diff --git a/.gitattributes b/.gitattributes index 7e671d473e9adb2bb47e30c6a3df475db8cac8db..ce53f571c9161fcdec23318c15aca56fcd38b10e 100644 --- a/.gitattributes +++ b/.gitattributes @@ -765,3 +765,28 @@ preprints/Uniform-Permanence-in-Weakly-Reversible-Mass-Action-Systems-October-5- preprints/Uniform-Pluricanonical-Iitaka-Fibrations-October-3-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text preprints/Uniform-quasipolynomial-time-trace-reconstruction-October-5-2026/uniform-trace-reconstruction.pdf filter=lfs diff=lfs merge=lfs -text preprints/Uniform-real-Lipschitz-surfaces-on-the-triangular-lattice-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Universal-cover-splitting-for-compact-Kahler-manifolds-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Universal-optimality-of-the-triangular-lattice-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Universal-strong-Kadison-Kastler-stability-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Universal-Tensor-Squares-for-Symmetric-Groups-September-24-2026/main.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Universality-of-critical-quench-autocorrelations-in-the-Sherrington-Kirkpatrick-model-October-5-2026/main.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Unrestricted-pro-modularity-at-the-prime-two-October-4-2026/two-adic-promodularity.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Vanishing-of-higher-bounded-Hochschild-cohomology-September-23-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Variable-dimension-Weisfeiler-Leman-equivalence-on-general-and-subcubic-graphs-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Variance-of-the-Random-k-SAT-Hitting-Time-September-27-2026/article.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Virasoro-Constraints-for-Projective-Complete-Intersections-September-24-2026/article.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Virasoro-Constraints-under-Projectivization-October-5-2026/virasoro-constraints-under-projectivization.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Virtual-compact-specialness-of-hyperbolic-one-relator-groups-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Weak-and-strong-normalization-in-pure-type-systems-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Weak-Hessian-bounds-along-every-geodesic-in-RCD-spaces-September-24-2026/weak-hessian-geodesics.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Weak-mixing-of-triangular-billiards-with-an-irrational-angle-October-5-2026/weak-mixing-triangular-billiards.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Weak-pure-infiniteness-and-O-infinity-absorption-September-25-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Weighted-Dilation-Graphs-Smooth-Shifted-Primes-and-Totient-Fibers-September-24-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Weil-classes-and-Hodge-classes-on-abelian-powers-September-30-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Witnessed-symmetric-choice-is-strictly-stronger-than-choiceless-polynomial-time-with-counting-September-24-2026/paper.pdf filter=lfs diff=lfs merge=lfs -text +preprints/Zero-Plane-Rigidity-for-Einstein-Four-Manifolds-October-4-2026/einstein-boundary.pdf filter=lfs diff=lfs merge=lfs -text diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/README.md b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/README.md new file mode 100644 index 0000000000000000000000000000000000000000..f7c89a3818f1a466e8d7a30f0dcb0a1aa5d87410 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/README.md @@ -0,0 +1,17 @@ +# [Uniform Stability of the Spherical Laughlin Gap](uniform-stability-spherical-laughlin-gap.pdf) + +**Author:** OpenAI + +**Date:** October 5, 2026 + +## Citation + +```bibtex +@misc{OAI:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026, + author = {{OpenAI}}, + title = {{Uniform Stability of the Spherical Laughlin Gap}}, + howpublished = {OpenAI Math Release preprint + \href{https://github.com/openai/math/blob/main/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf}{OAI:Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026}}, + year = {2026} +} +``` diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..474d7aec96aa1e6bc405af84f51f9110adfdfb60 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreexternal.code.tex @@ -0,0 +1,357 @@ + +\ProvidesFileRCS{pgfcoreexternal.code.tex} + + + +\newif\ifpgfexternal@aux@in@dpth +\newif\ifpgfexternal@info + +\pgfkeys{ + /pgf/images/include external/.code={\pgfimage{#1}}, + /pgf/images/aux in dpth/.is if=pgfexternal@aux@in@dpth, + /pgf/images/aux in dpth/.default=true, + /pgf/images/trim external/.code n args={4}{% + \def\pgf@external@kern@left{#1}% + \def\pgf@external@kern@bottom{#2}% + \def\pgf@external@kern@right{#3}% + \def\pgf@external@kern@top{#4}% + \ifx\pgf@external@kern@left\pgfutil@empty\def\pgf@external@kern@left{0sp}\fi% + \ifx\pgf@external@kern@bottom\pgfutil@empty\def\pgf@external@kern@bottom{0sp}\fi% + \ifx\pgf@external@kern@right\pgfutil@empty\def\pgf@external@kern@right{0sp}\fi% + \ifx\pgf@external@kern@top\pgfutil@empty\def\pgf@external@kern@top{0sp}\fi% + }, + /pgf/images/trim external={1truein}{1truein}{1truein}{1truein}, + /pgf/images/external info/.is if=pgfexternal@info, + /pgf/images/external info/.default=true, +} + + + +\newif\ifpgfexternalreadmainaux +\pgfexternalreadmainauxtrue + + +\def\pgfrealjobname#1{% + \global\let\pgfactualjobname=\jobname + \edef\pgf@tempa{\expandafter\string\csname #1\endcsname}% + \edef\pgf@tempb{\expandafter\string\csname\jobname\endcsname}% + \ifx\pgf@tempa\pgf@tempb% + \else% + \pgf@external@grabshipouttrue% + \pgfexternal@nofiles% + \ifpgfexternalreadmainaux + \gdef\jobname{#1}% + \fi + \ifpgfexternal@aux@in@dpth + \csname newwrite\endcsname\w@pgfexternal@auxout + \fi + \pgfexternal@geometry@compatibility + \fi% + \gdef\pgfrealjobname##1{}% +} + +\def\pgfexternal@geometry@compatibility{% + \pgfutil@ifundefined{geometry}{% + }{% + \pgf@typeout{Package TikZ externalization: calling \string\geometry{driver=none} during externalization.^^J}% + \geometry{driver=none}% + }% +}% + +\def\pgfexternal@nofiles{% + \let\pgfexternal@nofiles@=\relax + \def\relax{\relax}% + \csname nofiles\endcsname + \let\relax=\pgfexternal@nofiles@ +}% + +\newif\ifpgf@external@grabshipout +\newbox\pgfexternal@startupbox + +\pgfutil@ifundefined{AtBeginDocument}{}{% + \AtBeginDocument{% + \ifpgf@external@grabshipout% + \global\let\pgfexternal@originalshipout=\shipout% + \global\def\shipout{\setbox\pgfpic=}% + \maxdeadcycles=10000% + {% + \output{\global\setbox\pgfexternal@startupbox=\vbox{\csname @begindvi\endcsname\unvbox255}}% + \hbox{}\eject% + }% + \fi% + } +}% + +\pgfutil@ifundefined{AtEndDocument}{}{% + \AtEndDocument{% + \ifpgf@external@grabshipout + \pgfutil@ifundefined{pgfexternal@did@a@shipout}{% + \pgfexternal@error@no@shipout + }{}% + \fi + }% +} + +\def\pgfexternal@error@no@shipout{% + \pgferror{Sorry, image externalization failed: the resulting image was EMPTY. I tried to externalize '\pgfactualjobname'. Perhaps there was a typo somewhere? Please check that your document contains '\string\beginpgfgraphicnamed{\pgfactualjobname} ... \string\endpgfgraphicnamed'}% +}% + + + +\def\pgf@externalbegin#1{% + \let\pgf@next=\pgf@external@normal% + \ifpgf@external@grabshipout% + \edef\pgf@tempa{\expandafter\string\csname #1\endcsname}% + \edef\pgf@tempb{\expandafter\string\csname\pgfactualjobname\endcsname}% + \ifx\pgf@tempa\pgf@tempb% + \let\pgf@next=\pgf@external@grab% + \fi% + \fi% + \pgf@next{#1}% +} + + +\AtBeginDocument{ + \let\beginpgfgraphicnamed=\pgf@externalbegin% + \let\endpgfgraphicnamed=\unskip +} + + +\def\pgf@external@normal#1{% + \let\pgf@filename=\pgfutil@empty% + \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#1}% + \ifx\pgf@filename\pgfutil@empty% + \let\pgf@next=\relax% + \else% + \let\pgf@next=\pgf@replacepicturebygraphic% + \fi% + \pgf@next% +} + +\long\def\pgf@replacepicturebygraphic#1\endpgfgraphicnamed{% + \expandafter\pgfincludeexternalgraphics\expandafter{\pgf@filename}\unskip +} + +\def\pgfincludeexternalgraphics#1{% + \begingroup + \pgfexternalreaddpth{#1}% + \pgfkeysifdefined{/pgf/images/include external/#1/.@cmd}{% + \pgfkeysgetvalue{/pgf/images/include external/#1/.@cmd}\pgf@tempa + \pgfkeyslet{/pgf/images/include external/.@cmd}\pgf@tempa + }{}% + \setbox1=\hbox{\pgfkeysvalueof{/pgf/images/include external/.@cmd}{#1}\pgfeov}% + \ifdim\pgfexternaltrimleft=0sp \else \kern\pgfexternaltrimleft\relax \fi + \ifdim\pgfexternaldepth=0pt + \box1 + \else + \dimen0=\pgfexternaldepth\relax + \hbox{\lower\dimen0 \box1 }% + \fi + \ifdim\pgfexternaltrimright=0sp \else \kern\pgfexternaltrimright\relax \fi + \endgroup +} + +\def\pgfexternalreaddpth#1{% + \edef\pgfexternalreaddpth@restore{% + \noexpand\endlinechar=\the\endlinechar\space + \noexpand\catcode`\noexpand\@=\the\catcode`\@\space + }% + \def\pgfexternaldepth{0sp}% + \def\pgfexternaltrimleft{0sp}% + \def\pgfexternaltrimright{0sp}% + \endlinechar=-1 % + \catcode`\@=11 + \openin\r@pgf@reada=#1.dpth + \pgfincludeexternalgraphics@read@dpth + \pgfexternalreaddpth@restore +}% +\def\pgfincludeexternalgraphics@read@dpth{% + \ifeof\r@pgf@reada + \closein\r@pgf@reada + \else + \read\r@pgf@reada to\pgfincludeexternalgraphics@auxline + \ifx\pgfincludeexternalgraphics@auxline\pgfutil@empty + \else + \expandafter\pgfincludeexternalgraphics@read@dpth@line\pgfincludeexternalgraphics@auxline\pgfincludeexternalgraphics@read@dpth@line@EOI + \fi + \expandafter\pgfincludeexternalgraphics@read@dpth + \fi +}% + +\def\pgfexternal@restore#1{#1}% + +\long\def\pgfincludeexternalgraphics@read@dpth@line@getfirst#1#2\pgfincludeexternalgraphics@read@dpth@line@EOI{% + \def\pgf@first{#1}% +}% +\long\def\pgfincludeexternalgraphics@read@dpth@line#1\pgfincludeexternalgraphics@read@dpth@line@EOI{% + \pgfincludeexternalgraphics@read@dpth@line@getfirst#1\pgfincludeexternalgraphics@read@dpth@line@EOI + \expandafter\ifcat\expandafter\noexpand\pgf@first\relax + \expandafter\ifx\pgf@first\pgfexternal@restore + #1% + \else + \pgfutil@ifundefined{if@filesw}{% + }{% + \if@filesw + {% + \toks0={#1}% + \immediate\write\@auxout{% + \noexpand\def\noexpand\dpthimport{\the\toks0}\noexpand\dpthimport}% + }% + \fi + }% + \fi + \else% + \def\pgfexternaldepth{#1}% + \fi +}% + +\def\pgfexternalstorecommand#1{% +}% +\def\pgfexternalstorecommand@isexporting#1{% + \immediate\write\w@pgfexternal@auxout{\noexpand\pgfexternal@restore{#1}}% +}% + + + +\def\pgf@external@grab#1{% + \def\pgf@filename{#1}% + \ifpgfexternal@aux@in@dpth + \begingroup + \pgf@external@init@aux@in@dpth + \let\G@refundefinedtrue=\pgf@external@grab@refundefinedtrue + \fi + \gdef\pgf@trimleft@final{0sp}% + \gdef\pgf@trimright@final{0sp}% + \setbox\pgfpic=\hbox\bgroup\bgroup% + \let\endpgfgraphicnamed=\pgf@externalend% +} + +{\catcode`\^=12 \gdef\pgfexternal@hat{^}} + +\expandafter\let\expandafter\pgf@external@grab@refundefinedtrue@orig\csname G@refundefinedtrue\endcsname + +\def\pgf@external@grab@refundefinedtrue{% + \pgf@external@grab@refundefinedtrue@orig + \begingroup + \def\n{\pgfexternal@hat\pgfexternal@hat J}% + \pgfexternalstorecommand{% + \pgf@external@grab@refundefinedtrue@code + \noexpand\immediate\noexpand\write16{\pgf@external@grab@refundefinedtrue@warning}% + \noexpand\G@refundefinedtrue + }% + \endgroup +}% + +\def\pgf@external@grab@refundefinedtrue@code{} + +\def\pgf@external@grab@refundefinedtrue@warning{% + LaTeX Warning: External picture `\pgfactualjobname' contains undefined references\noexpand\on@line.\n +}% + +\let\pgf@external@@protected@write@orig=\protected@write +\long\def\pgf@external@@protected@write@immediate#1#2#3{% + \begingroup + \let\pgf@write@=\write + \def\write{\noexpand\immediate\pgf@write@}% + \pgf@external@@protected@write@orig{#1}{#2}{#3}% + \endgroup +}% + +\def\pgf@external@init@aux@in@dpth{% + \let\pgfexternalstorecommand=\pgfexternalstorecommand@isexporting + \csname @fileswtrue\endcsname + \immediate\openout\w@pgfexternal@auxout=\pgf@filename.dpth + \let\@auxout=\w@pgfexternal@auxout + \let\protected@write=\pgf@external@@protected@write@immediate +}% + +\def\pgf@externalend@storeshifts#1{% + \immediate\write#1{\the\dp\pgfpic}% + \ifx\pgf@trimleft@final\pgfutil@empty\else + \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternaltrimleft{\pgf@trimleft@final}}}% + \fi + \ifx\pgf@trimright@final\pgfutil@empty\else + \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternaltrimright{\pgf@trimright@final}}}% + \fi + \ifpgfexternal@info + \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternalwidth{\the\wd\pgfpic}}}% + \immediate\write#1{\noexpand\pgfexternal@restore{\noexpand\def\noexpand\pgfexternalheight{\the\dimen0}}}% + \fi +} +\def\pgf@externalend{% + \unskip\egroup\egroup% + {% + \def\pgf@external@trim{0}% + \def\pgf@external@store@dpth{0}% + \ifpgf@trim@lowlevel + \gdef\pgf@trimleft@final{}% + \gdef\pgf@trimright@final{}% + \else + \ifdim\pgf@trimleft@final=0sp \gdef\pgf@trimleft@final{} \else\def\pgf@external@trim{1}\fi + \ifdim\pgf@trimright@final=0sp \gdef\pgf@trimright@final{} \else\def\pgf@external@trim{1}\fi + \if1\pgf@external@trim + \setbox\pgfpic=\hbox{% + \ifx\pgf@trimleft@final\pgfutil@empty\else\kern-\pgf@trimleft@final\fi + \box\pgfpic + \ifx\pgf@trimright@final\pgfutil@empty\else\kern-\pgf@trimright@final\fi + }% + \def\pgf@external@store@dpth{1}% + \fi + \fi + \parindent0pt % + \hoffset=0pt % + \voffset=0pt + \dimen0\ht\pgfpic% + \advance\dimen0\dp\pgfpic% + \ifdim\dp\pgfpic=0pt\relax + \else% + \def\pgf@external@store@dpth{1}% + \fi + \ifpgfexternal@info + \def\pgf@external@store@dpth{1}% + \fi + \if1\pgf@external@store@dpth + \ifpgfexternal@aux@in@dpth + \pgf@externalend@storeshifts\@auxout + \immediate\closeout\@auxout + \else + \immediate\openout\pgf@plotwrite=\pgf@filename.dpth + \pgf@externalend@storeshifts\pgf@plotwrite + \immediate\closeout\pgf@plotwrite + \fi + \fi + \pgfsys@prepare@papersize{\the\wd\pgfpic}{\the\dimen0}% + \setbox0=\vbox{% + \kern -\pgf@external@kern@top\relax% + \hbox{% + \kern -\pgf@external@kern@left\relax% + \hbox to0pt{% + \wd\pgfexternal@startupbox=0pt % + \ht\pgfexternal@startupbox=0pt % + \dp\pgfexternal@startupbox=0pt % + \box\pgfexternal@startupbox% + \pgfsys@atbegindocument\hss}% + \box\pgfpic% + \kern\pgf@external@kern@right\relax% + }% + \kern\pgf@external@kern@bottom\relax% + }% + \let\pgfexternal@nointerlineskip@orig=\nointerlineskip + \let\nointerlineskip=\pgfexternal@nointerlineskip + \pgfexternal@originalshipout\box0 % + \gdef\pgfexternal@did@a@shipout{1}% + }% + \ifpgfexternal@aux@in@dpth + \endgroup + \fi +} + +\def\pgfexternal@nointerlineskip{% + \ifvmode + \pgfexternal@nointerlineskip@orig + \else + \relax% + \fi +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..dd4e49d0ee8b3406c37de2b947d125448812b8d7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoregraphicstate.code.tex @@ -0,0 +1,162 @@ + +\ProvidesFileRCS{pgfcoregraphicstate.code.tex} + + +\newdimen\pgflinewidth + + + +\def\pgfsetlinewidth#1{% + \pgfmathsetlength\pgflinewidth{#1}% + \global\pgflinewidth=\pgflinewidth% + \pgfsys@setlinewidth{\the\pgflinewidth}% + \ignorespaces} + + + +\def\pgfsetinnerlinewidth#1{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgfinnerlinewidth{\the\pgf@x}% +} +\def\pgfinnerlinewidth{0pt} + + + +\def\pgfsetinnerstrokecolor#1{\def\pgfinnerstrokecolor{#1}} +\def\pgfinnerstrokecolor{white} + + + +\def\pgfsetmiterlimit#1{% + \ifdim#1pt<1pt\pgferror{miter limit cannot be less than 1}\fi% + \pgfsys@setmiterlimit{#1}% + \ignorespaces} + + + +\def\pgfsetdash#1#2{% + \def\pgf@temp{}% + \def\pgf@next{\pgf@strip}% + \pgf@strip#1{pgf@stop}% + \pgfmathsetlength\pgf@x{#2}% + \pgfsys@setdash{\pgf@temp}{\the\pgf@x}% + \ignorespaces} + +\def\pgf@strip#1{% + \def\pgf@@temp{#1}% + \ifx\pgf@@temp\pgf@stop% + \let\pgf@next=\relax% + \else% + \pgfmathsetlength\pgf@x{#1}% + \ifx\pgf@temp\pgfutil@empty% + \edef\pgf@temp{\the\pgf@x}% + \else% + \edef\pgf@temp{\pgf@temp,\the\pgf@x}% + \fi% + \fi\pgf@next} + +\def\pgf@stop{pgf@stop} + + + +\def\pgfsetstrokecolor#1{% + \pgfutil@colorlet{pgfstrokecolor}{#1}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfstrokecolor}}% + \expandafter\let\expandafter\pgf@temp\csname\string\color@pgfstrokecolor\endcsname + \global\let\pgf@strokecolor@global=\pgf@temp + \expandafter\pgf@setstrokecolor\pgf@temp% +} +\def\pgf@setstrokecolor#1#2#3#4#5{% + \expandafter\ifx\csname pgfsys@color@#4@stroke\endcsname\relax% + \pgferror{Unsupported color model `#4'. Sorry}% + \else% + \edef\pgf@colmarshal{\expandafter\noexpand\csname pgfsys@color@#4@stroke\endcsname}% + \pgf@uncomma#5,,% + \pgf@colmarshal% + \fi} + +\def\pgf@uncomma#1,{% + \def\pgf@coltest{#1}% + \ifx\pgf@coltest\pgfutil@empty% + \let\pgf@colnext=\relax% + \else% + \expandafter\def\expandafter\pgf@colmarshal\expandafter{\pgf@colmarshal{#1}}% + \let\pgf@colnext=\pgf@uncomma% + \fi% + \pgf@colnext% +} + + + +\def\pgfsetfillcolor#1{% + \pgfutil@colorlet{pgffillcolor}{#1}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgffillcolor}}% + \expandafter\let\expandafter\pgf@temp\csname\string\color@pgffillcolor\endcsname + \global\let\pgf@fillcolor@global=\pgf@temp + \expandafter\pgf@setfillcolor\pgf@temp +} +\def\pgf@setfillcolor#1#2#3#4#5{% + \expandafter\ifx\csname pgfsys@color@#4@fill\endcsname\relax% + \pgferror{Unsupported color model `#4'. Sorry}% + \else% + \edef\pgf@colmarshal{\expandafter\noexpand\csname pgfsys@color@#4@fill\endcsname}% + \pgf@uncomma#5,,% + \pgf@colmarshal% + \fi} + + + + +\def\pgfsetcolor#1{% + \pgfutil@colorlet{pgfstrokecolor}{#1}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfstrokecolor}}% + \expandafter\let\expandafter\pgf@temp\csname\string\color@pgfstrokecolor\endcsname + \global\let\pgf@strokecolor@global=\pgf@temp + \global\let\pgf@fillcolor@global=\pgf@temp + \expandafter\pgf@setcolor\pgf@temp% +} +\def\pgf@setcolor#1#2#3#4#5{% + \expandafter\ifx\csname pgfsys@color@#4\endcsname\relax% + \pgferror{Unsupported color model `#4'. Sorry}% + \else% + \edef\pgf@colmarshal{\expandafter\noexpand\csname pgfsys@color@#4\endcsname}% + \pgf@uncomma#5,,% + \pgf@colmarshal% + \fi} + +\def\XC@bcolor{\pgfsys@color@reset} + + +\def\pgfsetbuttcap{\pgfsys@buttcap\ignorespaces} + + + +\def\pgfsetroundcap{\pgfsys@roundcap\ignorespaces} + + + +\def\pgfsetrectcap{\pgfsys@rectcap\ignorespaces} + + + +\def\pgfsetmiterjoin{\pgfsys@miterjoin\ignorespaces} + + + +\def\pgfsetbeveljoin{\pgfsys@beveljoin\ignorespaces} + + + +\def\pgfsetroundjoin{\pgfsys@roundjoin\ignorespaces} + + + +\def\pgfseteorule{\pgfsys@eoruletrue\ignorespaces} + + + +\def\pgfsetnonzerorule{\pgfsys@eorulefalse\ignorespaces} + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..28b82798aceeaf9e6843b1cbd26c0c04973e9e25 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreimage.code.tex @@ -0,0 +1,150 @@ + +\ProvidesFileRCS{pgfcoreimage.code.tex} + + + + +\def\pgfdeclareimage{\pgfutil@ifnextchar[{\pgf@declareimage}{\pgf@declareimage[]}} +\def\pgf@declareimage[#1]#2#3{% + \pgfqkeys{/pgf/images}{height=,width=,page=,interpolate=false,mask=,#1}% + \gdef\pgf@filename{}% + \ifx\pgf@imagepage\pgfutil@empty% + \else% + \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#3.page\pgf@imagepage}% + \fi% + \ifx\pgf@filename\pgfutil@empty% + \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#3}% + \else% + \pgfkeys{/pgf/images/page=}% + \fi% + \ifx\pgf@filename\pgfutil@empty% + \pgfwarning% + {File "#3" not found when defining image "#2". + Tried all extensions in "\pgfsys@imagesuffixlist"}% + \pgf@declaredraftimage{#2}{#3}% + \else% + \ifpgf@draftmode% + \pgf@declaredraftimage{#2}{#3}% + \else% + \pgfsys@defineimage% + \fi% + \fi% + \expandafter\global\expandafter\let\csname pgf@image@#2!\endcsname=\pgf@image% +} + + +\pgfkeys{ + /pgf/images/draft/.is if=pgf@draftmode, + /pgf/images/draft/.default=true} +\pgfkeys{/pgf/images/width/.estore in=\pgf@imagewidth} +\pgfkeys{/pgf/images/height/.estore in=\pgf@imageheight} +\pgfkeys{/pgf/images/page/.estore in=\pgf@imagepage} +\pgfkeys{/pgf/images/interpolate/.cd,.code=\edef\pgf@imageinterpolate{#1},.default=true} +\let\pgf@imageinterpolate\pgfutil@empty +\pgfkeys{/pgf/images/mask/.code=% + {% + \edef\pgf@imagemask{#1}% + \ifx\pgf@imagemask\pgfutil@empty% + \else% + \pgfutil@ifundefined{pgf@mask@#1}% + {\pgferror{Undefined mask "#1".}% + \edef\pgf@imagemask{}}% + {\edef\pgf@imagemask{\csname pgf@mask@#1\endcsname}% + }% + \fi% + }} + + +\def\pgf@findfile#1:#2+#3{% + \pgfutil@IfFileExists{#3#1}% + {\xdef\pgf@filename{#3#1}}% + {\def\pgf@mightbeempty{#2}% + \ifx\pgf@mightbeempty\pgfutil@empty\else% + \pgf@findfile#2+{#3}% + \fi}} + +\def\pgf@declaredraftimage#1#2{% + \ifx\pgf@imagewidth\pgfutil@empty% + \pgfwarning{Missing width for image "#1" ("#2") in draft mode. Using 1cm instead}% + \edef\pgf@imagewidth{1cm}% + \fi% + \ifx\pgf@imageheight\pgfutil@empty% + \pgfwarning{Missing height for image "#1" ("#2") in draft mode. Using 1cm instead}% + \edef\pgf@imageheight{1cm}% + \fi% + \ifx\pgf@imagepage\pgfutil@empty\else\edef\pgf@imagepagetext{ page \pgf@imagepage}\fi% + \edef\pgf@image{% + \hbox to \pgf@imagewidth{% + \vrule\kern-0.4pt% + \vbox to \pgf@imageheight{% + \hrule\vfil% + \hbox to \pgf@imagewidth{\hskip-10cm\hfil\noexpand\pgfutil@font@tiny#2\pgf@imagepage\hfil\hskip-10cm}% + \vfil\hrule}% + \kern-0.4pt\vrule}% + }% +} + + + + +\def\pgfdeclaremask{\pgfutil@ifnextchar[\pgf@declaremask{\pgf@declaremask[]}} +\def\pgf@declaremask[#1]#2#3{% + \pgfqkeys{/pgf/images/mask}{matte={1 1 1},#1}% + \def\pgf@mask{}% + \gdef\pgf@filename{}% + \expandafter\pgf@findfile\pgfsys@imagesuffixlist:+{#3}% + \ifx\pgf@filename\pgfutil@empty% + \pgfwarning% + {File "#3" not found when defining mask "#2". + Tried all extensions in "\pgfsys@imagesuffixlist"}% + \else% + \pgfsys@definemask% + \fi% + \expandafter\global\expandafter\let\csname pgf@mask@#2\endcsname=\pgf@mask% +} + +\pgfkeys{/pgf/images/mask/matte/.cd,.estore in=\pgf@maskmatte,.value required} + + + + +\def\pgfaliasimage#1#2{% + \expandafter\global\expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@image@#2!\endcsname% + \expandafter\global\expandafter\let\csname pgf@image@#1!\endcsname=\pgf@temp% + } + + + +\def\pgfuseimage#1{% + \def\pgf@imagename{pgf@image@#1}% + \pgf@tryextensions{\pgf@imagename}{\pgfalternateextension}% + \expandafter\pgfutil@ifundefined\expandafter{\pgf@imagename}% + {\pgferror{Undefined image "#1"}}% + {{\leavevmode\csname\pgf@imagename\endcsname}}} + +\def\pgf@tryextensions#1#2{% + \edef\pgf@args{[#2!]}\expandafter\pgf@@tryextensions\pgf@args{#1}} +\def\pgf@@tryextensions[#1!#2]#3{% + \expandafter\pgfutil@ifundefined\expandafter{#3#1!#2}% + {\def\pgf@temp{#2}% + \ifx\pgf@temp\pgfutil@empty% + \edef#3{#3!}% + \else% + \pgf@@tryextensions[#2]{#3}% + \fi}% + {\edef#3{#3#1!#2}}} + + + +\def\pgfalternateextension{} + + + + +\def\pgfimage{\pgfutil@ifnextchar[\pgf@imagecom{\pgf@imagecom[]}} +\def\pgf@imagecom[#1]#2{% + \pgfdeclareimage[#1]{pgflastimage}{#2}% + \pgfuseimage{pgflastimage}} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..5ab39e5f739afd3996261b8b63d8a09479a1aa96 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorelayers.code.tex @@ -0,0 +1,161 @@ + +\ProvidesFileRCS{pgfcorelayers.code.tex} + + + +\def\pgfdeclarelayer#1{% + \pgfutil@ifundefined{pgf@layerbox@#1}{% + \expandafter\expandafter\csname pgf@newbox\endcsname\csname pgf@layerbox@#1\endcsname% + \expandafter\expandafter\csname pgf@newbox\endcsname\csname pgf@layerboxsaved@#1\endcsname% + }{}% +} +\let\pgf@newbox=\newbox % + + +\def\pgfsetlayers#1{% + \let\pgf@layerlist\pgfutil@empty% + \pgf@dosetlayer#1,,\relax% +} + +\def\pgf@dosetlayer#1,#2,\relax{% + \ifx\pgf@layerlist\pgfutil@empty% + \edef\pgf@layerlist{\pgfutil@trimspaces{#1}}% + \else + \edef\pgf@layerlist{\pgf@layerlist,\pgfutil@trimspaces{#1}}% + \fi + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \else% + \pgf@dosetlayer#2,\relax% + \fi% +} + +\pgfsetlayers{main} + + +\def\pgfonlayer@name{main} + +\def\pgfonlayer#1{% + \pgfutil@ifundefined{pgf@layerbox@#1}{% + \pgferror{Sorry, the requested layer '#1' could not be found. Maybe you misspelled it?}% + \bgroup + \begingroup + }{% + \begingroup + \edef\pgf@temp{#1}% + \ifx\pgf@temp\pgfonlayer@name + \def\pgf@temp{% + \bgroup + \begingroup + }% + \else + \let\pgfonlayer@name=\pgf@temp + \pgfonlayer@assert@is@active + \def\pgf@temp{% + \expandafter\global\expandafter% + \setbox\csname pgf@layerbox@#1\endcsname=\hbox to 0pt% + \bgroup% + \expandafter\box\csname pgf@layerbox@#1\endcsname% + \begingroup% + }% + \fi + \pgfsetlinewidth{0.4pt}% + \pgf@temp + }% +} +\def\endpgfonlayer{% + \endgroup% + \hss + \egroup% + \endgroup +} + +\let\startpgfonlayer=\pgfonlayer +\let\stoppgfonlayer=\endpgfonlayer + +\def\pgfdiscardlayername{discard} + +\def\pgfonlayer@assert@is@active{% + \ifx\pgfonlayer@name\pgfdiscardlayername + \else + \begingroup + \def\pgfonlayer@isactive{0}% + \expandafter\pgf@assert@layer@is@active@loop\pgf@layerlist,,\relax% + \if0\pgfonlayer@isactive + \pgfonlayer@assert@fail + \fi + \endgroup + \fi +}% +\def\pgfonlayer@assert@fail{% + \pgferror{Sorry, the requested layer '\pgfonlayer@name' is not + part of the layer list. Please verify that you provided + \string\pgfsetlayers\space and that '\pgfonlayer@name' is part of this list}% +}% +\def\pgf@assert@layer@is@active@loop#1,#2,\relax{% + \edef\pgf@test{#1}% + \ifx\pgf@test\pgfonlayer@name + \def\pgfonlayer@isactive{1}% + \else + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \else% + \pgf@assert@layer@is@active@loop#2,\relax% + \fi% + \fi +} + + +\def\pgf@insertlayers{% + \expandafter\pgf@dolayer\pgf@layerlist,,\relax% +} +\def\pgf@maintext{main}% +\def\pgf@dolayer#1,#2,\relax{% + \def\pgf@test{#1}% + \ifx\pgf@test\pgf@maintext% + \box\pgf@layerbox@main% + \else% + \pgfsys@beginscope% + \expandafter\box\csname pgf@layerbox@#1\endcsname% + \pgfsys@endscope% + \fi% + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \else% + \pgf@dolayer#2,\relax% + \fi% +} + +\def\pgf@savelayers{% + \expandafter\pgf@dosavelayer\pgf@layerlist,,\relax% +} +\def\pgf@dosavelayer#1,#2,\relax{% + \def\pgf@test{#1}% + \ifx\pgf@test\pgf@maintext% + \else% + \setbox\csname pgf@layerboxsaved@#1\endcsname=\box\csname pgf@layerbox@#1\endcsname% + \fi% + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \else% + \pgf@dosavelayer#2,\relax% + \fi% +} + +\def\pgf@restorelayers{% + \expandafter\pgf@dorestorelayer\pgf@layerlist,,\relax% +} +\def\pgf@dorestorelayer#1,#2,\relax{% + \def\pgf@test{#1}% + \ifx\pgf@test\pgf@maintext% + \else% + \global\setbox\csname pgf@layerbox@#1\endcsname=\box\csname pgf@layerboxsaved@#1\endcsname% + \fi% + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \else% + \pgf@dorestorelayer#2,\relax% + \fi% +} + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..6cde5bb0e6ffe703f51af07df9a15cf12bb60a8e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreobjects.code.tex @@ -0,0 +1,29 @@ + +\ProvidesFileRCS{pgfcoreobjects.code.tex} + + + + + +\def\pgfdefobject#1#2#3#4{% + \pgfinterruptpath% + \pgf@relevantforpicturesizefalse% + \pgfsys@defobject{#1}{#2}{#3}{#4}% + \endpgfinterruptpath% + \ignorespaces% +} + + + +\def\pgfuseobject#1{\pgfsys@beginscope\pgfsys@useobject{#1}{}\pgfsys@endscope} + + + +\def\pgfuseobjectmagnify#1{% + \pgfsys@beginscope% + \pgfsys@useobject{#1}{\pgfsys@transformxyscale{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}}% + \pgfsys@endscope% +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..19c95bbf5019002e72f89b3fac94e6396b60e6fd --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathconstruct.code.tex @@ -0,0 +1,997 @@ + +\ProvidesFileRCS{pgfcorepathconstruct.code.tex} + + +\newdimen\pgf@path@lastx +\newdimen\pgf@path@lasty + +\let\pgfgetpath=\pgfsyssoftpath@getcurrentpath +\let\pgfsetpath=\pgfsyssoftpath@setcurrentpath + + + + +\newif\ifpgf@arccorners + +\def\pgfsetcornersarced#1{% + \pgf@process{#1}% + \edef\pgf@corner@arc{{\the\pgf@x}{\the\pgf@y}}% + \pgf@arccornerstrue% + \ifdim\pgf@x=0pt% + \ifdim\pgf@y=0pt\relax% + \pgf@arccornersfalse% + \fi% + \fi% +} + +\def\pgf@roundcornerifneeded{% + \ifpgf@arccorners\expandafter\pgfsyssoftpath@specialround\pgf@corner@arc\fi% +} + + + + +\def\pgf@lt@moveto#1#2{% + \pgf@protocolsizes{#1}{#2}% + \pgfsyssoftpath@moveto{\the#1}{\the#2}% +} +\def\pgf@lt@lineto#1#2{% + \pgf@protocolsizes{#1}{#2}% + \pgfsyssoftpath@lineto{\the#1}{\the#2}% +} +\def\pgf@lt@curveto#1#2#3#4#5#6{% + \pgf@protocolsizes{#1}{#2}% + \pgf@protocolsizes{#3}{#4}% + \pgf@protocolsizes{#5}{#6}% + \pgfsyssoftpath@curveto{\the#1}{\the#2}{\the#3}{\the#4}{\the#5}{\the#6}% +} + +\let\pgf@lt@closepath\pgfsyssoftpath@closepath + +\let\pgf@nlt@moveto\pgf@lt@moveto +\let\pgf@nlt@lineto\pgf@lt@lineto +\let\pgf@nlt@curveto\pgf@lt@curveto +\let\pgf@nlt@closepath\pgf@lt@closepath + +\let\pgf@nlt@list\pgfutil@empty % + + + +\def\pgfpathmoveto#1{% + \pgfpointtransformed{#1}% + \pgf@nlt@moveto{\pgf@x}{\pgf@y}% + \global\pgf@path@lastx=\pgf@x% + \global\pgf@path@lasty=\pgf@y% +} + +\def\pgf@protocolsizes#1#2{% + \ifpgf@relevantforpicturesize% + \ifdim#1<\pgf@picminx\global\pgf@picminx#1\fi% + \ifdim#1>\pgf@picmaxx\global\pgf@picmaxx#1\fi% + \ifdim#2<\pgf@picminy\global\pgf@picminy#2\fi% + \ifdim#2>\pgf@picmaxy\global\pgf@picmaxy#2\fi% + \ifpgf@size@hooked% + \let\pgf@size@hook@x#1\let\pgf@size@hook@y#2\pgf@path@size@hook% + \fi% + \fi% + \ifdim#1<\pgf@pathminx\global\pgf@pathminx#1\fi% + \ifdim#1>\pgf@pathmaxx\global\pgf@pathmaxx#1\fi% + \ifdim#2<\pgf@pathminy\global\pgf@pathminy#2\fi% + \ifdim#2>\pgf@pathmaxy\global\pgf@pathmaxy#2\fi% +} +\newif\ifpgf@size@hooked +\let\pgf@path@size@hook=\pgfutil@empty% + +\def\pgf@resetpathsizes{% + \global\pgf@pathmaxx=-16000pt\relax% + \global\pgf@pathminx=16000pt\relax% + \global\pgf@pathmaxy=-16000pt\relax% + \global\pgf@pathminy=16000pt\relax% +} + +\def\pgf@getpathsizes#1{% + \edef#1{{\the\pgf@pathmaxx}{\the\pgf@pathminx}{\the\pgf@pathmaxy}{\the\pgf@pathminy}}% +} +\def\pgf@setpathsizes#1{% + \expandafter\pgf@@setpathsizes#1% +} +\def\pgf@@setpathsizes#1#2#3#4{% + \global\pgf@pathmaxx=#1\relax% + \global\pgf@pathminx=#2\relax% + \global\pgf@pathmaxy=#3\relax% + \global\pgf@pathminy=#4\relax% +} + + + + + + +\def\pgfpathlineto#1{% + \pgfpointtransformed{#1}% + \pgf@roundcornerifneeded% + \pgf@nlt@lineto{\pgf@x}{\pgf@y}% + \global\pgf@path@lastx=\pgf@x% + \global\pgf@path@lasty=\pgf@y% +} + + + + +\def\pgfpathclose{% + \pgf@roundcornerifneeded% + \pgf@nlt@closepath% +} + + + +\def\pgfpathcurveto#1#2#3{% + \pgfpointtransformed{#3}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgfpointtransformed{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfpointtransformed{#1}% + \pgf@roundcornerifneeded% + \pgf@nlt@curveto{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}{\pgf@xb}{\pgf@yb}% + \global\pgf@path@lastx=\pgf@xb% + \global\pgf@path@lasty=\pgf@yb% +} + + + + +\def\pgfpathquadraticcurveto#1#2{% + \pgfpointtransformed{#2}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgfpointtransformed{#1}% + \pgf@xc=.6666666\pgf@x% + \pgf@yc=.6666666\pgf@y% + \pgf@xa=.33333333\pgf@xb% + \pgf@ya=.33333333\pgf@yb% + \advance\pgf@xa by\pgf@xc% + \advance\pgf@ya by\pgf@yc% + \advance\pgf@xc by.3333333\pgf@path@lastx% + \advance\pgf@yc by.3333333\pgf@path@lasty% + \pgf@roundcornerifneeded% + \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@xa}{\pgf@ya}{\pgf@xb}{\pgf@yb}% + \global\pgf@path@lastx=\pgf@xb% + \global\pgf@path@lasty=\pgf@yb% +} + + + + + +\def\pgfpatharc#1#2#3{% + {% + \pgfmathparse{#1}\let\pgf@temp@a=\pgfmathresult% + \pgfmathparse{#2}\let\pgf@temp@b=\pgfmathresult% + \pgfutil@in@{and }{#3}% + \ifpgfutil@in@% + \pgf@arc@get@radii#3\pgf@arc@stop% + \else + \pgf@arc@get@radii#3and #3\pgf@arc@stop% + \fi% + \pgf@arc@local@angle@a=\pgf@temp@a pt% + \pgf@arc@local@angle@b=\pgf@temp@b pt% + \loop% + \pgfutil@tempdima=\pgf@arc@local@angle@a% + \advance\pgfutil@tempdima by-\pgf@arc@local@angle@b\relax% + \ifdim\pgfutil@tempdima<0pt\relax% + \pgfutil@tempdima=-\pgfutil@tempdima\relax% + \fi% + \ifdim\pgfutil@tempdima>90pt\relax% + \ifdim\pgfutil@tempdima>115pt\relax% + \pgf@arc@temp=90pt% + \else% + \pgf@arc@temp=60pt% + \fi% + \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax% + {% + \pgf@arc@local@angle@b=\pgf@arc@local@angle@a\relax% + \advance\pgf@arc@local@angle@b by\pgf@arc@temp\relax% + \pgf@arc% + } + \advance\pgf@arc@local@angle@a by\pgf@arc@temp\relax% + \else + {% + \pgf@arc@local@angle@b=\pgf@arc@local@angle@a\relax% + \advance\pgf@arc@local@angle@b by-\pgf@arc@temp\relax% + \pgf@arc% + }% + \advance\pgf@arc@local@angle@a by-\pgf@arc@temp\relax% + \fi% + \repeat% + \pgf@roundcornerifneeded% + \pgf@arc% + }% +} +\dimendef\pgf@arc@local@angle@a=0 +\dimendef\pgf@arc@local@angle@b=1 +\dimendef\pgf@arc@temp=2 + +\def\pgf@arc@get@radii#1and #2\pgf@arc@stop{% + \pgfmathparse{#1}\let\pgf@arc@radius@a=\pgfmathresult% + \pgfmathparse{#2}\let\pgf@arc@radius@b=\pgfmathresult% +} + + +\def\pgf@arc{% + {% + \pgfutil@tempdima=\pgf@arc@radius@a pt% + \pgfutil@tempdimb=\pgf@arc@radius@b pt% + \pgf@xa=\pgf@arc@local@angle@a\relax% + \pgf@xb=\pgf@arc@local@angle@b\relax% + \advance\pgf@xb by-\pgf@xa\relax% + \ifdim\pgf@xb<0pt\relax% + \pgf@xb=-\pgf@xb\relax% + \fi% + \ifdim\pgf@xb=90.0pt% + \def\pgfmathresult{0.55228475}% + \else% + \pgfmathparse{1.333333333*tan(.25*\pgf@sys@tonumber{\pgf@xb})}% + \fi% + \pgfutil@tempdima=\pgfmathresult\pgfutil@tempdima% + \pgfutil@tempdimb=\pgfmathresult\pgfutil@tempdimb% + \pgf@xa=\pgf@arc@local@angle@a\relax% + \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax% + \advance\pgf@xa by 90pt\relax% + \else% + \advance\pgf@xa by -90pt\relax% + \fi% + \edef\pgf@arc@angle{\pgf@sys@tonumber{\pgf@xa}}% + \pgfpointtransformed{\pgfpointpolar{\pgf@arc@angle}{\pgfutil@tempdima and \pgfutil@tempdimb}}% + \advance\pgf@x by-\pgf@pt@x% + \advance\pgf@y by-\pgf@pt@y% + \pgf@xa=\pgf@path@lastx% + \pgf@ya=\pgf@path@lasty% + \advance\pgf@xa by \pgf@x% + \advance\pgf@ya by \pgf@y% + \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@a}}{\pgf@arc@radius@a pt and \pgf@arc@radius@b pt}}% + \pgf@xb=\pgf@path@lastx% + \pgf@yb=\pgf@path@lasty% + \advance\pgf@xb by -\pgf@x% + \advance\pgf@yb by -\pgf@y% + \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@b}}{\pgf@arc@radius@a pt and \pgf@arc@radius@b pt}}% + \advance\pgf@xb by \pgf@x% + \advance\pgf@yb by \pgf@y% + \ifdim\pgf@arc@local@angle@b>\pgf@arc@local@angle@a\relax% + \advance\pgf@arc@local@angle@b by -90pt\relax% + \else% + \advance\pgf@arc@local@angle@b by 90pt\relax% + \fi% + \pgfpointtransformed{\pgfpointpolar{\pgf@sys@tonumber{\pgf@arc@local@angle@b}}{\pgfutil@tempdima and \pgfutil@tempdimb}}% + \advance\pgf@x by-\pgf@pt@x% + \advance\pgf@y by-\pgf@pt@y% + \pgf@xc=\pgf@xb\relax% + \pgf@yc=\pgf@yb\relax% + \advance \pgf@xc by \pgf@x\relax% + \advance \pgf@yc by \pgf@y\relax% + \pgf@nlt@curveto{\pgf@xa}{\pgf@ya}{\pgf@xc}{\pgf@yc}{\pgf@xb}{\pgf@yb}% + \global\pgf@path@lastx=\pgf@xb% + \global\pgf@path@lasty=\pgf@yb% + }% +} + + + +\def\pgfpatharcaxes#1#2#3#4{% + {% + \pgftransformtriangle{\pgfpointorigin}{#3}{#4}% + \pgfpatharc{#1}{#2}{1pt}% + }% +} + + + + +\def\pgfpatharcto#1#2#3#4#5#6{% + {% + \pgfmathsetmacro\pgf@arcto@rx{abs(#1)}% + \pgfmathsetmacro\pgf@arcto@ry{abs(#2)}% + \ifdim\pgf@arcto@rx pt=0pt% + \gdef\pgf@marshal{\pgfpathlineto{#6}}% + \else + \ifdim\pgf@arcto@ry pt=0pt% + \gdef\pgf@marshal{\pgfpathlineto{#6}}% + \else + \pgfmathsetmacro\pgf@arcto@phi{#3}% + \pgfmathsetmacro\pgf@arcto@fA{#4}% + \ifdim\pgf@arcto@fA pt=0pt + \else + \pgfmathsetmacro\pgf@arcto@fA{1.0} % + \fi + \pgfmathsetmacro\pgf@arcto@fS{#5}% + \ifdim\pgf@arcto@fS pt=0pt + \else + \pgfmathsetmacro\pgf@arcto@fS{1.0} % + \fi + \pgf@process{#6} + \edef\pgf@arcto@xb{\the\pgf@x}% + \edef\pgf@arcto@yb{\the\pgf@y}% + \pgftransforminvert% + \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@path@lastx}{\pgf@path@lasty}}} + \edef\pgf@arcto@xa{\the\pgf@x} + \edef\pgf@arcto@ya{\the\pgf@y} + \edef\pgf@temp@a{\pgf@arcto@xa,\pgf@arcto@ya} + \edef\pgf@temp@b{\pgf@arcto@xb,\pgf@arcto@yb} + \ifx\pgf@temp@a\pgf@temp@b% + \global\let\pgf@marshal\pgfutil@empty + \else + \pgftransformreset + \pgftransformrotate{-\pgf@arcto@phi} + \pgf@process{ + \pgfpointtransformed{\pgfpointscale{.5}{\pgfpointdiff + {\pgfqpoint{\pgf@arcto@xb}{\pgf@arcto@yb}} + {\pgfqpoint{\pgf@arcto@xa}{\pgf@arcto@ya}} + } + } + } + \edef\pgf@arcto@xaprime{\pgf@sys@tonumber\pgf@x} + \edef\pgf@arcto@yaprime{\pgf@sys@tonumber\pgf@y} + \pgfmathsetmacro\pgf@arcto@frac@x{\pgf@arcto@xaprime/\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@frac@y{\pgf@arcto@yaprime/\pgf@arcto@ry} + \pgfmathsetmacro\pgf@arcto@lambda{ + \pgf@arcto@frac@x*\pgf@arcto@frac@x+\pgf@arcto@frac@y*\pgf@arcto@frac@y + } + \ifdim\pgf@arcto@lambda pt>1pt% + \pgfmathsetmacro\pgf@arcto@sqrt@lambda{sqrt(\pgf@arcto@lambda)} + \pgfmathsetmacro\pgf@arcto@rx{\pgf@arcto@sqrt@lambda*\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@ry{\pgf@arcto@sqrt@lambda*\pgf@arcto@ry} + \fi + \pgfmathsetmacro\pgf@arcto@xaprime@abs{abs(\pgf@arcto@xaprime)} + \pgfmathsetmacro\pgf@arcto@yaprime@abs{abs(\pgf@arcto@yaprime)} + \pgfmathmax@{\pgf@arcto@rx,\pgf@arcto@ry,\pgf@arcto@xaprime@abs,\pgf@arcto@yaprime@abs} + \pgfmathsetmacro\pgf@arcto@scaling{20/\pgfmathresult} + \pgfmathsetmacro\pgf@arcto@rx@scaled{\pgf@arcto@scaling*\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@ry@scaled{\pgf@arcto@scaling*\pgf@arcto@ry} + \pgfmathsetmacro\pgf@arcto@xaprime@scaled{\pgf@arcto@scaling*\pgf@arcto@xaprime} + \pgfmathsetmacro\pgf@arcto@yaprime@scaled{\pgf@arcto@scaling*\pgf@arcto@yaprime} + \ifdim\pgf@arcto@rx pt>\pgf@arcto@ry pt% + \pgfmathsetmacro\pgf@arcto@rx@over@ry{\pgf@arcto@rx/\pgf@arcto@ry} + \pgfmathsetmacro\pgf@arcto@ry@over@rx{\pgf@arcto@ry/\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@temp{\pgf@arcto@ry@over@rx*\pgf@arcto@xaprime@scaled} + \pgfmathsetmacro\pgf@arcto@numerator{ + \pgf@arcto@ry@scaled*\pgf@arcto@ry@scaled- + \pgf@arcto@yaprime@scaled*\pgf@arcto@yaprime@scaled- + \pgf@arcto@temp*\pgf@arcto@temp + } + \pgfmathsetmacro\pgf@arcto@denominator{ + \pgf@arcto@yaprime@scaled*\pgf@arcto@yaprime@scaled+ + \pgf@arcto@temp*\pgf@arcto@temp + } + \else + \pgfmathsetmacro\pgf@arcto@rx@over@ry{\pgf@arcto@rx/\pgf@arcto@ry} + \pgfmathsetmacro\pgf@arcto@ry@over@rx{\pgf@arcto@ry/\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@temp{\pgf@arcto@rx@over@ry*\pgf@arcto@yaprime@scaled} + \pgfmathsetmacro\pgf@arcto@numerator{ + \pgf@arcto@rx@scaled*\pgf@arcto@rx@scaled- + \pgf@arcto@xaprime@scaled*\pgf@arcto@xaprime@scaled- + \pgf@arcto@temp*\pgf@arcto@temp + } + \pgfmathsetmacro\pgf@arcto@denominator{ + \pgf@arcto@xaprime@scaled*\pgf@arcto@xaprime@scaled+ + \pgf@arcto@temp*\pgf@arcto@temp + } + \fi + \pgfmathsetmacro\pgf@arcto@frac{ + \pgf@arcto@numerator/\pgf@arcto@denominator + } + \ifdim\pgf@arcto@frac pt<0pt + \pgfmathsetmacro\pgf@arcto@factor{0} + \else + \pgfmathsetmacro\pgf@arcto@factor{sqrt(\pgf@arcto@frac)} + \fi + \ifx\pgf@arcto@fA\pgf@arcto@fS + \pgfmathsetmacro\pgf@arcto@factor{-\pgf@arcto@factor} + \fi + \pgfmathsetmacro\pgf@arcto@cxprime{ + \pgf@arcto@factor*\pgf@arcto@rx@over@ry*\pgf@arcto@yaprime + } + \pgfmathsetmacro\pgf@arcto@cyprime{ + -\pgf@arcto@factor*\pgf@arcto@ry@over@rx*\pgf@arcto@xaprime + } + \pgftransformreset + \pgftransformrotate{\pgf@arcto@phi} + \pgf@process{ + \pgfpointtransformed{\pgfqpoint{\pgf@arcto@cxprime pt}{\pgf@arcto@cyprime pt}} + } + \edef\pgf@arcto@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgf@process{\pgfpointadd{\pgf@arcto@temp}{ + \pgfpointscale{.5}{ + \pgfpointadd + {\pgfqpoint{\pgf@arcto@xa}{\pgf@arcto@ya}} + {\pgfqpoint{\pgf@arcto@xb}{\pgf@arcto@yb}} } + } + } + \edef\pgf@arcto@cx{\the\pgf@x} + \edef\pgf@arcto@cy{\the\pgf@y} + \pgfmathsetmacro\pgf@arcto@vec@x{(\pgf@arcto@xaprime-\pgf@arcto@cxprime)/\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@vec@y{(\pgf@arcto@yaprime-\pgf@arcto@cyprime)/\pgf@arcto@ry} + \pgfmathsetmacro\pgf@arcto@denominator{veclen(\pgf@arcto@vec@x,\pgf@arcto@vec@y)} + \pgfmathsetmacro\pgf@arcto@frac{\pgf@arcto@vec@x/\pgf@arcto@denominator} + \pgfmathsetmacro\pgf@arcto@theta@start{acos(\pgf@arcto@frac)} + \ifdim\pgf@arcto@vec@y pt<0pt + \pgfmathsetmacro\pgf@arcto@theta@start{-\pgf@arcto@theta@start} + \fi + \pgfmathsetmacro\pgf@arcto@vec@x{(-\pgf@arcto@xaprime-\pgf@arcto@cxprime)/\pgf@arcto@rx} + \pgfmathsetmacro\pgf@arcto@vec@y{(-\pgf@arcto@yaprime-\pgf@arcto@cyprime)/\pgf@arcto@ry} + \pgfmathsetmacro\pgf@arcto@denominator{veclen(\pgf@arcto@vec@x,\pgf@arcto@vec@y)} + \pgfmathsetmacro\pgf@arcto@frac{\pgf@arcto@vec@x/\pgf@arcto@denominator} + \pgfmathsetmacro\pgf@arcto@theta@end{acos(\pgf@arcto@frac)} + \ifdim\pgf@arcto@vec@y pt<0pt + \pgfmathsetmacro\pgf@arcto@theta@end{-\pgf@arcto@theta@end} + \fi + \pgfmathsetmacro\pgf@arcto@delta@theta{abs(\pgf@arcto@theta@start-\pgf@arcto@theta@end)} + \ifdim\pgf@arcto@fA pt=0pt% + \ifdim\pgf@arcto@delta@theta pt>180pt% + \ifdim\pgf@arcto@theta@end pt>\pgf@arcto@theta@start pt + \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end-360} + \else + \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end+360} + \fi + \fi + \else + \ifdim\pgf@arcto@delta@theta pt<180pt% + \ifdim\pgf@arcto@theta@end pt>\pgf@arcto@theta@start pt + \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end-360} + \else + \pgfmathsetmacro\pgf@arcto@theta@end{\pgf@arcto@theta@end+360} + \fi + \fi + \fi + \xdef\pgf@marshal{\noexpand + \pgfpatharcaxes{\pgf@arcto@theta@start}{\pgf@arcto@theta@end} + {\noexpand\pgfpointpolar{\pgf@arcto@phi}{\pgf@arcto@rx}} + {\noexpand\pgfpointpolar{\pgf@arcto@phi+90}{\pgf@arcto@ry}} + } + \fi\fi\fi + } + \pgf@marshal +} + + + +\def\pgfpatharctomaxstepsize{45} + +\def\pgfpatharctoprecomputed#1#2#3#4#5#6#7#8{% + \begingroup + \pgf@process{#1}% + \edef\pgfpath@center@x{\the\pgf@x}% + \edef\pgfpath@center@y{\the\pgf@y}% + \def\pgfpath@completearcend{#4}% + \pgf@xa=#2pt + \pgf@xb=#3pt + \edef\pgfpath@startangle{#2pt}% + \edef\pgfpath@endangle{\pgf@sys@tonumber\pgf@xb}% + \pgf@ya=\pgf@xb + \advance\pgf@ya by-\pgf@xa + \ifx\pgfpatharctomaxstepsize\pgfutil@empty + \def\pgfpath@N{1}% + \pgf@xc=\pgf@ya + \else + \pgf@xc=\pgf@ya% + \ifdim\pgf@xc<0pt + \multiply\pgf@xc by-1 + \fi + \divide\pgf@xc by\pgfpatharctomaxstepsize\relax + \afterassignment\pgfutil@gobble@until@relax + \c@pgf@counta=\the\pgf@xc\relax + \advance\c@pgf@counta by1 + \edef\pgfpath@N{\the\c@pgf@counta}% + \pgf@xc=\pgf@ya + \divide\pgf@xc by\c@pgf@counta + \fi + \edef\pgfpath@h{\pgf@sys@tonumber\pgf@xc}% + \pgf@xc=0.116355283466289\pgf@xc % + \divide\pgf@xc by20 + \pgf@xa=#7\pgf@xc + \edef\pgfpath@scale@A{\pgf@sys@tonumber\pgf@xa}% + \pgf@xa=#8\pgf@xc + \edef\pgfpath@scale@B{\pgf@sys@tonumber\pgf@xa}% + \c@pgf@countd=1 + \pgfutil@loop + \ifnum\c@pgf@countd<\pgfpath@N\relax + \pgf@xa=\pgfpath@startangle % + \pgf@xb=\pgfpath@h pt + \multiply\pgf@xb by\c@pgf@countd + \advance\pgf@xa by\pgf@xb + \edef\pgfpath@angle@i{\pgf@sys@tonumber\pgf@xa}% + \pgfpatharcofellipse@{% + \pgfpoint + {\pgfpath@center@x + #5*cos(\pgfpath@angle@i)} + {\pgfpath@center@y + #6*sin(\pgfpath@angle@i)}% + }% + \advance\c@pgf@countd by1 + \pgfutil@repeat + \pgfpatharcofellipse@{\pgfpath@completearcend}% + \endgroup +}% +\def\pgfpatharcofellipse@#1{% + \begingroup + \pgf@process{#1}% + \edef\pgfpath@endpt{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% + \pgfpathcurveto{ + \begingroup + \global\pgf@x=\pgf@path@lastx + \global\pgf@y=\pgf@path@lasty + \pgf@xa=\pgf@x \advance\pgf@xa by-\pgfpath@center@x + \pgf@ya=\pgf@y \advance\pgf@ya by-\pgfpath@center@y + \global\advance\pgf@x by-\pgfpath@scale@A\pgf@ya + \global\advance\pgf@y by \pgfpath@scale@B\pgf@xa + \endgroup + }{% + \begingroup + \pgfpath@endpt + \pgf@xa=\pgf@x \advance\pgf@xa by-\pgfpath@center@x + \pgf@ya=\pgf@y \advance\pgf@ya by-\pgfpath@center@y + \global\advance\pgf@x by \pgfpath@scale@A\pgf@ya + \global\advance\pgf@y by-\pgfpath@scale@B\pgf@xa + \endgroup + }{% + \pgfpath@endpt + }% + \endgroup +} + + + + + + + + + + +\def\pgfpathellipse#1#2#3{% + \pgfpointtransformed{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfpointtransformed{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \advance\pgf@xa by-\pgf@pt@x% + \advance\pgf@ya by-\pgf@pt@y% + \pgfpointtransformed{#3}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \advance\pgf@xb by-\pgf@pt@x% + \advance\pgf@yb by-\pgf@pt@y% + {% + \advance\pgf@xa by\pgf@xc% + \advance\pgf@ya by\pgf@yc% + \pgf@nlt@moveto{\pgf@xa}{\pgf@ya}% + }% + \pgf@x=0.55228475\pgf@xb% + \pgf@y=0.55228475\pgf@yb% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}% + \pgf@x=0.55228475\pgf@xa% + \pgf@y=0.55228475\pgf@ya% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + {% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \advance\pgf@xb by\pgf@xc% + \advance\pgf@yb by\pgf@yc% + \pgf@temp% + \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xb}{\pgf@yb}% + }% + \pgf@xa=-\pgf@xa% + \pgf@ya=-\pgf@ya% + \pgf@x=0.55228475\pgf@xa% + \pgf@y=0.55228475\pgf@ya% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}% + \pgf@x=0.55228475\pgf@xb% + \pgf@y=0.55228475\pgf@yb% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + {% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \advance\pgf@xa by\pgf@xc% + \advance\pgf@ya by\pgf@yc% + \pgf@temp% + \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}% + }% + \pgf@xb=-\pgf@xb% + \pgf@yb=-\pgf@yb% + \pgf@x=0.55228475\pgf@xb% + \pgf@y=0.55228475\pgf@yb% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}% + \pgf@x=0.55228475\pgf@xa% + \pgf@y=0.55228475\pgf@ya% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + {% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \advance\pgf@xb by\pgf@xc% + \advance\pgf@yb by\pgf@yc% + \pgf@temp% + \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xb}{\pgf@yb}% + }% + \pgf@xa=-\pgf@xa% + \pgf@ya=-\pgf@ya% + \pgf@x=0.55228475\pgf@xa% + \pgf@y=0.55228475\pgf@ya% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \edef\pgf@temp{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}% + \pgf@x=0.55228475\pgf@xb% + \pgf@y=0.55228475\pgf@yb% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + {% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \advance\pgf@xa by\pgf@xc% + \advance\pgf@ya by\pgf@yc% + \pgf@temp% + \pgf@nlt@curveto{\pgf@xc}{\pgf@yc}{\pgf@x}{\pgf@y}{\pgf@xa}{\pgf@ya}% + }% + \pgf@nlt@closepath% + \pgf@nlt@moveto{\pgf@xc}{\pgf@yc}% +} + + + + +\def\pgfpathcircle#1#2{\pgfpathellipse{#1}{\pgfpoint{#2}{0pt}}{\pgfpoint{0pt}{#2}}} + + + + + +\def\pgfpathrectangle{% + \let\pgfrect@next=\pgf@specialrect% + \ifpgf@pt@identity% + \ifpgf@arccorners% + \else% + \ifx\pgf@nlt@list\pgfutil@empty% + \let\pgfrect@next=\pgf@normalrect% + \fi% + \fi% + \fi% + \pgfrect@next% +} + +\def\pgf@normalrect#1#2{% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfpointtransformed{#1}% + \pgfsyssoftpath@rect{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \advance\pgf@x by\pgf@xa\relax% + \advance\pgf@y by\pgf@ya\relax% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% +} + +\def\pgf@specialrect#1#2{% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#1}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \advance\pgf@xa by\pgf@xb% + \advance\pgf@ya by\pgf@yb% + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}% + \pgfpathclose% + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yb}}% +} + + +\def\pgfpathrectanglecorners#1#2{% + \pgf@process{#2}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{#1}% + \advance\pgf@xc by-\pgf@x% + \advance\pgf@yc by-\pgf@y% + \pgfpathrectangle{#1}{\pgfqpoint{\pgf@xc}{\pgf@yc}}% +} + + + +\pgfkeys{ + /pgf/stepx/.initial=1cm, + /pgf/stepy/.initial=1cm, + /pgf/step/.code={\pgf@process{#1}\pgfkeysalso{/pgf/stepx/.expanded=\the\pgf@x,/pgf/stepy/.expanded=\the\pgf@y}}, + /pgf/step/.value required +} + +\def\pgfpathgrid{\pgfutil@ifnextchar[{\pgf@pathgrid}{\pgf@pathgrid[]}} +\def\pgf@pathgrid[#1]#2#3{% + \pgfset{#1}% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/stepx}}% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/stepy}}% + \pgf@process{#3}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \ifdim\pgf@xa>\pgf@xb% + \pgf@x=\pgf@xb% + \pgf@xb=\pgf@xa% + \pgf@xa=\pgf@x% + \fi% + \ifdim\pgf@ya>\pgf@yb% + \pgf@y=\pgf@yb% + \pgf@yb=\pgf@ya% + \pgf@ya=\pgf@y% + \fi% + \ifdim \pgf@yc > .01pt\relax% + \c@pgf@counta=\pgf@ya\relax% + \c@pgf@countb=\pgf@yc\relax% + \divide\c@pgf@counta by\c@pgf@countb\relax% + \pgfutil@tempdima=\c@pgf@counta\pgf@yc\relax% + \ifdim\pgfutil@tempdima<\pgf@ya% + \advance\pgfutil@tempdima by\pgf@yc% + \fi% + \pgfutil@tempdimb\pgf@x + \pgfutil@loop% + {% + \pgf@xa=\pgfutil@tempdimb% + \pgf@ya=\pgfutil@tempdima% + \pgf@pos@transform{\pgf@xa}{\pgf@ya} + \pgf@nlt@moveto{\pgf@xa}{\pgf@ya}% + \pgf@xa=\pgf@xb% + \pgf@ya=\pgfutil@tempdima% + \pgf@pos@transform{\pgf@xa}{\pgf@ya} + \pgf@nlt@lineto{\pgf@xa}{\pgf@ya}% + }% + \advance\pgfutil@tempdima by\pgf@yc% + \ifdim\pgfutil@tempdima<\pgf@yb% + \pgfutil@repeat% + \advance\pgfutil@tempdima by-0.01pt\relax% + \ifdim\pgfutil@tempdima<\pgf@yb% + {% + \pgf@xa=\pgfutil@tempdimb% + \pgf@ya=\pgfutil@tempdima% + \pgf@pos@transform{\pgf@xa}{\pgf@ya} + \pgf@nlt@moveto{\pgf@xa}{\pgf@ya}% + \pgf@xa=\pgf@xb% + \pgf@ya=\pgfutil@tempdima% + \pgf@pos@transform{\pgf@xa}{\pgf@ya} + \pgf@nlt@lineto{\pgf@xa}{\pgf@ya}% + }% + \fi% + \fi% + \ifdim \pgf@xc > .01pt\relax% + \c@pgf@counta=\pgf@xa\relax% + \c@pgf@countb=\pgf@xc\relax% + \divide\c@pgf@counta by\c@pgf@countb\relax% + \pgfutil@tempdimb=\c@pgf@counta\pgf@xc\relax% + \ifdim\pgfutil@tempdimb<\pgf@xa% + \advance\pgfutil@tempdimb by\pgf@xc% + \fi% + \pgfutil@loop% + {% + \pgf@xc=\pgfutil@tempdimb% + \pgf@yc=\pgf@ya% + \pgf@pos@transform{\pgf@xc}{\pgf@yc} + \pgf@nlt@moveto{\pgf@xc}{\pgf@yc}% + \pgf@xc=\pgfutil@tempdimb% + \pgf@yc=\pgf@yb% + \pgf@pos@transform{\pgf@xc}{\pgf@yc} + \pgf@nlt@lineto{\pgf@xc}{\pgf@yc}% + }% + \advance\pgfutil@tempdimb by\pgf@xc% + \ifdim\pgfutil@tempdimb<\pgf@xb% + \pgfutil@repeat% + \advance\pgfutil@tempdimb by-0.01pt\relax% + \ifdim\pgfutil@tempdimb<\pgf@xb% + {% + \pgf@xc=\pgfutil@tempdimb% + \pgf@yc=\pgf@ya% + \pgf@pos@transform{\pgf@xc}{\pgf@yc} + \pgf@nlt@moveto{\pgf@xc}{\pgf@yc}% + \pgf@xc=\pgfutil@tempdimb% + \pgf@yc=\pgf@yb% + \pgf@pos@transform{\pgf@xc}{\pgf@yc} + \pgf@nlt@lineto{\pgf@xc}{\pgf@yc}% + }% + \fi% + \fi% + \pgf@process{#3}% + \pgf@pos@transform{\pgf@x}{\pgf@y}% + \pgf@nlt@moveto{\pgf@x}{\pgf@y}% +} + + + + +\def\pgfpathparabola#1#2{% + {% + \pgf@process{#2}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfutil@tempswatrue% + \ifdim\pgf@xb=0pt\relax% + \ifdim\pgf@yb=0pt\relax% + \pgfutil@tempswafalse% + \fi% + \fi% + {% + \ifpgfutil@tempswa% + \pgf@arccornersfalse + \else% + \fi% + \pgfutil@tempswatrue% + \ifdim\pgf@xc=0pt\relax% + \ifdim\pgf@yc=0pt\relax% + \pgfutil@tempswafalse% + \fi% + \fi% + \ifpgfutil@tempswa + {% + \pgf@pt@x=\pgf@path@lastx% + \pgf@pt@y=\pgf@path@lasty% + \pgfpathcurveto% + {\pgfqpoint{.1125\pgf@xc}{.225\pgf@yc}}% + {\pgfqpoint{.5\pgf@xc}{\pgf@yc}}% + {\pgfqpoint{\pgf@xc}{\pgf@yc}}% + }% + \fi% + }% + \ifpgfutil@tempswa% + \pgf@xc=\pgf@xb% + \pgf@yc=\pgf@yb% + {% + \pgf@pt@x=\pgf@path@lastx% + \pgf@pt@y=\pgf@path@lasty% + \pgfpathcurveto% + {\pgfqpoint{.5\pgf@xc}{0\pgf@yc}}% + {\pgfqpoint{.8875\pgf@xc}{.775\pgf@yc}}% + {\pgfqpoint{\pgf@xc}{\pgf@yc}}% + }% + \fi% + }% +} + + + + + +\def\pgfpathsine#1{% + {% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@pt@x=\pgf@path@lastx% + \pgf@pt@y=\pgf@path@lasty% + \pgfpathcurveto% + {\pgfqpoint{.3260\pgf@xc}{.5120\pgf@yc}}% + {\pgfqpoint{.6380\pgf@xc}{\pgf@yc}}% + {\pgfqpoint{\pgf@xc}{\pgf@yc}}% + }% +} + + +\def\pgfpathcosine#1{% + {% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@pt@x=\pgf@path@lastx% + \pgf@pt@y=\pgf@path@lasty% + \pgfpathcurveto% + {\pgfqpoint{.3620\pgf@xc}{0pt}}% + {\pgfqpoint{.6740\pgf@xc}{.4880\pgf@yc}}% + {\pgfqpoint{\pgf@xc}{\pgf@yc}}% + }% +} + + + +\def\pgfpathcurvebetweentime{\pgf@ignoremovetofalse\pgf@@pathcurvebetweentime} +\def\pgfpathcurvebetweentimecontinue{\pgf@ignoremovetotrue\pgf@@pathcurvebetweentime} +\newif\ifpgf@ignoremoveto + +\def\pgf@@pathcurvebetweentime#1#2#3#4#5#6{% + \pgfmathparse{#1}% + \let\pgf@time@s=\pgfmathresult% + \pgfmathparse{#2}% + \let\pgf@time@t=\pgfmathresult% + \ifdim\pgf@time@s pt>\pgf@time@t pt\relax% + \pgfmathsetmacro\pgf@time@s{1-#1}% + \pgfmathsetmacro\pgf@time@t{1-#2}% + \pgf@@@pathcurvebetweentime{\pgf@time@t}{#6}{#5}{#4}{#3}% + \else% + \pgf@@@pathcurvebetweentime{\pgf@time@t}{#3}{#4}{#5}{#6}% + \fi% +} + +\def\pgf@@@pathcurvebetweentime#1#2#3#4#5{% + \pgf@process{#2}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{% + \pgf@process{#3}% + \pgf@xa=#1\pgf@x% + \pgf@ya=#1\pgf@y% + \pgf@process{#2}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \advance\pgf@x by-#1\pgf@xb% + \advance\pgf@y by-#1\pgf@yb% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + }% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{% + \pgf@process{#4}% + \pgf@xa=#1\pgf@x% + \pgf@ya=#1\pgf@y% + \pgf@process{#3}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xc by-#1\pgf@x% + \advance\pgf@yc by-#1\pgf@y% + \pgf@x=\pgf@xb% + \pgf@y=\pgf@yb% + \advance\pgf@x by#1\pgf@xa% + \advance\pgf@y by#1\pgf@ya% + \advance\pgf@x by-#1\pgf@xb% + \advance\pgf@y by-#1\pgf@yb% + \advance\pgf@x by#1\pgf@xc% + \advance\pgf@y by#1\pgf@yc% + }% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointcurveattime{#1}{#2}{#3}{#4}{#5}}% + \ifx#1\pgf@time@t% + \pgfmathdivide@{\pgf@time@s}{\pgf@time@t}% + \pgfmathadd@{-\pgfmathresult}{1}% + \let\pgf@time@s=\pgfmathresult% + \edef\pgf@marshal{% + \noexpand\pgf@@@pathcurvebetweentime{\noexpand\pgf@time@s}% + {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + }% + \else% + \ifpgf@ignoremoveto% + \edef\pgf@marshal{% + \noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + }% + \else% + \edef\pgf@marshal{% + \noexpand\pgfpathmoveto{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + }% + \fi% + \fi% + \pgf@marshal% +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..53ed8df15f694da9691d9e94a3074f9f1f63f32a --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathprocessing.code.tex @@ -0,0 +1,417 @@ + +\ProvidesFileRCS{pgfcorepathprocessing.code.tex} + + + +\def\pgfprocesssplitpath#1{% + \let\pgfprocessresultpathprefix\pgfutil@empty% + \let\pgfprocessresultpathsuffix\pgfutil@empty% + \let\pgf@next\pgf@process@split% + \expandafter\pgf@process@split#1\pgfsyssoftpath@movetotoken{}{}\pgf@stop% +} + +\def\pgf@process@split#1\pgfsyssoftpath@movetotoken#2#3#4{% + \ifx#4\pgf@stop% + \expandafter\def\expandafter\pgfprocessresultpathsuffix\expandafter{\pgfprocessresultpathsuffix#1}% + \let\pgf@next\pgfutil@gobble% + \else% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgfprocessresultpathprefix% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix#1}% + \def\pgfprocessresultpathsuffix{\pgfsyssoftpath@movetotoken{#2}{#3}}% + \fi% + \pgf@next#4% +} + + + + +\def\pgfprocesssplitsubpath#1{% + \let\pgf@tempa\pgfutil@emtpy% + \let\pgf@tempb\pgfutil@emtpy% + \let\pgf@tempc\pgfutil@emtpy% + \let\pgf@tempd\pgfutil@emtpy% + \let\pgfprocessresultsubpathprefix\pgfutil@empty% + \let\pgfprocessresultsubpathsuffix\pgfutil@empty% + \let\pgf@next\pgf@split@subpath% + \expandafter\pgf@split@subpath#1\pgf@stop% +} + +\newif\ifpgf@split@move + +\def\pgf@split@subpath#1#2#3#4{% + \ifx#4\pgf@stop% + \expandafter\def\expandafter\pgfprocessresultsubpathsuffix\expandafter{\pgfprocessresultsubpathsuffix#1{#2}{#3}}% + \let\pgf@next\pgfutil@gobble% + \else% + \pgf@split@movetrue% + \ifx#1\pgfsyssoftpath@curvetosupportatoken% + \pgf@split@movefalse% + \else + \ifx#1\pgfsyssoftpath@curvetosupportbtoken% + \pgf@split@movefalse% + \fi% + \fi% + \ifpgf@split@move% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgfprocessresultsubpathprefix% + \expandafter\expandafter\expandafter{% + \expandafter\pgfprocessresultsubpathprefix\pgfprocessresultsubpathsuffix}% + \def\pgfprocessresultsubpathsuffix{#1{#2}{#3}}% + \else% + \expandafter\def\expandafter\pgfprocessresultsubpathsuffix\expandafter{\pgfprocessresultsubpathsuffix#1{#2}{#3}}% + \fi% + \fi% + \pgf@next#4% +} + + + + + +\def\pgfprocesspathextractpoints#1{% + \ifx#1\pgfutil@empty% + \let\pgfpointfirstonpath=\pgfpointorigin% + \let\pgfpointsecondonpath=\pgfpointorigin% + \let\pgfpointsecondlastonpath=\pgfpointorigin% + \let\pgfpointlastonpath=\pgfpointorigin% + \else% + \expandafter\pgf@extractprocessorfirst#1\pgf@stop% + \fi% +} + +\def\pgf@extractprocessorfirst#1#2#3#4{% + \def\pgfpointfirstonpath{\pgfqpoint{#2}{#3}}% + \ifx#4\pgf@stop% + \let\pgfpointsecondonpath=\pgfpointfirstonpath% + \let\pgfpointsecondlastonpath=\pgfpointfirstonpath% + \let\pgfpointlastonpath=\pgfpointfirstonpath% + \let\next=\pgfutil@gobble% + \else + \let\next=\pgf@extractprocessorsecond% + \fi% + \next#4% +} + +\def\pgf@extractprocessorsecond#1{% + \ifx#1\pgfsyssoftpath@movetotoken% + \let\pgf@next=\pgf@extractprocessorfirst% + \else% + \let\pgf@next=\pgf@@extractprocessorsecond% + \fi% + \pgf@next#1% +} +\def\pgf@@extractprocessorsecond#1#2#3#4{% + \def\pgfpointsecondonpath{\pgfqpoint{#2}{#3}}% + \let\pgfpointsecondlastonpath=\pgfpointfirstonpath% + \let\pgfpointlastonpath=\pgfpointsecondonpath% + \ifx#4\pgf@stop% + \let\next=\pgfutil@gobble% + \else + \let\next=\pgf@extractprocessorother% + \fi% + \next#4% +} + +\def\pgf@extractprocessorother#1{% + \ifx#1\pgfsyssoftpath@movetotoken% + \let\pgf@next=\pgf@extractprocessorfirst% + \else% + \let\pgf@next=\pgf@@extractprocessorother% + \fi% + \pgf@next#1% +} +\def\pgf@@extractprocessorother#1#2#3#4{% + \let\pgfpointsecondlastonpath=\pgfpointlastonpath% + \def\pgfpointlastonpath{\pgfqpoint{#2}{#3}}% + \ifx#4\pgf@stop% + \let\next=\pgfutil@gobble% + \fi% + \next#4% +} + + + + +\def\pgfprocesscheckclosed#1#2{% + {% + \global\let\pgf@proc@todo=\relax% + \let\pgfsyssoftpath@movetotoken=\pgfutil@gobbletwo% + \let\pgfsyssoftpath@linetotoken=\pgfutil@gobbletwo% + \let\pgfsyssoftpath@curvetosupportatoken=\pgfutil@gobbletwo% + \let\pgfsyssoftpath@curvetosupportbtoken=\pgfutil@gobbletwo% + \let\pgfsyssoftpath@curvetotoken=\pgfutil@gobbletwo% + \def\pgfsyssoftpath@rectcornertoken{\gdef\pgf@proc@todo{#2}\pgfutil@gobbletwo}% + \def\pgfsyssoftpath@rectsizetoken{\gdef\pgf@proc@todo{#2}\pgfutil@gobbletwo}% + \def\pgfsyssoftpath@closepathtoken{\gdef\pgf@proc@todo{#2}\pgfutil@gobbletwo}% + #1% + }% + \pgf@proc@todo% +} + + + +\def\pgfprocessround#1#2{% + \expandafter\pgf@processroundcheck\expandafter#1\expandafter#2#1\pgfsyssoftpath@specialroundtoken\pgf@stop% +} + +\def\pgf@processroundcheck#1#2#3\pgfsyssoftpath@specialroundtoken#4\pgf@stop{% + \def\pgf@test{#4}% + \ifx\pgf@test\pgfutil@empty% + \let#2=#1% + \else% + \pgf@@processround#1#2% + \fi% +} + + +\def\pgf@@processround#1#2{% + \let\pgfprocess@newpath\pgfutil@empty% + \let\pgfprocess@moveto\pgfutil@empty% + \let\pgfprocess@firstto\pgfutil@empty% + \let\pgfprocess@segment\pgfutil@empty% + \pgf@xa=0pt% + \pgf@ya=0pt% + \expandafter\pgfprocess@round#1\pgf@stop{0pt}{0pt}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@moveto}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@segment}% + \let#2=\pgfprocess@newpath% +} + +\def\pgfprocess@round#1#2#3{% + \ifx#1\pgf@stop% + \let\next=\relax% + \else% + \ifx#1\pgfsyssoftpath@specialroundtoken% + \def\pgfprocess@savex{#2}% + \def\pgfprocess@savey{#3}% + \let\next=\pgfprocess@specialround% + \ifdim#2=0pt% + \ifdim#3=0pt% + \let\next=\pgfprocess@round% + \fi% + \fi% + \else% + \ifx\pgfprocess@firstto\pgfutil@empty% + \def\pgfprocess@firstto{{#2}{#3}}% + \fi% + \pgf@xa=#2% + \pgf@ya=#3% + \ifx#1\pgfsyssoftpath@movetotoken% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@moveto}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@newpath\expandafter{\pgfprocess@segment}% + \def\pgfprocess@moveto{#1{#2}{#3}}% + \let\pgfprocess@firstto=\pgfutil@empty% + \let\pgfprocess@segment=\pgfutil@empty% + \else% + \pgfutil@g@addto@macro\pgfprocess@segment{#1{#2}{#3}}% + \fi% + \let\next=\pgfprocess@round% + \fi% + \fi% + \next% +} + +\def\pgfprocess@specialround#1#2#3{% + \ifx\pgfprocess@firstto\pgfutil@empty% + \def\pgfprocess@firstto{{#2}{#3}}% + \fi% + \let\next=\pgfprocess@round% + \ifx#1\pgfsyssoftpath@linetotoken% + \let\next=\pgfprocess@specialroundcope% + \else% + \ifx#1\pgfsyssoftpath@curvetosupportatoken% + \let\next=\pgfprocess@specialroundcurveto% + \else% + \ifx#1\pgfsyssoftpath@closepathtoken% + \let\next=\pgfprocess@specialroundclose% + \fi% + \fi% + \fi% + \next#1{#2}{#3}% +}% + +\def\pgfprocess@specialroundcope#1#2#3#4#5#6{% + \let\next=\pgfprocess@round% + \let\pgfprocess@continueafterrounding=\pgfprocess@round% + \ifx#4\pgfsyssoftpath@linetotoken% + \pgf@xc=#5% + \pgf@yc=#6% + \let\next=\pgfprocess@@specialround% + \else% + \ifx#4\pgfsyssoftpath@curvetosupportatoken% + \pgf@xc=#5% + \pgf@yc=#6% + \let\next=\pgfprocess@@specialround% + \else% + \ifx#4\pgfsyssoftpath@closepathtoken% + \pgf@xc=#5% + \pgf@yc=#6% + \let\next=\pgfprocess@@specialround% + \else + \ifx#4\pgfsyssoftpath@specialroundtoken% + \let\next=\pgfprocess@@findrightcoordinates% + \fi% + \fi% + \fi% + \fi% + \next#1{#2}{#3}#4{#5}{#6}% +} + +\def\pgfprocess@@findrightcoordinates#1#2#3#4#5#6#7#8#9{% + \pgf@xc=#8% + \pgf@yc=#9% + \pgfprocess@@specialround#1{#2}{#3}#4{#5}{#6}#7{#8}{#9}% +} + +\def\pgfprocess@@specialround#1#2#3{% + \pgfutil@g@addto@macro\pgfprocess@segment{#1}% + \pgf@xb=#2% + \pgf@yb=#3% + \edef\pgf@marshal% + {\noexpand\pgfpointlineatdistance{\pgfprocess@savex}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}% + {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}}% + \pgf@process{\pgf@marshal}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \edef\pgfprocess@addition{{\the\pgf@x}{\the\pgf@y}}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}% + \edef\pgf@marshal% + {\noexpand\pgfpointlineatdistance{\pgfprocess@savey}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}% + {\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}}% + \pgf@process{\pgf@marshal}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + {% + \pgf@x=\pgf@xb% + \pgf@y=\pgf@yb% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@y by-\pgf@ya% + \advance\pgf@xa by 0.5522847\pgf@x% + \advance\pgf@ya by 0.5522847\pgf@y% + \edef\pgfprocess@addition{\noexpand\pgfsyssoftpath@curvetosupportatoken{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}% + }% + {% + \pgf@x=\pgf@xb% + \pgf@y=\pgf@yb% + \advance\pgf@x by-\pgf@xc% + \advance\pgf@y by-\pgf@yc% + \advance\pgf@xc by 0.5522847\pgf@x% + \advance\pgf@yc by 0.5522847\pgf@y% + \edef\pgfprocess@addition{\noexpand\pgfsyssoftpath@curvetosupportbtoken{\the\pgf@xc}{\the\pgf@yc}}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}% + }% + \edef\pgfprocess@addition{\noexpand\pgfsyssoftpath@curvetotoken{\the\pgf@xc}{\the\pgf@yc}}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfprocess@segment\expandafter{\pgfprocess@addition}% + \pgf@xa=#2% + \pgf@ya=#3% + \pgfprocess@continueafterrounding% +} + +\def\pgfprocess@specialroundcurveto#1#2#3#4#5#6{% + \pgfutil@g@addto@macro\pgfprocess@segment{#1{#2}{#3}#4{#5}{#6}}% + \pgf@xa=#5% + \pgf@ya=#6% + \pgfprocess@specialroundcope} + +\def\pgfprocess@specialroundclose{% + \let\next=\pgfprocess@round% + \ifx\pgfprocess@moveto\pgfutil@empty% + \else% + \ifx\pgfprocess@firstto\pgfutil@empty% + \else% + \expandafter\pgfprocess@@specialclosetarget\pgfprocess@firstto% + \let\pgfprocess@continueafterrounding=\pgfprocess@cleanupafterclose% + \edef\next{% + \noexpand\pgfprocess@@specialround% + \expandafter\expandafter\expandafter\noexpand\expandafter\pgfprocess@@specialclosemoveto\pgfprocess@moveto% + }% + \fi% + \fi% + \next% +} + +\def\pgfprocess@@specialclosetarget#1#2{% + \pgf@xc=#1% + \pgf@yc=#2% +} + +\def\pgfprocess@@specialclosemoveto#1#2#3{% + \pgfsyssoftpath@linetotoken{#2}{#3}% +} + + +\def\pgfprocess@cleanupafterclose#1#2#3{% + \edef\pgfprocess@moveto{\noexpand\pgfsyssoftpath@movetotoken{\the\pgf@xc}{\the\pgf@yc}}% + \edef\pgf@marshal{\noexpand\pgfprocess@round\noexpand\pgfsyssoftpath@closepathtoken{\the\pgf@xc}{\the\pgf@yc}}% + \pgf@marshal% +} + + + +\def\pgfprocesspathreplacestartandend#1#2#3{% + \ifx#1\pgfutil@empty% + \else% + {% + \pgfsyssoftpath@getcurrentpath\pgf@replace@origpath% + \let\pgf@prepath=\pgfutil@empty% + \pgf@process{#3}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#2}% + \expandafter\pgf@replaceprocessfirst#1\pgf@stop% + \pgfsyssoftpath@getcurrentpath\pgf@restpath% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter#1% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{% + \expandafter\expandafter\expandafter\pgf@prepath% + \expandafter\pgf@newstart\pgf@restpath}% + \pgfsyssoftpath@setcurrentpath\pgf@replace@origpath% + }% + \fi% +} + +\def\pgf@replaceprocessfirst#1#2#3#4{% + \def\pgf@origstart{#1{#2}{#3}}% + \edef\pgf@newstart{\noexpand#1{\the\pgf@x}{\the\pgf@y}}% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + \ifx#4\pgf@stop% + \let\pgf@next=\pgfutil@gobble% + \else% + \let\pgf@next=\pgf@replaceprocessother% + \let\pgf@@next=\pgf@@replaceprocessother% + \fi% + \pgf@next#4% +} + +\def\pgf@replaceprocessother#1{% + \ifx#1\pgfsyssoftpath@movetotoken% + \pgf@replace@handle@move% + \fi% + \pgf@@next#1% +} +\def\pgf@@replaceprocessother#1#2#3#4{% + \ifx#4\pgf@stop% + \edef\pgf@restpathaddition{{\noexpand#1{\the\pgf@xa}{\the\pgf@ya}}}% + \expandafter\pgfsyssoftpath@addtocurrentpath\pgf@restpathaddition% + \let\pgf@next=\pgfutil@gobble% + \else% + \pgfsyssoftpath@addtocurrentpath{#1{#2}{#3}}% + \fi% + \pgf@next#4% +} + +\def\pgf@replace@handle@move{% + \pgfsyssoftpath@getcurrentpath\pgf@restpath% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\pgf@prepath% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{% + \expandafter\expandafter\expandafter\pgf@prepath% + \expandafter\pgf@origstart\pgf@restpath}% + \let\pgf@@next=\pgf@replaceprocessfirst% +} + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3258ae3a96fbde780ca05f56cfa67fdfacd829f3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepathusage.code.tex @@ -0,0 +1,510 @@ + +\ProvidesFileRCS{pgfcorepathusage.code.tex} + + + +\pgfkeys{ + /pgf/stroke/.code=\let\pgf@up@stroke\pgf@up@stroke@text\pgf@up@path@neededtrue, + /pgf/draw/.code=\let\pgf@up@stroke\pgf@up@stroke@text\pgf@up@path@neededtrue, + /pgf/fill/.code=\let\pgf@up@fill\pgf@up@fill@text\pgf@up@path@neededtrue, + /pgf/clip/.code=\let\pgf@up@clip\pgf@up@clip@text\pgf@up@path@neededtrue, + /pgf/discard/.code=, + /pgf/use as bounding box/.code=\let\pgf@up@bb\pgf@do@up@bb, + /pgf/arrow keys/flex/.code=\pgferror{You need to say \string\usetikzlibrary{bending} for flexing and bending arrows}, + /pgf/arrow keys/flex'/.code=\pgferror{You need to say \string\usetikzlibrary{bending} for flexing and bending arrows}, + /pgf/arrow keys/bend/.code=\pgferror{You need to say \string\usetikzlibrary{bending} for flexing and bending arrows}, + /pgf/arrow keys/quick/.code=\pgfarrowsaddtooptions{\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@quick}, +} + +\pgfkeys{ + /pgf/.cd, + tips/.is choice, + tips/.default=true, + tips/proper/.code=\let\pgf@tips@mode\pgf@tips@mode@onproper, + tips/on proper draw/.code=\let\pgf@tips@mode\pgf@tips@mode@onproperdraw, + tips/true/.code=\let\pgf@tips@mode\pgf@tips@mode@true, + tips/on draw/.code=\let\pgf@tips@mode\pgf@tips@mode@ondraw, + tips/never/.code=\let\pgf@tips@mode\pgf@tips@mode@false, + tips/false/.code=\let\pgf@tips@mode\pgf@tips@mode@false, +} +\def\pgf@tips@mode@onproper{4} +\def\pgf@tips@mode@onproperdraw{3} +\def\pgf@tips@mode@true{2} +\def\pgf@tips@mode@ondraw{1} +\def\pgf@tips@mode@false{0} +\let\pgf@tips@mode\pgf@tips@mode@ondraw + + +\newif\ifpgf@precise@shortening +\def\pgf@arrow@mode@is@quick{0} +\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@quick + +\newif\ifpgf@up@path@needed +\newif\ifpgf@up@draw@arrows +\def\pgf@up@stroke@text{stroke} +\def\pgf@up@fill@text{fill} +\def\pgf@up@clip@text{clip} +\def\pgf@do@up@bb{\pgf@relevantforpicturesizefalse} + +\def\pgfusepath#1{% + \pgf@up@path@neededfalse% + \pgf@up@draw@arrowsfalse% + \let\pgf@up@stroke\pgfutil@empty% + \let\pgf@up@fill\pgfutil@empty% + \let\pgf@up@clip\pgfutil@empty% + \let\pgf@up@bb\pgfutil@empty% + \pgfset{#1}% + \expandafter\def\expandafter\pgf@up@action\expandafter{\csname pgfsys@\pgf@up@fill\pgf@up@stroke\endcsname}% + \ifnum\pgf@tips@mode=2\relax% + \pgf@up@path@neededtrue% + \fi% + \ifnum\pgf@tips@mode=4\relax% + \pgf@up@path@neededtrue% + \fi% + \ifpgf@up@path@needed% + \else% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + \fi% + \ifx\pgf@up@stroke\pgfutil@empty% + \ifx\pgf@up@fill\pgfutil@empty% + \let\pgf@up@action=\pgfutil@empty% + \ifx\pgf@up@clip\pgfutil@empty% + \else% + \let\pgf@up@action=\pgfsys@discardpath% + \fi% + \fi% + \fi% + \pgfsyssoftpath@getcurrentpath\pgf@last@processed@path + \pgfprocessround{\pgf@last@processed@path}{\pgf@last@processed@path}% + \pgfsyssoftpath@setcurrentpath\pgf@last@processed@path% + \ifpgf@relevantforpicturesize% + \ifx\pgf@up@stroke\pgfutil@empty% + \else% + \ifdim\pgf@picmaxx=-16000pt\relax% + \else% + \pgf@x=\pgf@pathminx\advance\pgf@x by-.5\pgflinewidth% + \ifdim\pgf@x<\pgf@picminx\global\pgf@picminx\pgf@x\fi% + \pgf@y=\pgf@pathminy\advance\pgf@y by-.5\pgflinewidth% + \ifdim\pgf@y<\pgf@picminy\global\pgf@picminy\pgf@y\fi% + \pgf@x=\pgf@pathmaxx\advance\pgf@x by.5\pgflinewidth% + \ifdim\pgf@x>\pgf@picmaxx\global\pgf@picmaxx\pgf@x\fi% + \pgf@y=\pgf@pathmaxy\advance\pgf@y by.5\pgflinewidth% + \ifdim\pgf@y>\pgf@picmaxy\global\pgf@picmaxy\pgf@y\fi% + \fi% + \fi% + \fi% + \ifx\pgf@up@clip\pgfutil@empty% + \ifx\pgf@up@stroke\pgfutil@empty% + \ifx\pgf@up@action\pgfutil@empty% + \ifnum\pgf@tips@mode=2\relax% + \pgf@up@draw@arrows@only% + \fi% + \ifnum\pgf@tips@mode=4\relax% + \pgf@up@draw@arrows@only% + \fi% + \else% + \pgfsyssoftpath@invokecurrentpath% + \pgf@up@action% + \fi% + \else% + \pgfgetpath\pgf@arrowpath% + \pgf@path@setup@tempswa% + \pgfprocesscheckclosed{\pgf@arrowpath}{\pgfutil@tempswafalse}% + \pgf@path@check@proper% + \ifpgfutil@tempswa% + \pgf@check@for@arrow@and@animation% + \pgf@prepare@end@of@path% + \begingroup% + \pgf@prepare@start@of@path% + \fi% + \pgfsyssoftpath@invokecurrentpath% + \pgf@up@action% + \ifdim\pgfinnerlinewidth>0pt\relax% + \pgf@stroke@inner@line% + \fi% + \ifpgfutil@tempswa% + \pgf@add@arrow@at@start% + \endgroup% + \pgf@add@arrow@at@end% + \fi% + \fi% + \else% + \pgfsyssoftpath@invokecurrentpath% + \pgfsys@clipnext% + \pgf@up@action% + \pgf@relevantforpicturesizefalse% + \fi% + \pgf@up@bb% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + \pgf@resetpathsizes% + \ignorespaces% +} +\def\pgf@path@setup@tempswa{% + \ifnum\pgf@tips@mode>0\relax + \pgfutil@tempswatrue% + \else + \pgfutil@tempswafalse% + \fi% +} +\def\pgf@up@draw@arrows@only{% + \pgfgetpath\pgf@arrowpath% + \pgfutil@tempswatrue% + \pgfprocesscheckclosed{\pgf@arrowpath}{\pgfutil@tempswafalse}% + \pgf@path@check@proper% + \ifpgfutil@tempswa% + \pgf@check@for@arrow@and@animation% + \pgf@prepare@end@of@path% + \begingroup% + \pgf@prepare@start@of@path% + \pgf@add@arrow@at@start% + \endgroup% + \pgf@add@arrow@at@end% + \fi% +} + +\def\pgf@check@for@arrow@and@animation{\pgfsys@if@fresh@currentid{\pgf@check@for@arrow@and@animation@}{}}% +\def\pgf@check@for@arrow@and@animation@{% + \expandafter\ifx\csname pgfsysanim@path@is@animated@\pgf@sys@id@current@id @\pgfsys@current@type\endcsname\pgfutil@empty% + \ifx\pgf@end@tip@sequence\pgfutil@empty% + \ifx\pgf@start@tip@sequence\pgfutil@empty% + \else% + \pgf@check@for@arrow@and@animation@error% + \fi% + \else% + \pgf@check@for@arrow@and@animation@error% + \fi% + \fi% +} +\def\pgf@check@for@arrow@and@animation@error{\pgferror{Animated path may not have normal arrow tips. Use a base path with arrow tips}} + +\def\pgf@path@check@proper{% + \ifpgfutil@tempswa% + \ifnum\pgf@tips@mode>2\relax% + \pgf@path@check@proper@% + \fi% + \fi% +} + +\def\pgf@path@check@proper@{% + {% + \pgf@x0pt\pgf@y\pgf@x% + \pgfutil@tempswatrue% + \let\pgfsyssoftpath@movetotoken\pgf@path@proper@init% + \let\pgfsyssoftpath@linetotoken\pgf@path@proper@test% + \let\pgfsyssoftpath@curvetosupportatoken\pgf@path@proper@test% + \let\pgfsyssoftpath@curvetosupportbtoken=\pgf@path@proper@test% + \let\pgfsyssoftpath@curvetotoken\pgf@path@proper@test% + \let\pgfsyssoftpath@rectcornertoken\pgf@path@proper@test% + \let\pgfsyssoftpath@rectsizetoken\pgf@path@proper@zero@test% + \let\pgfsyssoftpath@closepathtoken\pgf@path@proper@test% + \pgf@arrowpath% + \expandafter + }% + \ifpgfutil@tempswa\pgfutil@tempswafalse\else\pgfutil@tempswatrue\fi% +} + +\def\pgf@path@proper@init#1#2{\pgfutil@tempswatrue\pgf@x#1\pgf@y#2}% +\def\pgf@path@proper@test#1#2{% + \ifdim\pgf@x=#1\relax\else\pgfutil@tempswafalse\fi% + \ifdim\pgf@y=#2\relax\else\pgfutil@tempswafalse\fi} +\def\pgf@path@proper@zero@test#1#2{% + \ifdim\pgf@x=0pt\relax\else\pgfutil@tempswafalse\fi% + \ifdim\pgf@y=0pt\relax\else\pgfutil@tempswafalse\fi} + + + + +\def\pgf@stroke@inner@line{% + \let\pgf@temp@save=\pgf@strokecolor@global + \pgfsys@beginscope% + {% + \pgfsys@setlinewidth{\pgfinnerlinewidth}% + \pgfsetstrokecolor{\pgfinnerstrokecolor}% + \pgfsyssoftpath@invokecurrentpath% + \pgfsys@stroke% + }% + \pgfsys@endscope% + \global\let\pgf@strokecolor@global=\pgf@temp@save +} + +\let\pgf@prepare@start@of@path\relax% + + + + + +\def\pgfsetshortenstart#1{\pgfmathsetlength\pgf@shorten@start@additional{#1}} +\def\pgfsetshortenend#1{\pgfmathsetlength\pgf@shorten@end@additional{#1}} + +\newdimen\pgf@shorten@end@additional +\newdimen\pgf@shorten@start@additional + + + + +\newif\ifpgf@worry + + + +\def\pgf@prepare@end@of@path{% + \let\pgfprocessresultpathsuffix\relax% + \let\pgfprocessresultsubpathsuffix\relax% + \pgfsyssoftpath@getcurrentpath\pgf@arrowpath% + \ifx\pgf@arrowpath\pgfutil@empty\else% + \pgf@worryfalse% + \ifx\pgf@end@tip@sequence\pgfutil@empty% + \else% + \pgf@worrytrue% + \fi% + \pgf@precise@shorteningfalse% + \pgf@arrow@compute@shortening\pgf@end@tip@sequence% + \advance\pgf@xa by\pgf@shorten@end@additional% + \advance\pgf@xb by\pgf@shorten@end@additional% + \ifdim\pgf@xa=0pt\relax\else\pgf@worrytrue\fi% + \edef\pgf@path@shortening@distance{\the\pgf@xa}% + \edef\pgf@arrow@tip@total@length{\the\pgf@xb}% + \ifpgf@worry% + \pgfprocesssplitpath{\pgf@arrowpath}% + \pgfprocesssplitsubpath{\pgfprocessresultpathsuffix}% + \expandafter\pgf@parse@end\pgfprocessresultsubpathsuffix\pgf@stop\pgf@stop\pgf@stop% + \pgf@prep@end% + \ifdim\pgf@path@shortening@distance=0pt\else\pgf@do@shorten@end\fi% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@arrowpath% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix}% + \pgfsyssoftpath@setcurrentpath\pgf@arrowpath% + \fi% + \fi% +} + +\def\pgf@parse@end#1#2#3#4#5#6{% + \ifx#4\pgf@stop% + \def\pgfpointlastonpath{\pgfqpoint{#2}{#3}}% + \let\pgf@next\relax% + \let\pgf@do@shorten@end\relax% + \let\pgf@do@draw@end\pgf@do@draw@straightend% + \let\pgf@prep@end\pgf@prep@movetoend% + \else\ifx#4\pgfsyssoftpath@curvetosupportatoken% + \def\pgfsubpathfourthlasttoken{#1}% + \def\pgfpointfourthlastonpath{\pgfqpoint{#2}{#3}}% + \def\pgfpointthirdlastonpath{\pgfqpoint{#5}{#6}}% + \ifpgf@precise@shortening% + \let\pgf@do@shorten@end\pgf@do@shorten@curvedend% + \let\pgf@do@draw@end\pgf@do@draw@curvedend% + \let\pgf@prep@end\pgf@prep@curveend% + \else% + \def\pgfsubpathstart{\noexpand#1{#2}{#3}\noexpand#4{#5}{#6}}% + \let\pgf@do@shorten@end\pgf@do@shorten@straightend% + \let\pgf@do@draw@end\pgf@do@draw@straightend% + \let\pgf@prep@end\pgf@prep@straightend% + \fi% + \let\pgf@next\pgf@parse@end@curve@cont% + \else% + \def\pgfsubpathstart{\noexpand#1{#2}{#3}\noexpand#4}% + \def\pgfpointsecondlastonpath{\pgfqpoint{#2}{#3}}% + \def\pgfpointlastonpath{\pgfqpoint{#5}{#6}}% + \let\pgfpointfourthlastonpath\relax% + \let\pgfpointthirdlastonpath\relax% + \let\pgf@next\pgf@parse@end@gobble@three% + \let\pgf@do@shorten@end\pgf@do@shorten@straightend% + \let\pgf@do@draw@end\pgf@do@draw@straightend% + \let\pgf@prep@end\pgf@prep@straightend% + \fi\fi% + \pgf@next% +} + +\def\pgf@parse@end@gobble@three#1#2#3{}% +\def\pgf@parse@end@curve@cont#1#2#3#4#5#6#7#8#9{% + \def\pgfpointsecondlastonpath{\pgfqpoint{#2}{#3}}% + \def\pgfpointlastonpath{\pgfqpoint{#5}{#6}}% + \ifpgf@precise@shortening% + \else% + \expandafter\def\expandafter\pgfsubpathstart\expandafter{\pgfsubpathstart\noexpand#1{#2}{#3}\noexpand#4}% + \fi% +} + +\def\pgf@prep@movetoend{% + \pgf@process{\pgfpointlastonpath}% + \pgf@xb\pgf@x + \pgf@yb\pgf@y + \pgf@xc\pgf@x + \pgf@yc\pgf@y +} +\def\pgf@prep@straightend{% + \let\pgf@ref\pgfpointsecondlastonpath + \ifx\pgfpointlastonpath\pgfpointsecondlastonpath% + \ifx\pgfpointthirdlastonpath\relax% + \else% + \ifx\pgfpointlastonpath\pgfpointthirdlastonpath% + \let\pgf@ref\pgfpointfourthlastonpath% + \else + \let\pgf@ref\pgfpointthirdlastonpath% + \fi% + \fi% + \fi% + \pgfpointlineatdistance{\pgf@path@shortening@distance}{\pgfpointlastonpath}{\pgf@ref}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% +} + + +\def\pgf@do@shorten@straightend{% + \edef\pgfprocessresultsubpathsuffix{\pgfsubpathstart{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultsubpathprefix\pgfprocessresultsubpathsuffix}% +} + + + +\def\pgf@add@arrow@at@end{% + \ifx\pgf@arrowpath\pgfutil@empty\else% + \ifx\pgf@end@tip@sequence\pgfutil@empty\else% + \pgf@do@draw@end% + \fi% + \fi% +} + +\def\pgf@do@draw@straightend{% + {% + \pgftransformreset% + \pgftransformarrow{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgf@arrow@draw@arrow\pgf@end@tip@sequence\pgf@arrow@tip@total@length% + }% +} + + + + + + + +\def\pgf@prepare@start@of@path{% + \ifx\pgf@arrowpath\pgfutil@empty\else% + \pgf@worryfalse% + \ifx\pgf@start@tip@sequence\pgfutil@empty\else\pgf@worrytrue\fi% + \pgf@precise@shorteningfalse% + \pgf@arrow@compute@shortening\pgf@start@tip@sequence% + \advance\pgf@xa by\pgf@shorten@start@additional% + \advance\pgf@xb by\pgf@shorten@start@additional% + \ifdim\pgf@xa=0pt\relax\else\pgf@worrytrue\fi% + \edef\pgf@path@shortening@distance{\the\pgf@xa}% + \edef\pgf@arrow@tip@total@length{\the\pgf@xb}% + \ifpgf@worry% + \ifx\pgfprocessresultpathsuffix\relax% + \pgfprocesssplitpath{\pgf@arrowpath}% + \fi% + \expandafter\pgf@parse@start\pgfprocessresultpathsuffix\pgf@stop\pgf@stop\pgf@stop% + \pgf@prep@start% + \ifdim\pgf@path@shortening@distance=0pt\else\pgf@do@shorten@start\fi% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@arrowpath% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix}% + \pgfsyssoftpath@setcurrentpath\pgf@arrowpath% + \fi% + \fi% +} + +\def\pgf@parse@start#1#2#3#4#5#6{% + \def\pgfpointfirstonpath{\pgfqpoint{#2}{#3}}% + \def\pgfpointsecondonpath{\pgfqpoint{#5}{#6}}% + \let\pgfpointthirdonpath\relax% + \let\pgfpointfourthonpath\relax% + \def\pgfsubpathfirsttoken{\noexpand#1}% + \def\pgfsubpathsecondtoken{\noexpand#4}% + \ifx#4\pgf@stop% + \let\pgf@next\relax% + \let\pgf@do@shorten@start\relax% + \let\pgf@prep@start\pgf@prep@movetostart% + \let\pgf@do@draw@start\pgf@do@draw@straightstart% + \else\ifx#4\pgfsyssoftpath@curvetosupportatoken% + \ifpgf@precise@shortening% + \let\pgf@next\pgf@parse@start@curve@cont% + \let\pgf@do@shorten@start\pgf@do@shorten@curvedstart% + \let\pgf@do@draw@start\pgf@do@draw@curvedstart% + \let\pgf@prep@start\pgf@prep@curvedstart% + \else% + \let\pgf@next\pgf@parse@start@curve@cont@straight% + \let\pgf@do@shorten@start\pgf@do@shorten@straightstart% + \let\pgf@do@draw@start\pgf@do@draw@straightstart% + \let\pgf@prep@start\pgf@prep@straightstart% + \fi% + \else% + \let\pgf@next\pgf@parse@start@till@stop% + \let\pgf@do@shorten@start\pgf@do@shorten@straightstart% + \let\pgf@do@draw@start\pgf@do@draw@straightstart% + \let\pgf@prep@start\pgf@prep@straightstart% + \fi\fi% + \pgf@next% +} + +\def\pgf@parse@start@till@stop#1\pgf@stop\pgf@stop\pgf@stop{\def\pgfsubpathend{#1}}% + +\def\pgf@parse@start@curve@cont#1#2#3#4#5#6#7\pgf@stop\pgf@stop\pgf@stop{% + \def\pgfpointthirdonpath{\pgfqpoint{#2}{#3}}% + \def\pgfpointfourthonpath{\pgfqpoint{#5}{#6}}% + \def\pgfsubpathend{#7}% +} + +\def\pgf@parse@start@curve@cont@straight#1#2#3#4#5#6#7\pgf@stop\pgf@stop\pgf@stop{% + \def\pgfpointthirdonpath{\pgfqpoint{#2}{#3}}% + \def\pgfpointfourthonpath{\pgfqpoint{#5}{#6}}% + \def\pgfsubpathend{#1{#2}{#3}#4{#5}{#6}#7}% +} + +\def\pgf@prep@movetostart{% + \pgf@process{\pgfpointfirstonpath}% + \pgf@xb\pgf@x + \pgf@yb\pgf@y + \pgf@xc\pgf@x + \pgf@yc\pgf@y +} +\def\pgf@prep@straightstart{% + \let\pgf@ref\pgfpointsecondonpath + \ifx\pgfpointfirstonpath\pgfpointsecondonpath% + \ifx\pgfpointthirdonpath\relax% + \else% + \ifx\pgfpointfirstonpath\pgfpointthirdonpath% + \let\pgf@ref\pgfpointfourthonpath% + \else + \let\pgf@ref\pgfpointthirdonpath% + \fi% + \fi% + \fi% + \pgfpointlineatdistance{\pgf@path@shortening@distance}{\pgfpointfirstonpath}{\pgf@ref}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% +} + +\def\pgf@do@shorten@straightstart{% + \edef\pgfprocessresultpathsuffix{\pgfsubpathfirsttoken{\the\pgf@xa}{\the\pgf@ya}\pgfsubpathsecondtoken{\the\pgf@xc}{\the\pgf@yc}}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathsuffix\pgfsubpathend}% +} + + + +\def\pgf@add@arrow@at@start{% + \ifx\pgf@arrowpath\pgfutil@empty\else% + \ifx\pgf@start@tip@sequence\pgfutil@empty\else% + \pgf@do@draw@start% + \fi% + \fi% +} + +\def\pgf@do@draw@straightstart{% + {% + \pgftransformreset% + \pgftransformarrow{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgf@arrow@draw@arrow\pgf@start@tip@sequence\pgf@arrow@tip@total@length% + }% +} + + + +\let\pgf@shorten@end=\pgfutil@empty +\let\pgf@shorten@start=\pgfutil@empty + + +\endinput% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..60152c5d064e1c313b839399353e33ed207494c2 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepatterns.code.tex @@ -0,0 +1,197 @@ + +\ProvidesFileRCS{pgfcorepatterns.code.tex} + +\def\pgfdeclarepatternformonly{% + \def\pgf@pattern@type{formonly}% + \pgfutil@ifnextchar[{\pgf@declarepattern@checkarg}{\pgf@declarepattern@checkarg[]}% +} + + +\def\pgfdeclarepatterninherentlycolored{% + \def\pgf@pattern@type{inherentlycolored}% + \pgfutil@ifnextchar[{\pgf@declarepattern@checkarg}{\pgf@declarepattern@checkarg[]}% +} + + + + + +\def\pgf@declarepattern@checkarg[#1]{% + \def\pgf@pattern@tempvars{#1}% + \ifx\pgf@pattern@tempvars\pgfutil@empty% + \expandafter\let\expandafter\pgf@next\csname pgf@declarepattern\pgf@pattern@type\endcsname% + \else% + \expandafter\let\expandafter\pgf@next\csname pgf@declarepattern\pgf@pattern@type @mutable\endcsname% + \fi% + \pgf@next} + +\long\def\pgf@declarepatternformonly#1#2#3#4#5{\pgf@declarepattern{#1}{#2}{#3}{#4}{#5}{0}} + +\long\def\pgf@declarepatterninherentlycolored#1#2#3#4#5{\pgf@declarepattern{#1}{#2}{#3}{#4}{#5}{1}} + +\long\def\pgf@declarepatternformonly@mutable#1#2#3#4#5{% + \def\pgf@marshal{\pgf@declarepatternmutable{#1}}% + \expandafter\pgf@marshal\expandafter{\pgf@pattern@tempvars}{#2}{#3}{#4}{#5}{2}% +} + +\long\def\pgf@declarepatterninherentlycolored@mutable#1#2#3#4#5#6{% + \def\pgf@marshal{\pgf@declarepatternmutable{#1}}% + \expandafter\pgf@marshal\expandafter{\pgf@pattern@tempvars}{#2}{#3}{#4}{#5}{3}% +} + +\def\pgfsys@patternmatrix{{1.0}{0.0}{0.0}{1.0}{0.0pt}{0.0pt}} +\def\pgf@declarepattern#1#2#3#4#5#6{% + \pgfutil@ifundefined{pgf@pattern@name@#1}{% + \pgfsysprotocol@getcurrentprotocol\pgf@pattern@temp% + {% + \pgfinterruptpath% + \pgfpicturetrue% + \pgf@relevantforpicturesizefalse% + \pgftransformreset% + \pgfsysprotocol@setcurrentprotocol\pgfutil@empty% + \pgfsysprotocol@bufferedtrue% + \pgfsys@beginscope% + \pgfsetarrows{-}% + #5% + \pgfsys@endscope% + \pgfsysprotocol@getcurrentprotocol\pgf@pattern@code% + \global\let\pgf@pattern@code=\pgf@pattern@code% + \endpgfinterruptpath% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#3}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#4}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfutil@tempcnta=\pgf@pattern@number% + \advance\pgfutil@tempcnta by1\relax% + \xdef\pgf@pattern@number{\the\pgfutil@tempcnta}% + \expandafter\xdef\csname pgf@pattern@name@#1\endcsname{\the\pgfutil@tempcnta}% + \expandafter\gdef\csname pgf@pattern@type@#1\endcsname{#6}% + \xdef\pgf@marshal{\noexpand\pgfsys@declarepattern + {\csname pgf@pattern@name@#1\endcsname}% + {\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}% + {\the\pgf@xc}{\the\pgf@yc}% + \pgfsys@patternmatrix% + {\pgf@pattern@code}{#6}}% + }% + \pgfsysprotocol@setcurrentprotocol\pgf@pattern@temp% + \expandafter\global\expandafter\let\csname pgf@pattern@instantiate@#1\endcsname=\pgf@marshal% + } + {% + \pgferror{Pattern `#1' already defined}% + }% +} + +\def\pgf@pattern@number{0}% + +\def\pgf@declarepatternmutable#1#2#3#4#5#6#7{% + \pgfutil@ifundefined{pgf@pattern@name@#1}{% + \expandafter\gdef\csname pgf@pattern@name@#1\endcsname{#1}% + \expandafter\gdef\csname pgf@pattern@variables@#1\endcsname{#2}% + \expandafter\gdef\csname pgf@pattern@lowerleft@#1\endcsname{#3}% + \expandafter\gdef\csname pgf@pattern@upperright@#1\endcsname{#4}% + \expandafter\gdef\csname pgf@pattern@tilesize@#1\endcsname{#5}% + \expandafter\long\expandafter\gdef\csname pgf@pattern@code@#1\endcsname{#6}% + \expandafter\gdef\csname pgf@pattern@type@#1\endcsname{#7}% + }{\pgferror{The pattern `#1' is already defined}}% +} + +\def\pgf@ifpatternisinherentlycolored#1#2#3{% + \expandafter\ifodd\csname pgf@pattern@type@#1\endcsname\relax#2\else#3\fi% +} + +\def\pgf@ifpatternismutable#1#2#3{% + \expandafter\ifnum\csname pgf@pattern@type@#1\endcsname>1\relax#2\else#3\fi% +} + +\def\pgfpatternreleasename#1{\expandafter\let\csname pgf@pattern@name@#1\endcsname\relax} + + + + + + +\def\pgfsetfillpattern#1#2{% + \pgfutil@ifundefined{pgf@pattern@name@#1}% + {% + \pgferror{Undefined pattern `#1'}% + }% + {% + \pgf@ifpatternismutable{#1}% + {% + \let\pgf@pattern@tempvars\pgfutil@empty% + \expandafter\expandafter\expandafter\pgf@pattern@check@vars% + \csname pgf@pattern@variables@#1\endcsname,\pgf@stop,% + \edef\pgf@pattern@nametemp{pgf@pattern@#1@\pgf@pattern@tempvars}% + \expandafter\pgfutil@ifundefined\expandafter{\pgf@pattern@nametemp}% + {% + \pgf@ifpatternisinherentlycolored{#1}% + {\let\pgf@set@fillpattern@declare\pgfdeclarepatterninherentlycolored}% + {\let\pgf@set@fillpattern@declare\pgfdeclarepatternformonly}% + \pgf@set@fillpattern@declare% + {\pgf@pattern@nametemp}% + {\csname pgf@pattern@lowerleft@#1\endcsname}% + {\csname pgf@pattern@upperright@#1\endcsname}% + {\csname pgf@pattern@tilesize@#1\endcsname}% + {\csname pgf@pattern@code@#1\endcsname}% + }% + {% + }% + \expandafter\pgf@set@fillpattern\expandafter{\pgf@pattern@nametemp}{#2}% + \expandafter\gdef\csname\pgf@pattern@nametemp\endcsname{#1}% + }% + {% + \pgf@set@fillpattern{#1}{#2}% + }% + }% +} + + +\def\pgf@set@fillpattern#1#2{% + \pgfutil@ifundefined{pgf@pattern@name@#1}{% + \pgferror{Undefined pattern `#1'}} + {% + \csname pgf@pattern@instantiate@#1\endcsname% + \expandafter\global\expandafter\let\csname pgf@pattern@instantiate@#1\endcsname=\relax% + \pgf@ifpatternisinherentlycolored{#1}{% + \pgfsys@setpatterncolored{\csname pgf@pattern@name@#1\endcsname}% + }{% + \pgfutil@colorlet{pgf@tempcolor}{#2}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgf@tempcolor}}% + \pgfutil@extractcolorspec{pgf@tempcolor}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}% + \expandafter\pgf@set@fill@patternuncolored\pgf@rgbcolor\relax{#1}% + }% + }% +} + +\def\pgf@set@fill@patternuncolored#1,#2,#3\relax#4{% + \pgfsys@setpatternuncolored{\csname pgf@pattern@name@#4\endcsname}{#1}{#2}{#3}% +} + +\def\pgf@pattern@check@vars#1,{% + \ifx#1\pgf@stop% + \let\pgf@next\relax% + \else% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\let\expandafter\pgf@pattern@char#1#1\pgfmath@% + \ifx\pgf@pattern@char/% + \edef\pgf@pattern@tempvar{(\pgfkeysvalueof{#1})}% + \else% + \expandafter\ifcat\pgf@pattern@char\relax% + \edef\pgf@pattern@tempvar{(\the#1)}% + \else% + \edef\pgf@pattern@tempvar{(#1)}% + \fi% + \fi% + \edef\pgf@pattern@tempvars{\pgf@pattern@tempvars\pgf@pattern@tempvar}% + \let\pgf@next\pgf@pattern@check@vars% + \fi% + \pgf@next% +} + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ebc1f86d050c30cf277644f460057041551a022c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorepoints.code.tex @@ -0,0 +1,724 @@ + +\ProvidesFileRCS{pgfcorepoints.code.tex} + +\newdimen\pgf@picminx +\newdimen\pgf@picmaxx +\newdimen\pgf@picminy +\newdimen\pgf@picmaxy + +\newdimen\pgf@pathminx +\newdimen\pgf@pathmaxx +\newdimen\pgf@pathminy +\newdimen\pgf@pathmaxy + +\newif\ifpgf@relevantforpicturesize + +\def\pgf@process#1{{#1\global\pgf@x=\pgf@x\global\pgf@y=\pgf@y}} + + +\def\pgfextract@process#1#2{% + \pgf@process{#2}% + \edef#1{\noexpand\global\pgf@x=\the\pgf@x\noexpand\relax\noexpand\global\pgf@y=\the\pgf@y\noexpand\relax}% +} +\let\pgfsavepgf@process\pgfextract@process% + + + +\def\pgfpoint#1#2{% + \pgfmathsetlength\pgf@x{#1}% + \pgfmathsetlength\pgf@y{#2}\ignorespaces} + + + +\def\pgfqpoint#1#2{\global\pgf@x=#1\relax\global\pgf@y=#2\relax} + + + + +\def\pgfpointorigin{\global\pgf@x=0pt \global\pgf@y=\pgf@x\ignorespaces} + + + + +\def\pgfpointtransformed#1{% + \pgf@process{% + #1% + \pgf@pos@transform@glob% + }% +} + + + +\def\pgfpointdiff#1#2{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#2}% + \global\advance\pgf@x by-\pgf@xa\relax% + \global\advance\pgf@y by-\pgf@ya\relax\ignorespaces} + + +\def\pgfpointadd#1#2{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#2}% + \global\advance\pgf@x by\pgf@xa% + \global\advance\pgf@y by\pgf@ya} + + + + +\def\pgfpointscale#1#2{% + \pgf@process{#2}% + \pgfmathparse{#1}% + \global\pgf@x=\pgfmathresult\pgf@x% + \global\pgf@y=\pgfmathresult\pgf@y% +} +\def\pgfqpointscale#1#2{% + \pgf@process{#2}% + \global\pgf@x=#1\pgf@x% + \global\pgf@y=#1\pgf@y% +} + + + +\def\pgfpointintersectionoflines#1#2#3#4{% + {% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#1}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@ya=-\pgf@ya% + \c@pgf@counta=\pgf@xa% + \ifnum\c@pgf@counta<0\relax% + \c@pgf@counta=-\c@pgf@counta\relax% + \fi% + \c@pgf@countb=\pgf@ya% + \ifnum\c@pgf@countb<0\relax% + \c@pgf@countb=-\c@pgf@countb\relax% + \fi% + \advance\c@pgf@counta by\c@pgf@countb\relax% + \divide\c@pgf@counta by 65536\relax% + \ifnum\c@pgf@counta>0\relax% + \divide\pgf@xa by\c@pgf@counta\relax% + \divide\pgf@ya by\c@pgf@counta\relax% + \fi% + \pgf@xc=\pgf@sys@tonumber{\pgf@ya}\pgf@x% + \advance\pgf@xc by\pgf@sys@tonumber{\pgf@xa}\pgf@y% + \pgf@process{#4}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#3}% + \advance\pgf@xb by-\pgf@x% + \advance\pgf@yb by-\pgf@y% + \pgf@yb=-\pgf@yb% + \c@pgf@counta=\pgf@xb% + \ifnum\c@pgf@counta<0\relax% + \c@pgf@counta=-\c@pgf@counta\relax% + \fi% + \c@pgf@countb=\pgf@yb% + \ifnum\c@pgf@countb<0\relax% + \c@pgf@countb=-\c@pgf@countb\relax% + \fi% + \advance\c@pgf@counta by\c@pgf@countb\relax% + \divide\c@pgf@counta by 65536\relax% + \ifnum\c@pgf@counta>0\relax% + \divide\pgf@xb by\c@pgf@counta\relax% + \divide\pgf@yb by\c@pgf@counta\relax% + \fi% + \pgf@yc=\pgf@sys@tonumber{\pgf@yb}\pgf@x% + \advance\pgf@yc by\pgf@sys@tonumber{\pgf@xb}\pgf@y% + \pgfsettransform{{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@yb}{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@xb}{0pt}{0pt}}% + \pgftransforminvert% + \pgf@process{\pgfpointtransformed{\pgfpoint{\pgf@xc}{\pgf@yc}}}% + }% +} + + + +\def\pgfpointintersectionofcircles#1#2#3#4#5{% + {% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfmathsetlength{\pgf@xc}{#3}% + \pgf@process{#2}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgfmathsetlength{\pgf@yc}{#4}% + \c@pgf@counta=1\relax% + \loop% + \pgf@scale@downfalse% + \ifdim\pgf@xc>50pt\relax% + \pgf@scale@downtrue% + \fi% + \ifdim\pgf@yc>50pt\relax% + \pgf@scale@downtrue% + \fi% + \ifpgf@scale@down% + \multiply\c@pgf@counta by2\relax% + \divide\pgf@xa by2\relax% + \divide\pgf@ya by2\relax% + \divide\pgf@xb by2\relax% + \divide\pgf@yb by2\relax% + \divide\pgf@xc by2\relax% + \divide\pgf@yc by2\relax% + \repeat% + \dimen0=\pgf@xb% + \advance\dimen0 by-\pgf@xa% + \dimen1=\pgf@yb% + \advance\dimen1 by-\pgf@ya% + \pgf@x=\dimen0\relax% + \pgf@x=\pgf@sys@tonumber{\pgf@x}\pgf@x% + \dimen3=\pgf@x% + \pgf@x=\dimen1\relax% + \advance\dimen3 by\pgf@sys@tonumber{\pgf@x}\pgf@x% + \pgfmathparse{sqrt(\the\dimen3)}% + \dimen2=\pgfmathresult pt% + \pgfmathreciprocal@{\pgfmathresult}% + \dimen5=\pgfmathresult pt% + \dimen4=\dimen3\relax% + \pgf@x=\pgf@xc% + \advance\dimen4 by\pgf@sys@tonumber{\pgf@x}\pgf@x\relax% + \pgf@x=\pgf@yc% + \advance\dimen4 by-\pgf@sys@tonumber{\pgf@x}\pgf@x\relax% + \dimen4=.5\dimen4% + \dimen4=\pgf@sys@tonumber{\dimen5}\dimen4% + \dimen7=\pgf@sys@tonumber{\dimen4}\dimen4\relax% + \pgfmathparse{sqrt(\pgf@sys@tonumber{\pgf@xc}\pgf@xc-\the\dimen7)}% + \dimen6=\pgfmathresult pt% + \dimen8=\pgf@sys@tonumber{\dimen4}\dimen5\relax% + \dimen9=\pgf@sys@tonumber{\dimen6}\dimen5\relax% + \ifnum#5=1\relax% + \pgf@x=\pgf@xa% + \advance\pgf@x by\pgf@sys@tonumber{\dimen0}\dimen8\relax% + \advance\pgf@x by\pgf@sys@tonumber{\dimen1}\dimen9\relax% + \pgf@y=\pgf@ya% + \advance\pgf@y by\pgf@sys@tonumber{\dimen1}\dimen8\relax% + \pgf@xb=\pgf@sys@tonumber{\dimen0}\dimen9% + \pgf@xb=-\pgf@xb% + \advance\pgf@y by\pgf@xb\relax% + \else% + \pgf@x=\pgf@xa% + \advance\pgf@x by\pgf@sys@tonumber{\dimen0}\dimen8\relax% + \pgf@xb=\pgf@sys@tonumber{\dimen1}\dimen9% + \pgf@xb=-\pgf@xb% + \advance\pgf@x by\pgf@xb\relax% + \pgf@y=\pgf@ya% + \advance\pgf@y by\pgf@sys@tonumber{\dimen1}\dimen8\relax% + \advance\pgf@y by\pgf@sys@tonumber{\dimen0}\dimen9\relax% + \fi% + \pgf@x=\c@pgf@counta\pgf@x% + \pgf@y=\c@pgf@counta\pgf@y% + \pgf@process{}% + }% +} +\newif\ifpgf@scale@down + + + +\def\pgfpointlineattime#1#2#3{% + \pgf@process{#3}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgf@xc\pgf@x% + \pgf@yc\pgf@y% + \pgf@process{#2}% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgfmathsetmacro\pgf@temp{#1}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \global\advance\pgf@x by\pgf@temp\pgf@xa% + \global\advance\pgf@y by\pgf@temp\pgf@ya% +} + + + +\def\pgfpointlineatdistance#1#2#3{% + \pgfmathsetlength\pgf@xa{#1}% + \pgf@process{#2}% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@process{#3}% + \pgf@xc\pgf@x% + \pgf@yc\pgf@y% + \global\advance\pgf@x by-\pgf@xb\relax% + \global\advance\pgf@y by-\pgf@yb\relax% + \pgf@process{\pgfpointnormalised{}}% + \pgf@ya=\pgf@xa\relax% + \pgf@xa=\pgf@sys@tonumber{\pgf@x}\pgf@xa% + \pgf@ya=\pgf@sys@tonumber{\pgf@y}\pgf@ya% + \global\pgf@x=\pgf@xb\relax% + \global\pgf@y=\pgf@yb\relax% + \global\advance\pgf@x by\pgf@xa\relax% + \global\advance\pgf@y by\pgf@ya\relax% +} + + + +\def\pgfpointcurveattime#1#2#3#4#5{% + \pgfmathparse{#1}% + \let\pgf@time@s=\pgfmathresult% + \global\pgf@x=\pgfmathresult pt% + \global\pgf@x=-\pgf@x% + \advance\pgf@x by 1pt% + \edef\pgf@time@t{\pgf@sys@tonumber{\pgf@x}}% + \pgf@process{#5}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{#4}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#3}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#2}% + \global\pgf@x=\pgf@time@t\pgf@x\global\advance\pgf@x by\pgf@time@s\pgf@xa% + \global\pgf@y=\pgf@time@t\pgf@y\global\advance\pgf@y by\pgf@time@s\pgf@ya% + \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb% + \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb% + \pgf@xb=\pgf@time@t\pgf@xb\advance\pgf@xb by\pgf@time@s\pgf@xc% + \pgf@yb=\pgf@time@t\pgf@yb\advance\pgf@yb by\pgf@time@s\pgf@yc% + \global\pgf@x=\pgf@time@t\pgf@x\global\advance\pgf@x by\pgf@time@s\pgf@xa% + \global\pgf@y=\pgf@time@t\pgf@y\global\advance\pgf@y by\pgf@time@s\pgf@ya% + \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb% + \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \global\pgf@x=\pgf@time@t\pgf@x\global\advance\pgf@x by\pgf@time@s\pgf@xa% + \global\pgf@y=\pgf@time@t\pgf@y\global\advance\pgf@y by\pgf@time@s\pgf@ya% +} + + + + +\def\pgfpointarcaxesattime#1#2#3#4#5#6{% + \pgfmathsetmacro\pgf@angle@start{#5}% + \pgfmathsetmacro\pgf@angle@end{#6}% + \pgfmathparse{#1}% + \global\pgf@x=\pgfmathresult pt% + \global\pgf@x=-\pgf@x% + \advance\pgf@x by 1pt% + \pgfmathsetmacro\pgf@angle@mid{\pgf@angle@end*\pgfmathresult+\pgf@angle@start*\pgf@sys@tonumber{\pgf@x}}% + \pgfmathcos@{\pgf@angle@mid}% + \let\pgf@angle@cos\pgfmathresult% + \pgfmathsin@{\pgf@angle@mid}% + \let\pgf@angle@sin\pgfmathresult% + \pgf@process{#3}% + \edef\pgf@angle@zero@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgf@process{#4}% + \edef\pgf@angle@ninety@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgf@process{\pgfpointadd{\pgfpointscale{\pgf@angle@sin}{\pgf@angle@zero@axis}}% + {\pgfpointscale{-\pgf@angle@cos}{\pgf@angle@ninety@axis}}}% + \ifdim\pgf@angle@start pt>\pgf@angle@end pt% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \else% + \pgf@xa=-\pgf@x% + \pgf@ya=-\pgf@y% + \fi% + \pgf@process{\pgfpointadd{#2}{% + \pgfpointadd{\pgfpointscale{\pgf@angle@cos}{\pgf@angle@zero@axis}}% + {\pgfpointscale{\pgf@angle@sin}{\pgf@angle@ninety@axis}}}}% +} + + + +\newdimen\pgf@xx +\newdimen\pgf@xy +\newdimen\pgf@yx +\newdimen\pgf@yy +\newdimen\pgf@zx +\newdimen\pgf@zy + + + + +\def\pgfpointpolar#1#2{% + \pgfutil@in@{and }{#2}% + \ifpgfutil@in@% + \pgf@polar@#2\@@% + \else% + \pgf@polar@#2 and #2\@@% + \fi% + \pgfmathparse{#1}% + \let\pgfpoint@angle=\pgfmathresult% + \pgfmathcos@{\pgfpoint@angle}% + \global\pgf@x=\pgfmathresult\pgf@x% + \pgfmathsin@{\pgfpoint@angle}% + \global\pgf@y=\pgfmathresult\pgf@y% +} + +\def\pgf@polar@#1and #2\@@{% + \pgfmathsetlength{\pgf@y}{#2}% + \pgfmathsetlength{\pgf@x}{#1}% +} + + +\def\pgfqpointpolar#1#2{% + \global\pgf@x=#2% + \global\pgf@y=\pgf@x% + \pgfmathcos@{#1}% + \global\pgf@x=\pgfmathresult\pgf@x% + \pgfmathsin@{#1}% + \global\pgf@y=\pgfmathresult\pgf@y\relax% +} + + + + + +\def\pgfpointpolarxy#1#2{% + \pgfutil@in@{and }{#2}% + \ifpgfutil@in@% + \pgf@polarxy@#2\@@% + \else% + \pgf@polarxy@#2and #2\@@% + \fi% + \pgfmathparse{#1}% + \let\pgfpoint@angle=\pgfmathresult% + \pgfmathcos@{\pgfpoint@angle}% + \pgf@xa=\pgfmathresult\pgf@xa% + \pgfmathsin@{\pgfpoint@angle}% + \pgf@ya=\pgfmathresult\pgf@ya% + \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@xx% + \global\advance\pgf@x by \pgf@sys@tonumber{\pgf@ya}\pgf@yx% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xa}\pgf@xy% + \global\advance\pgf@y by \pgf@sys@tonumber{\pgf@ya}\pgf@yy} + +\def\pgf@polarxy@#1and #2\@@{% + \pgfmathsetlength{\pgf@xa}{#1}% + \pgfmathsetlength{\pgf@ya}{#2}% +} + + + + +\def\pgfpointcylindrical#1#2#3{% + \pgfpointpolarxy{#1}{#2}% + \pgfmathparse{#3}% + \global\advance\pgf@x by \pgfmathresult\pgf@zx% + \global\advance\pgf@y by \pgfmathresult\pgf@zy} + + + +\def\pgfpointspherical#1#2#3{% + \pgfmathparse{#1}% + \let\pgfpoint@angle=\pgfmathresult% + \pgfmathsin@{\pgfpoint@angle}% + \pgf@xb=\pgfmathresult\pgf@xx% + \pgf@yb=\pgfmathresult\pgf@xy% + \pgfmathcos@{\pgfpoint@angle}% + \advance\pgf@xb by \pgfmathresult\pgf@yx% + \advance\pgf@yb by \pgfmathresult\pgf@yy% + \pgfmathparse{#2}% + \let\pgfpoint@angle=\pgfmathresult% + \pgfmathcos@{\pgfpoint@angle}% + \pgf@xc=\pgfmathresult\pgf@xb% + \pgf@yc=\pgfmathresult\pgf@yb% + \pgfmathsin@{\pgfpoint@angle}% + \advance\pgf@xc by \pgfmathresult\pgf@zx% + \advance\pgf@yc by \pgfmathresult\pgf@zy% + \pgfmathparse{#3}% + \global\pgf@x=\pgfmathresult\pgf@xc% + \global\pgf@y=\pgfmathresult\pgf@yc\relax% +} + + + +\def\pgfpointxy#1#2{% + \pgfmathparse{#1}% + \let\pgftemp@x=\pgfmathresult% + \pgfmathparse{#2}% + \let\pgftemp@y=\pgfmathresult% + \global\pgf@x=\pgftemp@x\pgf@xx% + \global\advance\pgf@x by \pgftemp@y\pgf@yx% + \global\pgf@y=\pgftemp@x\pgf@xy% + \global\advance\pgf@y by \pgftemp@y\pgf@yy} + + +\def\pgfqpointxy#1#2{% + \global\pgf@x=#1\pgf@xx% + \global\advance\pgf@x by #2\pgf@yx% + \global\pgf@y=#1\pgf@xy% + \global\advance\pgf@y by #2\pgf@yy} + + +\def\pgfpointxyz#1#2#3{% + \pgfmathparse{#1}% + \let\pgftemp@x=\pgfmathresult% + \pgfmathparse{#2}% + \let\pgftemp@y=\pgfmathresult% + \pgfmathparse{#3}% + \let\pgftemp@z=\pgfmathresult% + \global\pgf@x=\pgftemp@x\pgf@xx% + \global\advance\pgf@x by \pgftemp@y\pgf@yx% + \global\advance\pgf@x by \pgftemp@z\pgf@zx% + \global\pgf@y=\pgftemp@x\pgf@xy% + \global\advance\pgf@y by \pgftemp@y\pgf@yy% + \global\advance\pgf@y by \pgftemp@z\pgf@zy} + +\def\pgfqpointxyz#1#2#3{% + \global\pgf@x=#1\pgf@xx% + \global\advance\pgf@x by #2\pgf@yx% + \global\advance\pgf@x by #3\pgf@zx% + \global\pgf@y=#1\pgf@xy% + \global\advance\pgf@y by #2\pgf@yy% + \global\advance\pgf@y by #3\pgf@zy} + + + + +\def\pgfsetxvec#1{% + \pgf@process{#1}% + \pgf@xx=\pgf@x% + \pgf@xy=\pgf@y% + \ignorespaces} + + + +\def\pgfsetyvec#1{% + \pgf@process{#1}% + \pgf@yx=\pgf@x% + \pgf@yy=\pgf@y% + \ignorespaces} + + + +\def\pgfsetzvec#1{% + \pgf@process{#1}% + \pgf@zx=\pgf@x% + \pgf@zy=\pgf@y% + \ignorespaces} + + + +\pgfsetxvec{\pgfpoint{1cm}{0cm}} +\pgfsetyvec{\pgfpoint{0cm}{1cm}} +\pgfsetzvec{\pgfpoint{-0.385cm}{-0.385cm}} + + + + + +\def\pgfpointnormalised#1{% + \pgf@process{#1}% + \pgfmathatantwo{\the\pgf@y}{\the\pgf@x}% + \let\pgf@tmp=\pgfmathresult% + \pgfmathcos@{\pgf@tmp}% + \pgf@x=\pgfmathresult pt\relax% + \pgfmathsin@{\pgf@tmp}% + \pgf@y=\pgfmathresult pt\relax% +} + + + + + + +\def\pgfpointborderrectangle#1#2{% + \pgf@process{#2}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \ifnum\pgf@xa<0\relax% + \global\pgf@x=-\pgf@x% + \fi% + \ifnum\pgf@ya<0\relax% + \global\pgf@y=-\pgf@y% + \fi% + \pgf@xc=.125\pgf@x% + \pgf@yc=.125\pgf@y% + \c@pgf@counta=\pgf@xc% + \c@pgf@countb=\pgf@yc% + \ifnum\c@pgf@countb<\c@pgf@counta% + \ifnum\c@pgf@counta<255\relax% + \global\pgf@y=\pgf@yb\relax% + \global\pgf@x=0pt\relax% + \else% + \pgf@xc=8192pt% + \divide\pgf@xc by\c@pgf@counta% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xb}\pgf@y% + \ifnum\pgf@y<\pgf@yb% + \global\pgf@x=\pgf@xb% + \else% + \ifnum\c@pgf@countb<255\relax% + \global\pgf@x=\pgf@xb\relax% + \global\pgf@y=0pt\relax% + \else% + \pgf@yc=8192pt% + \divide\pgf@yc by\c@pgf@countb% + \global\pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x% + \global\pgf@x=\pgf@sys@tonumber{\pgf@yb}\pgf@x% + \global\pgf@y=\pgf@yb% + \fi% + \fi% + \fi% + \else% + \ifnum\c@pgf@countb<255\relax% + \global\pgf@x=\pgf@xb\relax% + \global\pgf@y=0pt\relax% + \else% + \pgf@yc=8192pt% + \divide\pgf@yc by\c@pgf@countb% + \global\pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x% + \global\pgf@x=\pgf@sys@tonumber{\pgf@yb}\pgf@x% + \ifnum\pgf@x<\pgf@xb% + \global\pgf@y=\pgf@yb% + \else% + \ifnum\c@pgf@counta<255\relax% + \global\pgf@y=\pgf@yb\relax% + \global\pgf@x=0pt\relax% + \else% + \pgf@xc=8192pt% + \divide\pgf@xc by\c@pgf@counta% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xb}\pgf@y% + \global\pgf@x=\pgf@xb% + \fi% + \fi% + \fi% + \fi% + \ifnum\pgf@xa<0\relax\global\pgf@x=-\pgf@x\fi% + \ifnum\pgf@ya<0\relax\global\pgf@y=-\pgf@y\fi% +} + + + + + +\def\pgfpointborderellipse#1#2{% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \ifdim\pgf@xa=\pgf@ya% + \pgf@process{\pgfpointnormalised{#1}}% + \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xa}\pgf@y% + \else% + \ifdim\pgf@xa<\pgf@ya% + \c@pgf@countb=\pgf@ya% + \divide\c@pgf@countb by65536\relax% + \global\divide\pgf@x by\c@pgf@countb% + \global\divide\pgf@y by\c@pgf@countb% + \pgf@xc=\pgf@x% + \pgf@yc=8192pt% + \global\pgf@y=.125\pgf@y% + \c@pgf@countb=\pgf@y% + \divide\pgf@yc by\c@pgf@countb% + \pgf@process{#1}% + \global\pgf@y=\pgf@sys@tonumber{\pgf@yc}\pgf@y% + \global\pgf@y=\pgf@sys@tonumber{\pgf@xc}\pgf@y% + \pgf@process{\pgfpointnormalised{}}% + \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x% + \global\pgf@y=\pgf@sys@tonumber{\pgf@ya}\pgf@y% + \else% + \c@pgf@countb=\pgf@xa% + \divide\c@pgf@countb by65536\relax% + \global\divide\pgf@x by\c@pgf@countb% + \global\divide\pgf@y by\c@pgf@countb% + \pgf@yc=\pgf@y% + \pgf@xc=8192pt% + \global\pgf@x=.125\pgf@x% + \c@pgf@countb=\pgf@x% + \divide\pgf@xc by\c@pgf@countb% + \pgf@process{#1}% + \global\pgf@x=\pgf@sys@tonumber{\pgf@yc}\pgf@x% + \global\pgf@x=\pgf@sys@tonumber{\pgf@xc}\pgf@x% + \pgf@process{\pgfpointnormalised{}}% + \global\pgf@x=\pgf@sys@tonumber{\pgf@xa}\pgf@x% + \global\pgf@y=\pgf@sys@tonumber{\pgf@ya}\pgf@y% + \fi% + \fi% +} + + + + + + +\def\pgfextractx#1#2{% + \pgf@process{#2}% + #1=\pgf@x\relax} + + + +\def\pgfextracty#1#2{% + \pgf@process{#2}% + #1=\pgf@y\relax} + + +\def\pgfgetlastxy#1#2{% + \edef#1{\the\pgf@x}% + \edef#2{\the\pgf@y}% +}% + + +\def\pgf@def#1#2#3{\expandafter\def\csname pgf@#1#2\endcsname{#3}} +\pgf@def{cosfrac}{0}{1} +\pgf@def{cosfrac}{1}{0.99995} \pgf@def{cosfrac}{2}{0.9998} +\pgf@def{cosfrac}{3}{0.99955} \pgf@def{cosfrac}{4}{0.999201} +\pgf@def{cosfrac}{5}{0.998752} \pgf@def{cosfrac}{6}{0.998205} +\pgf@def{cosfrac}{7}{0.997559} \pgf@def{cosfrac}{8}{0.996815} +\pgf@def{cosfrac}{9}{0.995974} \pgf@def{cosfrac}{10}{0.995037} +\pgf@def{cosfrac}{11}{0.994004} \pgf@def{cosfrac}{12}{0.992877} +\pgf@def{cosfrac}{13}{0.991656} \pgf@def{cosfrac}{14}{0.990342} +\pgf@def{cosfrac}{15}{0.988936} \pgf@def{cosfrac}{16}{0.987441} +\pgf@def{cosfrac}{17}{0.985856} \pgf@def{cosfrac}{18}{0.984183} +\pgf@def{cosfrac}{19}{0.982424} \pgf@def{cosfrac}{20}{0.980581} +\pgf@def{cosfrac}{21}{0.978653} \pgf@def{cosfrac}{22}{0.976644} +\pgf@def{cosfrac}{23}{0.974555} \pgf@def{cosfrac}{24}{0.972387} +\pgf@def{cosfrac}{25}{0.970143} \pgf@def{cosfrac}{26}{0.967823} +\pgf@def{cosfrac}{27}{0.965429} \pgf@def{cosfrac}{28}{0.962964} +\pgf@def{cosfrac}{29}{0.960429} \pgf@def{cosfrac}{30}{0.957826} +\pgf@def{cosfrac}{31}{0.955157} \pgf@def{cosfrac}{32}{0.952424} +\pgf@def{cosfrac}{33}{0.949629} \pgf@def{cosfrac}{34}{0.946773} +\pgf@def{cosfrac}{35}{0.943858} \pgf@def{cosfrac}{36}{0.940887} +\pgf@def{cosfrac}{37}{0.937862} \pgf@def{cosfrac}{38}{0.934784} +\pgf@def{cosfrac}{39}{0.931655} \pgf@def{cosfrac}{40}{0.928477} +\pgf@def{cosfrac}{41}{0.925252} \pgf@def{cosfrac}{42}{0.921982} +\pgf@def{cosfrac}{43}{0.918669} \pgf@def{cosfrac}{44}{0.915315} +\pgf@def{cosfrac}{45}{0.911922} \pgf@def{cosfrac}{46}{0.90849} +\pgf@def{cosfrac}{47}{0.905024} \pgf@def{cosfrac}{48}{0.901523} +\pgf@def{cosfrac}{49}{0.89799} \pgf@def{cosfrac}{50}{0.894427} +\pgf@def{cosfrac}{51}{0.890835} \pgf@def{cosfrac}{52}{0.887217} +\pgf@def{cosfrac}{53}{0.883573} \pgf@def{cosfrac}{54}{0.879905} +\pgf@def{cosfrac}{55}{0.876216} \pgf@def{cosfrac}{56}{0.872506} +\pgf@def{cosfrac}{57}{0.868777} \pgf@def{cosfrac}{58}{0.865031} +\pgf@def{cosfrac}{59}{0.861269} \pgf@def{cosfrac}{60}{0.857493} +\pgf@def{cosfrac}{61}{0.853704} \pgf@def{cosfrac}{62}{0.849903} +\pgf@def{cosfrac}{63}{0.846092} \pgf@def{cosfrac}{64}{0.842271} +\pgf@def{cosfrac}{65}{0.838444} \pgf@def{cosfrac}{66}{0.834609} +\pgf@def{cosfrac}{67}{0.83077} \pgf@def{cosfrac}{68}{0.826927} +\pgf@def{cosfrac}{69}{0.82308} \pgf@def{cosfrac}{70}{0.819232} +\pgf@def{cosfrac}{71}{0.815383} \pgf@def{cosfrac}{72}{0.811534} +\pgf@def{cosfrac}{73}{0.807687} \pgf@def{cosfrac}{74}{0.803842} +\pgf@def{cosfrac}{75}{0.8} \pgf@def{cosfrac}{76}{0.796162} +\pgf@def{cosfrac}{77}{0.792329} \pgf@def{cosfrac}{78}{0.788502} +\pgf@def{cosfrac}{79}{0.784682} \pgf@def{cosfrac}{80}{0.780869} +\pgf@def{cosfrac}{81}{0.777064} \pgf@def{cosfrac}{82}{0.773268} +\pgf@def{cosfrac}{83}{0.769481} \pgf@def{cosfrac}{84}{0.765705} +\pgf@def{cosfrac}{85}{0.761939} \pgf@def{cosfrac}{86}{0.758185} +\pgf@def{cosfrac}{87}{0.754443} \pgf@def{cosfrac}{88}{0.750714} +\pgf@def{cosfrac}{89}{0.746997} \pgf@def{cosfrac}{90}{0.743294} +\pgf@def{cosfrac}{91}{0.739605} \pgf@def{cosfrac}{92}{0.735931} +\pgf@def{cosfrac}{93}{0.732272} \pgf@def{cosfrac}{94}{0.728628} +\pgf@def{cosfrac}{95}{0.724999} \pgf@def{cosfrac}{96}{0.721387} +\pgf@def{cosfrac}{97}{0.717792} \pgf@def{cosfrac}{98}{0.714213} +\pgf@def{cosfrac}{99}{0.710651} \pgf@def{cosfrac}{100}{0.707107} + + + + + +\let\pgfpointtransformednonlinear\pgfpointtransformed + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorequick.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorequick.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..49bd4f5b66c1e44feba662de724edfba868c03c1 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorequick.code.tex @@ -0,0 +1,67 @@ + +\ProvidesFileRCS{pgfcorequick.code.tex} + + + +\def\pgfpathqmoveto#1#2{\pgfsyssoftpath@moveto{#1}{#2}} + + + +\def\pgfpathqlineto#1#2{\pgfsyssoftpath@lineto{#1}{#2}} + + + +\def\pgfpathqcurveto#1#2#3#4#5#6{\pgfsyssoftpath@curveto{#1}{#2}{#3}{#4}{#5}{#6}} + + + + + +\def\pgfpathqcircle#1{% + {% + \pgf@x=#1% + \pgf@y=0.5522847\pgf@x% + \pgfsyssoftpath@moveto{\the\pgf@x}{0pt}% + \pgfsyssoftpath@curveto{\the\pgf@x}{\the\pgf@y}{\the\pgf@y}{\the\pgf@x}{0pt}{\the\pgf@x}% + \pgfsyssoftpath@curveto{-\the\pgf@y}{\the\pgf@x}{-\the\pgf@x}{\the\pgf@y}{-\the\pgf@x}{0pt}% + \pgfsyssoftpath@curveto{-\the\pgf@x}{-\the\pgf@y}{-\the\pgf@y}{-\the\pgf@x}{0pt}{-\the\pgf@x}% + \pgfsyssoftpath@curveto{\the\pgf@y}{-\the\pgf@x}{\the\pgf@x}{-\the\pgf@y}{\the\pgf@x}{0pt}% + \pgfsyssoftpath@closepath% + }% +} + + + + +\def\pgfusepathqstroke{% + \pgfsyssoftpath@flushcurrentpath% + \pgfsys@stroke% + \pgf@resetpathsizes% +} + + + +\def\pgfusepathqfill{% + \pgfsyssoftpath@flushcurrentpath% + \pgfsys@fill% + \pgf@resetpathsizes% +} + + + +\def\pgfusepathqfillstroke{% + \pgfsyssoftpath@flushcurrentpath% + \pgfsys@fillstroke% + \pgf@resetpathsizes% +} + + +\def\pgfusepathqclip{% + \pgfsyssoftpath@flushcurrentpath% + \pgfsys@clipnext% + \pgfsys@discardpath% + \pgf@resetpathsizes% +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..eef0d328b3a9d3938a85ef24d64a8d3d2c07792c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorerdf.code.tex @@ -0,0 +1,83 @@ + +\ProvidesFileRCS{pgfcorerdf.code.tex} + + + + + + + + + +\def\pgfrdfabout#1{\pgfsys@rdf@about{#1}} + + + + +\def\pgfrdfcontent#1{\pgfsys@rdf@content{#1}} + + + + +\def\pgfrdfdatatype#1{\pgfsys@rdf@datatype{#1}} + + + + +\def\pgfrdfhref#1{\pgfsys@rdf@href{#1}} + + + + +\def\pgfrdfinlist{\pgfsys@rdf@inlist} + + + + + +\def\pgfrdfprefix#1{\pgfsys@rdf@prefix{#1}} + + + + + +\def\pgfrdfproperty#1{\pgfsys@rdf@property{#1}} + + + + +\def\pgfrdfrel#1{\pgfsys@rdf@rel{#1}} + + + +\def\pgfrdfresource#1{\pgfsys@rdf@resource{#1}} + + + + + +\def\pgfrdfrev#1{\pgfsys@rdf@rev{#1}} + + + + + +\def\pgfrdfsrc#1{\pgfsys@rdf@src{#1}} + + + + + +\def\pgfrdftypeof#1{\pgfsys@rdf@typeof{#1}} + + + + + +\def\pgfrdfvocab#1{\pgfsys@rdf@vocab{#1}} + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..4036c90ff3df07178ae730c610104701b81b5195 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcorescopes.code.tex @@ -0,0 +1,496 @@ + +\ProvidesFileRCS{pgfcorescopes.code.tex} + + +\newbox\pgfpic +\newbox\pgf@hbox + +\newbox\pgf@layerbox@main + +\newcount\pgf@picture@serial@count + + + +\newif\ifpgfrememberpicturepositiononpage + + + + + + + +\def\pgfscope{% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + \pgfsys@beginscope% + \pgf@resetpathsizes% + \edef\pgfscope@linewidth{\the\pgflinewidth}% + \let\pgfscope@stroke@color=\pgf@strokecolor@global% + \let\pgfscope@fill@color=\pgf@fillcolor@global% + \begingroup} +\def\endpgfscope{% + \endgroup% + \global\pgflinewidth=\pgfscope@linewidth% + \global\let\pgf@strokecolor@global=\pgfscope@stroke@color% + \global\let\pgf@fillcolor@global=\pgfscope@fill@color% + \pgfsys@endscope} + + + + + +\def\pgfqbox#1{% + \pgfsys@hbox#1% +} + + + +\def\pgfqboxsynced#1{% + \pgfsys@hboxsynced#1% +} + + + +\def\pgftext{\pgfutil@ifnextchar[\pgf@text{\pgf@text[]}}% +\def\pgf@text[#1]{% + \def\pgf@text@options{#1}% + \pgf@maketext\pgf@after@text} +\def\pgf@after@text{% + {% + \def\pgf@text@hshift{center}% + \def\pgf@text@vshift{center}% + \expandafter\pgf@text@setkeys\expandafter{\pgf@text@options}% + \csname pgf@halign\pgf@text@hshift\endcsname% + \csname pgf@valign\pgf@text@vshift\endcsname% + \pgfapproximatenonlineartransformation% + \pgf@process{\pgfpointtransformed{\pgfqpoint{0pt}{\dp\pgf@hbox}}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \pgf@process{\pgfpointtransformed{\pgfqpoint{\wd\pgf@hbox}{\dp\pgf@hbox}}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \pgf@process{\pgfpointtransformed{\pgfqpoint{0pt}{\ht\pgf@hbox}}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \pgf@process{\pgfpointtransformed{\pgfqpoint{\wd\pgf@hbox}{\ht\pgf@hbox}}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \pgfqboxsynced{\pgf@hbox}% + }% +} +\def\pgf@text@setkeys{\pgfqkeys{/pgf/text}}% + +\pgfkeys{/pgf/text/left/.code=\def\pgf@text@hshift{left}} +\pgfkeys{/pgf/text/center/.code=} +\pgfkeys{/pgf/text/right/.code=\def\pgf@text@hshift{right}} +\pgfkeys{/pgf/text/top/.code=\def\pgf@text@vshift{top}} +\pgfkeys{/pgf/text/bottom/.code=\def\pgf@text@vshift{bottom}} +\pgfkeys{/pgf/text/base/.code=\def\pgf@text@vshift{base}} +\pgfkeys{/pgf/text/at/.cd,.code=\pgftransformshift{#1},.value required} +\pgfkeys{/pgf/text/x/.cd,.code=\pgftransformxshift{#1},.value required} +\pgfkeys{/pgf/text/y/.cd,.code=\pgftransformyshift{#1},.value required} +\pgfkeys{/pgf/text/rotate/.cd,.code=\pgftransformrotate{#1},.value required} + +\def\pgf@halignleft{}% +\def\pgf@haligncenter{\pgftransformxshift{+-.5\wd\pgf@hbox}} +\def\pgf@halignright{\pgftransformxshift{+-\wd\pgf@hbox}}% +\def\pgf@valignbase{}% +\def\pgf@valignbottom{\pgftransformyshift{+\dp\pgf@hbox}}% +\def\pgf@valigncenter{\pgftransformyshift{+.5\dp\pgf@hbox}\pgftransformyshift{+-.5\ht\pgf@hbox}}% +\def\pgf@valigntop{\pgftransformyshift{+-\ht\pgf@hbox}}% + + +\def\pgf@maketext#1{% + \def\pgf@@maketextafter{#1}% + \setbox\pgf@hbox=\hbox\bgroup% + \pgfinterruptpicture% + \bgroup% + \aftergroup\pgf@collectresetcolor% + \let\next=% +} +\def\pgf@collectresetcolor{% + \pgfutil@ifnextchar\reset@color% + {\reset@color\afterassignment\pgf@collectresetcolor\let\pgf@temp=}% + {\pgf@textdone}% +} +\def\pgf@textdone{% + \endpgfinterruptpicture% + \egroup% + \pgf@@maketextafter% +} + +\long\def\pgf@makehbox#1{% + \setbox\pgf@hbox=\hbox{{% + \pgfinterruptpicture% + #1% + \endpgfinterruptpicture% + }}} + + + + +\def\pgfresetboundingbox{% + \global\pgf@picmaxx=-16000pt\relax% + \global\pgf@picminx=16000pt\relax% + \global\pgf@picmaxy=-16000pt\relax% + \global\pgf@picminy=16000pt\relax% +}% + +\def\pgfpicture{% + \begingroup% + \pgfpicturetrue% + \global\advance\pgf@picture@serial@count by1\relax% + \edef\pgfpictureid{pgfid\the\pgf@picture@serial@count}% + \let\pgf@nodecallback=\pgfutil@gobble% + \pgf@picmaxx=-16000pt\relax% + \pgf@picminx=16000pt\relax% + \pgf@picmaxy=-16000pt\relax% + \pgf@picminy=16000pt\relax% + \pgf@relevantforpicturesizetrue% + \pgf@resetpathsizes% + \pgfutil@ifnextchar\bgroup\pgf@oldpicture\pgf@picture} +\def\pgf@oldpicture#1#2#3#4{% + \pgfmathsetlength\pgf@picminx{#1}% + \pgfmathsetlength\pgf@picminy{#2}% + \pgfmathsetlength\pgf@picmaxx{#3}% + \pgfmathsetlength\pgf@picmaxy{#4}% + \pgf@relevantforpicturesizefalse% + \pgf@picture} + +\def\pgf@picture{% + \setbox\pgfpic\hbox to0pt\bgroup% + \begingroup% + \pgfsys@beginpicture% + \pgfsys@beginscope% + \begingroup% + \pgfsetcolor{.}% + \pgfsetlinewidth{0.4pt}% + \pgftransformreset% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + \begingroup% + \let\pgf@setlengthorig=\setlength% + \let\pgf@addtolengthorig=\addtolength% + \let\pgf@selectfontorig=\selectfont% + \let\setlength=\pgf@setlength% + \let\addtolength=\pgf@addtolength% + \let\selectfont=\pgf@selectfont% + \nullfont\spaceskip0pt\xspaceskip0pt% + \tracinglostchars=% + \ifnum\tracinglostchars>2 2\else\tracinglostchars\fi + \setbox\pgf@layerbox@main\hbox to0pt\bgroup% + \begingroup% + } +\def\endpgfpicture{% + \ifpgfrememberpicturepositiononpage% + \hbox to0pt{\pgfsys@markposition{\pgfpictureid}}% + \fi% + \ifdim\pgf@picmaxx=-16000pt\relax% + \global\pgf@picmaxx=0pt\relax% + \global\pgf@picminx=0pt\relax% + \global\pgf@picmaxy=0pt\relax% + \global\pgf@picminy=0pt\relax% + \fi% + \pgf@relevantforpicturesizefalse% + \pgf@process{\pgf@baseline}% + \xdef\pgf@shift@baseline{\the\pgf@y}% + \pgf@process{\pgf@trimleft}% + \global\advance\pgf@x by-\pgf@picminx + \xdef\pgf@trimleft@final{-\the\pgf@x}% + \pgf@process{\pgf@trimright}% + \global\advance\pgf@x by-\pgf@picmaxx + \xdef\pgf@trimright@final{\the\pgf@x}% + \pgf@remember@layerlist@globally + \endgroup% + \hss% + \egroup% + \pgf@restore@layerlist@from@global + \pgf@insertlayers% + \endgroup% + \pgfsys@discardpath% + \endgroup% + \pgfsys@endscope% + \pgfsys@endpicture% + \endgroup% + \hss + \egroup% + \pgfsys@typesetpicturebox\pgfpic% + \endgroup% +} + +\def\pgf@remember@layerlist@globally{% + \global\let\pgf@layerlist@=\pgf@layerlist +}% +\def\pgf@restore@layerlist@from@global{% + \let\pgf@layerlist=\pgf@layerlist@ +}% +\def\pgf@insertlayers{% + \box\pgf@layerbox@main% +} + +\def\pgf@selectfont{\pgf@selectfontorig\nullfont} + +\def\pgf@setlength#1#2{% + \begingroup% + \pgfutil@selectfont% + \pgf@setlengthorig#1{#2}% + \expandafter% + \endgroup% + \expandafter#1\expandafter=\the#1\relax} +\def\pgf@addtolength#1#2{% + \begingroup% + \pgfutil@selectfont% + \pgf@addtolengthorig#1{#2}% + \expandafter% + \endgroup% + \expandafter#1\expandafter=\the#1\relax} + + + +\def\pgfsetbaselinepointlater#1{\def\pgf@baseline{#1}} + + + +\def\pgfsetbaselinepointnow#1{% + \pgf@process{#1}% + \edef\pgf@setter@baseline{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfsetbaselinepointlater{\pgf@setter@baseline}% +} + +\def\pgf@default@text{default}% + + +\def\pgfsetbaseline#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgf@default@text + \pgfsetbaseline{\pgf@picminy}% + \else + \pgfsetbaselinepointlater{\pgfpoint{0pt}{#1}}% + \fi +} +\pgfsetbaseline{\pgf@picminy} + +\newif\ifpgf@trim@lowlevel +\pgfkeys{ + /pgf/trim lowlevel/.is if=pgf@trim@lowlevel, + /pgf/trim lowlevel/.default=true, +} + +\def\pgfsettrimleftpointlater#1{\def\pgf@trimleft{#1}} +\def\pgfsettrimleftpointnow#1{% + \pgf@process{#1}% + \edef\pgf@setter@baseline{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfsettrimleftpointlater{\pgf@setter@baseline}% +} +\def\pgfsettrimleft#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgf@default@text + \pgfsettrimleft{\pgf@picminx} + \else + \pgfsettrimleftpointlater{\pgfpoint{#1}{0pt}}% + \fi +} +\pgfsettrimleft{\pgf@picminx} + +\def\pgfsettrimrightpointlater#1{\def\pgf@trimright{#1}} +\def\pgfsettrimrightpointnow#1{% + \pgf@process{#1}% + \edef\pgf@setter@baseline{\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfsettrimrightpointlater{\pgf@setter@baseline}% +} +\def\pgfsettrimright#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgf@default@text + \pgfsettrimright{\pgf@picmaxx}% + \else + \pgfsettrimrightpointlater{\pgfpoint{#1}{0pt}}% + \fi +} +\pgfsettrimright{\pgf@picmaxx} + + + +\def\pgfinterruptpath +{% + \begingroup% + \edef\pgf@interrupt@savex{\the\pgf@path@lastx}% + \edef\pgf@interrupt@savey{\the\pgf@path@lasty}% + \pgf@getpathsizes\pgf@interrupt@pathsizes% + \pgfsyssoftpath@getcurrentpath\pgf@interrupt@path% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + \let\pgf@interrupt@lastmoveto=\pgfsyssoftpath@lastmoveto% + \begingroup% +} +\def\endpgfinterruptpath +{% + \endgroup% + \pgfsyssoftpath@setcurrentpath\pgf@interrupt@path% + \pgf@setpathsizes\pgf@interrupt@pathsizes% + \global\pgf@path@lastx\pgf@interrupt@savex% + \global\pgf@path@lasty\pgf@interrupt@savey% + \global\let\pgfsyssoftpath@lastmoveto\pgf@interrupt@lastmoveto% + \endgroup% +} + + + + +\def\pgfinterruptboundingbox +{% + \begingroup% + \edef\pgf@interrupt@savemaxx{\the\pgf@picmaxx}% + \edef\pgf@interrupt@saveminx{\the\pgf@picminx}% + \edef\pgf@interrupt@savemaxy{\the\pgf@picmaxy}% + \edef\pgf@interrupt@saveminy{\the\pgf@picminy}% + \pgf@picmaxx=-16000pt\relax% + \pgf@picminx=16000pt\relax% + \pgf@picmaxy=-16000pt\relax% + \pgf@picminy=16000pt\relax% + \pgf@size@hookedfalse% + \let\pgf@path@size@hook=\pgfutil@empty% +} +\def\endpgfinterruptboundingbox +{% + \global\pgf@picmaxx=\pgf@interrupt@savemaxx% + \global\pgf@picmaxy=\pgf@interrupt@savemaxy% + \global\pgf@picminx=\pgf@interrupt@saveminx% + \global\pgf@picminy=\pgf@interrupt@saveminy% + \endgroup% +} + + + + + +\def\pgfidscope{\pgfsys@begin@idscope} +\def\endpgfidscope{\pgfsys@end@idscope} + +\let\startpgfidscope\pgfidscope +\let\stoppgfidscope\pgfendidscope + + + + + +\def\pgfuseid#1{% + \edef\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgf@lookup@id{#1}% + \pgfsys@use@id{\pgf@next@id}% + \expandafter\xdef\csname pgf@id@names@#1\endcsname{{\pgf@next@id}{}}% + \fi% +} + +\def\pgf@lookup@id#1{% + \expandafter\let\expandafter\pgf@id@name\csname pgf@id@names@#1\endcsname% + \ifx\pgf@id@name\relax% + \let\pgf@prev@id\pgfutil@empty% + \let\pgf@next@id\pgfutil@empty% + \else% + \expandafter\pgf@id@parse\pgf@id@name% + \fi% + \ifx\pgf@next@id\pgfutil@empty% + \pgfsys@new@id\pgf@next@id% + \expandafter\xdef\csname pgf@id@names@#1\endcsname{{\pgf@prev@id}{\pgf@next@id}}% + \fi% +} +\def\pgf@id@parse#1#2{% + \def\pgf@prev@id{#1}% + \def\pgf@next@id{#2}% +} + + + + +\def\pgfclearid{% + \pgfsys@clear@id% +} + + + +\def\pgfidrefnextuse#1#2{% + \edef\pgf@temp{#2}\ifx\pgf@temp\pgfutil@empty\pgferror{Missing name reference for ``\string#1''}\fi% + \pgf@lookup@id{#2}% + \let#1\pgf@next@id% +} + + + +\def\pgfidrefprevuse#1#2{% + \edef\pgf@temp{#2}\ifx\pgf@temp\pgfutil@empty\pgferror{Missing name reference for ``\string#1''}\fi% + \pgf@lookup@id{#2}% + \let#1\pgf@prev@id% +} + + + +\def\pgfusetype#1{% + \edef\pgf@temp{#1}% + \expandafter\pgfutil@ifnextchar\expandafter.\expandafter\pgf@id@use@type@add\expandafter\pgf@id@use@type@replace\pgf@temp\pgf@stop +} +\def\pgf@id@use@type@add.#1\pgf@stop{\pgfsys@append@type{#1}} +\def\pgf@id@use@type@replace#1\pgf@stop{\pgfsys@use@type{#1}} + + +\def\pgfpushtype{\pgfsys@push@type} + + + +\def\pgfpoptype{\pgfsys@pop@type} + + + + + +\def\pgfaliasid#1#2{% + \expandafter\let\expandafter\pgf@temp\csname pgf@id@names@#2\endcsname% + \expandafter\let\csname pgf@id@names@#1\endcsname\pgf@temp% +} +\def\pgfgaliasid#1#2{% + \expandafter\let\expandafter\pgf@temp\csname pgf@id@names@#2\endcsname% + \expandafter\global\expandafter\let\csname pgf@id@names@#1\endcsname\pgf@temp% +} + + + +\def\pgfifidreferenced#1#2#3{% + \expandafter\let\expandafter\pgf@id@name\csname pgf@id@names@#1\endcsname% + \ifx\pgf@id@name\relax% + #3% + \else + \expandafter\pgf@id@parse\pgf@id@name% + \ifx\pgf@next@id\pgfutil@empty% + #3% + \else% + #2% + \fi% + \fi% +} + + + +\def\pgfinterruptpicture +{% + \begingroup% + \csname tikz@inside@picturefalse\endcsname% + \pgfinterruptboundingbox% + \pgftransformreset% + \pgfinterruptpath% + \ifx\pgf@selectfontorig\@undefined% + \else% + \let\setlength\pgf@setlengthorig% + \let\addtolength\pgf@addtolengthorig% + \let\selectfont\pgf@selectfontorig% + \fi% + \pgfutil@selectfont% + \pgfpicturefalse% + \let\pgf@positionnodelater@macro\relax% + \pgf@savelayers% +} +\def\endpgfinterruptpicture +{% + \pgf@restorelayers% + \endpgfinterruptpath% + \endpgfinterruptboundingbox% + \endgroup% +} + +\let\pgf@savelayers=\relax +\let\pgf@restorelayers=\relax + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a26221b163a67580b304050051e277cf0e87caff --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoreshade.code.tex @@ -0,0 +1,700 @@ + +\ProvidesFileRCS{pgfcoreshade.code.tex} + +\newdimen\pgf@max +\newcount\pgf@sys@shading@range@num +\def\pgf@parsefunc#1{% + \edef\temp{{#1}}% + \expandafter\pgf@convertstring\temp% + \edef\temp{{\pgf@conv}}% + \expandafter\pgf@@parsefunc\temp} +\def\pgf@@parsefunc#1{% + \let\pgf@bounds=\pgfutil@empty% + \let\pgf@funcs=\pgfutil@empty% + \let\pgf@psfuncs=\pgfutil@empty% + \let\pgf@encode=\pgfutil@empty% + \let\pgf@sys@shading@ranges=\pgfutil@empty% + \pgf@sys@shading@range@num=0\relax% + \csname pgf@parsefirst\pgf@shading@model\endcsname[#1; ]% + \csname pgf@parselastdom\pgf@shading@model\endcsname[#1; ]% + \csname pgf@parsemid\pgf@shading@model\endcsname[#1; ]% + \ifx\pgf@bounds\pgfutil@empty% + \edef\pgf@pdfparseddomain{0 1}% + \edef\pgf@pdfparsedfunction{\pgf@singlefunc\space}% + \else% + \edef\pgf@pdfparseddomain{\pgf@doma\space\pgf@domb}% + \edef\pgf@pdfparsedfunction{% + << /FunctionType 3 /Domain [\pgf@doma\space\pgf@domb] /Functions + [\pgf@funcs\space] /Bounds [\pgf@bounds] /Encode [0 1 \pgf@encode] + >> }% + \fi% + \xdef\pgf@psfuncs{\pgf@psfuncs}% + } +\def\pgf@parsefirstrgb[rgb(#1)=(#2,#3,#4)#5]{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@start@pos{\the\pgf@x}% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@doma{\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}% + \pgf@getrgbtuplewithmixin{#2}{#3}{#4}% + \edef\pgf@sys@shading@start@rgb{\pgf@sys@rgb}% + \let\pgf@sys@prevcolor=\pgf@sys@shading@start@rgb% + \let\pgf@sys@prevpos=\pgf@sys@shading@start@pos% + \edef\pgf@prevcolor{\pgf@rgb}% + \edef\pgf@firstcolor{\pgf@rgb}} +\def\pgf@parselastdomrgb[rgb(#1)=(#2,#3,#4); {% + \pgfutil@ifnextchar]{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@end@pos{\the\pgf@x}% + \pgf@max=\pgf@x\relax% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@domb{\pgf@sys@tonumber{\pgf@x}}% + \pgf@getrgbtuplewithmixin{#2}{#3}{#4}% + \edef\pgf@sys@shading@end@rgb{\pgf@sys@rgb}% + \pgfutil@gobble}{\pgf@parselastdomrgb[}} +\def\pgf@parsemidrgb[rgb(#1)=(#2,#3,#4); {\pgf@parserestrgb[} +\def\pgf@parserestrgb[rgb(#1)=(#2,#3,#4); {% + \advance\pgf@sys@shading@range@num by1\relax% + \pgfutil@ifnextchar]{% + \pgf@getrgbtuplewithmixin{#2}{#3}{#4}% + \edef\pgf@singlefunc{\space% + << /FunctionType 2 /Domain [0 1] /C0 + [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }% + \edef\pgf@funcs{\pgf@funcs\space% + << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0 + [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }% + \edef\pgf@psfuncs{\pgf@prevx\space \pgf@rgb\space \pgf@prevcolor\space pgfshade \pgf@psfuncs}% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{{\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@rgb}}}% + \edef\pgf@sys@prevpos{\the\pgf@x}% + \let\pgf@sys@prevcolor=\pgf@sys@rgb% + \pgfutil@gobble}{% + \pgfmathsetlength\pgf@x{#1}% + \pgf@getrgbtuplewithmixin{#2}{#3}{#4}% + \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{{\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@rgb}}}% + \edef\pgf@sys@prevpos{\the\pgf@x}% + \let\pgf@sys@prevcolor=\pgf@sys@rgb% + \edef\pgf@psfuncs{\pgf@prevx\space \pgf@rgb\space \pgf@prevcolor\space pgfshade \pgf@psfuncs}% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@bounds{\pgf@bounds\space\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@encode{\pgf@encode\space0 1}% + \edef\pgf@singlefunc{\space% + << /FunctionType 2 /Domain [0 1] /C0 + [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }% + \edef\pgf@funcs{\pgf@funcs\space% + << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0 + [\pgf@prevcolor] /C1 [\pgf@rgb] /N 1 >> }% + \edef\pgf@prevcolor{\pgf@rgb}% + \pgf@parserestrgb[}} + +\def\pgf@getrgbtuplewithmixin#1#2#3{% + \pgfutil@definecolor{pgfshadetemp}{rgb}{#1,#2,#3}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfshadetemp}}% + \pgfutil@extractcolorspec{pgfshadetemp}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}% + \expandafter\pgf@getrgb@@\pgf@rgbcolor!} +\def\pgf@getrgb@@#1,#2,#3!{% + \def\pgf@rgb{#1 #2 #3}% + \def\pgf@sys@rgb{{#1}{#2}{#3}}% +} + +\def\pgf@parsefirstcmyk[cmyk(#1)=(#2,#3,#4,#5)#6]{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@start@pos{\the\pgf@x}% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@doma{\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}% + \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}% + \edef\pgf@sys@shading@start@cmyk{\pgf@sys@cmyk}% + \let\pgf@sys@prevcolor=\pgf@sys@shading@start@cmyk% + \let\pgf@sys@prevpos=\pgf@sys@shading@start@pos% + \edef\pgf@prevcolor{\pgf@cmyk}% + \edef\pgf@firstcolor{\pgf@cmyk}} +\def\pgf@parselastdomcmyk[cmyk(#1)=(#2,#3,#4,#5); {% + \pgfutil@ifnextchar]{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@end@pos{\the\pgf@x}% + \pgf@max=\pgf@x\relax% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@domb{\pgf@sys@tonumber{\pgf@x}}% + \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}% + \edef\pgf@sys@shading@end@cmyk{\pgf@sys@cmyk}% + \pgfutil@gobble}{\pgf@parselastdomcmyk[}} +\def\pgf@parsemidcmyk[cmyk(#1)=(#2,#3,#4,#5); {\pgf@parserestcmyk[} +\def\pgf@parserestcmyk[cmyk(#1)=(#2,#3,#4,#5); {% + \advance\pgf@sys@shading@range@num by1\relax% + \pgfutil@ifnextchar]{% + \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}% + \edef\pgf@singlefunc{\space% + << /FunctionType 2 /Domain [0 1] /C0 + [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }% + \edef\pgf@funcs{\pgf@funcs\space% + << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0 + [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }% + \edef\pgf@psfuncs{\pgf@prevx\space + \pgf@cmyk\space \pgf@prevcolor\space pgfshade \pgf@psfuncs}% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{% + {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@cmyk}}}% + \edef\pgf@sys@prevpos{\the\pgf@x}% + \let\pgf@sys@prevcolor=\pgf@sys@cmyk% + \pgfutil@gobble}{% + \pgfmathsetlength\pgf@x{#1}% + \pgf@getcmyktuplewithmixin{#2}{#3}{#4}{#5}% + \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{% + {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@cmyk}}}% + \edef\pgf@sys@prevpos{\the\pgf@x}% + \let\pgf@sys@prevcolor=\pgf@sys@cmyk% + \edef\pgf@psfuncs{\pgf@prevx\space \pgf@cmyk\space + \pgf@prevcolor\space pgfshade \pgf@psfuncs}% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@bounds{\pgf@bounds\space\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@encode{\pgf@encode\space0 1}% + \edef\pgf@singlefunc{\space% + << /FunctionType 2 /Domain [0 1] /C0 + [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }% + \edef\pgf@funcs{\pgf@funcs\space% + << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0 + [\pgf@prevcolor] /C1 [\pgf@cmyk] /N 1 >> }% + \edef\pgf@prevcolor{\pgf@cmyk}% + \pgf@parserestcmyk[}} + +\def\pgf@getcmyktuplewithmixin#1#2#3#4{% + \pgfutil@definecolor{pgfshadetemp}{cmyk}{#1,#2,#3,#4}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfshadetemp}}% + \pgfutil@extractcolorspec{pgfshadetemp}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{cmyk}{\pgf@cmykcolor}% + \expandafter\pgf@getcmyk@@\pgf@cmykcolor!} +\def\pgf@getcmyk@@#1,#2,#3,#4!{% + \def\pgf@cmyk{#1 #2 #3 #4}% + \def\pgf@sys@cmyk{{#1}{#2}{#3}{#4}}% +} + +\def\pgf@parsefirstgray[gray(#1)=(#2)#3]{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@start@pos{\the\pgf@x}% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@doma{\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}% + \pgf@getgraytuplewithmixin{#2}% + \edef\pgf@sys@shading@start@gray{\pgf@sys@gray}% + \let\pgf@sys@prevcolor=\pgf@sys@shading@start@gray% + \let\pgf@sys@prevpos=\pgf@sys@shading@start@pos% + \edef\pgf@prevcolor{\pgf@gray}% + \edef\pgf@firstcolor{\pgf@gray}} +\def\pgf@parselastdomgray[gray(#1)=(#2); {% + \pgfutil@ifnextchar]{% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@end@pos{\the\pgf@x}% + \pgf@max=\pgf@x\relax% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@domb{\pgf@sys@tonumber{\pgf@x}}% + \pgf@getgraytuplewithmixin{#2}% + \edef\pgf@sys@shading@end@gray{\pgf@sys@gray}% + \pgfutil@gobble}{\pgf@parselastdomgray[}} +\def\pgf@parsemidgray[gray(#1)=(#2); {\pgf@parserestgray[} +\def\pgf@parserestgray[gray(#1)=(#2); {% + \advance\pgf@sys@shading@range@num by1\relax% + \pgfutil@ifnextchar]{% + \pgf@getgraytuplewithmixin{#2}% + \edef\pgf@singlefunc{\space% + << /FunctionType 2 /Domain [0 1] /C0 + [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }% + \edef\pgf@funcs{\pgf@funcs\space% + << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0 + [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }% + \edef\pgf@psfuncs{\pgf@prevx\space \pgf@gray\space + \pgf@prevcolor\space pgfshade \pgf@psfuncs}% + \pgfmathsetlength\pgf@x{#1}% + \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{% + {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@gray}}}% + \edef\pgf@sys@prevpos{\the\pgf@x}% + \let\pgf@sys@prevcolor=\pgf@sys@gray% + \pgfutil@gobble}{% + \pgfmathsetlength\pgf@x{#1}% + \pgf@getgraytuplewithmixin{#2}% + \edef\pgf@sys@shading@ranges{\pgf@sys@shading@ranges{% + {\pgf@sys@prevpos}{\the\pgf@x}{\pgf@sys@prevcolor}{\pgf@sys@gray}}}% + \edef\pgf@sys@prevpos{\the\pgf@x}% + \let\pgf@sys@prevcolor=\pgf@sys@gray% + \edef\pgf@psfuncs{\pgf@prevx\space \pgf@gray\space + \pgf@prevcolor\space pgfshade \pgf@psfuncs}% + \pgf@sys@bp@correct\pgf@x% + \edef\pgf@prevx{\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@bounds{\pgf@bounds\space\pgf@sys@tonumber{\pgf@x}}% + \edef\pgf@encode{\pgf@encode\space0 1}% + \edef\pgf@singlefunc{\space% + << /FunctionType 2 /Domain [0 1] /C0 + [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }% + \edef\pgf@funcs{\pgf@funcs\space% + << /FunctionType 2 /Domain [\pgf@doma\space\pgf@domb] /C0 + [\pgf@prevcolor] /C1 [\pgf@gray] /N 1 >> }% + \edef\pgf@prevcolor{\pgf@gray}% + \pgf@parserestgray[}} + +\def\pgf@getgraytuplewithmixin#1{% + \pgfutil@definecolor{pgfshadetemp}{gray}{#1}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgfshadetemp}}% + \pgfutil@extractcolorspec{pgfshadetemp}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{gray}{\pgf@graycolor}% + \expandafter\pgf@getgray@@\pgf@graycolor!} +\def\pgf@getgray@@#1!{% + \def\pgf@gray{#1}% + \def\pgf@sys@gray{{#1}}% +} + +\def\pgf@convertstring#1{% + \def\pgf@conv{}% + \pgf@convert#1]% + } +\def\pgf@convert{% + \pgfutil@ifnextchar]{\pgfutil@gobble}% + {% + \pgfutil@ifnextchar;{\pgf@grabsemicolor}% + {% + \pgfutil@ifnextchar c{\pgf@gobblec}% + {% + \pgfutil@ifnextchar g{\pgf@grabgray}% + {% + \pgfutil@ifnextchar o{\pgf@grabcolor}% + {% + \pgfutil@ifnextchar m{\pgf@grabcmyk}% + {% + \pgfutil@ifnextchar r{\pgf@grabrgb}% + {\pgferror{Illformed shading + specification}\pgf@convert}% + }% + }% + }% + }% + }% + }% +} +\def\pgf@savecolor#1{% + \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor + {\pgf@shading@model}{\pgf@color}% + \expandafter\pgf@convget@\expandafter{\pgf@color}{#1}% +} +\def\pgf@grabsemicolor;{% + \edef\pgf@conv{\pgf@conv; }\pgf@convert} +\def\pgf@gobblec c{\pgf@convert} +\def\pgf@grabrgb rgb(#1)=(#2,#3,#4){% + \pgfutil@definecolor{pgf@tempcol}{rgb}{#2,#3,#4}% + \pgf@savecolor{#1}% +} +\def\pgf@grabcmyk myk(#1)=(#2,#3,#4,#5){% + \pgfutil@definecolor{pgf@tempcol}{cmyk}{#2,#3,#4,#5}% + \pgf@savecolor{#1}% +} +\def\pgf@grabgray gray(#1)=(#2){% + \pgfutil@definecolor{pgf@tempcol}{gray}{#2}% + \pgf@savecolor{#1}% +} +\def\pgf@grabcolor olor(#1)=(#2){% + \pgfutil@colorlet{pgf@tempcol}{#2}% + \pgf@savecolor{#1}% +} +\def\pgf@convget@#1#2{% + \edef\pgf@conv{\pgf@conv \pgf@shading@model(#2)=(#1)}\pgf@convert} + + +\newcount\pgf@shadingcount +\pgf@shadingcount=0 +{ + \catcode`\/=0 + \catcode`\\=12 + /gdef/pgf@shadingnum{\/the/pgf@shadingcount\} +} + + +\newif\ifpgfshadingmodelrgb +\newif\ifpgfshadingmodelcmyk +\newif\ifpgfshadingmodelgray +\def\pgf@setup@shading@model{% + \pgfshadingmodelrgbtrue + \pgfshadingmodelcmykfalse + \pgfshadingmodelgrayfalse + \XC@sdef\pgf@mod@test{\XC@tgt@mod{natural}}% + \def\pgf@shading@device{/DeviceRGB}% + \def\pgf@shading@ps@device{setrgbcolor}% + \def\pgf@shading@functional@range{0 1 0 1 0 1}% + \def\pgf@shading@model{rgb}% + \ifx\pgf@mod@test\XC@mod@cmyk + \def\pgf@shading@device{/DeviceCMYK}% + \def\pgf@shading@ps@device{setcmykcolor}% + \def\pgf@shading@functional@range{0 1 0 1 0 1 0 1}% + \def\pgf@shading@model{cmyk}% + \pgfshadingmodelrgbfalse + \pgfshadingmodelcmyktrue + \fi + \ifx\pgf@mod@test\XC@mod@gray + \def\pgf@shading@device{/DeviceGray}% + \def\pgf@shading@ps@device{setgray}% + \def\pgf@shading@functional@range{0 1}% + \def\pgf@shading@model{gray}% + \pgfshadingmodelrgbfalse + \pgfshadingmodelgraytrue + \fi + \edef\pgf@sys@driver@dvisvgm{pgfsys-dvisvgm.def}% + \ifx\pgfsysdriver\pgf@sys@driver@dvisvgm + \def\pgf@shading@model{rgb}% + \fi + \edef\pgf@sys@driver@texforht{pgfsys-tex4ht.def}% + \ifx\pgfsysdriver\pgf@sys@driver@texforht + \def\pgf@shading@model{rgb}% + \fi +} + + + +\def\pgfdeclarehorizontalshading{% + \pgf@setup@shading@model + \pgfutil@ifnextchar[% + \pgf@declarehorizontalshading{\pgf@declarehorizontalshading[]}} +\def\pgf@declarehorizontalshading[#1]#2#3#4{% + \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}% + \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty% + \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname\pgfutil@empty + \pgfsys@horishading{#2}{#3}{#4}% + \else% + \global\advance\pgf@shadingcount 1\relax + \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}% + \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfsys@horishading}% + \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}}% + \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty% + \fi} + + + +\def\pgfdeclareverticalshading{% + \pgf@setup@shading@model + \pgfutil@ifnextchar[% + \pgf@declareverticalshading{\pgf@declareverticalshading[]}} +\def\pgf@declareverticalshading[#1]#2#3#4{% + \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}% + \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty% + \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname=\pgfutil@empty + \pgfsys@vertshading{#2}{#3}{#4}% + \else% + \global\advance\pgf@shadingcount 1\relax + \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}% + \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfsys@vertshading}% + \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}}% + \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty% + \fi} + + + +\def\pgfdeclareradialshading{% + \pgf@setup@shading@model + \pgfutil@ifnextchar[% + \pgf@declareradialshading{\pgf@declareradialshading[]}} +\def\pgf@declareradialshading[#1]#2#3#4{% + \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}% + \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty% + \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname=\pgfutil@empty + \pgfsys@radialshading{#2}{#3}{#4}% + \else% + \global\advance\pgf@shadingcount 1\relax + \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}% + \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfsys@radialshading}% + \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}}% + \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty% + \fi} + + + + + +\def\pgfdeclarefunctionalshading{% + \pgf@setup@shading@model + \pgfutil@ifnextchar[% + \pgf@declarefunctionalshading{\pgf@declarefunctionalshading[]}} +\def\pgf@declarefunctionalshading[#1]#2#3#4#5#6{% + \expandafter\def\csname pgf@deps@pgfshading#2!\endcsname{#1}% + \expandafter\ifx\csname pgf@deps@pgfshading#2!\endcsname\pgfutil@empty% + \global\expandafter\let\csname pgf@num@pgfshading#2!\endcsname=\pgfutil@empty + \pgfshade@functionaldo{#2}{#3}{#4}{#5}{#6}% + \else% + \global\advance\pgf@shadingcount 1\relax + \global\expandafter\edef\csname pgf@num@pgfshading#2!\endcsname{\pgf@shadingnum}% + \expandafter\def\csname pgf@func@pgfshading#2!\endcsname{\pgfshade@functionaldo}% + \expandafter\def\csname pgf@args@pgfshading#2!\endcsname{{#3}{#4}{#5}{#6}}% + \expandafter\let\csname @pgfshading#2!\endcsname=\pgfutil@empty% + \fi} +\def\pgfshade@functionaldo#1#2#3#4#5{% + \begingroup + #4% + \pgfsys@functionalshading{#1}{#2}{#3}{#5}% + \expandafter\pgfmath@smuggleone\csname @pgfshading#1!\endcsname + \endgroup +} + +\def\pgfshadecolortorgb#1#2{% + \pgfutil@colorlet{pgf@tempcol}{#1}% + \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}% + \expandafter\pgfshading@rgb\pgf@rgbcolor\relax% + \edef#2{\pgf@sys@tonumber{\pgf@xa}\space\pgf@sys@tonumber{\pgf@xb}\space\pgf@sys@tonumber{\pgf@xc}\space}% + \c@pgf@counta\escapechar% + \escapechar-1\relax% + \expandafter\edef\csname\string#2red\endcsname{\pgf@sys@tonumber{\pgf@xa}\space}% + \expandafter\edef\csname\string#2green\endcsname{\pgf@sys@tonumber{\pgf@xb}\space}% + \expandafter\edef\csname\string#2blue\endcsname{\pgf@sys@tonumber{\pgf@xc}\space}% + \escapechar\c@pgf@counta% +} +\def\pgfshading@rgb#1,#2,#3\relax{% + \pgf@xa=#1pt% + \pgf@xb=#2pt% + \pgf@xc=#3pt% +} + +\def\pgfshadecolortocmyk#1#2{% + \pgfutil@colorlet{pgf@tempcol}{#1}% + \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{cmyk}{\pgf@cmykcolor}% + \expandafter\pgfshading@cmyk\pgf@cmykcolor\relax% + \edef#2{\pgf@sys@tonumber{\pgf@xa}\space\pgf@sys@tonumber{\pgf@xb}\space + \pgf@sys@tonumber{\pgf@xc}\space\pgf@sys@tonumber{\pgf@xd}\space}% + \c@pgf@counta\escapechar% + \escapechar-1\relax% + \expandafter\edef\csname\string#2cyan\endcsname{% + \pgf@sys@tonumber{\pgf@xa}\space}% + \expandafter\edef\csname\string#2magenta\endcsname{% + \pgf@sys@tonumber{\pgf@xb}\space}% + \expandafter\edef\csname\string#2yellow\endcsname{% + \pgf@sys@tonumber{\pgf@xc}\space}% + \expandafter\edef\csname\string#2black\endcsname{% + \pgf@sys@tonumber{\pgf@xd}\space}% + \escapechar\c@pgf@counta +} +\def\pgfshading@cmyk#1,#2,#3,#4\relax{% + \pgf@xa=#1pt% + \pgf@xb=#2pt% + \pgf@xc=#3pt% + \pgf@xd=#4pt% +} + +\def\pgfshadecolortogray#1#2{% + \pgfutil@colorlet{pgf@tempcol}{#1}% + \pgfutil@extractcolorspec{pgf@tempcol}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{gray}{\pgf@graycolor}% + \expandafter\pgfshading@gray\pgf@graycolor\relax + \edef#2{\pgf@sys@tonumber{\pgf@xa}\space}% + \c@pgf@counta\escapechar + \escapechar-1\relax + \expandafter\edef\csname\string#2gray\endcsname{% + \pgf@sys@tonumber{\pgf@xa}\space}% + \escapechar\c@pgf@counta +} +\def\pgfshading@gray#1\relax{% + \pgf@xa=#1pt% +} + + +\def\pgffuncshadingrgbtocmyk{% + 1.0 exch sub 3 1 roll + 1.0 exch sub 3 1 roll + 1.0 exch sub 3 1 roll + 3 copy + 2 copy gt { exch } if pop + 2 copy gt { exch } if pop + dup 3 1 roll sub + 0.0 2 copy lt { exch } if pop + 1.0 2 copy gt { exch } if pop + 4 1 roll + dup 3 1 roll sub + 0.0 2 copy lt { exch } if pop + 1.0 2 copy gt { exch } if pop + 4 1 roll + dup 3 1 roll sub + 0.0 2 copy lt { exch } if pop + 1.0 2 copy gt { exch } if pop + 4 1 roll +} + +\def\pgffuncshadingrgbtogray{% + 0.11 mul exch 0.59 mul add exch 0.3 mul add +} + +\def\pgffuncshadingcmyktorgb{% + dup 3 1 roll add + 1.0 2 copy gt { exch } if pop + 4 1 roll + dup 3 1 roll add + 1.0 2 copy gt { exch } if pop + 4 1 roll + add + 1.0 2 copy gt { exch } if pop + 3 1 roll + 1.0 exch sub + 3 1 roll + 1.0 exch sub + 3 1 roll + 1.0 exch sub + 3 1 roll +} + +\def\pgffuncshadingcmyktogray{% + exch 0.11 mul add exch 0.59 mul add exch 0.3 mul add + 1.0 2 copy gt { exch } if pop + 1.0 exch sub +} + +\def\pgffuncshadinggraytorgb{% + dup dup +} + +\def\pgffuncshadinggraytocmyk{% + 0.0 0.0 0.0 + 4 3 roll +} + + +\def\pgfuseshading#1{% + \edef\pgf@shadingname{@pgfshading#1}% + \pgf@tryextensions{\pgf@shadingname}{\pgfalternateextension}% + \expandafter\pgfutil@ifundefined\expandafter{\pgf@shadingname}% + {\pgferror{Undefined shading "#1"}}% + {% + \edef\pgf@shade@adds{\csname pgf@num\pgf@shadingname\endcsname}% + \pgfutil@ifundefined{pgf@deps\pgf@shadingname}% + {}% + {% + \pgf@setup@shading@model + \begingroup + \pgfutil@globalcolorsfalse + \edef\@list{\csname pgf@deps\pgf@shadingname\endcsname}% + \pgfutil@for\@temp:=\@list\do{% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{\@temp}}% + \pgfutil@extractcolorspec{\@temp}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{\pgf@shading@model}{\pgf@color}% + \edef\pgf@shade@adds{\pgf@shade@adds,\pgf@color}% + }% + \pgfmath@smuggleone\pgf@shade@adds + \endgroup + }% + \expandafter\pgf@strip@shadename\pgf@shadingname!!% + \edef\pgf@shadingxname{@pgfshading\pgf@basename\pgf@shade@adds!}% + \pgfutil@ifundefined{\pgf@shadingxname}% + {% + \begingroup + \edef\@temp{\expandafter\noexpand\csname pgf@func\pgf@shadingname\endcsname}% + \edef\@args{{\pgf@basename\pgf@shade@adds}}% + \expandafter\expandafter\expandafter\def + \expandafter\expandafter\expandafter\@@args + \expandafter\expandafter\expandafter{\csname pgf@args\pgf@shadingname\endcsname}% + \expandafter\expandafter\expandafter\@temp\expandafter\@args\@@args + \expandafter\pgfmath@smuggleone\csname\pgf@shadingxname\endcsname + \endgroup + }% + {}% + \pgf@invokeshading{\csname\pgf@shadingxname\endcsname}% + }% +} + +\def\pgf@strip@shadename @pgfshading#1!!!{\def\pgf@basename{#1}} + +\def\pgf@invokeshading#1{% + \ifpgfpicture% + \pgfsys@shadinginsidepgfpicture{#1}% + \else% + \pgfsys@shadingoutsidepgfpicture{#1}% + \fi% +} + + + +\def\pgfaliasshading#1#2{% + \expandafter\let\expandafter\pgf@temp\expandafter=\csname @pgfshading#2!\endcsname% + \expandafter\let\csname @pgfshading#1!\endcsname=\pgf@temp% + \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@num@pgfshading#2!\endcsname% + \expandafter\let\csname pgf@num@pgfshading#1!\endcsname=\pgf@temp% + \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@deps@pgfshading#2!\endcsname% + \expandafter\let\csname pgf@deps@pgfshading#1!\endcsname=\pgf@temp% + \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@func@pgfshading#2!\endcsname% + \expandafter\let\csname pgf@func@pgfshading#1!\endcsname=\pgf@temp% + \expandafter\let\expandafter\pgf@temp\expandafter=\csname pgf@args@pgfshading#2!\endcsname% + \expandafter\let\csname pgf@args@pgfshading#1!\endcsname=\pgf@temp% +} + + + + + +\def\pgfshadepath#1#2{% + \ifdim\pgf@pathminx=16000pt% + \pgfwarning{No path specified that can be filled}% + \else% + \begingroup% + \pgf@xb=.5\pgf@pathmaxx% + \advance\pgf@xb by.5\pgf@pathminx% + \pgf@yb=.5\pgf@pathmaxy% + \advance\pgf@yb by.5\pgf@pathminy% + \pgfmathparse{#2}% + \let\pgfshade@angle=\pgfmathresult + \pgfmathsin@\pgfshade@angle + \let\pgfshade@sin=\pgfmathresult + \pgfmathcos@\pgfshade@angle + \let\pgfshade@cos=\pgfmathresult + \pgf@xa=\pgf@pathmaxx + \advance\pgf@xa by-\pgf@pathminx + \pgf@ya=\pgf@pathmaxy + \advance\pgf@ya by-\pgf@pathminy + \pgfmathabs@\pgfshade@sin + \let\pgfshade@abssin=\pgfmathresult + \pgfmathabs@\pgfshade@cos + \let\pgfshade@abscos=\pgfmathresult + \pgf@xc=\pgfshade@abscos\pgf@xa + \advance\pgf@xc by\pgfshade@abssin\pgf@ya + \pgf@yc=\pgfshade@abssin\pgf@xa + \advance\pgf@yc by\pgfshade@abscos\pgf@ya + \pgfmathadd@\pgfshade@abscos\pgfshade@abssin + \pgfmathdivide@{.01992528}{\pgfmathresult}% + \pgf@xc=\pgfmathresult\pgf@xc + \pgf@yc=\pgfmathresult\pgf@yc + \ifdim\pgf@xc<0.0001pt + \ifdim\pgf@xc>-0.0001pt + \pgf@no@shadetrue + \fi + \fi + \ifdim\pgf@yc<0.0001pt + \ifdim\pgf@yc>-0.0001pt + \pgf@no@shadetrue + \fi + \fi + \ifpgf@no@shade\else + \pgfsys@beginscope + \pgfsyssoftpath@invokecurrentpath + \pgfsys@clipnext + \pgfsys@discardpath + \pgfsys@transformcm{1}{0}{0}{1}{\the\pgf@xb}{\the\pgf@yb}% + \pgf@x=\pgfshade@sin pt% + \pgf@xa=-\pgf@x% + \pgfsys@transformcm{\pgfshade@cos}{\pgfshade@sin}{\pgf@sys@tonumber{\pgf@xa}}{\pgfshade@cos}{0pt}{0pt}% + \pgfsys@transformcm{\pgf@sys@tonumber{\pgf@xc}}{0}{0}{\pgf@sys@tonumber{\pgf@yc}}{0pt}{0pt}% + \ifx\pgf@shade@extra@transform\pgfutil@empty% + \else% + \pgflowlevel{\pgf@shade@extra@transform}% + \fi% + \pgfuseshading{#1}% + \pgfsys@endscope% + \fi% + \endgroup% + \fi% +} + +\newif\ifpgf@no@shade + + +\def\pgfsetadditionalshadetransform#1{\def\pgf@shade@extra@transform{#1}} +\let\pgf@shade@extra@transform=\pgfutil@empty + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..35ace33ec43433a3066590603221058d82b4addc --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransformations.code.tex @@ -0,0 +1,503 @@ + +\ProvidesFileRCS{pgfcoretransformations.code.tex} + + + +\newdimen\pgf@pt@x +\newdimen\pgf@pt@y + +\newdimen\pgf@pt@temp + +\newif\ifpgf@pt@identity +\pgf@pt@identitytrue + +\def\pgf@pt@aa{1.0} \def\pgf@pt@ab{0.0} +\def\pgf@pt@ba{0.0} \def\pgf@pt@bb{1.0} + + + + +\def\pgfgettransform#1{% + \edef#1{{\pgf@pt@aa}{\pgf@pt@ab}{\pgf@pt@ba}{\pgf@pt@bb}{\the\pgf@pt@x}{\the\pgf@pt@y}}% +} + +\def\pgfgettransformentries#1#2#3#4#5#6{% + \edef#1{\pgf@pt@aa}% + \edef#2{\pgf@pt@ab}% + \edef#3{\pgf@pt@ba}% + \edef#4{\pgf@pt@bb}% + \edef#5{\the\pgf@pt@x}% + \edef#6{\the\pgf@pt@y}% +}% +\def\pgfsettransformentries#1#2#3#4#5#6{% + \pgfsettransform{{#1}{#2}{#3}{#4}{#5}{#6}}% +}% + + +\def\pgfsettransform#1{% + \edef\pgf@temp{#1}% + \expandafter\pgf@settransform\pgf@temp% +} +\def\pgf@settransform#1#2#3#4#5#6{% + \def\pgf@pt@aa{#1}% + \def\pgf@pt@ab{#2}% + \def\pgf@pt@ba{#3}% + \def\pgf@pt@bb{#4}% + \pgf@pt@x=#5% + \pgf@pt@y=#6% + \edef\pgf@idtest{#1,#2,#3,#4}% + \ifx\pgf@idtest\pgf@idmatrixtext% + \pgf@pt@identitytrue% + \else% + \pgf@pt@identityfalse% + \fi% +} + +\def\pgf@idmatrixtext{1.0,0.0,0.0,1.0} +\def\pgf@zerozerotext{0.0,0.0} +\def\pgf@one@text{1.0} +\def\pgf@zero@text{0.0} + + +\def\pgf@pos@transform#1#2{% + \ifpgf@pt@identity% + \else% + \pgf@pt@temp=#1% + #1=\pgf@pt@aa#1% + \advance#1 by\pgf@pt@ba#2% + #2=\pgf@pt@bb#2% + \advance#2 by\pgf@pt@ab\pgf@pt@temp% + \fi% + \advance#1 by\pgf@pt@x% + \advance#2 by\pgf@pt@y% +} +\def\pgf@pos@transform@glob{% + \ifpgf@pt@identity% + \else% + \pgf@pt@temp=\pgf@x% + \global\pgf@x=\pgf@pt@aa\pgf@x% + \global\advance\pgf@x by\pgf@pt@ba\pgf@y% + \global\pgf@y=\pgf@pt@bb\pgf@y% + \global\advance\pgf@y by\pgf@pt@ab\pgf@pt@temp% + \fi% + \global\advance\pgf@x by\pgf@pt@x% + \global\advance\pgf@y by\pgf@pt@y% +} + + + +\def\pgftransforminvert{% + \pgf@pt@x=-\pgf@pt@x + \pgf@pt@y=-\pgf@pt@y + \ifpgf@pt@identity% + \else% + \edef\pgf@zerotest{\pgf@pt@ab,\pgf@pt@ba}% + \ifx\pgf@zerotest\pgf@zerozerotext% + \pgfmathreciprocal@{\pgf@pt@aa}% + \let\pgf@pt@aa\pgfmathresult% + \pgfmathreciprocal@{\pgf@pt@bb}% + \let\pgf@pt@bb\pgfmathresult% + \else% + {% + \pgfutil@tempdima=\pgf@pt@aa pt% + \pgfutil@tempdima=\pgf@pt@bb\pgfutil@tempdima% + \pgfutil@tempdimb=\pgf@pt@ba pt% + \pgfutil@tempdimb=\pgf@pt@ab\pgfutil@tempdimb% + \advance\pgfutil@tempdima by -\pgfutil@tempdimb% + \pgfmathreciprocal@{\pgf@sys@tonumber{\pgfutil@tempdima}}% + \pgfutil@tempdima=\pgfmathresult pt% + \pgf@x=\pgf@pt@bb\pgfutil@tempdima% + \xdef\pgf@new@pt@aa{\pgf@sys@tonumber{\pgf@x}}% + \pgf@x=\pgf@pt@aa\pgfutil@tempdima% + \xdef\pgf@new@pt@bb{\pgf@sys@tonumber{\pgf@x}}% + \pgfutil@tempdima=-\pgfutil@tempdima% + \pgf@x=\pgf@pt@ba\pgfutil@tempdima% + \xdef\pgf@new@pt@ba{\pgf@sys@tonumber{\pgf@x}}% + \pgf@x=\pgf@pt@ab\pgfutil@tempdima% + \xdef\pgf@new@pt@ab{\pgf@sys@tonumber{\pgf@x}}% + }% + \let\pgf@pt@aa\pgf@new@pt@aa% + \let\pgf@pt@ab\pgf@new@pt@ab% + \let\pgf@pt@ba\pgf@new@pt@ba% + \let\pgf@pt@bb\pgf@new@pt@bb% + \fi% + \pgf@pt@temp=\pgf@pt@x% + \pgf@pt@x=\pgf@pt@aa\pgf@pt@x% + \advance\pgf@pt@x by\pgf@pt@ba\pgf@pt@y% + \pgf@pt@y=\pgf@pt@bb\pgf@pt@y% + \advance\pgf@pt@y by\pgf@pt@ab\pgf@pt@temp% + \fi% +} + + + + + +\def\pgftransformcm#1#2#3#4#5{% + \edef\pgf@marshal{\noexpand\pgf@transformcm{#1}{#2}{#3}{#4}}% + \pgf@marshal{#5}% +} +\def\pgf@transformcm#1#2#3#4#5{% + {% + \pgf@process{#5}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfmathsetlength\pgf@x{#1}% + \pgfmathsetlength\pgf@y{#2}% + \pgf@xa=\pgf@pt@aa\pgf@x% + \advance\pgf@xa by \pgf@pt@ba\pgf@y% + \pgf@ya=\pgf@pt@ab\pgf@x% + \advance\pgf@ya by \pgf@pt@bb\pgf@y% + \pgfmathsetlength\pgf@x{#3}% + \pgfmathsetlength\pgf@y{#4}% + \pgf@xb=\pgf@pt@aa\pgf@x% + \advance\pgf@xb by \pgf@pt@ba\pgf@y% + \pgf@yb=\pgf@pt@ab\pgf@x% + \advance\pgf@yb by \pgf@pt@bb\pgf@y% + \pgf@x=\pgf@pt@aa\pgf@xc% + \advance\pgf@x by\pgf@pt@ba\pgf@yc% + \advance\pgf@x by\pgf@pt@x% + \pgf@y=\pgf@pt@ab\pgf@xc% + \advance\pgf@y by\pgf@pt@bb\pgf@yc% + \advance\pgf@y by\pgf@pt@y% + \global\pgf@x=\pgf@x% + \global\pgf@y=\pgf@y% + \xdef\pgf@tempaa{\pgf@sys@tonumber{\pgf@xa}}% + \xdef\pgf@tempab{\pgf@sys@tonumber{\pgf@ya}}% + \xdef\pgf@tempba{\pgf@sys@tonumber{\pgf@xb}}% + \xdef\pgf@tempbb{\pgf@sys@tonumber{\pgf@yb}}% + }% + \pgf@pt@x=\pgf@x% + \pgf@pt@y=\pgf@y% + \let\pgf@pt@aa=\pgf@tempaa% + \let\pgf@pt@ba=\pgf@tempba% + \let\pgf@pt@ab=\pgf@tempab% + \let\pgf@pt@bb=\pgf@tempbb% + \edef\pgf@idtest{\pgf@pt@aa,\pgf@pt@ba,\pgf@pt@ab,\pgf@pt@bb}% + \ifx\pgf@idtest\pgf@idmatrixtext% + \pgf@pt@identitytrue% + \else% + \pgf@pt@identityfalse% + \fi% +} + + + + +\def\pgftransformtriangle#1#2#3{% + \pgf@process{#2}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#3}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#1}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \advance\pgf@xb by-\pgf@x% + \advance\pgf@yb by-\pgf@y% + \pgftransformcm% + {\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@ya}% + {\pgf@sys@tonumber\pgf@xb}{\pgf@sys@tonumber\pgf@yb}% + {\pgfpoint{\pgf@x}{\pgf@y}}% +} + + + + +\def\pgftransformreset{% + \pgf@pt@x=0pt% + \pgf@pt@y=0pt% + \let\pgf@pt@aa\pgf@one@text% + \let\pgf@pt@ba\pgf@zero@text% + \let\pgf@pt@ab\pgf@zero@text% + \let\pgf@pt@bb\pgf@one@text% + \pgf@pt@identitytrue% +} + + + +\def\pgftransformresetnontranslations{% + \let\pgf@pt@aa\pgf@one@text% + \let\pgf@pt@ba\pgf@zero@text% + \let\pgf@pt@ab\pgf@zero@text% + \let\pgf@pt@bb\pgf@one@text% + \pgf@pt@identitytrue% +} + + + + + +\def\pgftransformshift#1{\pgftransformcm{1}{0}{0}{1}{#1}} +\def\pgftransformxshift#1{\pgftransformcm{1}{0}{0}{1}{\pgfpoint{#1}{+0pt}}} +\def\pgftransformyshift#1{\pgftransformcm{1}{0}{0}{1}{\pgfpoint{+0pt}{#1}}} + + + + + +\def\pgftransformscale#1{\pgftransformcm{#1}{0}{0}{#1}{\pgfpointorigin}} +\def\pgftransformxscale#1{\pgftransformcm{#1}{0}{0}{1.0}{\pgfpointorigin}} +\def\pgftransformyscale#1{\pgftransformcm{1.0}{0}{0}{#1}{\pgfpointorigin}} + + + + +\def\pgftransformxslant#1{\pgftransformcm{1.0}{0}{#1}{1.0}{\pgfpointorigin}} +\def\pgftransformyslant#1{\pgftransformcm{1.0}{#1}{0}{1.0}{\pgfpointorigin}} + + + + +\def\pgftransformrotate#1{% + \pgfmathparse{#1}% + \let\pgftransform@angle=\pgfmathresult% + \pgfmathsin@{\pgftransform@angle}% + \let\pgftransform@sin=\pgfmathresult% + \pgfmathcos@{\pgftransform@angle}% + \let\pgftransform@cos=\pgfmathresult% + \pgf@x=\pgftransform@sin pt% + \pgf@xa=-\pgf@x% + \pgftransformcm{\pgftransform@cos}{\pgftransform@sin}{\pgf@sys@tonumber{\pgf@xa}}{\pgftransform@cos}{\pgfpointorigin}% +} + + + + +\newif\ifpgfslopedattime +\newif\ifpgfallowupsidedownattime +\newif\ifpgfresetnontranslationattime + + +\def\pgftransformlineattime#1#2#3{% + \pgf@process{#2}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{#3}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgftransformshift{\pgfpointlineattime{#1}{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}% + \ifpgfresetnontranslationattime% + \pgftransformresetnontranslations% + \fi% + \ifpgfslopedattime% + \advance\pgf@xc by-\pgf@xb% + \advance\pgf@yc by-\pgf@yb% + \ifpgfallowupsidedownattime% + \else% + \ifdim\pgf@xc<0pt% + \pgf@xc=-\pgf@xc% + \pgf@yc=-\pgf@yc% + \fi% + \fi% + \pgf@x=\pgf@xc% + \pgf@y=\pgf@yc% + \pgfpointnormalised{}% + \pgf@ya=-\pgf@y% + \pgftransformcm% + {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}% + {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}% + \fi% +} + + + +\def\pgftransformarcaxesattime#1#2#3#4#5#6{% + \pgfpointarcaxesattime{#1}{#2}{#3}{#4}{#5}{#6}% + \pgftransformshift{\pgfqpoint{\pgf@x}{\pgf@y}}% + \ifpgfresetnontranslationattime% + \pgftransformresetnontranslations% + \fi% + \ifpgfslopedattime% + \pgf@x=\pgf@xa% + \pgf@y=\pgf@ya% + \pgf@process{\pgfpointnormalised{}}% + \ifpgfallowupsidedownattime% + \else% + \ifdim\pgf@x<0pt% + \pgf@x=-\pgf@x% + \pgf@y=-\pgf@y% + \fi% + \fi% + \pgf@ya=-\pgf@y% + \pgftransformcm% + {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}% + {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}% + \fi% +} + + + + +\def\pgftransformcurveattime#1#2#3#4#5{% + \pgfpointcurveattime{#1}{#2}{#3}{#4}{#5}% + \pgftransformshift{\pgfqpoint{\pgf@x}{\pgf@y}}% + \ifpgfresetnontranslationattime% + \pgftransformresetnontranslations% + \fi% + \ifpgfslopedattime% + \pgf@x=\pgf@xa% + \pgf@y=\pgf@ya% + \advance\pgf@x by-\pgf@xb% + \advance\pgf@y by-\pgf@yb% + \ifpgfallowupsidedownattime% + \else% + \ifdim\pgf@x<0pt% + \pgf@x=-\pgf@x% + \pgf@y=-\pgf@y% + \fi% + \fi% + \pgfpointnormalised{}% + \pgf@ya=-\pgf@y% + \pgftransformcm% + {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}% + {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}% + \fi% +} + + + + + + +\def\pgftransformarrow#1#2{% + \pgf@process{#2}% + \pgftransformshift{}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#1}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@x=\pgf@xa% + \pgf@y=\pgf@ya% + \pgfpointnormalised{}% + \pgf@ya=-\pgf@y% + \pgftransformcm% + {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}% + {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfqpoint{0pt}{0pt}}% +} + + + + + +\def\pgftransformationadjustments{% + \ifpgf@pt@identity% + \let\pgfhorizontaltransformationadjustment\pgf@one@text% + \let\pgfverticaltransformationadjustment\pgf@one@text% + \else% + {% + \pgf@pt@x0pt% + \pgf@pt@y0pt% + \pgfpointtransformed{\pgfqpoint{1pt}{0pt}}% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgfmathreciprocal@{\pgfmathresult}% + \global\let\pgf@temp@hori\pgfmathresult + \pgfpointtransformed{\pgfqpoint{0pt}{1pt}}% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgfmathreciprocal@{\pgfmathresult}% + \global\let\pgf@temp@vert\pgfmathresult + \xdef\pgf@marshal@b{\def\noexpand\pgfverticaltransformationadjustment{\pgfmathresult}} + }% + \let\pgfhorizontaltransformationadjustment\pgf@temp@hori% + \let\pgfverticaltransformationadjustment\pgf@temp@vert% + \fi% +} + +\let\pgfhorizontaltransformationadjustment\pgf@one@text +\let\pgfverticaltransformationadjustment\pgf@one@text + + + + +\def\pgflowlevelsynccm{% + \pgfsys@transformcm% + {\pgf@pt@aa}{\pgf@pt@ab}% + {\pgf@pt@ba}{\pgf@pt@bb}% + {\pgf@pt@x}{\pgf@pt@y}% + \pgftransformreset% + \pgf@relevantforpicturesizefalse% +} + + + + +\def\pgflowlevel#1{% + {% + \pgftransformreset% + #1% + \pgflowlevelsynccm% + }% + \pgf@relevantforpicturesizefalse% +} + +\def\pgflowlevelscope#1{\pgfscope\pgflowlevel{#1}} +\def\endpgflowlevelscope{\endpgfscope} + +\long\def\pgflowlevelobj#1#2{\pgfscope{\pgflowlevel{#1}#2}\endpgfscope} + + + + + +\def\pgfviewboxscope#1#2#3#4#5{% + {% + \pgf@process{#1}% + \pgf@pos@transform@glob + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#2}% + \pgf@pos@transform@glob + \ifdim\pgf@x<\pgf@xa% + \pgf@xb\pgf@x% + \pgf@xc\pgf@xa% + \else% + \pgf@xb\pgf@xa% + \pgf@xc\pgf@x% + \fi% + \ifdim\pgf@y<\pgf@ya% + \pgf@yb\pgf@y% + \pgf@yc\pgf@ya% + \else% + \pgf@yb\pgf@ya% + \pgf@yc\pgf@y% + \fi% + \pgf@process{#3}% + \pgf@pos@transform@glob + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{#4}% + \pgf@pos@transform@glob + \ifdim\pgf@x<\pgf@xa% + \else% + \pgfutil@tempdima\pgf@x + \pgf@x\pgf@xa% + \pgf@xa\pgfutil@tempdima% + \fi% + \ifdim\pgf@y<\pgf@ya% + \else% + \pgfutil@tempdima\pgf@y + \pgf@y\pgf@ya% + \pgf@ya\pgfutil@tempdima% + \fi% + \pgfusetype{.view}% + \edef\pgf@marshal{\expandafter\noexpand\csname pgfsys@viewbox#5\endcsname{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}{\the\pgf@xc}{\the\pgf@yc}}% + \pgf@marshal% + }% + \pgf@relevantforpicturesizefalse% +} + +\def\endpgfviewboxscope{\pgfsys@endviewbox} + +\let\startpgfviewboxscope=\pgfviewboxscope +\let\stoppgfviewboxscope=\endpgfviewboxscope + + +\let\pgfapproximatenonlineartranslation\relax +\let\pgfapproximatenonlineartransformation\relax +\def\pgftransformnonlinear#1{\pgferror{You need to say + \string\usepgfmodule{nonlineartransformations} to use nonlinear transformations}} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..9cf7ea4496989baa39be6bd29e4009e96ac2476d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/basiclayer/pgfcoretransparency.code.tex @@ -0,0 +1,146 @@ + +\ProvidesFileRCS{pgfcoretransparency.code.tex} + + + +\def\pgfsetstrokeopacity#1{% + \pgfmathparse{#1}% + \expandafter\pgfsys@stroke@opacity\expandafter{\pgfmathresult}} + + + +\def\pgfsetfillopacity#1{% + \pgfmathparse{#1}% + \expandafter\pgfsys@fill@opacity\expandafter{\pgfmathresult}} + + + + +\def\pgfsetblendmode#1{\pgfsys@blend@mode{#1}} + + + +\def\pgfdeclarefading#1#2{% + \setbox\pgfutil@tempboxa=\hbox{{\pgfsys@beginscope\pgfutil@color{white}\ignorespaces#2\pgfsys@endscope}}% + \pgfsys@fadingfrombox{#1}\pgfutil@tempboxa% +} + +\pgfutil@colorlet{pgftransparent}{black} + + + +\def\pgfsetfading#1#2{% + {% + \pgftransformreset% + #2% + \pgfgettransform{\pgftrans@temp}% + \edef\pgf@marshal{\noexpand\pgfsys@usefading{#1}\pgftrans@temp}% + \pgf@marshal% + }% +} + + + + +\def\pgfsetfadingforcurrentpath#1#2{% + \ifdim\pgf@pathminx=16000pt% + \pgfsetfading{#1}{#2}% + \else% + \pgfsetfading{#1}{% + \pgf@xb=.5\pgf@pathmaxx% + \advance\pgf@xb by.5\pgf@pathminx% + \pgf@yb=.5\pgf@pathmaxy% + \advance\pgf@yb by.5\pgf@pathminy% + \pgf@xc=\pgf@pathmaxx% + \advance\pgf@xc by-\pgf@pathminx% + \ifdim\pgf@xc<0.1pt\pgf@xc=0.1pt\fi% + \pgf@yc=\pgf@pathmaxy% + \advance\pgf@yc by-\pgf@pathminy% + \ifdim\pgf@yc<0.1pt\pgf@yc=0.1pt\fi% + \pgf@xc=.02\pgf@xc% + \pgf@yc=.02\pgf@yc% + \pgftransformcm{1}{0}{0}{1}{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgftransformcm{\pgf@sys@tonumber{\pgf@xc}}{0}{0}{\pgf@sys@tonumber{\pgf@yc}}{\pgfpointorigin}% + \pgfsys@clipfading% + #2% + }% + \fi% +} + + + + + +\def\pgfsetfadingforcurrentpathstroked#1#2{% + \ifdim\pgf@pathminx=16000pt% + \pgfsetfading{#1}{#2}% + \else% + \pgfsetfading{#1}{% + \pgf@xb=.5\pgf@pathmaxx% + \advance\pgf@xb by.5\pgf@pathminx% + \pgf@yb=.5\pgf@pathmaxy% + \advance\pgf@yb by.5\pgf@pathminy% + \pgf@xc=\pgf@pathmaxx% + \advance\pgf@xc by-\pgf@pathminx% + \advance\pgf@xc by\pgflinewidth% + \ifdim\pgf@xc<0.1pt\pgf@xc=0.1pt\fi% + \pgf@yc=\pgf@pathmaxy% + \advance\pgf@yc by-\pgf@pathminy% + \advance\pgf@yc by\pgflinewidth% + \ifdim\pgf@yc<0.1pt\pgf@yc=0.1pt\fi% + \pgf@xc=.02\pgf@xc% + \pgf@yc=.02\pgf@yc% + \pgftransformcm{1}{0}{0}{1}{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgftransformcm{\pgf@sys@tonumber{\pgf@xc}}{0}{0}{\pgf@sys@tonumber{\pgf@yc}}{\pgfpointorigin}% + \pgfsys@clipfading% + #2% + }% + \fi% +} + + + +\def\pgftransparencygroup{% + \pgfutil@ifnextchar[{\pgftransparencygroup@}{\pgftransparencygroup@[]}% +} +\def\pgftransparencygroup@[#1]{% + \begingroup% + \pgfkeys{/pgf/transparency group options/.cd,% + isolated=false, + knockout=false, + #1}% + \setbox\pgfutil@tempboxa=\hbox\bgroup% +} +\pgfkeys{ + /pgf/transparency group options/.cd, + isolated/.is if=pgfsys@transparency@group@isolated, + knockout/.is if=pgfsys@transparency@group@knockout +} + +\def\endpgftransparencygroup{% + \egroup% + \ifdim\pgf@picminx=16000pt% + \else% + \advance\pgf@picminx by-1cm% + \advance\pgf@picmaxx by1cm% + \advance\pgf@picminy by-1cm% + \advance\pgf@picmaxy by1cm% + \setbox\pgfutil@tempboxa=\hbox{% + \vrule width0pt height\pgf@picmaxy depth-\pgf@picminy% + \hskip-\pgf@picminx% + \box\pgfutil@tempboxa% + \hskip\pgf@picmaxx% + }% + \pgfsys@transparencygroupfrombox\pgfutil@tempboxa% + \wd\pgfutil@tempboxa=0pt% + \ht\pgfutil@tempboxa=0pt% + \dp\pgfutil@tempboxa=0pt% + \hskip\pgf@picminx\box\pgfutil@tempboxa\hskip-\pgf@picminx% + \fi% + \endgroup% +} + +\let\startpgftransparencygroup=\pgftransparencygroup +\let\stoppgftransparencygroup=\endpgftransparencygroup + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..463c6ccf103f9f7c0a202f60222cbf6130e1c5e0 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.code.tex @@ -0,0 +1,205 @@ + +\usetikzlibrary{calc,decorations.markings}% + + +\tikzset{ + circuit/.style={ + every circuit/.try, + /utils/exec=\tikz@lib@circ@on@tofalse, + execute at begin to={ + \tikz@lib@circ@on@totrue + \let\tikz@lib@circ@start@node\pgfutil@empty + \def\tikz@lib@circ@end{-- (\tikztotarget) \tikztonodes} + } + } +}% + +\newif\iftikz@lib@circ@on@to + + + +\tikzset{ + circuit handle symbol/.code={% + \global\advance\tikz@lib@circ@count by1\relax% + \iftikz@lib@circ@on@to + {% + \pgfkeys{ + /pgf/key filters/active families or no family/.install key filter={/pgf/key filters/false}{/pgf/key filters/false}, + /tikz/circuits/pos grabber/.activate family} + \pgfqkeysfiltered{/tikz}{pos=.5,#1}% + \expandafter% + }% + \expandafter\def\expandafter\tikz@lib@circ@pos\expandafter{\tikz@time}% + \pgfkeysalso{to path={ + \pgfextra{\tikz@lib@circ@on@tofalse} + decorate [decoration={markings,mark connection node=mark node}] + { + \tikz@lib@circ@start@node + \tikz@lib@circ@end + } + }} + \ifdim\tikz@lib@circ@pos pt=0pt\relax% + \def\tikz@lib@circ@start@node{% + {\pgfextra{\tikz@lib@circ@compute@direction{\tikz@lib@circ@start}}% + node[alias=tikz@lib@circ@node@start,at={(0,0)},#1,pos=]{}}(tikz@lib@circ@node@start)}% + \else% + \ifdim\tikz@lib@circ@pos pt=1pt\relax% + \def\tikz@lib@circ@end{ + {\pgfextra{\tikz@lib@circ@compute@direction{\tikz@lib@circ@target}}% + node[alias=tikz@lib@circ@node\the\tikz@lib@circ@count,at={(0,0)},#1,pos=]{}} + --(tikz@lib@circ@node\the\tikz@lib@circ@count)\tikztonodes + }% + \else% + \edef\tikz@marshal{mark=at position \tikz@lib@circ@pos\space with}% + \def\tikz@marshala{decoration=}% + \expandafter\expandafter\expandafter\tikzset% + \expandafter\expandafter\expandafter{\expandafter\tikz@marshala\expandafter{\tikz@marshal{\node[alias=mark node,#1,pos=]{};}}} + \fi% + \fi% + \else + \pgfkeysalso{#1} + \fi + } +}% +\newcount\tikz@lib@circ@count + +\def\tikz@lib@circ@compute@direction#1{% + \tikz@scan@one@point\tikz@lib@circ@save@start(\tikztostart)% + \tikz@scan@one@point\tikz@lib@circ@save@target(\tikztotarget)% + \pgf@process{\pgfpointnormalised{\pgfpointdiff{\tikz@lib@circ@start}{\tikz@lib@circ@target}}}% + \pgf@ya=-\pgf@y% + \pgftransformcm{\the\pgf@x}{\the\pgf@y}{\the\pgf@ya}{\the\pgf@x}{#1}% +}% +\def\tikz@lib@circ@save@start#1{\def\tikz@lib@circ@start{#1}}% +\def\tikz@lib@circ@save@target#1{\def\tikz@lib@circ@target{#1}}% + +\tikzset{ + circuits/pos grabber/.is family, + pos/.belongs to family=/tikz/circuits/pos grabber, + at start/.belongs to family=/tikz/circuits/pos grabber, + very near start/.belongs to family=/tikz/circuits/pos grabber, + near start/.belongs to family=/tikz/circuits/pos grabber, + midway/.belongs to family=/tikz/circuits/pos grabber, + near end/.belongs to family=/tikz/circuits/pos grabber, + very near end/.belongs to family=/tikz/circuits/pos grabber, + at end/.belongs to family=/tikz/circuits/pos grabber +}% + + +\tikzset{ + circuit declare symbol/.style args={#1}{ + #1/.style={circuit handle symbol={ + inner sep=0.5pt, + every circuit symbol, + #1/graphic, + every #1/.try, + ##1} + }, + #1/graphic/.style={}, + set #1 graphic/.style={#1/graphic/.style={##1}} + }, + circuit symbol unit/.code=\pgfmathsetlength\tikzcircuitssizeunit{#1}, + circuit symbol size/.style args={width #1 height #2}{ + minimum width={(#1)*\tikzcircuitssizeunit}, + minimum height={(#2)*\tikzcircuitssizeunit} + }, + huge circuit symbols/.style={circuit symbol unit=10pt}, + large circuit symbols/.style={circuit symbol unit=8pt}, + medium circuit symbols/.style={circuit symbol unit=7pt}, + small circuit symbols/.style={circuit symbol unit=6pt}, + tiny circuit symbols/.style={circuit symbol unit=5pt}, +}% + +\newdimen\tikzcircuitssizeunit +\tikzcircuitssizeunit=7pt + + + +\tikzset{ + circuit declare annotation/.style args={#1#2#3}{% + #1/.style={ + append after command={% + \bgroup + [current point is local=true] + [every circuit annotation/.try] + [every #1/.try] + [shift={(\tikzlastnode.north)}] + [annotation arrow,->] + [label distance=#2,##1] + #3 + \tikz@after@path% + \egroup% + } + }, + #1'/.style={ + append after command={% + \bgroup + [current point is local=true] + [every circuit annotation/.try] + [every #1/.try] + [shift={(\tikzlastnode.south)},yscale=-1] + [annotation arrow,->] + [label distance=#2,##1] + #3 + \tikz@after@path% + \egroup% + } + } + }, + annotation arrow/.style = { + /utils/exec={\pgfsetarrowoptions{direction ee}{.4*\the\tikzcircuitssizeunit+.3*\the\pgflinewidth}}, + >=direction ee + } +}% + + + +\tikzset{ + point up/.style={rotate=90}, + point down/.style={rotate=-90}, + point left/.style={rotate=180}, + point right/.style={} +}% + + + + +\tikzset{ + every circuit symbol/.style={}, + circuit symbol open/.style={draw}, + circuit symbol filled/.style={draw,fill=black}, + circuit symbol lines/.style={draw}, + circuit symbol wires/.style={draw}, +}% + + + + + + +\tikzset{ + info/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@plain{\tikz@lib@circ@lab@plain[]}#1\pgf@stop},% + info'/.code={\pgfutil@ifnextchar[\tikz@lib@circ@labp@plain{\tikz@lib@circ@labp@plain[]}#1\pgf@stop},% + info sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@sloped@plain{\tikz@lib@circ@lab@sloped@plain[]}#1\pgf@stop},% + info' sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@slopedp@plain{\tikz@lib@circ@lab@slopedp@plain[]}#1\pgf@stop},% + circuit declare unit/.style 2 args={ + #1/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab{\tikz@lib@circ@lab[]}##1\pgf@stop{#2}{#1}},% + #1 sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@sloped{\tikz@lib@circ@lab@sloped[]}##1\pgf@stop{#2}{#1}},% + #1'/.code={\pgfutil@ifnextchar[\tikz@lib@circ@labp{\tikz@lib@circ@labp[]}##1\pgf@stop{#2}{#1}},% + #1' sloped/.code={\pgfutil@ifnextchar[\tikz@lib@circ@lab@slopedp{\tikz@lib@circ@lab@slopedp[]}##1\pgf@stop{#2}{#1}}% + } +}% + +\def\tikz@lib@circ@lab[#1]#2\pgf@stop#3#4{\tikzset{label={[every info/.try,every #4/.try,#1]$\mathrm{#2#3}$}}}% +\def\tikz@lib@circ@lab@sloped[#1]#2\pgf@stop#3#4{\tikzset{label={[every info/.try,every #4/.try,transform shape,#1]$\mathrm{#2#3}$}}}% +\def\tikz@lib@circ@labp[#1]#2\pgf@stop#3#4{\tikzset{label={[label position=below,every info/.try,every #4/.try,#1]$\mathrm{#2#3}$}}}% +\def\tikz@lib@circ@lab@slopedp[#1]#2\pgf@stop#3#4{\tikzset{label={[label position=below,every info/.try,every #4/.try,transform shape,#1]$\mathrm{#2#3}$}}}% + +\def\tikz@lib@circ@lab@plain[#1]#2\pgf@stop{\tikzset{label={[every info/.try,#1]#2}}}% +\def\tikz@lib@circ@lab@sloped@plain[#1]#2\pgf@stop{\tikzset{label={[every info/.try,transform shape,#1]#2}}}% +\def\tikz@lib@circ@labp@plain[#1]#2\pgf@stop{\tikzset{label={[label position=below,every info/.try,#1]#2}}}% +\def\tikz@lib@circ@lab@slopedp@plain[#1]#2\pgf@stop{\tikzset{label={[label position=below,every info/.try,transform shape,#1]#2}}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.IEC.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.IEC.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..4df278bff758fecf3baf97950bcf911e7d1c09f7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.IEC.code.tex @@ -0,0 +1,371 @@ + +\usetikzlibrary{arrows}% +\usetikzlibrary{circuits.ee}% + +\usepgflibrary{shapes.gates.ee.IEC}% + + + +\tikzset{ + circuit ee IEC/.style= + { + circuit ee, + set resistor graphic = resistor IEC graphic, + set inductor graphic = inductor IEC graphic, + set capacitor graphic = capacitor IEC graphic, + set contact graphic = contact IEC graphic, + set ground graphic = ground IEC graphic, + set battery graphic = battery IEC graphic, + set diode graphic = diode IEC graphic, + set Zener diode graphic = Zener diode IEC graphic, + set tunnel diode graphic = tunnel diode IEC graphic, + set backward diode graphic = backward diode IEC graphic, + set Schottky diode graphic = Schottky diode IEC graphic, + set breakdown diode graphic = breakdown diode IEC graphic, + set bulb graphic = bulb IEC graphic, + set voltage source graphic = voltage source IEC graphic, + set current source graphic = current source IEC graphic, + set make contact graphic = make contact IEC graphic, + set break contact graphic = break contact IEC graphic, + set amperemeter graphic = amperemeter graphic, + set voltmeter graphic = voltmeter graphic, + set ohmmeter graphic = ohmmeter graphic, + set ac source graphic = ac source graphic, + set dc source graphic = dc source graphic, + }, +}% + + + +\tikzset{ + resistor IEC graphic/.style={ + circuit symbol open, + circuit symbol size=width 4 height 1, + shape=rectangle ee, + transform shape, + }, + var resistor IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width 4.8 height 0.8, + shape=var resistor IEC, + transform shape, + outer sep=0pt, + cap=round, + }, +}% + + + + +\tikzset{ + inductor IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width 4 height .5, + transform shape, + shape=inductor IEC, + outer sep=0pt, + cap=round, + }, + var inductor IEC graphic/.style={ + circuit symbol filled, + circuit symbol size=width 4 height 1, + transform shape, + shape=rectangle ee, + }, +}% + + + + +\tikzset{ + capacitor IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width .5 height 2, + transform shape, + shape=capacitor IEC, + }, +}% + + + + +\tikzset{ + ground IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width .75 height 2, + transform shape, + shape=ground IEC, + }, +}% + + + + + +\tikzset{ + battery IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width .5 height 2.5, + transform shape, + shape=battery IEC, + transform shape, + }, +}% + + + + +\tikzset{ + diode IEC graphic/.style={ + circuit symbol open, + circuit symbol size=width 1.25 height 1.25, + transform shape, + shape=generic diode IEC, + /pgf/generic diode IEC/before background={ + \pgfpathmoveto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfusepathqstroke + }, + }, + var diode IEC graphic/.style={ + diode IEC graphic, + circuit symbol filled, + }, +}% + +\tikzset{ + Zener diode IEC graphic/.style={ + diode IEC graphic, + /pgf/generic diode IEC/before background={ + \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfusepathqstroke + }, + }, + var Zener diode IEC graphic/.style={ + Zener diode IEC graphic, + circuit symbol filled, + }, +}% + +\tikzset{ + Schottky diode IEC graphic/.style={ + diode IEC graphic, + /pgf/generic diode IEC/before background={ + \pgfpathmoveto{\pgfqpoint{-.4pt}{-.6pt}} + \pgfpathlineto{\pgfqpoint{-.4pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfpathlineto{\pgfqpoint{.4pt}{1pt}} + \pgfpathlineto{\pgfqpoint{.4pt}{.6pt}} + \pgfusepathqstroke + }, + }, + var Schottky diode IEC graphic/.style={ + Schottky diode IEC graphic, + circuit symbol filled, + }, +}% + +\tikzset{ + tunnel diode IEC graphic/.style={ + diode IEC graphic, + /pgf/generic diode IEC/before background={ + \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfpathlineto{\pgfqpoint{-.5pt}{1pt}} + \pgfusepathqstroke + }, + }, + var tunnel diode IEC graphic/.style={ + tunnel diode IEC graphic, + circuit symbol filled, + }, +}% + +\tikzset{ + backward diode IEC graphic/.style={ + diode IEC graphic, + /pgf/generic diode IEC/before background={ + \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{.5pt}{-1pt}} + \pgfpathmoveto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfpathmoveto{\pgfqpoint{-.5pt}{1pt}} + \pgfpathlineto{\pgfqpoint{.5pt}{1pt}} + \pgfusepathqstroke + }, + }, + var backward diode IEC graphic/.style={ + backward diode IEC graphic, + circuit symbol filled, + }, +}% + + +\tikzset{ + breakdown diode IEC graphic/.style={ + circuit symbol open, + circuit symbol size=width 2.5 height 1.25, + transform shape, + shape=breakdown diode IEC, + }, + var breakdown diode IEC graphic/.style={ + breakdown diode IEC graphic, + circuit symbol filled, + }, +}% + + + + +\tikzset{ + contact IEC graphic/.style={ + circuit symbol filled, + circuit symbol size=width .5 height .5, + shape=circle ee, + outer sep=.25\pgflinewidth, + }, +}% + + + +\tikzset{ + bulb IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width 1.5 height 1.5, + shape=generic circle IEC, + /pgf/generic circle IEC/before background={ + \pgfpathmoveto{\pgfpointpolar{-135}{1pt}} + \pgfpathlineto{\pgfpointpolar{45}{1pt}} + \pgfpathmoveto{\pgfpointpolar{-45}{1pt}} + \pgfpathlineto{\pgfpointpolar{135}{1pt}} + \pgfusepathqstroke + }, + transform shape, + }, +}% + + + +\tikzset{ + current source IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width 2 height 2, + shape=generic circle IEC, + /pgf/generic circle IEC/before background={ + \pgfpathmoveto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfusepathqstroke + }, + transform shape, + }, + voltage source IEC graphic/.style={ + circuit symbol lines, + circuit symbol size=width 2 height 2, + shape=generic circle IEC, + /pgf/generic circle IEC/before background={ + \pgfpathmoveto{\pgfqpoint{-1pt}{0pt}} + \pgfpathlineto{\pgfqpoint{1pt}{0pt}} + \pgfusepathqstroke + }, + transform shape, + }, +}% + + + + +\tikzset{ + make contact IEC graphic/.style={ + circuit symbol wires, + circuit symbol size=width 2 height 1, + transform shape, + shape=make contact IEC, + outer sep=0pt, + cap=round, + }, + var make contact IEC graphic/.style={ + circuit symbol wires, + circuit symbol size=width 2.4 height 1, + transform shape, + shape=var make contact IEC, + outer sep=0pt, + cap=round, + }, +}% + + +\tikzset{ + break contact IEC graphic/.style={ + circuit symbol wires, + circuit symbol size=width 2 height 1, + transform shape, + shape=break contact IEC, + outer sep=0pt, + cap=round, + }, +}% + + + + +\tikzset{ + amperemeter graphic/.style={ + circuit symbol open, + circuit symbol size=width 2 height 2, + transform shape, + shape=generic circle IEC, + info=center:A, + }, + voltmeter graphic/.style={ + circuit symbol open, + circuit symbol size=width 2 height 2, + transform shape, + shape=generic circle IEC, + info=center:V, + }, + ohmmeter graphic/.style={ + circuit symbol open, + circuit symbol size=width 2 height 2, + transform shape, + shape=generic circle IEC, + info=center:$\Omega$, + }, +}% + + + + +\tikzset{ + ac source graphic/.style={ + circuit symbol lines, + circuit symbol size=width 2 height 2, + shape=generic circle IEC, + /pgf/generic circle IEC/before background={ + \pgfpathmoveto{\pgfqpoint{0.7pt}{0pt}} + \pgfpathquadraticcurveto{\pgfqpoint{ 0.35pt}{-0.5pt}}{\pgfqpoint{0pt}{0pt}} + \pgfpathquadraticcurveto{\pgfqpoint{-0.35pt}{ 0.5pt}}{\pgfqpoint{-0.7pt}{0pt}} + \pgfusepathqstroke + }, + transform shape, + }, + dc source graphic/.style={ + circuit symbol lines, + circuit symbol size=width 2 height 2, + shape=generic circle IEC, + /pgf/generic circle IEC/before background={ + \pgfpathmoveto{\pgfqpoint{ 0.7pt}{ 0.2pt}} + \pgfpathlineto{\pgfqpoint{-0.7pt}{ 0.2pt}} + \pgfusepathqstroke + \pgfpathmoveto{\pgfqpoint{ 0.7pt}{-0.2pt}} + \pgfpathlineto{\pgfqpoint{-0.7pt}{-0.2pt}} + \pgfusepathqstroke + }, + transform shape, + }, +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..789f3fd6e13e97d3eea21261ece48458ecc664a8 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.ee.code.tex @@ -0,0 +1,121 @@ + + +\usetikzlibrary{circuits}% +\usepgflibrary{shapes.gates.ee}% + + +\tikzset{ + circuit ee/.style={ + circuit, + every circuit ee/.try + } +}% + + + +\tikzset{ + circuit declare symbol = resistor, + circuit declare symbol = inductor, + circuit declare symbol = capacitor, + circuit declare symbol = contact, + circuit declare symbol = ground, + circuit declare symbol = battery, + circuit declare symbol = diode, + circuit declare symbol = Zener diode, + circuit declare symbol = Schottky diode, + circuit declare symbol = tunnel diode, + circuit declare symbol = backward diode, + circuit declare symbol = breakdown diode, + circuit declare symbol = bulb, + circuit declare symbol = current source, + circuit declare symbol = voltage source, + circuit declare symbol = current direction, + circuit declare symbol = current direction', + circuit declare symbol = make contact, + circuit declare symbol = break contact, + circuit declare symbol = amperemeter, + circuit declare symbol = voltmeter, + circuit declare symbol = ohmmeter, + circuit declare symbol = ac source, + circuit declare symbol = dc source, + set current direction graphic = current direction ee graphic, + set current direction' graphic = current direction' ee graphic, +}% + + + +\tikzset{ + circuit declare unit={ampere}{A}, + circuit declare unit={volt}{V}, + circuit declare unit={ohm}{\Omega}, + circuit declare unit={siemens}{S}, + circuit declare unit={henry}{H}, + circuit declare unit={farad}{F}, + circuit declare unit={coulomb}{C}, + circuit declare unit={voltampere}{VA}, + circuit declare unit={watt}{W}, + circuit declare unit={hertz}{Hz}, +}% + + + + +\tikzset{ + current direction arrow/.style = { + /utils/exec={\pgfsetarrowoptions{direction ee}{1.3065*.5*\the\tikzcircuitssizeunit+1.3065*.3*\the\pgflinewidth}}, + >=direction ee, + direction ee arrow = direction ee, + } +}% + + + + +\tikzset{ + current direction ee graphic/.style = { + shape=direction ee, + circuit symbol filled, + current direction arrow, + minimum width = .5*\the\tikzcircuitssizeunit+.3*\the\pgflinewidth, + minimum height = .5*\the\tikzcircuitssizeunit+.3*\the\pgflinewidth, + transform shape + }, + current direction' ee graphic/.style = { + current direction ee graphic, + rotate=180 + } +}% + + + + +\tikzset{ + circuit declare annotation={direction info}{.5\tikzcircuitssizeunit} + { + (-1.25\tikzcircuitssizeunit,.3333\tikzcircuitssizeunit) edge[line to] (1.25\tikzcircuitssizeunit,.3333\tikzcircuitssizeunit) + }, + circuit declare annotation={light emitting}{1.75\tikzcircuitssizeunit} + { + (-.2\tikzcircuitssizeunit,.65\tikzcircuitssizeunit) edge[line to] ++(45:1.25\tikzcircuitssizeunit) + (.2\tikzcircuitssizeunit,.25\tikzcircuitssizeunit) edge[line to] ++(45:1.25\tikzcircuitssizeunit) + }, + circuit declare annotation={light dependent}{1.75\tikzcircuitssizeunit} + { + [shift=(135:1.25\tikzcircuitssizeunit)] + (.2\tikzcircuitssizeunit,.65\tikzcircuitssizeunit) edge[line to] ++(-45:1.25\tikzcircuitssizeunit) + (-.2\tikzcircuitssizeunit,.25\tikzcircuitssizeunit) edge[line to] ++(-45:1.25\tikzcircuitssizeunit) + }, + circuit declare annotation={adjustable}{1.5\tikzcircuitssizeunit} + { + [shift=(\tikzlastnode.center)] + (-1.5\tikzcircuitssizeunit,-1.5\tikzcircuitssizeunit) edge[line to] (1.5\tikzcircuitssizeunit,1.5\tikzcircuitssizeunit) + }, + circuit declare annotation={adjustable'}{1.5\tikzcircuitssizeunit} + { + [shift=(\tikzlastnode.center)] + (-1.5\tikzcircuitssizeunit,1.5\tikzcircuitssizeunit) edge[line to] (1.5\tikzcircuitssizeunit,-1.5\tikzcircuitssizeunit) + } +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.CDH.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.CDH.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..c2575d751bc7b57a49a8135ea47bf89bf9816cda --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.CDH.code.tex @@ -0,0 +1,20 @@ + +\usetikzlibrary{circuits.logic.US}% + +\tikzset{ + circuit logic CDH/.style = + { + circuit logic US, + set and gate graphic = and gate CDH graphic, + set nand gate graphic = nand gate CDH graphic, + } +}% + +\tikzset{ + circuit logic US make graphic=and gate CDH, + circuit logic US make graphic=nand gate CDH, +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.IEC.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.IEC.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a02ff8cb298ecc3c1910da256041cd3772ed1032 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.IEC.code.tex @@ -0,0 +1,59 @@ + +\usetikzlibrary{circuits.logic}% +\usepgflibrary{shapes.gates.logic.IEC}% + + + +\tikzset{ + circuit logic IEC/.style= + { + circuit logic, + set and gate graphic = and gate IEC graphic, + set nand gate graphic = nand gate IEC graphic, + set or gate graphic = or gate IEC graphic, + set nor gate graphic = nor gate IEC graphic, + set xor gate graphic = xor gate IEC graphic, + set xnor gate graphic = xnor gate IEC graphic, + set not gate graphic = not gate IEC graphic, + set buffer gate graphic = buffer gate IEC graphic, + and gate IEC symbol = {$\scriptstyle\char`\&$}, + nand gate IEC symbol = {$\scriptstyle\char`\&$}, + or gate IEC symbol = {$\scriptstyle\geq1$}, + nor gate IEC symbol = {$\scriptstyle\geq1$}, + xor gate IEC symbol = {$\scriptstyle=1$}, + xnor gate IEC symbol = {$\scriptstyle=1$}, + not gate IEC symbol = {$\scriptstyle1$}, + buffer gate IEC symbol = {$\scriptstyle1$}, + }, +}% + + +\tikzset{ + circuit logic IEC make graphic/.style= + { + #1 graphic/.style={ + circuit symbol open, + circuit symbol size=width 2.5 height 4, + shape=#1, + inner sep=.5ex + } + } +}% + + +\tikzset{ + circuit logic IEC make graphic=and gate IEC, + circuit logic IEC make graphic=nand gate IEC, + circuit logic IEC make graphic=or gate IEC, + circuit logic IEC make graphic=nor gate IEC, + circuit logic IEC make graphic=xor gate IEC, + circuit logic IEC make graphic=xnor gate IEC, + circuit logic IEC make graphic=not gate IEC, + circuit logic IEC make graphic=buffer gate IEC, + circuit logic IEC make graphic=and gate CDH, + circuit logic IEC make graphic=nand gate CDH, +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.US.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.US.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..1a68b94105a6a62e790035f7fed89ab394f08361 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.US.code.tex @@ -0,0 +1,49 @@ + +\usetikzlibrary{circuits.logic}% +\usepgflibrary{shapes.gates.logic.US}% + + + +\tikzset{ + circuit logic US/.style= + { + circuit logic, + set and gate graphic = and gate US graphic, + set nand gate graphic = nand gate US graphic, + set or gate graphic = or gate US graphic, + set nor gate graphic = nor gate US graphic, + set xor gate graphic = xor gate US graphic, + set xnor gate graphic = xnor gate US graphic, + set not gate graphic = not gate US graphic, + set buffer gate graphic = buffer gate US graphic + } +}% + + +\tikzset{ + circuit logic US make graphic/.style= + { + #1 graphic/.style={ + circuit symbol open, + circuit symbol size=width 0 height 2.5, + shape=#1, + transform shape + } + } +}% + + +\tikzset{ + circuit logic US make graphic=and gate US, + circuit logic US make graphic=nand gate US, + circuit logic US make graphic=or gate US, + circuit logic US make graphic=nor gate US, + circuit logic US make graphic=xor gate US, + circuit logic US make graphic=xnor gate US, + circuit logic US make graphic=not gate US, + circuit logic US make graphic=buffer gate US, +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..2a12f95e36d1330656c7d2dc6bfcb515c887a75c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/circuits/tikzlibrarycircuits.logic.code.tex @@ -0,0 +1,31 @@ + +\usetikzlibrary{circuits}% + + + + +\tikzset{ + circuit logic/.style={ + circuit, + inputs/.style={logic gate inputs={##1}}, + logic gate inverted radius=.25\tikzcircuitssizeunit, + every circuit logic/.try, + } +}% + + + + +\tikzset{ + circuit declare symbol = and gate, + circuit declare symbol = nand gate, + circuit declare symbol = or gate, + circuit declare symbol = nor gate, + circuit declare symbol = xor gate, + circuit declare symbol = xnor gate, + circuit declare symbol = not gate, + circuit declare symbol = buffer gate +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.3d.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.3d.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..b7e3beacc251a10b4db86b8aeaa24a85f02a6a06 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.3d.code.tex @@ -0,0 +1,61 @@ + +\ProvidesFileRCS{tikzlibrarydatavisualization.3d.code.tex} + +\usetikzlibrary{datavisualization}% + + + + + + + +\tikzdatavisualizationset{ + school book 3d plot/.style={ + xyz Cartesian, + x axis={ + visualize axis={y axis={goto=0},z axis={goto=0},styling/.style=->}, + visualize ticks={common={y axis={goto=0},z axis={goto=0},direction axis=y axis},only ticks={tick text at min extend}}, + }, + y axis={ + visualize axis={x axis={goto=0},z axis={goto=0},styling/.style=->}, + visualize ticks={common={x axis={goto=0},z axis={goto=0},direction axis=x axis},only ticks={tick text at min extend}}, + }, + z axis={ + visualize axis={x axis={goto=0},y axis={goto=0},styling/.style=->}, + visualize ticks={common={x axis={goto=0},y axis={goto=0},direction axis=x axis},only ticks={tick text at min extend}}, + }, + new line plot, + every school book plot/.try, + }, +}% + + + +\tikzdatavisualizationset{ + scientific 3d plot/length/.initial=100pt, + scientific 3d plot/.style={ + xyz Cartesian, + x axis={ + length=\pgfkeysvalueof{/tikz/data visualization/scientific 3d plot/length}, + visualize axis={y axis={goto=min},z axis={goto=min}}, + visualize axis={y axis={goto=max},z axis={goto=min}}, + visualize axis={y axis={goto=min},z axis={goto=max}}, + visualize axis={y axis={goto=max},z axis={goto=max}}, + }, + y axis={ + length=\pgfkeysvalueof{/tikz/data visualization/scientific 3d plot/length}, + visualize axis={x axis={goto=min},z axis={goto=min}}, + visualize axis={x axis={goto=max},z axis={goto=min}}, + visualize axis={x axis={goto=min},z axis={goto=max}}, + visualize axis={x axis={goto=max},z axis={goto=max}}, + }, + z axis={ + length=\pgfkeysvalueof{/tikz/data visualization/scientific 3d plot/length}, + visualize axis={x axis={goto=min},y axis={goto=min}}, + visualize axis={x axis={goto=max},y axis={goto=min}}, + visualize axis={x axis={goto=min},y axis={goto=max}}, + visualize axis={x axis={goto=max},y axis={goto=max}}, + }, + new line plot, + }, +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.barcharts.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.barcharts.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f76ac2f1ac1531cc40f4e197cd64570f2f53a21e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.barcharts.code.tex @@ -0,0 +1,35 @@ + +\ProvidesFileRCS{tikzlibrarydatavisualization.barcharts.code.tex} + +\usetikzlibrary{datavisualization}% +\usepgflibrary{datavisualization.barcharts}% + + +\tikzdatavisualizationset{% + candle stick plot/.style={ + new object={ + store=/tikz/data visualization/count, + class=count, + arg1=day + }, + new axis=y axis, + y axis/source=dax, + y axis/source max=100, + y axis/vec=\pgfqpoint{0cm}{1cm}, + new object={ + store=/tikz/data visualization/x line trans, + class=line transformer, + arg1=day, + arg2=\pgfqpoint{3mm}{0mm} + }, + new object={ + store=/tikz/data visualization/index, + class=candle stick visualizer, + arg1 from key=index/source + }, + }, + index/source/.initial=index, +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..4f372b51bf15de198f2d738f9bf5dab1fbd116f0 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.code.tex @@ -0,0 +1,2355 @@ + +\ProvidesFileRCS{tikzlibrarydatavisualization.code.tex} + +\usepgfmodule{datavisualization}% +\usetikzlibrary{backgrounds}% + + +\tikzset{/tikz/data visualization/.is family, + /tikz/data visualization/.unknown/.code={ + \let\tikz@dv@key\pgfkeyscurrentname% + \pgfkeys{/tikz/\tikz@dv@key/.try={#1}}% + \ifpgfkeyssuccess% + \else% + \edef\pgf@temp{/errors/unknown key={/tikz/data visualization/\tikz@dv@key}}% + \expandafter\pgfkeys\expandafter{\pgf@temp{#1}}% + \fi% + }, + /tikz/data visualization/data/.unknown/.code={% + \let\tikz@dv@key\pgfkeyscurrentname% + \pgfkeys{/pgf/data/\tikz@dv@key/.try={#1}}% + \ifpgfkeyssuccess% + \else% + \edef\pgf@temp{/errors/unknown key={/pgf/data/\tikz@dv@key}}% + \expandafter\pgfkeys\expandafter{\pgf@temp{#1}}% + \fi% + }, +}% + +\def\tikzdatavisualizationset{\pgfqkeys{/tikz/data visualization}}% + + + + + +\def\tikz@lib@datavisualization{ + \begingroup% + \let\tikz@path@do@at@end=\relax% + \pgfoonew \tikz@main@dv=new data visualization()% + \pgfset{local bounding box=data visualization bounding box}% + \pgfkeyslet{/tikz/data visualization/axes list}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/axes actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/label actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/legend actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/grid actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/major grid actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/minor grid actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/subminor grid actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/ticks actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/major ticks actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/minor ticks actions}\pgfutil@empty% + \pgfkeyslet{/tikz/data visualization/subminor ticks actions}\pgfutil@empty% + \tikz@main@dv.before visualization(% + )% + \tikz@main@dv.after visualization(% + \tikz@lib@dv@alias@dv@bb + \pgfkeysvalueof{/tikz/data visualization/grid actions} + \pgfkeysvalueof{/tikz/data visualization/subminor grid actions} + \pgfkeysvalueof{/tikz/data visualization/minor grid actions} + \pgfkeysvalueof{/tikz/data visualization/major grid actions} + \pgfkeysvalueof{/tikz/data visualization/ticks actions} + \pgfkeysvalueof{/tikz/data visualization/subminor ticks actions} + \pgfkeysvalueof{/tikz/data visualization/minor ticks actions} + \pgfkeysvalueof{/tikz/data visualization/major ticks actions} + \pgfkeysvalueof{/tikz/data visualization/axes actions} + \pgfkeysvalueof{/tikz/data visualization/label actions} + \pgfkeysvalueof{/tikz/data visualization/legend actions} + )% + \pgfset{/pgf/data/continue code=\tikz@lib@dv@parse@loop}% + \tikz@lib@dv@parse@loop +}% + +\def\tikz@lib@dv@parse@loop{% + \pgfutil@ifnextchar d\tikz@lib@dv@handle@data{% + \pgfutil@ifnextchar ;\tikz@lib@dv@parse@end{% + \pgfutil@ifnextchar \par\tikz@lib@dv@handle@par{% + \pgfutil@ifnextchar s\tikz@lib@dv@handle@beginscope{% + \pgfutil@ifnextchar i\tikz@lib@dv@handle@info{% + \pgfutil@ifnextchar [\tikz@lib@dv@handle@options{% + \pgfutil@ifnextchar \egroup\tikz@lib@dv@handle@endscope{% + \tikzerror{Semicolon expected}% + \endgroup% + }% + }% + }% + }% + }% + }% + }% +}% +\def\tikz@lib@dv@parse@end;{% + \tikz@main@dv.survey()% + \tikz@main@dv.visualize()% + \endgroup% + \tikz@path@do@at@end% +}% +\def\tikz@lib@dv@handle@par\par{\tikz@lib@dv@parse@loop}% + +\def\tikz@lib@dv@handle@options[#1]{% + \tikzdatavisualizationset{#1}% + \tikz@lib@dv@parse@loop% +}% + +\def\tikz@lib@dv@handle@beginscope scope{% + \begingroup% + \pgfutil@ifnextchar[\tikz@lib@dv@beg@opt{\tikz@lib@dv@beg@opt[]}% +}% +\def\tikz@lib@dv@beg@opt[#1]{% + \pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\begingroup\pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}}})}% + \pgfutil@ifnextchar\bgroup{ + \afterassignment\tikz@lib@dv@parse@loop% + \let\tikz@dummy=% + }{% + \tikzerror{Opening brace expected}% + \tikz@lib@dv@parse@loop% + }% +}% +\def\tikz@lib@dv@handle@endscope{% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data(\endgroup)}% + \endgroup% + \afterassignment\tikz@lib@dv@parse@loop% + \let\tikz@dummy=% +}% + +\def\tikz@lib@dv@handle@data data{% + \pgfutil@ifnextchar g{\tikz@lib@dv@handle@data@group}{% + \pgfutil@ifnextchar p{\tikz@lib@dv@handle@data@point}{% + \pgfdata}}}% + +\def\tikz@lib@dv@handle@data@group group{\pgfutil@ifnextchar[{\tikz@lib@dv@handle@data@group@opt}{\tikz@lib@dv@handle@data@group@opt[]}}% + +\def\tikz@lib@dv@handle@data@group@opt[#1]#2{% + \pgfutil@ifnextchar={\tikz@lib@dv@handle@data@group@def{#1}{#2}}{% + \pgfutil@ifnextchar+{\tikz@lib@dv@handle@data@group@extend{#1}{#2}}{% + \tikz@lib@dv@handle@data@group@use{#1}{#2}}}}% + +\def\tikz@lib@dv@handle@data@group@def#1#2={% + \pgfkeys{/pgf/data/new group={#2}}% + \tikz@lib@dv@handle@data@group@extend{#1}{#2}+=% +}% + +\def\tikz@lib@dv@handle@data@group@extend#1#2+={% + \pgfutil@ifnextchar\bgroup{ + \begingroup% + \pgfkeys{/pgf/data/store in group={#2}}% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\begingroup\pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}}})}% + \afterassignment\tikz@lib@dv@parse@loop% + \let\tikz@dummy=% + }{% + \tikzerror{Opening brace expected}% + \tikz@lib@dv@parse@loop% + }% +}% + +\def\tikz@lib@dv@handle@data@group@use#1#2{% + \pgfdata[#1,use group=#2]% +}% + +\def\tikz@lib@dv@handle@data@point point{\pgfutil@ifnextchar[{\tikz@lib@dv@handle@data@point@opt}{\tikz@lib@dv@handle@data@point@opt[]}}% +\def\tikz@lib@dv@handle@data@point@opt[#1]{% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\bgroup\pgfkeys{/data point/.cd,#1}\pgfdatapoint\egroup}})}% + \tikz@lib@dv@parse@loop% +}% + +\def\tikz@lib@dv@handle@info info{% + \pgfutil@ifnextchar'{\tikz@lib@dv@handle@info@prime}{\tikz@lib@dv@handle@info@noprime}}% +\def\tikz@lib@dv@handle@info@noprime{% + \pgfutil@ifnextchar[{\tikz@lib@dv@handle@info@block@opt}{\tikz@lib@dv@handle@info@block@opt[]}}% +\def\tikz@lib@dv@handle@info@block@opt[#1]#2{% + \tikz@main@dv.after visualization({\scope[#1]#2\endscope})% + \tikz@lib@dv@parse@loop +}% +\def\tikz@lib@dv@handle@info@prime'{% + \pgfutil@ifnextchar[{\tikz@lib@dv@handle@info@block@opt@prime}{\tikz@lib@dv@handle@info@block@opt@prime[]}}% +\def\tikz@lib@dv@handle@info@block@opt@prime[#1]#2{% + \tikz@main@dv.before visualization({\scope[#1]#2\endscope})% + \tikz@lib@dv@parse@loop +}% + + +\pgfset{/pgf/every data/.style={/tikz/every data/.try,/tikz/data visualization/every data/.try}}% + + + +\tikzdatavisualizationset{ + before survey/.code=\tikz@main@dv.before survey({#1}), + after survey/.code=\tikz@main@dv.after survey({#1}), + before visualization/.code=\tikz@main@dv.before visualization({#1}), + after visualization/.code=\tikz@main@dv.after visualization({#1}), + at start survey/.code=\tikz@main@dv.at start survey({#1}), + at end survey/.code=\tikz@main@dv.at end survey({#1}), + at start visualization/.code=\tikz@main@dv.at start visualization({#1}), + at end visualization/.code=\tikz@main@dv.at end visualization({#1}), +}% + + +\def\tikz@lib@dv@alias@dv@bb{ + \pgfnodealias{data bounding box}{data visualization bounding box}% + \pgfkeys{/pgf/freeze local bounding box=data bounding box}% +}% + +\tikzdatavisualizationset{ + data point/.code={ + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{\bgroup\pgfkeys{/data point/.cd,#1}\pgfdatapoint\egroup}})}% + } +}% + + + + +\tikzdatavisualizationset{% + new object/.code={% + \def\tikz@dv@grabbed@when{before survey}% + \let\tikz@dv@grabbed@store\pgfutil@empty + \pgfkeys{/tikz/data visualization/new object/grab/.cd,#1}% + \ifx\tikz@dv@grabbed@store\pgfutil@empty + \else + \pgfkeyslet{\tikz@dv@grabbed@store}\pgfutil@empty% + \fi + \edef\tikz@marshal{\noexpand\tikz@main@dv.\tikz@dv@grabbed@when(\noexpand\tikz@dv@newobject{\tikz@dv@grabbed@store}}% + \tikz@marshal{#1})% + }, + new object/grab/store/.store in=\tikz@dv@grabbed@store, + new object/grab/when/.store in=\tikz@dv@grabbed@when, + new object/grab/.unknown/.code={},% +}% + +\def\tikz@dv@newobject#1#2{% + \def\tikz@dv@new@obj@store{#1}% + \ifx\tikz@dv@new@obj@store\pgfutil@empty% + \let\tikz@dv@new@obj=\pgfutil@empty% + \else% + \pgfkeysgetvalue\tikz@dv@new@obj@store\tikz@dv@new@obj% + \fi% + \ifx\tikz@dv@new@obj\pgfutil@empty + \let\tikz@dv@arg@a=\tikz@lib@notused% + \let\tikz@dv@arg@b=\tikz@lib@notused% + \let\tikz@dv@arg@c=\tikz@lib@notused% + \let\tikz@dv@arg@d=\tikz@lib@notused% + \let\tikz@dv@arg@e=\tikz@lib@notused% + \let\tikz@dv@arg@f=\tikz@lib@notused% + \let\tikz@dv@arg@g=\tikz@lib@notused% + \let\tikz@dv@arg@h=\tikz@lib@notused% + \let\tikz@dv@new@after=\relax% + \pgfkeys{/tikz/data visualization/new object/parse/.cd,#2} + \edef\pgf@marshal{\noexpand\pgfoonew\noexpand\tikzdvobj=new \tikz@dv@new@class(}% + \tikz@dv@add@arg{}\tikz@dv@arg@a% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@b% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@c% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@d% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@e% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@f% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@g% + \tikz@dv@add@arg{\expandafter,}\tikz@dv@arg@h% + \expandafter\def\expandafter\pgf@marshal\expandafter{\pgf@marshal)}% + \pgf@marshal% + \tikzdvobj.default connects()% + \ifx\tikz@dv@new@obj@store\pgfutil@empty% + \else% + \pgfkeyslet\tikz@dv@new@obj@store\tikzdvobj% + \fi% + \tikz@dv@new@after% + \fi +}% +\def\tikz@lib@notused{\tikz@lib@notused}% + +\def\tikz@dv@add@arg#1#2{% + \ifx#2\tikz@lib@notused% + \else% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@marshal% + \expandafter\expandafter\expandafter{\expandafter\pgf@marshal#1#2}% + \fi% +}% + +\tikzdatavisualizationset{% + new object/parse/.cd, + store/.code=,% + when/.code=,% + class/.store in=\tikz@dv@new@class, + before creation/.code={#1}, + after creation/.store in=\tikz@dv@new@after, + arg1/.store in=\tikz@dv@arg@a, + arg2/.store in=\tikz@dv@arg@b, + arg3/.store in=\tikz@dv@arg@c, + arg4/.store in=\tikz@dv@arg@d, + arg5/.store in=\tikz@dv@arg@e, + arg6/.store in=\tikz@dv@arg@f, + arg7/.store in=\tikz@dv@arg@g, + arg8/.store in=\tikz@dv@arg@h, + arg1 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@a}, + arg2 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@b}, + arg3 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@c}, + arg4 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@d}, + arg5 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@e}, + arg6 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@f}, + arg7 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@g}, + arg8 from key/.code=\pgfkeysgetvalue{#1}{\tikz@dv@arg@h} + arg1 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@a}{\tikz@dv@arg@a}, + arg2 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@b}{\tikz@dv@arg@b}, + arg3 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@c}{\tikz@dv@arg@c}, + arg4 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@d}{\tikz@dv@arg@d}, + arg5 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@e}{\tikz@dv@arg@e}, + arg6 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@f}{\tikz@dv@arg@f}, + arg7 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@g}{\tikz@dv@arg@g}, + arg8 handle from key/.code=\tikz@dv@handle@from@key{#1}{\tikz@dv@handle@h}{\tikz@dv@arg@h} +}% + +\def\tikz@dv@handle@from@key#1#2#3{% + \pgfkeysvalueof{#1}.get handle(#2)% + \def#3{#2}% +}% + + + + + +\tikzdeclarecoordinatesystem{visualization} +{% + \tikzset{/data point/.cd,#1}% + \pgfpointdvlocaldatapoint% +}% + + + + + + + + +\tikzdatavisualizationset{% + new axis base/.style={ + new object={ + class=scaling mapper, + store=/tikz/data visualization/#1/scaling mapper, + before creation={ + \pgfkeysgetvalue{/tikz/data visualization/#1/scaling}\tikz@temp + \ifx\tikz@temp\pgfutil@empty% + \pgfkeysgetvalue{/tikz/data visualization/#1/scaling/default}\tikz@temp + \fi + \expandafter\tikz@dv@lib@parse@scaling\tikz@temp\pgf@stop% + \pgfkeyslet{/tikz/data visualization/#1/scaling}\tikz@temp + }, + arg1 from key=/tikz/data visualization/#1/attribute, + arg2/.expanded=\pgfkeysvalueof{/tikz/data visualization/#1/attribute}/scaled, + arg3 from key=/tikz/data visualization/#1/scaling, + arg4 from key=/tikz/data visualization/#1/function + }, + #1/attribute/.initial={#1}, + #1/function/.initial=, + #1/scaling/.initial=, + #1/scaling/default/.initial=0 at 0 and 1 at 1, + #1/ticks at/.initial=, + #1/default ticks at/.initial=, + #1/major ticks/.initial=, + #1/minor ticks/.initial=, + #1/subminor ticks/.initial=, + #1/grid at/.initial=, + #1/default grid at/.initial=, + #1/major grid/.initial=, + #1/minor grid/.initial=, + #1/subminor grid/.initial=, + #1/label/.initial=, + #1/padding min/.initial=, + #1/padding max/.initial=, + #1/.code={ + \let\tikz@temp\tikz@dv@axis% + \def\tikz@dv@axis{/tikz/data visualization/#1}% + \expandafter\tikz@do@axis@options\expandafter{\tikz@temp}{##1}% + }, + #1/@compute at positions/.initial=\tikz@lib@dv@compute@at@linear, + axes list/.append={\tikz@lib@dv@do@axis{#1}} + }, + all axes/.code={ + \def\tikz@lib@dv@args{#1}% + \pgfkeysvalueof{/tikz/data visualization/axes list}% + }, + styling/.style=, + style/.style={styling/.append style={#1}}, + @node styling/.initial=, + node styling/.style={% + /utils/exec={\pgfkeysgetvalue{/tikz/data visualization/@node styling}\tikz@temp\expandafter\tikzset\expandafter{\tikz@temp}}}, + node style/.style={/tikz/data visualization/@node styling/.append={,#1}}, + low/.initial=0, + high/.initial=0, + padded/.style={low=padded min,high=padded max}, + tick length/.style={low={-#1},high={#1}}, + common/.initial=, + major/.initial=, + minor/.initial=, + subminor/.initial=, + @setup at setters/.style={ + common/.code=\tikz@lib@dv@add@{common}{##1}, + major/.code=\tikz@lib@dv@add@{major}{##1}, + minor/.code=\tikz@lib@dv@add@{minor}{##1}, + subminor/.code=\tikz@lib@dv@add@{subminor}{##1} + }, + @setup at setters, + direction axis/.initial=, + tick text low even padding/.initial=0pt, + tick text high even padding/.initial=0pt, + tick text low odd padding/.initial=0pt, + tick text high odd padding/.initial=0pt, + tick text odd padding/.style={tick text low odd padding={-#1},tick text high odd padding={#1}}, + tick text even padding/.style={tick text low even padding={-#1},tick text high even padding={#1}}, + tick text padding/.style={tick text odd padding={#1},tick text even padding={#1}}, + stack/.style={tick text even padding={#1}}, + stack'/.style={tick text odd padding={#1}}, + stack/.default=1em, + stack'/.default=1em, + tick text at low/.is if=tikz@dv@min@tick@node, + tick text at high/.is if=tikz@dv@max@tick@node, + no tick text/.style={tick text at low=false,tick text at high=false}, + every major ticks/.style={style={line cap=round},tick length=2pt}, + every minor ticks/.style={style={solid, help lines,thin,line cap=round},tick length=1.4pt}, + every subminor ticks/.style={style={solid, help lines,line cap=round},tick length=0.8pt}, + clean ticks/.style={node style={fill=white}}, + every grid/.style={high=max,low=min}, + every major grid/.style={style={solid, help lines,thin,black!25}}, + every minor grid/.style={style={solid, help lines,black!25}}, + every subminor grid/.style={style={solid, help lines,black!10}}, + at default ticks/.code={% + \expandafter\pgfkeysalso\expandafter{\tikz@lib@dv@ticks@default@at}}, + at ticks/.code={% + \expandafter\pgfkeysalso\expandafter{\tikz@lib@dv@ticks@default@at}% + \expandafter\pgfkeysalso\expandafter{\tikz@lib@dv@ticks@at}}, +}% + +\def\tikz@lib@dv@add@#1#2{\pgfkeysaddvalue{/tikz/data visualization/#1}{}{,#2}}% + +\def\tikz@dv@lib@parse@scaling#1 at#2and #3 at#4\pgf@stop{% + \pgfmathsetmacro{\tikz@dv@lib@min@at}{#2} + \pgfmathsetmacro{\tikz@dv@lib@max@at}{#4} + \edef\tikz@temp{#1 at \tikz@dv@lib@min@at and #3 at \tikz@dv@lib@max@at}% +}% + + +\tikzdatavisualizationset{ + at/.code={\def\tikz@dv@at@list{#1}}, + also at/.code={\expandafter\def\expandafter\tikz@dv@at@list\expandafter{\tikz@dv@at@list,#1}}, + major at/.style={major={at={#1}}}, + minor at/.style={minor={at={#1}}}, + subminor at/.style={subminor={at={#1}}}, + major also at/.style={major={also at={#1}}}, + minor also at/.style={minor={also at={#1}}}, + subminor also at/.style={subminor={also at={#1}}}, + options at/.code={\expandafter\def\expandafter\tikz@dv@style@at@list\expandafter{\tikz@dv@style@at@list,{#1}}}, + no tick text at/.style={options at={#1 as [no tick text]}} +}% + + +\def\tikz@lib@dv@do@axis#1{% + \def\tikz@marshal{#1=} + \expandafter\expandafter\expandafter\tikzdatavisualizationset% + \expandafter\expandafter\expandafter{\expandafter\tikz@marshal\expandafter{\tikz@lib@dv@args}} +}% + +\def\tikz@do@axis@options#1#2{ + \pgfkeys{/tikz/data visualization/axis options/.cd,#2} + \def\tikz@dv@axis{#1} +}% +\let\tikz@dv@axis\pgfutil@empty + +\tikzdatavisualizationset{ + every ticks/.style={ + node style={% + font=\pgfutil@font@footnotesize, + inner sep=1pt, + outer sep=.1666em, + rounded corners=1.5pt + } + }, + every data set label/.style={ + every ticks, + node style={ + font=\pgfutil@font@small, + } + }, + @color of visualizer labels/.style={text=black}, + every label in legend/.style={ + node style={ + fill=none, + } + }, + every axis label/.style={ + node style={% + font=\pgfutil@font@small, + } + } +}% + + +\tikzset{ + /tikz/data visualization/axis options/.cd, + attribute/.style={\tikz@dv@axis/attribute={#1}}, + function/.style={\tikz@dv@axis/function={#1}}, + scaling/.style={\tikz@dv@axis/scaling={#1}}, + padding min/.style={\tikz@dv@axis/padding min={#1}}, + padding max/.style={\tikz@dv@axis/padding max={#1}}, + padding/.style={padding min={-#1},padding max={#1}}, + label/.code={% + \def\pgf@temp{#1}% + \ifx\pgf@temp\tikz@lib@dv@auto@attribute% + \tikzdatavisualizationset{\tikz@dv@axis/label/.expanded=$\noexpand\mathit{\pgfkeysvalueof{\tikz@dv@axis/attribute}}$}% + \else + \tikzdatavisualizationset{\tikz@dv@axis/label={#1}}% + \fi + }, + label/.default=\tikz@lib@dv@auto@attribute, + tick placement strategy/.style={\tikz@dv@axis/@compute at positions={#1}}, + linear steps/.style={tick placement strategy=\tikz@lib@dv@compute@at@linear}, + goto/.code={\tikz@dv@goto{\tikz@dv@axis}{#1}}, + goto pos/.code={\tikz@dv@goto@pos{\tikz@dv@axis}{#1}}, + anchor at min/.code={\tikz@lib@dv@special@at{\tikz@dv@axis}{\tikz@dv@min@anchor}}, + anchor at max/.code={\tikz@lib@dv@special@at{\tikz@dv@axis}{\tikz@dv@max@anchor}}, + visualize axis/.code=\expandafter\tikz@lib@dv@av\expandafter{\tikz@dv@axis}{#1}, + ticks/.style={\tikz@dv@axis/ticks at/.append={,#1}}, + ticks/.default=some, + visualize ticks/.code=\expandafter\tikz@lib@dv@tv\expandafter{\tikz@dv@axis}{#1}, + grid/.style={\tikz@dv@axis/grid at/.append={,#1}}, + grid/.default=at default ticks, + visualize grid/.code=\expandafter\tikz@lib@dv@gv\expandafter{\tikz@dv@axis}{#1}, + ticks and grid/.style={\tikz@dv@axis/ticks at/.append={,#1},\tikz@dv@axis/grid at/.append={,#1}}, + visualize label/.code=\expandafter\tikz@lib@dv@lv\expandafter{\tikz@dv@axis}{#1}, +}% + +\def\tikz@lib@dv@auto@attribute{\tikz@lib@dv@auto@attribute}% + + +\tikzdatavisualizationset{ + axis options/.cd, + include value/.style={% + /tikz/data visualization/before survey/.expanded={% + \noexpand\pgfkeysgetvalue{\tikz@dv@axis/scaling mapper}\noexpand\tikz@dv@axis@mapper% + \noexpand\foreach \noexpand\tikz@lib@dv@temp in {#1} {% + \noexpand\tikz@dv@axis@mapper.include in value(\noexpand\tikz@lib@dv@temp)% + }% + }% + }, + min value/.style={ + /tikz/data visualization/at end survey/.expanded={% + \noexpand\pgfkeysgetvalue{\tikz@dv@axis/scaling mapper}\noexpand\tikz@dv@axis@mapper% + \noexpand\tikz@lib@dv@set\noexpand\tikz@dv@axis@mapper{#1}{min}% + } + }, + max value/.style={ + /tikz/data visualization/at end survey/.expanded={% + \noexpand\pgfkeysgetvalue{\tikz@dv@axis/scaling mapper}\noexpand\tikz@dv@axis@mapper% + \noexpand\tikz@lib@dv@set\noexpand\tikz@dv@axis@mapper{#1}{max}% + } + }, +}% + +\def\tikz@lib@dv@set#1#2#3{% + \pgfdvmathenter{\pgf@dv@value}{#2}% + #1.get in range interval()% + \pgfdvinrangeinterval.let #3(\pgf@dv@value)% +}% + +\tikzdatavisualizationset{ + axis layer/.style=on background layer, + ticks layer/.style=on background layer, + ticks node layer/.style=, + grid layer/.style=on background layer, +}% + + + +\def\tikz@lib@dv@av#1#2{ + \tikzdatavisualizationset{ + axes actions/.append={\tikz@lib@dv@show@axis{#1}{#2}} + } +}% + +\def\tikz@lib@dv@show@axis#1#2{% + \scope[data visualization/axis layer,/tikz/data visualization/.cd,low=min,high=max,every axis/.try,#2] + \pgfkeysgetvalue{#1/scaling mapper}\tikz@dv@axis@mapper% + \tikzpointandanchordirection{\tikz@dv@axis@mapper.set in to(min)}{\tikz@dv@axis@mapper.set in to(max)} + \xdef\tikz@dv@axis@dir{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \path[draw,/tikz/data visualization/styling] + \pgfextra{ + { + \tikz@dv@goto{#1}{\pgfkeysvalueof{/tikz/data visualization/low}}% + \pgfpathdvmoveto% + } + { + \tikz@dv@goto{#1}{\pgfkeysvalueof{/tikz/data visualization/high}}% + \pgfpathdvlineto% + } + }; + \endscope +}% + +\def\tikz@dv@goto#1#2{% + \edef\pgf@@temp{#2}% + \ifx\pgf@@temp\tikz@lib@dv@padded@min@text% + \pgfkeysvalueof{#1/scaling mapper}.set in to(min)% + \pgfkeysvalueof{#1/scaling mapper}.get out()% + \pgfkeysgetvalue{#1/padding min}\pgf@temp% + \pgfmathparse{\pgf@temp}% + \pgfkeyslet{/data point/\pgfdvout/offset}\pgfmathresult% + \else% + \ifx\pgf@@temp\tikz@lib@dv@padded@max@text% + \pgfkeysvalueof{#1/scaling mapper}.set in to(max)% + \pgfkeysvalueof{#1/scaling mapper}.get out()% + \pgfkeysgetvalue{#1/padding max}\pgf@temp% + \pgfmathparse{\pgf@temp}% + \pgfkeyslet{/data point/\pgfdvout/offset}\pgfmathresult% + \else% + \pgfkeysvalueof{#1/scaling mapper}.set in to(#2)% + \fi% + \fi% +}% + +\def\tikz@dv@goto@pos#1#2{% + \pgfkeyssetvalue{/data point/\pgfkeysvalueof{#1/attribute}/out pos}{#2}% +}% + +\def\tikz@lib@dv@padded@min@text{padded min}% +\def\tikz@lib@dv@padded@max@text{padded max}% + +\def\tikz@lib@dv@special@at#1#2{% + \tikzpointandanchordirection{\pgfkeysvalueof{#1/scaling mapper}.set in to(min)}{\pgfkeysvalueof{#1/scaling mapper}.set in to(max)} + \tikzset{anchor/.expanded={#2}} +}% + + + +\def\tikz@lib@dv@tv#1#2{ + \tikzdatavisualizationset{ + ticks actions/.append={\tikz@lib@dv@default@action{ticks}{#1}{#2}}, + major ticks actions/.append={\tikz@lib@dv@show@ticks{major}{#1}{#2}}, + minor ticks actions/.append={\tikz@lib@dv@show@ticks{minor}{#1}{#2}}, + subminor ticks actions/.append={\tikz@lib@dv@show@ticks{subminor}{#1}{#2}} + } +}% + +\def\tikz@lib@dv@default@action#1#2#3{% + \let\tikz@marshal\pgfutil@empty% + {% + \let\tikz@lib@dv@ticks@at\pgfutil@empty% + \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@ticks@default@at% + \pgfkeysgetvalue{#2/#1 at}\tikz@lib@dv@settings% + \pgfkeysgetvalue{#2/scaling mapper}\tikz@lib@dv@mapper + \tikzdatavisualizationset{major/.code=,minor/.code=,subminor/.code=,common/.code=} + \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@settings}% + \tikzdatavisualizationset{@setup at setters}% + \pgfkeysgetvalue{/tikz/data visualization/compute step}\tikz@temp@step% + \ifx\tikz@temp@step\pgfutil@empty% + \else% + \pgfkeysvalueof{#2/@compute at positions}% + \xdef\tikz@marshal{ + major={\pgfkeysvalueof{/tikz/data visualization/major}}, + minor={\pgfkeysvalueof{/tikz/data visualization/minor}}, + subminor={\pgfkeysvalueof{/tikz/data visualization/subminor}}} + \fi + }% + \pgfkeyslet{#2/default #1 at}\tikz@marshal +}% + +\def\tikz@lib@dv@show@ticks#1#2#3{% + \pgfkeysgetvalue{#2/default ticks at}\tikz@lib@dv@default@settings% + \ifx\tikz@lib@dv@default@settings\pgfutil@empty% + \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@settings% + \else% + \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@settings% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@dv@settings% + \expandafter\expandafter\expandafter{\expandafter\tikz@lib@dv@default@settings\expandafter,\tikz@lib@dv@settings} + \fi% + \ifx\tikz@lib@dv@settings\pgfutil@empty% + \else + {% + \let\tikz@dv@at@list\pgfutil@empty% + \let\tikz@dv@style@at@list\pgfutil@empty% + \pgfkeysgetvalue{#2/scaling mapper}\tikz@lib@dv@mapper + \scope[/tikz/data visualization/.cd,every ticks/.try,every #1 ticks/.try,#3]% + \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@settings}% + \pgfkeysgetvalue{/tikz/data visualization/common}\tikz@temp + \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp} + \pgfkeysgetvalue{/tikz/data visualization/#1}\tikz@temp + \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp} + \pgfkeysgetvalue{/tikz/data visualization/\pgfkeysvalueof{/tikz/data visualization/direction axis}/scaling mapper}\pgf@dv@tick@dir@mapper + \foreach \tikz@dv@tick@pos[count=\tikz@dv@tick@count] in \tikz@dv@at@list + { + \ifx\tikz@dv@tick@pos\pgfutil@empty + \c@pgf@counta=\tikz@dv@tick@count\relax% + \advance\c@pgf@counta by-1\relax% + \edef\tikz@dv@tick@count{\the\c@pgf@counta}% + \else + \expandafter\tikz@lib@dv@parse\tikz@dv@tick@pos\pgf@stop% + \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@tick@opt}% + \tikz@lib@dv@mapper.set in to(\tikz@dv@tick@pos)% + \pgf@process{\pgfpointdvlocaldatapoint} + \xdef\pgf@dv@tick@origin{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \tikzpointandanchordirection{\pgf@dv@tick@dir@mapper.set in to(min)}{\pgf@dv@tick@dir@mapper.set in to(max)} + \xdef\pgf@dv@tick@dir{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \tikz@lib@handle@at@style% + \pgfkeysgetvalue{/tikz/data visualization/high}\tikz@dv@max@val% + \pgfkeysgetvalue{/tikz/data visualization/low}\tikz@dv@min@val% + \iftikz@dv@max@tick@node\pgfmathsetmacro\tikz@dv@max@val{% + \tikz@dv@max@val+(\pgfkeysvalueof{% + /tikz/data visualization/tick text high + \ifodd\tikz@dv@tick@count odd \else even \fi padding}% + )}% + \fi% + \iftikz@dv@min@tick@node\pgfmathsetmacro\tikz@dv@min@val{% + \tikz@dv@min@val+(\pgfkeysvalueof{% + /tikz/data visualization/tick text low + \ifodd\tikz@dv@tick@count odd \else even \fi padding}% + )}% + \fi% + \pgf@process{\pgfpointadd{\pgf@dv@tick@origin}{\pgfpointscale{\tikz@dv@max@val}{\pgf@dv@tick@dir}}} + \xdef\tikz@dv@max@tick{\the\pgf@x,\the\pgf@y} + \pgf@process{\pgfpointadd{\pgf@dv@tick@origin}{\pgfpointscale{\tikz@dv@min@val}{\pgf@dv@tick@dir}}} + \xdef\tikz@dv@min@tick{\the\pgf@x,\the\pgf@y} + \scope[data visualization/ticks layer] + \tikzdatavisualizationset{every \ifodd\tikz@dv@tick@count odd \else even \fi tick/.try} + \draw [/tikz/data visualization/styling] (\tikz@dv@min@tick) -- (\tikz@dv@max@tick); + \endscope + \iftikz@dv@min@tick@node + \scope[data visualization/ticks node layer] + \tikzdatavisualizationset{every \ifodd\tikz@dv@tick@count odd \else even \fi tick/.try} + \path [/tikz/data visualization/styling] (\tikz@dv@min@tick) \tikz@dv@handle@tick{\tikz@dv@min@anchor}; + \endscope + \fi + \iftikz@dv@max@tick@node + \scope[data visualization/ticks node layer] + \tikzdatavisualizationset{every \ifodd\tikz@dv@tick@count odd \else even \fi tick/.try} + \path [/tikz/data visualization/styling] (\tikz@dv@max@tick) \tikz@dv@handle@tick{\tikz@dv@max@anchor}; + \endscope + \fi + \fi + } + \endscope + } + \fi +}% + +\def\tikz@lib@dv@parse#1\pgf@stop{% + \pgfutil@in@{as}{#1}% + \ifpgfutil@in@% + \tikz@lib@dv@parse@as#1\pgf@stop% + \else% + \tikz@lib@dv@parse@as#1as\tikz@lib@dv@typeset\pgf@stop% + \fi% +}% +\def\tikz@lib@dv@parse@as#1as{% + \def\tikz@dv@tick@pos{#1}% + \pgfutil@ifnextchar[{\tikz@lib@dv@parse@as@opt}{\tikz@lib@dv@parse@as@opt[]}% +}% +\def\tikz@lib@dv@parse@as@opt[#1]{% + \def\tikz@lib@dv@tick@opt{#1}% + \pgfutil@ifnextchar\pgf@stop{\tikz@lib@dv@parse@as@text\tikz@lib@dv@typeset}{\tikz@lib@dv@parse@as@text} +}% +\def\tikz@lib@dv@parse@as@text#1\pgf@stop{% + \def\tikz@lib@dv@tick@text{#1}% +}% + +\def\tikz@lib@dv@typeset{% + \pgfdvmathenter{\tikz@lib@dv@typesetnum}{\tikz@dv@tick@pos}% + \pgfdvmathexitbyscientificformat{\tikz@lib@dv@typesetnum}{\tikz@lib@dv@typesetnum}% + \pgfkeysvalueof{/tikz/data visualization/tick prefix}% + \pgfkeys{/tikz/data visualization/tick typesetter=\tikz@lib@dv@typesetnum}% + \pgfkeysvalueof{/tikz/data visualization/tick suffix}% +}% + +\newif\iftikz@dv@min@tick@node +\newif\iftikz@dv@max@tick@node + +\def\tikz@dv@handle@tick#1{% + \pgfextra{ + \ifx\tikz@lib@dv@tick@text\pgfutil@empty% + \global\let\tikz@dv@tick@marshal=\pgfutil@empty% + \else + \def\tikz@dv@tick@marshal{node[anchor=#1,/tikz/data visualization/node styling]}% + \expandafter\pgfutil@g@addto@macro\expandafter\tikz@dv@tick@marshal\expandafter{\expandafter{\tikz@lib@dv@tick@text}} + \fi + \expandafter}% + \tikz@dv@tick@marshal +}% + + +\def\tikz@lib@handle@at@style{% + \ifx\tikz@dv@style@at@list\pgfutil@empty% + \else% + \let\tikz@dv@lib@this@at@style=\pgfutil@empty% + \pgfdvmathenter{\tikz@temp}{\tikz@dv@tick@pos}% + \pgfdvmathexitbyscientificformat{\tikz@dv@compare@to}{\tikz@temp}% + \foreach \tikz@dv@at@style in \tikz@dv@style@at@list {% + \ifx\tikz@dv@at@style\pgfutil@empty% + \else% + \expandafter\tikz@dv@lib@handle@one@at@style\tikz@dv@at@style\tikz@stop% + \fi% + } + \ifx\tikz@dv@lib@this@at@style\pgfutil@empty% + \else% + \expandafter\tikzdatavisualizationset\expandafter{\tikz@dv@lib@this@at@style}% + \fi% + \fi% +}% + +\def\tikz@dv@lib@handle@one@at@style#1as#2[#3]#4\tikz@stop{% + \pgfdvmathenter{\tikz@lib@dv@at@math@var}{#1}% + \pgfdvmathexitbyscientificformat{\tikz@dv@temp}{\tikz@lib@dv@at@math@var}% + \ifx\tikz@dv@temp\tikz@dv@compare@to% + \expandafter\gdef\expandafter\tikz@dv@lib@this@at@style\expandafter{\tikz@dv@lib@this@at@style,#3}% + \fi% +}% + + +\def\tikzpointandanchordirection#1#2{% + \pgf@process{\pgfpointdvdirection{#1}{#2}} + { + \pgf@ya=\pgf@y + \pgf@y=-\pgf@x + \pgf@x=\pgf@ya + \tikz@auto@anchor + \xdef\tikz@dv@max@anchor{\tikz@anchor} + \tikz@auto@anchor@prime + \xdef\tikz@dv@min@anchor{\tikz@anchor} + } +}% + + + + + +\def\tikz@lib@dv@gv#1#2{ + \tikzdatavisualizationset{ + grid actions/.append={\tikz@lib@dv@default@action{grid}{#1}{#2}}, + major grid actions/.append={\tikz@lib@dv@show@grid{major}{#1}{#2}}, + minor grid actions/.append={\tikz@lib@dv@show@grid{minor}{#1}{#2}}, + subminor grid actions/.append={\tikz@lib@dv@show@grid{subminor}{#1}{#2}}, + } +}% + +\def\tikz@lib@dv@show@grid#1#2#3{% + \pgfkeysgetvalue{#2/default grid at}\tikz@lib@dv@default@settings% + \ifx\tikz@lib@dv@default@settings\pgfutil@empty% + \pgfkeysgetvalue{#2/grid at}\tikz@lib@dv@settings% + \else% + \pgfkeysgetvalue{#2/grid at}\tikz@lib@dv@settings% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@dv@settings% + \expandafter\expandafter\expandafter{\expandafter\tikz@lib@dv@default@settings\expandafter,\tikz@lib@dv@settings} + \fi% + \ifx\tikz@lib@dv@settings\pgfutil@empty% + \else + {% + \let\tikz@dv@at@list\pgfutil@empty + \let\tikz@dv@style@at@list\pgfutil@empty + \pgfkeysgetvalue{#2/scaling mapper}\tikz@lib@dv@mapper + \let\tikz@lib@dv@ticks@default@at\pgfutil@empty% + \scope[data visualization/grid layer,/tikz/data visualization/.cd,every #1 grid/.try,every grid,#3] + \pgfkeysgetvalue{#2/ticks at}\tikz@lib@dv@ticks@at% + \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@settings}% + \pgfkeysgetvalue{/tikz/data visualization/common}\tikz@temp + \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp} + \pgfkeysgetvalue{/tikz/data visualization/#1}\tikz@temp + \expandafter\tikzdatavisualizationset\expandafter{\tikz@temp} + \edef\tikz@lib@dv@dir@axis{/tikz/data visualization/\pgfkeysvalueof{/tikz/data visualization/direction axis}}% + \foreach \tikz@dv@grid@pos in \tikz@dv@at@list + { + \ifx\tikz@dv@grid@pos\pgfutil@empty + \else + \expandafter\tikz@lib@dv@parse\tikz@dv@grid@pos\pgf@stop% + \expandafter\tikzdatavisualizationset\expandafter{\tikz@lib@dv@tick@opt}% + \tikz@lib@dv@mapper.set in to(\tikz@dv@tick@pos)% + \draw[/tikz/data visualization/styling] + \pgfextra{ + \tikz@dv@goto{\tikz@lib@dv@dir@axis}{\pgfkeysvalueof{/tikz/data visualization/low}}% + \pgfpathdvmoveto% + \tikz@dv@goto{\tikz@lib@dv@dir@axis}{\pgfkeysvalueof{/tikz/data visualization/high}}% + \pgfpathdvlineto% + }; + \fi + } + \endscope + } + \fi +}% + + + + + + + + + + +\def\tikz@lib@dv@lv#1#2{ + \tikzdatavisualizationset{ + label actions/.append={\tikz@lib@dv@show@label{#1}{#2}} + } +}% + +\def\tikz@lib@dv@show@label#1#2{% + \pgfkeysgetvalue{#1/label}\tikz@dv@lib@label% + \ifx\tikz@dv@lib@label\pgfutil@empty% + \else + \scope[anchor=center,/tikz/data visualization/.cd,every axis label/.try,#2] + \expandafter\tikz@lib@dv@parse@node\tikz@dv@lib@label\pgf@stop + \endscope + \fi +}% + +\def\tikz@lib@dv@parse@node{\pgfutil@ifnextchar[\tikz@lib@dv@parse@node@opt{\tikz@lib@dv@parse@node@opt[]}}% +\def\tikz@lib@dv@parse@node@opt[#1]#2\pgf@stop{ + \tikzdatavisualizationset{#1} + \pgftransformshift{\pgfpointdvlocaldatapoint}% + \node [/tikz/data visualization/node styling] {#2}; +}% + + + + +\tikzdatavisualizationset{ + compute step/.initial=, + step/.style={compute step=\def\tikz@lib@dv@step{#1}}, + minor steps between steps/.initial=, + minor steps between steps/.default=9, + phase/.initial=0, + tick typesetter/.code=\pgfmathprintnumber{#1}, + tick prefix/.initial=, + tick suffix/.initial=, + tick unit/.style={tick suffix={$\,\pgfutil@font@normalfont#1$}},% +}% + +\def\tikz@lib@dv@compute@at@linear{% + \let\tikz@lib@dv@compute@about=\tikz@lib@dv@about@linear% + \let\tikz@lib@dv@step\relax% + \pgfkeysvalueof{/tikz/data visualization/compute step} + \ifx\tikz@lib@dv@step\relax% + \else% + \tikz@lib@dv@mapper.get in range interval()% + \pgfdvinrangeinterval.get min and max()% + \pgfkeysgetvalue{/tikz/data visualization/phase}\tikz@temp + \pgfdvmathenter{\tikz@dv@lib@phase}{\tikz@temp} + \pgfdvmathenter{\tikz@dv@lib@step}{\tikz@lib@dv@step} + \pgfdvmathifless{\pgfdvmathalwayszero}{\tikz@dv@lib@step}{% + \pgfdvmathsub{\tikz@dv@lib@temp}{\pgfdvmin}{\tikz@dv@lib@phase}% + \pgfdvmathdiv{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}% + \pgfdvmathfloor{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}% + \pgfdvmathmul{\tikz@lib@dv@current}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}% + \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@phase}% + \let\tikz@lib@dv@ats\pgfutil@empty% + \let\tikz@lib@dv@minor@ats\pgfutil@empty% + \tikz@lib@dv@mapper.get function(\tikz@temp)% + \ifx\tikz@temp\pgfutil@empty% + \pgfdvmathenter{\tikz@one@hundreth}{0.001}% + \pgfdvmathsub{\tikz@lib@temp}{\pgfdvmax}{\pgfdvmin}% + \pgfdvmathmul{\tikz@lib@dv@epsilon}{\tikz@lib@temp}{\tikz@one@hundreth}% + \else + \let\tikz@lib@dv@epsilon\pgfdvmathalwayszero + \fi + \pgfdvmathsub{\tikz@lib@dv@min@minus@epsilon}{\pgfdvmin}{\tikz@lib@dv@epsilon}% + \pgfdvmathadd{\tikz@lib@dv@max@plus@epsilon}{\pgfdvmax}{\tikz@lib@dv@epsilon}% + \pgfkeysgetvalue{/tikz/data visualization/minor steps between steps}\tikz@lib@dv@substeps% + \ifx\tikz@lib@dv@substeps\pgfutil@empty + \else + \pgfmathsetmacro\tikz@temp{\tikz@lib@dv@substeps+1}% + \pgfdvmathenter{\tikz@dv@lib@substeps}{\tikz@temp}% + \pgfdvmathdiv{\tikz@lib@dv@substep}{\tikz@dv@lib@step}{\tikz@dv@lib@substeps}% + \fi + \loop% + \ifx\tikz@lib@dv@substeps\pgfutil@empty% + \else% + \let\tikz@lib@dv@subcurrent=\tikz@lib@dv@current% + \pgfmathsetcount{\c@pgf@counta}{\tikz@lib@dv@substeps}% + \let\tikz@lib@dv@next=\tikz@lib@dv@subloop% + \tikz@lib@dv@subloop + \fi% + \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@min@minus@epsilon}{}{% + \pgfdvmathexitbyserializing{\tikz@temp}{\tikz@lib@dv@current}% + \edef\tikz@lib@dv@ats{\tikz@lib@dv@ats,\tikz@temp}% + } + \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@step}% + \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@max@plus@epsilon}{\tikz@lib@dv@continuetrue}{\tikz@lib@dv@continuefalse}% + \iftikz@lib@dv@continue% + \repeat% + \tikzdatavisualizationset{major/.expanded={at={\tikz@lib@dv@ats}},minor/.expanded={at={\tikz@lib@dv@minor@ats}}}% + }{% + \pgfdvmathexitbyserializing{\tikz@temp}{\pgfdvmin}% + \tikzdatavisualizationset{major/.expanded={at={\tikz@temp}}}% + }% + \fi% +}% +\newif\iftikz@lib@dv@continue + +\def\tikz@lib@dv@subloop{ + \pgfdvmathadd{\tikz@lib@dv@subcurrent}{\tikz@lib@dv@subcurrent}{\tikz@lib@dv@substep}% + \pgfdvmathifless{\tikz@lib@dv@subcurrent}{\pgfdvmin}{}{% + \pgfdvmathifless{\tikz@lib@dv@subcurrent}{\pgfdvmax}{% + \pgfdvmathexitbyserializing{\tikz@temp}{\tikz@lib@dv@subcurrent}% + \edef\tikz@lib@dv@minor@ats{\tikz@lib@dv@minor@ats,\tikz@temp} + }{}} + \advance\c@pgf@counta by-1\relax% + \ifnum\c@pgf@counta=0\relax% + \let\tikz@lib@dv@next=\relax + \fi + \tikz@lib@dv@next +}% + + + + +\tikzdatavisualizationset{ + about/.style={compute step=\tikz@lib@dv@compute@about{#1}}, + about strategy/.initial=, + standard about strategy/.style={about strategy={1.5/1.0,2.3/2.0,4/2.5,7/5,11/10}}, + standard about strategy, + euro about strategy/.style={about strategy={1.5/1.0,3/2.0,7/5,11/10}}, + decimal about strategy/.style={about strategy={3/1.0,11/10}}, + half about strategy/.style={about strategy={2/1.0,7/5,11/10}}, + quarter about strategy/.style={about strategy={1.8/1.0,4/2.5,7/5,11/10}}, + int about strategy/.style={about strategy={1.5/1.0,2.5/2.0,3.5/3.0,4.5/4.0,7/5,11/10}}, + none/.style={compute step=}, + few/.style={about=3}, + some/.style={about=5}, + many/.style={about=10}, +}% + +\def\tikz@lib@dv@about@linear#1{% + \tikz@lib@dv@mapper.get in range interval()% + \pgfdvinrangeinterval.get min and max()% + \pgfdvmathsub{\tikz@lib@dv@diff}{\pgfdvmax}{\pgfdvmin} + \pgfdvmathenter{\tikz@lib@dv@about@val}{#1}% + \pgfdvmathdiv{\tikz@lib@dv@around}{\tikz@lib@dv@diff}{\tikz@lib@dv@about@val}% + \pgfmathfloattomacro{\tikz@lib@dv@around}{\tikz@lib@dv@flags}{\tikz@lib@dv@mant}{\tikz@lib@dv@exp}% + \pgf@xc=\tikz@lib@dv@mant pt % + \pgfkeysgetvalue{/tikz/data visualization/about strategy}\tikz@lib@dv@strat + \foreach \tikz@lib@dv@threshold/\tikz@lib@replace in \tikz@lib@dv@strat + { + \ifdim\pgf@xc<\tikz@lib@dv@threshold pt% + \global\pgf@xc=\tikz@lib@replace pt% + \breakforeach + \fi + }% + \ifdim\pgf@xc<10pt% + \pgfmathfloatcreate{\tikz@lib@dv@flags}{\pgf@sys@tonumber{\pgf@xc}}{\tikz@lib@dv@exp}% + \else + \begingroup + \c@pgf@countd=\tikz@lib@dv@exp + \advance\c@pgf@countd by1 + \edef\tikz@lib@dv@exp{\the\c@pgf@countd}% + \pgfmath@smuggleone\tikz@lib@dv@exp + \endgroup + \divide\pgf@xc by 10\relax + \pgfmathfloatcreate{\tikz@lib@dv@flags}{\pgf@sys@tonumber{\pgf@xc}}{\tikz@lib@dv@exp}% + \fi + \pgfmathfloattofixed{\pgfmathresult}% + \let\tikz@lib@dv@step=\pgfmathresult +}% + + + + + + +\tikzset{ + /tikz/data visualization/axis options/.cd, + exponential steps/.style={tick placement strategy=\tikz@lib@dv@compute@at@log}, + logarithmic/.style={ + \tikz@dv@axis/function=\pgfdvmathln{\pgfvalue}{\pgfvalue}, + \tikz@dv@axis/scaling/default=1 at 0 and 10 at 1, + exponential steps + } +}% + +\def\tikz@lib@dv@compute@at@log{% + \let\tikz@lib@dv@compute@about=\tikz@lib@dv@about@log% + \let\tikz@lib@dv@step\relax% + \pgfkeysvalueof{/tikz/data visualization/compute step} + \ifx\tikz@lib@dv@step\relax% + \else% + \tikz@lib@dv@mapper.get in range interval()% + \pgfdvinrangeinterval.get min and max()% + \pgfdvmathlog{\pgfdvminlog}{\pgfdvmin}% + \pgfdvmathlog{\pgfdvmaxlog}{\pgfdvmax}% + \pgfkeysgetvalue{/tikz/data visualization/phase}\tikz@temp + \pgfdvmathenter{\tikz@dv@lib@phase}{\tikz@temp} + \pgfdvmathenter{\tikz@dv@lib@step}{\tikz@lib@dv@step} + \pgfdvmathsub{\tikz@dv@lib@temp}{\pgfdvminlog}{\tikz@dv@lib@phase}% + \pgfdvmathdiv{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}% + \pgfdvmathfloor{\tikz@dv@lib@temp}{\tikz@dv@lib@temp}% + \pgfdvmathmul{\tikz@lib@dv@current}{\tikz@dv@lib@temp}{\tikz@dv@lib@step}% + \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@phase}% + \let\tikz@lib@dv@ats\pgfutil@empty% + \let\tikz@lib@dv@minor@ats\pgfutil@empty% + \pgfdvmathenter{\tikz@one@hundreth}{0.001}% + \pgfdvmathsub{\tikz@lib@temp}{\pgfdvmaxlog}{\pgfdvminlog}% + \pgfdvmathmul{\tikz@lib@dv@epsilon}{\tikz@lib@temp}{\tikz@one@hundreth}% + \pgfdvmathsub{\tikz@lib@dv@min@minus@epsilon}{\pgfdvminlog}{\tikz@lib@dv@epsilon}% + \pgfdvmathadd{\tikz@lib@dv@max@plus@epsilon}{\pgfdvmaxlog}{\tikz@lib@dv@epsilon}% + \pgfkeysgetvalue{/tikz/data visualization/minor steps between steps}\tikz@lib@dv@substeps% + \ifx\tikz@lib@dv@substeps\pgfutil@empty + \else + \pgfmathsetmacro\tikz@temp{\tikz@lib@dv@substeps+1}% + \pgfdvmathenter{\tikz@dv@lib@substeps}{\tikz@temp}% + \fi + \loop% + \ifx\tikz@lib@dv@substeps\pgfutil@empty% + \else% + \let\tikz@lib@dv@subcurrent=\tikz@lib@dv@current% + \pgfdvmathadd{\tikz@lib@dv@subcurrent@next}{\tikz@lib@dv@subcurrent}{\tikz@dv@lib@step}% + \pgfdvmathpowten{\tikz@lib@dv@subcurrent}{\tikz@lib@dv@subcurrent}% + \pgfdvmathpowten{\tikz@lib@dv@subcurrent@max}{\tikz@lib@dv@subcurrent@next}% + \pgfdvmathsub{\tikz@lib@dv@subcurrent@diff}{\tikz@lib@dv@subcurrent@max}{\tikz@lib@dv@subcurrent}% + \pgfdvmathdiv{\tikz@lib@dv@substep}{\tikz@lib@dv@subcurrent@diff}{\tikz@dv@lib@substeps}% + \pgfmathsetcount{\c@pgf@counta}{\tikz@lib@dv@substeps}% + \let\tikz@lib@dv@next=\tikz@lib@dv@subloop% + \tikz@lib@dv@subloop + \fi% + \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@min@minus@epsilon}{}{% + \pgfdvmathpowten{\tikz@lib@dv@current@pow}{\tikz@lib@dv@current}% + \pgfdvmathexitbyserializing{\tikz@temp}{\tikz@lib@dv@current@pow}% + \edef\tikz@lib@dv@ats{\tikz@lib@dv@ats,\tikz@temp}% + } + \pgfdvmathadd{\tikz@lib@dv@current}{\tikz@lib@dv@current}{\tikz@dv@lib@step}% + \pgfdvmathifless{\tikz@lib@dv@current}{\tikz@lib@dv@max@plus@epsilon}{\tikz@lib@dv@continuetrue}{\tikz@lib@dv@continuefalse}% + \iftikz@lib@dv@continue% + \repeat% + \tikzdatavisualizationset{major/.expanded={at={\tikz@lib@dv@ats}},minor/.expanded={at={\tikz@lib@dv@minor@ats}}}% + \fi% +}% + + +\def\tikz@lib@dv@about@log#1{% + \tikz@lib@dv@mapper.get in range interval()% + \pgfdvinrangeinterval.get min and max()% + \pgfdvmathlog{\pgfdvmin}{\pgfdvmin}% + \pgfdvmathlog{\pgfdvmax}{\pgfdvmax}% + \pgfdvmathsub{\tikz@lib@dv@diff}{\pgfdvmax}{\pgfdvmin} + \pgfdvmathenter{\tikz@lib@dv@about@val}{#1}% + \pgfdvmathdiv{\tikz@lib@dv@around}{\tikz@lib@dv@diff}{\tikz@lib@dv@about@val}% + \pgfmathfloattomacro{\tikz@lib@dv@around}{\tikz@lib@dv@flags}{\tikz@lib@dv@mant}{\tikz@lib@dv@exp} + \ifdim\tikz@lib@dv@exp pt<0pt% + \pgfmathfloatcreate{1}{1.0}{0}% + \else + \pgf@xc=\tikz@lib@dv@mant pt\relax% + \ifdim\pgf@xc<2.5pt + \pgfmathfloatcreate{1}{1.0}{\tikz@lib@dv@exp} + \else\ifdim\pgf@xc<5.1pt + \pgfmathfloatcreate{1}{3.0}{\tikz@lib@dv@exp} + \else + \pgfmathfloatcreate{1}{6.0}{\tikz@lib@dv@exp} + \fi\fi + \fi% + \pgfmathfloattofixed{\pgfmathresult} + \let\tikz@lib@dv@step=\pgfmathresult +}% + + + + + + + + +\tikzdatavisualizationset{% + new Cartesian axis/.style={ + new axis base={#1}, + new object={ + class=linear transformer, + store=/tikz/data visualization/#1/linear transformer, + arg1/.expanded=\pgfkeysvalueof{/tikz/data visualization/#1/attribute}/scaled, + arg2 from key=/tikz/data visualization/#1/unit vector, + }, + #1/scaling/default/.initial=0 at 0 and 1 at 1cm, + #1/unit vector/.initial=\pgfqpoint{1pt}{0pt}, + } +}% + +\tikzset{ + /tikz/data visualization/axis options/.cd, + unit vector/.code=\tikz@scan@one@point\tikz@lib@dv@uv#1, + length/.style={\tikz@dv@axis/scaling=min at 0 and max at {#1}}, + unit length/.code={\tikz@dv@parse@unit@length{#1}}, + power unit length/.style={\tikz@dv@axis/scaling=1 at 0 and 10 at {#1}} +}% + +\def\tikz@lib@dv@uv#1{% + \pgfkeyssetvalue{\tikz@dv@axis/unit vector}{#1} +}% + +\def\tikz@dv@parse@unit@length#1{ + \pgfutil@in@{per}{#1} + \ifpgfutil@in@% + \tikz@dv@parse@unit@length@#1\pgf@stop% + \else% + \tikz@dv@parse@unit@length@#1per1units\pgf@stop% + \fi% +}% +\def\tikz@dv@parse@unit@length@#1per#2units\pgf@stop{ + \pgfkeysalso{\tikz@dv@axis/scaling=0 at 0 and {#2} at {#1}} +}% + + + +\tikzdatavisualizationset{ + new visualizer/.style n args={3}{ + #1/.code={ + \def\tikz@visualizer{#1}% + \pgfkeys{/tikz/data visualization/visualizer options/.cd,##1} + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data(\pgfkeys{/data point/set={#1}})}% + }, + /utils/exec={ + \advance\tikzdvvisualizercounter by 1\relax + \edef\tikz@temp{/data point/set/#1/.initial=\the\tikzdvvisualizercounter} + \expandafter\tikzset\expandafter{\tikz@temp} + }, + /data point/#1/execute at begin/.initial={ + \pgfkeyssetvalue{/data point/set}{#1} + \scope[ + #2, + /tikz/data visualization/every visualizer/.try, + /tikz/data visualization/visualizers/#1/signal, + /tikz/data visualization/visualizers/#1/styling/.try] + }, + /data point/#1/execute at end/.initial={ + \path; % + \endscope + }, + /tikz/data visualization/visualizers/#1/signal/.code=\pgf@signalstyle.emit(), + /tikz/data visualization/visualizers/#1/styling/.style=, + /tikz/data visualization/visualizers/#1/label in legend options/.style={#3}, + }, + style sheet/.style={/data point/set/.style sheet={#1}}, + /pgf/data/set/.style={/data point/set={#1}}, +}% + +\tikzdatavisualizationset{ + new sub visualizer/.style n args={4}{ + #4/#1/.code={ + \def\tikz@visualizer{#4/#1}% + \pgfkeys{/tikz/data visualization/visualizer options/.cd,##1} + }, + /data point/#4/#1/execute at begin/.initial={ + \pgfkeyssetvalue{/data point/set}{#4} + \scope[ + #2, + /tikz/data visualization/every visualizer/.try, + /tikz/data visualization/visualizers/#4/signal, + /tikz/data visualization/visualizers/#4/styling/.try, + /tikz/data visualization/visualizers/#4/#1/styling/.try] + }, + /data point/#4/#1/execute at end/.initial={ + \path; % + \endscope + }, + /tikz/data visualization/visualizers/#4/#1/styling/.style=, + /tikz/data visualization/visualizers/#4/#1/label in legend options/.style={#3}, + } +}% + + +\def\tikz@do@visualizer#1#2{% + \tikzdatavisualizationset{ + #2={#1} + } +}% + +\newcount\tikzdvvisualizercounter + +\newif\iftikz@dv@visualizer@label@inline + +\tikzdatavisualizationset{visualizer options/.cd, + @set/.style 2 args={ + /tikz/data visualization/visualizers/\tikz@visualizer/styling/.append style={/utils/exec={\let\tikz@dv@plot@handler=#1}}, + /tikz/data visualization/visualizers/\tikz@visualizer/label in legend options/.append style={#2} + }, + no lines/.style={@set={\pgfplothandlerdiscard}{default label in legend mark}}, + smooth line/.style={@set={\pgfplothandlercurveto}{default label in legend path}}, + smooth cycle/.style={@set={\pgfplothandlerclosedcurve}{default label in legend closed path}}, + straight line/.style={@set={\pgfplothandlerlineto}{default label in legend path}}, + straight cycle/.style={@set={\pgfplothandlerpolygon}{default label in legend closed path}}, + polygon/.style={straight cycle},% + gap line/.style={@set={\pgfplothandlergaplineto}{default label in legend path}}, + gap cycle/.style={@set={\pgfplothandlergapcycle}{gap circular label in legend line}} +}% + + + + +\tikzdatavisualizationset{ + new label visualizer/.style 2 args={ + new object={ + when=before visualization, + class=label visualizer, + before creation={ + \begingroup + \def\tikz@visualizer{#1}% + \pgfkeys{/tikz/data visualization/visualizer label options/.cd, + #2} + \pgfkeysgetvalue{/tikz/data visualization/visualizer label options/text}\tikz@dv@temp@lab + \def\tikz@tempa{ + \scope[ + /utils/exec=\def\tikz@visualizer{#1},% + /tikz/data visualization/visualizer label options/.cd, + #2] + \tikzdatavisualizationset{every data set label/.try} + \path [ + /data point/set={#1},/utils/exec=\pgf@signalstyle.emit(), + /tikz/data visualization/.cd,every label in data/.try] + (label visualizer coordinate') -- + (label visualizer coordinate) + node [ + auto, + at end, + /tikz/data visualization/node styling] + } + \expandafter\def\expandafter\tikz@tempb\expandafter{\expandafter{\tikz@dv@temp@lab};}% + \expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\tikz@dv@label@code% + \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\relax% + \expandafter\expandafter\expandafter{\expandafter\tikz@tempa\tikz@tempb\endscope}} + \global\let\tikz@dv@label@attribute=\tikz@dv@label@attribute + \global\let\tikz@dv@label@threshold=\tikz@dv@label@threshold + \endgroup + }, + arg1/.expand once=\tikz@dv@label@attribute, + arg2=\tikz@dv@label@threshold, + arg3/.expand once=\tikz@dv@label@code, + arg4=\pgfdvvisualizerfilter{#1} + }, + /utils/exec=\tikz@create@label@count{#1} + }, + text colored/.style={node style={text=visualizer color}} +}% + +\def\tikz@create@label@count#1{ + \tikzdatavisualizationset{ + new object={ + when=before survey, + store=/tikz/data visualization/visualizers/#1/count/obj, + class=count, + arg1=set/#1/count, + after creation={\tikzdvobj.set filter(\pgfdvvisualizerfilter{#1})} + } + } +}% + +\pgfkeys{ + /tikz/data visualization/visualizer label options/.cd, + when/.code args={#1 is#2}{% + \def\tikz@dv@label@attribute{#1}% + \def\tikz@dv@label@threshold{#2}% + }, + index/.code={% + \edef\tikz@dv@label@attribute{set/\tikz@visualizer/count}% + \def\tikz@dv@label@threshold{#1}% + }, + pos/.code={% + \edef\tikz@dv@label@attribute{set/\tikz@visualizer/count}% + \pgfkeysvalueof{/tikz/data visualization/visualizers/\tikz@visualizer/count/obj}.get max(\tikz@lib@max) + \edef\tikz@dv@label@threshold{(#1*\tikz@lib@max)}% + }, + auto/.code={% + \edef\tikz@dv@label@attribute{set/\tikz@visualizer/count}% + \pgfkeysvalueof{/tikz/data visualization/visualizers/\tikz@visualizer/count/obj}.get max(\tikz@lib@max) + \edef\tikz@dv@label@threshold{({(\pgfkeysvalueof{/data point/set/\tikz@visualizer}-0.5)/\the\tikzdvvisualizercounter*\tikz@lib@max})} + }, + text/.initial=, + text'/.style={text={#1},node style=swap,/utils/exec=\def\tikz@lib@dv@pin@sign{-}}, + node style/.style={/tikz/data visualization/node style={#1}}, + text colored/.style=/tikz/data visualization/text colored, + pin angle/.store in=\tikz@lib@dv@pin@dir, + pin length/.style={node style={pin distance={#1}}}, +}% + +\let\tikz@lib@dv@pin@sign\pgfutil@empty + +\let\tikz@dv@label@attribute\pgfutil@empty +\let\tikz@dv@label@threshold\pgfutil@empty +\let\tikz@dv@label@code\pgfutil@empty + + + + + +\tikzdatavisualizationset{ + new legend/.code={ + \pgfkeysifdefined{/tikz/data visualization/#1/at}{} + {\tikzdatavisualizationset{ + new object={ + class=legend, + store=/tikz/data visualization/#1/obj, + arg1 from key=/tikz/data visualization/#1/@columns or rows, + arg2 from key=/tikz/data visualization/#1/@ideal, + arg3 from key=/tikz/data visualization/#1/max entries, + arg4 from key=/tikz/data visualization/#1/@strategy, + after creation={ + \tikzdatavisualizationset{ + legend actions/.append={ + \pgfkeysgetvalue{/tikz/data visualization/#1/obj}\pgf@dv@legend% + { + \pgf@dv@legend.get arrangement(\pgf@dv@temp)% + \pgfkeysgetvalue{/tikz/data visualization/#1/at}\pgf@dv@at% + \pgfkeysgetvalue{/tikz/data visualization/#1/anchor}\pgf@dv@anchor% + \let\pgfdvnextcell=\pgfmatrixnextcell% + \let\pgfdvendrow=\pgfmatrixendrow% + \def\pgf@marshal{ + \matrix[at/.expand once=\pgf@dv@at,matrix anchor/.expand + once=\pgf@dv@anchor,/tikz/data visualization/#1/matrix node styling] + } + \expandafter\pgf@marshal\expandafter{\pgf@dv@temp}; + } + } + } + } + }, + #1/@columns or rows/.initial=columns, + #1/@ideal/.initial=1, + #1/max entries/.initial=100, + #1/@strategy/.initial=down then right, + #1/anchor/.initial=west, + #1/at/.initial=(data visualization bounding box.east), + #1/matrix node styling/.style={row sep=0pt,column sep=.8em}, + #1/.code={ + \let\tikz@temp\tikz@dv@legend% + \def\tikz@dv@legend{/tikz/data visualization/#1}% + \expandafter\tikz@do@legend@options\expandafter{\tikz@temp}{##1}% + }, + #1={every new legend} + }}}, + new legend/.default=main legend, + legend/.style={ + new legend, + main legend={#1} + } +}% + +\def\tikz@do@legend@options#1#2{ + \pgfkeys{/tikz/data visualization/legend options/.cd,#2} + \def\tikz@dv@legend{#1} +}% +\let\tikz@dv@legend\pgfutil@empty + + +\tikzset{ + /tikz/data visualization/legend options/.cd, + ideal number of columns/.style={\tikz@dv@legend/@columns or rows=columns,\tikz@dv@legend/@ideal={#1}}, + ideal number of rows/.style={\tikz@dv@legend/@columns or rows=rows,\tikz@dv@legend/@ideal={#1}}, + columns/.style={ideal number of columns={#1}},% + rows/.style={ideal number of rows={#1}},% + max rows/.style={\tikz@dv@legend/@columns or rows=columns,\tikz@dv@legend/max entries={#1}}, + max columns/.style={\tikz@dv@legend/@columns or rows=rows,\tikz@dv@legend/max entries={#1}}, + down then right/.style={\tikz@dv@legend/@strategy=down then right}, + down then left/.style={\tikz@dv@legend/@strategy=down then left}, + up then right/.style={\tikz@dv@legend/@strategy=up then right}, + up then left/.style={\tikz@dv@legend/@strategy=up then left}, + right then down/.style={\tikz@dv@legend/@strategy=right then down}, + left then down/.style={\tikz@dv@legend/@strategy=left then down}, + right then up/.style={\tikz@dv@legend/@strategy=right then up}, + left then up/.style={\tikz@dv@legend/@strategy=left then up}, + anchor/.style={\tikz@dv@legend/anchor={#1}}, + at/.style={\tikz@dv@legend/at={#1}}, + right/.style={east outside}, + left/.style={west outside}, + above/.style={north outside}, + below/.style={south outside}, + east outside/.style={ + columns=1, + at={([xshift=.8em]data visualization bounding box.east)}, + anchor=west, + }, + north east outside/.style={ + columns=1, + at={([xshift=.8em]data visualization bounding box.north east|- + data bounding box.north)}, + anchor=north west, + }, + south east outside/.style={ + columns=1, + at={([xshift=.8em]data visualization bounding box.south east |- + data bounding box.south)}, + anchor=south west, + }, + west outside/.style={ + columns=1, + label style=text left, + at={([xshift=-.8em]data visualization bounding box.west)}, + anchor=east, + }, + north west outside/.style={ + columns=1, + label style=text left, + at={([xshift=-.8em]data visualization bounding box.north west |- + data bounding box.north)}, + anchor=north east, + }, + south west outside/.style={ + columns=1, + label style=text left, + at={([xshift=-.8em]data visualization bounding box.south west |- + data bounding box.south)}, + anchor=south east, + }, + south outside/.style={ + rows=1, + at={([yshift=-.5em]data visualization bounding box.south)}, + anchor=north, + }, + north outside/.style={ + rows=1, + at={([yshift=.5em]data visualization bounding box.north)}, + anchor=south, + }, + every new legend/.style={east outside,label style=text right}, + every legend inside/.style={ + opaque=white, + label style={node style={font=\pgfutil@font@footnotesize}} + }, + opaque/.style={ + matrix node style={ + inner sep=.333ex, + outer sep=.5ex, + rounded corners=3pt, + execute at begin cell={\tikzset{sharp corners}}, % + fill=#1 + }, + }, + opaque/.default=white, + transparent/.style={matrix node style={fill=none}}, + north east inside/.style={ + columns=1, + at={([xshift=-.3em]data bounding box.north east)}, + anchor=north east, + every legend inside + }, + south west inside/.style={ + columns=1, + at={([xshift=.3em]data bounding box.south west)}, + anchor=south west, + every legend inside + }, + north west inside/.style={ + columns=1, + at={([xshift=.3em]data bounding box.north west)}, + anchor=north west, + every legend inside + }, + south east inside/.style={ + columns=1, + at={([xshift=-.3em]data bounding box.south east)}, + anchor=south east, + every legend inside + }, + west inside/.style={ + columns=1, + at={([xshift=.3em]data bounding box.west)}, + anchor=west, + every legend inside + }, + east inside/.style={ + columns=1, + at={([xshift=.3em]data bounding box.east)}, + anchor=east, + every legend inside + }, + north inside/.style={ + rows=1, + at={(data bounding box.north)}, + anchor=north, + every legend inside + }, + south inside/.style={ + rows=1, + at={(data bounding box.south)}, + anchor=south, + every legend inside + }, + at values/.style={ + at={(visualization cs:#1)}, + anchor=center, + every legend inside + }, + right of/.style={ + at={(visualization cs:#1)}, + anchor=west, + every legend inside + }, + left of/.style={ + at={(visualization cs:#1)}, + anchor=east, + every legend inside + }, + above of/.style={ + at={(visualization cs:#1)}, + anchor=south, + every legend inside + }, + below of/.style={ + at={(visualization cs:#1)}, + anchor=north, + every legend inside + }, + above right of/.style={ + at={(visualization cs:#1)}, + anchor=south west, + every legend inside + }, + above left of/.style={ + at={(visualization cs:#1)}, + anchor=south east, + every legend inside + }, + below right of/.style={ + at={(visualization cs:#1)}, + anchor=north west, + every legend inside + }, + below left of/.style={ + at={(visualization cs:#1)}, + anchor=north east, + every legend inside + }, + label style/.style={ + matrix node style={/tikz/data visualization/every label in legend/.append style={#1}} + }, + matrix node style/.style={\tikz@dv@legend/matrix node styling/.append style={#1}}, +}% + + +\tikzdatavisualizationset{ + new legend entry/.code={ + \begingroup + \pgfkeys{/tikz/data visualization/legend entry options/.cd,#1} + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/legend}\tikz@dv@temp@legend + \global\let\tikz@dv@temp@legend\tikz@dv@temp@legend + \endgroup + \tikzdatavisualizationset{new legend/.expanded=\tikz@dv@temp@legend}% + \expandafter\tikz@dv@add@legend@entry\expandafter{\tikz@dv@temp@legend}{#1} + } +}% + +\def\tikz@dv@add@legend@entry#1#2{ + \tikz@main@dv.at start survey({ + \pgfkeysgetvalue{/tikz/data visualization/#1/obj}\pgf@temp + \pgf@temp.add entry(\tikz@dv@render@legend@entry{legend=#1,#2}) + }) +}% + +\def\tikz@dv@render@legend@entry#1{ + \pgfkeys{/tikz/data visualization/.cd,every data set label} + \pgfkeys{/tikz/data visualization/legend entry options/.cd, + /tikz/data visualization/every label in legend,#1}% + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/text}\tikz@dv@temp@lab + \pgfkeysgetvalue{/tikz/data visualization/@node styling}\tikz@dv@temp@style + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/setup}\tikz@dv@temp@setup + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/visualizer in legend styling}\tikz@dv@temp@visual@styling + \scope[/utils/exec=\expandafter\pgfkeysalso\expandafter{\tikz@dv@temp@setup}, + /utils/exec=\pgf@signalstyle.emit()] + \node[/tikz/data visualization/node styling, + /utils/exec=\expandafter\pgfkeysalso\expandafter{\tikz@dv@temp@style}] + {\tikz@dv@pre@height\tikz@dv@temp@lab\tikz@dv@post@height}; + \scope[/utils/exec=\expandafter\pgfkeysalso\expandafter{\tikz@dv@temp@visual@styling}] + \iftikz@lib@dv@text@only + \else + \pgfkeysvalueof{/tikz/data visualization/legend entry options/visualizer in legend} + \fi + \endscope + \endscope +}% + +\def\tikz@dv@pre@height{\hbox{\vrule height .75em width0pt}}% +\def\tikz@dv@post@height{\hbox{\vrule depth .25em width0pt}}% + + + +\pgfkeys{ + /tikz/data visualization/legend entry options/.cd, + text/.initial=, + node style/.style={/tikz/data visualization/node style={#1}}, + legend/.initial=main legend, + setup/.initial=, + visualizer in legend/.initial=, + visualizer in legend styling/.initial=, + visualizer in legend style/.style={visualizer in legend styling/.append={,#1}}, + text right/.style={ + node style={anchor=mid west,inner ysep=1pt,inner xsep=0pt,reset cm,xshift=.333em}, + visualizer in legend style={reset cm}, + }, + text left/.style={ + node style={anchor=mid east,inner ysep=1pt,inner xsep=0pt,reset + cm,xshift=-.333em,align=right}, + visualizer in legend style={reset cm,xscale=-1}, + }, + text only/.style={ + node style={anchor=mid west,inner ysep=1pt,inner xsep=0pt,reset cm,text=visualizer color}, + /utils/exec=\tikz@lib@dv@text@onlytrue + }, + text colored/.style=/tikz/data visualization/text colored, +}% +\let\tikz@lib@dv@pin@dir\pgfutil@empty +\newif\iftikz@lib@dv@text@only + +\pgfkeys{ + /tikz/data visualization/visualizer options/.cd, + label in legend/.code={\expandafter\tikz@dv@new@label@in@legend@for@visualizer\expandafter{\tikz@visualizer}{#1}}, + label in data/.code=\tikzdatavisualizationset{new label visualizer/.expand once=\expandafter{\tikz@visualizer}{auto,#1}}, + pin in data/.style={label in data={% + node style={% + /utils/exec={ + \ifx\tikz@lib@dv@pin@dir\pgfutil@empty + \pgf@process{\pgfpointnormalised{% + \pgfpointdiff% + {\pgfpointanchor{label visualizer coordinate}{center}}% + {\pgfpointanchor{label visualizer coordinate'}{center}}}}% + \pgf@x=-\pgf@x\relax% + \edef\tikz@lib@dv@temp@rot{\noexpand\pgfqpoint{\the\pgf@y}{\the\pgf@x}}% + \tikz@addtransform{\pgftransformshift{\pgfpointscale{\tikz@lib@dv@pin@sign\tikz@pin@distance}{\tikz@lib@dv@temp@rot}}} + \else% + \tikz@addtransform{\pgftransformshift{\pgfpointpolar{\tikz@lib@dv@pin@dir}{\tikz@lib@dv@pin@sign\tikz@pin@distance}}} + \fi% + }, + append after command={ + \bgroup + [current point is local=true] + (\tikzlastnode) edge [solid, every pin edge] (label visualizer coordinate) + \egroup% + }}, + ,#1}}, + style/.style={/tikz/data visualization/visualizers/\tikz@visualizer/styling/.append style={,#1}}, + label in legend options/.style={/tikz/data visualization/visualizers/\tikz@visualizer/label in legend options/.append style={,#1}}, + ignore style sheets/.style={/tikz/data visualization/visualizers/\tikz@visualizer/signal/.code=,/utils/exec=\advance\tikzdvvisualizercounter by -1\relax}, +}% + +\def\tikz@dv@new@label@in@legend@for@visualizer#1#2{ + \tikzdatavisualizationset{ + new legend entry={ + visualizer in legend style={/tikz/data visualization/visualizers/#1/styling/.try}, + /tikz/data visualization/every label in legend/.try, + /tikz/.cd, + every label/.try, + /tikz/data visualization/legend entry options/.cd, + setup={/data point/set={#1}}, + /tikz/data visualization/visualizers/#1/label in legend options/.try, + #2, + } + } +}% + +\def\tikz@dv@legend@entry@as@example{ + \pgfkeysgetvalue{/data point/set}{\tikz@visualizer} + \pgfkeysvalueof{/data point/\tikz@visualizer/execute at begin} + \tikz@dv@plot@handler + \pgfplotstreamstart + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/label in legend line coordinates}{\tikz@dv@temp} + \foreach \coordinate in \tikz@dv@temp + { \pgfplotstreampoint{\expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\coordinate} } + \pgfplotstreamend + \pgfkeysvalueof{/data point/\tikz@visualizer/execute at end} + \pgfkeysvalueof{/data point/\tikz@visualizer/execute at begin} + \tikz@dv@plot@mark@maker + \pgfplotstreamstart + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/label in legend mark coordinates}{\tikz@dv@temp} + \foreach \coordinate in \tikz@dv@temp + { \pgfplotstreampoint{\expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\coordinate} } + \pgfplotstreamend + \pgfkeysvalueof{/data point/\tikz@visualizer/execute at end} +}% + + +\tikzdatavisualizationset{ + legend entry options/.cd, + label in legend line coordinates/.initial=, + label in legend rectangle coordinates/.initial={(-1ex,-.5ex),(-1ex,0.968ex),(0ex,0.968ex),(0ex,-.5ex)}, + label in legend mark coordinates/.initial=, + label in legend one mark/.style={ + label in legend line coordinates={}, + label in legend mark coordinates={(0,0)}, + }, + label in legend three marks/.style={ + label in legend line coordinates={}, + label in legend mark coordinates={(-3ex,-.3ex),(-1.5ex,.3ex),(0,0)}, + }, + straight label in legend line/.style={ + label in legend line coordinates={(-2em,0),(-1.5em,0),(-.5em,0),(0,0)}, + label in legend mark coordinates={(-1.5em,0),(-.5em,0)}, + }, + zig zag label in legend line/.style={ + label in legend line coordinates={(-2em,0),(-1.5em,.3ex),(-.5em,-.3ex),(0,0)}, + label in legend mark coordinates={(-1.5em,.3ex),(-.5em,-.3ex)}, + }, + circular label in legend line/.style={ + label in legend line coordinates={% + ([xshift=-1em]0:.9em and .35ex),% + ([xshift=-1em]45:.9em and .35ex),% + ([xshift=-1em]90:.9em and .35ex),% + ([xshift=-1em]135:.9em and .35ex),% + ([xshift=-1em]180:.9em and .35ex),% + ([xshift=-1em]225:.9em and .35ex),% + ([xshift=-1em]270:.9em and .35ex),% + ([xshift=-1em]315:.9em and .35ex)},% + label in legend mark coordinates={([xshift=-1em]120:.9em and .35ex),([xshift=-1em]-60:.9em and .35ex)}, + }, + gap circular label in legend line/.style={ + label in legend line coordinates={% + ([xshift=-1em,yshift=.2ex]90:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]162:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]234:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]306:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]18:1.4ex and 0.9ex)}, + label in legend mark coordinates={ + ([xshift=-1em,yshift=.2ex]90:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]162:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]234:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]306:1.4ex and 0.9ex),% + ([xshift=-1em,yshift=.2ex]18:1.4ex and 0.9ex)} + }, + default label in legend path/.style={zig zag label in legend line}, + default label in legend closed path/.style={circular label in legend line}, + default label in legend mark/.style={label in legend one mark}, +}% + + +\def\tikz@dv@legend@entry@visualizer@visualizer{ +}% + + + + +\tikzdatavisualizationset{ + visualize as line/.style={ + new object={ + when=after survey, + store=/tikz/data visualization/visualizers/#1, + class=plot handler visualizer, + arg1=#1, + arg2={\tikz@dv@plot@handler,\tikz@dv@plot@mark@maker} + }, + new visualizer={#1}{% + every path/.style={draw}, + style={every mark/.append style={color=visualizer color}}, + mark size=2pt, + semithick, + color=visualizer color, + mark=none, + /tikz/data visualization/every visualize as line/.try, + }{visualizer in legend=\tikz@dv@legend@entry@as@example}, + #1={straight line} + }, + visualize as line/.default=line, + visualize as smooth line/.style={ + visualize as line={#1}, + #1={smooth line} + }, + visualize as smooth line/.default=line, + visualize as smooth cycle/.style={ + visualize as smooth line={#1}, + #1={smooth cycle} + }, + visualize as smooth cycle/.default=line, + visualize as scatter/.style={ + new object={ + when=after survey, + store=/tikz/data visualization/visualizers/#1, + class=plot handler visualizer, + arg1=#1, + arg2={\tikz@dv@plot@mark@maker} + }, + new visualizer={#1}{% + mark=x, + mark size=2pt, + style={every mark/.append style={color=visualizer color}}, + /tikz/data visualization/every visualize as scatter/.try, + }{visualizer in legend=\tikz@dv@legend@entry@as@example}, + #1={no lines} + }, + visualize as scatter/.default=scatter +}% + +\def\tikz@dv@plot@mark@maker{ + \let\tikz@options=\pgfutil@empty% + \let\tikz@transform=\pgfutil@empty% + \tikzset{solid,shift only,every mark}% + \tikz@options% + \ifx\tikz@plot@mark\pgfutil@empty% + \pgfplothandlerdiscard + \else + \pgfplothandlermark{\tikz@transform\pgfuseplotmark{\tikz@plot@mark}} + \fi +}% + + + + + +\tikzdatavisualizationset{ + visualize as rectangles/.style={ + new object={ + when=before survey, + store=/tikz/data visualization/visualizers/#1, + class=rectangle visualizer, + arg1=#1 + }, + /data point/#1/attribute 1/.initial=x, + /data point/#1/attribute 2/.initial=y, + new visualizer={#1}{% + every path/.style={draw}, + semithick, + color=visualizer color, + /tikz/data visualization/every visualize as rectangles/.try, + }{visualizer in legend=\tikz@dv@legend@entry@as@rectangle}, + #1={} + }, + visualize as rectangles/.default=rectangles, + visualizer options/.cd, + attribute 1/.style={/data point/\tikz@visualizer/attribute 1={#1}}, + attribute 2/.style={/data point/\tikz@visualizer/attribute 2={#1}}, +}% + + + +\def\tikz@dv@legend@entry@as@rectangle{ + \pgfkeysgetvalue{/data point/set}{\tikz@visualizer} + \pgfkeysvalueof{/data point/\tikz@visualizer/execute at begin} + \pgfplothandlerpolygon + \pgfplotstreamstart + \pgfkeysgetvalue{/tikz/data visualization/legend entry options/label in legend rectangle coordinates}{\tikz@dv@temp} + \foreach \coordinate in \tikz@dv@temp + { \pgfplotstreampoint{\expandafter\tikz@scan@one@point\expandafter\pgfutil@firstofone\coordinate} } + \pgfplotstreamend + \pgfkeysvalueof{/data point/\tikz@visualizer/execute at end} +}% + + + + + + +\pgfkeysdef{/handlers/.style sheet}{% + \edef\pgf@marshal{ + \noexpand \pgfoonew \noexpand\tikz@dv@temp=new style attribute(\pgfkeyscurrentpath,#1) + \noexpand \tikz@dv@temp.default connects() + } + \pgf@marshal +}% + +\tikzset{ + visualizer color/.code=\colorlet{visualizer color}{#1}, + visualizer color=black +}% + + +\pgfdvdeclarestylesheet{vary thickness} +{ + default style/.style={line width={0.3pt+(#1)*0.2pt}} +}% + +\pgfdvdeclarestylesheet{vary dashing} +{ + default style/.style=solid, + 1/.style=solid, + 2/.style={dash pattern=on 5\pgflinewidth off 2\pgflinewidth}, + 3/.style={dash pattern=on 1.5\pgflinewidth off 1.5\pgflinewidth}, + 4/.style={dash pattern=on 5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth}, + 5/.style={dash pattern=on 10\pgflinewidth off 3\pgflinewidth}, + 6/.style={dash pattern=on 10\pgflinewidth off 2\pgflinewidth on 2\pgflinewidth off 2\pgflinewidth}, + 7/.style={dash pattern=on 8\pgflinewidth off 2\pgflinewidth on + 1.5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off + 1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth} +}% + +\pgfdvdeclarestylesheet{vary thickness and dashing} +{ + default style/.style=thin, + 1/.style=thin, + 2/.style=thick, + 3/.style={ + dash pattern=on 5\pgflinewidth off 2\pgflinewidth, + thin + }, + 4/.style={ + dash pattern=on 5\pgflinewidth off 2\pgflinewidth, + thick, + }, + 5/.style={ + dash pattern=on 1.5\pgflinewidth off 1.5\pgflinewidth, + thin + }, + 6/.style={ + dash pattern=on 1.5\pgflinewidth off 1.5\pgflinewidth, + thick + }, + 7/.style={ + dash pattern=on 5\pgflinewidth off 1.5\pgflinewidth on + 1.5\pgflinewidth off 1.5\pgflinewidth, + thin + }, + 8/.style={ + dash pattern=on 5\pgflinewidth off 1.5\pgflinewidth on + 1.5\pgflinewidth off 1.5\pgflinewidth, + thick + }, + 9/.style={ + dash pattern=on 10\pgflinewidth off 3\pgflinewidth, + thin + }, + 10/.style={ + dash pattern=on 10\pgflinewidth off 3\pgflinewidth, + thick + }, + 11/.style={ + dash pattern=on 10\pgflinewidth off 2\pgflinewidth on + 2\pgflinewidth off 2\pgflinewidth, + thin + }, + 12/.style={ + dash pattern=on 10\pgflinewidth off 2\pgflinewidth on + 2\pgflinewidth off 2\pgflinewidth, + thick + }, + 13/.style={ + dash pattern=on 8\pgflinewidth off 2\pgflinewidth on + 1.5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off + 1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth, + thin + }, + 14/.style={ + dash pattern=on 8\pgflinewidth off 2\pgflinewidth on + 1.5\pgflinewidth off 1.5\pgflinewidth on 1.5\pgflinewidth off + 1.5\pgflinewidth on 1.5\pgflinewidth off 1.5\pgflinewidth, + thick + } +}% + + +\pgfdvdeclarestylesheet{strong colors} +{ + default style/.style={visualizer color=black}, + 1/.style={visualizer color=black}, + 2/.style={visualizer color=red!80!black}, + 3/.style={visualizer color=blue!80!black}, + 4/.style={visualizer color=green!60!black}, + 5/.style={visualizer color=orange!80!black}, + 6/.style={visualizer color=black!60} +}% + + +\pgfdvdeclarestylesheet{cross marks} +{ + default style/.style={mark=x,every mark/.append style=thin,mark size=2pt}, + 1/.style={mark=x,every mark/.append style=thin,mark size=2pt}, + 2/.style={mark=+,every mark/.append style=thin,mark size=2pt}, + 3/.style={mark=Mercedes star,every mark/.append style=thin,mark size=2pt}, + 4/.style={mark=Mercedes star flipped,every mark/.append style=thin,mark size=2pt}, + 5/.style={mark=star,every mark/.append style=thin,mark size=2pt}, + 6/.style={mark=10-pointed star,every mark/.append style={line width=.3pt,mark size=1.8pt}} +}% + + +\pgfdvdeclarestylesheet{* mark} +{ + default style/.style={mark=*,every mark/.append style=thin,mark size=1.4pt}, +}% + +\pgfdvdeclarestylesheet{dot mark} +{ + default style/.style={mark=*,every mark/.append style=thin,mark size=0.6pt}, +}% + + +\pgfdvdeclarestylesheet{o mark} +{ + default style/.style={mark=o,every mark/.append style=thin,mark size=1.4pt}, +}% + + + + +\def\tikzdvdeclarestylesheetcolorseries#1#2#3#4{% + \definecolorseries{tikzdvcolorseries#1}{#2}{step}[#2]{#3}{#4}% + \resetcolorseries{tikzdvcolorseries#1}% + \pgfdvdeclarestylesheet{#1} + { + default style/.style={ + /utils/exec=\colorlet{tikz@dv@temp}[rgb]{tikzdvcolorseries#1!![##1]}, + visualizer color=tikz@dv@temp + } + }% +}% + +\tikzdvdeclarestylesheetcolorseries{vary hue}{hsb}{.4,0.9,0.8}{.213,0,0}% +\tikzdvdeclarestylesheetcolorseries{shades of blue}{hsb}{.65,1.4,1}{0,-.4,-.0}% +\tikzdvdeclarestylesheetcolorseries{shades of red}{hsb}{0,1.4,1}{0,-.4,-.0}% +\tikzdvdeclarestylesheetcolorseries{gray scale}{hsb}{0,0,-.34}{0,0,.34}% + + + + + + + + +\tikzdatavisualizationset{ + xy Cartesian/.style={ + new Cartesian axis=x axis, + x axis={attribute=x,unit vector={(1pt,0cm)}}, + new Cartesian axis=y axis, + y axis={attribute=y,unit vector={(0cm,1pt)}} + }, + Xy axes/.style={x axis={#1},y axis={#1}}, + uv Cartesian/.style={ + new Cartesian axis=u axis, + u axis={attribute=u,unit vector={(1pt,0cm)}}, + new Cartesian axis=v axis, + v axis={attribute=v,unit vector={(0cm,1pt)}} + }, + uv axes/.style={u axis={#1},v axis={#1}}, +}% + +\tikzdatavisualizationset{ + xyz Cartesian cabinet/.style={ + xy Cartesian, + new Cartesian axis=z axis, + z axis={attribute=z,unit vector={(-0.353553pt,-0.353553pt)}} + }, + xyz axes/.style={x axis={#1},y axis={#1},z axis={#1}}, + uvw Cartesian cabinet/.style={ + uv Cartesian, + new Cartesian axis=w axis, + w axis={attribute=w,unit vector={(-0.353553pt,-0.353553pt)}} + } + uvw axes/.style={u axis={#1},v axis={#1},w axis={#1}}, +}% + + + + +\tikzdatavisualizationset{ + new axis system/.style n args={4}{ + #1/.style={ + #2, + #1/.cd, + #3, + /tikz/data visualization/every #1/.try, + ##1, + /tikz/data visualization/.cd, + #4, + } + } +}% + + + +\tikzdatavisualizationset{ + new axis system={school book axes}{% + xy Cartesian, + x axis={ + include value=0, + scaling=0 at 0 and \pgfkeysvalueof{/tikz/data visualization/school book axes/unit} at 1cm, + visualize axis={y axis={goto=0},style=->,padded}, + visualize ticks={common={y axis={goto=0},direction axis=y axis}, + major={tick text at low, + options at=0 as [{style={draw=none},no tick text}] + }}, + visualize grid={common={direction axis=y axis,padded}}, + ticks={step=\pgfkeysvalueof{/tikz/data visualization/school book axes/unit}}, + padding=0.75em + }, + y axis={ + include value=0, + scaling=0 at 0 and \pgfkeysvalueof{/tikz/data visualization/school book axes/unit} at 1cm, + visualize axis={x axis={goto=0},style=->,padded}, + visualize ticks={ + common={x axis={goto=0},direction axis=x axis}, + major={tick text at low,options at=0 as [{high=0,low=0,style={draw=none},node style={anchor=north east}}]} + }, + visualize grid={common={direction axis=x axis,padded}}, + ticks={step=\pgfkeysvalueof{/tikz/data visualization/school book axes/unit}}, + padding=0.75em + } + }{% + standard labels + }{% + @make labels + }, + school book axes/.cd, + standard labels/.style={ + /tikz/data visualization/@make labels/.style={ + x axis={ + visualize label={ + x axis={goto=padded max, anchor at max}, + y axis={goto=0} + } + }, + y axis={ + visualize label={ + y axis={goto=padded max, anchor at max}, + x axis={goto=0} + } + } + } + }, + unit/.initial=1, +}% + + + + + +\tikzdatavisualizationset{ + new axis system={scientific axes}{% + xy Cartesian, + every axis/.append style={style={draw=black!50}}, + every ticks/.append style={style={draw=black!50}}, + x axis={ + length=\pgfkeysvalueof{/tikz/data visualization/scientific axes/width}, + ticks + }, + y axis={ + length=\pgfkeysvalueof{/tikz/data visualization/scientific axes/height}, + ticks + } + }{% + standard labels, + outer ticks, + }{% + @make axes, + @make labels + }, + scientific axes/.cd, + width/.initial=5cm, + height/.initial=0.618*\pgfkeysvalueof{/tikz/data visualization/scientific axes/width},% + outer ticks/.style={ + /tikz/data visualization/@make axes/.style={ + x axis={ + visualize ticks={common={y axis={goto=padded min},direction axis=y axis,high=0pt},major={tick text at low}}, + visualize ticks={common={y axis={goto=padded max},direction axis=y axis,low=0pt}}, + visualize axis={y axis={goto=padded min},padded}, + visualize axis={y axis={goto=padded max},padded}, + visualize grid={common={direction axis=y axis,padded}}, + }, + y axis={ + visualize ticks={common={x axis={goto=padded min},direction axis=x axis,high=0pt},major={tick text at low}}, + visualize ticks={common={x axis={goto=padded max},direction axis=x axis,low=0pt}}, + visualize axis={x axis={goto=padded min},padded}, + visualize axis={x axis={goto=padded max},padded}, + visualize grid={common={direction axis=x axis,padded}}, + } + } + }, + inner ticks/.style={ + /tikz/data visualization/@make axes/.style={ + x axis={ + visualize ticks={common={y axis={goto=padded min},direction axis=y axis,low=0pt},major={tick text at low}}, + visualize ticks={common={y axis={goto=padded max},direction axis=y axis,high=0pt}}, + visualize axis={y axis={goto=padded min},padded}, + visualize axis={y axis={goto=padded max},padded}, + visualize grid={common={direction axis=y axis,padded}}, + }, + y axis={ + visualize ticks={common={x axis={goto=padded min},direction axis=x axis,low=0pt},major={tick text at low}}, + visualize ticks={common={x axis={goto=padded max},direction axis=x axis,high=0pt}}, + visualize axis={x axis={goto=padded min},padded}, + visualize axis={x axis={goto=padded max},padded}, + visualize grid={common={direction axis=x axis,padded}}, + } + } + }, + clean/.style={ + /tikz/data visualization/@make axes/.style={ + x axis={ + visualize ticks={common={y axis={goto=padded min},direction axis=y axis,high=0pt},major={tick text at low}}, + visualize axis={y axis={goto=padded min}}, + visualize axis={y axis={goto=min}, style={black!25, line cap=rect}}, + visualize axis={y axis={goto=max}, style={black!25, line cap=rect}}, + visualize grid={common={direction axis=y axis}}, + padding=.5em, + }, + y axis={ + visualize ticks={common={x axis={goto=padded min},direction axis=x axis,high=0pt},major={tick text at low}}, + visualize axis={x axis={goto=padded min}}, + visualize axis={x axis={goto=min}, style={black!25, line cap=rect}}, + visualize axis={x axis={goto=max}, style={black!25, line cap=rect}}, + visualize grid={common={direction axis=x axis}}, + padding=.5em + }, + } + }, + standard labels/.style={ + /tikz/data visualization/@make labels/.style={ + x axis={ + visualize label={ + x axis={goto pos=.5}, + node style={ + at={(0,0 |- data visualization bounding box.south)}, + below + } + } + }, + y axis={ + visualize label={ + y axis={goto pos=.5}, + node style={ + at={(0,0 -| data visualization bounding box.west)}, + rotate=90, + above} + } + } + } + }, + upright labels/.style={ + /tikz/data visualization/@make labels/.style={ + x axis={ + visualize label={ + x axis={goto pos=.5}, + node style={ + at={(0,0 |- data visualization bounding box.south)}, + below + } + } + }, + y axis={ + visualize label={ + y axis={goto pos=.5}, + node style={ + at={(0,0 -| data visualization bounding box.west)}, + left + } + } + } + } + }, + end labels/.style={ + /tikz/data visualization/@make labels/.style={ + x axis={ + visualize label={ + y axis={goto=padded min}, + node style={ + at={(0,0 -| data visualization bounding box.east)}, + right + } + } + }, + y axis={ + visualize label={ + x axis={goto=padded min}, + node style={ + at={(0,0 |- data visualization bounding box.north)}, + above + } + } + } + } + } +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.formats.functions.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.formats.functions.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..54966a83768e6e202cbec65c07642758ab6cf090 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.formats.functions.code.tex @@ -0,0 +1,8 @@ + +\ProvidesFileRCS{tikzlibrarydatavisualization.formats.functions.code.tex} + +\usetikzlibrary{datavisualization}% +\usepgflibrary{datavisualization.formats.functions}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.polar.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.polar.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..b4b707a8204b2e08785dc277a0d6a177895d52df --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.polar.code.tex @@ -0,0 +1,527 @@ + +\ProvidesFileRCS{tikzlibrarydatavisualization.polar.code.tex} + +\usetikzlibrary{datavisualization}% +\usepgflibrary{datavisualization.polar}% + + +\tikzdatavisualizationset{% + new polar axes/.style 2 args={ + new axis base=#1, + #1={attribute=angle}, + new axis base=#2, + #2={attribute=radius}, + #2/scaling/default=0 at 0 and 1 at 1cm, + new object={ + store=/tikz/data visualization/#1/polar transformer, + class=polar transformer, + arg1/.expanded=\pgfkeysvalueof{/tikz/data visualization/angle axis/attribute}/scaled, + arg2/.expanded=\pgfkeysvalueof{/tikz/data visualization/radius axis/attribute}/scaled, + arg3 from key=/tikz/data visualization/#1/unit vector 0 degrees, + arg4 from key=/tikz/data visualization/#1/unit vector 90 degrees + }, + /tikz/data visualization/#1/unit vector 0 degrees/.initial=\pgfqpoint{1pt}{0pt}, + /tikz/data visualization/#1/unit vector 90 degrees/.initial=\pgfqpoint{0pt}{1pt}, + }, + new polar axes/.default={angle axis}{radius axis} +}% +\def\tikz@lib@dv@polar@a#1{ + \pgfkeyssetvalue{\tikz@dv@axis/unit vector 0 degrees}{#1} +}% +\def\tikz@lib@dv@polar@b#1{ + \pgfkeyssetvalue{\tikz@dv@axis/unit vector 90 degrees}{#1} +}% + + + + +\tikzset{ + /tikz/data visualization/axis options/.cd, + unit vectors/.code 2 args={ + \tikz@scan@one@point\tikz@lib@dv@polar@a#1 + \tikz@scan@one@point\tikz@lib@dv@polar@b#2 + }, + degrees/.style={\tikz@dv@axis/scaling=0 at 0 and 1 at 1}, + radians/.style={\tikz@dv@axis/scaling=0 at 0 and 0.03141592653589793 at 1.8}, +}% + + + +\tikzdatavisualizationset{ + new axis system={scientific polar axes}{% + new polar axes, + angle axis={attribute=angle}, + radius axis={attribute=radius}, + every axis/.append style={style={draw=black!50}}, + every ticks/.append style={style={draw=black!50}}, + }{% + 0 to 360,% + outer ticks, + }{% + @make axes, + scientific polar axes/@setup axes, + /utils/exec={ + \edef\pgf@marshal{\noexpand\tikzdatavisualizationset{\pgfkeysvalueof{/tikz/data visualization/@which visualize radius axis}/.list={\pgfkeysvalueof{/tikz/data visualization/\pgfkeysvalueof{/tikz/data visualization/@which radius axes at}}}}} + \pgf@marshal + }, + @make labels + }, + @which radius axes at/.initial=@inner radius axes at, + @which visualize radius axis/.initial=@visualize radius axis, + @inner radius axes at/.initial=, + @clean radius axes at/.initial=, + @visualize radius axis/.style 2 args={ + radius axis={ + visualize axis={angle axis={goto=#1},high=padded max,low=0}, + visualize ticks={ + common={angle axis={goto=#1}, direction axis=angle axis}, + major={tick text at #2, + options at=0 as [{style={draw=none},no tick text}] + } + } + } + }, + @visualize clean radius axis/.style n args={5}{ + radius axis={ + visualize axis={angle + axis={goto=#1},high=max,low=0,style={black!25,line cap=rect}}, + visualize axis={angle + axis={goto=#1},high=max,low=0,style={line cap=rect,#4}}, + visualize ticks={ + style={#4}, + common={angle axis={goto=#1}, direction axis=angle axis, #3=0}, + major={tick text at #2,#5} + } + } + }, + @visualize zero/.style={@inner visualize zero={#1}}, + @clean visualize zero/.style={}, + @inner visualize zero/.style={ + radius axis={ + visualize ticks={ + common={angle axis={goto=0}, direction axis=angle axis}, + major={tick text at low,low=0,high=0,at=0 as + [{style={draw=none},node style={anchor=#1}}] + } + } + } + }, + @degrees/.style={ + angle axis={degrees, ticks={step=15, tick suffix=$^\circ$, major={ + options at=360 as [{style={draw=none},no tick text}], + options at=-180 as [{style={draw=none},no tick text}]}}} + }, + @rad/.style={ + angle axis={radians, ticks={ + step=(pi/12), + node style={ + /pgf/number format/frac, + /pgf/number format/frac shift={1} + }, + tick typesetter/.code={% + \pgfmathsetmacro{\tikz@lib@dv@pol}{round(####1*3.819718634205488)/12}% + \pgfmathapproxequalto{\tikz@lib@dv@pol}{0}% + \ifdim\pgfmathresult pt=1.0pt% + $0$% + \else% + \pgfmathapproxequalto{\tikz@lib@dv@pol}{1}% + \ifdim\pgfmathresult pt=1.0pt% + $\pi$% + \else + \pgfmathapproxequalto{\tikz@lib@dv@pol}{-1}% + \ifdim\pgfmathresult pt=1.0pt% + $-\pi$% + \else% + \pgfmathprintnumber{\tikz@lib@dv@pol}$\pi$% + \fi% + \fi% + \fi% + }, + major={ + options at=6.2831985e0 as [{style={draw=none},no tick text}], + options at=6.2831192e0 as [{style={draw=none},no tick text}], + options at=6.2830794e0 as [{style={draw=none},no tick text}], + options at=6.2828787e0 as [{style={draw=none},no tick text}], + options at=6.2831598e0 as [{style={draw=none},no tick text}], + options at=-3.1415991e0 as [{style={draw=none},no tick text}], + options at=-3.1415802e0 as [{style={draw=none},no tick text}], + options at=-3.1415602e0 as [{style={draw=none},no tick text}], + options at=-3.14153961e0 as [{style={draw=none},no tick text}], + options at=-3.1414406e0 as [{style={draw=none},no tick text}], + } + } + } + }, + @make labels/.style={}, +}% + +\tikzdatavisualizationset{ + scientific polar axes/.cd, + outer ticks/.style={ + /tikz/data visualization/@make axes/.style={ + radius axis={ + min value=0, + length=\pgfkeysvalueof{/tikz/data visualization/scientific polar axes/radius}, + padding=0em, + ticks={few}, + visualize grid={common={direction axis=angle axis,low=min,high=max}}, + }, + angle axis={ + visualize axis={radius axis={goto=padded max},low=min,high=max}, + visualize ticks={common={radius axis={goto=padded max},direction + axis=radius axis},common={low=0},major={tick text at high}}, + visualize grid={common={direction axis=radius axis},low=0,high=padded max}, + } + }, + /tikz/data visualization/@which radius axes at=@inner radius axes at, + /tikz/data visualization/@which visualize radius axis=@visualize radius axis, + /tikz/data visualization/@visualize zero/.style={@inner visualize zero={##1}}, + }, + inner ticks/.style={ + /tikz/data visualization/@make axes/.style={ + radius axis={ + min value=0, + length=\pgfkeysvalueof{/tikz/data visualization/scientific polar axes/radius}, + padding=0em, + ticks={few}, + visualize grid={common={direction axis=angle axis,low=min,high=max}}, + }, + angle axis={ + visualize axis={radius axis={goto=padded max},low=min,high=max}, + visualize ticks={common={radius axis={goto=padded max},direction + axis=radius axis},common={high=0},major={tick text at high}}, + visualize grid={common={direction axis=radius axis},low=0,high=padded max}, + } + }, + /tikz/data visualization/@which radius axes at=@inner radius axes at, + /tikz/data visualization/@which visualize radius axis=@visualize radius axis, + /tikz/data visualization/@visualize zero/.style={@inner visualize zero={##1}}, + }, + clean/.style={ + /tikz/data visualization/@make axes/.style={ + radius axis={ + min value=0, + length=\pgfkeysvalueof{/tikz/data visualization/scientific polar axes/radius}, + padding=.5em, + ticks={few}, + visualize grid={common={direction axis=angle axis,low=min,high=max}}, + }, + angle axis={ + padding=.5em, + visualize axis={radius axis={goto=max}, style={black!25, line cap=rect},low=min,high=max}, + visualize axis={radius axis={goto=padded max}, style={line cap=rect}, low=min,high=max}, + visualize ticks={common={radius axis={goto=padded max}, direction axis=radius axis},common={low=0},major={tick text at high}}, + visualize grid={common={direction axis=radius axis},low=0,high=max}, + } + }, + /tikz/data visualization/@which radius axes at=@clean radius axes at, + /tikz/data visualization/@which visualize radius axis=@visualize clean radius axis, + /tikz/data visualization/@visualize zero/.style={@clean visualize zero={##1}}, + }, + radius/.initial=3.25cm, + 0 to pi half/.style={ + @setup axes/.style={ + angle axis={min value=0, max value=1.570796326794897}, + @rad, + @visualize zero=north east, + @inner radius axes at={{0}{low},{1.570796326794897}{high}}, + @clean radius axes at={% + {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {1.570796326794897}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + 0 to 90/.style={ + @setup axes/.style={ + angle axis={min value=0, max value=90}, + @degrees, + @visualize zero=north east, + @inner radius axes at={{0}{low},{90}{high}}, + @clean radius axes at={% + {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {90}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + quadrant/.style={ + @setup axes/.style={ + angle axis={scaling=min at 0 and max at 90, ticks}, + @visualize zero=north east, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + quadrant clockwise/.style={ + @setup axes/.style={ + angle axis={scaling=min at 90 and max at 0, ticks}, + @visualize zero=north east, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {min}{low}{high}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + -pi half to 0/.style={ + @setup axes/.style={ + angle axis={min value=-1.570796326794897, max value=0}, + @rad, + @visualize zero=south east, + @inner radius axes at={{-1.570796326794897}{low},{0}{high}}, + @clean radius axes at={% + {-1.570796326794897}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {0}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + -90 to 0/.style={ + @setup axes/.style={ + angle axis={min value=-90, max value=0}, + @degrees, + @visualize zero=south east, + @inner radius axes at={{-90}{low},{0}{high}}, + @clean radius axes at={% + {-90}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {0}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + fourth quadrant/.style={ + @setup axes/.style={ + angle axis={scaling=min at -90 and max at 0, ticks}, + @visualize zero=south east, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + fourth quadrant clockwise/.style={ + @setup axes/.style={ + angle axis={scaling=min at 0 and max at -90, ticks}, + @visualize zero=south east, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {max}{high}{low}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding max}}{} + } + } + }, + 0 to pi/.style={ + @setup axes/.style={ + angle axis={min value=0, max value=3.141592653589793}, + @rad, + @visualize zero=north, + @inner radius axes at={{0}{low},{1.570796326794897}{high},{3.141592653589793}{high}}, + @clean radius axes at={% + {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {3.141592653589793}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + 0 to 180/.style={ + @setup axes/.style={ + angle axis={min value=0, max value=180}, + @degrees, + @visualize zero=north, + @inner radius axes at={{0}{low},{90}{high},{180}{high}}, + @clean radius axes at={% + {0}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {180}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + upper half/.style={ + @setup axes/.style={ + angle axis={scaling=min at 0 and max at 180, ticks}, + @visualize zero=north, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + upper half clockwise/.style={ + @setup axes/.style={ + angle axis={scaling=min at 180 and max at 0, ticks}, + @visualize zero=north, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{yshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{yshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + lower half/.style={ + @setup axes/.style={ + angle axis={scaling=min at -180 and max at 0, ticks}, + @visualize zero=south, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{yshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + lower half clockwise/.style={ + @setup axes/.style={ + angle axis={scaling=min at 0 and max at -180, ticks}, + @visualize zero=south, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{yshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{yshift=\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + -pi half to pi half/.style={ + @setup axes/.style={ + @rad, + angle axis={min value=-1.570796326794897, max value=1.570796326794897}, + @visualize zero=east, + @inner radius axes at={{0}{low},{1.570796326794897}{low},{-1.570796326794897}{high}}, + @clean radius axes at={% + {-1.570796326794897}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {1.570796326794897}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + -90 to 90/.style={ + @setup axes/.style={ + angle axis={min value=-90, max value=90}, + @degrees, + @visualize zero=east, + @inner radius axes at={{-90}{low},{0}{low},{90}{high}}, + @clean radius axes at={% + {-90}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {90}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + right half/.style={ + @setup axes/.style={ + angle axis={scaling=min at -90 and max at 90, ticks}, + @visualize zero=east, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + right half clockwise/.style={ + @setup axes/.style={ + angle axis={scaling=min at 90 and max at -90, ticks}, + @visualize zero=east, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{xshift=\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{xshift=-\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + left half/.style={ + @setup axes/.style={ + angle axis={scaling=min at 90 and max at 270, ticks}, + @visualize zero=west, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{xshift=\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + left half clockwise/.style={ + @setup axes/.style={ + angle axis={scaling=min at 270 and max at 90, ticks}, + @visualize zero=west, + @inner radius axes at={{min}{low},{max}{high}}, + @clean radius axes at={% + {min}{low}{high}{xshift=-\pgfkeysvalueof{/tikz/data visualization/angle axis/padding min}}{},% + {max}{high}{low}{xshift=\pgfkeysvalueof{/tikz/data + visualization/angle axis/padding max}}{options at=0 as + [{style={draw=none}, no tick text}]} + } + } + }, + 0 to 2pi/.style={ + @setup axes/.style={ + angle axis={min value=0, max value=6.283185307179586}, + @rad, + @visualize zero=north east, + @inner radius axes at={{0}{low},{1.570796326794897}{high},{3.141592653589793}{high},{4.71238898038469}{low}}, + @clean radius axes at={{0}{low}{high}{}{}} + } + }, + -pi to pi/.style={ + @setup axes/.style={ + angle axis={min value=-3.141592653589793, max value=3.141592653589793}, + @rad, + @visualize zero=north east, + @inner radius axes at={{0}{low},{1.570796326794897}{high},{3.141592653589793}{high},{-1.57079632679489}{low}}, + @clean radius axes at={{0}{low}{high}{}{}} + } + }, + 0 to 360/.style={ + @setup axes/.style={ + angle axis={min value=0, max value=360}, + @degrees, + @visualize zero=north east, + @inner radius axes at={{0}{low},{90}{high},{180}{high},{270}{low}}, + @clean radius axes at={{0}{low}{high}{}{}} + } + }, + -180 to 180/.style={ + @setup axes/.style={ + angle axis={min value=-180, max value=180}, + @degrees, + @visualize zero=north east, + @inner radius axes at={{0}{low},{90}{high},{180}{high},{-90}{low}}, + @clean radius axes at={{0}{low}{high}{}{}} + } + }, +}% + + + + + +\tikzset{ + /tikz/data visualization/axis options/.cd, + percent/.style={\tikz@dv@axis/scaling=0 at 0 and 1 at 3.6}, + full circle/.style={\tikz@dv@axis/scaling=min at 0 and max at 360}, + half circle/.style={\tikz@dv@axis/scaling=min at 0 and max at 180}, + quarter circle/.style={\tikz@dv@axis/scaling=min at 0 and max at 90} +}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.sparklines.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.sparklines.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..1bee17cdbf8812b8194925c866c0a83ab0f972d9 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/datavisualization/tikzlibrarydatavisualization.sparklines.code.tex @@ -0,0 +1,26 @@ + +\ProvidesFileRCS{tikzlibrarydatavisualization.sparklines.code.tex} + +\usetikzlibrary{datavisualization}% + + + + + +\tikzdatavisualizationset{ + spark line/.style={ + xy Cartesian, + x axis={ + unit length={1pt} + }, + y axis={ + scaling={min at -0.2em and max at 0.8em} + }, + new line plot, + every spark line plot/.try + } +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..46287a7552a777df4ad7b8246e493d25e7218321 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.code.tex @@ -0,0 +1,2275 @@ + +\ProvidesFileRCS{tikzlibrarygraphs.code.tex} + + + +\def\tikzgraphsset{\pgfqkeys{/tikz/graphs}}% + +\tikzgraphsset{ + new ->/.code n args={4}{% + \path [->,every new ->/.try] + (#1\tikzgraphleftanchor) + edge[#3] #4 + (#2\tikzgraphrightanchor);}, + new --/.code n args={4}{ + \path [-,every new --/.try] + (#1\tikzgraphleftanchor) + edge[#3] #4 + (#2\tikzgraphrightanchor);}, + new <->/.code n args={4}{ + \path [<->,every new <->/.try] + (#1\tikzgraphleftanchor) + edge[#3] #4 + (#2\tikzgraphrightanchor);}, + new -!-/.code n args={4}{}, + new <-/.code n args={4}{% + \path [<-,every new <-/.try] + (#1\tikzgraphleftanchor) + edge[#3] #4 + (#2\tikzgraphrightanchor); + } +}% + + +\def\tikz@lib@graph@store@anchor#1#2{% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \let#2\tikz@temp% + \else% + \def\tikz@temp{.#1}% + \let#2\tikz@temp% + \fi% +}% + +\tikzgraphsset{ + default edge kind/.initial=--, + --/.style={default edge kind=--}, + ->/.style={default edge kind=->}, + <-/.style={default edge kind=<-}, + <->/.style={default edge kind=<->}, + -!-/.style={default edge kind=-!-}, + default edge operator/.initial=matching and star, + left anchor/.code=\tikz@lib@graph@store@anchor{#1}{\tikzgraphleftanchor}, + right anchor/.code=\tikz@lib@graph@store@anchor{#1}{\tikzgraphrightanchor}, + left anchor=, + right anchor= +}% + + + +\tikzgraphsset{ + use existing nodes/.is if=tikz@lib@graph@all +}% + +\tikzset{ + new set/.code={ + \expandafter\global\expandafter\let\csname tikz@lg@node@set #1\endcsname\pgfutil@empty% + }, + set/.code={ + \tikz@fig@mustbenamed% + \ifcsname tikz@lg@node@set #1\endcsname\else + \tikzerror{Undefined set `#1'}% + \fi + \expandafter\def\expandafter\tikz@alias\expandafter{\tikz@alias% + \expandafter\def\expandafter\pgf@temp\expandafter{\csname tikz@lg@node@set #1\endcsname}% + \expandafter\expandafter\expandafter\pgfutil@g@addto@macro\expandafter\pgf@temp\expandafter{\expandafter\tikz@lg@do\expandafter{\tikz@fig@name}}% + }% + },% +}% + +\newif\iftikz@lib@graph@all + + +\tikzgraphsset{ + simple/.code={ + \iftikz@lib@graph@simple% + \else + \tikz@lib@graph@simpletrue% + \pgfkeysalso{operator=\tikz@lib@graph@simple@done}% + \fi% + }, + multi/.code={ + \tikz@lib@graph@simplefalse% + } +}% + +\newif\iftikz@lib@graph@simple + +\def\tikz@lib@graph@set@simple@edge#1#2#3#4#5{% + \ifcsname tikz@lg@e@#3@#2\endcsname% + \expandafter\global\expandafter\let\csname tikz@lg@e@#3@#2\endcsname\relax% + \fi% + \expandafter\gdef\csname tikz@lg@e@#2@#3\endcsname{\tikz@lib@graph@make@simple@edge{#1}{#2}{#3}{#4}{#5}}% +}% + +\def\tikz@lib@graph@make@simple@edge#1#2#3#4#5{% + \pgfqkeys{/tikz/graphs}{new #1={#2}{#3}{#4}{#5}}% +}% + + +\def\tikz@lib@graph@simple@done{% + \tikz@lib@graph@pack@node@list% + {% + \let\tikz@lg@do\tikz@lib@graph@simple@node% + \tikz@lib@graph@node@list + }% +}% + +\def\tikz@lib@graph@simple@node#1{% + {% + \def\tikz@lib@graph@simple@from@node{#1}% + \let\tikz@lg@do\tikz@lib@graph@simple@other@node% + \tikz@lib@graph@node@list% + }% +}% + +\def\tikz@lib@graph@simple@other@node#1{% + \ifcsname tikz@lg@e@\tikz@lib@graph@simple@from@node @#1\endcsname% + \csname tikz@lg@e@\tikz@lib@graph@simple@from@node @#1\endcsname% + \expandafter\global\expandafter\let\csname tikz@lg@e@\tikz@lib@graph@simple@from@node @#1\endcsname\relax% + \fi% +}% + + + +\tikzgraphsset{ + @nodes styling/.style=, + nodes/.style={/tikz/graphs/@nodes styling/.append style={,#1}}, + @edges styling/.initial=, + edges/.style={/tikz/graphs/@edges styling/.append={,#1}}, + edge/.style={edges={#1}}, + @edges node/.initial=, + edge node/.style={/tikz/graphs/@edges node/.append={#1}}, + edge label/.style={/tikz/graphs/@edges node/.append={node[auto]{#1}}}, + edge label'/.style={/tikz/graphs/@edges node/.append={node[auto,swap]{#1}}}, + @operators/.initial=, + operator/.style={/tikz/graphs/@operators/.append={#1}}, + @extra group options/.style=, +}% + + +\def\tikzgraphinvokeoperator#1{% + {% + \pgfkeyslet{/tikz/graphs/@operators}\pgfutil@empty% + \pgfkeys{/tikz/graphs/.cd,#1}% + \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@temp% + \global\let\tikz@lib@graph@temp\tikz@lib@graph@temp% + }% + \tikz@lib@graph@temp% + \global\let\tikz@lib@graph@temp\relax% +}% + + + +\def\tikz@lib@graph@parser{% + \pgfutil@ifnextchar[{\tikz@lib@graph@parser@}{\tikz@lib@graph@parser@[]}% +}% + +\def\tikz@lib@graph@parser@[#1]{% + \setbox\tikz@whichbox=\hbox\bgroup% + \unhbox\tikz@whichbox% + \hbox\bgroup + \bgroup% + \pgfinterruptpath% + \scope[graphs/.cd,@graph drawing setup/.try,@operators=,every graph/.try,#1]% + \begingroup% + \iftikz@graph@quick% + \expandafter\tikz@lib@graphs@parse@quick@graph% + \else% + \expandafter\tikz@lib@graphs@normal@main% + \fi% +}% + +\long\def\tikz@lib@graphs@normal@main#1{% + \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@outer@operators% + \let\tikz@lib@graph@options\pgfutil@empty% + \let\tikz@lib@graph@node@list\pgfutil@empty% + \pgfkeyssetvalue{/tikz/graphs/placement/depth}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/width}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/level}{0}% + \tikz@lib@graph@start@hint@group% + \tikz@lib@graph@parse@group{#1}% + \tikz@lib@graph@end@hint@group + \tikz@lib@graph@outer@operators% + \let\tikz@lg@do=\tikz@lib@graph@cleanup% + \tikz@lib@graph@node@list% + \tikz@lib@graph@main@done% +}% + +\def\tikz@lib@graph@main@done{% + \endgroup% + \endscope% + \endpgfinterruptpath% + \egroup + \egroup% + \egroup% + \tikz@lib@graph@parser@done% +}% + + + + + +\def\tikz@lib@graph@start@hint@group{% + \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/local width}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/chain count}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/element count}{0}% +}% + +\def\tikz@lib@graph@end@hint@group{% + \xdef\tikz@lib@graph@group@depth{\pgfkeysvalueof{/tikz/graphs/placement/local depth}} + \xdef\tikz@lib@graph@group@width{\pgfkeysvalueof{/tikz/graphs/placement/local width}} +}% + +\def\tikz@lib@graph@hint@aftergroup{% + \pgfkeysgetvalue{/tikz/graphs/placement/width}\tikz@temp@h% + \pgfkeysgetvalue{/tikz/graphs/placement/local width}\tikz@temp@lh% + \pgfkeysgetvalue{/tikz/graphs/placement/local depth}\tikz@temp@lw% + \pgfmathsetmacro\tikz@temp@h{\tikz@lib@graph@group@width+\tikz@temp@h} + \pgfmathsetmacro\tikz@temp@lh{\tikz@lib@graph@group@width+\tikz@temp@lh} + \pgfmathsetmacro\tikz@temp@lw{max(\tikz@lib@graph@group@depth,\tikz@temp@lw)} + \pgfkeyslet{/tikz/graphs/placement/width}\tikz@temp@h% + \pgfkeyslet{/tikz/graphs/placement/local width}\tikz@temp@lh% + \pgfkeyslet{/tikz/graphs/placement/local depth}\tikz@temp@lw% + \pgfkeysgetvalue{/tikz/graphs/placement/element count}\tikz@temp% + \c@pgf@counta=\tikz@temp\relax% + \advance\c@pgf@counta by1\relax% + \edef\tikz@temp{\the\c@pgf@counta}% + \pgfkeyslet{/tikz/graphs/placement/element count}\tikz@temp% +}% + +\def\tikz@lib@graph@placement@update{% + \pgfkeys{/tikz/graphs/placement/logical node depth/.expand once=\tikz@lib@graph@name} + \let\tikz@lib@graph@node@depth\pgfmathresult + \pgfkeys{/tikz/graphs/placement/logical node width/.expand once=\tikz@lib@graph@name} + \let\tikz@lib@graph@node@width\pgfmathresult + \pgfkeysgetvalue{/tikz/graphs/placement/width}\tikz@temp@h% + \pgfkeysgetvalue{/tikz/graphs/placement/local width}\tikz@temp@lh% + \pgfkeysgetvalue{/tikz/graphs/placement/local depth}\tikz@temp@lw% + \pgfmathsetmacro\tikz@temp@h{\tikz@lib@graph@node@width+\tikz@temp@h} + \pgfmathsetmacro\tikz@temp@lh{\tikz@lib@graph@node@width+\tikz@temp@lh} + \pgfmathsetmacro\tikz@temp@lw{max(\tikz@lib@graph@node@depth,\tikz@temp@lw)} + \pgfkeyslet{/tikz/graphs/placement/width}\tikz@temp@h% + \pgfkeyslet{/tikz/graphs/placement/local width}\tikz@temp@lh% + \pgfkeyslet{/tikz/graphs/placement/local depth}\tikz@temp@lw% + \pgfkeysgetvalue{/tikz/graphs/placement/element count}\tikz@temp% + \c@pgf@counta=\tikz@temp\relax% + \advance\c@pgf@counta by1\relax% + \edef\tikz@temp{\the\c@pgf@counta}% + \pgfkeyslet{/tikz/graphs/placement/element count}\tikz@temp% +}% + +\def\tikz@lib@graph@placement@after@chain@update{% + \pgfkeysgetvalue{/tikz/graphs/placement/depth}\tikz@temp@w% + \pgfkeysgetvalue{/tikz/graphs/placement/local width}\tikz@temp@lh% + \pgfkeysgetvalue{/tikz/graphs/placement/local depth}\tikz@temp@lw% + \pgfmathsetmacro\tikz@temp@w{\tikz@lib@graph@chain@depth+\tikz@temp@w}% + \pgfmathsetmacro\tikz@temp@lw{\tikz@lib@graph@chain@depth+\tikz@temp@lw}% + \pgfmathsetmacro\tikz@temp@lh{max(\tikz@lib@graph@chain@width,\tikz@temp@lh)}% + \pgfkeyslet{/tikz/graphs/placement/depth}\tikz@temp@w% + \pgfkeyslet{/tikz/graphs/placement/local width}\tikz@temp@lh% + \pgfkeyslet{/tikz/graphs/placement/local depth}\tikz@temp@lw% + \pgfkeysgetvalue{/tikz/graphs/placement/chain count}\tikz@temp% + \c@pgf@counta=\tikz@temp\relax% + \advance\c@pgf@counta by1\relax% + \edef\tikz@temp{\the\c@pgf@counta}% + \pgfkeyslet{/tikz/graphs/placement/chain count}\tikz@temp% +}% + + + +\long\def\tikz@lib@graph@parse@group#1{ + \let\tikz@lib@graph@group@qa\pgfutil@empty% + \let\tikz@lib@graph@group@q\pgfutil@empty% + \let\tikz@lib@graph@group@c\pgfutil@empty% + \let\tikz@lib@graph@group@cont\pgfutil@empty% + \let\tikz@lib@graph@group@conta\pgfutil@empty% + \tikz@lib@graph@group@check#1\par\pgf@stop@eogroup% +}% + + + +\def\tikz@lib@graph@group@check{% + \pgfutil@ifnextchar[\tikz@lib@graph@group@opt{\tikz@lib@graph@group@opt[]}% +}% + +\def\tikz@lib@graph@group@opt[#1]{% + \let\tikz@lib@graph@parse@extras\pgfutil@empty% + \tikzgraphsset{ + @operators=, + every group/.try, + @extra group options, + @extra group options/.style=,% + #1}% + \expandafter\tikz@lib@graph@par\tikz@lib@graph@parse@extras% +}% + +\tikzgraphsset{ + parse/.code={\expandafter\def\expandafter\tikz@lib@graph@parse@extras\expandafter{\tikz@lib@graph@parse@extras#1}}, +}% + + + + +\def\tikz@lib@graph@par{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@par@@}{\tikz@lib@graph@par@}% +}% +\long\def\tikz@lib@graph@par@#1\par{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \expandafter\tikz@lib@graph@quotes\tikz@lib@graph@group@c#1"}{% + \expandafter\def\expandafter\tikz@lib@graph@group@c\expandafter{\tikz@lib@graph@group@c#1}% + \tikz@lib@graph@par% + }% +}% +\long\def\tikz@lib@graph@par@@#1{% + \expandafter\def\expandafter\tikz@lib@graph@group@c\expandafter{\tikz@lib@graph@group@c{#1}}% + \tikz@lib@graph@par +}% + + + +\def\tikz@lib@graph@quotes{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@quotes@@}{\tikz@lib@graph@quotes@}% +}% +\def\tikz@lib@graph@quotes@#1"{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \tikz@lib@graph@passon{#1}% + }{% + \expandafter\def\expandafter\tikz@lib@graph@group@q\expandafter{\tikz@lib@graph@group@q#1"}% + \tikz@lib@graph@quotes@cont% + }% +}% + +\def\tikz@lib@graph@quotes@cont#1"#2"{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \tikz@lib@graph@passon{{#1}"#2}}{% + \expandafter\def\expandafter\tikz@lib@graph@group@q\expandafter{\tikz@lib@graph@group@q{#1}"#2"}% + \tikz@lib@graph@quotes@cont}% +}% + +\def\tikz@lib@graph@quotes@@#1{% + \expandafter\def\expandafter\tikz@lib@graph@group@q\expandafter{\tikz@lib@graph@group@q{#1}}% + \tikz@lib@graph@quotes% +}% + + + +{% + \catcode`\"=13\relax + + \gdef\tikz@lib@graph@passon#1{\expandafter\tikz@lib@graph@quotesactive\tikz@lib@graph@group@q#1"}% + + \gdef\tikz@lib@graph@quotesactive{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@quotesactive@@}{\tikz@lib@graph@quotesactive@}% + }% + \gdef\tikz@lib@graph@quotesactive@#1"{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \expandafter\tikz@lib@graph@encloser\tikz@lib@graph@group@qa#1[% + }{% + \expandafter\def\expandafter\tikz@lib@graph@group@qa\expandafter{\tikz@lib@graph@group@qa#1"}% + \tikz@lib@graph@quotesactive@cont% + }% + }% + + \gdef\tikz@lib@graph@quotesactive@cont#1"#2"{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \expandafter\tikz@lib@graph@encloser\tikz@lib@graph@group@qa{#1}"#2[}{% + \expandafter\def\expandafter\tikz@lib@graph@group@qa\expandafter{\tikz@lib@graph@group@qa{#1}"#2"}% + \tikz@lib@graph@quotesactive@cont}% + }% + + \gdef\tikz@lib@graph@quotesactive@@#1{% + \expandafter\def\expandafter\tikz@lib@graph@group@qa\expandafter{\tikz@lib@graph@group@qa{#1}}% + \tikz@lib@graph@quotesactive% + }% +}% + + + + +\def\tikz@lib@graph@encloser{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@encloser@@}{\tikz@lib@graph@encloser@}% +}% +\def\tikz@lib@graph@encloser@#1[{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \expandafter\tikz@lib@graph@semi\tikz@lib@graph@group@cont#1;% + }{% + \expandafter\def\expandafter\tikz@lib@graph@group@cont\expandafter{\tikz@lib@graph@group@cont#1[}% + \tikz@lib@graph@encloser@cont% + }% +}% + +\def\tikz@lib@graph@encloser@cont#1]#2[{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \expandafter\tikz@lib@graph@semi\tikz@lib@graph@group@cont{#1}]#2;}{% + \expandafter\def\expandafter\tikz@lib@graph@group@cont\expandafter{\tikz@lib@graph@group@cont{#1}]#2[}% + \tikz@lib@graph@encloser@cont}% +}% + +\def\tikz@lib@graph@encloser@@#1{% + \expandafter\def\expandafter\tikz@lib@graph@group@cont\expandafter{\tikz@lib@graph@group@cont{#1}}% + \tikz@lib@graph@encloser% +}% + + + + + +\def\tikz@lib@graph@semi{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@semi@@}{\tikz@lib@graph@semi@}% +}% +\def\tikz@lib@graph@semi@#1;{% + \pgfutil@ifnextchar\pgf@stop@eogroup{% + \expandafter\tikz@lib@graph@main@parser\tikz@lib@graph@group@conta#1,}{% + \expandafter\def\expandafter\tikz@lib@graph@group@conta\expandafter{\tikz@lib@graph@group@conta#1,}% + \tikz@lib@graph@semi% + }% +}% +\def\tikz@lib@graph@semi@@#1{% + \expandafter\def\expandafter\tikz@lib@graph@group@conta\expandafter{\tikz@lib@graph@group@conta{#1}}% + \tikz@lib@graph@semi% +}% + + + +\def\tikz@lib@graph@main@parser{% + \begingroup% + \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/local width}{0}% + \let\tikz@lib@graph@stored@actions\pgfutil@empty% + \let\tikz@lib@graph@node@list\pgfutil@empty% + \tikz@lib@graph@main@parser@start% +}% +\def\tikz@lib@graph@main@parser@start{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@protect@group}{\tikz@lib@graph@main@parser@cont}% +}% + +\def\tikz@lib@graph@protect@group#1{% + \pgfutil@ifnextchar\relax{\tikz@lib@graph@main@parser@cont{{#1}}}{\tikz@lib@graph@main@parser@cont{{#1}}}% +}% + +\def\tikz@lib@graph@main@parser@cont{\tikz@lib@graph@check@quotes\tikz@lib@graph@main@parser@cont@normal}% +\def\tikz@lib@graph@main@parser@cont@normal#1,{% + \tikz@lib@graph@parse@one#1-\pgf@stop@eodashes% +}% + +\def\tikz@lib@graph@parse@one{% + \pgfutil@ifnextchar\bgroup\tikz@lib@graph@scope\tikz@lib@graph@node% +}% + + + + +\def\tikz@lib@graph@check@quotes#1{% + \let\tikz@lib@graph@cont@quote#1% + \pgfutil@ifnextchar"{\begingroup\pgfkeys@temptoks{}\pgfutil@empty\tikz@lib@graph@quote@parser}{\tikz@lib@graph@check@quotes@active}% +}% +{% + \catcode`\"=13\relax + \gdef\tikz@lib@graph@check@quotes@active{% + \pgfutil@ifnextchar"{\begingroup\pgfkeys@temptoks{}\pgfutil@empty\tikz@lib@graph@quote@parser@active}{\tikz@lib@graph@cont@quote}% + }% + \gdef\tikz@lib@graph@quote@parser@active"#1"{% + \pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks #1}% + \pgfutil@ifnextchar"{\pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks "}\tikz@lib@graph@quote@parser@active}{\tikz@lib@graph@quote@parser@done}% + }% +}% + +\def\tikz@lib@graph@quote@parser"#1"{% + \pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks #1}% + \pgfutil@ifnextchar"{\pgfkeys@temptoks\expandafter{\the\pgfkeys@temptoks "}\tikz@lib@graph@quote@parser}{\tikz@lib@graph@quote@parser@done}% +}% + +\def\tikz@lib@graph@quote@parser@done{% + {\expandafter\scantokens\expandafter{% + \expandafter\expandafter\expandafter\tikzlibgraphactivations\expandafter\expandafter\expandafter\tikzlibgraphdoedef\expandafter{\the\pgfkeys@temptoks}% + }}% + {\expandafter\scantokens\expandafter{\expandafter\tikzlibgraphactivationsbrace\expandafter\xdef\expandafter\tikzlibgraphreplaced\expandafter<\tikzlibgraphreplaced>\catcode`\}=2\relax}}% + \edef\tikzlibgraphreplaced{\expandafter\detokenize\expandafter{\tikzlibgraphreplaced}} + \pgfutil@ifnextchar/\tikz@lib@graph@quotes@slash\tikz@lib@graph@quotes@no@slash% +}% +\def\tikz@lib@graph@quotes@no@slash{% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \tikz@smuggle\expandafter\expandafter\expandafter{\expandafter\tikzlibgraphreplaced\expandafter/\expandafter{\the\pgfkeys@temptoks}}% + \expandafter\endgroup\expandafter\tikz@lib@graph@cont@quote\tikz@smuggle% +}% +\def\tikz@lib@graph@quotes@slash/{% + \pgfutil@ifnextchar/% + {\tikz@lib@graph@quotes@no@slash/}{\expandafter\endgroup\expandafter\tikz@lib@graph@cont@quote\tikzlibgraphreplaced/}% +}% +\def\tikzlibgraphdoedef{\xdef\tikzlibgraphreplaced}% + +\def\tikz@lib@prepare@active#1#2#3{% + {% + \catcode`#1=13\relax% + \scantokens{\gdef\tikzlibgraphactivator{\def#2{@#3@}}}% + }% + \pgfutil@g@addto@macro\tikzlibgraphactivations{\catcode`#1=13\relax}% + \expandafter\pgfutil@g@addto@macro\expandafter\tikzlibgraphactivations\expandafter{\tikzlibgraphactivator}% +}% + +\let\tikzlibgraphactivations\pgfutil@empty + + +\outer\def\tikz@lib@outer@test{\tabalign}% +\ifx\+\tikz@lib@outer@test + \def\+{\tabalign} +\fi + +\tikz@lib@prepare@active{\$}{$}{DOLLAR SIGN}% +\tikz@lib@prepare@active{\&}{&}{AMPERSAND}% +\tikz@lib@prepare@active{\^}{^}{CIRCUMFLEX ACCENT}% +\tikz@lib@prepare@active{\~}{~}{TILDE}% +\tikz@lib@prepare@active{\_}{_}{LOW LINE}% +\tikz@lib@prepare@active{\|}{|}{VERTICAL LINE}% +\tikz@lib@prepare@active{\[}{[}{LEFT SQUARE BRACKET}% +\tikz@lib@prepare@active{\]}{]}{RIGHT SQUARE BRACKET}% +\tikz@lib@prepare@active{\(}{(}{LEFT PARENTHESIS}% +\tikz@lib@prepare@active{\)}{)}{RIGHT PARENTHESIS}% +\tikz@lib@prepare@active{\/}{/}{SOLIDUS}% +\tikz@lib@prepare@active{\.}{.}{FULL STOP}% +\tikz@lib@prepare@active{\-}{-}{HYPHEN MINUS}% +\tikz@lib@prepare@active{\,}{,}{COMMA}% +\tikz@lib@prepare@active{\+}{+}{PLUS SIGN}% +\tikz@lib@prepare@active{\*}{*}{ASTERISK}% +\tikz@lib@prepare@active{\'}{'}{APOSTROPHE}% +\tikz@lib@prepare@active{\!}{!}{EXCLAMATION MARK}% +\tikz@lib@prepare@active{\"}{"}{QUOTATION MARK}% +\tikz@lib@prepare@active{\:}{:}{COLON}% +\tikz@lib@prepare@active{\;}{;}{SEMINCOLON}% +\tikz@lib@prepare@active{\<}{<}{LESS THAN SIGN}% +\tikz@lib@prepare@active{\=}{=}{EQUALS SIGN}% +\tikz@lib@prepare@active{\>}{>}{GREATER THAN SIGN}% +\tikz@lib@prepare@active{\?}{?}{QUESTION MARK}% +\tikz@lib@prepare@active{\`}{`}{GRAVE ACCENT}% +{\catcode`\%=11\catcode`\#=11 +\tikz@lib@prepare@active{\%}{%}{PERCENT SIGN} +\tikz@lib@prepare@active{\#}{#}{NUMBER SIGN} +} + +\pgfutil@g@addto@macro\tikzlibgraphactivations{\catcode`\\=13\relax}% +{% + \catcode`\|=0\relax + \catcode`\\=13\relax + |pgfutil@g@addto@macro|tikzlibgraphactivations{|def\{@REVERSE SOLIDUS@}}% +}% +{% + \gdef\tikzlibgraphscommercialat{@COMMERCIAL AT@}% + \let\g=\pgfutil@g@addto@macro + \catcode`\@=13\relax + \g\tikzlibgraphactivations{\catcode`\@=13\relax\let@=\tikzlibgraphscommercialat}% +}% + +\def\tikzlibgraphactivationsbrace{% + \catcode`\{=13\relax% + \catcode`\}=13\relax% + \catcode`\<=1\relax% + \catcode`\>=2\relax% +}% +{% + \catcode`\{=13\relax% + \catcode`\}=13\relax% + \catcode`\<=1\relax% + \catcode`\>=2\relax% + \pgfutil@g@addto@macro\tikzlibgraphactivationsbrace<\def{<@LEFT CURLY BRACE@>> % + \pgfutil@g@addto@macro\tikzlibgraphactivationsbrace<\def}<@RIGHT CURLY BRACE@>> % +>% + + + +\def\tikz@lib@graph@node{\tikz@lib@graph@check@quotes\tikz@lib@graph@node@normal}% + +\def\tikz@lib@graph@node@normal{% + \pgfutil@ifnextchar({\tikz@lib@graph@node@dressed}{\tikz@lib@graph@node@naked}% +}% + +\def\tikz@lib@graph@node@dressed(#1){% + \tikz@lib@graph@node@naked{(#1)}% +}% + +\def\tikz@lib@graph@node@naked#1-{% + \tikz@lib@graph@@node#1<\pgf@stop% +}% + +\def\tikz@lib@graph@@node#1<#2\pgf@stop% +{ + \tikz@lib@graph@grab@name#1\pgf@stop% + \tikz@lib@graph@stored@actions% + \pgfutil@ifnextchar\pgf@stop@eodashes{% + \tikz@lib@graph@graph@done% + }{% + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \expandafter\tikz@lib@graph@no@back@arrow% + \else% + \expandafter\tikz@lib@graph@back@arrow% + \fi% + }% +}% + +\def\tikz@lib@graph@no@back@arrow{% + \pgfutil@ifnextchar>\tikz@lib@graph@forward@arrow{% + \pgfutil@ifnextchar-\tikz@lib@graph@undirected@arrow{% + \pgfutil@ifnextchar!\tikz@lib@graph@no@arrow{% + \tikzerror{One of the arrow types <-, --, ->, -!- or <-> expected}% + \tikz@lib@graph@undirected@arrow% + }% + }% + }% +}% + +\def\tikz@lib@graph@undirected@arrow-{% + \def\tikz@lib@graph@arrow@type{--}% + \tikz@lib@graph@after@arrow% +}% + +\def\tikz@lib@graph@forward@arrow>{% + \def\tikz@lib@graph@arrow@type{->}% + \tikz@lib@graph@after@arrow% +}% + +\def\tikz@lib@graph@bi@arrow>{% + \def\tikz@lib@graph@arrow@type{<->}% + \tikz@lib@graph@after@arrow% +}% + +\def\tikz@lib@graph@no@arrow!-{% + \def\tikz@lib@graph@arrow@type{-!-}% + \tikz@lib@graph@after@arrow% +}% + +\def\tikz@lib@graph@back@arrow{% + \pgfutil@ifnextchar>{\tikz@lib@graph@bi@arrow}{% + \def\tikz@lib@graph@arrow@type{<-}% + \tikz@lib@graph@after@arrow% + }% +}% + +\def\tikz@lib@graph@after@arrow{% + \pgfutil@ifnextchar[{\tikz@lib@graph@after@arrow@opt}{\tikz@lib@graph@after@arrow@opt[]}% +}% + +\def\tikz@lib@graph@after@arrow@opt[#1]{% + \tikzgraphinvokeoperator{recolor source by=source''} + \tikzgraphinvokeoperator{recolor target by=target'} + \expandafter\def\expandafter\tikz@lib@graph@stored@actions\expandafter{% + \expandafter\tikz@lib@graph@joiner\expandafter{\tikz@lib@graph@arrow@type}{#1}}% + \tikzgdeventgroupcallback{descendants}% + \tikz@lib@graph@parse@one% +}% + +\def\tikz@lib@graph@joiner#1#2{% + \tikzgraphinvokeoperator{recolor source by=source'} + \tikzgraphinvokeoperator{recolor source'' by=source} + {% + \tikz@enable@edge@quotes% + \pgfkeyssetvalue{/tikz/graphs/default edge kind}{#1}% + \pgfkeys{/tikz/graphs/.cd,@operators=,% + /tikz/graphs/.unknown/.code=\tikz@lib@graph@unknown@edge@option{##1},#2}% + \pgfkeysgetvalue{/tikz/graphs/@operators}\pgf@temp% + \ifx\pgf@temp\pgfutil@empty% + \edef\pgf@temp{\noexpand\pgfkeys{/tikz/graphs/.cd,\pgfkeysvalueof{/tikz/graphs/default edge operator}}}% + \pgf@temp% + \pgfkeysgetvalue{/tikz/graphs/@operators}\pgf@temp% + \fi% + \pgf@temp% + }% + \tikzgraphinvokeoperator{not source',not target'} +}% + +\def\tikz@lib@graph@unknown@edge@option#1{% + \def\tikz@temp{/tikz/graphs/@edges styling/.append=} + \expandafter\expandafter\expandafter\pgfkeys% + \expandafter\expandafter\expandafter{\expandafter\tikz@temp\expandafter{\expandafter,\pgfkeyscurrentname={#1}}} +}% + +\def\tikz@lib@graph@graph@done\pgf@stop@eodashes{% + \xdef\tikz@lib@graph@chain@depth{\pgfkeysvalueof{/tikz/graphs/placement/local depth}} + \xdef\tikz@lib@graph@chain@width{\pgfkeysvalueof{/tikz/graphs/placement/local width}} + \expandafter% + \endgroup% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@graph@node@list% + \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}% + \tikz@lib@graph@placement@after@chain@update + \pgfutil@ifnextchar\pgf@stop@eogroup% + \tikz@lib@graph@graph@group@done% + \tikz@lib@graph@main@parser% +}% + +\def\tikz@lib@graph@graph@group@done\pgf@stop@eogroup{% + \pgfkeysvalueof{/tikz/graphs/@operators}% +}% + + + +\def\tikz@lib@graph@grab@name{% + \pgfutil@ifnextchar\foreach\tikz@lib@graph@do@foreach\tikz@lib@graph@parse@node@text% +}% + +\def\tikz@lib@graph@do@foreach\foreach#1in{% + \pgfutil@ifnextchar\bgroup{\tikz@lib@graph@do@foreach@normal{#1}}{\def\tikz@temp{#1}\tikz@lib@graph@do@foreach@macro}% +}% +\def\tikz@lib@graph@do@foreach@macro#1{% + \expandafter\expandafter\expandafter\tikz@lib@graph@do@foreach@normal\expandafter\tikz@temp\expandafter{#1}% +}% + +\def\tikz@lib@graph@do@foreach@normal#1#2#3\pgf@stop{% + \begingroup + \let\tikz@lib@graph@node@list@saved\pgfutil@empty% + \xdef\tikz@lib@graph@saved@placement{% + {\pgfkeysvalueof{/tikz/graphs/placement/local depth}}% + {\pgfkeysvalueof{/tikz/graphs/placement/local width}}% + {\pgfkeysvalueof{/tikz/graphs/placement/chain count}}% + {\pgfkeysvalueof{/tikz/graphs/placement/element count}}% + {\pgfkeysvalueof{/tikz/graphs/placement/width}}% + {\pgfkeysvalueof{/tikz/graphs/placement/depth}}% + }% + \foreach #1 in {#2}% + {% + \let\tikz@lib@graph@node@list\tikz@lib@graph@node@list@saved% + \expandafter\tikz@lib@graph@setup@placement\tikz@lib@graph@saved@placement% + \tikz@lib@graph@parse@group{#3}% + \xdef\tikz@lib@graph@saved@placement{% + {\pgfkeysvalueof{/tikz/graphs/placement/local depth}}% + {\pgfkeysvalueof{/tikz/graphs/placement/local width}}% + {\pgfkeysvalueof{/tikz/graphs/placement/chain count}}% + {\pgfkeysvalueof{/tikz/graphs/placement/element count}}% + {\pgfkeysvalueof{/tikz/graphs/placement/width}}% + {\pgfkeysvalueof{/tikz/graphs/placement/depth}}% + }% + \global\let\tikz@lib@graph@node@list@saved\tikz@lib@graph@node@list% + }% + \expandafter% + \endgroup% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@graph@node@list% + \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list@saved}% + \expandafter\tikz@lib@graph@setup@placement\tikz@lib@graph@saved@placement% +}% + +\def\tikz@lib@graph@setup@placement#1#2#3#4#5#6{% + \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{#1}% + \pgfkeyssetvalue{/tikz/graphs/placement/local width}{#2}% + \pgfkeyssetvalue{/tikz/graphs/placement/chain count}{#3}% + \pgfkeyssetvalue{/tikz/graphs/placement/element count}{#4}% + \pgfkeyssetvalue{/tikz/graphs/placement/width}{#5}% + \pgfkeyssetvalue{/tikz/graphs/placement/depth}{#6}% +}% + +\def\tikz@lib@graph@parse@node@text#1\pgf@stop{% + \pgfutil@in@{//}{#1 } + \ifpgfutil@in@% + \tikz@lib@parse@layout@node#1\pgf@stop% + \else% + \tikz@lib@graph@fake@nodefalse + \let\tikz@lib@graph@node@parsed\tikz@lib@graph@node@opt@normal% + \def\tikz@lib@graph@empty@node@parsed{\tikzgdeventcallback{node}{}}% + \tikz@lib@parse@normal@node#1[\pgf@stop% + \fi% +}% + +\newif\iftikzgraphsautonumbernodes +\newcount\tikz@lib@auto@number + +\def\tikz@lib@do@autonumber{% + \ifx\tikz@lib@graph@name@only\pgfutil@empty% + \else% + \edef\tikz@lib@graph@name@only{\tikz@lib@graph@name@only\tikz@lib@auto@sep\the\tikz@lib@auto@number}% + \global\advance\tikz@lib@auto@number by1\relax% + \fi% +}% + + +\def\tikz@lib@parse@normal@node#1[{ + \pgfutil@in@{/}{#1}% + \ifpgfutil@in@% + \tikz@lib@parse@node@with@slash#1\pgf@stop% + \else + \pgfutil@in@{__}{#1}% + \ifpgfutil@in@% + \tikz@lib@parse@node@with@doubleunder#1\pgf@stop% + \else + \edef\pgf@marshal{\noexpand\pgfkeys@spdef\noexpand\tikz@lib@graph@name@only{#1}}% + \pgf@marshal% + \let\tikz@lib@graph@node@text\tikz@lib@graph@name@only% + \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}% + \fi% + \fi% + \tikz@lib@graph@handle@node@cont% +}% + +\def\tikz@lib@parse@node@with@slash#1/{ + \pgfkeys@spdef\tikz@lib@graph@name@only{#1}% + \ifx\tikz@lib@graph@name@only\pgfutil@empty% + \global\advance\tikz@fig@count by1\relax + \edef\tikz@lib@graph@name@only{tikz@f@\the\tikz@fig@count}% + \fi% + \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}% + \pgfutil@ifnextchar"\tikz@lg@slash@quote{\pgfutil@ifnextchar\tikz@active@quotes@token\tikz@lg@slash@quote@active\tikz@lg@slash@cont} +}% +\def\tikz@lg@slash@quote"#1"#2\pgf@stop{% + \iftikz@handle@active@nodes% + \def\tikz@lib@graph@node@text{\scantokens{#1}}% + \else + \def\tikz@lib@graph@node@text{#1}% + \fi% +}% +{\catcode`\"=13\relax + \gdef\tikz@lg@slash@quote@active"#1"#2\pgf@stop{% + \iftikz@handle@active@nodes% + \def\tikz@lib@graph@node@text{\scantokens{#1}}% + \else + \def\tikz@lib@graph@node@text{#1}% + \fi% + }% +}% +\def\tikz@lg@slash@cont#1\pgf@stop{% + \iftikz@handle@active@nodes% + \def\tikz@lib@graph@node@text{\scantokens{#1}}% + \else + \def\tikz@lib@graph@node@text{#1}% + \fi% +}% + +\def\tikz@lib@parse@node@with@doubleunder#1__{\tikz@lib@parse@node@with@slash{#1}/}% + +\def\tikz@lg@find@fresh@name{% + \edef\tikz@lib@graph@name@only{\tikz@lib@graph@name@only'}% + \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}% + \tikz@lg@if@local@node{\tikz@lib@graph@name}{\tikz@lg@find@fresh@name}{}% +}% + + + +\def\tikz@lib@graph@handle@node@cont{% + \iftikzgraphsautonumbernodes% + \tikz@lib@do@autonumber% + \fi% + \iftikz@lib@graph@fresh@node% + \tikz@lg@if@local@node{\tikz@lib@graph@name}{\tikz@lg@find@fresh@name}{}% + \fi% + \let\tikzgraphnodeas\tikzgraphnodeas@default% + \pgfutil@ifnextchar\pgf@stop{% + \ifx\tikz@lib@graph@name@only\pgfutil@empty% + \expandafter\tikz@lib@graph@node@empty@done% + \else + \expandafter\tikz@lib@graph@node@opt\expandafter[\expandafter]\expandafter[% + \fi% + }{\tikz@lib@graph@node@opt[}% +}% + +\def\tikzgraphnodeas@default{% + \tikz@lib@graph@typesetter% +}% + +\let\tikz@lib@graph@empty@node@parsed\relax% + +\def\tikz@lib@graph@node@opt[#1]#2[\pgf@stop{% + \tikz@lib@graph@node@parsed{#1}% +}% + +\def\tikz@lib@graph@node@empty@done\pgf@stop{\tikz@lib@graph@empty@node@parsed}% + + +\def\tikz@lib@parse@layout@node#1//{% + \pgf@lib@graph@empty@layout@nodefalse% + \let\tikz@lib@graph@node@parsed\tikz@lib@layout@node@parsed% + \let\tikz@lib@graph@empty@node@parsed\tikz@lib@graph@empty@layout@node@parsed + \tikz@lib@parse@normal@node#1[\pgf@stop% +}% + +\newif\ifpgf@lib@graph@empty@layout@node + +\def\tikz@lib@layout@node@parsed{% + \tikz@lib@layout@parse@rest% +}% + +\def\tikz@lib@graph@empty@layout@node@parsed{% + \pgf@lib@graph@empty@layout@nodetrue + \tikz@lib@layout@parse@rest{}% +}% + +\def\tikz@lib@layout@parse@rest#1{% + \def\tikz@lib@layout@node@options{#1}% + \pgfutil@ifnextchar[{\tikz@lib@layout@node@opt}{\tikz@lib@layout@node@opt[]}% +}% + +\def\tikz@lib@layout@node@parsed#1{% + \def\tikz@lib@layout@node@options{#1}% + \pgfutil@ifnextchar[{\tikz@lib@layout@node@opt}{\tikz@lib@layout@node@opt[]}% +}% + +\def\tikz@lib@layout@node@opt[#1]{% + \def\tikz@lib@layout@options{#1}% + \pgfutil@ifnextchar\bgroup{\tikz@lib@layout@start}{\tikzerror{Opening brace at beginning of sublayout expected}}% +}% + + + +\def\tikz@lib@graph@node@opt@normal#1{% + \expandafter\tikz@lib@graph@test@use@list\tikz@lib@graph@name@only\pgf@stop + \iftikz@lib@graph@use@list% + \let\tikz@lg@temp\pgfutil@empty% + \foreach \tikz@lg@node@name in \tikz@lib@graph@use@list {\expandafter\tikz@lib@graph@handle@use\expandafter{\tikz@lg@node@name}} + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@graph@node@list% + \expandafter\expandafter\expandafter{% + \expandafter\tikz@lib@graph@node@list\tikz@lg@temp}% + \let\tikz@lg@do\tikz@lib@graph@do@use% + \tikz@lg@temp% + \else% + \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}% + \expandafter\ifx\csname tikz@lib@graph@def@\tikz@lib@graph@name@only\endcsname\relax% + \pgfkeysgetvalue{/tikz/graphs/placement/level}\tikz@temp% + \c@pgf@counta=\tikz@temp\relax% + \advance\c@pgf@counta by1\relax% + \edef\tikz@temp{\the\c@pgf@counta}% + \pgfkeyslet{/tikz/graphs/placement/level}\tikz@temp% + \tikzgraphsset{ + level/.try=\pgfkeysvalueof{/tikz/graphs/placement/level}, + level \pgfkeysvalueof{/tikz/graphs/placement/level}/.try + } + {% + \edef\tikz@lib@graph@node@list{\noexpand\tikz@lg@do{\tikz@lib@graph@name}}% + \global\tikz@lib@graph@node@createdfalse% + \pgfkeyslet{/tikz/graphs/@operators}\pgfutil@empty% + \tikz@lib@activate@source@target@edge@syntax% + \tikz@lg@if@local@node{\tikz@lib@graph@name}% + {\tikz@lg@local@node@handle{#1}}% + {% + \tikz@lg@init@color{\tikz@lib@graph@name}{\tikz@lgc@all@true\tikz@lgc@source@true\tikz@lgc@target@true}% + \iftikz@lib@graph@all% + \tikzgraphsset{#1}\pgfkeysvalueof{/tikz/graphs/@operators}% + \else% + \pgfkeys{/tikz/graphs/placement/place}% + \let\tikzgraphnodetext\tikz@lib@graph@node@text% + \let\tikzgraphnodename\tikz@lib@graph@name@only% + \let\tikzgraphnodepath\tikz@lib@graph@path% + \let\tikzgraphnodefullname\tikz@lib@graph@name% + \iftikz@lib@graph@fake@node% + {% + \pgfkeys{ + /tikz/graphs/.cd,% + .unknown/.code=, + /tikz/graphs/@nodes styling,% + #1}% + \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@op@save% + \global\let\tikz@lib@graph@op@save\tikz@lib@graph@op@save% + }% + \else% + \node [% + name=\tikz@lib@graph@name,% + execute at end node={% + \pgfkeysgetvalue{/tikz/graphs/@operators}\tikz@lib@graph@op@save% + \global\let\tikz@lib@graph@op@save\tikz@lib@graph@op@save% + },% + graphs/redirect unknown to tikz, + /tikz/graphs/.cd,% + /tikz/graphs/@nodes styling,% + #1]% + {% + \tikzgraphnodeas% + };% + \fi% + \tikz@lib@graph@op@save\global\let\tikz@lib@graph@op@save\relax% + \global\tikz@lib@graph@node@createdtrue% + \fi + }% + }% + \iftikz@lib@graph@node@created\tikz@lib@graph@placement@update\fi% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@graph@node@list% + \expandafter\expandafter\expandafter{% + \expandafter\tikz@lib@graph@node@list\expandafter\tikz@lg@do\expandafter{\tikz@lib@graph@name}}% + \iftikz@lib@graph@trie\tikzgraphsset{name=\tikz@lib@graph@name@only}\fi% + \else + \tikz@lib@graph@handle@graph{#1}% + \fi + \fi% +}% + +\newif\iftikz@lib@graph@fake@node + +\newif\iftikz@lib@graph@use@list +\def\tikz@lib@graph@test@use@list{% + \pgfutil@ifnextchar({\tikz@lib@graph@use@list@grap}{\tikz@lib@graph@test@use@list@done}% +}% + +\def\tikz@lib@graph@test@use@list@done#1\pgf@stop{\tikz@lib@graph@use@listfalse}% +\def\tikz@lib@graph@use@list@grap(#1)\pgf@stop{\def\tikz@lib@graph@use@list{#1}\tikz@lib@graph@use@listtrue}% + + + +\def\tikz@lib@layout@start#1#2\pgf@stop{% + \tikz@lib@ensure@gd@loaded% + \tikz@lib@graph@fake@nodefalse% + \ifpgf@lib@graph@empty@layout@node% + \else% + \ifx\tikz@lib@graph@name\pgfutil@empty% + \tikzerror{Internal error: Node has no name, but it should!}% + \else + \tikz@lib@graph@fake@nodetrue% + \expandafter\tikz@lib@graph@node@opt@normal\expandafter{\tikz@lib@layout@node@options}% + \fi% + \fi% + \edef\tikz@lib@graph@name{\tikz@lib@graph@path\tikz@lib@graph@name@only}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@layout@node@options\expandafter\expandafter\expandafter{\expandafter\tikz@lib@layout@startup@node@options\tikz@lib@layout@node@options,}% + \begingroup + \iftikz@lib@graph@fake@node% + \expandafter\expandafter\expandafter% + \expandafter\expandafter\expandafter\expandafter\tikz@lib@make@subgraph@node% + \expandafter\expandafter\expandafter% + \expandafter\expandafter\expandafter\expandafter{% + \expandafter\expandafter\expandafter\tikz@lib@graph@name% + \expandafter\expandafter\expandafter}% + \expandafter\expandafter\expandafter{% + \expandafter\tikz@lib@graph@node@text\expandafter}\expandafter{\tikz@lib@layout@node@options} + \fi% + \expandafter\expandafter\expandafter\scope\expandafter\expandafter\expandafter[\expandafter\tikz@lib@layout@node@options@prefix\tikz@lib@layout@options] + \tikzgdeventgroupcallback{array}% + \let\tikz@lib@graph@node@list\pgfutil@empty% + \tikz@lib@graph@start@hint@group% + \tikz@lib@graph@parse@group{#1}% + \tikz@lib@graph@end@hint@group% + \def\tikz@lg@old@col{\tikz@lgc@source@true}% + \let\tikz@lg@new@col\pgfutil@empty% + \let\tikz@lg@do\tikz@lg@change@color% + \tikz@lib@graph@node@list% + \def\tikz@lg@old@col{\tikz@lgc@target@true}% + \tikz@lib@graph@node@list% + \expandafter% + \endscope\expandafter% + \endgroup% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@graph@node@list% + \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}% + \tikz@lib@graph@hint@aftergroup% +}% +\def\tikz@lib@make@subgraph@node#1#2#3{% + \pgfgdsubgraphnode{#1}{#3}{\pgfgdsubgraphnodecontents{#2}}% +}% +\def\tikz@lib@layout@startup@node@options{% + /utils/exec=\tikzlibignorecomparisonsINTERNAL, + /tikz/graphs/.cd,% + redirect unknown to tikz,% + anchor=base,% + /tikz/every subgraph node/.try,% +}% +\def\tikzlibignorecomparisonsINTERNAL{% + \pgfkeys{/handlers/first char syntax=true} + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string>}{\pgfutil@gobble}% + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string<}{\pgfutil@gobble}% +}% +\def\tikz@lib@layout@node@options@prefix{graphs/.cd,}% + +\ifx\tikz@lib@ensure@gd@loaded\pgfutil@undefined% +\def\tikz@lib@ensure@gd@loaded{\tikzerror{You must say \string\usetikzlibrary{graphdrawing} to use the (sub)layout syntax}}% +\fi + +\def\tikz@lg@local@node@handle#1{% + \tikzgraphsset{source,target,.unknown/.code=,#1}% + \tikzgdlatenodeoptionacallback{\tikz@pp@name\tikz@lib@graph@name}% + \node also[graphs/redirect unknown to tikz,/tikz/graphs/.cd,#1](\tikz@lib@graph@name);% + \pgfkeysvalueof{/tikz/graphs/@operators}% +}% + +\tikzgraphsset{redirect unknown to tikz/.style={ + /tikz/graphs/.unknown/.code={% + \let\tikz@key\pgfkeyscurrentname% + \pgfkeys{tikz/.cd,\tikz@key={##1},/tikz/graphs/.cd}% + }} +}% + +\def\tikz@lib@activate@source@target@edge@syntax{% + \pgfkeys{/handlers/first char syntax=true} + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string>}{\tikz@lg@parse@more}% + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string<}{\tikz@lg@parse@less}% +}% + +\def\tikz@lg@parse@less#1{\tikz@lg@parse@less@#1\pgf@stop}% +\def\tikz@lg@parse@less@<{\pgfutil@ifnextchar"{\tikz@lg@parse@quote{source}}{\tikz@lg@parse@noquote{source}}}% +\def\tikz@lg@parse@more#1{\tikz@lg@parse@more@#1\pgf@stop}% +\def\tikz@lg@parse@more@>{\pgfutil@ifnextchar"{\tikz@lg@parse@quote{target}}{\tikz@lg@parse@noquote{target}}}% + +\def\tikz@lg@parse@noquote#1#2\pgf@stop{{\tikzgraphsset{#1 edge style={#2}}}}% +\def\tikz@lg@parse@quote#1#2\pgf@stop{% + {\tikzgraphsset{/tikz/node quotes mean={#1 edge node={node [every edge quotes,##2]{##1}}},/utils/exec=\tikz@enable@node@quotes,#2}}% +}% + +\tikzgraphsset{ + clear >/.style=target edge clear, + clear , -!-, or <-> expected}% + }% + }% +}% + +\def\tikz@lib@graph@scope@minus-{ + \pgfutil@ifnextchar>\tikz@lib@graph@forward@arrow{% + \pgfutil@ifnextchar-\tikz@lib@graph@undirected@arrow{% + \pgfutil@ifnextchar!\tikz@lib@graph@no@arrow{% + \pgfutil@ifnextchar\pgf@stop@eodashes\tikz@lib@graph@graph@done{% + \tikzerror{One of the arrow types <-, --, ->, -!-, or <-> expected}% + \tikz@lib@graph@undirected@arrow% + }% + }% + }% + }% +}% + +\def\tikz@lib@graph@scope@less<-{\tikz@lib@graph@back@arrow}% + + + + + +\tikzgraphsset{ + declare/.code 2 args={\expandafter\def\csname tikz@lib@graph@def@#1\endcsname{\tikz@lib@graph@do@graph{#2}}}% +}% + +\def\tikz@lib@graph@handle@graph#1{% + \begingroup% + \let\tikz@lib@graph@node@list\pgfutil@empty% + \tikzgraphsset{@extra group options/.style={#1}}% + \tikz@lib@graph@start@hint@group% + \csname tikz@lib@graph@def@\tikz@lib@graph@name@only\endcsname% + \tikz@lib@graph@end@hint@group% + \expandafter% + \endgroup% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@lib@graph@node@list% + \expandafter\expandafter\expandafter{\expandafter\tikz@lib@graph@node@list\tikz@lib@graph@node@list}% + \tikz@lib@graph@hint@aftergroup% +}% + +\def\tikz@lib@graph@do@graph#1{% + \tikz@lib@graph@parse@group{#1}% +}% + +\let\tikz@lib@graph@path\pgfutil@empty + +\tikzgraphsset{ + name separator/.store in=\tikz@lib@graph@name@separator, + name separator=\space, + name/.code={% + \edef\tikz@lib@graph@path{\tikz@lib@graph@path#1\tikz@lib@graph@name@separator}% + }% +}% + + +\def\tikz@lg@newif{\csname newif\endcsname}% +\tikzgraphsset{ + as/.code=\def\tikzgraphnodeas{#1},% + color class/.style={% + /utils/exec=\expandafter\tikz@lg@newif\csname iftikz@lgc@#1@\endcsname, + #1/.style={operator={% + \edef\tikz@lg@col{\expandafter\noexpand\csname tikz@lgc@#1@true\endcsname}% + \let\tikz@lg@do\tikz@lg@colorize% + \tikz@lib@graph@node@list% + }}, + not #1/.style={operator={% + \edef\tikz@lg@old@col{\expandafter\noexpand\csname tikz@lgc@#1@true\endcsname}% + \let\tikz@lg@new@col\pgfutil@empty% + \let\tikz@lg@do\tikz@lg@change@color% + \tikz@lib@graph@node@list% + }}, + recolor #1 by/.style={operator={% + \edef\tikz@lg@old@col{\expandafter\noexpand\csname tikz@lgc@#1@true\endcsname}% + \edef\tikz@lg@new@col{\expandafter\noexpand\csname tikz@lgc@##1@true\endcsname}% + \let\tikz@lg@do\tikz@lg@change@color% + \tikz@lib@graph@node@list% + }}, + !#1/.style=not #1, + }, + color class=source, + color class=source', + color class=source'', + color class=target, + color class=target', + color class=all +}% + +\def\tikz@lg@init@color#1#2{% + \expandafter\gdef\csname tikz@lgc@#1\endcsname{#2}% +}% + +\def\tikz@lib@graph@cleanup#1{% + \expandafter\global\expandafter\let\csname tikz@lgc@#1\endcsname\relax% + \ifcsname tikz@lgca@@#1\endcsname\expandafter\global\expandafter\let\csname tikz@lgca@@#1\endcsname\relax\fi% + \ifcsname tikz@lgcb@@#1\endcsname\expandafter\global\expandafter\let\csname tikz@lgcb@@#1\endcsname\relax\fi% +}% + +\def\tikz@lg@colorize#1{% + \expandafter\let\expandafter\pgf@temp\csname tikz@lgc@#1\endcsname% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@temp% + \expandafter\expandafter\expandafter{% + \expandafter\tikz@lg@col\pgf@temp}% + \expandafter\global\expandafter\let\csname tikz@lgc@#1\endcsname\pgf@temp% +}% + +\def\tikz@lg@change@color#1{% + \def\tikz@lg@temp@save{#1}% + \let\tikz@lg@collect\pgfutil@empty% + \expandafter\let\expandafter\pgf@temp\csname tikz@lgc@#1\endcsname% + \expandafter\tikz@lg@change@check\pgf@temp\pgf@stop% +}% +\def\tikz@lg@change@check#1{% + \ifx#1\pgf@stop% + \tikz@lg@change@write@back% + \else% + \def\pgf@temp{#1}% + \ifx\pgf@temp\tikz@lg@old@col% + \expandafter\tikz@lg@change@add\expandafter{\tikz@lg@new@col}% + \else% + \tikz@lg@change@add{#1}% + \fi% + \expandafter\tikz@lg@change@check + \fi% +}% +\def\tikz@lg@change@add#1{% + \expandafter\def\expandafter\tikz@lg@collect\expandafter{\tikz@lg@collect#1}% +}% + +\def\tikz@lg@change@write@back{% + \expandafter\global\expandafter\let\csname tikz@lgc@\tikz@lg@temp@save\endcsname\tikz@lg@collect% +}% + + + +\def\tikz@lg@if@has@color#1#2#3#4{% + {% + \csname tikz@lgc@#1\endcsname% + \expandafter\let\expandafter\pgf@temp\csname iftikz@lgc@#2@\endcsname% + \ifx\pgf@temp\relax% + \tikz@lib@reset@temp% + \fi% + \pgf@temp% + \global\tikz@color@testtrue% + \else% + \global\tikz@color@testfalse% + \fi% + }% + \iftikz@color@test#3\else#4\fi% +}% +\newif\iftikz@color@test + +\def\tikz@lg@if@local@node#1#2#3{\expandafter\ifx\csname tikz@lgc@#1\endcsname\relax#3\else#2\fi}% + +\def\tikz@lib@reset@temp{\let\pgf@temp\iffalse}% + +\def\tikz@lib@annotate@#1#2#3#4{% + \expandafter\ifx\csname tikz@lgc#1@@#2\endcsname\relax% + \expandafter\gdef\csname tikz@lgc#1@@#2\endcsname{{#3}{#4}}% + \else% + \expandafter\expandafter\expandafter\tikz@lib@annotate@read\csname tikz@lgc#1@@#2\endcsname{#3}{#4}% + \expandafter\global\expandafter\let\csname tikz@lgc#1@@#2\endcsname\pgf@temp% + \fi% +}% +\def\tikz@lib@annotate@read#1#2#3#4{\def\pgf@temp{{#1,#3}{#2#4}}}% + +\tikzgraphsset{ + source edge style/.code=\tikz@lib@annotate@{a}{\tikz@lib@graph@name}{#1}{}, + source edge node/.code=\tikz@lib@annotate@{a}{\tikz@lib@graph@name}{}{#1}, + source edge clear/.code={ + \expandafter\global\expandafter\let\csname tikz@lgca@@\tikz@lib@graph@name\endcsname\relax% + }, + target edge style/.code=\tikz@lib@annotate@{b}{\tikz@lib@graph@name}{#1}{}, + target edge node/.code=\tikz@lib@annotate@{b}{\tikz@lib@graph@name}{}{#1}, + target edge clear/.code={% + \expandafter\global\expandafter\let\csname tikz@lgcb@@\tikz@lib@graph@name\endcsname\relax% + } +}% + + + + +\def\tikz@lib@graph@pack@node@list{% + {% + \let\tikz@lg@packed\pgfutil@empty% + \let\tikz@lg@do\tikz@lg@packer% + \tikz@lib@graph@node@list% + \expandafter + }\expandafter% + \def\expandafter\tikz@lib@graph@node@list\expandafter{\tikz@lg@packed}% +}% + +\def\tikz@lg@packer#1{% + \expandafter\ifx\csname tikz@lg@p@#1\endcsname\pgf@stop% + \else% + \expandafter\let\csname tikz@lg@p@#1\endcsname\pgf@stop% + \expandafter\def\expandafter\tikz@lg@packed\expandafter{\tikz@lg@packed\tikz@lg@do{#1}} + \fi +}% + + + +\def\tikzgraphforeachcolorednode#1#2{% + \tikz@lib@graph@pack@node@list% + \expandafter\def\expandafter\iftikz@lib@graph@color@picker\expandafter{\csname iftikz@lgc@#1@\endcsname}% + \let\tikz@lib@graph@action#2% + \let\tikz@lg@do\tikz@lg@pick% + \tikz@lib@graph@node@list% +}% +\def\tikz@lg@pick#1{ + {% + \csname tikz@lgc@#1\endcsname% + \iftikz@lib@graph@color@picker + \global\tikz@color@testtrue% + \else% + \global\tikz@color@testfalse% + \fi% + }% + \iftikz@color@test\tikz@lib@graph@action{#1}\fi% +}% + + + + +\def\tikzgraphpreparecolor#1#2#3{% + \let\tikz@lib@graph@count#2% + \tikz@lib@graph@count0\relax + \def\tikz@lib@graph@prefix{#3}% + \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@prepare% +}% + +\def\tikz@lib@graph@prepare#1{% + \advance\tikz@lib@graph@count by1\relax% + \expandafter\def\csname\tikz@lib@graph@prefix\the\tikz@lib@graph@count\endcsname{#1}% +}% + + + + + +\tikzgraphsset{ + complete bipartite/.style 2 args={operator={ + \def\tikz@lg@shoreb{#2}% + \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@bipartite@outer + }}, + complete bipartite/.default={target'}{source'}, + induced complete bipartite/.style 2 args={ + induced independent set={#1}, + induced independent set={#2}, + complete bipartite={#1}{#2} + }, + induced complete bipartite/.default={target'}{source'}, +}% + +\def\tikz@lib@graph@bipartite@outer#1{% + \def\tikz@lib@graph@from{#1}% + {% + \tikzgraphforeachcolorednode{\tikz@lg@shoreb}\tikz@lib@graph@bipartite@inner% + }% +}% + +\def\tikz@lib@graph@bipartite@inner#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\tikz@lib@graph@from\else% + \tikz@lib@graph@default@new@edge{\tikz@lib@graph@from}{#1}% + \fi% +}% + +\def\tikz@lib@graph@default@new@edge#1#2{% + \pgfkeysgetvalue{/tikz/graphs/@edges styling}\pgf@temp + \pgfkeysgetvalue{/tikz/graphs/@edges node}\pgf@temp@b + \let\tikz@lib@add@temp\pgfutil@empty% + \tikz@lib@graph@add@edge@annotations{a}{#1} + \tikz@lib@graph@add@edge@annotations{b}{#2} + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@temp% + \expandafter\expandafter\expandafter{\expandafter\pgf@temp\tikz@lib@add@temp}% + \expandafter\expandafter\expandafter\tikz@lib@graph@default@new@edge@% + \expandafter\expandafter\expandafter{\expandafter\pgf@temp\expandafter}\expandafter{\pgf@temp@b}{#1}{#2}% +}% +\def\tikz@lib@graph@default@new@edge@#1#2#3#4{% + \iftikz@lib@graph@simple% + \edef\tikz@temp{{\pgfkeysvalueof{/tikz/graphs/default edge kind}}{#3}{#4}} + \expandafter\tikz@lib@graph@set@simple@edge\tikz@temp{#1}{#2}% + \else% + \pgfkeys{/tikz/graphs/.cd,new \pgfkeysvalueof{/tikz/graphs/default edge kind}={#3}{#4}{#1}{#2}}% + \fi% +}% +\def\tikz@lib@graph@add@edge@annotations#1#2{% + \ifcsname tikz@lgc#1@@#2\endcsname% + \expandafter\let\expandafter\tikz@lg@temp@\csname tikz@lgc#1@@#2\endcsname% + \ifx\tikz@lg@temp@\relax\else + \expandafter\tikz@lib@graph@add@edge@annotations@\tikz@lg@temp@% + \let\tikz@lib@add@temp\tikz@lib@final@edge@style + \fi% + \fi% +}% +\def\tikz@lib@graph@add@edge@annotations@#1#2{ + \expandafter\def\expandafter\pgf@temp\expandafter{\pgf@temp,#1}% + \expandafter\def\expandafter\pgf@temp@b\expandafter{\pgf@temp@b#2}% +}% +\def\tikz@lib@final@edge@style{,after source and target edge/.try}% + + +\tikzgraphsset{ + clique/.style={operator={ + \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}% + \tikz@lg@clique@loop% + }}, + clique/.default=all +}% + +\def\tikz@lg@clique@loop{% + \ifnum\c@pgf@counta=0\relax% + \else + \c@pgf@countb=\c@pgf@counta\relax% + \tikz@lg@clique@loop@inner% + \advance\c@pgf@counta by-1\relax% + \expandafter\tikz@lg@clique@loop% + \fi% +}% + +\def\tikz@lg@clique@loop@inner{% + \advance\c@pgf@countb by-1\relax% + \ifnum\c@pgf@countb>0\relax% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{\csname tikz@lg\the\c@pgf@counta\endcsname}% + \expandafter\tikz@lg@clique@loop@inner% + \fi% +}% + + + +\tikzgraphsset{ + induced independent set/.style={operator={ + \pgfkeysgetvalue{/tikz/graphs/default edge kind}\tikz@lg@default% + \pgfkeyssetvalue{/tikz/graphs/default edge kind}{-!-}% + \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}% + \tikz@lg@indep@loop% + \pgfkeyslet{/tikz/graphs/default edge kind}\tikz@lg@default% + }}, + induced independent set/.default=all +}% + +\def\tikz@lg@indep@loop{% + \ifnum\c@pgf@counta=0\relax% + \else + \c@pgf@countb=\c@pgf@counta\relax% + \tikz@lg@indep@loop@inner% + \advance\c@pgf@counta by-1\relax% + \expandafter\tikz@lg@indep@loop% + \fi% +}% + +\def\tikz@lg@indep@loop@inner{% + \advance\c@pgf@countb by-1\relax% + \ifnum\c@pgf@countb>0\relax% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@counta\endcsname}{\csname tikz@lg\the\c@pgf@countb\endcsname}% + \expandafter\tikz@lg@indep@loop@inner% + \fi% +}% + + + +\tikzgraphsset{ + path/.style={operator={% + \let\tikz@lg@prev\relax% + \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@path@do% + }}, + path/.default=all, + induced path/.style={induced independent set={#1},path={#1}}, + induced path/.default=all, +}% + +\def\tikz@lib@graph@path@do#1{% + \ifx\tikz@lg@prev\relax% + \else% + \tikz@lib@graph@default@new@edge{\tikz@lg@prev}{#1}% + \fi + \def\tikz@lg@prev{#1}% +}% + + + +\tikzgraphsset{ + cycle/.style={operator={% + \let\tikz@lg@prev\relax% + \let\tikz@lg@first\relax% + \tikzgraphforeachcolorednode{#1}\tikz@lib@graph@cycle@do% + \ifx\tikz@lg@first\relax% + \else% + \tikz@lib@graph@default@new@edge{\tikz@lg@prev}{\tikz@lg@first}% + \fi% + }}, + cycle/.default=all, + induced cycle/.style={induced independent set={#1},cycle={#1}}, + induced cycle/.default=all, +}% + +\def\tikz@lib@graph@cycle@do#1{% + \ifx\tikz@lg@prev\relax% + \def\tikz@lg@prev{#1}% + \let\tikz@lg@first\tikz@lg@prev% + \else% + \tikz@lib@graph@default@new@edge{\tikz@lg@prev}{#1}% + \def\tikz@lg@prev{#1}% + \fi% +}% + + + + + +\tikzgraphsset{ + matching and star/.style 2 args={operator=% + {% + \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg} + \c@pgf@countb=0\relax% + \let\tikz@lg@prev\relax + \tikzgraphforeachcolorednode{#2}\tikz@lib@graph@flow@do% + \tikz@lib@graph@flow@rest% + }% + }, + matching and star/.default={target'}{source'} +}% + +\def\tikz@lib@graph@flow@do#1{% + \advance\c@pgf@countb by1\relax% + \ifnum\c@pgf@countb>\c@pgf@counta\relax% + \c@pgf@countb=\c@pgf@counta\relax% + \fi% + \ifnum\c@pgf@countb>0\relax% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{#1}% + \fi% + \def\tikz@lg@prev{#1}% +}% + +\def\tikz@lib@graph@flow@rest{% + \ifnum\c@pgf@countb<\c@pgf@counta\relax% + \ifnum\c@pgf@countb>0\relax% + \advance\c@pgf@countb by1\relax% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{\tikz@lg@prev}% + \expandafter\tikz@lib@graph@flow@rest% + \fi% + \fi% +}% + + + + +\tikzgraphsset{ + matching/.style 2 args={operator= + {% + \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg} + \c@pgf@countb=0\relax% + \tikzgraphforeachcolorednode{#2}\tikz@lib@graph@matching@do% + }% + }, + matching/.default={target'}{source'} +}% + +\def\tikz@lib@graph@matching@do#1{% + \advance\c@pgf@countb by1\relax% + \ifnum\c@pgf@countb>\c@pgf@counta\relax% + \else% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{#1}% + \fi% +}% + + + + + + +\tikzgraphsset{ + butterfly/.style={operator= + {}{% + \pgfkeys{/tikz/graphs/butterfly/.cd,#1}% + \ifnum\pgfkeysvalueof{/tikz/graphs/butterfly/level}=0\relax% + \tikzgraphinvokeoperator{matching and star={\pgfkeysvalueof{/tikz/graphs/butterfly/from}}{\pgfkeysvalueof{/tikz/graphs/butterfly/to}}}% + \else% + {% + \tikzgraphpreparecolor{\pgfkeysvalueof{/tikz/graphs/butterfly/from}}\c@pgf@counta{tikz@lg} + \c@pgf@countb=0\relax% + \tikzgraphforeachcolorednode{\pgfkeysvalueof{/tikz/graphs/butterfly/to}}\tikz@lib@graph@butterfly@do% + }% + \iftikz@butterfly@prime\else\tikzgraphinvokeoperator{matching and star={\pgfkeysvalueof{/tikz/graphs/butterfly/from}}{\pgfkeysvalueof{/tikz/graphs/butterfly/to}}}\fi% + \fi% + }% + }, + butterfly/.default=, + butterfly/level/.initial=1, + butterfly/from/.initial=target', + butterfly/to/.initial=source', + butterfly'/.style={operator={}{\tikz@butterfly@primetrue\pgfkeysalso{butterfly={#1}}}}, + butterfly'/.default=, +}% + +\newif\iftikz@butterfly@prime + +\def\tikz@lib@graph@butterfly@do#1{% + \advance\c@pgf@countb by1\relax% + \c@pgf@countc=\pgfkeysvalueof{/tikz/graphs/butterfly/level}\relax% + {% + \count0=\c@pgf@countc\relax% + \multiply\count0 by2\relax% + \count1=\c@pgf@countb\relax% + \advance\count1 by-1\relax% + \count2=\count1\relax% + \count3=\count1\relax% + \divide\count1 by\count0\relax% + \multiply\count1 by\count0\relax% + \advance\count2 by-\count1\relax% + \ifnum\count2<\c@pgf@countc\relax% + \advance\count3 by \c@pgf@countc\relax% + \else% + \advance\count3 by -\c@pgf@countc\relax% + \fi% + \expandafter% + }% + \expandafter\c@pgf@countc\the\count3\relax% + \advance\c@pgf@countc by1\relax% + \ifnum\c@pgf@countc>\c@pgf@counta\relax% + \c@pgf@countc=\c@pgf@counta\relax% + \fi% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countc\endcsname}{#1}% +}% + + + + +\tikzgraphsset{no edges/.style={operator=\relax}}% + + + + +\tikzgraphsset{ + grid/.style={operator={ + \tikzgraphpreparecolor{#1}\c@pgf@counta{tikz@lg}% + \c@pgf@countb=0\relax% + \tikzgraphpreparewrapafter% + \tikz@lg@grid@loop% + }% + }, + grid/.default=all +}% + +\def\tikzgraphpreparewrapafter{% + \pgfkeysgetvalue{/tikz/graphs/wrap after}\tikz@temp% + \ifnum\tikz@temp=0\relax% + \pgfmathparse{sqrt(\tikzgraphVnum)}% + \pgfmathint{\pgfmathresult}% + \edef\tikzgraphwrapafter{\pgfmathresult}% + \else% + \edef\tikzgraphwrapafter{\tikz@temp} + \fi% +}% + +\def\tikz@lg@grid@loop{% + \ifnum\c@pgf@counta=0\relax% + \else% + \advance\c@pgf@countb by 1\relax% + \pgfmathmod{\c@pgf@countb-1}{\tikzgraphwrapafter}% + \pgfmathint{\pgfmathresult}% + \ifnum\pgfmathresult>0% + \pgfmathsubtract{\c@pgf@countb}{1}% + \pgfmathint{\pgfmathresult}% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\the\c@pgf@countb\endcsname}{\csname tikz@lg\pgfmathresult\endcsname}% + \fi% + \pgfmathparse{\c@pgf@countb <= \tikzgraphwrapafter}% + \ifnum\pgfmathresult=0% + \pgfmathsubtract{\c@pgf@countb}{\tikzgraphwrapafter}% + \pgfmathint{\pgfmathresult}% + \tikz@lib@graph@default@new@edge{\csname tikz@lg\pgfmathresult\endcsname}{\csname tikz@lg\the\c@pgf@countb\endcsname}% + \fi% + \advance\c@pgf@counta by-1\relax% + \expandafter\tikz@lg@grid@loop% + \fi% +}% + + + + + +\tikzgraphsset{ + placement/.cd, + compute position/.code=\tikz@lib@graph@linear@pos, + place/.code={% + \pgfkeys{/tikz/graphs/placement/compute position}% + \aftergroup\tikz@lib@graph@reset@locals% + \pgfkeyssetvalue{/tikz/graphs/placement/element count}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/chain count}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/depth}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/width}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/local depth}{0}% + \pgfkeyssetvalue{/tikz/graphs/placement/local width}{0}% + }, + element count/.initial=0, + chain count/.initial=0, + depth/.initial=0, + width/.initial=0, + level/.initial=0, + logical node depth/.code=\def\pgfmathresult{1}, + logical node width/.code=\def\pgfmathresult{1}, +}% + +\def\tikz@lib@graph@reset@locals{% + \gdef\tikz@lib@graph@group@depth{0}% + \gdef\tikz@lib@graph@group@width{0}% +}% + + + +\tikzgraphsset{ + Cartesian placement/.style={ + placement/place, + placement/compute position/.code=\tikz@lib@graph@linear@pos% + }, + chain shift/.initial={(1,0)}, + group shift/.initial={(0,-1)}, + grow right/.style={ + placement/place, + chain shift={(#1,0)}, + @auto anchor horizontal=center, + placement/logical node width/.code=\def\pgfmathresult{1} + }, + grow right/.default=1, + grow left/.style={ + placement/place, + chain shift={(-#1,0)}, + @auto anchor horizontal=center, + placement/logical node width/.code=\def\pgfmathresult{1} + }, + grow left/.default=1, + grow up/.style={ + placement/place, + chain shift={(0,#1)}, + @auto anchor horizontal=center, + placement/logical node width/.code=\def\pgfmathresult{1} + }, + grow up/.default=1, + grow down/.style={ + placement/place, + chain shift={(0,-#1)}, + @auto anchor vertical=center, + placement/logical node width/.code=\def\pgfmathresult{1} + }, + grow down/.default=1, + branch right/.style={ + placement/place, + group shift={(#1,0)}, + @auto anchor horizontal=center, + placement/logical node depth/.code=\def\pgfmathresult{1} + }, + branch right/.default=1, + branch left/.style={ + placement/place, + group shift={(-#1,0)}, + @auto anchor horizontal=center, + placement/logical node depth/.code=\def\pgfmathresult{1} + }, + branch left/.default=1, + branch up/.style={ + placement/place, + group shift={(0,#1)}, + @auto anchor vertical=center, + placement/logical node depth/.code=\def\pgfmathresult{1} + }, + branch up/.default=1, + branch down/.style={ + placement/place, + group shift={(0,-#1)}, + @auto anchor vertical=center, + placement/logical node depth/.code=\def\pgfmathresult{1} + }, + branch down/.default=1, + grow right sep/.style={ + Cartesian placement, + chain shift={(1pt,0)}, + @auto anchor horizontal=west, + placement/logical node width/.code=\tikz@lib@graph@width@sep{##1}{#1} + }, + grow right sep/.default=1em, + grow left sep/.style={ + Cartesian placement, + chain shift={(-1pt,0)}, + @auto anchor horizontal=east, + placement/logical node width/.code=\tikz@lib@graph@width@sep{##1}{#1} + }, + grow left sep/.default=1em, + grow up sep/.style={ + Cartesian placement, + chain shift={(0,1pt)}, + @auto anchor vertical=south, + placement/logical node width/.code=\tikz@lib@graph@depth@sep{##1}{#1} + }, + grow up sep/.default=1em, + grow down sep/.style={ + Cartesian placement, + chain shift={(0,-1pt)}, + @auto anchor vertical=north, + placement/logical node width/.code=\tikz@lib@graph@depth@sep{##1}{#1} + }, + grow down sep/.default=1em, + grow right sep/.style={ + Cartesian placement, + chain shift={(1pt,0)}, + @auto anchor horizontal=west, + placement/logical node width/.code=\tikz@lib@graph@width@sep{##1}{#1} + }, + branch right sep/.style={ + Cartesian placement, + group shift={(1pt,0)}, + @auto anchor horizontal=west, + placement/logical node depth/.code=\tikz@lib@graph@width@sep{##1}{#1} + }, + branch right sep/.default=1em, + branch left sep/.style={ + Cartesian placement, + group shift={(-1pt,0)}, + @auto anchor horizontal=east, + placement/logical node depth/.code=\tikz@lib@graph@width@sep{##1}{#1} + }, + branch left sep/.default=1em, + branch up sep/.style={ + Cartesian placement, + group shift={(0,1pt)}, + @auto anchor vertical=south, + placement/logical node depth/.code=\tikz@lib@graph@depth@sep{##1}{#1} + }, + branch up sep/.default=1em, + branch down sep/.style={ + Cartesian placement, + group shift={(0,-1pt)}, + @auto anchor vertical=north, + placement/logical node depth/.code=\tikz@lib@graph@depth@sep{##1}{#1} + }, + branch down sep/.default=1em, + @auto anchor horizontal/.style={ + nodes={anchor=\csname tikz@lib@graph@auto@\tikz@lib@graph@auto@h @\tikz@lib@graph@auto@v\endcsname}, + /utils/exec=\def\tikz@lib@graph@auto@h{#1} + }, + @auto anchor vertical/.style={ + nodes={anchor=\csname tikz@lib@graph@auto@\tikz@lib@graph@auto@h @\tikz@lib@graph@auto@v\endcsname}, + /utils/exec=\def\tikz@lib@graph@auto@v{#1} + }, + no placement/.style={ + placement/place, + placement/compute position/.code=% + } +}% + +\def\tikz@lib@graph@auto@h{center}% +\def\tikz@lib@graph@auto@v{center}% + +\def\tikz@lib@graph@auto@center@center{center}% +\def\tikz@lib@graph@auto@west@center{west}% +\def\tikz@lib@graph@auto@east@center{east}% +\def\tikz@lib@graph@auto@center@north{north}% +\def\tikz@lib@graph@auto@west@north{north west}% +\def\tikz@lib@graph@auto@east@north{north east}% +\def\tikz@lib@graph@auto@center@south{south}% +\def\tikz@lib@graph@auto@west@south{south west}% +\def\tikz@lib@graph@auto@east@south{south east}% + +\def\tikz@lib@graph@linear@pos{% + \pgfkeysgetvalue{/tikz/graphs/chain shift}\tikz@temp + \expandafter\tikz@scan@one@point\expandafter\pgf@process\tikz@temp + \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/width}}{}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfkeysgetvalue{/tikz/graphs/group shift}\tikz@temp + \expandafter\tikz@scan@one@point\expandafter\pgf@process\tikz@temp + \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/depth}}{}}% + \advance\pgf@xa by\pgf@x% + \advance\pgf@ya by\pgf@y% + \edef\tikz@lib@graph@shift{(\the\pgf@xa,\the\pgf@ya)} + \pgfkeys{/tikz/graphs/nodes/.expanded={shift={\tikz@lib@graph@shift}}} +}% + + +\def\tikz@lib@graph@width@sep#1#2{% + \pgf@process{\pgfpointdiff{\pgfpointanchor{#1}{west}}{\pgfpointanchor{#1}{east}}}% + \pgfmathparse{#2+\the\pgf@x}% +}% + +\def\tikz@lib@graph@depth@sep#1#2{% + \pgf@process{\pgfpointdiff{\pgfpointanchor{#1}{south}}{\pgfpointanchor{#1}{north}}}% + \pgfmathparse{#2+\the\pgf@y}% +}% + + + +\tikzgraphsset{, + circular placement/.style={ + placement/place, + placement/compute position/.code=\tikz@lib@graph@circular@pos,% + placement/logical node depth/.code=\def\pgfmathresult{1}, + placement/logical node width/.code=\def\pgfmathresult{1}, + }, + clockwise/.style={ + circular placement, + group polar shift={(-360/#1:0)} + }, + clockwise/.default=\tikzgraphVnum, + counterclockwise/.style={ + circular placement, + group polar shift={(360/#1:0)} + }, + counterclockwise/.default=\tikzgraphVnum, + chain polar shift/.initial={(0:1cm)}, + group polar shift/.initial={(60:0)}, + radius/.initial=1cm, + phase/.initial=90, +}% + +\def\tikz@lib@graph@circular@pos{% + \pgfkeysgetvalue{/tikz/graphs/chain polar shift}\tikz@temp + \expandafter\tikz@lib@graph@decompose@polar\tikz@temp% + \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/width}}{}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfkeysgetvalue{/tikz/graphs/group polar shift}\tikz@temp + \expandafter\tikz@lib@graph@decompose@polar\tikz@temp% + \pgf@process{\pgfpointscale{\pgfkeysvalueof{/tikz/graphs/placement/depth}}{}}% + \advance\pgf@xa by\pgf@x% + \advance\pgf@ya by\pgf@y% + \pgfmathparse{\pgfkeysvalueof{/tikz/graphs/radius}}% + \advance\pgf@ya by\pgfmathresult pt% + \pgfmathsetmacro\tikz@temp{\the\pgf@xa+\pgfkeysvalueof{/tikz/graphs/phase}}% + \edef\tikz@lib@graph@shift{(\tikz@temp:\the\pgf@ya)} + \pgfkeys{/tikz/graphs/nodes/.expanded={shift={\tikz@lib@graph@shift}}} +}% + + +\def\tikz@lib@graph@decompose@polar(#1:#2){% + \pgfmathsetlength\pgf@x{#1}% + \pgfmathsetlength\pgf@y{#2}% +}% + + +\tikzgraphsset{ + grid placement/.style={ + placement/place, + placement/compute position/.code=\tikz@lib@graph@grid@pos,% + }, +}% + + +\def\tikz@lib@graph@grid@pos{% + \tikzgraphpreparewrapafter% + \pgfkeysgetvalue{/tikz/graphs/placement/depth}\tikz@temp@depth% + \pgfkeysgetvalue{/tikz/graphs/placement/width}\tikz@temp@width% + \pgfmathsetmacro{\tikz@temp}{max(\tikz@temp@depth, \tikz@temp@width)}% + \pgfmathsetmacro{\tikz@temp@col}{mod(\tikz@temp,\tikzgraphwrapafter)}% + \pgfmathsetmacro{\tikz@temp@row}{div(\tikz@temp,\tikzgraphwrapafter)}% + \pgfkeysgetvalue{/tikz/graphs/group shift}\tikz@temp% + \expandafter\tikz@scan@one@point\expandafter\tikz@lib@graph@grid@pos@a\tikz@temp% + \pgfkeysgetvalue{/tikz/graphs/chain shift}\tikz@temp% + \expandafter\tikz@scan@one@point\expandafter\tikz@lib@graph@grid@pos@b\tikz@temp% + \edef\tikz@lib@graph@shift{(\the\pgf@xa,\the\pgf@ya)} + \pgfkeys{/tikz/graphs/nodes/.expanded={shift={\tikz@lib@graph@shift}}} +}% + +\def\tikz@lib@graph@grid@pos@a#1{\pgf@process{\pgfpointscale{\tikz@temp@row}{#1}}\pgf@xa=\pgf@x\relax\pgf@ya=\pgf@y\relax}% +\def\tikz@lib@graph@grid@pos@b#1{\pgf@process{\pgfpointscale{\tikz@temp@col}{#1}}% + \advance\pgf@xa by\pgf@x\relax + \advance\pgf@ya by\pgf@y\relax}% + +\tikzgraphsset{ + wrap after/.initial=0, + V/.code={% + \def\tikzgraphV{#1}% + \c@pgf@counta=0\foreach \tikz@dummy in {#1} {\global\advance\c@pgf@counta by1\relax}% + \edef\tikzgraphVnum{\the\c@pgf@counta} + }, + V={1}, + n/.style={V={1,...,#1},name shore V/.style={name=V}}, + W/.code={% + \def\tikzgraphW{#1}% + \c@pgf@counta=0\foreach \tikz@dummy in {#1} {\global\advance\c@pgf@counta by1\relax}% + \edef\tikzgraphWnum{\the\c@pgf@counta} + }, + W={1}, + m/.style={W={1,...,#1},name shore W/.style={name=W}}, + name shore V/.style=, + name shore W/.style=, +}% + + + + +\tikzgraphsset{quick/.is if=tikz@graph@quick}% +\newif\iftikz@graph@quick + +\def\tikz@lib@graphs@parse@quick@graph{ + \begingroup% + \global\tikz@qnode@count0\relax% + \let\tikzgraphnodepath\pgfutil@empty% + \tikz@q@outertrue% + \afterassignment\tikz@lib@graphs@quick@main\let\pgf@temp=% +}% + +\newcount\tikz@qnode@count +\newif\iftikz@q@outer + +\def\tikz@lib@graphs@quick@main{% + \afterassignment\tikz@lib@graphs@quick@handle\let\pgf@let@token=% +}% +\def\tikz@lib@graphs@quick@handle{% + \ifx\pgf@let@token"% + \expandafter\tikz@lib@graphs@quick@first@node% + \else% + \expandafter\tikz@lib@graphs@quick@other% + \fi% +}% +\def\tikz@lib@graphs@quick@other{% + \let\tikz@next\tikz@lib@graphs@quick@error% + \ifx\pgf@let@token\egroup% + \let\tikz@next\tikz@lib@graphs@quick@end@group% + \else% + \ifx\pgf@let@token\bgroup% + \let\tikz@next\tikz@lib@graphs@quick@start@group% + \else% + \ifx\pgf@let@token\par% + \let\tikz@next\tikz@lib@graphs@quick@main% + \fi% + \fi + \fi% + \tikz@next% +}% + +\def\tikz@lib@graphs@quick@error#1{\tikzerror{Unexpected token '\string#1' in quick graph syntax}\tikz@lib@graphs@quick@main}% +\def\tikz@lib@graphs@quick@start@group{% + \pgfutil@ifnextchar[\tikz@lib@graphs@quick@start@group@{\tikzerror{Group + in quick graph syntax must start with options.}} +}% + +\def\tikz@lib@graphs@quick@start@group@[#1]{% + \begingroup% + \tikz@q@outerfalse% + \tikzgraphsset{#1}% + \tikz@lib@graphs@quick@main% +}% +\def\tikz@lib@graphs@quick@end@group{% + \iftikz@q@outer% + \endgroup% + \pgfutil@loop% + \ifnum\tikz@qnode@count>0\relax% + \expandafter\global\expandafter\let\csname tikz@gr@q@@\csname tikz@gr@qn@@\the\tikz@qnode@count\endcsname\endcsname\relax% + \expandafter\global\expandafter\let\csname tikz@gr@qn@@\the\tikz@qnode@count\endcsname\relax% + \global\advance\tikz@qnode@count by-1\relax% + \pgfutil@repeat% + \expandafter\tikz@lib@graph@main@done% + \else% + \endgroup% + \expandafter\tikz@lib@graphs@end@group@% + \fi% +}% +\def\tikz@lib@graphs@end@group@{% + \pgfutil@ifnextchar;{\expandafter\tikz@lib@graphs@quick@main\pgfutil@gobble}{% + \pgfutil@ifnextchar,{\expandafter\tikz@lib@graphs@quick@main\pgfutil@gobble}{% + \tikzerror{Graph groups in quick syntax must be followed by a semicolon or a comma.}% + }% + }% +}% + + +\def\tikz@lib@graphs@quick@first@node{% + \let\tikz@quick@prev@node\relax% + \tikz@lib@graphs@quick@node% +}% + +\def\tikz@lib@graphs@quick@node#1"{% + \def\tikzgraphnodename{#1}% + \let\tikzgraphnodetext\tikzgraphnodename% + \iftikzgraphsautonumbernodes + \edef\tikzgraphnodename{\tikzgraphnodename\tikz@lib@auto@sep\the\tikz@lib@auto@number}% + \global\advance\tikz@lib@auto@number by1\relax% + \fi + \pgfutil@ifnextchar/\tikz@lib@graphs@quick@text\tikz@lib@graphs@quick@opt% +}% +\def\tikz@lib@graphs@quick@text/"#1"{% + \def\tikzgraphnodetext{#1}% + \tikz@lib@graphs@quick@opt% +}% +\def\tikz@lib@graphs@quick@opt{% + \pgfutil@ifnextchar[\tikz@lib@graphs@quick@withopt{\tikz@lib@graphs@quick@withopt[]}% +}% +\def\tikz@lib@graphs@quick@withopt[#1]{% + \expandafter\ifx\csname tikz@gr@q@@\tikzgraphnodename\endcsname\relax% + \global\advance\tikz@qnode@count by1\relax% + \expandafter\global\expandafter\let\csname tikz@gr@q@@\tikzgraphnodename\endcsname\pgfutil@empty% + \expandafter\global\expandafter\let\csname tikz@gr@qn@@\the\tikz@qnode@count\endcsname\tikzgraphnodename% + \let\tikzgraphnodefullname\tikzgraphnodename% + \let\tikzgraphnodeas\tikzgraphnodeas@default% + \node [% + name=\tikzgraphnodename,% + graphs/redirect unknown to tikz, + /tikz/graphs/.cd,% + /tikz/graphs/@nodes styling,% + #1]% + {% + \tikzgraphnodeas% + };% + \else% + \tikzgdlatenodeoptionacallback{\tikzgraphnodename}% + \node also[graphs/redirect unknown to tikz,/tikz/graphs/.cd,#1](\tikzgraphnodename);% + \fi% + \tikz@lig@graph@quikc@make@edge@if@necessary% + \tikz@lib@graphs@quick@scan@after@node% +}% + +\def\tikz@lig@graph@quikc@make@edge@if@necessary{% + \ifx\tikz@quick@prev@node\relax% + \else% + \tikz@lib@graphs@quick@make@edge% + \fi% +}% + +\def\tikz@lib@graphs@quick@scan@after@node{% + \pgfutil@ifnextchar,\tikz@lib@graphs@quick@comma{% + \pgfutil@ifnextchar;\tikz@lib@graphs@quick@semi{% + \pgfutil@ifnextchar\egroup{\tikz@lib@graphs@quick@semi;}{% + \pgfutil@ifnextchar\par{\expandafter\tikz@lib@graphs@quick@scan@after@node\tikz@lib@graphs@quick@gobble@par}% + \tikz@lib@graphs@quick@connector}}}% +}% +\long\def\tikz@lib@graphs@quick@gobble@par#1{}% + +\def\tikz@lib@graphs@quick@comma,{\tikz@lib@graphs@quick@main}% +\def\tikz@lib@graphs@quick@semi;{\tikz@lib@graphs@quick@main}% +\def\tikz@lib@graphs@quick@connector#1#2{% + \def\tikz@lib@graphs@quick@edge@kind{#1#2}% + \pgfutil@ifnextchar>\tikz@lib@graphs@back@edge{% + \pgfutil@ifnextchar[\tikz@lib@graphs@quick@connector@handle@opt{\tikz@lib@graphs@quick@connector@handle@opt[]}% + }% +}% +\def\tikz@lib@graphs@back@edge#1{% + \expandafter\def\expandafter\tikz@lib@graphs@quick@edge@kind\expandafter{\tikz@lib@graphs@quick@edge@kind#1}% + \pgfutil@ifnextchar[\tikz@lib@graphs@quick@connector@handle@opt{\tikz@lib@graphs@quick@connector@handle@opt[]}% +}% +\def\tikz@lib@graphs@quick@connector@handle@opt[#1]{% + \def\tikz@lib@graphs@quick@edge@options{#1}% + \let\tikz@quick@prev@node\tikzgraphnodename% + \tikz@lib@graphs@quick@scan@after@connector% +}% +\def\tikz@lib@graphs@quick@scan@after@connector{% + \pgfutil@ifnextchar\par{\expandafter\tikz@lib@graphs@quick@scan@after@connector\tikz@lib@graphs@quick@gobble@par}{% + \pgfutil@ifnextchar"{\expandafter\tikz@lib@graphs@quick@node\pgfutil@gobble}{% + \tikzerror{Quotation marks expected after edge connector}% + }% + }% +}% + +\def\tikz@lib@graphs@quick@make@edge{% + { + \expandafter\tikz@lib@graphs@quick@make@edge@styling\expandafter{\tikz@lib@graphs@quick@edge@options}% + \expandafter\expandafter\expandafter\tikz@lib@graphs@quick@make@edge@for% + \expandafter\expandafter\expandafter{\expandafter\tikz@quick@prev@node\expandafter}\expandafter{\tikzgraphnodename}% + } +}% + +\def\tikz@lib@graphs@quick@make@edge@styling#1{% + \tikz@enable@edge@quotes% + \tikzgraphsset{.unknown/.code=\tikz@lib@graph@unknown@edge@option{##1},#1}% +}% + +\def\tikz@lib@graphs@quick@make@edge@for#1#2{% + \pgfkeysgetvalue{/tikz/graphs/@edges styling}\pgf@tempa + \pgfkeysgetvalue{/tikz/graphs/@edges node}\pgf@temp@b + \expandafter\expandafter\expandafter\tikz@lib@graphs@quick@make@edge@for@with% + \expandafter\expandafter\expandafter{\expandafter\pgf@tempa\expandafter}\expandafter{\pgf@temp@b}{#1}{#2}% +}% + +\def\tikz@lib@graphs@quick@make@edge@for@with#1#2#3#4{% + \tikzgraphsset{new \tikz@lib@graphs@quick@edge@kind={#3}{#4}{#1}{#2}}% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.standard.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.standard.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f3f2e199e27e84ee64ca489f9684e11ae17bf11b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/graphs/tikzlibrarygraphs.standard.code.tex @@ -0,0 +1,72 @@ + +\ProvidesFileRCS{tikzlibrarygraphs.standard.code.tex} + +\usetikzlibrary{graphs}% + + + +\tikzgraphsset{ + declare={subgraph I_n}% + { + \foreach \tikz@lib@graph@node@num in \tikzgraphV + { \tikz@lib@graph@node@num } + }, + declare={subgraph I_nm}% + { + subgraph I_n [name shore V] -- [no edges] + subgraph I_n [name shore W, V/.expand once=\tikzgraphW] + }, + declare={subgraph K_n}% + { + [clique] + subgraph I_n + }, + declare={subgraph K_nm}% + { + [color class=shore V, + color class=shore W, + complete bipartite={shore V}{shore W}] + subgraph I_n [name shore V, shore V] -- [no edges] + subgraph I_n [name shore W, V/.expand once=\tikzgraphW, shore W] + }, + declare={subgraph C_n}% + { + [cycle] + subgraph I_n + }, + declare={subgraph P_n}% + { + [path] + subgraph I_n + }, + declare={subgraph Grid_n}% + { + [grid] + subgraph I_n + }, + p/.initial=0.5, + declare={subgraph G_np}% + { + [/utils/exec={ + \pgfmathsetmacro\tikz@lib@lg@p{\pgfkeysvalueof{/tikz/graphs/p}} + \let\tikz@lib@gnp@edges\pgfutil@empty% + \foreach \tikz@lib@graph@node@a [count=\tikz@lib@g@count@a] in \tikzgraphV + \foreach \tikz@lib@graph@node@b [count=\tikz@lib@g@count@b] in \tikzgraphV + { + \ifnum\tikz@lib@g@count@a<\tikz@lib@g@count@b\relax + \pgfmathparse{rnd} + \ifdim\pgfmathresult pt<\tikz@lib@lg@p pt% + \ifx\tikz@lib@gnp@edges\pgfutil@empty + \xdef\tikz@lib@gnp@edges{\tikz@lib@graph@node@a--\tikz@lib@graph@node@b}% + \else + \xdef\tikz@lib@gnp@edges{\tikz@lib@gnp@edges,\tikz@lib@graph@node@a--\tikz@lib@graph@node@b}% + \fi + \fi + \fi + } + }] + \foreach \tikz@lg@temp in \tikz@lib@gnp@edges { + [parse/.expand once=\tikz@lg@temp] + } + }, +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzexternalshared.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzexternalshared.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..9de77a10684d30b30331506d998e75bf3171705d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzexternalshared.code.tex @@ -0,0 +1,1265 @@ + +\toksdef\t@tikzexternal@tmpa=0 +\toksdef\t@tikzexternal@tmpb=1 + +\newif\iftikzexternal@nestedflag +\newif\iftikzexternal@verboseuptodate +\newif\iftikzexternal@verboseio +\newif\iftikzexternal@genfigurelist +\newif\iftikzexternal@onlynamed +\newif\iftikzexternal@file@isuptodate +\newif\iftikzexternal@force@remake +\newif\iftikzexternal@optimize +\newif\iftikzexternal@export@enabled +\tikzexternal@export@enabledtrue + +\gdef\c@tikzexternal@version{2} + +\newif\iftikzexternalremakenext +\newif\iftikzexternal@verbose@optimize +\tikzexternal@verbose@optimizetrue + +\newif\iftikzexternalexportnext +\tikzexternalexportnexttrue + +\def\tikzifexternalizing#1#2{% + \ifpgf@external@grabshipout #1\else #2\fi +}% +\def\tikzifexternalizingnext#1#2{% + \ifpgf@external@grabshipout + \tikzexternalgetnextfilename\tikzexternal@temp + \tikzifexternaljobnamematches\tikzexternal@temp{#1}{#2}% + \else + #2% + \fi +}% +\def\tikzifexternalizingcurrent#1#2{% + \ifpgf@external@grabshipout + \tikzexternalgetcurrentfilename\tikzexternal@temp + \ifx\tikzexternal@temp\pgfutil@empty + #2% + \else + \tikzifexternaljobnamematches\tikzexternal@temp{#1}{#2}% + \fi + \else + #2% + \fi +}% + +\def\tikzifexternaljobnamematches#1#2#3{% + \edef\pgf@tempa{\expandafter\string\csname#1\endcsname}% + \edef\pgf@tempb{\expandafter\string\csname\pgfactualjobname\endcsname}% + \ifx\pgf@tempa\pgf@tempb #2\else#3 \fi% +}% + + +\pgfutil@IfUndefined{pdfshellescape}{% + \pgfutil@IfUndefined{pdf@shellescape}{% + \def\tikzexternalcheckshellescape{0}% + }{% + \let\tikzexternalcheckshellescape=\pdf@shellescape + }% +}{% + \let\tikzexternalcheckshellescape=\pdfshellescape +}% +\ifnum\tikzexternalcheckshellescape=1 + \def\tikzexternalcheckshellescape{\pgfkeysvalueof{/tikz/external/shell escape}\space}% +\else + \def\tikzexternalcheckshellescape{}% +\fi + +\newif\iftikzexternal@auto@detect@jobname + +\pgfqkeys{/tikz/external}{ + figure list/.is if=tikzexternal@genfigurelist, + aux in dpth/.style={/pgf/images/aux in dpth={#1}},% + disable dependency files/.code={% + \let\tikzexternalfiledependsonfile@ACTIVE=\tikzexternalfiledependsonfile + }, + mode/.is choice, + mode/only graphics/.code = {% + \def\tikzexternal@opmode{0}% + \pgfkeysalso{/pgf/images/aux in dpth=true}% + }, + mode/no graphics/.code = {\def\tikzexternal@opmode{1}}, + mode/only pictures/.code = {\def\tikzexternal@opmode{1}}, + mode/graphics if exists/.code= {% + \def\tikzexternal@opmode{2}% + \pgfkeysalso{/pgf/images/aux in dpth=true}% + }, + mode/list only/.code = {\def\tikzexternal@opmode{3}\tikzexternal@genfigurelisttrue}, + mode/convert with system call/.code={% + \def\tikzexternal@opmode{4}% + \pgfkeysalso{/tikz/external/figure list=false,/pgf/images/aux in dpth=true}% + }, + mode/list and make/.code = {% + \def\tikzexternal@opmode{5}% + \pgfkeysalso{/tikz/external/figure list=true,/pgf/images/aux in dpth=true}% + }, + mode=convert with system call, + force remake/.is if=tikzexternal@force@remake, + force remake/.default=true, + failed ref warnings for/.initial={\ref,\cite,\pageref}, + export next/.is if=tikzexternalexportnext, + export/.is if=tikzexternal@export@enabled, + remake next/.is if=tikzexternalremakenext, + remake next/.default=true, + verbose IO/.is if=tikzexternal@verboseio, + verbose IO/.default=true, + verbose IO=true, + verbose optimize/.is if=tikzexternal@verbose@optimize, + verbose up to date/.is if=tikzexternal@verboseuptodate, + verbose/.style={ + verbose IO=#1, + verbose optimize=#1, + verbose up to date=#1, + }, + shell escape/.initial=-shell-escape, + read main aux/.is if=pgfexternalreadmainaux, + image discarded text/.initial={% + [[ \textsc{Image Discarded Due To} \texttt{`/tikz/external/% + \ifcase\tikzexternal@opmode\relax + mode=only graphics% + \or + mode=no graphics% + \or + mode=graphics if exists% + \or + mode=list only% + \or + mode=convert with system call% + \or + mode=list and make% + \fi + '}~]]% + \pgfutil@ifundefined{tikzexternal@warning@at@end}{% + \pgfutil@ifundefined{AtEndDocument}{}{% + \AtEndDocument{% + \message{! Package tikz Warning: Some images are not up-to-date and need to be generated. }% + }% + }% + \gdef\tikzexternal@warning@at@end{1}% + }{}% + }, + optimize/.is choice, + optimize/true/.code={% + \tikzexternal@optimizetrue + \iftikzexternal@optimize + \ifpgf@external@grabshipout + \tikzexternal@optimize@REPLACE + \fi + \fi + }, + optimize/false/.code={% + \tikzexternal@optimizefalse% + \tikzexternal@optimize@RESTORE + },% + optimize=true, + optimize away text/.code={[ \textsc{\string#1\ optimized away because it does not contribute to exported PDF}]}, + optimize/install/.code={},% + optimize/restore/.code={},% + optimize command away/.code 2 args={% + \expandafter\global\expandafter\let\csname\string#1@ORIG\endcsname=#1% + \pgfkeysalso{% + /tikz/external/optimize/install/.append code={% + \def#1{\tikzexternal@optimize@away@cmd{#1}{#2}}% + }, + /tikz/external/optimize/restore/.append code={% + \expandafter\let\expandafter#1\csname\string#1@ORIG\endcsname + } + }% + \iftikzexternal@optimize + \ifpgf@external@grabshipout + \tikzexternal@optimize@REPLACE + \fi + \fi + }, + optimize command away=\includegraphics, + optimize command away=\pgfincludeexternalgraphics, + optimize latex env away/.code={% + \expandafter\let\expandafter\pgf@tempa\csname #1\endcsname + \expandafter\global\expandafter\let\csname #1@ORIG\endcsname=\pgf@tempa% + \pgfkeysalso{% + /tikz/external/optimize/install/.append code={% + \pgfutil@namedef{#1}{\tikzexternal@optimize@away@latex@env{#1}}% + }, + /tikz/external/optimize/restore/.append code={% + \pgfutil@namelet{#1}{#1@ORIG}% + }% + }% + }, + only named/.is if=tikzexternal@onlynamed, + only named/.default=true, + figure name/.initial=\tikzexternal@realjob-figure, + reset counter/.code={% + \expandafter\gdef\csname c@tikzext@no@#1\endcsname{0}% + },% + prefix/.code={\tikzsetexternalprefix{#1}}, + up to date check/.is choice, + up to date check/simple/.code={\def\tikzexternal@uptodate@mode{0}}, + up to date check/md5/.code={\def\tikzexternal@uptodate@mode{1}}, + up to date check/diff/.code={\def\tikzexternal@uptodate@mode{2}}, + up to date check=md5, +} + +\expandafter\def\csname tikzexternal@driver@pgfsys-luatex.def\endcsname{% + \pgfkeyssetvalue{/tikz/external/system call}{% + lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"% + }% +}% +\expandafter\def\csname tikzexternal@driver@pgfsys-pdftex.def\endcsname{% + \pgfutil@IfUndefined{directlua}{% + \pgfkeyssetvalue{/tikz/external/system call}{% + pdflatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"% + }% + }{% + \pgfkeyssetvalue{/tikz/external/system call}{% + lualatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"% + }% + }% +}% +\expandafter\def\csname tikzexternal@driver@pgfsys-xetex.def\endcsname{% + \pgfkeyssetvalue{/tikz/external/system call}{% + xelatex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource"% + }% +}% +\expandafter\def\csname tikzexternal@driver@pgfsys-dvips.def\endcsname{% + \pgfkeyssetvalue{/tikz/external/system call}{% + latex \tikzexternalcheckshellescape -halt-on-error -interaction=batchmode -jobname "\image" "\texsource" % + && dvips -o "\image".ps "\image".dvi % + }% +}% + +\pgfutil@ifundefined{tikzexternal@driver@\pgfsysdriver}{% + \csname tikzexternal@driver@pgfsys-pdftex.def\endcsname +}{% + \csname tikzexternal@driver@\pgfsysdriver\endcsname +}% + + +\def\tikzsetfigurename#1{\pgfkeyssetvalue{/tikz/external/figure name}{#1}}% +\def\tikzappendtofigurename#1{\pgfkeys{/tikz/external/figure name/.add={}{#1}}} + +\def\tikzsetexternalprefix#1{\def\tikzexternal@filenameprefix{#1}} +\tikzsetexternalprefix{} + +\def\tikzexternalize{% + \pgfutil@ifnextchar[{% + \tikzexternalize@opt + }{% + \tikzexternalize@opt[]% + }% +}% +\def\tikzexternalize@opt[#1]{% + \pgfutil@ifnextchar\bgroup{% + \tikzexternal@auto@detect@jobnamefalse + \tikzexternalize@opt@withname[#1]% + }{% + \tikzexternal@auto@detect@jobnametrue + \pgfutil@ifundefined{tikzexternalrealjob}{% + \let\tikzexternalrealjob=\jobname + }{}% + \def\pgf@tempa{\tikzexternalize@opt@withname[#1]}% + \expandafter\pgf@tempa\expandafter{\tikzexternalrealjob}% + }% +}% +\def\tikzexternalize@opt@withname[#1]#2{% + \gdef\tikzexternalrealjob{#2}% + \if1\tikzexternalize@hasbeencalled + \else + \pgfqkeys{/tikz/external}{#1}% + \def\tikzexternal@realjob{#2}% + \tikzexternalauxlock@init + \pgfrealjobname{#2}% + \def\tikzexternalize@hasbeencalled{1}% + \tikzexternalenable + \def\tikzexternal@determineimgextension##1:##2\relax{\gdef\tikzexternalimgextension{##1}}% + \xdef\pgf@tempa{\pgfsys@imagesuffixlist}% + \expandafter\tikzexternal@determineimgextension\pgf@tempa:\relax + \pgfutil@ifundefined{includegraphics}{% + \let\tikzexternal@orig@includegraphics=\relax + }{% + \let\tikzexternal@orig@includegraphics=\includegraphics + }% + \let\tikzexternalfiledependsonfile=\tikzexternalfiledependsonfile@ACTIVE + \let\tikzpicturedependsonfile=\tikzpicturedependsonfile@ACTIVE + \fi +} +\def\tikzexternalize@hasbeencalled{0}% + +\def\tikzifexternalizehasbeencalled#1#2{% + \if1\tikzexternalize@hasbeencalled + #1% + \else + #2% + \fi +}% + +\def\tikzexternalauxlock@init{% + \if4\tikzexternal@opmode + \ifpgfexternalreadmainaux + \edef\pgf@tempa{\expandafter\string\csname\tikzexternal@realjob\endcsname}% + \edef\pgf@tempb{\expandafter\string\csname\jobname\endcsname}% + \ifx\pgf@tempa\pgf@tempb + \tikzexternalauxlock@setlock{0}% + \else + \tikzexternalauxlock@getlockvalue + \if1\tikzexternallocked + \pgfexternalreadmainauxfalse + \else + \pgfexternalreadmainauxtrue + \fi + \fi + \else + \def\tikzexternalauxlock@setlock##1{}% + \fi + \fi +} +\def\tikzexternalauxlock@getlockvalue{% + \openin\r@pgf@reada=\tikzexternal@realjob.auxlock + \ifeof\r@pgf@reada + \def\tikzexternallocked{0}% + \else + \read\r@pgf@reada to\pgf@tempa + \pgf@tempa + \pgfutil@ifundefined + {tikzexternallocked} + {\def\tikzexternallocked{1}}% + {}% + \fi + \closein\r@pgf@reada +}% +\def\tikzexternalauxlock@setlock#1{% + \immediate\openout\w@pgf@writea=\tikzexternal@realjob.auxlock + \immediate\write\w@pgf@writea{\noexpand\def\noexpand\tikzexternallocked{#1}}% + \immediate\closeout\w@pgf@writea +} + + +\def\pgf@external@grab@refundefinedtrue@code{% + \gdef\noexpand\tikzexternal@systemcall@reschedule@to@end@document{1}% +}% + +\def\tikzexternalimgextension{}% + +\def\tikzexternaldisable{% + \tikzexternaldisable@nofading + \pgfutil@ifundefined{tikzexternal@orig@tikzfadingfrompicture} + {}% + {% + \let\tikzfadingfrompicture=\tikzexternal@orig@tikzfadingfrompicture + \let\endtikzfadingfrompicture=\tikzexternal@orig@endtikzfadingfrompicture + \let\tikzfading=\tikzexternal@orig@tikzfading + }% +}% +\def\tikzexternaldisable@nofading{% + \let\tikz=\tikzexternal@origtikz + \tikzexternal@TEXDIALECT@restore@picture + \iftikzexternal@optimize + \ifpgf@external@grabshipout + \tikzexternal@optimize@RESTORE + \fi + \fi +} +\def\tikzexternalenable{% + \if\tikzexternalize@hasbeencalled1% + \let\tikz=\tikzexternal@tikz@replacement + \tikzexternal@TEXDIALECT@installreplacement@picture + \pgfutil@ifundefined{tikzfadingfrompicture}% + {}% + {% + \pgfutil@ifundefined{tikzexternal@orig@tikzfadingfrompicture}{% + \let\tikzexternal@orig@tikzfadingfrompicture=\tikzfadingfrompicture + \let\tikzexternal@orig@endtikzfadingfrompicture=\endtikzfadingfrompicture + \let\tikzexternal@orig@tikzfading=\tikzfading + }{}% + \def\tikzfadingfrompicture{% + \begingroup + \tikzexternaldisable@nofading + \tikzexternal@orig@tikzfadingfrompicture}% + \def\endtikzfadingfrompicture{% + \tikzexternal@orig@endtikzfadingfrompicture + \endgroup}% + \def\tikzfading[##1]{% + \begingroup + \tikzexternaldisable@nofading + \tikzexternal@orig@tikzfading[##1]% + \endgroup}% + }% + \iftikzexternal@optimize + \ifpgf@external@grabshipout + \tikzexternal@optimize@REPLACE + \fi + \fi + \fi +}% + +\def\tikzsetnextfilename#1{\gdef\tikzexternal@nextfile{#1}} +\tikzsetnextfilename{} + + +\long\gdef\tikzexternal@TEXDIALECT@collectpicture#1#2\endtikzpicture{#1{#2}} +\def\tikzexternal@TEXDIALECT@begpicture{\tikzpicture} +\def\tikzexternal@TEXDIALECT@endpicture{\endtikzpicture}% +\def\tikzexternal@TEXDIALECT@installreplacement@picture{% + \let\tikzpicture=\tikzexternal@tikzpicture@replacement +}% +\def\tikzexternal@TEXDIALECT@restore@picture{% + \let\tikzpicture=\tikzexternal@origpicture +}% + + + + +\let\tikzexternal@origtikz=\tikz +\let\tikzexternal@origpicture=\tikzpicture +\let\tikzexternal@origendpicture=\endtikzpicture +\let\tikzexternal@curfilename=\relax + +\def\tikzexternal@tikzpicture@replacement{% + \leavevmode + \global\tikzexternal@file@isuptodatetrue% + \tikzexternal@getnextfilename\tikzexternal@curfilename + \ifx\tikzexternal@curfilename\pgfutil@empty + \ifpgf@external@grabshipout + \iftikzexternal@optimize + \let\tikzexternal@next=\tikzexternal@skipfigure + \else + \let\tikzexternal@next=\tikzexternal@normalpicture@nographics + \fi + \else + \let\tikzexternal@next=\tikzexternal@normalpicture@nographics + \fi + \else + \ifpgf@external@grabshipout + \tikzifexternaljobnamematches\tikzexternal@curfilename{% + \let\tikzexternal@next=\tikzexternal@externalizefig + }{% + \iftikzexternal@optimize + \let\tikzexternal@next=\tikzexternal@skipfigure + \else + \let\tikzexternal@next=\tikzexternal@normalpicture@nographics + \fi + }% + \else + \ifcase\tikzexternal@opmode\relax + \let\tikzexternal@next=\tikzexternal@forcegraphics + \or + \let\tikzexternal@next=\tikzexternal@normalpicture@nographics + \or + \let\tikzexternal@next=\tikzexternal@externalizefig + \or + \let\tikzexternal@next=\tikzexternal@listmodepicture + \or + \let\tikzexternal@next=\tikzexternal@externalizefig@systemcall + \or + \let\tikzexternal@next=\tikzexternal@list@and@makefile@mode@picture + \fi + \fi + \fi + \tikzexternal@next +}% + +\def\tikzexternal@tikz@replacement{% + \pgfutil@ifnextchar[{\tikzexternal@tikz@replacement@opt}{\tikzexternal@tikz@replacement@opt[]}% +}% +\def\tikzexternal@tikz@replacement@opt[#1]{% + \pgfutil@ifnextchar\bgroup{\tikzexternal@tikz@replacement@opt@{#1}}{\tikzexternal@tikz@replacement@opt@@{#1}}% +} +\long\def\tikzexternal@tikz@replacement@opt@#1#2{% + \tikzexternal@tikz@replacement@opt@process{#1}{#2}% +}% +\def\tikzexternal@tikz@replacement@opt@@#1{% + \def\tikz@next{\tikzexternal@tikz@replacement@collectnormalsemicolon{#1}}% + \ifnum\the\catcode`\;=\active\relax% + \def\tikz@next{\tikzexternal@tikz@replacement@collectactivesemicolon{#1}}% + \fi% + \tikz@next} +\long\def\tikzexternal@tikz@replacement@collectnormalsemicolon#1#2;{% + \tikzexternal@tikz@replacement@opt@process{#1}{#2;}% +}% +{ + \catcode`\;=\active + \long\gdef\tikzexternal@tikz@replacement@collectactivesemicolon#1#2;{% + \tikzexternal@tikz@replacement@opt@process{#1}{#2;}% + } +} +\long\def\tikzexternal@tikz@replacement@opt@process#1#2{% + \begingroup + \t@tikzexternal@tmpa=\expandafter{\tikzexternal@TEXDIALECT@begpicture[#1]#2}% + \t@tikzexternal@tmpb=\expandafter{\tikzexternal@TEXDIALECT@endpicture}% + \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb}% + \endgroup + \pgf@tempa +} + +\def\tikzexternal@getnextfilename@advancecount{% + \begingroup + \c@pgf@counta=\csname c@tikzext@no@\tikzexternal@figurename\endcsname\relax + \advance\c@pgf@counta by1 + \expandafter\xdef\csname c@tikzext@no@\tikzexternal@figurename\endcsname{\the\c@pgf@counta}% + \endgroup +}% + +\def\tikzexternalgetnextfilename#1{% + \begingroup + \let\tikzexternal@getnextfilename@advancecount\relax% + \let\tikzexternal@getnextfilename@resetglobals=\relax% + \def\tikzexternal@protocol@to@file##1{}% + \tikzexternal@getnextfilename#1% + \pgfmath@smuggleone#1% + \endgroup +}% + +\def\tikzexternalgetcurrentfilename#1{% + \ifx\tikzexternal@curfilename\relax + \let#1=\pgfutil@empty + \else + \let#1=\tikzexternal@curfilename + \fi +} + +\def\tikzexternal@getnextfilename#1{% + \let#1=\pgfutil@empty + \iftikzexternal@export@enabled + \iftikzexternalexportnext + \begingroup + \t@tikzexternal@tmpa=\expandafter{\tikzexternal@filenameprefix}% + \ifx\tikzexternal@nextfile\pgfutil@empty + \iftikzexternal@onlynamed + \xdef\pgf@tempa{}% + \else + \pgfkeysgetvalue{/tikz/external/figure name}\tikzexternal@figurename + \pgfutil@ifundefined{c@tikzext@no@\tikzexternal@figurename}{% + \expandafter\gdef\csname c@tikzext@no@\tikzexternal@figurename\endcsname{0}% + }{}% + \t@tikzexternal@tmpb=\expandafter{\tikzexternal@figurename}% + \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb\csname c@tikzext@no@\tikzexternal@figurename\endcsname}% + \tikzexternal@getnextfilename@advancecount + \fi + \else + \t@tikzexternal@tmpb=\expandafter{\tikzexternal@nextfile}% + \xdef\pgf@tempa{\the\t@tikzexternal@tmpa\the\t@tikzexternal@tmpb}% + \fi + \endgroup + \let#1=\pgf@tempa + \fi + \fi + \tikzexternal@getnextfilename@resetglobals% + \tikzexternal@protocol@to@file#1% +}% + +\def\tikzexternal@getnextfilename@resetglobals{% + \global\let\tikzexternal@nextfile=\pgfutil@empty + \global\tikzexternalexportnexttrue +}% + +\def\tikzexternal@protocol@to@file#1{% + \ifpgf@external@grabshipout% + \else + \iftikzexternal@genfigurelist + \edef\tikzexternal@temp{#1}% + \ifx\tikzexternal@temp\pgfutil@empty + \else + \pgfutil@ifundefined{tikzexternal@listmode@openedfile}{% + \message{Opening '\tikzexternal@realjob.figlist' for writing.}% + \begingroup + \globaldefs=1 + \csname newwrite\endcsname\tikzexternal@outfile + \endgroup + \immediate\openout\tikzexternal@outfile=\tikzexternal@realjob.figlist\relax + \gdef\tikzexternal@listmode@openedfile{1}% + \if\tikzexternal@opmode5% + \tikzexternal@list@and@make@prepare + \fi + }{}% + \iftikzexternal@verboseio + \pgf@typeout{Writing '#1' to '\tikzexternal@realjob.figlist'.}% + \fi + \immediate\write\tikzexternal@outfile{#1}% + \if\tikzexternal@opmode5% + \tikzexternal@list@and@make@gentarget{#1}% + \fi + \fi + \fi + \fi +}% + +\def\tikzexternal@list@and@make@gentarget#1{% + \tikzexternal@assemble@systemcall{#1}{\pgf@tempa}% + \def\tikzexternal@tempb{\pgfutilstrreplace{^^J}{^^J\tikzexternal@TABchar}}% + \expandafter\tikzexternal@tempb\expandafter{\pgf@tempa}% + \let\pgf@tempa=\pgfretval + \iftikzexternal@verboseio + \pgf@typeout{Writing '#1' to '\tikzexternal@realjob.makefile'.}% + \fi + \global\tikzexternal@file@isuptodatetrue% + \tikzexternal@checkforceremake% + \immediate\write\tikzexternal@outmakefile{#1\tikzexternalimgextension: \iftikzexternal@file@isuptodate\else FORCEREMAKE\fi}% + \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar\pgf@tempa}% + \immediate\write\tikzexternal@outmakefile{}% +} + +\def\tikzexternal@list@and@make@prepare{% + \iftikzexternal@verboseio + \pgf@typeout{Opening '\tikzexternal@realjob.makefile' for writing.}% + \fi + \begingroup + \globaldefs=1 + \csname newwrite\endcsname\tikzexternal@outmakefile + \endgroup + \immediate\openout\tikzexternal@outmakefile=\tikzexternal@realjob.makefile\relax + \immediate\write\tikzexternal@outmakefile{ALL_FIGURE_NAMES=\tikzexternal@DOLLARchar(shell cat \tikzexternal@realjob.figlist)}% + \immediate\write\tikzexternal@outmakefile{ALL_FIGURES=\tikzexternal@DOLLARchar(ALL_FIGURE_NAMES:\tikzexternal@PERCENTchar=\tikzexternal@PERCENTchar\tikzexternalimgextension)}% + \immediate\write\tikzexternal@outmakefile{}% + \immediate\write\tikzexternal@outmakefile{allimages: \tikzexternal@DOLLARchar(ALL_FIGURES)}% + \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar @echo All images exist now. Use make -B to re-generate them.}% + \immediate\write\tikzexternal@outmakefile{}% + \immediate\write\tikzexternal@outmakefile{FORCEREMAKE:}% + \immediate\write\tikzexternal@outmakefile{}% + \immediate\write\tikzexternal@outmakefile{-include $(ALL_FIGURE_NAMES:\tikzexternal@PERCENTchar=\tikzexternal@PERCENTchar.\tikzexternaldepext)}% + \immediate\write\tikzexternal@outmakefile{}% + \tikzexternalmakefiledefaultdeprule + \immediate\write\tikzexternal@outmakefile{}% + \tikzexternal@outmakefile@pendingcommands + \pgfutil@ifundefined{AtEndDocument}{}{% + \AtEndDocument{\pgf@typeout{===== mode=`list and make': Use 'make -f \tikzexternal@realjob.makefile' to generate all images. Then, re-run (pdf)latex \tikzexternal@realjob. =====}}% + }% +}% +\def\tikzexternaldepext{dep} + +\def\tikzexternalmakefiledefaultdeprule{% + \immediate\write\tikzexternal@outmakefile{\tikzexternal@PERCENTchar.\tikzexternaldepext:}% + \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar mkdir -p \tikzexternal@normal@dq $(dir $@)\tikzexternal@normal@dq}% + \immediate\write\tikzexternal@outmakefile{\tikzexternal@TABchar touch \tikzexternal@normal@dq $@\tikzexternal@normal@dq\space \tikzexternal@HASHchar\space will be filled later.}% +}% + +\def\tikzexternalifwritesmakefile#1#2{% + \if5\tikzexternal@opmode #1\else #2\fi +}% +\def\tikzexternal@outmakefile@pendingcommands{}% + +\def\tikzexternalwritetomakefile#1{% + \if\tikzexternal@opmode5% + \pgfutil@ifundefined{tikzexternal@outmakefile}{% + \expandafter\gdef\expandafter\tikzexternal@outmakefile@pendingcommands\expandafter{% + \tikzexternal@outmakefile@pendingcommands + \immediate\write\tikzexternal@outmakefile{#1}% + }% + }{% + \immediate\write\tikzexternal@outmakefile{#1}% + }% + \fi +}% + +\def\tikzexternal@dep@file@name{} + +\def\tikzexternalfiledependsonfile@ACTIVE#1#2{% + \begingroup + \def\tikzpicturedependsonfile@name{#1}% + \ifx\tikzpicturedependsonfile@name\pgfutil@empty + \else + \tikzifexternalizingcurrent + {\tikzexternalfiledependsonfile@append@to@dep@file{#1}{#2}}% + {\tikzexternalfiledependsonfile@append@to@makefile{#1}{#2}}% + \fi + \endgroup +}% +\def\tikzexternalfiledependsonfile#1#2{}% + +\def\tikzexternalfiledependsonfile@append@to@dep@file#1#2{% + \tikzexternalgetcurrentfilename\tikzpicturedependsonfile@name + \edef\tikzpicturedependsonfile@name{\tikzpicturedependsonfile@name.\tikzexternaldepext}% + \ifx\tikzexternal@dep@file@name\tikzpicturedependsonfile@name + \else + \pgfutil@ifundefined{tikzexternal@dep@file}{% + \begingroup + \globaldefs=1 + \csname newwrite\endcsname\tikzexternal@dep@file + \endgroup + }{}% + \ifx\tikzexternal@dep@file@name\pgfutil@empty + \else + \immediate\closeout\tikzexternal@dep@file + \fi + \global\let\tikzexternal@dep@file@name=\tikzpicturedependsonfile@name + \immediate\openout\tikzexternal@dep@file=\tikzexternal@dep@file@name\relax + \fi + \immediate\write\tikzexternal@dep@file{#1\tikzexternalimgextension: #2}% +} + +\def\tikzexternalfiledependsonfile@append@to@makefile#1#2{% + \edef\tikzexternal@temp{#1\tikzexternalimgextension: #2}% + \expandafter\tikzexternalwritetomakefile\expandafter{\tikzexternal@temp}% +} + +\def\tikzpicturedependsonfile@ACTIVE#1{% + \begingroup + \tikzexternalgetcurrentfilename\tikzpicturedependsonfile@name + \ifx\tikzpicturedependsonfile@name\pgfutil@empty + \tikzexternalgetnextfilename\tikzpicturedependsonfile@name + \fi + \expandafter\tikzexternalfiledependsonfile\expandafter{\tikzpicturedependsonfile@name}{#1}% + \endgroup +}% +\def\tikzpicturedependsonfile#1{}% + + +\def\tikzexternal@externalizefig{% + \ifpgf@external@grabshipout% + \expandafter\tikzexternal@externalizefig@GRAB% + \else + \expandafter\tikzexternal@externalizefig@mode@graphics@if@exists + \fi% +} +\def\tikzexternal@externalizefig@mode@graphics@if@exists{% + \gdef\pgf@filename{}% + \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}% + \pgf@tempa + \ifx\pgf@filename\pgfutil@empty% + \expandafter\tikzexternal@normalpicture@nographics + \else + \expandafter\tikzexternal@forcegraphics + \fi +}% + + +\def\tikzexternal@optimize@away@cmd#1#2{% + \pgfutil@ifnextchar[{% + \tikzexternal@optimize@away@cmd@{#1}{#2}% + }{% + \tikzexternal@optimize@away@cmd@{#1}{#2}[]% + }% +}% +\def\tikzexternal@optimize@away@cmd@#1#2[#3]{% + \def\tikz@temp{#2}% + \ifx\tikz@temp\pgfutil@empty + \def\tikz@temp{\tikzexternal@optimize@away@cmd@auto{#1}{#3}}% + \else + \ifcase#2\relax + \def\tikzexternal@optimize@away@cmd@manual{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7##8{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}{##8}}% + }% + \or + \def\tikzexternal@optimize@away@cmd@manual##1##2##3##4##5##6##7##8##9{% + \tikzexternal@optimize@away@cmd@@@{#1}{#3}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}{##8}{##9}}% + }% + \fi + \def\tikz@temp{\tikzexternal@optimize@away@cmd@manual}% + \fi + \tikz@temp +}% +\def\tikzexternal@optimize@away@cmd@auto#1#2{% + \pgfutil@ifnextchar\bgroup{% + \tikzexternal@optimize@away@cmd@auto@{#1}{#2}% + }{% + \tikzexternal@optimize@away@cmd@auto@{#1}{#2}{}% + } +}% + +\def\tikzexternal@optimize@away@cmd@auto@#1#2#3{% + \tikzexternal@optimize@away@cmd@@@{#1}{#2}{{#3}}% +}% +\def\tikzexternal@optimize@away@cmd@@@#1#2#3{% + \begingroup + \toks0={#1[#2]#3}% + \iftikzexternal@verbose@optimize + \pgf@typeout{The command '\the\toks0' has been optimized away. Use '/tikz/external/optimize=false' to disable this.}% + \fi + \endgroup + \begingroup + \pgfkeysvalueof{/tikz/external/optimize away text/.@cmd}#1\pgfeov% + \endgroup +}% + +\def\tikzexternal@optimize@away@latex@env#1{% + \def\tikzexternal@optimize@away@latex@env@{#1}% + \begingroup + \def\tikzexternal@laTeX@collect@until@end@tikzpicturetikzpicturestring{#1}% + \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@optimize@away@latex@env@close +}% +\long\def\tikzexternal@optimize@away@latex@env@close#1{% + \iftikzexternal@verbose@optimize + \pgf@typeout{The complete contents of \string\begin{tikzexternal@optimize@away@latex@env@} up to the next \end{tikzexternal@optimize@away@latex@env@} has been optimized away because it does not contribute to the exported PDF. Use '/tikz/external/optimize=false' to disable this.}% + \fi + \endgroup + \expandafter\let\csname end\tikzexternal@optimize@away@latex@env@\endcsname=\relax + \expandafter\end\expandafter{\tikzexternal@optimize@away@latex@env@}% +}% + +\def\tikzexternal@optimize@REPLACE{% + \pgfkeysvalueof{/tikz/external/optimize/install/.@cmd}\pgfeov +}% + +\def\tikzexternal@optimize@RESTORE{% + \pgfkeysvalueof{/tikz/external/optimize/restore/.@cmd}\pgfeov +}% + +\def\tikzexternal@closeenvironments{% + \let\endtikzpicture=\relax + \tikzexternal@TEXDIALECT@endpicture + \let\endtikzpicture=\tikzexternal@origendpicture + \let\tikzexternal@curfilename=\relax +} + +\def\tikzexternal@skipfigure{% + \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@skipfigure@@ +} +\long\def\tikzexternal@skipfigure@@#1{% + \iftikzexternal@verbose@optimize + \pgf@typeout{A tikzpicture has been optimized away. Use '/tikz/external/optimize=false' to disable this.}% + \fi + \tikzexternal@closeenvironments + \pgfkeysvalueof{/tikz/external/optimize away text/.@cmd}tikzpicture\pgfeov% +} + +\def\tikzexternal@normalpicture@nographics{% + \tikzexternal@nestedflagfalse + \let\tikzpicture=\tikzexternal@normalpicture@begreplace + \let\endtikzpicture=\tikzexternal@normalpicture@endreplace + \tikzpicture +} +\def\tikzexternal@normalpicture@begreplace{% + \begingroup + \tikzexternal@nestedflagtrue + \tikzexternal@origpicture +} +\def\tikzexternal@normalpicture@endreplace{% + \tikzexternal@origendpicture + \endgroup + \iftikzexternal@nestedflag + \else + \let\tikzpicture=\tikzexternal@tikzpicture@replacement + \let\endtikzpicture=\tikzexternal@origendpicture + \fi +}% + +\def\tikzexternal@forcegraphics{% + \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@forcegraphics@@ +} +\long\def\tikzexternal@forcegraphics@@#1{\tikzexternal@forcegraphics@@@}% +\def\tikzexternal@forcegraphics@@@{% + \if5\tikzexternal@opmode + \let\tikz@refundefinedtrue@@=\G@refundefinedtrue + \gdef\G@refundefinedtrue{% + \tikz@refundefinedtrue@@ + \tikzexternal@forceremake@undefined@reference@handler + }% + \fi + \expandafter\pgfincludeexternalgraphics\expandafter{\tikzexternal@curfilename}% + \if5\tikzexternal@opmode + \global\let\G@refundefinedtrue=\tikz@refundefinedtrue@@ + \fi + \tikzexternal@closeenvironments +} + +\def\tikzexternal@forceremake@undefined@reference@handler{% + \pgf@typeout{===== 'mode=list and make': encountered undefined reference in current picture. Adding dependency to FORCEREMAKE. Rerun make to update the picture.' ========^^J}% + \tikzpicturedependsonfile{FORCEREMAKE}% +}% + +\def\tikzexternal@listmodepicture{% + \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@listmodepicture@@ +} +\long\def\tikzexternal@listmodepicture@@#1{\tikzexternal@listmodepicture@@@} +\def\tikzexternal@listmodepicture@@@{% + \pgfkeysvalueof{/tikz/external/image discarded text}% + \tikzexternal@closeenvironments +} + +\def\tikzexternal@list@and@makefile@mode@picture{% + \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@list@and@makefile@mode@picture@ +}% +\long\def\tikzexternal@list@and@makefile@mode@picture@#1{% + \tikzexternal@check@uptodate@mode{#1}% + \gdef\pgf@filename{}% + \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}% + \pgf@tempa + \ifx\pgf@filename\pgfutil@empty% + \expandafter\tikzexternal@listmodepicture@@@ + \else + \expandafter\tikzexternal@forcegraphics@@@ + \fi +}% + +\def\tikzexternal@externalizefig@before@grab{% + \pgfutil@IfUndefined{TP@holdbox}{% + }{% + \global\setbox\TP@holdbox\vbox{}% + }% +}% + +\def\tikzexternal@externalizefig@GRAB{% + \ifpgf@external@grabshipout + \iftikzexternal@optimize + \tikzexternal@optimize@RESTORE + \fi + \tikzexternal@externalizefig@before@grab + \fi + \def\tikzpicture{% + \def\tikzpicture{% + \begingroup + \def\endtikzpicture{% + \tikzexternal@origendpicture + \endgroup + }% + \tikzexternal@origpicture + }% + \pgf@external@grab{\tikzexternal@curfilename}% + \tikzexternal@origpicture + }% + \def\endtikzpicture{% + \tikzexternal@origendpicture + \pgf@externalend + \tikzexternal@ensure@nonempty@floats + \let\tikzpicture=\tikzexternal@tikzpicture@replacement + \let\endtikzpicture=\tikzexternal@origendpicture + \iftikzexternal@optimize + \ifpgf@external@grabshipout + \tikzexternal@optimize@REPLACE + \fi + \fi + }% + \tikzpicture +}% + +\def\tikzexternal@ensure@nonempty@floats{% + tikzexternal: picture has been externalized. This text is required to avoid empty floats. +}% + +\def\tikzexternal@externalizefig@systemcall{% + \tikzexternal@TEXDIALECT@collectpicture\tikzexternal@externalizefig@systemcall@@ +} + +{ +\catcode`\"=12 +\catcode`\'=12 +\catcode`\;=12 +\catcode`\&=12 +\catcode`\-=12 +\xdef\tikzexternal@normal@dq{"} +\xdef\tikzexternal@normal@sq{'} +\xdef\tikzexternal@normal@semic{;} +\xdef\tikzexternal@normal@and{&} +\xdef\tikzexternal@normal@dash{-} +\catcode`\"=13 +\catcode`\'=13 +\catcode`\;=13 +\catcode`\&=13 +\catcode`\-=13 +\gdef\tikzexternal@activate@normal@dq{\let"=\tikzexternal@normal@dq} +\gdef\tikzexternal@activate@normal@sq{\let'=\tikzexternal@normal@sq} +\gdef\tikzexternal@activate@normal@semic{\let;=\tikzexternal@normal@semic} +\gdef\tikzexternal@activate@normal@and{\let&=\tikzexternal@normal@and} +\gdef\tikzexternal@activate@normal@dash{\let-=\tikzexternal@normal@dash} +\catcode`\|=0 +\catcode`\\=12 +|xdef|tikzexternal@normal@backslash{\}% +} +{ +\catcode`\^^I=12 +\catcode`\$=12 +\catcode`\%=12 +\catcode`\#=12 +\gdef\tikzexternal@HASHchar{#} +\gdef\tikzexternal@TABchar{^^I}\gdef\tikzexternal@PERCENTchar{%}\xdef\tikzexternal@DOLLARchar{$}} + +\def\tikzexternal@assemble@systemcall#1#2{% + \begingroup + \def\image{#1}% + \iftikzexternal@auto@detect@jobname + \edef\texsource{\string\def\string\tikzexternalrealjob{\tikzexternal@realjob}\string\input{\tikzexternal@realjob}}% + \else + \let\texsource=\tikzexternal@realjob + \fi + \ifnum\the\catcode`\"=13 \tikzexternal@activate@normal@dq\fi + \ifnum\the\catcode`\'=13 \tikzexternal@activate@normal@sq\fi + \ifnum\the\catcode`\;=13 \tikzexternal@activate@normal@semic\fi + \ifnum\the\catcode`\-=13 \tikzexternal@activate@normal@dash\fi + \let\\=\tikzexternal@normal@backslash + \xdef#2{\pgfkeysvalueof{/tikz/external/system call}}% + \endgroup +}% +\long\def\tikzexternal@externalizefig@systemcall@@#1{% + \tikzexternal@externalizefig@systemcall@uptodatecheck{#1}% + \tikzexternal@assemble@systemcall{\tikzexternal@curfilename}{\pgf@tempa}% + \global\let\tikzexternal@cursyscall=\pgf@tempa + \gdef\tikzexternal@typeset@picture@on@failure{1}% + \iftikzexternal@file@isuptodate + \iftikzexternal@verboseio + \pgf@typeout{===== Image '\tikzexternal@curfilename' is up-to-date. ======}% + \fi + \let\pgf@filename=\tikzexternal@curfilename + \else + \begingroup + \tikzexternalauxlock@setlock1% + \tikzexternal@externalizefig@systemcall@call{\tikzexternal@cursyscall}% + \tikzexternalauxlock@setlock0% + \expandafter\tikzexternal@externalizefig@systemcall@assertsuccess\expandafter{\tikzexternal@cursyscall}% + \pgfmath@smuggleone\pgf@filename + \endgroup + \fi + \ifx\pgf@filename\pgfutil@empty + \if1\tikzexternal@typeset@picture@on@failure + \begingroup + \toks0={% + \tikzexternaldisable + }% + \toks1={% + \tikzpicture + #1% + }% + \toks2={% + \tikzexternal@TEXDIALECT@endpicture + \tikzexternalenable + }% + \xdef\tikzexternal@externalizefig@systemcall@next{% + \the\toks0 + \noexpand\scantokens{\the\toks1 }% + \the\toks2 + }% + \endgroup + \else + \gdef\tikzexternal@externalizefig@systemcall@next{\tikzexternal@closeenvironments}% + \fi + \else + \gdef\tikzexternal@systemcall@reschedule@to@end@document{0}% + \expandafter\pgfincludeexternalgraphics\expandafter{\tikzexternal@curfilename}% + \if1\tikzexternal@systemcall@reschedule@to@end@document + \pgfutil@IfUndefined{AtVeryEndDocument}{% + }{% + \pgf@typeout{===== The previous system call resulted in undefined references inside of the output file. Rescheduling it for \string\end{document}. ========}% + \expandafter\tikzexternal@externalizefig@systemcall@reschedule\expandafter{\tikzexternal@cursyscall}% + }% + \fi + \gdef\tikzexternal@externalizefig@systemcall@next{\tikzexternal@closeenvironments}% + \fi + \tikzexternal@externalizefig@systemcall@next +}% + +\def\tikzexternal@externalizefig@systemcall@call#1{% + \iftikzexternal@verboseio + \pgf@typeout{===== 'mode=convert with system call': Invoking '#1' ========}% + \fi + \pgfutil@shellescape{#1}% +}% + +\def\tikzexternal@checkforceremake{% + \iftikzexternal@force@remake + \global\tikzexternal@file@isuptodatefalse + \else + \iftikzexternalremakenext + \global\tikzexternal@file@isuptodatefalse + \global\tikzexternalremakenextfalse + \fi + \fi +} + +\pgfutil@IfUndefined{pdfmdfivesum}{% +}{% + \let\tikzexternal@mdfivesum=\pdfmdfivesum +}% + +\long\def\tikzexternal@computemdfivesum#1{% + \t@tikzexternal@tmpb={#1}% + \edef\tikzexternal@temp{\the\t@tikzexternal@tmpb}% + \edef\pgfretval{\tikzexternal@mdfivesum{\meaning\tikzexternal@temp}}% +} +\long\def\tikzexternal@computemdfivesum@diff@fallback#1{% + \t@tikzexternal@tmpb={#1}% + \edef\tikzexternal@temp{\the\t@tikzexternal@tmpb}% + \edef\pgfretval{\meaning\tikzexternal@temp}% +} + +\long\def\tikzexternal@hashfct@serialize@std#1{% + \noexpand\def\noexpand\tikzexternallastkey{#1}% +}% + +\long\def\tikzexternal@hashfct@serialize@tok#1{% + \noexpand\begingroup + \noexpand\toks0={#1}% + \noexpand\xdef\noexpand\tikzexternallastkey{\noexpand\the\noexpand\toks0 }% + \noexpand\endgroup +}% + +\def\tikzexternal@check@uptodate@ext{.md5} + +\def\tikzexternal@check@uptodate@mode@warn@fallback{% + \message{Package tikz Warning: The key 'up to date check=md5' is impossible, there is no macro to compute MD5. Falling back to 'up to date check=diff'.}% + \global\let\tikzexternal@check@uptodate@mode@warn@fallback=\relax +}% + +\long\def\tikzexternal@check@uptodate@mode#1{% + \if1\tikzexternal@uptodate@mode + \pgfutil@IfUndefined{tikzexternal@mdfivesum}{% + \tikzexternal@check@uptodate@mode@warn@fallback + \def\tikzexternal@uptodate@mode{2}% + }{}% + \fi + \ifcase\tikzexternal@uptodate@mode + \let\tikzexternal@hashfct=\pgfutil@empty + \let\tikzexternal@hashfct@serialize=\pgfutil@empty + \or + \let\tikzexternal@hashfct=\tikzexternal@computemdfivesum + \let\tikzexternal@hashfct@serialize=\tikzexternal@hashfct@serialize@std + \or + \let\tikzexternal@hashfct=\tikzexternal@computemdfivesum@diff@fallback + \let\tikzexternal@hashfct@serialize=\tikzexternal@hashfct@serialize@tok + \fi + \ifx\tikzexternal@hashfct\pgfutil@empty + \else + \tikzpicturedependsonfile{\tikzexternal@curfilename\tikzexternal@check@uptodate@ext}% + \tikzexternal@hashfct{#1}% + \let\tikzexternal@lastkey@new=\pgfretval + \begingroup + \global\let\tikzexternallastkey=\pgfutil@empty + \openin\r@pgf@reada=\tikzexternal@curfilename\tikzexternal@check@uptodate@ext\relax % + \ifeof\r@pgf@reada + \else + \endlinechar=-1 % + \read\r@pgf@reada to\pgf@tempa + \pgf@tempa + \fi + \closein\r@pgf@reada + \let\tikzexternal@lastkey=\tikzexternallastkey + \pgfmath@smuggleone\tikzexternal@lastkey + \endgroup + \edef\tikzexternal@lastkey@normalized{\meaning\tikzexternal@lastkey}% + \edef\tikzexternal@lastkey@new@normalized{\meaning\tikzexternal@lastkey@new}% + \iftikzexternal@verboseuptodate + \pgf@typeout{Up-to-date check of \tikzexternal@curfilename: new \tikzexternal@lastkey@new@normalized; old \tikzexternal@lastkey@normalized.^^J}% + \fi + \ifx\tikzexternal@lastkey@normalized\tikzexternal@lastkey@new@normalized + \tikzexternal@file@isuptodatetrue + \else + \tikzexternal@file@isuptodatefalse + \immediate\openout\w@pgf@writea=\tikzexternal@curfilename\tikzexternal@check@uptodate@ext\relax% + \immediate\write\w@pgf@writea{\tikzexternal@hashfct@serialize{\tikzexternal@lastkey@new}\tikzexternal@PERCENTchar}% + \immediate\closeout\w@pgf@writea + \fi + \fi +} + +\long\def\tikzexternal@externalizefig@systemcall@uptodatecheck#1{% + \tikzexternal@check@uptodate@mode{#1}% + \tikzexternal@checkforceremake + \iftikzexternal@file@isuptodate + \gdef\pgf@filename{}% + \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}% + \pgf@tempa + \ifx\pgf@filename\pgfutil@empty% + \global\tikzexternal@file@isuptodatefalse + \fi + \fi +}% + +\def\tikzexternal@externalizefig@systemcall@assertsuccess#1{% + \gdef\pgf@filename{}% + \xdef\pgf@tempa{\noexpand\pgf@findfile\pgfsys@imagesuffixlist:+{\tikzexternal@curfilename}}% + \pgf@tempa + \ifx\pgf@filename\pgfutil@empty% + \tikzexternal@externalizefig@systemcall@handleexception{#1}% + \fi +}% +\def\tikzexternal@externalizefig@systemcall@handleexception@msg#1{% + \tikzerror{Sorry, the system call '#1' did NOT result in a usable output file '\tikzexternal@curfilename' (expected one of \pgfsys@imagesuffixlist). Please verify that you have enabled system calls. For pdflatex, this is 'pdflatex -shell-escape'. Sometimes it is also named 'write 18' or something like that. Or maybe the command simply failed? Error messages can be found in '\tikzexternal@curfilename.log'. If you continue now, I'll try to typeset the picture}{}% +} +\def\tikzexternal@externalizefig@systemcall@handleexception@retry@later#1{% + \gdef\tikzexternal@systemcall@reschedule@to@end@document{0}% + \expandafter\pgfexternalreaddpth\expandafter{\tikzexternal@curfilename}% + \if1\tikzexternal@systemcall@reschedule@to@end@document + \pgfutil@IfUndefined{AtVeryEndDocument}{% + \tikzexternal@externalizefig@systemcall@handleexception@msg{#1}% + }{% + \pgf@typeout{===== The last system call resulted in an EMPTY output file. Maybe it is part of \string\ref. Rescheduling it for \string\end{document}. ========}% + \gdef\tikzexternal@typeset@picture@on@failure{0}% + \tikzexternal@externalizefig@systemcall@reschedule{#1}% + }% + \else + \tikzexternal@externalizefig@systemcall@handleexception@msg{#1}% + \fi +} + +\def\tikzexternal@externalizefig@systemcall@reschedule#1{% + \t@tikzexternal@tmpb={% + \global\let\tikzexternal@externalizefig@systemcall@handleexception=\tikzexternal@externalizefig@systemcall@handleexception@msg% + \tikzexternal@externalizefig@systemcall@call{#1}% + \tikzexternal@externalizefig@systemcall@assertsuccess{#1}% + }% + \xdef\pgfutil@tempa{% + \noexpand\def\noexpand\tikzexternal@curfilename{\tikzexternal@curfilename}% + \the\t@tikzexternal@tmpb + }% + \expandafter\AtVeryEndDocument\expandafter{\pgfutil@tempa}% + \gdef\tikzexternal@has@rescheduled@something{1}% +}% +\let\tikzexternal@externalizefig@systemcall@handleexception=\tikzexternal@externalizefig@systemcall@handleexception@retry@later% + +\def\tikzexternal@has@rescheduled@something{0}% +\pgfutil@IfUndefined{AtVeryEndDocument}{}{% + \AtVeryEndDocument{% + \if1\tikzexternal@has@rescheduled@something + \pgf@typeout{===== tikzexternal: \string\end{document} reached. Working on rescheduled images to resolve references... ========}% + \fi + }% +} + +\def\pgfexternal@error@no@shipout{% + \begingroup + \begingroup + \immediate\openout\pgf@plotwrite=\pgfactualjobname.dpth + \let\w@pgfexternal@auxout=\pgf@plotwrite + \pgfexternalstorecommand@isexporting{\gdef\noexpand\tikzexternal@systemcall@reschedule@to@end@document{1}}% + \immediate\closeout\pgf@plotwrite + \endgroup + \tikzexternal@assemble@systemcall{\pgfactualjobname}{\pgf@tempa}% + \toks0=\expandafter{\pgf@tempa}% + \tikzerror{Sorry, image externalization failed: the resulting image was EMPTY. I tried to externalize '\pgfactualjobname', but it seems there is no such image in the document!? + \if\tikzexternal@opmode4 ^^J +\space\space You are currently using 'mode=convert with system call'. This problem can happen if the image (or one of the images preceding it) was declared inside of a \string\label{} (i.e. in the .aux file): 'convert with system call' has no access to the main aux file.^^J +\space\space Possible solutions in this case:^^J +\space\space (a) Try using 'mode=list and make',^^J +\space\space (b) Issue the externalization command '\the\toks0' *manually* (also check the preceding externalized images, perhaps the file name sequence is not correct).^^J +\space\space Repeat: the resulting image was EMPTY, your attention is required +\else + \if\tikzexternal@opmode5 ^^J +\space\space You are currently using 'mode=list and make'. Possible solutions:^^J +\space\space (a) Try to delete `\tikzexternal@realjob.makefile'. Perhaps it is not up-to-date.^^J +\space\space (b) Perhaps pictures are declared inside of \string\label{} and the .aux file is not up-to-date. Re-run latex, perhaps re-generate the graphics as well.^^J +\space\space Repeat: the resulting image was EMPTY, your attention is required + \fi +\fi}% + \endgroup +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary3d.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary3d.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a8a0090648183e4aa1af6875f90785745d7f02e7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrary3d.code.tex @@ -0,0 +1,97 @@ + +\ProvidesFileRCS{tikzlibrary3d.code.tex} + + + + +\tikzdeclarecoordinatesystem{xyz cylindrical} +{% + \pgfset{/tikz/cs/.cd,angle=0,radius=0,z=0,#1}% + \pgfpointcylindrical{\tikz@cs@angle}{\tikz@cs@xradius}{\tikz@cs@z}% +}% + +\tikzdeclarecoordinatesystem{xyz spherical} +{% + \pgfset{/tikz/cs/.cd,angle=0,radius=0,latitude=0,longitude=0,#1}% + \pgfpointspherical{\tikz@cs@angle}{\tikz@cs@latitude}{\tikz@cs@xradius}% +}% + +\pgfset{/tikz/cs/longitude/.store in=\tikz@cs@angle}% +\pgfset{/tikz/cs/latitude/.store in=\tikz@cs@latitude}% + + + +\tikzoption{plane origin}{\def\tikz@plane@origin{\tikz@scan@one@point\pgfutil@firstofone#1}}% +\tikzoption{plane x}{\def\tikz@plane@x{\tikz@scan@one@point\pgfutil@firstofone#1}}% +\tikzoption{plane y}{\def\tikz@plane@y{\tikz@scan@one@point\pgfutil@firstofone#1}}% + +\let\tikz@plane@origin=\pgfpointorigin +\def\tikz@plane@x{\pgfpointxy{1}{0}}% +\def\tikz@plane@y{\pgfpointxy{0}{1}}% + +\tikzoption{canvas is plane}[]{ + \tikz@canvas@is@plane +}% +\tikzoption{canvas is xy plane at z}[]{% + \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}% + \def\tikz@plane@x{\pgfpointxyz{1}{0}{#1}}% + \def\tikz@plane@y{\pgfpointxyz{0}{1}{#1}}% + \tikz@canvas@is@plane +}% +\tikzoption{canvas is yx plane at z}[]{% + \def\tikz@plane@origin{\pgfpointxyz{0}{0}{#1}}% + \def\tikz@plane@x{\pgfpointxyz{0}{1}{#1}}% + \def\tikz@plane@y{\pgfpointxyz{1}{0}{#1}}% + \tikz@canvas@is@plane +}% +\tikzoption{canvas is xz plane at y}[]{% + \def\tikz@plane@origin{\pgfpointxyz{0}{#1}{0}}% + \def\tikz@plane@x{\pgfpointxyz{1}{#1}{0}}% + \def\tikz@plane@y{\pgfpointxyz{0}{#1}{1}}% + \tikz@canvas@is@plane +}% +\tikzoption{canvas is zx plane at y}[]{% + \def\tikz@plane@origin{\pgfpointxyz{0}{#1}{0}}% + \def\tikz@plane@x{\pgfpointxyz{0}{#1}{1}}% + \def\tikz@plane@y{\pgfpointxyz{1}{#1}{0}}% + \tikz@canvas@is@plane +}% +\tikzoption{canvas is yz plane at x}[]{% + \def\tikz@plane@origin{\pgfpointxyz{#1}{0}{0}}% + \def\tikz@plane@x{\pgfpointxyz{#1}{1}{0}}% + \def\tikz@plane@y{\pgfpointxyz{#1}{0}{1}}% + \tikz@canvas@is@plane +}% +\tikzoption{canvas is zy plane at x}[]{% + \def\tikz@plane@origin{\pgfpointxyz{#1}{0}{0}}% + \def\tikz@plane@x{\pgfpointxyz{#1}{0}{1}}% + \def\tikz@plane@y{\pgfpointxyz{#1}{1}{0}}% + \tikz@canvas@is@plane +}% + + + + +\def\tikz@canvas@is@plane{ + \pgf@process{\tikz@plane@x}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@plane@y}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{\tikz@plane@origin}% + \edef\pgf@marshal{\noexpand\tikz@addtransform{% + \noexpand\pgftransformtriangle + {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}} + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}} + \noexpand\pgftransformscale{0.035146}% + \noexpand\pgfsetxvec{\noexpand\pgfpoint{1cm}{0cm}}% + \noexpand\pgfsetyvec{\noexpand\pgfpoint{0cm}{1cm}}% + \noexpand\pgfsetzvec{\noexpand\pgfpoint{0cm}{0cm}}% + }}% + \pgf@marshal% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..db9cbdd790621138bc5cfeb73252a7e70950daff --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryangles.code.tex @@ -0,0 +1,89 @@ + +\ProvidesFileRCS{tikzlibraryangles.code.tex} + + +\tikzset{ + pics/angle/.style = { + setup code = \tikz@lib@angle@parse#1\pgf@stop, + code = {}, + background code = \tikz@lib@angle@background#1\pgf@stop, + foreground code = \tikz@lib@angle@foreground#1\pgf@stop, + }, + pics/right angle/.style = { + setup code = \tikz@lib@angle@parse#1\pgf@stop, + code = {}, + background code = \tikz@lib@rightangle@background#1\pgf@stop, + foreground code = \tikz@lib@rightangle@foreground#1\pgf@stop, + }, + pics/angle/.default=A--B--C, + angle eccentricity/.initial=.6, + angle radius/.initial=5mm, +}% + +\def\tikz@lib@angle@background#1--#2--#3\pgf@stop{% + \path [name prefix ..] [pic actions, draw=none] (#2.center) + -- ++(\tikz@start@angle@temp:\tikz@lib@angle@rad pt) + arc [start angle=\tikz@start@angle@temp, end + angle=\tikz@end@angle@temp, radius=\tikz@lib@angle@rad pt] -- cycle; +}% + +\def\tikz@lib@angle@foreground#1--#2--#3\pgf@stop{% + \path [name prefix ..] [pic actions, fill=none, shade=none] + ([shift={(\tikz@start@angle@temp:\tikz@lib@angle@rad pt)}]#2.center) + arc [start angle=\tikz@start@angle@temp, end + angle=\tikz@end@angle@temp, radius=\tikz@lib@angle@rad pt]; + \ifx\tikzpictext\relax\else% + \def\pgf@temp{\node()[name prefix + ..,at={([shift={({.5*\tikz@start@angle@temp+.5*\tikz@end@angle@temp}:\pgfkeysvalueof{/tikz/angle + eccentricity}*\tikz@lib@angle@rad pt)}]#2.center)}]} + \expandafter\pgf@temp\expandafter[\tikzpictextoptions]{\tikzpictext};% + \fi +}% + +\def\tikz@lib@rightangle@background#1--#2--#3\pgf@stop{% + \path [name prefix ..] [pic actions, draw=none] (#2.center) + -- ++(\tikz@start@angle@temp:\tikz@lib@angle@rad pt) + -- ++(\tikz@end@angle@temp:\tikz@lib@angle@rad pt) + -- ++(\tikz@start@angle@temp:-\tikz@lib@angle@rad pt) + -- cycle; +}% + +\def\tikz@lib@rightangle@foreground#1--#2--#3\pgf@stop{% + \path [name prefix ..] [pic actions, fill=none, shade=none] + ([shift={(\tikz@start@angle@temp:\tikz@lib@angle@rad pt)}]#2.center) + -- ++(\tikz@end@angle@temp:\tikz@lib@angle@rad pt) + -- ++(\tikz@start@angle@temp:-\tikz@lib@angle@rad pt); + \ifx\tikzpictext\relax\else% + \def\pgf@temp{\node()[name prefix + ..,at={([shift={({.5*\tikz@start@angle@temp+.5*\tikz@end@angle@temp}:\pgfkeysvalueof{/tikz/angle + eccentricity}*1.4142136*\tikz@lib@angle@rad pt)}]#2.center)}]} + \expandafter\pgf@temp\expandafter[\tikzpictextoptions]{\tikzpictext};% + \fi +}% + +\def\tikz@lib@angle@parse#1--#2--#3\pgf@stop{% + \pgfmathsetmacro\tikz@lib@angle@rad{\pgfkeysvalueof{/tikz/angle radius}} + \ifdim\tikz@lib@angle@rad pt>0pt\else\def\tikz@lib@angle@rad{12}\fi% + \pgf@process{\pgfpointanchor{#2}{center}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointanchor{#1}{center}}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{\pgfpointanchor{#3}{center}}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \advance\pgf@xc by-\pgf@xa% + \advance\pgf@yc by-\pgf@ya% + \pgfmathsetmacro{\tikz@start@angle@temp}{atan2(\the\pgf@yb,\the\pgf@xb)} + \pgfmathsetmacro{\tikz@end@angle@temp}{atan2(\the\pgf@yc,\the\pgf@xc)} + \ifdim\tikz@end@angle@temp pt<\tikz@start@angle@temp pt% + \pgfmathsetmacro{\tikz@start@angle@temp}{\tikz@start@angle@temp-360}% + \fi% +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryanimations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryanimations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..703e103eaf1678632e5e2d95eeb4f0403c049786 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryanimations.code.tex @@ -0,0 +1,790 @@ + +\ProvidesFileRCS{tikzlibraryanimations.code.tex} + +\usepgfmodule{animations}% + + + + +\def\tikz@collect@scope@anims#1{% + \let\tikz@scope@anims\pgfutil@empty% + \let\tikz@collect@command#1% + \tikz@collect@scope@anims@parse% +}% +\def\tikz@collect@scope@anims@parse{% + \pgfutil@ifnextchar[{\tikz@collect@scope@anims@opt}{% + \pgfutil@ifnextchar:{\tikz@collect@scope@anims@go}{% + \tikz@collect@scope@anims@done}}% +}% +\def\tikz@collect@scope@anims@done{% + \expandafter\tikz@collect@command\expandafter[\tikz@scope@anims]% +}% +\def\tikz@collect@scope@anims@opt[{% + \expandafter\tikz@collect@command\expandafter[\tikz@scope@anims% +}% +\def\tikz@collect@scope@anims@go:#1=#2{% + \expandafter\def\expandafter\tikz@scope@anims\expandafter{\tikz@scope@anims animate={myself:={:{#1}={#2}}},}% + \tikz@collect@scope@anims@parse% +}% + + + + + +\def\tikzanimateset{\pgfqkeys{/tikz/animate}}% +\tikzanimateset{ + .code={ + \pgfkeys{/handlers/first char syntax=true} + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string"}{\tikz@animation@value}% + \def\tikz@anim@t{0}% + \def\tikz@anim@t@base{0}% + \def\tikz@anim@t@current{0}% + \tikzanimateset{#1} + }, + scope/.code=\tikz@anim@scope{#1}{}{}, + sync/.code=\tikz@anim@sync@scope{#1}{}{}, + entry/.code=\tikz@anim@make@entry, + object/.code=\tikz@anim@set@object{#1}, + attribute/.code=\tikz@anim@set@attr{#1}, + id/.code=\tikz@anim@set@id{#1}, + time/.code=\tikz@anim@set@time{#1}, + value/.code=\tikz@anim@add{\tikz@anim@value{#1}},% + remember/.code=\pgfmathadd@{\tikz@anim@t}{\tikz@anim@t@base}\global\let#1\pgfmathresult, + resume/.code=\tikz@anim@resume{#1}, + fork/.code={\tikz@anim@parse@time{#1}\pgfmathadd@\tikz@anim@t\tikz@anim@t@base\let\tikz@anim@t@base\pgfmathresult\def\tikz@anim@t{0}}, + fork/.default = 0later, + base/.style={scope={/utils/exec=\let\tikz@animation@time\tikz@anim@base@text,#1,entry}}, +}% + +\tikzset{ + make snapshot of/.code=\edef\tikz@temp{#1}\ifx\tikz@temp\pgfutil@empty\else\pgfsnapshot{#1}\fi, + make snapshot after/.code=\edef\tikz@temp{#1}\ifx\tikz@temp\pgfutil@empty\else\pgfsnapshotafter{#1}\fi, + make snapshot if necessary/.code=\ifpgfsysanimationsupported\else\pgfsnapshot{#1}\fi, + make snapshot if necessary/.default=0s, +}% + +\def\tikz@anim@scope#1#2#3{% + {#2\tikzanimateset{#1}#3}% +}% +\def\tikz@anim@sync@scope#1#2#3{% + {% + #2% + \tikzanimateset{#1}% + #3% + \pgfmathadd@{\tikz@anim@t}{\tikz@anim@t@base}% + \expandafter% + }\expandafter\pgfmathsubtract@\expandafter{\pgfmathresult}{\tikz@anim@t@base}% + \tikz@anim@set@time{\pgfmathresult}% +}% + +\def\tikz@anim@set@time#1{% + \tikz@anim@parse@time{#1}% + \let\tikz@anim@t@current\tikz@anim@t% + \pgfmathadd@\tikz@anim@t\tikz@anim@t@base% + \let\tikz@animation@time\pgfmathresult% +}% + +\def\tikz@anim@value#1{% + \def\tikz@anim@result{#1} + \ifx\tikz@anim@result\pgf@special@current@text% + \else% + \ifx\tikz@animation@parser\relax% + \else% + \tikz@animation@parser{#1}% + \fi% + \fi% +}% + + +\def\tikz@anim@resume#1{% + \pgfparsetime{#1}% + \pgfmathsubtract@{\pgftimeresult}{\tikz@anim@t@base}% + \tikz@anim@set@time{\pgfmathresult}% +}% + + + +\def\tikz@animation@syntax@check#1#2{% + \def\tikz@animation@rest{#1}% + \expandafter\pgfutil@in@\expandafter:\expandafter{\tikz@key}% + \ifpgfutil@in@% + \expandafter\tikz@anim@parse@colon\tikz@key\pgf@stop% + \else% + #2% + \fi% +}% + +\def\tikz@anim@parse@colon#1:#2\pgf@stop{% + \expandafter\tikz@anim@sync@scope\expandafter{\tikz@animation@rest}{% + \tikz@anim@set@object{#1}% + \pgfutil@in@_{#2}% + \ifpgfutil@in@% + \tikz@anim@parse@under#2\pgf@stop% + \else% + \tikz@anim@parse@under#2_\pgf@stop% + \fi% + }{\tikz@anim@make@entry}% +}% + +\def\tikz@anim@parse@under#1_#2\pgf@stop{% + \tikz@anim@set@attr{#1}% + \tikz@anim@set@id{#2}% +}% + +\def\tikz@anim@set@attr#1{% + \pgfkeys@spdef\tikz@anim@a{#1}% + \ifx\tikz@anim@a\pgfutil@empty% + \else% + \let\tikz@anim@tl@attributes\tikz@anim@a% + \fi% +}% + +\def\tikz@anim@set@id#1{% + \pgfkeys@spdef\tikz@anim@a{#1}% + \ifx\tikz@anim@a\pgfutil@empty% + \else% + \let\tikz@anim@tl@id\tikz@anim@a% + \fi% +}% + +\def\tikz@anim@set@object#1{% + \pgfkeys@spdef\tikz@anim@a{#1}% + \ifx\tikz@anim@a\pgfutil@empty% + \else% + \let\tikz@anim@tl@objects\tikz@anim@a% + \fi% +}% + + + +\def\tikz@animation@value#1{% + \tikz@animation@value@parser#1\pgf@stop% +}% + +\def\tikz@animation@value@parser"#1"{% + \def\tikz@animation@value@head{#1}% + \pgfutil@ifnextchar\pgf@stop{\tikz@animation@value@rest=}{% + \pgfutil@ifnextchar b\tikz@animation@value@rest@base\tikz@animation@value@rest% + }% +}% +\def\tikz@animation@value@rest=#1\pgf@stop{% + \tikz@anim@sync@scope{#1}{\expandafter\tikz@anim@add\expandafter{\expandafter\tikz@anim@value\expandafter{\tikz@animation@value@head}}}{\tikz@anim@make@entry}% +}% + +\def\tikz@animation@value@rest@base base{% + \tikz@anim@sync@scope{}{\let\tikz@animation@time\tikz@anim@base@text\expandafter\tikz@anim@add\expandafter{\expandafter\tikz@anim@value\expandafter{\tikz@animation@value@head}}}{\tikz@anim@make@entry}% + \pgfutil@ifnextchar\pgf@stop{\tikz@animation@value@rest=}{\tikz@animation@value@rest}% +}% + + + + + +\def\tikz@anim@simple@parse#1{} % + +\def\tikz@anim@slant@parse#1{\pgfmathsetmacro\tikz@anim@result{atan(#1)}}% + +\def\tikz@anim@dashpattern@parse#1{% + \pgfmathsetmacro\tikz@anim@dash@phase{\tikz@dashphase}% + \def\tikz@dashpattern{}% + \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil% + \edef\tikz@anim@result{{\tikz@dashpattern}{\tikz@anim@dash@phase pt}}% +}% +\def\tikz@anim@dashoffset@parse#1{% + \pgfmathparse{#1}% + \edef\tikz@anim@result{{\tikz@dashpattern}{\pgfmathresult pt}}% +}% +\def\tikz@anim@dash@parse#1{% + \tikz@anim@dash@parse@#1\pgf@stop% +}% +\def\tikz@anim@dash@parse@#1phase#2\pgf@stop{% + \pgfmathsetmacro\tikz@anim@dash@phase{#2}% + \def\tikz@dashpattern{}% + \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil% + \edef\tikz@anim@result{{\tikz@dashpattern}{\tikz@anim@dash@phase pt}}% +}% + +\def\tikz@anim@xshift@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{\noexpand\pgfqpoint{\pgfmathresult pt}{0pt}}}% +\def\tikz@anim@yshift@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{\noexpand\pgfqpoint{0pt}{\pgfmathresult pt}}}% + +\def\tikz@anim@xscale@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{\pgfmathresult,1}}% +\def\tikz@anim@yscale@parse#1{\pgfmathparse{#1}\edef\tikz@anim@result{1,\pgfmathresult}}% + +\def\tikz@anim@shift@parse#1{\tikz@scan@one@point\tikz@anim@do@shift#1}% +\def\tikz@anim@do@shift#1{\def\tikz@anim@result{#1}}% + +\def\tikz@anim@position@parse#1{% + \begingroup% + \let\tikz@transform=\relax% + \pgf@xc-\pgf@pt@x% + \pgf@yc-\pgf@pt@y% + \pgfsettransform\tikz@anim@saved@transform% + \tikz@scan@one@point\tikz@anim@do@position#1}% +\def\tikz@anim@do@position#1{% + \pgf@process{\pgfpointtransformed{#1}}% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \xdef\tikz@anim@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \endgroup% + \let\tikz@anim@result\tikz@anim@temp% +}% + +\def\tikz@anim@view@parse#1{\tikz@anim@view@parse@#1\pgf@stop}% +\def\tikz@anim@view@parse@{% + \pgfutil@ifnextchar({\tikz@scan@one@point\tikz@anim@view@parse@a}{\tikz@anim@view@node}% +}% +\def\tikz@anim@view@parse@a#1{% + \def\tikz@anim@result{{#1}}% + \pgfutil@ifnextchar r{\tikz@anim@view@parsed@rec}{\tikz@scan@one@point\tikz@anim@view@parse@b}% +}% +\def\tikz@anim@view@parsed@rec rectangle{\tikz@scan@one@point\tikz@anim@view@parse@b}% +\def\tikz@anim@view@parse@b#1{% + \expandafter\def\expandafter\tikz@anim@result\expandafter{\tikz@anim@result{#1}}% + \pgfutil@ifnextchar\pgf@stop\pgfutil@gobble{\tikzerror{Wrong view syntax}}% +}% +\def\tikz@anim@view@node#1\pgf@stop{% + \expandafter\ifx\csname pgf@sh@ns@#1\endcsname\relax% + \tikzerror{Undefined node '#1'}% + \else% + {% + \pgf@process{\pgfpointanchor{#1}{west}}% + \pgf@xa\pgf@x \pgf@ya\pgf@y + \pgf@xb\pgf@x \pgf@yb\pgf@y + \pgf@process{\pgfpointanchor{#1}{north}}% + \ifdim\pgf@x<\pgf@xa \pgf@xa=\pgf@x\fi% + \ifdim\pgf@x>\pgf@xb \pgf@xb=\pgf@x\fi% + \ifdim\pgf@y<\pgf@ya \pgf@ya=\pgf@y\fi% + \ifdim\pgf@y>\pgf@yb \pgf@yb=\pgf@y\fi% + \pgf@process{\pgfpointanchor{#1}{south}}% + \ifdim\pgf@x<\pgf@xa \pgf@xa=\pgf@x\fi% + \ifdim\pgf@x>\pgf@xb \pgf@xb=\pgf@x\fi% + \ifdim\pgf@y<\pgf@ya \pgf@ya=\pgf@y\fi% + \ifdim\pgf@y>\pgf@yb \pgf@yb=\pgf@y\fi% + \pgf@process{\pgfpointanchor{#1}{east}}% + \ifdim\pgf@x<\pgf@xa \pgf@xa=\pgf@x\fi% + \ifdim\pgf@x>\pgf@xb \pgf@xb=\pgf@x\fi% + \ifdim\pgf@y<\pgf@ya \pgf@ya=\pgf@y\fi% + \ifdim\pgf@y>\pgf@yb \pgf@yb=\pgf@y\fi% + \xdef\tikz@anim@result{{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}} + }% + \fi% +}% + +\def\tikz@anim@path@parse#1{% + {% + \setbox0=\hbox{{% + \pgfinterruptpath% + \expandafter\tikz@scan@next@command#1\pgf@stop% + \pgfsyssoftpath@getcurrentpath\tikz@anim@result% + \pgfprocessround{\tikz@anim@result}{\tikz@anim@result}% + \global\let\tikz@anim@result\tikz@anim@result% + \endpgfinterruptpath% + }}% + }% +}% + + + +\def\tikz@anim@along#1#2{% + {% + \setbox0=\hbox{{% + \pgfinterruptpath% + \pgf@relevantforpicturesizefalse% + \iftikz@anim@is@position% + \let\tikz@transform=\relax% + \pgf@x-\pgf@pt@x% + \pgf@y-\pgf@pt@y% + \edef\tikz@anim@along@shift{\pgf@xc\the\pgf@x\pgf@yc\the\pgf@y}% + \pgfsettransformentries#1% + \else% + \pgftransformreset% + \fi + \tikz@scan@next@command#2\pgf@stop% + \pgfsyssoftpath@getcurrentpath\tikz@anim@parsed@path% + \pgfprocessround{\tikz@anim@parsed@path}{\tikz@anim@parsed@path}% + \iftikz@anim@is@position% + \tikz@anim@shift@path% + \global\let\tikz@anim@parsed@path\tikz@anim@patched@path% + \else% + \global\let\tikz@anim@parsed@path\tikz@anim@parsed@path% + \fi% + \endpgfinterruptpath% + }}% + }% + \pgfanimationset{along softpath/.expand once=\tikz@anim@parsed@path}% +}% + +\def\tikz@anim@shift@path{% + \let\tikz@anim@patched@path\pgfutil@empty% + \tikz@anim@along@shift% + \expandafter\tikz@anim@shift@path@\tikz@anim@parsed@path\pgf@stop% +}% +\def\tikz@anim@shift@path@{% + \pgfutil@ifnextchar\pgf@stop\pgfutil@gobble{% + \pgfutil@ifnextchar\bgroup\tikz@anim@shift@path@sub\tikz@anim@shift@path@copy}% +}% +\def\tikz@anim@shift@path@copy#1{% + \expandafter\def\expandafter\tikz@anim@patched@path\expandafter{\tikz@anim@patched@path#1}% + \tikz@anim@shift@path@% +}% +\def\tikz@anim@shift@path@sub#1#2{% + \pgf@x#1% + \pgf@y#2% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \edef\tikz@temp{{\the\pgf@x}{\the\pgf@y}}% + \expandafter\tikz@anim@shift@path@copy\expandafter{\tikz@temp}% +}% + + + +\def\tikz@anim@parse@origin#1{% + \tikz@scan@one@point\tikz@anim@parse@origin@#1\relax% +}% +\def\tikz@anim@parse@origin@#1{\tikz@anim@add{\pgfanimationset{origin={#1}}}}% + + + +\def\tikz@anim@tl@objects{}% +\def\tikz@anim@tl@attributes{}% +\def\tikz@anim@tl@id{default}% + +\let\tikz@anim@tl@exec@options\pgfutil@empty +\let\tikz@anim@tl@early@options\pgfutil@empty + +\def\tikz@anim@add@early#1{\expandafter\def\expandafter\tikz@anim@tl@early@options\expandafter{\tikz@anim@tl@early@options#1}}% +\def\tikz@anim@add@once@early#1{% + \global\advance\tikz@anim@once@count by1\relax% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\tikz@anim@tl@early@options% + \expandafter\expandafter\expandafter{\expandafter\tikz@anim@tl@early@options\expandafter\tikz@anim@exec@once\expandafter{\the\tikz@anim@once@count}{#1}}% +}% +\def\tikz@anim@add#1{\expandafter\def\expandafter\tikz@anim@tl@exec@options\expandafter{\tikz@anim@tl@exec@options#1}}% +\def\tikz@anim@add@once#1{% + \global\advance\tikz@anim@once@count by1\relax% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\tikz@anim@tl@exec@options% + \expandafter\expandafter\expandafter{\expandafter\tikz@anim@tl@exec@options\expandafter\tikz@anim@exec@once\expandafter{\the\tikz@anim@once@count}{#1}}% +}% +\newcount\tikz@anim@once@count% +\def\tikz@anim@exec@once#1#2{% + \expandafter\ifx\csname tikz@anim@once@#1\endcsname\pgf@stop% + \else% + \expandafter\let\csname tikz@anim@once@#1\endcsname\pgf@stop% + #2% + \fi% +}% + +\newif\iftikz@anim@do@entry + +\def\tikz@anim@make@entry{% + \tikz@anim@do@entrytrue% + \ifx\tikz@anim@tl@objects\pgfutil@empty\tikz@anim@do@entryfalse\fi% + \ifx\tikz@anim@tl@attributes\pgfutil@empty\tikz@anim@do@entryfalse\fi% + \ifx\tikz@anim@tl@exec@options\pgfutil@empty\ifx\tikz@anim@tl@early@options\pgfutil@empty\tikz@anim@do@entryfalse\fi\fi% + \iftikz@anim@do@entry% + \foreach\tikz@anim@tl@object in\tikz@anim@tl@objects{% + \expandafter\tikzanimationattributesset\expandafter{\tikz@anim@tl@attributes}% + }% + \fi% +}% + +\def\tikzanimationattributesset#1{\pgfqkeys{/tikz/animate/attributes}{#1}}% + +\tikzanimationattributesset{ + .unknown/.code={ + \let\tikz@anim@attribute@name\pgfkeyscurrentname + \expandafter\let\expandafter\pgf@temp\csname tikz@anim@def@pgf@attr@\tikz@anim@attribute@name\endcsname% + \ifx\pgf@temp\relax% + \tikzerror{Unknown animation attribute '\tikz@anim@attribute@name'}% + \else% + \expandafter\tikz@timeline@config\expandafter\tikz@anim@tl@object\expandafter\tikz@anim@attribute@name\expandafter\tikz@anim@tl@id\expandafter{\tikz@anim@configs}% + \edef\pgf@marshal{\noexpand\tikz@timeline@entry{\tikz@anim@tl@object}{\tikz@anim@attribute@name}{\tikz@anim@tl@id}}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\pgf@marshal\expandafter{\tikz@anim@tl@early@options}}% + \expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\tikz@anim@entry\expandafter\expandafter\expandafter{\expandafter\tikz@anim@tl@exec@options\expandafter\def\expandafter\tikz@animation@time\expandafter{\tikz@animation@time}}}% + \fi% + } +}% +\let\tikz@anim@configs\pgfutil@empty + +\def\tikz@anim@entry#1{% + \let\tikz@anim@result\pgfutil@empty% + \pgf@anim@reset@linear% + #1% + \ifx\tikz@anim@result\pgfutil@empty% + \else% + \ifx\tikz@animation@time\pgfutil@empty% + \else% + \ifx\tikz@animation@time\tikz@anim@base@text% + \expandafter\pgf@anim@base\expandafter{\tikz@anim@result}% + \else% + \expandafter\expandafter\expandafter\pgf@anim@entry% + \expandafter\expandafter\expandafter{\expandafter\tikz@animation@time\expandafter}\expandafter{\tikz@anim@result}% + \fi% + \fi% + \fi% +}% +\let\tikz@animation@time\pgfutil@empty% +\def\tikz@anim@base@text{base}% + +\tikzanimateset{ + .unknown/.code={% + \let\tikz@key\pgfkeyscurrentname% + \tikz@animation@syntax@check{#1}{\tikz@anim@options{#1}}% + } +}% + + +\def\tikz@anim@options#1{ + \let\tikz@anim@key\pgfkeyscurrentname% + \pgfqkeys{/tikz/animate/options}{\tikz@anim@key/.try={#1}}% + \ifpgfkeyssuccess% + \else% + \def\tikz@anim@unparsed@value{#1}% + \expandafter\tikz@anim@time@test\tikz@anim@key\pgf@stop% + \fi% +}% + +\tikzanimateset{ + options/.cd, + name/.code=\tikz@anim@add{\pgfanimationset{name={#1}}}, + forever/.code=\tikz@anim@add{\pgfanimationset{freeze at end}}, + freeze/.code=\tikz@anim@add{\pgfanimationset{freeze at end}}, + restart/.code=\tikz@anim@add{\pgfanimationset{restart={#1}}}, + repeats/.code=\tikz@anim@add{\pgfanimationset{repeats={#1}}}, + repeats/.default=, + repeat/.code=\tikz@anim@add{\pgfanimationset{repeats={#1}}}, + repeat/.default=, + begin/.code=\tikz@anim@add@once{\pgfanimationset{begin={#1}}}, + end/.code=\tikz@anim@add@once{\pgfanimationset{end={#1}}}, + begin on/.code=\tikz@anim@event{begin}{#1}, + end on/.code=\tikz@anim@event{begin}{#1}, + begin snapshot/.code=\tikz@anim@add{\pgfanimationset{begin snapshot={#1}}}, + origin/.code=\tikz@anim@parse@origin{#1}, + transform/.code=\tikz@anim@add{\pgfanimationset{transform={\let\tikz@transform\relax\tikzset{#1}}}}, + along/.code=\tikz@anim@handle@along#1\pgf@stop, + entry control/.code=\tikz@anim@add{\pgfanimationset{entry control={#1}}}, + exit control/.code=\tikz@anim@add{\pgfanimationset{exit control={#1}}}, + stay/.code=\tikz@anim@add{\pgfanimationset{stay}}, + jump/.code=\tikz@anim@add{\pgfanimationset{jump}}, + ease/.style={ + entry control={1-(#1)}{1}, + exit control={#1}{0} + }, + ease/.default=0.5, + ease in/.style={ + entry control={1-(#1)}{1}, + }, + ease in/.default=0.5, + ease out/.style={ + exit control={#1}{0}, + }, + ease out/.default=0.5, + arrows/.code=\tikz@anim@add@early{\pgfanimationset{arrows={#1}}}, + shorten >/.code=\tikz@anim@add@early{\pgfanimationset{shorten >={#1}}}, + shorten ,double=none,every accepting by arrow] + -- + ([shift=(\tikz@accepting@angle:\tikz@accepting@distance)]\tikztostart.\tikz@accepting@angle) + node [shape=rectangle,anchor=\tikz@accepting@anchor] {\tikz@accepting@text} + }] + edge () + } +}}}% +\tikzset{every accepting by arrow/.style={}}% +\tikzset{accepting by double/.style= {double,outer sep=.5\pgflinewidth+.3pt}} % + +\tikzset{initial by arrow/.style= {after node path= +{ + { + [to path= + { + [->,double=none,every initial by arrow] + ([shift=(\tikz@initial@angle:\tikz@initial@distance)]\tikztostart.\tikz@initial@angle) + node [shape=rectangle,anchor=\tikz@initial@anchor] {\tikz@initial@text} + -- (\tikztostart)}] + edge () + } +}}}% +\tikzset{every initial by arrow/.style={}}% + +\tikzset{initial by diamond/.style={shape=diamond}}% + + +\tikzoption{initial text}{\tikzaddafternodepathoption{\def\tikz@initial@text{#1}}}% +\tikzoption{accepting text}{\tikzaddafternodepathoption{\def\tikz@accepting@text{#1}}}% + +\tikzoption{initial where}{\tikzaddafternodepathoption{\csname tikz@initial@compute@#1\endcsname}}% +\tikzoption{accepting where}{\tikzaddafternodepathoption{\csname tikz@accepting@compute@#1\endcsname}}% + +\tikzoption{initial distance}{\tikzaddafternodepathoption{\def\tikz@initial@distance{#1}}}% +\tikzoption{accepting distance}{\tikzaddafternodepathoption{\def\tikz@accepting@distance{#1}}}% + +\def\tikz@initial@text{start}% +\def\tikz@accepting@text{}% + +\def\tikz@initial@distance{3ex}% +\def\tikz@accepting@distance{3ex}% + +\def\tikz@initial@compute@above{\def\tikz@initial@angle{90}\def\tikz@initial@anchor{south}}% +\def\tikz@initial@compute@below{\def\tikz@initial@angle{270}\def\tikz@initial@anchor{north}}% +\def\tikz@initial@compute@left{\def\tikz@initial@angle{180}\def\tikz@initial@anchor{east}}% +\def\tikz@initial@compute@right{\def\tikz@initial@angle{0}\def\tikz@initial@anchor{west}}% + +\def\tikz@initial@angle{180}% +\def\tikz@initial@anchor{east}% + +\def\tikz@accepting@compute@above{\def\tikz@accepting@angle{90}\def\tikz@accepting@anchor{south}}% +\def\tikz@accepting@compute@below{\def\tikz@accepting@angle{270}\def\tikz@accepting@anchor{north}}% +\def\tikz@accepting@compute@left{\def\tikz@accepting@angle{180}\def\tikz@accepting@anchor{east}}% +\def\tikz@accepting@compute@right{\def\tikz@accepting@angle{0}\def\tikz@accepting@anchor{west}}% + +\def\tikz@accepting@angle{0}% +\def\tikz@accepting@anchor{west}% + + +\tikzset{initial above/.style= {initial by arrow,initial where=above}}% +\tikzset{initial below/.style= {initial by arrow,initial where=below}}% +\tikzset{initial left/.style= {initial by arrow,initial where=left}}% +\tikzset{initial right/.style= {initial by arrow,initial where=right}}% + +\tikzset{accepting above/.style= {accepting by arrow,accepting where=above}}% +\tikzset{accepting below/.style= {accepting by arrow,accepting where=below}}% +\tikzset{accepting left/.style= {accepting by arrow,accepting where=left}}% +\tikzset{accepting right/.style= {accepting by arrow,accepting where=right}}% + + + +\tikzset{state/.style= {state without output}}% +\tikzset{accepting/.style= {accepting by double}}% +\tikzset{initial/.style= {initial by arrow}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e413f1868be5cd7d1c7925298665334d9ee6ae48 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybabel.code.tex @@ -0,0 +1,9 @@ + +\ProvidesFileRCS{tikzlibrarybabel.code.tex} + +\tikzset{ + handle active characters in code, + handle active characters in nodes, +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..1be245170ada5c1fb41e76ccea58becd693a8a29 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybackgrounds.code.tex @@ -0,0 +1,134 @@ + +\ProvidesFileRCS{tikzlibrarybackgrounds.code.tex} + + + +\pgfdeclarelayer{background}% +\pgfsetlayers{background,main}% + + +\tikzset{on background layer/.style={ + execute at begin scope={% + \pgfonlayer{background}% + \let\tikz@options=\pgfutil@empty% + \tikzset{every on background layer/.try,#1}% + \tikz@options}, + execute at end scope={\endpgfonlayer} + } +}% + + + +\tikzset{background rectangle/.style= {draw}}% +\tikzset{background top/.style= {draw}}% +\tikzset{background bottom/.style= {draw}}% +\tikzset{background left/.style= {draw}}% +\tikzset{background right/.style= {draw}}% +\tikzset{background grid/.style= {help lines,draw}}% + +\tikzoption{inner frame sep}{\def\tikz@framexsep{#1}\def\tikz@frameysep{#1}}% +\tikzoption{inner frame xsep}{\def\tikz@framexsep{#1}}% +\tikzoption{inner frame ysep}{\def\tikz@frameysep{#1}}% +\def\tikz@framexsep{1ex}% +\def\tikz@frameysep{1ex}% + +\tikzoption{outer frame sep}{\def\tikz@outerframexsep{#1}\def\tikz@outerframeysep{#1}}% +\tikzoption{outer frame xsep}{\def\tikz@outerframexsep{#1}}% +\tikzoption{outer frame ysep}{\def\tikz@outerframeysep{#1}}% +\def\tikz@outerframexsep{0ex}% +\def\tikz@outerframeysep{0ex}% + + + +\tikzset{loose background/.style= {inner frame sep=2ex}}% +\tikzset{tight background/.style= {inner frame sep=0ex}}% + + + + +\tikzset{framed/.style= {style=show background rectangle}}% +\tikzset{gridded/.style= {style=show background grid}}% + +\tikzset{show background rectangle/.style={execute at end picture=\tikz@background@framed}}% +\tikzset{show background top/.style= {execute at end picture=\tikz@background@top}}% +\tikzset{show background bottom/.style= {execute at end picture=\tikz@background@bottom}}% +\tikzset{show background left/.style= {execute at end picture=\tikz@background@left}}% +\tikzset{show background right/.style= {execute at end picture=\tikz@background@right}}% +\tikzset{show background grid/.style= {execute at end picture=\tikz@background@grid}}% + + + +\def\tikz@background@save{% + \pgftransformreset% + \ifx\tikz@bg@minx\@undefined% + \pgf@xb=\pgf@picminx% + \pgf@yb=\pgf@picminy% + \pgf@xc=\pgf@picmaxx% + \pgf@yc=\pgf@picmaxy% + \pgfmathsetlength{\pgf@x}{\tikz@framexsep}% + \pgfmathsetlength{\pgf@y}{\tikz@frameysep}% + \advance\pgf@xb by-\pgf@x% + \advance\pgf@yb by-\pgf@y% + \advance\pgf@xc by\pgf@x% + \advance\pgf@yc by\pgf@y% + \edef\tikz@bg@minx{\the\pgf@xb}% + \edef\tikz@bg@miny{\the\pgf@yb}% + \edef\tikz@bg@maxx{\the\pgf@xc}% + \edef\tikz@bg@maxy{\the\pgf@yc}% + \pgfmathsetlength{\pgf@x}{\tikz@outerframexsep}% + \pgfmathsetlength{\pgf@y}{\tikz@outerframeysep}% + \advance\pgf@xb by-\pgf@x% + \advance\pgf@yb by-\pgf@y% + \advance\pgf@xc by\pgf@x% + \advance\pgf@yc by\pgf@y% + \edef\tikz@bg@outerminx{\the\pgf@xb}% + \edef\tikz@bg@outerminy{\the\pgf@yb}% + \edef\tikz@bg@outermaxx{\the\pgf@xc}% + \edef\tikz@bg@outermaxy{\the\pgf@yc}% + \fi% +}% + +\def\tikz@background@framed{% + \tikz@background@save% + \pgfonlayer{background} + \path[style=background rectangle] (\tikz@bg@minx,\tikz@bg@miny) rectangle (\tikz@bg@maxx,\tikz@bg@maxy); + \endpgfonlayer +}% + +\def\tikz@background@top{% + \tikz@background@save% + \pgfonlayer{background} + \path[style=background top] (\tikz@bg@outerminx,\tikz@bg@maxy) -- (\tikz@bg@outermaxx,\tikz@bg@maxy); + \endpgfonlayer +}% + +\def\tikz@background@bottom{% + \tikz@background@save% + \pgfonlayer{background} + \path[style=background bottom] (\tikz@bg@outerminx,\tikz@bg@miny) -- (\tikz@bg@outermaxx,\tikz@bg@miny); + \endpgfonlayer +}% + +\def\tikz@background@left{% + \tikz@background@save% + \pgfonlayer{background} + \path[style=background left] (\tikz@bg@minx,\tikz@bg@outerminy) -- (\tikz@bg@minx,\tikz@bg@outermaxy); + \endpgfonlayer +}% + +\def\tikz@background@right{% + \tikz@background@save% + \pgfonlayer{background} + \path[style=background right] (\tikz@bg@maxx,\tikz@bg@outerminy) -- (\tikz@bg@maxx,\tikz@bg@outermaxy); + \endpgfonlayer +}% + +\def\tikz@background@grid{% + \tikz@background@save% + \pgfonlayer{background} + \path[style=background grid] (\tikz@bg@minx,\tikz@bg@miny) grid (\tikz@bg@maxx,\tikz@bg@maxy); + \endpgfonlayer +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3a9ce5bb8a666b599303444e837dc0427dd5ad4c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarybending.code.tex @@ -0,0 +1,7 @@ + +\ProvidesFileRCS{tikzlibrarybending.code.tex} + +\usepgfmodule{bending}% +\tikzset{arrows=[flex]}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a9d0c5a915737625006897f0ef0279d52168e611 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalc.code.tex @@ -0,0 +1,455 @@ + +\ProvidesFileRCS{tikzlibrarycalc.code.tex} + + + + +\def\tikz@let@command et{% + \let\p=\tikz@cc@dop% + \let\x=\tikz@cc@dox% + \let\y=\tikz@cc@doy% + \let\n=\tikz@cc@don% + \pgfutil@ifnextchar i{\tikz@cc@stop@let}{\tikz@cc@handle@line}% +}% +\def\tikz@cc@handle@line{% + \pgfutil@ifnextchar\p{% + \tikz@cc@handle@coor% + }{% + \pgfutil@ifnextchar\n{% + \tikz@cc@handle@num% + }{% + \pgfutil@ifnextchar i{% + \tikz@cc@stop@let + }{% + \tikzerror{``\string\p'' or ``\string\n'' expected}% + }% + }% + }% +}% +\def\tikz@cc@handle@num\n#1#2=#3{% + \pgfmathparse{#3}% + \expandafter\edef\csname tikz@cc@n@#1\endcsname{\pgfmathresult\ifpgfmathunitsdeclared pt\fi} + \pgfutil@ifnextchar,{\tikz@cc@handle@nextline}{\tikz@cc@stop@let}% +}% +\def\tikz@cc@handle@coor\p#1#2={% + \def\tikz@cc@coord@name{#1}% + \tikz@scan@one@point\tikz@cc@dolet% +}% +\def\tikz@cc@dolet#1{% + \pgf@process{#1}% + \expandafter\edef\csname tikz@cc@p@\tikz@cc@coord@name\endcsname{\the\pgf@x,\the\pgf@y}% + \expandafter\edef\csname tikz@cc@x@\tikz@cc@coord@name\endcsname{\the\pgf@x}% + \expandafter\edef\csname tikz@cc@y@\tikz@cc@coord@name\endcsname{\the\pgf@y}% + \pgfutil@ifnextchar,{\tikz@cc@handle@nextline}{\tikz@cc@stop@let}% +}% +\def\tikz@cc@handle@nextline,{% + \tikz@cc@handle@line% +}% +\def\tikz@cc@stop@let in{% + \tikz@scan@next@command% +}% + +\def\tikz@cc@dop#1{\csname tikz@cc@p@#1\endcsname}% +\def\tikz@cc@dox#1{\csname tikz@cc@x@#1\endcsname}% +\def\tikz@cc@doy#1{\csname tikz@cc@y@#1\endcsname}% +\def\tikz@cc@don#1{\csname tikz@cc@n@#1\endcsname}% + + + + +\def\tikz@parse@calculator#1(${% + \def\tikz@cc@command{#1}% + \begingroup% + \pgf@xa=0pt% + \pgf@ya=0pt% + \tikz@cc@parse+% +}% + +\def\tikz@cc@parse{% + \pgfutil@ifnextchar${% + \tikz@cc@end% + } + {\pgfutil@ifnextchar+{% + \tikz@cc@add% + }{% + \pgfutil@ifnextchar-{% + \tikz@cc@sub% + }{% + \tikzerror{+ or - expected}% + \tikz@cc@end$% + }% + }% + }% +}% + +\def\tikz@cc@end$#1){% + \xdef\tikz@marshal{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \endgroup% + \expandafter\tikz@cc@command\expandafter{\tikz@marshal}% +}% + + +\def\tikz@cc@add+{% + \def\tikz@cc@factor{1}% + \tikz@cc@factororcoordinate% +}% +\def\tikz@cc@sub-{% + \def\tikz@cc@factor{-1}% + \tikz@cc@factororcoordinate% +}% + +\def\tikz@cc@factororcoordinate{% + \pgfutil@ifnextchar({% + \tikz@cc@coordinate% + }{% + \tikz@cc@parse@factor% + }% +}% + +\def\tikz@cc@parse@factor#1*({% + \pgfmathparse{#1*\tikz@cc@factor}% + \let\tikz@cc@factor=\pgfmathresult% + \tikz@cc@coordinate(% +}% + +\def\tikz@cc@coordinate{% + \tikz@scan@absolute\tikz@cc@after@coordinate% +}% +\def\tikz@cc@after@coordinate#1{% + \pgf@process{#1}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \tikz@cc@mid@checks% +}% + + + +\def\tikz@cc@mid@checks{% + \ifnum\the\catcode`\!=\active\relax + \expandafter\tikz@cc@mid@checks@active + \else + \expandafter\tikz@cc@mid@checks@nonactive + \fi +}% + +\def\tikz@cc@mid@checks@nonactive{% + \pgfutil@ifnextchar!{% + \tikz@cc@mid@nonactive% + }{% + \advance\pgf@xa by\tikz@cc@factor\pgf@xb + \advance\pgf@ya by\tikz@cc@factor\pgf@yb + \tikz@cc@parse% + }% +}% + +\def\tikz@cc@mid@nonactive!{% + \pgfutil@ifnextchar({% + \tikz@scan@one@point\tikz@cc@project% + }{% + \tikz@cc@mid@num@nonactive% + }% +}% + +\begingroup + \catcode`\!=\active + \gdef\tikz@cc@mid@checks@active{% + \pgfutil@ifnextchar!{% + \tikz@cc@mid@active% + }{% + \advance\pgf@xa by\tikz@cc@factor\pgf@xb + \advance\pgf@ya by\tikz@cc@factor\pgf@yb + \tikz@cc@parse% + }% + }% + + \gdef\tikz@cc@mid@active!{% + \pgfutil@ifnextchar({% + \tikz@scan@one@point\tikz@cc@project% + }{% + \tikz@cc@mid@num@active% + }% + }% +\endgroup + + +\def\tikz@cc@mid@num@nonactive#1!{\tikz@cc@mid@num{#1}}% + +\begingroup + \catcode`\!=\active + \gdef\tikz@cc@mid@num@active#1!{\tikz@cc@mid@num{#1}}% +\endgroup + +\def\tikz@cc@mid@num#1{% + \pgfmathparse{#1}% + \ifpgfmathunitsdeclared% + \let\tikz@cc@mid@unit=\pgfmathresult% + \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@unit% + \else% + \let\tikz@cc@mid@factor=\pgfmathresult% + \pgfmathparse{1-\tikz@cc@mid@factor}% + \let\tikz@cc@mid@factor@one=\pgfmathresult% + \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@num% + \fi% +}% + +\def\tikz@cc@after@num#1{% + \pgf@process{#1}% + \pgf@xb=\tikz@cc@mid@factor@one\pgf@xb% + \pgf@yb=\tikz@cc@mid@factor@one\pgf@yb% + \advance\pgf@xb by\tikz@cc@mid@factor\pgf@x% + \advance\pgf@yb by\tikz@cc@mid@factor\pgf@y% + \tikz@cc@mid@checks% +}% + + + + +\def\tikz@cc@after@unit#1{% + \pgf@process{#1}% + \advance\pgf@x by-\pgf@xb% + \advance\pgf@y by-\pgf@yb% + \pgf@process{\pgfpointnormalised{}}% + \advance\pgf@xb by\tikz@cc@mid@unit\pgf@x% + \advance\pgf@yb by\tikz@cc@mid@unit\pgf@y% + \tikz@cc@mid@checks% +}% + +\def\tikz@cc@project#1{% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \begingroup + \ifnum\the\catcode`\!=\active + \def\tikz@next{% + \endgroup + \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@project + \tikz@cc@scan@ex@active}% + \else + \def\tikz@next{% + \endgroup + \expandafter\tikz@cc@scan@rot\expandafter\tikz@cc@after@project + \tikz@cc@scan@ex@nonactive}% + \fi + \tikz@next% +}% + +\def\tikz@cc@scan@ex@nonactive!{}% + +\begingroup + \catcode`\!=\active + \gdef\tikz@cc@scan@ex@active!{}% +\endgroup + +\def\tikz@cc@after@project#1{% + \pgf@process{#1}% + \advance\pgf@x by-\pgf@xb% + \advance\pgf@y by-\pgf@yb% + \advance\pgf@xc by-\pgf@xb% + \advance\pgf@yc by-\pgf@yb% + \pgf@process{\pgfpointnormalised{}}% + \pgf@xc=\pgf@sys@tonumber{\pgf@xc}\pgf@x% + \advance\pgf@xc by\pgf@sys@tonumber{\pgf@yc}\pgf@y% + \advance\pgf@xb by\pgf@sys@tonumber{\pgf@xc}\pgf@x% + \advance\pgf@yb by\pgf@sys@tonumber{\pgf@xc}\pgf@y% + \tikz@cc@mid@checks% +}% + + +\def\tikz@cc@scan@rot#1{% + \pgfutil@ifnextchar({% + \tikz@scan@one@point#1% + }% + {% + \def\tikz@cc@scan@rot@cmd{#1}% + \ifnum\the\catcode`\:=\active\relax + \expandafter\tikz@cc@scan@one@rot@active% + \else + \expandafter\tikz@cc@scan@one@rot@nonactive% + \fi + }% +}% + +\def\tikz@cc@scan@one@rot@nonactive#1:{% + \def\tikz@cc@scan@rot@angle{#1}% + \tikz@scan@one@point\tikz@cc@handle@rot% +}% + +\begingroup + \catcode`\:=\active + \gdef\tikz@cc@scan@one@rot@active#1:{% + \def\tikz@cc@scan@rot@angle{#1}% + \tikz@scan@one@point\tikz@cc@handle@rot% + }% +\endgroup + +\def\tikz@cc@handle@rot#1{% + \pgf@process{#1}% + {% + \pgftransformreset% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgftransformshift{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgftransformrotate{\tikz@cc@scan@rot@angle}% + \pgftransformshift{\pgfqpoint{-\pgf@xb}{-\pgf@yb}}% + \pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \expandafter + }% + \edef\tikz@marshal{\noexpand\tikz@cc@scan@rot@cmd{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + \tikz@marshal% +}% + + + + + + +\tikzdeclarecoordinatesystem{tangent} +{% + \tikzset{cs/.cd,#1}% + \expandafter\ifx\csname tikz@tangent@\tikz@cs@type\endcsname\relax% + \tikzerror{I do not know how to compute the tangent to + a \tikz@cs@type}% + \pgfpointorigin% + \else% + \expandafter\tikz@scan@one@point\expandafter\tikz@lib@do@tangent\tikz@cs@point% + \fi% +}% + +\tikzset{cs/node/.code=\tikz@cs@unpack{\tikz@cs@node}{\tikz@cs@type}{#1}}% +\tikzset{cs/point/.store in=\tikz@cs@point}% + +\def\tikz@lib@do@tangent{\csname tikz@tangent@\tikz@cs@type\endcsname}% + +\def\tikz@tangent@coordinate#1{% + \pgfpointanchor{\tikz@cs@node}{center}% +}% + +\def\tikz@tangent@circle#1{% + {% + \pgf@process{\pgfpointtransformed{#1}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikz@cs@node}{center}}}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgftransformreset% + \pgftransformshift{\pgfpointanchor{\tikz@cs@node}{center}}% + \pgf@process{\pgfpointanchor{\tikz@cs@node}{east}}% + \pgf@xc=\pgf@x% + \pgfmathparse{veclen(\the\pgf@xa,\the\pgf@ya)} + \pgfmathparse{acos(\the\pgf@xc/\pgfmathresult)} + \ifnum\pgfkeysvalueof{/tikz/cs/solution}>1\relax% + \pgfmathparse{0-\pgfmathresult}% + \fi% + \let\tikz@lib@temp=\pgfmathresult% + \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgf@xa}{\pgf@ya}}}% + \pgf@ya=-\pgf@y% + \pgftransformcm{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}{\pgfpointorigin}% + \pgf@process{\pgfpointtransformed{\pgfpointpolar{\tikz@lib@temp}{\the\pgf@xc}}}% + }% + {% + \pgftransforminvert% + \pgf@process{\pgfpointtransformed{}}% + }% +}% + + + + +\def\tikz@intersect@circle@and@circle{% + {% + \pgftransformreset% + \pgf@process{\pgfpointanchor{\tikz@cs@node@a}{center}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointanchor{\tikz@cs@node@a}{east}}% + \advance\pgf@x by-\pgf@xa% + \pgf@xc=\pgf@x% + \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{center}}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{east}}% + \advance\pgf@x by-\pgf@xb% + \pgf@yc=\pgf@x% + \pgf@process{% + \pgfpointintersectionofcircles{\pgfqpoint{\pgf@xa}{\pgf@ya}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgf@xc}{\pgf@yc}{\pgfkeysvalueof{/tikz/cs/solution}}% + }% + }% + {% + \pgftransforminvert% + \pgf@process{\pgfpointtransformed{}}% + }% +}% + + +\def\tikz@intersect@line@and@circle{% + {% + \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@a% + \pgf@process{\pgfpointtransformed{}}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikz@cs@node@b}{center}}}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \advance\pgf@xb by-\pgf@x% + \advance\pgf@yb by-\pgf@y% + \pgftransformreset% + \pgftransformshift{\pgfpointanchor{\tikz@cs@node@b}{center}}% + \pgf@process{\pgfpointanchor{\tikz@cs@node@b}{east}}% + \edef\tikz@lib@saved@radius{\pgf@sys@tonumber{\pgf@x}}% + \pgf@x=\pgf@xb% + \pgf@y=\pgf@yb% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@y by-\pgf@ya% + \pgf@process{\pgfpointnormalised{}}% + \pgf@xc=\pgf@sys@tonumber{\pgf@xa}\pgf@x% + \advance\pgf@xc by\pgf@sys@tonumber{\pgf@ya}\pgf@y% + \pgf@xc=-\pgf@xc% + \advance\pgf@xa by\pgf@sys@tonumber{\pgf@xc}\pgf@x% + \advance\pgf@ya by\pgf@sys@tonumber{\pgf@xc}\pgf@y% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@xb=\tikz@lib@saved@radius pt% + \c@pgf@counta=1\relax% + \loop% + \ifdim\pgf@xb>50pt% + \multiply\c@pgf@counta by2\relax% + \divide\pgf@xa by2\relax% + \divide\pgf@ya by2\relax% + \divide\pgf@xb by2\relax% + \repeat% + \pgf@xb=\pgf@sys@tonumber{\pgf@xb}\pgf@xb% + \pgf@yb=\pgf@sys@tonumber{\pgf@xa}\pgf@xa% + \advance\pgf@xb by-\pgf@yb% + \pgf@yb=\pgf@sys@tonumber{\pgf@ya}\pgf@ya% + \advance\pgf@xb by-\pgf@yb% + \ifdim\pgf@xb<0pt% + \pgf@xb=0pt% + \fi% + \pgfmathsqrt@{\pgf@sys@tonumber{\pgf@xb}}% + \pgfmathmultiply@{\pgfmathresult}{\the\c@pgf@counta}% + \multiply\pgf@xa by\c@pgf@counta\relax% + \multiply\pgf@ya by\c@pgf@counta\relax% + \ifnum\pgfkeysvalueof{/tikz/cs/solution}>1\relax% + \pgfmathsubtract{0}{\pgfmathresult}% + \fi% + \advance\pgf@xa by \pgfmathresult\pgf@xc% + \advance\pgf@ya by \pgfmathresult\pgf@yc% + \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@xa}{\pgf@ya}}}% + }% + {% + \pgftransforminvert% + \pgf@process{\pgfpointtransformed{}}% + }% +}% + +\def\tikz@intersect@circle@and@line{% + {% + \let\tikz@cs@node@b=\tikz@cs@node@a% + \let\tikz@cs@line@a=\tikz@cs@line@b% + \tikz@intersect@line@and@circle% + }% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalendar.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalendar.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..4078484c2a2b7389ae95d739dab82046136e2924 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarycalendar.code.tex @@ -0,0 +1,398 @@ + +\ProvidesFileRCS{tikzlibrarycalendar.code.tex} + + +\pgfutil@usemodule{pgfcalendar} + + + +\tikzoption{dates}{\tikz@lib@cal@parse#1\relax} +\def\tikz@lib@cal@parse#1to#2\relax{% + \def\tikz@lib@cal@start{#1} + \def\tikz@lib@cal@end{#2}% +} +\tikzoption{execute at begin day scope}{\expandafter\def\expandafter\tikz@atbegin@day\expandafter{\tikz@atbegin@day#1}} +\tikzoption{execute at end day scope}{% + \def\pgf@temp{#1}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@atend@day% + \expandafter\expandafter\expandafter{\expandafter\pgf@temp\tikz@atend@day}} +\tikzoption{execute before day scope}{\expandafter\def\expandafter\tikz@before@day\expandafter{\tikz@before@day#1}} +\tikzoption{execute after day scope}{\expandafter\def\expandafter\tikz@after@day\expandafter{\tikz@after@day#1}} + +\let\tikz@atbegin@day=\pgfutil@empty +\let\tikz@atend@day=\pgfutil@empty +\let\tikz@before@day=\pgfutil@empty +\let\tikz@after@day=\pgfutil@empty + + + + + + +\tikzoption{day xshift}{\def\tikz@lib@cal@xshift{#1}} +\tikzoption{day yshift}{\def\tikz@lib@cal@yshift{#1}} + +\def\tikz@lib@cal@yshift{3ex} +\def\tikz@lib@cal@xshift{3.5ex} + + + +\tikzoption{month xshift}{\def\tikz@lib@cal@month@xshift{#1}} +\tikzoption{month yshift}{\def\tikz@lib@cal@month@yshift{#1}} + +\def\tikz@lib@cal@month@yshift{9ex} +\def\tikz@lib@cal@month@xshift{9ex} + + + + + +\tikzoption{day code}{\def\tikzdaycode{#1}} +\tikzoption{day text}{\def\tikzdaytext{#1}} +\tikzoption{days}{\tikzset{every day/.append style={#1}}} +\tikzset{every day/.style={anchor=base east}} + +\tikzoption{month code}{\def\tikzmonthcode{#1}} +\tikzoption{month text}{\def\tikzmonthtext{#1}} +\tikzset{every month/.style={}} + +\tikzoption{year code}{\def\tikzyearcode{#1}} +\tikzoption{year text}{\def\tikzyeartext{#1}} +\tikzset{every year/.style={}} + +\def\tikzdaycode{\node[name=\pgfcalendarsuggestedname,every day]{\tikzdaytext};} +\def\tikzmonthcode{\node[every month]{\tikzmonthtext};} +\def\tikzyearcode{\node[every year]{\tikzyeartext};} + +\def\tikzdaytext{\%d-} +\def\tikzmonthtext{\%mt} +\def\tikzyeartext{\%y0} + + + +\tikzoption{tikz@lib@cal@width}{\def\tikz@lib@cal@width{#1}} + +\def\tikz@lib@cal@width{1} + + +\tikzset{day list downward/.style={% + execute before day scope={ + \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{} + {% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@month@yshift}% + \pgftransformyshift{-\pgf@y} + }% + }{}% + }, + execute after day scope={\pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}\pgftransformyshift{-\pgf@y}}, + tikz@lib@cal@width=1 +}} +\tikzset{day list upward/.style={% + execute before day scope={ + \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{} + {% + \pgftransformyshift{\tikz@lib@cal@month@yshift}% + }% + }{}% + }, + execute after day scope={\pgftransformyshift\tikz@lib@cal@yshift}, + tikz@lib@cal@width=1 +}} +\tikzset{day list right/.style={% + execute before day scope={ + \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{} + {% + \pgftransformxshift{\tikz@lib@cal@month@xshift}% + }% + }{}% + }, + execute after day scope={\pgftransformxshift\tikz@lib@cal@xshift}, + tikz@lib@cal@width=30% +}} + +\tikzset{day list left/.style={% + execute before day scope={ + \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{} + {% + \pgfmathsetlength{\pgf@x}{\tikz@lib@cal@month@xshift} + \pgftransformxshift{-\pgf@x}% + }% + }{}% + }, + execute after day scope={ + \pgfmathsetlength{\pgf@x}{\tikz@lib@cal@xshift} + \pgftransformxshift{-\pgf@x}% + }, + tikz@lib@cal@width=30% +}} + + + + +\tikzset{week list/.style={% + execute before day scope={% + \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{} + {% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@month@yshift}% + \pgftransformyshift{-\pgf@y} + }% + }{}% + }, + execute at begin day scope={% + \pgfmathsetlength\pgf@x{\tikz@lib@cal@xshift}% + \pgf@x=\pgfcalendarcurrentweekday\pgf@x% + \pgftransformxshift{\pgf@x}% + }, + execute after day scope={% + \ifdate{Sunday}{% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}% + \pgftransformyshift{-\pgf@y} + }{}% + }, + tikz@lib@cal@width=7 +}} + + + + +\tikzset{month list/.style={% + execute before day scope={% + \ifdate{day of month=1}{\ifdate{equals=\pgfcalendarbeginiso}{} + {% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@month@yshift}% + \pgftransformyshift{-\pgf@y} + }% + }{}% + \ifdate{day of month=1} + {% + \edef\tikz@lib@cal@month@list@start{\pgfcalendarcurrentweekday}% + }{}% + \ifdate{equals=\pgfcalendarbeginiso}% + {% + {% + \c@pgf@counta=\pgfcalendarcurrentjulian% + \advance\c@pgf@counta by-\pgfcalendarcurrentday% + \advance\c@pgf@counta by1\relax% + \pgfcalendarjuliantoweekday{\c@pgf@counta}{\c@pgf@countb}% + \xdef\pgf@temp{\the\c@pgf@countb}% + }% + \let\tikz@lib@cal@month@list@start=\pgf@temp% + }{}% + }, + execute at begin day scope={% + \pgfmathsetlength\pgf@xa{\tikz@lib@cal@xshift}% + \pgf@xb=\pgfcalendarcurrentday\pgf@xa% + \advance\pgf@xb by\tikz@lib@cal@month@list@start\pgf@xa% + \advance\pgf@xb by-\pgf@xa\relax% + \pgftransformxshift{\pgf@xb}% + }, + tikz@lib@cal@width=37 +}} + + + + + +\tikzset{month label left/.style={% + execute before day scope={\ifdate{day of month=1}{\tikzmonthcode}{}}, + every month/.append style={anchor=base east,xshift=-3.5ex} +}} + +\tikzset{month label left vertical/.style={% + execute before day scope={\ifdate{day of month=1}{\tikzmonthcode}{}}, + every month/.append style={anchor=base east,xshift=-4.5ex,yshift=2.25ex,rotate=90} +}} + +\tikzset{month label right/.style={% +execute before day scope={\ifdate{day of month=1}{% + {% + \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}% + \pgftransformxshift{\tikz@lib@cal@width\pgf@xa}% + \pgftransformxshift{-\pgf@xa}% + \tikzmonthcode% + }}{}}, + every month/.append style={anchor=base west,xshift=1ex} +}} + +\tikzset{month label right vertical/.style={% + execute before day scope={\ifdate{day of month=1}{% + {% + \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}% + \pgftransformxshift{\tikz@lib@cal@width\pgf@xa}% + \pgftransformxshift{-\pgf@xa}% + \tikzmonthcode% + }}{}}, + every month/.append style={anchor=base west,xshift=2ex,yshift=2.25ex,rotate=-90} +}} + +\tikzset{month label above centered/.style={% + execute before day scope={% + \ifdate{day of month=1}{% + { + \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}% + \pgf@xb=\tikz@lib@cal@width\pgf@xa% + \advance\pgf@xb by-\pgf@xa% + \pgf@xb=.5\pgf@xb% + \pgftransformxshift{\pgf@xb}% + \pgftransformxshift{-1.5ex}% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}% + \pgftransformyshift{1.25\pgf@y} + \tikzmonthcode% + } + }{}}, + every month/.append style={anchor=base} +}} + +\tikzset{month label above left/.style={% + execute before day scope={% + \ifdate{day of month=1}{% + { + \pgftransformxshift{-3.25ex}% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}% + \pgftransformyshift{1.25\pgf@y} + \tikzmonthcode% + } + }{}}, + every month/.append style={anchor=base west} +}} + + + +\tikzset{month label above right/.style={% + execute before day scope={% + \ifdate{day of month=1}{% + { + \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}% + \pgf@xb=\tikz@lib@cal@width\pgf@xa% + \advance\pgf@xb by-\pgf@xa% + \pgftransformxshift{\pgf@xb}% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}% + \pgftransformyshift{1.25\pgf@y} + \tikzmonthcode% + } + }{}}, + every month/.append style={anchor=base east} +}} + +\tikzset{month label below centered/.style={% + execute before day scope={% + \ifdate{day of month=1}{% + { + \pgfmathsetlength{\pgf@xa}{\tikz@lib@cal@xshift}% + \pgf@xb=\tikz@lib@cal@width\pgf@xa% + \advance\pgf@xb by-\pgf@xa% + \pgf@xb=.5\pgf@xb% + \pgftransformxshift{\pgf@xb}% + \pgftransformxshift{-1.5ex}% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}% + \pgftransformyshift{-1.25\pgf@y} + \tikzmonthcode% + } + }{}}, + every month/.append style={anchor=base} +}} + +\tikzset{month label below left/.style={% + execute before day scope={% + \ifdate{day of month=1}{% + { + \pgftransformxshift{-3.25ex}% + \pgfmathsetlength{\pgf@y}{\tikz@lib@cal@yshift}% + \pgftransformyshift{-1.25\pgf@y} + \tikzmonthcode% + } + }{}}, + every month/.append style={anchor=base west} +}} + + + + +\def\tikz@lib@cal@calendar{% + \begingroup% + \let\tikz@lib@cal@ifs=\pgfutil@empty% + \tikz@resetexpandcount + \tikzset{name=,at={(0,0)}}% + \let\%=\pgfcalendarshorthand% + \tikzset{every calendar/.try}% + \tikz@lib@cal@scanner% +} + +\def\tikz@lib@cal@scanner{% + \afterassignment\tikz@lib@cal@handle\let\pgf@let@token=% +} + +\def\tikz@lib@cal@handle{% + \pgfutil@switch\pgfutil@ifx\pgf@let@token{% + {;}{\let\pgfutil@next\tikz@lib@cal@stop}% + {(}{\let\pgfutil@next\tikz@lib@cal@name}% + {a}{\let\pgfutil@next\tikz@lib@cal@at}% + {[}{\let\pgfutil@next\tikz@lib@cal@option}% + {i}{\let\pgfutil@next\tikz@lib@cal@if}% + }{\tikz@resetexpandcount\pgfutil@next}{\tikz@lib@cal@expand}% +} +\def\tikz@lib@cal@expand{% + \advance\tikz@expandcount by -1 + \ifnum\tikz@expandcount<0\relax% + \tikzerror{Giving up on this calendar}% + \let\pgfutil@next=\tikz@lib@cal@end% + \else% + \let\pgfutil@next=\tikz@lib@cal@@expand + \fi% + \pgfutil@next} + +\def\tikz@lib@cal@@expand{\expandafter\tikz@lib@cal@scanner\pgf@let@token} + + +\def\tikz@lib@cal@name#1){% + \tikzset{name=#1}% + \tikz@lib@cal@scanner% +} +\def\tikz@lib@cal@at t#1(#2){% + \tikzset{at={(#2)}}% + \tikz@lib@cal@scanner% +} +\def\tikz@lib@cal@option#1]{% + \tikzset{#1}% + \tikz@lib@cal@scanner% +} +\def\tikz@lib@cal@if f#1(#2){% + \pgfutil@ifnextchar[{\tikz@lib@cal@if@opt{#2}}{\tikz@lib@cal@if@code{#2}}}% + +\def\tikz@lib@cal@if@opt#1[#2]{\tikz@lib@cal@if@code{#1}{\tikzset{#2}}} +\def\tikz@lib@cal@if@code#1#2{% + \pgfutil@ifnextchar e{\tikz@lib@cal@if@else{#1}{#2}}{\tikz@lib@cal@if@else{#1}{#2}else{}}} + +\def\tikz@lib@cal@if@else#1#2else{% + \pgfutil@ifnextchar[{\tikz@lib@cal@if@else@opt{#1}{#2}}{\tikz@lib@cal@if@else@code{#1}{#2}}}% +\def\tikz@lib@cal@if@else@opt#1#2[#3]{\tikz@lib@cal@if@else@code{#1}{#2}{\tikzset{#3}}} +\def\tikz@lib@cal@if@else@code#1#2#3{% + \expandafter\def\expandafter\tikz@lib@cal@ifs\expandafter{\tikz@lib@cal@ifs\ifdate{#1}{#2}{#3}}% + \tikz@lib@cal@scanner% +} +\def\tikz@lib@cal@stop{% + \pgftransformshift{\tikz@node@at}% + \expandafter\pgfcalendar\expandafter{\tikz@fig@name}{\tikz@lib@cal@start}{\tikz@lib@cal@end}% + {% + \tikz@before@day% + \scope% + \tikz@atbegin@day% + \tikz@lib@cal@ifs% + \tikzdaycode% + \tikz@atend@day% + \endscope% + \tikz@after@day% + }% + \endgroup% +} + +\tikzoption{if}{% + \let\tikz@lib@cal@scanner@orig=\tikz@lib@cal@scanner% + \let\tikz@lib@cal@scanner=\relax% + \tikz@lib@cal@if f#1\relax% + \let\tikz@lib@cal@scanner=\tikz@lib@cal@scanner@orig} + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarychains.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarychains.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..473edcdf5761a27d279c0935afd5a3eb0ac1ad30 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarychains.code.tex @@ -0,0 +1,198 @@ + +\ProvidesFileRCS{tikzlibrarychains.code.tex} + +\usetikzlibrary{positioning}% + +\tikzset{start chain/.default=, + start chain/.code={% + \tikz@lib@chain@parse{#1}% + \ifx\tikz@lib@chain@name\pgfutil@empty% + \def\tikz@lib@chain@name{chain}% + \fi% + \ifx\tikz@lib@chain@direction\relax% + \let\tikz@lib@chain@direction=\tikz@lib@chain@default@direction% + \fi% + \expandafter\ifx\csname tikz@lib@chain@active@\tikz@lib@chain@name\endcsname\relax% + \expandafter\let\csname tikz@lib@chain@active@\tikz@lib@chain@name\endcsname=\pgfutil@empty% + \expandafter\global\expandafter\let\csname tikz@lib@chain@exists@\tikz@lib@chain@name\endcsname=\pgfutil@empty% + \expandafter\gdef\csname tikz@lib@chain@count@\tikz@lib@chain@name\endcsname{0}% + \expandafter\global\expandafter\let\csname tikz@lib@chain@dir@\tikz@lib@chain@name\endcsname\tikz@lib@chain@direction% + \let\tikz@lib@current@chain=\tikz@lib@chain@name% + \let\chainin=\tikz@lib@chainin% + \else% + \tikzerror{Chain ``\tikz@lib@chain@name'' is already active}% + \fi% + }, + continue chain/.default=, + continue chain/.code={% + \tikz@lib@chain@parse{#1}% + \ifx\tikz@lib@chain@name\pgfutil@empty% + \let\tikz@lib@chain@name\tikz@lib@current@chain% + \fi% + \expandafter\ifx\csname tikz@lib@chain@exists@\tikz@lib@chain@name\endcsname\relax% + \tikzerror{Unknown chain ``#1''}% + \else% + \let\tikz@lib@current@chain=\tikz@lib@chain@name% + \expandafter\let\csname tikz@lib@chain@active@\tikz@lib@chain@name\endcsname=\pgfutil@empty% + \ifx\tikz@lib@chain@direction\relax% + \else% + \expandafter\global\expandafter\let\csname tikz@lib@chain@dir@\tikz@lib@chain@name\endcsname\tikz@lib@chain@direction% + \fi% + \fi% + }, + join/.code=\tikz@lib@parse@join{#1}, + join/.default={}% +}% + +\def\tikz@lib@chain@parse#1{% + \pgfutil@in@{going }{#1}% + \ifpgfutil@in@% + \tikz@lib@chain@going#1\pgf@stop% + \else% + \pgfutil@in@{placed }{#1}% + \ifpgfutil@in@% + \tikz@lib@chain@positioning#1\pgf@stop% + \else% + \def\tikz@lib@chain@name{#1}% + \let\tikz@lib@chain@direction\relax% + \fi% + \fi% +}% + +\def\tikz@lib@chain@going#1going #2\pgf@stop{% + \def\tikz@lib@chain@name{#1}% + \ifx\tikz@lib@chain@name\pgfutil@empty% + \else% + \tikz@lib@chain@strip#1\pgf@stop% + \fi% + \tikz@lib@chain@is@goingtrue% + \def\tikz@lib@chain@direction{% + \ifx\tikzchainprevious\pgfutil@empty% + \else% + \tikz@lib@chain@place{#2}% + \fi% + }% +}% + +\def\tikz@lib@chain@positioning#1placed #2\pgf@stop{% + \def\tikz@lib@chain@name{#1}% + \ifx\tikz@lib@chain@name\pgfutil@empty% + \else% + \tikz@lib@chain@strip#1\pgf@stop% + \fi% + \tikz@lib@chain@is@goingfalse% + \def\tikz@lib@chain@direction{\tikz@lib@chain@place{#2}}% +}% +\newif\iftikz@lib@chain@is@going + + +\tikzset{/tikz/chain default direction/.code=% + {% + \tikz@lib@chain@parse{#1}% + \let\tikz@lib@chain@default@direction=\tikz@lib@chain@direction% + },% + /tikz/chain default direction=going right +}% + +\def\tikz@lib@current@chain{chain}% + +\pgfutil@g@addto@macro\tikz@node@reset@hook{\let\tikz@lib@chain@caller=\relax}% +\pgfutil@g@addto@macro\tikz@node@begin@hook{\tikz@lib@chain@caller}% + +\tikzset{ + on chain/.default=, + on chain/.code=\tikz@lib@on@chain{#1}% +}% +\def\tikz@lib@on@chain#1{% + \tikz@lib@chain@parse{#1}% + \ifx\tikz@lib@chain@name\pgfutil@empty% + \let\tikz@lib@chain@name\tikz@lib@current@chain% + \fi% + \expandafter\ifx\csname tikz@lib@chain@exists@\tikz@lib@chain@name\endcsname\relax% + \tikzerror{Unknown chain ``\tikz@lib@chain@name''}% + \else% + \c@pgf@counta\csname tikz@lib@chain@count@\tikz@lib@chain@name\endcsname\relax% + \ifnum\c@pgf@counta=0\relax% + \global\let\tikzchainprevious=\pgfutil@empty% + \else + \xdef\tikzchainprevious{\tikz@lib@chain@name-\the\c@pgf@counta}% + \fi% + \advance\c@pgf@counta by1\relax% + \xdef\tikzchaincount{\the\c@pgf@counta}% + \ifx\tikz@lib@chain@direction\relax% + \csname tikz@lib@chain@dir@\tikz@lib@chain@name\endcsname% + \else% + \tikz@lib@chain@direction% + \fi% + \edef\tikz@lib@chain@caller{\noexpand\tikz@lib@chain@last@found{\tikz@lib@chain@name}}% + \fi% +}% +\def\tikz@lib@chain@last@found#1{% + \c@pgf@counta\csname tikz@lib@chain@count@#1\endcsname\relax% + \advance\c@pgf@counta by1\relax% + \xdef\tikzchaincurrent{#1-\the\c@pgf@counta}% + \expandafter\xdef\csname tikz@lib@chain@count@#1\endcsname{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=1\relax% + \tikzset{alias/.expanded={#1-begin}} % + \fi% + \tikzset{alias/.expanded={#1-end}} % + \tikzset{alias/.expanded={#1-\the\c@pgf@counta}} % + \tikz@lib@chain@direction% + \tikzset{every on chain/.try}% +}% + + +\def\tikz@lib@chain@place#1{% + \pgfutil@in@{=}{#1}% + \ifpgfutil@in@% + \tikzset{#1}% + \else% + \tikzset{#1=of \tikzchainprevious}% + \fi% +}% + +\def\tikz@lib@chain@strip#1 \pgf@stop{% + \def\tikz@lib@chain@name{#1}% +}% + +\def\tikz@lib@parse@join#1{% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \tikz@lib@parse@join@by by \pgf@stop% + \else% + \pgfutil@in@{with }{#1}% + \ifpgfutil@in@% + \pgfutil@in@{by }{#1}% + \ifpgfutil@in@% + \tikz@lib@parse@join@with@by#1\pgf@stop% + \else% + \tikz@lib@parse@join@with@by#1 by \pgf@stop% + \fi% + \else% + \tikz@lib@parse@join@by#1\pgf@stop% + \fi% + \fi% +}% +\def\tikz@lib@parse@join@with@by with #1 by #2\pgf@stop{% + \tikzset{after node path={(#1)edge[every join,#2](\tikzchaincurrent)}}% +}% +\def\tikz@lib@parse@join@by by #1\pgf@stop{% + \tikzset{after node path={\ifx\tikzchainprevious\pgfutil@empty\else (\tikzchainprevious)edge[every join,#1](\tikzchaincurrent)\fi}}% +}% +\tikzset{every join/.style=}% + + +\def\tikz@lib@chainin#1(#2){\pgfutil@ifnextchar[{\tikz@lib@chainin@{#2}}{\tikz@lib@chainin@{#2}[]}}% +\def\tikz@lib@chainin@#1[#2]{\path[late options={name=#1,on chain,every chain in/.try,#2}]}% + + + +\tikzset{start branch/.code={% + \let\tikz@lib@save@current\tikz@lib@current@chain% + \pgfkeysalso{/tikz/start chain/.expand once=\tikz@lib@current@chain/#1}% + \path[late options={name=\tikz@lib@save@current-end,on chain}];% + }% +}% +\tikzset{continue branch/.style={continue chain/.expand once=\tikz@lib@current@chain/#1}}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ee19fe154ccd8557b7b3dc4e400e676e21172040 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex @@ -0,0 +1,173 @@ + +\usepgfmodule{decorations}% + + +\tikzset{decorate/.is if=tikz@decoratepath, + /pgf/decoration/name/.store in=\tikz@decoration@name, + /pgf/decoration/.unknown/.code=% + \pgfifdecoration{\pgfkeyscurrentname}{\edef\tikz@decoration@name{\pgfkeyscurrentname}} + {\pgfifmetadecoration{\pgfkeyscurrentname}{\edef\tikz@decoration@name{\pgfkeyscurrentname}} + {\pgfkeys{/errors/unknown + key/.expanded={/pgf/decoration/\pgfkeyscurrentname}{\pgfutil@unexpanded{#1}}}}},% + /pgf/decoration/raise/.code={\def\tikz@dec@shift{\pgftransformyshift{#1}}\tikz@dec@trans}, + /pgf/decoration/mirror/.code={% + \csname if#1\endcsname + \def\tikz@dec@mirror{\pgftransformyscale{-1}}% + \else% + \let\tikz@dec@mirror=\relax% + \fi% + \tikz@dec@trans% + }, + /pgf/decoration/mirror/.default=true, + /pgf/decoration/transform/.code={% + {% + \pgftransformreset% + \def\tikz@transform{}% + \pgfkeysalso{/tikz/.cd, #1}% + \expandafter\gdef\expandafter\tikz@g@temptransform\expandafter{\tikz@transform}% + }% + \let\tikz@dec@user@transform=\tikz@g@temptransform% + \tikz@dec@trans% + },% + /pgf/decoration/pre/.initial=lineto, + /pgf/decoration/post/.initial=lineto, + /pgf/decoration/pre length/.initial=0pt, + /pgf/decoration/post length/.initial=0pt, +}% + +\let\tikz@decoration@name=\tikz@nonetext + +\def\tikz@dec@trans{\pgfsetdecorationsegmenttransformation{\tikz@dec@user@transform\tikz@dec@mirror\tikz@dec@shift}}% +\let\tikz@dec@user@transform=\relax +\let\tikz@dec@shift=\relax +\let\tikz@dec@mirror=\relax + +\pgfdeclaremetadecoration{tikz@internal}{pre}{% + \state{pre}[width=\pgfkeysvalueof{/pgf/decoration/pre length}, next state=main] + { + \tikz@dec@trans + \decoration{\pgfkeysvalueof{/pgf/decoration/pre}} + }% + \state{main}[width=\pgfmetadecoratedremainingdistance-\pgfkeysvalueof{/pgf/decoration/post length}, next state=final] + { + \tikz@dec@trans + \decoration{\tikz@decoration@name} + }% + \state{final} + { + \tikz@dec@trans + \decoration{\pgfkeysvalueof{/pgf/decoration/post}} + }% +}% + + +\newif\iftikz@metadecoration + +\def\tikz@lib@dec@addtomacro#1#2{\expandafter\def\expandafter#1\expandafter{#1#2}}% + +\def\tikz@lib@decoration[#1]{% + \begingroup% + \tikzset{#1}% + \ifx\tikz@decoration@name\tikz@nonetext% + \else + \expandafter\tikz@lib@do@dec% + \fi% + \pgfutil@ifnextchar\bgroup{% + \begingroup% + \tikz@auto@end@pathfalse% + \aftergroup\tikz@enddecoration% + \afterassignment\tikz@scan@next@command% + \let\tikz@lib@next% + }% + {% + \tikzerror{A decoration must begin with a brace}% + \tikz@enddecoration% + }% +}% +\def\tikz@lib@do@dec{% + \pgfifmetadecoration{\tikz@decoration@name}% + {\expandafter\pgfmetadecoration\expandafter{\tikz@decoration@name}}% + {% + \pgfifdecoration{\tikz@decoration@name}% + {\tikz@lib@dec@startdecoration}% + {\tikzerror{Unknown (meta-)decoration '\tikz@decoration@name'. Perhaps you + misspelled it?}}% + }% + \ifx\pgfdecorateexistingpath\pgfutil@empty% + \pgfpathmoveto{\pgfqpoint{\the\tikz@lastxsaved}{\the\tikz@lastysaved}}% + \fi% +}% +\newbox\tikz@lib@dec@box +\def\tikz@enddecoration{% + \global\setbox\tikz@lib@dec@box=\box\tikz@tempbox% + \ifx\tikz@decoration@name\tikz@nonetext% + \else + \iftikz@metadecoration% + \endpgfmetadecoration% + \else% + \tikz@lib@dec@stopdecoration% + \fi% + \fi + \endgroup% + \setbox\tikz@tempbox=\box\tikz@lib@dec@box% +}% + + +\def\tikz@lib@dec@decorate@path{% + \ifx\tikz@decoration@name\tikz@nonetext% + \else% + \pgfgetpath\tikz@lib@dec@currentpath% + \pgfsetpath\pgfutil@empty% + \pgfifmetadecoration{\tikz@decoration@name} + { + \expandafter\pgfmetadecoration\expandafter{\tikz@decoration@name}% + \pgfsetpath\tikz@lib@dec@currentpath% + \endpgfmetadecoration% + } + { + \pgfifdecoration{\tikz@decoration@name} + { + \tikz@lib@dec@startdecoration% + \pgfsetpath\tikz@lib@dec@currentpath% + \tikz@lib@dec@stopdecoration% + } + { + \tikzerror{Unknown (meta-)decoration '\tikz@decoration@name'. Perhaps + you misspelled it?} + } + } + \fi% +}% + +\def\tikz@lib@dec@zpttext{0pt}% + +\newif\iftikz@lib@dec@temp +\def\tikz@lib@dec@startdecoration{% + \pgfkeysgetvalue{/pgf/decoration/pre length}{\tikz@lib@pre}% + \pgfkeysgetvalue{/pgf/decoration/post length}{\tikz@lib@post}% + \tikz@lib@dec@tempfalse% + \ifx\tikz@lib@pre\tikz@lib@dec@zpttext% + \ifx\tikz@lib@post\tikz@lib@dec@zpttext% + \else% + \tikz@lib@dec@temptrue% + \fi% + \else% + \tikz@lib@dec@temptrue% + \fi% + \iftikz@lib@dec@temp% + \pgfmetadecoration{tikz@internal}% + \else% + \expandafter\pgfdecoration\expandafter{\expandafter{\tikz@decoration@name}{\pgfdecoratedpathlength}{}{}}% + \fi% +}% + +\def\tikz@lib@dec@stopdecoration{% + \iftikz@lib@dec@temp% + \endpgfmetadecoration% + \else% + \endpgfdecoration% + \fi% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.footprints.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.footprints.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..0122cfbdfd48155e69cd0cfe31dec7048cacbaa9 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.footprints.code.tex @@ -0,0 +1,5 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.footprints}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.fractals.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.fractals.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..35f86d83e76aec0435ec9497dbe6178af7c22831 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.fractals.code.tex @@ -0,0 +1,5 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.fractals}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.markings.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.markings.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..88ecf5084808d7d96570d6c802c5f56f03f4a31b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.markings.code.tex @@ -0,0 +1,22 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.markings}% + +\def\pgf@lib@dec@doarrowhead{% + \pgfutil@ifnextchar[{\tikz@lib@dec@doarrowhead}{\tikz@lib@dec@doarrowhead[]}% +}% +\def\tikz@lib@dec@doarrowhead[#1]#2{% + \scope[#1] + \pgf@lib@dec@arrowhead{1}{#2}% + \endscope +}% +\def\pgf@lib@dec@doarrowheadrev{% + \pgfutil@ifnextchar[{\tikz@lib@dec@doarrowheadrev}{\tikz@lib@dec@doarrowheadrev[]}% +}% +\def\tikz@lib@dec@doarrowheadrev[#1]#2{% + \scope[#1] + \pgf@lib@dec@arrowhead{-1}{#2}% + \endscope +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8e80621a6401255c160c198ff391b2c2e087d4e2 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathmorphing.code.tex @@ -0,0 +1,5 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.pathmorphing}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..b357e7a59580ec6c44fcfb401cb240c106c2735b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.pathreplacing.code.tex @@ -0,0 +1,25 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.pathreplacing}% + + +\def\tikz@lib@dec@installinputsegmentpoints{% + \pgf@process{\pgf@decorate@inputsegment@first}% + \edef\tikzinputsegmentfirst{\the\pgf@x,\the\pgf@y}% + \pgf@process{\pgf@decorate@inputsegment@last}% + \edef\tikzinputsegmentlast{\the\pgf@x,\the\pgf@y}% + \pgf@process{\pgf@decorate@inputsegment@supporta}% + \edef\tikzinputsegmentsupporta{\the\pgf@x,\the\pgf@y}% + \pgf@process{\pgf@decorate@inputsegment@supportb}% + \edef\tikzinputsegmentsupportb{\the\pgf@x,\the\pgf@y}% +}% + +\pgfkeys{ + /pgf/decoration/.cd, + moveto code/.code=\def\pgfdecoratedinputsegmentmovetocode{\tikz@lib@dec@installinputsegmentpoints#1}, + lineto code/.code=\def\pgfdecoratedinputsegmentlinetocode{\tikz@lib@dec@installinputsegmentpoints#1}, + curveto code/.code=\def\pgfdecoratedinputsegmentcurvetocode{\tikz@lib@dec@installinputsegmentpoints#1}, + closepath code/.code=\def\pgfdecoratedinputsegmentclosepathcode{\tikz@lib@dec@installinputsegmentpoints#1} +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.shapes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.shapes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ec7c71f51aa0ad725b508ffde715318cf31f6c7b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.shapes.code.tex @@ -0,0 +1,5 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.shapes}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.text.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.text.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..47c503a707383efa50bb258b382d4d95f44f72b8 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarydecorations.text.code.tex @@ -0,0 +1,596 @@ + +\usetikzlibrary{decorations}% +\usepgflibrary{decorations.text}% + + + +\def\tikz@lib@dec@te@space@text{space}% +\def\tikz@lib@dec@align@left@text{left}% +\def\tikz@lib@dec@align@right@text{right}% +\def\tikz@lib@dec@align@center@text{center}% +\def\tikz@lib@dec@te@none@text{none}% + +\newif\iftikz@lib@dec@te@pathfromtext% +\newif\iftikz@lib@dec@te@segmentfromwidth% +\newif\iftikz@lib@dec@te@scaletexttopath% +\newif\iftikz@lib@dec@te@fittexttopath% +\newif\iftikz@lib@dec@te@wordsep% +\newif\iftikz@lib@dec@te@finalletter% + + +\def\tikz@lib@dec@te@addto@macro#1#2{% + \expandafter\def\expandafter#1\expandafter{#1#2}% +}% + +\def\tikz@lib@dec@te@namelet#1#2{% + \expandafter\expandafter\expandafter\let\expandafter\expandafter\csname\expandafter#1\expandafter\endcsname\expandafter=\csname#2\endcsname% +}% + +\def\tikz@lib@dec@te@advancecountmacro#1#2{% + \pgfutil@tempcnta=#1\relax% + \advance\pgfutil@tempcnta by#2\relax% + \edef#1{\the\pgfutil@tempcnta}% +}% + +\def\tikz@lib@dec@te@advancedimenmacro#1#2{% + \pgf@x=#1\relax% + \advance\pgf@x by#2\relax% + \edef#1{\the\pgf@x}% +}% + +\def\tikz@lib@dec@te@start@parameters#1{% + \expandafter\let\csname tikz@lib@dec@te@character@#1\endcsname=\pgfutil@empty% +}% + +\def\tikz@lib@dec@te@addto@parameters#1#2{% + \expandafter\tikz@lib@dec@te@addto@macro\expandafter% + {\csname tikz@lib@dec@te@character@#1\endcsname}{#2}% +}% +\def\tikz@lib@dec@te@addmacroto@parameters#1#2{% + \def\tikz@lib@dec@te@marshal{\expandafter\tikz@lib@dec@te@addto@macro\expandafter% + {\csname tikz@lib@dec@te@character@#1\endcsname}}% + \expandafter\tikz@lib@dec@te@marshal\expandafter{\expandafter\def\expandafter#2\expandafter{#2}}% +}% + +\def\tikz@lib@dec@te@getparameters#1{\csname tikz@lib@dec@te@character@#1\endcsname}% + + + +\let\tikz@lib@dec@te@textoptions=\pgfutil@empty +\let\tikz@lib@dec@te@widthoptions=\pgfutil@empty +\let\tikz@lib@dec@te@charactercountvar=\pgfutil@empty +\let\tikz@lib@dec@te@charactertotalvar=\pgfutil@empty +\let\tikz@lib@dec@te@lettercountvar=\pgfutil@empty +\let\tikz@lib@dec@te@lettertotalvar=\pgfutil@empty +\let\tikz@lib@dec@te@wordcountvar=\pgfutil@empty +\let\tikz@lib@dec@te@wordctotalvar=\pgfutil@empty +\let\tikz@lib@dec@te@transformtext=\pgfutil@empty% + + +\pgfkeys{/pgf/decoration/text effects/.cd, + .unknown/.code={\let\tikz@lib@dec@te@key@tmp=\pgfkeyscurrentname% + \pgfkeysalso{/tikz/\tikz@lib@dec@te@key@tmp={#1}}}, + path from text/.is if=tikz@lib@dec@te@pathfromtext, + path from text angle/.store in=\tikz@lib@dec@te@pathfromtextangle, + path from text angle=0, + fit text to path/.is if=tikz@lib@dec@te@fittexttopath, + characters/.style={/pgf/decoration/text effects/every character/.style={#1}}, + characters/.append/.code={\pgfkeysalso{/pgf/decoration/text effects/every character/.append style={#1}}}, + character widths/.code={\pgfkeysalso{/pgf/decoration/text effects/every character width/.style={#1}}}, + character widths/.append/.code={\pgfkeysalso{/pgf/decoration/text effects/every character width/.append style={#1}}}, + character count/.store in=\tikz@lib@dec@te@charactercountvar, + character count=, + character total/.store in=\tikz@lib@dec@te@charactertotalvar, + character total=, + letter count/.store in=\tikz@lib@dec@te@lettercountvar, + letter count=, + letter total/.store in=\tikz@lib@dec@te@lettertotalvar, + letter total=, + word count/.store in=\tikz@lib@dec@te@wordcountvar, + word count=, + word total/.store in=\tikz@lib@dec@te@wordtotalvar, + word total=, + style characters/.code args={#1 with #2}{\tikz@lib@dec@te@parse@stylecharacters{#1}{#2}}, + text along path/.style={ + inner xsep=0pt, + anchor=base, + transform shape + }, + segment from width/.is if=tikz@lib@dec@te@segmentfromwidth, + segment from width=true, + word separator/.code={% + \def\tikz@lib@dec@te@tmp{#1}% + \ifx\tikz@lib@dec@te@tmp\tikz@lib@dec@te@space@text% + \let\tikz@lib@dec@te@wordsep=\tikz@lib@dec@te@spacetoken% + \else% + \def\tikz@lib@dec@te@wordsep{#1} + \fi}, + word separator=space, + character command/.code={% + \def\tikz@lib@dec@te@tmp{#1}% + \ifx\tikz@lib@dec@te@tmp\pgfutil@empty% + \def\tikz@lib@dec@te@charactercommand{\tikz@lib@dec@te@charactertypesetonly}% + \else% + \def\tikz@lib@dec@te@charactercommand{#1}% + \fi% + }, + character command=, + every character width/.style={/pgf/decoration/text effects/every character/.try}, + every character/.style={}, + reverse text/.code={\tikz@lib@dec@te@addto@macro\tikz@lib@dec@te@transformtext% + {\tikz@lib@dec@te@reversetext}}, + group letters into words/.code={\tikz@lib@dec@te@addto@macro\tikz@lib@dec@te@transformtext% + {\tikz@lib@dec@te@groupletters}}, + group letters/.code={\tikz@lib@dec@te@addto@macro\tikz@lib@dec@te@transformtext% + {\tikz@lib@dec@te@groupletters}}, + replace characters/.code args={#1 with #2}{\tikz@lib@dec@te@parse@replacecharacters{#1}{#2}}, + scale text to path/.is if=tikz@lib@dec@te@scaletexttopath, + fit text to path/.is if=tikz@lib@dec@te@fittexttopath, + repeat text/.store in=\tikz@lib@dec@te@repeattext, + repeat text/.default=-1, + repeat text=0, +}% + + +\def\tikz@lib@dec@te@charactertypesetonly#1{#1}% + +\tikzset{% + text effects/.code={\pgfkeysalso{/pgf/decoration/text effects/.cd,#1}}, +}% + + + + + + +\def\tikz@lib@dec@te@preparetext{% + \let\tikz@lib@dec@te@text=\pgfdecorationtext% + \tikz@lib@dec@te@scancharacters{% + \expandafter\let\csname tikz@lib@dec@te@character@\tikz@lib@dec@te@scancount @token\endcsname=% + \tikz@lib@dec@te@character% + }% + \let\tikz@lib@dec@te@charactertotalcount=\tikz@lib@dec@te@scancount% + \ifx\tikz@lib@dec@te@transformtext\pgfutil@empty% + \else% + \tikz@lib@dec@te@transformtext% + \fi% + \def\tikz@lib@dec@te@charactercount{0}% + \def\tikz@lib@dec@te@wordcount{0}% + \def\tikz@lib@dec@te@wordsepcount{0}% + \def\tikz@lib@dec@te@lettercount{0}% + \def\tikz@lib@dec@te@lastcharacter{0}% + \pgfmathloop% + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount% + \ifnum\tikz@lib@dec@te@lettercount>0\relax% + \tikz@lib@dec@te@addto@parameters{\tikz@lib@dec@te@lastcharactercount}{\tikz@lib@dec@te@finallettertrue}% + \fi + \else% + \expandafter\let\expandafter\tikz@lib@dec@te@character\expandafter=\csname tikz@lib@dec@te@character@\pgfmathcounter @token\endcsname% + \tikz@lib@dec@te@advancecountmacro{\tikz@lib@dec@te@charactercount}{1}% + \tikz@lib@dec@te@start@parameters{\tikz@lib@dec@te@charactercount}% + \tikz@lib@dec@te@addmacroto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@charactercount}% + \ifx\tikz@lib@dec@te@character\tikz@lib@dec@te@wordsep% + \tikz@lib@dec@te@advancecountmacro{\tikz@lib@dec@te@wordsepcount}{1}% + \ifnum\tikz@lib@dec@te@lettercount>0\relax% + \tikz@lib@dec@te@addto@parameters{\tikz@lib@dec@te@lastcharactercount}{\tikz@lib@dec@te@finallettertrue}% + \fi + \def\tikz@lib@dec@te@lettercount{0}% + \tikz@lib@dec@te@addto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@wordseptrue}% + \else + \ifnum\tikz@lib@dec@te@lettercount=0\relax% + \tikz@lib@dec@te@advancecountmacro\tikz@lib@dec@te@wordcount{1}% + \fi% + \tikz@lib@dec@te@addto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@finalletterfalse}% + \tikz@lib@dec@te@advancecountmacro{\tikz@lib@dec@te@lettercount}{1}% + \tikz@lib@dec@te@addto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@wordsepfalse}% + \expandafter\let\csname tikz@lib@dec@te@word \tikz@lib@dec@te@wordcount @lettercount\endcsname=\tikz@lib@dec@te@lettercount% + \fi% + \tikz@lib@dec@te@addmacroto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@lettercount}% + \tikz@lib@dec@te@addmacroto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@wordcount}% + \tikz@lib@dec@te@addmacroto@parameters{\tikz@lib@dec@te@charactercount}{\tikz@lib@dec@te@character}% + \let\tikz@lib@dec@te@lastcharactercount=\pgfmathcounter% + \repeatpgfmathloop% + \let\tikz@lib@dec@te@wordtotal=\tikz@lib@dec@te@wordcount% + \pgfmathloop + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount% + \else% + \tikz@lib@dec@te@addmacroto@parameters{\pgfmathcounter}{\tikz@lib@dec@te@charactertotalcount}% + \tikz@lib@dec@te@addmacroto@parameters{\pgfmathcounter}{\tikz@lib@dec@te@wordtotal}% + \expandafter\let\expandafter\tikz@lib@dec@te@lettertotalcount\expandafter=\csname tikz@lib@dec@te@word \tikz@lib@dec@te@wordcount @lettercount\endcsname% + \tikz@lib@dec@te@addmacroto@parameters{\pgfmathcounter}{\tikz@lib@dec@te@lettertotalcount}% + \repeatpgfmathloop% + \def\tikz@lib@dec@te@textwidth{0pt}% + \pgfmathloop% + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount% + \else% + \def\tikz@lib@dec@te@characterwidth{0pt}% + \tikz@lib@dec@te@getcharacterwidth{\pgfmathcounter}% + \expandafter\let\csname tikz@lib@dec@te@character@\pgfmathcounter @width\endcsname=\tikz@lib@dec@te@characterwidth% + \pgf@x=\tikz@lib@dec@te@characterwidth\relax% + \pgf@x=0.5\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@\pgfmathcounter @prewidth\endcsname{\the\pgf@x}% + \expandafter\edef\csname tikz@lib@dec@te@character@\pgfmathcounter @postwidth\endcsname{\the\pgf@x}% + \tikz@lib@dec@te@advancedimenmacro{\tikz@lib@dec@te@textwidth}{\tikz@lib@dec@te@characterwidth}% + \repeatpgfmathloop% +}% + +\def\tikz@lib@dec@te@spacetoken{ }% + +\let\tikz@lib@dec@te@wordsep=\tikz@lib@dec@te@spacetoken + + +\def\tikz@lib@dec@te@scancharacters#1{% + \def\tikz@lib@dec@te@@@scancharacters@process{#1}% + \def\tikz@lib@dec@te@scancount{0}% + \expandafter\tikz@lib@dec@te@@scancharacters\tikz@lib@dec@te@text\tikz@lib@dec@te@scancharacters}% + +\def\tikz@lib@dec@te@@scancharacters{% + \futurelet\tikz@lib@dec@te@token\tikz@lib@dec@te@@@scancharacters}% + +\def\tikz@lib@dec@te@@@scancharacters{% + \ifx\tikz@lib@dec@te@token\tikz@lib@dec@te@scancharacters% + \let\tikz@lib@dec@te@next=\tikz@lib@dec@te@@@@scancharacters% + \else% + \tikz@lib@dec@te@advancecountmacro\tikz@lib@dec@te@scancount{1}% + \ifx\tikz@lib@dec@te@token\pgfutil@sptoken% + \let\tikz@lib@dec@te@next=\tikz@lib@dec@te@@@scancharacters@space% + \else% + \ifx\tikz@lib@dec@te@token\bgroup% + \let\tikz@lib@dec@te@next=\tikz@lib@dec@te@@@scancharacters@bgroup% + \else% + \let\tikz@lib@dec@te@next=\tikz@lib@dec@te@@@scancharacters@normal% + \fi% + \fi% + \fi% + \tikz@lib@dec@te@next% +}% + +\def\tikz@lib@dec@te@@@scancharacters@space{% + \let\tikz@lib@dec@te@character=\tikz@lib@dec@te@spacetoken% + \tikz@lib@dec@te@@@scancharacters@process% + \pgfutil@ifnextchar x\tikz@lib@dec@te@@scancharacters\tikz@lib@dec@te@@scancharacters% +}% + +\def\tikz@lib@dec@te@@@scancharacters@bgroup#1{% + \def\tikz@lib@dec@te@character{{#1}}% + \tikz@lib@dec@te@@@scancharacters@process% + \tikz@lib@dec@te@@scancharacters% +}% + +\def\tikz@lib@dec@te@@@scancharacters@normal#1{% + \def\tikz@lib@dec@te@character{#1}% + \tikz@lib@dec@te@@@scancharacters@process% + \tikz@lib@dec@te@@scancharacters% +}% + + +\def\tikz@lib@dec@te@@@@scancharacters#1\tikz@lib@dec@te@scancharacters{}% + + +\def\tikz@lib@dec@te@reversetext{% + \c@pgf@counta=\tikz@lib@dec@te@charactertotalcount% + \pgfmathloop% + \ifnum\pgfmathcounter>\c@pgf@counta% + \else% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@tmp}{tikz@lib@dec@te@character@\pgfmathcounter @token}% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@character@\pgfmathcounter @token}{tikz@lib@dec@te@character@\the\c@pgf@counta @token}% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@character@\the\c@pgf@counta @token}{tikz@lib@dec@te@tmp}% + \advance\c@pgf@counta by-1\relax% + \repeatpgfmathloop% +}% + +\def\tikz@lib@dec@te@groupletters{% + \c@pgf@counta=0\relax% + \let\tikz@lib@dec@te@tmp=\pgfutil@empty% + \let\tikz@lib@dec@te@@tmp=\pgfutil@empty% + \pgfmathloop% + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount% + \ifx\tikz@lib@dec@te@@tmp\pgfutil@empty% + \else% + \advance\c@pgf@counta by1\relax% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@character@\the\c@pgf@counta @token}{tikz@lib@dec@te@@tmp}% + \fi% + \else% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@tmp}{tikz@lib@dec@te@character@\pgfmathcounter @token}% + \ifx\tikz@lib@dec@te@tmp\tikz@lib@dec@te@wordsep% + \advance\c@pgf@counta by1\relax% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@character@\the\c@pgf@counta @token}{tikz@lib@dec@te@@tmp}% + \let\tikz@lib@dec@te@@tmp=\pgfutil@empty% + \advance\c@pgf@counta by1\relax% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@character@\the\c@pgf@counta @token}{tikz@lib@dec@te@wordsep}% + \else% + \expandafter\tikz@lib@dec@te@addto@macro\expandafter{\expandafter\tikz@lib@dec@te@@tmp\expandafter}\expandafter{\tikz@lib@dec@te@tmp}% + \fi% + \repeatpgfmathloop% + \edef\tikz@lib@dec@te@charactertotalcount{\the\c@pgf@counta}% +}% + + +\def\tikz@lib@dec@te@getcharacterwidth#1{% + \csname tikz@lib@dec@te@character@#1\endcsname% + \tikz@lib@dec@te@getoptions{every character width/.try}% + \let\tikz@lib@dec@te@lastcharacterwidth=\tikz@lib@dec@te@characterwidth% + \pgfpositionnodelater\tikz@lib@dec@te@@getcharacterwidth% + \pgfutil@ifundefined{tikz@lib@dec@te@character@replacements@\meaning\tikz@lib@dec@te@character @code}{% + \expandafter\node\expandafter[\tikz@lib@dec@te@options,scale=\tikz@lib@dec@scaledcharacterwidthfactor]% + {\hbox{\tikz@lib@dec@te@charactercommand{\tikz@lib@dec@te@character}}};% + \let\tikz@lib@dec@te@characterwidth=\tikz@lib@dec@te@characterwidth@tmp% + }{% + \tikz@lib@dec@te@getcharacter@replacementwidth{\tikz@lib@dec@te@character}% + \let\tikz@lib@dec@te@characterwidth=\tikz@lib@dec@te@character@replacementwidth% + }% +}% + +\def\tikz@lib@dec@te@addwidthstoparameters{% + \pgfmathloop% + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount% + \else% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@characterwidth}{tikz@lib@dec@te@character@\pgfmathcounter @width}% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@characterprewidth}{tikz@lib@dec@te@character@\pgfmathcounter @prewidth}% + \tikz@lib@dec@te@namelet{tikz@lib@dec@te@characterpostwidth}{tikz@lib@dec@te@character@\pgfmathcounter @postwidth}% + \tikz@lib@dec@te@addmacroto@parameters{\pgfmathcounter}{\tikz@lib@dec@te@characterwidth}% + \tikz@lib@dec@te@addmacroto@parameters{\pgfmathcounter}{\tikz@lib@dec@te@characterprewidth}% + \tikz@lib@dec@te@addmacroto@parameters{\pgfmathcounter}{\tikz@lib@dec@te@characterpostwidth}% + \repeatpgfmathloop% +}% + + +\def\tikz@lib@dec@te@addoptions#1{% + \expandafter\def\expandafter\tikz@lib@dec@te@options\expandafter{\tikz@lib@dec@te@options,#1}% +}% + +\def\tikz@lib@dec@te@getoptions#1{% + \let\tikz@lib@dec@te@lastcharactercommand=\tikz@lib@dec@te@charactercommand% + \def\tikz@lib@dec@te@options{/pgf/decoration/text effects/.cd}% + \tikz@lib@dec@te@addoptions{#1}% + \let\tikzdecorationcharactercount=\tikz@lib@dec@te@charactercount% + \let\tikzdecorationcharactertotal=\tikz@lib@dec@te@charactertotalcount% + \let\tikzdecorationlettercount=\tikz@lib@dec@te@lettercount% + \let\tikzdecorationlettertotal=\tikz@lib@dec@te@lettertotalcount% + \let\tikzdecorationwordcount=\tikz@lib@dec@te@wordcount% + \let\tikzdecorationwordtotal=\tikz@lib@dec@te@wordtotal% + \let\tikzdecorationcharacter=\tikz@lib@dec@te@character% + \ifx\tikz@lib@dec@te@charactercountvar\pgfutil@empty% + \else% + \expandafter\let\tikz@lib@dec@te@charactercountvar=\tikz@lib@dec@te@charactercount% + \fi% + \ifx\tikz@lib@dec@te@charactertotalvar\pgfutil@empty% + \else% + \expandafter\let\tikz@lib@dec@te@charactertotalvar=\tikz@lib@dec@te@charactertotalcount% + \fi% + \ifx\tikz@lib@dec@te@wordcountvar\pgfutil@empty% + \else% + \expandafter\let\tikz@lib@dec@te@wordcountvar=\tikz@lib@dec@te@wordcount% + \fi% + \ifx\tikz@lib@dec@te@wordtotalvar\pgfutil@empty% + \else% + \expandafter\let\tikz@lib@dec@te@wordtotalvar=\tikz@lib@dec@te@wordtotal% + \fi% + \ifx\tikz@lib@dec@te@lettercountvar\pgfutil@empty% + \else% + \expandafter\let\tikz@lib@dec@te@lettercountvar=\tikz@lib@dec@te@lettercount% + \fi% + \ifx\tikz@lib@dec@te@lettertotalvar\pgfutil@empty% + \else% + \expandafter\let\tikz@lib@dec@te@lettertotalvar=\tikz@lib@dec@te@lettetotal% + \fi% + \edef\tikz@lib@dec@te@tmp{character \tikz@lib@dec@te@charactercount/.try,% + character {\meaning\tikz@lib@dec@te@character}/.try}% + \expandafter\tikz@lib@dec@te@addoptions\expandafter{\tikz@lib@dec@te@tmp}% + \ifx\tikz@lib@dec@te@character\tikz@lib@dec@te@wordsep% + \tikz@lib@dec@te@addoptions{/pgf/decoration/text effects/every word separator/.try}% + \else% + \ifnum\tikz@lib@dec@te@wordcount>0\relax% + \edef\tikz@lib@dec@te@tmp{every word/.try, word \tikz@lib@dec@te@wordcount/.try}% + \expandafter\tikz@lib@dec@te@addoptions\expandafter{\tikz@lib@dec@te@tmp}% + \ifnum\tikz@lib@dec@te@lettercount>0\relax% + \edef\tikz@lib@dec@te@tmp{every letter/.try,every \tikz@lib@dec@te@lettercount\space letter/.try}% + \expandafter\tikz@lib@dec@te@addoptions\expandafter{\tikz@lib@dec@te@tmp}% + \ifnum\tikz@lib@dec@te@lettercount=1\relax% + \edef\tikz@lib@dec@te@tmp{every first letter/.try}% + \expandafter\tikz@lib@dec@te@addoptions\expandafter{\tikz@lib@dec@te@tmp}% + \fi% + \iftikz@lib@dec@te@finalletter% + \tikz@lib@dec@te@addoptions{every final letter/.try}% + \fi% + \fi% + \fi% + \fi% +}% + +\def\tikz@lib@dec@te@@getcharacterwidth{% + \iftikz@lib@dec@te@segmentfromwidth% + \pgf@x=\pgfpositionnodelatermaxx\relax% + \advance\pgf@x by-\pgfpositionnodelaterminx\relax% + \else% + \pgf@x=\pgfpositionnodelatermaxy\relax% + \advance\pgf@x by-\pgfpositionnodelaterminy\relax% + \fi% + \xdef\tikz@lib@dec@te@characterwidth@tmp{\the\pgf@x}% +}% + + +\def\tikz@lib@dec@te@drawcharacter{% + \csname tikz@lib@dec@te@character@\tikz@lib@dec@te@charactercount\endcsname% + \tikz@lib@dec@te@getoptions{every character/.try}% + \pgfpositionnodelater\relax% + \pgfutil@ifundefined{tikz@lib@dec@te@character@replacements@\meaning\tikz@lib@dec@te@character @code}{% + \expandafter\node\expandafter[\tikz@lib@dec@te@options, scale=\tikz@lib@dec@scaledcharacterwidthfactor]{\hbox{\tikz@lib@dec@te@charactercommand{\tikz@lib@dec@te@character}}};% + }{\tikz@lib@dec@te@drawcharacter@replacement{\tikz@lib@dec@te@character}}% +}% + +\def\tikz@lib@dec@te@drawcharacter@replacement#1{% + \pgfscope% + \expandafter\tikzset\expandafter{\tikz@lib@dec@te@options}% + \csname tikz@lib@dec@te@character@replacements@\meaning#1@code\endcsname% + \endpgfscope% +}% + +\newbox\tikz@lib@dec@te@box +\def\tikz@lib@dec@te@getcharacter@replacementwidth#1{% + \pgfinterruptpicture% + \setbox\tikz@lib@dec@te@box=\hbox{% + \pgfpicture + \expandafter\tikzset\expandafter{\tikz@lib@dec@te@options}% + \csname tikz@lib@dec@te@character@replacements@\meaning#1@code\endcsname% + \endpgfpicture}% + \xdef\tikz@lib@dec@te@character@replacementwidth{\the\wd\tikz@lib@dec@te@box}% + \endpgfinterruptpicture% +}% + +\def\tikz@lib@dec@scaledcharacterwidthfactor{1}% + +\def\tikz@lib@dec@te@state@setup@precomputation{% + \def\tikz@lib@te@alignshift{0pt}% + \iftikz@lib@dec@te@pathfromtext% + \else% + \let\tikz@lib@dec@te@text=\pgfdecorationtext% + \tikz@lib@dec@te@preparetext% + \iftikz@lib@dec@te@scaletexttopath% + \pgfmathdivide{\pgfdecoratedpathlength}{\tikz@lib@dec@te@textwidth}% + \let\tikz@lib@dec@scaledcharacterwidthfactor=\pgfmathresult% + \expandafter\pgfkeys\expandafter{\tikz@lib@dec@te@tmp}% + \pgfmathloop + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount% + \else% + \pgf@x=\csname tikz@lib@dec@te@character@\pgfmathcounter @prewidth\endcsname\relax% + \pgf@x=\tikz@lib@dec@scaledcharacterwidthfactor\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@\pgfmathcounter @prewidth\endcsname{\the\pgf@x}% + \pgf@x=\csname tikz@lib@dec@te@character@\pgfmathcounter @postwidth\endcsname\relax% + \pgf@x=\tikz@lib@dec@scaledcharacterwidthfactor\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@\pgfmathcounter @postwidth\endcsname{\the\pgf@x}% + \repeatpgfmathloop% + \tikz@lib@dec@te@addwidthstoparameters% + \let\tikz@lib@dec@te@textwidth=\pgfdecoratedpathlength% + \else% + \iftikz@lib@dec@te@fittexttopath% + \pgf@x=\pgfdecoratedpathlength% + \pgf@xa=\csname tikz@lib@dec@te@character@1@postwidth\endcsname\relax% + \pgf@xb=\csname tikz@lib@dec@te@character@\tikz@lib@dec@te@charactertotalcount @prewidth\endcsname\relax% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@x by-\pgf@xb% + \pgf@y=\tikz@lib@dec@te@textwidth\relax% + \advance\pgf@y by-\pgf@xa% + \advance\pgf@y by-\pgf@xb% + \pgfmathdivide{\the\pgf@x}{\the\pgf@y}% + \let\tikz@lib@dec@characterwidthscale=\pgfmathresult% + \pgfmathloop + \ifnum\pgfmathcounter>\tikz@lib@dec@te@charactertotalcount\relax% + \else% + \ifnum\pgfmathcounter>1\relax% + \pgf@x=\csname tikz@lib@dec@te@character@\pgfmathcounter @prewidth\endcsname\relax% + \pgf@x=\tikz@lib@dec@characterwidthscale\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@\pgfmathcounter @prewidth\endcsname{\the\pgf@x}% + \fi% + \ifnum\pgfmathcounter<\tikz@lib@dec@te@charactertotalcount\relax% + \pgf@x=\csname tikz@lib@dec@te@character@\pgfmathcounter @postwidth\endcsname\relax% + \pgf@x=\tikz@lib@dec@characterwidthscale\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@\pgfmathcounter @postwidth\endcsname{\the\pgf@x}% + \fi% + \repeatpgfmathloop% + \tikz@lib@dec@te@addwidthstoparameters% + \let\tikz@lib@dec@te@textwidth=\pgfdecoratedpathlength% + \else% + \pgfkeysgetvalue{/pgf/decoration/text align/align}{\tikz@lib@dec@align}% + \ifx\tikz@lib@dec@align\tikz@lib@dec@align@center@text% + \pgf@x=\pgfdecoratedpathlength\relax% + \advance\pgf@x by-\tikz@lib@dec@te@textwidth\relax% + \ifdim\pgf@x<0pt\relax% + \pgf@x=0pt\relax% + \fi% + \divide\pgf@x by2\relax% + \pgf@xa=\csname tikz@lib@dec@te@character@1@prewidth\endcsname\relax% + \advance\pgf@xa by\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@1@prewidth\endcsname{\the\pgf@xa}% + \pgf@xa=\csname tikz@lib@dec@te@character@\tikz@lib@dec@te@charactertotalcount @postwidth\endcsname\relax% + \advance\pgf@xa by\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@\tikz@lib@dec@te@charactertotalcount @postwidth\endcsname{\the\pgf@xa}% + \else% + \ifx\tikz@lib@dec@align\tikz@lib@dec@align@right@text% + \pgf@x=\pgfdecoratedpathlength\relax% + \advance\pgf@x by-\tikz@lib@dec@te@textwidth\relax% + \ifdim\pgf@x<0pt\relax% + \pgf@x=0pt\relax% + \fi% + \pgf@xa=\csname tikz@lib@dec@te@character@1@prewidth\endcsname\relax% + \advance\pgf@xa by\pgf@x% + \expandafter\edef\csname tikz@lib@dec@te@character@1@prewidth\endcsname{\the\pgf@xa}% + \fi% + \fi% + \tikz@lib@dec@te@addwidthstoparameters% + \fi% + \fi% + \fi% +}% + + +\def\pgf@decorate@path@check@moveto#1{% + \expandafter\pgf@decorate@path@@check@moveto#1\pgf@decorate@stop\pgf@decorate@@stop}% + +\def\pgf@decorate@token@stop{\pgf@decorate@stop}% +\def\pgf@decorate@path@@check@moveto#1#2#3#4\pgf@decorate@@stop#5#6{% + \def\pgf@decorate@temp{#4}% + \pgf@x=#2\relax% + \pgf@y=#3\relax% + \ifx\pgf@decorate@temp\pgf@decorate@token@stop% + \iftikz@lib@dec@te@pathfromtext% + \pgfextract@process\tikz@lib@dec@te@pathstart{}% + \tikz@lib@dec@te@preparetext% + \tikz@lib@dec@te@addwidthstoparameters% + \pgfsetpath\pgfutil@empty% + \pgfpathmoveto{\tikz@lib@dec@te@pathstart}% + \pgfpathlineto{\pgfpointadd{\tikz@lib@dec@te@pathstart}% + {\pgfpointpolar{\tikz@lib@dec@te@pathfromtextangle}{\tikz@lib@dec@te@textwidth}}}% + \pgfgetpath\pgfdecoratedpath% + \pgfsetpath\pgfutil@empty% + \else% + #5% + \fi% + \else% + \tikz@lib@dec@te@pathfromtextfalse% + #6% + \fi% +}% + + +\pgfdeclaredecoration{text effects along path}{setup}{% + \state{setup}[width=+0pt, next state=scan, persistent precomputation={% + \tikz@lib@dec@te@state@setup@precomputation% + \def\tikz@lib@dec@te@charactercount{0}% + }]{}% +\state{scan}[width=+0pt, next state=pre token, persistent precomputation={% + \tikz@lib@dec@te@advancecountmacro\tikz@lib@dec@te@charactercount{1}% + \ifnum\tikz@lib@dec@te@charactercount>\tikz@lib@dec@te@charactertotalcount\relax% + \ifnum\tikz@lib@dec@te@repeattext=0\relax% + \def\pgf@decorate@next@state{final}% + \else% + \tikz@lib@dec@te@advancecountmacro\tikz@lib@dec@te@repeattext{-1}% + \def\tikz@lib@dec@te@charactercount{1}% + \fi% + \fi% + \csname tikz@lib@dec@te@character@\tikz@lib@dec@te@charactercount\endcsname% +}]{}% +\state{pre token}[width=+\tikz@lib@dec@te@characterprewidth, next state=token]{}% +\state{token}[width=+0pt, next state=post token] +{% + \tikz@lib@dec@te@drawcharacter% +}% +\state{post token}[width=+\tikz@lib@dec@te@characterpostwidth, next state=scan]{}% +}% + + +\def\tikz@lib@dec@te@parse@stylecharacters#1#2{% + \def\tikz@lib@dec@te@text{#1}% + \tikz@lib@dec@te@scancharacters{% + \pgfkeysalso{/pgf/decoration/text effects/character {\meaning\tikz@lib@dec@te@character}/.style={#2}}% + }% +}% + +\def\tikz@lib@dec@te@parse@replacecharacters#1#2{% + \def\tikz@lib@dec@te@text{#1}% + \tikz@lib@dec@te@scancharacters{% + \expandafter\def\csname tikz@lib@dec@te@character@replacements@\meaning\tikz@lib@dec@te@character @code\endcsname{#2}% + }% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryer.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryer.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..1d5c0f75dd3a9392136cdffeb75b464e8b4b407f --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryer.code.tex @@ -0,0 +1,29 @@ + +\ProvidesFileRCS{tikzlibraryer.code.tex} + +\usetikzlibrary{shapes.geometric}% + + +\tikzset{every entity/.style= {}}% +\tikzset{entity/.style= {rectangle,draw, + minimum height=2\baselineskip, + minimum width=4\baselineskip,every entity}}% + + + +\tikzset{every relationship/.style= {}}% +\tikzset{relationship/.style= {diamond,draw, + minimum size=1.5\baselineskip, + inner sep=1pt, + every relationship}}% + + + +\tikzset{every attribute/.style= {}}% +\tikzset{attribute/.style= {minimum size=1.5\baselineskip,ellipse,draw,every attribute}}% +\tikzset{key attribute/.style= {font=\itshape,attribute}}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfadings.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfadings.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ed8871062f13563a9c2ce91110d3d11a5f3cca8a --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfadings.code.tex @@ -0,0 +1,36 @@ + +\ProvidesFileRCS{tikzlibraryfadings.code.tex} + +\usepgflibrary{fadings}% + + +\def\tikzfadingfrompicture{% + \begingroup% + \setbox\pgfpic=\hbox\bgroup% + \tikzpicture% +}% +\def\endtikzfadingfrompicture{% + \global\let\tikz@smuggle=\tikz@fig@name% + \endtikzpicture + \egroup% + \pgfdeclarefading{\tikz@smuggle}{\box\pgfpic}% + \endgroup% +}% + +\def\starttikzfadingfrompicture{\tikzfadingfrompicture}% +\def\stopttikzfadingfrompicture{\endtikzfadingfrompicture}% + +\def\tikzfading[#1]{% + {% + \setbox\pgfpic=\hbox{% + \tikzset{#1}% + \global\let\tikz@smuggle=\tikz@fig@name% + \tikz{% + \useasboundingbox(0,0) (100bp,100bp); + \node at (50bp,50bp) [rotate=\tikz@shade@angle] + {\pgfuseshading{\tikz@shading}}; + }% + }% + \pgfdeclarefading{\tikz@smuggle}{\box\pgfpic}% + }% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..4a254d0a53797ed7b61d8b8cc82adec687525261 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfit.code.tex @@ -0,0 +1,118 @@ + +\ProvidesFileRCS{tikzlibraryfit.code.tex} + +\pgfqkeys{/tikz}{% + fit/.code=\tikz@lib@fit{#1}, + rotate fit/.code={% + \pgfmathsetmacro\tikz@lib@fit@rotate{#1}% + \pgfkeysalso{/tikz/rotate=\tikz@lib@fit@rotate}% + }, +}% + +\def\tikz@lib@fit@rotate{0}% + +\def\tikz@lib@fit#1{% + \pgf@xb=-16000pt\relax% + \pgf@xa=16000pt\relax% + \pgf@yb=-16000pt\relax% + \pgf@ya=16000pt\relax% + \tikz@lib@fit@scan#1\pgf@stop% + \ifdim\pgf@xa>\pgf@xa% + \else% + \pgf@x=\pgf@xb% + \advance\pgf@x by-\pgf@xa% + \pgf@y=\pgf@yb% + \advance\pgf@y by-\pgf@ya% + \advance\pgf@xa by.5\pgf@x% + \advance\pgf@ya by.5\pgf@y% + \ifdim\tikz@lib@fit@rotate pt=0pt\relax% + {% + \pgftransforminvert% + \pgf@pos@transform{\pgf@xa}{\pgf@ya}% + \global\pgf@xa\pgf@xa + \global\pgf@ya\pgf@ya + } + \else% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + {% + \pgf@xc=\pgf@xa% + \pgf@yc=\pgf@ya% + \pgftransforminvert% + \pgf@pos@transform{\pgf@xc}{\pgf@yc}% + \pgftransformreset% + \pgftransformrotate{\tikz@lib@fit@rotate}% + \pgf@pos@transform{\pgf@xc}{\pgf@yc}% + \global\pgf@x=\pgf@xc% + \global\pgf@y=\pgf@yc% + }% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@x=\pgf@xc% + \pgf@y=\pgf@yc% + \fi% + \edef\tikz@node@at{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \pgfkeysalso{/tikz/anchor=center,/tikz/text badly centered}% + \pgfkeysalso{/tikz/text width/.expanded=\the\pgf@x}% + \pgf@x=\pgf@y% + \pgf@y=.5\pgf@y% + \pgfkeysalso{ + /tikz/transform shape=false, + /tikz/text height/.expanded=\the\pgf@y-.5\dp\pgfnodeparttextbox, + /tikz/text depth/.expanded=\the\pgf@x-\noexpand\the\ht\pgfnodeparttextbox}% + \pgfkeysalso{every fit/.try}% + \fi% +}% + +\def\tikz@lib@fit@scan{% + \pgfutil@ifnextchar\pgf@stop{\pgfutil@gobble} + {\tikz@scan@one@point\tikz@lib@fit@scan@handle}}% + +\def\tikz@lib@fit@scan@handle#1{% + \iftikz@shapeborder% + \tikz@lib@fit@adjust{\pgfpointanchor{\tikz@shapeborder@name}{west}}% + \tikz@lib@fit@adjust{\pgfpointanchor{\tikz@shapeborder@name}{east}}% + \tikz@lib@fit@adjust{\pgfpointanchor{\tikz@shapeborder@name}{north}}% + \tikz@lib@fit@adjust{\pgfpointanchor{\tikz@shapeborder@name}{south}}% + \else% + \tikz@lib@fit@adjust{#1}% + \fi% + \tikz@lib@fit@scan% +}% + +\def\tikz@lib@fit@adjust#1{% + \ifdim\tikz@lib@fit@rotate pt=0pt\relax% + \pgf@process{\pgfpointtransformed{#1}}% + \else% + {% + \pgf@process{\pgfpointtransformed{#1}}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfgettransform\tikz@lib@fit@transform% + \pgftransforminvert% + \pgf@pos@transform{\pgf@xc}{\pgf@yc}% + \pgftransformreset% + \pgftransformrotate{-\tikz@lib@fit@rotate}% + \pgf@pos@transform{\pgf@xc}{\pgf@yc}% + \pgfsettransform\tikz@lib@fit@transform% + \pgf@pos@transform{\pgf@xc}{\pgf@yc}% + \global\pgf@x=\pgf@xc% + \global\pgf@y=\pgf@yc% + }% + \fi% + \ifdim\pgf@x<\pgf@xa% + \pgf@xa=\pgf@x% + \fi% + \ifdim\pgf@y<\pgf@ya% + \pgf@ya=\pgf@y% + \fi% + \ifdim\pgf@x>\pgf@xb% + \pgf@xb=\pgf@x% + \fi% + \ifdim\pgf@y>\pgf@yb% + \pgf@yb=\pgf@y% + \fi% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfixedpointarithmetic.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfixedpointarithmetic.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..5e2537a995c551ca012c7c543c9dea329785dcdd --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfixedpointarithmetic.code.tex @@ -0,0 +1,2 @@ + +\usepgflibrary{fixedpointarithmetic}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfolding.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfolding.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..16b28f8c559931c16600c8a27441fede3666be5e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfolding.code.tex @@ -0,0 +1,2409 @@ + +\ProvidesFileRCS{tikzlibraryfolding.code.tex} + + + +\tikzoption{folding line length}{\pgfmathsetlength\tikz@lib@fold@length{#1}}% +\newdimen\tikz@lib@fold@length +\tikz@lib@fold@length=2cm + + + +\def\tikz@lib@fold@triangle#1#2#3#4{% + \scope[xshift=.5\tikz@lib@fold@length,yshift=.28868\tikz@lib@fold@length] + #1 + \endscope + \scope[shift={(60:\tikz@lib@fold@length)},rotate=-60] + #2 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #3 + \endscope + \scope[rotate=60] + #4 + \endscope +}% + +\def\tikz@lib@fold@square#1#2#3#4#5{% + \scope[xshift=.5\tikz@lib@fold@length,yshift=.5\tikz@lib@fold@length] + #1 + \endscope + \scope[yshift=\tikz@lib@fold@length] + #2 + \endscope + \scope[xshift=\tikz@lib@fold@length,yshift=\tikz@lib@fold@length,rotate=-90] + #3 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #4 + \endscope + \scope[rotate=90] + #5 + \endscope +}% + +\def\tikz@lib@fold@squarerhombusr#1#2#3#4#5{% + \scope[xshift=.63\tikz@lib@fold@length,yshift=.4755\tikz@lib@fold@length,xslant=0.34] + #1 + \endscope + \scope[shift={(70.529:\tikz@lib@fold@length)}] + #2 + \endscope + \scope[shift={(35.264:1.63299\tikz@lib@fold@length)},rotate=-109.471] + #3 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #4 + \endscope + \scope[rotate=70.529] + #5 + \endscope +}% + +\def\tikz@lib@fold@squarerhombusl#1#2#3#4#5{% + \scope[xshift=.33\tikz@lib@fold@length,yshift=.4755\tikz@lib@fold@length,xslant=-0.34] + #1 + \endscope + \scope[shift={(109.471:\tikz@lib@fold@length)}] + #2 + \endscope + \scope[shift={(54.736:1.1547\tikz@lib@fold@length)},rotate=-70.529] + #3 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #4 + \endscope + \scope[rotate=109.471] + #5 + \endscope +}% + +\def\tikz@lib@fold@goldenrhombusr#1#2#3#4#5{% + \scope[xshift=.724\tikz@lib@fold@length,yshift=.447\tikz@lib@fold@length, xslant=0.447] + #1 + \endscope + \scope[shift={(63.435:\tikz@lib@fold@length)}] + #2 + \endscope + \scope[shift={(31.717:1.701\tikz@lib@fold@length)},rotate=-116.565] + #3 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #4 + \endscope + \scope[rotate=63.435] + #5 + \endscope +}% + +\def\tikz@lib@fold@goldenrhombusl#1#2#3#4#5{% + \scope[xshift=.276\tikz@lib@fold@length,yshift=.447\tikz@lib@fold@length, xslant=-0.447] + #1 + \endscope + \scope[shift={(116.565:\tikz@lib@fold@length)}] + #2 + \endscope + \scope[shift={(58.283:1.051\tikz@lib@fold@length)},rotate=-63.435] + #3 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #4 + \endscope + \scope[rotate=116.565] + #5 + \endscope +}% + +\def\tikz@lib@fold@pentagon#1#2#3#4#5#6{% + \scope[xshift=.5\tikz@lib@fold@length,yshift=0.68819\tikz@lib@fold@length] + #1 + \endscope + \scope[shift={(108:\tikz@lib@fold@length)},shift={(36:\tikz@lib@fold@length)},rotate=-36] + #2 + \endscope + \scope[xshift=\tikz@lib@fold@length,shift={(72:\tikz@lib@fold@length)},rotate=-108] + #3 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #4 + \endscope + \scope[rotate=108] + #5 + \endscope + \scope[shift={(108:\tikz@lib@fold@length)},rotate=36] + #6 + \endscope +}% + +\def\tikz@lib@fold@hexagon#1#2#3#4#5#6#7{% + \scope + [shift={(60:\tikz@lib@fold@length)}] + #1 + \endscope + \scope + [shift={(120:\tikz@lib@fold@length)}, + shift={(60:\tikz@lib@fold@length)}] + #2 + \endscope + \scope + [shift={(120:\tikz@lib@fold@length)}, + shift={(60:\tikz@lib@fold@length)}, + xshift=\tikz@lib@fold@length, + rotate=-60] + #3 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + shift={(60:\tikz@lib@fold@length)}, + rotate=-120] + #4 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + rotate=180] + #5 + \endscope + \scope + [rotate=120] + #6 + \endscope + \scope + [shift={(120:\tikz@lib@fold@length)}, + rotate=60] + #7 + \endscope +}% + +\def\tikz@lib@fold@octagon#1#2#3#4#5#6#7#8#9{% + \scope[xshift=.5\tikz@lib@fold@length,yshift=1.20711\tikz@lib@fold@length] + #1 + \endscope + \scope[yshift=2.41421\tikz@lib@fold@length] + #2 + \endscope + \scope[xshift=\tikz@lib@fold@length,yshift=2.41421\tikz@lib@fold@length,rotate=-45] + #3 + \endscope + \scope[xshift=1.70711\tikz@lib@fold@length,yshift=1.70711\tikz@lib@fold@length,rotate=-90] + #4 + \endscope + \scope[xshift=1.70711\tikz@lib@fold@length,yshift=.70711\tikz@lib@fold@length,rotate=-135] + #5 + \endscope + \scope[xshift=\tikz@lib@fold@length,rotate=180] + #6 + \endscope + \scope[rotate=135] + #7 + \endscope + \scope[xshift=-.70711\tikz@lib@fold@length,yshift=.70711\tikz@lib@fold@length,rotate=90] + #8 + \endscope + \scope[xshift=-.70711\tikz@lib@fold@length,yshift=1.70711\tikz@lib@fold@length,rotate=45] + #9 + \endscope +}% + +\def\tikz@lib@fold@decagon#1#2#3#4#5#6#7{% + \scope[shift={(72:1.61803\tikz@lib@fold@length)}] % + #1 + \endscope + \scope + [shift={(36:\tikz@lib@fold@length)}, + shift={(72:\tikz@lib@fold@length)}, + shift={(108:\tikz@lib@fold@length)}, + shift={(144:\tikz@lib@fold@length)}] + #2 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + shift={(36:\tikz@lib@fold@length)}, + shift={(72:\tikz@lib@fold@length)}, + shift={(108:\tikz@lib@fold@length)}, + shift={(144:\tikz@lib@fold@length)}, + rotate=-36] + #3 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + shift={(36:\tikz@lib@fold@length)}, + shift={(72:\tikz@lib@fold@length)}, + shift={(108:\tikz@lib@fold@length)}, + rotate=-72] + #4 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + shift={(36:\tikz@lib@fold@length)}, + shift={(72:\tikz@lib@fold@length)}, + rotate=-108] + #5 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + shift={(36:\tikz@lib@fold@length)}, + rotate=-144] + #6 + \endscope + \scope + [xshift=\tikz@lib@fold@length, + rotate=180] + #7 + \endscope + \tikz@lib@fold@decagonbis +}% + +\def\tikz@lib@fold@decagonbis#1#2#3#4{% + \scope + [rotate=144] + #1 + \endscope + \scope + [shift={(144:\tikz@lib@fold@length)}, + rotate=108] + #2 + \endscope + \scope + [shift={(144:\tikz@lib@fold@length)}, + shift={(108:\tikz@lib@fold@length)}, + rotate=72] + #3 + \endscope + \scope + [shift={(144:\tikz@lib@fold@length)}, + shift={(108:\tikz@lib@fold@length)}, + shift={(72:\tikz@lib@fold@length)}, + rotate=36] + #4 + \endscope +}% + +\def\tikz@lib@fold@path{\draw[every fold](0,0) -- (\tikz@lib@fold@length,0pt);}% +\def\tikz@lib@fold@cut@path{\draw[every cut](0,0) -- (\tikz@lib@fold@length,0pt);}% +\def\tikz@lib@fold@ear@path{ + \path[every ear] (0,0) -- (.5\tikz@lib@fold@length,.2\tikz@lib@fold@length) --(\tikz@lib@fold@length,0pt) --(0,0) -- cycle; + \draw[every fold](0,0) -- (\tikz@lib@fold@length,0pt); + \draw[every cut] (0,0) -- (.5\tikz@lib@fold@length,.2\tikz@lib@fold@length) --(\tikz@lib@fold@length,0pt);}% +\def\tikz@lib@fold@ear@custom@left@path#1{ + \path[every ear] (0,0) -- (#1:.66\tikz@lib@fold@length) -- (\tikz@lib@fold@length,0pt) --(0,0) -- cycle; + \draw[every fold](0,0) -- (\tikz@lib@fold@length,0pt); + \draw[every cut] (0,0) -- (#1:.66\tikz@lib@fold@length) -- (\tikz@lib@fold@length,0pt);}% +\def\tikz@lib@fold@ear@custom@right@path#1{ + \path[every ear] (0,0) -- (\tikz@lib@fold@length,0pt) -- ++(-#1:-.66\tikz@lib@fold@length) --(0,0) -- cycle; + \draw[every fold](0,0) -- (\tikz@lib@fold@length,0pt); + \draw[every cut] (\tikz@lib@fold@length,0pt) -- ++(-#1:-.66\tikz@lib@fold@length) -- (0,0);}% + +\tikzset{every ear/.style={}}% +\tikzset{every cut/.style={}}% +\tikzset{every fold/.style={help lines}}% + +\tikzoption{face 1}{\def\tikz@lib@fold@face@A{#1}}% +\tikzoption{face 2}{\def\tikz@lib@fold@face@B{#1}}% +\tikzoption{face 3}{\def\tikz@lib@fold@face@C{#1}}% +\tikzoption{face 4}{\def\tikz@lib@fold@face@D{#1}}% +\tikzoption{face 5}{\def\tikz@lib@fold@face@E{#1}}% +\tikzoption{face 6}{\def\tikz@lib@fold@face@F{#1}}% +\tikzoption{face 7}{\def\tikz@lib@fold@face@G{#1}}% +\tikzoption{face 8}{\def\tikz@lib@fold@face@H{#1}}% +\tikzoption{face 9}{\def\tikz@lib@fold@face@I{#1}}% +\tikzoption{face 10}{\def\tikz@lib@fold@face@J{#1}}% +\tikzoption{face 11}{\def\tikz@lib@fold@face@K{#1}}% +\tikzoption{face 12}{\def\tikz@lib@fold@face@L{#1}}% +\tikzoption{face 13}{\def\tikz@lib@fold@face@M{#1}}% +\tikzoption{face 14}{\def\tikz@lib@fold@face@N{#1}}% +\tikzoption{face 15}{\def\tikz@lib@fold@face@O{#1}}% +\tikzoption{face 16}{\def\tikz@lib@fold@face@P{#1}}% +\tikzoption{face 17}{\def\tikz@lib@fold@face@Q{#1}}% +\tikzoption{face 18}{\def\tikz@lib@fold@face@R{#1}}% +\tikzoption{face 19}{\def\tikz@lib@fold@face@S{#1}}% +\tikzoption{face 20}{\def\tikz@lib@fold@face@T{#1}}% +\tikzoption{face 21}{\def\tikz@lib@fold@face@U{#1}}% +\tikzoption{face 22}{\def\tikz@lib@fold@face@V{#1}}% +\tikzoption{face 23}{\def\tikz@lib@fold@face@W{#1}}% +\tikzoption{face 24}{\def\tikz@lib@fold@face@X{#1}}% +\tikzoption{face 25}{\def\tikz@lib@fold@face@Y{#1}}% +\tikzoption{face 26}{\def\tikz@lib@fold@face@Z{#1}}% +\tikzoption{face 27}{\def\tikz@lib@fold@face@AA{#1}}% +\tikzoption{face 28}{\def\tikz@lib@fold@face@AB{#1}}% +\tikzoption{face 29}{\def\tikz@lib@fold@face@AC{#1}}% +\tikzoption{face 30}{\def\tikz@lib@fold@face@AD{#1}}% +\tikzoption{face 31}{\def\tikz@lib@fold@face@AE{#1}}% +\tikzoption{face 32}{\def\tikz@lib@fold@face@AF{#1}}% +\tikzoption{face 33}{\def\tikz@lib@fold@face@AG{#1}}% +\tikzoption{face 34}{\def\tikz@lib@fold@face@AH{#1}}% +\tikzoption{face 35}{\def\tikz@lib@fold@face@AI{#1}}% +\tikzoption{face 36}{\def\tikz@lib@fold@face@AJ{#1}}% +\tikzoption{face 37}{\def\tikz@lib@fold@face@AK{#1}}% +\tikzoption{face 38}{\def\tikz@lib@fold@face@AL{#1}}% +\tikzoption{face 39}{\def\tikz@lib@fold@face@AM{#1}}% +\tikzoption{face 40}{\def\tikz@lib@fold@face@AN{#1}}% +\tikzoption{face 41}{\def\tikz@lib@fold@face@AO{#1}}% +\tikzoption{face 42}{\def\tikz@lib@fold@face@AP{#1}}% +\tikzoption{face 43}{\def\tikz@lib@fold@face@AQ{#1}}% +\tikzoption{face 44}{\def\tikz@lib@fold@face@AR{#1}}% +\tikzoption{face 45}{\def\tikz@lib@fold@face@AS{#1}}% +\tikzoption{face 46}{\def\tikz@lib@fold@face@AT{#1}}% +\tikzoption{face 47}{\def\tikz@lib@fold@face@AU{#1}}% +\tikzoption{face 48}{\def\tikz@lib@fold@face@AV{#1}}% +\tikzoption{face 49}{\def\tikz@lib@fold@face@AW{#1}}% +\tikzoption{face 50}{\def\tikz@lib@fold@face@AX{#1}}% +\tikzoption{face 51}{\def\tikz@lib@fold@face@AY{#1}}% +\tikzoption{face 52}{\def\tikz@lib@fold@face@AZ{#1}}% +\tikzoption{face 53}{\def\tikz@lib@fold@face@BA{#1}}% +\tikzoption{face 54}{\def\tikz@lib@fold@face@BB{#1}}% +\tikzoption{face 55}{\def\tikz@lib@fold@face@BC{#1}}% +\tikzoption{face 56}{\def\tikz@lib@fold@face@BD{#1}}% +\tikzoption{face 57}{\def\tikz@lib@fold@face@BE{#1}}% +\tikzoption{face 58}{\def\tikz@lib@fold@face@BF{#1}}% +\tikzoption{face 59}{\def\tikz@lib@fold@face@BG{#1}}% +\tikzoption{face 60}{\def\tikz@lib@fold@face@BH{#1}}% +\tikzoption{face 61}{\def\tikz@lib@fold@face@BI{#1}}% +\tikzoption{face 62}{\def\tikz@lib@fold@face@BJ{#1}}% +\tikzoption{face 63}{\def\tikz@lib@fold@face@BK{#1}}% +\tikzoption{face 64}{\def\tikz@lib@fold@face@BL{#1}}% +\tikzoption{face 65}{\def\tikz@lib@fold@face@BM{#1}}% +\tikzoption{face 66}{\def\tikz@lib@fold@face@BN{#1}}% +\tikzoption{face 67}{\def\tikz@lib@fold@face@BO{#1}}% +\tikzoption{face 68}{\def\tikz@lib@fold@face@BP{#1}}% +\tikzoption{face 69}{\def\tikz@lib@fold@face@BQ{#1}}% +\tikzoption{face 70}{\def\tikz@lib@fold@face@BR{#1}}% +\tikzoption{face 71}{\def\tikz@lib@fold@face@BS{#1}}% +\tikzoption{face 72}{\def\tikz@lib@fold@face@BT{#1}}% +\tikzoption{face 73}{\def\tikz@lib@fold@face@BU{#1}}% +\tikzoption{face 74}{\def\tikz@lib@fold@face@BV{#1}}% +\tikzoption{face 75}{\def\tikz@lib@fold@face@BW{#1}}% +\tikzoption{face 76}{\def\tikz@lib@fold@face@BX{#1}}% +\tikzoption{face 77}{\def\tikz@lib@fold@face@BY{#1}}% +\tikzoption{face 78}{\def\tikz@lib@fold@face@BZ{#1}}% +\tikzoption{face 79}{\def\tikz@lib@fold@face@CA{#1}}% +\tikzoption{face 80}{\def\tikz@lib@fold@face@CB{#1}}% +\tikzoption{face 81}{\def\tikz@lib@fold@face@CC{#1}}% +\tikzoption{face 82}{\def\tikz@lib@fold@face@CD{#1}}% +\tikzoption{face 83}{\def\tikz@lib@fold@face@CE{#1}}% +\tikzoption{face 84}{\def\tikz@lib@fold@face@CF{#1}}% +\tikzoption{face 85}{\def\tikz@lib@fold@face@CG{#1}}% +\tikzoption{face 86}{\def\tikz@lib@fold@face@CH{#1}}% +\tikzoption{face 87}{\def\tikz@lib@fold@face@CI{#1}}% +\tikzoption{face 88}{\def\tikz@lib@fold@face@CJ{#1}}% +\tikzoption{face 89}{\def\tikz@lib@fold@face@CK{#1}}% +\tikzoption{face 90}{\def\tikz@lib@fold@face@CL{#1}}% +\tikzoption{face 91}{\def\tikz@lib@fold@face@CM{#1}}% +\tikzoption{face 92}{\def\tikz@lib@fold@face@CN{#1}}% + + +\let\tikz@lib@fold@face@A=\pgfutil@empty +\let\tikz@lib@fold@face@B=\pgfutil@empty +\let\tikz@lib@fold@face@C=\pgfutil@empty +\let\tikz@lib@fold@face@D=\pgfutil@empty +\let\tikz@lib@fold@face@E=\pgfutil@empty +\let\tikz@lib@fold@face@F=\pgfutil@empty +\let\tikz@lib@fold@face@G=\pgfutil@empty +\let\tikz@lib@fold@face@H=\pgfutil@empty +\let\tikz@lib@fold@face@I=\pgfutil@empty +\let\tikz@lib@fold@face@J=\pgfutil@empty +\let\tikz@lib@fold@face@K=\pgfutil@empty +\let\tikz@lib@fold@face@L=\pgfutil@empty +\let\tikz@lib@fold@face@M=\pgfutil@empty +\let\tikz@lib@fold@face@N=\pgfutil@empty +\let\tikz@lib@fold@face@O=\pgfutil@empty +\let\tikz@lib@fold@face@P=\pgfutil@empty +\let\tikz@lib@fold@face@Q=\pgfutil@empty +\let\tikz@lib@fold@face@R=\pgfutil@empty +\let\tikz@lib@fold@face@S=\pgfutil@empty +\let\tikz@lib@fold@face@T=\pgfutil@empty +\let\tikz@lib@fold@face@U=\pgfutil@empty +\let\tikz@lib@fold@face@V=\pgfutil@empty +\let\tikz@lib@fold@face@W=\pgfutil@empty +\let\tikz@lib@fold@face@X=\pgfutil@empty +\let\tikz@lib@fold@face@Y=\pgfutil@empty +\let\tikz@lib@fold@face@Z=\pgfutil@empty +\let\tikz@lib@fold@face@AA=\pgfutil@empty +\let\tikz@lib@fold@face@AB=\pgfutil@empty +\let\tikz@lib@fold@face@AC=\pgfutil@empty +\let\tikz@lib@fold@face@AD=\pgfutil@empty +\let\tikz@lib@fold@face@AE=\pgfutil@empty +\let\tikz@lib@fold@face@AF=\pgfutil@empty +\let\tikz@lib@fold@face@AG=\pgfutil@empty +\let\tikz@lib@fold@face@AH=\pgfutil@empty +\let\tikz@lib@fold@face@AI=\pgfutil@empty +\let\tikz@lib@fold@face@AJ=\pgfutil@empty +\let\tikz@lib@fold@face@AK=\pgfutil@empty +\let\tikz@lib@fold@face@AL=\pgfutil@empty +\let\tikz@lib@fold@face@AM=\pgfutil@empty +\let\tikz@lib@fold@face@AN=\pgfutil@empty +\let\tikz@lib@fold@face@AO=\pgfutil@empty +\let\tikz@lib@fold@face@AP=\pgfutil@empty +\let\tikz@lib@fold@face@AQ=\pgfutil@empty +\let\tikz@lib@fold@face@AR=\pgfutil@empty +\let\tikz@lib@fold@face@AS=\pgfutil@empty +\let\tikz@lib@fold@face@AT=\pgfutil@empty +\let\tikz@lib@fold@face@AU=\pgfutil@empty +\let\tikz@lib@fold@face@AV=\pgfutil@empty +\let\tikz@lib@fold@face@AW=\pgfutil@empty +\let\tikz@lib@fold@face@AX=\pgfutil@empty +\let\tikz@lib@fold@face@AY=\pgfutil@empty +\let\tikz@lib@fold@face@AZ=\pgfutil@empty +\let\tikz@lib@fold@face@BA=\pgfutil@empty +\let\tikz@lib@fold@face@BB=\pgfutil@empty +\let\tikz@lib@fold@face@BC=\pgfutil@empty +\let\tikz@lib@fold@face@BD=\pgfutil@empty +\let\tikz@lib@fold@face@BE=\pgfutil@empty +\let\tikz@lib@fold@face@BF=\pgfutil@empty +\let\tikz@lib@fold@face@BG=\pgfutil@empty +\let\tikz@lib@fold@face@BH=\pgfutil@empty +\let\tikz@lib@fold@face@BI=\pgfutil@empty +\let\tikz@lib@fold@face@BJ=\pgfutil@empty +\let\tikz@lib@fold@face@BK=\pgfutil@empty +\let\tikz@lib@fold@face@BL=\pgfutil@empty +\let\tikz@lib@fold@face@BM=\pgfutil@empty +\let\tikz@lib@fold@face@BN=\pgfutil@empty +\let\tikz@lib@fold@face@BO=\pgfutil@empty +\let\tikz@lib@fold@face@BP=\pgfutil@empty +\let\tikz@lib@fold@face@BQ=\pgfutil@empty +\let\tikz@lib@fold@face@BR=\pgfutil@empty +\let\tikz@lib@fold@face@BS=\pgfutil@empty +\let\tikz@lib@fold@face@BT=\pgfutil@empty +\let\tikz@lib@fold@face@BU=\pgfutil@empty +\let\tikz@lib@fold@face@BV=\pgfutil@empty +\let\tikz@lib@fold@face@BW=\pgfutil@empty +\let\tikz@lib@fold@face@BX=\pgfutil@empty +\let\tikz@lib@fold@face@BY=\pgfutil@empty +\let\tikz@lib@fold@face@BZ=\pgfutil@empty +\let\tikz@lib@fold@face@CA=\pgfutil@empty +\let\tikz@lib@fold@face@CB=\pgfutil@empty +\let\tikz@lib@fold@face@CC=\pgfutil@empty +\let\tikz@lib@fold@face@CD=\pgfutil@empty +\let\tikz@lib@fold@face@CE=\pgfutil@empty +\let\tikz@lib@fold@face@CF=\pgfutil@empty +\let\tikz@lib@fold@face@CG=\pgfutil@empty +\let\tikz@lib@fold@face@CH=\pgfutil@empty +\let\tikz@lib@fold@face@CI=\pgfutil@empty +\let\tikz@lib@fold@face@CJ=\pgfutil@empty +\let\tikz@lib@fold@face@CK=\pgfutil@empty +\let\tikz@lib@fold@face@CL=\pgfutil@empty +\let\tikz@lib@fold@face@CM=\pgfutil@empty +\let\tikz@lib@fold@face@CN=\pgfutil@empty + + +\tikzset{numbered faces/.style={% + face 1={\node{1};}, + face 2={\node{2};}, + face 3={\node{3};}, + face 4={\node{4};}, + face 5={\node{5};}, + face 6={\node{6};}, + face 7={\node{7};}, + face 8={\node{8};}, + face 9={\node{9};}, + face 10={\node{10};}, + face 11={\node{11};}, + face 12={\node{12};}, + face 13={\node{13};}, + face 14={\node{14};}, + face 15={\node{15};}, + face 16={\node{16};}, + face 17={\node{17};}, + face 18={\node{18};}, + face 19={\node{19};}, + face 20={\node{20};}, + face 21={\node{21};}, + face 22={\node{22};}, + face 23={\node{23};}, + face 24={\node{24};}, + face 25={\node{25};}, + face 26={\node{26};}, + face 27={\node{27};}, + face 28={\node{28};}, + face 29={\node{29};}, + face 30={\node{30};}, + face 31={\node{31};}, + face 32={\node{32};}, + face 33={\node{33};}, + face 34={\node{34};}, + face 35={\node{35};}, + face 36={\node{36};}, + face 37={\node{37};}, + face 38={\node{38};}, + face 39={\node{39};}, + face 40={\node{40};}, + face 41={\node{41};}, + face 42={\node{42};}, + face 43={\node{43};}, + face 44={\node{44};}, + face 45={\node{45};}, + face 46={\node{46};}, + face 47={\node{47};}, + face 48={\node{48};}, + face 49={\node{49};}, + face 50={\node{50};}, + face 51={\node{51};}, + face 52={\node{52};}, + face 53={\node{53};}, + face 54={\node{54};}, + face 55={\node{55};}, + face 56={\node{56};}, + face 57={\node{57};}, + face 58={\node{58};}, + face 59={\node{59};}, + face 60={\node{60};}, + face 61={\node{61};}, + face 62={\node{62};}, + face 63={\node{63};}, + face 64={\node{64};}, + face 65={\node{65};}, + face 66={\node{66};}, + face 67={\node{67};}, + face 68={\node{68};}, + face 69={\node{69};}, + face 70={\node{70};}, + face 71={\node{71};}, + face 72={\node{72};}, + face 73={\node{73};}, + face 74={\node{74};}, + face 75={\node{75};}, + face 76={\node{76};}, + face 77={\node{77};}, + face 78={\node{78};}, + face 79={\node{79};}, + face 80={\node{80};}, + face 81={\node{81};}, + face 82={\node{82};}, + face 83={\node{83};}, + face 84={\node{84};}, + face 85={\node{85};}, + face 86={\node{86};}, + face 87={\node{87};}, + face 88={\node{88};}, + face 89={\node{89};}, + face 90={\node{90};}, + face 91={\node{91};}, + face 92={\node{92};}}}% + + +\tikzset{ + pics/dodecahedron folding/.style = {code=\tikzfoldingdodecahedron[];}, + pics/tetrahedron folding/.style = {code=\tikzfoldingtetrahedron[];}, + pics/tetrahedron truncated folding/.style = {code=\tikzfoldingtruncatedtetrahedron[];}, + pics/cube folding/.style = {code=\tikzfoldingcube[];}, + pics/cube truncated folding/.style = {code=\tikzfoldingtruncatedcube[];}, + pics/octahedron folding/.style = {code=\tikzfoldingoctahedron[];}, + pics/octahedron truncated folding/.style = {code=\tikzfoldingtruncatedoctahedron[];}, + pics/dodecahedron folding/.style = {code=\tikzfoldingdodecahedron[];}, + pics/dodecahedron' folding/.style = {code=\tikzfoldingalternatedodecahedron[];}, + pics/dodecahedron rhombic folding/.style = {code=\tikzfoldingrhombicdodecahedron[];}, + pics/dodecahedron golden folding/.style = {code=\tikzfoldinggoldenrhombicdodecahedron[];}, + pics/cuboctahedron folding/.style = {code=\tikzfoldingcuboctahedron[];}, + pics/cuboctahedron truncated folding/.style = {code=\tikzfoldingtruncatedcuboctahedron[];}, + pics/icosahedron folding/.style = {code=\tikzfoldingicosahedron[];}, + pics/rhombicuboctahedron folding/.style = {code=\tikzfoldingrhombicuboctahedron[];}, + pics/snub cube folding/.style = {code=\tikzfoldingsnubcube[];}, + pics/icosidodecahedron folding/.style = {code=\tikzfoldingicosidodecahedron[];} +}% + + + + +\def\tikzfoldingdodecahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@pentagon + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + +\def\tikzfoldingalternatedodecahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@pentagon + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + } + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@pentagon + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + \endgroup +}% + + + +\def\tikzfoldingtetrahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@triangle + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + +\def\tikzfoldingcube#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@square{\tikz@lib@fold@face@A} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@B} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + { + \tikz@lib@fold@square{\tikz@lib@fold@face@C} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@square{\tikz@lib@fold@face@D} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + { + \tikz@lib@fold@square{\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + + +\def\tikzfoldingoctahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@triangle + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + \endgroup +}% + + + +\def\tikzfoldingicosahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@triangle + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@M} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@N} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@O} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@P} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@Q} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@R} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@S} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@T} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + \endgroup +}% + + + +\def\tikzfoldingtruncatedtetrahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@hexagon + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + +\def\tikzfoldingcuboctahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@square + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@M} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@N} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + +\def\tikzfoldingtruncatedcube#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@octagon + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@M} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@N} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + \endgroup +}% + + + +\def\tikzfoldingtruncatedoctahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@hexagon + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@M} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@N} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + \endgroup +}% + + + +\def\tikzfoldingrhombicuboctahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@square + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@M} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@N} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@O} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@P} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@Q} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@R} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@S} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@T} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@U} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@V} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@W} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@triangle + {\tikz@lib@fold@face@X} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@square + {\tikz@lib@fold@face@Y} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@Z} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + \endgroup +}% + + +\def\tikzfoldingtruncatedcuboctahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@square + {\tikz@lib@fold@face@A} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@B} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@C} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@D} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@E} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@I} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@J} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@K} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@L} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@M} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@N} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@O} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@P} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@Q} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@R} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@S} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@T} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@U} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@V} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@W} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@square + {\tikz@lib@fold@face@X} + {\tikz@lib@fold@octagon + {\tikz@lib@fold@face@Y} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@hexagon + {\tikz@lib@fold@face@Z} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{15}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@custom@left@path{15}} + {\tikz@lib@fold@ear@path} + } + \endgroup +}% + + +\def\tikzfoldingsnubcube#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@square{\tikz@lib@fold@face@A} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@B} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@C} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@E} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@F} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@I} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@J} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@K} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@L} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@M} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@N} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@O} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@P} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@Q} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@R} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@S} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@T} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@U} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@V} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@W} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@X} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@Y} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@Z} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AA} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AB} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AC} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AD} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AE} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@AF} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AG} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AH} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AI} + { + \tikz@lib@fold@square{\tikz@lib@fold@face@AJ} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AK} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AL} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + +\def\tikzfoldingicosidodecahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@A} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@B} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@C} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@D} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@E} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@F} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@G} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@I} + {\tikz@lib@fold@ear@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@J} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@K} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@L} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@M} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@N} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@O} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@P} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@Q} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@R} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@S} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@T} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@U} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@V} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@W} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@X} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@Y} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@Z} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + } + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AA} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@AB} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AC} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { + \tikz@lib@fold@pentagon{\tikz@lib@fold@face@AD} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AE} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + { + \tikz@lib@fold@triangle{\tikz@lib@fold@face@AF} + {\tikz@lib@fold@ear@custom@right@path{24}} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + +\def\tikzfoldingrhombicdodecahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@squarerhombusr{\tikz@lib@fold@face@B} + {\tikz@lib@fold@squarerhombusl{\scope[rotate=90]\tikz@lib@fold@face@C\endscope} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@squarerhombusr{\tikz@lib@fold@face@E} + {\tikz@lib@fold@squarerhombusl{\scope[rotate=90]\tikz@lib@fold@face@F\endscope} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@squarerhombusr{\scope[rotate=180]\tikz@lib@fold@face@D\endscope} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@squarerhombusl{\scope[rotate=-90]\tikz@lib@fold@face@H\endscope} + {\tikz@lib@fold@squarerhombusr{\scope[rotate=180]\tikz@lib@fold@face@G\endscope} + {\tikz@lib@fold@squarerhombusl{\scope[rotate=-90]\tikz@lib@fold@face@L\endscope} + {\tikz@lib@fold@squarerhombusr{\scope[rotate=180]\tikz@lib@fold@face@K\endscope} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@squarerhombusl{\scope[rotate=90]\tikz@lib@fold@face@J\endscope} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@squarerhombusl{\tikz@lib@fold@face@H} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@squarerhombusr{\tikz@lib@fold@face@F} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + +\def\tikzfoldinggoldenrhombicdodecahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@A} + {\tikz@lib@fold@goldenrhombusl{\scope[rotate=180]\tikz@lib@fold@face@B\endscope} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@goldenrhombusr{\scope[rotate=180]\tikz@lib@fold@face@E\endscope} + {\tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@H} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@G} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@goldenrhombusl{\scope[rotate=180]\tikz@lib@fold@face@D\endscope} + {\tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@I} + {\tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@L} + {\tikz@lib@fold@goldenrhombusr{\scope[rotate=180]\tikz@lib@fold@face@K\endscope} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@goldenrhombusl{\scope[rotate=180]\tikz@lib@fold@face@J\endscope} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@F} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@goldenrhombusr{\scope[rotate=180]\tikz@lib@fold@face@C\endscope} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + \endgroup +}% + + +\def\tikzfoldingrhombictricontahedron#1[#2]#3;{% + \begingroup% + \tikzset{#2}% + \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@A} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@B} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@F} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@I} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@J} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@K} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@H} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@G} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@L} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@N} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@M} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@C} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@N} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@N} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@N} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@N} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@D} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@D} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@D} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@D} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@D} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + } + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@D} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@E} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@E} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@E} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@E} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@E} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@cut@path} + } + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@E} + { \tikz@lib@fold@goldenrhombusl{\tikz@lib@fold@face@E} + { \tikz@lib@fold@goldenrhombusr{\tikz@lib@fold@face@E} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@ear@path} + } + {\tikz@lib@fold@ear@path} + {\tikz@lib@fold@path} + {\tikz@lib@fold@path} + } + } + \endgroup +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfpu.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfpu.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..772914b7e633893aa84c42afd91e1d7eb56dc6c6 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryfpu.code.tex @@ -0,0 +1,2 @@ + +\usepgflibrary{fpu}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..c8179769364158182e046e9779738de837c6393d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryintersections.code.tex @@ -0,0 +1,127 @@ + +\usepgflibrary{intersections}% + + +\pgfkeys{% + /tikz/name path global/.code={% + \expandafter\global\expandafter\let\csname tikz@intersect@path@name@#1\endcsname=\relax + \tikz@key@name@path{#1}{\gdef}% + }, + /tikz/name path local/.code={% + \pgfkeys{/tikz/name path={#1}}% + }, + /tikz/name path/.code={% + \tikz@key@name@path{#1}{\def}% + }, +}% + +\def\tikz@key@name@path#1#2{% + \tikz@addmode{% + \pgfsyssoftpath@getcurrentpath\tikz@intersect@temppath@round% + \pgfprocessround\tikz@intersect@temppath@round\tikz@intersect@temppath% + \ifx\tikz@intersect@namedpaths\pgfutil@empty% + \else% + \tikz@intersect@namedpaths% + \fi% + \tikz@intersect@addto@path@names{#1}{#2}% + }% +}% + +\def\tikz@intersect@addto@path@names#1#2{% + \edef\tikz@marshal{#2\expandafter\noexpand\csname tikz@intersect@path@name@#1\endcsname}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\tikz@marshal% + \expandafter\expandafter\expandafter{\expandafter\tikz@marshal\expandafter{\tikz@intersect@temppath}}% + \expandafter\pgfutil@g@addto@macro\expandafter\tikz@intersect@namedpaths\expandafter{\tikz@marshal}% +}% + +\let\tikz@finish@orig=\tikz@finish +\def\tikz@finish{% + \tikz@finish@orig% + \tikz@intersect@finish% +}% + +\def\tikz@intersect@finish{% + \tikz@intersect@namedpaths% +}% + +\let\tikz@intersect@namedpaths=\pgfutil@empty +\let\tikz@intersect@path@a=\pgfutil@empty +\let\tikz@intersect@path@b=\pgfutil@empty +\let\tikz@intersect@name=\pgfutil@empty +\let\tikz@intersect@total=\pgfutil@empty + +\tikzset{ + every scope/.append style={ + execute at begin scope={\let\tikz@intersect@namedpaths@outside\tikz@intersect@namedpaths}, + execute at end scope={\global\let\tikz@intersect@namedpaths\tikz@intersect@namedpaths@outside}, + }, + name intersections/.code={% + \tikzset{/tikz/intersection/.cd, + by=, + #1}% + \pgfutil@ifundefined{tikz@intersect@path@name@\tikz@intersect@path@a}{% + \tikzerror{I do not know the path named `\tikz@intersect@path@a'. Perhaps you misspelt it}}% + {\pgfutil@ifundefined{tikz@intersect@path@name@\tikz@intersect@path@b}{% + \tikzerror{I do not know the path named `\tikz@intersect@path@b'. Perhaps you misspelt it}}% + {% + \pgfintersectionofpaths% + {% + \expandafter\pgfsetpath\csname tikz@intersect@path@name@\tikz@intersect@path@a\endcsname% + }% + {% + \expandafter\pgfsetpath\csname tikz@intersect@path@name@\tikz@intersect@path@b\endcsname% + }% + \ifx\tikz@intersect@total\pgfutil@empty% + \else% + \expandafter\let\tikz@intersect@total=\pgfintersectionsolutions% + \fi% + \ifx\tikz@intersect@name\pgfutil@empty% + \def\tikz@intersect@@name{intersection}% + \else% + \let\tikz@intersect@@name=\tikz@intersect@name% + \fi% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgfintersectionsolutions\relax% + \else% + \path[reset cm]\pgfextra{\pgftransformshift{\pgfpointintersectionsolution{\pgfmathcounter}}}% + coordinate (\tikz@intersect@@name-\pgfmathcounter); + \repeatpgfmathloop% + \ifx\tikz@intersect@by\pgfutil@empty% + \else% + \foreach\tikz@intersect@name[count=\tikz@intersection@count] in \tikz@intersect@by% + {\expandafter\tikz@intersect@name@parse\tikz@intersect@name\pgf@stop}% + \fi% + }% + }% + },% + intersection/.cd, + of/.code=\tikz@intersect@path@names@parse#1\tikz@stop,% + name/.store in=\tikz@intersect@name, + total/.store in=\tikz@intersect@total, + by/.store in=\tikz@intersect@by, + sort by/.code=\edef\tikz@intersect@sort@by{#1}\tikz@intersect@check@sort@by% +}% + + +\def\tikz@intersect@check@sort@by{% + \ifx\tikz@intersect@sort@by\tikz@intersect@path@a% + \pgfintersectionsortbyfirstpath% + \else% + \ifx\tikz@intersect@sort@by\tikz@intersect@path@b% + \pgfintersectionsortbysecondpath% + \else% + \pgf@intersect@sortfalse% + \fi% + \fi% +}% +\def\tikz@intersect@path@names@parse#1 and #2\tikz@stop{% + \def\tikz@intersect@path@a{#1}% + \def\tikz@intersect@path@b{#2}% +}% + +\def\tikz@intersect@name@parse{\pgfutil@ifnextchar[\tikz@intersect@name@parse@opt{\tikz@intersect@name@parse@opt[]}}% +\def\tikz@intersect@name@parse@opt[#1]#2\pgf@stop{% + \coordinate [#1] (#2) at (\tikz@intersect@@name-\tikz@intersection@count); +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarylindenmayersystems.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarylindenmayersystems.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3160f8c7cf5e9d6d7bce29d3c933bce263069f55 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarylindenmayersystems.code.tex @@ -0,0 +1,73 @@ + +\usepgflibrary{lindenmayersystems}% + +\def\tikz@@lsystem-system{% + \pgfutil@ifnextchar[{\tikz@lsystem@options}{\tikz@lsystem@options[]}}% + +\def\tikz@lsystem indenmayer system{% + \pgfutil@ifnextchar[{\tikz@lsystem@options}{\tikz@lsystem@options[]}}% + +\def\tikz@lsystem@options[#1]{% + \tikzset{#1}% + \ifx\tikz@lsystem@rules\pgfutil@empty% + \else% + \tikz@lsystem@declare% + \def\tikz@lsystem@name{tikz@temp}% + \fi% + \ifx\tikz@lsystem@anchor\pgfutil@empty% + \pgfpathmoveto{\pgfqpoint{\tikz@lastxsaved}{\tikz@lastysaved}}% + \pgflindenmayersystem{\tikz@lsystem@name}{\tikz@lsystem@axiom}{\tikz@lsystem@order}% + \else% + \pgfextract@process\tikz@lsystem@pos{\pgfqpoint{\tikz@lastxsaved}{\tikz@lastysaved}}% + \setbox\pgfnodeparttextbox=\hbox{% + \pgfinterruptpicture% + \pgfpicture% + \pgfpathmoveto{\pgfpointorigin}% + \pgflindenmayersystem{\tikz@lsystem@name}{\tikz@lsystem@axiom}{\tikz@lsystem@order}% + \begingroup% + \tikz@finish% + \endpgfpicture% + \endpgfinterruptpicture% + }% + {% + \pgftransformshift{\tikz@lsystem@pos}% + \tikzset{inner sep=0pt, outer sep=0pt, minimum size=0pt}% + \pgfmultipartnode{rectangle}{\tikz@lsystem@anchor}{lindenmayer system}{\pgfusepath{discard}}% + }% + \fi% + \tikz@scan@next@command}% + +\tikzset{% + lindenmayer system/.style={/pgf/lindenmayer system/.cd, #1,/tikz/.cd}, + l-system/.style={lindenmayer system={#1}}, +}% +\pgfkeys{/pgf/lindenmayer system/.cd, + name/.code=\edef\tikz@lsystem@name{#1}\let\tikz@lsystem@rules=\pgfutil@empty,% + axiom/.store in=\tikz@lsystem@axiom,% + order/.store in=\tikz@lsystem@order, + .unknown/.code={% + \pgfutil@ifundefined{pgf@lsystem@\pgfkeyscurrentname}{% + \pgfkeys{/errors/unknown key={/pgf/lindenmayer system/\pgfkeyscurrentname}{#1}}% + \let\tikz@lsystem@name=\pgfutil@empty% + }% + {\edef\tikz@lsystem@name{\pgfkeyscurrentname}} + },% + anchor/.store in=\tikz@lsystem@anchor,% + rule set/.store in=\tikz@lsystem@rules +}% +\let\tikz@lsystem@anchor=\pgfutil@empty% +\let\tikz@lsystem@rules=\pgfutil@empty% + +\def\tikz@lsystem@declare{% + \expandafter\let\csname pgf@lsystem@tikz@temp\endcsname=\relax% + \pgfdeclarelindenmayersystem{tikz@temp}{% + \expandafter\tikz@lsystem@parse@rules\tikz@lsystem@rules,\tikz@stop,% + }% +}% +\def\tikz@lsystem@parse@rules#1,{% + \ifx#1\tikz@stop% + \else% + \rule{#1}% + \expandafter\tikz@lsystem@parse@rules% + \fi% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymath.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymath.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..763eacf21638f255cc759cd695f5cb9dd3d12acd --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymath.code.tex @@ -0,0 +1,722 @@ + +\usetikzlibrary{fpu} + +\edef\tikz@math@at@catcode{\the\catcode`\@}% +\catcode`\@=11 + +\def\tikz@math@gobblespaces#1{\pgfutil@ifnextchar x{#1}{#1}}% + +\def\tikz@math@meaning@macro{macro}% +\def\tikz@math@meaning@dimen{dimen}% +\def\tikz@math@meaning@count{count}% +\def\tikz@math@meaning@null{null}% + +\def\tikz@math@getmeaning#1{\expandafter\tikz@math@@getmeaning\meaning#1\tikz@math@getmeaning@stop}% + +\def\tikz@math@@getmeaning#1#2#3#4#5\tikz@math@getmeaning@stop{% + \if#1u% + \let\tikz@math@meaning=\tikz@math@meaning@macro% + \else% + \if#1m% + \let\tikz@math@meaning=\tikz@math@meaning@macro% + \else% + \if#2d% + \let\tikz@math@meaning=\tikz@math@meaning@dimen% + \else% + \if#2c% + \let\tikz@math@meaning=\tikz@math@meaning@count% + \else% + \if#3k% + \let\tikz@math@meaning=\tikz@math@meaning@dimen% + \else% + \let\tikz@math@meaning=\tikz@math@meaning@null% + \fi% + \fi% + \fi% + \fi% + \fi% +}% + +\def\tikz@math@firstoftwo#1#2{#1}% +\def\tikz@math@secondoftwo#1#2{#2}% + + +\def\tikz@math@getvarstring#1{% + \begingroup% + \escapechar=-1\relax% + \expandafter\tikz@math@@getvarstring\string#1\tikz@math}% + +\def\tikz@math@@getvarstring#1\tikz@math#2{% + \endgroup% + \def#2{#1}% +}% + +\long\def\tikz@math@collecttosemicolon@other#1#2;{% + \def\tikz@math@collected{#2}#1}% +\def\tikz@math@semicolon@other{;}% + +{\catcode`\;=13 +\long\gdef\tikz@math@collecttosemicolon@active#1#2;{% + \def\tikz@math@collected{#2}#1}% +\gdef\tikz@math@semicolon@active{;}% +}% + + +\def\tikz@math@setvartype#1#2{% + \expandafter\let\csname tikz@math@var@vartype@\string#1\endcsname=#2% +}% + + +\def\tikz@math@getvartype#1#2{% + \def\tikz@math@marshal{\let#1=}% + \expandafter\tikz@math@marshal\csname + tikz@math@var@vartype@\string#2\endcsname% +}% + + + +\def\tikz@math@ifvarcoordinate#1{% + \expandafter\ifx\csname + tikz@math@var@vartype@\string#1\endcsname\tikz@math@keyword@coordinate% + \let\tikz@math@next=\tikz@math@firstoftwo% + \else% + \let\tikz@math@next=\tikz@math@secondoftwo% + \fi% + \tikz@math@next% +}% + +\def\tikz@math@ifvarinteger#1{% + \expandafter\ifx\csname + tikz@math@var@vartype@\string#1\endcsname\tikz@math@keyword@integer% + \let\tikz@math@next=\tikz@math@firstoftwo% + \else% + \let\tikz@math@next=\tikz@math@secondoftwo% + \fi% + \tikz@math@next% +}% + + +\def\tikz@math@setvarindexed#1{% + \expandafter\let\csname + tikz@math@var@subtype@\string#1\endcsname=\tikz@math@subtype@indexed% +}% + +\def\tikz@math@clearvarindexed#1{% + \expandafter\let\csname tikz@math@var@subtype@\string#1\endcsname=\relax% +}% + +\def\tikz@math@ifvarindexed#1{% + \expandafter\ifx\csname tikz@math@var@subtype@\string#1\endcsname\relax% + \let\tikz@math@next=\tikz@math@secondoftwo% + \else% + \let\tikz@math@next=\tikz@math@firstoftwo% + \fi% + \tikz@math@next% +}% + +\def\tikz@math@stop{@}% + +\let\tikz@math@parse@hook@before=\pgfutil@empty +\let\tikz@math@parse@hook@after=\pgfutil@empty + +\def\tikz@math{% + \ifnum\catcode`\;=13\relax% + \let\tikz@math@semicolon=\tikz@math@semicolon@active% + \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@active% + \else% + \let\tikz@math@semicolon=\tikz@math@semicolon@other% + \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@other% + \fi% + \tikz@math@parse@hook@before% + \tikz@@math}% + + + + +\long\def\tikz@@math#1{% + \def\tikz@math@marshal{\tikz@math@parse#1}% + \expandafter\expandafter\expandafter\tikz@math@marshal\expandafter\tikz@math@stop\tikz@math@semicolon}% + +\def\tikz@math@parse{\pgfutil@ifnextchar\bgroup\tikz@math@@parse@bgroup\tikz@math@@parse@nobgroup}% + + +\def\tikz@math@@parse@bgroup{% + \tikz@math@collecttosemicolon{% + \ifx\pgf@selectfontorig\tikz@math@undefined% + \begingroup\tikz@math@collected\endgroup% + \else% + \begingroup\csname nullfont\endcsname\tikz@math@collected\endgroup% + \fi\tikz@math@parse}}% + + + +\def\tikz@math@@parse@nobgroup{\tikz@math@collecttosemicolon{\tikz@math@@parse@@nobgroup}}% + +\def\tikz@math@@parse@@nobgroup{% + \let\tikz@math@tmp=\tikz@math@collected% + \ifx\tikz@math@tmp\tikz@math@stop% + \def\tikz@math@next{\expandafter\tikz@math@parse@finish\tikz@math@semicolon}% + \else% + \def\tikz@math@next{\expandafter\expandafter\expandafter\tikz@math@parse@keyword@check\expandafter\tikz@math@tmp\tikz@math@semicolon}% + \fi% + \tikz@math@next% +}% + +\def\tikz@math@parse@finish{% + \tikz@math@collecttosemicolon{\tikz@math@parse@hook@after}% +}% + + + +\newif\iftikz@math@let +\def\tikz@math@parse@keyword@check#1{% + \tikz@math@letfalse% + \tikz@math@getmeaning{#1}% + \ifx\tikz@math@meaning\tikz@math@meaning@null% + \let\tikz@math@next=\tikz@math@parse@keyword% + \else% + \let\tikz@math@next=\tikz@math@parse@nokeyword% + \fi% + \tikz@math@next#1}% + + +\def\tikz@math@parse@keyword{% + \let\tikz@math@parsed@keyword=\pgfutil@empty% + \futurelet\tikz@math@parse@token\tikz@math@@parse@keyword}% + +\def\tikz@math@@parse@keyword{% + \ifx\tikz@math@parse@token\pgfutil@sptoken% + \let\tikz@math@next=\tikz@math@@@parse@keyword% + \else% + \ifx\tikz@math@parse@token(% + \let\tikz@math@next=\tikz@math@@@parse@keyword% + \else% + \ifx\tikz@math@parse@token\bgroup% + \let\tikz@math@next=\tikz@math@@@parse@keyword% + \else% + \let\tikz@math@next=\tikz@math@@@@parse@keyword% + \fi% + \fi% + \fi% + \tikz@math@next}% + +\def\tikz@math@error#1{\pgfutil@packageerror{tikz}{tikz math library: #1}{}}% + +\def\tikz@math@@@parse@keyword{% + \expandafter\ifx\csname tikz@math@process@keyword@\tikz@math@parsed@keyword\endcsname\relax% + \expandafter\ifx\csname pgfmath\tikz@math@parsed@keyword\endcsname\relax% + \tikz@math@error{Unknown function or keyword '\tikz@math@parsed@keyword'}% + \else% + \def\tikz@math@next{\tikz@math@collecttosemicolon{\tikz@math@function@noassign}}% + \fi% + \else% + \expandafter\def\expandafter\tikz@math@next\expandafter{\csname tikz@math@process@keyword@\tikz@math@parsed@keyword\endcsname}% + \fi% + \tikz@math@next}% + +\def\tikz@math@@@@parse@keyword#1{% + \edef\tikz@math@parsed@keyword{\tikz@math@parsed@keyword#1}% + \futurelet\tikz@math@parse@token\tikz@math@@parse@keyword% +}% + +\def\tikz@math@function@noassign{% + \pgfmathparse{\tikz@math@parsed@keyword\tikz@math@collected}% + \tikz@math@parse% +}% + + + + +\def\tikz@math@process@keyword@count{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@count}}% +\def\tikz@math@process@keyword@@count{% +\def\tikz@math@assign@register{\csname newcount\endcsname}% +\expandafter\tikz@math@gobblespaces\expandafter\tikz@math@process@registers\tikz@math@collected,@,}% + +\def\tikz@math@process@keyword@length{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@length}}% +\def\tikz@math@process@keyword@@length{% +\def\tikz@math@assign@register{\csname newdimen\endcsname}% +\expandafter\tikz@math@gobblespaces\expandafter\tikz@math@process@registers\tikz@math@collected,@,}% + + +\def\tikz@math@process@registers#1#2,{% + \def\tikz@math@var{#1}% + \ifx\tikz@math@var\tikz@math@stop% + \let\tikz@math@next=\tikz@math@parse% + \else% + \tikz@math@assign@register#1\relax% + \let\tikz@math@next=\tikz@math@process@registers% + \fi% + \tikz@math@gobblespaces\tikz@math@next% +}% + + +\def\tikz@math@process@keyword@if#1then{% + \def\tikz@math@if@condition{#1}% + \tikz@math@gobblespaces\tikz@math@parse@if@iftrue% +}% +\def\tikz@math@parse@if@iftrue#1{% + \def\tikz@math@if@trueaction{#1}% + \pgfutil@ifnextchar e{\tikz@math@parse@else}{\tikz@math@if@doif}}% + +\def\tikz@math@parse@else else{\tikz@math@gobblespaces\tikz@math@if@doifelse}% + +\def\tikz@math@if@doif{\tikz@math@collecttosemicolon{\tikz@math@if@@doif}}% + +\def\tikz@math@if@@doif{% + \pgfmathparse{\tikz@math@if@condition}% + \ifpgfmathfloatparseactive% + \pgfmathfloattofixed{\pgfmathresult}% + \fi% + \ifdim\pgfmathresult pt=0pt\relax% + \else% + \expandafter\tikz@math\expandafter{\tikz@math@if@trueaction}% + \fi% + \tikz@math@parse% +}% +\def\tikz@math@if@doifelse{\tikz@math@collecttosemicolon{\tikz@math@if@@doifelse}}% +\def\tikz@math@if@@doifelse{% + \pgfmathparse{\tikz@math@if@condition}% + \ifpgfmathfloatparseactive% + \pgfmathfloattofixed{\pgfmathresult}% + \fi% + \let\tikz@math@if@falseaction=\tikz@math@collected% + \ifdim\pgfmathresult pt=0pt\relax% + \expandafter\tikz@math\expandafter{\tikz@math@if@falseaction}% + \else% + \expandafter\tikz@math\expandafter{\tikz@math@if@trueaction}% + \fi% + \tikz@math@parse% +}% +\def\tikz@math@process@keyword@let{% + \tikz@math@lettrue% + \tikz@math@gobblespaces\tikz@math@parse@nokeyword% +}% + + +\def\tikz@math@parse@nokeyword#1{% + \def\tikz@math@var{#1}% + \tikz@math@getvarstring{#1}\tikz@math@varstring% + \let\tikz@math@vartype=\pgfutil@empty% + \ifx\tikz@math@var\tikz@math@stop% + \let\tikz@math@next=\tikz@math@parse@finish% + \else% + \ifx\tikz@math@semicolon\tikz@math@var% + \let\tikz@math@next=\tikz@math@parse% + \else% + \let\tikz@math@next=\tikz@math@parse@index@check% + \fi% + \fi% + \tikz@math@next}% + +\def\tikz@math@parse@index@check{% + \pgfutil@ifnextchar={\tikz@math@parse@noindex}{\tikz@math@parse@index}}% + +\def\tikz@math@parse@noindex{% + \expandafter\tikz@math@clearvarindexed\tikz@math@var% + \let\tikz@math@current@index=\pgfutil@empty% + \tikz@math@parse@afterindex% +}% + +\def\tikz@math@parse@index#1{% + \def\tikz@math@tmp{#1}% + \expandafter\tikz@math@setvarindexed\tikz@math@var% + \edef\tikz@math@current@index{#1}% + \tikz@math@parse@afterindex% +}% +\def\tikz@math@parse@afterindex#1={\tikz@math@gobblespaces\tikz@math@parse@assignment}% + +\def\tikz@math@parse@assignment{\tikz@math@collecttosemicolon{\tikz@math@parse@@assignment}}% +\def\tikz@math@parse@@assignment{% + \expandafter\expandafter\expandafter\tikz@math@doassignment\expandafter\expandafter\expandafter% + {\expandafter\tikz@math@var\expandafter}\expandafter{\tikz@math@collected}% + \tikz@math@parse% +}% + +\def\tikz@math@dollar@char{$}% +\def\tikz@math@dollar@char{$}% + +\def\tikz@math@doassignment#1#2{% + \tikz@math@ifvarcoordinate{#1}{% + \def\tikz@math@var{#1}% + \tikz@math@getvarstring{#1}\tikz@math@varstring% + \expandafter\pgfutil@in@\tikz@math@dollar@char{#2}% + \edef\tikz@math@expression{#2}% + \ifpgfutil@in@% + \expandafter\tikz@scan@one@point\expandafter\tikz@math@assign@coordinate\tikz@math@expression% + \else% + \expandafter\ifx\csname tikz@library@calc@loaded\endcsname\relax% + \expandafter\tikz@scan@one@point\expandafter\tikz@math@assign@coordinate\tikz@math@expression% + \else% + \expandafter\tikz@scan@one@point\expandafter\tikz@math@assign@coordinate\expandafter% + (\expandafter$\tikz@math@expression$)% + \fi% + \fi% + }{% + \iftikz@math@let% + \ifx\tikz@math@current@index\pgfutil@empty% + \edef#1{#2}% + \else% + \edef\tikz@math@tmp{#2}% + \expandafter\expandafter\expandafter\tikz@math@assign@index\expandafter\expandafter\expandafter% + {\expandafter\tikz@math@varstring\expandafter}\expandafter{\tikz@math@tmp}% + \fi% + \tikz@math@letfalse% + \else% + \ifx\tikz@math@current@index\pgfutil@empty% + \tikz@math@getmeaning{#1}% + \ifx\tikz@math@meaning\tikz@math@meaning@dimen% + \pgfmathsetlength{#1}{#2}% + \let\tikz@math@last@assigned@value=\pgfmathresult% + \else% + \ifx\tikz@math@meaning\tikz@math@meaning@count% + \pgfmathsetcount{#1}{#2}% + \let\tikz@math@last@assigned@value=\pgfmathresult% + \else% + \tikz@math@ifvarinteger{#1}{\pgfmathparse{int(#2)}}{\pgfmathparse{#2}}% + \let\tikz@math@last@assigned@value=\pgfmathresult% + \let#1=\pgfmathresult% + \fi% + \fi% + \else% + \tikz@math@ifvarinteger{#1}{\pgfmathparse{int(#2)}}{\pgfmathparse{#2}}% + \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring}\pgfmathresult% + \let\tikz@math@last@assigned@value=\pgfmathresult% + \fi% + \fi% + }% +}% + + + +\def\tikz@math@assign@index#1#2{% + \expandafter\def\csname#1\endcsname##1{\csname + tikz@math@var@indexed@#1@##1\endcsname}% + \expandafter\edef\csname + tikz@math@var@indexed@#1@\tikz@math@current@index\endcsname{#2}\relax% +}% + + + +\def\tikz@math@assign@coordinate#1{% + \pgf@process{#1}% + \ifx\tikz@math@current@index\pgfutil@empty% + \expandafter\edef\csname\tikz@math@varstring\endcsname{\the\pgf@x,\the\pgf@y}% + \expandafter\edef\csname\tikz@math@varstring x\endcsname{\the\pgf@x}% + \expandafter\edef\csname\tikz@math@varstring y\endcsname{\the\pgf@y}% + \else% + \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring}{\the\pgf@x,\the\pgf@y}% + \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring x}{\the\pgf@x}% + \expandafter\tikz@math@assign@index\expandafter{\tikz@math@varstring y}{\the\pgf@y}% + \fi% +}% + + + +\def\tikz@math@keyword@coordinate{coordinate}% +\def\tikz@math@process@keyword@coordinate{% + \let\tikz@math@vartype=\tikz@math@keyword@coordinate% + \tikz@math@gobblespaces\tikz@math@process@vartypes% +}% + +\def\tikz@math@keyword@integer{integer}% +\def\tikz@math@process@keyword@integer{% + \let\tikz@math@vartype=\tikz@math@keyword@integer% + \tikz@math@gobblespaces\tikz@math@process@vartypes% +}% +\def\tikz@math@process@keyword@int{% + \tikz@math@process@keyword@integer% +}% + +\def\tikz@math@keyword@real{real}% +\def\tikz@math@process@keyword@real{% + \let\tikz@math@vartype=\tikz@math@keyword@real% + \tikz@math@gobblespaces\tikz@math@process@vartypes% +}% + +\def\tikz@math@process@keyword@point{\tikz@math@process@keyword@coordinate}% + + +\def\tikz@math@process@vartypes{\tikz@math@collecttosemicolon{\tikz@math@process@@vartypes}}% + +\def\tikz@math@process@@vartypes{% + \expandafter\tikz@math@@process@vartypes\tikz@math@collected,@,\tikz@math% +}% + +\def\tikz@math@@process@vartypes#1#2,{% + \def\tikz@math@var{#1}% + \tikz@math@getvarstring{#1}\tikz@math@varstring% + \ifx\tikz@math@var\tikz@math@stop% + \let\tikz@math@next=\tikz@math@@@process@vartypes% + \else% + \expandafter\tikz@math@setvartype\tikz@math@var\tikz@math@vartype% + \def\tikz@math@next{\tikz@math@gobblespaces\tikz@math@@process@vartypes}% + \fi% + \tikz@math@next% +}% + +\def\tikz@math@process@keyword@print{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@print}}% +\def\tikz@math@process@keyword@@print{% + \begingroup\tikz@math@collected\endgroup\tikz@math@parse% +}% + +\def\tikz@math@@@process@vartypes#1\tikz@math{% + \tikz@math@parse% +}% + +\newcount\tikz@math@for@depth + +\def\tikz@math@for@namedef#1{\expandafter\def\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}% +\def\tikz@math@for@nameedef#1{\expandafter\edef\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}% +\def\tikz@math@for@namelet#1{\expandafter\let\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}% + +\def\tikz@math@for@namegetvalue#1#2{% + \def\tikz@math@marshal{\let#2=}% + \expandafter\tikz@math@marshal\csname tikz@math@for@def@#1@\the\tikz@math@for@depth\endcsname}% + +\def\tikz@math@process@keyword@for{% + \tikz@math@for% +}% + +\def\tikz@math@for@external{% + \ifnum\catcode`\;=13\relax% + \let\tikz@math@semicolon=\tikz@math@semicolon@active% + \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@active% + \else% + \let\tikz@math@semicolon=\tikz@math@semicolon@other% + \let\tikz@math@collecttosemicolon=\tikz@math@collecttosemicolon@other% + \fi + \advance\tikz@math@for@depth by1\relax% + \tikz@math@for@namedef{execute}{\tikz@math@for@external@execute}% + \tikz@math@for@namedef{finished}{\relax}% + \tikz@math@gobblespaces\tikz@math@for@parsevar}% + +\def\tikz@math@for@external@execute#1{#1}% + +\def\tikz@math@for{% + \advance\tikz@math@for@depth by1\relax% + \tikz@math@for@namedef{execute}{\tikz@math}% + \tikz@math@for@namedef{finished}{\tikz@math@parse}% + \tikz@math@gobblespaces\tikz@math@for@parsevar}% + + +\def\tikz@math@for@parsevar#1{% + \tikz@math@for@namedef{var}{#1}% + \tikz@math@for@parsein}% + +\def\tikz@math@getindex#1{% + \tikz@math@@getindex#1\tikz@math@getindex\tikz@math@@getindex% +}% + +\def\tikz@math@@getindex#1#2\tikz@math@@getindex{#1}% + +\def\tikz@math@for@parsein#1in{% + \def\tikz@math@tmp{#1}% + \ifx\tikz@math@tmp\pgfutil@empty% + \tikz@math@for@namedef{index}{}% + \else% + \tikz@math@for@nameedef{index}{\tikz@math@getindex{#1}}% + \fi% + \tikz@math@gobblespaces\tikz@math@for@parselist% +}% + + +\long\def\tikz@math@for@parselist#1{% + \edef\tikz@math@for@list{#1}% + \tikz@math@gobblespaces{% + \tikz@math@collecttosemicolon{\tikz@math@for@parseaction}}}% + +\def\tikz@math@for@parseaction{% + \tikz@math@for@namedef{prevvalue}{}% + \tikz@math@for@namedef{prevprevvalue}{}% + \tikz@math@for@namelet{action}=\tikz@math@collected% + \expandafter\tikz@math@for@scan\tikz@math@for@list,\tikz@math,\tikz@@math% +}% + +\def\tikz@math@token{\tikz@math}% + + +\def\tikz@math@for@scan#1,{% + \def\tikz@math@for@value{#1}% + \ifx\tikz@math@for@value\tikz@math@token% + \let\tikz@math@next=\tikz@math@for@scan@end% + \else% + \ifx\tikz@math@for@value\pgfutil@empty% + \let\tikz@math@next=\tikz@math@for@scan@end% + \else% + \pgfutil@in@{...}{#1}% + \ifpgfutil@in@% + \let\tikz@math@next=\tikz@math@for@scan@dots% + \else% + \tikz@math@for@namegetvalue{var}{\tikz@math@var}% + \tikz@math@for@namegetvalue{index}{\tikz@math@current@index}% + \tikz@math@for@namegetvalue{action}{\tikz@math@action}% + \expandafter\tikz@math@getvarstring\expandafter{\tikz@math@var}\tikz@math@varstring% + \expandafter\tikz@math@doassignment\expandafter{\tikz@math@var}{#1}% + \tikz@math@for@namelet{value}=\tikz@math@last@assigned@value% + \tikz@math@for@namegetvalue{execute}{\tikz@math@execute}% + \expandafter\tikz@math@execute\expandafter{\tikz@math@action}% + \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}% + \tikz@math@for@namelet{prevprevvalue}=\tikz@math@prevvalue% + \tikz@math@for@namegetvalue{value}{\tikz@math@value}% + \tikz@math@for@namelet{prevvalue}=\tikz@math@value% + \let\tikz@math@next=\tikz@math@for@scan% + \fi% + \fi% + \fi% + \tikz@math@next% +}% + +\newdimen\tikz@math@dimen + +\def\tikz@math@for@scan@dots#1,{% + \pgfmathparse{#1}\let\tikz@math@value=\pgfmathresult% + \tikz@math@for@nameedef{endvalue}{\tikz@math@value}% + \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}% + \tikz@math@for@namegetvalue{prevprevvalue}{\tikz@math@prevprevvalue}% + \tikz@math@dimen=\tikz@math@prevvalue pt\relax% + \ifx\tikz@math@prevprevvalue\pgfutil@empty% + \ifdim\tikz@math@prevvalue pt<\tikz@math@value pt\relax% + \def\tikz@math@step{1pt}% + \else% + \def\tikz@math@step{-1pt}% + \fi% + \else% + \tikz@math@dimen=\tikz@math@prevvalue pt\relax% + \advance\tikz@math@dimen by-\tikz@math@prevprevvalue pt\relax% + \edef\tikz@math@step{\the\tikz@math@dimen}% + \fi% + \ifdim\tikz@math@step<0pt\relax% + \tikz@math@for@namedef{comparitor}{<}% + \else% + \tikz@math@for@namedef{comparitor}{>}% + \fi% + \tikz@math@for@nameedef{step}{\tikz@math@step}% + \tikz@math@for@doloop% +}% + +\def\tikz@math@for@doloop{% + \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}% + \tikz@math@for@namegetvalue{step}{\tikz@math@step}% + \tikz@math@for@namegetvalue{comparitor}{\tikz@math@comparitor}% + \tikz@math@for@namegetvalue{endvalue}{\tikz@math@endvalue}% + \tikz@math@dimen=\tikz@math@prevvalue pt\relax% + \advance\tikz@math@dimen by\tikz@math@step\relax% + \ifdim\tikz@math@dimen\tikz@math@comparitor\tikz@math@endvalue pt\relax% + \let\tikz@math@next=\tikz@math@for@endloop% + \else% + \tikz@math@for@nameedef{value}{\pgfmath@tonumber{\tikz@math@dimen}}% + \tikz@math@for@namegetvalue{var}{\tikz@math@var}% + \expandafter\tikz@math@getvarstring\expandafter{\tikz@math@var}\tikz@math@varstring% + \tikz@math@for@namegetvalue{index}{\tikz@math@current@index}% + \tikz@math@for@namegetvalue{action}{\tikz@math@action}% + \tikz@math@for@namegetvalue{value}{\tikz@math@value}% + \expandafter\expandafter\expandafter\tikz@math@doassignment\expandafter\expandafter\expandafter% + {\expandafter\tikz@math@var\expandafter}\expandafter{\tikz@math@value}% + \tikz@math@for@namegetvalue{execute}{\tikz@math@execute}% + \expandafter\tikz@math@execute\expandafter{\tikz@math@action}% + \tikz@math@for@namegetvalue{prevvalue}{\tikz@math@prevvalue}% + \tikz@math@for@namelet{prevprevvalue}=\tikz@math@prevvalue% + \tikz@math@for@namegetvalue{value}{\tikz@math@value}% + \tikz@math@for@namelet{prevvalue}=\tikz@math@value% + \let\tikz@math@next=\tikz@math@for@doloop% + \fi% + \tikz@math@next% +}% + +\def\tikz@math@for@endloop{% +\tikz@math@for@scan}% + + + + +\def\tikz@math@for@scan@end#1\tikz@@math{% +\tikz@math@for@namegetvalue{finished}{\tikz@math@next}% +\advance\tikz@math@for@depth by-1\relax% +\tikz@math@next}% + + + + + +\def\tikz@math@process@keyword@return{% + \tikz@math@collecttosemicolon{\pgfmathparse{\tikz@math@collected}\tikz@math@parse}}% + +\def\tikz@math@process@keyword@function{\tikz@math@collecttosemicolon{\tikz@math@process@keyword@@function}}% +\def\tikz@math@process@keyword@@function{% + \let\tikz@math@function@name=\pgfutil@empty% + \let\tikz@math@function@arguments=\pgfutil@empty% + \let\tikz@math@function@body=\pgfutil@empty% + \expandafter\expandafter\expandafter\tikz@math@@declarefunction\expandafter\tikz@math@collected\tikz@math@semicolon% +}% + +\def\tikz@math@@declarefunction{% + \pgfutil@ifnextchar\bgroup\tikz@math@@@collectbody\tikz@math@@@declarefunction}% + + +\def\tikz@math@@@declarefunction#1{% + \if#1(% + \let\tikz@math@next=\tikz@math@@@collectarguments% + \else% + \expandafter\def\expandafter\tikz@math@function@name\expandafter{\tikz@math@function@name#1}% + \let\tikz@math@next=\tikz@math@@declarefunction% + \fi% + \tikz@math@next% +}% +\def\tikz@math@@@collectarguments#1){% + \def\tikz@math@function@arguments{#1}% + \tikz@math@@declarefunction% +}% + +\newtoks\tikz@math@toks +\tikz@math@toks={#}% +\edef\tikz@math@char@hash{\the\tikz@math@toks}% +\tikz@math@toks={}% + +\def\tikz@math@@@collectbody{\tikz@math@collecttosemicolon{\tikz@math@@@@collectbody}}% + +\def\tikz@math@@@@collectbody{% + \tikz@math@toks={}% + \c@pgf@counta=0\relax% + \ifx\tikz@math@function@arguments\pgfutil@empty% + \else% + \expandafter\tikz@math@createargumentlist\tikz@math@function@arguments,,% + \expandafter\tikz@math@addto@toks\expandafter{\tikz@math@collected}% + \fi% + \edef\tikz@math@local@temp{% + \noexpand\pgfmathdeclarefunction{\tikz@math@function@name}{\the\c@pgf@counta}% + {\noexpand\def\noexpand\return{0}\noexpand\tikz@math{\the\tikz@math@toks}}% + }% + \tikz@math@local@temp + \tikz@math@parse% +}% + +\def\tikz@math@addto@toks#1{% + \expandafter\tikz@math@toks\expandafter{\the\tikz@math@toks#1}}% + +\def\tikz@math@createargumentlist{% + \pgfutil@ifnextchar + x\tikz@math@@createargumentlist\tikz@math@@createargumentlist}% + +\def\tikz@math@comma{,}% +\def\tikz@math@@createargumentlist#1,{% + \def\tikz@math@tmp{#1}% + \ifx\tikz@math@tmp\pgfutil@empty% + \let\tikz@math@next=\relax% + \else% + \advance\c@pgf@counta by1\relax% + \tikz@math@addto@toks{#1=}% + \expandafter\expandafter\expandafter\tikz@math@addto@toks\expandafter\expandafter\expandafter% + {\expandafter\tikz@math@char@hash\the\c@pgf@counta;}% + \let\tikz@math@next=\tikz@math@createargumentlist% + \fi% + \tikz@math@next% +}% + + + +\let\tikzmath=\tikz@math +\tikzset{evaluate/.code={\tikz@math{#1}}}% +\let\tikzmathfor=\tikz@math@for@external + + +\catcode`\@=\tikz@math@at@catcode\relax diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..90b6833b9c400ba2631b7e1bd599ef944eeddd15 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymatrix.code.tex @@ -0,0 +1,130 @@ + +\ProvidesFileRCS{tikzlibrarymatrix.code.tex} + + + +\tikzset{matrix of nodes/.style={% + matrix,% + cells={anchor=base},% + execute at begin cell=\tikz@lib@matrix@start@cell,% + execute at end cell=\tikz@lib@matrix@end@cell,% + execute at empty cell=\tikz@lib@matrix@empty@cell, + execute at begin matrix=\iftikz@handle@active@code\tikz@orig@shorthands\fi,% +}}% + +\def\tikz@lib@matrix@empty@cell{\iftikz@lib@matrix@empty\node[name=\tikzmatrixname-\the\pgfmatrixcurrentrow-\the\pgfmatrixcurrentcolumn]{};\fi}% + +\newif\iftikz@lib@matrix@plain + +\def\tikz@lib@matrix@start@cell{% + \pgfutil@ifnextchar|{\tikz@lib@matrix@with@options}{\tikz@lib@matrix@normal@start@cell}}% + +\def\tikz@lib@matrix@with@options|#1|{\tikz@lib@matrix@plainfalse\node% + [name=\tikzmatrixname-\the\pgfmatrixcurrentrow-\the\pgfmatrixcurrentcolumn]#1\bgroup\tikz@lib@matrix@startup}% + + +\def\tikz@lib@matrix@normal@start@cell{\pgfutil@ifnextchar\let{\tikz@lib@matrix@check}{\tikz@lib@matrix@plainfalse\node + [name=\tikzmatrixname-\the\pgfmatrixcurrentrow-\the\pgfmatrixcurrentcolumn]\bgroup\tikz@lib@matrix@startup}}% + +\def\tikz@lib@matrix@check#1{% + \pgfutil@ifnextchar\tikz@signal@path{\tikz@lib@matrix@plaintrue\let}{\tikz@lib@matrix@plainfalse\node + [name=\tikzmatrixname-\the\pgfmatrixcurrentrow-\the\pgfmatrixcurrentcolumn]\bgroup\tikz@lib@matrix@startup\let}% +}% + +\def\tikz@lib@matrix@end@cell{% + \iftikz@lib@matrix@plain% + \else% + \expandafter\egroup\expandafter;% + \fi% +}% + +\def\tikz@lib@matrix@startup{% + \pgfutil@ifnextchar\bgroup{% + \let\tikz@lib@matrix@saved@eol=\\% + \let\\=\pgfmatrixendrow% + \afterassignment\tikz@lib@matrix@smuggle% + \let\tikz@next} + {\let\\=\pgfmatrixendrow}% +}% +\def\tikz@lib@matrix@smuggle{% + \bgroup% + \let\\=\tikz@lib@matrix@saved@eol% +}% + + + +\newif\iftikz@lib@matrix@empty + +\tikzoption{nodes in empty cells}[true]{\csname tikz@lib@matrix@empty#1\endcsname}% + + +\tikzset{matrix of math nodes/.style={% + matrix of nodes, + nodes={% + execute at begin node=$,% + execute at end node=$% + }% +}}% + + + + +\tikzoption{left delimiter}{\tikzset{append after command={\tikz@delimiter% + {south east}% + {south west}% + {every delimiter,every left delimiter}% + {south}% + {north}% + {#1}% + {.}% + {\pgf@y}}}}% + +\tikzoption{right delimiter}{\tikzset{append after command={\tikz@delimiter% + {south west}% + {south east}% + {every delimiter,every right delimiter}% + {south}% + {north}% + {.}% + {#1}% + {\pgf@y}}}}% + +\tikzoption{above delimiter}{\tikzset{append after command={\tikz@delimiter% + {south east}% + {north west}% + {every delimiter,every above delimiter,rotate=-90}% + {west}% + {east}% + {#1}% + {.}% + {\pgf@x}}}}% + +\tikzoption{below delimiter}{\tikzset{append after command={\tikz@delimiter% + {south west}% + {south west}% + {every delimiter,every below delimiter,rotate=-90}% + {west}% + {east}% + {.}% + {#1}% + {\pgf@x}}}}% + +\def\tikz@delimiter#1#2#3#4#5#6#7#8{% + \bgroup + \pgfextra{\let\tikz@save@last@fig@name=\tikz@last@fig@name\tikz@node@is@a@labelfalse}% + node[outer sep=0pt,inner sep=0pt,draw=none,fill=none,anchor=#1,at=(\tikz@last@fig@name.#2),#3] + {% + {\nullfont\pgf@process{\pgfpointdiff{\pgfpointanchor{\tikz@last@fig@name}{#4}}{\pgfpointanchor{\tikz@last@fig@name}{#5}}}}% + $\left#6\vcenter{\hrule height .5#8 depth .5#8 width0pt}\right#7$% + } + \pgfextra{\global\let\tikz@last@fig@name=\tikz@save@last@fig@name}% + \egroup% +}% + +\tikzset{every delimiter/.style={}}% +\tikzset{every left delimiter/.style={}}% +\tikzset{every right delimiter/.style={}}% +\tikzset{every above delimiter/.style={}}% +\tikzset{every below delimiter/.style={}}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymindmap.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymindmap.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..75987d67570accd3541a954ae6658de374c80f5d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarymindmap.code.tex @@ -0,0 +1,396 @@ + +\ProvidesFileRCS{tikzlibrarymindmap.code.tex} + + +\usetikzlibrary{trees,decorations}% + + + +\pgfdeclaredecoration{circle connection bar}{initial} +{% + \state{initial}[width=0pt,next state=bar] + { + { + \pgftransformxshift{-\pgfkeysvalueof{/pgf/decoration/start radius}}% + \pgfpathmoveto{\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}}} + \pgfpatharc{\pgfdecorationsegmentangle}{-\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}} + \pgfutil@tempcnta=-\pgfdecorationsegmentangle\relax + \advance\pgfutil@tempcnta by90\relax + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/decoration/start radius}} + \pgfmathsetlength\pgfutil@tempdimb{\pgfdecorationsegmentamplitude} + \pgfpathcurveto + {\pgfpointadd + {\pgfpointpolar{-\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}}} + {\pgfpointpolar{\the\pgfutil@tempcnta}{.25\pgfutil@tempdima}}} + {\pgfqpoint{1.25\pgfutil@tempdima}{-.5\pgfutil@tempdimb}} + {\pgfqpoint{1.5\pgfutil@tempdima}{-.5\pgfutil@tempdimb}} + \pgfpathlineto{\pgfpoint{1.5\pgfutil@tempdima}{.5\pgfutil@tempdimb}} + \pgfutil@tempcnta=\pgfdecorationsegmentangle\relax + \advance\pgfutil@tempcnta by-90\relax + \pgfpathcurveto + {\pgfpoint{1.25\pgfutil@tempdima}{.5\pgfutil@tempdimb}} + {\pgfpointadd + {\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}}} + {\pgfpointpolar{\the\pgfutil@tempcnta}{.25\pgfutil@tempdima}}} + {\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}}} + \pgfpathclose + } + }% + \state{bar}[width=0pt,next state=end] + { + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/decoration/start radius}}% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/decoration/end radius}}% + \pgfmathsetlength\pgf@xc{\pgfdecorationsegmentamplitude}% + \pgfpathrectangle + {\pgfqpoint{.5\pgfutil@tempdima}{-.5\pgf@xc}} + {\pgfpoint{\pgfdecoratedremainingdistance+-.5\pgfutil@tempdimb+-.5\pgfutil@tempdima}{\pgf@xc}} + }% + \state{end}[width=0pt,next state=final] + { + { + \pgftransformxshift{\pgfdecoratedremainingdistance}% + \pgftransformxscale{-1}% + \pgftransformxshift{-\pgfkeysvalueof{/pgf/decoration/end radius}}% + \pgfpathmoveto{\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/end radius}}} + \pgfpatharc{\pgfdecorationsegmentangle}{-\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/end radius}} + \pgfutil@tempcnta=-\pgfdecorationsegmentangle\relax + \advance\pgfutil@tempcnta by90\relax + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/decoration/end radius}} + \pgfmathsetlength\pgfutil@tempdimb{\pgfdecorationsegmentamplitude}% + \pgfpathcurveto + {\pgfpointadd + {\pgfpointpolar{-\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/end radius}}} + {\pgfpointpolar{\the\pgfutil@tempcnta}{.25\pgfutil@tempdima}}} + {\pgfqpoint{1.25\pgfutil@tempdima}{-.5\pgfutil@tempdimb}} + {\pgfqpoint{1.5\pgfutil@tempdima}{-.5\pgfutil@tempdimb}} + \pgfpathlineto{\pgfpoint{1.5\pgfutil@tempdima}{.5\pgfutil@tempdimb}} + \pgfutil@tempcnta=\pgfdecorationsegmentangle\relax + \advance\pgfutil@tempcnta by-90\relax + \pgfpathcurveto + {\pgfpoint{1.25\pgfutil@tempdima}{.5\pgfutil@tempdimb}} + {\pgfpointadd + {\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/end radius}}} + {\pgfpointpolar{\the\pgfutil@tempcnta}{.25\pgfutil@tempdima}}} + {\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/end radius}}} + \pgfpathclose + } + }% + \state{final} + {}% +}% + + + +\pgfkeys{/pgf/decoration/angle=20}% + + +\tikzset{circle connection bar/.style= +{to path={ + \pgfextra{% + \tikz@lib@mindmap@check{\tikztostart}% + \tikz@compute@circle@radii\tikz@compute@segmentamplitude% + } + [every circle connection bar] + decorate [decoration=circle connection bar] + { -- (\tikztotarget) \tikztonodes} +}, +append after command={[fill=\tikz@concept@color,draw=none]} +}}% +\tikzset{every circle connection bar/.style={}}% + +\def\tikz@compute@circle@radii{% + \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikztostart}{center}}}% + \pgf@xa=\pgf@x% + \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikztostart}{west}}}% + \advance\pgf@xa by-\pgf@x% + \pgfkeys{/pgf/decoration/start radius/.expanded=\the\pgf@xa}% + \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikztotarget}{center}}}% + \pgf@xa=\pgf@x% + \pgf@process{\pgfpointtransformed{\pgfpointanchor{\tikztotarget}{west}}}% + \advance\pgf@xa by-\pgf@x% + \pgfkeys{/pgf/decoration/end radius/.expanded=\the\pgf@xa}% +}% +\def\tikz@compute@segmentamplitude{% + \pgf@x=\pgfkeysvalueof{/pgf/decoration/start radius}\relax% + \ifdim\pgf@x>\pgfkeysvalueof{/pgf/decoration/end radius}\relax% + \pgf@x=\pgfkeysvalueof{/pgf/decoration/end radius}\relax% + \fi% + \pgf@x=.175\pgf@x\relax% + \edef\pgfdecorationsegmentamplitude{\the\pgf@x}% +}% + + + + +\def\tikz@lib@mindmap@check#1{% + \pgfutil@ifundefined{pgf@sh@ns@#1}% + {\tikzerror{You are attempting to connect two things by a circle + connection bar where one is not a node}}{% + \expandafter\ifx\csname pgf@sh@ns@#1\endcsname\tikz@lib@coordinate@text% + \tikzerror{You are attempting to connect node of shape + 'coordinate' by a circle connection bar. The shape should be + 'circle' or something similar, instead.} + \fi% + } +}% + +\def\tikz@lib@coordinate@text{coordinate}% + + + +\tikzoption{circle connection bar switch color}{\tikz@parse@switch#1\pgf@unique}% +\def\tikz@parse@switch from (#1) to (#2)\pgf@unique{% + \tikzset{to path={% + \pgfextra{% + \tikz@lib@mindmap@check{\tikztostart}% + \tikz@compute@circle@radii\tikz@compute@segmentamplitude% + \global\let\tikz@lib@save@start=\tikztostart% + \global\let\tikz@lib@save@target=\tikztotarget% + \pgfkeysgetvalue{/pgf/decoration/start radius}\pgf@temp% + \global\let\tikz@lib@saved@start@radius=\pgf@temp% + \pgfkeysgetvalue{/pgf/decoration/end radius}\pgf@temp% + \global\let\tikz@lib@saved@end@radius=\pgf@temp% + }% + [every circle connection bar] + decorate [decoration=circle connection bar] + { -- (\tikztotarget) \tikztonodes} + }, + append after command={ + [fill=none,draw=none,path picture=\tikz@lib@shade@pic] + \pgfextra{ + \pgfutil@colorlet{tikz@switch@from}{#1}% + \pgfutil@colorlet{tikz@switch@to}{#2}% + }} + } +}% + +\def\tikz@lib@shade@pic{% + \pgftransformreset% + \pgf@process{\pgfpointnormalised{\pgfpointdiff{\pgfpointanchor{\tikz@lib@save@start}{center}}{\pgfpointanchor{\tikz@lib@save@target}{center}}}}% + \edef\tikz@lib@mm@vec{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfmathsetlength\pgf@xc{\tikz@lib@saved@start@radius} + \pgf@process{\pgfpointadd{\pgfpointtransformed{\pgfpointanchor{\tikz@lib@save@start}{center}}} + {\pgfpointscale{\pgf@sys@tonumber{\pgf@xc}}{\tikz@lib@mm@vec}}} + \edef\tikz@lib@mm@start{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfmathsetlength\pgf@xc{\tikz@lib@saved@end@radius} + \pgf@process{\pgfpointdiff{\tikz@lib@mm@start}{\pgfpointadd{\pgfpointtransformed{\pgfpointanchor{\tikz@lib@save@target}{center}}} + {\pgfpointscale{-\pgf@sys@tonumber{\pgf@xc}}{\tikz@lib@mm@vec}}}} + \edef\tikz@lib@mm@end{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgftransformshift{\tikz@lib@mm@start} + \pgflowlevelsynccm + \pgf@process{\tikz@lib@mm@vec} + { + \pgf@xa=-\pgf@x% + \pgftransformcm{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}% + {\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@xa}}% + {\pgfpointorigin}% + \pgf@process{\pgfpointtransformed{\tikz@lib@mm@end}}% + \expandafter + } + \edef\tikz@lib@mm@length{\the\pgf@x}% + \pgf@process{\tikz@lib@mm@vec} + \pgf@ya=-\pgf@y% + \pgftransformcm{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}% + {\pgf@sys@tonumber{\pgf@ya}}{\pgf@sys@tonumber{\pgf@x}}% + {\pgfpointorigin}% + \pgfmathsetlength\pgf@y{\tikz@lib@saved@start@radius}% + \pgfmathsetlength\pgf@ya{\tikz@lib@saved@end@radius}% + \ifdim\pgf@y<\pgf@ya% + \pgf@y=\pgf@ya% + \fi% + \pgf@y=0.01992528\pgf@y% + \pgftransformyscale{\pgf@sys@tonumber{\pgf@y}}% + \pgfpathrectanglecorners + {\pgfpoint{-\tikz@lib@saved@start@radius}{-50bp}} + {\pgfpoint{1pt}{50bp}} + \pgfsetfillcolor{tikz@switch@from} + \pgfusepath{fill} + \pgfpathrectanglecorners + {\pgfpoint{\tikz@lib@mm@length+\tikz@lib@saved@end@radius}{-50bp}} + {\pgfpoint{\tikz@lib@mm@length-1pt}{50bp}} + \pgfsetfillcolor{tikz@switch@to} + \pgfusepath{fill} + \pgf@x=\tikz@lib@mm@length% + \pgf@x=0.009962\pgf@x% + \pgftransformxscale{\pgf@sys@tonumber{\pgf@x}}% + \pgftransformxshift{50bp} + \pgflowlevelsynccm% + \pgfuseshading{tikz@shade@bar} +}% + +\tikzoption{concept color}{% + \let\tikz@old@concept@color=\tikz@concept@color% + \def\tikz@edge@to@parent@path{ + (\tikzparentnode) + to[circle connection bar switch color=from (\tikz@old@concept@color) to (#1)] + (\tikzchildnode)} + \def\tikz@concept@color{#1}% +}% + +\pgfdeclarehorizontalshading[tikz@switch@from,tikz@switch@to]{tikz@shade@bar}{100bp}{% + color(0pt)=(tikz@switch@from); + color(100bp)=(tikz@switch@to)}% + + + + + +\tikzset{concept/.style= {circle,fill=\tikz@concept@color,draw=\tikz@concept@color,every concept}}% +\tikzset{every concept/.style= {}}% + +\def\tikz@concept@color{black}% + +\tikzset{tikz@concept@setting/.style={edge from parent path={(\tikzparentnode) to [circle connection bar] (\tikzchildnode)}}}% +\tikzset{tikz@concept@color@set/.style={}}% + + +\tikzset{extra concept/.style= {concept color=black!50,level 2 concept,concept,every extra concept}}% +\tikzset{every extra concept/.style={}}% + +\tikzset{concept connection/.style={line width=1mm,shorten <=2mm,shorten >=2mm,cap=round,draw=black!50}}% + + + +\tikzset{mindmap/.style= + {fill,draw,very thick,outer sep=0pt,inner sep=1pt,% + every child/.append style={style=tikz@concept@setting,style=tikz@concept@color@set},% + root concept, + level 1/.append style={level 1 concept}, + level 2/.append style={level 2 concept}, + level 3/.append style={level 3 concept}, + level 4/.append style={level 4 concept}, + text centered,% + segment angle=20, + style=every mindmap, + }}% +\tikzset{every mindmap/.style={}}% + + +\tikzset{root concept/.style= {minimum size=4cm,text width=3.5cm,font=\pgfutil@font@large}}% +\tikzset{level 1 concept/.style={minimum size=2.25cm, + level distance=5cm, + text width=2cm, + sibling angle=60, + font=\pgfutil@font@small}}% +\tikzset{level 2 concept/.style={minimum size=1.75cm,% + level distance=2.9cm,% + text width=1.5cm,% + sibling angle=60,% + font=\pgfutil@font@footnotesize}}% +\tikzset{level 3 concept/.style={minimum size=1.15cm,% + text width=1cm,% + level distance=2.4cm,% + sibling angle=30,% + font=\pgfutil@font@tiny}}% +\tikzset{level 4 concept/.style={minimum size=0.9cm,% + text width=0.7cm, + level distance=1.85cm,% + sibling angle=30,% + font=\pgfutil@font@tiny}}% + +\tikzset{small mindmap/.style= + {% + root concept/.style={minimum size=2.3cm,text width=2.1cm,font=\pgfutil@font@footnotesize}, + level 1 concept/.style={% + minimum size=1.5cm, + level distance=2.8cm, + text width=1.4cm, + sibling angle=75, + font=\pgfutil@font@scriptsize},% + level 2 concept/.style={% + minimum size=1.1cm,% + level distance=2.2cm,% + text width=1.1cm,% + sibling angle=60,% + font=\pgfutil@font@tiny},% + level 3 concept/.style={% + level 2 concept, + sibling angle=30,% + font=\pgfutil@font@tiny},% + level 4 concept/.style={% + level 3 concept, + }, + mindmap,% + line width=2pt, + }}% + +\tikzset{large mindmap/.style= + {% + root concept/.style={minimum size=5.6cm,text width=4.5cm,font=\pgfutil@font@Large}, + level 1 concept/.style={% + minimum size=3.2cm, + level distance=7cm, + text width=2.8cm, + sibling angle=60, + font=},% + level 2 concept/.style={% + minimum size=2.45cm,% + level distance=4cm,% + text width=2.2cm,% + sibling angle=60,% + font=\pgfutil@font@small% + },% + level 3 concept/.style={% + minimum size=1.63cm,% + text width=1.4cm,% + level distance=3.38cm,% + sibling angle=30,% + font=\pgfutil@font@scriptsize},% + level 4 concept/.style={% + minimum size=1.27cm,% + text width=1cm, + level distance=2.60cm,% + sibling angle=30,% + font=\pgfutil@font@tiny},% + mindmap,% + line width=2pt, + }}% + +\tikzset{huge mindmap/.style= + {% + root concept/.style={minimum size=8cm,text width=7cm,font=\pgfutil@font@huge}, + level 1 concept/.style={% + minimum size=4.5cm, + level distance=10cm, + text width=4cm, + sibling angle=60, + font=\pgfutil@font@large},% + level 2 concept/.style={% + minimum size=3.5cm,% + level distance=5.8cm,% + text width=3cm,% + sibling angle=60,% + font=% + },% + level 3 concept/.style={% + minimum size=2.3cm,% + text width=2cm,% + level distance=4.8cm,% + sibling angle=30,% + font=\pgfutil@font@footnotesize},% + level 4 concept/.style={% + minimum size=1.7cm,% + text width=1.4cm, + level distance=3.7cm,% + sibling angle=30,% + font=\pgfutil@font@scriptsize},% + mindmap,% + line width=3pt, + }}% + + + +\tikzset{annotation/.style={shape=rectangle, + minimum size=0pt, + text width=3.5cm, + outer sep=1.5mm, + inner sep=1mm, + text badly ragged, + rounded corners, + font=\pgfutil@font@tiny, + every annotation}}% +\tikzset{every annotation/.style={}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..de39128cdda2c1cc0fcb6f6419b77c4152b57203 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.code.tex @@ -0,0 +1,23 @@ + +\ProvidesFileRCS{tikzlibrarypatterns.code.tex} + +\usepgflibrary{patterns}% + +\tikzoption{pattern color}{\edef\tikz@pattern@color{#1}}% +\tikzoption{pattern}[]{% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@fillfalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \tikz@addoption{\pgfsetfillpattern{#1}{\tikz@pattern@color}}% + \def\tikz@pattern{#1}% + \fi% + \tikz@addmode{\tikz@mode@filltrue}% + \fi% +}% +\def\tikz@pattern@color{black}% +\def\tikz@pattern{dots}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.meta.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.meta.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ee3ca9f3b32c89fdba08fb650a3a90bd541d6cc6 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypatterns.meta.code.tex @@ -0,0 +1,86 @@ + +\usepgflibrary{patterns.meta}% + +\tikzset{% + pattern color/.code=\edef\tikz@pattern@color{#1}, + pattern/.code={% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@fillfalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \tikz@addoption{\pgfsetfillpattern{#1}{\tikz@pattern@color}}% + \def\tikz@pattern{#1}% + \fi% + \tikz@addmode{\tikz@mode@filltrue}% + \fi% + } +}% + +\def\tikz@pattern@color{black}% +\def\tikz@pattern{}% + +\tikzset{patterns/.cd, + .unknown/.code={% + \let\tikz@pat@key=\pgfkeyscurrentname% + \pgfkeys{/pgf/patterns/\tikz@pat@key/.try={#1}}% + }, + bottom left/.style={/pgf/patterns/bottom left={\tikz@scan@one@point\pgf@pat@process#1}}, + top right/.style={/pgf/patterns/top right={\tikz@scan@one@point\pgf@pat@process#1}}, + bounding box/.style args={#1(#2)#3and#4(#5)#6}{% + /tikz/patterns/bottom left={(#2)}, + /tikz/patterns/top right={#4(#5)}, + }, + tile size/.style={/pgf/patterns/tile size={\tikz@scan@one@point\pgf@pat@process#1}}, + tile transformation/.style={/pgf/patterns/tile transformation={% + \let\tikz@transform=\relax\pgfkeys{/tikz/.cd,#1}}% + }, + infer tile bounding box/.code={ + \def\pgf@pat@codeafter{% + \xdef\tikz@pat@installbb{% + \noexpand\pgfkeys{/tikz/patterns/bounding box={% + (\the\pgf@picminx-#1,\the\pgf@picminy-#1) and + (\the\pgf@picmaxx+#1,\the\pgf@picmaxy+#1) + }, + /tikz/patterns/tile size={% + (\the\pgf@picmaxx-\the\pgf@picminx, + \the\pgf@picmaxy-\the\pgf@picminy)}}}% + }% + \let\pgf@pat@declarepost=\tikz@pat@installbb% + }, + infer tile bounding box/.default=0pt, +}% + +\def\tikzdeclarepattern#1{% + \begingroup% + \def\pgf@pat@codebefore{% + \let\tikz@transform=\relax% + \pgftransformreset% + \tikz@declarepattern@install% + \ifnum\pgf@pat@type=0\relax% + \let\pgfsetstrokecolor=\pgfutil@gobble% + \let\pgfsetfillcolor=\pgfutil@gobble% + \fi% + \def\tikz@fig{\tikzerror{You cannot use `\string\node' inside a pattern}}% + \def\tikz@edge@plain{\tikzerror{You cannot use `edge' inside a pattern}}% + \def\tikz@to{\tikzerror{You cannot use `to' paths inside a pattern}}% + \tikzset{pattern/.code={\tikzerror{You cannot nest patterns}}, + pattern color/.style={pattern}}% + }% + \pgfdeclarepattern{/tikz/patterns/.cd,#1}% + \endgroup% + }% + +\def\tikz@declarepattern@install{% + \let\tikz@compat@color@set=\tikz@compat@color@set@insidepatttern% + \tikz@installcommands% +}% + +\let\tikz@compat@color@set@orig=\tikz@compat@color@set +\def\tikz@compat@color@set@insidepatttern#1{% + \tikz@compat@color@set@orig{#1}% + \pgfsetfillcolor{#1}\pgfsetstrokecolor{#1}% +}% + + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryperspective.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryperspective.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..db4e9424de422b6706e542772c7f2a654a891351 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryperspective.code.tex @@ -0,0 +1,94 @@ + +\ProvidesFileRCS{tikzlibraryperspective.code.tex} + +\pgfmathsetmacro\pgf@H@tpp@aa{+1} + \pgfmathsetmacro\pgf@H@tpp@ab{+0} + \pgfmathsetmacro\pgf@H@tpp@ac{+0} +\pgfmathsetmacro\pgf@H@tpp@ba{+0} + \pgfmathsetmacro\pgf@H@tpp@bb{+1} + \pgfmathsetmacro\pgf@H@tpp@bc{+0} +\pgfmathsetmacro\pgf@H@tpp@ca{+0} + \pgfmathsetmacro\pgf@H@tpp@cb{+0} + \pgfmathsetmacro\pgf@H@tpp@cc{+1} +\pgfmathsetmacro\pgf@H@tpp@da{+0} + \pgfmathsetmacro\pgf@H@tpp@db{+0} + \pgfmathsetmacro\pgf@H@tpp@dc{+0} + +\def\pgfpointperspectivexyz#1#2#3{% + \pgfmathsetmacro\pgf@pp@w% + { \pgf@H@tpp@da*(#1) + \pgf@H@tpp@db*(#2) + \pgf@H@tpp@dc*(#3) + 1} + \pgfmathsetmacro\pgf@pp@x% + {(\pgf@H@tpp@aa*(#1) + \pgf@H@tpp@ab*(#2) + \pgf@H@tpp@ac*(#3))/\pgf@pp@w} + \pgfmathsetmacro\pgf@pp@y% + {(\pgf@H@tpp@ba*(#1) + \pgf@H@tpp@bb*(#2) + \pgf@H@tpp@bc*(#3))/\pgf@pp@w} + \pgfmathsetmacro\pgf@pp@z% + {(\pgf@H@tpp@ca*(#1) + \pgf@H@tpp@cb*(#2) + \pgf@H@tpp@cc*(#3))/\pgf@pp@w} + \pgf@x=\pgf@pp@x\pgf@xx% + \advance\pgf@x by \pgf@pp@y\pgf@yx% + \advance\pgf@x by \pgf@pp@z\pgf@zx% + \pgf@y=\pgf@pp@x\pgf@xy% + \advance\pgf@y by \pgf@pp@y\pgf@yy% + \advance\pgf@y by \pgf@pp@z\pgf@zy} + +\tikzdeclarecoordinatesystem{three point perspective} +{% + \tikzset{cs/.cd,x=0,y=0,z=0,#1}% + \pgfpointperspectivexyz{\tikz@cs@x}{\tikz@cs@y}{\tikz@cs@z} +} +\tikzaliascoordinatesystem{tpp}{three point perspective} + +\pgfkeys{ + /perspective/.cd, + p/.code args={(#1,#2,#3)}{ + \pgfmathparse{ifthenelse(#1,int(1),int(0))} + \ifnum\pgfmathresult=0\else + \pgfmathsetmacro\pgf@H@tpp@ba{#2/#1} + \pgfmathsetmacro\pgf@H@tpp@ca{#3/#1} + \pgfmathsetmacro\pgf@H@tpp@da{ 1/#1} + \fi + }, + q/.code args={(#1,#2,#3)}{ + \pgfmathparse{ifthenelse(#2,int(1),int(0))} + \ifnum\pgfmathresult=0\else + \pgfmathsetmacro\pgf@H@tpp@ab{#1/#2} + \pgfmathsetmacro\pgf@H@tpp@cb{#3/#2} + \pgfmathsetmacro\pgf@H@tpp@db{ 1/#2} + \fi + }, + r/.code args={(#1,#2,#3)}{ + \pgfmathparse{ifthenelse(#3,int(1),int(0))} + \ifnum\pgfmathresult=0\else + \pgfmathsetmacro\pgf@H@tpp@ac{#1/#3} + \pgfmathsetmacro\pgf@H@tpp@bc{#2/#3} + \pgfmathsetmacro\pgf@H@tpp@dc{ 1/#3} + \fi + }, +} + +\tikzset{ + perspective/.append code={\pgfkeys{/perspective/.cd,#1}}, + perspective/.default={ + p={(10,0,0)}, + q={(0,10,0)}, + r={(0,0,20)}}, +} + +\tikzset{ + 3d view/.code 2 args={% + \pgfmathsetmacro\pgf@view@az{#1}% + \pgfmathsetmacro\pgf@view@el{#2}% + \pgfmathsetmacro\pgf@xvec@x{cos(\pgf@view@az)}% + \pgfmathsetmacro\pgf@xvec@y{-sin(\pgf@view@az)*sin(\pgf@view@el)}% + \pgfmathsetmacro\pgf@yvec@x{sin(\pgf@view@az)}% + \pgfmathsetmacro\pgf@yvec@y{cos(\pgf@view@az)*sin(\pgf@view@el)}% + \pgfmathsetmacro\pgf@zvec@x{+0}% + \pgfmathsetmacro\pgf@zvec@y{cos(\pgf@view@el)}% + \pgfsetxvec{\pgfpoint{\pgf@xvec@x cm}{\pgf@xvec@y cm}}% + \pgfsetyvec{\pgfpoint{\pgf@yvec@x cm}{\pgf@yvec@y cm}}% + \pgfsetzvec{\pgfpoint{\pgf@zvec@x cm}{\pgf@zvec@y cm}}% + }, + 3d view/.default={-30}{15}, + isometric view/.style={3d view={-45}{atan(1/sqrt(2))}}, +} + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypetri.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypetri.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f39cb7e8e7092dbf625382ae7adcaee68aeff2b2 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypetri.code.tex @@ -0,0 +1,125 @@ + +\ProvidesFileRCS{tikzlibrarypetri.code.tex} + + + +\tikzset{every place/.style= {}}% +\tikzset{place/.style= {circle,draw,inner sep=0pt, + minimum size=5ex, + every place}}% + + + +\tikzset{every transition/.style= {}}% +\tikzset{transition/.style= {rectangle,draw,inner sep=0pt, + minimum size=4mm, + every transition}}% + + + +\tikzset{pre/.style= {<-,shorten <=1pt}}% +\tikzset{post/.style= {->,shorten >=1pt}}% +\tikzset{pre and post/.style= {<->,shorten >=1pt,shorten <=1pt}}% + + + + +\tikzset{every token/.style= {}}% +\tikzset{token/.style= {fill=black,draw=none,circle, + inner sep=0.5pt,minimum size=1ex, + text=white,font=\pgfutil@font@tiny,every token}}% + +\tikzoption{token distance}{\def\tikz@token@distance{#1}}% +\def\tikz@token@distance{1.5ex}% + +\tikzset{children are tokens/.style= {growth function=\tikz@grow@tokens,edge from parent path=}}% + +\tikzoption{tokens}{% + \ifnum#1>0\relax% + \tikzset{append after command={} + {[children are tokens]child foreach \tikz@dummy in {1,...,#1} {node[token]{}}}}% + \fi}% + +\tikzoption{colored tokens}{% + \tikzset{append after command={}% + {[children are tokens]child foreach \tikz@child@color in {#1} {node[token,\tikz@child@color]{}}}}% + }% + +\tikzoption{structured tokens}{% + \tikzset{append after command={}% + {[children are tokens]child foreach \tikzpetrichildname in {#1} {node[token]{\tikzpetrichildname}}}}% + }% + + +\def\tikz@grow@tokens{% + \pgfmathsetlength{\pgf@xa}{\tikz@token@distance}% + \pgfmathsetlength{\pgf@ya}{\tikz@token@distance}% + \pgf@xc=0pt% + \pgf@yc=0pt% + \csname tikz@grow@tokens@placer@\the\tikznumberofchildren @\the\tikznumberofcurrentchild\endcsname% + \pgftransformshift{\pgfqpoint{\pgf@xc}{\pgf@yc}}% +}% + +\def\tikz@def@grow@tokens#1#2#3#4{% + \expandafter\def\csname tikz@grow@tokens@placer@#1@#2\endcsname{% + \pgf@xc=#3\pgf@xa% + \pgf@yc=#4\pgf@ya}% +}% + + +\tikz@def@grow@tokens{1}{1}{0}{0}% + +\tikz@def@grow@tokens{2}{1}{-.5}{0}% +\tikz@def@grow@tokens{2}{2}{.5}{0}% + +\tikz@def@grow@tokens{3}{1}{0} {0.57}% +\tikz@def@grow@tokens{3}{2}{-.5}{-.306025}% +\tikz@def@grow@tokens{3}{3}{.5} {-.306025}% + +\tikz@def@grow@tokens{4}{1}{-.5}{.5}% +\tikz@def@grow@tokens{4}{2}{.5}{.5}% +\tikz@def@grow@tokens{4}{3}{-.5}{-.5}% +\tikz@def@grow@tokens{4}{4}{.5}{-.5}% + +\tikz@def@grow@tokens{5}{1}{0}{.85}% +\tikz@def@grow@tokens{5}{2}{-0.808398}{0.26266}% +\tikz@def@grow@tokens{5}{3}{0.808398}{0.26266}% +\tikz@def@grow@tokens{5}{4}{-0.499617}{-0.687664}% +\tikz@def@grow@tokens{5}{5}{0.499617}{-0.687664}% + +\tikz@def@grow@tokens{6}{1}{-1}{.5}% +\tikz@def@grow@tokens{6}{2}{0}{.5}% +\tikz@def@grow@tokens{6}{3}{1}{.5}% +\tikz@def@grow@tokens{6}{4}{-1}{-.5}% +\tikz@def@grow@tokens{6}{5}{0}{-.5}% +\tikz@def@grow@tokens{6}{6}{1}{-.5}% + +\tikz@def@grow@tokens{7}{1}{0}{1}% +\tikz@def@grow@tokens{7}{2}{-1}{.5}% +\tikz@def@grow@tokens{7}{3}{0}{0}% +\tikz@def@grow@tokens{7}{4}{1}{.5}% +\tikz@def@grow@tokens{7}{5}{-1}{-.5}% +\tikz@def@grow@tokens{7}{6}{0}{-1}% +\tikz@def@grow@tokens{7}{7}{1}{-.5}% + +\tikz@def@grow@tokens{8}{1}{-.5}{1}% +\tikz@def@grow@tokens{8}{2}{.5}{1}% +\tikz@def@grow@tokens{8}{3}{-1}{0}% +\tikz@def@grow@tokens{8}{4}{0}{0}% +\tikz@def@grow@tokens{8}{5}{1}{0}% +\tikz@def@grow@tokens{8}{6}{-1}{-1}% +\tikz@def@grow@tokens{8}{7}{0}{-1}% +\tikz@def@grow@tokens{8}{8}{1}{-1}% + +\tikz@def@grow@tokens{9}{1}{-1}{1}% +\tikz@def@grow@tokens{9}{2}{0}{1}% +\tikz@def@grow@tokens{9}{3}{1}{1}% +\tikz@def@grow@tokens{9}{4}{-1}{0}% +\tikz@def@grow@tokens{9}{5}{0}{0}% +\tikz@def@grow@tokens{9}{6}{1}{0}% +\tikz@def@grow@tokens{9}{7}{-1}{-1}% +\tikz@def@grow@tokens{9}{8}{0}{-1}% +\tikz@def@grow@tokens{9}{9}{1}{-1}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplothandlers.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplothandlers.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..25c8c7d4156f90d858722e1a81f29032663271c3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplothandlers.code.tex @@ -0,0 +1,6 @@ + +\ProvidesFileRCS{tikzlibraryplothandlers.code.tex} + +\usepgflibrary{plothandlers}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e00aec682bfbd657444b4d88112dc1170edecdf6 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryplotmarks.code.tex @@ -0,0 +1,6 @@ + +\ProvidesFileRCS{tikzlibraryplotmarks.code.tex} + +\usepgflibrary{plotmarks}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8836ee58559c690ce7550b42c10ad42e33e2f23f --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarypositioning.code.tex @@ -0,0 +1,107 @@ + +\ProvidesFileRCS{tikzlibrarypositioning.code.tex} + + +\tikzset{above/.code=\tikz@lib@place@handle@{#1}{south}{0}{1}{north}{1}}% +\tikzset{above left/.code=\tikz@lib@place@handle@{#1}{south east}{-1}{1}{north west}{0.707106781}}% +\tikzset{above right/.code=\tikz@lib@place@handle@{#1}{south west}{1}{1}{north east}{0.707106781}}% +\tikzset{base left/.code =\tikz@lib@place@handle@{#1}{base east}{-1}{0}{base west}{1}}% +\tikzset{base right/.code=\tikz@lib@place@handle@{#1}{base west}{1}{0}{base east}{1}}% +\tikzset{below/.code=\tikz@lib@place@handle@{#1}{north}{0}{-1}{south}{1}}% +\tikzset{below left/.code=\tikz@lib@place@handle@{#1}{north east}{-1}{-1}{south west}{0.707106781}}% +\tikzset{below right/.code=\tikz@lib@place@handle@{#1}{north west}{1}{-1}{south east}{0.707106781}}% +\tikzset{left/.code =\tikz@lib@place@handle@{#1}{east}{-1}{0}{west}{1}}% +\tikzset{mid left/.code =\tikz@lib@place@handle@{#1}{mid east}{-1}{0}{mid west}{1}}% +\tikzset{mid right/.code=\tikz@lib@place@handle@{#1}{mid west}{1}{0}{mid east}{1}}% +\tikzset{right/.code=\tikz@lib@place@handle@{#1}{west}{1}{0}{east}{1}}% + +\newif\iftikz@lib@ignore@size + +\pgfutil@g@addto@macro\tikz@node@reset@hook{\tikz@addtransform{\tikz@lib@pos@call}\let\tikz@lib@pos@call=\relax}% + +\tikzset{on grid/.is if=tikz@lib@ignore@size}% + +\tikzset{node distance=1cm and 1cm}% + +\def\tikz@lib@place@handle@#1#2#3#4#5#6{% + \def\tikz@anchor{#2}% + \let\tikz@do@auto@anchor=\relax% + \edef\tikz@temp{#1}% + \def\tikz@lib@place@single@factor{#6}% + \expandafter\tikz@lib@place@handle@@\expandafter{\tikz@temp}{#3}{#4}{#5}% +}% +\def\tikz@lib@place@handle@@#1#2#3#4{% + \pgfutil@in@{of }{#1}% + \ifpgfutil@in@% + \tikz@lib@place@of#1\tikz@stop{#4}% + \else% + \edef\tikz@lib@place@nums{#1}% + \fi% + \ifx\tikz@lib@place@nums\pgfutil@empty% + \else% + \expandafter\tikz@lib@place@parse@nums\expandafter{\tikz@lib@place@nums}% + \pgf@x=#2\pgf@x% + \pgf@y=#3\pgf@y% + \edef\tikz@lib@pos@call{\noexpand\pgftransformshift{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + \fi% +}% + +\def\tikz@lib@place@parse@nums#1{% + \pgfutil@in@{and}{#1}% + \ifpgfutil@in@% + \tikz@lib@place@parse@nums@#1\tikz@stop% + \else% + \tikz@lib@place@parse@nums@#1and#1\tikz@stop% + \pgf@x=\tikz@lib@place@single@factor\pgf@x% + \pgf@y=\tikz@lib@place@single@factor\pgf@y% + \fi +}% +\def\tikz@lib@place@parse@nums@#1and#2\tikz@stop{% + \pgfmathparse{#2}% + \ifpgfmathunitsdeclared% + \pgf@xa=\pgfmathresult pt% + \pgf@ya=0pt% + \else% + \let\tikz@lib@temp=\pgfmathresult% + \pgf@process{\pgfpointxy{\tikz@lib@temp}{0}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \fi% + \pgfmathparse{#1}% + \ifpgfmathunitsdeclared% + \advance\pgf@ya by\pgfmathresult pt% + \else% + \let\tikz@lib@temp=\pgfmathresult% + \pgf@process{\pgfpointxy{0}{\tikz@lib@temp}}% + \advance\pgf@xa by\pgf@x% + \advance\pgf@ya by\pgf@y% + \fi% + \pgf@x=\pgf@xa% + \pgf@y=\pgf@ya% +}% + +\def\tikz@lib@place@of#1of #2\tikz@stop#3{% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \tikz@lib@place@of@{\tikz@node@distance}{#2}{#3}% + \else% + \tikz@lib@place@of@{#1}{#2}{#3}% + \fi% +}% +\def\tikz@lib@place@of@#1#2#3{% + \tikz@scan@one@point\tikz@lib@place@remember(#2)% + \iftikz@shapeborder% + \iftikz@lib@ignore@size% + \edef\tikz@node@at{\noexpand\pgfpointanchor{\tikz@shapeborder@name}{center}}% + \def\tikz@anchor{center}% + \else% + \edef\tikz@node@at{\noexpand\pgfpointanchor{\tikz@shapeborder@name}{#3}}% + \fi% + \fi% + \edef\tikz@lib@place@nums{#1}% +}% +\def\tikz@lib@place@remember#1{\def\tikz@node@at{#1}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryquotes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryquotes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..eb6bfc5afde15024314e7b43c38f3f9ed9c1370e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryquotes.code.tex @@ -0,0 +1,82 @@ + +\ProvidesFileRCS{tikzlibraryquotes.code.tex} + +\def\tikz@quote@parser#1{\tikz@quote@@parser#1\pgf@stop}% +\def\tikz@quote@@parser"#1"{% + \pgfutil@ifnextchar\bgroup{% + \tikz@quote@@parser@group{#1}}{% + \pgfutil@ifnextchar'{% + \tikz@quote@@parser@apo{#1}}{% + \tikz@quote@@parser@normal{#1}}}}% +\def\tikz@quote@@parser@apo#1'{% + \pgfutil@ifnextchar\bgroup{\tikz@quote@@parser@apo@group{#1}}{\tikz@quote@@parser@apo@normal{#1}}}% +\def\tikz@quote@@parser@group#1#2#3\pgf@stop{% + \expandafter\def\expandafter\tikz@temp\expandafter{\tikz@quotes@as{#1}{#2}}% + \expandafter\pgfkeysalso\expandafter{\tikz@temp}% +}% +\def\tikz@quote@@parser@normal#1#2\pgf@stop{% + \expandafter\def\expandafter\tikz@temp\expandafter{\tikz@quotes@as{#1}{#2}}% + \expandafter\pgfkeysalso\expandafter{\tikz@temp}% +}% +\def\tikz@quote@@parser@apo@group#1#2#3\pgf@stop{% + \expandafter\def\expandafter\tikz@temp\expandafter{\tikz@quotes@as{#1}{',#2}}% + \expandafter\pgfkeysalso\expandafter{\tikz@temp}% +}% +\def\tikz@quote@@parser@apo@normal#1#2\pgf@stop{% + \expandafter\def\expandafter\tikz@temp\expandafter{\tikz@quotes@as{#1}{',#2}}% + \expandafter\pgfkeysalso\expandafter{\tikz@temp}% +}% + +\pgfkeys{/handlers/first char syntax=true}% + +\def\tikz@enable@node@quotes{% + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string"}{\tikz@quote@parser}% + \let\tikz@quotes@as\tikz@node@quotes@as% +}% +\def\tikz@enable@edge@quotes{% + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string"}{\tikz@quote@parser}% + \let\tikz@quotes@as\tikz@edge@quotes@as% +}% +\def\tikz@enable@pic@quotes{% + \pgfkeyssetvalue{/handlers/first char syntax/\expandafter\meaning\string"}{\tikz@quote@parser}% + \let\tikz@quotes@as\tikz@pic@quotes@as% +}% + +\tikzset{ + node quotes mean/.code={\def\tikz@node@quotes@as##1##2{#1}}, + edge quotes mean/.code={\def\tikz@edge@quotes@as##1##2{#1}}, + pic quotes mean/.code={\def\tikz@pic@quotes@as##1##2{#1}}, + quotes mean pin/.style={node quotes mean={ + pin={[direction shorthands,every pin quotes/.try,##2]##1}}}, + quotes mean label/.style={node quotes mean={ + label={[direction shorthands,every label quotes/.try,##2]##1}}}, + quotes mean label, + edge quotes mean={edge node={node [every edge quotes,#2]{#1}}}, + pic quotes mean={pic text={#1},pic text options={every pic quotes/.try,#2}}, + every edge quotes/.style={auto}, + direction shorthands/.code={% + \pgfkeyslet{/tikz/centered/.@cmd}\tikz@label@@centered + \pgfkeyslet{/tikz/above/.@cmd}\tikz@label@@above + \pgfkeyslet{/tikz/below/.@cmd}\tikz@label@@below + \pgfkeyslet{/tikz/left/.@cmd}\tikz@label@@left + \pgfkeyslet{/tikz/right/.@cmd}\tikz@label@@right + \pgfkeyslet{/tikz/above left/.@cmd}\tikz@label@@above@left + \pgfkeyslet{/tikz/above right/.@cmd}\tikz@label@@above@right + \pgfkeyslet{/tikz/below left/.@cmd}\tikz@label@@below@left + \pgfkeyslet{/tikz/below right/.@cmd}\tikz@label@@below@right + } +}% + +\def\tikz@label@@centered#1\pgfeov{\pgfkeysalso{label position=center,pin position=center}}% +\def\tikz@label@@above#1\pgfeov{\pgfkeysalso{label position=90,pin position=90}}% +\def\tikz@label@@below#1\pgfeov{\pgfkeysalso{label position=-90,pin position=-90}}% +\def\tikz@label@@left#1\pgfeov{\pgfkeysalso{label position=180,pin position=180}}% +\def\tikz@label@@right#1\pgfeov{\pgfkeysalso{label position=0,pin position=0}}% +\def\tikz@label@@above@left#1\pgfeov{\pgfkeysalso{label position=135,pin position=135}}% +\def\tikz@label@@below@left#1\pgfeov{\pgfkeysalso{label position=-135,pin position=-135}}% +\def\tikz@label@@above@right#1\pgfeov{\pgfkeysalso{label position=45,pin position=45}}% +\def\tikz@label@@below@right#1\pgfeov{\pgfkeysalso{label position=-45,pin position=-45}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryrdf.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryrdf.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3512fa15f6caac6c11065361a652e05ae0b2799e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryrdf.code.tex @@ -0,0 +1,257 @@ + +\ProvidesFileRCS{tikzlibraryrdf.code.tex} + + + +\def\tikz@add@rdf@pre@option#1{\expandafter\def\expandafter\tikz@rdf@pre@options\expandafter{\tikz@rdf@pre@options#1}}% +\def\tikz@add@rdf@post@option#1{\expandafter\def\expandafter\tikz@rdf@post@options\expandafter{\tikz@rdf@post@options#1}}% + +\let\tikz@rdf@pre@options\pgfutil@empty +\let\tikz@rdf@post@options\pgfutil@empty + +\tikzset{ + rdf engine on/.code={% + \def\tikz@clear@rdf@options{\let\tikz@rdf@pre@options\pgfutil@empty\let\tikz@rdf@post@options\pgfutil@empty}% + \def\tikz@do@rdf@pre@options{\tikz@rdf@pre@options\let\tikz@rdf@pre@options\pgfutil@empty}% + \def\tikz@do@rdf@post@options{\tikz@rdf@post@options\let\tikz@rdf@post@options\pgfutil@empty}% + \pgfkeys{/tikz/rdf engine/.code=\tikz@add@rdf@pre@option{\pgfqkeys{/tikz/rdf engine}{##1}}}% + }, + rdf engine/.cd, + every statement/.style=, + prefix/.code=\pgfrdfprefix{#1}, + statement/.code={% + {% + \pgfkeys{/tikz/rdf engine/every statement}% + \pgfqkeys{/tikz/rdf engine/statements}{#1}% + \iftikz@rdf@is@a@container\tikz@rdf@init@container\fi% + \iftikz@rdf@is@a@member\tikz@rdf@make@member\fi% + \tikz@rdf@make@triple% + \expandafter}\tikz@rdf@action% + }, + get scope curie/.code={% + \ifx\tikz@id@name\pgfutil@empty% + \def\tikz@id@name{@rdf}% + \fi% + \pgfidrefnextuse\tikz@temp{\tikz@id@name}% + \edef#1{\tikzrdfhashmark\tikz@temp}% + }, + get new resource curie/.code={% + \pgfsys@new@id\tikz@temp% + \edef#1{\tikzrdfhashmark\tikz@temp}% + }, + scope is new context/.style={get scope curie=\tikzrdfcontext} +}% + +\def\tikzrdfcontext{\tikzrdfhashmark}% + +\tikzset{ + rdf engine/statements/.cd, + subject/.code={% + \def\tikz@rdf@target{\tikz@rdf@subject}% + \tikz@rdf@parse{#1}% + }, + predicate/.code={% + \def\tikz@rdf@target{\tikz@rdf@predicate}% + \tikz@rdf@parse{#1}% + }, + object/.code={% + \let\tikz@rdf@object@literal\relax% + \let\tikz@rdf@object\relax% + \def\tikz@temp{#1}% + \ifx\tikz@temp\tikz@rdf@current@scope@text% + \tikz@rdf@object@scope@contenttrue% + \else% + \tikz@rdf@object@scope@contentfalse% + \def\tikz@rdf@target{\tikz@rdf@object}% + \tikz@rdf@parse{#1}% + \fi% + }, + has type/.style={predicate=rdf:type,object={#1}}, + is a bag/.style={has type=rdf:Bag, is a container}, + is a sequence/.style={has type=rdf:Seq, is a container}, + is an alternative/.style={has type=rdf:Alt, is a container}, + is a container/.code={\tikz@rdf@is@a@containertrue}, + has as member/.code={\tikz@rdf@is@a@membertrue},% +}% + +\def\tikz@rdf@current@scope@text{scope content}% + +\let\tikz@rdf@subject\relax +\let\tikz@rdf@predicate\pgfutil@empty +\let\tikz@rdf@object\relax +\let\tikz@rdf@object@literal\relax +\let\tikz@rdf@container\relax + +\newif\iftikz@rdf@object@scope@content +\newif\iftikz@rdf@is@a@container +\newif\iftikz@rdf@is@a@member + + +\def\tikz@rdf@parse#1{% + \edef\tikz@temp{#1}% + \expandafter\tikz@rdf@parse@#1\relax% +}% + +\def\tikz@rdf@parse@{% + \pgfutil@ifnextchar({\tikz@rdf@parse@name}{% + \pgfutil@ifnextchar"{\tikz@rdf@parse@literals}{% + \tikz@rdf@parse@curie% + }% + }% +}% + +\def\tikz@rdf@parse@name(#1)\relax{% + \pgfidrefprevuse\tikz@rdf@the@id{#1}\expandafter\edef\tikz@rdf@target{\tikzrdfhashmark\tikz@rdf@the@id}% +}% +\def\tikz@rdf@parse@literals"#1"{% + \ifx\tikz@rdf@target\tikz@rdf@object@name% + \def\tikz@rdf@object@literal{#1}% + \else% + \tikzerror{Only RDF objects can be literals}% + \fi% + \pgfutil@ifnextchar\relax\pgfutil@gobble\tikz@rdf@parse@literals@rest% +}% +\def\tikz@rdf@parse@literals@rest and scope content\relax{% + \tikz@rdf@object@scope@contenttrue% +}% + +\def\tikz@rdf@object@name{\tikz@rdf@object}% +\def\tikz@rdf@parse@curie#1\relax{% + \expandafter\def\tikz@rdf@target{#1}% +}% + +{% + \catcode`\#=11 + \gdef\tikzrdfhashmark{#}% +}% + + +\def\tikz@rdf@make@triple{% + \ifx\tikz@rdf@subject\relax% + \tikzerror{RDF statement misses subject}% + \else% + \ifx\tikz@rdf@predicate\relax% + \tikzerror{RDF statement misses predicate}% + \else% + \iftikz@rdf@object@scope@content% + \edef\tikz@marshal{\noexpand\tikz@rdf@make@content@triple{\tikz@rdf@subject}{\tikz@rdf@predicate}{\tikz@rdf@object@literal}}% + \tikz@marshal% + \else% + \ifx\tikz@rdf@object\relax% + \ifx\tikz@rdf@object@literal\relax% + \tikzerror{RDF statement misses object}% + \else% + \edef\tikz@marshal{\noexpand\tikz@rdf@make@literal@triple{\tikz@rdf@subject}{\tikz@rdf@predicate}{\tikz@rdf@object@literal}}% + \tikz@marshal% + \fi% + \else% + \edef\tikz@marshal{\noexpand\tikz@rdf@make@normal@triple{\tikz@rdf@subject}{\tikz@rdf@predicate}{\tikz@rdf@object}}% + \tikz@marshal% + \fi% + \fi% + \fi% + \fi% +}% + +\def\tikz@rdf@make@content@triple#1#2#3{% + \def\tikz@rdf@action{% + \def\tikz@rdf@invoke@code{% + \def\tikz@temp{#3}% + \ifx\tikz@temp\tikz@rdf@object@literal@text\else% + \pgfrdfcontent{#3}% + \fi% + \pgfrdfabout{#1}% + \pgfrdfdatatype{rdf:XMLLiteral}% + \foreach \tikz@rdf@pred in {#2}{% + \ifx\tikz@rdf@pred\pgfutil@empty\else% + \expandafter\pgfrdfproperty\expandafter{\tikz@rdf@pred}% + \fi% + }% + }% + }% +}% + +\def\tikz@rdf@make@literal@triple#1#2#3{% + \def\tikz@rdf@action{% + \tikz@add@rdf@post@option{% + {% + \pgfrdfabout{#1}% + \foreach \tikz@rdf@pred in {#2}{% + \ifx\tikz@rdf@pred\pgfutil@empty\else% + \expandafter\pgfrdfproperty\expandafter{\tikz@rdf@pred}% + \fi% + }% + \pgfrdfcontent{#3}% + \pgfidscope% + \endpgfidscope% + }% + }% + }% +}% + +\def\tikz@rdf@make@normal@triple#1#2#3{% + \def\tikz@rdf@action{% + \tikz@add@rdf@post@option{% + {% + \pgfrdfabout{#1}% + \foreach \tikz@rdf@pred in {#2}{% + \ifx\tikz@rdf@pred\pgfutil@empty\else% + \expandafter\pgfrdfproperty\expandafter{\tikz@rdf@pred}% + \fi% + }% + \pgfrdfresource{#3}% + \pgfidscope% + \endpgfidscope% + }% + }% + }% +}% + +\def\tikz@rdf@object@literal@text{\tikz@rdf@object@literal}% + + + + + +\def\tikz@rdf@init@container{% + \ifx\tikz@rdf@subject\relax% + \tikzerror{RDF statement misses subject}% + \else% + \expandafter\gdef\csname tikz@rdf@c@\tikz@rdf@subject\endcsname{0}% + \fi% +}% + + +\def\tikz@rdf@make@member{% + \ifx\tikz@rdf@subject\relax% + \tikzerror{RDF statement misses subject}% + \else% + \expandafter\let\expandafter\tikz@temp\csname tikz@rdf@c@\tikz@rdf@subject\endcsname% + \ifx\tikz@temp\relax% + \tikzerror{RDF subject is not a container}% + \else% + \c@pgf@counta\tikz@temp% + \advance\c@pgf@counta by1\relax% + \expandafter\xdef\csname tikz@rdf@c@\tikz@rdf@subject\endcsname{\the\c@pgf@counta}% + \edef\tikz@rdf@predicate{rdf:_\the\c@pgf@counta}% + \fi% + \fi% +}% + + + + + + +\let\tikz@rdf@invoke@code\relax + +\def\tikz@rdf@id@hook{% + \tikz@rdf@invoke@code% + \let\tikz@rdf@invoke@code\relax% +}% + +\expandafter\def\expandafter\tikz@id@hook\expandafter{\tikz@id@hook\tikz@rdf@id@hook}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryscopes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryscopes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..43636ddd24b431b4bfb75f0c04985b57d1525b94 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryscopes.code.tex @@ -0,0 +1,32 @@ + +\ProvidesFileRCS{tikzlibraryscopes.code.tex} + + +\def\tikz@lib@scope@check{% + \pgfutil@ifnextchar\tikz@intersect@finish{% + \tikz@intersect@finish\afterassignment\tikz@lib@scope@check\let\tikz@next% + }{% + \pgfutil@ifnextchar\par{% + \afterassignment\tikz@lib@scope@check\let\tikz@next% + }% + {\pgfutil@ifnextchar\bgroup{% + \afterassignment\tikz@lib@scope@gotcha\let\tikz@next% + }% + {}% + }% + }% +}% + +\def\tikz@lib@scope@gotcha{% + \pgfutil@ifnextchar[{% + \tikz@lib@scope@action% + }{% + \bgroup% + }% +}% +\def\tikz@lib@scope@action[#1]{% + \scope[#1]\bgroup\aftergroup\endscope% + \tikz@lib@scope@check% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshadings.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshadings.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..0ab6173b1f2f3b969ce3b0dadb54358124214487 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshadings.code.tex @@ -0,0 +1,13 @@ + +\ProvidesFileRCS{tikzlibraryshadings.code.tex} + +\usepgflibrary{shadings}% + +\tikzset{ + lower left/.style={shading=bilinear interpolation,/utils/exec=\colorlet{lower left}{#1}}, + upper left/.style={shading=bilinear interpolation,/utils/exec=\colorlet{upper left}{#1}}, + lower right/.style={shading=bilinear interpolation,/utils/exec=\colorlet{lower right}{#1}}, + upper right/.style={shading=bilinear interpolation,/utils/exec=\colorlet{upper right}{#1}} +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshadows.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshadows.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..d70a06abc3a0d80672d2b34d73bf1caa5007ac10 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshadows.code.tex @@ -0,0 +1,121 @@ + +\ProvidesFileRCS{tikzlibraryshadows.code.tex} + +\usetikzlibrary{fadings}% + + +\tikzset{ + /tikz/shadow scale/.initial=1, + /tikz/shadow xshift/.initial=0pt, + /tikz/shadow yshift/.initial=0pt, +}% + +\tikzset{ + general shadow/.style={ + preaction={ + #1, + transform canvas={ + scale around=\pgfkeysvalueof{/tikz/shadow scale}:(current path bounding box.center), + shift={(\pgfkeysvalueof{/tikz/shadow xshift},\pgfkeysvalueof{/tikz/shadow yshift})} + }, + } + }, + every shadow/.style={} +}% + + + + +\tikzset{ + /tikz/drop shadow/.style={ + general shadow={% + shadow scale=1, + shadow xshift=.5ex, + shadow yshift=-.5ex, + opacity=.5, + fill=black!50, + every shadow, + #1 + } + } +}% + + + +\tikzset{ + /tikz/circular drop shadow/.style={ + general shadow={% + shadow scale=1.1, + shadow xshift=.3ex, + shadow yshift=-.3ex, + fill=black!50, + path fading={circle with fuzzy edge 15 percent}, + every shadow, + #1 + } + } +}% + + + + +\tikzset{ + /tikz/circular glow/.style={ + general shadow={% + shadow scale=1.25, + shadow xshift=0pt, + shadow yshift=0pt, + fill=black!50, + path fading={circle with fuzzy edge 15 percent}, + every shadow, + #1, + } + } +}% + + + + + + +\tikzset{ + /tikz/copy shadow/.style={ + general shadow={% + /utils/exec={\let\tikz@lib@shadow@fill=\tikz@fillcolor\let\tikz@lib@shadow@draw=\tikz@strokecolor}, + shadow scale=1, + shadow xshift=.5ex, + shadow yshift=.5ex, + fill=\tikz@lib@shadow@fill, + draw=\tikz@lib@shadow@draw, + every shadow, + #1 + } + } +}% + + + +\tikzset{ + /tikz/double copy shadow/.style={ + general shadow={% + /utils/exec={\let\tikz@lib@shadow@fill=\tikz@fillcolor\let\tikz@lib@shadow@draw=\tikz@strokecolor}, + shadow scale=1, + shadow xshift=.5ex, + shadow yshift=.5ex, + fill=\tikz@lib@shadow@fill, + draw=\tikz@lib@shadow@draw, + #1, + shadow xshift/.expanded=2*\pgfkeysvalueof{/tikz/shadow xshift}, + shadow yshift/.expanded=2*\pgfkeysvalueof{/tikz/shadow yshift}, + }, + general shadow={% + /utils/exec={\let\tikz@lib@shadow@fill=\tikz@fillcolor\let\tikz@lib@shadow@draw=\tikz@strokecolor}, + shadow scale=1, + shadow xshift=.5ex, + shadow yshift=.5ex, + fill=\tikz@lib@shadow@fill, + draw=\tikz@lib@shadow@draw, + #1, + }, + } +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.arrows.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.arrows.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..1f4f033eca50cd1d16b5a40486b478b7f72153be --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.arrows.code.tex @@ -0,0 +1,8 @@ + +\ProvidesFileRCS{tikzlibraryshapes.arrows.code.tex} + +\usepgflibrary{shapes.arrows}% + +\pgfkeys{/tikz/arrow box arrows/.code={\pgf@lib@arrowbox@parsearrows{#1}}}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.callouts.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.callouts.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..af8cf41c0406dab988ebfd0b40c2648a34a12f80 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.callouts.code.tex @@ -0,0 +1,27 @@ + +\usepgflibrary{shapes.callouts}% + +\pgfkeys{/tikz/callout absolute pointer/.code={% + \tikz@scan@one@point\tikz@lib@callout@checkforplus#1\relax% + }% +}% + +\def\tikz@lib@callout@checkforplus#1{% + \pgfutil@ifnextchar+{\def\tikz@lib@callout@originalpoint{#1}\tikz@lib@callout@scan@relative}% + {\pgf@lib@callout@makeabsolutepointer{#1}}}% + +\def\tikz@lib@callout@scan@relative+{% + \pgfutil@ifnextchar+{\tikz@lib@callout@scan@plusplus}{\tikz@lib@callout@scan@plus}}% +\def\tikz@lib@callout@scan@plusplus+{\tikz@scan@one@point\tikz@lib@callout@add}% +\def\tikz@lib@callout@scan@plus{\tikz@scan@one@point\tikz@lib@callout@add}% +\def\tikz@lib@callout@add#1{% + \expandafter\pgf@lib@callout@makeabsolutepointer\expandafter{% + \expandafter\pgfpointadd\expandafter{\tikz@lib@callout@originalpoint}{#1}}% +}% + +\pgfkeys{/tikz/callout relative pointer/.code={% + \tikz@scan@one@point\pgf@lib@callout@makerelativepointer#1\relax% + }% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..94c0aa296e3c9ebeeb6beccd3d6604e4ed101d70 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.code.tex @@ -0,0 +1,11 @@ + +\ProvidesFileRCS{tikzlibraryshapes.code.tex} + +\usetikzlibrary{shapes.geometric}% +\usetikzlibrary{shapes.misc}% +\usetikzlibrary{shapes.symbols}% +\usetikzlibrary{shapes.arrows}% +\usetikzlibrary{shapes.callouts}% +\usetikzlibrary{shapes.multipart}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.gates.logic.IEC.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.gates.logic.IEC.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..c124b93586ca67320cc57541d8947785ff3e9fa8 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.gates.logic.IEC.code.tex @@ -0,0 +1,30 @@ + +\ProvidesFileRCS{tikzlibraryshapes.gates.logic.IEC.code.tex} + +\usepgflibrary{shapes.gates.logic.IEC}% + +\tikzset{% + use IEC style logic gates/.code={% + \tikzset{% + and gate/.style={shape=and gate IEC}, + nand gate/.style={shape=nand gate IEC}, + or gate/.style={shape=or gate IEC}, + nor gate/.style={shape=nor gate IEC}, + xor gate/.style={shape=xor gate IEC}, + xnor gate/.style={shape=xnor gate IEC}, + not gate/.style={shape=not gate IEC}, + buffer gate/.style={shape=buffer gate IEC}, + and gate symbol/.style={and gate IEC symbol={##1}}, + nand gate symbol/.style={nand gate IEC symbol={##1}}, + or gate symbol/.style={or gate IEC symbol={##1}}, + nor gate symbol/.style={nor gate IEC symbol={##1}}, + xor gate symbol/.style={xor gate IEC symbol={##1}}, + xnor gate symbol/.style={xnor gate IEC symbol={##1}}, + not gate symbol/.style={not gate IEC symbol={##1}}, + buffer gate symbol/.style={buffer gate IEC symbol={##1}}, + logic gate symbol align/.style={/pgf/logic gate IEC symbol align={##1}}, + logic gate symbol color/.style={/pgf/logic gate IEC symbol color={##1}} + }% + }% +}% +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.gates.logic.US.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.gates.logic.US.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..33cd782cb1c113500aa8de748d91d2a11a9c5438 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.gates.logic.US.code.tex @@ -0,0 +1,32 @@ + +\ProvidesFileRCS{tikzlibraryshapes.gates.logic.US.code.tex} + +\usepgflibrary{shapes.gates.logic.US}% + +\tikzset{% + use US style logic gates/.code={% + \tikzset{% + and gate/.style={shape=and gate US}, + nand gate/.style={shape=nand gate US}, + or gate/.style={shape=or gate US}, + nor gate/.style={shape=nor gate US}, + xor gate/.style={shape=xor gate US}, + xnor gate/.style={shape=xnor gate US}, + not gate/.style={shape=not gate US}, + buffer gate/.style={shape=buffer gate US} + }% + }, + use CDH style logic gates/.code={% + \tikzset{% + and gate/.style={shape=and gate CDH}, + nand gate/.style={shape=nand gate CDH}, + or gate/.style={shape=or gate US}, + nor gate/.style={shape=nor gate US}, + xor gate/.style={shape=xor gate US}, + xnor gate/.style={shape=xnor gate US}, + not gate/.style={shape=not gate US}, + buffer gate/.style={shape=buffer gate US} + } + } +}% +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.geometric.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.geometric.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..7d96e1301c8242bce0f5ea6e26d6f1c53dba351f --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.geometric.code.tex @@ -0,0 +1,6 @@ + +\ProvidesFileRCS{tikzlibraryshapes.geometric.code.tex} + +\usepgflibrary{shapes.geometric}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.misc.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.misc.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ea924e8b37db28d4155f37176324f139837ccb8a --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.misc.code.tex @@ -0,0 +1,6 @@ + +\ProvidesFileRCS{tikzlibraryshapes.misc.code.tex} + +\usepgflibrary{shapes.misc}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..eb513d5e78bc0baf351c8e32661f2f0751b664c7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.multipart.code.tex @@ -0,0 +1,28 @@ + +\ProvidesFileRCS{tikzlibraryshapes.multipart.code.tex} + +\usepgflibrary{shapes.multipart}% + +\pgfkeys{/tikz/rectangle split/parts/.code={% + \pgfkeys{/pgf/rectangle split parts={#1}}% + }% +}% + +\pgfkeys{/tikz/rectangle split use custom fill/.code={% + \pgfkeys{/pgf/rectangle split use custom fill={#1}}% + \pgfkeys{/tikz/fill=none}}% +}% + +\pgfkeys{/tikz/rectangle split draw splits/.is if=pgfrectanglesplitdrawsplits}% + +\pgfkeys{/tikz/rectangle split part align/.code={% + \pgfkeys{/pgf/rectangle split part align={#1}}% + }% +}% + +\pgfkeys{/tikz/rectangle split part fill/.code={% + \pgfkeys{/pgf/rectangle split part fill={#1}}% + }% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.symbols.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.symbols.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..34df509277ed87828ade663043ed095c9046e48a --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryshapes.symbols.code.tex @@ -0,0 +1,9 @@ + +\ProvidesFileRCS{tikzlibraryshapes.symbols.code.tex} + +\pgfkeysifdefined{/tikz/shape border uses incircle}{}{% + \pgfkeys{/tikz/shape border uses incircle/.is if=pgfshapeborderusesincircle}}% + +\usepgflibrary{shapes.symbols}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysnakes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysnakes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..bd026a5b9b4a7bf066e4b0262b018dcc086f8de7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysnakes.code.tex @@ -0,0 +1,68 @@ + +\ProvidesFileRCS{tikzlibrarysnakes.code.tex} + +\pgfwarning{Snakes have been superseded by +decorations. Please use the decoration libraries instead of the snakes +library}% + +\usetikzlibrary{decorations.pathmorphing,decorations.pathreplacing,decorations.shapes}% + + + +\tikzoption{snake}[]{% + \def\tikz@@snake{#1}% + \ifx\tikz@@snake\pgfutil@empty% + \tikz@snakedtrue% + \else% + \ifx\tikz@@snake\tikz@nonetext% + \tikz@snakedfalse% + \else% + \tikz@snakedtrue% + \let\tikz@snake=\tikz@@snake% + \fi% + \fi}% + +\tikzoption{raise snake}{\def\pgf@snake@raise{\pgftransformyshift{#1}}}% +\tikzoption{mirror snake}[true]{% + \csname if#1\endcsname + \def\pgf@snake@mirror{\pgftransformyscale{-1}}% + \else% + \let\pgf@snake@mirror=\pgfutil@empty% + \fi +}% + +\tikzoption{gap before snake}{\def\tikz@presnake{{moveto}{#1}{\noexpand\tikz@snake@install@trans}{}}}% +\tikzoption{line before snake}{\def\tikz@presnake{{lineto}{#1}{\noexpand\tikz@snake@install@trans}{}}}% + +\tikzoption{gap after snake}{\def\tikz@postsnake{{moveto}{#1}{\noexpand\tikz@snake@install@trans}{}}\def\tikz@mainsnakelength{\pgfsnakeremainingdistance-#1}}% +\tikzoption{line after snake}{\def\tikz@postsnake{{lineto}{#1}{\noexpand\tikz@snake@install@trans}{}}\def\tikz@mainsnakelength{\pgfsnakeremainingdistance-#1}}% + +\tikzoption{gap around snake}{% + \def\tikz@presnake{{moveto}{#1}{\noexpand\tikz@snake@install@trans}{}}% + \def\tikz@postsnake{{moveto}{#1}{\noexpand\tikz@snake@install@trans}{}}% + \def\tikz@mainsnakelength{\pgfsnakeremainingdistance-#1}% +}% +\tikzoption{line around snake}{% + \def\tikz@presnake{{lineto}{#1}{\noexpand\tikz@snake@install@trans}{}}% + \def\tikz@postsnake{{lineto}{#1}{\noexpand\tikz@snake@install@trans}{}}% + \def\tikz@mainsnakelength{\pgfsnakeremainingdistance-#1}% +}% +\let\pgf@snake@mirror=\pgfutil@empty +\let\pgf@snake@raise=\pgfutil@empty + +\def\tikz@snake@install@trans{\pgfsetsnakesegmenttransformation{\pgf@snake@mirror\pgf@snake@raise}}% + +\def\tikz@snake{zigzag}% + +\let\tikz@presnake=\pgfutil@empty +\let\tikz@postsnake=\pgfutil@empty +\def\tikz@mainsnakelength{\pgfsnakeremainingdistance}% + + +\tikzset{snake triangles 45/.style= {snake=triangles,segment object length=2.41421356\pgfsnakesegmentamplitude}}% +\tikzset{snake triangles 60/.style= {snake=triangles,segment object length=1.73205081\pgfsnakesegmentamplitude}}% +\tikzset{snake triangles 90/.style= {snake=triangles,segment object length=\pgfsnakesegmentamplitude}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryspy.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryspy.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..d8917c407014c7b3a18a3552ecb511a3a3605f8d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryspy.code.tex @@ -0,0 +1,125 @@ + +\ProvidesFileRCS{tikzlibraryspy.code.tex} + + + + +\tikzset{ + spy using outlines/.style={ + spy scope={ + every spy on node/.style={very thin,draw}, + every spy in node/.style={thick,draw}, + #1 + } + }, + spy using overlays/.style={ + spy scope={ + every spy on node/.style={fill,fill opacity=0.2,text opacity=1}, + every spy in node/.style={fill,fill opacity=0.2,text opacity=1}, + #1 + } + }, + connect spies/.style={ + spy connection path={\draw[thin] (tikzspyonnode) -- (tikzspyinnode);} + } +}% + +\newbox\tikz@lib@spybox + +\let\tikz@lib@spy@collection=\pgfutil@empty% + +\tikzset{spy scope/.style={ + size/.style={minimum size={##1}}, + height/.style={minimum height={##1}}, + width/.style={minimum width={##1}}, + execute at begin scope={% + \let\tikz@lib@spy@save=\tikz@lib@spy@collection% + \setbox\tikz@lib@spybox=\hbox\bgroup\bgroup% + \let\spy=\tikz@lib@spy@parse}, + execute at end scope={% + \egroup\egroup% + {% + \copy\tikz@lib@spybox% + \tikz@lib@spy@collection% + }% + \global\let\tikz@lib@spy@collection=\tikz@lib@spy@save% + },% + tikz@lib@spy@style/.style={#1}, + tikz@lib@reset@gs + }, + lens/.store in=\tikz@lib@spy@lens, + lens=, + magnification/.style={lens={scale={#1}}}, + spy connection path/.store in=\tikz@lib@spy@path, + spy connection path= +}% + +\tikzset{ + tikz@lib@reset@gs/.style={black,thin,solid,opaque,line cap=butt,line join=miter} +}% + +\def\tikz@lib@spy@parse{% + \pgfutil@ifnextchar[{\tikz@lib@spy@parse@opt}{\tikz@lib@spy@parse@opt[]}% +}% +\def\tikz@lib@spy@parse@opt[#1]{ + \pgfutil@ifnextchar x{\tikz@lib@spy@parse@opta[#1]}{\tikz@lib@spy@parse@opta[#1]}% +}% +\def\tikz@lib@spy@parse@opta[#1]on#2in node#3;{% + \pgfutil@g@addto@macro\tikz@lib@spy@collection{\tikz@lib@spy@do{#1}{#2}{#3}}% +}% + +\def\tikz@lib@spy@do#1#2#3{% + \scope[tikz@lib@spy@style,#1] + \node [alias=tikzspyonnode,inner sep=0pt,outer sep=0pt,every spy on node/.try, + /utils/exec={ + {% + \let\tikz@transform=\relax + \pgftransformreset% + \expandafter\tikzset\expandafter{\tikz@lib@spy@lens} + \pgftransforminvert% + \pgfgettransformentries\a\b\c\d\e\f% + \global\let\pgf@lib@svg@a=\a% + \global\let\pgf@lib@svg@b=\b% + \global\let\pgf@lib@svg@c=\c% + \global\let\pgf@lib@svg@d=\d% + }% + \tikz@addtransform{% + \tikz@scan@one@point\pgftransformshift#2% + \pgftransformcm{\pgf@lib@svg@a}{\pgf@lib@svg@b}{\pgf@lib@svg@c}{\pgf@lib@svg@d}{\pgfpointorigin}% + } + }]{}; + \expandafter\pgfutil@switch\expandafter\pgfutil@ifstrequal\expandafter{\tikz@anchor}{% + {north} {\def\tikz@spy@anchor{south}}% + {north east}{\def\tikz@spy@anchor{south west}}% + {east} {\def\tikz@spy@anchor{west}}% + {south east}{\def\tikz@spy@anchor{north west}}% + {south} {\def\tikz@spy@anchor{north}}% + {south west}{\def\tikz@spy@anchor{north east}}% + {west} {\def\tikz@spy@anchor{east}}% + {north west}{\def\tikz@spy@anchor{south east}}% + }{}{\def\tikz@spy@anchor{center}}% + \node [alias=tikzspyinnode,inner sep=0pt,outer sep=0pt,at={#2},every spy in node/.try, + path picture={\node[anchor=\tikz@spy@anchor,tikz@lib@reset@gs]{\nullfont% + \pgfpicture\relax\pgfsetbaseline{default}\pgfsettrimleft{default}\pgfsettrimright{default}% + \pgftransformreset% + \let\tikz@transform=\relax% + \expandafter\tikzset\expandafter{\tikz@lib@spy@lens}% + \pgflowlevelsynccm% + \tikz@scan@one@point\tikz@lib@spy@shift#2% + \pgflowlevelsynccm% + \copy\tikz@lib@spybox% + \endpgfpicture};}]#3{}; + \tikz@lib@spy@path + \endscope +}% + +\def\tikz@lib@spy@shift#1{% + \pgf@process{#1}% + \pgf@x=-\pgf@x% + \pgf@y=-\pgf@y% + \pgftransformshift{}% +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysvg.path.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysvg.path.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..2888c1e64c238a5f1dad837bb866feda508b28b0 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarysvg.path.code.tex @@ -0,0 +1,25 @@ + +\ProvidesFileRCS{tikzlibrarysvg.path.code.tex} + +\usepgflibrary{svg.path}% + +\def\tikz@svg@path vg{\pgfutil@ifnextchar[\tikz@svg@@path{\tikz@svg@@path[]}}% + +\def\tikz@svg@@path[#1]{\pgfutil@ifnextchar"{\tikz@svg@@path@old{#1}}{\tikz@svg@@path@new{#1}}}% +\def\tikz@svg@@path@new#1#2{\tikz@svg@@path@old{#1}"#2"}% +\def\tikz@svg@@path@old#1"#2"{ + {% + \tikzset{#1}% + \pgfpathsvg{#2}% + }% + { + \pgftransforminvert + \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@path@lastx}{\pgf@path@lasty}}} + } + \tikz@lastx=\pgf@x% + \tikz@lasty=\pgf@y% + \tikz@lastxsaved=\tikz@lastx% + \tikz@lastysaved=\tikz@lasty% + \tikz@updatecurrenttrue% + \tikz@scan@next@command +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarythrough.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarythrough.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..6bffd70293b45274955247f22e6c3d34832212d3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarythrough.code.tex @@ -0,0 +1,27 @@ + +\ProvidesFileRCS{tikzlibrarythrough.code.tex} + + + +\tikzset{circle through/.code={% + \pgfkeysalso{shape=circle,inner sep=0pt,outer sep=0pt}% + \pgfgettransform{\tikz@lib@saved@transform}% + \tikz@scan@one@point\tikz@lib@circle@through#1% + }}% + +\def\tikz@lib@circle@through#1{% + \tikz@addoption{% + {% + \pgfsettransform{\tikz@lib@saved@transform}% + \pgf@process{\pgfpointtransformed{#1}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointtransformed{\tikz@node@at}}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgfmathparse{2*veclen(\the\pgf@xa,\the\pgf@ya)}% + \global\let\tikz@lib@circle@size=\pgfmathresult% + }% + \pgfset{/pgf/minimum size/.expanded=\tikz@lib@circle@size}% + }% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e337077c18fe6c57c751057be8d10c286a65c396 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex @@ -0,0 +1,347 @@ + +\ProvidesFileRCS{tikzlibrarytopaths.code.tex} + + + +\tikzset{move to/.style= {to path={(\tikztotarget) \tikztonodes}}} + + + +\tikzset{line to/.style= {to path={-- (\tikztotarget) \tikztonodes}}} + + + +\tikzset{every curve to/.style= {}} +\tikzset{curve to/.style= {to path=\tikz@to@curve@path}} + +\tikzoption{bend angle}{\pgfmathsetmacro\tikz@to@bend{#1}} + +\tikzoption{bend left}[]{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgfmathsetmacro\tikz@to@bend{#1}% + \fi% + \let\tikz@to@out=\tikz@to@bend% + \pgfmathsetmacro\tikz@to@in{180-(\tikz@to@out)}% + \tikz@to@switch@on% + \tikz@to@relativetrue% +} + +\tikzoption{bend right}[]{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgfmathsetmacro\tikz@to@bend{#1}% + \fi% + \pgfmathsetmacro\tikz@to@out{-(\tikz@to@bend)} + \pgfmathsetmacro\tikz@to@in{180-(\tikz@to@out)} + \tikz@to@switch@on% + \tikz@to@relativetrue% +} + +\tikzoption{relative}[true]{\csname tikz@to@relative#1\endcsname} +\newif\iftikz@to@relative +\tikz@to@relativefalse + +\tikzoption{in}{\def\tikz@to@in{#1}\tikz@to@switch@on} +\tikzoption{out}{\def\tikz@to@out{#1}\tikz@to@switch@on} + +\tikzoption{in looseness}{\tikz@to@set@in@looseness{#1}} +\tikzoption{out looseness}{\tikz@to@set@out@looseness{#1}} +\tikzoption{looseness}{\tikz@to@set@in@looseness{#1}\tikz@to@set@out@looseness{#1}} + +\tikzoption{in control}{\tikz@to@set@in@control{#1}} +\tikzoption{out control}{\tikz@to@set@out@control{#1}} +\tikzoption{controls}{\tikz@to@parse@controls#1\pgf@stop} + +\tikzoption{in min distance}{\tikz@to@set@distances{#1}{}{}{}} +\tikzoption{in max distance}{\tikz@to@set@distances{}{#1}{}{}} +\tikzoption{in distance}{\tikz@to@set@distances{#1}{#1}{}{}} +\tikzoption{out min distance}{\tikz@to@set@distances{}{}{#1}{}} +\tikzoption{out max distance}{\tikz@to@set@distances{}{}{}{#1}} +\tikzoption{out distance}{\tikz@to@set@distances{}{}{#1}{#1}} +\tikzoption{min distance}{\tikz@to@set@distances{#1}{}{#1}{}} +\tikzoption{max distance}{\tikz@to@set@distances{}{#1}{}{#1}} +\tikzoption{distance}{\tikz@to@set@distances{#1}{#1}{#1}{#1}} + +\def\tikz@to@set@distances#1#2#3#4{% + \tikz@to@setifnotempy{#1}{\tikz@to@in@min}{\let\tikz@to@end@compute=\tikz@to@end@compute@looseness}% + \tikz@to@setifnotempy{#2}{\tikz@to@in@max}{\let\tikz@to@end@compute=\tikz@to@end@compute@looseness}% + \tikz@to@setifnotempy{#3}{\tikz@to@out@min}{\let\tikz@to@start@compute=\tikz@to@start@compute@looseness}% + \tikz@to@setifnotempy{#4}{\tikz@to@out@max}{\let\tikz@to@start@compute=\tikz@to@start@compute@looseness}% + \tikz@to@switch@on% +} + +\def\tikz@to@setifnotempy#1#2#3{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty\else\def#2{#1}#3\fi% +} + + +\def\tikz@to@set@in@looseness#1{% + \pgfmathsetmacro\tikz@to@in@looseness{#1}% + \let\tikz@to@end@compute=\tikz@to@end@compute@looseness% + \tikz@to@switch@on% +} +\def\tikz@to@set@out@looseness#1{% + \pgfmathsetmacro\tikz@to@out@looseness{#1}% + \let\tikz@to@start@compute=\tikz@to@start@compute@looseness% + \tikz@to@switch@on% +} + +\def\tikz@to@parse@controls#1and#2\pgf@stop{\tikz@to@set@in@control{#2}\tikz@to@set@out@control{#1}} + +\def\tikz@to@set@in@control#1{% + \def\tikz@to@in@control{#1}% + \let\tikz@to@end@compute=\tikz@to@end@compute@control% + \tikz@to@switch@on% +} +\def\tikz@to@set@out@control#1{% + \def\tikz@to@out@control{#1}% + \let\tikz@to@start@compute=\tikz@to@start@compute@control% + \tikz@to@switch@on% +} + + +\def\tikz@to@bend{30} + +\def\tikz@to@out{45} +\def\tikz@to@in{135} + +\def\tikz@to@out@looseness{1} +\def\tikz@to@in@looseness{1} + +\def\tikz@to@in@min{0pt} +\def\tikz@to@in@max{10000pt} +\def\tikz@to@out@min{0pt} +\def\tikz@to@out@max{10000pt} + +\def\tikz@to@switch@on{\let\tikz@to@path=\tikz@to@curve@path} + +\def\tikz@to@curve@path{% + [every curve to] + \pgfextra{\iftikz@to@relative\tikz@to@compute@relative\else\tikz@to@compute\fi} + \tikz@computed@path + \pgfextra{\tikz@updatenexttrue\tikz@updatecurrenttrue}% + \tikztonodes% +} + +\def\tikz@to@modify#1#2{% + \pgfutil@ifundefined{pgf@sh@ns@#1} + {}% + {\edef#1{#1.#2}} +}% + +\def\tikz@to@compute{% + \let\tikz@tofrom=\tikztostart% + \let\tikz@toto=\tikztotarget% + \tikz@to@modify\tikz@tofrom\tikz@to@out% + \tikz@to@modify\tikz@toto\tikz@to@in% + \ifx\tikz@to@start@compute\tikz@to@start@compute@looseness% + \tikz@to@compute@distance% + \else% + \ifx\tikz@from@start@compute\tikz@to@start@compute@looseness% + \tikz@to@compute@distance% + \fi% + \fi% + \tikz@to@start@compute% + \tikz@to@end@compute% + \edef\tikz@computed@path{.. controls \tikz@computed@start and \tikz@computed@end .. (\tikztotarget)} +} + +\def\tikz@to@compute@distance{\tikz@scan@one@point\tikz@@to@compute@distance(\tikz@tofrom)} +\def\tikz@@to@compute@distance#1{% + \def\tikz@first@point{#1}% + \tikz@scan@one@point\tikz@@@to@compute@distance(\tikz@toto)} +\def\tikz@@@to@compute@distance#1{% + \iftikz@updatecurrent\else + \tikz@updatenextfalse + \fi + \def\tikz@second@point{#1}% + \tikz@to@compute@distance@main% +} +\def\tikz@to@compute@distance@main{% + \pgf@process{\pgfpointdiff{\tikz@first@point}{\tikz@second@point}}% + \ifdim\pgf@x<0pt\pgf@xa=-\pgf@x\else\pgf@xa=\pgf@x\fi% + \ifdim\pgf@y<0pt\pgf@ya=-\pgf@y\else\pgf@ya=\pgf@y\fi% + \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgf@xa}{\pgf@ya}}}% + \ifdim\pgf@x>\pgf@y% + \c@pgf@counta=\pgf@x% + \ifnum\c@pgf@counta=0\relax% + \else% + \divide\c@pgf@counta by 255\relax% + \pgf@xa=16\pgf@xa\relax% + \divide\pgf@xa by\c@pgf@counta% + \pgf@xa=16\pgf@xa\relax% + \fi% + \else% + \c@pgf@counta=\pgf@y% + \ifnum\c@pgf@counta=0\relax% + \else% + \divide\c@pgf@counta by 255\relax% + \pgf@ya=16\pgf@ya\relax% + \divide\pgf@ya by\c@pgf@counta% + \pgf@xa=16\pgf@ya\relax% + \fi% + \fi% + \pgf@x=0.3915\pgf@xa% + \pgf@xa=\tikz@to@out@looseness\pgf@x% + \pgf@xb=\tikz@to@in@looseness\pgf@x% + \pgfmathsetlength{\pgf@ya}{\tikz@to@out@min} + \ifdim\pgf@xa<\pgf@ya% + \pgf@xa=\pgf@ya% + \fi% + \pgfmathsetlength{\pgf@ya}{\tikz@to@out@max} + \ifdim\pgf@xa>\pgf@ya% + \pgf@xa=\pgf@ya% + \fi% + \pgfmathsetlength{\pgf@ya}{\tikz@to@in@min} + \ifdim\pgf@xb<\pgf@ya% + \pgf@xb=\pgf@ya% + \fi% + \pgfmathsetlength{\pgf@ya}{\tikz@to@in@max} + \ifdim\pgf@xb>\pgf@ya% + \pgf@xb=\pgf@ya% + \fi% +} + +\def\tikz@to@start@compute@looseness{% + \edef\tikz@computed@start{([shift=({\tikz@to@out}:\the\pgf@xa)]\tikz@tofrom)}% +} +\def\tikz@to@end@compute@looseness{% + \edef\tikz@computed@end{([shift=({\tikz@to@in}:\the\pgf@xb)]\tikz@toto)}% +} +\def\tikz@to@start@compute@control{% + \let\tikz@computed@start=\tikz@to@out@control% +} +\def\tikz@to@end@compute@control{% + \let\tikz@computed@end=\tikz@to@in@control% +} + +\let\tikz@to@start@compute=\tikz@to@start@compute@looseness% +\let\tikz@to@end@compute=\tikz@to@end@compute@looseness% + + + + + +\def\tikz@to@compute@relative{% + \tikz@scan@one@point\tikz@@to@compute@relative(\tikztostart)% +} +\def\tikz@@to@compute@relative#1{% + \def\tikz@tofrom{#1}% + \tikz@scan@one@point\tikz@@@to@compute@relative(\tikztotarget)% +} +\def\tikz@@@to@compute@relative#1{% + \def\tikz@toto{#1}% + \begingroup + \pgfutil@ifundefined{pgf@sh@ns@\tikztostart} + {% + \let\tikz@first@point=\tikz@tofrom% + \let\tikz@tostart@tikz=\pgfutil@empty + }% + {% + {% + \tikz@tofrom% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + {% + \pgftransformreset% + \pgftransformshift{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \pgftransformrotate{\tikz@to@out}% + \pgftransformshift{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}% + \pgf@process{\pgfpointtransformed{\tikz@toto}}% + }% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfpointshapeborder{\tikztostart}{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \xdef\tikz@tofrom@smuggle{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + }% + \let\tikz@first@point=\tikz@tofrom@smuggle% + \tikz@first@point% + \edef\tikz@tostart@tikz{(\the\pgf@x,\the\pgf@y)}% + }% + \pgfutil@ifundefined{pgf@sh@ns@\tikztotarget} + {% + \let\tikz@second@point=\tikz@toto% + }% + {% + {% + \tikz@toto% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + {% + \pgftransformreset% + \pgftransformshift{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \pgftransformrotate{180}% + \pgftransformrotate{\tikz@to@in}% + \pgftransformshift{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}% + \pgf@process{\pgfpointtransformed{\tikz@tofrom}}% + }% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfpointshapeborder{\tikztotarget}{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \xdef\tikz@toto@smuggle{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + }% + \let\tikz@second@point=\tikz@toto@smuggle% + }% + \tikz@second@point% + \edef\tikz@totarget@tikz{(\the\pgf@x,\the\pgf@y)}% + \tikz@to@compute@distance@main% + \edef\tikz@to@first@distance{\the\pgf@xa}% + \edef\tikz@to@second@distance{\the\pgf@xb}% + \pgftransformreset% + \pgf@process{\tikz@first@point}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@second@point}% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@y by-\pgf@ya% + \pgfpointnormalised{}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@xb=-\pgf@x% + \pgf@yb=-\pgf@y% + {% + \pgftransformshift{\tikz@first@point}% + \pgftransformcm{\pgf@sys@tonumber\pgf@xc}{\pgf@sys@tonumber\pgf@yc}{\pgf@sys@tonumber\pgf@yb}{\pgf@sys@tonumber\pgf@xc}% + {\pgfpointorigin}% + \pgf@process{\pgfpointtransformed{\pgfpointpolar{\tikz@to@out}{\tikz@to@first@distance}}}% + \xdef\tikz@computed@start{(\the\pgf@x,\the\pgf@y)}% + } + {% + \pgftransformshift{\tikz@second@point}% + \pgftransformcm{\pgf@sys@tonumber\pgf@xc}{\pgf@sys@tonumber\pgf@yc}{\pgf@sys@tonumber\pgf@yb}{\pgf@sys@tonumber\pgf@xc}% + {\pgfpointorigin}% + \pgf@process{\pgfpointtransformed{\pgfpointpolar{\tikz@to@in}{\tikz@to@second@distance}}}% + \xdef\tikz@computed@end{(\the\pgf@x,\the\pgf@y)}% + } + \xdef\tikz@computed@path{ + \tikz@tostart@tikz + .. controls \tikz@computed@start and \tikz@computed@end .. + \tikz@totarget@tikz}% + \endgroup +} + + + + +\tikzset{loop/.style= {to path={ + \pgfextra{\let\tikztotarget=\tikztostart} + [looseness=8,min distance=5mm,every loop] + \tikz@to@curve@path + }}} + +\tikzset{every loop/.style= {->,shorten >=1pt}} + +\tikzset{loop right/.style= {right,out=15,in=-15,loop}} +\tikzset{loop above/.style= {above,out=105,in=75,loop}} +\tikzset{loop left/.style= {left,out=195,in=165,loop}} +\tikzset{loop below/.style= {below,out=285,in=255,loop}} + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytrees.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytrees.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..dc4e123d5d3b361a6619b914c95ee2f1b69f0eaa --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibrarytrees.code.tex @@ -0,0 +1,92 @@ + +\ProvidesFileRCS{tikzlibrarytrees.code.tex} + + + + +\tikzoption{grow via three points}{\let\tikz@grow=\tikz@grow@three\tikz@parse@three#1}% + +\def\tikz@parse@three one child at#1(#2)#3and two children at#4(#5)#6and#7(#8){% + \def\tikz@tree@one@child{\tikz@scan@one@point\pgf@process(#2)} + \def\tikz@tree@left@child{\tikz@scan@one@point\pgf@process(#5)} + \def\tikz@tree@right@child{\tikz@scan@one@point\pgf@process(#8)} +}% + +\def\tikz@grow@three{% + \pgf@process{\tikz@tree@one@child}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@tree@left@child}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \pgf@process{\tikz@tree@right@child}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xc by-\pgf@xa% + \advance\pgf@yc by-\pgf@ya% + \advance\pgf@xc by-\pgf@xb% + \advance\pgf@yc by-\pgf@yb% + \advance\tikznumberofchildren by-1\relax% + \pgf@xb=\tikznumberofchildren\pgf@xb\relax% + \pgf@yb=\tikznumberofchildren\pgf@yb\relax% + \advance\tikznumberofcurrentchild by-1\relax% + \pgf@xc=\tikznumberofcurrentchild\pgf@xc\relax% + \pgf@yc=\tikznumberofcurrentchild\pgf@yc\relax% + \advance\pgf@xa by\pgf@xb% + \advance\pgf@xa by\pgf@xc% + \advance\pgf@ya by\pgf@yb% + \advance\pgf@ya by\pgf@yc% + \edef\pgf@temp{\noexpand\pgftransformshift{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}}% + \pgf@temp% +}% + + + + +\tikzset{ + grow cyclic/.style={ + edge from parent/.append style={reset cm}, + growth function=\tikz@grow@circle, + } +}% + +\tikzset{sibling angle/.initial=20}% + +\def\tikz@grow@circle{% + \pgftransformrotate{% + (\pgfkeysvalueof{/tikz/sibling angle})*(-.5-.5*\tikznumberofchildren+\tikznumberofcurrentchild)}% + \pgftransformxshift{\the\tikzleveldistance}% +}% + +\tikzoption{counterclockwise from}{\let\tikz@grow=\tikz@grow@circle@from\def\tikz@grow@circle@from@start{#1}}% + +\def\tikz@grow@circle@from{% + \pgftransformshift{\pgfpointpolar{\tikz@grow@circle@from@start+(\pgfkeysvalueof{/tikz/sibling angle})*(\tikznumberofcurrentchild-1)}{\the\tikzleveldistance}}% +}% + +\tikzoption{clockwise from}{\let\tikz@grow=\tikz@grow@circle@from@\def\tikz@grow@circle@from@start{#1}}% + +\def\tikz@grow@circle@from@{% + \pgftransformshift{\pgfpointpolar{\tikz@grow@circle@from@start-(\pgfkeysvalueof{/tikz/sibling angle})*(\tikznumberofcurrentchild-1)}{\the\tikzleveldistance}}% +}% + + + + +\tikzset{edge from parent fork down/.style= + {edge from parent path={(\tikzparentnode\tikzparentanchor) -- +(0pt,-.5\tikzleveldistance) -| (\tikzchildnode\tikzchildanchor)}}}% + +\tikzset{edge from parent fork up/.style= + {edge from parent path={(\tikzparentnode\tikzparentanchor) -- +(0pt,.5\tikzleveldistance) -| (\tikzchildnode\tikzchildanchor)}}}% + +\tikzset{edge from parent fork left/.style= + {edge from parent path={(\tikzparentnode\tikzparentanchor) -- +(-.5\tikzleveldistance,0pt) |- (\tikzchildnode\tikzchildanchor)}}}% + +\tikzset{edge from parent fork right/.style= + {edge from parent path={(\tikzparentnode\tikzparentanchor) -- +(.5\tikzleveldistance,0pt) |- (\tikzchildnode\tikzchildanchor)}}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryturtle.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryturtle.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..c8357dd072985626d39ecd5438b9d84bb27ac33e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryturtle.code.tex @@ -0,0 +1,65 @@ + +\ProvidesFileRCS{tikzlibraryturtle.code.tex} + + +\tikzset{turtle/.style={/tikz/turtle/.cd,#1}}% + +\tikzset{turtle/direction/.code=\gdef\tikz@lib@turtle@dir{#1},turtle/direction=90}% + +\tikzset{turtle/distance/.initial=1cm}% + +\tikzset{turtle/how/.style=}% + +\tikzset{turtle/home/.style={/tikz/insert path={(0,0) [turtle/direction=90]}}}% + +\tikzset{ + turtle/forward/.default=\pgfkeysvalueof{/tikz/turtle/distance}, + turtle/forward/.style={/tikz/insert path={to[/tikz/turtle/how]++({\tikz@lib@turtle@dir}:{#1})}} +}% + + + +\tikzset{ + turtle/back/.default=\pgfkeysvalueof{/tikz/turtle/distance}, + turtle/back/.style={turtle forward={-(#1)}} +}% + + + +\tikzset{ + turtle/left/.default=90, + turtle/left/.code={% + \pgfmathparse{(#1)+(\tikz@lib@turtle@dir)}% + \ifdim\pgfmathresult pt>360pt\relax% + \pgfmathparse{\pgfmathresult-360}% + \fi% + \global\let\tikz@lib@turtle@dir\pgfmathresult + } +}% + + +\tikzset{ + turtle/right/.default=90, + turtle/right/.code={% + \pgfmathparse{#1} + \pgfmathparse{(\tikz@lib@turtle@dir)-\pgfmathresult}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathparse{\pgfmathresult+360}% + \fi% + \global\let\tikz@lib@turtle@dir\pgfmathresult + } +}% + + +\tikzset{turtle/.cd, + fd/.style={forward={#1}}, + fd/.default=\pgfkeysvalueof{/tikz/turtle/distance}, + bk/.style={back={#1}}, + bk/.default=\pgfkeysvalueof{/tikz/turtle/distance}, + lt/.style={left={#1}}, + lt/.default=90, + rt/.style={right={#1}}, + rt/.default=90}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryviews.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryviews.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..83cef25f61f266664c4c6a583066222b6f73d5a3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/libraries/tikzlibraryviews.code.tex @@ -0,0 +1,37 @@ + +\ProvidesFileRCS{tikzlibraryviews.code.tex} + + +\tikzset{ + meet/.style={execute at begin scope={\tikz@lib@view@parse{meet}#1\pgf@stop},execute at end scope={\endpgfviewboxscope}}, + view/.style={meet = {#1}}, + slice/.style={execute at begin scope={\tikz@lib@view@parse{slice}#1\pgf@stop},execute at end scope={\endpgfviewboxscope}}, +}% + +\def\tikz@lib@view@parse#1#2\pgf@stop{% + \tikz@scan@one@point\tikz@lib@view@a#2\pgf@stop% + \pgfviewboxscope{\tikz@lib@view@stored@a}{\tikz@lib@view@stored@b}{\tikz@lib@view@stored@c}{\tikz@lib@view@stored@d}{#1}% +}% +\def\tikz@lib@view@a#1{% + \def\tikz@lib@view@stored@a{#1}% + \pgfutil@ifnextchar r{\tikz@lib@view@a@rec}{\tikz@scan@one@point\tikz@lib@view@b}% +}% +\def\tikz@lib@view@a@rec rectangle{\tikz@scan@one@point\tikz@lib@view@b}% +\def\tikz@lib@view@b#1{% + \def\tikz@lib@view@stored@b{#1}% + \pgfutil@ifnextchar\pgf@stop{% + \let\tikz@lib@view@stored@c\tikz@lib@view@stored@a% + \let\tikz@lib@view@stored@d\tikz@lib@view@stored@b% + \pgfutil@gobble% + }{\tikz@lib@view@b@at}% +}% +\def\tikz@lib@view@b@at at{\tikz@scan@one@point\tikz@lib@view@c}% +\def\tikz@lib@view@c#1{% + \def\tikz@lib@view@stored@c{#1}% + \pgfutil@ifnextchar r{\tikz@lib@view@c@rec}{\tikz@scan@one@point\tikz@lib@view@d}% +}% +\def\tikz@lib@view@c@rec rectangle{\tikz@scan@one@point\tikz@lib@view@d}% +\def\tikz@lib@view@d#1{\def\tikz@lib@view@stored@d{#1}\pgfutil@ifnextchar\pgf@stop\pgfutil@gobble{\tikzerror{Wrong syntax for meet or slice key}}}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..db51c43d5d52f8771c1d78f8a4034c57fba1f40e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex @@ -0,0 +1,5119 @@ + +\ProvidesPackageRCS{tikz.code.tex} + + +\def\tikzerror#1{\pgfutil@packageerror{tikz}{#1}{}} + +\usepgflibrary{plothandlers} + +\newdimen\tikz@lastx +\newdimen\tikz@lasty +\newdimen\tikz@lastxsaved +\newdimen\tikz@lastysaved +\newdimen\tikz@lastmovetox +\newdimen\tikz@lastmovetoy + +\newdimen\tikzleveldistance +\newdimen\tikzsiblingdistance + +\newbox\tikz@figbox +\newbox\tikz@figbox@bg +\newbox\tikz@tempbox +\newbox\tikz@tempbox@bg + +\newcount\tikztreelevel +\newcount\tikznumberofchildren +\newcount\tikznumberofcurrentchild + +\newcount\tikz@fig@count + +\newif\iftikz@node@is@a@label +\newif\iftikz@snaked +\newif\iftikz@decoratepath + +\let\tikz@options\pgfutil@empty +\def\tikz@addoption#1{% + \expandafter\def\expandafter\tikz@options\expandafter{\tikz@options#1}}% +\def\tikz@addmode#1{% + \expandafter\def\expandafter\tikz@mode\expandafter{\tikz@mode#1}}% +\def\tikz@addtransform#1{% + \ifx\tikz@transform\relax + #1% + \else + \expandafter\def\expandafter\tikz@transform\expandafter{\tikz@transform#1}% + \fi +}% + + + +\pgfkeys{/tikz/.is family}% + +\def\tikzset{\pgfqkeys{/tikz}}% + +\def\tikzoption#1{% + \pgfutil@ifnextchar[% + {\tikzoption@opt{#1}}{\tikzoption@noopt{#1}}}% +\def\tikzoption@opt#1[#2]#3{% + \pgfkeysdef{/tikz/#1}{#3}% + \pgfkeyssetvalue{/tikz/#1/.@def}{#2}}% +\def\tikzoption@noopt#1#2{% + \pgfkeysdef{/tikz/#1}{#2}% + \pgfkeyssetvalue{/tikz/#1/.@def}{\pgfkeysvaluerequired}}% + +\tikzoption{baseline}[0pt]{% + \pgfutil@ifnextchar(% + {\tikz@baseline@coordinate}{\tikz@baseline@simple}#1\@nil}% +\def\tikz@baseline@simple#1\@nil{\pgfsetbaseline{#1}}% +\def\tikz@baseline@coordinate#1\@nil{% + \pgfsetbaselinepointlater{\tikz@scan@one@point\pgfutil@firstofone#1}}% + +\tikzoption{trim left}[0pt]{\pgfutil@ifnextchar({\tikz@trim@coordinate{left}}{\tikz@trim@simple{left}}#1\@nil}% +\tikzoption{trim right}{\pgfutil@ifnextchar({\tikz@trim@coordinate{right}}{\tikz@trim@simple{right}}#1\@nil}% +\def\tikz@trim@simple#1#2\@nil{\csname pgfsettrim#1\endcsname{#2}}% +\def\tikz@trim@coordinate#1#2\@nil{\csname pgfsettrim#1pointlater\endcsname{\tikz@scan@one@point\pgfutil@firstofone#2}}% + +\tikzoption{line width}{\tikz@semiaddlinewidth{#1}}% + +\def\tikz@semiaddlinewidth#1{\tikz@addoption{\pgfsetlinewidth{#1}}\pgfmathsetlength\pgflinewidth{#1}}% + +\tikzoption{cap}{\tikz@addoption{\csname pgfset#1cap\endcsname}}% +\tikzoption{join}{\tikz@addoption{\csname pgfset#1join\endcsname}}% +\tikzoption{line cap}{\tikz@addoption{\csname pgfset#1cap\endcsname}}% +\tikzoption{line join}{\tikz@addoption{\csname pgfset#1join\endcsname}}% +\tikzoption{miter limit}{\tikz@addoption{\pgfsetmiterlimit{#1}}}% + +\tikzoption{dash pattern}{% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \def\tikz@dashpattern{}% + \tikz@addoption{\pgfsetdash{}{0pt}}% + \else% + \def\tikz@dashpattern{}% + \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil% + \edef\tikz@temp{{\tikz@dashpattern}{\noexpand\tikz@dashphase}}% + \expandafter\tikz@addoption\expandafter{\expandafter\pgfsetdash\tikz@temp}% + \fi}% +\tikzoption{dash phase}{% + \def\tikz@dashphase{#1}% + \edef\tikz@temp{{\tikz@dashpattern}{\noexpand\tikz@dashphase}}% + \expandafter\tikz@addoption\expandafter{\expandafter\pgfsetdash\tikz@temp}% +}% +\tikzoption{dash}{\tikz@parse@full@dash#1\pgf@stop}% +\def\tikz@parse@full@dash#1phase#2\pgf@stop{% + \def\tikz@dashphase{#2}% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \def\tikz@dashpattern{}% + \tikz@addoption{\pgfsetdash{}{0pt}}% + \else% + \def\tikz@dashpattern{}% + \expandafter\tikz@scandashon\pgfutil@gobble#1o\@nil% + \edef\tikz@temp{{\tikz@dashpattern}{\noexpand\tikz@dashphase}}% + \expandafter\tikz@addoption\expandafter{\expandafter\pgfsetdash\tikz@temp}% + \fi% +}% +\def\tikz@dashphase{0pt}% +\def\tikz@dashpattern{}% + +\def\tikz@scandashon n#1o{% + \expandafter\def\expandafter\tikz@dashpattern\expandafter{\tikz@dashpattern{#1}}% + \pgfutil@ifnextchar\@nil{\pgfutil@gobble}{\tikz@scandashoff}}% +\def\tikz@scandashoff ff#1o{% + \expandafter\def\expandafter\tikz@dashpattern\expandafter{\tikz@dashpattern{#1}}% + \pgfutil@ifnextchar\@nil{\pgfutil@gobble}{\tikz@scandashon}}% + +\tikzset{ + dash expand off/.code={% + \ifcsname tikz@library@decorations@loaded\endcsname\else + \tikzerror{You need \string\usetikzlibrary{decorations} for ``dash expand off''}% + \fi + \tikz@addoption{% + \pgfgetpath\currentpath + \pgfprocessround{\currentpath}{\currentpath}% + \pgf@decorate@parsesoftpath{\currentpath}{\currentpath}% + \pgfmathsetmacro\on{\expandafter\pgfutil@firstoftwo\tikz@dashpattern}% + \pgfmathsetmacro\off{\expandafter\pgfutil@secondoftwo\tikz@dashpattern}% + \pgfmathsetmacro\tikz@dashphase{\tikz@dashphase}% + \pgfmathsubtract@{\on}{\tikz@dashphase}% + \pgfmathmax@{\pgfmathresult,0}% + \let\dashphase=\pgfmathresult + \edef\rest{\pgf@sys@tonumber\dimexpr\pgf@decorate@totalpathlength - \on pt + 2\dimexpr\dashphase pt\relax\relax}% + \edef\onoff{\pgf@sys@tonumber\dimexpr\on pt+\off pt\relax}% + \pgfmathdivide@{\rest}{\onoff}% + \pgfmathfloor@{\pgfmathresult}% + \pgfmathmax@{\pgfmathresult,1}% + \pgfmathdivide@{\rest}{\pgfmathresult}% + \pgfmathsubtract@{\pgfmathresult}{\on}% + \pgfmathmax@{\pgfmathresult,\off}% + \edef\tikz@marshal{\noexpand\pgfsetdash{{+\on pt}{+\pgfmathresult pt}}{+\dashphase pt}}% + \tikz@marshal + }% + } +} + +\tikzoption{draw opacity}{\tikz@addoption{\pgfsetstrokeopacity{#1}}}% + +\tikzoption{double}[]{% + \def\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@doublefalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \pgfsetinnerstrokecolor{#1}% + \fi% + \tikz@addmode{\tikz@mode@doubletrue}% + \tikzset{every double/.try}% + \fi}% +\tikzoption{double distance}{% + \pgfmathsetlength{\pgf@x}{#1}% + \edef\tikz@double@setup{% + \pgf@x=\the\pgf@x% + \advance\pgf@x by2\pgflinewidth% + \pgflinewidth=\pgf@x% + \noexpand\pgfsetlinewidth{\pgflinewidth}% + \noexpand\pgfsetinnerlinewidth{\the\pgf@x}% + }% + \tikzset{double}}% +\def\tikz@double@setup{% + \pgf@x=2\pgflinewidth% + \advance\pgf@x by0.6pt% + \pgflinewidth=\pgf@x% + \pgfsetlinewidth{\pgflinewidth}% + \pgfsetinnerlinewidth{0.6pt}% +}% +\tikzset{double distance between line centers/.code={ + \pgfmathsetlength{\pgf@x}{#1}% + \edef\tikz@double@setup{% + \pgf@x=\pgflinewidth% + \pgf@xa=\the\pgf@x% + \advance\pgf@x by\pgf@xa% + \advance\pgf@xa by-\pgflinewidth% + \pgflinewidth=\pgf@x% + \noexpand\pgfsetlinewidth{\pgflinewidth}% + \noexpand\pgfsetinnerlinewidth{\pgf@xa}% + }% + \tikzset{double}}}% +\tikzset{double equal sign distance/.style={double distance between line centers=0.45ex}}% + + + + + +\tikzoption{even odd rule}[]{\tikz@addoption{\pgfseteorule}}% +\tikzoption{nonzero rule}[]{\tikz@addoption{\pgfsetnonzerorule}}% + +\tikzoption{fill opacity}{\tikz@addoption{\pgfsetfillopacity{#1}}}% + + + +\tikzoption{opacity}{\tikz@addoption{\pgfsetstrokeopacity{#1}\pgfsetfillopacity{#1}}}% + + + +\tikzset{blend mode/.code={\tikz@addoption{\pgfsetblendmode{#1}}}}% + + +\tikzoption{color}{% + \tikz@addoption{% + \ifx\tikz@fillcolor\pgfutil@empty% + \ifx\tikz@strokecolor\pgfutil@empty% + \else% + \pgfsys@color@reset@inorderfalse% + \let\tikz@strokecolor\pgfutil@empty% + \let\tikz@fillcolor\pgfutil@empty% + \fi% + \else% + \pgfsys@color@reset@inorderfalse% + \let\tikz@strokecolor\pgfutil@empty% + \let\tikz@fillcolor\pgfutil@empty% + \fi% + \pgfutil@colorlet{tikz@color}{#1}% + \pgfutil@colorlet{.}{tikz@color}% + \pgfsetcolor{.}% + \pgfsys@color@reset@inordertrue% + }% + \def\tikz@textcolor{#1}}% + + + +\tikzoption{rounded corners}[4pt]{\pgfsetcornersarced{\pgfpoint{#1}{#1}}}% +\tikzoption{sharp corners}[]{\pgfsetcornersarced{\pgfpointorigin}}% + +\tikzset{x radius/.initial=0pt}% +\tikzset{y radius/.initial=0pt}% +\tikzset{% + radius/.code={% + \pgfmathparse{#1}% + \ifpgfmathunitsdeclared + \pgfkeyssetevalue{/tikz/x radius}{\pgfmathresult pt}% + \pgfkeyssetevalue{/tikz/y radius}{\pgfmathresult pt}% + \else + \pgfkeyssetevalue{/tikz/x radius}{\pgfmathresult}% + \pgfkeyssetevalue{/tikz/y radius}{\pgfmathresult}% + \fi + }% +}% +\tikzset{start angle/.initial=}% +\tikzset{end angle/.initial=}% +\tikzset{delta angle/.initial=}% + + +\tikzoption{x}{\tikz@handle@vec{\pgfsetxvec}{\tikz@handle@x}#1\relax}% +\tikzoption{y}{\tikz@handle@vec{\pgfsetyvec}{\tikz@handle@y}#1\relax}% +\tikzoption{z}{\tikz@handle@vec{\pgfsetzvec}{\tikz@handle@z}#1\relax}% + +\def\tikz@handle@vec#1#2{\pgfutil@ifnextchar({\tikz@handle@coordinate#1}{\tikz@handle@single#2}}% +\def\tikz@handle@coordinate#1{\tikz@scan@one@point#1}% +\def\tikz@handle@single#1#2\relax{#1{#2}}% +\def\tikz@handle@x#1{\pgfsetxvec{\pgfpoint{#1}{0pt}}}% +\def\tikz@handle@y#1{\pgfsetyvec{\pgfpoint{0pt}{#1}}}% +\def\tikz@handle@z#1{\pgfsetzvec{\pgfpoint{#1}{#1}}}% + + +\tikzoption{scale}{\tikz@addtransform{\pgftransformscale{#1}}}% +\tikzoption{scale around}{\tikz@addtransform{\def\tikz@aroundaction{\pgftransformscale}\tikz@doaround{#1}}}% +\tikzoption{xscale}{\tikz@addtransform{\pgftransformxscale{#1}}}% +\tikzoption{xslant}{\tikz@addtransform{\pgftransformxslant{#1}}}% +\tikzoption{yscale}{\tikz@addtransform{\pgftransformyscale{#1}}}% +\tikzoption{yslant}{\tikz@addtransform{\pgftransformyslant{#1}}}% +\tikzoption{rotate}{\tikz@addtransform{\pgftransformrotate{#1}}}% +\tikzoption{rotate around}{\tikz@addtransform{\def\tikz@aroundaction{\pgftransformrotate}\tikz@doaround{#1}}}% +\def\tikz@doaround#1{% + \edef\tikz@temp{#1}% + \expandafter\tikz@doparseA\tikz@temp% +}% +\def\tikz@doparseA#1:{% + \def\tikz@temp@rot{#1}% + \tikz@scan@one@point\tikz@doparseB% +}% +\def\tikz@doparseB#1{% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgftransformshift{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \tikz@aroundaction{\tikz@temp@rot}% + \pgftransformshift{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}% +}% + +\tikzoption{shift}{\tikz@addtransform{\tikz@scan@one@point\pgftransformshift#1\relax}}% +\tikzoption{xshift}{\tikz@addtransform{\pgftransformxshift{#1}}}% +\tikzoption{yshift}{\tikz@addtransform{\pgftransformyshift{#1}}}% +\tikzoption{cm}{\tikz@addtransform{\tikz@parse@cm#1\relax}}% +\tikzoption{reset cm}[]{\tikz@addtransform{\pgftransformreset}}% +\tikzoption{shift only}[]{\tikz@addtransform{\pgftransformresetnontranslations}}% + +\def\tikz@parse@cm#1,#2,#3,#4,{% + \def\tikz@p@cm{{#1}{#2}{#3}{#4}}% + \tikz@scan@one@point\tikz@parse@cmA}% +\def\tikz@parse@cmA#1{% + \expandafter\pgftransformcm\tikz@p@cm{#1}% +}% + +\tikzset{transform canvas/.code=% + {% + \tikz@addoption + {% + {% + \pgftransformreset% + \let\tikz@transform=\relax% + \tikzset{#1}% + \pgflowlevelsynccm% + }% + \pgf@relevantforpicturesizefalse% + }% + }% +}% + +\tikzset{turn/.code={% + \pgf@x=0pt% + \pgf@y\pgf@x% + \pgf@process{\tikz@tangent}% + \advance\pgf@x by-\tikz@lastx% + \advance\pgf@y by-\tikz@lasty% + \pgfpointnormalised{}% + \pgf@x=-\pgf@x% + \pgf@ya=-\pgf@y% + \pgftransformcm% + {\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@ya}}% + {\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@x}}{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}% + }% +}% + +\def\tikz@tangent@lookup{% + \pgfgetpath\tikz@temp% + \pgfprocesspathextractpoints\tikz@temp% + \pgfpointsecondlastonpath% +}% + +\def\tikz@xyz@rotate@let{% + \let\pgf@z=\pgf@yc% + \let\pgf@za=\pgf@xc% +}% + +\def\tikz@xyz@rotate@xyz@xaxis#1#2#3#4{% + \tikz@xyz@rotate@let% + \pgf@x=#1\relax% + \pgf@ya=#2\relax% + \pgf@za=#3\relax% + \pgfmathsin@{#4}\let\tikz@xyz@sin=\pgfmathresult% + \pgfmathcos@{#4}\let\tikz@xyz@cos=\pgfmathresult% + \pgf@y=\tikz@xyz@cos\pgf@ya% + \advance\pgf@y by-\tikz@xyz@sin\pgf@za% + \pgf@z=\tikz@xyz@sin\pgf@ya% + \advance\pgf@z by\tikz@xyz@cos\pgf@za% +}% + +\def\tikz@xyz@rotate@xyz@yaxis#1#2#3#4{% + \tikz@xyz@rotate@let% + \pgf@xa=#1\relax% + \pgf@y=#2\relax% + \pgf@za=#3\relax% + \pgfmathsin@{#4}\let\tikz@xyz@sin=\pgfmathresult% + \pgfmathcos@{#4}\let\tikz@xyz@cos=\pgfmathresult% + \pgf@x=\tikz@xyz@cos\pgf@xa% + \advance\pgf@x by\tikz@xyz@sin\pgf@za% + \pgf@z=-\tikz@xyz@sin\pgf@xa% + \advance\pgf@z by\tikz@xyz@cos\pgf@za% +}% + +\def\tikz@xyz@rotate@xyz@zaxis#1#2#3#4{% + \tikz@xyz@rotate@let% + \pgf@xa=#1\relax% + \pgf@ya=#2\relax% + \pgf@z=#3\relax% + \pgfmathsin@{#4}\let\tikz@xyz@sin=\pgfmathresult% + \pgfmathcos@{#4}\let\tikz@xyz@cos=\pgfmathresult% + \pgf@x=\tikz@xyz@cos\pgf@xa% + \advance\pgf@x by-\tikz@xyz@sin\pgf@ya% + \pgf@y=\tikz@xyz@sin\pgf@xa% + \advance\pgf@y by\tikz@xyz@cos\pgf@ya% +}% + +\tikzset{rotate around x/.code={% + \tikz@xyz@rotate@let% + \pgfmathparse{#1}\let\tikz@xyz@angle=\pgfmathresult% + \tikz@xyz@rotate@xyz@xaxis{0pt}{1pt}{0pt}{\tikz@xyz@angle}% + \pgfextract@process\tikz@xyz@rotate@yvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}% + \tikz@xyz@rotate@xyz@xaxis{0pt}{0pt}{1pt}{\tikz@xyz@angle}% + \pgfsetzvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}% + \pgfsetyvec{\tikz@xyz@rotate@yvec}% + }, + rotate around y/.code={% + \tikz@xyz@rotate@let% + \pgfmathparse{#1}\let\tikz@xyz@angle=\pgfmathresult% + \tikz@xyz@rotate@xyz@yaxis{1pt}{0pt}{0pt}{\tikz@xyz@angle}% + \pgfextract@process\tikz@xyz@rotate@xvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}% + \tikz@xyz@rotate@xyz@yaxis{0pt}{0pt}{1pt}{\tikz@xyz@angle}% + \pgfsetzvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}% + \pgfsetxvec{\tikz@xyz@rotate@xvec}% + }, + rotate around z/.code={% + \tikz@xyz@rotate@let% + \pgfmathparse{#1}\let\tikz@xyz@angle=\pgfmathresult% + \tikz@xyz@rotate@xyz@zaxis{1pt}{0pt}{0pt}{\tikz@xyz@angle}% + \pgfextract@process\tikz@xyz@rotate@xvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}% + \tikz@xyz@rotate@xyz@zaxis{0pt}{1pt}{0pt}{\tikz@xyz@angle}% + \pgfsetyvec{\pgfpointxyz{\pgf@sys@tonumber{\pgf@x}}{\pgf@sys@tonumber{\pgf@y}}{\pgf@sys@tonumber{\pgf@z}}}% + \pgfsetxvec{\tikz@xyz@rotate@xvec}% + }, +}% + +\tikzoption{xstep}{\def\tikz@grid@x{#1}}% +\tikzoption{ystep}{\def\tikz@grid@y{#1}}% +\tikzoption{step}{\tikz@handle@vec{\tikz@step@point}{\tikz@step@single}#1\relax}% +\def\tikz@step@single#1{\def\tikz@grid@x{#1}\def\tikz@grid@y{#1}}% +\def\tikz@step@point#1{\pgf@process{#1}\edef\tikz@grid@x{\the\pgf@x}\edef\tikz@grid@y{\the\pgf@y}}% + +\def\tikz@grid@x{1cm}% +\def\tikz@grid@y{1cm}% + + +\newif\iftikz@current@point@local +\tikzset{current point is local/.is if=tikz@current@point@local}% + +\newif\iftikz@mode@double +\newif\iftikz@mode@fill +\newif\iftikz@mode@draw +\newif\iftikz@mode@clip +\newif\iftikz@mode@boundary +\newif\iftikz@mode@shade +\newif\iftikz@mode@fade@path +\newif\iftikz@mode@fade@scope +\let\tikz@mode=\pgfutil@empty + +\def\tikz@nonetext{none}% + +\tikzoption{path only}[]{\let\tikz@mode=\pgfutil@empty}% +\tikzset{ + shade/.is choice, + shade/.default=true, + shade/true/.code=\tikz@addmode{\tikz@mode@shadetrue}, + shade/false/.code=\tikz@addmode{\tikz@mode@shadefalse}, + shade/none/.code=\tikz@addmode{\tikz@mode@shadefalse}, +}% + +\tikzoption{fill}[]{% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@fillfalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \tikz@addoption{\pgfsetfillcolor{#1}}% + \def\tikz@fillcolor{#1}% + \fi% + \tikz@addmode{\tikz@mode@filltrue}% + \fi% +}% +\tikzoption{draw}[]{% + \edef\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@drawfalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \tikz@addoption{\pgfsetstrokecolor{#1}}% + \def\tikz@strokecolor{#1}% + \fi% + \tikz@addmode{\tikz@mode@drawtrue}% + \fi% +}% +\tikzoption{clip}[]{\tikz@addmode{\tikz@mode@cliptrue}}% +\tikzoption{use as bounding box}[]{\tikz@addmode{\tikz@mode@boundarytrue}}% + +\tikzoption{save path}{\tikz@addmode{\pgfsyssoftpath@getcurrentpath#1\global\let#1=#1}}% +\tikzoption{use path}{\tikz@addmode{\pgfsyssoftpath@setcurrentpath#1}}% + +\let\tikz@fillcolor=\pgfutil@empty +\let\tikz@strokecolor=\pgfutil@empty + +\tikzset{insert path/.code=\tikz@scan@next@command#1\pgf@stop}% + +\tikzset{pattern/.code=\tikzerror{You need to say \string\usetikzlibrary{patterns}}, + pattern color/.style=pattern}% + +\tikzset{path picture/.code=\tikz@addmode{\def\tikz@path@picture{#1}}}% + +\tikzset{path fading/.code={ + \def\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@fade@pathfalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \def\tikz@path@fading{#1}% + \fi% + \tikz@addmode{\tikz@mode@fade@pathtrue}% + \fi% + }, + path fading/.default=, + scope fading/.code={ + \def\tikz@temp{#1}% + \ifx\tikz@temp\tikz@nonetext% + \tikz@addmode{\tikz@mode@fade@scopefalse}% + \else% + \ifx\tikz@temp\pgfutil@empty% + \else% + \def\tikz@scope@fading{#1}% + \fi% + \tikz@addmode{\tikz@mode@fade@scopetrue}% + \fi% + }, + scope fading/.default=}% +\tikzset{fit fading/.is if=tikz@fade@adjust}% +\tikzset{fading transform/.store in=\tikz@fade@transform}% +\tikzset{fading angle/.style={fading transform={rotate={#1}}}}% + +\newif\iftikz@fade@adjust% +\tikz@fade@adjusttrue% +\let\tikz@fade@transform\pgfutil@empty% + +\pgfutil@colorlet{transparent}{pgftransparent}% +\def\tikz@do@fade@transform{\let\tikz@transform=\relax\expandafter\tikzset\expandafter{\tikz@fade@transform}}% + + + +\newif\iftikz@transparency@group% +\tikzset{/tikz/transparency group/.code=\tikz@transparency@grouptrue\def\tikz@transparency@group@options{isolated=true,#1}\let\tikz@blend@group\pgfutil@empty}% +\tikzset{/tikz/blend group/.code=\tikz@transparency@grouptrue\def\tikz@transparency@group@options{isolated=true}\def\tikz@blend@group{\pgfsetblendmode{#1}}}% + +\let\tikz@blend@group\pgfutil@empty + +\tikzoption{shading}{\def\tikz@shading{#1}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{shading angle}{\def\tikz@shade@angle{#1}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{top color}{% + \pgfutil@colorlet{tikz@axis@top}{#1}% + \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}% + \def\tikz@shading{axis}\def\tikz@shade@angle{0}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{bottom color}{% + \pgfutil@colorlet{tikz@axis@bottom}{#1}% + \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}% + \def\tikz@shading{axis}\def\tikz@shade@angle{0}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{middle color}{% + \pgfutil@colorlet{tikz@axis@middle}{#1}% + \def\tikz@shading{axis}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{left color}{% + \pgfutil@colorlet{tikz@axis@top}{#1}% + \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}% + \def\tikz@shading{axis}\def\tikz@shade@angle{90}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{right color}{% + \pgfutil@colorlet{tikz@axis@bottom}{#1}% + \pgfutil@colorlet{tikz@axis@middle}{tikz@axis@top!50!tikz@axis@bottom}% + \def\tikz@shading{axis}\def\tikz@shade@angle{90}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{ball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{ball}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{inner color}{\pgfutil@colorlet{tikz@radial@inner}{#1}\def\tikz@shading{radial}\tikz@addmode{\tikz@mode@shadetrue}}% +\tikzoption{outer color}{\pgfutil@colorlet{tikz@radial@outer}{#1}\def\tikz@shading{radial}\tikz@addmode{\tikz@mode@shadetrue}}% + +\def\tikz@shading{axis}% +\def\tikz@shade@angle{0}% + +\pgfdeclareverticalshading[tikz@axis@top,tikz@axis@middle,tikz@axis@bottom]{axis}{100bp}{% + color(0bp)=(tikz@axis@bottom); + color(25bp)=(tikz@axis@bottom); + color(50bp)=(tikz@axis@middle); + color(75bp)=(tikz@axis@top); + color(100bp)=(tikz@axis@top)}% + +\pgfutil@colorlet{tikz@axis@top}{gray}% +\pgfutil@colorlet{tikz@axis@middle}{gray!50!white}% +\pgfutil@colorlet{tikz@axis@bottom}{white}% + +\pgfdeclareradialshading[tikz@ball]{ball}{\pgfqpoint{-10bp}{10bp}}{% + color(0bp)=(tikz@ball!15!white); + color(9bp)=(tikz@ball!75!white); + color(18bp)=(tikz@ball!70!black); + color(25bp)=(tikz@ball!50!black); + color(50bp)=(black)}% + +\pgfutil@colorlet{tikz@ball}{blue}% + +\pgfdeclareradialshading[tikz@radial@inner,tikz@radial@outer]{radial}{\pgfpointorigin}{% + color(0bp)=(tikz@radial@inner); + color(25bp)=(tikz@radial@outer); + color(50bp)=(tikz@radial@outer)}% + +\pgfutil@colorlet{tikz@radial@inner}{gray}% +\pgfutil@colorlet{tikz@radial@outer}{white}% + + +\tikzset{ + pin distance/.store in=\tikz@pin@distance, + pin distance=3ex, + pin position/.store in=\tikz@pin@default@pos, + pin position=above, + pin edge/.store in=\tikz@pin@edge@style, + pin edge={}, + tikz@pin@post/.code={\global\let\tikz@pin@edge@style@smuggle=\tikz@pin@edge@style}, + tikz@pre@pin@edge/.code={% + \toks0=\expandafter{\tikz@pin@edge@style@smuggle}% + \edef\pgf@marshal{\noexpand\tikzset{tikz@pin@options/.style={\the\toks0}}}% + \pgf@marshal + },% +}% + +\tikzset{% + pin/.code={% + \begingroup + \ifnum\the\catcode`\:=\active\relax + \def\tikz@next{% + \endgroup + \tikz@parse@pin@active@i{#1}}% + \else + \def\tikz@next{% + \endgroup + \pgfutil@ifnextchar[% + {\tikz@parse@pin@nonactive} + {\tikz@parse@pin@nonactive[]}#1:\pgf@nil}% + \fi + \tikz@next}}% + +\begingroup + \catcode`\:=\active\relax + + \gdef\tikz@parse@pin@active@i#1{% + \pgfutil@ifnextchar[% + {\tikz@parse@pin@active} + {\tikz@parse@pin@active[]}#1:\pgf@nil}% + + \long\gdef\tikz@parse@pin@active[#1]#2:#3\pgf@nil{% + \def\tikz@temp{#3}% + \ifx\tikz@temp\pgfutil@empty + \tikz@@parse@pin@active[#1]\tikz@pin@default@pos:#2:\pgf@nil% + \else + \tikz@@parse@pin@active[#1]#2:#3\pgf@nil% + \fi}% + + \long\gdef\tikz@@parse@pin@active[#1]#2:#3:\pgf@nil{% + \tikzset{% + append after command = {% + \bgroup + [current point is local = true] + \pgfextra{\let\tikz@save@last@node=\tikzlastnode\tikz@node@is@a@labelfalse}% + node [tikz@label@angle = #2, + anchor=@auto, + every pin, + #1, + append after command = {% + (\tikz@save@last@node) + edge [every pin edge, + tikz@pre@pin@edge, + tikz@pin@options] + (\tikzlastnode)}, + tikz@label@post = \tikz@pin@distance, + tikz@pin@post] {#3} + \egroup}}}% +\endgroup + +\long\def\tikz@parse@pin@nonactive[#1]#2:#3\pgf@nil{% + \def\tikz@temp{#3}% + \ifx\tikz@temp\pgfutil@empty + \tikz@@parse@pin@nonactive[#1]\tikz@pin@default@pos:#2:\pgf@nil% + \else + \tikz@@parse@pin@nonactive[#1]#2:#3\pgf@nil% + \fi}% + +\long\def\tikz@@parse@pin@nonactive[#1]#2:#3:\pgf@nil{% + \tikzset{% + append after command = {% + \bgroup + [current point is local = true] + \pgfextra{\let\tikz@save@last@node=\tikzlastnode\tikz@node@is@a@labelfalse}% + node [tikz@label@angle = #2, + anchor=@auto, + every pin, + #1, + append after command = {% + (\tikz@save@last@node) + edge [every pin edge, + tikz@pre@pin@edge, + tikz@pin@options] + (\tikzlastnode)}, + tikz@label@post = \tikz@pin@distance, + tikz@pin@post] {#3} + \egroup}}}% + + +\tikzset{ + label distance/.store in=\tikz@label@distance, + label distance=0pt, + label position/.store in=\tikz@label@default@pos, + label position=above, + absolute/.is if=tikz@absolute, + tikz@label@angle/.store in=\tikz@label@angle +}% + +\newif\iftikz@absolute +\def\tikz@on@text{center}% + +\tikzset{tikz@label@post/.code 2 args={ + \edef\tikz@label@angle{\tikz@label@angle}% + \expandafter\pgfkeys@spdef\expandafter\tikz@label@angle\expandafter{\tikz@label@angle}% + \csname tikz@label@angle@is@\tikz@label@angle\endcsname + \ifx\tikz@label@angle\tikz@on@text% + \def\tikz@node@at{\pgfpointanchor{\tikzlastnode}{center}}% + \def\tikz@anchor{center}% + \else% + \iftikz@absolute% + \pgftransformreset% + \pgf@process{% + \pgfpointshapeborder{\tikzlastnode}% + {\pgfpointadd{\pgfpointanchor{\tikzlastnode}{center}}{\pgfpointpolar{\tikz@label@angle}{1pt}}}}% + \edef\tikz@node@at{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \tikz@compute@direction{\tikz@label@angle}% + \tikz@addtransform{\pgftransformshift{\pgfpointpolar{\tikz@label@angle}{#1}}}% + \else% + \pgf@process{\pgfpointanchor{\tikzlastnode}{\tikz@label@angle}}% + \edef\tikz@node@at{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@process{\pgfpointanchor{\tikzlastnode}{center}}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \tikz@label@simplefalse% + \ifdim\pgf@xc=\pgf@xb\relax% + \ifdim\pgf@yc=\pgf@yb\relax% + \tikz@label@simpletrue% + \fi% + \fi% + \iftikz@label@simple% + \tikz@compute@direction{\tikz@label@angle}% + \tikz@addtransform{\pgftransformshift{\pgfpointpolar{\tikz@label@angle}{#1}}}% + \else% + \pgf@process{\pgfpointnormalised{% + \pgfpointdiff{\pgfpointtransformed{\pgfqpoint{\pgf@xc}{\pgf@yc}}}{\pgfpointtransformed{\pgfqpoint{\pgf@xb}{\pgf@yb}}}}}% + \edef\pgf@marshal{% + \noexpand\tikz@addtransform{\noexpand\pgftransformshift{\noexpand\pgfpointscale{#1}{ + \noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}}}% + \pgf@marshal% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@x=\pgf@yc% + \pgf@y=-\pgf@xc% + \ifx\tikz@anchor\tikz@auto@text% + \tikz@auto@anchor% + \fi% + \fi% + \fi% + \fi} +}% + +\newif\iftikz@label@simple% + +\tikzset{% + label/.code={% + \begingroup + \ifnum\the\catcode`\:=\active\relax + \def\tikz@next{% + \endgroup + \tikz@parse@label@active@i{#1}}% + \else + \def\tikz@next{% + \endgroup + \pgfutil@ifnextchar[% + {\tikz@parse@label@nonactive} + {\tikz@parse@label@nonactive[]}#1:\pgf@nil}% + \fi + \tikz@next}}% + +\begingroup + \catcode`\:=\active\relax + + \gdef\tikz@parse@label@active@i#1{% + \pgfutil@ifnextchar[% + {\tikz@parse@label@active} + {\tikz@parse@label@active[]}#1:\pgf@nil}% + + \gdef\tikz@parse@label@active[#1]#2:#3\pgf@nil{% + \def\tikz@temp{#3}% + \ifx\tikz@temp\pgfutil@empty + \tikz@@parse@label@active[#1]\tikz@label@default@pos:#2:\pgf@nil% + \else + \def\tikz@temp{#2}% + \ifx\tikz@temp\pgfutil@empty + \tikz@@parse@label@active[#1]\tikz@label@default@pos:#3\pgf@nil% + \else + \tikz@@parse@label@active[#1]#2:#3\pgf@nil% + \fi + \fi + }% + + \gdef\tikz@@parse@label@active[#1]#2:#3:\pgf@nil{% + \tikzset{% + append after command = {% + \bgroup + [current point is local=true] + \pgfextra{\let\tikz@save@last@fig@name=\tikz@last@fig@name\tikz@node@is@a@labelfalse} + node [tikz@label@angle = #2, + anchor=@auto, + every label, + #1, + tikz@label@post = \tikz@label@distance] {\iftikz@handle@active@nodes\expandafter\scantokens\else\expandafter\pgfutil@firstofone\fi{#3\noexpand}} + \pgfextra{\global\let\tikz@last@fig@name=\tikz@save@last@fig@name} + \egroup}}}% +\endgroup + +\def\tikz@parse@label@nonactive[#1]#2:#3\pgf@nil{% + \def\tikz@temp{#3}% + \ifx\tikz@temp\pgfutil@empty + \tikz@@parse@label@nonactive[#1]\tikz@label@default@pos:#2:\pgf@nil% + \else + \def\tikz@temp{#2}% + \ifx\tikz@temp\pgfutil@empty + \tikz@@parse@label@nonactive[#1]\tikz@label@default@pos:#3\pgf@nil% + \else + \tikz@@parse@label@nonactive[#1]#2:#3\pgf@nil% + \fi + \fi +}% + +\def\tikz@@parse@label@nonactive[#1]#2:#3:\pgf@nil{% + \tikzset{% + append after command = {% + \bgroup + [current point is local=true] + \pgfextra{\let\tikz@save@last@fig@name=\tikz@last@fig@name\tikz@node@is@a@labelfalse} + node [tikz@label@angle = #2, + anchor=@auto, + every label, + #1, + tikz@label@post = \tikz@label@distance] {\iftikz@handle@active@nodes\expandafter\scantokens\else\expandafter\pgfutil@firstofone\fi{#3\noexpand}} + \pgfextra{\global\let\tikz@last@fig@name=\tikz@save@last@fig@name} + \egroup}}}% + +\expandafter\def\csname tikz@label@angle@is@right\endcsname{\def\tikz@label@angle{0}}% +\expandafter\def\csname tikz@label@angle@is@above right\endcsname{\def\tikz@label@angle{45}}% +\expandafter\def\csname tikz@label@angle@is@above\endcsname{\def\tikz@label@angle{90}}% +\expandafter\def\csname tikz@label@angle@is@above left\endcsname{\def\tikz@label@angle{135}}% +\expandafter\def\csname tikz@label@angle@is@left\endcsname{\def\tikz@label@angle{180}}% +\expandafter\def\csname tikz@label@angle@is@below left\endcsname{\def\tikz@label@angle{225}}% +\expandafter\def\csname tikz@label@angle@is@below\endcsname{\def\tikz@label@angle{270}}% +\expandafter\def\csname tikz@label@angle@is@below right\endcsname{\def\tikz@label@angle{315}}% + +\def\tikz@compute@direction#1{% + \ifx\tikz@anchor\tikz@auto@text% + \let\tikz@do@auto@anchor=\relax + \pgfmathsetcount{\c@pgf@counta}{#1}% + \ifnum\c@pgf@counta<0\relax + \advance\c@pgf@counta by 360\relax% + \fi% + \ifnum\c@pgf@counta>359\relax + \advance\c@pgf@counta by-360\relax% + \fi% + \ifnum\c@pgf@counta<4\relax% + \def\tikz@anchor{west}% + \else\ifnum\c@pgf@counta<87\relax% + \def\tikz@anchor{south west}% + \else\ifnum\c@pgf@counta<94\relax% + \def\tikz@anchor{south}% + \else\ifnum\c@pgf@counta<177\relax% + \def\tikz@anchor{south east}% + \else\ifnum\c@pgf@counta<184\relax% + \def\tikz@anchor{east}% + \else\ifnum\c@pgf@counta<267\relax% + \def\tikz@anchor{north east}% + \else\ifnum\c@pgf@counta<274\relax% + \def\tikz@anchor{north}% + \else\ifnum\c@pgf@counta<357\relax% + \def\tikz@anchor{north west}% + \else% + \def\tikz@anchor{west}% + \fi\fi\fi\fi\fi\fi\fi\fi% + \fi% +}% +\def\tikz@auto@text{@auto}% + +\tikzset{ + name/.code={\edef\tikz@fig@name{\tikz@pp@name{#1}}\let\tikz@id@name\tikz@fig@name},% + name prefix/.initial=,% + name suffix/.initial=,% + local bounding box/.style={/pgf/local bounding box/.expanded=\tikz@pp@name{#1}} +}% +\def\tikz@pp@name#1{\csname pgfk@/tikz/name prefix\endcsname#1\csname pgfk@/tikz/name suffix\endcsname}% + + +\tikzset{ + node contents/.code=\def\tikz@node@content{#1}, + pic type/.code=\def\tikz@node@content{#1}, % +}% + +\tikzset{ + behind path/.code=\def\tikz@whichbox{\tikz@figbox@bg}, + in front of path/.code=\def\tikz@whichbox{\tikz@figbox} +}% +\def\tikz@whichbox{\tikz@figbox}% + +\tikzoption{at}{\tikz@scan@one@point\tikz@set@at#1}% +\def\tikz@set@at#1{\def\tikz@node@at{#1}}% + +\tikzoption{shape}{\edef\tikz@shape{#1}}% + +\tikzoption{nodes}{\tikzset{every node/.append style={#1}}}% + +\tikzset{alias/.code={% + \tikz@fig@mustbenamed + \begingroup + \toks0=\expandafter{\tikz@alias}% + \edef\pgf@temp{\noexpand\pgfnodealias{\tikz@pp@name{#1}}{\noexpand\tikz@fig@name}}% + \toks1=\expandafter{\pgf@temp}% + \xdef\pgf@marshal{% + \noexpand\def\noexpand\tikz@alias{\the\toks0 \the\toks1 }% + }% + \endgroup + \pgf@marshal +}}% + +\def\tikzaddafternodepathoption#1{#1\tikzset{prefix after command={\pgfextra{#1}}}}% +\tikzset{after node path/.style={append after command={#1}}}% + + +\tikzset{pic text/.store in=\tikzpictext}% +\let\tikzpictext\relax +\tikzset{pic text options/.store in=\tikzpictextoptions}% +\let\tikzpictextoptions\pgfutil@empty + + + +\tikzoption{anchor}{\def\tikz@anchor{#1}\let\tikz@do@auto@anchor=\relax}% + +\tikzoption{left}[]{\def\tikz@anchor{east}\tikz@possibly@transform{x}{-}{#1}}% +\tikzoption{right}[]{\def\tikz@anchor{west}\tikz@possibly@transform{x}{}{#1}}% +\tikzoption{above}[]{\def\tikz@anchor{south}\tikz@possibly@transform{y}{}{#1}}% +\tikzoption{below}[]{\def\tikz@anchor{north}\tikz@possibly@transform{y}{-}{#1}}% +\tikzoption{above left}[]% + {\def\tikz@anchor{south east}% + \tikz@possibly@transform{x}{-}{#1}\tikz@possibly@transform{y}{}{#1}}% +\tikzoption{above right}[]% + {\def\tikz@anchor{south west}% + \tikz@possibly@transform{x}{}{#1}\tikz@possibly@transform{y}{}{#1}}% +\tikzoption{below left}[]% + {\def\tikz@anchor{north east}% + \tikz@possibly@transform{x}{-}{#1}\tikz@possibly@transform{y}{-}{#1}}% +\tikzoption{below right}[]% + {\def\tikz@anchor{north west}% + \tikz@possibly@transform{x}{}{#1}\tikz@possibly@transform{y}{-}{#1}}% +\tikzset{centered/.code=\def\tikz@anchor{center}}% + +\tikzoption{node distance}{\def\tikz@node@distance{#1}}% +\def\tikz@node@distance{1cm}% + +\tikzoption{above of}{\tikz@of{#1}{90}}% +\tikzoption{below of}{\tikz@of{#1}{-90}}% +\tikzoption{left of}{\tikz@of{#1}{180}}% +\tikzoption{right of}{\tikz@of{#1}{0}}% +\tikzoption{above left of}{\tikz@of{#1}{135}}% +\tikzoption{below left of}{\tikz@of{#1}{-135}}% +\tikzoption{above right of}{\tikz@of{#1}{45}}% +\tikzoption{below right of}{\tikz@of{#1}{-45}}% +\def\tikz@of#1#2{% + \def\tikz@anchor{center}% + \let\tikz@do@auto@anchor=\relax% + \tikz@addtransform{% + \expandafter\tikz@extract@node@dist\tikz@node@distance and\pgf@stop% + \pgftransformshift{\pgfpointpolar{#2}{\tikz@extracted@node@distance}}}% + \def\tikz@node@at{\pgfpointanchor{\tikz@pp@name{#1}}{center}}}% +\def\tikz@extract@node@dist#1and#2\pgf@stop{% + \def\tikz@extracted@node@distance{#1}}% + +\tikzset{ + transform shape nonlinear/.is choice, + transform shape nonlinear/.default=true, + transform shape nonlinear/true/.code=\let\tikz@nlt\relax, + transform shape nonlinear/false/.code=\def\tikz@nlt{\pgfapproximatenonlineartranslation}, + transform shape nonlinear=false, +}% + + +\tikzoption{transform shape}[true]{% + \csname tikz@fullytransformed#1\endcsname% + \iftikz@fullytransformed% + \pgfresetnontranslationattimefalse% + \else% + \pgfresetnontranslationattimetrue% + \fi% +}% + +\newif\iftikz@fullytransformed +\pgfresetnontranslationattimetrue% + +\def\tikz@anchor{center}% +\def\tikz@shape{rectangle}% + +\def\tikz@possibly@transform#1#2#3{% + \let\tikz@do@auto@anchor=\relax% + \def\tikz@test{#3}% + \ifx\tikz@test\pgfutil@empty% + \else% + \pgfmathsetlength{\pgf@x}{#3}% + \pgf@x=#2\pgf@x\relax% + \edef\tikz@marshal{\noexpand\tikz@addtransform{% + \expandafter\noexpand\csname pgftransform#1shift\endcsname{\the\pgf@x}}}% + \tikz@marshal% + \fi% +}% + + +\tikzoption{remember picture}[true]{\csname pgfrememberpicturepositiononpage#1\endcsname} +\tikzset{ + overlay/.is choice, + overlay/true/.code={\pgf@relevantforpicturesizefalse}, + overlay/false/.code={\pgf@relevantforpicturesizetrue}, + overlay/.default=true +} + + + +\tikzoption{sloped}[true]{\csname pgfslopedattime#1\endcsname}% +\tikzoption{allow upside down}[true]{\csname pgfallowupsidedownattime#1\endcsname}% + +\tikzoption{pos}{\edef\tikz@time{#1}\ifx\tikz@time\pgfutil@empty\else\pgfmathsetmacro\tikz@time{\tikz@time}\fi}% + +\tikzoption{auto}[]{\csname tikz@install@auto@anchor@#1\endcsname}% +\tikzoption{swap}[]{% + \def\tikz@temp{left}% + \ifx\tikz@auto@anchor@direction\tikz@temp% + \def\tikz@auto@anchor@direction{right}% + \else% + \def\tikz@auto@anchor@direction{left}% + \fi% +}% +\tikzset{'/.style=swap}% + + +\def\tikz@install@auto@anchor@{\let\tikz@do@auto@anchor=\tikz@auto@anchor@on}% +\def\tikz@install@auto@anchor@false{\let\tikz@do@auto@anchor=\relax}% +\def\tikz@install@auto@anchor@left{\let\tikz@do@auto@anchor=\tikz@auto@anchor@on\def\tikz@auto@anchor@direction{left}}% +\def\tikz@install@auto@anchor@right{\let\tikz@do@auto@anchor=\tikz@auto@anchor@on\def\tikz@auto@anchor@direction{right}}% + +\let\tikz@do@auto@anchor=\relax% + +\def\tikz@auto@anchor@on{\csname tikz@auto@anchor@\tikz@auto@anchor@direction\endcsname} + +\def\tikz@auto@anchor@left{\tikz@auto@pre\tikz@auto@anchor\tikz@auto@post}% +\def\tikz@auto@anchor@right{\tikz@auto@pre\tikz@auto@anchor@prime\tikz@auto@post}% + +\def\tikz@auto@anchor@direction{left}% + +\tikzoption{text}{\def\tikz@textcolor{#1}}% +\tikzoption{font}{\def\tikz@textfont{#1}}% +\tikzoption{node font}{\def\tikz@node@textfont{#1}}% +\tikzoption{text opacity}{\def\tikz@textopacity{#1}}% +\tikzoption{text width}{\def\tikz@text@width{#1}}% +\tikzoption{text height}{\def\tikz@text@height{#1}}% +\tikzoption{text depth}{\def\tikz@text@depth{#1}}% +\tikzoption{text ragged}[]% +{\def\tikz@text@action{\pgfutil@raggedright\rightskip0pt plus2em \spaceskip.3333em \xspaceskip.5em\relax}}% +\tikzoption{text badly ragged}[]{\def\tikz@text@action{\pgfutil@raggedright\relax}}% +\tikzoption{text ragged left}[]% +{\def\tikz@text@action{\pgfutil@raggedleft\leftskip0pt plus2em \spaceskip.3333em \xspaceskip.5em\relax}}% +\tikzoption{text badly ragged left}[]{\def\tikz@text@action{\pgfutil@raggedleft\relax}}% +\tikzoption{text justified}[]{\def\tikz@text@action{\leftskip0pt\rightskip0pt\relax}}% +\tikzoption{text centered}[]{\def\tikz@text@action{% + \leftskip0pt plus2em% + \rightskip0pt plus2em% + \spaceskip.3333em \xspaceskip.5em% + \parfillskip=0pt% + \iftikz@warn@for@narrow@centered\else\hbadness10000\fi% + \let\\=\@centercr% + \relax}}% +\tikzoption{text badly centered}[]% +{\def\tikz@text@action{% + \let\\=\@centercr% + \parfillskip=0pt% + \rightskip\pgfutil@flushglue% + \leftskip\pgfutil@flushglue\relax}}% +\tikzset{badness warnings for centered text/.is if=tikz@warn@for@narrow@centered}% +\newif\iftikz@warn@for@narrow@centered + +\def\tikz@text@reset{% + \let\tikz@text@width=\pgfutil@empty + \let\tikz@text@height=\pgfutil@empty + \let\tikz@text@depth=\pgfutil@empty + \let\tikz@textcolor=\pgfutil@empty + \let\tikz@textfont=\pgfutil@empty + \let\tikz@textopacity=\pgfutil@empty + \let\tikz@node@textfont=\pgfutil@empty + \def\tikz@text@action{\pgfutil@raggedright\rightskip0pt plus2em \spaceskip.3333em \xspaceskip.5em\relax}% +} +\tikz@text@reset + + +\tikzset{ + node halign header/.initial=, + align/.is choice, + align/left/.style ={text ragged,node halign header=\tikz@align@left@header}, + align/flush left/.style ={text badly ragged,node halign header=\tikz@align@left@header}, + align/right/.style ={text ragged left,node halign header=\tikz@align@right@header}, + align/flush right/.style ={text badly ragged left,node halign header=\tikz@align@right@header}, + align/center/.style={text centered,node halign header=\tikz@align@center@header}, + align/flush center/.style={text badly centered,node halign header=\tikz@align@center@header}, + align/justify/.style ={text justified,node halign header=\tikz@align@left@header}, + align/none/.style ={text justified,node halign header=}, +}% +\def\tikz@align@left@header{##\hfil\cr}% +\def\tikz@align@right@header{\hfil##\cr}% +\def\tikz@align@center@header{\hfil##\hfil\cr}% + + + +\tikzoption{arrows}{\tikz@processarrows{#1}}% + + +\tikzoption{>}{\pgfdeclarearrow{name=<->,means={#1}}}% +\pgfdeclarearrow{name=|<->|, means={>[sep=0pt].|}}% + +\tikzoption{shorten <}{\pgfsetshortenstart{#1}}% +\tikzoption{shorten >}{\pgfsetshortenend{#1}}% + +\def\tikz@processarrows#1{% + \def\tikz@current@arrows{#1}% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \else% + \pgfsetarrows{#1}% + \fi% +}% + +\def\tikz@current@arrows{-}% + +\tikzoption{bend}{\tikz@scan@one@point\tikz@set@parabola@bend#1\relax}% +\tikzoption{bend pos}{\def\tikz@parabola@bend@factor{#1}}% +\tikzoption{parabola height}{% + \def\tikz@parabola@bend@factor{.5}% + \def\tikz@parabola@bend{\pgfpointadd{\pgfpoint{0pt}{#1}}{\tikz@last@position@saved}}}% + +\def\tikz@parabola@bend{\tikz@last@position@saved}% +\def\tikz@parabola@bend@factor{0}% + +\def\tikz@set@parabola@bend#1{\def\tikz@parabola@bend{#1}}% + +\tikzoption{domain}{\edef\tikz@plot@domain{#1}\expandafter\tikz@plot@samples@recalc\tikz@plot@domain\relax}% +\tikzoption{range}{\def\tikz@plot@range{#1}}% +\tikzoption{yrange}{\def\tikz@plot@range{#1}}% +\let\tikz@plot@range=\pgfutil@empty +\tikzoption{xrange}{\def\tikz@plot@xrange{#1}}% +\let\tikz@plot@xrange=\pgfutil@empty + +\tikzoption{smooth}[]{\let\tikz@plot@handler=\pgfplothandlercurveto}% +\tikzoption{smooth cycle}[]{\let\tikz@plot@handler=\pgfplothandlerclosedcurve}% +\tikzoption{sharp plot}[]{\let\tikz@plot@handler\pgfplothandlerlineto}% +\tikzoption{sharp cycle}[]{\let\tikz@plot@handler\pgfplothandlerpolygon}% + +\tikzoption{tension}{\pgfsetplottension{#1}}% + +\tikzoption{xcomb}[]{\let\tikz@plot@handler=\pgfplothandlerxcomb}% +\tikzoption{ycomb}[]{\let\tikz@plot@handler=\pgfplothandlerycomb}% +\tikzoption{polar comb}[]{\let\tikz@plot@handler=\pgfplothandlerpolarcomb}% +\tikzoption{ybar}[]{\let\tikz@plot@handler=\pgfplothandlerybar}% +\tikzoption{ybar interval}[]{\let\tikz@plot@handler=\pgfplothandlerybarinterval}% +\tikzoption{xbar interval}[]{\let\tikz@plot@handler=\pgfplothandlerxbarinterval}% +\tikzoption{xbar}[]{\let\tikz@plot@handler=\pgfplothandlerxbar}% +\tikzoption{const plot}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlineto}% +\tikzoption{const plot mark left}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlineto}% +\tikzoption{const plot mark right}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlinetomarkright}% +\tikzoption{const plot mark mid}[]{\let\tikz@plot@handler=\pgfplothandlerconstantlinetomarkmid}% +\tikzoption{jump mark right}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkright}% +\tikzoption{jump mark mid}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkmid}% +\tikzoption{jump mark left}[]{\let\tikz@plot@handler=\pgfplothandlerjumpmarkleft}% + +\tikzoption{raw gnuplot}[true]{\csname tikz@plot@raw@gnuplot#1\endcsname}% +\tikzoption{prefix}{\def\tikz@plot@prefix{#1}}% +\tikzoption{id}{\def\tikz@plot@id{#1}}% + +\tikzoption{samples}{\pgfmathsetmacro\tikz@plot@samples{max(2,#1)}\expandafter\tikz@plot@samples@recalc\tikz@plot@domain\relax}% +\tikzoption{samples at}{\def\tikz@plot@samplesat{#1}}% +\tikzoption{parametric}[true]{\csname tikz@plot@parametric#1\endcsname}% + +\tikzoption{variable}{\def\tikz@plot@var{#1}}% + +\tikzoption{only marks}[]{\let\tikz@plot@handler\pgfplothandlerdiscard}% + +\tikzoption{mark}{% + \def\tikz@plot@mark{#1}% + \def\tikz@temp{none}% + \ifx\tikz@temp\tikz@plot@mark + \let\tikz@plot@mark=\pgfutil@empty + \fi +}% +\tikzset{ + no marks/.style={mark=none},% + no markers/.style={mark=none},% + every mark/.style={}, + mark options/.style={% + every mark/.style={#1}% + }}% +\tikzoption{mark size}{\pgfsetplotmarksize{#1}}% + +\tikzoption{mark indices}{\def\tikz@mark@list{#1}}% +\tikzoption{mark phase}{\pgfsetplotmarkphase{#1}}% +\tikzoption{mark repeat}{\pgfsetplotmarkrepeat{#1}}% + +\let\tikz@mark@list=\pgfutil@empty + +\let\tikz@plot@handler=\pgfplothandlerlineto +\let\tikz@plot@mark=\pgfutil@empty + +\def\tikz@plot@samples{25}% +\def\tikz@plot@domain{-5:5}% +\def\tikz@plot@var{\x}% +\def\tikz@plot@samplesat{-5,-4.5833333,...,5}% +\def\tikz@plot@samples@recalc#1:#2\relax{% + \begingroup + \pgfmathparse{#1}% + \let\tikz@temp@start=\pgfmathresult% + \pgfmathparse{#2}% + \let\tikz@temp@end=\pgfmathresult% + \pgfmathsetmacro\tikz@temp@diff{(\tikz@temp@end-\tikz@temp@start)/(\tikz@plot@samples-1)}% + \pgfkeys{/pgf/fpu/output format/fixed/.try}% + \pgfmathsetmacro\tikz@temp@diff@abs{abs(\tikz@temp@diff)}% + \ifdim\tikz@temp@diff@abs pt<0.0001pt\relax% + \edef\tikz@plot@samplesat{\tikz@temp@start,\tikz@temp@end}% + \else% + \pgfmathparse{\tikz@temp@start+\tikz@temp@diff}% + \edef\tikz@plot@samplesat{\tikz@temp@start,\pgfmathresult,...,\tikz@temp@end}% + \fi% + \pgfmath@smuggleone\tikz@plot@samplesat + \endgroup +}% + + +\def\tikz@plot@prefix{\jobname.}% +\def\tikz@plot@id{pgf-plot}% + +\newif\iftikz@plot@parametric +\newif\iftikz@plot@raw@gnuplot + + +\tikzoption{to path}{\def\tikz@to@path{#1}}% + +\def\tikz@to@path{-- (\tikztotarget) \tikztonodes}% + +\tikzset{edge macro/.store in=\tikz@edge@macro}% +\let\tikz@edge@macro\pgfutil@empty + +\tikzset{ + edge node/.code={ + \expandafter\def\expandafter\tikz@tonodes\expandafter{\tikz@tonodes #1} + }, + edge label/.style={/tikz/edge node={node[auto]{#1}}}, + edge label'/.style={/tikz/edge node={node[auto,swap]{#1}}}, +}% + + +\tikzset{ + append after command/.code=\expandafter\def\expandafter\tikz@after@path\expandafter{\tikz@after@path#1}, + prefix after command/.code={% + \def\tikz@temp{#1}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@after@path% + \expandafter\expandafter\expandafter{% + \expandafter\tikz@temp\tikz@after@path}% + }, +}% +\let\tikz@after@path\pgfutil@empty + + +\newif\iftikz@child@missing +\pgfkeys{/tikz/missing/.is if=tikz@child@missing}% + +\tikzset{edge from parent macro/.initial=\tikz@edge@from@parent@macro}% +\def\tikz@edge@from@parent@macro#1#2{ + [style=edge from parent, #1, /utils/exec=\tikz@node@is@a@labeltrue] \tikz@edge@to@parent@path #2}% + +\tikzoption{edge from parent path}{\def\tikz@edge@to@parent@path{#1}}% + +\tikzoption{parent anchor}{\def\tikzparentanchor{.#1}\ifx\tikzparentanchor\tikz@border@text\let\tikzparentanchor\pgfutil@empty\fi}% +\tikzoption{child anchor}{\def\tikzchildanchor{.#1}\ifx\tikzchildanchor\tikz@border@text\let\tikzchildanchor\pgfutil@empty\fi}% + +\tikzoption{level distance}{\pgfmathsetlength\tikzleveldistance{#1}}% +\tikzoption{sibling distance}{\pgfmathsetlength\tikzsiblingdistance{#1}}% + +\tikzoption{growth function}{\let\tikz@grow=#1}% + +\tikzset{grow siblings on line/.style={growth function=\tikz@grow@direction}}% + +\tikzoption{growth parent anchor}{\def\tikz@growth@anchor{#1}}% +\tikzoption{grow}{\tikz@set@growth{#1}\edef\tikz@special@level{\the\tikztreelevel}}% +\tikzoption{grow'}{\tikz@set@growth{#1}\tikz@swap@growth\edef\tikz@special@level{\the\tikztreelevel}}% + +\def\tikz@growth@anchor{center}% + +\def\tikz@special@level{-1}% + +\def\tikz@swap@growth{% + \let\tikz@temp=\tikz@angle@grow@right% + \let\tikz@angle@grow@right=\tikz@angle@grow@left% + \let\tikz@angle@grow@left=\tikz@temp% +}% + +\def\tikz@set@growth#1{% + \let\tikz@grow=\tikz@grow@direction% + \expandafter\ifx\csname tikz@grow@direction@#1\endcsname\relax% + \c@pgf@counta=#1\relax% + \else% + \c@pgf@counta=\csname tikz@grow@direction@#1\endcsname% + \fi% + \edef\tikz@angle@grow{\the\c@pgf@counta}% + \advance\c@pgf@counta by-90\relax% + \edef\tikz@angle@grow@left{\the\c@pgf@counta}% + \advance\c@pgf@counta by180\relax% + \edef\tikz@angle@grow@right{\the\c@pgf@counta}% +}% + +\def\tikz@border@text{.border}% +\let\tikzparentanchor=\pgfutil@empty +\let\tikzchildanchor=\pgfutil@empty +\def\tikz@edge@to@parent@path{(\tikzparentnode\tikzparentanchor) -- (\tikzchildnode\tikzchildanchor)}% + +\tikzleveldistance=15mm% +\tikzsiblingdistance=15mm% + +\def\tikz@grow@direction@down{-90}% +\def\tikz@grow@direction@up{90}% +\def\tikz@grow@direction@left{180}% +\def\tikz@grow@direction@right{0}% + +\def\tikz@grow@direction@south{-90}% +\def\tikz@grow@direction@north{90}% +\def\tikz@grow@direction@west{180}% +\def\tikz@grow@direction@east{0}% + +\expandafter\def\csname tikz@grow@direction@north east\endcsname{45}% +\expandafter\def\csname tikz@grow@direction@north west\endcsname{135}% +\expandafter\def\csname tikz@grow@direction@south east\endcsname{-45}% +\expandafter\def\csname tikz@grow@direction@south west\endcsname{-135}% + +\def\tikz@grow@direction{% + \pgftransformshift{\pgfpointpolar{\tikz@angle@grow}{\tikzleveldistance}}% + \ifnum\tikztreelevel=\tikz@special@level% + \else% + \pgf@xc=.5\tikzsiblingdistance% + \c@pgf@counta=\tikznumberofchildren% + \advance\c@pgf@counta by1\relax% + \pgfutil@tempdima=\c@pgf@counta\pgf@xc% + \pgftransformshift{\pgfpointpolar{\tikz@angle@grow@left}{\pgfutil@tempdima}}% + \pgftransformshift{\pgfpointpolar{\tikz@angle@grow@right}{\tikznumberofcurrentchild\tikzsiblingdistance}}% + \fi% +}% + +\tikzset{grow=down}% + + +\tikzset{snake/.code=\tikzerror{You need to say \string\usetikzlibrary{snakes}}}% + +\tikzset{decorate/.code=\tikzerror{You need to load a decoration library}}% + +\usepgfmodule{matrix}% + +\tikzoption{matrix}[true]{\csname tikz@is@matrix#1\endcsname}% + +\tikzoption{matrix anchor}{\def\tikz@matrix@anchor{#1}}% + +\tikzoption{column sep}{\def\pgfmatrixcolumnsep{#1}}% +\tikzoption{row sep}{\def\pgfmatrixrowsep{#1}}% + +\tikzoption{cells}{\tikzset{every cell/.append style={#1}}}% + +\tikzoption{ampersand replacement}{\def\tikz@ampersand@replacement{#1}}% + +\newif\iftikz@is@matrix +\let\tikz@matrix@anchor=\pgfutil@empty +\let\tikz@ampersand@replacement=\pgfutil@empty + + +\tikzset{% + handle active characters in code/.is if=tikz@handle@active@code, + handle active characters in nodes/.is if=tikz@handle@active@nodes, +}% +\newif\iftikz@handle@active@code +\newif\iftikz@handle@active@nodes + + +\tikzoption{execute at begin picture}{\expandafter\def\expandafter\tikz@atbegin@picture\expandafter{\tikz@atbegin@picture#1}}% +\tikzoption{execute at end picture}{\expandafter\def\expandafter\tikz@atend@picture\expandafter{\tikz@atend@picture#1}}% +\tikzoption{execute at begin scope}{\expandafter\def\expandafter\tikz@atbegin@scope\expandafter{\tikz@atbegin@scope#1}}% +\tikzoption{execute at end scope}{\expandafter\def\expandafter\tikz@atend@scope\expandafter{\tikz@atend@scope#1}}% +\tikzoption{execute at begin to}{\expandafter\def\expandafter\tikz@atbegin@to\expandafter{\tikz@atbegin@to#1}}% +\tikzoption{execute at end to}{\expandafter\def\expandafter\tikz@atend@to\expandafter{\tikz@atend@to#1}}% +\tikzoption{execute at begin node}{\expandafter\def\expandafter\tikz@atbegin@node\expandafter{\tikz@atbegin@node#1}}% +\tikzoption{execute at end node}{\expandafter\def\expandafter\tikz@atend@node\expandafter{\tikz@atend@node#1}}% +\tikzoption{execute at begin matrix}{\expandafter\def\expandafter\tikz@atbegin@matrix\expandafter{\tikz@atbegin@matrix#1}}% +\tikzoption{execute at end matrix}{\expandafter\def\expandafter\tikz@atend@matrix\expandafter{\tikz@atend@matrix#1}}% +\tikzoption{execute at begin cell}{\expandafter\def\expandafter\tikz@atbegin@cell\expandafter{\tikz@atbegin@cell#1}}% +\tikzoption{execute at end cell}{\expandafter\def\expandafter\tikz@atend@cell\expandafter{\tikz@atend@cell#1}}% +\tikzoption{execute at empty cell}{\expandafter\def\expandafter\tikz@at@emptycell\expandafter{\tikz@at@emptycell#1}}% + +\let\tikz@atbegin@picture=\pgfutil@empty +\let\tikz@atend@picture=\pgfutil@empty +\let\tikz@atbegin@scope=\pgfutil@empty +\let\tikz@atend@scope=\pgfutil@empty +\let\tikz@atbegin@to=\pgfutil@empty +\let\tikz@atend@to=\pgfutil@empty +\let\tikz@atbegin@node=\pgfutil@empty +\let\tikz@atend@node=\pgfutil@empty +\let\tikz@atbegin@cell=\pgfutil@empty +\let\tikz@atend@cell=\pgfutil@empty +\let\tikz@at@emptycell=\pgfutil@empty +\let\tikz@atbegin@matrix=\pgfutil@empty +\let\tikz@atend@matrix=\pgfutil@empty + + +\tikzset{preaction/.code=\expandafter\def\expandafter\tikz@preactions\expandafter{\tikz@preactions\tikz@extra@preaction{#1}}}% +\tikzset{postaction/.code=\expandafter\def\expandafter\tikz@postactions\expandafter{\tikz@postactions\tikz@extra@postaction{#1}}}% +\let\tikz@preactions=\pgfutil@empty +\let\tikz@postactions=\pgfutil@empty + +\tikzoption{set style}{\tikzstyle#1}% + +\def\tikzstyle{\pgfutil@ifnextchar\bgroup\tikz@style@parseA\tikz@style@parseB}% +\def\tikz@style@parseB#1={\tikz@style@parseA{#1}=}% +\def\tikz@style@parseA#1#2=#3[#4]{% + \pgfutil@in@[{#2}% + \ifpgfutil@in@% + \tikz@style@parseC{#1}#2={#4}% + \else% + \tikz@style@parseD{#1}#2={#4}% + \fi% +}% + +\def\tikz@style@parseC#1[#2]#3=#4{% + \pgfkeys{/tikz/#1/.default={#2}}% + \pgfutil@in@+{#3}% + \ifpgfutil@in@% + \pgfkeys{/tikz/#1/.append style={#4}}% + \else% + \pgfkeys{/tikz/#1/.style={#4}}% + \fi}% +\def\tikz@style@parseD#1#2=#3{% + \pgfutil@in@+{#2}% + \ifpgfutil@in@% + \pgfkeys{/tikz/#1/.append style={#3}}% + \else% + \pgfkeys{/tikz/#1/.style={#3}}% + \fi}% + + + +\tikzset{help lines/.style= {color=gray,line width=0.2pt}}% + +\tikzset{every picture/.style= {}}% +\tikzset{every path/.style= {}}% +\tikzset{every scope/.style= {}}% +\tikzset{every plot/.style= {}}% +\tikzset{every node/.style= {}}% +\tikzset{every child/.style= {}}% +\tikzset{every child node/.style= {}}% +\tikzset{every to/.style= {}}% +\tikzset{every cell/.style= {}}% +\tikzset{every matrix/.style= {}}% +\tikzset{every edge/.style= {draw}}% +\tikzset{every label/.style= {draw=none,fill=none}}% +\tikzset{every pin/.style= {draw=none,fill=none}}% +\tikzset{every pin edge/.style= {help lines}}% + +\tikzset{ultra thin/.style= {line width=0.1pt}}% +\tikzset{very thin/.style= {line width=0.2pt}}% +\tikzset{thin/.style= {line width=0.4pt}}% +\tikzset{semithick/.style= {line width=0.6pt}}% +\tikzset{thick/.style= {line width=0.8pt}}% +\tikzset{very thick/.style= {line width=1.2pt}}% +\tikzset{ultra thick/.style= {line width=1.6pt}}% + +\tikzset{solid/.style= {dash pattern=}}% +\tikzset{dotted/.style= {dash pattern=on \pgflinewidth off 2pt}}% +\tikzset{densely dotted/.style= {dash pattern=on \pgflinewidth off 1pt}}% +\tikzset{loosely dotted/.style= {dash pattern=on \pgflinewidth off 4pt}}% +\tikzset{dashed/.style= {dash pattern=on 3pt off 3pt}}% +\tikzset{densely dashed/.style= {dash pattern=on 3pt off 2pt}}% +\tikzset{loosely dashed/.style= {dash pattern=on 3pt off 6pt}}% +\tikzset{dashdotted/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt}}% +\tikzset{dash dot/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt}}% +\tikzset{densely dashdotted/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt}}% +\tikzset{densely dash dot/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt}}% +\tikzset{loosely dashdotted/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt}}% +\tikzset{loosely dash dot/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt}}% +\tikzset{dashdotdotted/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt on \the\pgflinewidth off 2pt}}% +\tikzset{densely dashdotdotted/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt on \the\pgflinewidth off 1pt}}% +\tikzset{loosely dashdotdotted/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt on \the\pgflinewidth off 4pt}}% +\tikzset{dash dot dot/.style= {dash pattern=on 3pt off 2pt on \the\pgflinewidth off 2pt on \the\pgflinewidth off 2pt}}% +\tikzset{densely dash dot dot/.style= {dash pattern=on 3pt off 1pt on \the\pgflinewidth off 1pt on \the\pgflinewidth off 1pt}}% +\tikzset{loosely dash dot dot/.style= {dash pattern=on 3pt off 4pt on \the\pgflinewidth off 4pt on \the\pgflinewidth off 4pt}}% + + +\tikzset{transparent/.style= {opacity=0}}% +\tikzset{ultra nearly transparent/.style={opacity=0.05}}% +\tikzset{very nearly transparent/.style= {opacity=0.1}}% +\tikzset{nearly transparent/.style= {opacity=0.25}}% +\tikzset{semitransparent/.style= {opacity=0.5}}% +\tikzset{nearly opaque/.style= {opacity=0.75}}% +\tikzset{very nearly opaque/.style= {opacity=0.9}}% +\tikzset{ultra nearly opaque/.style= {opacity=0.95}}% +\tikzset{opaque/.style= {opacity=1}}% + +\tikzset{at start/.style= {pos=0}}% +\tikzset{very near start/.style= {pos=0.125}}% +\tikzset{near start/.style= {pos=0.25}}% +\tikzset{midway/.style= {pos=0.5}}% +\tikzset{near end/.style= {pos=0.75}}% +\tikzset{very near end/.style= {pos=0.875}}% +\tikzset{at end/.style= {pos=1}}% + +\tikzset{bend at start/.style= {bend pos=0,bend={+(0,0)}}}% +\tikzset{bend at end/.style= {bend pos=1,bend={+(0,0)}}}% + +\tikzset{edge from parent/.style= {draw}}% + + + +\tikzset{ + animate/.code=\tikzerror{You need to say \string\usetikzlibrary{animations} to use animations} +} + +\newif\iftikz@is@node +\let\tikz@id@name\pgfutil@empty +\let\tikz@id@hook\pgfutil@empty +\def\tikz@call@id@hook{\ifx\tikz@id@hook\pgfutil@empty\else\tikz@id@hook\pgfuseid{\tikz@id@name}\fi}% + + +\let\tikz@clear@rdf@options\relax +\let\tikz@do@rdf@post@options\relax +\let\tikz@do@rdf@pre@options\relax + + + +\pgfkeys{/tikz/style/.style={#1}}% + +\pgfkeys{/tikz/.unknown/.code=% + \let\tikz@key\pgfkeyscurrentname% + \pgfkeys{/pgf/\tikz@key/.try={#1}}% + \ifpgfkeyssuccess% + \else% + \expandafter\pgfutil@in@\expandafter!\expandafter{\tikz@key}% + \ifpgfutil@in@% + \expandafter\tikz@addoption\expandafter{\expandafter\tikz@compat@color@set\expandafter{\tikz@key}}% + \edef\tikz@textcolor{\tikz@key}% + \else% + \pgfutil@doifcolorelse{\tikz@key} + {% + \expandafter\tikz@addoption\expandafter{\expandafter\tikz@compat@color@set\expandafter{\tikz@key}}% + \edef\tikz@textcolor{\tikz@key}% + }% + {% + \expandafter\pgfutil@in@\expandafter-\expandafter{\tikz@key}% + \ifpgfutil@in@% + \expandafter\tikz@processarrows\expandafter{\tikz@key}% + \else% + \expandafter\ifx\csname pgf@sh@s@\tikz@key\endcsname\relax% + \pgfkeys{/errors/unknown key/.expand + once=\expandafter{\expandafter/\expandafter t\expandafter i\expandafter k\expandafter z\expandafter/\tikz@key}{#1}}% + \else% + \edef\tikz@shape{\tikz@key}% + \fi% + \fi% + }% + \fi% + \fi% +}% +\def\tikz@compat@color@set#1{% + \pgfutil@color{#1}\pgfutil@colorlet{pgffillcolor}{#1}% + \expandafter\let\expandafter\pgf@temp\csname\string\color@pgffillcolor\endcsname% + \global\let\pgf@strokecolor@global=\pgf@temp + \global\let\pgf@fillcolor@global=\pgf@temp +}% + +\def\tikz@startup@env{% + \ifnum\the\catcode`\;=\active\relax\expandafter\let\expandafter\tikz@origsemi\expandafter=\tikz@activesemicolon\fi% + \ifnum\the\catcode`\:=\active\relax\expandafter\let\expandafter\tikz@origcolon\expandafter=\tikz@activecolon\fi% + \ifnum\the\catcode`\|=\active\relax\expandafter\let\expandafter\tikz@origbar\expandafter=\tikz@activebar\fi% + \tikz@deactivatthings% + \iftikz@handle@active@code% + \tikz@switchoff@shorthands% + \fi% +}% + +\newif\iftikz@inside@picture +\tikz@inside@picturefalse +\def\tikz@check@inside@picture{% + \iftikz@inside@picture% + \pgfwarning{Nesting tikzpictures is NOT supported}% + \fi% + \tikz@inside@picturetrue% +} + +\def\tikzpicture{% + \begingroup% + \tikz@startup@env% + \tikz@collect@scope@anims\tikz@picture}% +\def\tikz@picture[#1]{% + \pgfpicture% + \let\tikz@atbegin@picture=\pgfutil@empty% + \let\tikz@atend@picture=\pgfutil@empty% + \let\tikz@transform=\relax% + \def\tikz@time{.5}% + \tikz@installcommands% + \scope[every picture,#1]% + \iftikz@handle@active@code% + \tikz@switchoff@shorthands% + \fi% + \expandafter\tikz@atbegin@picture% + \tikz@lib@scope@check% +}% +\def\endtikzpicture{% + \tikz@atend@picture% + \global\let\pgf@shift@baseline@smuggle=\pgf@baseline% + \global\let\pgf@trimleft@final@smuggle=\pgf@trimleft% + \global\let\pgf@trimright@final@smuggle=\pgf@trimright% + \global\let\pgf@remember@smuggle=\ifpgfrememberpicturepositiononpage% + \pgf@remember@layerlist@globally + \endscope% + \let\pgf@baseline=\pgf@shift@baseline@smuggle% + \let\pgf@trimleft=\pgf@trimleft@final@smuggle% + \let\pgf@trimright=\pgf@trimright@final@smuggle% + \let\ifpgfrememberpicturepositiononpage=\pgf@remember@smuggle% + \pgf@restore@layerlist@from@global + \endpgfpicture\endgroup}% + + + + +\def\tikz{% + \begingroup% + \tikz@startup@env% + \tikz@collect@scope@anims\tikz@opt}% +\def\tikz@opt[#1]{\tikzpicture[#1]\pgfutil@ifnextchar\bgroup{\tikz@}{\tikz@@single}}% +\def\tikz@{\bgroup\tikz@auto@end@pathtrue\aftergroup\endtikzpicture\aftergroup\endgroup\let\pgf@temp=}% +\def\tikz@@single#1{% + \expandafter\ifx\csname tikz@protected@command\string#1\endcsname\relax% + \expandafter\tikz@@% + \else% + \begingroup\def\tikz@path@do@at@end{\endgroup\endtikzpicture\endgroup}% + \fi% + #1% +}% + +\expandafter\let\csname tikz@protected@command\string\draw\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\pattern\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\fill\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\filldraw\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\shade\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\shadedraw\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\clip\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\graph\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\useasboundingbox\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\node\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\coordinate\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\matrix\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\datavisualization\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\path\endcsname\pgfutil@empty% +\expandafter\let\csname tikz@protected@command\string\pic\endcsname\pgfutil@empty% + +\def\tikz@@{% + \let\tikz@next=\tikz@collectnormalsemicolon% + \ifnum\the\catcode`\;=\active\relax% + \let\tikz@next=\tikz@collectactivesemicolon% + \fi% + \tikz@next}% +\def\tikz@collectnormalsemicolon#1;{#1;\endtikzpicture\endgroup} +{ + \catcode`\;=\active + \gdef\tikz@collectactivesemicolon#1;{#1;\endtikzpicture\endgroup} +}% + +\def\tikzifinpicture#1#2{% + \pgfutil@ifundefined{filldraw}{#2}{#1}% +}% + + +\def\tikz@collect@scope@anims#1{% + \pgfutil@ifnextchar[#1{#1[]}% +}% + +\def\tikz@scope@env{% + \pgfscope% + \begingroup% + \let\tikz@atbegin@scope=\pgfutil@empty% + \let\tikz@atend@scope=\pgfutil@empty% + \let\tikz@options=\pgfutil@empty% + \tikz@clear@rdf@options% + \let\tikz@mode=\pgfutil@empty% + \let\tikz@id@name=\pgfutil@empty% + \tikz@transparency@groupfalse% + \tikzset{every scope/.try}% + \tikz@collect@scope@anims\tikz@scope@opt% +}% +\def\tikz@scope@opt[#1]{% + \tikzset{#1}% + \tikz@options% + \tikz@do@rdf@pre@options% + \iftikz@transparency@group\expandafter\pgftransparencygroup\expandafter[\tikz@transparency@group@options]\tikz@blend@group\fi% + \tikz@is@nodefalse% + \tikz@call@id@hook% + \pgfidscope% + \tikz@do@rdf@post@options% + \begingroup% + \let\tikz@id@name\pgfutil@empty% + \expandafter\tikz@atbegin@scope% + \expandafter\pgfclearid% + \tikz@lib@scope@check% +}% +\def\endtikz@scope@env{% + \tikz@atend@scope% + \endgroup% + \endpgfidscope% + \iftikz@transparency@group\endpgftransparencygroup\fi% + \endgroup% + \endpgfscope% + \tikz@lib@scope@check% +}% + + +\def\tikz@scoped{\tikz@collect@scope@anims\tikz@scoped@opt}% +\def\tikz@scoped@opt[#1]{\scope[#1]\pgfutil@ifnextchar\bgroup{\tikz@scoped@}{\tikz@scoped@@single}}% +\def\tikz@scoped@{\bgroup\tikz@auto@end@pathtrue\aftergroup\endscope\let\pgf@temp=}% +\def\tikz@scoped@@single#1{% + \expandafter\ifx\csname tikz@scoped@protected@command\string#1\endcsname\relax% + \expandafter\tikz@scoped@@% + \else% + \begingroup\def\tikz@scoped@path@do@at@end{\endgroup\endscope}% + \fi% + #1% +}% +\def\tikz@scoped@@{% + \let\tikz@scoped@next=\tikz@scoped@collectnormalsemicolon% + \ifnum\the\catcode`\;=\active\relax% + \let\tikz@scoped@next=\tikz@scoped@collectactivesemicolon% + \fi% + \tikz@scoped@next}% +\def\tikz@scoped@collectnormalsemicolon#1;{#1;\endscope} +{ + \catcode`\;=\active + \gdef\tikz@scoped@collectactivesemicolon#1;{#1;\endscope} +}% + + +\def\tikzaddtikzonlycommandshortcutlet#1#2{% + \expandafter\def\expandafter\tikz@installcommands\expandafter{\tikz@installcommands + \let#1=#2% + }% +}% + +\def\tikzaddtikzonlycommandshortcutdef#1#2{% + \expandafter\def\expandafter\tikz@installcommands\expandafter{\tikz@installcommands + \def#1{#2}% + }% +}% + +\def\tikz@installcommands{% + \let\tikz@origscope=\scope% + \let\tikz@origscoped=\scoped% + \let\tikz@origendscope=\endscope% + \let\tikz@origstartscope=\startscope% + \let\tikz@origstopscope=\stopscope% + \let\tikz@origpath=\path% + \let\tikz@origagainpath=\againpath% + \let\tikz@origdraw=\draw% + \let\tikz@origpattern=\pattern% + \let\tikz@origfill=\fill% + \let\tikz@origfilldraw=\filldraw% + \let\tikz@origshade=\shade% + \let\tikz@origshadedraw=\shadedraw% + \let\tikz@origclip=\clip% + \let\tikz@origuseasboundingbox=\useasboundingbox% + \let\tikz@orignode=\node% + \let\tikz@origpic=\pic% + \let\tikz@origcoordinate=\coordinate% + \let\tikz@origmatrix=\matrix% + \let\tikz@origcalendar=\calendar% + \let\tikz@origdv=\datavisualization% + \let\tikz@origgraph=\graph% + \let\scope=\tikz@scope@env% + \let\scoped=\tikz@scoped% + \let\endscope=\endtikz@scope@env% + \let\startscope=\scope% + \let\stopscope=\endscope% + \let\path=\tikz@command@path% + \let\againpath=\tikz@command@againpath% + \def\draw{\path[draw]}% + \def\pattern{\path[pattern]}% + \def\fill{\path[fill]}% + \def\filldraw{\path[fill,draw]}% + \def\shade{\path[shade]}% + \def\shadedraw{\path[shade,draw]}% + \def\clip{\path[clip]}% + \def\graph{\path graph}% + \def\useasboundingbox{\path[use as bounding box]}% + \def\node{\tikz@path@overlay{node}}% + \def\pic{\tikz@path@overlay{pic}}% + \def\coordinate{\tikz@path@overlay{coordinate}}% + \def\matrix{\tikz@path@overlay{node[matrix]}}% + \def\calendar{\tikz@lib@cal@calendar}% + \def\datavisualization{\tikz@lib@datavisualization}% +}% +\ifx\tikz@lib@cal@calendar\@undefined +\def\tikz@lib@cal@calendar{\tikzerror{You need to say \string\usetikzlibrary{calendar} to use the \string\calendar{} command}}% +\fi +\ifx\tikz@lib@datavisualization\@undefined +\def\tikz@lib@datavisualization{\tikzerror{You need to say \string\usetikzlibrary{datavisualization} to use the \string\datavisualization{} command}}% +\fi + +\def\tikz@path@overlay#1{% + \let\tikz@signal@path=\tikz@signal@path% + \pgfutil@ifnextchar<{\tikz@path@overlayed{#1}}{\path #1}}% +\def\tikz@path@overlayed#1<#2>{\path<#2> #1}% + +\def\tikz@uninstallcommands{% + \let\scope=\tikz@origscope% + \let\scoped=\tikz@origscoped% + \let\endscope=\tikz@origendscope% + \let\startscope=\tikz@origstartscope% + \let\stopscope=\tikz@origstopscope% + \let\path=\tikz@origpath% + \let\againpath=\tikz@origagainpath% + \let\draw=\tikz@origdraw% + \let\pattern=\tikz@origpattern% + \let\fill=\tikz@origfill% + \let\filldraw=\tikz@origfilldraw% + \let\shade=\tikz@origshade% + \let\shadedraw=\tikz@origshadedraw% + \let\clip=\tikz@origclip% + \let\useasboundingbox=\tikz@origuseasboundingbox% + \let\node=\tikz@orignode% + \let\pic=\tikz@origpic% + \let\coordinate=\tikz@origcoordinate% + \let\matrix=\tikz@origmatrix% + \let\calendar=\tikz@origcalendar% + \let\datavisualization=\tikz@origdv% + \let\graph=\tikz@origgraph% +}% + + +{% + \catcode`\;=12 + \gdef\tikz@nonactivesemicolon{;}% + \catcode`\:=12 + \gdef\tikz@nonactivecolon{:}% + \catcode`\|=12 + \gdef\tikz@nonactivebar{|}% + \catcode`\!=12 + \gdef\tikz@nonactiveexlmark{!}% + \catcode`\;=\active + \catcode`\:=\active + \catcode`\|=\active + \catcode`\"=\active + \catcode`\!=\active + \gdef\tikz@activesemicolon{;}% + \gdef\tikz@activecolon{:}% + \gdef\tikz@activebar{|}% + \gdef\tikz@activequotes{"}% + \global\let\tikz@active@quotes@token="% + \gdef\tikz@activeexlmark{!}% + \gdef\tikz@deactivatthings{% + \def;{\tikz@nonactivesemicolon}% + \def:{\tikz@nonactivecolon}% + \def|{\tikz@nonactivebar}% + \def!{\tikz@nonactiveexlmark}% + }% +}% + +\let\tikz@orig@shorthands\pgfutil@empty +\def\tikz@switchoff@shorthands{% + \ifx\tikz@orig@shorthands\pgfutil@empty% + \edef\tikz@orig@shorthands{% + \catcode\noexpand`\noexpand\;\the\catcode`\;\relax% + \catcode\noexpand`\noexpand\:\the\catcode`\:\relax% + \catcode\noexpand`\noexpand\|\the\catcode`\|\relax% + \catcode\noexpand`\noexpand\!\the\catcode`\!\relax% + \catcode\noexpand`\noexpand\,\the\catcode`\,\relax% + \catcode\noexpand`\noexpand\<\the\catcode`\<\relax% + \catcode\noexpand`\noexpand\>\the\catcode`\>\relax% + \catcode\noexpand`\noexpand\"\the\catcode`\"\relax% + \catcode\noexpand`\noexpand\'\the\catcode`\'\relax% + \catcode\noexpand`\noexpand\-\the\catcode`\-\relax% + \catcode\noexpand`\noexpand\=\the\catcode`\=\relax% + \catcode\noexpand`\noexpand\.\the\catcode`\.\relax% + \catcode\noexpand`\noexpand\$\the\catcode`\$\relax% + }% + \catcode`\;12\relax% + \catcode`\:12\relax% + \catcode`\|12\relax% + \catcode`\!12\relax% + \catcode`\,12\relax% + \catcode`\<12\relax% + \catcode`\>12\relax% + \catcode`\"12\relax% + \catcode`\'12\relax% + \catcode`\-12\relax% + \catcode`\=12\relax% + \catcode`\.12\relax% + \catcode`\$3\relax% + \fi% +}% + + + + +\def\tikz@command@path{% + \let\tikz@signal@path=\tikz@signal@path% + \pgfutil@ifnextchar[{\tikz@check@earg}% + {\pgfutil@ifnextchar<{\tikz@doopt}{\tikz@@command@path}}}% +\pgfutil@protected\def\tikz@signal@path{\tikz@signal@path}% +\def\tikz@check@earg[#1]{% + \pgfutil@ifnextchar<{\tikz@swap@args[#1]}{\tikz@@command@path[#1]}} +\def\tikz@swap@args[#1]<#2>{\tikz@command@path<#2>[#1]}% + +\def\tikz@doopt{% + \let\tikz@next=\tikz@eargnormalsemicolon% + \ifnum\the\catcode`\;=\active\relax% + \let\tikz@next=\tikz@eargactivesemicolon% + \fi% + \tikz@next}% +\long\def\tikz@eargnormalsemicolon<#1>#2;{\alt<#1>{\tikz@@command@path#2;}{\tikz@path@do@at@end}}% +{ + \catcode`\;=\active + \long\global\def\tikz@eargactivesemicolon<#1>#2;{\alt<#1>{\tikz@@command@path#2;}{\tikz@path@do@at@end}}% +} + +\def\tikz@@command@path{% + \edef\tikzscope@linewidth{\the\pgflinewidth}% + \begingroup% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \let\tikz@path@do@at@end=\tikz@lib@scope@check% + \let\tikz@options=\pgfutil@empty% + \tikz@clear@rdf@options% + \let\tikz@mode=\pgfutil@empty% + \let\tikz@moveto@waiting=\relax% + \let\tikz@timer=\relax% + \let\tikz@tangent=\relax% + \let\tikz@collected@onpath=\pgfutil@empty% + \let\tikz@preactions=\pgfutil@empty% + \let\tikz@postactions=\pgfutil@empty% + \tikz@snakedfalse% + \tikz@decoratepathfalse% + \tikz@node@is@a@labelfalse% + \tikz@resetexpandcount + \pgf@path@lastx=0pt% + \pgf@path@lasty=0pt% + \tikz@lastx=0pt% + \tikz@lasty=0pt% + \tikz@lastxsaved=0pt% + \tikz@lastysaved=0pt% + \tikzset{every path/.try}% + \tikz@scan@next@command% +}% +\def\tikz@scan@next@command{% + \ifx\tikz@collected@onpath\pgfutil@empty% + \else% + \tikz@invoke@collected@onpath% + \fi% + \afterassignment\tikz@handle\let\pgf@let@token=% +}% +\newcount\tikz@expandcount +\def\tikz@resetexpandcount{\tikz@expandcount=100\relax} +\let\tikz@collected@onpath=\pgfutil@empty% + +\edef\tikz@frozen@relax@token{\ifnum0=0\fi} + +\def\tikz@handle{% + \pgfutil@switch\pgfutil@ifx\pgf@let@token{% + {(}{\let\pgfutil@next\tikz@movetoabs}% + {+}{\let\pgfutil@next\tikz@movetorel}% + {-}{\let\pgfutil@next\tikz@lineto}% + {.}{\let\pgfutil@next\tikz@dot}% + {r}{\let\pgfutil@next\tikz@rect}% + {n}{\let\pgfutil@next\tikz@fig}% + {[}{\let\pgfutil@next\tikz@parse@options}% + {c}{\let\pgfutil@next\tikz@cchar}% + {\bgroup}{\let\pgfutil@next\tikz@beginscope}% + {\egroup}{\let\pgfutil@next\tikz@endscope}% + {;}{\let\pgfutil@next\tikz@finish}% + {a}{\let\pgfutil@next\tikz@a@char}% + {e}{\let\pgfutil@next\tikz@e@char}% + {g}{\let\pgfutil@next\tikz@g@char}% + {s}{\let\pgfutil@next\tikz@schar}% + {|}{\let\pgfutil@next\tikz@vh@lineto}% + {p}{\pgfsetmovetofirstplotpoint\let\pgfutil@next\tikz@pchar}% + {t}{\let\pgfutil@next\tikz@to}% + {\pgfextra}{\let\pgfutil@next\tikz@extra}% + {\foreach}{\let\pgfutil@next\tikz@foreach}% + {f}{\let\pgfutil@next\tikz@fchar}% + {\pgf@stop}{\let\pgfutil@next\relax}% + {\par}{\let\pgfutil@next\tikz@scan@next@command}% + {d}{\let\pgfutil@next\tikz@decoration}% + {l}{\let\pgfutil@next\tikz@l@char}% + {:}{\let\pgfutil@next\tikz@colon@char}% + {\relax}{\relax\let\pgfutil@next\tikz@scan@next@command}% + }{\tikz@resetexpandcount\pgfutil@next}{\tikz@expand}% +}% + +\def\tikz@l@char{% + \pgfutil@ifnextchar e{\tikz@let@command}{% + \pgfutil@ifnextchar i{\tikz@lsystem}{% + \pgfutil@ifnextchar-{\tikz@@lsystem}{\tikz@expand}% + }% + }% +}% + +\def\tikz@lsystem{% + \tikzerror{You need to say \string\usetikzlibrary{lindenmayersystems} to draw Lindenmayer systems} +}% + +\def\tikz@@lsystem{% + \tikzerror{You need to say \string\usetikzlibrary{lindenmayersystems} to draw L-systems} +}% + +\def\tikz@pchar{\pgfutil@ifnextchar l{\tikz@plot}{\pgfutil@ifnextchar i{\tikz@subpicture}{\tikz@parabola}}}% +\def\tikz@cchar{% + \pgfutil@ifnextchar i{\tikz@circle}% + {\pgfutil@ifnextchar h{\tikz@children}{\tikz@cochar}}}% +\def\tikz@cochar o{% + \pgfutil@ifnextchar o{\tikz@coordinate}{\tikz@cosine}}% +\def\tikz@e@char{% + \pgfutil@ifnextchar l{\tikz@ellipse}{\tikz@@e@char}}% +\def\tikz@a@char{% + \pgfutil@ifnextchar r{\tikz@arcA}{\tikzerror{Arc expected}}}% +\def\tikz@@e@char dge{% + \pgfutil@ifnextchar f{\tikz@edgetoparent}{\tikz@edge@plain}}% + +\def\tikz@schar{\pgfutil@ifnextchar i{\tikz@sine}{\tikz@svg@path}}% + +\def\tikz@g@char r{\pgfutil@ifnextchar i{\tikz@grid}{\tikz@graph}}% + + +\def\tikz@svg@path{% + \tikzerror{You need to say \string\usetikzlibrary{svg.path} to use the svg path command} +}% + + +\def\tikz@finish{% + \box\tikz@figbox@bg% + \iftikz@decoratepath% + \tikz@lib@dec@decorate@path% + \fi% + \pgfsyssoftpath@getcurrentpath\tikz@actions@path% + \edef\tikz@restorepathsize{% + \global\pgf@pathmaxx=\the\pgf@pathmaxx% + \global\pgf@pathmaxy=\the\pgf@pathmaxy% + \global\pgf@pathminx=\the\pgf@pathminx% + \global\pgf@pathminy=\the\pgf@pathminy% + }% + \tikz@preactions% + \let\tikz@path@picture=\pgfutil@empty% + \tikz@mode@fillfalse% + \tikz@mode@drawfalse% + \tikz@mode@doublefalse% + \tikz@mode@clipfalse% + \tikz@mode@boundaryfalse% + \tikz@mode@fade@pathfalse% + \tikz@mode@fade@scopefalse% + \edef\tikz@pathextend{% + {\noexpand\pgfqpoint{\the\pgf@pathminx}{\the\pgf@pathminy}}% + {\noexpand\pgfqpoint{\the\pgf@pathmaxx}{\the\pgf@pathmaxy}}% + }% + \tikz@mode% + \iftikz@mode@fade@path% + \tikz@addoption{% + \iftikz@fade@adjust% + \iftikz@mode@draw% + \pgfsetfadingforcurrentpathstroked{\tikz@path@fading}{\tikz@do@fade@transform}% + \else% + \pgfsetfadingforcurrentpath{\tikz@path@fading}{\tikz@do@fade@transform}% + \fi% + \else% + \pgfsetfading{\tikz@path@fading}{\tikz@do@fade@transform}% + \fi% + \tikz@mode@fade@pathfalse% + }% + \fi% + \iftikz@mode@fade@scope% + \iftikz@fade@adjust% + \iftikz@mode@draw% + \pgfsetfadingforcurrentpathstroked{\tikz@scope@fading}{\tikz@do@fade@transform}% + \else% + \pgfsetfadingforcurrentpath{\tikz@scope@fading}{\tikz@do@fade@transform}% + \fi% + \else% + \pgfsetfading{\tikz@scope@fading}{\tikz@do@fade@transform}% + \fi% + \tikz@mode@fade@scopefalse% + \fi% + \ifx\tikz@options\pgfutil@empty% + \else% + \pgfsys@beginscope% + \let\pgfscope@stroke@color=\pgf@strokecolor@global% + \let\pgfscope@fill@color=\pgf@fillcolor@global% + \begingroup% + \tikz@options% + \fi% + \tikz@do@rdf@pre@options% + \tikz@is@nodefalse% + \tikz@call@id@hook% + \iftikz@mode@clip\else% + \pgfidscope% + \tikz@do@rdf@post@options% + \begingroup% + \fi% + \iftikz@mode@fill% + \iftikz@mode@shade% + \pgfsyssoftpath@getcurrentpath\tikz@temppath + \pgfprocessround{\tikz@temppath}{\tikz@temppath}% + \pgfsyssoftpath@setcurrentpath\tikz@temppath% + \pgfsyssoftpath@invokecurrentpath% + \pgfpushtype% + \pgfusetype{.path fill}% + \pgfsys@fill% + \pgfpoptype% + \tikz@mode@fillfalse% + \else% + \ifx\tikz@path@picture\pgfutil@empty% + \else% + \pgfsyssoftpath@getcurrentpath\tikz@temppath + \pgfprocessround{\tikz@temppath}{\tikz@temppath}% + \pgfsyssoftpath@setcurrentpath\tikz@temppath% + \pgfsyssoftpath@invokecurrentpath% + \pgfpushtype% + \pgfusetype{.path fill}% + \pgfsys@fill% + \pgfpoptype% + \tikz@mode@fillfalse% + \fi% + \fi% + \fi% + \iftikz@mode@shade% + \pgfsyssoftpath@getcurrentpath\tikz@temppath + \pgfprocessround{\tikz@temppath}{\tikz@temppath}% + \pgfsyssoftpath@setcurrentpath\tikz@temppath% + \pgfpushtype% + \pgfusetype{.path shade}% + \pgfshadepath{\tikz@shading}{\tikz@shade@angle}% + \pgfpoptype% + \tikz@mode@shadefalse% + \fi% + \ifx\tikz@path@picture\pgfutil@empty% + \else% + \begingroup% + \pgfusetype{.path picture}% + \pgfidscope% + \pgfsys@beginscope% + \let\tikz@id@name\pgfutil@empty% + \pgfclearid% + \pgfsyssoftpath@getcurrentpath\tikz@temppath + \pgfprocessround{\tikz@temppath}{\tikz@temppath}% + \pgfsyssoftpath@setcurrentpath\tikz@temppath% + \pgfsyssoftpath@invokecurrentpath% + \pgfsys@clipnext% + \pgfsys@discardpath% + \pgf@relevantforpicturesizefalse% + \expandafter\def\csname pgf@sh@ns@path picture bounding box\endcsname{rectangle} + \expandafter\edef\csname pgf@sh@np@path picture bounding box\endcsname{% + \def\noexpand\southwest{\noexpand\pgfqpoint{\the\pgf@pathminx}{\the\pgf@pathminy}}% + \def\noexpand\northeast{\noexpand\pgfqpoint{\the\pgf@pathmaxx}{\the\pgf@pathmaxy}}% + } + \expandafter\def\csname pgf@sh@nt@path picture bounding box\endcsname{{1}{0}{0}{1}{0pt}{0pt}} + \expandafter\def\csname pgf@sh@pi@path picture bounding box\endcsname{\pgfpictureid} + \pgfinterruptpath% + \tikz@path@picture% + \endpgfinterruptpath% + \pgfsys@endscope% + \endpgfidscope% + \endgroup% + \let\tikz@path@picture=\pgfutil@empty% + \fi% + \iftikz@mode@draw% + \iftikz@mode@double% + \begingroup% + \pgfsys@beginscope% + \tikz@double@setup% + \fi% + \fi% + \pgfpushtype% + \edef\tikz@temp{\noexpand\pgfusepath{% + \iftikz@mode@fill fill,\fi% + \iftikz@mode@draw draw,\fi% + \iftikz@mode@clip clip\fi% + }}% + \pgfusetype{.path}% + \tikz@temp% + \pgfpoptype% + \tikz@mode@fillfalse% + \iftikz@mode@draw% + \iftikz@mode@double% + \pgfsys@endscope% + \endgroup% + \fi% + \fi% + \tikz@mode@drawfalse% + \tikz@postactions% + \box\tikz@figbox% + \iftikz@mode@clip\else\endgroup\endpgfidscope\fi% + \ifx\tikz@options\pgfutil@empty% + \else% + \endgroup% + \global\let\pgf@strokecolor@global=\pgfscope@stroke@color% + \global\let\pgf@fillcolor@global=\pgfscope@fill@color% + \pgfsys@endscope% + \iftikz@mode@clip% + \tikzerror{Extra options not allowed for clipping path command.}% + \fi% + \fi% + \iftikz@mode@clip% + \aftergroup\pgf@relevantforpicturesizefalse% + \fi% + \iftikz@mode@boundary% + \aftergroup\pgf@relevantforpicturesizefalse% + \fi% + \endgroup% + \global\pgflinewidth=\tikzscope@linewidth% + \tikz@path@do@at@end% +}% +\let\tikz@lib@scope@check\pgfutil@empty% +\def\tikz@path@do@at@end{\tikz@lib@scope@check}% +\def\tikz@@pathtext{@path}% + +\def\pgf@outer@auto@adjust@hook{% + {% + \tikz@mode@drawfalse% + \tikz@mode% + \expandafter% + }% + \iftikz@mode@draw\else% + \pgfkeyslet{/pgf/outer xsep}\pgf@zero@text + \pgfkeyslet{/pgf/outer ysep}\pgf@zero@text + \fi% +}% + + +\def\tikz@extra@preaction#1{% + {% + \pgfsys@beginscope% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \path[#1];% + \pgfsyssoftpath@setcurrentpath\tikz@actions@path% + \tikz@restorepathsize% + \pgfsys@endscope% + }% +}% + +\def\tikz@extra@postaction#1{% + {% + \pgfsys@beginscope% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \tikz@restorepathsize% + \path[#1]\pgfextra{\pgfsyssoftpath@setcurrentpath\tikz@actions@path};% + \pgf@resetpathsizes% + \pgfsys@endscope% + }% +}% + + + +\def\tikz@skip#1{\tikz@scan@next@command#1}% +\def\tikz@expand{% + \advance\tikz@expandcount by -1 + \ifnum\tikz@expandcount<0\relax% + \expandafter\pgfutil@firstoftwo + \else + \expandafter\pgfutil@secondoftwo + \fi + {% + \tikzerror{Giving up on this path. Did you forget a semicolon?}% + \global\let\tikz@expand@last@token=\pgf@let@token + \tikz@finish% + \expandafter\let\expandafter\tikz@expand@last@token@\csname tikz@expand@last@token\endcsname + \global\let\tikz@expand@last@token=\relax + \tikz@expand@last@token@ + }{% + \tikz@@expand + }% +} + +\def\tikz@@expand{% + \expandafter\tikz@scan@next@command\pgf@let@token}% + + + + +\newif\iftikz@auto@end@path + +\def\tikz@beginscope{\begingroup\tikz@auto@end@pathfalse\tikz@scan@next@command}% +\def\tikz@endscope{% + \iftikz@auto@end@path\expandafter\tikz@finish\expandafter\egroup\else\expandafter\tikz@@endscope\fi% +}% +\def\tikz@@endscope{% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \global\let\tikz@tangent@temp\tikz@tangent% + \edef\tikz@marshal{% + \tikz@lastx=\the\tikz@lastx% + \tikz@lasty=\the\tikz@lasty% + \iftikz@current@point@local% + \else% + \tikz@lastxsaved=\the\tikz@lastxsaved% + \tikz@lastysaved=\the\tikz@lastysaved% + \ifx\tikz@moveto@waiting\relax% + \let\tikz@moveto@waiting\relax% + \else% + \def\noexpand\tikz@moveto@waiting{\tikz@moveto@waiting}% + \fi% + \iftikz@shapeborder% + \noexpand\tikz@shapebordertrue% + \def\noexpand\tikz@shapeborder@name{\tikz@shapeborder@name}% + \else% + \noexpand\tikz@shapeborderfalse% + \fi% + \fi% + }% + \expandafter% + \endgroup\tikz@marshal% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \let\tikz@tangent\tikz@tangent@temp% + \tikz@scan@next@command}% + + + +\def\tikz@extra{\pgfutil@ifnextchar\bgroup\tikz@@extra\relax}% +\long\def\tikz@@extra#1{#1\tikz@scan@next@command}% +\let\endpgfextra=\tikz@scan@next@command + +\def\pgfextra{pgfextra}% + + + +\def\tikz@fchar oreach{\tikz@foreach}% + +\def\tikz@foreach{% + \def\pgffor@beginhook{% + \tikz@lastx=\tikz@foreach@save@lastx% + \tikz@lasty=\tikz@foreach@save@lasty% + \tikz@lastxsaved=\tikz@foreach@save@lastxsaved% + \tikz@lastysaved=\tikz@foreach@save@lastysaved% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \expandafter\tikz@scan@next@command\pgfutil@firstofone}% + \def\pgffor@endhook{\pgfextra{% + \xdef\tikz@foreach@save@lastx{\the\tikz@lastx}% + \xdef\tikz@foreach@save@lasty{\the\tikz@lasty}% + \xdef\tikz@foreach@save@lastxsaved{\the\tikz@lastxsaved}% + \xdef\tikz@foreach@save@lastysaved{\the\tikz@lastysaved}% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \pgfutil@gobble}}% + \def\pgffor@afterhook{% + \tikz@lastx=\tikz@foreach@save@lastx% + \tikz@lasty=\tikz@foreach@save@lasty% + \tikz@lastxsaved=\tikz@foreach@save@lastxsaved% + \tikz@lastysaved=\tikz@foreach@save@lastysaved% + \let\pgffor@beginhook\relax% + \let\pgffor@endhook\relax% + \let\pgffor@afterhook\relax% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \tikz@scan@next@command}% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \xdef\tikz@foreach@save@lastx{\the\tikz@lastx}% + \xdef\tikz@foreach@save@lasty{\the\tikz@lasty}% + \xdef\tikz@foreach@save@lastxsaved{\the\tikz@lastxsaved}% + \xdef\tikz@foreach@save@lastysaved{\the\tikz@lastysaved}% + \foreach}% + + + +\def\tikz@command@againpath#1{% + \pgfextra{% + \pgfsyssoftpath@getcurrentpath\tikz@temp% + \expandafter\pgfutil@g@addto@macro\expandafter\tikz@temp\expandafter{#1}% + \pgfsyssoftpath@setcurrentpath\tikz@temp% + }% +}% + + + +\def\tikz@colon@char#1=#2{% + \tikz@scan@next@command{[animate={myself:{#1}={#2}}]}% +}% + + + + +\newif\iftikz@shapeborder + + +\def\tikz@movetoabs{\tikz@moveto(}% +\def\tikz@movetorel{\tikz@moveto+}% +\def\tikz@moveto{% + \tikz@scan@one@point{\tikz@@moveto}}% +\def\tikz@@moveto#1{% + \tikz@make@last@position{#1}% + \iftikz@shapeborder% + \edef\tikz@moveto@waiting{\tikz@shapeborder@name}% + \else% + \tikz@@movetosave{\tikz@last@position}% + \let\tikz@moveto@waiting=\relax% + \fi% + \tikz@scan@next@command% +}% + +\def\tikz@@movetosave#1{% + {\pgftransformreset + \pgf@process{#1}% + \xdef\tikz@marshal{% + \tikz@lastmovetox=\the\pgf@x\relax% + \tikz@lastmovetoy=\the\pgf@y\relax% + }% + }% + \tikz@marshal + \pgfpathmoveto{#1}% +}% + + +\let\tikz@moveto@waiting=\relax % + +\def\tikz@flush@moveto{% + \ifx\tikz@moveto@waiting\relax% + \else% + \tikz@@movetosave{\tikz@last@position}% + \fi% + \let\tikz@moveto@waiting=\relax% +}% + + +\def\tikz@flush@moveto@toward#1#2#3{% + \ifx\tikz@moveto@waiting\relax% + \else% + \pgf@process{\pgfpointshapeborder{\tikz@moveto@waiting}{#1}}% + #2=\pgf@x% + #3=\pgf@y% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \tikz@@movetosave{\pgfqpoint{\pgf@x}{\pgf@y}}% + \fi% + \let\tikz@moveto@waiting=\relax% +}% + + + +\def\tikz@collect@coordinate@onpath#1c{% + \pgfutil@ifnextchar y{\tikz@cycle@expander@add#1}{\tikz@collect@coordinate@onpath@{#1}}}% +\def\tikz@collect@coordinate@onpath@#1oordinate{% + \pgfutil@ifnextchar[{\tikz@@collect@coordinate@opt#1}{\tikz@@collect@coordinate@opt#1[]}}% +\def\tikz@@collect@coordinate@opt#1[#2]{% + \pgfutil@ifnextchar({\tikz@@collect@coordinate#1[#2]}{% + \tikz@collect@label@onpath#1node[shape=coordinate,#2]{}}}% +\def\tikz@@collect@coordinate#1[#2](#3){% + \tikz@collect@label@onpath#1node[shape=coordinate,#2](#3){}}% + +\newif\iftikz@collect@pic + +\def\tikz@collect@label@onpath#1node{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath node}% + \let\tikz@collect@cont#1% + \tikz@collect@picfalse% + \tikz@collect@label@scan}% + +\def\tikz@collect@pic@onpath#1pic{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath pic}% + \let\tikz@collect@cont#1 + \tikz@collect@pictrue% + \tikz@collect@label@scan}% + +\def\tikz@collect@label@scan{% + \pgfutil@ifnextchar f{\tikz@collect@nodes}{% + \pgfutil@ifnextchar({\tikz@collect@paran}% + {\pgfutil@ifnextchar[{\tikz@collect@options}% + {\pgfutil@ifnextchar:{\tikz@collect@animation}% + {\pgfutil@ifnextchar\bgroup{\tikz@collect@arg}% + {\tikz@collect@cont}}}}}% +}% + +\def\tikz@collect@nodes foreach#1in{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath foreach#1in}% + \pgfutil@ifnextchar\bgroup\tikz@collect@nodes@group\tikz@collect@nodes@one% +}% +\def\tikz@collect@nodes@one#1{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath #1}% + \tikz@collect@label@scan% +}% +\def\tikz@collect@nodes@group#1{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{#1}}% + \tikz@collect@label@scan% +}% + +\def\tikz@collect@animation#1=#2{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath#1={#2}}% + \tikz@collect@label@scan% +}% +\def\tikz@collect@paran#1){% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath#1)}% + \tikz@collect@label@scan% +}% +\def\tikz@collect@options#1]{% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath#1]}% + \tikz@collect@label@scan% +}% +\def\tikz@collect@arg#1{% + \iftikz@handle@active@nodes% + \iftikz@collect@pic% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{#1}}% + \else% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{\scantokens{#1}}}% + \fi% + \else% + \expandafter\def\expandafter\tikz@collected@onpath\expandafter{\tikz@collected@onpath{#1}}% + \fi% + \tikz@collect@cont% +}% + +\def\tikz@invoke@collected@onpath{% + \tikz@node@is@a@labeltrue% + \let\tikz@temp=\tikz@collected@onpath% + \let\tikz@collected@onpath=\pgfutil@empty% + \expandafter\tikz@scan@next@command\tikz@temp\pgf@stop% + \tikz@node@is@a@labelfalse% +}% + + + +\def\tikz@cycle@expander#1{\pgfutil@ifnextchar c{\tikz@cycle@expander@{#1}}{#1}}% +\def\tikz@cycle@expander@#1c{\pgfutil@ifnextchar y{\tikz@cycle@expander@add{#1}}{#1c}}% +\def\tikz@cycle@expander@add#1ycle{#1(current subpath start)--cycle}% + + + + + +\def\tikz@lineto{% + \pgfutil@ifnextchar |% + {\expandafter\tikz@hv@lineto\pgfutil@gobble}% + {\expandafter\pgfutil@ifnextchar\tikz@activebar{\expandafter\tikz@hv@lineto\pgfutil@gobble}% + {\expandafter\tikz@lineto@mid\pgfutil@gobble}}}% +\def\tikz@lineto@mid{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@lineto@mid}% + {% + \pgfutil@ifnextchar c{\tikz@close}{% + \pgfutil@ifnextchar p{\tikz@lineto@plot@or@pic}{\tikz@scan@one@point{\tikz@@lineto}}}}}% +\def\tikz@lineto@plot@or@pic p{% + \pgfutil@ifnextchar i{\tikz@collect@pic@onpath\tikz@lineto@mid p}{% + \pgfsetlinetofirstplotpoint\tikz@plot}% +}% +\def\tikz@@lineto#1{% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}} + \iftikz@shapeborder% + \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\tikz@last@position}}% + \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}% + \tikz@flush@moveto@toward{\tikz@last@position}\pgf@x\pgf@y% + \tikz@path@lineto{\tikz@last@position}% + \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \tikz@make@last@position{#1}% + \edef\tikz@moveto@waiting{\tikz@shapeborder@name}% + \else% + \tikz@make@last@position{#1}% + \tikz@flush@moveto@toward{\tikz@last@position}\pgf@x\pgf@y% + \tikz@path@lineto{\tikz@last@position}% + \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \fi% + \let\tikz@timer=\tikz@timer@line% + \let\tikz@tangent\tikz@timer@start% + \tikz@scan@next@command% +}% + +\def\tikz@path@lineto#1{% + \iftikz@snaked% + { + \pgfsyssoftpathmovetorelevantfalse% + \pgfpathsnakesto{\tikz@presnake,{\tikz@snake}{\tikz@mainsnakelength}{\noexpand\tikz@snake@install@trans}{},\tikz@postsnake}{#1}% + } + \else% + \pgfpathlineto{#1}% + \fi% +}% + +\def\tikz@path@close#1{% + \iftikz@snaked% + {% + \pgftransformreset% + \pgfpathsnakesto{\tikz@presnake,{\tikz@snake}{\tikz@mainsnakelength}{\noexpand\tikz@snake@install@trans}{},\tikz@postsnake}{#1}% + }% + \fi% + \pgfpathclose% +}% + + + +\def\tikz@hv@lineto{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@hv@lineto}{% + \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@hv@lineto}% + {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@hv@lineto}% + {\tikz@scan@one@point{\tikz@@hv@lineto}}}}}% +\def\tikz@@hv@lineto#1{% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \pgf@yc=\tikz@lasty% + \tikz@make@last@position{#1}% + \edef\tikz@tangent{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\pgf@yc}}% + \tikz@flush@moveto@toward{\pgfqpoint{\tikz@lastx}{\pgf@yc}}\pgf@x\pgf@yc% + \iftikz@shapeborder% + {% + \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\pgfqpoint{\tikz@lastx}{\pgf@yc}}}% + \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}% + \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\pgf@yc}}% + \tikz@path@lineto{\tikz@last@position}% + \xdef\tikz@timer@end@temp{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + }% + \let\tikz@timer@end=\tikz@timer@end@temp% + \edef\tikz@moveto@waiting{\tikz@shapeborder@name}% + \else% + \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\pgf@yc}}% + \tikz@path@lineto{\tikz@last@position}% + \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \fi% + \let\tikz@timer=\tikz@timer@hvline% + \tikz@scan@next@command% +}% + + +\def\tikz@vh@lineto-{\tikz@vh@lineto@next}% +\def\tikz@vh@lineto@next{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@vh@lineto@next}{% + \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@vh@lineto@next}% + {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@vh@lineto@next}% + {\tikz@scan@one@point\tikz@@vh@lineto}}}}% +\def\tikz@@vh@lineto#1{% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \pgf@xc=\tikz@lastx% + \tikz@make@last@position{#1}% + \edef\tikz@tangent{\noexpand\pgfqpoint{\the\pgf@xc}{\the\tikz@lasty}}% + \tikz@flush@moveto@toward{\pgfqpoint{\pgf@xc}{\tikz@lasty}}\pgf@xc\pgf@y% + \iftikz@shapeborder% + {% + \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\pgfqpoint{\pgf@xc}{\tikz@lasty}}}% + \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}% + \tikz@path@lineto{\pgfqpoint{\pgf@xc}{\tikz@lasty}}% + \tikz@path@lineto{\tikz@last@position}% + \xdef\tikz@timer@end@temp{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + }% + \let\tikz@timer@end=\tikz@timer@end@temp% + \edef\tikz@moveto@waiting{\tikz@shapeborder@name}% + \else% + \tikz@path@lineto{\pgfqpoint{\pgf@xc}{\tikz@lasty}}% + \tikz@path@lineto{\tikz@last@position}% + \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \fi% + \let\tikz@timer=\tikz@timer@vhline% + \tikz@scan@next@command% +}% + +\def\tikz@close c{% + \pgfutil@ifnextchar o{\tikz@collect@coordinate@onpath\tikz@lineto@mid c}% + {\tikz@@close c}}% +\def\tikz@@close cycle{% + \tikz@flush@moveto% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}} + \tikz@make@last@position{\expandafter\pgfpoint\pgfsyssoftpath@lastmoveto}% + \tikz@path@close{\expandafter\pgfpoint\pgfsyssoftpath@lastmoveto}% + \def\pgfstrokehook{}% + \edef\tikz@timer@end{% + \noexpand\pgfqpoint{\the\tikz@lastmovetox}{\the\tikz@lastmovetoy}}% + \let\tikz@timer=\tikz@timer@line% + \let\tikz@tangent\tikz@timer@start% + \tikz@scan@next@command% +}% + + +\def\tikz@parse@options#1]{% + \tikzset{#1}% + \tikz@scan@next@command% +}% + +\def\tikz@edge@plain{% + \begingroup% + \ifx\tikz@to@use@whom\pgfutil@undefined\else\tikz@to@use@whom\fi + \let\tikz@to@or@edge@function=\tikz@do@edge% + \let\tikz@@to@local@options\pgfutil@empty% + \let\tikz@collected@onpath=\pgfutil@empty% + \tikz@to@or@edge}% + +\def\tikz@to o{% + \tikz@to@use@last@coordinate% + \let\tikz@to@or@edge@function=\tikz@do@to% + \let\tikz@@to@local@options\pgfutil@empty% + \let\tikz@collected@onpath=\pgfutil@empty% + \tikz@to@or@edge}% + +\def\tikz@to@or@edge{% + \pgfutil@ifnextchar[{\tikz@to@or@edge@option}{% + \pgfutil@ifnextchar:{\tikz@to@or@edge@animation}{% + \tikz@@to@collect}}% +}% +\def\tikz@to@or@edge@option[#1]{% + \expandafter\def\expandafter\tikz@@to@local@options\expandafter{\tikz@@to@local@options,#1}% + \tikz@to@or@edge% +}% +\def\tikz@to@or@edge@animation:#1=#2{% + \expandafter\def\expandafter\tikz@@to@local@options\expandafter{\tikz@@to@local@options,% + animate={myself:{#1}={#2}}}% + \tikz@to@or@edge% +}% +\def\tikz@@to@collect{% + \pgfutil@ifnextchar(\tikz@@to@or@edge@coordinate% + {\pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@@to@collect}% + {\pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@@to@collect}% + {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@@to@collect}% + {\pgfutil@ifnextchar +{\tikz@scan@one@point\tikz@@to@or@edge@math}% + {\tikzerror{(, +, coordinate, pic, or node expected}% + \tikz@@to@or@edge@coordinate()}}}}}% +}% + +\def\tikz@@to@or@edge@coordinate({% + \pgfutil@ifnextchar${% + \tikz@scan@one@point\tikz@@to@or@edge@math(% + }{% + \pgfutil@ifnextchar[{% + \tikz@scan@one@point\tikz@@to@or@edge@math(% + }{% + \tikz@@to@or@edge@@coordinate(% + }% + }% +}% +\def\tikz@@to@or@edge@math#1{% + \pgf@process{#1}% + \iftikz@updatecurrent\else + \tikz@updatenextfalse + \fi + \edef\tikztotarget{\the\pgf@x,\the\pgf@y}% + \tikz@to@or@edge@function% +}% + +\def\tikz@@to@or@edge@@coordinate(#1){% + \def\tikztotarget{#1}% + \tikz@to@or@edge@function% +}% + +\def\tikz@do@edge{% + \ifx\tikz@edge@macro\pgfutil@empty% + \setbox\tikz@whichbox=\hbox\bgroup% + \unhbox\tikz@whichbox% + \hbox\bgroup + \bgroup% + \pgfinterruptpath% + \pgfscope% + \let\tikz@transform=\pgfutil@empty% + \let\tikz@options=\pgfutil@empty% + \tikz@clear@rdf@options% + \let\tikz@tonodes=\tikz@collected@onpath% + \def\tikztonodes{{\pgfextra{\tikz@node@is@a@labeltrue}\tikz@tonodes}}% + \let\tikz@collected@onpath=\pgfutil@empty% + \tikz@options% + \tikz@do@rdf@pre@options% + \pgfidscope% + \tikz@do@rdf@post@options% + \tikz@transform% + \let\tikz@transform=\relax% + \let\tikz@after@path\pgfutil@empty% + \tikz@atbegin@to% + \tikz@enable@edge@quotes% + \path[style=every edge]\expandafter[\tikz@@to@local@options](\tikztostart)\tikz@to@path + \pgfextra{\global\let\tikz@after@path@smuggle=\tikz@after@path};% + \tikz@atend@to% + \endpgfidscope% + \endpgfscope% + \endpgfinterruptpath% + \egroup + \egroup% + \egroup% + \global\setbox\tikz@tempbox=\box\tikz@whichbox% + \expandafter\endgroup% + \expandafter\setbox\tikz@whichbox=\box\tikz@tempbox% + \else% + \expandafter\expandafter\expandafter\tikz@edge@macro% + \expandafter\expandafter\expandafter{\expandafter\tikz@@to@local@options\expandafter}\expandafter{\tikz@collected@onpath}% + \endgroup% + \let\tikz@after@path@smuggle=\pgfutil@empty% + \fi% + \expandafter\tikz@scan@next@command\tikz@after@path@smuggle% +}% + +\def\tikz@do@to{% + \let\tikz@tonodes=\tikz@collected@onpath% + \def\tikztonodes{{\pgfextra{\tikz@node@is@a@labeltrue}\tikz@tonodes}}% + \let\tikz@collected@onpath=\pgfutil@empty% + \tikz@scan@next@command% + {% + \pgfextra{\let\tikz@after@path\pgfutil@empty}% + \pgfextra{\tikz@atbegin@to}% + \pgfextra{\tikz@enable@edge@quotes}% + [style=every to]\expandafter[\tikz@@to@local@options]\tikz@to@path% + \pgfextra{\tikz@atend@to}% + \pgf@stop% + \expandafter\tikz@scan@next@command\expandafter% + }\tikz@after@path% + \pgfextra{\tikz@updatenexttrue\tikz@updatecurrenttrue}% +}% + + +\def\tikz@to@use@last@coordinate{% + \iftikz@shapeborder% + \edef\tikztostart{\tikz@shapeborder@name}% + \else% + \edef\tikztostart{\the\tikz@lastx,\the\tikz@lasty}% + \fi% +}% +\def\tikz@to@use@last@fig@name{% + \edef\tikztostart{\tikz@to@last@fig@name}% +}% + + + + +\def\tikz@graph aph{\tikz@lib@graph@parser}% + +\def\tikz@lib@graph@parser{\pgfutil@ifnextchar[\tikz@graph@error{\tikz@graph@error[]}}% +\def\tikz@graph@error[#1]#2{% + \tikzerror{You need to say \string\usetikzlibrary{graphs} in order to use the graph syntax}% + \tikz@lib@graph@parser@done% +}% + +\def\tikz@lib@graph@parser@done{% + \tikz@scan@next@command% +}% + + + + +\def\tikz@edgetoparent from parent{\pgfutil@ifnextchar[\tikz@@edgetoparent{\tikz@@edgetoparent[]}}% +\def\tikz@@edgetoparent[#1]{% + \let\tikz@edge@to@parent@needed=\pgfutil@empty% + \def\tikz@edgetoparent@options{#1}% + \begingroup% + \let\tikz@collected@onpath=\pgfutil@empty% + \tikz@edgetoparentcollect% +}% +\def\tikz@edgetoparentcollect{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@edgetoparentcollect}% + {% + \expandafter% + \endgroup% + \expandafter\tikz@edgetoparent@rollout\expandafter{\tikz@collected@onpath}% + }% +}% + +\def\tikz@edgetoparent@rollout#1{% + \pgfkeysgetvalue{/tikz/edge from parent macro}\tikz@etop@temp + \expandafter\tikz@scan@next@command\expandafter\tikz@etop@temp\expandafter{\tikz@edgetoparent@options}{#1}% +}% + + + +\def\tikz@dot.{\tikz@@dot}% +\def\tikz@@dot{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@@dot}{% + \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@@dot}% + {\pgfutil@ifnextchar c{\tikz@curveto@double}{\tikz@curveto@auto}}}% +}% + +\def\tikz@curveto@double co{% + \pgfutil@ifnextchar o{\tikz@collect@coordinate@onpath\tikz@@dot co} + {\tikz@cureveto@@double}}% +\def\tikz@cureveto@@double ntrols#1{% + \tikz@scan@one@point\tikz@curveA#1% +}% +\def\tikz@curveA#1{% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + {% + \tikz@lastxsaved=\tikz@lastx% + \tikz@lastysaved=\tikz@lasty% + \tikz@make@last@position{#1}% + \xdef\tikz@curve@first{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + }% + \pgfutil@ifnextchar a + {\tikz@curveBand}% + {\let\tikz@curve@second\tikz@curve@first\tikz@curveCdots}% +}% +\def\tikz@curveBand and{% + \tikz@scan@one@point\tikz@curveB% +}% +\def\tikz@curveB#1{% + \def\tikz@curve@second{#1}% + \tikz@curveCdots} +\def\tikz@curveCdots{% + \afterassignment\tikz@curveCdot\let\pgfutil@next=}% +\def\tikz@curveCdot.{% + \ifx\pgfutil@next.% + \else% + \tikzerror{Dot expected}% + \fi% + \iftikz@updatenext + \tikz@updatecurrenttrue% + \fi + \tikz@curveCcheck% +}% +\def\tikz@curveCcheck{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@curveCcheck}{% + \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@curveCcheck}% + {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@curveCcheck} + {\tikz@scan@one@point\tikz@curveC}}}% +}% +\def\tikz@curveC#1{% + \tikz@make@last@position{#1}% + \edef\tikz@curve@third{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + {% + \tikz@lastxsaved=\tikz@lastx% + \tikz@lastysaved=\tikz@lasty% + \tikz@make@last@position{\tikz@curve@second}% + \xdef\tikz@curve@second{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + }% + \ifx\tikz@moveto@waiting\relax% + \else% + \pgf@process{\pgfpointshapeborder{\tikz@moveto@waiting}{\tikz@curve@first}}% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \tikz@@movetosave{\pgfqpoint{\pgf@x}{\pgf@y}}% + \fi% + \let\tikz@timer@cont@one=\tikz@curve@first% + \let\tikz@timer@cont@two=\tikz@curve@second% + \iftikz@shapeborder% + {% + \pgf@process{\pgfpointshapeborder{\tikz@shapeborder@name}{\tikz@curve@second}}% + \tikz@make@last@position{\pgfqpoint{\pgf@x}{\pgf@y}}% + \edef\tikz@curve@third{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \pgfpathcurveto{\tikz@curve@first}{\tikz@curve@second}{\tikz@curve@third}% + \global\let\tikz@timer@end@temp=\tikz@curve@third% + }% + \let\tikz@timer@end=\tikz@timer@end@temp% + \edef\tikz@moveto@waiting{\tikz@shapeborder@name}% + \else% + \pgfpathcurveto{\tikz@curve@first}{\tikz@curve@second}{\tikz@curve@third}% + \let\tikz@timer@end=\tikz@curve@third + \let\tikz@moveto@waiting=\relax% + \fi% + \let\tikz@timer=\tikz@timer@curve% + \let\tikz@tangent=\tikz@curve@second% + \tikz@scan@next@command% +}% + + +\def\tikz@rect ectangle{% + \tikz@flush@moveto% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \tikz@@rect}% +\def\tikz@@rect{% + \pgfutil@ifnextchar n{\tikz@collect@label@onpath\tikz@@rect}{% + \pgfutil@ifnextchar p{\tikz@collect@pic@onpath\tikz@@rect}% + {\pgfutil@ifnextchar c{\tikz@collect@coordinate@onpath\tikz@@rect}% + { + \pgf@xa=\tikz@lastx\relax% + \pgf@ya=\tikz@lasty\relax% + \tikz@scan@one@point\tikz@rectB}}}}% +\def\tikz@rectB#1{% + \tikz@make@last@position{#1}% + \edef\tikz@timer@end{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \let\tikz@timer=\tikz@timer@line% + \tikz@@movetosave{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \tikz@path@lineto{\pgfqpoint{\pgf@xa}{\tikz@lasty}}% + \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}% + \tikz@path@lineto{\pgfqpoint{\tikz@lastx}{\pgf@ya}}% + \iftikz@snaked% + \tikz@path@lineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \fi% + \pgfpathclose% + \tikz@@movetosave{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}% + \def\pgfstrokehook{}% + \let\tikz@tangent\relax% + \tikz@scan@next@command% +}% + + + +\def\tikz@grid id{% + \tikz@flush@moveto% + \pgf@xa=\tikz@lastx\relax% + \pgf@ya=\tikz@lasty\relax% + \pgfutil@ifnextchar[{\tikz@gridA}{\tikz@gridA[]}}% +\def\tikz@gridA[#1]{% + \def\tikz@grid@options{#1}% + \tikz@cycle@expander{\tikz@scan@one@point\tikz@gridB}}% +\def\tikz@gridB#1{% + \tikz@make@last@position{#1}% + \let\tikz@tangent\relax% + {% + \let\tikz@after@path\pgfutil@empty% + \expandafter\tikzset\expandafter{\tikz@grid@options} + \tikz@checkunit{\tikz@grid@x}% + \iftikz@isdimension% + \pgf@process{\pgfpoint{\tikz@grid@x}{0pt}}% + \else% + \pgf@process{\pgfpointxy{\tikz@grid@x}{0}}% + \fi% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \tikz@checkunit{\tikz@grid@y}% + \iftikz@isdimension% + \pgf@process{\pgfpoint{0pt}{\tikz@grid@y}}% + \else% + \pgf@process{\pgfpointxy{0}{\tikz@grid@y}}% + \fi% + \advance\pgf@xb by\pgf@x% + \advance\pgf@yb by\pgf@y% + \pgfpathgrid[stepx=\pgf@xb,stepy=\pgf@yb]% + {\pgfqpoint{\pgf@xa}{\pgf@ya}}{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}% + \expandafter}% + \expandafter\tikz@scan@next@command\tikz@after@path% +}% + + + +\def\tikz@plot lot{% + \tikz@flush@moveto% + \pgfutil@ifnextchar[{\tikz@@plot}{\tikz@@plot[]}}% +\def\tikz@@plot[#1]{% + \let\tikz@tangent\tikz@tangent@lookup% + \begingroup% + \let\tikz@after@path\pgfutil@empty% + \let\tikz@options=\pgfutil@empty% + \tikzset{every plot/.try}% + \tikzset{#1}% + \pgfutil@ifnextchar f{\tikz@plot@f}% + {\pgfutil@ifnextchar c{\tikz@plot@scan@points}% + {\pgfutil@ifnextchar ({\tikz@plot@expression}{% + \tikzerror{Cannot parse this plotting data}% + \endgroup}}}}% +\def\tikz@plot@f f{\pgfutil@ifnextchar i{\tikz@plot@file}{\tikz@plot@function}}% + +\def\tikz@plot@file ile#1{\def\tikz@plot@data{\pgfplotxyfile{#1}}\tikz@@@plot}% +\def\tikz@plot@scan@points coordinates#1{% + \pgfplothandlerrecord\tikz@plot@data% + \pgfplotstreamstart% + \pgfutil@ifnextchar\pgf@stop{\pgfplotstreamend\expandafter\tikz@@@plot\pgfutil@gobble} + {\tikz@scan@one@point\tikz@plot@next@point}% + #1\pgf@stop% +}% +\def\tikz@plot@next@point#1{% + \pgfplotstreampoint{#1}% + \pgfutil@ifnextchar\pgf@stop{\pgfplotstreamend\expandafter\tikz@@@plot\pgfutil@gobble}% + {\tikz@scan@one@point\tikz@plot@next@point}% +}% +\def\tikz@plot@function unction#1{% + \def\tikz@plot@filename{\tikz@plot@prefix\tikz@plot@id}% + \iftikz@plot@raw@gnuplot% + \def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{#1}}% + \else% + \iftikz@plot@parametric% + \def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{% + set samples \tikz@plot@samples; + set parametric; + plot [t=\tikz@plot@domain] + [\tikz@plot@xrange] + [\tikz@plot@range] + #1}}% + \else% + \def\tikz@plot@data{\pgfplotgnuplot[\tikz@plot@filename]{% + set samples \tikz@plot@samples; + plot [x=\tikz@plot@domain] + \ifx\tikz@plot@range\pgfutil@empty\else[\tikz@plot@range]\fi + #1}}% + \fi% + \fi% + \tikz@@@plot% +}% + +\def\tikz@plot@no@resample{% + \pgfutil@IfFileExists{\tikz@plot@filename.table}% + {\def\tikz@plot@data{\pgfplotxyfile{\tikz@plot@filename.table}}}% + {}% +}% + +\def\tikz@plot@expression(#1){% + \edef\tikz@plot@data{\noexpand\pgfplotfunction{\expandafter\noexpand\tikz@plot@var}{\tikz@plot@samplesat}}% + \expandafter\def\expandafter\tikz@plot@data\expandafter{\tikz@plot@data{\tikz@scan@one@point\pgfutil@firstofone(#1)}}% + \tikz@@@plot% +}% + +\def\tikz@@@plot{% + \def\pgfplotlastpoint{\pgfpointorigin}% + \tikz@plot@handler% + \tikz@plot@data% + \global\let\tikz@@@temp=\pgfplotlastpoint% + \ifx\tikz@plot@mark\pgfutil@empty% + \else% + \setbox\tikz@whichbox=\hbox{% + \unhbox\tikz@whichbox% + \hbox{{% + \pgfinterruptpath% + \pgfscope% + \let\tikz@options=\pgfutil@empty% + \let\tikz@transform=\pgfutil@empty% + \tikzset{every mark}% + \tikz@options% + \ifx\tikz@mark@list\pgfutil@empty% + \pgfplothandlermark{\tikz@transform\pgfuseplotmark{\tikz@plot@mark}}% + \else + \pgfplothandlermarklisted{\tikz@transform\pgfuseplotmark{\tikz@plot@mark}}{\tikz@mark@list}% + \fi + \tikz@plot@data% + \endpgfscope + \endpgfinterruptpath% + }}% + }% + \fi% + \global\setbox\tikz@tempbox=\box\tikz@whichbox% + \global\let\tikz@after@path@smuggle=\tikz@after@path + \expandafter\endgroup% + \expandafter\setbox\tikz@whichbox=\box\tikz@tempbox% + \tikz@make@last@position{\tikz@@@temp}% + \expandafter\tikz@scan@next@command\tikz@after@path@smuggle% +}% + + +\pgfdeclareplotmark{ball} +{% + \def\tikz@shading{ball}% + \shade (0pt,0pt) circle (\pgfplotmarksize);% +}% + + + + +\def\tikz@cosine s{\tikz@cycle@expander{\tikz@scan@one@point\tikz@@cosine}} +\def\tikz@@cosine#1{% + \let\tikz@tangent\tikz@tangent@lookup% + \tikz@flush@moveto% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xc by-\tikz@lastx% + \advance\pgf@yc by-\tikz@lasty% + \advance\tikz@lastx by\pgf@xc% + \advance\tikz@lasty by\pgf@yc% + \tikz@lastxsaved=\tikz@lastx% + \tikz@lastysaved=\tikz@lasty% + \tikz@updatecurrenttrue% + \pgfpathcosine{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \tikz@scan@next@command% +}% + +\def\tikz@sine in{\tikz@cycle@expander{\tikz@scan@one@point\tikz@@sine}} +\def\tikz@@sine#1{% + \let\tikz@tangent\tikz@tangent@lookup% + \tikz@flush@moveto% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xc by-\tikz@lastx% + \advance\pgf@yc by-\tikz@lasty% + \advance\tikz@lastx by\pgf@xc% + \advance\tikz@lasty by\pgf@yc% + \tikz@lastxsaved=\tikz@lastx% + \tikz@lastysaved=\tikz@lasty% + \tikz@updatecurrenttrue% + \pgfpathsine{\pgfqpoint{\pgf@xc}{\pgf@yc}}% + \tikz@scan@next@command% +}% + +\def\tikz@parabola arabola{% + \let\tikz@tangent\tikz@tangent@lookup% + \pgfutil@ifnextchar[{\tikz@parabola@options}{\tikz@parabola@options[]}}% + +\def\tikz@parabola@options[#1]{% + \def\tikz@parabola@option{#1}% + \pgfutil@ifnextchar b{\tikz@parabola@scan@bend}{\tikz@cycle@expander{\tikz@scan@one@point\tikz@parabola@semifinal}}}% +\def\tikz@parabola@scan@bend bend{\tikz@scan@one@point\tikz@parabola@scan@bendB}% +\def\tikz@parabola@scan@bendB#1{% + \def\tikz@parabola@bend{#1}% + \tikz@cycle@expander{\tikz@scan@one@point\tikz@parabola@semifinal}% +}% +\def\tikz@parabola@semifinal#1{% + \tikz@flush@moveto% + \pgf@xb=\tikz@lastx% + \pgf@yb=\tikz@lasty% + \tikz@make@last@position{#1}% + \pgf@xc=\tikz@lastx% + \pgf@yc=\tikz@lasty% + \begingroup% + \let\tikz@after@path\pgfutil@empty% + \expandafter\tikzset\expandafter{\tikz@parabola@option}% + \tikz@lastxsaved=\tikz@parabola@bend@factor\tikz@lastx% + \tikz@lastysaved=\tikz@parabola@bend@factor\tikz@lasty% + \advance\tikz@lastxsaved by\pgf@xb% + \advance\tikz@lastysaved by\pgf@yb% + \advance\tikz@lastxsaved by-\tikz@parabola@bend@factor\pgf@xb% + \advance\tikz@lastysaved by-\tikz@parabola@bend@factor\pgf@yb% + \expandafter\tikz@make@last@position\expandafter{\tikz@parabola@bend}% + \advance\pgf@xc by-\tikz@lastx% + \advance\pgf@yc by-\tikz@lasty% + \advance\tikz@lastx by-\pgf@xb% + \advance\tikz@lasty by-\pgf@yb% + \xdef\tikz@parabola@b{{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}}% + \expandafter\endgroup% + \expandafter\expandafter\expandafter\pgfpathparabola\expandafter\tikz@parabola@b% + \expandafter\tikz@scan@next@command\tikz@after@path% +}% + + +\def\tikz@circle ircle{\tikz@flush@moveto\tikz@@circle}% +\def\tikz@ellipse llipse{\tikz@flush@moveto\tikz@@circle}% +\def\tikz@@circle{% + \let\tikz@tangent\relax% + \pgfutil@ifnextchar(\tikz@@@circle + {\pgfutil@ifnextchar[\tikz@circle@opt{% + \advance\tikz@expandcount by -10\relax% + \ifnum\tikz@expandcount<0\relax% + \let\pgfutil@next=\tikz@@circle@normal% + \else% + \let\pgfutil@next=\tikz@@circle@scanexpand% + \fi% + \pgfutil@next% + }}% +}% +\def\tikz@@circle@scanexpand{\expandafter\tikz@@circle}% +\def\tikz@@circle@normal{\tikz@circle@opt[]}% + +\def\tikz@circle@opt[#1]{% + {% + \def\tikz@node@at{\tikz@last@position}% + \let\tikz@transform=\pgfutil@empty% + \tikzset{every circle/.try,#1}% + \pgftransformshift{\tikz@node@at}% + \tikz@transform% + \tikz@do@ellipse{\pgfkeysvalueof{/tikz/x radius}}{\pgfkeysvalueof{/tikz/y radius}} + }% + \tikz@scan@next@command% +}% + +\def\tikz@@@circle(#1){% + {% + \pgftransformshift{\tikz@last@position}% + \pgfutil@in@{ and }{#1}% + \ifpgfutil@in@% + \tikz@@ellipseB(#1)% + \else% + \tikz@do@circle{#1}% + \fi% + }% + \tikz@scan@next@command% +}% +\def\tikz@@ellipseB(#1 and #2){% + \tikz@do@ellipse{#1}{#2}% +}% +\def\tikz@do@circle#1{% + \pgfmathparse{#1}% + \let\tikz@ellipse@x=\pgfmathresult + \ifpgfmathunitsdeclared + \pgfpathellipse{\pgfpointorigin}% + {\pgfqpoint{\tikz@ellipse@x pt}{0pt}}% + {\pgfpoint{0pt}{\tikz@ellipse@x pt}}% + \else + \pgfpathellipse{\pgfpointorigin}% + {\pgfpointxy{\tikz@ellipse@x}{0}}% + {\pgfpointxy{0}{\tikz@ellipse@x}}% + \fi +} +\def\tikz@do@ellipse#1#2{ + \pgfmathparse{#1}% + \let\tikz@ellipse@x=\pgfmathresult% + \ifpgfmathunitsdeclared% + \pgfmathparse{#2}% + \let\tikz@ellipse@y=\pgfmathresult% + \ifpgfmathunitsdeclared% + \pgfpathellipse{\pgfpointorigin}{% + \pgfqpoint{\tikz@ellipse@x pt}{0pt}}{\pgfpoint{0pt}{\tikz@ellipse@y pt}}% + \else% + \tikzerror{You cannot mix dimensions and dimensionless values in an ellipse}% + \fi% + \else% + \pgfmathparse{#2}% + \let\tikz@ellipse@y=\pgfmathresult% + \ifpgfmathunitsdeclared% + \tikzerror{You cannot mix dimensions and dimensionless values in an ellipse}% + \else% + \pgfpathellipse{\pgfpointorigin}{% + \pgfpointxy{\tikz@ellipse@x}{0}}{\pgfpointxy{0}{\tikz@ellipse@y}}% + \fi% + \fi% +}% + +\def\tikz@arcA rc{\tikz@flush@moveto\tikz@arc@cont}% +\def\tikz@arc@cont{% + \pgfutil@ifnextchar(% + {\tikz@@arcto}{% + \pgfutil@ifnextchar[% + {\tikz@arc@opt}% + {% + \advance\tikz@expandcount by -10\relax% + \ifnum\tikz@expandcount<0\relax% + \let\pgfutil@next=\tikz@@arc@normal% + \else% + \let\pgfutil@next=\tikz@@arc@scanexpand% + \fi% + \pgfutil@next% + }% + }% +}% +\def\tikz@@arc@scanexpand{\expandafter\tikz@arc@cont}% +\def\tikz@@arc@normal{\tikz@arc@opt[]}% + + +\def\tikz@arc@opt[#1]{% + {% + \tikzset{every arc/.try,#1}% + \pgfkeysgetvalue{/tikz/start angle}\tikz@s + \pgfkeysgetvalue{/tikz/end angle}\tikz@e + \pgfkeysgetvalue{/tikz/delta angle}\tikz@d + \ifx\tikz@s\pgfutil@empty% + \pgfmathsetmacro\tikz@s{\tikz@e-\tikz@d} + \else + \ifx\tikz@e\pgfutil@empty% + \pgfmathsetmacro\tikz@e{\tikz@s+\tikz@d} + \fi% + \fi% + \xdef\pgf@marshal{\noexpand% + \tikz@do@arc{\tikz@s}{\tikz@e} + {\pgfkeysvalueof{/tikz/x radius}} + {\pgfkeysvalueof{/tikz/y radius}}}% + }% + \pgf@marshal% + \tikz@arcfinal% +}% + +\def\tikz@@arcto(#1){% + \edef\tikz@temp{(#1)}% + \expandafter\tikz@@@arcto@check@slashand\tikz@temp% +}% + +\def\tikz@@@arcto@check@slashand(#1:#2:#3){% + \pgfutil@in@{ and }{#3}% + \ifpgfutil@in@% + \tikz@parse@arc@and(#1:#2:#3)% + \else% + \tikz@parse@arc@and(#1:#2:{#3} and {#3})% + \fi% + \tikz@arcfinal% +}% + +\def\tikz@parse@arc@and(#1:#2:#3 and #4){% + \tikz@do@arc{#1}{#2}{#3}{#4}% +}% +\def\tikz@do@arc#1#2#3#4{% + \let\tikz@tangent\tikz@tangent@lookup% + \edef\tikz@timer@start{\noexpand\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \pgfmathsetmacro\tikz@timer@start@angle{#1}% + \pgfmathsetmacro\tikz@timer@end@angle{#2}% + \pgfmathparse{#3}% + \let\tikz@arc@x=\pgfmathresult% + \ifpgfmathunitsdeclared% + \pgfmathparse{#4}% + \let\tikz@arc@y=\pgfmathresult% + \ifpgfmathunitsdeclared% + \tikz@@@arcfinal{\pgfpatharc{\tikz@timer@start@angle}{\tikz@timer@end@angle}{\tikz@arc@x pt and \tikz@arc@y pt}} + {\pgfpointpolar{\tikz@timer@start@angle}{\tikz@arc@x pt and \tikz@arc@y pt}} + {\pgfpointpolar{\tikz@timer@end@angle}{\tikz@arc@x pt and \tikz@arc@y pt}}% + \edef\tikz@timer@zero@axis{\noexpand\pgfqpoint{\tikz@arc@x pt}{0pt}} + \edef\tikz@timer@ninety@axis{\noexpand\pgfqpoint{0pt}{\tikz@arc@y pt}} + \else% + \tikzerror{You cannot mix dimensions and dimensionless values in an arc}% + \fi% + \else% + \pgfmathparse{#4}% + \let\tikz@arc@y=\pgfmathresult% + \ifpgfmathunitsdeclared% + \tikzerror{You cannot mix dimensions and dimensionless values in an arc}% + \else% + \tikz@@@arcfinal{\pgfpatharcaxes{\tikz@timer@start@angle}{\tikz@timer@end@angle}{\pgfpointxy{\tikz@arc@x}{0}}{\pgfpointxy{0}{\tikz@arc@y}}} + {\pgfpointpolarxy{\tikz@timer@start@angle}{\tikz@arc@x and \tikz@arc@y}}{\pgfpointpolarxy{\tikz@timer@end@angle}{\tikz@arc@x and \tikz@arc@y}}% + \pgf@process{\pgfpointxy{\tikz@arc@x}{0}} + \edef\tikz@timer@zero@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgf@process{\pgfpointxy{0}{\tikz@arc@y}} + \edef\tikz@timer@ninety@axis{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \fi% + \fi% +}% + +\def\tikz@@@arcfinal#1#2#3{% + #1% + \pgf@process{#2} + \xdef\tikz@arc@save@first{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@process{#3} + \xdef\tikz@arc@save@second{\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% +}% + +\def\tikz@arcfinal{% + \pgf@process{\tikz@arc@save@first}% + \advance\tikz@lastx by-\pgf@x% + \advance\tikz@lasty by-\pgf@y% + \pgf@process{\tikz@arc@save@second}% + \advance\tikz@lastx by\pgf@x% + \advance\tikz@lasty by\pgf@y% + \tikz@lastxsaved=\tikz@lastx% + \tikz@lastysaved=\tikz@lasty% + \let\tikz@timer=\tikz@timer@arc% + \tikz@scan@next@command% +}% + + +\def\tikz@coordinate ordinate{% + \pgfutil@ifnextchar[{\tikz@@coordinate@opt}{\tikz@@coordinate@opt[]}}% +\def\tikz@@coordinate@opt[#1]{% + \pgfutil@ifnextchar({\tikz@@coordinate[#1]} + {\tikz@fig ode[shape=coordinate,#1]{}}}% +\def\tikz@@coordinate[#1](#2){% + \pgfutil@ifnextchar a{\tikz@@coordinate@at[#1](#2)} + {\tikz@fig ode[shape=coordinate,#1](#2){}}}% +\def\tikz@@coordinate@at[#1](#2)a{% + \pgfutil@ifnextchar t{\tikz@@coordinate@@at[#1](#2)a}% + {\tikz@fig ode[shape=coordinate,#1](#2){}a}% +}% +\def\tikz@@coordinate@@at[#1](#2)at#3({% + \def\tikz@coordinate@caller{\tikz@fig ode[shape=coordinate,#1](#2)at}% + \tikz@scan@one@point\tikz@@coordinate@at@math(% +}% +\def\tikz@@coordinate@at@math#1{% + \pgf@process{#1}% + \edef\tikz@temp{(\the\pgf@x,\the\pgf@y)}% + \expandafter\tikz@coordinate@caller\tikz@temp{}% +}% + + + +\def\tikz@fig ode{% + \pgfutil@ifnextchar a\tikz@test@also{% + \pgfutil@ifnextchar f{\tikz@nodes@start}\tikz@normal@fig}}% +\def\tikz@test@also a{\pgfutil@ifnextchar l\tikz@node@also{\tikz@normal@fig a}}% +\def\tikz@normal@fig{% + \edef\tikz@save@line@width{\the\pgflinewidth}% + \begingroup% + \let\tikz@fig@name=\pgfutil@empty% + \begingroup% + \tikz@is@matrixfalse% + \let\nodepart=\tikz@nodepart% + \let\tikz@atbegin@scope=\pgfutil@empty% + \let\tikz@atend@scope=\pgfutil@empty% + \let\tikz@do@after@node=\tikz@scan@next@command% + \let\tikz@options=\pgfutil@empty% + \tikz@clear@rdf@options% + \let\tikz@id@name=\pgfutil@empty% + \let\tikz@after@path=\pgfutil@empty% + \let\tikz@transform=\pgfutil@empty% + \let\tikz@mode=\pgfutil@empty% + \tikz@decoratepathfalse% + \let\tikz@preactions=\pgfutil@empty% + \let\tikz@postactions=\pgfutil@empty% + \let\tikz@alias=\pgfutil@empty% + \def\tikz@node@at{\pgfqpoint{\the\tikz@lastx}{\the\tikz@lasty}}% + \let\tikz@time@for@matrix\tikz@time% + \let\tikz@node@content\relax% + \pgfgetpath\tikzpathuptonow% + \iftikz@node@is@a@label% + \else% + \let\tikz@time\pgfutil@empty% + \fi% + \tikz@node@reset@hook% + \tikzset{every node/.try}% + \tikz@@scan@fig}% +\def\tikz@@scan@fig{% + \pgfutil@ifnextchar a{\tikz@fig@scan@at} + {\pgfutil@ifnextchar({\tikz@fig@scan@name} + {\pgfutil@ifnextchar[{\tikz@fig@scan@options}% + {\pgfutil@ifnextchar:{\tikz@fig@scan@animation}% + {\pgfutil@ifnextchar\bgroup{\tikz@fig@main}% + {\tikzerror{A node must have a (possibly empty) label text}% + \tikz@fig@main{}}}}}}}% +\def\tikz@fig@scan@at at{% + \tikz@scan@one@point\tikz@@fig@scan@at}% +\def\tikz@@fig@scan@at#1{% + \def\tikz@node@at{#1}\tikz@@scan@fig}% +\def\tikz@fig@scan@name(#1){% + \pgfkeysvalueof{/tikz/name/.@cmd}#1\pgfeov% + \tikz@@scan@fig}% +\long\def\tikz@fig@scan@options[#1]{\iftikz@node@is@pic\tikz@enable@pic@quotes\else\tikz@enable@node@quotes\fi\tikzset{#1}\ifx\tikz@node@content\relax\expandafter\tikz@@scan@fig\else\tikz@expand@node@contents\fi}% +\def\tikz@fig@scan@animation:#1=#2{\tikzset{animate={myself:{#1}={#2}}}\tikz@@scan@fig}% +\def\tikz@expand@node@contents{% + \expandafter\tikz@@scan@fig\expandafter{\tikz@node@content}% +}% +\let\tikz@node@reset@hook=\pgfutil@empty% +\let\tikz@node@begin@hook=\pgfutil@empty% +\def\tikz@fig@main{% + \iftikz@node@is@pic% + \tikz@node@is@picfalse% + \expandafter\tikz@subpicture@handle% + \else% + \afterassignment\tikz@@fig@main\expandafter\let\expandafter\next\expandafter=% + \fi}% +\def\tikz@@fig@main{% + \pgfutil@ifundefined{pgf@sh@s@\tikz@shape}% + {\tikzerror{Unknown shape ``\tikz@shape.'' Using ``rectangle'' instead}% + \def\tikz@shape{rectangle}}% + {}% + \expandafter\xdef\csname tikz@dcl@coord@\tikz@fig@name\endcsname{% + \csname tikz@scan@point@coordinate\endcsname}% + \tikzset{every \tikz@shape\space node/.try}% + \tikz@node@textfont% + \tikz@node@begin@hook% + \iftikz@is@matrix% + \let\tikz@next=\tikz@do@matrix% + \else% + \let\tikz@next=\tikz@do@fig% + \fi% + \tikz@next% +}% +\let\tikz@nodepart@list\pgfutil@empty +\def\tikz@do@fig{% + \pgfutil@for\tikz@temp:=\tikz@nodepart@list\do{% + \expandafter\setbox\csname pgfnodepart\tikz@temp box\endcsname=\box\pgfutil@voidb@x% + }% + \setbox\pgfnodeparttextbox=\hbox% + \bgroup% + \pgfinterruptpicture% + \pgfsys@begin@text% + \pgfsys@text@to@black@hook% + \tikzset{every text node part/.try}% + \ifx\tikz@textopacity\pgfutil@empty% + \else% + \pgfsetfillopacity{\tikz@textopacity}% + \pgfsetstrokeopacity{\tikz@textopacity}% + \fi% + \ifx\tikz@text@width\pgfutil@empty% + \tikz@textfont% + \else% + \begingroup% + \pgfmathsetlength{\pgf@x}{\tikz@text@width}% + \pgfutil@minipage[t]{\pgf@x}\leavevmode\hbox{}% + \tikz@textfont% + \tikz@text@action% + \fi% + \tikz@atbegin@node% + \bgroup% + \aftergroup\unskip% + \ifx\tikz@textcolor\pgfutil@empty% + \else% + \pgfutil@colorlet{.}{\tikz@textcolor}% + \pgfutil@color{\tikz@textcolor}% + \fi% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \tikz@uninstallcommands% + \iftikz@handle@active@code% + \tikz@orig@shorthands% + \let\tikz@orig@shorthands\pgfutil@empty% + \fi% + \ifnum\the\catcode`\;=\active\relax\expandafter\let\tikz@activesemicolon=\tikz@origsemi\fi% + \ifnum\the\catcode`\:=\active\relax\expandafter\let\tikz@activecolon=\tikz@origcolon\fi% + \ifnum\the\catcode`\|=\active\relax\expandafter\let\tikz@activebar=\tikz@origbar\fi% + \aftergroup\tikz@fig@collectresetcolor% + \tikz@signal@halign@check% + \tikz@text@reset% + \tikz@halign@check% + \ignorespaces% +}% +\def\tikz@fig@collectresetcolor{% + \pgfutil@ifnextchar\reset@color% + {\reset@color\afterassignment\tikz@fig@collectresetcolor\let\tikz@temp=}\tikz@fig@boxdone% +}% +\def\tikz@fig@boxdone{% + \tikz@atend@node% + \ifx\tikz@text@width\pgfutil@empty% + \else% + \pgfutil@endminipage% + \endgroup% + \fi% + \pgfsys@end@text% + \endpgfinterruptpicture% + \egroup% + \pgfutil@ifnextchar c{\tikz@fig@mustbenamed\tikz@fig@continue}% + {\pgfutil@ifnextchar[{\tikz@fig@mustbenamed\tikz@fig@continue}% + {\pgfutil@ifnextchar t{\tikz@fig@mustbenamed\tikz@fig@continue} + {\pgfutil@ifnextchar e{\tikz@fig@mustbenamed\tikz@fig@continue} + {\ifx\tikz@after@path\pgfutil@empty\expandafter\tikz@fig@continue\else\expandafter\tikz@fig@mustbenamed\expandafter\tikz@fig@continue\fi}}}}}% + +\tikzset{ + matrix/inner style/every cell/.code={% + \tikzset{every cell/.try={\the\pgfmatrixcurrentrow}{\the\pgfmatrixcurrentcolumn}}% + }, + matrix/inner style/column/.code={% + \tikzset{column \the\pgfmatrixcurrentcolumn/.try}% + }, + matrix/inner style/even odd column/.code={ + \ifodd\pgfmatrixcurrentcolumn% + \tikzset{every odd column/.try}% + \else% + \tikzset{every even column/.try}% + \fi + }, + matrix/inner style/row/.code={% + \tikzset{row \the\pgfmatrixcurrentrow/.try}% + }, + matrix/inner style/even odd row/.code={% + \ifodd\pgfmatrixcurrentrow% + \tikzset{every odd row/.try}% + \else% + \tikzset{every even row/.try}% + \fi + }, + matrix/inner style/cell/.code={% + \tikzset{row \the\pgfmatrixcurrentrow\space column \the\pgfmatrixcurrentcolumn/.try}% + }, + matrix/inner style order/.store in=\tikz@common@matrix@code@styleorder, + matrix/inner style order={ + every cell, + column, + even odd column, + row, + even odd row, + cell + }, +}% + +\def\tikz@do@matrix{% + \tikzset{every matrix/.try}% + \tikz@node@transformations% + \tikz@fig@mustbenamed% + \setbox\tikz@whichbox=\hbox\bgroup% + \unhbox\tikz@whichbox% + \hbox\bgroup\bgroup% + \pgfinterruptpath% + \pgfscope% + \ifx\tikz@time\pgfutil@empty\let\tikz@time\tikz@time@for@matrix\fi% + \tikz@options% + \tikz@do@rdf@pre@options% + \tikz@is@nodefalse% + \tikz@call@id@hook% + \pgfidscope% + \tikz@do@rdf@post@options% + \begingroup% + \let\tikz@id@name\pgfutil@empty% + \pgfclearid% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \let\tikzmatrixname=\tikz@fig@name% + \edef\tikz@m@anchor{\ifx\tikz@matrix@anchor\pgfutil@empty\tikz@anchor\else\tikz@matrix@anchor\fi}% + \expandafter\pgfutil@in@\expandafter{\expandafter.\expandafter}\expandafter{\tikz@m@anchor}% + \ifpgfutil@in@% + \expandafter\tikz@matrix@split\tikz@m@anchor\relax% + \else% + \def\tikz@matrix@shift{\pgfpointorigin}% + \fi% + \let\tikz@transform=\relax% + \pgfmatrixbeforeassemblenode{\tikzset{every outer matrix/.try}}% + \pgfmatrix% + {\tikz@shape}% + {\tikz@m@anchor}% + {\tikz@fig@name}% + {% + \pgfutil@tempdima=\pgflinewidth% + {\begingroup\tikz@finish}% + \global\pgflinewidth=\pgfutil@tempdima% + }% + {\tikz@matrix@shift}% + {% + \tikz@matrix@make@active@ampersand% + \def\pgfmatrixbegincode{% + \pgfsys@beginscope% + \tikz@common@matrix@code% + \tikz@atbegin@cell% + }% + \def\tikz@common@matrix@code{% + \let\tikz@options=\pgfutil@empty% + \let\tikz@mode=\pgfutil@empty% + \pgfutil@for\pgf@temp:=\tikz@common@matrix@code@styleorder\do{% + \toks0=\expandafter{\romannumeral-`0\expandafter\pgfutil@trimspaces\expandafter{\pgf@temp}}% + \def\pgf@marshal{}% + \pgfutil@ifxempty\pgf@temp{}{% + \edef\pgf@marshal{\noexpand\tikzset{matrix/inner style/.cd,\the\toks0}}% + }% + \pgf@marshal + }% + \tikz@options% + }% + \def\pgfmatrixendcode{% + \tikz@atend@cell% + \pgfsys@endscope% + }% + \def\pgfmatrixemptycode{% + \pgfsys@beginscope% + \tikz@common@matrix@code% + \tikz@at@emptycell% + \pgfsys@endscope% + }% + \tikz@atbegin@matrix% + \aftergroup\tikz@do@matrix@cont}% + \bgroup% +}% +\def\tikz@do@matrix@cont{% + \tikz@atend@matrix% + \endgroup% + \endpgfidscope% + \endpgfscope + \endpgfinterruptpath% + \egroup\egroup% + \egroup% + \tikz@node@finish% +}% +{% + \catcode`\&=13 + \gdef\tikz@matrix@make@active@ampersand{% + \ifx\tikz@ampersand@replacement\pgfutil@empty% + \catcode`\&=13% + \let&=\pgfmatrixnextcell% + \else% + \expandafter\let\tikz@ampersand@replacement=\pgfmatrixnextcell% + \fi% + }% +}% + + +\def\tikz@matrix@split#1.#2\relax{% + \def\tikz@m@anchor{text}% + \def\tikz@matrix@shift{\pgfpointanchor{#1}{#2}}% +}% + +\def\tikz@fig@continue{% + \ifx\tikz@text@width\pgfutil@empty% + \else% + \pgfmathsetlength{\pgf@x}{\tikz@text@width}% + \wd\pgfnodeparttextbox=\pgf@x% + \fi% + \ifx\tikz@text@height\pgfutil@empty% + \else% + \pgfmathsetlength{\pgf@x}{\tikz@text@height}% + \ht\pgfnodeparttextbox=\pgf@x% + \fi% + \ifx\tikz@text@depth\pgfutil@empty% + \else% + \pgfmathsetlength{\pgf@x}{\tikz@text@depth}% + \dp\pgfnodeparttextbox=\pgf@x% + \fi% + \tikz@node@transformations% + \tikz@nlt% + \setbox\tikz@whichbox=\hbox{% + \unhbox\tikz@whichbox% + \hbox{{% + \pgfinterruptpath% + \pgfscope% + \tikz@options% + \tikz@do@rdf@pre@options% + \tikz@is@nodetrue% + \tikz@call@id@hook% + \pgfidscope% + \tikz@do@rdf@post@options% + \let\tikz@id@name\pgfutil@empty% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \setbox\pgfnodeparttextbox=\hbox{{% + \pgfsys@begin@text% + \ifx\tikz@textcolor\pgfutil@empty% + \else% + \pgfutil@colorlet{.}{\tikz@textcolor}% + \fi% + \pgfsetcolor{.}% + \pgfusetype{.text}% + \pgfidscope% + \box\pgfnodeparttextbox% + \endpgfidscope% + \pgfsys@end@text% + }}% + \pgfmultipartnode{\tikz@shape}{\tikz@anchor}{\tikz@fig@name}{% + \pgfutil@tempdima=\pgflinewidth% + {\begingroup\tikz@finish}% + \global\pgflinewidth=\pgfutil@tempdima% + }% + \endpgfidscope% + \endpgfscope% + \endpgfinterruptpath% + }}% + }% + \tikz@alias% + \tikz@node@finish% +}% + + +\def\tikz@fig@mustbenamed{% + \ifx\tikz@fig@name\pgfutil@empty% + \global\advance\tikz@fig@count by1\relax + \edef\tikz@fig@name{tikz@f@\the\tikz@fig@count}% + \let\tikz@id@name\tikz@fig@name% + \fi% +}% + +\def\tikz@node@transformations{% + \ifx\tikz@time\pgfutil@empty% + \pgftransformshift{\tikz@node@at}% + \iftikz@fullytransformed% + \else% + \pgftransformresetnontranslations% + \fi% + \else% + \tikz@do@auto@anchor% + \tikz@timer% + \fi% + \tikz@transform% +}% + +\def\tikz@node@finish{% + \global\let\tikz@last@fig@name=\tikz@fig@name% + \global\let\tikz@after@path@smuggle=\tikz@after@path% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \endgroup\endgroup% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \global\pgflinewidth=\tikz@save@line@width% + \tikz@do@after@path@smuggle% + \tikz@node@is@picfalse + \tikz@do@after@node% +}% +\let\tikz@fig@continue@orig=\tikz@fig@continue + +\def\tikz@do@after@node{\tikz@scan@next@command}% + +\def\tikz@do@after@path@smuggle{% + \let\tikz@to@last@fig@name=\tikz@last@fig@name% + \let\tikz@to@use@whom=\tikz@to@use@last@fig@name% + \let\tikzlastnode=\tikz@last@fig@name% + \ifx\tikz@after@path@smuggle\pgfutil@empty% + \else% + \ifpgflatenodepositioning% + \expandafter\expandafter\expandafter\tikz@call@late% + \expandafter\expandafter\expandafter{\expandafter\tikz@last@fig@name\expandafter}\expandafter{\tikz@after@path@smuggle}% + \else% + \tikz@scan@next@command{\tikz@after@path@smuggle}\pgf@stop% + \fi% + \fi% +}% + +\def\tikz@call@late#1#2{\pgfnodepostsetupcode{#1}{\path[late options={name={#1},append after command={#2}}];}}% + +\newif\iftikz@do@align + +\def\tikz@signal@halign@check{% + \tikz@do@alignfalse + \ifx\tikz@text@width\pgfutil@empty% + \pgfkeysgetvalue{/tikz/node halign header}\tikz@align@header% + \ifx\tikz@align@header\pgfutil@empty% + \else% + \tikz@do@aligntrue% + \fi% + \fi% +} +\def\tikz@halign@check{% + \iftikz@do@align% + \setbox\tikz@align@aligned@box=\box\pgfutil@voidb@x% + \let\\=\tikz@align@newline% + \expandafter\tikz@start@align% + \fi% +}% +\def\tikz@align@newline{\pgfutil@protect\tikz@align@newline@}% +\def\tikz@align@newline@{\unskip\pgfutil@ifnextchar[\tikz@@align@newline{\tikz@@align@newline[0pt]}}% +\def\tikz@@align@newline[#1]{\egroup\tikz@align@continue\pgfmathparse{#1}\let\tikz@align@temp=\pgfmathresult\tikz@start@align}% +\let\tikz@align@aligned@box=\pgfnodeparttextbox +\let\tikz@align@line@box=\tikz@figbox + +\def\tikz@start@align{% + \setbox\tikz@align@line@box=\hbox\bgroup\bgroup% + \aftergroup\tikz@align@collectresetcolor\ignorespaces% +}% +\def\tikz@align@collectresetcolor{% + \pgfutil@ifnextchar\reset@color% + {\reset@color\afterassignment\tikz@align@collectresetcolor\let\tikz@temp=}% + {\tikz@align@end@check}% +}% +\def\tikz@align@end@check{% + \egroup% + \ifvoid\tikz@align@aligned@box% + \setbox\tikz@align@aligned@box=\box\tikz@align@line@box% + \else% + \setbox\tikz@align@aligned@box=\vbox{% + \expandafter\expandafter\expandafter\halign\expandafter\expandafter\expandafter{\tikz@align@header% + \box\tikz@align@aligned@box\cr% + \noalign{\vskip\tikz@align@temp pt}% + \unhbox\tikz@align@line@box\unskip\cr}}% + \fi% + \pgfutil@ifnextchar\tikz@align@continue{} + {% + \box\tikz@align@aligned@box% + \egroup% + }% +}% +\def\tikz@align@continue{\tikz@@align@continue}% +\let\tikz@@align@continue=\pgfutil@empty + + +\def\tikz@node@also lso{\pgfutil@ifnextchar[\tikz@node@also@opt{\tikz@node@also@opt[]}}% +\def\tikz@node@also@opt[#1]{ + \pgfutil@ifnextchar(% + {\tikz@node@also@opt@cont[#1]}% + {\tikzerror{Syntax error in node also: ``('' expected.}% + \tikz@scan@next@command}% +}% +\def\tikz@node@also@opt@cont[#1](#2){\tikzset{late options={name=#2,#1}}\tikz@scan@next@command}% + + + + +\def\tikz@nodepart{\pgfutil@ifnextchar[\tikz@@nodepart{\tikz@@nodepart[]}}% +\def\tikz@@nodepart[#1]#2{% + \tikz@atend@node% + \unskip% + \gdef\tikz@nodepart@options{#1}% + \gdef\tikz@nodepart@name{#2}% + \global\let\tikz@fig@continue=\tikz@nodepart@continue% + \pgfutil@ifnextchar x{\egroup\relax}{\egroup\relax}% +}% +\def\tikz@nodepart@continue{% + \global\let\tikz@fig@continue=\tikz@fig@continue@orig% + \ifx\tikz@nodepart@list\pgfutil@empty% + \let\tikz@nodepart@list\tikz@nodepart@name% + \else% + \edef\tikz@nodepart@list{\tikz@nodepart@list,\tikz@nodepart@name}% + \fi% + \expandafter\setbox\csname pgfnodepart\tikz@nodepart@name box\endcsname=\hbox% + \bgroup% + \pgfinterruptpicture% + \pgfsys@begin@text% + \pgfsys@text@to@black@hook% + \tikzset{every \tikz@nodepart@name\space node part/.try}% + \expandafter\tikzset\expandafter{\tikz@nodepart@options}% + \ifx\tikz@textopacity\pgfutil@empty% + \else% + \pgfsetfillopacity{\tikz@textopacity}% + \pgfsetstrokeopacity{\tikz@textopacity}% + \fi% + \ifx\tikz@textcolor\pgfutil@empty% + \else% + \pgfutil@colorlet{.}{\tikz@textcolor}% + \fi% + \pgfsetcolor{.}% + \ifx\tikz@text@width\pgfutil@empty% + \tikz@textfont% + \else% + \begingroup% + \pgfmathsetlength{\pgf@x}{\tikz@text@width}% + \pgfutil@minipage[t]{\pgf@x}\leavevmode\hbox{}% + \tikz@textfont% + \tikz@text@action% + \fi% + \bgroup% + \aftergroup\unskip% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \tikz@uninstallcommands% + \iftikz@handle@active@code% + \tikz@orig@shorthands% + \let\tikz@orig@shorthands\pgfutil@empty% + \fi% + \ifnum\the\catcode`\;=\active\relax\expandafter\let\tikz@activesemicolon=\tikz@origsemi\fi% + \ifnum\the\catcode`\:=\active\relax\expandafter\let\tikz@activecolon=\tikz@origcolon\fi% + \ifnum\the\catcode`\|=\active\relax\expandafter\let\tikz@activebar=\tikz@origbar\fi% + \tikz@atbegin@node% + \aftergroup\tikz@fig@collectresetcolor% + \tikz@signal@halign@check% + \tikz@text@reset% + \tikz@halign@check% + \ignorespaces% +}% + + + +\def\tikz@nodes@start{% + \let\tikz@nodes@list\pgfutil@empty% + \iftikz@node@is@pic% + \def\tikz@nodes@collect{pic }% + \else% + \def\tikz@nodes@collect{node }% + \fi% + \tikz@nodes% +}% +\def\tikz@nodes foreach{\pgfutil@ifnextchar x\tikz@nodes@\tikz@nodes@}% +\def\tikz@nodes@#1in{% + \expandafter\def\expandafter\tikz@nodes@list\expandafter{\tikz@nodes@list\foreach#1in}% + \pgfutil@ifnextchar\bgroup\tikz@nodes@group\tikz@nodes@one% +}% +\def\tikz@nodes@one#1{% + \expandafter\def\expandafter\tikz@nodes@list\expandafter{\tikz@nodes@list#1}% + \pgfutil@ifnextchar f\tikz@nodes\tikz@nodes@scan% +}% +\def\tikz@nodes@group#1{% + \expandafter\def\expandafter\tikz@nodes@list\expandafter{\tikz@nodes@list{#1}}% + \pgfutil@ifnextchar f\tikz@nodes\tikz@nodes@scan% +}% +\def\tikz@nodes@scan{% + \pgfutil@ifnextchar a{\tikz@nodes@at}% + {\pgfutil@ifnextchar({\tikz@nodes@name}% + {\pgfutil@ifnextchar[{\tikz@nodes@opt}% + {\pgfutil@ifnextchar\bgroup{\tikz@nodes@main}% + {\tikzerror{Nodes must have a (possibly empty) label text}% + \tikz@fig@main{}}}}}}% + +\def\tikz@nodes@at at{\pgfutil@ifnextchar({\tikz@nodes@at@}{\tikz@nodes@at@@}}% +\def\tikz@nodes@at@#1){% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect at#1)}% + \tikz@nodes@scan}% +\def\tikz@nodes@at@@#1{% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect at#1}% + \tikz@nodes@scan}% + +\def\tikz@nodes@name#1){% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect#1)}% + \tikz@nodes@scan}% +\def\tikz@nodes@opt#1]{% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect#1]}% + \tikz@nodes@scan}% +\def\tikz@nodes@main#1{% + \iftikz@handle@active@nodes% + \iftikz@node@is@pic% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect{#1}}% + \else% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect{\scantokens{#1}}}% + \fi% + \else% + \expandafter\def\expandafter\tikz@nodes@collect\expandafter{\tikz@nodes@collect{#1}}% + \fi% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \tikz@nodes@list{% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \expandafter\tikz@scan@next@command\tikz@nodes@collect\pgfextra\relax% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + }% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \tikz@scan@next@command% +}% + + + +\tikzset{late options/.code=\tikz@late@options{#1}}% +\def\tikz@late@options#1{% + \begingroup% + \iftikz@shapeborder% + \let\tikz@fig@name=\tikz@shapeborder@name% + \else% + \let\tikz@fig@name=\pgfutil@empty% + \fi% + \tikz@is@matrixfalse% + \let\tikz@options=\pgfutil@empty% + \tikz@clear@rdf@options% + \let\tikz@after@path=\pgfutil@empty% + \let\tikz@afternodepathoptions=\pgfutil@empty% + \let\tikz@alias=\pgfutil@empty% + \let\tikz@transform=\pgfutil@empty% + \tikz@decoratepathfalse% + \tikz@node@reset@hook% + \tikz@enable@node@quotes% + \tikzset{every node/.try,#1}% + \ifx\tikz@fig@name\pgfutil@empty% + \tikzerror{Late options must reference some existing node}% + \fi% + \tikz@node@begin@hook% + \tikz@alias% + \tikzgdlatenodeoptionacallback{\tikz@fig@name}% + \global\let\tikz@last@fig@name=\tikz@fig@name% + \global\let\tikz@after@path@smuggle=\tikz@after@path% + \endgroup% + \tikz@do@after@path@smuggle% +}% + + + +\def\tikz@auto@pre{% + \begingroup + \pgfresetnontranslationattimefalse + \ifpgfslopedattime + \pgfslopedattimefalse% + \else + \pgfslopedattimetrue% + \fi + \pgfallowupsidedownattimetrue% + \tikz@timer% + \pgf@x=\pgf@pt@aa pt% + \pgf@y=\pgf@pt@ab pt% + \pgfpointnormalised{}% +}% + +\def\tikz@auto@post{% + \global\let\tikz@anchor@smuggle=\tikz@anchor% + \endgroup% + \let\tikz@anchor=\tikz@anchor@smuggle% +}% + +\def\tikz@auto@anchor{% + \ifdim\pgf@x>0.05pt% + \ifdim\pgf@y>0.05pt% + \def\tikz@anchor{south east}% + \else\ifdim\pgf@y<-0.05pt% + \def\tikz@anchor{south west}% + \else + \def\tikz@anchor{south}% + \fi\fi% + \else\ifdim\pgf@x<-0.05pt% + \ifdim\pgf@y>0.05pt% + \def\tikz@anchor{north east}% + \else\ifdim\pgf@y<-0.05pt% + \def\tikz@anchor{north west}% + \else + \def\tikz@anchor{north}% + \fi\fi% + \else% + \ifdim\pgf@y>0pt% + \def\tikz@anchor{east}% + \else% + \def\tikz@anchor{west}% + \fi% + \fi\fi% +}% + +\def\tikz@auto@anchor@prime{% + \ifdim\pgf@x>0.05pt% + \ifdim\pgf@y>0.05pt% + \def\tikz@anchor{north west}% + \else\ifdim\pgf@y<-0.05pt% + \def\tikz@anchor{north east}% + \else + \def\tikz@anchor{north}% + \fi\fi% + \else\ifdim\pgf@x<-0.05pt% + \ifdim\pgf@y>0.05pt% + \def\tikz@anchor{south west}% + \else\ifdim\pgf@y<-0.05pt% + \def\tikz@anchor{south east}% + \else + \def\tikz@anchor{south}% + \fi\fi% + \else% + \ifdim\pgf@y>0pt% + \def\tikz@anchor{west}% + \else% + \def\tikz@anchor{east}% + \fi% + \fi\fi% +}% + + +\def\tikzgdeventcallback#1#2{}% +\def\tikzgdeventgroupcallback#1{}% +\def\tikzgdlatenodeoptionacallback#1{}% + + +\def\tikz@children{% + \let\tikz@children@list=\pgfutil@empty% + \tikznumberofchildren=0\relax% + \tikz@collect@children c}% + +\def\tikz@collect@children{\pgfutil@ifnextchar c{\tikz@collect@children@cchar}{\tikz@children@collected}}% +\def\tikz@collect@children@cchar c{\pgfutil@ifnextchar h{\tikz@collect@child}{\tikz@children@collected c}}% +\def\tikz@collect@child hild{\pgfutil@ifnextchar[{\tikz@collect@childA}{\tikz@collect@childA[]}}% +\def\tikz@collect@childA[#1]{\pgfutil@ifnextchar f{\tikz@collect@children@foreach[#1]}{\tikz@collect@childB[#1]}}% +\def\tikz@collect@childB[#1]{% + \advance\tikznumberofchildren by1\relax + \expandafter\def\expandafter\tikz@children@list\expandafter{\tikz@children@list \tikz@childnode[#1]}% + \pgfutil@ifnextchar\bgroup{\tikz@collect@child@code}{\tikz@collect@child@code{}}}% +\def\tikz@collect@child@code#1{% + \expandafter\def\expandafter\tikz@children@list\expandafter{\tikz@children@list{#1}}% + \tikz@collect@children% +}% +\def\tikz@collect@children@foreach[#1]foreach#2in#3{% + \pgfutil@ifnextchar\bgroup{\tikz@collect@children@foreachA{#1}{#2}{#3}}{\tikz@collect@children@foreachA{#1}{#2}{#3}{}}}% +\def\tikz@collect@children@foreachA#1#2#3#4{% + \expandafter\def\expandafter\tikz@children@list\expandafter + {\tikz@children@list\tikz@childrennodes[#1]{#2}{#3}{#4}}% + \c@pgf@counta=\tikznumberofchildren% + \foreach#2in{#3}% + {% + \global\advance\c@pgf@counta by1\relax% + }% + \tikznumberofchildren=\c@pgf@counta% + \tikz@collect@children% +}% +\long\def\tikz@children@collected{% + \begingroup% + \advance\tikztreelevel by 1\relax% + \tikzgdeventgroupcallback{descendants}% + \let\tikz@options=\pgfutil@empty% + \tikz@clear@rdf@options% + \let\tikz@transform=\pgfutil@empty% + \tikzset{level/.try=\the\tikztreelevel,level \the\tikztreelevel/.try}% + \tikz@transform% + \let\tikz@transform=\relax% + \let\tikzparentnode=\tikz@last@fig@name% + \ifx\tikz@grow\relax\else% + \pgftransformshift{\pgfpointanchor{\tikzparentnode}{\tikz@growth@anchor}}% + \fi% + \tikznumberofcurrentchild=0\relax% + \tikz@children@list% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \endgroup% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \tikz@scan@next@command% +}% + +\def\tikz@childrennodes[#1]#2#3#4{% + \c@pgf@counta=\tikznumberofcurrentchild\relax% + \setbox\tikz@tempbox=\box\tikz@figbox% + \setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + \foreach#2in{#3}{% + \tikznumberofcurrentchild=\c@pgf@counta\relax% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% + \tikz@childnode[#1]{#4}% + \global\c@pgf@counta=\tikznumberofcurrentchild\relax% + \global\setbox\tikz@tempbox=\box\tikz@figbox% + \global\setbox\tikz@tempbox@bg=\box\tikz@figbox@bg% + }% + \tikznumberofcurrentchild=\c@pgf@counta\relax% + \setbox\tikz@figbox=\box\tikz@tempbox% + \setbox\tikz@figbox@bg=\box\tikz@tempbox@bg% +}% + + + +\def\tikz@childnode[#1]#2{% + \advance\tikznumberofcurrentchild by1\relax% + {\tikzset{every child/.try,#1}\expandafter}% + \iftikz@child@missing% + \tikzgdeventcallback{node}{}% + \else% + \setbox\tikz@whichbox=\hbox\bgroup% + \unhbox\tikz@whichbox% + \hbox\bgroup\bgroup% + \pgfinterruptpath% + \pgfscope% + \let\tikz@transform=\pgfutil@empty% + \tikzset{every child/.try,#1}% + \tikz@options% + \tikz@transform% + \let\tikz@transform=\relax% + \tikz@grow% + \edef\tikz@parent@node@name{[name=\tikzparentnode-\the\tikznumberofcurrentchild,style=every child node]}% + \def\tikz@child@node@text{[shape=coordinate]{}} + \tikz@parse@child@node#2\pgf@stop% + \expandafter\expandafter\expandafter\node + \expandafter\tikz@parent@node@name + \tikz@child@node@text + \pgfextra{\global\let\tikz@childnode@name=\tikz@last@fig@name};% + \let\tikzchildnode=\tikz@childnode@name% + {% + \def\tikz@edge@to@parent@needed{edge from parent} + \ifx\tikz@child@node@rest\pgfutil@empty% + \path edge from parent;% + \else% + \path \tikz@child@node@rest \tikz@edge@to@parent@needed;% + \fi% + }% + \endpgfscope% + \endpgfinterruptpath% + \egroup\egroup% + \egroup% + \fi% +}% + +\def\tikz@parse@child@node{% + \pgfutil@ifnextchar n{\tikz@parse@child@node@n}% + {\pgfutil@ifnextchar c{\tikz@parse@child@node@c}% + {\pgfutil@ifnextchar\pgf@stop\tikz@parse@child@node@rest\tikz@parse@child@node@expand}}}% +\def\tikz@parse@child@node@expand{% + \advance\tikz@expandcount by-1\relax% + \ifnum\tikz@expandcount<0\relax% + \expandafter\tikz@parse@child@node@rest% + \else% + \expandafter\expandafter\expandafter\tikz@parse@child@node% + \fi% +}% +\def\tikz@parse@child@node@rest#1\pgf@stop{\tikz@resetexpandcount\def\tikz@child@node@rest{#1}}% +\def\tikz@parse@child@node@c c{\tikz@resetexpandcount\pgfutil@ifnextchar o{\tikz@parse@child@node@co}{\tikz@parse@child@node@rest c}}% +\def\tikz@parse@child@node@co o{\pgfutil@ifnextchar o{\tikz@parse@child@node@coordinate}{\tikz@parse@child@node@rest co}}% +\def\tikz@parse@child@node@coordinate ordinate{% + \pgfutil@ifnextchar ({\tikz@@parse@child@node@coordinate}{% + \def\tikz@child@node@text{[shape=coordinate]{}}% + \tikz@parse@child@node@rest}}% +\def\tikz@@parse@child@node@coordinate(#1){% + \pgfutil@ifnextchar a{\tikz@p@c@n@c@at(#1)}{% + \def\tikz@child@node@text{[shape=coordinate,name=#1]{}}% + \tikz@parse@child@node@rest}}% +\def\tikz@p@c@n@c@at(#1)at#2({% + \def\tikz@child@node@text@pre{[shape=coordinate,name=#1]at}% + \tikz@scan@one@point\tikz@p@c@n@c@at@math(% +}% +\def\tikz@p@c@n@c@at@math#1{% + \pgf@process{#1}% + \edef\tikz@marshal{(\the\pgf@x,\the\pgf@y){}}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@child@node@text% + \expandafter\expandafter\expandafter{\expandafter\tikz@child@node@text@pre\tikz@marshal}% + \tikz@parse@child@node@rest% +}% +\def\tikz@parse@child@node@n node{\tikz@resetexpandcount% + \let\tikz@child@node@text=\pgfutil@empty% + \tikz@p@c@s}% +\def\tikz@p@c@s{% + \pgfutil@ifnextchar a{\tikz@p@c@s@at} + {\pgfutil@ifnextchar ({\tikz@p@c@s@paran} + {\pgfutil@ifnextchar [{\tikz@p@c@s@bra} + {\pgfutil@ifnextchar \bgroup{\tikz@p@c@s@group} + {\tikzerror{Cannot parse this node}}}}}}% +\def\tikz@p@c@s@at at#1({% + \tikz@scan@one@point\tikz@p@c@s@at@math(% +}% +\def\tikz@p@c@s@at@math#1{% + \pgf@process{#1}% + \edef\tikz@marshal{ at(\the\pgf@x,\the\pgf@y)}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\tikz@child@node@text% + \expandafter\expandafter\expandafter{\expandafter\tikz@child@node@text\tikz@marshal} + \tikz@p@c@s}% +\def\tikz@p@c@s@paran(#1){% + \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text(#1)} + \tikz@p@c@s}% +\def\tikz@p@c@s@bra[#1]{% + \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text[#1]} + \tikz@p@c@s}% +\def\tikz@p@c@s@group#1{% + \iftikz@handle@active@nodes% + \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text{\scantokens{#1}}}% + \else% + \expandafter\def\expandafter\tikz@child@node@text\expandafter{\tikz@child@node@text{#1}} + \fi% + \tikz@parse@child@node@rest% +}% + + + +\def\tikz@decoration ecorate{% + \pgfutil@ifnextchar[{\tikz@lib@decoration}{\tikz@lib@decoration[]}% +}% + +\def\tikz@lib@decoration[#1]#2{\tikzerror{You need to load a decoration library}}% + +\def\tikz@lib@dec@decorate@path{\tikzerror{You need to load a decoration library}}% + + + +\def\tikz@let@command et#1in{% + \tikzerror{You need to say \string\usetikzlibrary{calc} to use the let command}% + \tikz@scan@next@command% +}% + + +\newif\iftikz@node@is@pic +\def\tikz@subpicture ic{\tikz@node@is@pictrue\tikz@scan@next@command node}% +\def\tikz@subpicture@handle#1{% + \pgfkeys@spdef\tikz@temp{#1}% + \expandafter\tikz@subpicture@handle@\expandafter{\tikz@temp}% +}% +\def\tikz@subpicture@handle@#1{ + \pgfkeys{/tikz/pics/.cd,#1}% + \tikz@node@transformations% + \let\tikz@transform=\relax% + \let\tikz@picmode\tikz@mode% + \tikzset{name prefix ../.style/.expanded={/tikz/name prefix=\pgfkeysvalueof{/tikz/name prefix}}}% + \ifx\tikz@fig@name\pgfutil@empty\else% + \tikzset{name prefix/.expanded=\tikz@fig@name}% + \fi% + \pgfkeysvalueof{/tikz/pics/setup code}% + \pgfkeysgetvalue{/tikz/pics/code}{\tikz@pic@code} + \ifx\tikz@pic@code\pgfutil@empty\else% + \setbox\tikz@whichbox=\hbox\bgroup% + \unhbox\tikz@whichbox% + \hbox\bgroup + \bgroup% + \pgfinterruptpath% + \pgfscope% + \tikz@options% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \tikz@atbegin@scope% + \scope[every pic/.try]% + \tikz@pic@code% + \endscope% + \tikz@atend@scope% + \endpgfscope% + \endpgfinterruptpath% + \egroup + \egroup% + \egroup% + \fi% + \pgfkeysgetvalue{/tikz/pics/foreground code}{\tikz@pic@code} + \ifx\tikz@pic@code\pgfutil@empty\else% + \setbox\tikz@figbox=\hbox\bgroup% + \unhbox\tikz@figbox% + \hbox\bgroup + \bgroup% + \pgfinterruptpath% + \pgfscope% + \tikz@options% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \tikz@atbegin@scope% + \scope[every front pic/.try]% + \tikz@pic@code% + \endscope% + \tikz@atend@scope% + \endpgfscope% + \endpgfinterruptpath% + \egroup + \egroup% + \egroup% + \fi% + \pgfkeysgetvalue{/tikz/pics/background code}{\tikz@pic@code} + \ifx\tikz@pic@code\pgfutil@empty\else% + \setbox\tikz@figbox@bg=\hbox\bgroup% + \unhbox\tikz@figbox@bg% + \hbox\bgroup + \bgroup% + \pgfinterruptpath% + \pgfscope% + \tikz@options% + \setbox\tikz@figbox=\box\pgfutil@voidb@x% + \setbox\tikz@figbox@bg=\box\pgfutil@voidb@x% + \tikz@atbegin@scope% + \scope[every behind pic/.try]% + \tikz@pic@code% + \endscope% + \tikz@atend@scope% + \endpgfscope% + \endpgfinterruptpath% + \egroup + \egroup% + \egroup% + \fi% + \tikz@node@finish% +}% +\tikzset{ + pic actions/.code=\tikz@addmode{\tikz@picmode} +}% + +\tikzset{ + pics/setup code/.initial=, + pics/code/.initial=, + pics/background code/.initial=, + pics/foreground code/.initial= +}% + + +\def\tikzdeclarepic#1#2{\pgfkeys{/tikz/#1/.cd,#2}}% + +\pgfkeysdef{/handlers/.pic}{% + \edef\pgf@temp{\pgfkeyscurrentpath}% + \edef\pgf@temp{\expandafter\tikz@smuggle@pics@in\pgf@temp\pgf@stop}% + \expandafter\pgfkeys\expandafter{\pgf@temp/.style={code={#1}}}% +}% +\def\tikz@smuggle@pics@in/tikz/#1\pgf@stop{/tikz/pics/#1}% + + +\def\tikz@timer@line{% + \pgftransformlineattime{\tikz@time}{\tikz@timer@start}{\tikz@timer@end}% +}% + +\def\tikz@timer@vhline{% + \ifdim\tikz@time pt<0.5pt% + \pgf@process{\tikz@timer@start}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@timer@end}% + \pgf@xb=\tikz@time pt% + \pgf@xb=2\pgf@xb% + \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}{\noexpand\tikz@timer@start}{% + \noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@y}}}% + \tikz@marshal% + \else% + \pgf@process{\tikz@timer@start}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@timer@end}% + \pgf@xb=\tikz@time pt% + \pgf@xb=2\pgf@xb% + \advance\pgf@xb by-1pt% + \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}% + {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@y}}{\noexpand\tikz@timer@end}}% + \tikz@marshal% + \fi% +}% + +\def\tikz@timer@hvline{% + \ifdim\tikz@time pt<0.5pt% + \pgf@process{\tikz@timer@start}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@timer@end}% + \pgf@xb=\tikz@time pt% + \pgf@xb=2\pgf@xb% + \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}{\noexpand\tikz@timer@start}{% + \noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@ya}}}% + \tikz@marshal% + \else% + \pgf@process{\tikz@timer@start}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\tikz@timer@end}% + \pgf@xb=\tikz@time pt% + \pgf@xb=2\pgf@xb% + \advance\pgf@xb by-1pt% + \edef\tikz@marshal{\noexpand\pgftransformlineattime{\pgf@sys@tonumber{\pgf@xb}}% + {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@ya}}{\noexpand\tikz@timer@end}}% + \tikz@marshal% + \fi% +}% + +\def\tikz@timer@curve{% + \pgftransformcurveattime{\tikz@time}{\tikz@timer@start}{\tikz@timer@cont@one}{\tikz@timer@cont@two}{\tikz@timer@end}% +}% + + +\def\tikz@timer@arc{% + \pgfmathcos@{\tikz@timer@start@angle}% + \let\tikz@angle@cos\pgfmathresult% + \pgfmathsin@{\tikz@timer@start@angle}% + \let\tikz@angle@sin\pgfmathresult% + \pgftransformarcaxesattime{\tikz@time}{% + \pgfpointdiff{% + \pgfpointadd{% + \pgfpointscale{\tikz@angle@cos}{\tikz@timer@zero@axis}% + }{% + \pgfpointscale{\tikz@angle@sin}{\tikz@timer@ninety@axis}% + }% + }% + {\tikz@timer@start}% + }% + {\tikz@timer@zero@axis}% + {\tikz@timer@ninety@axis}% + {\tikz@timer@start@angle}{\tikz@timer@end@angle}% +}% + + + + +\def\tikzdeclarecoordinatesystem#1#2{% + \expandafter\def\csname tikz@parse@cs@#1\endcsname(##1){% + \pgf@process{% + #2% + \global\let\tikz@smubble@b=\tikz@shapeborder@name% + }% + \let\tikz@shapeborder@name=\tikz@smubble@b% + \edef\tikz@return@coordinate{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% +}% +\def\tikzaliascoordinatesystem#1#2{% + \edef\pgf@marshal{\noexpand\let\expandafter\noexpand\csname + tikz@parse@cs@#1\endcsname=\expandafter\noexpand\csname + tikz@parse@cs@#2\endcsname}% + \pgf@marshal% +}% + + + +\tikzdeclarecoordinatesystem{canvas} +{% + \tikzset{cs/.cd,x=0pt,y=0pt,#1}% + \pgfpoint{\tikz@cs@x}{\tikz@cs@y}% +}% + +\tikzdeclarecoordinatesystem{canvas polar} +{% + \tikzset{cs/.cd,angle=0,radius=0cm,#1}% + \pgfpointpolar{\tikz@cs@angle}{\tikz@cs@xradius and \tikz@cs@yradius}% +}% + +\tikzdeclarecoordinatesystem{xyz} +{% + \tikzset{cs/.cd,x=0,y=0,z=0,#1}% + \pgfpointxyz{\tikz@cs@x}{\tikz@cs@y}{\tikz@cs@z}% +}% + +\tikzdeclarecoordinatesystem{xyz polar} +{% + \tikzset{cs/.cd,angle=0,radius=0,#1}% + \pgfpointpolarxy{\tikz@cs@angle}{\tikz@cs@xradius and \tikz@cs@yradius}% +}% +\tikzaliascoordinatesystem{xy polar}{xyz polar}% + + +\tikzdeclarecoordinatesystem{node} +{% + \tikzset{cs/.cd,name=,anchor=none,angle=none,#1}% + \ifx\tikz@cs@anchor\tikz@nonetext% + \ifx\tikz@cs@angle\tikz@nonetext% + \expandafter\ifx\csname pgf@sh@ns@\tikz@cs@node\endcsname\tikz@coordinate@text% + \else + \aftergroup\tikz@shapebordertrue% + \edef\tikz@shapeborder@name{\tikz@pp@name{\tikz@cs@node}}% + \fi% + \pgfpointanchor{\tikz@pp@name{\tikz@cs@node}}{center}% + \else% + \pgfpointanchor{\tikz@pp@name{\tikz@cs@node}}{\tikz@cs@angle}% + \fi% + \else% + \pgfpointanchor{\tikz@pp@name{\tikz@cs@node}}{\tikz@cs@anchor}% + \fi% +}% + +\tikzset{cs/first line/.code=\def\tikz@cs@line@a{#1}\def\tikz@cs@type@a{line}}% +\tikzset{cs/second line/.code=\def\tikz@cs@line@b{#1}\def\tikz@cs@type@b{line}}% + +\tikzset{cs/first node/.code=\tikz@cs@unpack{\tikz@cs@node@a}{\tikz@cs@type@a}{#1}}% +\tikzset{cs/second node/.code=\tikz@cs@unpack{\tikz@cs@node@b}{\tikz@cs@type@b}{#1}}% + +\def\tikz@cs@unpack#1#2#3{% + \expandafter\ifx\csname pgf@sh@ns@#3\endcsname\relax% + \tikzerror{Undefined node ``#3''}% + \else% + \def#1{#3}% + \edef#2{\csname pgf@sh@ns@#3\endcsname}% + \fi% +}% + +\tikzset{cs/solution/.initial=1}% + +\tikzset{cs/horizontal line through/.store in=\tikz@cs@hori@line}% +\tikzset{cs/vertical line through/.store in=\tikz@cs@vert@line}% + +\tikzdeclarecoordinatesystem{intersection} +{% + \tikzset{cs/.cd,#1}% + \expandafter\ifx\csname tikz@intersect@\tikz@cs@type@a @and@\tikz@cs@type@b\endcsname\relax% + \tikzerror{I do not know how to compute the intersection + of a \tikz@cs@type@a and a \tikz@cs@type@b. Try saying + \string\usetikzlibrary{calc}}% + \pgfpointorigin% + \else% + \csname tikz@intersect@\tikz@cs@type@a @and@\tikz@cs@type@b\endcsname% + \fi% +}% + +\def\tikz@intersect@line@and@line{% + \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@a% + \pgf@xa=\pgf@xc% + \pgf@ya=\pgf@yc% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \expandafter\tikz@scan@one@point\expandafter\tikz@parse@line\tikz@cs@line@b% + \edef\pgf@marshal{% + {\noexpand\pgfpointintersectionoflines% + {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}% + {\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}}% + \pgf@marshal% +}% + +\def\tikz@parse@line#1--{% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \tikz@scan@one@point\pgf@process% +}% + + +\tikzdeclarecoordinatesystem{perpendicular} +{% + \tikzset{cs/.cd,#1}% + \expandafter\tikz@scan@one@point\expandafter\tikz@parse@intersection@a\tikz@cs@hori@line% + \expandafter\tikz@scan@one@point\expandafter\tikz@parse@intersection@b\tikz@cs@vert@line% + \pgfqpoint{\the\pgf@xb}{\the\pgf@ya} +}% + +\tikzdeclarecoordinatesystem{barycentric} +{% + {% + \pgf@xa=0pt% + \pgf@ya=0pt% + \pgf@xb=0pt% + \tikz@bary@dolist#1,=,% + \pgfmathparse{1/\the\pgf@xb}% + \global\pgf@x=\pgfmathresult\pgf@xa% + \global\pgf@y=\pgfmathresult\pgf@ya% + }% +}% + +\def\tikz@bary@dolist#1=#2,{% + \def\tikz@temp{#1}% + \ifx\tikz@temp\pgfutil@empty% + \else + \pgf@process{\pgfpointanchor{#1}{center}}% + \pgfmathparse{#2}% + \advance\pgf@xa by\pgfmathresult\pgf@x% + \advance\pgf@ya by\pgfmathresult\pgf@y% + \advance\pgf@xb by\pgfmathresult pt% + \expandafter\tikz@bary@dolist% + \fi% +}% + +\tikzset{cs/x/.store in=\tikz@cs@x}% +\tikzset{cs/y/.store in=\tikz@cs@y}% +\tikzset{cs/z/.store in=\tikz@cs@z}% +\tikzset{cs/angle/.store in=\tikz@cs@angle}% +\tikzset{cs/x radius/.store in=\tikz@cs@xradius}% +\tikzset{cs/y radius/.store in=\tikz@cs@yradius}% +\tikzset{cs/radius/.style={/tikz/cs/x radius={#1},/tikz/cs/y radius={#1}}}% +\tikzset{cs/name/.store in=\tikz@cs@node}% +\tikzset{cs/anchor/.store in=\tikz@cs@anchor}% + + + + + +\def\tikz@last@position{\pgfqpoint{\tikz@lastx}{\tikz@lasty}}% +\def\tikz@last@position@saved{\pgfqpoint{\tikz@lastxsaved}{\tikz@lastysaved}}% + +\def\tikz@make@last@position#1{% + \pgf@process{#1}% + \tikz@lastx=\pgf@x\relax% + \tikz@lasty=\pgf@y\relax% + \iftikz@updatecurrent% + \tikz@lastxsaved=\pgf@x\relax% + \tikz@lastysaved=\pgf@y\relax% + \fi% + \iftikz@updatenext + \tikz@updatecurrenttrue% + \fi +}% + +\newif\iftikz@updatecurrent +\tikz@updatecurrenttrue +\newif\iftikz@updatenext +\tikz@updatenexttrue + + + + +\def\tikz@scan@one@point#1{% + \let\tikz@to@use@whom=\tikz@to@use@last@coordinate% + \tikz@shapeborderfalse% + \pgfutil@ifnextchar+{\tikz@scan@relative#1}{\tikz@scan@absolute#1}}% +\def\tikz@scan@absolute#1{% + \pgfutil@ifnextchar({\tikz@scan@@absolute#1}% + {% + \advance\tikz@expandcount by -1 + \ifnum\tikz@expandcount<0\relax% + \let\pgfutil@next=\tikz@@scangiveup% + \else% + \let\pgfutil@next=\tikz@@scanexpand% + \fi% + \pgfutil@next{#1}% + }% +}% +\def\tikz@@scanexpand#1{\expandafter\tikz@scan@one@point\expandafter#1}% +\def\tikz@@scangiveup#1{\tikzerror{Cannot parse this coordinate}#1{\pgfpointorigin}}% +\def\tikz@scan@@absolute#1({% + \pgfutil@ifnextchar[% + {\def\tikz@scan@point@recall{#1}\tikz@scan@options}% + {\tikz@@@scan@@absolute#1(}% +}% + +\def\tikz@scan@options[#1]#2{% + \def\tikz@scan@point@options{#1}% + \tikz@@@scan@@absolute\tikz@scan@handle@options(#2% +}% + +\def\tikz@scan@handle@options#1{% + {% + \pgftransformreset% + \let\tikz@transform=\pgfutil@empty% + \expandafter\tikzset\expandafter{\tikz@scan@point@options}% + \tikz@transform% + \pgf@process{\pgfpointtransformed{#1}}% + \xdef\tikz@marshal{\expandafter\noexpand\tikz@scan@point@recall{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + }% + \tikz@marshal% +}% + +\def\tikz@@@scan@@absolute#1({% + \pgfutil@ifnextchar{$}% + {\tikz@parse@calculator#1(} + {\tikz@scan@no@calculator#1(}% +}% +\def\tikz@scan@no@calculator#1(#2){% + \edef\tikz@scan@point@coordinate{(#2)}% + \expandafter\tikz@@scan@@no@calculator\expandafter#1\tikz@scan@point@coordinate% +}% +\def\tikz@@scan@@no@calculator#1(#2){% + \pgfutil@in@{cs:}{#2}% + \ifpgfutil@in@% + \let\pgfutil@next\tikz@parse@coordinatesystem% + \else% + \pgfutil@in@{intersection }{#2}% + \ifpgfutil@in@% + \let\pgfutil@next\tikz@parse@intersection% + \else% + \pgfutil@in@|{#2}% + \ifpgfutil@in@ + \pgfutil@in@{-|}{#2}% + \ifpgfutil@in@ + \let\pgfutil@next\tikz@parse@hv% + \else% + \let\pgfutil@next\tikz@parse@vh% + \fi% + \else% + \pgfutil@in@:{#2}% + \ifpgfutil@in@ + \let\pgfutil@next\tikz@parse@polar% + \else% + \pgfutil@in@,{#2}% + \ifpgfutil@in@% + \let\pgfutil@next\tikz@parse@regular% + \else% + \let\pgfutil@next\tikz@parse@node% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgfutil@next#1(#2)% +}% + +\def\tikz@parse@calculator#1($#2$){% + \tikzerror{You need to say \string\usetikzlibrary{calc} for coordinate calculation}% + #1{\pgfpointorigin}% +}% + +\def\tikz@parse@coordinatesystem#1(#2 cs:#3){% + \let\tikz@return@coordinate=\pgfpointorigin% + \pgfutil@ifundefined{tikz@parse@cs@#2} + {\tikzerror{Unknown coordinate system '#2'}} + {\csname tikz@parse@cs@#2\endcsname(#3)}% + \expandafter#1\expandafter{\tikz@return@coordinate}% +}% + + +\newif\iftikz@isdimension +\def\tikz@checkunit#1{% + \pgfmathparse{#1}% + \let\iftikz@isdimension=\ifpgfmathunitsdeclared% +}% + +\def\tikz@parse@polar#1(#2:#3){% + \pgfutil@ifundefined{tikz@polar@dir@#2} + {\tikz@@parse@polar#1({#2}:{#3})} + {\tikz@@parse@polar#1(\csname tikz@polar@dir@#2\endcsname:{#3})}% +}% +\def\tikz@@parse@polar#1(#2:#3){% + \pgfutil@in@{ and }{#3}% + \ifpgfutil@in@% + \edef\tikz@args{({#2}:#3)}% + \else% + \edef\tikz@args{({#2}:{#3} and {#3})}% + \fi% + \expandafter\tikz@@@parse@polar\expandafter#1\tikz@args% +}% +\def\tikz@@@parse@polar#1(#2:#3 and #4){% + \tikz@checkunit{#3}% + \iftikz@isdimension% + \tikz@checkunit{#4}% + \iftikz@isdimension% + \def\tikz@next{#1{\pgfpointpolar{#2}{#3 and #4}}}% + \else% + \tikzerror{You cannot mix dimension and dimensionless values for polar coordinates} + \def\tikz@next{#1{\pgfpointorigin}}% + \fi% + \else% + \tikz@checkunit{#4}% + \iftikz@isdimension% + \tikzerror{You cannot mix dimension and dimensionless values for polar coordinates} + \def\tikz@next{#1{\pgfpointorigin}}% + \else% + \def\tikz@next{#1{\pgfpointpolarxy{#2}{#3 and #4}}}% + \fi% + \fi% + \tikz@next% +}% +\def\tikz@polar@dir@up{90}% +\def\tikz@polar@dir@down{-90}% +\def\tikz@polar@dir@left{180}% +\def\tikz@polar@dir@right{0}% +\def\tikz@polar@dir@north{90}% +\def\tikz@polar@dir@south{-90}% +\def\tikz@polar@dir@east{0}% +\def\tikz@polar@dir@west{180}% +\expandafter\def\csname tikz@polar@dir@north east\endcsname{45}% +\expandafter\def\csname tikz@polar@dir@north west\endcsname{135}% +\expandafter\def\csname tikz@polar@dir@south east\endcsname{-45}% +\expandafter\def\csname tikz@polar@dir@south west\endcsname{-135}% + + +\def\tikz@parse@regular#1(#2,{% + \pgfutil@ifnextchar\bgroup{\tikz@@parse@regular#1{#2}}{\tikz@@@parse@regular#1{#2}}% +}% +\def\tikz@@parse@regular#1#2#3{% + \pgfutil@ifnextchar[{% + \tikz@@@parse@regular#1{#2}{#3}}% + {\tikz@@@parse@regular#1{#2}{{#3}}}}% + +\def\tikz@@@parse@regular#1#2#3){% + \pgfutil@in@,{#3}% + \ifpgfutil@in@% + \tikz@parse@splitxyz{#1}{#2}#3,% + \else% + \tikz@checkunit{#2}% + \iftikz@isdimension% + \tikz@checkunit{#3}% + \iftikz@isdimension% + \def\pgfutil@next{#1{\pgfpoint{#2}{#3}}}% + \else% + \def\pgfutil@next{#1{\pgfpointadd{\pgfpoint{#2}{0pt}}{\pgfpointxy{0}{#3}}}}% + \fi% + \else% + \tikz@checkunit{#3}% + \iftikz@isdimension% + \def\pgfutil@next{#1{\pgfpointadd{\pgfpoint{0pt}{#3}}{\pgfpointxy{#2}{0}}}}% + \else% + \def\pgfutil@next{#1{\pgfpointxy{#2}{#3}}}% + \fi% + \fi% + \fi% + \pgfutil@next% +}% + +\def\tikz@parse@splitxyz#1#2#3,#4,{% + \def\pgfutil@next{#1{\pgfpointxyz{#2}{#3}{#4}}}% +}% + +\def\tikz@coordinate@text{coordinate}% + +\def\tikz@parse@node#1(#2){% + \pgfutil@in@.{#2}% + \ifpgfutil@in@ + \tikz@calc@anchor#2\tikz@stop% + \else% + \tikz@calc@anchor#2.center\tikz@stop% + \ifcsname pgf@sh@ns@\tikz@pp@name{#2}\endcsname + \expandafter\ifx\csname pgf@sh@ns@\tikz@pp@name{#2}\endcsname\tikz@coordinate@text% + \else + \tikz@shapebordertrue% + \def\tikz@shapeborder@name{\tikz@pp@name{#2}}% + \fi% + \else\ifcsname pgf@sh@ns@#2\endcsname + \expandafter\ifx\csname pgf@sh@ns@#2\endcsname\tikz@coordinate@text% + \else + \tikz@shapebordertrue% + \def\tikz@shapeborder@name{#2}% + \fi% + \fi\fi + \fi% + \edef\tikz@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + \tikz@marshal% +}% + +\def\tikz@calc@anchor#1.#2\tikz@stop{% + \ifcsname pgf@sh@ns@\tikz@pp@name{#1}\endcsname% + \pgfpointanchor{\tikz@pp@name{#1}}{#2}% + \else + \pgfpointanchor{#1}{#2}% + \fi +}% + + +\def\tikz@parse@hv#1(#2){% + \pgfutil@in@{ -| }{#2}% + \ifpgfutil@in@% + \let\tikz@next=\tikz@parse@hvboth% + \else% + \pgfutil@in@{ -|}{#2}% + \ifpgfutil@in@% + \let\tikz@next=\tikz@parse@hvleft% + \else% + \pgfutil@in@{-| }{#2}% + \ifpgfutil@in@% + \let\tikz@next=\tikz@parse@hvright% + \else% + \let\tikz@next=\tikz@parse@hvdone% + \fi% + \fi% + \fi% + \tikz@next#1(#2)}% +\def\tikz@parse@hvboth#1(#2 -| #3){\tikz@parse@vhdone#1({#3}|-{#2})}% +\def\tikz@parse@hvleft#1(#2 -|#3){\tikz@parse@vhdone#1({#3}|-{#2})}% +\def\tikz@parse@hvright#1(#2-| #3){\tikz@parse@vhdone#1({#3}|-{#2})}% +\def\tikz@parse@hvdone#1(#2-|#3){\tikz@parse@vhdone#1({#3}|-{#2})}% + +\def\tikz@parse@vh#1(#2){% + \pgfutil@in@{ |- }{#2}% + \ifpgfutil@in@% + \let\tikz@next=\tikz@parse@vhboth% + \else% + \pgfutil@in@{ |-}{#2}% + \ifpgfutil@in@% + \let\tikz@next=\tikz@parse@vhleft% + \else% + \pgfutil@in@{|- }{#2}% + \ifpgfutil@in@% + \let\tikz@next=\tikz@parse@vhright% + \else% + \let\tikz@next=\tikz@parse@vhdone% + \fi% + \fi% + \fi% + \tikz@next#1(#2)}% +\def\tikz@parse@vhboth#1(#2 |- #3){\tikz@parse@vhdone#1({#2}|-{#3})}% +\def\tikz@parse@vhleft#1(#2 |-#3){\tikz@parse@vhdone#1({#2}|-{#3})}% +\def\tikz@parse@vhright#1(#2|- #3){\tikz@parse@vhdone#1({#2}|-{#3})}% +\def\tikz@parse@vhdone#1(#2|-#3){% + {% + \tikz@@@scan@@absolute\tikz@parse@vh@mid(#2)% + \tikz@@@scan@@absolute\tikz@parse@vh@end(#3)% + \xdef\tikz@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}}% + }% + \tikz@marshal% +}% +\def\tikz@parse@vh@mid#1{\pgf@process{#1}\pgf@xa=\pgf@x}% +\def\tikz@parse@vh@end#1{\pgf@process{#1}\pgf@ya=\pgf@y}% + +\def\tikz@parse@intersection#1(intersection{% + \pgfutil@ifnextchar o{% + \tikz@parse@main@intersection#1 1% + }{% + \tikz@parse@main@intersection#1% + }% +}% +\def\tikz@parse@main@intersection#1#2of #3 and #4){% + \tikzset{cs/solution={#2}}% + \pgfutil@in@{--}{#3}% + \ifpgfutil@in@% + \tikz@reparse@line{first}#3\pgf@stop% + \else% + \tikzset{cs/first node={#3}}% + \fi% + \pgfutil@in@{--}{#4}% + \ifpgfutil@in@% + \tikz@reparse@line{second}#4\pgf@stop% + \else% + \tikzset{cs/second node={#4}}% + \fi% + \tikz@parse@cs@intersection()% + \edef\pgf@marshal{\noexpand#1{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + \pgf@marshal% +}% +\def\tikz@reparse@line#1#2--#3\pgf@stop{% + \tikzset{cs/#1 line={(#2)--(#3)}}% +}% + + +\def\tikz@parse@intersection@a#1{\pgf@process{#1}\pgf@xa=\pgf@x\pgf@ya=\pgf@y}% +\def\tikz@parse@intersection@b#1{\pgf@process{#1}\pgf@xb=\pgf@x\pgf@yb=\pgf@y}% + +\def\tikz@scan@relative#1+{% + \pgfutil@ifnextchar+{\tikz@scan@plusplus#1}{\tikz@scan@oneplus#1}}% + +\def\tikz@scan@plusplus#1+{% + \def\tikz@doafter{#1}% + \tikz@scan@absolute\tikz@add% +}% +\def\tikz@add#1{% + \tikz@doafter{\pgfpointadd{#1}{\tikz@last@position@saved}}% +}% +\def\tikz@scan@oneplus#1{% + \def\tikz@doafter{#1}% + \tikz@updatecurrentfalse% + \tikz@scan@absolute\tikz@add% +}% + + + + +\let\tikz@enable@node@quotes\relax +\let\tikz@enable@edge@quotes\relax +\let\tikz@enable@pic@quotes\relax + + + + + +\def\usetikzlibrary{\pgfutil@ifnextchar[{\use@tikzlibrary}{\use@@tikzlibrary}}% +\def\use@tikzlibrary[#1]{\use@@tikzlibrary{#1}}% +\def\use@@tikzlibrary#1{% + \edef\pgf@list{#1}% + \pgfutil@for\pgf@temp:=\pgf@list\do{% + \expandafter\pgfkeys@spdef\expandafter\pgf@temp\expandafter{\pgf@temp}% + \ifx\pgf@temp\pgfutil@empty + \else + \expandafter\ifx\csname tikz@library@\pgf@temp @loaded\endcsname\relax% + \expandafter\global\expandafter\let\csname tikz@library@\pgf@temp @loaded\endcsname=\pgfutil@empty% + \expandafter\edef\csname tikz@library@#1@atcode\endcsname{\the\catcode`\@} + \expandafter\edef\csname tikz@library@#1@barcode\endcsname{\the\catcode`\|} + \expandafter\edef\csname tikz@library@#1@dollarcode\endcsname{\the\catcode`\$} + \catcode`\@=11 + \catcode`\|=12 + \catcode`\$=3 + \pgfutil@InputIfFileExists{tikzlibrary\pgf@temp.code.tex}{}{ + \pgfutil@IfFileExists{pgflibrary\pgf@temp.code.tex}{% + \expandafter\usepgflibrary\expandafter{\pgf@temp}% + }{% + \tikzerror{I did not find the tikz library + '\pgf@temp'. I looked for files named + tikzlibrary\pgf@temp.code.tex and + pgflibrary\pgf@temp.code.tex, but neither + could be found in the current texmf trees.} + }}% + \catcode`\@=\csname tikz@library@#1@atcode\endcsname + \catcode`\|=\csname tikz@library@#1@barcode\endcsname + \catcode`\$=\csname tikz@library@#1@dollarcode\endcsname + \fi% + \fi + }% +}% + + + +\usetikzlibrary{topaths}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/experimental/tikzlibrarygraphdrawing.evolving.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/experimental/tikzlibrarygraphdrawing.evolving.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8667798adb68ce0eab47ac78c7fb30478031d52d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/experimental/tikzlibrarygraphdrawing.evolving.code.tex @@ -0,0 +1,13 @@ + +\usepgflibrary{graphdrawing} + +\usegdlibrary{evolving} + +\newcount\mycount +\tikzgraphsset{ + nodes = {supernode/.expanded=\tikzgraphnodename}, + when/.code = {\pgfparsetime{#1}\mycount=\pgftimeresult pt\tikzgraphsset{name/.expanded=\the\mycount,snapshot/.expanded=\the\mycount}} +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.circular.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.circular.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..0571816262347709ef1652d3342218978f9092a2 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.circular.code.tex @@ -0,0 +1,7 @@ + +\ProvidesFileRCS{pgflibrarygraphdrawing.circular.code.tex} + + +\usegdlibrary{circular}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..286863c1a006a6cfe44acd403ff0030aa31bdb34 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.code.tex @@ -0,0 +1,631 @@ + +\ProvidesFileRCS{pgflibrarygraphdrawing.code.tex} + + + + +\ifx\directlua\relax% + \pgferror{You need to run LuaTeX to use the graph drawing library} + \expandafter\endinput +\fi +\ifx\directlua\undefined% + \pgferror{You need to run LuaTeX to use the graph drawing library} + \expandafter\endinput +\fi + + + + + +\def\pgfgdset{\pgfqkeys{/graph drawing}}% + + + +\def\pgfgd@callbackkey#1{% + \pgf@gd@setup@forwards{#1}% + \pgfutil@g@addto@macro\pgf@gd@forwards@list{\pgf@gd@setup@forwards{#1}}% +}% +\def\pgf@gd@setup@forwards#1{% + \let\pgf@temp\pgfutil@empty + \foreach \pgf@gd@path in \pgf@gd@forwarding@list {% + \ifx\pgf@gd@path\pgfutil@empty\else% + \expandafter\pgfutil@g@addto@macro% + \expandafter\pgf@temp\expandafter{% + \expandafter\pgfkeys\expandafter{\pgf@gd@path#1/.forward to=/graph drawing/#1}}% + \fi% + }% + \pgf@temp +}% + +\let\pgf@gd@forwards@list\pgfutil@empty + + + +\def\pgfgdappendtoforwardinglist#1{% + \let\pgf@gd@forwarding@list@orig\pgf@gd@forwarding@list + \def\pgf@gd@forwarding@list{#1}% + \pgf@gd@forwards@list% + \expandafter\def\expandafter\pgf@gd@forwarding@list\expandafter{\pgf@gd@forwarding@list@orig,#1}% +}% +\let\pgf@gd@forwarding@list\pgfutil@empty + + + + + + +\def\pgfgdcallbackdeclareparameter#1#2{% + \pgfkeysdef{/graph drawing/#1}{\pgf@gd@handle@parameter{#1}{#2}{##1}}% + \pgfgd@callbackkey{#1}% +}% +\def\pgf@gd@handle@parameter#1#2#3{% + \def\pgf@temp{#3}% + \ifx\pgf@temp\pgfkeysnovalue@text% + \let\pgfgdresult\pgfgd@niltext% + \else% + \pgfkeys{/graph drawing/conversions/#2={#3}}% + \fi% + \advance\pgf@gd@parameter@stack@height by1\relax% + \pgf@gd@parameter@stack@height\directlua{% + local new, main = pgf.gd.interface.InterfaceToDisplay.pushOption('\pgfutil@luaescapestring{#1}',\pgfgdresult,\the\pgf@gd@parameter@stack@height) + tex.print(new..'\pgfutil@luaescapestring{\relax}') + if main then + tex.print('\pgfutil@luaescapestring{\noexpand\pgfgdtriggerrequest}') + end}% +}% +\newcount\pgf@gd@parameter@stack@height + +\def\pgfgdtriggerrequest{\pgfgdset{@request scope and layout}}% + + + +\pgfgdset{ + conversions/string/.code=\def\pgfgdresult{'\pgfutil@luaescapestring{\detokenize{#1}}'}, + conversions/raw/.code=\def\pgfgdresult{#1}, + conversions/nil/.code=\let\pgfgdresult\pgfgd@niltext, + conversions/boolean/.code=\def\pgf@test{#1}\ifx\pgf@test\pgf@truetext\def\pgfgdresult{true}\else\ifx\pgf@test\pgfkeysnovalue@text\def\pgfgdresult{true}\else\def\pgfgdresult{false}\fi\fi, + conversions/number/.code=\pgfmathparse{#1}\let\pgfgdresult\pgfmathresult, + conversions/length/.code=\pgfmathparse{#1}\let\pgfgdresult\pgfmathresult, + conversions/time/.code=\pgfparsetime{#1}\let\pgfgdresult\pgftimeresult, + conversions/direction/.code=\pgf@lib@gd@grow@dir{#1}\let\pgfgdresult\pgfmathresult, + conversions/canvas coordinate/.code args={(#1pt,#2pt)}{\edef\pgfgdresult{pgf.gd.model.Coordinate.new(#1,#2)}}, + conversions/coordinate/.code args={(#1pt,#2pt)}{\edef\pgfgdresult{{#1,#2}}} +}% +\def\pgf@truetext{true}% +\def\pgfgd@niltext{nil}% + +\def\pgf@lib@gd@grow@dir#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgf@gd@lib@active@bar% + \def\pgfmathresult{-90} + \else% + \ifcsname pgf@orient@direction@#1\endcsname% + \expandafter\let\expandafter\pgfmathresult\csname pgf@orient@direction@#1\endcsname% + \else + \pgfmathparse{#1}% + \fi + \fi +}% + +\def\pgf@orient@direction@down{-90}% +\def\pgf@orient@direction@up{90}% +\def\pgf@orient@direction@left{180}% +\def\pgf@orient@direction@right{0}% + +\def\pgf@orient@direction@south{-90}% +\def\pgf@orient@direction@north{90}% +\def\pgf@orient@direction@west{180}% +\def\pgf@orient@direction@east{0}% + +\expandafter\def\csname pgf@orient@direction@north east\endcsname{45}% +\expandafter\def\csname pgf@orient@direction@north west\endcsname{135}% +\expandafter\def\csname pgf@orient@direction@south east\endcsname{-45}% +\expandafter\def\csname pgf@orient@direction@south west\endcsname{-135}% + +\expandafter\def\csname pgf@orient@direction@-\endcsname{0}% +\expandafter\def\csname pgf@orient@direction@|\endcsname{-90}% + +{% + \catcode`\|=13 + \gdef\pgf@gd@lib@active@bar{|}% +}% + + + + + + +\def\pgfgdcallbackrendercollectionkindstart#1#2{% + \ifnum#2<0\relax + \setbox\pgf@gd@prekind@box=\hbox\bgroup% + \unhbox\pgf@gd@prekind@box% + \else% + \setbox\pgf@gd@postkind@box=\hbox\bgroup% + \unhbox\pgf@gd@postkind@box% + \fi% + \pgfgdset{/graph drawing/#1/begin rendering/.try}% +}% + + +\def\pgfgdcallbackrendercollectionkindstop#1#2{% + \pgfgdset{/graph drawing/#1/end rendering/.try}% + \egroup % +}% + + + + +\def\pgfgdcallbackrendercollection#1#2{ + \pgfgdset{/graph drawing/#1/render/.try={#2}} +}% + + + + + + + + + +\def\pgfgdevent#1#2{% + \directlua{pgf.gd.interface.InterfaceToDisplay.createEvent('\pgfutil@luaescapestring{#1}', '\pgfutil@luaescapestring{#2}')}% +}% + + + +\def\pgfgdbegineventgroup#1{% + \pgfgdevent{begin}{#1}% +}% + + +\def\pgfgdendeventgroup{% + \pgfgdevent{end}{}% +}% + + + +\def\pgfgdeventgroup#1{% + \pgfgdbegineventgroup{#1}% + \aftergroup\pgfgdendeventgroup% +}% + + + + + + + + +\def\pgf@gd@positionnode@callback{% + {% + \pgfmathsetmacro{\pgf@gd@node@minx}{\pgfpositionnodelaterminx}% + \pgfmathsetmacro{\pgf@gd@node@miny}{\pgfpositionnodelaterminy}% + \pgfmathsetmacro{\pgf@gd@node@maxx}{\pgfpositionnodelatermaxx}% + \pgfmathsetmacro{\pgf@gd@node@maxy}{\pgfpositionnodelatermaxy}% + \directlua{pgf.temp = require 'pgf.gd.model.Path'.new ()}% + \let\pgfsyssoftpath@movetotoken\pgf@gd@movetotoken% + \let\pgfsyssoftpath@linetotoken\pgf@gd@linetotoken% + \let\pgfsyssoftpath@rectcornertoken\pgf@gd@rectcornertoken% + \let\pgfsyssoftpath@curvetosupportatoken\pgf@gd@curvetosupportatoken% + \let\pgfsyssoftpath@closepathtoken\pgf@gd@closepathtoken% + \pgfpositionnodelaterpath% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + {% + \pgf@process{\pgfpointanchor{\pgfpositionnodelatername}{center}} + \pgfsettransform{\csname pgf@sh@nt@\pgfpositionnodelatername\endcsname}% + \pgf@pos@transform{\pgf@x}{\pgf@y}% + \global\pgf@x=\pgf@x% + \global\pgf@y=\pgf@y% + }% + \directlua{ + pgf.gd.interface.InterfaceToDisplay.createVertex( + string.sub('\pgfutil@luaescapestring{\pgfpositionnodelatername}',30), % + '\pgfutil@luaescapestring{\csname pgf@sh@ns@\pgfpositionnodelatername\endcsname}', + pgf.temp:pad((\pgf@sys@tonumber\pgf@xa+\pgf@sys@tonumber\pgf@ya)/2), % + \the\pgf@gd@parameter@stack@height, % + {% + x_min = \pgf@gd@node@minx, + y_min = \pgf@gd@node@miny, + x_max = \pgf@gd@node@maxx, + y_max = \pgf@gd@node@maxy, + tex_box_number = \pgfpositionnodelaterbox + }, + {% + center = require 'pgf.gd.model.Coordinate'.new(\pgf@sys@tonumber\pgf@x,\pgf@sys@tonumber\pgf@y) + } + ) + pgf.temp = nil + } + }% +}% + + +\def\pgf@gd@movetotoken#1#2{\directlua{pgf.temp:appendMoveto(\Pgf@geT#1,\Pgf@geT#2)}}% +\def\pgf@gd@linetotoken#1#2{\directlua{pgf.temp:appendLineto(\Pgf@geT#1,\Pgf@geT#2)}}% +\def\pgf@gd@rectcornertoken#1#2#3#4#5{% + \directlua{% + local x,y,dx,dy=\Pgf@geT#1,\Pgf@geT#2,\Pgf@geT#4,\Pgf@geT#5 + pgf.temp:appendMoveto(x,y) + pgf.temp:appendLineto(x,y+dy) + pgf.temp:appendLineto(x+dx,y+dy) + pgf.temp:appendLineto(x+dx,y) + pgf.temp:appendClosepath()% + }% +}% +\def\pgf@gd@curvetosupportatoken#1#2#3#4#5#6#7#8{\directlua{pgf.temp:appendCurveto(\Pgf@geT#1,\Pgf@geT#2,\Pgf@geT#4,\Pgf@geT#5,\Pgf@geT#7,\Pgf@geT#8)}}% +\def\pgf@gd@closepathtoken#1#2{\directlua{pgf.temp:appendClosepath()}}% + + + +\def\pgfgdsetlatenodeoption#1{% + \directlua{ + pgf.gd.interface.InterfaceToDisplay.addToVertexOptions('\pgfutil@luaescapestring{#1}',\the\pgf@gd@parameter@stack@height) + } +}% + + + + +\def\pgfgdcallbackrendernode#1#2#3#4#5#6#7#8#9{% + {% + \def\pgfpositionnodelatername{#1} + \def\pgfpositionnodelaterminx{#2} + \def\pgfpositionnodelatermaxx{#3} + \def\pgfpositionnodelaterminy{#4} + \def\pgfpositionnodelatermaxy{#5} + \directlua{pgf.gd.interface.InterfaceCore.binding:retrieveBox(#8,\pgfpositionnodelaterbox)} + \def\pgf@temp{#9}% + \ifx\pgf@temp\pgfutil@empty% + \pgfpositionnodenow{\pgfqpoint{#6}{#7}}% + \else% + \pgfset{every graphdrawing animation/.try}% + \pgfset{every graphdrawing node animation/.try}% + #9% + \pgfuseid{pgf@gd}% + \pgfidscope% + \pgfpositionnodenow{\pgfqpoint{#6}{#7}}% + \endpgfidscope% + \fi% + }% +}% + +\ifx\pgfanimateattribute\pgfutil@undefined + \def\pgfanimateattribute#1#2{\tikzerror{You need to say \string\usetikzlibrary{animations} for animated graphs}}% +\fi + + +\def\pgfgdedge#1#2#3#4#5{% + \begingroup% + \setbox0=\hbox{{% + \pgfinterruptpath% + \pgfgdprepareedge% + \pgfkeys{#4}% + \toks0={#4}% + \toks1={#5}% + \directlua{ + pgf.gd.interface.InterfaceToDisplay.createEdge( + '\pgfutil@luaescapestring{#1}','\pgfutil@luaescapestring{#2}','\pgfutil@luaescapestring{#3}', + \the\pgf@gd@parameter@stack@height, + { pgf_options = '\pgfutil@luaescapestring{\the\toks0}', + pgf_edge_nodes = '\pgfutil@luaescapestring{\the\toks1}', + }) + }% + \endpgfinterruptpath% + }}% + \endgroup% +}% + +\let\pgfgdprepareedge=\pgfutil@empty +\def\pgfgdaddprepareedgehook#1{\expandafter\def\expandafter\pgfgdprepareedge\expandafter{\pgfgdprepareedge#1}}% + + +\newif\ifpgf@gd@nodes@behind@edges + + + + +\def\pgfgdsetedgecallback#1{\let\pgfgdcallbackedge=#1}% + +\def\pgfgddefaultedgecallback#1#2#3#4#5#6#7#8{% + {% + \def\pgf@temp{#8}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgfset{every graphdrawing animation/.try}% + \pgfset{every graphdrawing edge animation/.try}% + #8% + \pgfuseid{pgf@gd}% + \pgfidscope% + \fi% + \pgfscope + \pgfpathmoveto{ + \pgfutil@in@.{#1}% + \ifpgfutil@in@ + \pgf@gd@unravel#1\relax% + \else + \pgfpointshapeborder{#1}{\pgfpointanchor{#2}{center}} + \fi + } + \pgfpathlineto{ + \pgfutil@in@.{#2}% + \ifpgfutil@in@ + \pgf@gd@unravel#2\relax% + \else + \pgfpointshapeborder{#2}{\pgfpointanchor{#1}{center}} + \fi + } + \pgfusepath{stroke} + \endpgfscope + \ifx\pgf@temp\pgfutil@empty% + \else% + \endpgfidscope% + \fi% + } +}% + +\pgfgdsetedgecallback{\pgfgddefaultedgecallback}% + +\def\pgf@gd@unravel#1.#2\relax{% + \pgfpointanchor{#1}{#2}% +}% + + + + + +\def\pgfgdcallbackbeginshipout{% + \pgfscope% + \catcode`\@=11\relax% + \setbox\pgf@gd@prekind@box=\box\pgfutil@voidb@x% + \setbox\pgf@gd@postkind@box=\box\pgfutil@voidb@x% +}% +\def\pgfgdcallbackendshipout{% + \box\pgf@gd@prekind@box% + \ifpgf@gd@nodes@behind@edges% + \box\pgf@gd@node@box% + \box\pgf@gd@edge@box% + \else% + \box\pgf@gd@edge@box% + \box\pgf@gd@node@box% + \fi% + \box\pgf@gd@postkind@box% + \endpgfscope +}% + +\newbox\pgf@gd@node@box +\newbox\pgf@gd@edge@box +\newbox\pgf@gd@prekind@box +\newbox\pgf@gd@postkind@box + +\def\pgfgdcallbackbeginnodeshipout{% + \setbox\pgf@gd@node@box=\hbox\bgroup% +}% +\def\pgfgdcallbackendnodeshipout{% + \egroup% +}% + +\def\pgfgdcallbackbeginedgeshipout{% + \setbox\pgf@gd@edge@box=\hbox\bgroup% +}% + +\def\pgfgdcallbackendedgeshipout{% + \egroup +}% + + + + + +\def\pgfgdcallbackcreatevertex#1#2#3#4{% + { + \pgfkeys{#3} + \pgfnode{#2}{\pgfkeysvalueof{/graph drawing/generated + node/anchor}}{#4}{#1}{\pgfkeysvalueof{/graph drawing/generated + node/use path}} + } +}% + +\pgfkeys{ + /graph drawing/generated node/anchor/.initial=center, + /graph drawing/generated node/use path/.initial=\pgfusepath{} +}% + + + + +\def\pgfgdbeginlayout{ + \begingroup + \pgfgdlayoutscopeactivetrue + \advance\pgf@gd@parameter@stack@height by1\relax% + \directlua{pgf.gd.interface.InterfaceToDisplay.pushLayout(\the\pgf@gd@parameter@stack@height)} +}% + +\def\pgfgdendlayout{ + \endgroup% +}% + + + + + +\def\pgfgdsubgraphnode#1#2#3{% + \advance\pgf@gd@parameter@stack@height by1\relax% + {% + \toks0={#2}% + \toks1={#3}% + \directlua{pgf.gd.interface.InterfaceToDisplay.pushSubgraphVertex% + ('\pgfutil@luaescapestring{#1}',\the\pgf@gd@parameter@stack@height, + { + shape = 'rectangle', % + pgf_options = '\pgfutil@luaescapestring{\the\toks0}', + text = '\pgfutil@luaescapestring{\the\toks1}', + }) + }% + } +}% + +\def\pgfgdsubgraphnodecontents#1{% + \hbox to \pgfkeysvalueof{/graph drawing/subgraph bounding box width}{% + \vrule width0pt height\pgfkeysvalueof{/graph drawing/subgraph bounding box height}\hfil}% +}% + +\pgfgdset{ + subgraph point cloud/.initial=, + subgraph bounding box width/.initial=, + subgraph bounding box height/.initial=, +}% + + + +\pgfgdset{@request scope and layout/.code=\pgfgd@requestcallback{\pgfgdbeginrequest}{\pgfgdendrequest}}% + +\def\pgfgd@requestcallback#1#2{% + #1\def\pgf@gd@after@request{#2\egroup}\bgroup\aftergroup\pgf@gd@after@request% +}% + +\def\pgfgdbeginrequest{% + \ifpgfgdlayoutscopeactive% + \else% + \expandafter\pgfgdbeginscope% + \fi% + \pgfgdbeginlayout% +}% +\def\pgfgdendrequest{% + \pgfgdendlayout% + \ifpgfgdlayoutscopeactive% + \else% + \expandafter\pgfgdendscope% + \fi% +}% +\newif\ifpgfgdlayoutscopeactive + + + +\def\pgfgdsetrequestcallback#1{\let\pgfgd@requestcallback#1}% + + + + + +\newif\ifpgfgdgraphdrawingscopeactive + + + +\def\pgfgdbeginscope{% + \begingroup % + \directlua{ + pgf.gd.interface.InterfaceToDisplay.beginGraphDrawingScope(\the\pgf@gd@parameter@stack@height) + }% + \begingroup % + \pgfgdgraphdrawingscopeactivetrue + \pgfpositionnodelater{\pgf@gd@positionnode@callback} + \pgfgd@latecallback% + \pgftransformreset +}% + + + +\newif\ifpgfgdresumecoroutine + + + +\def\pgfgdendscope{% + \pgfgdresumecoroutinefalse% + \directlua{ + pgf.gd.interface.InterfaceToDisplay.runGraphDrawingAlgorithm() + }% + \pgfutil@loop% + \ifpgfgdresumecoroutine% + \pgfgdresumecoroutinefalse% + \directlua{ + pgf.gd.interface.InterfaceToDisplay.resumeGraphDrawingCoroutine() + }% + \pgfutil@repeat% + \endgroup% + \directlua{pgf.gd.interface.InterfaceToDisplay.renderGraph()}% + \directlua{pgf.gd.interface.InterfaceToDisplay.endGraphDrawingScope()}% + \endgroup% +}% + + + + + + + +\def\pgfgdaddspecificationhook#1{ + \expandafter\def\expandafter\pgfgd@latecallback\expandafter{\pgfgd@latecallback#1} +}% +\let\pgfgd@latecallback\pgfutil@empty + + + + + + + + + + +\def\usegdlibrary{\pgfutil@ifnextchar[{\use@gdlibrary}{\use@@gdlibrary}}% +\def\use@gdlibrary[#1]{\use@@gdlibrary{#1}}% +\def\use@@gdlibrary#1{% + \edef\pgf@list{#1}% + \pgfutil@for\pgf@temp:=\pgf@list\do{% + \expandafter\pgfkeys@spdef\expandafter\pgf@temp\expandafter{\pgf@temp}% + \ifx\pgf@temp\pgfutil@empty + \else + \directlua{if not pgf_lookup_and_require('\pgf@temp') then + tex.print('\pgfutil@luaescapestring{\noexpand\pgferror{Graph drawing library '\pgf@temp' not found}}') + end} + \fi + } +}% + +{% +\catcode`\%=11 +\directlua{ + function pgf_lookup_and_require(name) + local sep = package.config:sub(1,1) + local function lookup(name) + local sub = name:gsub('%.',sep) + local find_file = context and + resolvers.findfile or + kpse.find_file + if find_file(sub, 'lua') then + require(name) + elseif find_file(sub, 'clua') then + collectgarbage('stop') + require(name) + collectgarbage('restart') + else + return false + end + return true + end + return + lookup('pgf.gd.' .. name .. '.library') or + lookup('pgf.gd.' .. name) or + lookup(name .. '.library') or + lookup(name) + end +} +}% + + +\directlua{ + require 'pgf.gd.interface.InterfaceToDisplay' + pgf.gd.interface.InterfaceToDisplay.bind(require 'pgf.gd.bindings.BindingToPGF') +}% + + + + +\pgfkeys{/graph drawing/nodes behind edges/.append code=\csname pgf@gd@nodes@behind@edges#1\endcsname}% +\pgfkeys{/graph drawing/nodes behind edges/.default=true}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.examples.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.examples.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..615036a7c0194c13edb07e93e338543ca9bec44e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.examples.code.tex @@ -0,0 +1,9 @@ + +\ProvidesFileRCS{pgflibrarygraphdrawing.examples.code.tex} + +\usepgflibrary{graphdrawing}% + +\usegdlibrary{examples}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.force.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.force.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ec81214b2872df35e8450cad3e13ce1b9561eb82 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.force.code.tex @@ -0,0 +1,82 @@ + +\ProvidesFileRCS{pgflibrarygraphdrawing.force.code.tex} + + + +\usepgflibrary{graphdrawing}% + +\usegdlibrary{force}% + +\endinput + + + + +\pgfgdset{ + force based/.cd, + iterations/.graph parameter=number, + iterations/.parameter initial=500, + cooling factor/.graph parameter=number, + cooling factor/.parameter initial=0.95, + initial step dimension/.graph parameter=number, + initial step dimension/.parameter initial=0, + convergence tolerance/.graph parameter=number, + convergence tolerance/.parameter initial=0.01, + spring constant/.graph parameter=number, + spring constant/.parameter initial=0.01, + approximate electric forces/.graph parameter=boolean, + approximate electric forces/.parameter initial=false, + approximate electric forces/.default=true, + electric force order/.graph parameter=number, + electric force order/.parameter initial=1, + coarsen/.graph parameter=boolean, + coarsen/.parameter initial=true, + coarsen/.default=true, + coarsening/.code=\pgfkeys{ + /graph drawing/force based/coarsening/.cd, + #1 + }, + coarsening/downsize ratio/.graph parameter=number, + coarsening/downsize ratio/.parameter initial=0.25, + coarsening/minimum graph size/.graph parameter=number, + coarsening/minimum graph size/.parameter initial=2, + coarsening/collapse independent edges/.graph parameter=boolean, + coarsening/collapse independent edges/.parameter initial=true, + coarsening/collapse independent edges/.default=true, + coarsening/connect independent nodes/.graph parameter=boolean, + coarsening/connect independent nodes/.parameter initial=false, + coarsening/connect independent nodes/.default=true, +}% + +\pgfgddeclareforwardedkeys{/graph drawing}{ + electric charge/.node parameter=number, + electric charge/.parameter initial=1, +} + + +\pgfgddeclarealgorithmkey + {spring layout} + {force based} + { + algorithm=pgf.gd.force.SpringHu2006 + } + + +\pgfgddeclarealgorithmkey + {spring electrical layout} + {force based} + { + algorithm=pgf.gd.force.SpringElectricalHu2006, + force based/spring constant=0.2, + } + + + +\pgfgddeclarealgorithmkey + {spring electrical layout'} + {force based} + { + algorithm=pgf.gd.force.SpringElectricalWalshaw2000, + force based/spring constant=0.01, + force based/convergence tolerance=0.001, + } diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.layered.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.layered.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..274b6e46f1ef5e7136e9ae2c6fe7106af1fc258d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.layered.code.tex @@ -0,0 +1,9 @@ + +\ProvidesFileRCS{pgflibrarygraphdrawing.layered.code.tex} + +\usepgflibrary{graphdrawing}% + +\usegdlibrary{layered}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.trees.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.trees.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..60c72ae9152810423c7a9cc41b5ebd52fa2c4c38 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/pgflibrarygraphdrawing.trees.code.tex @@ -0,0 +1,10 @@ + +\ProvidesFileRCS{pgflibrarygraphdrawing.trees.code.tex} + + +\usepgflibrary{graphdrawing}% +\usepgflibrary{graphdrawing.layered}% + +\usegdlibrary{trees}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/tikzlibrarygraphdrawing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/tikzlibrarygraphdrawing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..b48ccc9798268d87d3d065ffe040561c9dfe1d5f --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/graphdrawing/tex/tikzlibrarygraphdrawing.code.tex @@ -0,0 +1,224 @@ + +\ProvidesFileRCS{tikzlibrarygraphdrawing.code.tex} + +\usepgflibrary{graphdrawing}% + +\def\tikz@lib@ensure@gd@loaded{}% + + +\tikzset{level distance=1cm, sibling distance=1cm}% + + +\pgfkeysgetvalue{/graph drawing/node distance/.@cmd}\tikz@lib@gd@node@dist@path +\pgfkeyslet{/graph drawing/node distance/orig/.@cmd}\tikz@lib@gd@node@dist@path + +\pgfkeysdef{/graph drawing/node distance}{ + \pgfutil@in@{ and }{#1}% + \ifpgfutil@in@% + \tikz@gd@convert@and#1\pgf@stop% + \else% + \tikz@gd@convert@and#1 and #1\pgf@stop% + \fi% +}% +\def\tikz@gd@convert@and#1 and #2\pgf@stop{\pgfkeys{/graph drawing/node distance/orig={#1}}}% + + + + + +\def\tikz@gd@request@callback#1#2{% + \tikzset{ + execute at begin scope={ + \tikzset{ + --/.style={arrows=-}, + -!-/.style={draw=none,fill=none}, + } + \pgfgdsetedgecallback{\pgfgdtikzedgecallback}% + \pgfgdaddspecificationhook{\tikz@lib@gd@spec@hook}% + #1 + \let\tikzgdeventcallback\pgfgdevent% + \let\tikzgdeventgroupcallback\pgfgdeventgroup% + \let\tikzgdlatenodeoptionacallback\pgfgdsetlatenodeoption% + }, + execute at end scope={% + #2% + } + }% +}% + +\pgfgdsetrequestcallback\tikz@gd@request@callback + + + +\pgfgdappendtoforwardinglist{/tikz/,/tikz/graphs/}% + +\def\tikz@lib@gd@spec@hook{% + \tikzset{ + edge macro=\tikz@gd@plain@edge@macro, + /tikz/at/.style={/graph drawing/desired at={##1}}, + /tikz/growth function=\relax, + /tikz/edge from parent macro=\tikz@gd@edge@from@parent@macro, + /tikz/graphs/new ->/.code n args={4}{\tikz@lib@gd@edge{##1}{##2}{->}{/tikz,##3}{##4}}, + /tikz/graphs/new <-/.code n args={4}{\tikz@lib@gd@edge{##1}{##2}{<-}{/tikz,##3}{##4}}, + /tikz/graphs/new --/.code n args={4}{\tikz@lib@gd@edge{##1}{##2}{--}{/tikz,##3}{##4}}, + /tikz/graphs/new <->/.code n args={4}{\tikz@lib@gd@edge{##1}{##2}{<->}{/tikz,##3}{##4}}, + /tikz/graphs/new -!-/.code n args={4}{\tikz@lib@gd@edge{##1}{##2}{-!-}{/tikz,##3}{##4}}, + /tikz/graphs/placement/compute position/.code=,% + } +}% + +\def\tikz@lib@gd@edge#1#2{% + \pgfgdedge{\tikz@pp@name{#1}}{\tikz@pp@name{#2}}% +} + +\pgfgdaddprepareedgehook{ + \tikz@enable@edge@quotes% + \let\tikz@transform=\pgfutil@empty% + \let\tikz@options=\pgfutil@empty% + \let\tikz@tonodes=\pgfutil@empty% +}% + + +\tikzset{ + parent anchor/.forward to=/graph drawing/tail anchor, + child anchor/.forward to=/graph drawing/head anchor +}% + +\def\pgfgdtikzedgecallback#1#2#3#4#5#6#7#8{% + \def\pgf@temp{#8}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgfscope% + \pgfset{every graphdrawing animation/.try}% + \pgfset{every graphdrawing edge animation/.try}% + #8% + \pgfuseid{pgf@gd}% + \pgfidscope% + \fi% + \begingroup + \draw (#1) + edge [to path={#7 \tikztonodes},#3,#4,/graph drawing/.cd,#6,/tikz/.cd] + #5 + (#2); + \endgroup + \ifx\pgf@temp\pgfutil@empty% + \else% + \endpgfidscope% + \endpgfscope% + \fi% +}% + +\def\tikz@gd@edge@from@parent@macro#1#2{ + [/utils/exec=\tikz@lib@gd@edge{\tikzparentnode}{\tikzchildnode}{--}{/tikz,#1}{#2}] +}% + +\def\tikz@gd@plain@edge@macro#1#2{ + \tikz@lib@gd@edge{\tikztostart}{\tikztotarget}{--}{/tikz,#1}{#2} +}% + + + + +\pgfgdset{ + conversions/canvas coordinate/.code={% + \tikz@scan@one@point\pgf@process#1% + \pgfmathsetmacro{\tikz@gd@temp@x}{\pgf@x} + \pgfmathsetmacro{\tikz@gd@temp@y}{\pgf@y} + \edef\pgfgdresult{pgf.gd.model.Coordinate.new(\tikz@gd@temp@x,\tikz@gd@temp@y)} + }, + conversions/coordinate/.code={% + \tikz@scan@one@point\pgf@process#1% + \pgfmathsetmacro{\tikz@gd@temp@x}{\pgf@x} + \pgfmathsetmacro{\tikz@gd@temp@y}{\pgf@y} + \edef\pgfgdresult{pgf.gd.model.Coordinate.new(\tikz@gd@temp@x,\tikz@gd@temp@y)} + } +}% + + + + +\def\pgfgdcallbackcreatevertex#1#2#3#4{% + \node[every generated node/.try,name={#1},shape={#2},/graph drawing/.cd,#3]{#4};% +}% + + + + +\tikzset{ + subgraph text top/.code=\tikz@lg@simple@contents@top{#1},% + subgraph text top/.default=text ragged, + subgraph text bottom/.code=\tikz@lg@simple@contents@bottom{#1},% + subgraph text bottom/.default=text ragged, + subgraph text sep/.initial=.1em, + subgraph text none/.code={ + \def\pgfgdsubgraphnodecontents##1{% + \pgf@y=\pgfkeysvalueof{/graph drawing/subgraph bounding box height}\relax% + \hbox to \pgfkeysvalueof{/graph drawing/subgraph bounding box width}{% + \vrule width0pt height.5\pgf@y depth.5\pgf@y\hfil}% + }% + }, +}% + +\def\tikz@lg@simple@contents@top#1{% + \def\pgfgdsubgraphnodecontents##1{% + \vbox{% + \def\pgf@temp{##1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \ifx\pgf@temp\pgfutil@sptoken% + \else% + \hbox to \pgfkeysvalueof{/graph drawing/subgraph bounding box width}{% + \hsize=\pgfkeysvalueof{/graph drawing/subgraph bounding box width}\relax% + \vbox{\noindent\strut\tikzset{#1}\tikz@text@action\pgf@temp}% + }% + \fi% + \fi% + \pgfmathparse{\pgfkeysvalueof{/tikz/subgraph text sep}}% + \kern\pgfmathresult pt\relax% + \pgf@y=\pgfkeysvalueof{/graph drawing/subgraph bounding box height}\relax% + \hbox to \pgfkeysvalueof{/graph drawing/subgraph bounding box width}{% + \vrule width0pt height.5\pgf@y depth.5\pgf@y\hfil}% + }% + }% +}% + +\def\tikz@lg@simple@contents@bottom#1{% + \def\pgfgdsubgraphnodecontents##1{% + {% + \pgf@y=\pgfkeysvalueof{/graph drawing/subgraph bounding box height}\relax% + \setbox0=\vbox{% + \hbox to \pgfkeysvalueof{/graph drawing/subgraph bounding box width}{\vrule width0pt height\pgf@y\hfil}% + \pgfmathparse{\pgfkeysvalueof{/tikz/subgraph text sep}}% + \kern\pgfmathresult pt\relax% + \def\pgf@temp{##1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \ifx\pgf@temp\pgfutil@sptoken% + \else% + \hbox to \pgfkeysvalueof{/graph drawing/subgraph bounding box width}{% + \hsize=\pgfkeysvalueof{/graph drawing/subgraph bounding box width}\relax% + \vbox{\noindent\strut\tikzset{#1}\tikz@text@action\pgf@temp}% + }% + \fi% + \fi% + }% + \pgf@ya=\ht0\relax% + \advance\pgf@ya by-.5\pgf@y\relax% + \ht0=.5\pgf@y\relax% + \dp0=\pgf@ya\relax% + \box0\relax% + }% + }% +}% + +\tikzset{subgraph text top}% + +\tikzset{ + subgraph nodes/.style={/tikz/every subgraph node/.style={#1}}, + graphs/subgraph nodes/.style={/tikz/every subgraph node/.style={#1}}, + graphs/@graph drawing setup/.style={/graph drawing/anchor at={(\tikz@lastx,\tikz@lasty)}} +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.barcharts.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.barcharts.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a0f1ed2cff8093b2b5c1295cadf715b2c79a6b1c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.barcharts.code.tex @@ -0,0 +1,118 @@ + +\ProvidesFileRCS{pgflibrarydatavisualization.barcharts.code.tex} + +\usepgfmodule{datavisualization}% + + + + +\pgfooclass{candle stick visualizer} +{% + \attribute attribute;% + \attribute offset;% + \attribute use path rise=\pgfsetfillcolor{white}\pgfusepath{fill,stroke};% + \attribute use path fall=\pgfsetfillcolor{black}\pgfusepath{fill,stroke};% + \attribute use path wick=\pgfusepath{stroke};% + + \method candle stick visualizer(#1) { + \pgfooeset{attribute}{#1} + \pgfoothis.set stick width(4pt) + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,visualize,visualize datapoint signal) + }% + + \method set stick width(#1) { + \pgfmathparse{#1} + \pgfmathdivide{\pgfmathresult}{2} + \let\pgf@dv@lib@w=\pgfmathresult + \pgfkeyssetvalue{/data point/\pgfoovalueof{attribute}}{1} + \pgfcanvaspositionofdatapoint% + \pgfsettocanvasposition\pgf@dv@lib@lower% + \pgfkeyssetvalue{/data point/\pgfoovalueof{attribute}}{10} + \pgfcanvaspositionofdatapoint% + \pgfsettocanvasposition\pgf@dv@lib@upper% + \pgf@process{\pgfpointnormalised{\pgfpointdiff{\pgf@dv@lib@upper}{\pgf@dv@lib@lower}}}% + \pgf@xa=\pgf@x% + \pgf@x=-\pgf@dv@lib@w\pgf@y% + \pgf@y=\pgf@dv@lib@w\pgf@xa% + \edef\pgf@dv@lib@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfoolet{offset}\pgf@dv@lib@temp + }% + + \method set use path rise(#1) { + \pgfooset{use path rise}{#1} + }% + + \method set use path fall(#1) { + \pgfooset{use path fall}{#1} + }% + + \method visualize() { + { + \pgfooget{attribute}\pgf@lib@attribute% + \pgfkeysgetvalue{/data point/\pgf@lib@attribute/low}\pgf@lib@low + \pgfkeysgetvalue{/data point/\pgf@lib@attribute/high}\pgf@lib@high + \pgfkeysgetvalue{/data point/\pgf@lib@attribute/entry}\pgf@lib@entry + \pgfkeysgetvalue{/data point/\pgf@lib@attribute/exit}\pgf@lib@exit + \ifx\pgf@lib@low\pgfutil@empty\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@low\relax\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@high\pgfutil@empty\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@high\relax\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@entry\pgfutil@empty\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@entry\relax\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@exit\pgfutil@empty\pgf@dv@lib@cs@skiptrue\fi + \ifx\pgf@lib@exit\relax\pgf@dv@lib@cs@skiptrue\fi + \ifpgf@dv@lib@cs@skip% + \else% + \begin{pgfscope} + \pgfkeyssetvalue{/data point/\pgf@lib@attribute}\pgf@lib@low + \pgfcanvaspositionofdatapoint% + \pgfsettocanvasposition\pgf@dv@lib@lowpoint% + \pgfkeyssetvalue{/data point/\pgf@lib@attribute}\pgf@lib@high + \pgfcanvaspositionofdatapoint% + \pgfsettocanvasposition\pgf@dv@lib@highpoint% + \pgfkeyssetvalue{/data point/\pgf@lib@attribute}\pgf@lib@entry + \pgfcanvaspositionofdatapoint% + \pgfsettocanvasposition\pgf@dv@lib@entrypoint% + \pgfkeyssetvalue{/data point/\pgf@lib@attribute}\pgf@lib@exit + \pgfcanvaspositionofdatapoint% + \pgfsettocanvasposition\pgf@dv@lib@exitpoint% + \ifdim\pgf@lib@entry pt<\pgf@lib@exit pt\relax% + \pgf@dv@lib@risetrue% + \fi% + \ifpgf@dv@lib@rise + \let\pgf@dv@lib@a=\pgf@dv@lib@entrypoint + \let\pgf@dv@lib@b=\pgf@dv@lib@exitpoint + \else + \let\pgf@dv@lib@a=\pgf@dv@lib@exitpoint + \let\pgf@dv@lib@b=\pgf@dv@lib@entrypoint + \fi + \pgfpathmoveto{\pgf@dv@lib@lowpoint} + \pgfpathlineto{\pgf@dv@lib@a} + \pgfpathmoveto{\pgf@dv@lib@highpoint} + \pgfpathlineto{\pgf@dv@lib@b} + \pgfoovalueof{use path wick} + \pgfpathmoveto{\pgfpointadd{\pgf@dv@lib@a}{\pgfoovalueof{offset}}} + \pgfpathlineto{\pgfpointadd{\pgf@dv@lib@b}{\pgfoovalueof{offset}}} + \pgfpathlineto{\pgfpointadd{\pgf@dv@lib@b}{\pgfpointscale{-1}{\pgfoovalueof{offset}}}} + \pgfpathlineto{\pgfpointadd{\pgf@dv@lib@a}{\pgfpointscale{-1}{\pgfoovalueof{offset}}}} + \pgfpathclose + \ifpgf@dv@lib@rise + \pgfoovalueof{use path rise} + \else + \pgfoovalueof{use path fall} + \fi + \end{pgfscope}% + \fi + } + }% + + \newif\ifpgf@dv@lib@cs@skip + \newif\ifpgf@dv@lib@rise +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.formats.functions.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.formats.functions.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8e37353c8b2709736a79dc89b639a874631c8136 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.formats.functions.code.tex @@ -0,0 +1,130 @@ + +\ProvidesFileRCS{pgflibrarydatavisualization.formats.functions.code.tex} + +\usepgfmodule{datavisualization}% + + + + + +\pgfdeclaredataformat{function} +{ % +} +{ % + \let\value=\relax% + \pgfkeysgetvalue{/pgf/data/vars}\pgf@lib@dv@collector +} +{% + #1% +} +{ % + \edef\pgf@lib@dv@collector{\pgf@lib@dv@collector\space #1}% +} +{% +} +{% + \edef\pgf@lib@dv@collector{\pgf@lib@dv@collector\space \pgfkeysvalueof{/pgf/data/funcs}}% + \let\pgf@lib@dv@parsed\pgfutil@empty% + \expandafter\pgf@lib@dv@func@parse \pgf@lib@dv@collector\pgf@stop% + \let\value\pgf@lib@dv@getval + \pgf@lib@dv@parsed\pgfdatapoint\pgfutil@gobble\pgf@stop% +}% + +\pgfkeys{ + /pgf/data/vars/.initial=, + /pgf/data/funcs/.initial=, + /pgf/data/evaluator/.initial=\pgfmathparse, + /pgf/data/samples/.initial=25}% + +\def\pgf@lib@dv@getval#1{\pgfkeysvalueof{/data point/#1}}% + +\def\pgf@lib@dv@func@parse{% + \pgfutil@ifnextchar\pgf@stop{% + \pgfutil@gobble% + } + {% + \pgfutil@ifnextchar v{% + \pgf@lib@dv@var% + }{% + \pgf@lib@dv@func% + }% + }% +}% + +\def\pgf@lib@dv@func func #1 =#2;{% + \expandafter\def\expandafter\pgf@lib@dv@parsed\expandafter{\pgf@lib@dv@parsed\pgf@lib@dv@eval@func{#1}{#2}} + \pgf@lib@dv@func@parse% +}% +\def\pgf@lib@dv@var var #1 :{\pgfutil@ifnextchar\bgroup{\pgf@lib@dv@var@group{#1}}{\pgf@lib@dv@var@int{#1}}}% +\def\pgf@lib@dv@var@group#1#2;{% + \expandafter\def\expandafter\pgf@lib@dv@parsed\expandafter{\pgf@lib@dv@parsed\pgf@lib@dv@group@var{#1}{#2}}% + \pgf@lib@dv@func@parse% +}% +\def\pgf@lib@dv@var@int#1#2[#3:#4]{% + \pgfutil@ifnextchar s{% + \pgf@lib@dv@samplesorsteps{#1}{#3}{#4}% + }{% + \expandafter\def\expandafter\pgf@lib@dv@parsed\expandafter{% + \pgf@lib@dv@parsed\pgf@lib@dv@samples@var{#1}{#3}{#4}{\pgfkeysvalueof{/pgf/data/samples}}}% + \expandafter\pgf@lib@dv@func@parse\pgfutil@gobble% + } +}% +\def\pgf@lib@dv@samplesorsteps#1#2#3s{% + \pgfutil@ifnextchar t{% + \pgf@lib@dv@step{#1}{#2}{#3}% + }{% + \pgf@lib@dv@samples{#1}{#2}{#3}% + }% +}% +\def\pgf@lib@dv@step#1#2#3tep#4;{% + \expandafter\def\expandafter\pgf@lib@dv@parsed\expandafter{\pgf@lib@dv@parsed\pgf@lib@dv@step@var{#1}{#2}{#3}{#4}}% + \pgf@lib@dv@func@parse% +}% +\def\pgf@lib@dv@samples#1#2#3amples#4;{% + \expandafter\def\expandafter\pgf@lib@dv@parsed\expandafter{\pgf@lib@dv@parsed\pgf@lib@dv@samples@var{#1}{#2}{#3}{#4}}% + \pgf@lib@dv@func@parse% +}% + +\def\pgf@lib@dv@samples@var#1#2#3#4{% + \pgfmathparse{#3}% + \let\pgf@lib@dv@temp=\pgfmathresult% + \pgfmathparse{#2}% + \pgfmathparse{\pgf@lib@dv@temp-\pgfmathresult}% + \pgfmathparse{\pgfmathresult/(#4-1)}% + \let\pgf@lib@dv@temp=\pgfmathresult% + \pgf@lib@dv@step@var{#1}{#2}{#3}{\pgf@lib@dv@temp}% +}% + +\def\pgf@lib@dv@step@var#1#2#3#4#5\pgf@stop{% + {% + \def\pgf@loop@body{#5}% + \pgfmathparse{#2}% + \pgfkeyslet{/data point/#1}{\pgfmathresult}% + \pgfmathparse{#3}% + \let\pgf@loop@end\pgfmathresult% + \pgfmathparse{#4}% + \let\pgf@loop@step\pgfmathresult% + \pgfmathloop% + \pgfmathlessthan{\pgf@loop@end}{\pgfkeysvalueof{/data point/#1}} + \ifdim\pgfmathresult pt<1pt\relax% + \pgf@loop@body\pgf@stop% + \pgfmathparse{\pgfkeysvalueof{/data point/#1}+\pgf@loop@step}% + \pgfkeyslet{/data point/#1}{\pgfmathresult}% + \repeatpgfmathloop% + }% +}% + +\def\pgf@lib@dv@group@var#1#2#3\pgf@stop{% + \foreach \pgf@lib@dv@iterator in {#2} {% + \pgfkeyslet{/data point/#1}{\pgf@lib@dv@iterator}% + #3\pgf@stop% + }% +}% + +\def\pgf@lib@dv@eval@func#1#2{% + \pgfkeysvalueof{/pgf/data/evaluator}{#2}% + \pgfkeyslet{/data point/#1}{\pgfmathresult}% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.polar.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.polar.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a14acc7910d5c1e64eafa07037d145f269ab5b0c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/datavisualization/pgflibrarydatavisualization.polar.code.tex @@ -0,0 +1,144 @@ + +\ProvidesFileRCS{pgflibrarydatavisualization.polar.code.tex} + +\usepgfmodule{datavisualization}% + + + + +\pgfooclass{polar transformer} +{% + + \attribute angle;% + + \attribute radius;% + + \attribute unit vector 0 degrees;% + + \attribute unit vector 90 degrees;% + + + + \method polar transformer(#1,#2,#3,#4) { + \pgfooset{angle}{#1} + \pgfooset{radius}{#2} + \pgfooset{unit vector 0 degrees}{#3} + \pgfooset{unit vector 90 degrees}{#4} + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,transform,transform datapoint signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,path,path signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,direction,direction signal) + }% + + \method get angle attribute(#1) { + \pgfooget{angle}{#1} + }% + + \method get radius attribute(#1) { + \pgfooget{radius}{#1} + }% + + + \method transform() { + \pgfkeysgetvalue{/data point/\pgfoovalueof{angle}/const}\pgf@dv@angle% + \ifx\pgf@dv@angle\relax + \pgfkeysgetvalue{/data point/\pgfoovalueof{angle}}\pgf@dv@angle% + \fi + \ifx\pgf@dv@angle\relax\else% + \ifx\pgf@dv@angle\pgfutil@empty\else% + \pgfkeysgetvalue{/data point/\pgfoovalueof{radius}/const}\pgf@dv@radius% + \ifx\pgf@dv@radius\relax + \pgfkeysgetvalue{/data point/\pgfoovalueof{radius}}\pgf@dv@radius% + \fi + \ifx\pgf@dv@radius\pgfutil@empty\else% + \ifx\pgf@dv@radius\relax\else% + \pgfdvmathenter{\pgf@dv@val}{\pgf@dv@angle}% + \pgfdvmathexitbyscientificformat{\pgf@dv@angle}{\pgf@dv@val}% + \pgfdvmathenter{\pgf@dv@val}{\pgf@dv@radius}% + \pgfdvmathexitbyscientificformat{\pgf@dv@radius}{\pgf@dv@val}% + \pgfmathsincos{\pgf@dv@angle}% + \pgfmathmultiply{\pgfmathresultx}{\pgf@dv@radius}% + \let\pgf@dv@polar@temp=\pgfmathresult + \pgftransformshift{\pgfpointscale{\pgf@dv@polar@temp}{\pgfoovalueof{unit vector 0 degrees}}}% + \pgfmathmultiply{\pgfmathresulty}{\pgf@dv@radius}% + \let\pgf@dv@polar@temp=\pgfmathresult + \pgftransformshift{\pgfpointscale{\pgf@dv@polar@temp}{\pgfoovalueof{unit vector 90 degrees}}}% + \fi% + \fi% + \fi% + \fi% + }% + + + + + \attribute prev angle;% + \attribute prev radius;% + + \method path(#1) {% + \ifpgfdvhandled% + \else% + \ifx#1\pgfdvpathlinetotoken + \pgfooget{prev radius}\pgf@dv@prev@rad + \pgfkeysgetvalue{/data point/\pgfoovalueof{radius}}\pgf@dv@current@rad + \ifx\pgf@dv@current@rad\relax + \else + \ifx\pgf@dv@current@rad\pgf@dv@prev@rad% + \pgfooget{prev angle}\pgf@dv@prev@angle + \pgfkeysgetvalue{/data point/\pgfoovalueof{angle}}\pgf@dv@current@angle + \ifx\pgf@dv@current@angle\relax + \else + \ifx\pgf@dv@current@angle\pgf@dv@prev@angle% + \else% + \pgfdvmathenter{\pgf@dv@val}{\pgf@dv@prev@angle}% + \pgfdvmathexitbyscientificformat{\pgf@dv@prev@angle}{\pgf@dv@val}% + \pgfdvmathenter{\pgf@dv@val}{\pgf@dv@prev@rad}% + \pgfdvmathexitbyscientificformat{\pgf@dv@prev@rad}{\pgf@dv@val}% + \pgfdvmathenter{\pgf@dv@val}{\pgf@dv@current@angle}% + \pgfdvmathexitbyscientificformat{\pgf@dv@current@angle}{\pgf@dv@val}% + \pgfdvmathenter{\pgf@dv@val}{\pgf@dv@current@rad}% + \pgfdvmathexitbyscientificformat{\pgf@dv@current@rad}{\pgf@dv@val}% + \pgfpatharcaxes{\pgf@dv@prev@angle}{\pgf@dv@current@angle} + {\pgfpointscale{\pgf@dv@current@rad}{\pgfoovalueof{unit vector 0 degrees}}} + {\pgfpointscale{\pgf@dv@current@rad}{\pgfoovalueof{unit vector 90 degrees}}}% + \pgfdvhandledtrue% + \fi% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgfooeset{prev angle}{\pgfkeysvalueof{/data point/\pgfoovalueof{angle}}} + \pgfooeset{prev radius}{\pgfkeysvalueof{/data point/\pgfoovalueof{radius}}} + }% + + \method direction(#1) {% + \ifx#1\pgfdvdirectionfromtoken + \xdef\pgf@dv@polar@from@angle{\pgfkeysvalueof{/data point/\pgfoovalueof{angle}}} + \xdef\pgf@dv@polar@from@radius{\pgfkeysvalueof{/data point/\pgfoovalueof{radius}}} + \else\ifx#1\pgfdvdirectiontotoken% + \xdef\pgf@dv@polar@to@angle{\pgfkeysvalueof{/data point/\pgfoovalueof{angle}}} + \xdef\pgf@dv@polar@to@radius{\pgfkeysvalueof{/data point/\pgfoovalueof{radius}}} + \else% + \ifx\pgf@dv@polar@from@radius\pgf@dv@polar@to@radius% + \pgfdvmathenter{\pgf@dv@a}{\pgf@dv@polar@from@angle}% + \pgfdvmathenter{\pgf@dv@b}{\pgf@dv@polar@to@angle}% + \pgfdvmathifless{\pgf@dv@a}{\pgf@dv@b}{\def\pgf@dv@temp@sign{+}}{\def\pgf@dv@temp@sign{-}}% + \pgfkeysgetvalue{/data point/\pgfoovalueof{angle}}\pgf@temp% + \ifx\pgf@temp\relax% + \else% + \pgfdvmathenter{\pgf@dv@val}{\pgf@temp}% + \pgfdvmathexitbyscientificformat{\pgf@dv@polar@angle}{\pgf@dv@val}% + \pgf@process{\pgfpointpolar{\pgf@dv@polar@angle\pgf@dv@temp@sign90}{1pt}}% + \pgfdvhandledtrue% + \fi% + \fi% + \fi\fi% + }% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.footprints.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.footprints.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f98f79c3fe670d468697add160f53bba57b79764 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.footprints.code.tex @@ -0,0 +1,181 @@ + +\usepgfmodule{decorations}% + + +\pgfset{ + /pgf/decoration/foot length/.initial=10pt, + /pgf/decoration/stride length/.initial=30pt, + /pgf/decoration/foot sep/.initial=4pt, + /pgf/decoration/foot angle/.initial=10, + /pgf/decoration/foot of/.initial=human, +}% + + + +\pgfdeclaredecoration{footprints}{left} +{% + \state{left}[width=\pgfkeysvalueof{/pgf/decoration/stride length}/2,next state=right] + { + \pgftransformyshift{\pgfkeysvalueof{/pgf/decoration/foot sep}/2} + \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/foot length}} + \pgftransformscale{\pgfmathresult} + \pgftransformrotate{\pgfkeysvalueof{/pgf/decoration/foot angle}} + \csname pgf@lib@foot@of@\pgfkeysvalueof{/pgf/decoration/foot of}\endcsname + }% + \state{right}[width=\pgfkeysvalueof{/pgf/decoration/stride length}/2,next state=left] + { + \pgftransformyscale{-1} + \pgftransformyshift{\pgfkeysvalueof{/pgf/decoration/foot sep}/2} + \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/foot length}} + \pgftransformscale{\pgfmathresult} + \pgftransformrotate{\pgfkeysvalueof{/pgf/decoration/foot angle}} + \csname pgf@lib@foot@of@\pgfkeysvalueof{/pgf/decoration/foot of}\endcsname + }% +}% + + + + + +\def\pgf@lib@foot@of@gnome{ + \pgftransformcm{0}{-1}{-1}{0}{\pgfqpoint{1pt}{0.8pt}} + \pgftransformscale{0.83333} + \pgfpathmoveto{\pgfqpoint{.86068pt}{0pt}} + \pgfpathcurveto{\pgfqpoint{.61466pt}{0pt}}{\pgfqpoint{.56851pt}{.35041pt}}{\pgfqpoint{.70691pt}{.35041pt}} + \pgfpathcurveto{\pgfqpoint{.84529pt}{.35041pt}}{\pgfqpoint{1.10671pt}{0pt}}{\pgfqpoint{.86068pt}{0pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.45217pt}{.30699pt}} + \pgfpathcurveto{\pgfqpoint{.52586pt}{.31149pt}}{\pgfqpoint{.60671pt}{.02577pt}}{\pgfqpoint{.46821pt}{.04374pt}} + \pgfpathcurveto{\pgfqpoint{.32976pt}{.06171pt}}{\pgfqpoint{.37845pt}{.30249pt}}{\pgfqpoint{.45217pt}{.30699pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.11445pt}{.48453pt}} + \pgfpathcurveto{\pgfqpoint{.16686pt}{.46146pt}}{\pgfqpoint{.1212pt}{.23581pt}}{\pgfqpoint{.03208pt}{.29735pt}} + \pgfpathcurveto{\pgfqpoint{-.057pt}{.3589pt}}{\pgfqpoint{.06204pt}{.50759pt}}{\pgfqpoint{.11445pt}{.48453pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.26212pt}{.36642pt}} + \pgfpathcurveto{\pgfqpoint{.32451pt}{.3537pt}}{\pgfqpoint{.32793pt}{.09778pt}}{\pgfqpoint{.21667pt}{.14369pt}} + \pgfpathcurveto{\pgfqpoint{.10539pt}{.18961pt}}{\pgfqpoint{.19978pt}{.37916pt}}{\pgfqpoint{.26212pt}{.36642pt}} + \pgfpathlineto{\pgfqpoint{.26212pt}{.36642pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.58791pt}{.93913pt}} + \pgfpathcurveto{\pgfqpoint{.59898pt}{1.02367pt}}{\pgfqpoint{.52589pt}{1.06542pt}}{\pgfqpoint{.45431pt}{1.01092pt}} + \pgfpathcurveto{\pgfqpoint{.22644pt}{.83743pt}}{\pgfqpoint{.8316pt}{.75088pt}}{\pgfqpoint{.79171pt}{.51386pt}} + \pgfpathcurveto{\pgfqpoint{.7586pt}{.31712pt}}{\pgfqpoint{.15495pt}{.37769pt}}{\pgfqpoint{.08621pt}{.68553pt}} + \pgfpathcurveto{\pgfqpoint{.03968pt}{.89374pt}}{\pgfqpoint{.27774pt}{1.1826pt}}{\pgfqpoint{.52614pt}{1.1826pt}} + \pgfpathcurveto{\pgfqpoint{.64834pt}{1.1826pt}}{\pgfqpoint{.78929pt}{1.07226pt}}{\pgfqpoint{.81566pt}{.93248pt}} + \pgfpathcurveto{\pgfqpoint{.8358pt}{.82589pt}}{\pgfqpoint{.57867pt}{.8686pt}}{\pgfqpoint{.58791pt}{.93913pt}} + \pgfpathlineto{\pgfqpoint{.58791pt}{.93913pt}} + \pgfpathclose +}% + + + +\def\pgf@lib@foot@of@bird{ + \pgftransformcm{0}{.11}{.11}{0}{\pgfqpoint{.37pt}{.52pt}} + \pgfpathmoveto{\pgfqpoint{-.886pt}{1.652pt}} + \pgfpathcurveto{\pgfqpoint{-.4632pt}{2.669pt}}{\pgfqpoint{-.5092pt}{4.3712pt}}{\pgfqpoint{-.4512pt}{5.6734pt}} + \pgfpathcurveto{\pgfqpoint{-.4374pt}{5.9842pt}}{\pgfqpoint{-.3182pt}{6.0686pt}}{\pgfqpoint{-.2484pt}{5.644pt}} + \pgfpathcurveto{\pgfqpoint{-.0534pt}{4.459pt}}{\pgfqpoint{.087pt}{3.0132pt}}{\pgfqpoint{.5206pt}{1.8464pt}} + \pgfpathcurveto{\pgfqpoint{.714pt}{1.326pt}}{\pgfqpoint{.692pt}{1.416pt}}{\pgfqpoint{1.0864pt}{1.759pt}} + \pgfpathcurveto{\pgfqpoint{1.7662pt}{2.3504pt}}{\pgfqpoint{2.665pt}{3.1756pt}}{\pgfqpoint{3.2028pt}{4.02pt}} + \pgfpathcurveto{\pgfqpoint{3.4708pt}{4.4408pt}}{\pgfqpoint{3.4258pt}{4.0814pt}}{\pgfqpoint{3.3366pt}{3.8708pt}} + \pgfpathcurveto{\pgfqpoint{2.9068pt}{2.8562pt}}{\pgfqpoint{.8502pt}{.645pt}}{\pgfqpoint{.4808pt}{-.0864pt}} + \pgfpathcurveto{\pgfqpoint{.0808pt}{-.8788pt}}{\pgfqpoint{.1664pt}{-2.1246pt}}{\pgfqpoint{.0024pt}{-2.7868pt}} + \pgfpathcurveto{\pgfqpoint{-.172pt}{-3.4908pt}}{\pgfqpoint{-.2726pt}{-3.704pt}}{\pgfqpoint{-.3812pt}{-2.9558pt}} + \pgfpathcurveto{\pgfqpoint{-.5316pt}{-1.9202pt}}{\pgfqpoint{-.88pt}{-.256pt}}{\pgfqpoint{-1.332pt}{.128pt}} + \pgfpathcurveto{\pgfqpoint{-1.716pt}{.4542pt}}{\pgfqpoint{-3.7928pt}{2.3136pt}}{\pgfqpoint{-4.5044pt}{3.3524pt}} + \pgfpathcurveto{\pgfqpoint{-4.7618pt}{3.728pt}}{\pgfqpoint{-4.709pt}{3.7864pt}}{\pgfqpoint{-4.4212pt}{3.5818pt}} + \pgfpathcurveto{\pgfqpoint{-3.4844pt}{2.9162pt}}{\pgfqpoint{-2.6164pt}{1.654pt}}{\pgfqpoint{-1.454pt}{1.3886pt}} + \pgfpathcurveto{\pgfqpoint{-1.0876pt}{1.305pt}}{\pgfqpoint{-1.0296pt}{1.3066pt}}{\pgfqpoint{-.886pt}{1.652pt}} + \pgfpathclose +}% + + +\expandafter\def\csname pgf@lib@foot@of@felis silvestris\endcsname{ + \pgftransformcm{0}{.1}{.1}{0}{\pgfqpoint{.48pt}{.5pt}} + \pgfpathmoveto{\pgfqpoint{2.7312pt}{-1.992pt}} + \pgfpathcurveto{\pgfqpoint{1.8716pt}{-1.4226pt}}{\pgfqpoint{2.1404pt}{.0436pt}}{\pgfqpoint{.9202pt}{.0436pt}} + \pgfpathcurveto{\pgfqpoint{-.1146pt}{.0436pt}}{\pgfqpoint{-.7386pt}{.0178pt}}{\pgfqpoint{-1.319pt}{-1.0288pt}} + \pgfpathcurveto{\pgfqpoint{-1.7922pt}{-1.8822pt}}{\pgfqpoint{-2.072pt}{-1.5488pt}}{\pgfqpoint{-2.9638pt}{-1.968pt}} + \pgfpathcurveto{\pgfqpoint{-3.9244pt}{-2.4198pt}}{\pgfqpoint{-4.4394pt}{-3.348pt}}{\pgfqpoint{-4.1136pt}{-4.041pt}} + \pgfpathcurveto{\pgfqpoint{-3.3862pt}{-5.5882pt}}{\pgfqpoint{-1.6156pt}{-3.83pt}}{\pgfqpoint{-1.1684pt}{-4.312pt}} + \pgfpathcurveto{\pgfqpoint{-.5806pt}{-4.9454pt}}{\pgfqpoint{.5032pt}{-4.8822pt}}{\pgfqpoint{1.1748pt}{-4.2878pt}} + \pgfpathcurveto{\pgfqpoint{1.5822pt}{-3.9272pt}}{\pgfqpoint{2.6524pt}{-5.0652pt}}{\pgfqpoint{3.3506pt}{-4.1066pt}} + \pgfpathcurveto{\pgfqpoint{3.839pt}{-3.4356pt}}{\pgfqpoint{3.1192pt}{-2.249pt}}{\pgfqpoint{2.7312pt}{-1.992pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{5.0576pt}{.4996pt}} + \pgfpathcurveto{\pgfqpoint{4.6056pt}{.6536pt}}{\pgfqpoint{4.0596pt}{.2516pt}}{\pgfqpoint{3.8382pt}{-.398pt}} + \pgfpathcurveto{\pgfqpoint{3.6168pt}{-1.0478pt}}{\pgfqpoint{3.8038pt}{-1.6996pt}}{\pgfqpoint{4.2558pt}{-1.8536pt}} + \pgfpathcurveto{\pgfqpoint{4.7078pt}{-2.0076pt}}{\pgfqpoint{5.2538pt}{-1.6056pt}}{\pgfqpoint{5.4752pt}{-.9558pt}} + \pgfpathcurveto{\pgfqpoint{5.6966pt}{-.3062pt}}{\pgfqpoint{5.5096pt}{.3456pt}}{\pgfqpoint{5.0576pt}{.4996pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{3.1212pt}{3.5542pt}} + \pgfpathcurveto{\pgfqpoint{2.5874pt}{3.6726pt}}{\pgfqpoint{1.975pt}{3.1756pt}}{\pgfqpoint{1.7538pt}{2.4442pt}} + \pgfpathcurveto{\pgfqpoint{1.5324pt}{1.7128pt}}{\pgfqpoint{1.7858pt}{1.0238pt}}{\pgfqpoint{2.3196pt}{.9052pt}} + \pgfpathcurveto{\pgfqpoint{2.8534pt}{.7868pt}}{\pgfqpoint{3.4658pt}{1.2838pt}}{\pgfqpoint{3.6872pt}{2.0152pt}} + \pgfpathcurveto{\pgfqpoint{3.9084pt}{2.7466pt}}{\pgfqpoint{3.655pt}{3.4358pt}}{\pgfqpoint{3.1212pt}{3.5542pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{-.6182pt}{5.0456pt}} + \pgfpathcurveto{\pgfqpoint{-1.2132pt}{5.0456pt}}{\pgfqpoint{-1.6956pt}{4.3104pt}}{\pgfqpoint{-1.6956pt}{3.4038pt}} + \pgfpathcurveto{\pgfqpoint{-1.6956pt}{2.4972pt}}{\pgfqpoint{-1.2132pt}{1.7618pt}}{\pgfqpoint{-.6182pt}{1.7618pt}} + \pgfpathcurveto{\pgfqpoint{-.0232pt}{1.7618pt}}{\pgfqpoint{.4592pt}{2.4972pt}}{\pgfqpoint{.4592pt}{3.4038pt}} + \pgfpathcurveto{\pgfqpoint{.4592pt}{4.3104pt}}{\pgfqpoint{-.0232pt}{5.0456pt}}{\pgfqpoint{-.6182pt}{5.0456pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{-4.1176pt}{1.8248pt}} + \pgfpathcurveto{\pgfqpoint{-4.6334pt}{1.7534pt}}{\pgfqpoint{-4.9806pt}{1.0312pt}}{\pgfqpoint{-4.8928pt}{.212pt}} + \pgfpathcurveto{\pgfqpoint{-4.8052pt}{-.6072pt}}{\pgfqpoint{-4.3158pt}{-1.2136pt}}{\pgfqpoint{-3.8pt}{-1.1422pt}} + \pgfpathcurveto{\pgfqpoint{-3.2842pt}{-1.0708pt}}{\pgfqpoint{-2.9372pt}{-.3486pt}}{\pgfqpoint{-3.0248pt}{.4706pt}} + \pgfpathcurveto{\pgfqpoint{-3.1126pt}{1.2898pt}}{\pgfqpoint{-3.6018pt}{1.8962pt}}{\pgfqpoint{-4.1176pt}{1.8248pt}} + \pgfpathclose +}% + + + +\def\pgf@lib@foot@of@human{% + \pgftransformcm{0}{.5}{.5}{0}{\pgfqpoint{.48pt}{.2pt}} + \pgfpathmoveto{\pgfqpoint{.20175pt}{-.72633pt}} + \pgfpathcurveto{\pgfqpoint{.16314pt}{-.88194pt}}{\pgfqpoint{.07386pt}{-1.0167pt}}{\pgfqpoint{-.08385pt}{-1.0167pt}} + \pgfpathcurveto{\pgfqpoint{-.24153pt}{-1.0167pt}}{\pgfqpoint{-.36942pt}{-.84897pt}}{\pgfqpoint{-.36942pt}{-.72633pt}} + \pgfpathcurveto{\pgfqpoint{-.36942pt}{-.60372pt}}{\pgfqpoint{-.32505pt}{-.54825pt}}{\pgfqpoint{-.27633pt}{-.51192pt}} + \pgfpathcurveto{\pgfqpoint{-.23937pt}{-.48435pt}}{\pgfqpoint{-.17031pt}{-.46539pt}}{\pgfqpoint{-.10611pt}{-.40323pt}} + \pgfpathcurveto{\pgfqpoint{-.04191pt}{-.3411pt}}{\pgfqpoint{.00495pt}{-.27783pt}}{\pgfqpoint{.00495pt}{-.14787pt}} + \pgfpathcurveto{\pgfqpoint{.00495pt}{-.01794pt}}{\pgfqpoint{-.08526pt}{.12648pt}}{\pgfqpoint{-.22194pt}{.22467pt}} + \pgfpathcurveto{\pgfqpoint{-.35862pt}{.32286pt}}{\pgfqpoint{-.40863pt}{.50226pt}}{\pgfqpoint{-.32703pt}{.5979pt}} + \pgfpathcurveto{\pgfqpoint{-.24543pt}{.69354pt}}{\pgfqpoint{-.00564pt}{.66543pt}}{\pgfqpoint{.17172pt}{.53484pt}} + \pgfpathcurveto{\pgfqpoint{.34908pt}{.40422pt}}{\pgfqpoint{.39363pt}{.27192pt}}{\pgfqpoint{.37416pt}{.10971pt}} + \pgfpathcurveto{\pgfqpoint{.35472pt}{-.0525pt}}{\pgfqpoint{.26736pt}{-.46203pt}}{\pgfqpoint{.20175pt}{-.72633pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{-.27138pt}{1.01451pt}} + \pgfpathcurveto{\pgfqpoint{-.21198pt}{1.01451pt}}{\pgfqpoint{-.1638pt}{.94509pt}}{\pgfqpoint{-.1638pt}{.8595pt}} + \pgfpathcurveto{\pgfqpoint{-.1638pt}{.77388pt}}{\pgfqpoint{-.21198pt}{.70446pt}}{\pgfqpoint{-.27138pt}{.70446pt}} + \pgfpathcurveto{\pgfqpoint{-.33078pt}{.70446pt}}{\pgfqpoint{-.37896pt}{.77388pt}}{\pgfqpoint{-.37896pt}{.8595pt}} + \pgfpathcurveto{\pgfqpoint{-.37896pt}{.94509pt}}{\pgfqpoint{-.33078pt}{1.01451pt}}{\pgfqpoint{-.27138pt}{1.01451pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{-.05769pt}{.90573pt}} + \pgfpathcurveto{\pgfqpoint{-.01659pt}{.90573pt}}{\pgfqpoint{.01674pt}{.86445pt}}{\pgfqpoint{.01674pt}{.81354pt}} + \pgfpathcurveto{\pgfqpoint{.01674pt}{.7626pt}}{\pgfqpoint{-.01659pt}{.72132pt}}{\pgfqpoint{-.05769pt}{.72132pt}} + \pgfpathcurveto{\pgfqpoint{-.09879pt}{.72132pt}}{\pgfqpoint{-.13209pt}{.7626pt}}{\pgfqpoint{-.13209pt}{.81354pt}} + \pgfpathcurveto{\pgfqpoint{-.13209pt}{.86445pt}}{\pgfqpoint{-.09879pt}{.90573pt}}{\pgfqpoint{-.05769pt}{.90573pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.10497pt}{.81636pt}} + \pgfpathcurveto{\pgfqpoint{.14214pt}{.81096pt}}{\pgfqpoint{.16722pt}{.77193pt}}{\pgfqpoint{.16104pt}{.72918pt}} + \pgfpathcurveto{\pgfqpoint{.15483pt}{.68646pt}}{\pgfqpoint{.11964pt}{.65619pt}}{\pgfqpoint{.08247pt}{.66159pt}} + \pgfpathcurveto{\pgfqpoint{.0453pt}{.66699pt}}{\pgfqpoint{.02019pt}{.70602pt}}{\pgfqpoint{.0264pt}{.74874pt}} + \pgfpathcurveto{\pgfqpoint{.03261pt}{.79149pt}}{\pgfqpoint{.0678pt}{.82176pt}}{\pgfqpoint{.10497pt}{.81636pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.24054pt}{.70842pt}} + \pgfpathcurveto{\pgfqpoint{.27513pt}{.70842pt}}{\pgfqpoint{.30318pt}{.67686pt}}{\pgfqpoint{.30318pt}{.63795pt}} + \pgfpathcurveto{\pgfqpoint{.30318pt}{.59904pt}}{\pgfqpoint{.27513pt}{.56751pt}}{\pgfqpoint{.24054pt}{.56751pt}} + \pgfpathcurveto{\pgfqpoint{.20598pt}{.56751pt}}{\pgfqpoint{.17793pt}{.59904pt}}{\pgfqpoint{.17793pt}{.63795pt}} + \pgfpathcurveto{\pgfqpoint{.17793pt}{.67686pt}}{\pgfqpoint{.20598pt}{.70842pt}}{\pgfqpoint{.24054pt}{.70842pt}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{.35973pt}{.57501pt}} + \pgfpathcurveto{\pgfqpoint{.3918pt}{.57501pt}}{\pgfqpoint{.41781pt}{.54852pt}}{\pgfqpoint{.41781pt}{.51585pt}} + \pgfpathcurveto{\pgfqpoint{.41781pt}{.48318pt}}{\pgfqpoint{.3918pt}{.45669pt}}{\pgfqpoint{.35973pt}{.45669pt}} + \pgfpathcurveto{\pgfqpoint{.32769pt}{.45669pt}}{\pgfqpoint{.30168pt}{.48318pt}}{\pgfqpoint{.30168pt}{.51585pt}} + \pgfpathcurveto{\pgfqpoint{.30168pt}{.54852pt}}{\pgfqpoint{.32769pt}{.57501pt}}{\pgfqpoint{.35973pt}{.57501pt}} + \pgfpathclose +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.fractals.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.fractals.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8d9fb15558d3893f3d55bca079becdcf195621e9 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.fractals.code.tex @@ -0,0 +1,57 @@ + +\usepgfmodule{decorations}% + + + +\pgfdeclaredecoration{Koch curve type 1}{init} +{% + \state{init}[width=\pgfdecoratedinputsegmentremainingdistance] + { + \pgfpathlineto{\pgfpoint{.33333\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{.33333\pgfdecoratedinputsegmentremainingdistance}{.33333\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.66666\pgfdecoratedinputsegmentremainingdistance}{.33333\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.66666\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + }% +}% + +\pgfdeclaredecoration{Koch curve type 2}{init} +{% + \state{init}[width=\pgfdecoratedinputsegmentremainingdistance] + { + \pgfpathlineto{\pgfpoint{.25\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{.25\pgfdecoratedinputsegmentremainingdistance}{.25\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.5\pgfdecoratedinputsegmentremainingdistance}{.25\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.5\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{.5\pgfdecoratedinputsegmentremainingdistance}{-.25\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.75\pgfdecoratedinputsegmentremainingdistance}{-.25\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.75\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + }% +}% + +\pgfdeclaredecoration{Koch snowflake}{init} +{% + \state{init}[width=\pgfdecoratedinputsegmentremainingdistance] + { + \pgfpathlineto{\pgfpoint{.3333\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{.5\pgfdecoratedinputsegmentremainingdistance}{0.2886751347\pgfdecoratedinputsegmentremainingdistance}} + \pgfpathlineto{\pgfpoint{.6666\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + }% +}% + + +\pgfdeclaredecoration{Cantor set}{init} +{% + \state{init}[width=\pgfdecoratedinputsegmentremainingdistance] + { + \pgfpathlineto{\pgfpoint{.3333\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathmoveto{\pgfpoint{.6666\pgfdecoratedinputsegmentremainingdistance}{0pt}} + \pgfpathlineto{\pgfpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + }% +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.markings.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.markings.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..603d35250677fdbb7accfc153e359c69659b613b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.markings.code.tex @@ -0,0 +1,160 @@ + +\usepgfmodule{decorations}% + + + +\pgfkeys{ + /pgf/decoration/reset marks/.code=\let\pgf@lib@dec@mark@marks\pgfutil@empty, + /pgf/decoration/mark/.code=\pgf@lib@dec@parsemark#1\pgf@lib@dec@stop, +}% + +\let\pgf@lib@dec@mark@marks=\pgfutil@empty + +\def\pgf@lib@dec@parsemark{\pgfutil@ifnextchar b{\pgf@lib@dec@parsebetween}{\pgf@lib@dec@parseat}}% +\def\pgf@lib@dec@parseat at position#1with#2\pgf@lib@dec@stop{% + \expandafter\def\expandafter\pgf@lib@dec@mark@marks\expandafter{\pgf@lib@dec@mark@marks% + \pgf@lib@dec@domark{#1}{#2}% + }% +}% +\def\pgf@lib@dec@parsebetween between positions#1and#2step#3with#4\pgf@lib@dec@stop{% + \expandafter\def\expandafter\pgf@lib@dec@mark@marks\expandafter{\pgf@lib@dec@mark@marks% + \pgf@lib@dec@dobetweenmark{#1}{#2}{#3}{#4}% + }% +}% + +\def\pgf@lib@dec@arrowhead#1#2{% + \pgftransformxscale{#1} + \pgfarrowdraw{#2}% +}% + +\def\pgf@lib@dec@doarrowhead#1{% + \pgf@lib@dec@arrowhead{1}{#1}% +}% +\def\pgf@lib@dec@doarrowheadrev#1{% + \pgf@lib@dec@arrowhead{-1}{#1}% +}% + + +\pgfdeclaredecoration{markings}{init} +{% + \state{init} + [ + width=0pt, + persistent precomputation={% + \pgfkeys{/pgf/decoration/mark info/sequence number/.initial=0}% + \pgfkeys{/pgf/decoration/mark info/distance from start/.initial=}% + }, + next state=pre + ] + {}% + + \state{pre} + [ + width=0pt, + persistent precomputation={% + \def\pgf@lib@dec@computed@width{0pt}% + \pgf@lib@dec@mark@marks\pgf@lib@dec@mark@last% + \let\arrow=\pgf@lib@dec@doarrowhead% + \let\arrowreversed=\pgf@lib@dec@doarrowheadrev% + }, + next state=skipper + ] + {}% + + \state{skipper}[width=\pgf@lib@dec@computed@width-\pgfdecoratedcompleteddistance-1sp, + next state=\pgf@lib@dec@next@state]{}% + + \state{main} + [ + width=1sp, + next state=pre, + persistent precomputation={% + \pgfutil@tempcnta=\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}\relax% + \advance\pgfutil@tempcnta by1\relax% + \pgfkeys{/pgf/decoration/mark info/sequence number/.expanded=\the\pgfutil@tempcnta}% + \pgfkeys{/pgf/decoration/mark info/distance from start/.expanded=\pgf@lib@dec@computed@width}% + }% + ] + {% + \pgfinterruptpath% + \pgfscope% + \let\pgf@lib@dec@mark@marks=\pgfutil@empty% + \pgfslopedattimefalse + \pgf@lib@dec@computed@action% + \endpgfscope% + \endpgfinterruptpath% + \ifx\pgf@lib@mark@node\pgfutil@empty% + \else% + \pgf@lib@mark@connect@node% + \fi% + }% + + \state{final}[width=\pgfdecoratedremainingdistance]{ + \ifx\pgf@lib@mark@node\pgfutil@empty% + \pgfpathmoveto{\pgfpointdecoratedpathlast} + \else% + \pgfpathlineto{\pgfpointdecoratedpathlast} + \fi% + }% +}% + +\def\pgf@lib@dec@domark#1#2#3\pgf@lib@dec@mark@last{% + \def\pgf@lib@dec@mark@marks{#3}% + \pgf@lib@dec@parsenum{#1}% + \def\pgf@lib@dec@computed@action{#2}% + \def\pgf@lib@dec@next@state{main}% +}% + + +\def\pgf@lib@dec@dobetweenmark#1#2#3#4#5\pgf@lib@dec@mark@last{% + \pgf@lib@dec@parsenum{#1}% + \let\pgf@lib@dec@mark@start=\pgf@lib@dec@computed@width% + \pgf@lib@dec@parsenum{#2}% + \let\pgf@lib@dec@mark@end=\pgf@lib@dec@computed@width% + \ifdim\pgf@lib@dec@mark@end<\pgf@lib@dec@mark@start\relax% + #5\pgf@lib@dec@mark@last% + \else% + \pgf@lib@dec@parsenum{#3}% + \pgfmathparse{\pgf@lib@dec@mark@start+\pgf@lib@dec@computed@width}% + \edef\pgf@temp{\noexpand\pgf@lib@dec@dobetweenmark{\pgfmathresult pt}{\pgf@lib@dec@mark@end}{\pgf@lib@dec@computed@width}}% + \expandafter\def\expandafter\pgf@lib@dec@mark@marks\expandafter{\pgf@temp{#4}#5}% + \let\pgf@lib@dec@computed@width\pgf@lib@dec@mark@start% + \def\pgf@lib@dec@computed@action{#4}% + \def\pgf@lib@dec@next@state{main}% + \fi% +}% + + +\def\pgf@lib@dec@parsenum#1{% + \pgfmathparse{#1}% + \ifpgfmathunitsdeclared% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathparse{\pgfdecoratedpathlength\pgfmathresult pt}% + \else% + \pgfmathparse{\pgfmathresult pt}% + \fi% + \else% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathparse{\pgfdecoratedpathlength\pgfmathresult*\pgfdecoratedpathlength}% + \else% + \pgfmathparse{\pgfmathresult*\pgfdecoratedpathlength}% + \fi% + \fi% + \edef\pgf@lib@dec@computed@width{\pgfmathresult pt}% +}% + +\def\pgf@lib@dec@mark@last{% + \def\pgf@lib@dec@next@state{final}% +}% + + + +\pgfkeys{/pgf/decoration/mark connection node/.store in=\pgf@lib@mark@node, + /pgf/decoration/mark connection node=}% +\def\pgf@lib@mark@connect@node{% + \pgfpathlineto{\pgfpointshapeborder{\pgf@lib@mark@node}{\pgfqpoint{-1pt}{0pt}}} + \pgfpathmoveto{\pgfpointshapeborder{\pgf@lib@mark@node}{\pgfqpoint{1pt}{0pt}}} +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..396ffa543e6312ec92718060f4b2491b20d0ee5c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathmorphing.code.tex @@ -0,0 +1,242 @@ + +\usepgfmodule{decorations}% + + + + + + +\pgfdeclaredecoration{zigzag}{up from center}{% + \state{up from center}[width=+.5\pgfdecorationsegmentlength, next state=big down] + { + \pgfpathlineto{\pgfqpoint{.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + }% + \state{big down}[switch if less than=+.5\pgfdecorationsegmentlength to center finish, + width=+.5\pgfdecorationsegmentlength, + next state=big up] + { + \pgfpathlineto{\pgfqpoint{.25\pgfdecorationsegmentlength}{-\pgfdecorationsegmentamplitude}} + }% + \state{big up}[switch if less than=+.5\pgfdecorationsegmentlength to center finish, + width=+.5\pgfdecorationsegmentlength, + next state=big down] + { + \pgfpathlineto{\pgfqpoint{.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + }% + \state{center finish}[width=0pt, next state=final]{ + \pgfpathlineto{\pgfpointorigin} + }% + \state{final} + { + \pgfpathlineto{\pgfpointdecoratedpathlast} + }% +}% + + + + + +\pgfdeclaredecoration{saw}{initial} +{% + \state{initial}[auto end on length=+\pgfdecorationsegmentlength, + auto corner on length=+\pgfdecorationsegmentlength, + width=+\pgfdecorationsegmentlength] + { + \pgfpathlineto{\pgfqpoint{\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + \pgfpathlineto{\pgfqpoint{\pgfdecorationsegmentlength}{0pt}} + }% + \state{final} + {}% +}% + + + + + +\pgfdeclaredecoration{random steps}{start} +{% + \state{start}[width=+0pt,next state=step,persistent precomputation=\pgfdecoratepathhascornerstrue]{}% + \state{step}[auto end on length=1.5\pgfdecorationsegmentlength, + auto corner on length=1.5\pgfdecorationsegmentlength, + width=+\pgfdecorationsegmentlength] + { + \pgfpathlineto{ + \pgfpointadd + {\pgfpoint{\pgfdecorationsegmentlength}{0pt}} + {\pgfpoint{rand*\pgfdecorationsegmentamplitude}{rand*\pgfdecorationsegmentamplitude}} + } + }% + \state{final} + {}% +}% + + + + +\pgfdeclaremetadecoration{straight zigzag}{line to}{% + \state{line to}[width=\pgfmetadecorationsegmentlength, next state=zigzag] + { + \decoration{curveto} + }% + \state{zigzag}[width=\pgfmetadecorationsegmentlength, next state=line to] + { + \decoration{zigzag} + }% + \state{final} + { + \decoration{curveto} + }% +}% + + + + + + + + + +\pgfdeclaredecoration{bent}{bent} +{% + \state{bent}[width=+\pgfdecoratedinputsegmentremainingdistance] + { + \pgfpathcurveto + {\pgfqpoint{\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude}} + {\pgfpointadd{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + {\pgfqpoint{-\pgfdecorationsegmentaspect\pgfdecoratedinputsegmentremainingdistance}{\pgfdecorationsegmentamplitude}}} + {\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + }% + \state{final} + {}% +}% + + + + +\pgfdeclaredecoration{snake}{initial} +{% + \state{initial}[switch if less than=+.625\pgfdecorationsegmentlength to final, + width=+.3125\pgfdecorationsegmentlength, + next state=down] + { + \pgfpathcurveto + {\pgfqpoint{.125\pgfdecorationsegmentlength}{0pt}} + {\pgfqpoint{.1875\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.3125\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + }% + \state{down}[switch if less than=+.8125\pgfdecorationsegmentlength to end down, + width=+.5\pgfdecorationsegmentlength, + next state=up] + { + \pgfpathcosine{\pgfqpoint{.25\pgfdecorationsegmentlength}{-1\pgfdecorationsegmentamplitude}} + \pgfpathsine{\pgfqpoint{.25\pgfdecorationsegmentlength}{-1\pgfdecorationsegmentamplitude}} + }% + \state{up}[switch if less than=+.8125\pgfdecorationsegmentlength to end up, + width=+.5\pgfdecorationsegmentlength, + next state=down] + { + \pgfpathcosine{\pgfqpoint{.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + \pgfpathsine{\pgfqpoint{.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + }% + \state{end down}[width=+.3125\pgfdecorationsegmentlength, + next state=final] + { + \pgfpathcurveto + {\pgfqpoint{.125\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.1875\pgfdecorationsegmentlength}{0pt}} + {\pgfqpoint{.3125\pgfdecorationsegmentlength}{0pt}} + }% + \state{end up}[width=+.3125\pgfdecorationsegmentlength, + next state=final] + { + \pgfpathcurveto + {\pgfqpoint{.125\pgfdecorationsegmentlength}{-\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.1875\pgfdecorationsegmentlength}{0pt}} + {\pgfqpoint{.3125\pgfdecorationsegmentlength}{0pt}} + }% + \state{final} + { + \pgfpathlineto{\pgfpointdecoratedpathlast} + }% +}% + + + +\pgfdeclaredecoration{coil}{coil} +{% + \state{coil}[switch if less than=% + 1.5\pgfdecorationsegmentlength+% + \pgfdecorationsegmentaspect\pgfdecorationsegmentamplitude+% + \pgfdecorationsegmentaspect\pgfdecorationsegmentamplitude to last, + width=+\pgfdecorationsegmentlength] + { + \pgfpathcurveto + {\pgfpoint@oncoil{0 }{ 0.555}{1}} + {\pgfpoint@oncoil{0.445}{ 1 }{2}} + {\pgfpoint@oncoil{1 }{ 1 }{3}} + \pgfpathcurveto + {\pgfpoint@oncoil{1.555}{ 1 }{4}} + {\pgfpoint@oncoil{2 }{ 0.555}{5}} + {\pgfpoint@oncoil{2 }{ 0 }{6}} + \pgfpathcurveto + {\pgfpoint@oncoil{2 }{-0.555}{7}} + {\pgfpoint@oncoil{1.555}{-1 }{8}} + {\pgfpoint@oncoil{1 }{-1 }{9}} + \pgfpathcurveto + {\pgfpoint@oncoil{0.445}{-1 }{10}} + {\pgfpoint@oncoil{0 }{-0.555}{11}} + {\pgfpoint@oncoil{0 }{ 0 }{12}} + }% + \state{last}[width=.5\pgfdecorationsegmentlength+% + \pgfdecorationsegmentaspect\pgfdecorationsegmentamplitude+% + \pgfdecorationsegmentaspect\pgfdecorationsegmentamplitude,next state=final] + { + \pgfpathcurveto + {\pgfpoint@oncoil{0 }{ 0.555}{1}} + {\pgfpoint@oncoil{0.445}{ 1 }{2}} + {\pgfpoint@oncoil{1 }{ 1 }{3}} + \pgfpathcurveto + {\pgfpoint@oncoil{1.555}{ 1 }{4}} + {\pgfpoint@oncoil{2 }{ 0.555}{5}} + {\pgfpoint@oncoil{2 }{ 0 }{6}} + }% + \state{final} + { + \pgfpathlineto{\pgfpointdecoratedpathlast} + }% +}% + +\def\pgfpoint@oncoil#1#2#3{% + \pgf@x=#1\pgfdecorationsegmentamplitude% + \pgf@x=\pgfdecorationsegmentaspect\pgf@x% + \pgf@y=#2\pgfdecorationsegmentamplitude% + \pgf@xa=0.083333333333\pgfdecorationsegmentlength% + \advance\pgf@x by#3\pgf@xa% +}% + + + +\pgfdeclaredecoration{bumps}{initial} +{% + \state{initial}[auto end on length=+.51\pgfdecorationsegmentlength, + auto corner on length=+.51\pgfdecorationsegmentlength, + width=+.5\pgfdecorationsegmentlength] + { + \pgfpathcurveto + {\pgfqpoint{0pt}{.555\pgfdecorationsegmentamplitude}} + {\pgfqpoint{0.11125\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + \pgfpathcurveto + {\pgfqpoint{.38875\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.5\pgfdecorationsegmentlength}{.5\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.5\pgfdecorationsegmentlength}{0\pgfdecorationsegmentamplitude}} + }% + \state{final} + { + \pgfpathlineto{\pgfpointdecoratedpathlast} + }% +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..2292b281c09b3998987f3120e415d44d96c7c0b4 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.pathreplacing.code.tex @@ -0,0 +1,203 @@ + +\usepgfmodule{decorations}% + + + + + + + + +\pgfdeclaredecoration{ticks}{ticks} +{% + \state{ticks}[width=+\pgfdecorationsegmentlength] + { + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfdecorationsegmentamplitude}} + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfdecorationsegmentamplitude}} + }% + \state{final} + { + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfdecorationsegmentamplitude}} + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfdecorationsegmentamplitude}} + \pgfpathmoveto{\pgfpointdecoratedpathlast} + }% +}% + + + + +\pgfdeclaredecoration{expanding waves}{initial} +{% + \state{initial}[width=+\pgfdecorationsegmentlength,next state=wave] + {}% + + \state{wave}[switch if less than=+\pgfdecorationsegmentlength to last, + width=+\pgfdecorationsegmentlength] + { + \pgfpathmoveto{ + \pgfpointadd + {\pgfqpoint{-\pgfdecoratedcompleteddistance}{0pt}}% + {\pgfpointpolar{\pgfdecorationsegmentangle}{+\pgfdecoratedcompleteddistance}}}% + \pgfpatharc{\pgfdecorationsegmentangle}{-\pgfdecorationsegmentangle}{+\pgfdecoratedcompleteddistance}% + }% + \state{last}[width=+0pt,next state=final] + { + \pgfpathmoveto{ + \pgfpointadd + {\pgfqpoint{-\pgfdecoratedcompleteddistance}{0pt}}% + {\pgfpointpolar{\pgfdecorationsegmentangle}{+\pgfdecoratedcompleteddistance}}}% + \pgfpatharc{\pgfdecorationsegmentangle}{-\pgfdecorationsegmentangle}{+\pgfdecoratedcompleteddistance}% + }% + \state{final} + { + \pgfpathmoveto{\pgfpointdecoratedpathlast} + }% +}% + + + + +\pgfdeclaredecoration{waves}{wave} +{% + \state{wave}[width=\pgfdecorationsegmentlength] + { + \pgftransformxshift{+\pgfdecorationsegmentlength} + \pgfpathmoveto{ + \pgfpointadd + {\pgfqpoint{-\pgfkeysvalueof{/pgf/decoration/start radius}}{0pt}}% + {\pgfpointpolar{\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}}}}% + \pgfpatharc{\pgfdecorationsegmentangle}{-\pgfdecorationsegmentangle}{\pgfkeysvalueof{/pgf/decoration/start radius}}% + }% + \state{final} + { + \pgfpathmoveto{\pgfpointdecoratedpathlast} + }% +}% + + + + +\pgfdeclaredecoration{border}{tick} +{% + \state{tick}[switch if less than=+\pgfdecorationsegmentlength to last, + width=+\pgfdecorationsegmentlength] + { + \pgfpathmoveto{\pgfpointorigin} + \pgfpathlineto{\pgfpointpolar{\pgfdecorationsegmentangle}{+\pgfdecorationsegmentamplitude}} + }% + \state{last}[width=+\pgfdecorationsegmentamplitude,next state=final] + { + \pgfpathmoveto{\pgfpointorigin} + \pgfpathlineto{\pgfpointpolar{\pgfdecorationsegmentangle}{+\pgfdecorationsegmentamplitude}} + }% + \state{final} + { + \pgfpathmoveto{\pgfpointdecoratedpathlast} + }% +}% + + + + + + + +\pgfdeclaredecoration{brace}{brace} +{% + \state{brace}[width=+\pgfdecoratedremainingdistance,next state=final] + { + \pgf@yc=\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance + \ifdim2\pgfdecorationsegmentamplitude>\pgf@yc + \pgf@yc=0.5\pgf@yc + \else + \pgf@yc=\pgfdecorationsegmentamplitude + \fi + \pgf@xc=\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance + \advance\pgf@xc-\pgfdecoratedremainingdistance + \ifdim-2\pgfdecorationsegmentamplitude<\pgf@xc + \pgf@xc=-0.5\pgf@xc + \else + \pgf@xc=\pgfdecorationsegmentamplitude + \fi + \pgfpathmoveto{\pgfpointorigin} + \pgfpathcurveto + {\pgfqpoint{.15\pgf@yc}{.3\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.5\pgf@yc}{.5\pgfdecorationsegmentamplitude}} + {\pgfqpoint{\pgf@yc}{.5\pgfdecorationsegmentamplitude}} + { + \pgftransformxshift{+\pgfdecorationsegmentaspect\pgfdecoratedremainingdistance} + \pgfpathlineto{\pgfqpoint{-\pgf@yc}{.5\pgfdecorationsegmentamplitude}} + \pgfpathcurveto + {\pgfqpoint{-.5\pgf@yc}{.5\pgfdecorationsegmentamplitude}} + {\pgfqpoint{-.15\pgf@yc}{.7\pgfdecorationsegmentamplitude}} + {\pgfqpoint{0\pgf@yc}{1\pgfdecorationsegmentamplitude}} + \pgfpathcurveto + {\pgfqpoint{.15\pgf@xc}{.7\pgfdecorationsegmentamplitude}} + {\pgfqpoint{.5\pgf@xc}{.5\pgfdecorationsegmentamplitude}} + {\pgfqpoint{\pgf@xc}{.5\pgfdecorationsegmentamplitude}} + } + { + \pgftransformxshift{+\pgfdecoratedremainingdistance} + \pgfpathlineto{\pgfqpoint{-\pgf@xc}{.5\pgfdecorationsegmentamplitude}} + \pgfpathcurveto + {\pgfqpoint{-.5\pgf@xc}{.5\pgfdecorationsegmentamplitude}} + {\pgfqpoint{-.15\pgf@xc}{.3\pgfdecorationsegmentamplitude}} + {\pgfqpoint{0pt}{0pt}} + } + }% + \state{final} + {}% +}% + + + + +\pgfdeclaredecoration{show path construction}{check for moveto}{% + \state{check for moveto}[width=0pt, next state=segment, + persistent precomputation={% + \begingroup% + \pgf@lib@decoraions@installinputsegmentpoints% + \ifx\pgfdecorationpreviousinputsegment\pgfdecorationinputsegmentmoveto% + \pgfdecoratedinputsegmentmovetocode% + \fi% + \endgroup% + }]{}% + \state{segment}[width=\pgfdecoratedinputsegmentremainingdistance, next state=check for moveto, + persistent precomputation={% + \begingroup% + \pgf@lib@decoraions@installinputsegmentpoints% + \csname pgfdecoratedinputsegment\pgfdecorationcurrentinputsegment code\endcsname% + \endgroup% + }]{}% + \state{final}{% + \egroup% + \begingroup% + \pgf@lib@decoraions@installinputsegmentpoints% + \csname pgfdecoratedinputsegment\pgfdecorationcurrentinputsegment code\endcsname% + \endgroup% + \bgroup% + }% +}% + +\pgfkeys{ + /pgf/decoration/.cd, + moveto code/.code=\def\pgfdecoratedinputsegmentmovetocode{#1}, + lineto code/.code=\def\pgfdecoratedinputsegmentlinetocode{#1}, + curveto code/.code=\def\pgfdecoratedinputsegmentcurvetocode{#1}, + closepath code/.code=\def\pgfdecoratedinputsegmentclosepathcode{#1} +}% + +\let\pgfdecoratedinputsegmentmovetocode\pgfutil@empty% +\let\pgfdecoratedinputsegmentlinetocode\pgfutil@empty% +\let\pgfdecoratedinputsegmentcurvetocode\pgfutil@empty% +\let\pgfdecoratedinputsegmentclosepathcode\pgfutil@empty% + +\def\pgf@lib@decoraions@installinputsegmentpoints{% + \let\pgfpointdecoratedinputsegmentfirst\pgf@decorate@inputsegment@first% + \let\pgfpointdecoratedinputsegmentlast\pgf@decorate@inputsegment@last% + \let\pgfpointdecoratedinputsegmentsupporta\pgf@decorate@inputsegment@supporta% + \let\pgfpointdecoratedinputsegmentsupportb\pgf@decorate@inputsegment@supportb% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.shapes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.shapes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..541a3ed78bbea0d7ed0c3319da0214bf12c5e406 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.shapes.code.tex @@ -0,0 +1,353 @@ + +\usepgfmodule{decorations}% + + + +\pgfkeys{ + /pgf/decoration/.cd, + shape/.initial=circle, + anchor/.initial=center, + shape start width/.initial=2.5pt, + shape start height/.initial=2.5pt, + shape end width/.initial=2.5pt, + shape end height/.initial=2.5pt, + shape sep/.store in=\pgf@lib@shapedecoration@sep, + shape sloped/.is if=pgfshapedecorationsloped, + shape scaled/.is if=pgfshapedecorationscaled, + shape evenly spread/.store in=\pgf@lib@shapedecoration@spread, + shape start size/.style={% + shape start width={#1}, + shape start height={#1}% + },% + shape end size/.style={% + shape end width={#1}, + shape end height={#1}% + },% + shape size/.style={% + shape start size={#1}, + shape end size={#1}% + },% + shape width/.style={% + shape start width={#1}, + shape end width={#1} + }, + shape height/.style={% + shape start height={#1}, + shape end height={#1} + } +}% + +\def\pgf@lib@shapedecoration@sep{.25cm, between centers}% +\newif\ifpgfshapedecorationsloped +\pgfshapedecorationslopedtrue +\newif\ifpgfshapedecorationscaled +\let\pgf@lib@shapedecoration@spread\pgfutil@empty% + + + + +\pgfdeclaredecoration{triangles}{init} +{% + \state{init}[width=+0pt,next state=triangle,persistent precomputation={ + \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/shape start width}} + \edef\pgf@lib@dec@ssw{\pgfmathresult pt} + \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/shape start height}/2} + \edef\pgf@lib@dec@ssh{\pgfmathresult pt} + }]{}% + \state{triangle}[switch if less than=+\pgfdecorationsegmentlength to last, + width=+\pgfdecorationsegmentlength] + { + \pgfpathmoveto{\pgfqpoint{0pt}{\pgf@lib@dec@ssh}} + \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{0pt}} + \pgfpathlineto{\pgfqpoint{0pt}{-\pgf@lib@dec@ssh}} + \pgfpathclose + }% + \state{last}[switch if less than=\pgf@lib@dec@ssw to skip, + width=\pgfdecoratedremainingdistance,next state=final] + { + \pgfpathmoveto{\pgfqpoint{0pt}{\pgf@lib@dec@ssh}} + \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{0pt}} + \pgfpathlineto{\pgfqpoint{0pt}{-\pgf@lib@dec@ssh}} + \pgfpathclose + }% + \state{skip}[width=\pgfdecoratedremainingdistance] + {}% + \state{final} + { + \pgfpathmoveto{\pgfpointdecoratedpathlast} + }% +}% + + + + + +\pgfdeclaredecoration{crosses}{init} +{% + \state{init}[width=+0pt,next state=crosses,persistent precomputation={ + \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/shape start width}/2} + \edef\pgf@lib@dec@ssw{\pgfmathresult pt} + \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/shape start height}/2} + \edef\pgf@lib@dec@ssh{\pgfmathresult pt} + }]{}% + \state{crosses}[switch if less than=+\pgfdecorationsegmentlength to last, + width=+\pgfdecorationsegmentlength] + { + \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}} + \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}} + \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}} + \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}} + }% + \state{last}[width=+\pgfdecoratedremainingdistance] + { + \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}} + \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}} + \pgfpathmoveto{\pgfqpoint{-\pgf@lib@dec@ssw}{-\pgf@lib@dec@ssh}} + \pgfpathlineto{\pgfqpoint{\pgf@lib@dec@ssw}{\pgf@lib@dec@ssh}} + }% + \state{final}{ + \pgfpathmoveto{\pgfpointdecoratedpathlast} + }% +}% + + + + + + + +\newif\ifpgf@lib@shapedecoration@betweenborders + +\edef\pgf@lib@shapedecoration@initialise{0pt}% + +\pgfdeclaredecoration{shape backgrounds}{initialise} +{% + \state{initialise} + [ + width=+\pgf@lib@shapedecoration@initialise, + next state=shape, + persistent precomputation= + { + \pgfutil@ifundefined{pgf@sh@bg@\pgfkeysvalueof{/pgf/decoration/shape}}{% + \pgferror{I do not know the shape `\pgfkeysvalueof{/pgf/decoration/shape}', + so I cannot use it in a decoration. Check if its library been loaded or if you + simply mistyped the name}}{}% + \pgfinterruptpath% + \pgfinterruptboundingbox% + \pgftransformreset% + \pgf@relevantforpicturesizetrue% + \pgfkeys{/pgf/inner sep=50pt, /pgf/minimum size=1pt}% + \setbox\pgfnodeparttextbox\hbox{}% + \let\pgf@sh@savedmacros\pgfutil@empty% + \let\pgf@sh@savedpoints\pgfutil@empty% + \csname pgf@sh@s@\pgfkeysvalueof{/pgf/decoration/shape}\endcsname% + \pgf@sh@savedpoints% + \pgf@sh@savedmacros% + \expandafter\gdef\expandafter\pgf@lib@shapedecoration@points\expandafter{\pgf@sh@savedpoints}% + \expandafter\gdef\expandafter\pgf@lib@shapedecoration@macros\expandafter{\pgf@sh@savedmacros}% + \csname pgf@sh@bg@\pgfkeysvalueof{/pgf/decoration/shape}\endcsname% + \pgf@x\pgf@picmaxx% + \pgf@y\pgf@picmaxy% + \advance\pgf@x-\pgf@picminx% + \advance\pgf@y-\pgf@picminy% + \xdef\pgf@lib@shapedecoration@shapepathsize{% + \noexpand\pgf@x\the\pgf@x% + \noexpand\pgf@y\the\pgf@y% + }% + \endpgfinterruptboundingbox% + \endpgfinterruptpath% + \edef\pgf@lib@shapedecoration@beforeshape{0pt}% + \edef\pgf@lib@shapedecoration@aftershape{0pt}% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/decoration/shape start width}}% + \edef\pgf@lib@shapedecoration@startwidth{\the\pgf@x}% + \edef\pgf@lib@shapedecoration@width{\the\pgf@x}% + \pgf@x-\pgf@x% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/decoration/shape end width}}% + \edef\pgf@lib@shapedecoration@widthchange{\the\pgf@x}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/decoration/shape start height}}% + \edef\pgf@lib@shapedecoration@initialheight{\the\pgf@y}% + \edef\pgf@lib@shapedecoration@height{\the\pgf@y}% + \pgf@y-\pgf@y% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/decoration/shape end height}}% + \edef\pgf@lib@shapedecoration@heightchange{\the\pgf@y}% + \ifx\pgf@lib@shapedecoration@spread\pgfutil@empty% + \def\pgf@lib@shapedecoration@borderstext{between borders}% + \afterassignment\pgf@lib@shapedecoration@setkeyword% + \expandafter\pgf@x\pgf@lib@shapedecoration@sep,\pgf@stop% + \edef\pgf@lib@shapedecoration@sep{\the\pgf@x}% + \else% + \def\pgf@lib@shapedecoration@borderstext{by borders}% + \afterassignment\pgf@lib@shapedecoration@setkeyword% + \expandafter\c@pgf@counta\pgf@lib@shapedecoration@spread,\pgf@stop% + \ifpgf@lib@shapedecoration@betweenborders% + \ifnum\c@pgf@counta>1\relax% + \advance\c@pgf@counta-1\relax% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/decoration/shape start width}}% + \ifpgfshapedecorationscaled% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/decoration/shape end width}}% + \else% + \advance\pgf@x\pgf@x% + \fi% + \pgf@x.5\pgf@x% + \multiply\pgf@x-\c@pgf@counta% + \advance\pgf@x\pgfdecoratedremainingdistance% + \divide\pgf@x\c@pgf@counta% + \pgf@x.9999\pgf@x% + \ifpgfshapedecorationscaled% + \pgf@xa\pgf@lib@shapedecoration@widthchange\relax% + \divide\pgf@xa\c@pgf@counta% + \edef\pgf@lib@shapedecoration@specialwidth{\the\pgf@xa}% + \fi% + \else% + \pgf@lib@shapedecoration@betweenbordersfalse% + \pgf@x\pgfdecoratedremainingdistance% + \ifnum\c@pgf@counta=1\relax% + \pgf@y.5\pgf@x% + \edef\pgf@lib@shapedecoration@initialise{\the\pgf@y}% + \else% + \advance\pgf@x5pt\relax% + \edef\pgf@lib@shapedecoration@initialise{\the\pgf@x}% + \fi% + \fi% + \else% + \pgf@x\pgfdecoratedremainingdistance% + \ifnum\c@pgf@counta>1\relax% + \advance\c@pgf@counta-1\relax% + \divide\pgf@x\c@pgf@counta\relax% + \else% + \ifnum\c@pgf@counta=1\relax% + \pgf@y.5\pgf@x% + \edef\pgf@lib@shapedecoration@initialise{\the\pgf@y}% + \else% + \advance\pgf@x5pt\relax% + \edef\pgf@lib@shapedecoration@initialise{\the\pgf@x}% + \fi% + \fi% + \fi% + \edef\pgf@lib@shapedecoration@sep{\the\pgf@x}% + \fi% + }] + {}% + \state{before shape} + [ + width=\pgf@lib@shapedecoration@beforeshape-1sp, + next state=shape, + persistent precomputation= + { + \ifpgfshapedecorationscaled% + \ifpgf@lib@shapedecoration@betweenborders% + \ifx\pgf@lib@shapedecoration@spread\pgfutil@empty% + \pgf@x\pgfdecoratedcompleteddistance% + \advance\pgf@x\pgfdecoratedremainingdistance% + \pgf@xa\pgf@lib@shapedecoration@startwidth\relax% + \pgf@xa.5\pgf@xa% + \advance\pgf@xa\pgfdecoratedcompleteddistance% + \pgf@xb\pgf@lib@shapedecoration@widthchange\relax% + \pgf@xb-.5\pgf@xb% + \advance\pgf@xb\pgf@x% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@xb}}% + \fi% + \else% + \pgf@y\pgfdecoratedcompleteddistance% + \advance\pgf@y\pgfdecoratedremainingdistance% + \pgfmathdivide@{\pgfmath@tonumber{\pgfdecoratedcompleteddistance}}{\pgfmath@tonumber{\pgf@y}}% + \fi% + \ifx\pgf@lib@shapedecoration@spread\pgfutil@empty% + \pgf@x\pgf@lib@shapedecoration@widthchange\relax% + \pgf@x\pgfmathresult\pgf@x% + \advance\pgf@x\pgf@lib@shapedecoration@startwidth\relax% + \else% + \ifpgf@lib@shapedecoration@betweenborders% + \pgf@x\pgf@lib@shapedecoration@width\relax% + \advance\pgf@x\pgf@lib@shapedecoration@specialwidth\relax% + \pgf@xa\pgf@x% + \advance\pgf@xa-\pgf@lib@shapedecoration@startwidth\relax% + \pgf@xb\pgf@lib@shapedecoration@widthchange\relax% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@xb}}% + \else% + \pgf@x\pgf@lib@shapedecoration@widthchange\relax% + \pgf@x\pgfmathresult\pgf@x% + \advance\pgf@x\pgf@lib@shapedecoration@startwidth\relax% + \fi% + \fi% + \edef\pgf@lib@shapedecoration@width{\the\pgf@x}% + \pgf@y\pgf@lib@shapedecoration@heightchange\relax% + \pgf@y\pgfmathresult\pgf@y% + \advance\pgf@y\pgf@lib@shapedecoration@initialheight\relax% + \edef\pgf@lib@shapedecoration@height{\the\pgf@y}% + \fi% + \ifpgf@lib@shapedecoration@betweenborders% + \pgf@x\pgf@lib@shapedecoration@width\relax% + \pgf@x.5\pgf@x% + \edef\pgf@lib@shapedecoration@beforeshape{\the\pgf@x}% + \else% + \def\pgf@lib@shapedecoration@beforeshape{0pt}% + \fi% + }] + {}% + \state{shape}[width=+0sp,next state=after shape] + { + \ifpgfshapedecorationsloped% + \else% + \pgftransformrotate{-\pgfdecoratedangle}% + \fi% + \pgf@lib@shapedecoration@shapepathsize% + \pgfutil@tempdima\pgf@x% + \pgfutil@tempdimb\pgf@y% + \pgf@xa\pgf@lib@shapedecoration@width\relax% + \pgf@xb\pgfutil@tempdima% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@xb}}% + \expandafter\pgftransformxscale\expandafter{\pgfmathresult}% + \pgf@ya\pgf@lib@shapedecoration@height\relax% + \pgf@yb\pgfutil@tempdimb% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@ya}}{\pgfmath@tonumber{\pgf@yb}}% + \expandafter\pgftransformyscale\expandafter{\pgfmathresult}% + \pgf@lib@shapedecoration@points% + \pgf@lib@shapedecoration@macros% + \pgftransformshift{% + \pgf@sh@reanchor{\pgfkeysvalueof{/pgf/decoration/shape}}{\pgfkeysvalueof{/pgf/decoration/anchor}}% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }% + \csname pgf@sh@bg@\pgfkeysvalueof{/pgf/decoration/shape}\endcsname% + }% + \state{after shape} + [ + width=\pgf@lib@shapedecoration@aftershape-1sp, + next state=sep, + persistent precomputation= + { + \ifpgf@lib@shapedecoration@betweenborders% + \pgf@x\pgf@lib@shapedecoration@width\relax% + \pgf@x.5\pgf@x% + \edef\pgf@lib@shapedecoration@aftershape{\the\pgf@x}% + \else% + \edef\pgf@lib@shapedecoration@aftershape{0pt}% + \fi% + } + ] + {}% + \state{sep}[width=\pgf@lib@shapedecoration@sep,next state=before shape, + persistent precomputation=\def\pgf@lib@shapedecoration@beforeshape{0pt}] + {}% + \state{final} + { + \pgfpathmoveto{\pgfpointdecoratedpathlast}% + }% +}% + +\def\pgf@lib@shapedecoration@setkeyword,{% + \pgfutil@ifnextchar\pgf@stop{\def\pgf@temp{}\pgf@lib@@@shapedecoration@setkeyword}{\pgf@lib@@shapedecoration@setkeyword}% +}% +\def\pgf@lib@@shapedecoration@setkeyword#1,{\def\pgf@temp{#1}\pgf@lib@@@shapedecoration@setkeyword}% +\def\pgf@lib@@@shapedecoration@setkeyword\pgf@stop{% + \ifx\pgf@temp\pgf@lib@shapedecoration@borderstext% + \pgf@lib@shapedecoration@betweenborderstrue% + \else% + \pgf@lib@shapedecoration@betweenbordersfalse% + \fi% +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.text.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.text.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..7e7ee03ae532231209a6065392d0a848f8674c73 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/decorations/pgflibrarydecorations.text.code.tex @@ -0,0 +1,328 @@ + +\usepgfmodule{decorations}% + + + +\pgfkeys{ + /pgf/decoration/.cd, + text/.store in=\pgfdecorationtext,% + text color/.store in=\pgf@lib@decorationtextcolor,% + text format delimiters/.code={\expandafter\pgfsetdecoratetextformatdelimiters#1}, + text align/.code={\pgfkeys{/pgf/decoration/text align/.cd,#1}}, + text align/.cd, + align/.initial=left, + left/.style={/pgf/decoration/text align/align=left}, + right/.style={/pgf/decoration/text align/align=right}, + center/.style={/pgf/decoration/text align/align=center}, + left indent/.initial=0pt, + right indent/.initial=0pt, + fit to path/.is if=pgf@lib@dec@text@fit, + fit to path stretching spaces/.default=true, + fit to path stretching spaces/.code={% + \csname pgf@lib@dec@text@fit#1\endcsname% + \csname pgf@lib@dec@text@stretch@spaces#1\endcsname% + }% +}% + +\newif\ifpgf@lib@dec@text@scan@space +\newif\ifpgf@lib@dec@text@stretch@spaces +\newif\ifpgf@lib@dec@text@fit + +\def\pgf@lib@decorationtextcolor{black}% + +\def\pgf@lib@dec@text@left@text{left}% +\def\pgf@lib@dec@text@right@text{right}% +\def\pgf@lib@dec@text@right@center{center}% + + +\pgfdeclaredecoration{text along path}{initial}{% + \state{initial}[ + width=+0pt, next state=left indent, + persistent precomputation={% + \edef\pgf@lib@dec@text@indent@left{\pgfkeysvalueof{/pgf/decoration/text align/left indent}}% + \edef\pgf@lib@dec@text@indent@right{\pgfkeysvalueof{/pgf/decoration/text align/right indent}}% + \edef\pgf@lib@dec@text@align{\pgfkeysvalueof{/pgf/decoration/text align/align}}% + \pgfdecoratedremainingdistance=\pgfdecoratedpathlength% + \advance\pgfdecoratedremainingdistance by-\pgf@lib@dec@text@indent@right\relax% + \edef\pgfdecoratedpathlength{\the\pgfdecoratedremainingdistance}% + \pgf@lib@dec@text@getwidth% + \pgf@x=\pgf@lib@dec@text@width\relax% + \pgf@y=\pgfdecoratedremainingdistance% + \ifpgf@lib@dec@text@fit% + \advance\pgf@y by-\pgf@lib@dec@text@indent@left\relax% + \advance\pgf@y by-\pgf@x% + \ifpgf@lib@dec@text@stretch@spaces% + \def\pgf@lib@dec@text@character@shift{0pt}% + \divide\pgf@y by\pgf@lib@dec@space@count\relax% + \edef\pgf@lib@dec@text@space@shift{\the\pgf@y}% + \else% + \c@pgf@counta=\pgf@lib@dec@character@count\relax% + \advance\c@pgf@counta by-1\relax% + \divide\pgf@y by\c@pgf@counta\relax% + \edef\pgf@lib@dec@text@character@shift{\the\pgf@y}% + \def\pgf@lib@dec@text@space@shift{0pt}% + \fi% + \ifdim\pgf@y<0pt\relax% + \pgf@lib@dec@text@fitfalse% + \pgf@lib@dec@text@stretch@spacesfalse% + \def\pgf@lib@dec@text@character@shift{0pt}% + \def\pgf@lib@dec@text@space@shift{0pt}% + \fi% + \else% + \def\pgf@lib@dec@text@character@shift{0pt}% + \def\pgf@lib@dec@text@space@shift{0pt}% + \ifx\pgf@lib@dec@text@align\pgf@lib@dec@text@left@text% + \else% + \ifx\pgf@lib@dec@text@align\pgf@lib@dec@text@right@text% + \advance\pgf@y by-\pgf@x% + \edef\pgf@lib@dec@text@indent@left{\the\pgf@y}% + \else% + \advance\pgf@y by-\pgf@x% + \advance\pgf@y by-\pgf@lib@dec@text@indent@left\relax% + \pgf@y=0.5\pgf@y% + \advance\pgf@y by\pgf@lib@dec@text@indent@left\relax% + \edef\pgf@lib@dec@text@indent@left{\the\pgf@y}% + \fi% + \fi% + \fi% + \let\pgfdecorationrestoftext=\pgfdecorationtext% + }]{}% +\state{left indent}[width=+\pgf@lib@dec@text@indent@left, next state=scan]{}% +\state{scan}[ + width=+0pt, + next state=before typeset, + persistent precomputation={ + \pgf@lib@dec@text@scanchar% + \ifvoid\pgf@lib@dec@text@box% + \setbox\pgf@lib@dec@text@box\hbox{}% + \wd\pgf@lib@dec@text@box16383pt\relax% + \fi% +}]{}% +\state{before typeset}[width=+.5\wd\pgf@lib@dec@text@box, next state=typeset]{}% +\state{typeset}[width=+0pt, next state=after typeset] +{% + \pgftransformxshift{+-.5\wd\pgf@lib@dec@text@box}% + \setbox\pgf@hbox\hbox{\copy\pgf@lib@dec@text@box}% + \pgfqboxsynced\pgf@hbox% +}% +\state{after typeset}[width=+.5\wd\pgf@lib@dec@text@box, next state=shift, + persistent precomputation={% + \ifpgf@lib@dec@text@fit% + \ifpgf@lib@dec@text@stretch@spaces% + \ifpgf@lib@dec@text@scan@space% + \let\pgf@lib@dec@text@shift=\pgf@lib@dec@text@space@shift% + \else% + \def\pgf@lib@dec@text@shift{0pt}% + \fi% + \else% + \let\pgf@lib@dec@text@shift=\pgf@lib@dec@text@character@shift% + \fi% + \else% + \def\pgf@lib@dec@text@shift{0pt}% + \fi% + }]{}% +\state{shift}[width=+\pgf@lib@dec@text@shift, next state=scan]{}% +\state{final}{}% +}% + + +\def\pgfsetdecoratetextformatdelimiters#1#2{% + \def\pgf@lib@dec@text@formatchar{#1}% + \def\pgf@test{#2}% + \ifx\pgf@test\pgfutil@empty% + \def\pgf@lib@dec@text@collectformat##1#1{% + \pgf@lib@dec@text@@collectformat##1\pgf@stop}% + \else% + \def\pgf@lib@dec@text@collectformat##1#2{% + \pgf@lib@dec@text@@collectformat##1\pgf@stop}% + \fi% +}% + +\pgfsetdecoratetextformatdelimiters{|}{}% + +\newbox\pgf@lib@dec@text@box +\newif\ifpgf@lib@decorate@textmathmode + +\let\pgfdecorationtext=\pgfutil@empty +\let\pgfdecorationrestoftext=\pgfutil@empty% +\let\pgf@lib@dec@text@format=\pgfutil@empty + +\def\pgf@lib@dec@text@scanchar{% + \pgf@lib@dec@text@scan@spacefalse% + \ifx\pgfdecorationrestoftext\pgfutil@empty% + \let\pgf@lib@dec@text@char\pgfutil@empty% + \setbox\pgf@lib@dec@text@box\box\pgfutil@voidb@x% + \let\pgf@next\relax% + \else\ifx\pgfdecorationrestoftext\pgf@lib@dec@mathshift% + \ifpgf@lib@decorate@textmathmode% + \pgf@lib@decorate@textmathmodefalse% + \fi% + \let\pgf@lib@dec@text@char\pgfutil@empty% + \setbox\pgf@lib@dec@text@box\box\pgfutil@voidb@x% + \let\pgf@next\relax% + \else + \let\pgf@next\pgf@lib@dec@text@@scanchar% + \fi\fi% + \pgf@next}% + +\def\pgf@lib@dec@text@@scanchar{% + \expandafter\pgf@lib@dec@text@@@scanchar\pgfdecorationrestoftext\pgf@stop}% + +\def\pgf@lib@dec@text@@@scanchar{% + \futurelet\pgf@lib@dec@lettoken% + \pgf@lib@dec@text@@@@scanchar}% + +\def\pgf@lib@dec@text@@@@scanchar{% + \ifx\pgf@lib@dec@lettoken\pgfutil@sptoken% + \let\pgf@next\pgf@lib@dec@text@insertspace% + \else% + \let\pgf@next\pgf@lib@dec@text@@@@@scanchar% + \fi% + \pgf@next}% + +\def\pgf@lib@dec@text@@@@@scanchar{% + \pgfutil@ifnextchar\bgroup{\pgf@lib@dec@text@collectgroup}% + {\pgf@lib@dec@text@@@@@@scanchar}}% + +\def\pgf@lib@dec@text@collectgroup#1{% + \def\pgf@lib@dec@text@char{#1}% + \pgf@lib@dec@text@collectrestoftext}% + +\def\pgf@lib@dec@text@@@@@@scanchar#1{% + \ifx#1\pgf@stop% + \pgf@lib@dec@text@box\box\pgfutil@voidb@x% + \let\pgf@next\pgf@lib@dec@text@endoftext% + \else% + \def\pgf@lib@dec@text@char{#1}% + \ifx#1\space% + \let\pgf@next\pgf@lib@dec@text@collectrestoftext% + \else% + \ifx#1\ % + \let\pgf@next\pgf@lib@dec@text@collectrestoftext% + \else% + \ifx\pgf@lib@dec@text@char\pgf@lib@dec@text@formatchar% + \let\pgf@next\pgf@lib@dec@text@collectformat% + \else% + \expandafter\ifcat\noexpand#1\relax% + \let\pgf@next\pgf@lib@dec@text@expandcs% + \else% + \ifnum\catcode`#1=3\relax% + \ifpgf@lib@decorate@textmathmode% + \pgf@lib@decorate@textmathmodefalse% + \else% + \pgf@lib@decorate@textmathmodetrue% + \fi% + \let\pgf@next\pgf@lib@dec@text@@@scanchar% + \else% + \let\pgf@next\pgf@lib@dec@text@collectrestoftext% + \fi% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgf@next% +}% + +\def\pgf@lib@dec@text@@collectformat{% + \pgfutil@ifnextchar+{\pgf@lib@dec@text@addtoformat}{\pgf@lib@dec@text@setformat}}% + +\def\pgf@lib@dec@text@setformat#1\pgf@stop{% + \def\pgf@lib@dec@text@format{#1}% + \pgf@lib@dec@text@@@scanchar% +}% + +\def\pgf@lib@dec@text@addtoformat+#1\pgf@stop{% + \expandafter\def\expandafter\pgf@lib@dec@text@format\expandafter{\pgf@lib@dec@text@format#1}% + \pgf@lib@dec@text@@@scanchar% +}% + +\def\pgf@lib@dec@text@insertspace{% + \pgf@lib@dec@text@scan@spacetrue% + \pgfutil@ifnextchar\bgroup{\pgf@lib@dec@text@@insertspacegrp}% + {\pgf@lib@dec@text@@insertspace}}% + +\def\pgf@lib@dec@text@@insertspacegrp#1{% + \pgf@lib@dec@text@@@@@@scanchar\space{#1}}% + +\def\pgf@lib@dec@text@@insertspace#1{% + \pgf@lib@dec@text@@@@@@scanchar\space#1}% + +\def\pgf@lib@dec@text@expandcs{% + \expandafter\expandafter\expandafter\pgf@lib@dec@text@@@@@scanchar% + \pgf@lib@dec@text@char}% + +\def\pgf@lib@dec@text@endoftext{% + \let\pgfdecorationrestoftext\pgfutil@empty% + \let\pgf@lib@dec@text@char\pgfutil@empty% +}% +\def\pgf@lib@dec@text@collectrestoftext{% + \pgf@lib@dec@text@dobox% + \futurelet\pgf@lib@dec@text@lettoken% + \pgf@lib@dec@text@@collectrestoftext}% + +\def\pgf@lib@dec@text@@collectrestoftext{% + \ifx\bgroup\pgf@lib@dec@text@lettoken% + \let\pgf@next\pgf@lib@dec@text@@@collectrestoftextgrp% + \else% + \let\pgf@next\pgf@lib@dec@text@@@collectrestoftext% + \fi% + \pgf@next}% + +\def\pgf@lib@dec@text@@@collectrestoftextgrp#1#2\pgf@stop{\def\pgfdecorationrestoftext{{#1}#2}% +}% + +\def\pgf@lib@dec@text@@@collectrestoftext#1\pgf@stop{\def\pgfdecorationrestoftext{#1}}% + +{% + \catcode`\$3 % + \gdef\pgf@lib@dec@mathshift{$}% + \catcode`\$9 $% +}% + +\def\pgf@lib@dec@text@dobox{% + \setbox\pgf@lib@dec@text@box\hbox{% + \pgfinterruptpicture% + \begingroup% + \pgfsetcolor{\pgf@lib@decorationtextcolor}% + \ifpgf@lib@decorate@textmathmode\pgf@lib@dec@mathshift\fi% + \pgf@lib@dec@text@format\relax% + \pgf@lib@dec@text@char% + \ifpgf@lib@decorate@textmathmode\pgf@lib@dec@mathshift\fi% + \endgroup% + \endpgfinterruptpicture% + }% +}% + +\def\pgf@lib@dec@text@getwidth{% + \begingroup% + \let\c@pgf@lib@dec@characters=\c@pgf@counta% + \let\c@pgf@lib@dec@spaces=\c@pgf@countb% + \let\pgfdecorationrestoftext=\pgfdecorationtext% + \c@pgf@lib@dec@spaces=0\relax% + \c@pgf@lib@dec@characters=0\relax% + \pgfmathloop% + \pgf@lib@dec@text@scanchar% + \ifvoid\pgf@lib@dec@text@box% + \else% + \setbox\pgf@hbox=\hbox{{% + \unhbox\pgf@hbox% + \unhbox\pgf@lib@dec@text@box% + }}% + \advance\c@pgf@lib@dec@characters by1\relax% + \ifpgf@lib@dec@text@scan@space% + \advance\c@pgf@lib@dec@spaces by1\relax% + \fi% + \repeatpgfmathloop% + \global\pgf@x=\the\wd\pgf@hbox% + \xdef\pgf@lib@dec@temp{\the\c@pgf@lib@dec@characters}% + \xdef\pgf@lib@dec@@temp{\the\c@pgf@lib@dec@spaces}% + \endgroup% + \edef\pgf@lib@dec@text@width{\the\pgf@x}% + \let\pgf@lib@dec@character@count=\pgf@lib@dec@temp% + \let\pgf@lib@dec@space@count=\pgf@lib@dec@@temp% +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/luamath/pgflibraryluamath.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/luamath/pgflibraryluamath.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..cbeef8b8c73041113ea5d4ecc6d4aa85d1763467 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/luamath/pgflibraryluamath.code.tex @@ -0,0 +1,365 @@ + + +\edef\pgfliblua@oldcatcodedoublequote{\the\catcode`\"}% +\catcode`\"=12 + +\let\pgfutil@ifluatex\iffalse +\begingroup\expandafter\expandafter\expandafter\endgroup +\expandafter\ifx\csname directlua\endcsname\relax +\else + \expandafter\let\csname pgfutil@ifluatex\expandafter\endcsname + \csname iftrue\endcsname +\fi + +\pgfutil@ifluatex + \let\pgfutil@directlua\directlua + \pgfutil@directlua{% + tex.enableprimitives('pgfutil@',{'luaescapestring'})}% +\else + \def\pgfutil@directlua#1{}% + \def\pgfutil@luaescapestring#1{}% +\fi + +\pgfutil@directlua{% + pgfluamathfunctions = require("pgf.luamath.functions") + pgfluamathparser = require("pgf.luamath.parser")}% + + +\pgfkeys{ + /pgf/trig format/deg/.add code={}{\directlua{pgfluamathfunctions.setTrigFormat("deg")}\aftergroup\pgfmath@settrigformat}, + /pgf/trig format/rad/.add code={}{\directlua{pgfluamathfunctions.setTrigFormat("rad")}\aftergroup\pgfmath@settrigformat}, +}% +\pgfmathiftrigonometricusesdeg{% + \pgfkeys{/pgf/trig format/deg}% +}{% + \pgfkeys{/pgf/trig format/rad}% +}% + +\def\pgfmath@settrigformat{% + \pgfmathiftrigonometricusesdeg{% + \directlua{pgfluamathfunctions.setTrigFormat("deg")}% + }{% + \directlua{pgfluamathfunctions.setTrigFormat("rad")}% + }% +}% + +\let\pgfmathsetseed@pgfbasic = \pgfmathsetseed +\def\pgfmathsetseed#1{% + \pgfmathsetseed@pgfbasic{#1}% + \directlua{pgfluamathfunctions.setRandomSeed(pgfluamathfunctions.tonumber("\pgfmathresult"))}% +}% + +\let\pgfmathnotifynewdeclarefunction@orig=\pgfmathnotifynewdeclarefunction +\def\pgfmathnotifynewdeclarefunction#1#2#3{% + \pgfmathnotifynewdeclarefunction@orig{#1}{#2}{#3}% + \begingroup + \toks0={#3}% + \xdef\pgf@marshal@glob{\the\toks0 }% + \endgroup + \pgfutil@command@to@string\pgf@marshal@glob\pgf@marshal + \expandafter\pgfutilifcontainsmacro\expandafter{\pgf@marshal}{% + \def\pgf@temp{1}% + }{% + \def\pgf@temp{0}% + }% + \if1\pgf@temp + \directlua{pgfluamathparser.pushLocalExpressionFunction(% + "\pgfutil@luaescapestring{#1}",% + #2,% + "functionMustBeEvaluatedInTeX")}% + \else + \directlua{pgfluamathparser.pushLocalExpressionFunction(% + "\pgfutil@luaescapestring{#1}",% + #2,% + "\pgfutil@luaescapestring{#3}")}% + \fi + \aftergroup\pgfluamathparse@pop@local@function +}% + +\def\pgfluamathparse@pop@local@function{% + \directlua{pgfluamathparser.popLocalExpressionFunction()}% +}% + + + + +\newif\ifpgfluamathshowerrormessage + +\newif\ifpgfluamathenableTeXfallback + +\newif\ifpgfluamathcomputationactive +\newif\ifpgfluamathparseractive + +\def\pgfluamath@makecomputationactive{% + \ifpgfluamathcomputationactive + \else + \pgfluamath@checkuninstallcmd% + \pgfluamath@install% + \pgfluamathcomputationactivetrue + \fi}% + +\def\pgfluamath@makecomputationinactive{% + \ifpgfluamathcomputationactive + \pgfluamath@uninstall% + \pgfluamathcomputationactivefalse + \fi}% + +\let\pgfluamath@pgfmathparse\pgfmathparse +\def\pgfluamath@makeparseractive{% + \ifpgfluamathparseractive + \else + \let\pgfluamath@pgfmathparse\pgfmathparse + \let\pgfmathparse\pgfluamathparse + \let\pgfmath@iftrue=\pgfmathluamath@iftrue + \pgfluamathparseractivetrue + \fi}% + +\let\pgfmath@iftrue@basic=\pgfmath@iftrue + +\def\pgfluamath@makeparserinactive{% + \ifpgfluamathparseractive + \let\pgfmathparse\pgfluamath@pgfmathparse + \let\pgfmath@iftrue=\pgfmath@iftrue@basic + \pgfluamathparseractivefalse + \fi}% + +\pgfqkeys{/pgf}{% + luamath/.is choice, + luamath/only computation/.code={% + \pgfutil@ifluatex + \pgfluamath@makecomputationactive + \pgfluamath@makeparserinactive + \else + \pgfmath@error{Sorry, you need the luaTeX engine to use the + luamath library}{}% + \fi}, + luamath/parser and computation/.code={% + \pgfutil@ifluatex + \pgfluamath@makecomputationactive + \pgfluamath@makeparseractive + \else + \pgfmath@error{Sorry, you need the luaTeX engine to use the + luamath library}{}% + \fi}, + luamath/off/.code={% + \pgfluamath@makecomputationinactive + \pgfluamath@makeparserinactive}, + luamath/.default=only computation, + luamath/parser/.code={% + \pgfutil@ifluatex + \pgfluamath@makeparseractive + \else + \pgfmath@error{Sorry, you need the luaTeX engine to use the + luamath library}{}% + \fi + }, + luamath/output format/.is choice, + luamath/output format/fixed/.code= {\def\pgfluamath@outputformat@choice{0}}, + luamath/output format/float/.code= {\def\pgfluamath@outputformat@choice{1}}, + luamath/output format/fixed, + luamath/show error message/.is if=pgfluamathshowerrormessage, + luamath/enable TeX fallback/.is choice, + luamath/enable TeX fallback/true/.code={\pgfluamathenableTeXfallbacktrue\pgfluamathshowerrormessagefalse}, + luamath/enable TeX fallback/false/.code={\pgfluamathenableTeXfallbackfalse\pgfluamathshowerrormessagetrue}, + luamath/enable TeX fallback/.default=true, + luamath/enable TeX fallback=true, +}% + +\def\pgfluamath@uninstall@appendcmd#1{% + \expandafter\gdef\expandafter\pgfluamath@uninstall\expandafter{% + \pgfluamath@uninstall #1}}% + +\def\pgfluamath@checkuninstallcmd{% + \pgfutil@ifundefined{pgfluamath@uninstall}{% + \global\let\pgfluamath@uninstall=\pgfutil@empty + }{% + \def\pgfluamath@uninstall@appendcmd##1{}% + \def\pgfluamath@prepareuninstallcmd##1{}% + }% +}% + +\def\pgfluamath@prepareuninstallcmd#1{% + \expandafter\global\expandafter\let + \csname pgfluamath@backup@\string#1\endcsname=#1% + \expandafter\gdef\expandafter\pgfluamath@uninstall\expandafter{% + \pgfluamath@uninstall + \expandafter\let\expandafter#1\csname pgfluamath@backup@\string#1\endcsname}% +}% + +\def\pgfluamath@install@function#1=#2{% + \pgfluamath@prepareuninstallcmd{#1}% + \let#1=#2% +}% + +\def\pgfluamath@install{% + \pgfluamath@install@function\pgfmathadd@=\pgfluamathadd@% + \pgfluamath@install@function\pgfmathsubtract@=\pgfluamathsubtract@% + \pgfluamath@install@function\pgfmathneg@=\pgfluamathneg@% + \pgfluamath@install@function\pgfmathmultiply@=\pgfluamathmultiply@% + \pgfluamath@install@function\pgfmath@iftrue=\pgfmathluamath@iftrue% + \pgfluamath@install@function\pgfmathdivide@=\pgfluamathdivide@% + \pgfluamath@install@function\pgfmathfactorial@=\pgfluamathfactorial@% + \pgfluamath@install@function\pgfmathsqrt@=\pgfluamathsqrt@% + \pgfluamath@install@function\pgfmathe@=\pgfluamathe@% + \pgfluamath@install@function\pgfmathexp@=\pgfluamathexp@% + \pgfluamath@install@function\pgfmathln@=\pgfluamathln@% + \pgfluamath@install@function\pgfmathlogten@=\pgfluamathlogten@% + \pgfluamath@install@function\pgfmathabs@=\pgfluamathabs@% + \pgfluamath@install@function\pgfmathmod@=\pgfluamathmod@% + \pgfluamath@install@function\pgfmathMod@=\pgfluamathMod@% + \pgfluamath@install@function\pgfmathround@=\pgfluamathround@% + \pgfluamath@install@function\pgfmathfloor@=\pgfluamathfloor@% + \pgfluamath@install@function\pgfmathceil@=\pgfluamathceil@% + \pgfluamath@install@function\pgfmathgcd@=\pgfluamathgcd@% + \pgfluamath@install@function\pgfmathisprime@=\pgfluamathisprime@% + \pgfluamath@install@function\pgfmathpi@=\pgfluamathpi@% + \pgfluamath@install@function\pgfmathrad@=\pgfluamathrad@% + \pgfluamath@install@function\pgfmathdeg@=\pgfluamathdeg@% + \pgfluamath@install@function\pgfmathsin@=\pgfluamathsin@% + \pgfluamath@install@function\pgfmathcos@=\pgfluamathcos@% + \pgfluamath@install@function\pgfmathtan@=\pgfluamathtan@% + \pgfluamath@install@function\pgfmathsec@=\pgfluamathsec@% + \pgfluamath@install@function\pgfmathcosec@=\pgfluamathcosec@% + \pgfluamath@install@function\pgfmathcot@=\pgfluamathcot@% + \pgfluamath@install@function\pgfmathasin@=\pgfluamathasin@% + \pgfluamath@install@function\pgfmathacos@=\pgfluamathacos@% + \pgfluamath@install@function\pgfmathatan@=\pgfluamathatan@% + \pgfluamath@install@function\pgfmathatantwo@=\pgfluamathatantwo@% + \pgfluamath@install@function\pgfmathmax@=\pgfluamathmax@% + \pgfluamath@install@function\pgfmathmin@=\pgfluamathmin@% + \pgfluamath@install@function\pgfmathrand@=\pgfluamathrand@ + \pgfluamath@install@function\pgfmathrand=\pgfluamathrand@ + \pgfluamath@install@function\pgfmathrnd@=\pgfluamathrnd@ + \pgfluamath@install@function\pgfmathrnd=\pgfluamathrnd@ + \pgfluamath@install@function\pgfmathreciprocal=\pgfluamathreciprocal% + \pgfluamath@install@function\pgfpointnormalised=\pgfluamathpointnormalised +}% + +\def\pgfluamathgetresult#1{% + \edef\pgfmathresult{\pgfutil@directlua{tex.print(-1,#1)}}}% + +\def\pgfmathluamath@iftrue{% + \if 0\pgfluamath@outputformat@choice + \let\pgfmathluamath@@iftrue@v=\pgfluamathone + \else + \let\pgfmathluamath@@iftrue@v=\pgfluamathfloatone + \fi + \pgfmathluamath@iftrue@ +}% +\def\pgfluamathone{1.0}% +\def\pgfluamathfloatone{1Y1.0e+00]}% +\def\pgfmathluamath@iftrue@#1#2{% + \ifx\pgfmathresult\pgfmathluamath@@iftrue@v + \def\pgfmath@next{#1}% + \else + \def\pgfmath@next{#2}% + \fi + \pgfmath@next +}% + +\def\pgfluamathpi@{% + \pgfluamathgetresult{pgfluamathfunctions.pi()}}% +\def\pgfluamathe@{% + \pgfluamathgetresult{pgfluamathfunctions.e()}}% +\def\pgfluamathadd@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.add(#1,#2)}}% +\def\pgfluamathsubtract@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.subtract(#1,#2)}}% +\def\pgfluamathneg@#1{% + \pgfluamathgetresult{pgfluamathfunctions.neg(#1)}}% +\def\pgfluamathmultiply@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.multiply(#1,#2)}}% +\def\pgfluamathdivide@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.divide(#1,#2)}}% +\def\pgfluamathabs@#1{% + \pgfluamathgetresult{pgfluamathfunctions.abs(#1)}}% +\def\pgfluamathround@#1{% + \pgfluamathgetresult{pgfluamathfunctions.round(#1)}}% +\def\pgfluamathfloor@#1{% + \pgfluamathgetresult{pgfluamathfunctions.floor(#1)}}% +\def\pgfluamathceil@#1{% + \pgfluamathgetresult{pgfluamathfunctions.ceil(#1)}}% +\def\pgfluamathgcd@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.gcd(#1,#2)}}% +\def\pgfluamathisprime@#1{% + \pgfluamathgetresult{pgfluamathfunctions.isprime(#1)}}% +\def\pgfluamathmax@#1{% + \pgfluamathgetresult{% + math.max(pgfluamathfunctions.split_braces_to_explist("#1"))}}% +\def\pgfluamathmin@#1{% + \pgfluamathgetresult{% + math.min(pgfluamathfunctions.split_braces_to_explist("#1"))}}% +\def\pgfluamathsin@#1{% + \pgfluamathgetresult{pgfluamathfunctions.Sin(#1)}}% +\def\pgfluamathcos@#1{% + \pgfluamathgetresult{pgfluamathfunctions.Cos(#1)}}% +\def\pgfluamathtan@#1{% + \pgfluamathgetresult{pgfluamathfunctions.Tan(#1)}}% +\def\pgfluamathmod@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.mod(#1,#2)}}% +\def\pgfluamathMod@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.Mod(#1,#2)}}% +\def\pgfluamathrad@#1{% + \pgfluamathgetresult{pgfluamathfunctions.rad(#1)}}% +\def\pgfluamathdeg@#1{% + \pgfluamathgetresult{pgfluamathfunctions.deg(#1)}}% +\def\pgfluamathatan@#1{% + \pgfluamathgetresult{pgfluamathfunctions.aTan(#1)}}% +\def\pgfluamathatantwo@#1#2{% + \pgfluamathgetresult{pgfluamathfunctions.aTan2(#1,#2)}}% +\def\pgfluamathasin@#1{% + \pgfluamathgetresult{pgfluamathfunctions.aSin(#1)}}% +\def\pgfluamathacos@#1{% + \pgfluamathgetresult{pgfluamathfunctions.aCos(#1)}}% +\def\pgfluamathcot@#1{% + \pgfluamathgetresult{1/pgfluamathfunctions.Tan(#1)}}% +\def\pgfluamathsec@#1{% + \pgfluamathgetresult{1/pgfluamathfunctions.Cos(#1)}}% +\def\pgfluamathcosec@#1{% + \pgfluamathgetresult{1/pgfluamathfunctions.Sin(#1)}}% +\def\pgfluamathexp@#1{% + \pgfluamathgetresult{pgfluamathfunctions.exp(#1)}}% +\def\pgfluamathln@#1{% + \pgfluamathgetresult{pgfluamathfunctions.log(#1)}}% +\def\pgfluamathlogten@#1{% + \pgfluamathgetresult{pgfluamathfunctions.log10(#1)}}% +\def\pgfluamathsqrt@#1{% + \pgfluamathgetresult{pgfluamathfunctions.sqrt(#1)}}% +\def\pgfluamathrnd@{% + \pgfluamathgetresult{pgfluamathfunctions.rnd()}}% +\def\pgfluamathrand@{% + \pgfluamathgetresult{pgfluamathfunctions.rand(-1,1)}}% +\def\pgfluamathfactorial@#1{% + \pgfluamathgetresult{pgfluamathfunctions.factorial(#1)}}% +\def\pgfluamathreciprocal#1{% + \pgfluamathgetresult{1/#1}}% + +\def\pgfluamathpointnormalised#1{% + \pgf@process{#1}% + \pgfutil@directlua{% + pgfluamathfunctions.pointnormalised(% + \pgf@sys@tonumber{\pgf@x},\pgf@sys@tonumber{\pgf@y})}% + \ignorespaces}% + + +\newif\ifpgfluamathunitsdeclared + +\newif\ifpgfluamathusedTeXfallback + +\def\pgfluamathparse#1{% + \pgfluamathusedTeXfallbackfalse + \pgfutil@directlua{pgfluamathparser.texCallParser( + "\pgfutil@luaescapestring{#1}", + \pgfluamath@outputformat@choice, + \ifpgfluamathshowerrormessage true\else false\fi)% + }% + \ifx\pgfmathresult\pgfutil@empty + \ifpgfluamathenableTeXfallback + \pgfluamathusedTeXfallbacktrue + \pgfluamath@pgfmathparse{#1}% + \fi + \fi +}% + +\catcode`\"=\pgfliblua@oldcatcodedoublequote +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..d5476b114d307ea0beab14e1d53275de374dbbd6 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.code.tex @@ -0,0 +1,898 @@ + +\ProvidesFileRCS{pgflibraryarrows.code.tex} + + + +\pgfarrowsdeclare{square bracket}{square bracket} +{ + \pgfutil@tempdima=1pt% + \advance\pgfutil@tempdima by1.25\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdima} + \pgfarrowsrightextend{+.5\pgflinewidth} +} +{ + \pgfutil@tempdima=2pt% + \advance\pgfutil@tempdima by1.5\pgflinewidth% + \pgfutil@tempdimb=\pgfutil@tempdima% + \advance\pgfutil@tempdimb by\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfsetbuttcap + \pgfpathmoveto{\pgfqpoint{-.5\pgfutil@tempdimb}{-1\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0pt}{-1\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0pt}{\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-.5\pgfutil@tempdimb}{\pgfutil@tempdima}} + \pgfusepathqstroke +}% +\pgfdeclarearrow{name=[-], means=square bracket}% + +\pgfarrowsdeclarereversed{]}{[}{[}{]}% + + + +\pgfarrowsdeclare{(}{)} +{ + \pgfutil@tempdima=2pt% + \advance\pgfutil@tempdima by1.5\pgflinewidth% + \pgfutil@tempdimb=0.0625\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} + \pgfutil@tempdimb=0.5\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=2pt% + \advance\pgfutil@tempdima by1.5\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfpathmoveto{\pgfqpoint{-.5\pgfutil@tempdima}{-1\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{.25\pgfutil@tempdima}{-.5\pgfutil@tempdima}} + {\pgfqpoint{.25\pgfutil@tempdima}{.5\pgfutil@tempdima}} + {\pgfqpoint{-.5\pgfutil@tempdima}{\pgfutil@tempdima}} + \pgfusepathqstroke +}% + +\pgfarrowsdeclarereversed{)}{(}{(}{)}% + + + + + +\pgfarrowsdeclare{angle 90}{angle 90} +{ + \pgfutil@tempdima=0.3pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfutil@tempdimb=5.5\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=.5\pgfutil@tempdima\advance\pgfutil@tempdimb by0.707\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.3pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetmiterjoin + \pgfpathmoveto{\pgfqpoint{-5.5\pgfutil@tempdima}{-6\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-5.5\pgfutil@tempdima}{6\pgfutil@tempdima}} + \pgfusepathqstroke +}% + +\pgfarrowsdeclarereversed{angle 90 reversed}{angle 90 reversed}{angle 90}{angle 90}% + + +\pgfarrowsdeclare{angle 60}{angle 60} +{ + \pgfutil@tempdima=0.3pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfutil@tempdimb=7.29\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=.5\pgfutil@tempdima\advance\pgfutil@tempdimb by\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.3pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetmiterjoin + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{150}{9\pgfutil@tempdima}}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{-150}{9\pgfutil@tempdima}}} + \pgfusepathqstroke +}% + +\pgfarrowsdeclarereversed{angle 60 reversed}{angle 60 reversed}{angle 60}{angle 60}% + + + +\pgfarrowsdeclare{angle 45}{angle 45} +{ + \pgfutil@tempdima=0.3pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfutil@tempdimb=8.705\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=.5\pgfutil@tempdima\advance\pgfutil@tempdimb by1.28\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.3pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetmiterjoin + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{157}{10\pgfutil@tempdima}}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{-157}{10\pgfutil@tempdima}}} + \pgfusepathqstroke +}% + +\pgfarrowsdeclarereversed{angle 45 reversed}{angle 45 reversed}{angle 45}{angle 45}% + + + + +\pgfarrowsdeclare{*}{*} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfutil@tempdimb=7.5\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=1.5\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfpathcircle{\pgfqpoint{-3\pgfutil@tempdima}{0pt}}{+4.5\pgfutil@tempdima} + \pgfusepathqfillstroke +}% + + + +\pgfarrowsdeclare{o}{o} +{ + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfutil@tempdimb=9\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfpathcircle{\pgfqpoint{4.5\pgfutil@tempdima}{0bp}}{4.5\pgfutil@tempdima} + \pgfusepathqstroke +}% + + + + +\pgfarrowsdeclare{diamond}{diamond} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.275\pgflinewidth% + \pgfutil@tempdimb=13\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=1\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.275\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{1\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-6\pgfutil@tempdima}{4\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-13\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-6\pgfutil@tempdima}{-4\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfarrowsdeclare{open diamond}{open diamond}% +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.275\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=14\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.275\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{14\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{7\pgfutil@tempdima}{4\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{7\pgfutil@tempdima}{-4\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqstroke +}% + + +\newdimen\arrowsize +\pgfarrowsdeclare{square}{square} +{ + \arrowsize=0.4pt + \advance\arrowsize by.275\pgflinewidth% + \pgfarrowsleftextend{-7\arrowsize-.5\pgflinewidth} + \advance\arrowsize by.5\pgflinewidth + \pgfarrowsrightextend{+\arrowsize} +} +{ + \arrowsize=0.4pt + \advance\arrowsize by.275\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{1\arrowsize}{4\arrowsize}} + \pgfpathlineto{\pgfqpoint{-7\arrowsize}{4\arrowsize}} + \pgfpathlineto{\pgfqpoint{-7\arrowsize}{-4\arrowsize}} + \pgfpathlineto{\pgfqpoint{1\arrowsize}{-4\arrowsize}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfarrowsdeclare{open square}{open square}% +{ + \arrowsize=0.4pt + \advance\arrowsize by.275\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \advance\arrowsize by7\arrowsize + \advance\arrowsize by.5\pgflinewidth + \pgfarrowsrightextend{+\arrowsize} +} +{ + \arrowsize=0.4pt + \advance\arrowsize by.275\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{8\arrowsize}{4\arrowsize}} + \pgfpathlineto{\pgfqpoint{0\arrowsize}{4\arrowsize}} + \pgfpathlineto{\pgfqpoint{0\arrowsize}{-4\arrowsize}} + \pgfpathlineto{\pgfqpoint{8\arrowsize}{-4\arrowsize}} + \pgfpathclose + \pgfusepathqstroke +}% + + + + +\pgfarrowsdeclare{triangle 90}{triangle 90} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfutil@tempdimb=5.5\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=.5\pgfutil@tempdima\advance\pgfutil@tempdimb by0.707\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfqpoint{-5.5\pgfutil@tempdima}{-6\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-5.5\pgfutil@tempdima}{6\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfarrowsdeclarereversed{triangle 90 reversed}{triangle 90 reversed}{triangle 90}{triangle 90}% + + +\pgfarrowsdeclare{triangle 60}{triangle 60} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfutil@tempdimb=7.29\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=.5\pgfutil@tempdima\advance\pgfutil@tempdimb by\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{150}{9\pgfutil@tempdima}}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{-150}{9\pgfutil@tempdima}}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfarrowsdeclarereversed{triangle 60 reversed}{triangle 60 reversed}{triangle 60}{triangle 60}% + + + + +\pgfarrowsdeclare{triangle 45}{triangle 45} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfutil@tempdimb=8.705\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=.5\pgfutil@tempdima\advance\pgfutil@tempdimb by1.28\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{157}{10\pgfutil@tempdima}}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{0.5\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{-157}{10\pgfutil@tempdima}}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfarrowsdeclarereversed{triangle 45 reversed}{triangle 45 reversed}{triangle 45}{triangle 45}% + + + + +\pgfarrowsdeclare{open triangle 90}{open triangle 90} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=6\pgfutil@tempdima\advance\pgfutil@tempdimb by0.707\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfqpoint{0\pgfutil@tempdima}{-6\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{6\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0\pgfutil@tempdima}{6\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqstroke +}% + +\pgfarrowsdeclare{open triangle 90 reversed}{open triangle 90 reversed}% +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfarrowsleftextend{+-.707\pgflinewidth} + \pgfutil@tempdimb=6\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfqpoint{6\pgfutil@tempdima}{-6\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{6\pgfutil@tempdima}{6\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqstroke +}% + + + +\pgfarrowsdeclare{open triangle 60}{open triangle 60} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=7.794\pgfutil@tempdima\advance\pgfutil@tempdimb by\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{7.794\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{150}{9\pgfutil@tempdima}}} + \pgfpathlineto{\pgfqpoint{7.794\pgfutil@tempdima}{0pt}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{7.794\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{-150}{9\pgfutil@tempdima}}} + \pgfpathclose + \pgfusepathqstroke +}% + + + +\pgfarrowsdeclare{open triangle 60 reversed}{open triangle 60 reversed} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfarrowsleftextend{+-\pgflinewidth} + \pgfutil@tempdimb=7.794\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfqpointpolar{30}{9\pgfutil@tempdima}} + \pgfpathlineto{\pgfpointorigin} + \pgfpathlineto{\pgfqpointpolar{-30}{9\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqstroke +}% + + + +\pgfarrowsdeclare{open triangle 45}{open triangle 45} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=9.205\pgfutil@tempdima\advance\pgfutil@tempdimb by1.28\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{9.205\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{157}{10\pgfutil@tempdima}}} + \pgfpathlineto{\pgfqpoint{9.205\pgfutil@tempdima}{0pt}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{9.205\pgfutil@tempdima}{0pt}}{\pgfqpointpolar{-157}{10\pgfutil@tempdima}}} + \pgfpathclose + \pgfusepathqstroke +}% + + + +\pgfarrowsdeclare{open triangle 45 reversed}{open triangle 45 reversed} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfarrowsleftextend{+-1.28\pgflinewidth} + \pgfutil@tempdimb=9.205\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.5pt% + \advance\pgfutil@tempdima by.25\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetmiterjoin + \pgfpathmoveto{\pgfqpointpolar{23}{10\pgfutil@tempdima}} + \pgfpathlineto{\pgfpointorigin} + \pgfpathlineto{\pgfqpointpolar{-23}{10\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqstroke +}% + + + + +\pgfarrowsdeclare{latex'}{latex'} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfarrowsleftextend{+-4\pgfutil@tempdima} + \pgfarrowsrightextend{+6\pgfutil@tempdima} +} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfpathmoveto{\pgfqpoint{6\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{3.5\pgfutil@tempdima}{.5\pgfutil@tempdima}} + {\pgfqpoint{-1\pgfutil@tempdima}{1.5\pgfutil@tempdima}} + {\pgfqpoint{-4\pgfutil@tempdima}{3.75\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-1.5\pgfutil@tempdima}{1\pgfutil@tempdima}} + {\pgfqpoint{-1.5\pgfutil@tempdima}{-1\pgfutil@tempdima}} + {\pgfqpoint{-4\pgfutil@tempdima}{-3.75\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-1\pgfutil@tempdima}{-1.5\pgfutil@tempdima}} + {\pgfqpoint{3.5\pgfutil@tempdima}{-.5\pgfutil@tempdima}} + {\pgfqpoint{6\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfill +}% + +\pgfarrowsdeclarereversed{latex' reversed}{latex' reversed}{latex'}{latex'}% + + + +\pgfarrowsdeclare{stealth'}{stealth'} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfutil@tempdimb=6\pgfutil@tempdima\advance\pgfutil@tempdimb by.5\pgflinewidth% + \pgfarrowsleftextend{+-\pgfutil@tempdimb} + \pgfutil@tempdimb=2\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{2\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-.5\pgfutil@tempdima}{.5\pgfutil@tempdima}} + {\pgfqpoint{-3\pgfutil@tempdima}{1.5\pgfutil@tempdima}} + {\pgfqpoint{-6\pgfutil@tempdima}{3.25\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-3\pgfutil@tempdima}{1\pgfutil@tempdima}} + {\pgfqpoint{-3\pgfutil@tempdima}{-1\pgfutil@tempdima}} + {\pgfqpoint{-6\pgfutil@tempdima}{-3.25\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-3\pgfutil@tempdima}{-1.5\pgfutil@tempdima}} + {\pgfqpoint{-.5\pgfutil@tempdima}{-.5\pgfutil@tempdima}} + {\pgfqpoint{2\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfarrowsdeclarereversed{stealth' reversed}{stealth' reversed}{stealth'}{stealth'}% + + + + +\pgfarrowsdeclare{left to}{left to} +{ + \pgfutil@tempdima=-0.84pt% + \advance\pgfutil@tempdima by-1.3\pgflinewidth% + \pgfutil@tempdimb=0.21pt% + \advance\pgfutil@tempdimb by.625\pgflinewidth% + \pgfarrowsleftextend{+\pgfutil@tempdima} + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfsetlinewidth{0.8\pgflinewidth} + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{-3\pgfutil@tempdima}{4\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-2.75\pgfutil@tempdima}{2.5\pgfutil@tempdima}} + {\pgfqpoint{0pt}{0.25\pgfutil@tempdima}} + {\pgfqpoint{0.75\pgfutil@tempdima}{0pt}} + \pgfpathcurveto + {\pgfqpoint{0.55\pgfutil@tempdima}{-0.125\pgflinewidth}} + {\pgfqpoint{0.5\pgfutil@tempdima}{-0.125\pgflinewidth}} + {\pgfqpoint{0.5\pgfutil@tempdima}{-0.125\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{0pt}{-0.125\pgflinewidth}} + \pgfusepathqstroke +}% + + +\pgfarrowsdeclare{right to}{right to} +{ + \pgfutil@tempdima=-0.84pt% + \advance\pgfutil@tempdima by-1.3\pgflinewidth% + \pgfutil@tempdimb=0.21pt% + \advance\pgfutil@tempdimb by.625\pgflinewidth% + \pgfarrowsleftextend{+\pgfutil@tempdima} + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfsetlinewidth{0.8\pgflinewidth} + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{-3\pgfutil@tempdima}{-4\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-2.75\pgfutil@tempdima}{-2.5\pgfutil@tempdima}} + {\pgfqpoint{0pt}{-0.25\pgfutil@tempdima}} + {\pgfqpoint{0.75\pgfutil@tempdima}{0pt}} + \pgfpathcurveto + {\pgfqpoint{0.55\pgfutil@tempdima}{0.125\pgflinewidth}} + {\pgfqpoint{0.5\pgfutil@tempdima}{0.125\pgflinewidth}} + {\pgfqpoint{0.5\pgfutil@tempdima}{0.125\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{0pt}{0.125\pgflinewidth}} + \pgfusepathqstroke +}% + + + + +\pgfarrowsdeclare{left to reversed}{left to reversed} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfarrowsleftextend{+-.1\pgflinewidth} + \pgfutil@tempdimb=3.75\pgfutil@tempdima\advance\pgfutil@tempdimb by0.9\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfsetbuttcap + \pgfpathmoveto{\pgfqpoint{0.5\pgflinewidth}{0pt}} + \pgfpathlineto{\pgfqpoint{-0.1\pgflinewidth}{0pt}} + \pgfusepathqstroke + \pgfsetroundcap + \pgfsetlinewidth{.8\pgflinewidth} + {\pgftransformxshift{0.625\pgflinewidth} + \pgfpathmoveto{\pgfqpoint{3.75\pgfutil@tempdima}{4\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.5\pgfutil@tempdima}{2.5\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{0.25\pgfutil@tempdima}}{\pgfqpoint{0pt}{0.125\pgflinewidth}} + \pgfpathmoveto{\pgfqpoint{3.75\pgfutil@tempdima}{4\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.5\pgfutil@tempdima}{2.5\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{0.25\pgfutil@tempdima}}{\pgfqpoint{0pt}{-0.125\pgflinewidth}} + } + \pgfusepathqstroke% +}% + +\pgfarrowsdeclare{right to reversed}{right to reversed} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfarrowsleftextend{+-.1\pgflinewidth} + \pgfutil@tempdimb=3.75\pgfutil@tempdima\advance\pgfutil@tempdimb by0.9\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.28pt% + \advance\pgfutil@tempdima by.3\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfsetbuttcap + \pgfpathmoveto{\pgfqpoint{0.5\pgflinewidth}{0pt}} + \pgfpathlineto{\pgfqpoint{-0.1\pgflinewidth}{0pt}} + \pgfusepathqstroke + \pgfsetroundcap + \pgfsetlinewidth{.8\pgflinewidth} + {\pgftransformxshift{0.625\pgflinewidth} + \pgfpathmoveto{\pgfqpoint{3.75\pgfutil@tempdima}{-4\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.5\pgfutil@tempdima}{-2.5\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{-0.25\pgfutil@tempdima}}{\pgfqpoint{0pt}{-0.125\pgflinewidth}} + \pgfpathmoveto{\pgfqpoint{3.75\pgfutil@tempdima}{-4\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.5\pgfutil@tempdima}{-2.5\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{-0.25\pgfutil@tempdima}}{\pgfqpoint{0pt}{0.125\pgflinewidth}} + } + \pgfusepathqstroke% +}% + + + + +\pgfarrowsdeclare{left hook}{left hook} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=3.75\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfpathmoveto{\pgfqpoint{0\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0.75\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{2.415\pgfutil@tempdima}{0\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{1.665\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{3\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.75\pgfutil@tempdima}{4.665\pgfutil@tempdima}}{\pgfqpoint{2.415\pgfutil@tempdima}{6\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{6\pgfutil@tempdima}} + \pgfusepathqstroke% +}% + +\pgfarrowsdeclarereversed{left hook reversed}{left hook reversed}{left hook}{left hook}% + + + + +\pgfarrowsdeclare{right hook}{right hook} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=3.75\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfpathmoveto{\pgfqpoint{0\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0.75\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{2.415\pgfutil@tempdima}{0\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{-1.665\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{-3\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.75\pgfutil@tempdima}{-4.665\pgfutil@tempdima}}{\pgfqpoint{2.415\pgfutil@tempdima}{-6\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{-6\pgfutil@tempdima}} + \pgfusepathqstroke% +}% + +\pgfarrowsdeclarereversed{right hook reversed}{right hook reversed}{right hook}{right hook}% + + + +\pgfarrowsdeclare{hooks}{hooks} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfarrowsleftextend{+-.5\pgflinewidth} + \pgfutil@tempdimb=3.75\pgfutil@tempdima\advance\pgfutil@tempdimb by0.5\pgflinewidth% + \pgfarrowsrightextend{+\pgfutil@tempdimb} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.2\pgflinewidth% + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfpathmoveto{\pgfqpoint{0\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0.75\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{2.415\pgfutil@tempdima}{0\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{1.665\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{3\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.75\pgfutil@tempdima}{4.665\pgfutil@tempdima}}{\pgfqpoint{2.415\pgfutil@tempdima}{6\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{6\pgfutil@tempdima}} + \pgfpathmoveto{\pgfqpoint{0.75\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{2.415\pgfutil@tempdima}{0\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{-1.665\pgfutil@tempdima}}{\pgfqpoint{3.75\pgfutil@tempdima}{-3\pgfutil@tempdima}} + \pgfpathcurveto{\pgfqpoint{3.75\pgfutil@tempdima}{-4.665\pgfutil@tempdima}}{\pgfqpoint{2.415\pgfutil@tempdima}{-6\pgfutil@tempdima}}{\pgfqpoint{0.75\pgfutil@tempdima}{-6\pgfutil@tempdima}} + \pgfusepathqstroke% +}% + +\pgfarrowsdeclarereversed{hooks reversed}{hooks reversed}{hooks}{hooks}% + + + +\pgfarrowsdeclare{serif cm}{serif cm} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.45\pgflinewidth% + \pgfarrowsleftextend{+-.75\pgfutil@tempdima} + \pgfarrowsrightextend{+.04\pgflinewidth} +} +{ + \pgfutil@tempdima=0.4pt% + \advance\pgfutil@tempdima by.45\pgflinewidth% + \pgftransformxshift{.04\pgflinewidth} + \pgfpathmoveto{\pgfqpoint{-.75\pgfutil@tempdima}{.5\pgflinewidth}} + \pgfpathcurveto + {\pgfqpoint{-.375\pgfutil@tempdima}{.5\pgflinewidth}} + {\pgfqpoint{-.375\pgfutil@tempdima}{.7\pgflinewidth}} + {\pgfqpoint{-.375\pgfutil@tempdima}{1.95\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0pt}{1.95\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-.04\pgflinewidth}{.5\pgfutil@tempdima}} + {\pgfqpoint{-.04\pgflinewidth}{-.5\pgfutil@tempdima}} + {\pgfqpoint{0pt}{-1.95\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-.375\pgfutil@tempdima}{-1.95\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfqpoint{-.375\pgfutil@tempdima}{-.7\pgflinewidth}} + {\pgfqpoint{-.375\pgfutil@tempdima}{-.5\pgflinewidth}} + {\pgfqpoint{-.75\pgfutil@tempdima}{-.5\pgflinewidth}} + \pgfpathclose + \pgfusepathqfill +}% + + + + +\pgfarrowsdeclare{round cap}{round cap} +{\pgfarrowsleftextend{+0pt}\pgfarrowsrightextend{+\pgflinewidth}} +{ + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfpathmoveto{\pgfpointorigin} + \pgfpathlineto{\pgfqpoint{0.5\pgflinewidth}{0pt}} + \pgfusepathqstroke +}% + + + +\pgfarrowsdeclare{butt cap}{butt cap} +{\pgfarrowsleftextend{+-.1\pgflinewidth}\pgfarrowsrightextend{+.5\pgflinewidth}} +{ + \pgfsetdash{}{+0pt} + \pgfsetbuttcap + \pgfpathmoveto{\pgfqpoint{-.1\pgflinewidth}{0pt}} + \pgfpathlineto{\pgfqpoint{0.5\pgflinewidth}{0pt}} + \pgfusepathqstroke +}% + + + + +\pgfarrowsdeclare{triangle 90 cap}{triangle 90 cap} +{\pgfarrowsleftextend{+-.1\pgflinewidth}\pgfarrowsrightextend{+\pgflinewidth}} +{ + \pgfpathmoveto{\pgfqpoint{-.1\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{.5\pgflinewidth}{.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{\pgflinewidth}{0pt}} + \pgfpathlineto{\pgfqpoint{.5\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{-.1\pgflinewidth}{-0.5\pgflinewidth}} + \pgfpathclose + \pgfusepathqfill +}% + + + +\pgfarrowsdeclare{triangle 90 cap reversed}{triangle 90 cap reversed} +{\pgfarrowsleftextend{+-.1\pgflinewidth}\pgfarrowsrightextend{+\pgflinewidth}} +{ + \pgfpathmoveto{\pgfqpoint{1\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{-.1\pgflinewidth}{.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{-.1\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{0.5\pgflinewidth}{0\pgflinewidth}} + \pgfpathclose + \pgfusepathqfill +}% + + + + +\pgfarrowsdeclare{fast cap}{fast cap} +{\pgfarrowsleftextend{+-.1\pgflinewidth}\pgfarrowsrightextend{+2\pgflinewidth}} +{ + \pgfpathmoveto{\pgfqpoint{-.1\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{.5\pgflinewidth}{.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1\pgflinewidth}{0\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{.5\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{-.1\pgflinewidth}{-0.5\pgflinewidth}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{1\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1.5\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{2\pgflinewidth}{0\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1.5\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1\pgflinewidth}{-0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1.5\pgflinewidth}{0\pgflinewidth}} + \pgfpathclose + \pgfusepathqfill +}% + + +\pgfarrowsdeclare{fast cap reversed}{fast cap reversed} +{\pgfarrowsleftextend{+-.1\pgflinewidth}\pgfarrowsrightextend{+2\pgflinewidth}} +{ + \pgfpathmoveto{\pgfqpoint{-.1\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1\pgflinewidth}{.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{.5\pgflinewidth}{0\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{-.1\pgflinewidth}{-0.5\pgflinewidth}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{1.5\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{2\pgflinewidth}{0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1.5\pgflinewidth}{0\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{2\pgflinewidth}{-.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1.5\pgflinewidth}{-0.5\pgflinewidth}} + \pgfpathlineto{\pgfqpoint{1\pgflinewidth}{0\pgflinewidth}} + \pgfpathclose + \pgfusepathqfill +}% + + + + + + + + +\pgfarrowsdeclare{implies}{implies} +{ + \pgfmathsetlength{\pgfutil@tempdima}{.25\pgflinewidth+.25*\pgfinnerlinewidth}% + \pgfmathsetlength{\pgfutil@tempdimb}{.5\pgflinewidth-.5*\pgfinnerlinewidth}% + \pgfarrowsrightextend{2.06\pgfutil@tempdima+.5\pgfutil@tempdimb} + \pgfarrowsleftextend{-1.36\pgfutil@tempdima-.5\pgfutil@tempdimb} +} +{ + \pgfmathsetlength{\pgfutil@tempdima}{.25\pgflinewidth+.25*\pgfinnerlinewidth}% + \pgfmathsetlength{\pgfutil@tempdimb}{.5\pgflinewidth-.5*\pgfinnerlinewidth}% + \pgftransformxshift{.06\pgfutil@tempdima} + \pgfsetlinewidth{\pgfutil@tempdimb} + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetroundjoin + \pgfpathmoveto{\pgfpoint{-1.4\pgfutil@tempdima}{2.65\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfpoint{-0.75\pgfutil@tempdima}{1.25\pgfutil@tempdima}} + {\pgfpoint{1\pgfutil@tempdima}{0.05\pgfutil@tempdima}} + {\pgfpoint{2\pgfutil@tempdima}{0pt}} + \pgfpathcurveto + {\pgfpoint{1\pgfutil@tempdima}{-0.05\pgfutil@tempdima}} + {\pgfpoint{-.75\pgfutil@tempdima}{-1.25\pgfutil@tempdima}} + {\pgfpoint{-1.4\pgfutil@tempdima}{-2.65\pgfutil@tempdima}} + \pgfusepathqstroke +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..12652d298bc990ffd195ad807a38da14e00ebbcb --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.meta.code.tex @@ -0,0 +1,1436 @@ + +\ProvidesFileRCS{pgflibraryarrows.meta.code.tex} + + + + + +\newdimen\pgfarrowinset +\newdimen\pgfarrowlength +\newdimen\pgfarrowwidth +\newdimen\pgfarrowlinewidth +\newif\ifpgfarrowroundcap +\newif\ifpgfarrowroundjoin + +\pgfarrowsaddtolengthscalelist\pgfarrowlength +\pgfarrowsaddtolengthscalelist\pgfarrowinset +\pgfarrowsaddtowidthscalelist\pgfarrowwidth + + +\pgfkeys{ + /pgf/arrow keys/.cd, + length/.code={% + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtooptions\expandafter{\expandafter\pgfarrowslinewidthdependent\pgfarrowstheparameters\pgfarrowlength\pgf@x}% + }, + inset/.code={% + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtolateoptions\expandafter{\expandafter\pgfarrowslinewidthdependent\pgfarrowstheparameters\pgfarrowinset\pgf@x}% + }, + inset'/.code={ + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtolateoptions\expandafter{\expandafter\pgfarrowslengthdependent\pgfarrowstheparameters\pgfarrowinset}% + }, + line width/.code={% + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtolateoptions\expandafter{\expandafter\pgfarrowslinewidthdependent\pgfarrowstheparameters\pgfarrowlinewidth\pgf@x}% + }, + line width'/.code={ + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtolateoptions\expandafter{\expandafter\pgfarrowslengthdependent\pgfarrowstheparameters\pgfarrowlinewidth}% + }, + width/.code={% + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtolateoptions\expandafter{\expandafter\pgfarrowslinewidthdependent\pgfarrowstheparameters\pgfarrowwidth\pgf@x}% + }, + width'/.code={% + \pgfarrowsthreeparameters{#1}% + \expandafter\pgfarrowsaddtolateoptions\expandafter{\expandafter\pgfarrowslengthdependent\pgfarrowstheparameters\pgfarrowwidth}% + }, + angle/.code={% + \pgfarrowsfourparameters{#1}% + \expandafter\pgfarrowsaddtooptions\expandafter{\expandafter\pgfarrows@angle@setup\pgfarrowstheparameters}% + }, + angle'/.code={ + \pgfarrowsaddtolateoptions{\pgfarrows@angle@setup@prime{#1}}% + }, + line cap/.is choice, + line cap/butt/.code=\pgfarrowsaddtooptions{\pgfarrowroundcapfalse}, + line cap/round/.code=\pgfarrowsaddtooptions{\pgfarrowroundcaptrue}, + line join/.is choice, + line join/miter/.code=\pgfarrowsaddtooptions{\pgfarrowroundjoinfalse}, + line join/round/.code=\pgfarrowsaddtooptions{\pgfarrowroundjointrue}, + round/.style={line cap=round,line join=round}, + sharp/.style={line cap=butt,line join=miter}, +}% + + + + + + +\pgfdeclarearrow{ + name = Straight Barb, + defaults = { + length = +1.5pt 2, + width' = +0pt 2, + line width = +0pt 1 1, + }, + setup code = { + \pgfmathdivide@{\pgf@sys@tonumber\pgfarrowlength}{\pgf@sys@tonumber\pgfarrowwidth}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x4\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@xc\pgfmathresult\pgfarrowlinewidth% + \pgf@xc.5\pgf@xc + \pgf@xa\pgf@temp@quot\pgfarrowlinewidth% + \ifpgfarrowroundjoin + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth} + \else + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by\pgf@xc\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi} + \fi + \pgfarrowssetvisualbackend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth} + \pgfarrowssetbackend{-.5\pgfarrowlinewidth} + \ifpgfarrowreversed + \pgfarrowssetlineend{\pgfarrowlength\ifpgfarrowharpoon\advance\pgf@x by.5\pgfarrowlinewidth\fi} + \else + \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth} + \fi + \ifpgfarrowroundjoin + \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else0pt\fi}% + \else% + \ifpgfarrowharpoon + \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by\pgf@xc\advance\pgf@x by\pgf@xa}{-.5\pgfarrowlinewidth}% + \else + \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by\pgf@xc\advance\pgf@x by\pgf@xa}{0pt}% + \fi% + \fi + \pgfarrowsupperhullpoint{.5\pgfarrowlinewidth}{.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}% + \pgfarrowsupperhullpoint{-.5\pgfarrowlinewidth}{.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}% + \ifpgfarrowharpoon + \pgfarrowshullpoint{-.5\pgfarrowlinewidth}{-.5\pgfarrowlinewidth}% + \fi + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowwidth + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \pgfpathmoveto{\pgfqpoint{0pt}{.5\pgfarrowwidth}} + \pgfpathlineto{\pgfqpoint{\pgfarrowlength}{0pt}} + \ifpgfarrowharpoon + \pgfpathlineto{\pgfqpoint{\pgfarrowlength\advance\pgf@x by\ifpgfarrowreversed\else-\fi\pgfarrowlinewidth}{0pt}} + \else + \pgfpathlineto{\pgfqpoint{0pt}{-.5\pgfarrowwidth}} + \fi + \pgfusepathqstroke + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowroundjoin j\fi% + \ifpgfarrowroundcap c\fi% + }, +}% + +\pgfkeys{ + /pgf/arrow keys/.cd, + arc/.code={% + \pgfmathparse{#1}% + \expandafter\pgfarrowsaddtooptions\expandafter{\expandafter\def\expandafter\pgfarrowarc\expandafter{\pgfmathresult}} + } +}% + +\def\pgfarrowarc{180}% + +\pgfdeclarearrow{ + name = Hooks, + defaults = { + length = +0.75pt 1.25, + width' = +0pt 4 -1, + line width = +0pt 1 1, + }, + setup code = { + \ifpgfarrowharpoon + \pgfarrowshullpoint{.5\pgfarrowlength}{-.5\pgfarrowlinewidth} + \pgfarrowshullpoint{\pgfarrowlength}{-.5\pgfarrowlinewidth\advance\pgf@y by.125\pgfarrowwidth} + \fi + \ifdim\pgfarrowarc pt<90.1pt + \pgfarrowsupperhullpoint{0pt}{.25\pgfarrowwidth\ifpgfarrowroundcap\else\advance\pgf@y by-.25\pgfarrowlinewidth\fi} + \pgfarrowsupperhullpoint{\pgfarrowlength}{.25\pgfarrowwidth\ifpgfarrowroundcap\else\advance\pgf@y by-.25\pgfarrowlinewidth\fi} + \else% + \pgfarrowsupperhullpoint{\pgfarrowlength}{.375\pgfarrowwidth} + \pgfarrowsupperhullpoint{.5\pgfarrowlength}{.5\pgfarrowwidth} + \ifdim\pgfarrowarc pt>180pt + \pgfarrowsupperhullpoint{-.5\pgfarrowlength}{.5\pgfarrowwidth} + \pgfarrowsupperhullpoint{-\pgfarrowlength}{.375\pgfarrowwidth} + \pgfarrowsupperhullpoint{-\pgfarrowlength}{.25\pgfarrowwidth} + \else + \pgfarrowsupperhullpoint{\ifpgfarrowroundcap-.5\pgfarrowlinewidth\else0pt\fi}{.25\pgfarrowwidth} + \pgfarrowsupperhullpoint{\ifpgfarrowroundcap-.5\pgfarrowlinewidth\else0pt\fi}{.5\pgfarrowwidth} + \fi + \fi + \advance\pgfarrowlength by-.5\pgfarrowlinewidth + \advance\pgfarrowwidth by-\pgfarrowlinewidth + \ifpgfarrowreversed + \ifpgfarrowroundjoin + \pgfarrowssetbackend{-.5\pgfarrowlinewidth} + \fi + \fi + \ifdim\pgfarrowarc pt<90pt% + \pgfmathsin@{\pgfarrowarc} + \pgfarrowssettipend{\pgfmathresult\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}% + \else\ifdim\pgfarrowarc pt<180pt% + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}% + \ifpgfarrowroundcap\pgfarrowssetbackend{-.5\pgfarrowlinewidth}\fi% + \else\ifdim\pgfarrowarc pt<270pt% + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}% + \ifdim\pgfarrowarc pt>180pt + \pgfmathsin@{\pgfarrowarc} + \pgfarrowssetbackend{\pgfmathresult\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth}% + \else + \ifpgfarrowroundcap\pgfarrowssetbackend{-.5\pgfarrowlinewidth}\fi% + \fi% + \else% + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by.5\pgfarrowlinewidth}% + \pgfarrowssetbackend{-\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth}% + \fi\fi\fi% + \ifpgfarrowreversed + \pgfarrowssetlineend{.5\pgfarrowlinewidth} + \else% + \ifpgfarrowharpoon + \pgfarrowssetlineend{0pt} + \else + \pgfarrowssetlineend{.25\pgfarrowlinewidth} + \fi + \fi + \pgf@x\pgfarrowarc pt% + \advance\pgf@x by-90pt% + \edef\pgfarrowarc{\pgf@sys@tonumber\pgf@x}% + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowwidth + \pgfarrowssave\pgfarrowarc + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + {% + \pgftransformxscale{+\pgfarrowlength} + \pgftransformyscale{+.25\pgfarrowwidth} + \pgfpathmoveto{\pgfpointpolar{+\pgfarrowarc}{+1pt}\advance\pgf@y by1pt} + \pgfpatharc{\pgfarrowarc}{+-90}{+1pt} + \ifpgfarrowharpoon + \else + \pgfpatharc{+90}{+-\pgfarrowarc}{+1pt} + \fi + } + \ifpgfarrowharpoon\ifpgfarrowreversed + \pgfpathlineto{\pgfqpoint{\pgflinewidth}{0pt}} + \fi\fi + \pgfusepathqstroke + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \pgfarrowarc,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowroundjoin j\fi% + \ifpgfarrowroundcap c\fi% + }, +}% + + +\pgfdeclarearrow{ + name = Arc Barb, + defaults = { + length = +1.5pt 2, + width' = +0pt 2, + line width = +0pt 1 1, + }, + setup code = { + \pgf@x\pgfarrowarc pt% + \pgf@x.5\pgf@x% + \edef\pgfarrowarc{\pgf@sys@tonumber\pgf@x}% + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowssetvisualbackend{\pgfarrowlength} + \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth} + \pgfarrowsupperhullpoint{\pgfarrowlength}{.25\pgfarrowwidth} + \ifpgfarrowharpoon\pgfarrowshullpoint{\pgfarrowlength}{-.5\pgflinewidth}\fi + \pgfmathsincos@{\pgfarrowarc}% + \pgf@xa.5\pgfarrowwidth% + \pgfarrowsupperhullpoint{\pgfmathresultx\pgfarrowlength}{\pgfmathresulty\pgf@xa} + \ifdim\pgfarrowarc pt>60pt + \pgfarrowsupperhullpoint{.5\pgfarrowlength}{\ifdim\pgfarrowarc pt<90pt\pgfmathresulty\pgf@xa\else.5\pgfarrowwidth\fi} + \fi + \ifdim\pgfarrowarc pt>90pt + \ifdim\pgfarrowarc pt<120pt + \pgfarrowsupperhullpoint{\pgfmathresultx\pgfarrowlength}{.5\pgfarrowwidth} + \else + \pgfarrowsupperhullpoint{-.5\pgfarrowlength}{.5\pgfarrowwidth} + \ifdim\pgfarrowarc pt>150pt + \pgfarrowsupperhullpoint{-\pgfarrowlength}{.25\pgfarrowwidth} + \fi + \fi + \fi + \pgfutil@tempswafalse + \ifdim\pgfarrowarc pt<90pt + \pgfutil@tempswatrue + \fi + \ifpgfarrowharpoon + \pgfutil@tempswatrue + \fi + \ifpgfutil@tempswa + \pgf@xa.5\pgfarrowwidth\advance\pgf@xa by-\pgfarrowlinewidth% + \pgf@ya\pgfarrowlength\advance\pgf@ya by-\pgfarrowlinewidth% + \pgfarrowsupperhullpoint{\pgfmathresultx\pgf@ya}{\pgfmathresulty\pgf@xa} + \fi + \ifpgfarrowroundcap + \pgf@y\pgfarrowlength + \advance\pgf@y by-.5\pgfarrowlinewidth + \pgf@x\pgfmathresultx\pgf@y% + \else + \ifdim\pgfarrowarc pt<90pt + \pgf@y\pgfarrowlength + \advance\pgf@y by-\pgfarrowlinewidth + \pgf@x\pgfmathresultx\pgf@y% + \else + \pgf@x\pgfmathresultx\pgfarrowlength% + \fi + \fi + \pgfarrowssetbackend{\pgf@x\ifpgfarrowroundcap\advance\pgf@x by-.5\pgfarrowlinewidth\fi} + \advance\pgfarrowlength by-.5\pgfarrowlinewidth + \advance\pgfarrowwidth by-\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowwidth + \pgfarrowssave\pgfarrowarc + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + {% + \pgftransformxscale{+\pgfarrowlength} + \pgftransformyscale{+.5\pgfarrowwidth} + \pgfpathmoveto{\pgfpointpolar{+\pgfarrowarc}{+1pt}} + \ifpgfarrowharpoon + \pgfpatharc{+\pgfarrowarc}{0pt}{+1pt} + \else + \pgfpatharc{+\pgfarrowarc}{+-\pgfarrowarc}{+1pt} + \fi + } + \ifpgfarrowharpoon + \pgfpathlineto{\pgfqpoint{\pgfarrowlength\advance\pgf@x by\ifpgfarrowreversed\else-\fi.5\pgflinewidth}{0pt}} + \fi + \pgfusepathqstroke + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \pgfarrowarc,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowroundcap c\fi% + \ifpgfarrowroundjoin j\fi% + }, +}% + + + + +\pgfdeclarearrow{ + name = Tee Barb, + defaults = { + length = +1.5pt 2, + width = +3pt 4, + inset' = +0pt .5, + line width = +0pt 1 1, + }, + bending mode=polar, + setup code = { + \pgfutil@tempswafalse% + \pgfutil@tempswbfalse% + \pgfutil@tempdima\pgfarrowlength\advance\pgfutil@tempdima by-\pgfarrowinset\ifdim\pgfutil@tempdima<.5\pgfarrowlinewidth\pgfutil@tempdima.5\pgfarrowlinewidth\pgfutil@tempswatrue\fi% + \pgfutil@tempdimb-\pgfarrowinset\ifdim\pgfutil@tempdimb>-.5\pgfarrowlinewidth\pgfutil@tempdimb-.5\pgfarrowlinewidth\pgfutil@tempswbtrue\fi + \pgfarrowssavethe\pgfarrowwidth + \pgfarrowssavethe\pgfutil@tempdima + \pgfarrowssavethe\pgfutil@tempdimb + \pgfarrowssettipend{\pgfutil@tempdima\ifpgfarrowroundcap\ifpgfutil@tempswa\else\advance\pgf@x by.5\pgfarrowlinewidth\fi\fi} + \pgfarrowssetvisualbackend{.5\pgfarrowlinewidth} + \pgfarrowssetbackend{\pgfutil@tempdimb\ifpgfarrowroundcap\ifpgfutil@tempswb\else\advance\pgf@x by-.5\pgfarrowlinewidth\fi\fi} + \pgfarrowssetlineend{\ifpgfarrowreversed\else-\fi.25\pgfarrowlinewidth}% + \pgfarrowsupperhullpoint{\pgfutil@tempdima\ifpgfarrowroundcap\ifpgfutil@tempswa\else\advance\pgf@x by.5\pgfarrowlinewidth\fi\fi}{.5\pgfarrowwidth}% + \pgfarrowsupperhullpoint{\pgfutil@tempdimb\ifpgfarrowroundcap\ifpgfutil@tempswb\else\advance\pgf@x by-.5\pgfarrowlinewidth\fi\fi}{.5\pgfarrowwidth}% + \ifpgfarrowharpoon + \pgfarrowshullpoint{.5\pgfarrowlinewidth}{-.5\pgfarrowlinewidth}% + \fi + }, + drawing code = { + \pgfsetdash{}{+0pt} + \pgf@yc\pgflinewidth% + \ifdim\pgflinewidth=\pgfarrowlinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \pgf@x\pgfutil@tempdima\advance\pgf@x by-.5\pgfarrowlinewidth% + \pgf@y\pgfutil@tempdimb\advance\pgf@y by.5\pgfarrowlinewidth% + \ifdim\pgf@x=\pgf@y% + \pgfpathmoveto{\pgfqpoint{0pt}{.5\pgfarrowwidth}} + \pgfpathlineto{\pgfqpoint{0pt}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else-.5\pgfarrowwidth\fi}} + \else + \ifdim\pgfutil@tempdima=.5\pgfarrowlinewidth% + \pgfpathmoveto{\pgfqpoint{\pgfutil@tempdimb}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \pgfpathlineto{\pgfqpoint{0pt}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \ifpgfarrowharpoon% + \pgfpathlineto{\pgfqpoint{0pt}{-.5\pgf@yc}}% + \else% + \pgfpathlineto{\pgfqpoint{0pt}{-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}} + \pgfpathlineto{\pgfqpoint{\pgfutil@tempdimb}{-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}} + \fi + \else% + \pgfpathmoveto{\pgfqpoint{\pgfutil@tempdimb}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \pgfpathlineto{\pgfqpoint{\pgfutil@tempdima}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \pgfpathmoveto{\pgfqpoint{0pt}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \ifpgfarrowharpoon% + \pgfpathlineto{\pgfqpoint{0pt}{-.5\pgf@yc}}% + \else% + \pgfpathlineto{\pgfqpoint{0pt}{-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}} + \pgfpathmoveto{\pgfqpoint{\pgfutil@tempdimb}{-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}} + \pgfpathlineto{\pgfqpoint{\pgfutil@tempdima}{-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth}} + \fi + \fi + \fi + \pgfusepathqstroke + }, + parameters = { + \the\pgfarrowwidth,% + \the\pgfarrowlength,% + \the\pgfarrowinset,% + \the\pgfarrowlinewidth,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowroundjoin j\fi% + \ifpgfarrowroundcap c\fi% + }, +}% + + + + + + +\pgfdeclarearrow{ + name = Classical TikZ Rightarrow, + defaults = { + length = +1.05pt 1.925, + width' = +0pt 1.9237, + line width = 0pt 0.8 1, + round + }, + setup code = + { + \ifpgfarrowharpoon\pgfarrowroundjointrue\fi + \pgfutil@tempdima\pgfarrowlength + \advance\pgfutil@tempdima by-\pgfarrowlinewidth + \pgfutil@tempdimb\pgfarrowwidth + \advance\pgfutil@tempdimb by-\pgfarrowlinewidth + \ifpgfarrowroundjoin% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\pgfutil@tempdima}{\pgf@sys@tonumber\pgfutil@tempdimb}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x40.96\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@xc\pgfmathresult\pgfarrowlinewidth% + \pgf@xc.5\pgf@xc + \fi% + \pgfarrowssavethe\pgfutil@tempdima + \pgfarrowssavethe\pgfutil@tempdimb + \pgfarrowssettipend{\pgfutil@tempdima\ifpgfarrowroundjoin\advance\pgf@x by.5\pgfarrowlinewidth\else\advance\pgf@x by\pgf@xc\fi}% + \pgfarrowssetvisualbackend{\pgfutil@tempdima\advance\pgf@x by.5\pgfarrowlinewidth}% + \ifpgfarrowreversed% + \ifpgfarrowharpoon% + \pgfarrowssetlineend{\pgfutil@tempdima\advance\pgf@x by.5\pgflinewidth}% + \else% + \pgfarrowssetlineend{\pgfutil@tempdima\advance\pgf@x by-.25\pgflinewidth}% + \fi% + \else% + \pgfarrowssetlineend{\pgfutil@tempdima\advance\pgf@x by-.6\pgflinewidth}% + \fi% + \pgfarrowssetbackend{-.5\pgfarrowlinewidth}% + \pgfarrowshullpoint{\pgfutil@tempdima\ifpgfarrowroundjoin\advance\pgf@x by.5\pgfarrowlinewidth\else\advance\pgf@x by\pgf@xc\fi}{.5\pgfarrowlinewidth}% + \pgfarrowshullpoint{\pgfutil@tempdima\ifpgfarrowroundjoin\advance\pgf@x by.5\pgfarrowlinewidth\else\advance\pgf@x by\pgf@xc\fi}{-.5\pgfarrowlinewidth}% + \pgfarrowsupperhullpoint{.5\pgfarrowlinewidth}{.5\pgfutil@tempdimb\advance\pgf@y by.5\pgfarrowlinewidth}% + \pgfarrowsupperhullpoint{-.5\pgfarrowlinewidth}{.5\pgfutil@tempdimb\advance\pgf@y by.5\pgfarrowlinewidth}% + \ifpgfarrowharpoon + \pgfarrowshullpoint{\pgfutil@tempdima\advance\pgf@x by-\pgflinewidth}{-.5\pgflinewidth}% + \pgfarrowshullpoint{-.5\pgfarrowlinewidth}{.5\pgfutil@tempdimb\advance\pgf@y by-.5\pgflinewidth}% + \fi + }, + drawing code = + { + \pgfsetdash{}{+0pt} + \edef\pgf@orig@linewidth{\the\pgflinewidth} + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \ifpgfarrowharpoon\pgfarrowroundjointrue\fi + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \pgfpathmoveto + {\pgfqpoint{0pt}{.5\pgfutil@tempdimb}} + \ifpgfarrowharpoon + \pgf@arrows@old@tikz@harpoon + \else + \pgfpathcurveto + {\pgfqpoint{0.066666\pgfutil@tempdima}{0.3125\pgfutil@tempdimb}} + {\pgfqpoint{.8\pgfutil@tempdima}{0.03125\pgfutil@tempdimb}} + {\pgfqpoint{\pgfutil@tempdima}{0pt}} + \pgfpathcurveto + {\pgfqpoint{.8\pgfutil@tempdima}{-.03125\pgfutil@tempdimb}} + {\pgfqpoint{0.066666\pgfutil@tempdima}{-.3125\pgfutil@tempdimb}} + {\pgfqpoint{0pt}{-.5\pgfutil@tempdimb}} + \pgfsetlinewidth{+\pgfarrowlinewidth} + \pgfusepathqstroke + \fi + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowroundjoin j\fi% + \ifpgfarrowroundcap c\fi% + }, +}% + +\def\pgf@arrows@old@tikz@harpoon{ + \ifpgfarrowreversed + \pgf@arrows@old@tikz@harpoon@reversed + \else + \pgfpathcurveto + {\pgfqpoint{0.066666\pgfutil@tempdima}{0.3125\pgfutil@tempdimb}} + {\pgfqpoint{.8\pgfutil@tempdima}{0.03125\pgfutil@tempdimb}} + {\pgfqpoint{\pgfutil@tempdima}{0pt}} + \pgfpathcurveto + {\pgfqpoint{0.95\pgfutil@tempdima}{-0.125\pgflinewidth}} + {\pgfqpoint{0.933333\pgfutil@tempdima}{-0.125\pgflinewidth}} + {\pgfqpoint{0.933333\pgfutil@tempdima}{-0.125\pgflinewidth}} + \pgfpathlineto + {\pgfqpoint{0.8\pgfutil@tempdima\advance\pgf@x by-.5\pgflinewidth}{-0.125\pgflinewidth}} + \pgfusepathqstroke + \fi +}% +\def\pgf@arrows@old@tikz@harpoon@reversed{ + \pgfpathcurveto + {\pgfqpoint{0.066666\pgfutil@tempdima}{0.3125\pgfutil@tempdimb}} + {\pgfqpoint{.8\pgfutil@tempdima}{0.03125\pgfutil@tempdimb}} + {\pgfqpoint{\pgfutil@tempdima}{0.125\pgflinewidth}} + \pgfpathmoveto + {\pgfqpoint{0pt}{.5\pgfutil@tempdimb}} + \pgfpathcurveto + {\pgfqpoint{0.066666\pgfutil@tempdima}{0.3125\pgfutil@tempdimb}} + {\pgfqpoint{.8\pgfutil@tempdima}{0.03125\pgfutil@tempdimb}} + {\pgfqpoint{\pgfutil@tempdima}{-0.125\pgflinewidth}} + \pgfusepathqstroke + \pgfsetlinewidth{+\pgf@orig@linewidth} + \pgfsetroundcap + \pgfpathmoveto{\pgfqpoint{\pgfutil@tempdima\advance\pgf@x by0.6\pgflinewidth}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgfutil@tempdima}{0pt}} + \pgfusepathqstroke +}% + + + +\pgfdeclarearrow{ + name = Computer Modern Rightarrow, + defaults = { + length = +1.6pt 2.2, % + width' = +0pt 2.096774, + line width = 0pt 1 1, + round + }, + setup code = + { + \pgfutil@tempdima\pgfarrowlength + \advance\pgfutil@tempdima by-\pgfarrowlinewidth + \pgfutil@tempdimb\pgfarrowwidth + \advance\pgfutil@tempdimb by-\pgfarrowlinewidth + \pgfarrowssavethe\pgfutil@tempdima + \pgfarrowssavethe\pgfutil@tempdimb + \ifpgfarrowroundjoin% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\pgfutil@tempdima}{\pgf@sys@tonumber\pgfutil@tempdimb}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x49.44662\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@xc\pgfmathresult\pgfarrowlinewidth% + \pgf@xc.5\pgf@xc + \pgf@xa\pgf@temp@quot\pgfarrowlinewidth% + \pgf@xa3.51591\pgf@xa% + \fi% + \pgfarrowssettipend{\ifpgfarrowroundjoin.5\pgfarrowlinewidth\else\pgf@xc\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi\fi}% + \pgfarrowssetvisualbackend{.5\pgfarrowlinewidth}% + \ifpgfarrowreversed% + \ifpgfarrowharpoon% + \pgfarrowssetlineend{.5\pgfarrowlinewidth}% + \else% + \pgfarrowssetlineend{-.5\pgfarrowlinewidth}% + \fi% + \else% + \pgfarrowssetlineend{-.5\pgfarrowlinewidth}% + \fi% + \pgfarrowssetbackend{-\pgfutil@tempdima\advance\pgf@x by-.5\pgfarrowlinewidth}% + \pgfarrowshullpoint{\ifpgfarrowroundjoin.5\pgfarrowlinewidth\else\pgf@xc\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi\fi}{.5\pgfarrowlinewidth}% + \pgfarrowshullpoint{\ifpgfarrowroundjoin.5\pgfarrowlinewidth\else\pgf@xc\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi\fi}{-.5\pgfarrowlinewidth}% + \pgfarrowsupperhullpoint{-\pgfutil@tempdima\advance\pgf@x by.5\pgfarrowlinewidth}{.5\pgfutil@tempdimb\advance\pgf@y by.5\pgfarrowlinewidth}% + \pgfarrowsupperhullpoint{-\pgfutil@tempdima\advance\pgf@x by-.5\pgfarrowlinewidth}{.5\pgfutil@tempdimb\advance\pgf@y by.5\pgfarrowlinewidth}% + \ifpgfarrowharpoon + \pgfarrowshullpoint{-\pgfarrowlinewidth}{-.5\pgfarrowlinewidth}% + \pgfarrowshullpoint{-\pgfutil@tempdima\advance\pgf@x by-.5\pgfarrowlinewidth}{.5\pgfutil@tempdimb\advance\pgf@y by-.5\pgfarrowlinewidth}% + \fi + }, + drawing code = + { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \pgfpathmoveto + {\pgfqpoint{-\pgfutil@tempdima}{.5\pgfutil@tempdimb}} + \pgfpathcurveto + {\pgfqpoint{-0.81731\pgfutil@tempdima}{.2\pgfutil@tempdimb}} + {\pgfqpoint{-0.41019\pgfutil@tempdima}{0.05833333\pgfutil@tempdimb}} + {\pgfpointorigin} + \ifpgfarrowharpoon + \pgfpathlineto + {\pgfqpoint{\ifpgfarrowreversed.5\else-\fi\pgfarrowlinewidth}{0pt}} + \else + \pgfpathcurveto + {\pgfqpoint{-0.41019\pgfutil@tempdima}{-0.05833333\pgfutil@tempdimb}} + {\pgfqpoint{-0.81731\pgfutil@tempdima}{-.2\pgfutil@tempdimb}} + {\pgfqpoint{-\pgfutil@tempdima}{-.5\pgfutil@tempdimb}} + \fi + \pgfusepathqstroke + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \ifpgfarrowharpoon h\fi + \ifpgfarrowharpoon r\fi + \ifpgfarrowroundjoin j\fi% + \ifpgfarrowroundcap c\fi% + }, +}% + + + + +\pgfdeclarearrow{ + name = Implies, + setup code = { + \pgf@xa\pgfinnerlinewidth + \pgfutil@tempdima.25\pgflinewidth + \advance\pgfutil@tempdima by.25\pgf@xa% + \pgfutil@tempdimb.5\pgflinewidth + \advance\pgfutil@tempdimb by-.5\pgf@xa% + \pgfarrowssettipend{2.06\pgfutil@tempdima\advance\pgf@x by.5\pgfutil@tempdimb} + \pgfarrowssetbackend{-1.36\pgfutil@tempdima\advance\pgf@x by.5\pgfutil@tempdimb} + \pgfarrowsupperhullpoint{-1.4\pgfutil@tempdima}{2.8\pgfutil@tempdima} + \pgfarrowsupperhullpoint{2\pgfutil@tempdima}{.5\pgfutil@tempdimb} + \pgfarrowssavethe\pgfutil@tempdima + \pgfarrowssavethe\pgfutil@tempdimb + }, + drawing code = { + \pgftransformxshift{.06\pgfutil@tempdima} + \pgfsetlinewidth{\pgfutil@tempdimb} + \pgfsetdash{}{+0pt} + \pgfsetroundcap + \pgfsetroundjoin + \pgfpathmoveto{\pgfpoint{-1.4\pgfutil@tempdima}{2.65\pgfutil@tempdima}} + \pgfpathcurveto + {\pgfpoint{-0.75\pgfutil@tempdima}{1.25\pgfutil@tempdima}} + {\pgfpoint{1\pgfutil@tempdima}{0.05\pgfutil@tempdima}} + {\pgfpoint{2\pgfutil@tempdima}{0pt}} + \pgfpathcurveto + {\pgfpoint{1\pgfutil@tempdima}{-0.05\pgfutil@tempdima}} + {\pgfpoint{-.75\pgfutil@tempdima}{-1.25\pgfutil@tempdima}} + {\pgfpoint{-1.4\pgfutil@tempdima}{-2.65\pgfutil@tempdima}} + \pgfusepathqstroke + }, + parameters = {\the\pgfarrowlength} +}% + + + + + + + +\pgfdeclarearrow{ + name = Latex, + defaults = { + length = +3pt 4.5 .8,% + width' = +0pt .75, + line width = +0pt 1 1, + }, + setup code = { + \pgf@x.2\pgfarrowlength + \ifdim\pgf@x<\pgfarrowlinewidth + \pgfarrowlinewidth\pgf@x + \fi + \pgfarrowssavethe\pgfarrowlinewidth% + \pgfmathdivide@{\pgf@sys@tonumber\pgfarrowlength}{\pgf@sys@tonumber\pgfarrowwidth}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x9\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@xc\pgfmathresult\pgfarrowlinewidth% + \pgf@xa\pgf@temp@quot\pgfarrowlinewidth + \pgfutil@tempdima\pgfarrowlength% + \advance\pgfutil@tempdima by-.5\pgf@xc% + \advance\pgfutil@tempdima by-.5\pgfarrowlinewidth% + \pgfarrowssetbackend{-.5\pgfarrowlinewidth} + \ifpgfarrowreversed + \ifdim\pgfinnerlinewidth>0pt + \pgfarrowssetlineend{0pt} + \else + \pgfarrowssetlineend{\pgfutil@tempdima\advance\pgf@x by-.5\pgflinewidth} + \fi + \else + \pgfarrowssetlineend{0pt} + \fi + \ifpgfarrowroundjoin + \pgfarrowssettipend{\pgfutil@tempdima\advance\pgf@x by.5\pgfarrowlinewidth} + \else + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth\ifpgfarrowharpoon\advance\pgf@x by1.5\pgf@xa\fi} + \fi + \pgfarrowssavethe\pgfutil@tempdima + \pgf@process{\pgfpointnormalised{\pgfqpoint{.3\pgfarrowlength}{.2333333\pgfarrowwidth}}}% + \advance\pgf@y by1pt% + \pgf@yc\pgf@y\pgf@xc\pgf@x% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@yc}{\pgf@sys@tonumber\pgf@xc}% + \pgfutil@tempdimb\pgfmathresult\pgfarrowlinewidth% + \pgfutil@tempdimb-.5\pgfutil@tempdimb% + \advance\pgfutil@tempdimb by.5\pgfarrowwidth% + \pgfarrowssavethe\pgfutil@tempdimb% + \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth\ifpgfarrowroundjoin\else\ifpgfarrowharpoon\advance\pgf@x by1.5\pgf@xa\fi\fi}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else0pt\fi}% + \pgfarrowshullpoint{-.5\pgfarrowlinewidth}{.5\pgfarrowwidth\ifpgfarrowharpoon\advance\pgf@y by-.5\pgfarrowlinewidth\fi}% + \pgfarrowshullpoint{-.5\pgfarrowlinewidth}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else-.5\pgfarrowwidth\fi}% + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \pgfpathmoveto {\pgfqpoint{\pgfutil@tempdima}{0pt}} + \pgfpathcurveto {\pgfqpoint{.877192\pgfutil@tempdima}{.077922\pgfutil@tempdimb}} + {\pgfqpoint{.337381\pgfutil@tempdima}{.519480\pgfutil@tempdimb}} + {\pgfqpoint{0pt}{\pgfutil@tempdimb}} + \ifpgfarrowharpoon + \pgfpathlineto {\pgfpointorigin} + \else + \pgfpathlineto {\pgfqpoint{0pt}{-\pgfutil@tempdimb}} + \pgfpathcurveto {\pgfqpoint{.337381\pgfutil@tempdima}{-.519480\pgfutil@tempdimb}} + {\pgfqpoint{.877192\pgfutil@tempdima}{-.077922\pgfutil@tempdimb}} + {\pgfqpoint{\pgfutil@tempdima}{0pt}} + \fi + \pgfpathclose + \ifpgfarrowopen\pgfusepathqstroke\else\ifdim\pgfarrowlinewidth>0pt\pgfusepathqfillstroke\else\pgfusepathqfill\fi\fi + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowopen o\fi% + \ifpgfarrowroundjoin j\fi% + }, +}% + + + + +\pgfdeclarearrow{ + name = Stealth, + defaults = { + length = +3pt 4.5 .8, + width' = +0pt .75, + inset' = +0pt 0.325, + line width = +0pt 1 1, + }, + setup code = { + \pgf@x\pgfarrowlength + \advance\pgf@x by-\pgfarrowinset + \pgf@x.25\pgf@x + \ifdim\pgf@x<\pgfarrowlinewidth + \pgfarrowlinewidth\pgf@x + \fi + \pgfmathdivide@{\pgf@sys@tonumber\pgfarrowlength}{\pgf@sys@tonumber\pgfarrowwidth}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x4\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@xc\pgfmathresult\pgfarrowlinewidth% + \pgf@xc.5\pgf@xc + \pgf@xa\pgf@temp@quot\pgfarrowlinewidth% + \pgf@ya.5\pgfarrowwidth% + \csname pgfmathatan2@\endcsname{\pgfmath@tonumber\pgfarrowlength}{\pgfmath@tonumber\pgf@ya}% + \pgf@yb\pgfmathresult pt% + \csname pgfmathatan2@\endcsname{\pgfmath@tonumber\pgfarrowinset}{\pgfmath@tonumber\pgf@ya}% + \pgf@ya\pgfmathresult pt% + \advance\pgf@yb by-\pgf@ya% + \pgf@yb.5\pgf@yb% + \pgfmathtan@{\pgf@sys@tonumber\pgf@yb}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@yc\pgfmathresult\pgfarrowlinewidth% + \pgf@yc.5\pgf@yc% + \advance\pgf@ya by\pgf@yb% + \pgfmathsincos@{\pgf@sys@tonumber\pgf@ya}% + \pgf@ya\pgfmathresulty\pgf@yc% + \pgf@yb\pgfmathresultx\pgf@yc% + \ifdim\pgfarrowinset=0pt% + \pgf@ya.5\pgfarrowlinewidth% + \fi + \pgfmathdivide@{\pgf@sys@tonumber\pgfarrowinset}{\pgf@sys@tonumber\pgfarrowwidth}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x4\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@yc\pgfmathresult\pgfarrowlinewidth% + \pgf@yc.5\pgf@yc% + \pgfutil@tempdima\pgfarrowlength% + \advance\pgfutil@tempdima by-\pgf@xc% + \advance\pgfutil@tempdima by-\pgf@ya% + \pgfutil@tempdimb.5\pgfarrowwidth% + \advance\pgfutil@tempdimb by-\pgf@yb% + \ifpgfarrowroundjoin + \pgfarrowssetbackend{\pgf@ya\advance\pgf@x by-.5\pgfarrowlinewidth} + \else + \pgfarrowssetbackend{0pt} + \fi + \ifpgfarrowharpoon + \pgfarrowssetlineend{\pgfarrowinset\advance\pgf@x + by\pgf@yc\advance\pgf@x by.5\pgfarrowlinewidth} + \else + \pgfarrowssetlineend{\pgfarrowinset\advance\pgf@x by\pgf@yc\advance\pgf@x by-.25\pgfarrowlinewidth} + \ifpgfarrowreversed + \ifdim\pgfinnerlinewidth>0pt + \pgfarrowssetlineend{\pgfarrowinset} + \else + \pgfarrowssetlineend{\pgfutil@tempdima\advance\pgf@x by\pgf@ya\advance\pgf@x by-.25\pgfarrowlinewidth} + \fi + \fi + \fi + \ifpgfarrowroundjoin + \pgfarrowssettipend{\pgfutil@tempdima\advance\pgf@x by\pgf@ya\advance\pgf@x by.5\pgfarrowlinewidth} + \else + \pgfarrowssettipend{\pgfarrowlength\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi} + \fi + \pgfarrowshullpoint{\pgfarrowlength\ifpgfarrowroundjoin\else\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi\fi}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else0pt\fi}% + \pgfarrowsupperhullpoint{0pt}{.5\pgfarrowwidth}% + \pgfarrowshullpoint{\pgfarrowinset}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else 0pt\fi}% + \pgfarrowssetvisualbackend{\pgfarrowinset} + \advance\pgfarrowinset by\pgf@yc% + \pgfarrowssavethe\pgfutil@tempdima + \pgfarrowssavethe\pgfutil@tempdimb + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgf@ya + \pgfarrowssavethe\pgfarrowinset + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \pgfpathmoveto{\pgfqpoint{\pgfutil@tempdima\advance\pgf@x by\pgf@ya}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgf@ya}{\pgfutil@tempdimb}} + \pgfpathlineto{\pgfqpoint{\pgfarrowinset}{0pt}} + \ifpgfarrowharpoon \else + \pgfpathlineto{\pgfqpoint{\pgf@ya}{-\pgfutil@tempdimb}} + \fi + \pgfpathclose + \ifpgfarrowopen\pgfusepathqstroke\else\ifdim\pgfarrowlinewidth>0pt\pgfusepathqfillstroke\else\pgfusepathqfill\fi\fi + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \the\pgfarrowinset,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowopen o\fi% + \ifpgfarrowroundjoin j\fi% + }, +}% + + + + +\pgfdeclarearrow{ + name = Kite, + defaults = { + length = +3.6pt +5.4, + width' = +0pt +0.5, + inset' = +0pt 0.25, + line width = +0pt 1 1, + }, + setup code = { + \pgf@x.4\pgfarrowlength + \ifdim\pgf@x<\pgfarrowlinewidth + \pgfarrowlinewidth\pgf@x + \fi + \pgf@x.4\pgfarrowwidth + \ifdim\pgf@x<\pgfarrowlinewidth + \pgfarrowlinewidth\pgf@x + \fi + \pgf@xa\pgfarrowlength% + \advance\pgf@xa by-\pgfarrowinset% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgfarrowwidth}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x4\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@xc\pgfmathresult\pgfarrowlinewidth% + \pgf@xc.5\pgf@xc + \pgf@xa\pgf@temp@quot\pgfarrowlinewidth% + \pgfmathdivide@{\pgf@sys@tonumber\pgfarrowinset}{\pgf@sys@tonumber\pgfarrowwidth}% + \let\pgf@temp@quot\pgfmathresult% + \pgf@x\pgfmathresult pt% + \pgf@x\pgfmathresult\pgf@x% + \pgf@x4\pgf@x% + \advance\pgf@x by1pt% + \pgfmathsqrt@{\pgf@sys@tonumber\pgf@x}% + \pgf@yc\pgfmathresult\pgfarrowlinewidth% + \pgf@yc.5\pgf@yc + \pgf@ya\pgf@temp@quot\pgfarrowlinewidth% + {% + \pgfutil@tempdimb.5\pgfarrowwidth% + \pgfutil@tempdima\pgfarrowlength\advance\pgfutil@tempdima by-\pgfarrowinset% + \csname pgfmathatan2@\endcsname{\pgfmath@tonumber\pgfutil@tempdima}{\pgfmath@tonumber\pgfutil@tempdimb}% + \pgf@yb\pgfmathresult pt% + \csname pgfmathatan2@\endcsname{\pgfmath@tonumber\pgfarrowinset}{\pgfmath@tonumber\pgfutil@tempdimb}% + \pgf@ya\pgfmathresult pt% + \advance\pgf@yb by\pgf@ya% + \pgf@yb.5\pgf@yb% + \ifdim\pgf@yb=45pt% + \def\pgfmathresult{1.414213}% + \else% + \pgfmathsin@{\pgf@sys@tonumber\pgf@yb}% + \pgfmathreciprocal@{\pgfmathresult}% + \fi% + \pgf@yc\pgfmathresult\pgfarrowlinewidth% + \pgf@yc.5\pgf@yc% + \pgf@ya-\pgf@ya% + \advance\pgf@ya by-90pt% + \advance\pgf@ya by\pgf@yb% + \pgfmathsincos@{\pgf@sys@tonumber\pgf@ya}% + \pgf@xb\pgfmathresultx\pgf@yc% + \pgf@yb\pgfmathresulty\pgf@yc% + \expandafter\expandafter\expandafter% + }\expandafter\expandafter\expandafter\pgf@xb\expandafter\the\expandafter\pgf@xb\expandafter\pgf@yb\the\pgf@yb% + \pgfutil@tempdima\pgfarrowlength% + \advance\pgfutil@tempdima by-\pgf@xc% + \pgfutil@tempdimb.5\pgfarrowwidth% + \advance\pgfutil@tempdimb by\pgf@yb% + \ifpgfarrowroundjoin + \pgfarrowssetbackend{\pgf@ya\advance\pgf@x by-.5\pgfarrowlinewidth} + \else + \pgfarrowssetbackend{0pt} + \fi + \ifpgfarrowreversed + \pgfarrowssetlineend{\pgfutil@tempdima\advance\pgf@x by-\pgflinewidth\advance\pgf@x by\pgfarrowlinewidth} + \else + \pgfarrowssetlineend{\pgf@yc\advance\pgf@x by\pgflinewidth\advance\pgf@x by-\pgfarrowlinewidth} + \fi + \ifpgfarrowroundjoin + \pgfarrowssettipend{\pgfutil@tempdima\advance\pgf@x by.5\pgfarrowlinewidth} + \else + \pgfarrowssettipend{\pgfarrowlength\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi} + \fi + \pgfarrowshullpoint{\pgfarrowlength\ifpgfarrowroundjoin\else\ifpgfarrowharpoon\advance\pgf@x by\pgf@xa\fi\fi}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else0pt\fi}% + \pgfarrowsupperhullpoint{\pgfarrowinset}{.5\pgfarrowwidth}% + \pgfarrowshullpoint{0pt}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else0pt\fi}% + \advance\pgfarrowinset by\pgf@xb% + \pgfarrowssavethe\pgfutil@tempdima + \pgfarrowssavethe\pgfutil@tempdimb + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgf@yc + \pgfarrowssavethe\pgfarrowinset + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{\pgfarrowlinewidth}\fi + \pgfpathmoveto{\pgfqpoint{\pgfutil@tempdima}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgfarrowinset}{\pgfutil@tempdimb}} + \pgfpathlineto{\pgfqpoint{\pgf@yc}{0pt}} + \ifpgfarrowharpoon \else + \pgfpathlineto{\pgfqpoint{\pgfarrowinset}{-\pgfutil@tempdimb}} + \fi + \pgfpathclose + \ifpgfarrowopen\pgfusepathqstroke\else\ifdim\pgfarrowlinewidth>0pt\pgfusepathqfillstroke\else\pgfusepathqfill\fi\fi + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \the\pgfarrowinset,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowopen o\fi% + \ifpgfarrowroundjoin j\fi% + }, +}% + + + + + +\pgfdeclarearrow{ + name = Square, + defaults = { + length = +2.12132pt +2.828427, + width' = +0pt +1, + line width = +0pt +1 +1, + }, + setup code = { + \pgf@x.5\pgfarrowlength + \ifdim\pgf@x<\pgfarrowlinewidth + \pgfarrowlinewidth\pgf@x + \fi + \ifpgfarrowreversed + \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth} + \else + \pgfarrowssetlineend{.5\pgfarrowlinewidth} + \fi + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowshullpoint{\pgfarrowlength}{.5\pgfarrowwidth} + \pgfarrowshullpoint{0pt}{.5\pgfarrowwidth} + \pgfarrowshullpoint{\pgfarrowlength}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else-.5\pgfarrowwidth\fi} + \pgfarrowshullpoint{0pt}{\ifpgfarrowharpoon-.5\pgfarrowlinewidth\else-.5\pgfarrowwidth\fi} + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowwidth + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \pgfpathmoveto{\pgfqpoint{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \pgfpathlineto{\pgfqpoint{.5\pgfarrowlinewidth}{.5\pgfarrowwidth\advance\pgf@y by-.5\pgfarrowlinewidth}} + \pgfpathlineto{\pgfqpoint{.5\pgfarrowlinewidth}{\ifpgfarrowharpoon0pt\else-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth\fi}} + \pgfpathlineto{\pgfqpoint{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth}{\ifpgfarrowharpoon0pt\else-.5\pgfarrowwidth\advance\pgf@y by.5\pgfarrowlinewidth\fi}} + \pgfpathclose + \ifpgfarrowopen\pgfusepathqstroke\else\ifdim\pgfarrowlinewidth>0pt\pgfusepathqfillstroke\else\pgfusepathqfill\fi\fi + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowopen o\fi% + \ifpgfarrowroundjoin j\fi% + }, +}% + + + +\pgfdeclarearrow{ + name = Circle, + defaults = { + length = +2.39365pt +3.191538, + width' = +0pt 1, + line width = +0pt 1 1, + }, + setup code = { + \pgf@x.5\pgfarrowlength + \ifdim\pgf@x<\pgfarrowlinewidth + \pgfarrowlinewidth\pgf@x + \fi + \ifpgfarrowreversed + \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by-.5\pgfarrowlinewidth} + \else + \pgfarrowssetlineend{.5\pgfarrowlinewidth} + \fi + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowsupperhullpoint{\pgfarrowlength}{.25\pgfarrowwidth} + \pgfarrowsupperhullpoint{.75\pgfarrowlength}{.5\pgfarrowwidth} + \pgfarrowsupperhullpoint{.25\pgfarrowlength}{.5\pgfarrowwidth} + \pgfarrowsupperhullpoint{0pt}{.25\pgfarrowwidth} + \ifpgfarrowharpoon% + \pgfarrowshullpoint{0pt}{-.5\pgfarrowlinewidth} + \pgfarrowshullpoint{\pgfarrowlength}{-.5\pgfarrowlinewidth} + \fi% + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowwidth + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundjoin\pgfsetroundjoin\else\pgfsetmiterjoin\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + \ifpgfarrowharpoon + \pgfpathmoveto{\pgfqpoint{\pgfarrowlength\advance\pgf@x + by-.5\pgfarrowlinewidth}{0pt}} + {% + \pgf@xa.5\pgfarrowlength + \advance\pgf@xa by-.5\pgfarrowlinewidth + \pgftransformxscale{+\the\pgf@xa} + \pgf@xa.5\pgfarrowwidth + \advance\pgf@xa by-.5\pgfarrowlinewidth + \pgftransformyscale{+\the\pgf@xa} + \pgfpatharc{0}{180}{1pt} + } + \pgfpathclose + \else% + \pgfpathellipse{\pgfqpoint{.5\pgfarrowlength}{0pt}}{\pgfqpoint{.5\pgfarrowlength\advance\pgf@x + by-.5\pgfarrowlinewidth}{0pt}}{\pgfqpoint{0pt}{.5\pgfarrowwidth\advance\pgf@y + by-.5\pgfarrowlinewidth}} + \fi + \ifpgfarrowopen\pgfusepathqstroke\else\ifdim\pgfarrowlinewidth>0pt\pgfusepathqfillstroke\else\pgfusepathqfill\fi\fi + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowopen o\fi% + \ifpgfarrowroundjoin j\fi% + }, +}% + + +\pgfdeclarearrow{ + name = Round Cap, + defaults = { + length = +0pt .5 + }, + setup code = { + \ifpgfarrowreversed + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by.5\pgflinewidth} + \else + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowssetlineend{-.5\pgflinewidth} + \fi + \pgfarrowssavethe\pgfarrowlength + \pgfarrowsupperhullpoint{0pt}{.5\pgflinewidth} + \pgfarrowsupperhullpoint{\pgfarrowlength}{.5\pgflinewidth} + }, + drawing code = { + \ifpgfarrowreversed + \pgftransformxscale{-1} + \pgftransformxshift{-\pgfarrowlength} + \fi + \pgfutil@tempdima.5\pgflinewidth + \pgfpathmoveto {\pgfqpoint{-0.75\pgflinewidth}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{0pt}{\pgfutil@tempdima}} + \ifpgfarrowreversed + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{\pgfutil@tempdima}} + \begingroup + \pgftransformxshift{\pgfarrowlength} + \pgftransformxscale{-1} + \fi + \pgfpathcurveto {\pgfqpoint{0.55228475\pgfarrowlength}{\pgfutil@tempdima}} + {\pgfqpoint{\pgfarrowlength}{0.55228475\pgfutil@tempdima}} + {\pgfqpoint{\pgfarrowlength}{0pt}} + \pgfpathcurveto {\pgfqpoint{\pgfarrowlength}{-0.55228475\pgfutil@tempdima}} + {\pgfqpoint{0.55228475\pgfarrowlength}{-\pgfutil@tempdima}} + {\pgfqpoint{0pt}{-\pgfutil@tempdima}} + \ifpgfarrowreversed + \endgroup + \fi + \pgfpathlineto {\pgfqpoint{-.75\pgflinewidth}{-\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfill + }, + parameters = {\the\pgfarrowlength} +}% + + + +\pgfdeclarearrow{ + name = Butt Cap, + defaults = { + length = +0pt .5 + }, + setup code = { + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowssetlineend{-.5\pgflinewidth} + \pgfarrowssavethe\pgfarrowlength + \pgfarrowsupperhullpoint{0pt}{.5\pgflinewidth} + \pgfarrowsupperhullpoint{\pgfarrowlength}{.5\pgflinewidth} + }, + drawing code = { + \pgfutil@tempdima.5\pgflinewidth + \pgfpathmoveto {\pgfqpoint{-0.75\pgflinewidth}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{0pt}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{-\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{-.75\pgflinewidth}{-\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfill + }, + parameters = {\the\pgfarrowlength} +}% + + + +\pgfkeys{ + /pgf/arrow keys/.cd, + cap angle/.code={% + \pgfmathsetlength\pgf@x{#1}% + \pgf@x.5\pgf@x + \pgfmathtan@{\pgf@sys@tonumber\pgf@x}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@x\pgfmathresult pt% + \pgf@x.5\pgf@x% + \edef\pgf@marshal{\noexpand\pgfarrowsaddtooptions{\noexpand\pgfarrowslinewidthdependent{+0pt}{\pgf@sys@tonumber\pgf@x}{0}\pgfarrowlength\pgf@x}} + \pgf@marshal + } +}% + + +\pgfdeclarearrow{ + name = Triangle Cap, + defaults = { + length = +0pt .5 + }, + setup code = { + \ifpgfarrowreversed + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by.5\pgflinewidth} + \else + \pgfarrowssettipend{\pgfarrowlength} + \pgfarrowssetlineend{-.5\pgflinewidth} + \fi + \pgfarrowssavethe\pgfarrowlength + \pgfarrowsupperhullpoint{0pt}{.5\pgflinewidth} + \pgfarrowshullpoint{\pgfarrowlength}{0pt} + }, + drawing code = { + \ifpgfarrowreversed + \pgftransformxscale{-1} + \pgftransformxshift{-\pgfarrowlength} + \fi + \pgfutil@tempdima.5\pgflinewidth + \pgfpathmoveto {\pgfqpoint{-0.75\pgflinewidth}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{0pt}{\pgfutil@tempdima}} + \ifpgfarrowreversed + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{\pgfutil@tempdima}} + \begingroup + \pgftransformxshift{\pgfarrowlength} + \pgftransformxscale{-1} + \fi + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{0pt}} + \ifpgfarrowreversed + \endgroup + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{-\pgfutil@tempdima}} + \fi + \pgfpathlineto {\pgfqpoint{0pt}{-\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{-.75\pgflinewidth}{-\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfill + }, + parameters = {\the\pgfarrowlength} +}% + + + +\pgfdeclarearrow{ + name = Fast Triangle, + defaults = { + length = +0pt .5, + inset = +0pt .5, + }, + setup code = { + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by\pgfarrowinset} + \ifpgfarrowreversed\pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by\pgfarrowinset}\fi + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowinset + \pgfarrowsupperhullpoint{0pt}{.5\pgflinewidth} + \pgfarrowsupperhullpoint{\pgfarrowinset}{.5\pgflinewidth} + \pgfarrowshullpoint{\pgfarrowlength\advance\pgf@x by\pgfarrowinset}{0pt} + }, + drawing code = { + \pgfutil@tempdima.5\pgflinewidth + \pgfpathmoveto {\pgfqpoint{0pt}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{\pgfarrowinset}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{\pgfarrowinset\advance\pgf@x by\pgfarrowlength}{0pt}} + \pgfpathlineto {\pgfqpoint{\pgfarrowinset}{-\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{0pt}{-\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{\pgfarrowlength}{0pt}} + \pgfpathclose + \pgfusepathqfill + }, + parameters = {\the\pgfarrowlength,\the\pgfarrowinset} +}% + + +\pgfdeclarearrow{ + name = Fast Round, + defaults = { + length = +0pt .5, + inset = +0pt .5, + }, + setup code = { + \pgfarrowssettipend{\pgfarrowlength\advance\pgf@x by\pgfarrowinset} + \ifpgfarrowreversed\pgfarrowssetlineend{\pgfarrowlength\advance\pgf@x by\pgfarrowinset}\fi + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowinset + \pgfarrowsupperhullpoint{0pt}{.5\pgflinewidth} + \pgfarrowsupperhullpoint{\pgfarrowlength\advance\pgf@x by\pgfarrowinset}{.5\pgflinewidth} + }, + drawing code = { + \pgfutil@tempdima.5\pgflinewidth + \pgfpathmoveto {\pgfqpoint{0pt}{\pgfutil@tempdima}} + \pgfpathlineto {\pgfqpoint{\pgfarrowinset}{\pgfutil@tempdima}} + { + \pgftransformxshift{\pgfarrowinset} + \pgfpathcurveto{\pgfqpoint{0.55228475\pgfarrowlength}{\pgfutil@tempdima}} + {\pgfqpoint{\pgfarrowlength}{0.55228475\pgfutil@tempdima}} + {\pgfqpoint{\pgfarrowlength}{0pt}} + \pgfpathcurveto{\pgfqpoint{\pgfarrowlength}{-0.55228475\pgfutil@tempdima}} + {\pgfqpoint{0.55228475\pgfarrowlength}{-\pgfutil@tempdima}} + {\pgfqpoint{0pt}{-\pgfutil@tempdima}} + } + \pgfpathlineto {\pgfqpoint{0pt}{-\pgfutil@tempdima}} + \pgfpathcurveto {\pgfqpoint{0.55228475\pgfarrowlength}{-\pgfutil@tempdima}} + {\pgfqpoint{\pgfarrowlength}{-0.55228475\pgfutil@tempdima}} + {\pgfqpoint{\pgfarrowlength}{0pt}} + \pgfpathcurveto {\pgfqpoint{\pgfarrowlength}{0.55228475\pgfutil@tempdima}} + {\pgfqpoint{0.55228475\pgfarrowlength}{\pgfutil@tempdima}} + {\pgfqpoint{0pt}{\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfill + }, + parameters = {\the\pgfarrowlength,\the\pgfarrowinset} +}% + + + + + + +\pgfkeys{ + /pgf/arrow keys/.cd, + n/.code={% + \pgfmathparse{#1}% + \expandafter\pgf@lib@meta@strip@dot\pgfmathresult.\relax% + } +}% +\def\pgf@lib@meta@strip@dot#1.#2\relax{% + \pgfarrowsaddtooptions{\def\pgfarrown{#1}}% +}% + +\def\pgfarrown{4}% + +\pgfdeclarearrow{ + name = Rays, + defaults = { + length = +3pt 4, + width' = +0pt 1, + line width = +0pt 1 1, + }, + setup code = { + \pgfmathdivide@{360}{\pgfarrown}% + \let\pgfarrow@inc\pgfmathresult% + \pgf@xa\pgfarrow@inc pt% + \ifodd\pgfarrown\pgf@ya.25\pgf@xa\else\pgf@ya.5\pgf@xa\fi% + \pgfmathsincos@{\pgf@sys@tonumber\pgf@ya}% + \pgf@x.5\pgfarrowlength% + \pgf@xa\pgfmathresultx\pgf@x% + \ifpgfarrowroundcap + \advance\pgf@xa by.5\pgfarrowlinewidth + \else + \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgfmathresultx\pgfarrowlength}{\pgfmathresulty\pgfarrowwidth}}}% + \pgf@x.5\pgfarrowlinewidth% + \advance\pgf@xa by\pgf@sys@tonumber{\pgf@y}\pgf@x% + \fi% + \pgfarrowssettipend{\pgf@xa} + \pgfarrowssetbackend{-\pgf@xa} + \pgfarrowsupperhullpoint{\pgf@xa}{.25\pgfarrowwidth} + \pgfarrowsupperhullpoint{.25\pgfarrowlength}{.5\pgfarrowwidth\ifpgfarrowroundcap\advance\pgf@y by.5\pgfarrowlinewidth\fi} + \pgfarrowsupperhullpoint{-.25\pgfarrowlength}{.5\pgfarrowwidth\ifpgfarrowroundcap\advance\pgf@y by.5\pgfarrowlinewidth\fi} + \pgfarrowsupperhullpoint{-\pgf@xa}{.25\pgfarrowwidth} + \ifpgfarrowharpoon + \pgfarrowshullpoint{-.5\pgfarrowlength\ifpgfarrowroundcap\advance\pgf@x by-.5\pgfarrowlinewidth\fi}{-.5\pgfarrowlinewidth} + \pgfarrowshullpoint{.5\pgfarrowlength\ifpgfarrowroundcap\advance\pgf@x by.5\pgfarrowlinewidth\fi}{-.5\pgfarrowlinewidth} + \fi + \pgfarrowssavethe\pgfarrowlinewidth + \pgfarrowssavethe\pgfarrowlength + \pgfarrowssavethe\pgfarrowwidth + \pgfarrowssave\pgfarrow@inc + \pgfarrowssave\pgfarrown + }, + drawing code = { + \pgfsetdash{}{+0pt} + \ifpgfarrowroundcap\pgfsetroundcap\else\pgfsetbuttcap\fi + \ifdim\pgfarrowlinewidth=\pgflinewidth\else\pgfsetlinewidth{+\pgfarrowlinewidth}\fi + {% + \pgfgettransform\pgf@temp@trans + \pgftransformxscale{+.5\pgfarrowlength} + \pgftransformyscale{+.5\pgfarrowwidth} + \pgf@xa\pgfarrow@inc pt% + \ifodd\pgfarrown\pgf@ya.25\pgf@xa\else\pgf@ya.5\pgf@xa\fi% + \ifpgfarrowharpoon\pgf@yb180pt\else\pgf@yb360pt\fi + \pgfutil@loop% + \ifdim\pgf@ya<\pgf@yb% + \pgfpathmoveto{\pgfpointpolar{+\pgf@ya}{+1pt}} + \pgfpathlineto{\pgfpointorigin} + \ifpgfarrowharpoon\ifdim\pgf@ya>\pgf@xa\else{\pgfsettransform\pgf@temp@trans\pgfpathlineto{\pgfqpoint{-.5\pgflinewidth}{0pt}}}\fi\fi + \advance\pgf@ya by\pgf@xa\relax% + \pgfutil@repeat% + } + \pgfusepathqstroke + }, + parameters = { + \the\pgfarrowlinewidth,% + \the\pgfarrowlength,% + \the\pgfarrowwidth,% + \pgfarrown,% + \ifpgfarrowharpoon h\fi% + \ifpgfarrowroundcap c\fi% + } +}% + + + + +\pgfkeys{ + LaTeX /.tip = {Latex}, + Triangle /.tip = {Stealth[inset=+0pt, angle=+60:+2.7pt +3.6]}, + Rectangle /.tip = {Square[length=+3pt +4.5,width'=+0pt +.5]}, + Ellipse /.tip = {Circle[length=+3.3pt +4.95, width'=+0pt +0.5]}, + Diamond /.tip = {Kite[inset'=+0pt .5]}, + Turned Square /.tip = {Kite[length=+3pt 4,width'= +0pt 1,inset'= +0pt 0.5]}, + To /.tip = {Computer Modern Rightarrow}, + Bar /.tip = {Tee Barb[length=+0pt]}, + Bracket /.tip = {Tee Barb[inset'=+0pt +1,length=+0.75pt +1]}, + Parenthesis /.tip = {Arc Barb[arc=+120,length=+1.725pt +2.3]} +}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.spaced.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.spaced.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f972d7afdbc163ffb238c12c9b848c035780fbe4 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryarrows.spaced.code.tex @@ -0,0 +1,78 @@ + +\ProvidesFileRCS{pgflibraryarrows.spaced.code.tex} + + +\usepgflibrary{arrows}% + + + + +\pgfarrowsdeclarecombine*{spaced to}{spaced to}{to}{to}{space}{space}% +\pgfarrowsdeclarecombine*{spaced to reversed}{spaced to reversed}{to reversed}{to reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced implies}{spaced implies}{implies}{implies}{space}{space}% +\pgfarrowsdeclarecombine*{spaced latex}{spaced latex}{latex}{latex}{space}{space}% +\pgfarrowsdeclarecombine*{spaced latex reversed}{spaced latex reversed}{latex reversed}{latex reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced latex'}{spaced latex'}{latex'}{latex'}{space}{space}% +\pgfarrowsdeclarecombine*{spaced latex' reversed}{spaced latex' reversed}{latex' reversed}{latex' reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced stealth}{spaced stealth}{stealth}{stealth}{space}{space}% +\pgfarrowsdeclarecombine*{spaced stealth reversed}{spaced stealth reversed}{stealth reversed}{stealth reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced stealth'}{spaced stealth'}{stealth'}{stealth'}{space}{space}% +\pgfarrowsdeclarecombine*{spaced stealth' reversed}{spaced stealth' reversed}{stealth' reversed}{stealth' reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 90}{spaced triangle 90}{triangle 90}{triangle 90}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 90 reversed}{spaced triangle 90 reversed}{triangle 90 reversed}{triangle 90 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 60}{spaced triangle 60}{triangle 60}{triangle 60}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 60 reversed}{spaced triangle 60 reversed}{triangle 60 reversed}{triangle 60 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 45}{spaced triangle 45}{triangle 45}{triangle 45}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 45 reversed}{spaced triangle 45 reversed}{triangle 45 reversed}{triangle 45 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open triangle 90}{spaced open triangle 90}{open triangle 90}{open triangle 90}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open triangle 90 reversed}{spaced open triangle 90 reversed}{open triangle 90 reversed}{open triangle 90 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open triangle 60}{spaced open triangle 60}{open triangle 60}{open triangle 60}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open triangle 60 reversed}{spaced open triangle 60 reversed}{open triangle 60 reversed}{open triangle 60 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open triangle 45}{spaced open triangle 45}{open triangle 45}{open triangle 45}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open triangle 45 reversed}{spaced open triangle 45 reversed}{open triangle 45 reversed}{open triangle 45 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced angle 90}{spaced angle 90}{angle 90}{angle 90}{space}{space}% +\pgfarrowsdeclarecombine*{spaced angle 90 reversed}{spaced angle 90 reversed}{angle 90 reversed}{angle 90 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced angle 60}{spaced angle 60}{angle 60}{angle 60}{space}{space}% +\pgfarrowsdeclarecombine*{spaced angle 60 reversed}{spaced angle 60 reversed}{angle 60 reversed}{angle 60 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced angle 45}{spaced angle 45}{angle 45}{angle 45}{space}{space}% +\pgfarrowsdeclarecombine*{spaced angle 45 reversed}{spaced angle 45 reversed}{angle 45 reversed}{angle 45 reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced hooks}{spaced hooks}{hooks}{hooks}{space}{space}% +\pgfarrowsdeclarecombine*{spaced hooks reversed}{spaced hooks reversed}{hooks reversed}{hooks reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced o}{spaced o}{o}{o}{space}{space}% +\pgfarrowsdeclarecombine*{spaced *}{spaced *}{*}{*}{space}{space}% +\pgfarrowsdeclarecombine*{spaced diamond}{spaced diamond}{diamond}{diamond}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open diamond}{spaced open diamond}{open diamond}{open diamond}{space}{space}% +\pgfarrowsdeclarecombine*{spaced square}{spaced square}{square}{square}{space}{space}% +\pgfarrowsdeclarecombine*{spaced open square}{spaced open square}{open square}{open square}{space}{space}% +\pgfarrowsdeclarecombine*{spaced serif cm}{spaced serif cm}{serif cm}{serif cm}{space}{space}% +\pgfarrowsdeclarecombine*{spaced left to}{spaced left to}{left to}{left to}{space}{space}% +\pgfarrowsdeclarecombine*{spaced left to reversed}{spaced left to reversed}{left to reversed}{left to reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced right to}{spaced right to}{right to}{right to}{space}{space}% +\pgfarrowsdeclarecombine*{spaced right to reversed}{spaced right to reversed}{right to reversed}{right to reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced left hook}{spaced left hook}{left hook}{left hook}{space}{space}% +\pgfarrowsdeclarecombine*{spaced left hook reversed}{spaced left hook reversed}{left hook reversed}{left hook reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced right hook}{spaced right hook}{right hook}{right hook}{space}{space}% +\pgfarrowsdeclarecombine*{spaced right hook reversed}{spaced right hook reversed}{right hook reversed}{right hook reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced round cap}{spaced round cap}{round cap}{round cap}{space}{space}% +\pgfarrowsdeclarecombine*{spaced butt cap}{spaced butt cap}{butt cap}{butt cap}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 90 cap}{spaced triangle 90 cap}{triangle 90 cap}{triangle 90 cap}{space}{space}% +\pgfarrowsdeclarecombine*{spaced triangle 90 cap reversed}{spaced triangle 90 cap reversed}{triangle 90 cap reversed}{triangle 90 cap reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced fast cap}{spaced fast cap}{fast cap}{fast cap}{space}{space}% +\pgfarrowsdeclarecombine*{spaced fast cap reversed}{spaced fast cap reversed}{fast cap reversed}{fast cap reversed}{space}{space}% +\pgfarrowsdeclarecombine*{spaced (}{spaced )}{(}{)}{space}{space}% +\pgfarrowsdeclarecombine*{spaced )}{spaced (}{)}{(}{space}{space}% +\pgfarrowsdeclarecombine*{spaced |}{spaced |}{|}{|}{space}{space}% + +\pgfdeclarearrow{ + name = spaced [-spaced ], + means = square bracket[].space +}% + +\pgfdeclarearrow{ + name = spaced ]-spaced [, + means = square bracket[reversed].space +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarycurvilinear.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarycurvilinear.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..791ef1269b3b204fcfc4490ec587c0431492ff6b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarycurvilinear.code.tex @@ -0,0 +1,263 @@ + +\ProvidesFileRCS{pgflibrarycurvilinear.code.tex} + + + + + + + +\def\pgfsetcurvilinearbeziercurve#1#2#3#4{% + \pgf@process{#1}% + \edef\pgf@curvilinear@line@a{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xa=-\pgf@x% + \pgf@ya=-\pgf@y% + \pgf@process{#2}% + \edef\pgf@curvilinear@line@b{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xb=-\pgf@x% + \pgf@yb=-\pgf@y% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@lenab\pgfmathresult% + \pgf@process{#3}% + \edef\pgf@curvilinear@line@c{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xc=-\pgf@x% + \pgf@yc=-\pgf@y% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@lenbc\pgfmathresult% + \pgf@process{#4}% + \edef\pgf@curvilinear@line@d{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@lencd\pgfmathresult + \pgf@x=\pgf@curvilinear@lenab pt% + \advance\pgf@x by\pgf@curvilinear@lenbc pt% + \advance\pgf@x by\pgf@curvilinear@lencd pt% + \pgfmathreciprocal@{\pgf@sys@tonumber\pgf@x}% + \pgf@curvilinear@time@a\pgfmathresult pt% + \pgf@process{\pgfpointcurveattime{\pgf@curvilinear@time@a}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}}% + \pgf@xb=-\pgf@x% + \pgf@yb=-\pgf@y% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgf@curvilinear@length@a\pgfmathresult pt% + \ifdim\pgf@curvilinear@length@a>1pt\relax% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@curvilinear@time@a}{\pgf@sys@tonumber\pgf@curvilinear@length@a}% + \pgf@curvilinear@time@a\pgfmathresult pt% + \pgf@process{\pgfpointcurveattime{\pgf@curvilinear@time@a}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}} + \pgf@xb=-\pgf@x% + \pgf@yb=-\pgf@y% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgf@curvilinear@length@a\pgfmathresult pt% + \fi% + \pgf@process{\pgfpointcurveattime{2\pgf@curvilinear@time@a}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}} + \pgf@xa=-\pgf@x% + \pgf@ya=-\pgf@y% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgf@curvilinear@length@b\pgfmathresult pt% + \advance\pgf@curvilinear@length@b by\pgf@curvilinear@length@a% + \pgf@process{\pgfpointcurveattime{4\pgf@curvilinear@time@a}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}} + \pgf@xb=-\pgf@x% + \pgf@yb=-\pgf@y% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgf@curvilinear@length@c\pgfmathresult pt% + \advance\pgf@curvilinear@length@c by\pgf@curvilinear@length@b% + \pgf@process{\pgfpointcurveattime{8\pgf@curvilinear@time@a}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}} + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + \pgfmathveclen@{\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + \pgf@curvilinear@length@d\pgfmathresult pt% + \advance\pgf@curvilinear@length@d by\pgf@curvilinear@length@c% + \let\pgf@curvilinear@comp@a\pgf@curvilinear@comp@a@initial% + \let\pgf@curvilinear@comp@b\pgf@curvilinear@comp@b@initial% + \let\pgf@curvilinear@comp@c\pgf@curvilinear@comp@c@initial% + \let\pgf@curvilinear@comp@d\pgf@curvilinear@comp@d@initial% + \let\pgf@curvilinear@comp@e\pgf@curvilinear@comp@e@initial% + \let\pgf@curvilinear@point\pgf@curvilinear@curve@point% +}% +\newdimen\pgf@curvilinear@time@a +\newdimen\pgf@curvilinear@length@a +\newdimen\pgf@curvilinear@length@b +\newdimen\pgf@curvilinear@length@c +\newdimen\pgf@curvilinear@length@d + + +\def\pgf@curvilinear@comp@a@initial{% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@curvilinear@time@a}{\pgf@sys@tonumber\pgf@curvilinear@length@a}% + \let\pgf@curvilinear@quot@a\pgfmathresult% + \let\pgf@curvilinear@comp@a\pgf@curvilinear@comp@a@cont% + \pgf@curvilinear@comp@a@cont% +}% +\def\pgf@curvilinear@comp@a@cont{% + \pgf@x\pgf@curvilinear@quot@a\pgf@x% +}% + +\def\pgf@curvilinear@comp@b@initial{% + \pgf@y=\pgf@curvilinear@length@b% + \advance\pgf@y by-\pgf@curvilinear@length@a% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@curvilinear@time@a}{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@quot@b\pgfmathresult% + \pgf@y\pgfmathresult\pgf@curvilinear@length@a% + \pgf@y-\pgf@y% + \advance\pgf@y by\pgf@curvilinear@time@a% + \edef\pgf@curvilinear@correct@b{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@comp@b\pgf@curvilinear@comp@b@cont% + \pgf@curvilinear@comp@b@cont% +}% +\def\pgf@curvilinear@comp@b@cont{% + \pgf@x\pgf@curvilinear@quot@b\pgf@x% + \advance\pgf@x by\pgf@curvilinear@correct@b pt% +}% + +\def\pgf@curvilinear@comp@c@initial{% + \pgf@y=\pgf@curvilinear@length@c% + \advance\pgf@y by-\pgf@curvilinear@length@b% + \pgf@y.5\pgf@y% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@curvilinear@time@a}{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@quot@c\pgfmathresult% + \pgf@y\pgf@curvilinear@quot@c\pgf@curvilinear@length@b% + \pgf@y-\pgf@y% + \advance\pgf@y by2\pgf@curvilinear@time@a% + \edef\pgf@curvilinear@correct@c{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@comp@c\pgf@curvilinear@comp@c@cont% + \pgf@curvilinear@comp@c@cont% +}% +\def\pgf@curvilinear@comp@c@cont{% + \pgf@x\pgf@curvilinear@quot@c\pgf@x% + \advance\pgf@x by\pgf@curvilinear@correct@c pt% +}% + +\def\pgf@curvilinear@comp@d@initial{% + \pgf@y=\pgf@curvilinear@length@d% + \advance\pgf@y by-\pgf@curvilinear@length@c% + \pgf@y.25\pgf@y% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@curvilinear@time@a}{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@quot@d\pgfmathresult% + \pgf@y\pgf@curvilinear@quot@d\pgf@curvilinear@length@c% + \pgf@y-\pgf@y% + \advance\pgf@y by4\pgf@curvilinear@time@a% + \edef\pgf@curvilinear@correct@d{\pgf@sys@tonumber\pgf@y}% + \let\pgf@curvilinear@comp@d\pgf@curvilinear@comp@d@cont% + \pgf@curvilinear@comp@d@cont% +}% +\def\pgf@curvilinear@comp@d@cont{% + \pgf@x\pgf@curvilinear@quot@d\pgf@x% + \advance\pgf@x by\pgf@curvilinear@correct@d pt% +}% + +\def\pgf@curvilinear@comp@e@initial{% + \pgfmathmultiply@{8}{\pgf@sys@tonumber\pgf@curvilinear@time@a}% + \expandafter\pgfmathdivide@\expandafter{\pgfmathresult}{\pgf@sys@tonumber\pgf@curvilinear@length@d}% + \let\pgf@curvilinear@quot@e\pgfmathresult% + \let\pgf@curvilinear@comp@e\pgf@curvilinear@comp@e@cont% + \pgf@curvilinear@comp@e@cont% +}% +\def\pgf@curvilinear@comp@e@cont{% + \pgf@x\pgf@curvilinear@quot@e\pgf@x% +}% + + + +\def\pgfcurvilineardistancetotime#1{% + \pgfmathsetlength{\pgf@x}{#1}% + \ifdim\pgf@x<\pgf@curvilinear@length@c\relax% + \ifdim\pgf@x<\pgf@curvilinear@length@a\relax% + \pgf@curvilinear@comp@a% + \else\ifdim\pgf@x<\pgf@curvilinear@length@b\relax% + \pgf@curvilinear@comp@b% + \else% + \pgf@curvilinear@comp@c% + \fi\fi% + \else\ifdim\pgf@x<\pgf@curvilinear@length@d\relax% + \pgf@curvilinear@comp@d% + \else% + \pgf@curvilinear@comp@e% + \fi\fi% +}% + + + + +\def\pgfpointcurvilinearbezierorthogonal#1#2{% + \pgfmathsetmacro\pgf@curvilinear@yfactor{#2}% + \pgfcurvilineardistancetotime{#1}% + \pgfpointcurveattime{\pgf@x}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d} + \pgf@xc\pgf@x% + \pgf@yc\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \ifdim\pgf@xb<0.0001pt\ifdim\pgf@xb>-0.0001pt\ifdim\pgf@yb<0.0001pt\ifdim\pgf@yb>-0.0001pt\pgf@diff@curvi@ac\fi\fi\fi\fi + \pgf@process{\pgfpointnormalised{\pgf@x=\pgf@yb\pgf@y=-\pgf@xb}} + \pgf@x\pgf@curvilinear@yfactor\pgf@x% + \pgf@y\pgf@curvilinear@yfactor\pgf@y% + \advance\pgf@x by\pgf@xc% + \advance\pgf@y by\pgf@yc% +}% + +\def\pgf@diff@curvi@ac{% + \pgf@curvilinear@line@a% + \pgf@xa\pgf@x\pgf@ya\pgf@y% + \pgf@curvilinear@line@c% + \pgf@xb\pgf@x\pgf@yb\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \ifdim\pgf@xb<0.0001pt\ifdim\pgf@xb>-0.0001pt\ifdim\pgf@yb<0.0001pt\ifdim\pgf@yb>-0.0001pt% + \pgf@curvilinear@line@d% + \pgf@xb\pgf@x\pgf@yb\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \fi\fi\fi\fi% + \pgf@xb-\pgf@xb% + \pgf@yb-\pgf@yb% +}% + + + + +\def\pgfpointcurvilinearbezierpolar#1#2{% + \pgfmathsetlength\pgfutil@tempdima{#1}% + \pgfmathsetlength\pgfutil@tempdimb{#2}% + \pgfpointnormalised{\pgfqpoint{\pgfutil@tempdima}{\pgfutil@tempdimb}}% + \ifdim\pgfutil@tempdimb=0pt\relax\ifdim\pgfutil@tempdima=0pt\pgf@x1pt\pgf@y0pt\fi\fi% + \ifdim\pgfutil@tempdima<0pt% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + \fi% + \pgf@ya=-\pgf@y% + \pgfsettransformentries% + {\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + {\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@x}{0pt}{0pt}% + \pgftransformshift{\pgfpointscale{-1}{\pgf@curvilinear@line@a}}% + \pgfmathveclen@{\pgf@sys@tonumber\pgfutil@tempdima}{\pgf@sys@tonumber\pgfutil@tempdimb}% + \ifdim\pgfutil@tempdima<0pt% + \edef\pgfmathresult{-\pgfmathresult}% + \fi% + \pgfcurvilineardistancetotime{\pgfmathresult}% + \pgf@process{% + \pgfpointadd{% + \pgfpointtransformed{% + \pgfpointcurveattime% + {\pgf@x}% + {\pgf@curvilinear@line@a}% + {\pgf@curvilinear@line@b}% + {\pgf@curvilinear@line@c}% + {\pgf@curvilinear@line@d}% + }% + }% + \pgf@curvilinear@line@a% + }% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfadings.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfadings.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ce86574f22b01adeb3162df7c0683d3c8ab75050 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfadings.code.tex @@ -0,0 +1,47 @@ + +\ProvidesFileRCS{pgflibraryfadings.code.tex} + + + +\pgfdeclarehorizontalshading{pgf@lib@fade@east}{100bp} +{color(0bp)=(pgftransparent!0); color(25bp)=(pgftransparent!0); + color(75bp)=(pgftransparent!100); color(100bp)=(pgftransparent!100)}% + +\pgfdeclarehorizontalshading{pgf@lib@fade@west}{100bp} +{color(0bp)=(pgftransparent!100); color(25bp)=(pgftransparent!100); + color(75bp)=(pgftransparent!0); color(100bp)=(pgftransparent!0)}% + +\pgfdeclareverticalshading{pgf@lib@fade@north}{100bp} +{color(0bp)=(pgftransparent!0); color(25bp)=(pgftransparent!0); + color(75bp)=(pgftransparent!100); color(100bp)=(pgftransparent!100)}% + +\pgfdeclareverticalshading{pgf@lib@fade@south}{100bp} +{color(0bp)=(pgftransparent!100); color(25bp)=(pgftransparent!100); + color(75bp)=(pgftransparent!0); color(100bp)=(pgftransparent!0)}% + +\pgfdeclarefading{east}{\pgfuseshading{pgf@lib@fade@east}}% +\pgfdeclarefading{west}{\pgfuseshading{pgf@lib@fade@west}}% +\pgfdeclarefading{north}{\pgfuseshading{pgf@lib@fade@north}}% +\pgfdeclarefading{south}{\pgfuseshading{pgf@lib@fade@south}}% + + + +\pgfdeclareradialshading{tikz@lib@fade@circle@10}{\pgfpointorigin}{ + color(0pt)=(pgftransparent!0); color(22.5bp)=(pgftransparent!0); + color(25bp)=(pgftransparent!100); color(50bp)=(pgftransparent!100)}% +\pgfdeclarefading{circle with fuzzy edge 10 percent}{\pgfuseshading{tikz@lib@fade@circle@10}}% + +\pgfdeclareradialshading{tikz@lib@fade@circle@15}{\pgfpointorigin}{ + color(0pt)=(pgftransparent!0); color(21.25bp)=(pgftransparent!0); + color(25bp)=(pgftransparent!100); color(50bp)=(pgftransparent!100)}% +\pgfdeclarefading{circle with fuzzy edge 15 percent}{\pgfuseshading{tikz@lib@fade@circle@15}}% + +\pgfdeclareradialshading{tikz@lib@fade@circle@20}{\pgfpointorigin}{ + color(0pt)=(pgftransparent!0); color(20bp)=(pgftransparent!0); + color(25bp)=(pgftransparent!100); color(50bp)=(pgftransparent!100)}% +\pgfdeclarefading{circle with fuzzy edge 20 percent}{\pgfuseshading{tikz@lib@fade@circle@20}}% + +\pgfdeclareradialshading{tikz@lib@fade@fuzzy@15}{\pgfpointorigin}{ + color(0pt)=(pgftransparent!100); color(21.25bp)=(pgftransparent!100); color(23.125bp)=(pgftransparent!0); + color(25bp)=(pgftransparent!100); color(50bp)=(pgftransparent!100)}% +\pgfdeclarefading{fuzzy ring 15 percent}{\pgfuseshading{tikz@lib@fade@fuzzy@15}}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfixedpointarithmetic.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfixedpointarithmetic.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..45943b188b4178325f08720060ac60c733adf238 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfixedpointarithmetic.code.tex @@ -0,0 +1,562 @@ + + +\pgfkeys{/pgf/.cd, + fixed point arithmetic/.code={% + \pgfmathfp@plots@install% + \pgfmathfp@parser@install% + \let\pgfmathparse=\pgfmathfpparse% + \pgfkeys{/pgf/fixed point/.cd, #1}% + },% + fixed point/.cd, + scale results/.code={% + \pgfmathfpparse{#1}% + \let\pgfmathfpscale=\pgfmathresult% + }% +}% + +\def\pgfmathfpscale{1}% + +\def\pgfmathfpparse{% + \begingroup% + \let\pgfmathpostparse=\relax% + \pgfmath@catcodes% + \pgfmath@quickparsefalse% + \pgfmathfpparse@}% + +\def\pgfmathfpparse@#1{% + \edef\pgfmathfp@expression{#1}% + \expandafter\pgfmathfpparse@@\pgfmathfp@expression\pgfmathfp@}% + +\def\pgfmathfp@char@asterisk{*}% +\def\pgfmathfpparse@@#1#2\pgfmathfp@{% + \def\pgfmathfp@test{#1}% + \ifx\pgfmathfp@test\pgfmathfp@char@asterisk% + \edef\pgfmathfp@expression{\pgfmathfpscale#1#2}% + \else% + \edef\pgfmathfp@expression{#1#2}% + \fi% + \expandafter\pgfmathparse@\expandafter{\pgfmathfp@expression}% +}% + +\pgfkeys{/pgf/fixed point/.cd, + scale file plot x/.code=\pgfmathfpparse{#1}\edef\pgfmathfpplotscalex{\pgfmathresult*}, + scale file plot y/.code=\pgfmathfpparse{#1}\edef\pgfmathfpplotscaley{\pgfmathresult*}, + scale file plot z/.code=\pgfmathfpparse{#1}\edef\pgfmathfpplotscalez{\pgfmathresult*}, +}% + +\def\pgfmathfp@plots@install{% + \let\pgfmathfpplotscalex=\pgfutil@empty + \let\pgfmathfpplotscaley=\pgfutil@empty + \let\pgfmathfpplotscalez=\pgfutil@empty + \let\pgf@parsexyline=\pgfmathfp@parsexyline% + \let\pgf@parsexyzline=\pgfmathfp@parsexyzline% +}% + +\def\pgfmathfp@parsexyline#1 #2 #3\pgf@stop{% + \edef\pgfmathfp@marshal{% + \noexpand\pgfplotstreampoint{\noexpand\pgfpointxy{\pgfmathfpplotscalex#1}{\pgfmathfpplotscaley#2}}% + }% + \pgfmathfp@marshal% +}% + +\def\pgfmathfp@parsexyzline#1 #2 #3 #4\pgf@stop{% + \edef\pgfmathfp@marshal{% + \noexpand\pgfplotstreampoint{% + \noexpand\pgfpointxyz{\pgfmathfpplotscalex#1}{\pgfmathfpplotscaley#2}{\pgfmathfpplotscalez#3}% + }% + }% + \pgfmathfp@marshal% +}% + +\def\pgfmathfp@parser@install{% + \expandafter\ifx\csname FP@version\endcsname\relax% + \pgferror{You need to say `\string\usepackage{fp}' to use % + fixed point arithmetic}% + \else% + \FPmessagesfalse% + \FPdebugfalse% + \let\pgfmathadd@=\pgfmathfpadd@% + \let\pgfmathsubtract@=\pgfmathfpsubtract@% + \let\pgfmathmultiply@=\pgfmathfpmultiply@% + \let\pgfmathdivide@=\pgfmathfpdivide@% + \let\pgfmathabs@=\pgfmathfpabs@% + \let\pgfmathneg@=\pgfmathfpneg@% + \let\pgfmathround@=\pgfmathfpround@% + \let\pgfmathfloor@=\pgfmathfpfloor@% + \let\pgfmathceil@=\pgfmathfpceil@% + \let\pgfmathmod@=\pgfmathfpmod@% + \let\pgfmathmax@=\pgfmathfpmax@% + \let\pgfmathmin@=\pgfmathfpmin@% + \let\pgfmathsin@=\pgfmathfpsin@% + \let\pgfmathcos@=\pgfmathfpcos@% + \let\pgfmathtan@=\pgfmathfptan@% + \let\pgfmathdeg@=\pgfmathfpdeg@% + \let\pgfmathrad@=\pgfmathfprad@% + \let\pgfmathatan@=\pgfmathfpatan@% + \let\pgfmathasin@=\pgfmathfpasin@% + \let\pgfmathacos@=\pgfmathfpacos@% + \let\pgfmathcot@=\pgfmathfpcot@% + \let\pgfmathsec@=\pgfmathfpsec@% + \let\pgfmathcosec@=\pgfmathfpcosec@% + \let\pgfmathpow@=\pgfmathfppow@% + \let\pgfmathexp@=\pgfmathfpexp@% + \let\pgfmathln@=\pgfmathfpln@% + \let\pgfmathsqrt@=\pgfmathfpsqrt@% + \let\pgfmath@pi=\pgfmathfppi@% + \let\pgfmathveclen@=\pgfmathfpveclen@% + \let\pgfmathe@=\pgfmathfpe@% + \let\pgfmathlessthan@=\pgfmathfplessthan@% + \let\pgfmathgreaterthan@=\pgfmathfpgreaterthan@% + \let\pgfmathequalto@=\pgfmathfpequalto@% + \let\pgfmathrnd=\pgfmathfprnd% + \let\pgfmathrand=\pgfmathfprand% + \let\pgfmathsetseed=\pgfmathfpsetseed% + \let\pgfmathscientific=\pgfmathfpscientific% + \fi% +}% + +\def\pgfmathfpe@{let\pgfmathresult=\FPe}% +\def\pgfmathfppi@{let\pgfmathresult=\FPpi}% + + + +\def\pgfmathfpscientific#1#2{% + \begingroup% + \FPpow\pgfmathresult{10}{#2}\unskip% + \FPmul\pgfmathresult{#1}{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + + +\def\pgfmathfplessthan#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfplessthan@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfplessthan@#1#2{% + \begingroup% + \FPiflt{#1}{#2}% + \def\pgfmathresult{1.0}% + \else% + \def\pgfmathresult{0.0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpgreaterthan#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpgreaterthan@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpgreaterthan@#1#2{% + \begingroup% + \FPifgt{#1}{#2}% + \def\pgfmathresult{1.0}% + \else% + \def\pgfmathresult{0.0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpequalto#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpequalto@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpequalto@#1#2{% + \begingroup% + \FPifeq{#1}{#2}% + \def\pgfmathresult{1.0}% + \else% + \def\pgfmathresult{0.0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + + + +\def\pgfmathfpadd#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpadd@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpadd@#1#2{% + \begingroup% + \FPadd\pgfmathresult{#1}{#2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpsubtract#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpsubtract@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpsubtract@#1#2{% + \begingroup% + \FPsub\pgfmathresult{#1}{#2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpmultiply#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpmultiply@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpmultiply@#1#2{% + \begingroup% + \FPmul\pgfmathresult{#1}{#2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpdivide#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpdivide@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpdivide@#1#2{% + \begingroup% + \FPdiv\pgfmathresult{#1}{#2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpabs#1{% + \pgfmathfpparse{#1}% + \pgfmathfpabs@{\pgfmathresult}% +}% +\def\pgfmathfpabs@#1{% + \begingroup% + \FPabs\pgfmathresult{#1}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpneg#1{% + \pgfmathfpparse{#1}% + \pgfmathfpneg@{\pgfmathresult}% +}% +\def\pgfmathfpneg@#1{% + \begingroup% + \FPneg\pgfmathresult{#1}% + \pgfmath@smuggleone\pgfmathresult + \endgroup% +}% + +\def\pgfmathfpround#1{% + \pgfmathfpparse{#1}% + \pgfmathfpround@{\pgfmathresult}% +}% +\def\pgfmathfpround@#1{% + \begingroup% + \FPround\pgfmathresult{#1}{0}% + \edef\pgfmathresult{\pgfmathresult.0}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpfloor#1{% + \pgfmathfpparse{#1}% + \pgfmathfpfloor@{\pgfmathresult}% +}% +\def\pgfmathfpfloor@#1{% + \begingroup% + \FPtrunc\pgfmathresult{#1}{0}% + \FPifneg{#1}% + \FPsub\pgfmathresult{\pgfmathresult}{1}% + \fi% + \edef\pgfmathresult{\pgfmathresult.0}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpceil#1{% + \pgfmathfpparse{#1}% + \pgfmathfpceil@{\pgfmathresult}% +}% +\def\pgfmathfpceil@#1{% + \begingroup% + \FPtrunc\pgfmathresult{#1}{0}% + \FPifpos{#1}% + \FPadd\pgfmathresult{\pgfmathresult}{1}% + \fi% + \edef\pgfmathresult{\pgfmathresult.0}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpmod#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpmod@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpmod@#1#2{% + \begingroup% + \FPdiv\pgfmathresult{#1}{#2}% + \FPtrunc\pgfmathresult{\pgfmathresult}{0}% + \FPmul\pgfmathresult{\pgfmathresult}{#2}% + \FPsub\pgfmathresult{#1}{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpmax#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpmax@@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpmax@#1{% + \pgfmathfpmax@@#1% +}% +\def\pgfmathfpmax@@#1#2{% + \begingroup% + \FPifgt{#1}{#2}% + \def\pgfmathresult{#1}% + \else% + \def\pgfmathresult{#2}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpmin#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpmin@@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpmin@#1{% + \pgfmathfpmin@@#1% +}% +\def\pgfmathfpmin@@#1#2{% + \begingroup% + \FPiflt{#1}{#2}% + \def\pgfmathresult{#1}% + \else% + \def\pgfmathresult{#2}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + + +\def\pgfmathfppow#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfppow@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfppow@#1#2{% + \begingroup% + \FPpow\pgfmathresult{#1}{#2}\unskip% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpexp#1{% + \pgfmathfpparse{#1}% + \pgfmathfpexp@{\pgfmathresult}% +}% +\def\pgfmathfpexp@#1{% + \begingroup% + \FPexp\pgfmathresult{#1}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpln#1{% + \pgfmathfpparse{#1}% + \pgfmathfpln@{\pgfmathresult}% +}% +\def\pgfmathfpln@#1{% + \begingroup% + \FPln\pgfmathresult{#1}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpsqrt#1{% + \pgfmathfpparse{#1}% + \pgfmathfpsqrt@{\pgfmathresult}% +}% +\def\pgfmathfpsqrt@#1{% + \begingroup% + \FProot\pgfmathresult{#1}{2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpveclen#1#2{% + \pgfmathfpparse{#2}\let\pgfmath@result=\pgfmathresult% + \pgfmathfpparse{#1}% + \pgfmathfpveclen@{\pgfmathresult}{\pgfmath@result}% +}% +\def\pgfmathfpveclen@#1#2{% + \begingroup% + \FPmul\pgfmath@result{#1}{#1}% + \FPmul\pgfmath@@result{#2}{#2}% + \FPadd\pgfmathresult{\pgfmath@result}{\pgfmath@@result}% + \FProot\pgfmathresult{\pgfmathresult}{2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + + +\def\pgfmathfpsin#1{% + \pgfmathfpparse{#1}% + \pgfmathfpsin@{\pgfmathresult}% +}% +\def\pgfmathfpsin@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.017453292519943295}% + \FPsin\pgfmathresult{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpcos#1{% + \pgfmathfpparse{#1}% + \pgfmathfpcos@{\pgfmathresult}% +}% +\def\pgfmathfpcos@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.017453292519943295}% + \FPcos\pgfmathresult{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfptan#1{% + \pgfmathfpparse{#1}% + \pgfmathfptan@{\pgfmathresult}% +}% +\def\pgfmathfptan@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.017453292519943295}% + \FPtan\pgfmathresult{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpacos#1{% + \pgfmathfpparse{#1}% + \pgfmathfpacos@{\pgfmathresult}% +}% +\def\pgfmathfpacos@#1{% + \begingroup% + \FParccos\pgfmathresult{#1}% + \FPmul\pgfmathresult{\pgfmathresult}{57.295779513082320885}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpasin#1{% + \pgfmathfpparse{#1}% + \pgfmathfpasin@{\pgfmathresult}% +}% +\def\pgfmathfpasin@#1{% + \begingroup% + \FParcsin\pgfmathresult{#1}% + \FPmul\pgfmathresult{\pgfmathresult}{57.295779513082320885}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpatan#1{% + \pgfmathfpparse{#1}% + \pgfmathfpatan@{\pgfmathresult}% +}% +\def\pgfmathfpatan@#1{% + \begingroup% + \FParctan\pgfmathresult{#1}% + \FPmul\pgfmathresult{\pgfmathresult}{57.295779513082320885}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpcot#1{% + \pgfmathfpparse{#1}% + \pgfmathfpcot@{\pgfmathresult}% +}% +\def\pgfmathfpcot@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.017453292519943295}% + \FPcot\pgfmathresult{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpsec#1{% + \pgfmathfpparse{#1}% + \pgfmathfpsec@{\pgfmathresult}% +}% +\def\pgfmathfpsec@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.017453292519943295}% + \FPcos\pgfmathresult{\pgfmathresult}% + \FPdiv\pgfmathresult{1}{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpcosec#1{% + \pgfmathfpparse{#1}% + \pgfmathfpcosec@{\pgfmathresult}% +}% +\def\pgfmathfpcosec@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.017453292519943295}% + \FPsin\pgfmathresult{\pgfmathresult}% + \FPdiv\pgfmathresult{1}{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfpdeg#1{% + \pgfmathfpparse{#1}% + \pgfmathfpdeg@{\pgfmathresult}% +}% +\def\pgfmathfpdeg@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{57.295779513082320885}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfprad#1{% + \pgfmathfpparse{#1}% + \pgfmathfprad@{\pgfmathresult}% +}% +\def\pgfmathfprad@#1{% + \begingroup% + \FPmul\pgfmathresult{#1}{0.01745329251994325}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + + +\def\pgfmathfpsetseed#1{% + \pgfmathfpparse{#1}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \FPseed\pgfmathresult\relax\pgfmath@% +}% + +\def\pgfmathfprnd{% + \begingroup% + \FPrandom\pgfmathresult% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% + +\def\pgfmathfprand{% + \begingroup% + \FPrandom\pgfmathresult% + \FPmul\pgfmathresult{2}{\pgfmathresult}% + \FPsub\pgfmathresult{\pgfmathresult}{1}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfpu.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfpu.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..df6d66d75a6d23d892e495aa4b45ec7a782bd6d0 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryfpu.code.tex @@ -0,0 +1,1961 @@ + +\newif\ifpgfmathfloatparseactive +\newif\ifpgfmathfloat@scaleactive + +\def\pgflibraryfpuifactive#1#2{% + \ifpgfmathfloatparseactive + #1% + \else + #2% + \fi +}% + +\pgfqkeys{/pgf}{ + fpu/.is choice, + fpu/true/.code={% + \ifpgfmathfloatparseactive + \else + \pgfutil@ifundefined{pgfmathdeclarefunction}{% + \pgfmathfloat@parser@install@pgf@two@null@null% + }{% + \pgfmathfloat@parser@install% + }% + \pgfmathfloatparseactivetrue + \pgfkeysalso{/pgf/fixed point arithmetic/.prefix style={/pgf/fpu=false}}% + \fi + },% + fpu/false/.code={% + \ifpgfmathfloatparseactive + \pgfmathfloat@uninstall% + \pgfmathfloatparseactivefalse + \fi + },% + fpu/.default=true, + fpu/scale results/.code={% + \ifpgfmathfloatparseactive + \pgfmathparse{#1}% + \else + \pgfmathfloatparsenumber{#1}% + \fi + \let\pgfmathfloatscale=\pgfmathresult% + },% + fpu/output format/.is choice, + fpu/output format/float/.code= {% + \def\pgfmathfloatparse@output@choice{Y}% + \let\pgfmathfloatparse@output=\relax + }, + fpu/output format/sci/.code= {% + \def\pgfmathfloatparse@output@choice{S}% + \def\pgfmathfloatparse@output{\pgfmathfloattosci@{\pgfmathresult}}% + }, + fpu/output format/fixed/.code= {% + \def\pgfmathfloatparse@output@choice{F}% + \def\pgfmathfloatparse@output{\pgfmathfloattofixed@{\pgfmathresult}}% + }, + fpu/output format/float, + fpu/rel thresh/.code={% + \pgfmathfloatparsenumber{#1}% + \let\pgfmathfloat@relthresh=\pgfmathresult + }, + fpu/rel thresh=1e-4, + fpu/install only/.code={ + \edef\pgf@list{#1}% + \pgfutil@for\pgf@temp:=\pgf@list\do{% + \expandafter\pgfmath@float@install@singlefunction\expandafter{% + \romannumeral-`0\expandafter\pgfutil@trimspaces\expandafter{\pgf@temp}}% + }% + }, +}% + +\pgfmathfloatcreate{1}{1.0}{0}\let\pgfmathfloatscale=\pgfmathresult + +\let\pgfmathfloatone=\pgfmathresult + +\def\pgfmathfloatparse{% + \begingroup% + \let\pgfmathpostparse=\relax% + \pgfmath@catcodes% + \pgfmath@quickparsefalse% + \ifpgfmathfloatparseactive\else + \pgfmathfloat@parser@install + \fi + \pgfmathfloatparse@}% + +\def\pgfmathfloatparse@pgf@two@null@null{% + \pgfmath@quickparsefalse% + \pgfmathfloatparse@}% + +\def\pgfmathfloatparse@#1{% + \edef\pgfmathfloat@expression{#1}% + \expandafter\pgfmathfloatparse@@\pgfmathfloat@expression\pgfmathfloat@ + \ifpgfmathfloat@scaleactive + \expandafter\pgfmathfloatmultiply@\expandafter{\pgfmathresult}{\pgfmathfloatscale}% + \pgfmathfloattofixed{\pgfmathresult}% + \else + \pgfmathfloatparse@output + \fi + \ignorespaces +}% + +\def\pgfmathfloat@char@asterisk{*}% +\def\pgfmathfloatparse@@#1#2\pgfmathfloat@{% + \def\pgfmathfloat@test{#1}% + \ifx\pgfmathfloat@test\pgfmathfloat@char@asterisk% + \def\pgfmathfloat@expression{#2}% + \pgfmathfloat@scaleactivetrue + \fi% + \expandafter\pgfmathparse@\expandafter{\pgfmathfloat@expression}% +}% + +\pgfkeys{/pgf/fpu/.cd, + scale file plot x/.code=\pgfmathfloatparse{#1}\edef\pgfmathfloatplotscalex{\pgfmathresult*}, + scale file plot y/.code=\pgfmathfloatparse{#1}\edef\pgfmathfloatplotscaley{\pgfmathresult*}, + scale file plot z/.code=\pgfmathfloatparse{#1}\edef\pgfmathfloatplotscalez{\pgfmathresult*} +}% + +\def\pgfmathfloat@uninstall@appendcmd#1{% + \expandafter\gdef\expandafter\pgfmathfloat@uninstall\expandafter{\pgfmathfloat@uninstall #1}% +}% + +\def\pgfmathfloat@plots@checkuninstallcmd{% + \pgfutil@ifundefined{pgfmathfloat@uninstall}{% + \global\let\pgfmathfloat@uninstall=\pgfutil@empty + }{% + \def\pgfmathfloat@uninstall@appendcmd##1{}% + \def\pgfmathfloat@prepareuninstallcmd##1{}% + }% +}% + +\def\pgfmathfloat@prepareuninstallcmd#1{% + \expandafter\global\expandafter\let\csname pgfmathfloat@backup@\string#1\endcsname=#1% + \expandafter\gdef\expandafter\pgfmathfloat@uninstall\expandafter{\pgfmathfloat@uninstall + \expandafter\let\expandafter#1\csname pgfmathfloat@backup@\string#1\endcsname% + }% +}% + +\def\pgfmathfloat@install#1=#2{% + \pgfmathfloat@prepareuninstallcmd{#1}% + \let#1=#2% +}% +\def\pgfmathfloat@install@csname#1#2{% + \expandafter\pgfmathfloat@prepareuninstallcmd\csname #1\endcsname% + \pgfutil@namelet{#1}{#2}% +}% +\def\pgfmathfloat@install@unimplemented#1{% + \expandafter\pgfmathfloat@prepareuninstallcmd\csname pgfmath#1@\endcsname% + \expandafter\def\csname pgfmath#1@\endcsname##1{\pgfmathfloat@notimplemented{#1}}% +}% +\def\pgfmathfloat@plots@install{% + \let\pgfmathfloatplotscalex=\pgfutil@empty + \let\pgfmathfloatplotscaley=\pgfutil@empty + \let\pgfmathfloatplotscalez=\pgfutil@empty + \pgfmathfloat@install\pgf@parsexyline=\pgfmathfloat@parsexyline% + \pgfmathfloat@install\pgf@parsexyzline=\pgfmathfloat@parsexyzline% +}% +\def\pgfmathfloat@parsexyline#1 #2 #3\pgf@stop{% + \edef\pgfmathfloat@marshal{% + \noexpand\pgfplotstreampoint{\noexpand\pgfpointxy{\pgfmathfloatplotscalex#1}{\pgfmathfloatplotscaley#2}}% + }% + \pgfmathfloat@marshal% +}% +\def\pgfmathfloat@parsexyzline#1 #2 #3 #4\pgf@stop{% + \edef\pgfmathfloat@marshal{% + \noexpand\pgfplotstreampoint{% + \noexpand\pgfpointxyz{\pgfmathfloatplotscalex#1}{\pgfmathfloatplotscaley#2}{\pgfmathfloatplotscalez#3}% + }% + }% + \pgfmathfloat@marshal% +}% + +\def\pgfmathfloat@parser@install@functions{% + \pgfmathfloat@install\pgfmathadd@=\pgfmathfloatadd@% + \pgfmathfloat@install\pgfmathsubtract@=\pgfmathfloatsubtract@% + \pgfmathfloat@install\pgfmathneg@=\pgfmathfloatneg@% + \pgfmathfloat@install\pgfmathmultiply@=\pgfmathfloatmultiply@% + \pgfmathfloat@install\pgfmathdivide@=\pgfmathfloatdivide@% + \pgfmathfloat@install\pgfmathabs@=\pgfmathfloatabs@% + \pgfmathfloat@install\pgfmathsign@=\pgfmathfloatsign@% + \pgfmathfloat@install\pgfmathround@=\pgfmathfloatround@% + \pgfmathfloat@install\pgfmathfloor@=\pgfmathfloatfloor@% + \pgfmathfloat@install\pgfmathceil@=\pgfmathfloatceil@ + \pgfmathfloat@install\pgfmathint@=\pgfmathfloatint@ + \pgfmathfloat@install\pgfmathmod@=\pgfmathfloatmod@% + \pgfmathfloat@install\pgfmathmax@=\pgfmathfloatmax@% + \pgfmathfloat@install\pgfmathmin@=\pgfmathfloatmin@% + \pgfmathfloat@install\pgfmathsin@=\pgfmathfloatsin@% + \pgfmathfloat@install\pgfmathcos@=\pgfmathfloatcos@% + \pgfmathfloat@install\pgfmathtan@=\pgfmathfloattan@% + \pgfmathfloat@install\pgfmathdeg@=\pgfmathfloatdeg@% + \pgfmathfloat@install\pgfmathrad@=\pgfmathfloatrad@% + \pgfmathfloat@install\pgfmathatan@=\pgfmathfloatatan@% + \pgfmathfloat@install\pgfmathasin@=\pgfmathfloatasin@% + \pgfmathfloat@install\pgfmathacos@=\pgfmathfloatacos@% + \pgfmathfloat@install\pgfmathcot@=\pgfmathfloatcot@% + \pgfmathfloat@install\pgfmathsec@=\pgfmathfloatsec@% + \pgfmathfloat@install\pgfmathcosec@=\pgfmathfloatcosec@% + \pgfmathfloat@install\pgfmathexp@=\pgfmathfloatexp@% + \pgfmathfloat@install\pgfmathln@=\pgfmathfloatln@% + \pgfmathfloat@install@csname{pgfmathlog10@}{pgfmathfloatlog10@}% + \pgfmathfloat@install@csname{pgfmathlog2@}{pgfmathfloatlog2@}% + \pgfmathfloat@install\pgfmathsqrt@=\pgfmathfloatsqrt@% + \pgfmathfloat@install\pgfmath@pi=\pgfmathfloatpi@% + \pgfmathfloat@install\pgfmathpi=\pgfmathfloatpi@% + \pgfmathfloat@install\pgfmathe@=\pgfmathfloate@% + \pgfmathfloat@install\pgfmathe=\pgfmathfloate@% + \pgfmathfloat@install\pgfmathlessthan@=\pgfmathfloatlessthan@% + \pgfmathfloat@install\pgfmathnotless@=\pgfmathfloatnotless@% + \pgfmathfloat@install\pgfmathnotgreater@=\pgfmathfloatnotgreater@% + \pgfmathfloat@install\pgfmathless@=\pgfmathfloatlessthan@% + \pgfmathfloat@install\pgfmathgreaterthan@=\pgfmathfloatgreaterthan@% + \pgfmathfloat@install\pgfmathgreater@=\pgfmathfloatgreaterthan@% + \pgfmathfloat@install\pgfmathifthenelse@=\pgfmathfloatifthenelse@% + \pgfmathfloat@install\pgfmathequal@=\pgfmathfloatequal@% + \pgfmathfloat@install\pgfmathequalto@=\pgfmathfloatequal@% + \pgfmathfloat@install\pgfmathnotequal@=\pgfmathfloatnotequal@% + \pgfmathfloat@install\pgfmathnotequalto@=\pgfmathfloatnotequal@% + \pgfmathfloat@install\pgfmathpow@=\pgfmathfloatpow@ + \pgfmathfloat@install\pgfmathrand@=\pgfmathfloatrand@ + \pgfmathfloat@install\pgfmathrand=\pgfmathfloatrand@ + \pgfmathfloat@install\pgfmathrnd@=\pgfmathfloatrnd@ + \pgfmathfloat@install\pgfmathrnd=\pgfmathfloatrnd@ + \pgfmathfloat@install\pgfmathtrue@=\pgfmathfloattrue@ + \pgfmathfloat@install\pgfmathfalse@=\pgfmathfloatfalse@ + \pgfmathfloat@install\pgfmathnot@=\pgfmathfloatnot@ + \pgfmathfloat@install\pgfmathhex@=\pgfmathfloathex@ + \pgfmathfloat@install\pgfmathHex@=\pgfmathfloatHex@ + \pgfmathfloat@install\pgfmathoct@=\pgfmathfloatoct@ + \pgfmathfloat@install\pgfmathbin@=\pgfmathfloatbin@ + \pgfmathfloat@install\pgfmathand@=\pgfmathfloatand@ + \pgfmathfloat@install\pgfmathor@=\pgfmathfloator@ + \pgfmathfloat@install\pgfmathfactorial@=\pgfmathfloatfactorial@ + \pgfmathfloat@install\pgfmathveclen@=\pgfmathfloatveclen@ + \pgfmathfloat@install\pgfmathcosh@=\pgfmathfloatcosh@ + \pgfmathfloat@install\pgfmathsinh@=\pgfmathfloatsinh@ + \pgfmathfloat@install\pgfmathtanh@=\pgfmathfloattanh@ + \pgfmathfloat@install\pgfmath@iftrue=\pgfmathfloat@iftrue% + \expandafter\pgfmathfloat@install\csname pgfmathatan2@\endcsname=\pgfmathfloatatantwo@ + \pgfmathfloat@install@unimplemented{isprime}% + \pgfmathfloat@install@unimplemented{iseven}% + \pgfmathfloat@install@unimplemented{isodd}% + \pgfmathfloat@install@unimplemented{gcd}% + \pgfmathfloat@install@unimplemented{frac}% + \pgfmathfloat@install@unimplemented{random}% + \pgfmathfloat@install@unimplemented{setseed}% + \pgfmathfloat@install@unimplemented{Mod}% + \pgfmathfloat@install@unimplemented{div}% + \pgfmathfloat@install@unimplemented{real}% + \pgfmathfloat@install\pgfmathscientific=\pgfmathfloatscientific% +}% + +\def\pgfmath@float@install@singlefunction#1{% + \ifcsname pgfmath@function@#1\endcsname\else + \pgfmath@error{The function `#1' does not exist}{}% + \fi + \pgfmath@toks={}% + \pgfmathloop + \ifnum\pgfmathcounter>\csname pgfmath@operation@#1@arity\endcsname\relax% + \else + \expandafter\pgfmath@addto@toks\expandafter{\pgfmath@char@hash}% + \expandafter\pgfmath@addto@toks\expandafter{\pgfmathcounter}% + \repeatpgfmathloop + \edef\pgfmath@head{\noexpand\def\expandafter\noexpand\csname pgfmath#1@\endcsname\the\pgfmath@toks}% + \pgfmath@toks={}% + \def\pgfmath@arguments{}% + \pgfmathloop + \ifnum\pgfmathcounter>\csname pgfmath@operation@#1@arity\endcsname\relax% + \else + \pgfmath@addto@toks{\pgfmathfloatparsenumber}% + \expandafter\expandafter\expandafter\pgfmath@addto@toks + \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter + {\expandafter\pgfmath@char@hash\pgfmathcounter}}% + \pgfmath@addto@toks{\let}% + \expandafter\pgfmath@addto@toks\expandafter{% + \csname pgfmath@argument@\pgfmathcounter\endcsname=\pgfmathresult}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter + \pgfmath@arguments\expandafter\expandafter\expandafter{\expandafter + \pgfmath@arguments\expandafter{\csname pgfmath@argument@\pgfmathcounter\endcsname}}% + \repeatpgfmathloop + \expandafter\pgfmath@addto@toks\expandafter{\csname pgfmathfloat#1@\expandafter\endcsname\pgfmath@arguments}% + \pgfmath@addto@toks{\pgfmathfloattofixed{\pgfmathresult}}% + \edef\pgfmath@body{{\the\pgfmath@toks}}% + \expandafter\pgfmath@head\pgfmath@body +} + +\def\pgfmathfloat@iftrue{% + \if Y\pgfmathfloatparse@output@choice + \let\pgfmathfloat@@iftrue@v=\pgfmathfloatone + \let\pgfmathfloat@@iftrue@next=\pgfmathfloat@iftrue@ + \else + \if S\pgfmathfloatparse@output@choice + \def\pgfmathfloat@@iftrue@v{1.0e0}% + \let\pgfmathfloat@@iftrue@next=\pgfmathfloat@iftrue@ + \else + \def\pgfmath@next{\pgfutilifstartswith{1.0}}% + \expandafter\pgfmath@next\expandafter{\pgfmathresult}{% + \ifdim\pgfmathresult pt=1.0pt % + \let\pgfmathfloat@@iftrue@next=\pgfutil@firstoftwo + \else + \let\pgfmathfloat@@iftrue@next=\pgfutil@secondoftwo + \fi + }{% + \let\pgfmathfloat@@iftrue@next=\pgfutil@secondoftwo + }% + \fi + \fi + \pgfmathfloat@@iftrue@next% +}% +\def\pgfmathfloat@iftrue@{% + \ifx\pgfmathresult\pgfmathfloat@@iftrue@v + \let\pgfmath@next=\pgfutil@firstoftwo + \else + \let\pgfmath@next=\pgfutil@secondoftwo + \fi + \pgfmath@next% +}% + +\def\pgfmathfloat@parser@install{% + \pgfmathfloat@plots@checkuninstallcmd + \pgfmathfloat@plots@install% + \pgfmathfloat@parser@install@functions + \pgfmath@tokens@make{exponent}{\pgfmathfloat@POSTFLAGSCHAR}% + \pgfmathfloat@uninstall@appendcmd{% + \expandafter\let\csname pgfmath@token@exponent@\pgfmathfloat@POSTFLAGSCHAR\endcsname=\relax + }% + \let\pgfmath@basic@parse@exponent=\pgfmath@parse@exponent% + \let\pgfmath@basic@stack@push@operand=\pgfmath@stack@push@operand + \pgfmathfloat@install\pgfmath@stack@push@operand=\pgfmathfloat@stack@push@operand + \pgfmathfloat@install\pgfmath@parse@operand@quote=\pgfmathfloat@parse@operand@quote + \pgfmathfloat@install\pgfmath@parse@exponent=\pgfmathfloat@parse@float@or@exponent + \pgfmathfloat@install\pgfmathparse=\pgfmathfloatparse% + \pgfmathfloat@install\pgfmathparse@expression@is@number=\pgfmathfloat@parse@expression@is@number +}% + + +\def\pgfmathfloat@parse@expression@is@number{% + \pgfmathfloatparsenumber{\pgfmath@expression}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup + \ignorespaces +}% + +\def\pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG#1{% + \edef\pgfmathfloat@loc@TMPa{% + \noexpand\def\expandafter\noexpand\csname pgfmath@parsefunction@#1\endcsname{% + \noexpand\let\noexpand\pgfmath@parsepostgroup\expandafter\noexpand\csname pgfmath@parsefunction@#1@\endcsname% + \noexpand\expandafter\noexpand\pgfmath@parse@}% + \noexpand\def\expandafter\noexpand\csname pgfmath@parsefunction@#1@\endcsname{% + \noexpand\expandafter\expandafter\noexpand\csname pgfmath#1@\endcsname\noexpand\expandafter{\noexpand\pgfmathresult}% + \noexpand\pgfmath@postfunction% + }% + }% + \pgfmathfloat@loc@TMPa +}% +\def\pgfmathfloat@parser@install@pgf@two@null@null{% + \pgfmathfloat@plots@checkuninstallcmd + \pgfmathfloat@plots@install% + \pgfmathfloat@parser@install@functions + \let\pgfmathrand@=\pgfmath@basic@rand@ + \let\pgfmathrnd@=\pgfmath@basic@rnd@ + \pgfmathfloat@install\pgfmathmax@=\pgfmathfloatmaxtwo% + \pgfmathfloat@install\pgfmathmin@=\pgfmathfloatmintwo% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{factorial}% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{hex}% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{bin}% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{oct}% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{tanh}% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{sinh}% + \pgfmathfloat@defineadapter@for@pgf@two@null@null@ONEARG{cosh}% + \let\pgfmath@basic@parsedecimalpoint=\pgfmath@parsedecimalpoint% + \let\pgfmath@basic@stack@push@operand=\pgfmath@stackpushoperand + \pgfmathfloat@install\pgfmath@stackpushoperand=\pgfmathfloat@stack@push@operand + \pgfmathfloat@install\pgfmath@parsedecimalpoint=\pgfmathfloat@parsedecimalpoint@pgf@two@null@null + \pgfmathfloat@install\pgfmath@endparse=\pgfmathfloat@endparse@pgf@two@null@null + \pgfmathfloat@install\pgfmath@endparsegroup=\pgfmathfloat@endparsegroup@pgf@two@null@null + \pgfmathfloat@install\pgfmath@postfunction=\pgfmathfloat@postfunction@pgf@two@null@null + \pgfmathfloat@install\pgfmath@@parseoperandgroup=\pgfmathfloat@@parseoperandgroup + \pgfmathfloat@install\pgfmathparse=\pgfmathfloatparse@pgf@two@null@null% +}% + +\pgfutil@ifundefined{pgfmathdeclarefunction}{% + \def\pgfmathdeclarepseudoconstant#1#2{% + \begingroup + \toks0=\expandafter{\csname pgfmath#1@\endcsname}% + \toks1={\pgfmath@postfunction}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }% + \xdef\pgfmathfloat@glob@TMPb{\the\toks0 }% + \endgroup + \expandafter\let\csname pgfmath@parsefunction@#1\endcsname=\pgfmathfloat@glob@TMP + \expandafter\let\csname pgfmath#1\endcsname=\pgfmathfloat@glob@TMPb + \expandafter\def\csname pgfmath#1@\endcsname{#2}% + }% + \let\pgfmathredeclarepseudoconstant=\pgfmathdeclarepseudoconstant +}{% + \pgfutil@ifundefined{pgfmathdeclarepseudoconstant}{% + \def\pgfmathdeclarepseudoconstant#1#2{\pgfmathdeclarefunction*{#1}{0}{#2}} + }{}% +}% + +\pgfmathdeclarepseudoconstant{inf}{\def\pgfmathresult{inf}}% +\pgfmathdeclarepseudoconstant{INF}{\def\pgfmathresult{inf}}% +\pgfmathdeclarepseudoconstant{Inf}{\def\pgfmathresult{inf}}% +\pgfmathdeclarepseudoconstant{infty}{\def\pgfmathresult{inf}}% +\pgfmathdeclarepseudoconstant{nan}{\def\pgfmathresult{nan}}% +\pgfmathdeclarepseudoconstant{NaN}{\def\pgfmathresult{nan}}% + + +\def\pgfmathfloat@parsedecimalpoint@pgf@two@null@null#1{% + \expandafter\ifx\pgfmathfloat@POSTFLAGSCHAR#1% + \let\pgfmath@next=\pgfmathfloat@return@float@pgf@two@null@null% + \else + \def\pgfmath@next{\pgfmath@basic@parsedecimalpoint#1}% + \fi + \pgfmath@next +}% +\def\pgfmathfloat@return@float@pgf@two@null@null#1]{% + \edef\pgfmathresult{\the\c@pgfmath@parsecounta\pgfmathfloat@POSTFLAGSCHAR#1]}% + \let\pgfmath@resulttemp=\pgfmathresult + \pgfmath@parseoperator% +}% +\def\pgfmathfloat@endparse@pgf@two@null@null#1\pgfmath@empty{% + \pgfmath@processalloperations% + \pgfmath@stackpop{\pgfmathresult}% + \pgfmath@smuggleone{\pgfmathresult}% + \endgroup% + \ignorespaces% +}% +\def\pgfmathfloat@endparsegroup@pgf@two@null@null{% + \pgfmath@processalloperations% + \pgfmath@stackpop{\pgfmathresult}% + \pgfmath@smuggleone{\pgfmathresult}% + \endgroup% + \pgfmath@parsepostgroup% +}% +\def\pgfmathfloat@postfunction@pgf@two@null@null{% + \let\pgfmath@parsepostgroup\pgfmath@parseoperator% + \ifnum\pgfmath@sign1<0 + \pgfmathfloatneg@{\pgfmathresult}% + \let\pgfmath@sign\pgfutil@empty + \fi + \pgfmath@parseoperator}% +\def\pgfmathfloat@@parseoperandgroup{% + \let\pgfmath@postparsegroup\pgfmath@parseoperator% + \ifnum\pgfmath@sign1<0 + \pgfmathfloatneg@{\pgfmathresult}% + \let\pgfmath@sign\pgfutil@empty + \fi + \pgfmath@parseoperator% +}% + + + + + + +\def\pgfmathfloat@parse@float@or@exponent{% + \if\pgfmath@token \pgfmathfloat@POSTFLAGSCHAR% + \expandafter\pgfmathfloat@return@float\expandafter\pgfmath@token@next + \else + \expandafter\pgfmath@basic@parse@exponent + \fi +}% +\def\pgfmathfloat@return@float#1]{% + \edef\pgfmathresult{\pgfmath@number \pgfmathfloat@POSTFLAGSCHAR#1]}% + \expandafter\pgfmath@basic@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +}% + +\def\pgfmathfloat@parse@operand@quote#1"{% + \edef\pgfmathresult{\pgfmath@fpu@stringmarker #1}% + \expandafter\pgfmath@basic@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +} + +\def\pgfmath@fpu@stringmarker{@@str@@:}% + +\def\pgfmathfloat@stack@push@operand#1{% + \pgfutil@ifnextchar\bgroup{% + \let\pgfmathfloat@stack@push@operand@list@=\pgfutil@empty + \pgfmathfloat@stack@push@operand@list + }{% + \pgfmathfloat@stack@push@operand@single + }% + #1\relax +}% + +\def\pgfmathfloat@stack@push@operand@single#1\relax{% + \expandafter\pgfutil@in@\pgfmathfloat@POSTFLAGSCHAR{#1}% + \ifpgfutil@in@ + \pgfmath@basic@stack@push@operand{#1}% + \else + \expandafter\pgfutil@in@\expandafter{\pgfmath@fpu@stringmarker}{#1}% + \ifpgfutil@in@ + \pgfmathfloat@stack@push@operand@single@str#1\relax + \else + \pgfmathfloatparsenumber{#1}% + \expandafter\pgfmath@basic@stack@push@operand\expandafter{\pgfmathresult}% + \fi + \fi +}% + +\expandafter\def\expandafter\pgfmathfloat@stack@push@operand@single@str\pgfmath@fpu@stringmarker #1\relax{% + \pgfmath@basic@stack@push@operand{#1}% +}% + +\def\pgfmathfloat@stack@push@operand@GOBBLE#1\relax{}% +\def\pgfmathfloat@stack@push@operand@list#1{% + \expandafter\pgfutil@in@ \pgfmathfloat@POSTFLAGSCHAR{#1}% + \ifpgfutil@in@ + \expandafter\def\expandafter\pgfmathfloat@stack@push@operand@list@\expandafter{% + \pgfmathfloat@stack@push@operand@list@{#1}% + }% + \else + \pgfmathfloatparsenumber{#1}% + \begingroup + \toks0=\expandafter{\pgfmathfloat@stack@push@operand@list@}% + \toks1=\expandafter{\pgfmathresult}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 {\the\toks1}}% + \endgroup + \let\pgfmathfloat@stack@push@operand@list@=\pgfmathfloat@glob@TMP + \fi + \pgfutil@ifnextchar\relax{% + \expandafter\pgfmath@basic@stack@push@operand\expandafter{\pgfmathfloat@stack@push@operand@list@}% + \pgfmathfloat@stack@push@operand@GOBBLE + }{% + \pgfmathfloat@stack@push@operand@list + }% +}% + + + + +\let\pgfmath@basic@add@=\pgfmathadd@ +\let\pgfmath@basic@subtract@=\pgfmathsubtract@ +\let\pgfmath@basic@multiply@=\pgfmathmultiply@ +\let\pgfmath@basic@divide@=\pgfmathdivide@ +\let\pgfmath@basic@reciprocal@=\pgfmathreciprocal@ +\let\pgfmath@basic@abs@=\pgfmathabs@ +\let\pgfmath@basic@round@=\pgfmathround@ +\let\pgfmath@basic@rand@=\pgfmathrand@ +\let\pgfmath@basic@rnd@=\pgfmathrnd@ +\let\pgfmath@basic@setseed@=\pgfmathsetseed@ +\let\pgfmath@basic@random@=\pgfmathrandom@ +\let\pgfmath@basic@floor@=\pgfmathfloor@ +\let\pgfmath@basic@ceil@=\pgfmathceil@ +\let\pgfmath@basic@mod@=\pgfmathmod@ +\let\pgfmath@basic@max@=\pgfmathmax@ +\let\pgfmath@basic@min@=\pgfmathmin@ +\let\pgfmath@basic@sin@=\pgfmathsin@ +\let\pgfmath@basic@cos@=\pgfmathcos@ +\let\pgfmath@basic@tan@=\pgfmathtan@ +\let\pgfmath@basic@deg@=\pgfmathdeg@ +\let\pgfmath@basic@rad@=\pgfmathrad@ +\let\pgfmath@basic@atan@=\pgfmathatan@ +\let\pgfmath@basic@asin@=\pgfmathasin@ +\let\pgfmath@basic@acos@=\pgfmathacos@ +\let\pgfmath@basic@cot@=\pgfmathcot@ +\let\pgfmath@basic@sec@=\pgfmathsec@ +\let\pgfmath@basic@cosec@=\pgfmathcosec@ +\let\pgfmath@basic@pow@=\pgfmathpow@ +\let\pgfmath@basic@exp@=\pgfmathexp@ +\let\pgfmath@basic@ln@=\pgfmathln@ +\let\pgfmath@basic@sqrt@=\pgfmathsqrt@ +\let\pgfmath@basic@@pi=\pgfmath@pi +\let\pgfmath@basic@veclen@=\pgfmathveclen@ +\let\pgfmath@basic@e@=\pgfmathe@ +\let\pgfmath@basic@lessthan@=\pgfmathlessthan@ +\let\pgfmath@basic@greaterthan@=\pgfmathgreaterthan@ +\let\pgfmath@basic@equalto@=\pgfmathequalto@ +\let\pgfmath@basic@equal@=\pgfmathequal@ +\let\pgfmath@basic@true@=\pgfmathtrue@ +\let\pgfmath@basic@false@=\pgfmathfalse@ + +\def\pgfmathfloatscientific#1#2{% + \edef\pgfmathresult{#1e#2}% + \expandafter\pgfmathfloatparsenumber\expandafter{\pgfmathresult}% +}% +\def\pgfmathfloatlessthan@#1#2{% + \global\pgfmathfloatcomparisonfalse + \begingroup + \edef\pgfmathfloat@loc@TMPa{#1}% + \edef\pgfmathfloat@loc@TMPb{#2}% + \expandafter\pgfmathfloat@decompose\pgfmathfloat@loc@TMPa\relax\pgfmathfloat@a@S\pgfmathfloat@a@M\pgfmathfloat@a@E + \expandafter\pgfmathfloat@decompose\pgfmathfloat@loc@TMPb\relax\pgfmathfloat@b@S\pgfmathfloat@b@M\pgfmathfloat@b@E + \ifcase\pgfmathfloat@a@S + \ifcase\pgfmathfloat@b@S + \or% + \global\pgfmathfloatcomparisontrue + \or% + \or% + \or% + \global\pgfmathfloatcomparisontrue + \or% + \fi + \or + \ifcase\pgfmathfloat@b@S + \or% + \pgfmathfloatlessthan@positive + \or% + \or% + \or% + \global\pgfmathfloatcomparisontrue + \or% + \fi + \or + \ifcase\pgfmathfloat@b@S + \global\pgfmathfloatcomparisontrue + \or% + \global\pgfmathfloatcomparisontrue + \or% + \pgfmathfloatgreaterthan@positive + \or% + \or% + \global\pgfmathfloatcomparisontrue + \or% + \fi + \or + \or + \or + \ifnum\pgfmathfloat@b@S=3 + \else + \global\pgfmathfloatcomparisontrue + \fi + \fi + \endgroup + \ifpgfmathfloatcomparison + \def\pgfmathresult{1.0}% + \else + \def\pgfmathresult{0.0}% + \fi +}% +\let\pgfmathfloatlessthan=\pgfmathfloatlessthan@ +\let\pgfmathfloatless@=\pgfmathfloatlessthan@ + +\def\pgfmathfloatnotless@#1#2{% + \pgfmathfloatless@{#1}{#2}% + \ifpgfmathfloatcomparison + \def\pgfmathresult{0.0}% + \else + \def\pgfmathresult{1.0}% + \fi +}% +\def\pgfmathfloatnotgreater@#1#2{% + \pgfmathfloatless@{#2}{#1}% + \ifpgfmathfloatcomparison + \def\pgfmathresult{0.0}% + \else + \def\pgfmathresult{1.0}% + \fi +}% + +\def\pgfmathfloatlessthan@positive{% + \ifnum\pgfmathfloat@a@E<\pgfmathfloat@b@E + \global\pgfmathfloatcomparisontrue + \else + \ifnum\pgfmathfloat@a@E=\pgfmathfloat@b@E + \ifdim\pgfmathfloat@a@M<\pgfmathfloat@b@M + \global\pgfmathfloatcomparisontrue + \fi + \fi + \fi +}% + +\def\pgfmathfloatgreaterthan@positive{% + \ifnum\pgfmathfloat@a@E>\pgfmathfloat@b@E + \global\pgfmathfloatcomparisontrue + \else + \ifnum\pgfmathfloat@a@E=\pgfmathfloat@b@E + \ifdim\pgfmathfloat@a@M>\pgfmathfloat@b@M + \global\pgfmathfloatcomparisontrue + \fi + \fi + \fi +}% + + +\def\pgfmathfloatgreaterthan@#1#2{\pgfmathfloatlessthan@{#2}{#1}}% +\let\pgfmathfloatgreaterthan=\pgfmathfloatgreaterthan@ +\let\pgfmathfloatgreater@=\pgfmathfloatgreaterthan@ + +\def\pgfmathfloatmax@#1{% + \begingroup + \pgfmathfloatcreate{2}{1.0}{2147483644}% + \let\pgfmathmaxsofar=\pgfmathresult + \pgfmathfloatmax@@#1{}% +}% +\def\pgfmathfloatmax@@#1{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \expandafter\pgfmathfloatmax@@@% + \else% + \pgfmathfloatlessthan{\pgfmathmaxsofar}{#1}% + \ifpgfmathfloatcomparison + \edef\pgfmathmaxsofar{#1}% + \fi + \expandafter\pgfmathfloatmax@@% + \fi% +}% +\def\pgfmathfloatmax@@@{% + \let\pgfmathresult=\pgfmathmaxsofar + \pgfmath@smuggleone{\pgfmathresult}% + \endgroup +}% +\def\pgfmathfloatmin@#1{% + \begingroup + \pgfmathfloatcreate{1}{1.0}{2147483644}% + \let\pgfmathminsofar=\pgfmathresult + \pgfmathfloatmin@@#1{}% +}% +\def\pgfmathfloatmin@@#1{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \expandafter\pgfmathfloatmin@@@% + \else% + \pgfmathfloatlessthan{#1}{\pgfmathminsofar}% + \ifpgfmathfloatcomparison + \edef\pgfmathminsofar{#1}% + \fi + \expandafter\pgfmathfloatmin@@% + \fi% +}% +\def\pgfmathfloatmin@@@{% + \let\pgfmathresult=\pgfmathminsofar + \pgfmath@smuggleone{\pgfmathresult}% + \endgroup +}% + +\def\pgfmathfloatmaxtwo#1#2{% + \pgfmathfloatlessthan{#1}{#2}% + \ifpgfmathfloatcomparison + \edef\pgfmathresult{#2}% + \else + \edef\pgfmathresult{#1}% + \fi +}% +\let\pgfmathfloatmax=\pgfmathfloatmaxtwo + +\def\pgfmathfloatmintwo#1#2{% + \pgfmathfloatlessthan{#1}{#2}% + \ifpgfmathfloatcomparison + \edef\pgfmathresult{#1}% + \else + \edef\pgfmathresult{#2}% + \fi +}% +\let\pgfmathfloatmin=\pgfmathfloatmintwo + +\def\pgfmathfloattoextentedprecision#1{% + \begingroup + \pgfmathfloattoextentedprecision@a{#1}% + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\pgfmathresult}{\the\pgfmathfloat@a@E}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloattoextentedprecision@@zero#1\pgfmathfloat@EOI{% + \edef\pgfmathresult{#1}% +}% +\def\pgfmathfloattoextentedprecision@@one#1.#2#3\pgfmathfloat@EOI{% + \edef\pgfmathresult{#1#2.#3}% +}% +\def\pgfmathfloattoextentedprecision@@two#1.#2#3#4\pgfmathfloat@EOI{% + \edef\pgfmathresult{#1#2#3.#4}% +}% +\def\pgfmathfloattoextentedprecision@@three#1.#2#3#4#5\pgfmathfloat@EOI{% + \edef\pgfmathresult{#1#2#3#4.#5}% +}% + +\def\pgfmathfloatsetextprecision#1{% + \ifcase#1\relax + \let\pgfmathfloattoextentedprecision@@=\pgfmathfloattoextentedprecision@@zero + \def\pgfmathfloatextprec@shift{0}% + \or + \let\pgfmathfloattoextentedprecision@@=\pgfmathfloattoextentedprecision@@one + \def\pgfmathfloatextprec@shift{1}% + \or + \let\pgfmathfloattoextentedprecision@@=\pgfmathfloattoextentedprecision@@two + \def\pgfmathfloatextprec@shift{2}% + \else + \let\pgfmathfloattoextentedprecision@@=\pgfmathfloattoextentedprecision@@three + \def\pgfmathfloatextprec@shift{3}% + \fi +}% +\pgfmathfloatsetextprecision{2}% + +\def\pgfmathfloattoextentedprecision@a#1{% + \edef\pgfmathresult{#1}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifnum\pgfmathfloat@a@S<3 + \advance\pgfmathfloat@a@E by-\pgfmathfloatextprec@shift\relax% + \expandafter\pgfmathfloattoextentedprecision@@\the\pgfmathfloat@a@Mtok 000\pgfmathfloat@EOI + \fi +}% + + +\def\pgfmathfloattoextentedprecision@b#1{% + \edef\pgfmathresult{#1}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@b@S\pgfmathfloat@a@Mtok\pgfmathfloat@b@E + \ifnum\pgfmathfloat@b@S<3 + \advance\pgfmathfloat@b@E by-\pgfmathfloatextprec@shift\relax + \expandafter\pgfmathfloattoextentedprecision@@\the\pgfmathfloat@a@Mtok 00\pgfmathfloat@EOI + \fi +}% + +\def\pgfmathfloatadd@#1#2{% + \begingroup + \pgfmathfloattoextentedprecision@a{#1}% + \let\pgfmathfloat@arga=\pgfmathresult + \pgfmathfloattoextentedprecision@b{#2}% + \let\pgfmathfloat@argb=\pgfmathresult + \pgfmathfloatcomparisontrue% + \ifcase\pgfmathfloat@a@S + \edef\pgfmathresult{#2}% + \pgfmathfloatcomparisonfalse + \or + \or + \edef\pgfmathfloat@arga{-\pgfmathfloat@arga}% + \else + \pgfmathfloatcomparisonfalse + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{0.0}{0}% + \fi + \ifcase\pgfmathfloat@b@S + \edef\pgfmathresult{#1}% + \pgfmathfloatcomparisonfalse + \or + \or + \edef\pgfmathfloat@argb{-\pgfmathfloat@argb}% + \else + \pgfmathfloatcomparisonfalse + \pgfmathfloatcreate{\the\pgfmathfloat@b@S}{0.0}{0}% + \fi + \ifpgfmathfloatcomparison + \ifnum\pgfmathfloat@a@E<\pgfmathfloat@b@E + \pgfmathfloatadd@shift{\pgfmathfloat@arga}{\pgfmathfloat@a@E}{\pgfmathfloat@b@E}% + \else + \pgfmathfloatadd@shift{\pgfmathfloat@argb}{\pgfmathfloat@b@E}{\pgfmathfloat@a@E}% + \fi + \pgfmath@basic@add@{\pgfmathfloat@arga}{\pgfmathfloat@argb}% + \edef\pgfmathresult{\pgfmathresult e\the\pgfmathfloat@a@E}% + \expandafter\pgfmathfloatqparsenumber\expandafter{\pgfmathresult}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloatifzero#1#2#3{% + \pgfmathfloatgetflagstomacro{#1}\pgfmathfloat@loc@TMPa + \if\pgfmathfloat@loc@TMPa0 #2\else#3\fi +}% + +\def\pgfmathfloatiffinite#1#2#3{% + \pgfmathfloatgetflagstomacro{#1}\pgfmathfloatiffinite@ + \ifnum\pgfmathfloatiffinite@>2 #3\else #2\fi +}% + +\def\pgfmathfloatifthenelse@#1#2#3{% + \pgfmathfloatifflags{#1}{0}{% + \edef\pgfmathresult{#3}% + }{% + \edef\pgfmathresult{#2}% + }% +}% +\def\pgfmathfloatequal@#1#2{% + \pgfmathfloatifapproxequalrel{#1}{#2}{% + \def\pgfmathresult{1}% + \pgfmathfloatcomparisontrue + }{% + \def\pgfmathresult{0}% + \pgfmathfloatcomparisonfalse + }% +}% +\let\pgfmathfloatequalto@=\pgfmathfloatequal@ + +\def\pgfmathfloatnotequal@#1#2{% + \pgfmathfloatifapproxequalrel{#1}{#2}{% + \def\pgfmathresult{0}% + \pgfmathfloatcomparisonfalse + }{% + \def\pgfmathresult{1}% + \pgfmathfloatcomparisontrue + }% +}% +\let\pgfmathfloatnotequalto@=\pgfmathfloatnotequal@ + +\long\def\pgfmathfloatifapproxequalrel#1#2#3#4{% + \begingroup + \pgfmathfloatparsenumber{#1}% + \let\pgfmathfloatarga=\pgfmathresult + \pgfmathfloatparsenumber{#2}% + \let\pgfmathfloatargb=\pgfmathresult + \pgfmathfloatrelerror@\pgfmathfloatarga\pgfmathfloatargb + \let\pgfmathfloatarga=\pgfmathresult + \pgfmathfloatlessthan@\pgfmathfloatarga\pgfmathfloat@relthresh + \ifpgfmathfloatcomparison + \def\pgfmathfloat@loc@TMPa{#3}% + \else + \def\pgfmathfloat@loc@TMPa{#4}% + \fi + \expandafter\endgroup + \pgfmathfloat@loc@TMPa +}% + +\def\pgfmathfloatifflags#1#2#3#4{% + \if#2-% + \pgfmathfloatifflags{#1}{2}{#3}{#4}% + \else + \if#2+% + \pgfmathfloatifflags{#1}{1}{#3}{#4}% + \else + \pgfmathfloatgetflagstomacro{#1}\pgfmathfloat@loc@TMPa + \if#2u% + \ifnum\pgfmathfloat@loc@TMPa>2 + #3\relax + \else + #4\relax + \fi + \else + \if\pgfmathfloat@loc@TMPa#2% + #3\relax + \else + #4\relax + \fi + \fi + \fi + \fi +}% + +\def\pgfmathfloatadd@shift#1#2#3{% + \pgf@xa=#1 pt% + \pgfmathfloat@a@S=#3\relax + \advance\pgfmathfloat@a@S by-#2\relax + \ifcase\pgfmathfloat@a@S + \or + \divide\pgf@xa by10\relax + \or + \divide\pgf@xa by100\relax + \or + \divide\pgf@xa by1000\relax + \or + \divide\pgf@xa by10000\relax + \or + \divide\pgf@xa by10000\relax + \divide\pgf@xa by10\relax + \or + \divide\pgf@xa by10000\relax + \divide\pgf@xa by100\relax + \or + \divide\pgf@xa by10000\relax + \divide\pgf@xa by1000\relax + \or + \divide\pgf@xa by10000\relax + \divide\pgf@xa by10000\relax + \else + \pgf@xa=0pt% + \fi + #2=#3\relax + \edef#1{\pgf@sys@tonumber\pgf@xa}% +}% + +\let\pgfmathfloatadd=\pgfmathfloatadd@ + + +\def\pgfmathfloatsubtract@#1#2{% + \begingroup + \edef\pgfmathresult{#2}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@b@S\pgfmathfloat@a@Mtok\pgfmathfloat@b@E + \ifcase\pgfmathfloat@b@S + \edef\pgfmathresult{#1}% + \or + \pgfmathfloatcreate{2}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@b@E}% + \let\pgfmathfloatsub@arg=\pgfmathresult + \pgfmathfloatadd@{#1}{\pgfmathfloatsub@arg}% + \or + \pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@b@E}% + \let\pgfmathfloatsub@arg=\pgfmathresult + \pgfmathfloatadd@{#1}{\pgfmathfloatsub@arg}% + \else + \pgfmathfloatcreate{\the\pgfmathfloat@b@S}{0.0}{0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\let\pgfmathfloatsubtract=\pgfmathfloatsubtract@ + +\def\pgfmathfloatmultiplyfixed@#1#2{% + \begingroup + \pgfmathfloattoextentedprecision@a{#1}% + \let\pgfmathfloat@arga=\pgfmathresult + \pgfmathfloatcomparisontrue% + \ifcase\pgfmathfloat@a@S + \edef\pgfmathresult{#1}% + \pgfmathfloatcomparisonfalse + \or + \or + \edef\pgfmathfloat@arga{-\pgfmathfloat@arga}% + \else + \pgfmathfloatcomparisonfalse + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{0.0}{0}% + \fi + \ifpgfmathfloatcomparison + \pgfmath@basic@multiply@{\pgfmathfloat@arga}{#2}% + \edef\pgfmathresult{\pgfmathresult e\the\pgfmathfloat@a@E}% + \expandafter\pgfmathfloatqparsenumber\expandafter{\pgfmathresult}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\let\pgfmathfloatmultiplyfixed=\pgfmathfloatmultiplyfixed@ + + +\def\pgfmathfloatmultiply@#1#2{% + \begingroup + \pgfmathfloatsetextprecision{1}% + \pgfmathfloattoextentedprecision@a{#1}% + \let\pgfmathfloat@arga=\pgfmathresult + \pgfmathfloattoextentedprecision@b{#2}% + \let\pgfmathfloat@argb=\pgfmathresult + \pgfmathfloatcomparisontrue% + \ifcase\pgfmathfloat@a@S + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \def\pgfmathresult@S{1}% + \or + \def\pgfmathresult@S{2}% + \else + \expandafter\pgfmathfloatcreate\the\pgfmathfloat@b@S{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \def\pgfmathresult@S{2}% + \or + \def\pgfmathresult@S{1}% + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \or% + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \fi + \ifpgfmathfloatcomparison + \pgfmath@basic@multiply@{\pgfmathfloat@arga}{\pgfmathfloat@argb}% + \advance\pgfmathfloat@a@E by\pgfmathfloat@b@E + \edef\pgfmathresult{\pgfmathresult e\the\pgfmathfloat@a@E}% + \expandafter\pgfmathfloatqparsenumber\expandafter{\pgfmathresult}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \pgfmathfloatcreate{\pgfmathresult@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatmultiply=\pgfmathfloatmultiply@ + +\def\pgfmathfloatdivide@#1#2{% + \begingroup + \pgfmathfloatsetextprecision{1}% + \edef\pgfmathfloat@arga{#1}% + \pgfmathfloattoextentedprecision@a{\pgfmathfloat@arga}% + \let\pgfmathfloat@arga=\pgfmathresult + \edef\pgfmathfloat@argb{#2}% + \pgfmathfloattoextentedprecision@b{\pgfmathfloat@argb}% + \let\pgfmathfloat@argb=\pgfmathresult + \pgfmathfloatcomparisontrue% + \ifcase\pgfmathfloat@a@S + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \def\pgfmathresult@S{1}% + \or + \def\pgfmathresult@S{2}% + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \else + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \def\pgfmathresult@S{2}% + \or + \def\pgfmathresult@S{1}% + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \else + \pgfmathfloatcreate{0}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \or% + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \or% + \ifcase\pgfmathfloat@b@S + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{3}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{5}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \or + \pgfmathfloatcreate{4}{0.0}{0}% + \pgfmathfloatcomparisonfalse + \fi + \fi + \ifpgfmathfloatcomparison + \pgfmath@basic@divide@{\pgfmathfloat@arga}{\pgfmathfloat@argb}% + \advance\pgfmathfloat@a@E by-\pgfmathfloat@b@E + \edef\pgfmathresult{\pgfmathresult e\the\pgfmathfloat@a@E}% + \expandafter\pgfmathfloatqparsenumber\expandafter{\pgfmathresult}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \pgfmathfloatcreate{\pgfmathresult@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatdivide=\pgfmathfloatdivide@ + +\def\pgfmathfloatreciprocal@#1{% + \begingroup + \edef\pgfmathfloat@loc@TMPa{#1}% + \pgfmathfloatcreate{1}{1.0}{0}% + \pgfmathfloatdivide@{\pgfmathresult}{\pgfmathfloat@loc@TMPa}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloatsqrt@#1{% + \begingroup + \pgfmathfloatsetextprecision{3}% + \edef\pgfmathfloat@arga{#1}% + \pgfmathfloattoextentedprecision@a{\pgfmathfloat@arga}% + \let\pgfmathfloat@arga=\pgfmathresult + \ifcase\pgfmathfloat@a@S + \pgfmathfloatcreate{0}{0.0}{0}% + \or% + \pgfmath@basic@sqrt@{\pgfmathfloat@arga}% + \ifodd\pgfmathfloat@a@E + \ifnum\pgfmathfloat@a@E>0 + \expandafter\pgfmath@basic@multiply@\expandafter{\pgfmathresult}{3.16227766}% + \else + \expandafter\pgfmath@basic@multiply@\expandafter{\pgfmathresult}{0.316227766}% + \fi + \fi + \divide\pgfmathfloat@a@E by2 % + \edef\pgfmathfloat@arga{\pgfmathresult e\the\pgfmathfloat@a@E}% + \pgfmathfloatqparsenumber{\pgfmathfloat@arga}% + \or% + \pgfmathfloatcreate{3}{0.0}{0}% + \or% + \pgfmathfloatcreate{3}{0.0}{0}% + \or% + \pgfmathfloatcreate{4}{0.0}{0}% + \or% + \pgfmathfloatcreate{3}{0.0}{0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatsqrt=\pgfmathfloatsqrt@ + +\def\pgfmathfloatint@#1{% + \begingroup + \edef\pgfmathfloatint@input{#1}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathfloatint@input\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \gdef\pgfmathfloatintwasnoop{1}% + \gdef\pgfmathfloatintremainder{}% + \ifcase\pgfmathfloat@a@S + \or% + \expandafter\pgfmathfloatint@@\the\pgfmathfloat@a@Mtok\pgfmathfloat@EOI + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \or% + \expandafter\pgfmathfloatint@@\the\pgfmathfloat@a@Mtok\pgfmathfloat@EOI + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \else + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\def\pgfmathfloatint@@#1.{% + \ifnum\pgfmathfloat@a@E<0 + \pgfmathfloat@a@S=0 + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0 + \gdef\pgfmathfloatintwasnoop{0}% + \expandafter\pgfmathfloatint@@loop@gobble + \else + \pgfmathfloat@a@Mtok={#1.}% + \pgfmathfloat@b@E=\pgfmathfloat@a@E + \expandafter\pgfmathfloatint@@loop + \fi +}% +\def\pgfmathfloatint@@loop#1{% + \def\pgfmathfloatint@@loop@{#1}% + \ifx\pgfmathfloatint@@loop@\pgfmathfloat@EOI + \gdef\pgfmathfloatintwasnoop{1}% + \let\pgfmathfloatint@@loop@next=\relax + \else + \ifnum\pgfmathfloat@b@E=0 + \def\pgfmathfloatint@@loop@next{\pgfmathfloatint@@loop@gobble#1}% + \else + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}% + \advance\pgfmathfloat@b@E by-1 + \let\pgfmathfloatint@@loop@next=\pgfmathfloatint@@loop + \fi + \fi + \pgfmathfloatint@@loop@next +}% +\def\pgfmathfloatint@@loop@gobble#1\pgfmathfloat@EOI{% + \if0\pgfmathfloatintwasnoop + \else + \gdef\pgfmathfloatintwasnoop{2}% + \gdef\pgfmathfloatintremainder{#1}% + \fi +}% +\let\pgfmathfloatint=\pgfmathfloatint@ + +\def\pgfmathfloatfloor#1{% + \edef\pgfmath@orig{#1}% + \pgfmathfloatint@{#1}% + \pgfmathfloatifflags{\pgfmath@orig}{2}{% + \let\pgfmath@trunc=\pgfmathresult + \ifcase\pgfmathfloatintwasnoop\relax + \pgfmathfloatcreate{2}{1.0}{0}% + \expandafter\pgfmathfloatadd@\expandafter{\pgfmathresult}{\pgfmath@trunc}% + \or + \let\pgfmathresult=\pgfmath@trunc + \else + \pgfmathfloatparsenumber{0.\pgfmathfloatintremainder}% + \pgfmathfloatifflags{\pgfmathresult}{1}{% + \pgfmathfloatcreate{2}{1.0}{0}% + \expandafter\pgfmathfloatadd@\expandafter{\pgfmathresult}{\pgfmath@trunc}% + }{% + \let\pgfmathresult=\pgfmath@trunc + }% + \fi + }{}% +}% +\let\pgfmathfloatfloor@=\pgfmathfloatfloor + +\def\pgfmathfloatceil#1{% + \edef\pgfmath@orig{#1}% + \pgfmathfloatint@{#1}% + \pgfmathfloatifflags{\pgfmath@orig}{1}{% + \let\pgfmath@trunc=\pgfmathresult + \ifcase\pgfmathfloatintwasnoop\relax + \pgfmathfloatcreate{1}{1.0}{0}% + \expandafter\pgfmathfloatadd@\expandafter{\pgfmathresult}{\pgfmath@trunc}% + \or + \let\pgfmathresult=\pgfmath@trunc + \else + \pgfmathfloatparsenumber{0.\pgfmathfloatintremainder}% + \pgfmathfloatifflags{\pgfmathresult}{1}{% + \pgfmathfloatcreate{1}{1.0}{0}% + \expandafter\pgfmathfloatadd@\expandafter{\pgfmathresult}{\pgfmath@trunc}% + }{% + \let\pgfmathresult=\pgfmath@trunc + }% + \fi + }{}% +}% +\let\pgfmathfloatceil@=\pgfmathfloatceil + +\def\pgfmathfloat@notimplemented#1{% + \pgfmath@error{Sorry, the operation '#1' has not yet been implemented in the floating point unit}{}% + \pgfmathfloatcreate{0}{0.0}{0}% +}% + +\def\pgfmathfloatshift@#1#2{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \advance\pgfmathfloat@a@E by#2\relax + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatshift=\pgfmathfloatshift@ + +\def\pgfmathfloatabs@#1{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S + \or + \or + \pgfmathfloat@a@S=1 + \or + \or + \or + \pgfmathfloat@a@S=4 + \fi + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\def\pgfmathfloatsign@#1{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S + \pgfmathfloatcreate{0}{0.0}{0}% + \or + \pgfmathfloatcreate{1}{1.0}{0}% + \or + \pgfmathfloatcreate{2}{1.0}{0}% + \or + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \or + \pgfmathfloatcreate{1}{1.0}{0}% + \or + \pgfmathfloatcreate{2}{1.0}{0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatsign=\pgfmathfloatsign@ + +\def\pgfmathfloatabserror@#1#2{% + \pgfmathfloatsubtract@{#1}{#2}% + \pgfmathfloatabs@{\pgfmathresult}% +}% +\let\pgfmathfloatabserror=\pgfmathfloatabserror@ + +\def\pgfmathfloatrelerror@#1#2{% + \pgfmathfloatsubtract@{#1}{#2}% + \let\pgfmathfloat@subtract=\pgfmathresult + \pgfmathfloatifflags{#2}{0}{% + \let\pgfmathresult=\pgfmathfloat@subtract + }{% + \pgfmathfloatdivide@{\pgfmathfloat@subtract}{#2}% + }% + \pgfmathfloatabs@{\pgfmathresult}% +}% +\let\pgfmathfloatrelerror=\pgfmathfloatrelerror@ + +\def\pgfmathfloatmod@#1#2{% + \begingroup + \pgfmathfloattoint{#1}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloattoint{#2}% + \let\pgfmathfloat@loc@TMPb=\pgfmathresult + \c@pgfmath@counta=\pgfmathfloat@loc@TMPa\relax + \divide\c@pgfmath@counta by\pgfmathfloat@loc@TMPb\relax + \expandafter\pgfmathfloatparsenumber\expandafter{\the\c@pgfmath@counta}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloatmultiply@{\pgfmathfloat@loc@TMPa}{#2}% + \let\pgfmathfloat@loc@TMPb=\pgfmathresult + \pgfmathfloatsubtract@{#1}{\pgfmathfloat@loc@TMPb}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatmod=\pgfmathfloatmod@ + + +\def\pgfmathfloatmodknowsinverse@#1#2#3{% + \pgfmathfloatmod@{#1}{#2}% +}% +\let\pgfmathfloatmodknowsinverse=\pgfmathfloatmodknowsinverse@ + +\def\pgfmathfloatpi@{% + \pgfmathfloatcreate{1}{3.14159265358979}{0}% +}% +\let\pgfmathfloatpi=\pgfmathfloatpi@ + +\def\pgfmathfloate@{% + \pgfmathfloatcreate{1}{2.71828182845905}{0}% +}% +\let\pgfmathfloate=\pgfmathfloate@ + +\def\pgfmathfloatdeg@#1{% + \expandafter\ifx\csname pgfmfltdeg@factor\endcsname\relax + \pgfmathfloatcreate{1}{5.72957795130823}{1}% + \global\let\pgfmfltdeg@factor=\pgfmathresult + \fi + \pgfmathfloatmultiply@{#1}\pgfmfltdeg@factor% +}% +\let\pgfmathfloatdeg=\pgfmathfloatdeg@ + +\def\pgfmathfloatrad@#1{% + \expandafter\ifx\csname pgfmfltrad@factor\endcsname\relax + \pgfmathfloatcreate{1}{1.74532925199433}{-2}% + \global\let\pgfmfltrad@factor=\pgfmathresult + \fi + \pgfmathfloatmultiply@{#1}\pgfmfltrad@factor% +}% +\let\pgfmathfloatrad=\pgfmathfloatrad@ + +\def\pgfmathfloatTRIG@#1#2{% + \if0\pgfmath@trig@format@choice + \expandafter\ifx\csname pgfmathfloatTRIG@NUM\endcsname\relax% + \pgfmathfloatcreate{1}{3.6}{2}% + \global\let\pgfmathfloatTRIG@NUM=\pgfmathresult + \pgfmathfloatcreate{1}{2.77777777777778}{-3}% + \global\let\pgfmathfloatTRIG@NUM@INV=\pgfmathresult + \fi + \pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@NUM}{\pgfmathfloatTRIG@NUM@INV}% + \else + \expandafter\ifx\csname pgfmathfloatTRIG@rad@NUM\endcsname\relax% + \pgfmathfloatcreate{1}{6.28318530717959}{0}% + \global\let\pgfmathfloatTRIG@rad@NUM=\pgfmathresult + \pgfmathfloatcreate{1}{1.59154943091895}{-1}% + \global\let\pgfmathfloatTRIG@rad@NUM@INV=\pgfmathresult + \fi + \pgfmathfloatmodknowsinverse@{#2}{\pgfmathfloatTRIG@rad@NUM}{\pgfmathfloatTRIG@rad@NUM@INV}% + \fi + \pgfmathfloattofixed@{\pgfmathresult}% + \expandafter#1\expandafter{\pgfmathresult}% + \pgfmathfloatparsenumber{\pgfmathresult}% +}% + +\def\pgfmathfloatsin@#1{\pgfmathfloatTRIG@\pgfmath@basic@sin@{#1}}% +\let\pgfmathfloatsin=\pgfmathfloatsin@ +\def\pgfmathfloatcos@#1{\pgfmathfloatTRIG@\pgfmath@basic@cos@{#1}}% +\let\pgfmathfloatcos=\pgfmathfloatcos@ +\def\pgfmathfloattan@#1{% + \begingroup + \pgfmathfloatcos@{#1}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloatsin@{#1}% + \expandafter\pgfmathfloatdivide@\expandafter{\pgfmathresult}{\pgfmathfloat@loc@TMPa}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloattan=\pgfmathfloattan@ + +\def\pgfmathfloatcot@#1{% + \begingroup + \pgfmathfloatsin@{#1}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloatcos@{#1}% + \expandafter\pgfmathfloatdivide@\expandafter{\pgfmathresult}{\pgfmathfloat@loc@TMPa}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatcot=\pgfmathfloatcot@ + +\def\pgfmathfloatatan@#1{% + \begingroup + \expandafter\ifx\csname pgfmathfloatatan@TMP\endcsname\relax% + \pgfmathfloatcreate{1}{1.6}{4}% + \global\let\pgfmathfloatatan@TMP=\pgfmathresult + \pgfmathfloatcreate{2}{1.6}{4}% + \global\let\pgfmathfloatatan@TMPB=\pgfmathresult + \fi + \pgfmathfloatgreaterthan@{#1}{\pgfmathfloatatan@TMP}% + \ifpgfmathfloatcomparison + \pgfmathiftrigonometricusesdeg{% + \pgfmathfloatcreate{1}{9.0}{1}% + }{% + \pgfmathfloatcreate{1}{1.570796326794}{0}% + }% + \else + \pgfmathfloatlessthan{#1}{\pgfmathfloatatan@TMPB}% + \ifpgfmathfloatcomparison + \pgfmathiftrigonometricusesdeg{% + \pgfmathfloatcreate{2}{9.0}{1}% + }{% + \pgfmathfloatcreate{2}{1.570796326794}{0}% + }% + \else + \pgfmathfloattofixed@{#1}% + \expandafter\pgfmath@basic@atan@\expandafter{\pgfmathresult}% + \pgfmathfloatparsenumber{\pgfmathresult}% + \fi + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloatatan=\pgfmathfloatatan@ + +\def\pgfmathfloatatantwo#1#2{% + \begingroup% + \let\pgfmath@trig@format@choice@@=\pgfmath@trig@format@choice + \def\pgfmath@trig@format@choice{0}% + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \expandafter\pgfmathfloat@decompose#2\relax\pgfmathfloat@b@S\pgfmathfloat@b@M\pgfmathfloat@b@E + \ifnum\pgfmathfloat@a@S=0 + \pgfmathfloat@a@E=-16 % + \fi + \ifnum\pgfmathfloat@a@E<-3 % + \ifnum\pgfmathfloat@b@S=2 % + \pgfmathfloatcreate{1}{1.8}{2}% + \else + \ifnum\pgfmathfloat@b@S=1 % + \pgfmathfloatcreate{0}{0.0}{0}% + \else + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{9.0}{1}% + \fi + \fi + \else% + \pgfmathfloatabs@{#1}\let\pgfmath@tempa\pgfmathresult% + \pgfmathfloatabs@{#2}\let\pgfmath@tempb\pgfmathresult% + \pgfmathfloatgreaterthan@{\pgfmath@tempa}{\pgfmath@tempb}% + \ifpgfmathfloatcomparison + \pgfmathfloatdivide@{#2}{\pgfmath@tempa}% + \expandafter\pgfmathfloatatan@\expandafter{\pgfmathresult}% + \let\pgfmath@tempa=\pgfmathresult + \pgfmathfloatcreate{1}{9.0}{1}% + \let\pgfmath@tempb=\pgfmathresult + \pgfmathfloatsubtract@{\pgfmath@tempb}{\pgfmath@tempa}% + \else% + \pgfmathfloatdivide@{\pgfmath@tempa}{#2}% + \expandafter\pgfmathfloatatan@\expandafter{\pgfmathresult}% + \expandafter\pgfmathfloatifflags\expandafter{\pgfmathresult}{2}{% + \let\pgfmath@tempa=\pgfmathresult + \pgfmathfloatcreate{1}{1.8}{2}% + \let\pgfmath@tempb=\pgfmathresult + \pgfmathfloatadd@{\pgfmath@tempa}{\pgfmath@tempb}% + }{}% + \fi% + \pgfmathfloatifflags{#1}{-}{% + \pgfmathfloatmultiplyfixed@{\pgfmathresult}{-1}% + }{}% + \fi% + \if1\pgfmath@trig@format@choice@@ + \pgfmathfloat@scale@deg@to@rad\pgfmathresult + \fi + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +}% +\let\pgfmathfloatatantwo@=\pgfmathfloatatantwo +\expandafter\let\csname pgfmathfloatatan2\endcsname=\pgfmathfloatatantwo +\expandafter\let\csname pgfmathfloatatan2@\endcsname=\pgfmathfloatatantwo@ + +\def\pgfmathfloat@scale@deg@to@rad#1{% + \edef\pgfmathfloat@loc@TMPb{#1}% + \pgfmathfloatcreate{1}{1.74532925199433}{-2}% + \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@loc@TMPb}% +}% + +\def\pgfmathfloatsec@#1{\pgfmathfloatTRIG@\pgfmath@basic@cos@{#1}\pgfmathfloatreciprocal@{\pgfmathresult}}% +\let\pgfmathfloatsec=\pgfmathfloatsec@ +\def\pgfmathfloatcosec@#1{\pgfmathfloatTRIG@\pgfmath@basic@sin@{#1}\pgfmathfloatreciprocal@{\pgfmathresult}}% +\let\pgfmathfloatcosec=\pgfmathfloatcosec@ + +\def\pgfmathlog@invoke@expanded#1#2{% + \edef\pgfmath@resulttemp{#2}% + \expandafter#1\pgfmath@resulttemp +}% + +\def\pgfmathfloatln@#1{% + \pgfmathlog@float{#1}% + \ifx\pgfmathresult\pgfutil@empty + \pgfmathfloatcreate{3}{0.0}{0}% + \else + \pgfmathfloatparsenumber{\pgfmathresult}% + \fi +}% +\let\pgfmathfloatln=\pgfmathfloatln@ + +\expandafter\def\csname pgfmathfloatlog10@\endcsname#1{% + \pgfmathfloatln@{#1}% + \let\pgfmathfloat@log@e=\pgfmathresult + \pgfmathfloatcreate{1}{4.34294481903252}{-1}% + \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@log@e}% +}% +\pgfutil@namelet{pgfmathfloatlog10}{pgfmathfloatlog10@}% + +\expandafter\def\csname pgfmathfloatlog2@\endcsname#1{% + \pgfmathfloatln@{#1}% + \let\pgfmathfloat@log@e=\pgfmathresult + \pgfmathfloatcreate{1}{1.44269504088896}{0}% + \pgfmathfloatmultiply@{\pgfmathresult}{\pgfmathfloat@log@e}% +}% +\pgfutil@namelet{pgfmathfloatlog2}{pgfmathfloatlog2@}% + +\expandafter\let\expandafter\pgfmathfloatlogtwo\csname pgfmathfloatlog2\endcsname +\expandafter\let\expandafter\pgfmathfloatlogtwo@\csname pgfmathfloatlog2@\endcsname +\expandafter\let\expandafter\pgfmathfloatlogten\csname pgfmathfloatlog10\endcsname +\expandafter\let\expandafter\pgfmathfloatlogten@\csname pgfmathfloatlog10@\endcsname + +\def\pgfmathlog@#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathlog@float{\pgfmathresult}% +}% +\let\pgfmathlog=\pgfmathlog@ +\def\pgfmathlog@float#1{% + \begingroup% + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifnum\pgfmathfloat@a@S=1 + \expandafter\pgfmath@basic@ln@\expandafter{\the\pgfmathfloat@a@Mtok}% + \pgfmathfloat@b@M=\pgfmathresult pt% + \pgfmathfloat@a@M=2.302585pt% + \multiply\pgfmathfloat@a@M by\pgfmathfloat@a@E\relax + \advance\pgfmathfloat@b@M by\pgfmathfloat@a@M + \edef\pgfmathresult{\pgf@sys@tonumber{\pgfmathfloat@b@M}}% + \else + \let\pgfmathresult=\pgfutil@empty% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup% +}% + + +\def\pgfmathfloatexp@#1{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S + \pgfmathfloatcreate{1}{1.0}{0}% + \or% + \pgfmathfloatexp@@{#1}% + \or% + \pgfmathfloatexp@@{#1}% + \else + \edef\pgfmathresult{#1}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\def\pgfmathfloatexp@@#1{% + \pgfmathfloattofixed@{#1}% + \pgf@xa=\pgfmathresult pt + \pgf@xa=0.434294481\pgf@xa\relax + \edef\pgfmathfloat@loc@TMPa{\pgf@sys@tonumber{\pgf@xa}}% + \expandafter\pgfmathfloatexp@@toint\pgfmathfloat@loc@TMPa\relax + \pgf@xa=2.302585092pt + \multiply\pgf@xa by-\pgfmathfloat@k\relax + \advance\pgf@xa by\pgfmathresult pt + \edef\pgfmathfloat@loc@TMPa{\pgf@sys@tonumber{\pgf@xa}}% + \pgfmath@basic@exp@{\pgfmathfloat@loc@TMPa}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloatparsenumber{\pgfmathfloat@loc@TMPa}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloatshift@{\pgfmathfloat@loc@TMPa}{\pgfmathfloat@k}% +}% +\def\pgfmathfloatexp@@toint#1.#2\relax{% + \c@pgf@counta=#1\relax + \ifnum\c@pgf@counta<0 +\advance\c@pgf@counta by-1 % + \c@pgf@countb=#2\relax + \ifnum\c@pgf@countb>0 + \advance\c@pgf@counta by-1 + \fi + \fi + \edef\pgfmathfloat@k{\the\c@pgf@counta}% +}% +\let\pgfmathfloatexp=\pgfmathfloatexp@ + +\def\pgfmathfloatround@#1{% + \begingroup + \pgfkeysvalueof{/pgf/number format/precision/.@cmd}0\pgfeov + \pgfmathfloattofixed{#1}% + \pgfmathroundto{\pgfmathresult}% + \pgfmathfloatparsenumber{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + + +\def\pgfmathfloatneg@#1{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S\relax + \edef\pgfmathresult{#1}% + \or + \pgfmathfloatcreate{2}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \or + \pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \or + \edef\pgfmathresult{#1}% + \or + \pgfmathfloatcreate{5}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \or + \pgfmathfloatcreate{4}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + + +\def\pgfmathfloatpow@#1#2{% + \begingroup% + \expandafter\pgfmathfloat@decompose@tok#2\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S\relax + \pgfmathfloatcreate{1}{1.0}{0}% + \or + \pgfmathfloatpow@@{#1}{#2}% + \or + \pgfmathfloatpow@@{#1}{#2}% + \or + \edef\pgfmathresult{#2}% + \or + \edef\pgfmathresult{#2}% + \or + \pgfmathfloatcreate{0}{0.0}{0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloatpow@@#1#2{% + \pgfmathfloattofixed@{#2}% + \afterassignment\pgfmath@x% + \expandafter\c@pgfmath@counta\pgfmathresult pt\relax% + \ifdim\pgfmath@x=0pt % + \ifnum\c@pgfmath@counta<0 + \pgfmathfloatreciprocal@{#1}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \c@pgfmath@counta=-\c@pgfmath@counta + \else + \edef\pgfmathfloat@loc@TMPa{#1}% + \fi + \pgfmathfloatcreate{1}{1.0}{0}% + \let\pgfmathfloat@loc@TMPb=\pgfmathresult + \pgfmathloop + \ifnum\c@pgfmath@counta>0\relax% + \ifodd\c@pgfmath@counta% + \pgfmathfloatmultiply@{\pgfmathfloat@loc@TMPb}{\pgfmathfloat@loc@TMPa}% + \let\pgfmathfloat@loc@TMPb=\pgfmathresult + \fi + \ifnum\c@pgfmath@counta>1\relax% + \pgfmathfloatmultiply@{\pgfmathfloat@loc@TMPa}{\pgfmathfloat@loc@TMPa}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \fi% + \divide\c@pgfmath@counta by2\relax% + \repeatpgfmathloop% + \else + \pgfmathfloatgetflags{#1}\c@pgfmath@counta + \ifnum0=\c@pgfmath@counta + \pgfmathfloatgetflags{#2}\c@pgfmath@counta + \ifnum0=\c@pgfmath@counta + \pgfmathfloatcreate{1}{1.0}{0}% + \else + \pgfmathfloatcreate{0}{0.0}{0}% + \fi + \else + \pgfmathfloatln@{#1}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \edef\pgfmathfloat@loc@TMPb{#2}% + \pgfmathfloatmultiply@{\pgfmathfloat@loc@TMPa}{\pgfmathfloat@loc@TMPb}% + \pgfmathfloatexp@{\pgfmathresult}% + \fi + \fi +}% + +\def\pgfmathfloat@definemethodfrombasic@NOARG#1{% + \pgfutil@ifundefined{pgfmath@basic@#1@}{% + \pgfutil@namelet{pgfmath@basic@#1@}{pgfmath#1@}% + }{}% + \edef\pgfmathfloat@glob@TMP{% + \expandafter\noexpand\csname pgfmath@basic@#1@\endcsname + \noexpand\pgfmathfloatparsenumber{\noexpand\pgfmathresult}% + }% + \expandafter\let\csname pgfmathfloat#1@\endcsname=\pgfmathfloat@glob@TMP% + \expandafter\let\csname pgfmathfloat#1\endcsname=\pgfmathfloat@glob@TMP% +}% +\def\pgfmathfloat@definemethodfrombasic@ONEARG#1{% + \pgfutil@ifundefined{pgfmath@basic@#1@}{% + \pgfutil@namelet{pgfmath@basic@#1@}{pgfmath#1@}% + }{}% + \edef\pgfmathfloat@glob@TMP##1{% + \noexpand\pgfmathfloattofixed{##1}% + \noexpand\expandafter + \expandafter\noexpand\csname pgfmath@basic@#1@\endcsname\noexpand\expandafter% + {\noexpand\pgfmathresult}% + \noexpand\pgfmathfloatparsenumber{\noexpand\pgfmathresult}% + }% + \expandafter\let\csname pgfmathfloat#1@\endcsname=\pgfmathfloat@glob@TMP% + \expandafter\let\csname pgfmathfloat#1\endcsname=\pgfmathfloat@glob@TMP% +}% +\def\pgfmathfloat@definemethodfrombasic@TWOARGS#1{% + \pgfutil@ifundefined{pgfmath@basic@#1@}{% + \pgfutil@namelet{pgfmath@basic@#1@}{pgfmath#1@}% + }{}% + \edef\pgfmathfloat@glob@TMP##1##2{% + \noexpand\pgfmathfloattofixed{##2}% + \noexpand\let\noexpand\pgfmathfloat@loc@TMPa=\noexpand\pgfmathresult + \noexpand\pgfmathfloattofixed{##1}% + \noexpand\expandafter + \expandafter\noexpand\csname pgfmath@basic@#1@\endcsname\noexpand\expandafter% + {\noexpand\pgfmathresult}{\noexpand\pgfmathfloat@loc@TMPa}% + \noexpand\pgfmathfloatparsenumber{\noexpand\pgfmathresult}% + }% + \expandafter\let\csname pgfmathfloat#1@\endcsname=\pgfmathfloat@glob@TMP% + \expandafter\let\csname pgfmathfloat#1\endcsname=\pgfmathfloat@glob@TMP% +}% +\pgfmathfloat@definemethodfrombasic@NOARG{rand}% +\pgfmathfloat@definemethodfrombasic@NOARG{rnd}% +\pgfmathfloat@definemethodfrombasic@NOARG{false}% +\pgfmathfloat@definemethodfrombasic@NOARG{true}% +\pgfmathfloat@definemethodfrombasic@ONEARG{asin}% +\pgfmathfloat@definemethodfrombasic@ONEARG{acos}% +\pgfmathfloat@definemethodfrombasic@ONEARG{not}% +\pgfmathfloat@definemethodfrombasic@ONEARG{hex}% +\pgfmathfloat@definemethodfrombasic@ONEARG{Hex}% +\pgfmathfloat@definemethodfrombasic@ONEARG{oct}% +\pgfmathfloat@definemethodfrombasic@ONEARG{bin}% +\pgfmathfloat@definemethodfrombasic@TWOARGS{and}% +\pgfmathfloat@definemethodfrombasic@TWOARGS{or}% + +\pgfutil@ifundefined{pgfmathdeclarefunction}{% + \let\pgfmath@basic@rand=\pgfmathrand + \let\pgfmath@basic@rand@=\pgfmathrand@ + \def\pgfmathfloatrand@{% + \pgfmath@basic@rand + \pgfmathfloatparsenumber{\pgfmathresult}% + }% + \let\pgfmathfloatrand=\pgfmathfloatrand@% + \let\pgfmath@basic@rnd=\pgfmathrnd + \let\pgfmath@basic@rnd@=\pgfmathrnd@ + \def\pgfmathfloatrnd@{% + \pgfmath@basic@rnd + \pgfmathfloatparsenumber{\pgfmathresult}% + }% + \let\pgfmathfloatrnd=\pgfmathfloatrnd@% +}{}% + +\def\pgfmathfloatfactorial@#1{% + \begingroup + \pgfmathfloattofixed{#1}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgfmath@counta\pgfmathresult\relax\pgfmath@% + \pgfmathfloatcreate{1}{1.0}{0}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathloop + \ifnum\c@pgfmath@counta<2 % + \else + \expandafter\pgfmathfloatparsenumber\expandafter{\the\c@pgfmath@counta}% + \expandafter\pgfmathfloatmultiply@\expandafter{\pgfmathresult}{\pgfmathfloat@loc@TMPa}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \advance\c@pgfmath@counta by-1\relax% + \repeatpgfmathloop + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloatveclen@#1#2{% + \begingroup + \edef\pgfmathfloat@@a{#1}% + \pgfmathfloatmultiply@{\pgfmathfloat@@a}{\pgfmathfloat@@a}% + \let\pgfmathfloat@@a=\pgfmathresult + \edef\pgfmathfloat@@b{#2}% + \pgfmathfloatmultiply@{\pgfmathfloat@@b}{\pgfmathfloat@@b}% + \let\pgfmathfloat@@b=\pgfmathresult + \pgfmathfloatadd@{\pgfmathfloat@@a}{\pgfmathfloat@@b}% + \pgfmathfloatsqrt@{\pgfmathresult}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloatcosh@#1{% + \begingroup + \pgfmathfloatexp@{#1}% + \let\pgfmathfloat@@a=\pgfmathresult + \pgfmathfloatneg@{#1}% + \pgfmathfloatexp@{\pgfmathresult}% + \pgfmathfloatadd@{\pgfmathresult}{\pgfmathfloat@@a}% + \expandafter\pgfmathfloatmultiplyfixed@\expandafter{\pgfmathresult}{0.5}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\def\pgfmathfloatsinh@#1{% + \begingroup + \pgfmathfloatexp@{#1}% + \let\pgfmathfloat@@a=\pgfmathresult + \pgfmathfloatneg@{#1}% + \pgfmathfloatexp@{\pgfmathresult}% + \pgfmathfloatsubtract@{\pgfmathfloat@@a}{\pgfmathresult}% + \expandafter\pgfmathfloatmultiplyfixed@\expandafter{\pgfmathresult}{0.5}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\def\pgfmathfloattanh@#1{% + \begingroup + \pgfmathfloatsinh@{#1}% + \let\pgfmathfloat@@a=\pgfmathresult + \pgfmathfloatcosh@{#1}% + \let\pgfmathfloat@@b=\pgfmathresult + \pgfmathfloatdivide@{\pgfmathfloat@@a}{\pgfmathfloat@@b}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryintersections.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryintersections.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..da237fb375a01bdec340de5664a1d4c74ba6e360 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryintersections.code.tex @@ -0,0 +1,899 @@ + + +\usepgflibrary{fpu}% + +\newcount\pgf@intersect@solutions + +\newif\ifpgf@intersect@sort +\newif\ifpgf@intersect@sort@by@second@path + +\def\pgfintersectionsortbyfirstpath{% + \pgf@intersect@sorttrue% + \pgf@intersect@sort@by@second@pathfalse% +}% + +\def\pgfintersectionsortbysecondpath{% + \pgf@intersect@sorttrue% + \pgf@intersect@sort@by@second@pathtrue% +}% + +\def\pgfpointintersectionsolution#1{% + \ifnum#1<1\relax% + \pgfpoint@intersect@solution@orgin% + \else% + \ifnum#1>\pgfintersectionsolutions\relax% + \pgfpoint@intersect@solution@orgin% + \else% + \csname pgfpoint@intersect@solution@#1\endcsname% + \fi% + \fi% +}% + +\def\pgfintersectiongetsolutionsegmentindices#1#2#3{% + \ifnum#1<1\relax% + \let#2=\pgfutil@empty + \let#3=\pgfutil@empty + \else% + \ifnum#1>\pgfintersectionsolutions\relax% + \let#2=\pgfutil@empty + \let#3=\pgfutil@empty + \else% + \def\pgf@temp##1##2##3##4{% + \edef#2{##1}% + \edef#3{##2}% + }% + \expandafter\let\expandafter\pgf@tempb\csname pgf@intersect@solution@props@#1\endcsname + \expandafter\pgf@temp\pgf@tempb + \fi% + \fi% +}% + +\def\pgfintersectiongetsolutiontimes#1#2#3{% + \ifnum#1<1\relax% + \let#2=\pgfutil@empty + \let#3=\pgfutil@empty + \else% + \ifnum#1>\pgfintersectionsolutions\relax% + \let#2=\pgfutil@empty + \let#3=\pgfutil@empty + \else% + \def\pgf@temp##1##2##3##4{% + \edef#2{##3}% + \edef#3{##4}% + \ifx#2\pgfutil@empty \edef#2{##1}\fi + \ifx#3\pgfutil@empty \edef#3{##2}\fi + }% + \expandafter\let\expandafter\pgf@tempb\csname pgf@intersect@solution@props@#1\endcsname + \expandafter\pgf@temp\pgf@tempb + \fi% + \fi% +}% + +\def\pgfpoint@intersect@solution@orgin{% + \begingroup% + \pgftransforminvert% + \pgfpointorigin% + \pgf@pos@transform@glob + \global\pgf@x=\pgf@x% + \global\pgf@y=\pgf@y% + \endgroup% +}% + +\long\def\pgfintersectionofpaths#1#2{% + \begingroup% + \pgfinterruptpath% + #1% + \pgfgetpath\pgf@intersect@path@a% + \global\let\pgf@intersect@path@temp=\pgf@intersect@path@a% + \endpgfinterruptpath% + \endgroup% + \let\pgf@intersect@path@a=\pgf@intersect@path@temp% + \begingroup% + \pgfinterruptpath% + #2% + \pgfgetpath\pgf@intersect@path@b% + \global\let\pgf@intersect@path@temp=\pgf@intersect@path@b% + \endpgfinterruptpath% + \endgroup% + \let\pgf@intersect@path@b=\pgf@intersect@path@temp% + \pgf@intersect@solutions=0\relax% + \pgf@intersect@path@reset@a + \ifpgf@intersect@sort@by@second@path% + \let\pgf@intersect@temp=\pgf@intersect@path@a% + \let\pgf@intersect@path@a=\pgf@intersect@path@b% + \let\pgf@intersect@path@b=\pgf@intersect@temp% + \fi% + \pgfprocessround\pgf@intersect@path@a\pgf@intersect@path@a% + \pgfprocessround\pgf@intersect@path@b\pgf@intersect@path@b% + \let\pgf@intersect@token@after=\pgf@intersect@path@process@a% + \expandafter\pgf@intersectionofpaths\pgf@intersect@path@a\pgf@stop% + \edef\pgfintersectionsolutions{\the\pgf@intersect@solutions}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgfintersectionsolutions\relax% + \else% + \pgfutil@namelet{pgfpoint@intersect@solution@\pgfmathcounter}% + {pgfpoint@g@intersect@solution@\pgfmathcounter}% + \edef\pgf@marshal{\noexpand\pgf@intersection@set@properties{\csname pgfpoint@g@intersect@solution@\pgfmathcounter @props\endcsname}}% + \pgf@marshal + \ifpgf@intersect@sort% + \pgfutil@namelet{pgf@intersect@solution@\pgfmathcounter @time@a}% + {pgf@g@intersect@solution@\pgfmathcounter @time@a}% + \fi% + \repeatpgfmathloop% + \ifpgf@intersect@sort% + \pgfintersectionsolutionsortbytime% + \fi% +}% + +\def\pgf@intersection@set@properties#1{% + \pgfutil@namedef{pgf@intersect@solution@props@\pgfmathcounter}{#1}% +}% + +\def\pgf@intersection@store@properties#1{% + \expandafter\xdef\csname #1@props\endcsname{{\pgf@intersect@time@offset}{\pgf@intersect@time@offset@b}{\pgf@intersect@time@a}{\pgf@intersect@time@b}}% +}% + +\def\pgf@intersectionofpaths#1{% + \ifx#1\pgf@stop% + \let\pgf@intersect@next=\relax% + \else% + \ifx#1\pgfsyssoftpath@movetotoken% + \let\pgf@intersect@next=\pgf@intersect@token@moveto% + \else% + \ifx#1\pgfsyssoftpath@linetotoken% + \let\pgf@intersect@next=\pgf@intersect@token@lineto% + \else% + \ifx#1\pgfsyssoftpath@closepathtoken% + \let\pgf@intersect@next=\pgf@intersect@token@lineto% + \else% + \ifx#1\pgfsyssoftpath@curvetosupportatoken% + \let\pgf@intersect@next=\pgf@intersect@token@curveto% + \else% + \ifx#1\pgfsyssoftpath@rectcornertoken% + \let\pgf@intersect@next=\pgf@intersect@token@rect% + \fi% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgf@intersect@next}% + +\def\pgf@intersect@token@moveto#1#2{% + \def\pgfpoint@intersect@start{\pgfqpoint{#1}{#2}}% + \pgf@intersectionofpaths% +}% + +\def\pgf@intersect@token@lineto#1#2{% + \def\pgfpoint@intersect@end{\pgfqpoint{#1}{#2}}% + \def\pgf@intersect@type{line}% + \pgf@intersect@token@after% +}% +\def\pgf@intersect@token@curveto#1#2\pgfsyssoftpath@curvetosupportbtoken#3#4\pgfsyssoftpath@curvetotoken#5#6{% + \def\pgfpoint@intersect@firstsupport{\pgfqpoint{#1}{#2}}% + \def\pgfpoint@intersect@secondsupport{\pgfqpoint{#3}{#4}}% + \def\pgfpoint@intersect@end{\pgfqpoint{#5}{#6}}% + \def\pgf@intersect@type{curve}% + \pgf@intersect@token@after% +}% + +\def\pgf@intersect@token@rect#1#2\pgfsyssoftpath@rectsizetoken#3#4{% + \pgf@xa=#1\relax% + \advance\pgf@xa by#3\relax% + \pgf@ya=#2\relax% + \advance\pgf@ya by#4\relax% + \edef\pgf@marshal{% + \noexpand\pgfsyssoftpath@movetotoken{#1}{#2}% + \noexpand\pgfsyssoftpath@linetotoken{#1}{\the\pgf@ya}% + \noexpand\pgfsyssoftpath@linetotoken{\the\pgf@xa}{\the\pgf@ya}% + \noexpand\pgfsyssoftpath@linetotoken{\the\pgf@xa}{#2}% + \noexpand\pgfsyssoftpath@closepathtoken{#1}{#2}% + }% + \expandafter\pgf@intersectionofpaths\pgf@marshal% +}% + +\def\pgf@intersect@path@process@a{% + \pgf@intersect@path@getpoints@a% + \let\pgf@intersect@token@after=\pgf@intersect@path@process@b% + \pgf@intersect@path@reset@b + \expandafter\pgf@intersectionofpaths\pgf@intersect@path@b\pgf@stop% + \let\pgfpoint@intersect@start=\pgfpoint@intersect@end@a% + \let\pgf@intersect@token@after=\pgf@intersect@path@process@a% + \c@pgf@counta=\pgf@intersect@time@offset\relax% + \advance\c@pgf@counta by1\relax% + \edef\pgf@intersect@time@offset{\the\c@pgf@counta}% + \pgf@intersectionofpaths% +}% + +\def\pgf@intersect@path@reset@a{% + \def\pgf@intersect@time@offset{0}% + \def\pgf@intersect@time@a{}% +}% + +\def\pgf@intersect@path@reset@b{% + \def\pgf@intersect@time@offset@b{0}% + \def\pgf@intersect@time@b{}% +}% + +\def\pgf@intersect@path@getpoints@a{% + \let\pgfpoint@intersect@start@a=\pgfpoint@intersect@start% + \let\pgfpoint@intersect@end@a=\pgfpoint@intersect@end% + \let\pgfpoint@intersect@firstsupport@a=\pgfpoint@intersect@firstsupport% + \let\pgfpoint@intersect@secondsupport@a=\pgfpoint@intersect@secondsupport% + \let\pgf@intersect@type@a=\pgf@intersect@type% +}% + +\def\pgf@intersect@path@process@b{% + \pgf@intersect@path@getpoints@b% + \csname pgf@intersect@\pgf@intersect@type@a @and@\pgf@intersect@type@b\endcsname% + \let\pgfpoint@intersect@start=\pgfpoint@intersect@end@b% + \c@pgf@counta=\pgf@intersect@time@offset@b\relax% + \advance\c@pgf@counta by1\relax% + \edef\pgf@intersect@time@offset@b{\the\c@pgf@counta}% + \pgf@intersectionofpaths}% + +\def\pgf@intersect@path@getpoints@b{% + \let\pgfpoint@intersect@start@b=\pgfpoint@intersect@start% + \let\pgfpoint@intersect@end@b=\pgfpoint@intersect@end% + \let\pgfpoint@intersect@firstsupport@b=\pgfpoint@intersect@firstsupport% + \let\pgfpoint@intersect@secondsupport@b=\pgfpoint@intersect@secondsupport% + \let\pgf@intersect@type@b=\pgf@intersect@type% +}% + +\def\pgf@intersect@line@and@line{% + \pgf@intersectionoflines{\pgfpoint@intersect@start@a}{\pgfpoint@intersect@end@a}% + {\pgfpoint@intersect@start@b}{\pgfpoint@intersect@end@b}% +}% + +\def\pgf@intersect@line@and@curve{% + \pgf@intersectionoflineandcurve% + {\pgf@process{\pgfpoint@intersect@start@a}}{\pgf@process{\pgfpoint@intersect@end@a}}% + {\pgf@process{\pgfpoint@intersect@start@b}}{\pgf@process{\pgfpoint@intersect@firstsupport@b}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@b}}{\pgf@process{\pgfpoint@intersect@end@b}}% +}% + +\def\pgf@intersect@curve@and@line{% + \pgf@intersectionofcurveandline% + {\pgf@process{\pgfpoint@intersect@start@a}}{\pgf@process{\pgfpoint@intersect@firstsupport@a}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@a}}{\pgf@process{\pgfpoint@intersect@end@a}}% + {\pgf@process{\pgfpoint@intersect@start@b}}{\pgf@process{\pgfpoint@intersect@end@b}}% +}% + +\def\pgf@intersect@curve@and@curve{% + \pgf@intersectionofcurves% + {\pgf@process{\pgfpoint@intersect@start@a}}{\pgf@process{\pgfpoint@intersect@firstsupport@a}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@a}}{\pgf@process{\pgfpoint@intersect@end@a}}% + {\pgf@process{\pgfpoint@intersect@start@b}}{\pgf@process{\pgfpoint@intersect@firstsupport@b}}% + {\pgf@process{\pgfpoint@intersect@secondsupport@b}}{\pgf@process{\pgfpoint@intersect@end@b}}% +}% + + +\def\pgfintersectionoflines#1#2#3#4{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionoflines{#1}{#2}{#3}{#4}% +}% + +\def\pgf@intersectionoflines#1#2#3#4{% + \pgf@iflinesintersect{#1}{#2}{#3}{#4}% + {% + \pgfextract@process\pgf@intersect@solution@candidate{% + }% + \pgf@ifsolution@duplicate{\pgf@intersect@solution@candidate}{% + }{% + \global\advance\pgf@intersect@solutions by1\relax% + \expandafter\global\expandafter\let\csname pgfpoint@g@intersect@solution@\the\pgf@intersect@solutions\endcsname=\pgf@intersect@solution@candidate + \ifpgf@intersect@sort% + \pgf@process{\pgf@intersect@solution@candidate}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\pgfpointdiff{\pgfpoint@intersect@start@a}{\pgfpoint@intersect@end@a}}% + \edef\pgf@marshal{% + \noexpand\pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + }% + \pgf@marshal% + \let\pgf@intersect@length@a=\pgfmathresult% + \pgf@process{\pgfpointdiff{\pgfpoint@intersect@start@a}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}% + \edef\pgf@marshal{% + \noexpand\pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + }% + \pgf@marshal% + \pgfmathdivide@{\pgfmathresult}{\pgf@intersect@length@a}% + \pgf@x=\pgfmathresult pt\relax% + \advance\pgf@x by\pgf@intersect@time@offset pt\relax% + \edef\pgf@intersect@time@a{\pgfmath@tonumber{\pgf@x}}% + \expandafter\global\expandafter\let\csname pgf@g@intersect@solution@\the\pgf@intersect@solutions @time@a\endcsname= + \pgf@intersect@time@a + \else + \let\pgf@intersect@time@a=\pgfutil@empty + \fi% + \let\pgf@intersect@time@b=\pgfutil@empty + \pgf@intersection@store@properties{pgfpoint@g@intersect@solution@\the\pgf@intersect@solutions}% + }% + }{% + }% +}% + +\newif\ifpgf@s +\newif\ifpgf@t +\def\pgfiflinesintersect#1#2#3#4{% + \begingroup% + \pgf@iflinesintersect{\pgf@process{#1}}{\pgf@process{#2}}{\pgf@process{#3}}{\pgf@process{#4}}% + {\aftergroup\pgfutil@firstoftwo}{\aftergroup\pgfutil@secondoftwo}% + \endgroup% +}% + +\def\pgf@intersections@version{2}% + +\def\pgf@iflinesintersect#1#2#3#4{% + \pgf@intersect@boundingbox@reset% + \pgf@intersect@boundingbox@update{#1}% + \pgf@intersect@boundingbox@update{#2}% + \pgf@intersect@boundingbox@assign@b% + \pgf@intersect@boundingbox@reset% + \pgf@intersect@boundingbox@update{#3}% + \pgf@intersect@boundingbox@update{#4}% + \pgf@intersect@boundingbox@assign@a% + \pgf@intersect@boundingbox@a% + \pgf@intersect@boundingbox@b% + \pgf@intersect@boundingbox@ifoverlap@upperbound{% + \pgf@iflinesintersect@{#1}{#2}{#3}{#4}% + }{% + \let\pgf@intersect@next=\pgfutil@secondoftwo% + }% + \pgf@intersect@next% +}% + +\def\pgf@iflinesintersect@#1#2#3#4{% + #1\relax% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + #2\relax% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + #3\relax% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + #4\relax% + \edef\pgf@intersect@A{% + \pgf@xa=\the\pgf@xa\space + \pgf@ya=\the\pgf@ya\space + }% + \advance\pgf@xb by-\pgf@xa + \advance\pgf@yb by-\pgf@ya + \advance\pgf@xa by-\pgf@xc + \advance\pgf@ya by-\pgf@yc + \pgf@xa=-\pgf@xa + \pgf@ya=-\pgf@ya + \advance\pgf@xc by-\pgf@x + \advance\pgf@yc by-\pgf@y + \begingroup + \ifdim\pgf@xb<0sp \pgf@xb=-\pgf@xb\fi + \ifdim\pgf@yb<0sp \pgf@yb=-\pgf@yb\fi + \advance\pgf@xb by\pgf@yb + \xdef\pgf@intersect@len@a{\pgf@sys@tonumber\pgf@xb}% + \ifdim\pgf@xc<0sp \pgf@xc=-\pgf@xc\fi + \ifdim\pgf@yc<0sp \pgf@yc=-\pgf@yc\fi + \advance\pgf@xc by\pgf@yc + \xdef\pgf@intersect@len@b{\pgf@sys@tonumber\pgf@xc}% + \endgroup + \edef\pgf@marshal{% + \noexpand\pgfutilsolvetwotwoleqfloat{% + {\pgf@sys@tonumber\pgf@xb}{\pgf@sys@tonumber\pgf@xc}% + {\pgf@sys@tonumber\pgf@yb}{\pgf@sys@tonumber\pgf@yc}% + }{% + {\pgf@sys@tonumber\pgf@xa}% + {\pgf@sys@tonumber\pgf@ya}% + }% + }% + \pgf@marshal + \let\pgf@intersect@next=\pgfutil@secondoftwo% + \ifx\pgfmathresult\pgfutil@empty + \else + \def\pgf@marshal##1##2{% + \global\pgf@x=##1pt % + \global\pgf@y=##2pt % + }% + \expandafter\pgf@marshal\pgfmathresult + \def\pgf@marshal{XXXX}% + \ifdim\pgf@x<0sp + \pgf@xa=-\pgf@intersect@len@a\pgf@x + \ifdim\pgf@xa<\pgfintersectiontolerance\relax + \def\pgf@marshal{1}% + \else + \def\pgf@marshal{0}% + \fi + \else + \ifdim\pgf@x>1pt + \pgf@xa=\pgf@intersect@len@a\pgf@x + \advance\pgf@xa by-\pgf@intersect@len@a pt % + \ifdim\pgf@xa<\pgfintersectiontolerance\relax + \def\pgf@marshal{1}% + \else + \def\pgf@marshal{0}% + \fi + \else + \def\pgf@marshal{1}% + \fi + \fi + \if1\pgf@marshal + \ifdim\pgf@y<0sp + \pgf@xa=-\pgf@intersect@len@b\pgf@y + \ifdim\pgf@xa<\pgfintersectiontolerance\relax + \def\pgf@marshal{1}% + \else + \def\pgf@marshal{0}% + \fi + \else + \ifdim\pgf@y>1pt + \pgf@xa=\pgf@intersect@len@b\pgf@y + \advance\pgf@xa by-\pgf@intersect@len@b pt % + \ifdim\pgf@xa<\pgfintersectiontolerance\relax + \def\pgf@marshal{1}% + \else + \def\pgf@marshal{0}% + \fi + \else + \def\pgf@marshal{1}% + \fi + \fi + \fi + \if1\pgf@marshal + \pgf@intersect@A + \pgf@yc=\pgf@x + \global\pgf@x=\pgf@sys@tonumber\pgf@xb\pgf@yc + \global\pgf@y=\pgf@sys@tonumber\pgf@yb\pgf@yc + \global\advance\pgf@x by \pgf@xa + \global\advance\pgf@y by \pgf@ya + \let\pgf@intersect@next=\pgfutil@firstoftwo% + \fi + \fi +}% + + + + +\def\pgfintersectionoflineandcurve#1#2#3#4#5#6{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionoflineandcurve{#1}{#2}{#3}{#4}{#5}{#6}% +}% + +\def\pgf@intersectionoflineandcurve#1#2#3#4#5#6{% + \pgf@intersectionofcurves% + {\pgf@process{#1}}% + {% + \pgf@process{% + \pgfpointadd{#1\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + {#2\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + }% + }% + {% + \pgf@process{% + \pgfpointadd{#1\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + {#2\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + }% + }% + {\pgf@process{#2}}% + {\pgf@process{#3}}% + {\pgf@process{#4}}% + {\pgf@process{#5}}% + {\pgf@process{#6}}% +}% + +\def\pgf@intersectionofcurveandline#1#2#3#4#5#6{% + \pgf@intersectionofcurves% + {\pgf@process{#1}}% + {\pgf@process{#2}}% + {\pgf@process{#3}}% + {\pgf@process{#4}}% + {\pgf@process{#5}}% + {% + \pgf@process{% + \pgfpointadd{#5\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + {#6\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + }% + }% + {% + \pgf@process{% + \pgfpointadd{#5\relax\pgf@x=0.333333\pgf@x\pgf@y=0.333333\pgf@y}% + {#6\relax\pgf@x=0.666666\pgf@x\pgf@y=0.666666\pgf@y}% + }% + }% + {\pgf@process{#6}}% +}% + + + + +\def\pgfintersectiontolerance{0.1pt}% +\def\pgfintersectiontoleranceupperbound{1pt}% +\def\pgfintersectiontolerancefactor{0.1}% + + + +\def\pgfpointintersectionofcurves#1#2#3#4#5#6#7#8#9{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionofcurves% + {\pgf@process{#1}}{\pgf@process{#2}}{\pgf@process{#3}}{\pgf@process{#4}}% + {\pgf@process{#5}}{\pgf@process{#6}}{\pgf@process{#7}}{\pgf@process{#8}}% + \pgfpointintersectionsolution{#9}% +}% + +\def\pgfintersectionofcurves#1#2#3#4#5#6#7#8{% + \pgf@intersect@solutions=0\relax% + \pgf@intersectionofcurves% + {\pgf@process{#1}}{\pgf@process{#2}}{\pgf@process{#3}}{\pgf@process{#4}}% + {\pgf@process{#5}}{\pgf@process{#6}}{\pgf@process{#7}}{\pgf@process{#8}}% +}% +\def\pgf@intersectionofcurves#1#2#3#4#5#6#7#8{% + \begingroup% + \dimendef\pgf@time@a=2\relax% + \dimendef\pgf@time@aa=4\relax% + \dimendef\pgf@time@b=6\relax% + \dimendef\pgf@time@bb=8\relax% + \pgf@time@a=0pt\relax% + \pgf@time@aa=1pt\relax% + \pgf@time@b=0pt\relax% + \pgf@time@bb=1pt\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@b% + \let\pgf@curve@subdivde@after=\pgf@@intersectionofcurves% + \pgf@@intersectionofcurves{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \endgroup% +}% + +\def\pgf@intersect@boundingbox@assign@a{% + \edef\pgf@intersect@boundingbox@a{% + \noexpand\pgf@xb=\the\pgf@xa\space% + \noexpand\pgf@yb=\the\pgf@ya\space% + \noexpand\pgf@xc=\the\pgf@xb\space% + \noexpand\pgf@yc=\the\pgf@yb\space% + }% +}% +\def\pgf@intersect@boundingbox@assign@b{% + \edef\pgf@intersect@boundingbox@b{% + \noexpand\global\noexpand\pgf@x=\the\pgf@xa\space% + \noexpand\global\noexpand\pgf@y=\the\pgf@ya\space% + \noexpand\pgf@xa=\the\pgf@xb\space% + \noexpand\pgf@ya=\the\pgf@yb\space% + }% +}% + +\def\pgf@intersect@boundingbox@ifoverlap{% + \def\pgf@intersect@next{\pgfutil@secondoftwo}% + \ifdim\pgf@xa<\pgf@xb% + \else% + \ifdim\pgf@x>\pgf@xc% + \else% + \ifdim\pgf@ya<\pgf@yb% + \else% + \ifdim\pgf@y>\pgf@yc% + \else% + \def\pgf@intersect@next{\pgfutil@firstoftwo}% + \fi + \fi + \fi + \fi + \pgf@intersect@next +}% +\def\pgf@intersect@boundingbox@ifoverlap@upperbound{% + \begingroup + \def\pgf@intersect@next{\pgfutil@secondoftwo}% + \advance\pgf@xa by+\pgfintersectiontolerance\relax + \ifdim\pgf@xa<\pgf@xb% + \else% + \global\advance\pgf@x by-\pgfintersectiontolerance\relax + \ifdim\pgf@x>\pgf@xc% + \else% + \advance\pgf@ya by\pgfintersectiontolerance\relax + \ifdim\pgf@ya<\pgf@yb% + \else% + \global\advance\pgf@y by-\pgfintersectiontolerance\relax + \ifdim\pgf@y>\pgf@yc% + \else% + \def\pgf@intersect@next{\pgfutil@firstoftwo}% + \fi + \fi + \fi + \fi + \expandafter + \endgroup + \pgf@intersect@next +}% +\def\pgf@intersect@boundingbox@ifoverlap@UNUSED{% + \let\pgf@intersect@next=\pgfutil@secondoftwo% + \ifdim\pgf@xa<\pgf@xb% + \else% + \ifdim\pgf@x>\pgf@xc% + \else% + \ifdim\pgf@ya<\pgf@yb% + \else% + \ifdim\pgf@y>\pgf@yc% + \else% + \let\pgf@intersect@next=\pgfutil@firstoftwo% + \fi + \fi + \fi + \fi + \pgf@intersect@next +}% +\def\pgf@@intersectionofcurves#1#2#3#4#5#6#7#8{% + \pgf@intersect@boundingbox@reset% + \pgf@intersect@boundingbox@update{#1}% + \pgf@intersect@boundingbox@update{#2}% + \pgf@intersect@boundingbox@update{#3}% + \pgf@intersect@boundingbox@update{#4}% + \pgf@intersect@boundingbox@assign@b% + \pgf@intersect@boundingbox@reset% + \pgf@intersect@boundingbox@update{#5}% + \pgf@intersect@boundingbox@update{#6}% + \pgf@intersect@boundingbox@update{#7}% + \pgf@intersect@boundingbox@update{#8}% + \pgf@intersect@boundingbox@assign@a% + \pgf@intersect@boundingbox@a% + \pgf@intersect@boundingbox@b% + \pgf@intersect@boundingbox@ifoverlap{% + \pgf@@@intersectionofcurves{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + }{% + }% +}% + +\def\pgf@@@intersectionofcurves#1#2#3#4#5#6#7#8{% + \advance\pgf@xc by-\pgf@xb% + \advance\pgf@yc by-\pgf@yb% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \let\pgf@intersect@subdivde=\relax% + \ifdim\pgf@xc<\pgfintersectiontolerance\relax% + \ifdim\pgf@xa<\pgfintersectiontolerance\relax% + \ifdim\pgf@yc<\pgfintersectiontolerance\relax% + \ifdim\pgf@ya<\pgfintersectiontolerance\relax% + \pgfextract@process\pgf@intersect@solution@candidate{% + \pgf@intersect@boundingbox@a% + \pgf@intersect@boundingbox@b% + \pgf@x=0.25\pgf@x% + \advance\pgf@x by0.25\pgf@xa% + \advance\pgf@x by0.25\pgf@xb% + \advance\pgf@x by0.25\pgf@xc% + \pgf@y=0.25\pgf@y% + \advance\pgf@y by0.25\pgf@ya% + \advance\pgf@y by0.25\pgf@yb% + \advance\pgf@y by0.25\pgf@yc% + }% + \let\pgf@intersect@subdivde=\pgf@stop% + \pgf@ifsolution@duplicate\pgf@intersect@solution@candidate{}% + {% + \global\advance\pgf@intersect@solutions by1\relax% + \begingroup + \advance\pgf@time@a by\pgf@time@aa% + \divide\pgf@time@a by2\relax% + \advance\pgf@time@a by\pgf@intersect@time@offset pt\relax% + \edef\pgf@intersect@time@a{\pgfmath@tonumber{\pgf@time@a}}% + \advance\pgf@time@b by\pgf@time@bb% + \divide\pgf@time@b by2\relax% + \advance\pgf@time@b by\pgf@intersect@time@offset@b pt\relax% + \edef\pgf@intersect@time@b{\pgfmath@tonumber{\pgf@time@b}}% + \pgf@intersection@store@properties{pgfpoint@g@intersect@solution@\the\pgf@intersect@solutions}% + \expandafter\global\expandafter\let% + \csname pgfpoint@g@intersect@solution@\the\pgf@intersect@solutions\endcsname=% + \pgf@intersect@solution@candidate% + \ifpgf@intersect@sort% + \expandafter\xdef% + \csname pgf@g@intersect@solution@\the\pgf@intersect@solutions @time@a\endcsname% + {\pgf@intersect@time@a}% + \fi% + \endgroup + }% + \fi% + \fi% + \fi% + \fi% + \ifx\pgf@intersect@subdivde\pgf@stop% + \else% + \pgf@intersect@subdivide@curve{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \fi% +}% + +\def\pgf@intersect@subdivide@curve@b#1#2#3#4#5#6#7#8{% + \begingroup% + \advance\pgf@time@bb by\pgf@time@b\relax% + \divide\pgf@time@bb by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@a% + \pgf@curve@subdivide@left{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% + \begingroup% + \advance\pgf@time@b by\pgf@time@bb\relax% + \divide\pgf@time@b by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@a% + \pgf@curve@subdivide@right{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% +}% + +\def\pgf@intersect@subdivide@curve@a#1#2#3#4#5#6#7#8{% + \begingroup% + \advance\pgf@time@aa by\pgf@time@a\relax% + \divide\pgf@time@aa by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@b% + \pgf@curve@subdivide@left{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% + \begingroup% + \advance\pgf@time@a by\pgf@time@aa\relax% + \divide\pgf@time@a by2\relax% + \let\pgf@intersect@subdivide@curve=\pgf@intersect@subdivide@curve@b% + \pgf@curve@subdivide@right{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% + \endgroup% +}% + +\def\pgf@intersect@boundingbox@reset{% + \pgf@xa=16000pt\relax% + \pgf@ya=16000pt\relax% + \pgf@xb=-16000pt\relax% + \pgf@yb=-16000pt\relax% +}% + +\def\pgf@intersect@boundingbox@update#1{% + #1\relax% + \ifdim\pgf@x<\pgf@xa\pgf@xa=\pgf@x\fi% + \ifdim\pgf@y<\pgf@ya\pgf@ya=\pgf@y\fi% + \ifdim\pgf@x>\pgf@xb\pgf@xb=\pgf@x\fi% + \ifdim\pgf@y>\pgf@yb\pgf@yb=\pgf@y\fi% +}% + + +\def\pgf@float@adapter@setxy{% + \pgfmathfloatparsenumber{\pgf@sys@tonumber\pgf@x}\let\pgf@fpu@x=\pgfmathresult + \pgfmathfloatparsenumber{\pgf@sys@tonumber\pgf@y}\let\pgf@fpu@y=\pgfmathresult +}% +\def\pgf@float@adapter@mult#1=#2*#3{% + \pgfmathfloatmultiplyfixed@{#3}{#2}% + \let#1=\pgfmathresult +}% +\def\pgf@float@adapter@advance#1by#2*#3{% + \pgfmathfloatmultiplyfixed@{#3}{#2}% + \let\pgfutil@temp=\pgfmathresult + \pgfmathfloatadd@{#1}{\pgfutil@temp}% + \let#1=\pgfmathresult +}% + +\def\pgf@float@adapter@tostring#1{% + \pgfmathfloattofixed{#1}\edef#1{\pgfmathresult pt }% +}% + +\def\pgf@curve@subdivide@left#1#2#3#4{% + \begingroup + #1\relax% + \pgfutil@tempdima=\pgf@x% + \pgfutil@tempdimb=\pgf@y% + \pgf@float@adapter@setxy + \pgf@float@adapter@mult\pgf@fpu@xa=.5*\pgf@fpu@x \pgf@float@adapter@mult\pgf@fpu@ya=.5*\pgf@fpu@y% + \pgf@float@adapter@mult\pgf@fpu@xb=.25*\pgf@fpu@x \pgf@float@adapter@mult\pgf@fpu@yb=.25*\pgf@fpu@y% + \pgf@float@adapter@mult\pgf@fpu@xc=.125*\pgf@fpu@x\pgf@float@adapter@mult\pgf@fpu@yc=.125*\pgf@fpu@y% + #2\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@advance\pgf@fpu@xa by.5*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@ya by.5*\pgf@fpu@y% + \pgf@float@adapter@advance\pgf@fpu@xb by.5*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@yb by.5*\pgf@fpu@y% + \pgf@float@adapter@advance\pgf@fpu@xc by.375*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@yc by.375*\pgf@fpu@y% + #3\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@advance\pgf@fpu@xb by.25*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@yb by.25*\pgf@fpu@y% + \pgf@float@adapter@advance\pgf@fpu@xc by.375*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@yc by.375*\pgf@fpu@y% + #4\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@advance\pgf@fpu@xc by.125*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@yc by.125*\pgf@fpu@y% + \pgf@float@adapter@tostring\pgf@fpu@xa + \pgf@float@adapter@tostring\pgf@fpu@ya + \pgf@float@adapter@tostring\pgf@fpu@xb + \pgf@float@adapter@tostring\pgf@fpu@yb + \pgf@float@adapter@tostring\pgf@fpu@xc + \pgf@float@adapter@tostring\pgf@fpu@yc + \edef\pgf@marshal{% + \noexpand\pgf@curve@subdivde@after% + {\noexpand\pgf@x=\the\pgfutil@tempdima\noexpand\pgf@y=\the\pgfutil@tempdimb}% + {\noexpand\pgf@x=\pgf@fpu@xa\noexpand\pgf@y=\pgf@fpu@ya}% + {\noexpand\pgf@x=\pgf@fpu@xb\noexpand\pgf@y=\pgf@fpu@yb}% + {\noexpand\pgf@x=\pgf@fpu@xc\noexpand\pgf@y=\pgf@fpu@yc}% + }% + \expandafter + \endgroup + \pgf@marshal% +}% + +\def\pgf@curve@subdivide@right#1#2#3#4{% + \begingroup + #1\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@mult\pgf@float@tmpa=.125*\pgf@fpu@x\pgf@float@adapter@mult\pgf@float@tmpb=.125*\pgf@fpu@y% + #2\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@advance\pgf@float@tmpa by.375*\pgf@fpu@x\pgf@float@adapter@advance\pgf@float@tmpb by.375*\pgf@fpu@y% + \pgf@float@adapter@mult\pgf@fpu@xa=.25*\pgf@fpu@x\pgf@float@adapter@mult\pgf@fpu@ya=.25*\pgf@fpu@y% + #3\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@advance\pgf@float@tmpa by.375*\pgf@fpu@x\pgf@float@adapter@advance\pgf@float@tmpb by.375*\pgf@fpu@y% + \pgf@float@adapter@advance\pgf@fpu@xa by.5*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@ya by.5*\pgf@fpu@y% + \pgf@float@adapter@mult\pgf@fpu@xb=.5*\pgf@fpu@x\pgf@float@adapter@mult\pgf@fpu@yb=.5*\pgf@fpu@y% + #4\relax% + \pgf@float@adapter@setxy + \pgf@float@adapter@advance\pgf@float@tmpa by.125*\pgf@fpu@x\pgf@float@adapter@advance\pgf@float@tmpb by.125*\pgf@fpu@y% + \pgf@float@adapter@advance\pgf@fpu@xa by.25*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@ya by.25*\pgf@fpu@y% + \pgf@float@adapter@advance\pgf@fpu@xb by.5*\pgf@fpu@x\pgf@float@adapter@advance\pgf@fpu@yb by.5*\pgf@fpu@y% + \let\pgf@fpu@xc=\pgf@fpu@x\let\pgf@fpu@yc=\pgf@fpu@y% + \pgf@float@adapter@tostring\pgf@float@tmpa + \pgf@float@adapter@tostring\pgf@float@tmpb + \pgf@float@adapter@tostring\pgf@fpu@xa + \pgf@float@adapter@tostring\pgf@fpu@ya + \pgf@float@adapter@tostring\pgf@fpu@xb + \pgf@float@adapter@tostring\pgf@fpu@yb + \pgf@float@adapter@tostring\pgf@fpu@xc + \pgf@float@adapter@tostring\pgf@fpu@yc + \edef\pgf@marshal{% + \noexpand\pgf@curve@subdivde@after% + {\noexpand\pgf@x=\pgf@float@tmpa\noexpand\pgf@y=\pgf@float@tmpb}% + {\noexpand\pgf@x=\pgf@fpu@xa\noexpand\pgf@y=\pgf@fpu@ya}% + {\noexpand\pgf@x=\pgf@fpu@xb\noexpand\pgf@y=\pgf@fpu@yb}% + {\noexpand\pgf@x=\pgf@fpu@xc\noexpand\pgf@y=\pgf@fpu@yc}% + }% + \expandafter + \endgroup + \pgf@marshal% +}% + + +\def\pgf@ifsolution@duplicate#1{% + #1% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \let\pgf@intersect@next=\pgfutil@secondoftwo% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@intersect@solutions\relax% + \else% + \pgf@ifsolution@duplicate@{\pgfmathcounter}% + \repeatpgfmathloop% + \pgf@intersect@next% +}% + +\def\pgf@ifsolution@duplicate@#1{% + \pgf@process{\csname pgfpoint@g@intersect@solution@#1\endcsname}% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@y by-\pgf@ya% + \ifdim\pgf@x<0pt\relax\pgf@x=-\pgf@x\fi% + \ifdim\pgf@y<0pt\relax\pgf@y=-\pgf@y\fi% + \pgf@x=\pgfintersectiontolerancefactor\pgf@x% + \pgf@y=\pgfintersectiontolerancefactor\pgf@y% + \ifdim\pgf@x<\pgfintersectiontolerance\relax% + \ifdim\pgf@y<\pgfintersectiontolerance\relax% + \let\pgf@intersect@next=\pgfutil@firstoftwo% + \fi% + \fi% +}% + +\newif\ifpgf@intersect@solutions@sortfinish + +\def\pgfintersectionsolutionsortbytime{% + \pgf@intersect@solutions@sortfinishtrue% + \pgfmathloop% + \ifnum\pgfmathcounter<\pgfintersectionsolutions\relax% + \pgfutil@tempcnta=\pgfmathcounter% + \advance\pgfutil@tempcnta by1\relax% + \ifdim\csname pgf@intersect@solution@\pgfmathcounter @time@a\endcsname pt>% + \csname pgf@intersect@solution@\the\pgfutil@tempcnta @time@a\endcsname pt\relax% + \pgf@intersect@solutions@sortfinishfalse% + \pgfintersectionsolutionsortbytime@swap{pgfpoint@intersect@solution@\pgfmathcounter}% + {pgfpoint@intersect@solution@\the\pgfutil@tempcnta}% + \pgfintersectionsolutionsortbytime@swap{pgf@intersect@solution@\pgfmathcounter @time@a}% + {pgf@intersect@solution@\the\pgfutil@tempcnta @time@a}% + \pgfintersectionsolutionsortbytime@swap{pgf@intersect@solution@props@\pgfmathcounter}% + {pgf@intersect@solution@props@\the\pgfutil@tempcnta}% + \fi% + \repeatpgfmathloop% + \ifpgf@intersect@solutions@sortfinish% + \else% + \expandafter\pgfintersectionsolutionsortbytime% + \fi% +}% + +\def\pgfintersectionsolutionsortbytime@swap#1#2{% + \pgfutil@namelet{pgf@intersect@temp}{#1}% + \pgfutil@namelet{#1}{#2}% + \pgfutil@namelet{#2}{pgf@intersect@temp}% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarylindenmayersystems.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarylindenmayersystems.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..273940595b05cb82747c8de4f1e6dd4f44387682 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarylindenmayersystems.code.tex @@ -0,0 +1,213 @@ + +\newdimen\pgflsystemstep +\newcount\c@pgf@lsystem@iteration + +\newif\ifpgf@lsystem@randomize@step +\newif\ifpgf@lsystem@randomize@angle + +\pgfkeys{/pgf/lindenmayer system/.cd,% + step/.code={\pgfmathsetlength\pgflsystemstep{#1}},% + randomize step percent/.code={% + \pgfmathparse{#1}% + \let\pgflsystemrandomizesteppercent=\pgfmathresult% + \ifdim\pgfmathresult pt=0pt\relax% + \pgf@lsystem@randomize@stepfalse% + \else% + \pgf@lsystem@randomize@steptrue% + \fi% + },% + left angle/.code={\pgfmathparse{#1}\let\pgflsystemleftangle=\pgfmathresult},% + right angle/.code={\pgfmathparse{#1}\let\pgflsystemrightangle=\pgfmathresult},% + angle/.style={/pgf/lindenmayer system/left angle={#1}, /pgf/lindenmayer system/right angle={#1}},% + randomize angle percent/.code={% + \pgfmathparse{#1}% + \let\pgflsystemrandomizeanglepercent=\pgfmathresult% + \ifdim\pgfmathresult pt=0pt\relax% + \pgf@lsystem@randomize@anglefalse% + \else% + \pgf@lsystem@randomize@angletrue% + \fi% + }% +}% + +\pgfkeys{/pgf/lindenmayer system/.cd, + step=5pt,% + randomize step percent=0,% + angle=90,% + randomize angle percent=0% +}% + +\long\def\pgfdeclarelindenmayersystem#1#2{% + \pgfutil@ifundefined{pgf@lsystem@#1}% + {% + \begingroup% + \edef\pgf@lsystem@name{#1}% + \expandafter\global\expandafter\let\csname pgf@lsystem@#1\endcsname=\pgf@lsystem@name% + \let\symbol=\pgf@lsystem@symbol% + \let\rule=\pgf@lsystem@rule% + #2% + \endgroup% + }% + {\pgferror{Lindenmayer system `#1' is already defined}}% +}% + +\def\pgf@lsystem@symbol#1#2{% + \expandafter\gdef\csname pgf@lsystem@\pgf@lsystem@name @symbol@#1\endcsname{#2}% +}% + +\def\pgf@lsystem@rule#1{\expandafter\pgf@lsystem@rule@#1\pgf@stop}% +\def\pgf@lsystem@rule@#1{\def\pgf@lsystem@rule@head{#1}\pgf@lsystem@rule@@}% +\def\pgf@lsystem@rule@@#1->{% + \let\pgf@lsystem@rule@body=\pgfutil@empty% + \pgfutil@ifnextchar x{\pgf@lsystem@rule@@@}{\pgf@lsystem@rule@@@}}% +\def\pgf@lsystem@rule@@@#1{% + \ifx#1\pgf@stop% + \expandafter\global\expandafter\let% + \csname pgf@lsystem@\pgf@lsystem@name @rule@\pgf@lsystem@rule@head\endcsname=\pgf@lsystem@rule@body% + \else% + \edef\pgf@lsystem@rule@body{\pgf@lsystem@rule@body#1}% + \expandafter\pgf@lsystem@rule@@@% + \fi% +}% + +\def\pgflindenmayersystem#1#2#3{% + \begingroup% + \edef\pgf@lsystem@name{#1}% + \edef\pgf@lsystem@axiom{#2}% + \pgfmathtruncatemacro\pgf@lsystem@order{#3}% + \let\pgf@lsystem@current@symbol=\relax% + \c@pgf@lsystem@iteration=0\relax% + \ifnum\pgf@lsystem@order=0\relax% + \expandafter\pgf@lsystem@draw\pgf@lsystem@axiom\pgf@stop + \let\pgf@lsystem@next=\pgf@lsystem@end% + \else% + \let\pgf@lsystem@next=\pgf@lsystem@run% + \fi% + \expandafter\pgf@lsystem@next\pgf@lsystem@axiom\pgf@lsystem@stop% +}% + +\def\pgf@lsystem@run#1{% + \ifx#1\pgf@lsystem@stop% + \def\pgf@lsystem@token{\pgf@lsystem@stop}% + \let\pgf@lsystem@next=\pgf@lsystem@end% + \else% + \ifx#1\pgf@stop% + \advance\c@pgf@lsystem@iteration by-1\relax% + \let\pgf@system@token=\pgfutil@empty% + \let\pgf@lsystem@next=\pgf@lsystem@run% + \else% + \expandafter\let\expandafter\pgf@lsystem@token\expandafter=% + \csname pgf@lsystem@\pgf@lsystem@name @rule@#1\endcsname% + \ifx\pgf@lsystem@token\relax% + \pgf@lsystem@draw#1\pgf@stop% + \let\pgf@lsystem@token=\pgfutil@empty% + \else% + \advance\c@pgf@lsystem@iteration by1\relax% + \ifnum\c@pgf@lsystem@iteration=\pgf@lsystem@order% + \expandafter\pgf@lsystem@draw\pgf@lsystem@token \pgf@stop% + \advance\c@pgf@lsystem@iteration by-1\relax% + \let\pgf@lsystem@token=\pgfutil@empty% + \else% + \expandafter\def\expandafter\pgf@lsystem@token\expandafter{\pgf@lsystem@token \pgf@stop}% + \fi% + \fi% + \let\pgf@lsystem@next=\pgf@lsystem@run% + \fi% + \fi% + \expandafter\pgf@lsystem@next\pgf@lsystem@token}% + +\def\pgf@lsystem@end#1\pgf@lsystem@stop{\endgroup}% + +\def\pgf@lsystem@draw#1{% + \ifx#1\pgf@stop% + \let\pgf@lsystem@next=\relax% + \else% + \expandafter\let\expandafter\pgf@lsystem@current@symbol\expandafter=% + \csname pgf@lsystem@\pgf@lsystem@name @symbol@#1\endcsname% + \ifx\pgf@lsystem@current@symbol\relax% + \expandafter\let\expandafter\pgf@lsystem@current@symbol\expandafter=% + \csname pgf@lsystem@symbol@default@#1\endcsname% + \fi% + \let\pgf@lsystem@next=\pgf@lsystem@@draw% + \fi% + \pgf@lsystem@next}% + +\def\pgf@lsystem@@draw{% + \edef\pgflsystemcurrentstep{\the\pgflsystemstep}% + \let\pgflsystemcurrentrightangle=\pgflsystemrightangle% + \let\pgflsystemcurrentrightangle=\pgflsystemleftangle% + \pgf@lsystem@current@symbol% + \pgf@lsystem@draw}% + +\expandafter\def\csname +pgf@lsystem@symbol@default@F\endcsname{\pgflsystemdrawforward}% +\expandafter\def\csname +pgf@lsystem@symbol@default@f\endcsname{\pgflsystemmoveforward}% +\expandafter\def\csname +pgf@lsystem@symbol@default@+\endcsname{\pgflsystemturnleft}% +\expandafter\def\csname +pgf@lsystem@symbol@default@-\endcsname{\pgflsystemturnright}% +\expandafter\def\csname +pgf@lsystem@symbol@default@[\endcsname{\pgflsystemsavestate}% +\expandafter\def\csname +pgf@lsystem@symbol@default@]\endcsname{\pgflsystemrestorestate}% + +\def\pgflsystemradonmizestep{% + \ifpgf@lsystem@randomize@step% + \pgfmathrand% + \pgf@x=\pgflsystemrandomizesteppercent pt\relax% + \pgf@x=\pgfmathresult\pgf@x% + \divide\pgf@x by20\relax% + \advance\pgf@x by\pgflsystemstep\relax% + \edef\pgflsystemcurrentstep{\the\pgf@x}% + \else% + \edef\pgflsystemcurrentstep{\the\pgflsystemstep}% + \fi% +}% + +\def\pgflsystemdrawforward{% + \pgflsystemradonmizestep + \pgftransformxshift{+\pgflsystemcurrentstep}% + \pgfpathlineto{\pgfpointorigin}}% + +\def\pgflsystemmoveforward{% + \pgflsystemradonmizestep + \pgftransformxshift{+\pgflsystemcurrentstep}% + \pgfpathmoveto{\pgfpointorigin}}% + +\def\pgflsystemranomizerightangle{% + \ifpgf@lsystem@randomize@angle% + \pgf@x=\pgflsystemrandomizeanglepercent pt\relax% + \divide\pgf@x by20\relax% + \pgfmathrand% + \pgf@x=\pgfmathresult\pgf@x% + \advance\pgf@x by\pgflsystemrightangle pt\relax% + \edef\pgflsystemcurrentrightangle{\pgfmath@tonumber{\pgf@x}}% + \else% + \let\pgflsystemcurrentrightangle=\pgflsystemrightangle% + \fi% +}% + +\def\pgflsystemranomizeleftangle{% + \ifpgf@lsystem@randomize@angle% + \pgf@x=\pgflsystemrandomizeanglepercent pt\relax% + \divide\pgf@x by20\relax% + \pgfmathrand% + \pgf@x=\pgfmathresult\pgf@x% + \advance\pgf@x by\pgflsystemleftangle pt\relax% + \edef\pgflsystemcurrentleftangle{\pgfmath@tonumber{\pgf@x}}% + \else% + \let\pgflsystemcurrentleftangle=\pgflsystemleftangle% + \fi% +}% + +\def\pgflsystemturnright{% + \pgflsystemranomizerightangle + \pgftransformrotate{-\pgflsystemcurrentrightangle}}% + +\def\pgflsystemturnleft{% + \pgflsystemranomizeleftangle + \pgftransformrotate{\pgflsystemcurrentleftangle}}% + +\def\pgflsystemsavestate{\begingroup}% +\def\pgflsystemrestorestate{\endgroup\pgfpathmoveto{\pgfpointorigin}}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarypatterns.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarypatterns.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..2a7dbcd33ff0e7e96db67a7296c946653c6b42db --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarypatterns.code.tex @@ -0,0 +1,246 @@ + +\ProvidesFileRCS{pgflibrarypatterns.code.tex} + + + +\pgfdeclarepatternformonly{horizontal lines}{\pgfpointorigin}{\pgfqpoint{100pt}{1pt}}{\pgfqpoint{100pt}{3pt}}% +{% + \pgfsetlinewidth{0.4pt}% + \pgfpathmoveto{\pgfqpoint{0pt}{0.5pt}}% + \pgfpathlineto{\pgfqpoint{100pt}{0.5pt}}% + \pgfusepath{stroke}% +}% + +\pgfdeclarepatternformonly{vertical lines}{\pgfpointorigin}{\pgfqpoint{1pt}{100pt}}{\pgfqpoint{3pt}{100pt}}% +{% + \pgfsetlinewidth{0.4pt}% + \pgfpathmoveto{\pgfqpoint{0.5pt}{0pt}}% + \pgfpathlineto{\pgfqpoint{0.5pt}{100pt}}% + \pgfusepath{stroke}% +}% + +\pgfdeclarepatternformonly{north east lines}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{4pt}{4pt}}{\pgfqpoint{3pt}{3pt}}% +{% + \pgfsetlinewidth{0.4pt}% + \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}% + \pgfpathlineto{\pgfqpoint{3.1pt}{3.1pt}}% + \pgfusepath{stroke}% +}% + +\pgfdeclarepatternformonly{north west lines}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{4pt}{4pt}}{\pgfqpoint{3pt}{3pt}}% +{% + \pgfsetlinewidth{0.4pt}% + \pgfpathmoveto{\pgfqpoint{0pt}{3pt}}% + \pgfpathlineto{\pgfqpoint{3.1pt}{-0.1pt}}% + \pgfusepath{stroke}% +}% + + +\pgfdeclarepatternformonly{grid}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{4pt}{4pt}}{\pgfqpoint{3pt}{3pt}}% +{% + \pgfsetlinewidth{0.4pt}% + \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{3.1pt}}% + \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}% + \pgfpathlineto{\pgfqpoint{3.1pt}{0pt}}% + \pgfusepath{stroke}% +}% + +\pgfdeclarepatternformonly{crosshatch}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{4pt}{4pt}}{\pgfqpoint{3pt}{3pt}}% +{% + \pgfsetlinewidth{0.4pt}% + \pgfpathmoveto{\pgfqpoint{3.1pt}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{3.1pt}}% + \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}% + \pgfpathlineto{\pgfqpoint{3.1pt}{3.1pt}}% + \pgfusepath{stroke}% +}% + + + +\pgfdeclarepatternformonly{dots}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{1pt}{1pt}}{\pgfqpoint{3pt}{3pt}}% +{% + \pgfpathcircle{\pgfqpoint{0pt}{0pt}}{.5pt}% + \pgfusepath{fill}% +}% + +\pgfdeclarepatternformonly{crosshatch dots}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{2.5pt}{2.5pt}}{\pgfqpoint{3pt}{3pt}}% +{% + \pgfpathcircle{\pgfqpoint{0pt}{0pt}}{.5pt}% + \pgfpathcircle{\pgfqpoint{1.5pt}{1.5pt}}{.5pt}% + \pgfusepath{fill}% +}% + + + + + +\pgfdeclarepatternformonly{fivepointed stars}{\pgfpointorigin}{\pgfqpoint{3mm}{3mm}}{\pgfqpoint{3mm}{3mm}}% +{% + \pgftransformshift{\pgfqpoint{1mm}{1mm}}% + \pgfpathmoveto{\pgfqpointpolar{18}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{162}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{306}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{90}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{234}{1mm}}% + \pgfpathclose% + \pgfusepath{fill}% +}% + +\pgfdeclarepatternformonly{sixpointed stars}{\pgfpointorigin}{\pgfqpoint{3mm}{3mm}}{\pgfqpoint{3mm}{3mm}}% +{% + \pgftransformshift{\pgfqpoint{1mm}{1mm}}% + \pgfpathmoveto{\pgfqpointpolar{30}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{150}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{270}{1mm}}% + \pgfpathclose% + \pgfpathmoveto{\pgfqpointpolar{-30}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{-270}{1mm}}% + \pgfpathlineto{\pgfqpointpolar{-150}{1mm}}% + \pgfpathclose% + \pgfsetnonzerorule% + \pgfusepath{fill}% +}% + + + + +\pgfdeclarepatternformonly{bricks}{\pgfqpoint{-1pt}{-1pt}}{\pgfqpoint{5mm}{5mm}}{\pgfqpoint{4mm}{4mm}}% +{% + \pgfsetlinewidth{0.8pt}% + \pgfpathmoveto{\pgfqpoint{0mm}{1mm}}% + \pgfpathlineto{\pgfqpoint{4mm}{1mm}}% + \pgfpathmoveto{\pgfqpoint{0mm}{3mm}}% + \pgfpathlineto{\pgfqpoint{4mm}{3mm}}% + \pgfpathmoveto{\pgfqpoint{1mm}{0mm}}% + \pgfpathlineto{\pgfqpoint{1mm}{1mm}}% + \pgfpathmoveto{\pgfqpoint{3mm}{1mm}}% + \pgfpathlineto{\pgfqpoint{3mm}{3mm}}% + \pgfpathmoveto{\pgfqpoint{1mm}{3mm}}% + \pgfpathlineto{\pgfqpoint{1mm}{4mm}}% + \pgfusepath{stroke}% +}% + + + +\pgfdeclarepatternformonly{checkerboard}{\pgfpointorigin}{\pgfqpoint{4mm}{4mm}}{\pgfqpoint{4mm}{4mm}}% +{% + \pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{2mm}{2mm}}% + \pgfpathrectangle{\pgfqpoint{2mm}{2mm}}{\pgfqpoint{2mm}{2mm}}% + \pgfusepath{fill}% +}% + + + + +\pgfdeclarepatterninherentlycolored{checkerboard light gray} +{\pgfpointorigin}{\pgfqpoint{4mm}{4mm}}{\pgfqpoint{4mm}{4mm}}% +{% + \pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.1mm}{4.1mm}}% + \pgfusepath{fill}% + \pgfsetfillcolor{black!20}% + \pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{2mm}{2mm}}% + \pgfpathrectangle{\pgfqpoint{2mm}{2mm}}{\pgfqpoint{2mm}{2mm}}% + \pgfusepath{fill}% +}% + +\pgfdeclarepatterninherentlycolored{horizontal lines light gray} +{\pgfpointorigin}{\pgfpoint{100pt}{4pt}} +{\pgfpoint{100pt}{4pt}} +{% + \pgfsetfillcolor{black!10}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{black!15}% + \pgfpathrectangle{\pgfpoint{0pt}{2pt}}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% +}% + +\pgfdeclarepatterninherentlycolored{horizontal lines gray} +{\pgfpointorigin}{\pgfpoint{100pt}{4pt}} +{\pgfpoint{100pt}{4pt}} +{% + \pgfsetfillcolor{black!30}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{black!35}% + \pgfpathrectangle{\pgfpoint{0pt}{2pt}}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% +}% + +\pgfdeclarepatterninherentlycolored{horizontal lines dark gray} +{\pgfpointorigin}{\pgfpoint{100pt}{4pt}} +{\pgfpoint{100pt}{4pt}} +{% + \pgfsetfillcolor{black!90}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{black!85}% + \pgfpathrectangle{\pgfpoint{0pt}{2pt}}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% +}% + +\pgfdeclarepatterninherentlycolored{horizontal lines light blue} +{\pgfpointorigin}{\pgfpoint{100pt}{4pt}} +{\pgfpoint{100pt}{4pt}} +{% + \pgfsetfillcolor{blue!10}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{blue!15}% + \pgfpathrectangle{\pgfpoint{0pt}{2pt}}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% +}% + +\pgfdeclarepatterninherentlycolored{horizontal lines dark blue} +{\pgfpointorigin}{\pgfpoint{100pt}{4pt}} +{\pgfpoint{100pt}{4pt}} +{% + \pgfsetfillcolor{blue!90}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{blue!85}% + \pgfpathrectangle{\pgfpoint{0pt}{2pt}}{\pgfpoint{100pt}{2.5pt}}% + \pgfusepath{fill}% +}% + + +\pgfdeclarepatterninherentlycolored{crosshatch dots gray} +{\pgfpointorigin}{\pgfpoint{8pt}{8pt}} +{\pgfpoint{8pt}{8pt}} +{% + \pgfsetfillcolor{black!20}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{black!10}% + \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{1pt}% + \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{1pt}% + \pgfusepath{fill}% + \pgfsetfillcolor{black!70}% + \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{1pt}% + \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{1pt}% + \pgfusepath{fill}% +}% + +\pgfutil@definecolor{pgf@lightsteelblue}{rgb}{0.6875,0.765625,0.8671875}% +\pgfutil@colorlet{pgf@darklightsteelblue}{black!50!pgf@lightsteelblue}% + +\pgfdeclarepatterninherentlycolored{crosshatch dots light steel blue} +{\pgfpointorigin}{\pgfpoint{8pt}{8pt}} +{\pgfpoint{8pt}{8pt}} +{% + \pgfsetfillcolor{pgf@lightsteelblue}% + \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}% + \pgfusepath{fill}% + \pgfsetfillcolor{pgf@darklightsteelblue!10}% + \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{1pt}% + \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{1pt}% + \pgfusepath{fill}% + \pgfsetfillcolor{pgf@darklightsteelblue!70}% + \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{1pt}% + \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{1pt}% + \pgfusepath{fill}% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarypatterns.meta.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarypatterns.meta.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..6550546cf872590ed38fd10380881ca7908133a3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarypatterns.meta.code.tex @@ -0,0 +1,429 @@ + +\def\pgf@pat@type@uncolored{0}% +\def\pgf@pat@type@colored{1}% +\newif\ifpgf@pat@makepatternimmutable + +\pgfkeys{/pgf/patterns/.cd, + name/.store in=\pgf@pat@name, + number ../.store in=\pgf@pat@number, + type/.is choice, + type/uncolored/.code={\let\pgf@pat@type=\pgf@pat@type@uncolored}, + type/colored/.code={\let\pgf@pat@type=\pgf@pat@type@colored}, + type/form only/.style={/pgf/patterns/type=uncolored}, + type/inherently colored/.style={/pgf/patterns/type=colored}, + x/.store in=\pgf@pat@xvec, + y/.store in=\pgf@pat@yvec, + parameters/.store in=\pgf@pat@parameters, + defaults/.store in=\pgf@pat@defaults, + append to defaults/.code={% + \pgf@pat@addto@macro\pgf@pat@defaults{,#1}% + }, + bottom left/.store in=\pgf@pat@bottomleft, + top right/.store in=\pgf@pat@topright, + tile size/.store in=\pgf@pat@tilesize, + tile transformation/.store in=\pgf@pat@transformation, + code/.store in=\pgf@pat@code, + set up code/.store in=\pgf@pat@declarebefore, + name=, + number ..=, + type=uncolored, + x=1cm, y=1cm, + parameters=, + defaults=, + bottom left=, + top right=, + tile size=, + tile transformation=, + code=, + set up code=, +}% + +\def\pgf@pat@name@prefix{pgf@pattern@name@meta@}% + +\def\pgfifpatternundefined#1{% + \pgfutil@ifundefined{\pgf@pat@name@prefix#1}% +}% + +\def\pgf@pat@adddef@to@macro#1#2{% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter#1% + \expandafter\expandafter\expandafter{\expandafter#1\expandafter% + \def\expandafter#2\expandafter{#2}}% +}% + +\def\pgf@pat@addto@macro#1#2{% + \expandafter\def\expandafter#1\expandafter{#1#2}}% + +\def\pgf@pat@process#1{% + \pgf@process{#1}% +}% + +\def\pgf@pat@doifnotempty#1{% + \ifx#1\pgfutil@empty% + \let\pgf@pat@next=\relax% + \else% + \let\pgf@pat@next=#1% + \fi% + \pgf@pat@next% +}% + +\def\pgf@pat@processtransformations#1{#1}% +\def\pgf@pat@processpoint#1{% + \pgf@process{#1}% +}% + + +\def\pgfdeclarepattern#1{% + \begingroup% + \nullfont% + \def\pgf@pat@options{,#1}% + \pgfkeys{/pgf/patterns/.cd,#1}% + \ifx\pgf@pat@name\pgfutil@empty + \pgferror{Declaring unnamed pattern}% + \fi + \ifx\pgf@pat@bottomleft\pgfutil@empty + \pgferror{Bottom left corner of the bounding box unset}% + \fi + \ifx\pgf@pat@topright\pgfutil@empty + \pgferror{Top right corner of the bounding box unset}% + \fi + \ifx\pgf@pat@tilesize\pgfutil@empty + \pgferror{Tile size unset}% + \fi + \ifx\pgf@pat@code\pgfutil@empty + \pgferror{Pattern code is empty}% + \fi + \pgf@declarepattern@meta% + \endgroup% +}% +\def\pgf@declarepattern@meta{% + \pgfifpatternundefined{\pgf@pat@name}{% + \ifx\pgf@pat@parameters\pgfutil@empty% + \pgf@pat@declare% + \edef\pgf@marshal{% + \noexpand\pgf@pat@addto@macro\noexpand\pgf@pat@options{,number ..=\pgf@pattern@number}}% + \pgf@marshal% + \fi% + \expandafter\global\expandafter\let\csname\pgf@pat@name@prefix\pgf@pat@name\endcsname=\pgf@pat@options% + }{% + \pgferror{Pattern `\pgf@pat@name' already defined}% + }% +}% +\let\pgf@pat@declarebefore=\pgfutil@empty +\let\pgf@pat@declareafter=\pgfutil@empty +\let\pgf@pat@codebefore=\pgfutil@empty +\let\pgf@pat@codeafter=\pgfutil@empty + +\def\pgf@pat@declare{% + \pgfsysprotocol@getcurrentprotocol\pgf@pattern@temp% + {% + \pgfsetxvec{\pgfpoint{\pgf@pat@xvec}{+0pt}}% + \pgfsetyvec{\pgfpoint{+0pt}{\pgf@pat@yvec}}% + \pgf@pat@doifnotempty\pgf@pat@declarebefore% + \pgfinterruptpath% + \pgfpicturetrue% + \pgf@relevantforpicturesizetrue% + \pgftransformreset% + \pgfsysprotocol@setcurrentprotocol\pgfutil@empty% + \pgfsysprotocol@bufferedtrue% + \pgfsys@beginscope% + \pgfinterruptboundingbox% + \pgfsetarrows{-}% + \pgf@pat@doifnotempty\pgf@pat@codebefore + \pgf@pat@code% + \pgf@pat@doifnotempty\pgf@pat@codeafter% + \endpgfinterruptboundingbox% + \pgfsys@endscope% + \pgfsysprotocol@getcurrentprotocol\pgf@pattern@code% + \global\let\pgf@pattern@code=\pgf@pattern@code% + \endpgfinterruptpath% + \pgf@pat@doifnotempty\pgf@pat@declareafter% + \pgf@pat@processpoint{\pgf@pat@bottomleft}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@pat@processpoint{\pgf@pat@topright}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@pat@processpoint{\pgf@pat@tilesize}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \begingroup% + \pgftransformreset% + \pgf@pat@processtransformations\pgf@pat@transformation% + \pgfgettransformentries\aa\ab\ba\bb\shiftx\shifty% + \global\edef\pgf@pattern@matrix{{\aa}{\ab}{\ba}{\bb}{\shiftx}{\shifty}}% + \endgroup% + \pgfutil@tempcnta=\pgf@pattern@number\relax% + \advance\pgfutil@tempcnta by1\relax% + \xdef\pgf@pattern@number{\the\pgfutil@tempcnta}% + \xdef\pgf@marshal{\noexpand\pgfsys@declarepattern% + {\pgf@pattern@number}% + {\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}{\the\pgf@xc}{\the\pgf@yc}\pgf@pattern@matrix{\pgf@pattern@code}{\pgf@pat@type}}% + }% + \pgf@marshal% + \pgfsysprotocol@setcurrentprotocol\pgf@pattern@temp% +}% + +\def\pgf@pat@checkname#1{% + \pgf@pat@@checkname#1[]\pgf@patstop}% + +\def\pgf@pat@@checkname#1[#2]#3\pgf@patstop{% + \expandafter\def\expandafter\pgf@pat@onlinename\expandafter{\romannumeral-`0\pgfutil@trimspaces{#1}}% + \def\pgf@pat@onlineoptions{#2}% +}% + + +\def\pgf@pat@unravel#1/{% + \pgfutil@ifnextchar\pgf@stop{\def\pgf@pat@unravelled{#1}}{\pgf@pat@unravel}}% + +\pgfkeys{/handlers/.pattern/.code={% + \expandafter\expandafter\expandafter\pgf@pat@unravel\pgfkeyscurrentpath/\pgf@stop% + \pgfpatternalias{#1}{\pgf@pat@unravelled}% +}}% + +\def\pgfpatternalias#1#2{% + \begingroup% + \pgf@pat@checkname{#1}% + \expandafter\let\expandafter\pgf@pat@options\expandafter=% + \csname\pgf@pat@name@prefix\pgf@pat@onlinename\endcsname% + \pgf@pat@macroaskeys{/pgf/patterns/.cd}{\pgf@pat@options}% + \pgfutil@toks@\expandafter{\pgf@pat@onlineoptions}% + \edef\pgf@pat@tmp{append to defaults={\the\pgfutil@toks@}}% + \expandafter\pgf@pat@addto@macro\expandafter\pgf@pat@options\expandafter{\expandafter,\pgf@pat@tmp}% + \pgf@pat@addto@macro\pgf@pat@options{,name=#2}% + \expandafter\global\expandafter\let\csname\pgf@pat@name@prefix#2\endcsname=\pgf@pat@options% + \endgroup% +}% + + +\let\pgfsetfillpattern@old=\pgfsetfillpattern + +\def\pgf@pat@macroaskeys#1#2{% + \pgfutil@toks@\expandafter{#2}% + \edef\pgf@marshal{\noexpand\pgfkeys{,#1,\the\pgfutil@toks@}}% + \pgf@marshal% +}% +\def\pgfsetfillpattern#1#2{% + \pgf@pat@checkname{#1}% + \pgfutil@ifundefined{\pgf@pat@name@prefix\pgf@pat@onlinename}{% + \pgfsetfillpattern@old{\pgf@pat@onlinename}{#2}% + }{% + \let\pgf@pat@parameters=\pgfutil@empty% + \expandafter\let\expandafter\pgf@pat@options\expandafter=% + \csname\pgf@pat@name@prefix\pgf@pat@onlinename\endcsname% + \pgf@pat@macroaskeys{/pgf/patterns/.cd}{\pgf@pat@options}% + \ifx\pgf@pat@parameters\pgfutil@empty% + \else% + \begingroup% + \pgf@pat@macroaskeys{/pgf/pattern keys/.cd}{\pgf@pat@defaults}% + \pgf@pat@macroaskeys{/pgf/pattern keys/.cd}{\pgf@pat@onlineoptions}% + \edef\pgf@pat@current@parameters{\pgf@pat@parameters}% + \edef\pgf@pat@onlinename{\pgf@pat@onlinename\pgf@pat@current@parameters}% + \let\pgf@pat@name=\pgf@pat@onlinename% + \pgfutil@ifundefined{\pgf@pat@name@prefix\pgf@pat@onlinename}{% + \let\pgf@pat@parameters=\pgfutil@empty% + \pgf@declarepattern@meta% + }{}% + \expandafter% + \endgroup% + \expandafter\def\expandafter\pgf@pat@onlinename\expandafter{\pgf@pat@onlinename}% + \expandafter\let\expandafter\pgf@pat@options\expandafter=% + \csname\pgf@pat@name@prefix\pgf@pat@onlinename\endcsname% + \pgf@pat@macroaskeys{/pgf/patterns/.cd}{\pgf@pat@options}% + \fi% + \ifx\pgf@pat@type\pgf@pat@type@uncolored% + \pgf@pat@setpatternuncolored{\pgf@pat@number}{#2}% + \else% + \pgfsys@setpatterncolored{\pgf@pat@number}% + \fi% + }% +}% + +\def\pgf@pat@setpatternuncolored#1#2{% + \pgfutil@colorlet{pgf@tempcolor}{#2}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgf@tempcolor}}% + \pgfutil@extractcolorspec{pgf@tempcolor}{\pgf@tempcolor}% + \expandafter\pgfutil@convertcolorspec\pgf@tempcolor{rgb}{\pgf@rgbcolor}% + \expandafter\pgf@pat@set@fill@patternuncolored\pgf@rgbcolor\relax{#1}% +}% +\def\pgf@pat@set@fill@patternuncolored#1,#2,#3\relax#4{% + \pgfsys@setpatternuncolored{#4}{#1}{#2}{#3}% +}% + + +\pgfdeclarepattern{ + name=Lines, + parameters={ + \pgfkeysvalueof{/pgf/pattern keys/distance}, + \pgfkeysvalueof{/pgf/pattern keys/angle}, + \pgfkeysvalueof{/pgf/pattern keys/xshift}, + \pgfkeysvalueof{/pgf/pattern keys/yshift}, + \pgfkeysvalueof{/pgf/pattern keys/line width}, + }, + bottom left={% + \pgfpoint + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + top right={% + \pgfpoint + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + tile size={% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/distance}}% + {\pgfkeysvalueof{/pgf/pattern keys/distance}}}, + tile transformation={% + \pgftransformshift{% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/xshift}}% + {\pgfkeysvalueof{/pgf/pattern keys/yshift}}}% + \pgftransformrotate{\pgfkeysvalueof{/pgf/pattern keys/angle}}}, + defaults={ + distance/.initial=3pt, + angle/.initial=0, + xshift/.initial=0pt, + yshift/.initial=0pt, + line width/.initial=\the\pgflinewidth, + }, + code={% + \pgfsetlinewidth{\pgfkeysvalueof{/pgf/pattern keys/line width}}% + \pgfpathmoveto{\pgfpoint{-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}{0pt}}% + \pgfpathlineto{\pgfpoint{.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}{0pt}}% + \pgfusepath{stroke}% + }, +} + +\pgfdeclarepattern{ + name=Hatch, + parameters={ + \pgfkeysvalueof{/pgf/pattern keys/distance}, + \pgfkeysvalueof{/pgf/pattern keys/angle}, + \pgfkeysvalueof{/pgf/pattern keys/xshift}, + \pgfkeysvalueof{/pgf/pattern keys/yshift}, + \pgfkeysvalueof{/pgf/pattern keys/line width}, + }, + bottom left={% + \pgfpoint + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + top right={% + \pgfpoint + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + tile size={% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/distance}}% + {\pgfkeysvalueof{/pgf/pattern keys/distance}}}, + tile transformation={% + \pgftransformshift{% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/xshift}}% + {\pgfkeysvalueof{/pgf/pattern keys/yshift}}}% + \pgftransformrotate{\pgfkeysvalueof{/pgf/pattern keys/angle}}}, + defaults={ + distance/.initial=3pt, + angle/.initial=0, + xshift/.initial=0pt, + yshift/.initial=0pt, + line width/.initial=\the\pgflinewidth, + }, + code={% + \pgfsetlinewidth{\pgfkeysvalueof{/pgf/pattern keys/line width}}% + \pgfpathmoveto{\pgfpoint{-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}{0pt}}% + \pgfpathlineto{\pgfpoint{.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}{0pt}}% + \pgfpathmoveto{\pgfpoint{0pt}{-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}% + \pgfpathlineto{\pgfpoint{0pt}{.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}% + \pgfusepath{stroke}% + }, +} + +\pgfdeclarepattern{ + name=Dots, + parameters={ + \pgfkeysvalueof{/pgf/pattern keys/distance}, + \pgfkeysvalueof{/pgf/pattern keys/angle}, + \pgfkeysvalueof{/pgf/pattern keys/xshift}, + \pgfkeysvalueof{/pgf/pattern keys/yshift}, + \pgfkeysvalueof{/pgf/pattern keys/radius}, + }, + bottom left={% + \pgfpoint + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + top right={% + \pgfpoint + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + tile size={% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/distance}}% + {\pgfkeysvalueof{/pgf/pattern keys/distance}}}, + tile transformation={% + \pgftransformshift{% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/xshift}}% + {\pgfkeysvalueof{/pgf/pattern keys/yshift}}}% + \pgftransformrotate{\pgfkeysvalueof{/pgf/pattern keys/angle}}}, + defaults={ + distance/.initial=3pt, + angle/.initial=0, + xshift/.initial=0pt, + yshift/.initial=0pt, + radius/.initial=.5pt, + }, + code={% + \pgfpathcircle% + {\pgfpointorigin}% + {\pgfkeysvalueof{/pgf/pattern keys/radius}} + \pgfusepath{fill}% + }, +} + +\pgfdeclarepattern{ + name=Stars, + parameters={ + \pgfkeysvalueof{/pgf/pattern keys/distance}, + \pgfkeysvalueof{/pgf/pattern keys/angle}, + \pgfkeysvalueof{/pgf/pattern keys/xshift}, + \pgfkeysvalueof{/pgf/pattern keys/yshift}, + \pgfkeysvalueof{/pgf/pattern keys/radius}, + \pgfkeysvalueof{/pgf/pattern keys/points}, + }, + bottom left={% + \pgfpoint + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {-.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + top right={% + \pgfpoint + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}% + {.5*(\pgfkeysvalueof{/pgf/pattern keys/distance})}}, + tile size={% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/distance}}% + {\pgfkeysvalueof{/pgf/pattern keys/distance}}}, + tile transformation={% + \pgftransformshift{% + \pgfpoint + {\pgfkeysvalueof{/pgf/pattern keys/xshift}}% + {\pgfkeysvalueof{/pgf/pattern keys/yshift}}}% + \pgftransformrotate{\pgfkeysvalueof{/pgf/pattern keys/angle}}}, + defaults={ + distance/.initial=3mm, + angle/.initial=0, + xshift/.initial=0pt, + yshift/.initial=0pt, + radius/.initial=1mm, + points/.initial=5, + }, + code={% + \pgfmathsetmacro\a{180/(\pgfkeysvalueof{/pgf/pattern keys/points})}% + \pgfpathmoveto{\pgfpointpolar{90}{\pgfkeysvalueof{/pgf/pattern keys/radius}}}% + \foreach \i in {1,...,\pgfkeysvalueof{/pgf/pattern keys/points}}{% + \pgfpathlineto{\pgfpointpolar{90+2*\i*\a-\a}{.5*(\pgfkeysvalueof{/pgf/pattern keys/radius})}}% + \pgfpathlineto{\pgfpointpolar{90+2*\i*\a}{\pgfkeysvalueof{/pgf/pattern keys/radius}}}% + }% + \pgfpathclose% + \pgfusepath{fill}% + }, +} + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..dc578cc1feed49ddfad9021c5d332e6140796e9f --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryplothandlers.code.tex @@ -0,0 +1,773 @@ + +\ProvidesFileRCS{pgflibraryplothandlers.code.tex} + + + +\pgfdeclareplothandler{\pgfplothandlercurveto}{}{% + point macro=\pgf@plot@curveto@handler@initial, + jump macro=\pgf@plot@smooth@next@moveto, + end macro=\pgf@plot@curveto@handler@finish +}% + +\def\pgf@plot@smooth@next@moveto{% + \pgf@plot@curveto@handler@finish% + \global\pgf@plot@startedfalse% + \global\let\pgf@plotstreampoint\pgf@plot@curveto@handler@initial% +}% + +\def\pgf@plot@curveto@handler@initial#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@plot@first@action{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@curveto@first{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \global\let\pgf@plot@curveto@first@support=\pgf@plot@curveto@first% + \global\let\pgf@plotstreampoint=\pgf@plot@curveto@handler@second% +}% + +\def\pgf@plot@curveto@handler@second#1{% + \pgf@process{#1}% + \xdef\pgf@plot@curveto@second{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \global\let\pgf@plotstreampoint=\pgf@plot@curveto@handler@third% + \global\pgf@plot@startedtrue% +}% + +\def\pgf@plot@curveto@handler@third#1{% + \pgf@process{#1}% + \xdef\pgf@plot@curveto@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgf@plot@curveto@first} + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@xa=\pgf@plottension\pgf@xa% + \pgf@ya=\pgf@plottension\pgf@ya% + \pgf@process{\pgf@plot@curveto@second}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \advance\pgf@xc by\pgf@xa% + \advance\pgf@yc by\pgf@ya% + \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@curveto@first@support}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@curveto@second}}% + {\pgf@marshal}% + \global\let\pgf@plot@curveto@first=\pgf@plot@curveto@second% + \global\let\pgf@plot@curveto@second=\pgf@plot@curveto@current% + \xdef\pgf@plot@curveto@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% +}% + +\def\pgf@plot@curveto@handler@finish{% + \ifpgf@plot@started% + \pgfpathcurveto{\pgf@plot@curveto@first@support}{\pgf@plot@curveto@second}{\pgf@plot@curveto@second}% + \fi% +}% + + + +\def\pgfsetplottension#1{% + \pgf@x=#1pt\relax% + \pgf@x=0.2775\pgf@x\relax% + \edef\pgf@plottension{\pgf@sys@tonumber\pgf@x}}% +\pgfsetplottension{0.5}% + + + +\pgfdeclareplothandler{\pgfplothandlerclosedcurve}{}{% + point macro=\pgf@plot@closedcurve@handler@initial, + end macro=\pgf@plot@closedcurve@handler@finish, + jump macro=\pgf@plot@closedsmooth@next@moveto +}% + +\def\pgf@plot@closedsmooth@next@moveto{% + \pgf@plot@closedcurve@handler@finish% + \global\pgf@plot@startedfalse% + \global\let\pgf@plotstreampoint\pgf@plot@closedcurve@handler@initial% +}% + +\def\pgf@plot@closedcurve@handler@initial#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \xdef\pgf@plot@closedcurve@initial{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@second% + \global\pgf@plot@startedfalse% +}% + +\def\pgf@plot@closedcurve@handler@second#1{% + \pgf@process{#1}% + \xdef\pgf@plot@closedcurve@after@initial{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + {\pgfpathmoveto{}}% + \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@third% +}% + +\def\pgf@plot@closedcurve@handler@third#1{% + \global\pgf@plot@startedtrue% + \pgf@process{#1}% + \xdef\pgf@plot@closedcurve@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgf@plot@closedcurve@initial} + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@xa=\pgf@plottension\pgf@xa% + \pgf@ya=\pgf@plottension\pgf@ya% + \pgf@process{\pgf@plot@closedcurve@after@initial}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \advance\pgf@xc by\pgf@xa% + \advance\pgf@yc by\pgf@ya% + \global\let\pgf@plot@closedcurve@first=\pgf@plot@closedcurve@after@initial% + \global\let\pgf@plot@closedcurve@second=\pgf@plot@closedcurve@current% + \xdef\pgf@plot@closedcurve@after@initial@presupport{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}% + \xdef\pgf@plot@closedcurve@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + \global\let\pgf@plotstreampoint=\pgf@plot@closedcurve@handler@fourth% +}% + +\def\pgf@plot@closedcurve@handler@fourth#1{% + \pgf@process{#1}% + \xdef\pgf@plot@closedcurve@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgf@plot@closedcurve@first} + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@xa=\pgf@plottension\pgf@xa% + \pgf@ya=\pgf@plottension\pgf@ya% + \pgf@process{\pgf@plot@closedcurve@second}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \advance\pgf@xc by\pgf@xa% + \advance\pgf@yc by\pgf@ya% + \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@closedcurve@first@support}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@closedcurve@second}}% + {\pgf@marshal}% + \global\let\pgf@plot@closedcurve@first=\pgf@plot@closedcurve@second% + \global\let\pgf@plot@closedcurve@second=\pgf@plot@closedcurve@current% + \xdef\pgf@plot@closedcurve@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% +}% + +\def\pgf@plot@closedcurve@handler@finish{% + \ifpgf@plot@started + \pgf@process{\pgf@plot@closedcurve@initial}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgf@plot@closedcurve@first}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@xa=\pgf@plottension\pgf@xa% + \pgf@ya=\pgf@plottension\pgf@ya% + \pgf@process{\pgf@plot@closedcurve@second}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \advance\pgf@xc by\pgf@xa% + \advance\pgf@yc by\pgf@ya% + \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@closedcurve@first@support}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@closedcurve@second}}% + {\pgf@marshal}% + \xdef\pgf@plot@closedcurve@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + \pgf@process{\pgf@plot@closedcurve@after@initial}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgf@plot@closedcurve@second}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@xa=\pgf@plottension\pgf@xa% + \pgf@ya=\pgf@plottension\pgf@ya% + \pgf@process{\pgf@plot@closedcurve@initial}% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \advance\pgf@xc by\pgf@xa% + \advance\pgf@yc by\pgf@ya% + \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@closedcurve@first@support}% + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@closedcurve@initial}}% + {\pgf@marshal}% + \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + {\noexpand\pgf@plot@closedcurve@after@initial@presupport}{\noexpand\pgf@plot@closedcurve@after@initial}}% + {\pgf@marshal}% + \pgfpathclose% + \fi% +}% + + + + + + +\pgfdeclareplothandler{\pgfplothandlerxcomb}{}{% + start macro=\pgfplotxzerolevelstreamstart, + point macro=\pgf@plot@xcomb@handler, + end macro=\pgfplotxzerolevelstreamend, +}% + +\def\pgf@plot@xcomb@handler#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \begingroup + \pgfplotxzerolevelstreamnext + \endgroup + \pgf@yb=\pgf@x + \pgfpathmoveto{\pgfqpoint{\pgf@yb}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% +}% + + + +\pgfdeclareplothandler{\pgfplothandlerycomb}{}{% + start macro=\pgfplotyzerolevelstreamstart, + point macro=\pgf@plot@ycomb@handler, + end macro=\pgfplotyzerolevelstreamend +}% + +\def\pgf@plot@ycomb@handler#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \begingroup + \pgfplotyzerolevelstreamnext + \endgroup + \pgf@yb=\pgf@x + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% +}% + +\def\pgfplotxzerolevelstreamstart{\pgf@plotxzerolevelstreamstart}% +\def\pgfplotxzerolevelstreamend{\pgf@plotxzerolevelstreamend}% +\def\pgfplotxzerolevelstreamnext{\pgf@plotxzerolevelstreamnext} +\def\pgfplotyzerolevelstreamstart{\pgf@plotyzerolevelstreamstart}% +\def\pgfplotyzerolevelstreamend{\pgf@plotyzerolevelstreamend}% +\def\pgfplotyzerolevelstreamnext{\pgf@plotyzerolevelstreamnext}% + +\def\pgfplotxzerolevelstreamconstant#1{% + \edef\pgfplotxzerolevelstreamconstant@val{#1}% + \def\pgf@plotxzerolevelstreamstart{% + \global\let\pgf@plotxzerolevelstreamend=\relax + \gdef\pgf@plotxzerolevelstreamnext{\global\pgf@x=\pgfplotxzerolevelstreamconstant@val\relax}% + }% +}% +\pgfplotxzerolevelstreamconstant{0pt}% + +\def\pgfplotyzerolevelstreamconstant#1{% + \edef\pgfplotyzerolevelstreamconstant@val{#1}% + \def\pgf@plotyzerolevelstreamstart{% + \global\let\pgf@plotyzerolevelstreamend=\relax + \gdef\pgf@plotyzerolevelstreamnext{\global\pgf@x=\pgfplotyzerolevelstreamconstant@val\relax}% + }% +}% +\pgfplotyzerolevelstreamconstant{0pt}% + +\def\pgfplotbarwidth{\pgfkeysvalueof{/pgf/bar width}}% +\def\pgfplotbarshift{\pgfkeysvalueof{/pgf/bar shift}}% + +\pgfqkeys{/pgf}{% + bar width/.initial=10pt, + bar shift/.initial=0pt, + bar interval width/.initial=1, + bar interval shift/.initial=0.5, + at begin bar/.initial=, + at end bar/.initial=, +}% + + +\pgfdeclareplothandler{\pgfplothandlerybar}{}{% + start={ + \pgfmathparse{\pgfplotbarwidth}% + \xdef\pgfplotbarwidth@{\pgfmathresult pt}% + \pgfmathparse{\pgfplotbarshift}% + \xdef\pgfplotbarshift@{\pgfmathresult pt}% + \pgfplotyzerolevelstreamstart + }, + end macro=\pgfplotyzerolevelstreamend, + point macro=\pgf@plot@ybar@handler +}% + +\def\pgf@plot@ybar@handler#1{% + \pgfkeysvalueof{/pgf/at begin bar}% + \pgf@process{#1}% + \pgf@ya=\pgf@y + \expandafter\pgf@xb\pgfplotbarwidth@\relax + \pgf@xc=\pgf@x + \advance\pgf@xc by-.5\pgf@xb + \advance\pgf@xc by\pgfplotbarshift@\relax + \begingroup + \pgfplotyzerolevelstreamnext + \endgroup + \pgf@yb=\pgf@x + \advance\pgf@ya by-\pgf@yb + \pgfpathrectangle + {\pgfqpoint{\pgf@xc}{\pgf@yb}}% + {\pgfqpoint{\pgf@xb}{\pgf@ya}}% + \pgfkeysvalueof{/pgf/at end bar}% +}% + +\pgfdeclareplothandler{\pgfplothandlerxbar}{}{% + start={ + \pgfmathparse{\pgfplotbarwidth}% + \xdef\pgfplotbarwidth@{\pgfmathresult pt}% + \pgfmathparse{\pgfplotbarshift}% + \xdef\pgfplotbarshift@{\pgfmathresult pt}% + \pgfplotxzerolevelstreamstart + }, + end macro=\pgfplotxzerolevelstreamend, + point macro=\pgf@plot@xbar@handler +}% + +\def\pgf@plot@xbar@handler#1{% + \pgfkeysvalueof{/pgf/at begin bar}% + \pgf@process{#1}% + \pgf@ya=\pgf@x + \expandafter\pgf@xb\pgfplotbarwidth@\relax + \pgf@xc=\pgf@y + \advance\pgf@xc by-.5\pgf@xb + \advance\pgf@xc by\pgfplotbarshift@\relax + \begingroup + \pgfplotxzerolevelstreamnext + \endgroup + \pgf@yb=\pgf@x + \advance\pgf@ya by-\pgf@yb + \pgfpathrectangle + {\pgfqpoint{\pgf@yb}{\pgf@xc}}% + {\pgfqpoint{\pgf@ya}{\pgf@xb}}% + \pgfkeysvalueof{/pgf/at end bar}% +}% + +\pgfdeclareplothandler{\pgfplothandlerybarinterval}{}{% + start={ + \pgfmathparse{\pgfkeysvalueof{/pgf/bar interval width}}% + \xdef\pgfplotbarintervalwidth@{\pgfmathresult}% + \pgfmathparse{\pgfkeysvalueof{/pgf/bar interval shift}}% + \xdef\pgfplotbarintervalshift@{\pgfmathresult}% + \pgfplotyzerolevelstreamstart + }, + end macro=\pgfplotyzerolevelstreamend, + point macro=\pgf@plot@ybarinterval@handler@first +}% + +\def\pgf@plot@ybarinterval@handler@first#1{% + \pgf@process{#1}% + \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@x}% + \xdef\pgf@plot@barinterval@bar{\the\pgf@y}% + \global\let\pgf@plotstreampoint=\pgf@plot@ybarinterval@handler% +}% +\def\pgf@plot@ybarinterval@handler#1{% + \pgfkeysvalueof{/pgf/at begin bar}% + \pgf@process{#1}% + \pgf@ya=\pgf@plot@barinterval@bar + \xdef\pgf@plot@barinterval@bar{\the\pgf@y}% + \pgf@xc=\pgf@plot@barinterval@intervalstart\relax + \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@x}% + \pgf@xb=\pgf@x + \advance\pgf@xb by-\pgf@xc + \advance\pgf@xc by\pgfplotbarintervalshift@\pgf@xb + \pgf@xb=\pgfplotbarintervalwidth@\pgf@xb + \advance\pgf@xc by-.5\pgf@xb% + \begingroup + \pgfplotyzerolevelstreamnext + \endgroup + \pgf@yb=\pgf@x + \advance\pgf@ya by-\pgf@yb + \pgfpathrectangle + {\pgfqpoint{\pgf@xc}{\pgf@yb}}% + {\pgfqpoint{\pgf@xb}{\pgf@ya}}% + \pgfkeysvalueof{/pgf/at end bar}% +}% + +\pgfdeclareplothandler{\pgfplothandlerxbarinterval}{}{% + start={ + \pgfmathparse{\pgfkeysvalueof{/pgf/bar interval width}}% + \xdef\pgfplotbarintervalwidth@{\pgfmathresult}% + \pgfmathparse{\pgfkeysvalueof{/pgf/bar interval shift}}% + \xdef\pgfplotbarintervalshift@{\pgfmathresult}% + \pgfplotxzerolevelstreamstart + }, + end macro=\pgfplotxzerolevelstreamend, + point macro=\pgf@plot@xbarinterval@handler@first +}% + +\def\pgf@plot@xbarinterval@handler@first#1{% + \pgf@process{#1}% + \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@y}% + \xdef\pgf@plot@barinterval@bar{\the\pgf@x}% + \global\let\pgf@plotstreampoint=\pgf@plot@xbarinterval@handler% +}% +\def\pgf@plot@xbarinterval@handler#1{% + \pgfkeysvalueof{/pgf/at begin bar}% + \pgf@process{#1}% + \pgf@ya=\pgf@plot@barinterval@bar + \xdef\pgf@plot@barinterval@bar{\the\pgf@x}% + \pgf@xc=\pgf@plot@barinterval@intervalstart\relax + \xdef\pgf@plot@barinterval@intervalstart{\the\pgf@y}% + \pgf@xb=\pgf@y + \advance\pgf@xb by-\pgf@xc + \advance\pgf@xc by\pgfplotbarintervalshift@\pgf@xb + \pgf@xb=\pgfplotbarintervalwidth@\pgf@xb + \advance\pgf@xc by-.5\pgf@xb% + \begingroup + \pgfplotxzerolevelstreamnext + \endgroup + \pgf@yb=\pgf@x + \advance\pgf@ya by-\pgf@yb + \pgfpathrectangle + {\pgfqpoint{\pgf@yb}{\pgf@xc}}% + {\pgfqpoint{\pgf@ya}{\pgf@xb}}% + \pgfkeysvalueof{/pgf/at end bar}% +}% + + + +\pgfdeclareplothandler{\pgfplothandlerconstantlineto}{}{% + point macro=\pgf@plot@const@line@handler +}% + +\def\pgf@plot@const@line@handler#1{% + \pgf@process{#1}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@y}% + \pgf@plot@first@action{}% + \global\let\pgf@plotstreampoint=\pgf@plot@const@line@handler@@% +}% +\def\pgf@plot@const@line@handler@@#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x + \pgf@ya=\pgf@y + \pgf@yb\pgf@plot@const@line@handler@last\relax + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@ya}% +}% + + +\pgfdeclareplothandler{\pgfplothandlerconstantlinetomarkright}{}{% + point macro=\pgf@plot@const@line@mark@right@handler +}% + +\def\pgf@plot@const@line@mark@right@handler#1{% + \pgf@process{#1}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@x}% + \pgf@plot@first@action{}% + \global\let\pgf@plotstreampoint=\pgf@plot@const@line@mark@right@handler@@% +}% +\def\pgf@plot@const@line@mark@right@handler@@#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x + \pgf@ya=\pgf@y + \pgf@yb\pgf@plot@const@line@handler@last\relax + \pgfpathlineto{\pgfqpoint{\pgf@yb}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@xa}% +}% + + +\pgfdeclareplothandler{\pgfplothandlerconstantlinetomarkmid}{}{% + point macro=\pgf@plot@const@line@mark@mid@handler +}% + +\def\pgf@plot@const@line@mark@mid@handler#1{% + \pgf@process{#1}% + \xdef\pgf@plot@const@line@handler@last{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% + \pgf@plot@first@action{}% + \global\let\pgf@plotstreampoint=\pgf@plot@const@line@mark@mid@handler@@% +}% +\def\pgf@plot@const@line@mark@mid@handler@@#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x + \pgf@ya=\pgf@y + \pgf@plot@const@line@handler@last + \pgf@xc=.5\pgf@xa + \advance\pgf@xc by.5\pgf@x + \pgfpathlineto{\pgfqpoint{\pgf@xc}{\pgf@y}}% + \pgfpathlineto{\pgfqpoint{\pgf@xc}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@const@line@handler@last{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% +}% + + +\pgfdeclareplothandler{\pgfplothandlerjumpmarkright}{}{% + point macro=\pgf@plot@jumpmarkright@handler +}% + +\def\pgf@plot@jumpmarkright@handler#1{% + \pgf@process{#1}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@x}% + \pgf@plot@first@action{}% + \global\let\pgf@plotstreampoint=\pgf@plot@jumpmarkright@handler@@% +}% +\def\pgf@plot@jumpmarkright@handler@@#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x + \pgf@ya=\pgf@y + \pgf@yb\pgf@plot@const@line@handler@last\relax + \pgfpathmoveto{\pgfqpoint{\pgf@yb}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@xa}% +}% + + +\pgfdeclareplothandler{\pgfplothandlerjumpmarkleft}{}{% + point macro=\pgf@plot@jumpmarkleft@handler +}% +\def\pgf@plot@jumpmarkleft@handler#1{% + \pgf@process{#1}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@y}% + \pgf@plot@first@action{}% + \global\let\pgf@plotstreampoint=\pgf@plot@jumpmarkleft@handler@@% +}% +\def\pgf@plot@jumpmarkleft@handler@@#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x + \pgf@ya=\pgf@y + \pgf@yb\pgf@plot@const@line@handler@last\relax + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}% + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@const@line@handler@last{\the\pgf@ya}% +}% + + +\pgfdeclareplothandler{\pgfplothandlerjumpmarkmid}{}{% + point macro=\pgf@plot@jump@mark@mid@handler +}% + +\def\pgf@plot@jump@mark@mid@handler#1{% + \pgf@process{#1}% + \xdef\pgf@plot@const@line@handler@last{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% + \pgf@plot@first@action{}% + \global\let\pgf@plotstreampoint=\pgf@plot@jump@mark@mid@handler@@% +}% +\def\pgf@plot@jump@mark@mid@handler@@#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x + \pgf@ya=\pgf@y + \pgf@plot@const@line@handler@last + \pgf@xc=.5\pgf@xa + \advance\pgf@xc by.5\pgf@x + \pgfpathlineto{\pgfqpoint{\pgf@xc}{\pgf@y}}% + \pgfpathmoveto{\pgfqpoint{\pgf@xc}{\pgf@ya}}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \xdef\pgf@plot@const@line@handler@last{\global\pgf@x=\the\pgf@x\space\global\pgf@y=\the\pgf@y\space}% +}% + + + +\pgfdeclareplothandler{\pgfplothandlerpolarcomb}{}{% + point macro=\pgf@plot@polarcomb@handler +}% + +\def\pgf@plot@polarcomb@handler#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfpathmoveto{\pgfpointorigin}% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% +}% + + + + + +\pgfdeclareplothandler{\pgfplothandlermark}{#1}{% + start={ + \def\pgf@plot@mark{% + \ifnum\pgf@plot@mark@count<\pgf@plot@mark@repeat\relax% + \else% + \global\pgf@plot@mark@count=0\relax% + #1% + \fi% + }% + \global\pgf@plot@mark@count=\pgf@plot@mark@repeat\relax% + \global\advance\pgf@plot@mark@count by-\pgf@plot@mark@phase\relax% + }, + point macro=\pgf@plot@mark@handler +}% + +\newcount\pgf@plot@mark@count +\def\pgf@plot@mark@phase{0}% + +\def\pgf@plot@mark@handler#1{% + \global\advance\pgf@plot@mark@count by1\relax% + {\pgftransformshift{#1}\pgf@plot@mark}% +}% + + + +\def\pgfsetplotmarkrepeat#1{\def\pgf@plot@mark@repeat{#1}}% +\pgfsetplotmarkrepeat{1}% + + + +\def\pgfsetplotmarkphase#1{\def\pgf@plot@mark@phase{#1}}% +\pgfsetplotmarkphase{1}% + + + + +\pgfdeclareplothandler{\pgfplothandlermarklisted}{#1#2}{% + start={ + \let\pgf@plot@mark@list=\pgfutil@empty% + \edef\pgf@marshal{\noexpand\foreach\noexpand\pgf@temp in{#2}} + \pgf@marshal{\xdef\pgf@plot@mark@list{\pgf@plot@mark@list(\pgf@temp)}}% + \def\pgf@plot@mark{% + \edef\pgf@marshal{\noexpand\pgfutil@in@{(\the\pgf@plot@mark@count)}{\pgf@plot@mark@list}}% + \pgf@marshal% + \ifpgfutil@in@#1\fi% + }% + \global\pgf@plot@mark@count=\pgf@plot@mark@repeat\relax% + \global\advance\pgf@plot@mark@count by-\pgf@plot@mark@phase\relax% + }, + point macro=\pgf@plot@mark@handler +}% + + + + +\def\pgfdeclareplotmark#1#2{\expandafter\def\csname pgf@plot@mark@#1\endcsname{#2}}% + + + +\def\pgfsetplotmarksize#1{\pgfmathsetlength\pgfplotmarksize{#1}}% + +\newdimen\pgfplotmarksize +\pgfplotmarksize=2pt + + + +\def\pgfuseplotmark#1{\csname pgf@plot@mark@#1\endcsname}% + + + +\pgfdeclareplotmark{*} +{% + \pgfpathellipse{\pgfpointorigin}{\pgfqpoint{\pgfplotmarksize}{0sp}}{\pgfqpoint{0sp}{\pgfplotmarksize}}% + \pgfusepathqfillstroke +}% + + + +\pgfdeclareplotmark{+} +{% + \pgfpathmoveto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{x} +{% + \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + + + + +\pgfkeys{/pgf/gap around stream point/.initial=1.5pt}% + +\pgfdeclareplothandler{\pgfplothandlergaplineto}{}{% + point macro=\pgf@plot@gap@lineto@handler@initial, + jump macro=\pgf@plot@gap@next@moveto +}% + +\def\pgf@plot@gap@next@moveto{% + \global\let\pgf@plotstreampoint=\pgf@plot@gap@lineto@handler@initial% +}% + +\def\pgf@plot@gap@lineto@handler@initial#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \xdef\pgf@plot@gap@lineto@last{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \global\let\pgf@plotstreampoint=\pgf@plot@gap@lineto@handler% +}% + +\def\pgf@plot@gap@lineto@handler#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \xdef\pgf@plot@gap@lineto@next{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \pgf@process{\pgfpointnormalised{\pgfpointdiff{\pgf@plot@gap@lineto@last}{\pgf@plot@gap@lineto@next}}}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfpathmoveto{\pgfpointadd{\pgfpointscale{\pgfkeysvalueof{/pgf/gap + around stream point}}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}{\pgf@plot@gap@lineto@last}}% + \pgfpathlineto{\pgfpointadd{\pgfpointscale{\pgfkeysvalueof{/pgf/gap + around stream point}}{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}}{\pgf@plot@gap@lineto@next}}% + \global\let\pgf@plot@gap@lineto@last=\pgf@plot@gap@lineto@next% +}% + + + + + +\pgfdeclareplothandler{\pgfplothandlergapcycle}{}{% + point macro=\pgf@plot@gap@cycle@handler@initial, + jump macro=\pgf@plot@gapcycle@next@moveto, + end macro=\pgf@plot@gap@cycle@handler@finish, + start={\global\let\pgf@plot@gap@cycle@first\relax} +}% + +\def\pgf@plot@gapcycle@next@moveto{% + \pgf@plot@gap@cycle@handler@finish% + \global\let\pgf@plot@gap@cycle@first=\relax% + \global\let\pgf@plotstreampoint=\pgf@plot@gap@cycle@handler@initial% +}% + +\def\pgf@plot@gap@cycle@handler@initial#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \xdef\pgf@plot@gap@cycle@last{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \global\let\pgf@plot@gap@cycle@first=\pgf@plot@gap@cycle@last% + \global\let\pgf@plotstreampoint=\pgf@plot@gap@cycle@handler% +}% + +\def\pgf@plot@gap@cycle@handler#1{% + \pgf@process{#1}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \xdef\pgf@plot@gap@cycle@next{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \pgf@process{\pgfpointnormalised{\pgfpointdiff{\pgf@plot@gap@cycle@last}{\pgf@plot@gap@cycle@next}}}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfpathmoveto{\pgfpointadd{\pgfpointscale{\pgfkeysvalueof{/pgf/gap + around stream point}}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}{\pgf@plot@gap@cycle@last}}% + \pgfpathlineto{\pgfpointadd{\pgfpointscale{\pgfkeysvalueof{/pgf/gap + around stream point}}{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}}{\pgf@plot@gap@cycle@next}}% + \global\let\pgf@plot@gap@cycle@last=\pgf@plot@gap@cycle@next% +}% + +\def\pgf@plot@gap@cycle@handler@finish{% + \ifx\pgf@plot@gap@cycle@first\relax% + \else + \pgf@plot@gap@cycle@handler{\pgf@plot@gap@cycle@first}% + \fi +}% + + + +\endinput + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..70389b648854fcc5367a9a0d054142e242da18e0 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryplotmarks.code.tex @@ -0,0 +1,412 @@ + +\ProvidesFileRCS{pgflibraryplotmarks.code.tex} + + + +\pgfdeclareplotmark{o} +{% + \pgfpathellipse{\pgfpointorigin}{\pgfqpoint{\pgfplotmarksize}{0sp}}{\pgfqpoint{0sp}{\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{Mercedes star} +{% + \pgfpathmoveto{\pgfqpointpolar{90}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfpointorigin}% + \pgfpathmoveto{\pgfqpointpolar{-30}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfpointorigin}% + \pgfpathmoveto{\pgfqpointpolar{-150}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfpointorigin}% + \pgfusepathqstroke +}% + +\pgfdeclareplotmark{Mercedes star flipped} +{% + \pgfpathmoveto{\pgfqpointpolar{-90}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfpointorigin}% + \pgfpathmoveto{\pgfqpointpolar{30}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfpointorigin}% + \pgfpathmoveto{\pgfqpointpolar{150}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfpointorigin}% + \pgfusepathqstroke +}% + + + + + +\pgfdeclareplotmark{asterisk} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpointpolar{30}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{210}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpointpolar{-30}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-210}{\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{star} +{% + \pgfpathmoveto{\pgfpointorigin}\pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfpointorigin}\pgfpathlineto{\pgfqpointpolar{18}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfpointorigin}\pgfpathlineto{\pgfqpointpolar{-54}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfpointorigin}\pgfpathlineto{\pgfqpointpolar{234}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfpointorigin}\pgfpathlineto{\pgfqpointpolar{162}{\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{10-pointed star} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfplotmarksize}}\pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpointpolar{18}{-\pgfplotmarksize}}\pgfpathlineto{\pgfqpointpolar{18}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpointpolar{-54}{-\pgfplotmarksize}}\pgfpathlineto{\pgfqpointpolar{-54}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpointpolar{234}{-\pgfplotmarksize}}\pgfpathlineto{\pgfqpointpolar{234}{\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpointpolar{162}{-\pgfplotmarksize}}\pgfpathlineto{\pgfqpointpolar{162}{\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{oplus} +{% + \pgfpathcircle{\pgfpointorigin}{\pgfplotmarksize}% + \pgfpathmoveto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfusepathqstroke +}% + +\pgfdeclareplotmark{oplus*} +{% + \pgfpathcircle{\pgfpointorigin}{\pgfplotmarksize}% + \pgfpathmoveto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfusepathqfillstroke +}% + + + +\pgfdeclareplotmark{otimes} +{% + \pgfpathcircle{\pgfpointorigin}{\pgfplotmarksize}% + \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}% + \pgfusepathqstroke +}% + +\pgfdeclareplotmark{otimes*} +{% + \pgfpathcircle{\pgfpointorigin}{\pgfplotmarksize}% + \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}% + \pgfpathmoveto{\pgfqpoint{-.70710678\pgfplotmarksize}{.70710678\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.70710678\pgfplotmarksize}{-.70710678\pgfplotmarksize}}% + \pgfusepathqfillstroke +}% + + + +\pgfdeclareplotmark{|} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + + + +\pgfdeclareplotmark{-} +{% + \pgfpathmoveto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{square} +{% + \pgfpathrectangle{\pgfqpoint{-\pgfplotmarksize}{-\pgfplotmarksize}}{\pgfqpoint{2\pgfplotmarksize}{2\pgfplotmarksize}}% + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{square*} +{% + \pgfpathrectangle{\pgfqpoint{-\pgfplotmarksize}{-\pgfplotmarksize}}{\pgfqpoint{2\pgfplotmarksize}{2\pgfplotmarksize}}% + \pgfusepathqfillstroke +}% + + + +\pgfdeclareplotmark{triangle} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-30}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-150}{\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{triangle*} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-30}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-150}{\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqfillstroke +}% + + + + +\pgfdeclareplotmark{diamond} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.75\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-.75\pgfplotmarksize}{0pt}}% + \pgfpathclose + \pgfusepathqstroke +}% + + + +\pgfdeclareplotmark{diamond*} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.75\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-.75\pgfplotmarksize}{0pt}}% + \pgfpathclose + \pgfusepathqfillstroke +}% + + + + +\pgfdeclareplotmark{pentagon} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{18}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-54}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{234}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{162}{\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{pentagon*} +{% + \pgfpathmoveto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{18}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{-54}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{234}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpointpolar{162}{\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqfillstroke +}% + +\newif\ifpgfmarktext@usetikznode +\pgfkeys{ + /pgf/text mark/.initial=p, + /pgf/text mark style/.initial=, + /pgf/text mark as node/.is if=pgfmarktext@usetikznode, + /pgf/text mark as node/.default=true, + /pgf/text mark/style/.style={/pgf/text mark style={#1}},% + /pgf/text mark/as node/.style={/pgf/text mark as node={#1}},% +}% + +\pgfdeclareplotmark{text} +{ + \pgfkeysgetvalue{/pgf/text mark style}\pgfmarktext@style + \pgfkeysgetvalue{/pgf/text mark}\pgfmarktext@ + \ifpgfmarktext@usetikznode + \expandafter\node\expandafter[\pgfmarktext@style]{\pgfmarktext@}; + \else + \expandafter\pgftext\expandafter[\pgfmarktext@style]{\pgfmarktext@}% + \fi +}% + +\pgfkeysdef{/pgf/mark color}{\def\pgf@mark@color{#1}}% +\let\pgf@mark@color\pgfutil@empty + +\def\pgf@set@mark@color{% + \ifx\pgf@mark@color\pgfutil@empty + \pgfsys@color@rgb@fill{1}{1}{1}% + \else + \pgfsetfillcolor{\pgf@mark@color}% + \fi +}% +\def\pgf@mark@color@none{none}% + + +\pgfdeclareplotmark{halfcircle}{% + \ifx\pgf@mark@color@none\pgf@mark@color + \else + \pgfscope + \pgf@set@mark@color + \pgfpathmoveto + {\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpatharc{180}{360}{\pgfplotmarksize}% + \pgfusepathqfill + \endpgfscope% + \fi + \pgfpathmoveto + {\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto + {\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathcircle{\pgfpointorigin}% + {\pgfplotmarksize}% + \pgfusepathqstroke +}% +\pgfdeclareplotmark{halfcircle*}{% + \pgfpathmoveto + {\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpatharc{0}{180}{\pgfplotmarksize}% + \pgfpathclose + \pgfusepathqfill + \ifx\pgf@mark@color@none\pgf@mark@color + \else + \pgfscope + \pgf@set@mark@color + \pgfpathmoveto + {\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpatharc{180}{360}{\pgfplotmarksize}% + \pgfusepathqfill + \endpgfscope% + \fi + \pgfpathcircle{\pgfpointorigin}% + {\pgfplotmarksize}% + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{halfdiamond*}{% + \pgfpathmoveto{\pgfqpoint{-.75\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{.75\pgfplotmarksize}{0pt}}% + \pgfusepathqfill + \ifx\pgf@mark@color@none\pgf@mark@color + \else + \pgfscope + \pgf@set@mark@color + \pgfpathmoveto{\pgfqpoint{.75\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-.75\pgfplotmarksize}{0pt}}% + \pgfusepathqfill + \endpgfscope + \fi + \pgfpathmoveto{\pgfqpoint{.75\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-.75\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{halfsquare*}{% + \pgfpathmoveto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfusepathqfill + \ifx\pgf@mark@color@none\pgf@mark@color + \else + \pgfscope + \pgf@set@mark@color + \pgfpathmoveto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfusepathqfill + \endpgfscope + \fi + \pgfpathmoveto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{halfsquare right*}{% + \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfusepathqfill + \ifx\pgf@mark@color@none\pgf@mark@color + \else + \pgfscope + \pgf@set@mark@color + \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfusepathqfill + \endpgfscope + \fi + \pgfpathmoveto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{halfsquare left*}{% + \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfusepathqfill + \ifx\pgf@mark@color@none\pgf@mark@color + \else + \pgfscope + \pgf@set@mark@color + \pgfpathmoveto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfusepathqfill + \endpgfscope + \fi + \pgfpathmoveto{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgfplotmarksize}}% + \pgfpathlineto{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqstroke +}% + + +\pgfdeclareplotmark{heart}{% + \pgfpathmoveto{\pgfqpoint{0pt}{-1.75\pgfplotmarksize}}% + \pgfpathcurveto{\pgfqpoint{0pt}{-1.75\pgfplotmarksize}}{\pgfqpoint{0pt}{-1.66\pgfplotmarksize}}{\pgfqpoint{-.5\pgfplotmarksize}{-1.165\pgfplotmarksize}}% + \pgfpathcurveto{\pgfqpoint{-.5\pgfplotmarksize}{-1.165\pgfplotmarksize}}{\pgfqpoint{-\pgfplotmarksize}{-.75\pgfplotmarksize}}{\pgfqpoint{-\pgfplotmarksize}{0pt}}% + \pgfpathcurveto{\pgfqpoint{-\pgfplotmarksize}{0pt}}{\pgfqpoint{-\pgfplotmarksize}{.5825\pgfplotmarksize}}{\pgfqpoint{-.5825\pgfplotmarksize}{.5825\pgfplotmarksize}}% + \pgfpathcurveto{\pgfqpoint{-.5825\pgfplotmarksize}{.5825\pgfplotmarksize}}{\pgfqpoint{0pt}{.5825\pgfplotmarksize}}{\pgfqpoint{0pt}{0pt}}% + \pgfpathcurveto{\pgfqpoint{0pt}{0pt}}{\pgfqpoint{0pt}{.5825\pgfplotmarksize}}{\pgfqpoint{.5825\pgfplotmarksize}{.5825\pgfplotmarksize}}% + \pgfpathcurveto{\pgfqpoint{.5825\pgfplotmarksize}{.5825\pgfplotmarksize}}{\pgfqpoint{\pgfplotmarksize}{.5825\pgfplotmarksize}}{\pgfqpoint{\pgfplotmarksize}{0pt}}% + \pgfpathcurveto{\pgfqpoint{\pgfplotmarksize}{0pt}}{\pgfqpoint{\pgfplotmarksize}{-.75\pgfplotmarksize}}{\pgfqpoint{.5\pgfplotmarksize}{-1.165\pgfplotmarksize}}% + \pgfpathcurveto{\pgfqpoint{.5\pgfplotmarksize}{-1.165\pgfplotmarksize}}{\pgfqpoint{0pt}{-1.66\pgfplotmarksize}}{\pgfqpoint{0pt}{-1.75\pgfplotmarksize}}% + \pgfpathclose + \pgfusepathqfillstroke +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryprofiler.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryprofiler.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..11401cef33cd2b0f9030bbca6436362201447269 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryprofiler.code.tex @@ -0,0 +1,427 @@ + +\pgfutil@ifundefined{pdfelapsedtime}{% + \pgfutil@ifluatex + \def\pgfutil@pdfelapsedtime{% + \numexpr\pgfutil@directlua{% + tex.print(math.floor((os.clock())*65536+0.5))}\relax} + \else + \pgferror{% + Library 'profiler' can only be used with pdftex Rev. >= 1.671 + because it needs the \string\pdfelapsedtime\space command or + with luatex}% + \global\let\pgfutil@pdfelapsedtime=\c@pgf@counta + \fi}{% + \let\pgfutil@pdfelapsedtime\pdfelapsedtime}% + + +\def\pgfprofilenew#1{% + \pgfutil@ifundefined{c@pgfprofile@elapsedtotal@#1}{% + \expandafter\gdef\csname c@pgfprofile@elapsedtotal@#1\endcsname{0}% + \expandafter\gdef\csname c@pgfprofile@elapsedself@#1\endcsname{0}% + \expandafter\gdef\csname c@pgfprofile@numinvocations@#1\endcsname{0}% + \expandafter\gdef\csname c@pgfprofile@subtractforself@#1\endcsname{0}% + \expandafter\gdef\csname c@pgfprofile@semaphor@#1\endcsname{0}% + \expandafter\gdef\csname c@pgfprofile@elapsed@at@start@#1\endcsname{0}% + \pgfprofile@all@registered@list@add{#1}% + }{% + }% +}% + +\def\pgfprofile@TeX@DIALECT@toenvironment@begin#1{\csname #1\endcsname}% +\def\pgfprofile@TeX@DIALECT@toenvironment@end#1{\csname end#1\endcsname}% + +\def\pgfprofile@@to@pgfretval#1{% + \expandafter\let\expandafter\pgfretval#1% +}% + +\def\pgfprofilenewforenvironment{\pgfutil@ifnextchar[{\pgfprofilenewforenvironment@}{\pgfprofilenewforenvironment@[]}}% +\def\pgfprofilenewforenvironment@[#1]#2{% + \expandafter\pgfprofile@@to@pgfretval\pgfprofile@TeX@DIALECT@toenvironment@begin{#2}% + \ifx\pgfretval\relax + \pgferror{\string\pgfprofilenewforenvironment{#2} doesn't work: the environment `#2' is (not yet?) known or not known in this context}{}% + \else + \expandafter\global\expandafter\let\csname pgfprofile@orig@begin@#2\endcsname=\pgfretval + \expandafter\pgfprofile@@to@pgfretval\pgfprofile@TeX@DIALECT@toenvironment@end{#2}% + \expandafter\global\expandafter\let\csname pgfprofile@orig@end@#2\endcsname=\pgfretval + \def\pgfprofile@temp{#1}% + \ifx\pgfprofile@temp\pgfutil@empty + \pgfprofilenewforenvironment@@{\pgfprofileenv #2}{#2}% + \else + \pgfprofilenewforenvironment@@{#1}{#2}% + \fi + \fi +}% +\def\pgfprofilenewforenvironment@@#1#2{% + \pgfprofilenew{#1}% + \expandafter\expandafter\expandafter\gdef\pgfprofile@TeX@DIALECT@toenvironment@begin{#2}{% + \pgfprofilestart{#1}% + \csname pgfprofile@orig@begin@#2\endcsname + }% + \expandafter\expandafter\expandafter\gdef\pgfprofile@TeX@DIALECT@toenvironment@end{#2}{% + \csname pgfprofile@orig@end@#2\endcsname + \pgfprofileend{#1}% + }% +}% + + +\def\pgfprofilecs{}% +\def\pgfprofileenv{}% + +\def\pgfprofilenewforcommand{\pgfutil@ifnextchar[{\pgfprofilenewforcommand@}{\pgfprofilenewforcommand@[]}}% +\def\pgfprofilenewforcommand@[#1]#2#3{% + \def\pgfprofile@temp{#3}% + \ifx\pgfprofile@temp\pgfutil@empty + \pgfprofilenewforcommandpattern[#1]{#2}{}{}% + \else + \ifcase#3\relax + \pgfprofilenewforcommandpattern[#1]{#2}{}{}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1}{{##1}}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1##2}{{##1}{##2}}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1##2##3}{{##1}{##2}{##3}}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1##2##3##4}{{##1}{##2}{##3}{##4}}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1##2##3##4##5}{{##1}{##2}{##3}{##4}{##5}}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1##2##3##4##5##6}{{##1}{##2}{##3}{##4}{##5}{##6}}% + \or + \pgfprofilenewforcommandpattern[#1]{#2}{##1##2##3##4##5##6##7}{{##1}{##2}{##3}{##4}{##5}{##6}{##7}}% + \else + \pgferror{library 'profiler' can't replace control sequences with '#3' arguments automatically, sorry.}{}% + \fi + \fi +}% + +\def\pgfprofilenewforcommandpattern{\pgfutil@ifnextchar[{\pgfprofilenewforcommandpattern@}{\pgfprofilenewforcommandpattern@[]}}% +\def\pgfprofilenewforcommandpattern@[#1]#2#3#4{% + \def\pgfprofile@known{1}% + \ifx#2\undefined + \def\pgfprofile@known{0}% + \else + \ifx#2\relax + \def\pgfprofile@known{0}% + \fi + \fi + \if\pgfprofile@known0% + \pgferror{\string\pgfprofilenewforcommandpattern{\string#2} doesn't work: the command `\string#2' is (not yet?) known or not known in this context}% + \else + \begingroup + \pgfprofile@cs@to@name{#2}% + \let\pgfprofilenew@cmdname=\pgfretval + \def\pgfprofile@temp{#1}% + \ifx\pgfprofile@temp\pgfutil@empty + \edef\pgfprofilenew@profilerentryname{\pgfprofilecs\pgfprofilenew@cmdname}% + \else + \edef\pgfprofilenew@profilerentryname{#1}% + \fi + \expandafter\global\expandafter\let\csname pgfprofile@name@for@\pgfprofilenew@cmdname\endcsname=\pgfprofilenew@profilerentryname + \pgfprofilenew{\pgfprofilenew@profilerentryname}% + \expandafter\gdef\csname b@pgfprofile@show@\pgfprofilenew@profilerentryname\endcsname{0}% + \expandafter\global\expandafter\let\csname pgfprofile@orig@\pgfprofilenew@cmdname\endcsname=#2% + \toks0={#3}% + \edef\pgfprofile@temp{\the\toks0}% + \def\pgfprofile@tempb{}% + \ifx\pgfprofile@temp\pgfprofile@tempb + \expandafter\global\expandafter\let\csname pgfprofile@repl@\pgfprofilenew@cmdname\endcsname=\pgfprofileinvokecommand@uptoonearg + \else + \expandafter\gdef\csname pgfprofile@repl@\pgfprofilenew@cmdname\endcsname#3{% + \pgfprofile@invokeorig{#4}% + }% + \fi + \xdef#2{\noexpand\pgfprofileinvokecommand{\pgfprofilenew@cmdname}}% + \endgroup + \fi +}% + +\def\pgfprofileshowinvocationsfor#1{% + \pgfutil@ifundefined{b@pgfprofile@show@#1}{% + \pgferror{\string\pgfprofileshowinvocationsfor{#1} doesn't work: the argument is no profiler entry}% + }{% + \expandafter\gdef\csname b@pgfprofile@show@#1\endcsname{1}% + \expandafter\gdef\csname b@pgfprofile@show@edef@#1\endcsname{0}% + }% +}% +\def\pgfprofileshowinvocationsexpandedfor#1{% + \pgfutil@ifundefined{b@pgfprofile@show@#1}{% + \pgferror{\string\pgfprofileshowinvocationsfor{#1} doesn't work: the argument is no profiler entry}% + }{% + \expandafter\gdef\csname b@pgfprofile@show@#1\endcsname{1}% + \expandafter\gdef\csname b@pgfprofile@show@edef@#1\endcsname{1}% + }% +}% + +\def\pgfprofile@no@optional@arg@text{}% +\def\pgfprofileinvokecommand#1{% + \pgfutil@ifnextchar[{\pgfprofileinvokecommand@{#1}}{\pgfprofileinvokecommand@{#1}[]}% +}% +\def\pgfprofileinvokecommand@#1[#2]{% + \def\pgfprofileinvokecommand@cs{#1}% + \def\pgfprofileinvokecommand@optarg{#2}% + \edef\pgfprofileinvokecommand@profilerentryname{\csname pgfprofile@name@for@#1\endcsname}% + \csname pgfprofile@repl@#1\endcsname% +}% + +\def\pgfprofile@invokeorig#1{% + \begingroup + \toks1=\expandafter{\pgfprofileinvokecommand@optarg}% + \toks2={#1}% + \toks3=\expandafter{\csname pgfprofile@orig@\pgfprofileinvokecommand@cs\endcsname}% + \ifx\pgfprofileinvokecommand@optarg\pgfprofile@no@optional@arg@text + \xdef\pgfprofile@invokeorig@doitfinally{\the\toks3 \the\toks2 }% + \else + \xdef\pgfprofile@invokeorig@doitfinally{\the\toks3[\the\toks1]\the\toks2 }% + \fi + \if1\csname b@pgfprofile@show@\pgfprofileinvokecommand@profilerentryname\endcsname + \pgfprofile@orig@show + \fi + \endgroup + \edef\pgfprofile@temp{{\pgfprofileinvokecommand@cs}{\pgfprofileinvokecommand@profilerentryname}}% + \expandafter\pgfprofile@invokeorig@\pgfprofile@temp% +}% +\def\pgfprofile@orig@show{% + \toks4=\expandafter{\csname\pgfprofileinvokecommand@cs\endcsname}% + \ifx\pgfprofileinvokecommand@optarg\pgfprofile@no@optional@arg@text + \def\pgfprofile@orig@show@args{\the\toks2 }% + \else + \def\pgfprofile@orig@show@args{[\the\toks1] \the\toks2 }% + \fi + \if1\csname b@pgfprofile@show@edef@\pgfprofileinvokecommand@profilerentryname\endcsname + \edef\pgfprofile@orig@show@args{\pgfprofile@orig@show@args}% + \edef\pgfprofile@orig@show@args{\pgfprofile@orig@show@args}% + \fi + \pgf@typeout{pgflibraryprofiler: calling + \#\csname c@pgfprofile@numinvocations@\pgfprofileinvokecommand@profilerentryname\endcsname\space + (\the\toks4 \pgfprofile@orig@show@args)}% +}% + +\def\pgfprofile@invokeorig@#1#2{% + \pgfprofileifisrunning{#2}{% + \pgfprofile@invokeorig@doitfinally% + }{% + \pgfprofilestart{#2}% + \pgfprofile@invokeorig@doitfinally% + \pgfprofileend{#2}% + }% +}% + + +\def\pgfprofileinvokecommand@uptoonearg{% + \pgfutil@ifnextchar\bgroup{\pgfprofileinvokecommand@onearg}{\pgfprofileinvokecommand@noarg}% +}% +\def\pgfprofileinvokecommand@onearg#1{% + \pgfprofile@invokeorig{{#1}}% +}% +\def\pgfprofileinvokecommand@noarg{% + \pgfprofile@invokeorig{}% +}% + + + +\def\pgfprofilestart#1{% + \pgfprofileifisrunning{#1}{% + \relax + }{% + \expandafter\xdef\csname c@pgfprofile@elapsed@at@start@#1\endcsname{\the\pgfutil@pdfelapsedtime}% + \expandafter\gdef\csname c@pgfprofile@subtractforself@#1\endcsname{0}% + \pgfprofile@advance{c@pgfprofile@numinvocations@#1}{1}% + \pgfprofilestackpush{#1}% + }% + \pgfprofile@advance{c@pgfprofile@semaphor@#1}{1}% +}% + +\def\pgfprofileend#1{% + \pgfprofile@advance{c@pgfprofile@semaphor@#1}{-1}% + \pgfprofileifisrunning{#1}{% + \relax + }{% + \begingroup + \c@pgf@countb=\pgfutil@pdfelapsedtime\relax + \advance\c@pgf@countb by-\csname c@pgfprofile@elapsed@at@start@#1\endcsname\relax + \pgfprofilestackpop\pgfretval + \edef\pgfprofile@temp{#1}% + \ifx\pgfprofile@temp\pgfretval + \else + \pgf@typeout{pgflibraryprofiler WARNING: possible error in self time computation...}% + \fi + \pgfprofilestackifempty{% + \relax + }{% + \pgfprofilestacktop\pgfretval + \pgfprofile@advance{c@pgfprofile@subtractforself@\pgfretval}{\c@pgf@countb}% + }% + \pgfprofile@advance{c@pgfprofile@elapsedtotal@#1}{\c@pgf@countb}% + \advance\c@pgf@countb by-\csname c@pgfprofile@subtractforself@#1\endcsname\relax + \pgfprofile@advance{c@pgfprofile@elapsedself@#1}{\c@pgf@countb}% + \endgroup + }% +}% + +\def\pgfprofileifisrunning#1#2#3{% + \ifnum\csname c@pgfprofile@semaphor@#1\endcsname=0 \def\pgfprofileifisrunning@next{#3}\else \def\pgfprofileifisrunning@next{#2}\fi + \pgfprofileifisrunning@next +}% + +\def\pgfprofilesetrel#1{\edef\pgfprofile@rel{#1}}% + +\def\pgfprofilepostprocess{% + \begingroup + \c@pgf@countb=\time + \divide\c@pgf@countb by60 + \c@pgf@countd=\c@pgf@countb + \multiply\c@pgf@countd by60 + \c@pgf@countc=\time + \advance\c@pgf@countc by-\c@pgf@countd + \immediate\openout\w@pgf@writea=\jobname.profiler.\the\year-\pgfprofiletotwodigitstr\month-\pgfprofiletotwodigitstr\day_\pgfprofiletotwodigitstr\c@pgf@countb h_\pgfprofiletotwodigitstr\c@pgf@countc m.dat + \immediate\write\w@pgf@writea{% + \pgfprofile@percent relative values are measured against the totaltime of `\pgfprofile@rel'.% + }% + \pgf@typeout{pgflibraryprofiler: relative values are measured against the totaltime of `\pgfprofile@rel'.}% + \immediate\write\w@pgf@writea{% + profilerentry\pgfprofile@TAB + totaltime[s]\pgfprofile@TAB + totaltime[percent]\pgfprofile@TAB + selftime[s]\pgfprofile@TAB + selftime[percent]\pgfprofile@TAB + numinvocations\pgfprofile@TAB}% + \pgfprofileifisrunning{\pgfprofile@rel}{% + \pgfprofileend{\pgfprofile@rel}% + }{}% + \pgf@xa=\csname c@pgfprofile@elapsedtotal@\pgfprofile@rel\endcsname sp + \edef\pgfprofiletotaltime{\pgf@sys@tonumber\pgf@xa}% + \pgfmathreciprocal@{\pgfprofiletotaltime}% + \let\pgfprofiletotaltime@inv=\pgfmathresult + \pgfprofile@all@registered@list@foreach{% + \pgfprofileifisrunning{##1}{% + \pgfprofileend{##1}% + }{}% + \pgfprofilepostprocess@single{##1}% + }% + \immediate\write\w@pgf@writea{% + \pgfprofile@percent\space vim: ts=40 nowrap nostartofline + }% + \immediate\closeout\w@pgf@writea + \endgroup +}% + +{% +\catcode`\[=1 % +\catcode`\]=2 % +\catcode`\{=12 % +\catcode`\}=12 % +\catcode`\^^I=12 +\gdef\pgfprofile@lbrace[{]% +\gdef\pgfprofile@rbrace[}]% +\gdef\pgfprofile@TAB[^^I]% +] +{ +\catcode`\%=12 \gdef\pgfprofile@percent{%}} + +\def\pgfprofilepostprocess@single#1{% + \begingroup + \pgf@xa=\csname c@pgfprofile@elapsedtotal@#1\endcsname sp + \pgf@xb=\csname c@pgfprofile@elapsedself@#1\endcsname sp + \pgf@ya=\pgfprofiletotaltime@inv\pgf@xa + \pgf@yb=\pgfprofiletotaltime@inv\pgf@xb + \multiply\pgf@ya by100 + \multiply\pgf@yb by100 + \edef\pgfprofilecur@total{\pgf@sys@tonumber\pgf@xa}% + \edef\pgfprofilecur@self{\pgf@sys@tonumber\pgf@xb}% + \edef\pgfprofilecur@total@rel{\pgf@sys@tonumber\pgf@ya}% + \edef\pgfprofilecur@self@rel{\pgf@sys@tonumber\pgf@yb}% + \pgf@typeout{ + pgflibraryprofiler(#1) + \pgfprofile@lbrace + total time=\pgfprofilecur@total sec; (\pgfprofilecur@total@rel\pgfprofile@percent) + self time=\pgfprofilecur@self sec; (\pgfprofilecur@self@rel\pgfprofile@percent) + invocations=\csname c@pgfprofile@numinvocations@#1\endcsname; + \pgfprofile@rbrace + }% + \immediate\write\w@pgf@writea{% + #1\pgfprofile@TAB + \pgfprofilecur@total\pgfprofile@TAB + \pgfprofilecur@total@rel\pgfprofile@TAB + \pgfprofilecur@self\pgfprofile@TAB + \pgfprofilecur@self@rel\pgfprofile@TAB + \csname c@pgfprofile@numinvocations@#1\endcsname\pgfprofile@TAB + }% + \endgroup +}% +\long\def\pgfprofileforeachentryinCSV#1#2{% + \long\def\pgfprofileinvokeforeach@@##1{#2}% + \pgfprofileforeachentryinCSVisterminated@loop#1,\pgfeov +}% +\long\def\pgfprofileforeachentryinCSVisterminated@loop{% + \pgfutil@ifnextchar\pgfeov{\pgfutil@gobble}{\pgfprofileforeachentryinCSV@next}% +}% +\long\def\pgfprofileforeachentryinCSV@next#1,{% + \pgfprofileinvokeforeach@@{#1}% + \pgfprofileforeachentryinCSVisterminated@loop% +}% + +\xdef\pgfprofile@all@registered@list{}% +\xdef\pgfprofile@currently@running@list{}% + +\def\pgfprofile@all@registered@list@add#1{% + \ifx\pgfprofile@all@registered@list\pgfutil@empty + \xdef\pgfprofile@all@registered@list{#1}% + \else + \xdef\pgfprofile@all@registered@list{\pgfprofile@all@registered@list,#1}% + \fi +}% + +\def\pgfprofile@all@registered@list@foreach#1{% + \expandafter\pgfprofileforeachentryinCSV\expandafter{\pgfprofile@all@registered@list}{#1}% +}% + +\def\pgfprofile@advance#1#2{% + \begingroup + \c@pgf@counta=\csname #1\endcsname\relax + \advance\c@pgf@counta by#2\relax + \expandafter\xdef\csname #1\endcsname{\the\c@pgf@counta}% + \endgroup +}% + +\def\pgfprofile@cs@to@name@#1#2\relax{\def\pgfretval{#2}} + +\def\pgfprofile@cs@to@name#1{% + \expandafter\pgfprofile@cs@to@name@\string#1\relax +}% + +\newcount\c@pgfprofile@stacktop + +\c@pgfprofile@stacktop=-1 +\def\pgfprofilestackpush#1{% + \global\advance\c@pgfprofile@stacktop by1 + \expandafter\xdef\csname pgfprofile@stack@\the\c@pgfprofile@stacktop\endcsname{#1}% +}% +\def\pgfprofilestackpop#1{% + \pgfprofilestacktop#1% + \global\advance\c@pgfprofile@stacktop by-1 +}% +\def\pgfprofilestacktop#1{% + \expandafter\let\expandafter#1\csname pgfprofile@stack@\the\c@pgfprofile@stacktop\endcsname +}% +\def\pgfprofilestackifempty#1#2{% + \ifnum\c@pgfprofile@stacktop<0 #1\else #2\fi +}% + + +\def\pgfprofiletotwodigitstr#1{\ifnum#1<10 0\the#1\else\the#1\fi}% + +\pgfprofilenew{main job}% +\pgfprofilestart{main job}% +\expandafter\xdef\csname c@pgfprofile@elapsed@at@start@main job\endcsname{0}% +\pgfprofilesetrel{main job}% + +\pgfutil@ifundefined{AtEndDocument}{% +}{% + \pgfprofilenew{preamble} + \pgfprofilestart{preamble} + \expandafter\xdef\csname c@pgfprofile@elapsed@at@start@preamble\endcsname{0}% + \AtBeginDocument{\pgfprofileend{preamble}}% + \AtEndDocument{\pgfprofilepostprocess}% +}% +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryshadings.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryshadings.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..95437bca50cc9548e0598263b845726f57eb5884 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibraryshadings.code.tex @@ -0,0 +1,351 @@ + +\ProvidesFileRCS{pgflibraryshadings.code.tex} + + + +\pgfdeclarefunctionalshading[black]{color wheel white center} +{\pgfpoint{-50bp}{-50bp}} +{\pgfpoint{50bp}{50bp}} +{} +{ % + 2 copy % + 2 copy abs exch abs add 0.0001 ge + {atan 360.0 div} % + { pop } % + ifelse % + 3 1 roll % + dup mul % + exch dup mul % + add sqrt % + 25.0 div % + dup 1.0 ge % + { pop 1.0 }{} ifelse % + 1.0 % + 3 2 roll 6.0 mul dup 4 1 roll % + floor cvr % + dup 5 1 roll % + 3 index sub neg % + 1.0 3 index sub % + 2 index mul % + 6 1 roll % + dup 3 index mul neg 1.0 add % + 2 index mul % + 7 1 roll % + neg 1.0 add % + 2 index mul neg 1.0 add % + 1 index mul % + 7 2 roll % + pop pop % + dup 0.5 le % + { % + pop exch pop + } + { dup 1.5 le % + { % + pop exch 4 1 roll exch pop + } + { dup 2.5 le % + { % + pop 4 1 roll pop + } + { dup 3.5 le % + { % + pop exch 4 2 roll pop + } + { dup 4.5 le % + { % + pop exch pop 3 -1 roll + } + { % + pop 3 1 roll exch pop + } + ifelse + } + ifelse % + } + ifelse % + } + ifelse % + } + ifelse % + \ifpgfshadingmodelcmyk + \pgffuncshadingrgbtocmyk + \fi + \ifpgfshadingmodelgray + \pgffuncshadingrgbtogray + \fi +}% + +\pgfdeclarefunctionalshading[black]{color wheel black center} +{\pgfpoint{-50bp}{-50bp}} +{\pgfpoint{50bp}{50bp}} +{} +{ % + 2 copy % + 2 copy abs exch abs add 0.0001 ge + {atan 360.0 div} % + { pop } % + ifelse % + 3 1 roll % + dup mul % + exch dup mul % + add sqrt % + 25.0 div % + dup 1.0 ge % + { pop 1.0 }{} ifelse % + 1.0 exch % + 3 2 roll 6.0 mul dup 4 1 roll % + floor cvr % + dup 5 1 roll % + 3 index sub neg % + 1.0 3 index sub % + 2 index mul % + 6 1 roll % + dup 3 index mul neg 1.0 add % + 2 index mul % + 7 1 roll % + neg 1.0 add % + 2 index mul neg 1.0 add % + 1 index mul % + 7 2 roll % + pop pop % + dup 0.5 le % + { % + pop exch pop + } + { dup 1.5 le % + { % + pop exch 4 1 roll exch pop + } + { dup 2.5 le % + { % + pop 4 1 roll pop + } + { dup 3.5 le % + { % + pop exch 4 2 roll pop + } + { dup 4.5 le % + { % + pop exch pop 3 -1 roll + } + { % + pop 3 1 roll exch pop + } + ifelse + } + ifelse % + } + ifelse % + } + ifelse % + } + ifelse % + \ifpgfshadingmodelcmyk + \pgffuncshadingrgbtocmyk + \fi + \ifpgfshadingmodelgray + \pgffuncshadingrgbtogray + \fi +}% + +\pgfdeclarefunctionalshading[black]{color wheel} +{\pgfpoint{-50bp}{-50bp}} +{\pgfpoint{50bp}{50bp}} +{} +{ % + 2 copy abs exch abs add 0.0001 ge + {atan 360.0 div} % + { pop } % + ifelse % + 1.0 1.0 % + 3 2 roll 6.0 mul dup 4 1 roll % + floor cvr % + dup 5 1 roll % + 3 index sub neg % + 1.0 3 index sub % + 2 index mul % + 6 1 roll % + dup 3 index mul neg 1.0 add % + 2 index mul % + 7 1 roll % + neg 1.0 add % + 2 index mul neg 1.0 add % + 1 index mul % + 7 2 roll % + pop pop % + dup 0.5 le % + { % + pop exch pop + } + { dup 1.5 le % + { % + pop exch 4 1 roll exch pop + } + { dup 2.5 le % + { % + pop 4 1 roll pop + } + { dup 3.5 le % + { % + pop exch 4 2 roll pop + } + { dup 4.5 le % + { % + pop exch pop 3 -1 roll + } + { % + pop 3 1 roll exch pop + } + ifelse + } + ifelse % + } + ifelse % + } + ifelse % + } + ifelse % + \ifpgfshadingmodelcmyk + \pgffuncshadingrgbtocmyk + \fi + \ifpgfshadingmodelgray + \pgffuncshadingrgbtogray + \fi +}% + + + +\colorlet{lower left}{white}% +\colorlet{lower right}{white}% +\colorlet{upper left}{white}% +\colorlet{upper right}{white}% + +\pgfdeclarefunctionalshading[lower left,lower right,upper left,upper right]{bilinear interpolation} +{\pgfpointorigin} +{\pgfpoint{100bp}{100bp}} +{ + \pgfshadecolortorgb{lower left}{\pgf@lib@shadings@ll}\pgfshadecolortorgb{lower right}{\pgf@lib@shadings@lr} + \pgfshadecolortorgb{upper right}{\pgf@lib@shadings@ur}\pgfshadecolortorgb{upper left}{\pgf@lib@shadings@ul} +}{ + 25 sub 50 div exch 25 sub 50 div 2 copy % + neg 1 add exch neg 1 add % + 3 1 roll 2 copy exch 5 2 roll 6 copy 6 copy % + \pgf@lib@shadings@llred mul exch \pgf@lib@shadings@lrred mul add mul % + 4 1 roll + \pgf@lib@shadings@urred mul exch \pgf@lib@shadings@ulred mul add mul + add + 13 1 roll + \pgf@lib@shadings@llgreen mul exch \pgf@lib@shadings@lrgreen mul add mul % + 4 1 roll + \pgf@lib@shadings@urgreen mul exch \pgf@lib@shadings@ulgreen mul add mul + add + 7 1 roll + \pgf@lib@shadings@llblue mul exch \pgf@lib@shadings@lrblue mul add mul % + 4 1 roll + \pgf@lib@shadings@urblue mul exch \pgf@lib@shadings@ulblue mul add mul + add + \ifpgfshadingmodelcmyk + \pgffuncshadingrgbtocmyk + \fi + \ifpgfshadingmodelgray + \pgffuncshadingrgbtogray + \fi +}% + + + +\pgfdeclarefunctionalshading[black]{Mandelbrot set} +{\pgfpoint{-50bp}{-50bp}} +{\pgfpoint{50bp}{50bp}}{} +{ + 12.5 div exch 12.5 div exch + 1 index 1 index + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul 1 index dup mul add + 4 lt { + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul 1 index dup mul add + 4 lt { + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + 1 index dup mul % + 1 index dup mul % + sub % + 4 index add % + 3 1 roll + mul 2 mul % + 2 index add % + } { pop pop 1000.0 1000.0 } ifelse + } { pop pop 1000.0 1000.0 } ifelse + dup mul exch + dup mul + add sqrt + dup 4 1 roll + 2 gt { pop pop 2.0 exch div 1.0 exch sub dup dup} {pop pop pop 0.0 0.0 0.0} ifelse + \ifpgfshadingmodelcmyk + \pgffuncshadingrgbtocmyk + \fi + \ifpgfshadingmodelgray + \pgffuncshadingrgbtogray + \fi +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarysnakes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarysnakes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e6319bacee96d39d77c15a8ebc3e3dd6b57654a2 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarysnakes.code.tex @@ -0,0 +1,8 @@ + +\ProvidesFileRCS{pgflibrarysnakes.code.tex} + +\pgfwarning{Snakes have been superseded by decorations. Use the decoration libraries instead of the snakes library}% + +\usepgflibrary{decorations.pathmorphing,decorations.pathreplacing,decorations.shapes}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarysvg.path.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarysvg.path.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3dc1a7b8a14c30a74587370acff572e0a2ba70af --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarysvg.path.code.tex @@ -0,0 +1,735 @@ + +\ProvidesFileRCS{pgflibrarysvg.path.code.tex} + + +\usepgfmodule{parser}% + + + +\def\pgfpathsvg#1{% + \let\pgf@lib@svg@finish@prev\relax% + {% + \pgftransforminvert% + \pgf@process{\pgfpointtransformed{\pgfqpoint{\pgf@path@lastx}{\pgf@path@lasty}}}% + }% + \pgf@lib@svg@last@x\pgf@x% + \pgf@lib@svg@last@y\pgf@y% + \let\pgf@lib@svg@num=\pgfutil@empty% + \let\pgf@lib@svg@exp=\pgfutil@empty% + \pgfparserparse{svgpath}#1"% +}% + + + +\newdimen\pgf@lib@svg@last@x +\newdimen\pgf@lib@svg@last@y +\newdimen\pgf@lib@svg@last@c@x +\newdimen\pgf@lib@svg@last@c@y + +\newcount\pgf@lib@svg@count +\newcount\pgf@lib@svg@max@num + +\newif\pgf@lib@svg@relative + + + + +\def\pgf@lib@svg@clear@bezier@quad{% + \let\pgf@lib@svg@bezier@last=\pgfutil@empty + \let\pgf@lib@svg@quad@last=\pgfutil@empty +}% +\pgf@lib@svg@clear@bezier@quad + + + +\pgfparserdef{svgpath}{all}{the letter M} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@moveto}% +}% + +\def\pgf@lib@svg@moveto{% + \pgf@lib@svg@clear@bezier@quad% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{0}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{1}pt% + \pgfpathmoveto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@lineto}% +}% + + + +\pgfparserdef{svgpath}{all}{the letter m} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@moveto@rel}% +}% + +\def\pgf@lib@svg@moveto@rel{% + \pgf@lib@svg@clear@bezier@quad% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{0}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{1}pt% + \pgfpathmoveto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@lineto@rel}% +}% + + + +\pgfparserdef{svgpath}{all}{the letter L} +{% + \pgf@lib@svg@finish@prev% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@lineto}% +}% + +\def\pgf@lib@svg@lineto{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{0}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{1}pt% + \pgfpathlineto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@lineto}% + \fi +}% + + + +\pgfparserdef{svgpath}{all}{the letter l} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@lineto@rel}% +}% + +\def\pgf@lib@svg@lineto@rel{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{0}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{1}pt% + \pgfpathlineto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@lineto@rel}% + \fi +}% + + + +\pgfparserdef{svgpath}{all}{the letter Z} +{% + \pgf@lib@svg@closepath +}% + +\pgfparserdef{svgpath}{all}{the letter z} +{% + \pgf@lib@svg@closepath +}% + +\def\pgf@lib@svg@closepath{% + \pgf@lib@svg@finish@prev + \pgfpathclose + \let\pgf@lib@svg@finish@prev=\relax + \pgf@lib@svg@clear@bezier@quad% + \pgfparserswitch{initial}% +}% + + + +\pgfparserdef{svgpath}{all}{blank space \space}{}% + + + + + +\pgfparserdef{svgpath}{all}{the letter H} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@hlineto}% +}% + +\def\pgf@lib@svg@hlineto{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{0}pt% + \pgfpathlineto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@hlineto}% + \fi +}% + +\pgfparserdef{svgpath}{all}{the letter h} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@hlineto@rel}% +}% + +\def\pgf@lib@svg@hlineto@rel{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{0}pt% + \pgfpathlineto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@hlineto@rel}% + \fi +}% + + + +\pgfparserdef{svgpath}{all}{the letter V} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@vlineto}% +}% + +\def\pgf@lib@svg@vlineto{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{0}pt% + \pgfpathlineto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@vlineto}% + \fi +}% + +\pgfparserdef{svgpath}{all}{the letter v} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@vlineto@rel}% +}% + +\def\pgf@lib@svg@vlineto@rel{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{0}pt% + \pgfpathlineto{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{1}{\pgf@lib@svg@vlineto@rel}% + \fi +}% + + + + + +\pgfparserdef{svgpath}{all}{the letter C} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{6}{\pgf@lib@svg@curveto}% +}% + +\def\pgf@lib@svg@curveto{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \let\pgf@lib@svg@quad@last=\pgfutil@empty% + \edef\pgf@lib@svg@bezier@last{% + \noexpand\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{4}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{5}pt% + \pgfpathcurveto + {\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}% + {\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{6}{\pgf@lib@svg@curveto}% + \fi +}% + + +\pgfparserdef{svgpath}{all}{the letter c} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{6}{\pgf@lib@svg@curveto@rel}% +}% + +\def\pgf@lib@svg@curveto@rel{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \let\pgf@lib@svg@quad@last=\pgfutil@empty% + \pgf@process{\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}}% + \edef\pgf@lib@svg@bezier@last{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfpathcurveto + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}}% + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}}% + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{4}pt}{\pgf@lib@svg@get@num{5}pt}}}% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{4}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{5}pt% + \pgf@lib@svg@read@nums{6}{\pgf@lib@svg@curveto@rel}% + \fi +}% + + + + + +\pgfparserdef{svgpath}{all}{the letter S} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@curveto@smooth}% +}% + +\def\pgf@lib@svg@curveto@smooth{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \ifx\pgf@lib@svg@bezier@last\pgfutil@empty% + \def\pgf@lib@svg@first@cp{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \else + \def\pgf@lib@svg@first@cp{% + \pgfpointadd + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + {\pgfpointdiff + {\pgf@lib@svg@bezier@last}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + }% + }% + \fi + \pgfpathcurveto + {\pgf@lib@svg@first@cp}% + {\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}% + {\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}% + \let\pgf@lib@svg@quad@last=\pgfutil@empty% + \edef\pgf@lib@svg@bezier@last{% + \noexpand\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{2}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{3}pt% + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@curveto@smooth}% + \fi +}% + + +\pgfparserdef{svgpath}{all}{the letter s} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@curveto@rel@smooth}% +}% + +\def\pgf@lib@svg@curveto@rel@smooth{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \ifx\pgf@lib@svg@bezier@last\pgfutil@empty% + \def\pgf@lib@svg@first@cp{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \else + \def\pgf@lib@svg@first@cp{% + \pgfpointadd + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + {\pgfpointdiff + {\pgf@lib@svg@bezier@last}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + }% + }% + \fi + \pgfpathcurveto + {\pgf@lib@svg@first@cp}% + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}}% + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}}% + \let\pgf@lib@svg@quad@last=\pgfutil@empty% + \pgf@process{\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}}% + \edef\pgf@lib@svg@bezier@last{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{2}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{3}pt% + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@curveto@rel@smooth}% + \fi +}% + + + + + +\pgfparserdef{svgpath}{all}{the letter Q} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@quad@curveto}% +}% + +\def\pgf@lib@svg@quad@curveto{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \let\pgf@lib@svg@bezier@last=\pgfutil@empty% + \edef\pgf@lib@svg@quad@last{% + \noexpand\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{2}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{3}pt% + \pgfpathquadraticcurveto + {\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@quad@curveto}% + \fi +}% + + +\pgfparserdef{svgpath}{all}{the letter q} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@quad@curveto@rel}% +}% + +\def\pgf@lib@svg@quad@curveto@rel{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \let\pgf@lib@svg@bezier@last=\pgfutil@empty% + \pgf@process{\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}}% + \edef\pgf@lib@svg@quad@last{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfpathquadraticcurveto + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}}% + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{2}pt}{\pgf@lib@svg@get@num{3}pt}}}% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{2}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{3}pt% + \pgf@lib@svg@read@nums{4}{\pgf@lib@svg@quad@curveto@rel}% + \fi +}% + + + + +\pgfparserdef{svgpath}{all}{the letter T} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@quad@curveto@smooth}% +}% + +\def\pgf@lib@svg@quad@curveto@smooth{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@process{% + \ifx\pgf@lib@svg@quad@last\pgfutil@empty% + \pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}% + \else + \pgfpointadd + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + {\pgfpointdiff + {\pgf@lib@svg@quad@last}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + }% + \fi + }% + \edef\pgf@lib@svg@first@cp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfpathquadraticcurveto + {\pgf@lib@svg@first@cp}% + {\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}% + \let\pgf@lib@svg@bezier@last=\pgfutil@empty% + \let\pgf@lib@svg@quad@last=\pgf@lib@svg@first@cp% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{0}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{1}pt% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@quad@curveto@smooth}% + \fi +}% + + +\pgfparserdef{svgpath}{all}{the letter t} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@quad@curveto@rel@smooth}% +}% + +\def\pgf@lib@svg@quad@curveto@rel@smooth{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@process{% + \ifx\pgf@lib@svg@quad@last\pgfutil@empty% + \pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}% + \else + \pgfpointadd + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + {\pgfpointdiff + {\pgf@lib@svg@quad@last}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + }% + \fi + }% + \edef\pgf@lib@svg@first@cp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgfpathquadraticcurveto + {\pgf@lib@svg@first@cp}% + {\pgfpointadd{\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}{\pgfqpoint{\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}}}% + \let\pgf@lib@svg@bezier@last=\pgfutil@empty% + \let\pgf@lib@svg@quad@last=\pgf@lib@svg@first@cp% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{0}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{1}pt% + \pgf@lib@svg@read@nums{2}{\pgf@lib@svg@quad@curveto@rel@smooth}% + \fi +}% + + + + +\pgfparserdef{svgpath}{all}{the letter A} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{7}{\pgf@lib@svg@arcto}% +}% + +\def\pgf@lib@svg@arcto{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \pgf@lib@svg@last@x=\pgf@lib@svg@get@num{5}pt% + \pgf@lib@svg@last@y=\pgf@lib@svg@get@num{6}pt% + \pgfpatharcto + {\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}% + {\pgf@lib@svg@get@num{2}}% + {\pgf@lib@svg@get@num{3}}% + {\pgf@lib@svg@get@num{4}}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{7}{\pgf@lib@svg@arcto}% + \fi +}% + +\pgfparserdef{svgpath}{all}{the letter a} +{% + \pgf@lib@svg@finish@prev + \pgf@lib@svg@read@nums{7}{\pgf@lib@svg@arcto@rel}% +}% + +\def\pgf@lib@svg@arcto@rel{% + \ifnum\pgf@lib@svg@count=0\relax% + \else% + \pgf@lib@svg@clear@bezier@quad% + \advance\pgf@lib@svg@last@x by\pgf@lib@svg@get@num{5}pt% + \advance\pgf@lib@svg@last@y by\pgf@lib@svg@get@num{6}pt% + \pgfpatharcto + {\pgf@lib@svg@get@num{0}pt}{\pgf@lib@svg@get@num{1}pt}% + {\pgf@lib@svg@get@num{2}}% + {\pgf@lib@svg@get@num{3}}% + {\pgf@lib@svg@get@num{4}}% + {\pgfqpoint{\pgf@lib@svg@last@x}{\pgf@lib@svg@last@y}}% + \pgf@lib@svg@read@nums{7}{\pgf@lib@svg@arcto@rel}% + \fi +}% + + + + + + +\pgfparserdef{svgpath}{all}{the character "} +{% + \pgf@lib@svg@finish@prev + \pgfparserswitch{final}% +}% + + + + + +\def\pgf@lib@svg@read@nums#1#2{% + \pgf@lib@svg@count=0\relax + \pgf@lib@svg@max@num=#1\relax + \pgfparserswitch{num}% + \def\pgf@lib@svg@finish@prev{% + \ifx\pgf@lib@svg@num\pgfutil@empty% + \else% + \ifx\pgf@lib@svg@exp\pgfutil@empty + \else + \pgfmathfloatparsenumber{\pgf@lib@svg@num e\pgf@lib@svg@exp}% + \pgfmathfloattofixed{\pgfmathresult}% + \let\pgf@lib@svg@num=\pgfmathresult + \fi + \expandafter\let\csname pgf@lib@svg@num@\the\pgf@lib@svg@count\endcsname=\pgf@lib@svg@num + \advance\pgf@lib@svg@count by1\relax% + \let\pgf@lib@svg@num=\pgfutil@empty% + \let\pgf@lib@svg@exp=\pgfutil@empty% + \fi + #2% + }% +}% + +\def\pgf@lib@svg@get@num#1{\csname pgf@lib@svg@num@#1\endcsname}% + + +\pgfparserdef{svgpath}{num}{the character ,} +{% + \pgf@lib@svg@handle@spacer +}% +\pgfparserlet{svgpath}{after.}{the character ,}[num]{the character ,} +\pgfparserlet{svgpath}{exp},[num], +\pgfparserlet{svgpath}{exp sign},[num], + +\pgfparserdef{svgpath}{num}{\meaning\pgfutil@sptoken} +{% + \pgf@lib@svg@handle@spacer +}% +\pgfparserlet{svgpath}{after.}{blank space}[num]{blank space} +\pgfparserlet{svgpath}{exp}{blank space}, +\pgfparserlet{svgpath}{exp sign}{blank space}, + +\pgfparserdef{svgpath}{num}{the character -} +{% + \pgf@lib@svg@handle@spacer + \def\pgf@lib@svg@num{-}% +}% +\pgfparserlet{svgpath}{after.}{the character -}[num]{the character -} +\pgfparserlet{svgpath}{exp}-[num]- +\pgfparserdef{svgpath}{num}{the character +} +{% + \pgf@lib@svg@handle@spacer + \def\pgf@lib@svg@num{+}% +} +\pgfparserlet{svgpath}{after.}{the character +}[num]{the character +} +\pgfparserlet{svgpath}{exp}+[num]+ + +\def\pgf@lib@svg@handle@spacer{% + \ifx\pgf@lib@svg@num\pgfutil@empty% + \else + \ifx\pgf@lib@svg@exp\pgfutil@empty + \else + \pgfmathfloatparsenumber{\pgf@lib@svg@num e\pgf@lib@svg@exp}% + \pgfmathfloattofixed{\pgfmathresult}% + \let\pgf@lib@svg@num=\pgfmathresult + \fi + \expandafter\let\csname pgf@lib@svg@num@\the\pgf@lib@svg@count\endcsname=\pgf@lib@svg@num + \advance\pgf@lib@svg@count by1\relax% + \ifnum\pgf@lib@svg@count=\pgf@lib@svg@max@num\relax% + \pgf@lib@svg@finish@prev% + \fi + \let\pgf@lib@svg@num=\pgfutil@empty% + \let\pgf@lib@svg@exp=\pgfutil@empty% + \pgfparserswitch{num}% + \fi +}% + + + +\pgfparserdef{svgpath}{num}e + {% + \pgfparserswitch{exp sign}% + \let\pgf@lib@svg@exp=\pgfutil@empty + } +\pgfparserlet{svgpath}{after.}e[num]e +\pgfparserdef{svgpath}{exp sign}- + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp-}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}+ + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp+}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}0 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp0}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}1 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp1}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}2 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp2}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}3 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp3}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}4 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp4}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}5 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp5}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}6 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp6}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}7 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp7}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}8 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp8}% + \pgfparserswitch{exp}% + } +\pgfparserdef{svgpath}{exp sign}9 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp9}% + \pgfparserswitch{exp}% + } + +\pgfparserdef{svgpath}{exp}0 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp0}% + } +\pgfparserdef{svgpath}{exp}1 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp1}% + } +\pgfparserdef{svgpath}{exp}2 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp2}% + } +\pgfparserdef{svgpath}{exp}3 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp3}% + } +\pgfparserdef{svgpath}{exp}4 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp4}% + } +\pgfparserdef{svgpath}{exp}5 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp5}% + } +\pgfparserdef{svgpath}{exp}6 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp6}% + } +\pgfparserdef{svgpath}{exp}7 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp7}% + } +\pgfparserdef{svgpath}{exp}8 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp8}% + } +\pgfparserdef{svgpath}{exp}9 + {% + \expandafter\def\expandafter\pgf@lib@svg@exp\expandafter{\pgf@lib@svg@exp9}% + } + +\pgfparserdef{svgpath}{num}{the character .} + {% + \expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num.}% + \pgfparserswitch{after.}% + }% +\pgfparserdef{svgpath}{after.}{the character .} + {% + \pgf@lib@svg@handle@spacer + \def\pgf@lib@svg@num{.}% + \pgfparserswitch{after.}% + }% +\pgfparserlet{svgpath}{exp}{the character .}[after.]{the character .} + +\pgfparserdef{svgpath}{all}{the character 0} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num0}}% + +\pgfparserdef{svgpath}{all}{the character 1} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num1}}% + +\pgfparserdef{svgpath}{all}{the character 2} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num2}}% + +\pgfparserdef{svgpath}{all}{the character 3} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num3}}% + +\pgfparserdef{svgpath}{all}{the character 4} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num4}}% + +\pgfparserdef{svgpath}{all}{the character 5} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num5}}% + +\pgfparserdef{svgpath}{all}{the character 6} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num6}}% + +\pgfparserdef{svgpath}{all}{the character 7} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num7}}% + +\pgfparserdef{svgpath}{all}{the character 8} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num8}}% + +\pgfparserdef{svgpath}{all}{the character 9} +{\expandafter\def\expandafter\pgf@lib@svg@num\expandafter{\pgf@lib@svg@num9}}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarytimelines.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarytimelines.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e0e5a4437be77ca673f024733ff32ee41d03aac4 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/pgflibrarytimelines.code.tex @@ -0,0 +1,124 @@ + +\ProvidesFileRCS{pgflibrarytimelines.code.tex} + + + +\usepgfmodule{animations}% + + + +\def\pgftimelinebegin{% + \pgf@timeline@todo@saved=\pgf@timeline@todo% + \begingroup% + \advance\pgf@timeline@depth by1\relax% + \pgf@timeline@todo{}% +}% + +\newcount\pgf@timeline@depth +\newtoks\pgf@timeline@todo +\newtoks\pgf@timeline@todo@saved + + + +\def\pgftimelineend{% + \the\pgf@timeline@todo% + \endgroup% + \global\pgf@timeline@todo=\pgf@timeline@todo@saved% +}% + + + +\def\pgftimelineentry#1#2#3#4{% + \begingroup% + \pgfparsetime{#1}% + \edef\pgf@timeline@whom{#2}% + \edef\pgf@timeline@attr{#3}% + \expandafter\let\expandafter\pgf@timeline@entry\csname pgf@tl@\pgf@timeline@whom @\pgf@timeline@attr @\the\pgf@timeline@depth\endcsname% + \ifx\pgf@timeline@entry\relax% + \edef\pgf@timeline@entry{\noexpand\pgf@timeline@setup{\pgf@timeline@whom}{\pgf@timeline@attr}}% + \fi% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@timeline@entry\expandafter\expandafter\expandafter% + {\expandafter\pgf@timeline@entry\expandafter\pgf@timeline@doentry\expandafter{\pgftimeresult}{#4}}% + \expandafter\global\expandafter\let\csname pgf@tl@\pgf@timeline@whom @\pgf@timeline@attr @\the\pgf@timeline@depth\endcsname\pgf@timeline@entry% + \global\pgf@timeline@todo\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgf@timeline@todo\expandafter\pgf@timeline@handle\csname pgf@tl@\pgf@timeline@whom @\pgf@timeline@attr @\the\pgf@timeline@depth\endcsname}% + \endgroup% +}% + + +\newtoks\pgf@timeline@sort@toks +\countdef\pgf@timeline@sort@count=0\relax% +\countdef\pgf@timeline@count@down=1\relax% +\countdef\pgf@timeline@count@down@next=2\relax% + + +\def\pgf@timeline@handle#1{% + \ifx#1\relax% + \else% + {% + \pgf@timeline@sort@count=1\relax% + #1% + \pgf@timeline@count@down=1\relax% + \pgf@timeline@sort@toks{}% + \pgfutil@loop% + \ifnum\pgf@timeline@count@down<\pgf@timeline@sort@count\relax% + \edef\pgf@temp{\the\pgf@timeline@sort@toks\noexpand\pgf@timeline@donow{\the\dimen\pgf@timeline@count@down}{\the\toks\pgf@timeline@count@down}}% + \pgf@timeline@sort@toks\expandafter{\pgf@temp}% + \advance\pgf@timeline@count@down by1\relax% + \pgfutil@repeat% + \pgf@timeline@compute@duration% + \edef\pgf@temp{\noexpand\pgf@timeline@call@attribute{\pgf@timeline@whom}{\pgf@timeline@attr}{\the\pgf@timeline@sort@toks}} + \expandafter% + \endgroup% + \pgf@temp% + }% + \global\let#1\relax% + \fi% +}% + +\def\pgf@timeline@compute@duration{% + \advance\pgf@timeline@sort@count by-1\relax% + \pgfmathparse{\the\dimen\pgf@timeline@sort@count}% + \global\let\pgf@timeline@duration\pgfmathresult% +}% + + +\def\pgf@timeline@setup#1#2{% + \def\pgf@timeline@whom{#1}% + \def\pgf@timeline@attr{#2}% + \begingroup% +}% + +\def\pgf@timeline@doentry#1#2{% + \dimen\pgf@timeline@sort@count=#1pt\relax% + \toks\pgf@timeline@sort@count{#2}% + \pgf@timeline@count@down\pgf@timeline@sort@count\relax% + \pgfutil@loop% + \ifnum\pgf@timeline@count@down>1\relax% + \pgf@timeline@count@down@next\pgf@timeline@count@down% + \advance\pgf@timeline@count@down@next by-1\relax% + \ifdim\dimen\pgf@timeline@count@down<\dimen\pgf@timeline@count@down@next\relax% + \toks0=\toks\pgf@timeline@count@down% + \dimen0=\dimen\pgf@timeline@count@down% + \toks\pgf@timeline@count@down=\toks\pgf@timeline@count@down@next% + \dimen\pgf@timeline@count@down=\dimen\pgf@timeline@count@down@next% + \toks\pgf@timeline@count@down@next=\toks0\relax% + \dimen\pgf@timeline@count@down@next=\dimen0\relax% + \pgf@timeline@count@down\pgf@timeline@count@down@next\relax% + \else% + \pgf@timeline@count@down1\relax% + \fi% + \pgfutil@repeat% + \advance\pgf@timeline@sort@count by1\relax% +}% + + +\def\pgf@timeline@call@attribute#1#2#3{% + \pgfanimateattributecode{#2}{\pgfkeys{/pgf/animation/whom={#1},/pgf/animation/duration=\pgf@timeline@duration}#3}% +}% + +\def\pgf@timeline@donow#1#2{% + \pgfkeys{/pgf/animation/key time={#1/\pgf@timeline@duration}}% + \pgfkeys{/pgf/animation/value={#2}}% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.ee.IEC.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.ee.IEC.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..cd0438bf9c950129f73eb0981b320fc23c6a0af3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.ee.IEC.code.tex @@ -0,0 +1,596 @@ + + + +\pgfdeclareshape{var resistor IEC} +{% + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgf@yc=.5\pgf@ya + \advance\pgf@yc by.5\pgf@yb + \pgf@xc=-.5\pgf@ya + \advance\pgf@xc by.5\pgf@yb + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yc}} + \advance\pgf@xb by.1pt% + \pgfutil@loop% + \advance\pgf@xa by4\pgf@xc\relax% + \ifdim\pgf@xa<\pgf@xb% + \advance\pgf@xa by-3\pgf@xc% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}}% + \advance\pgf@xa by2\pgf@xc% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@ya}}% + \advance\pgf@xa by\pgf@xc% + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yc}}% + \pgfutil@repeat% + \advance\pgf@xb by-.1pt% + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yc}}% + }% +}% + + + + +\pgfdeclareshape{inductor IEC} +{% + \savedanchor\northeast{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=\pgf@xa% + \advance\pgf@x by .5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y=\pgf@ya% + \advance\pgf@y by\pgf@yb% + }% + \savedanchor\southwest{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=-\pgf@xa% + \advance\pgf@x by -.5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgf@y=-\pgf@ya% + }% + + \anchor{center}{\pgfpointorigin}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + + \anchorborder{% + \ifdim\pgf@y<0pt% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\southwest}% + \advance\pgf@y by-0.5pt% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\pgfqpoint{-\pgf@xa}{-\pgf@ya}}}% + \else% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\northeast}}% + \fi% + }% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xa=-\pgf@x \pgf@ya=0pt + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgf@xc=\pgf@yb% + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{0pt}} + \advance\pgf@xb by.1pt% + \pgfutil@loop% + \advance\pgf@xa by2\pgf@xc\relax% + \ifdim\pgf@xa<\pgf@xb% + \pgfpatharc{180}{0}{\pgf@xc}% + \pgfutil@repeat% + \advance\pgf@xb by-.1pt% + \pgfpathlineto{\pgfqpoint{\pgf@xb}{0pt}}% + }% +}% + + + + + +\pgfdeclareshape{capacitor IEC} +{% + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + }% +}% + + + + + +\pgfdeclareshape{ground IEC} +{% + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \pgfmathsetlength\pgf@xa{.5\pgf@xa+.5\pgf@xb} + \pgfmathsetlength\pgf@yc{.16666\pgf@yb-.16666\pgf@ya} + \advance\pgf@ya by\pgf@yc + \advance\pgf@yb by-\pgf@yc + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \advance\pgf@ya by\pgf@yc + \advance\pgf@yb by-\pgf@yc + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + }% +}% + + + + +\pgfdeclareshape{battery IEC} +{% + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \pgfmathsetlength\pgf@yc{.25\pgf@yb-.25\pgf@ya} + \advance\pgf@ya by\pgf@yc + \advance\pgf@yb by-\pgf@yc + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + }% +}% + + + + +\pgfdeclareshape{breakdown diode IEC} +{% + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgf@xc=.5\pgf@xa \advance\pgf@xc by.5\pgf@xb + \pgf@yc=.5\pgf@ya + \advance\pgf@yc by .5\pgf@yb + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xc}{\pgf@yc}} + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \pgfpathclose + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xc}{\pgf@yc}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + \pgfpathclose + }% + + + \beforebackgroundpath{ + { + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgf@yc=.5\pgf@ya + \advance\pgf@yc by.5\pgf@yb + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yc}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yc}} + \pgfusepathqstroke + \pgf@xc=.5\pgf@xa + \advance\pgf@xc by.5\pgf@xb + \pgftransformshift{\pgfqpoint{\pgf@xc}{\pgf@yc}} + \pgf@yc=.5\pgf@yb + \advance\pgf@yc by-.5\pgf@ya + \pgftransformscale{\pgf@sys@tonumber{\pgf@yc}} + \pgfpathmoveto{\pgfqpoint{-.5pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{-1pt}} + \pgfpathlineto{\pgfqpoint{0pt}{1pt}} + \pgfpathlineto{\pgfqpoint{.5pt}{1pt}} + \pgfusepathqstroke + } + }% +}% + + + + + + + + +\pgfdeclareshape{generic circle IEC} +{% + + \inheritsavedanchors[from=circle ee]% + \inheritanchorborder[from=circle ee]% + \inheritanchor[from=circle ee]{north}% + \inheritanchor[from=circle ee]{north west}% + \inheritanchor[from=circle ee]{north east}% + \inheritanchor[from=circle ee]{center}% + \inheritanchor[from=circle ee]{west}% + \inheritanchor[from=circle ee]{east}% + \inheritanchor[from=circle ee]{south}% + \inheritanchor[from=circle ee]{south west}% + \inheritanchor[from=circle ee]{south east}% + \inheritanchor[from=circle ee]{input}% + \inheritanchor[from=circle ee]{output}% + \inheritbackgroundpath[from=circle ee]% + + \beforebackgroundpath{ + { + \centerpoint% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgftransformshift{} + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgfutil@tempdima by-\pgf@yb% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \pgftransformscale{\pgf@sys@tonumber{\pgfutil@tempdima}} + \pgfkeysvalueof{/pgf/generic circle IEC/before background} + } + }% +}% + + + + +\pgfdeclareshape{generic diode IEC} +{% + + \inheritsavedanchors[from=rectangle ee]% + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \advance\pgf@xb by-.5\pgflinewidth + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \pgf@yc=.5\pgf@ya + \advance\pgf@yc by .5\pgf@yb + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yc}} + \pgfpathclose + }% + + + \beforebackgroundpath{ + { + \pgf@process{\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgf@yc=.5\pgf@ya + \advance\pgf@yc by.5\pgf@yb + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yc}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yc}} + \pgfusepathqstroke + \pgftransformshift{\pgfqpoint{\pgf@xb}{\pgf@yc}} + \pgf@yc=.5\pgf@yb + \advance\pgf@yc by-.5\pgf@ya + \pgftransformscale{\pgf@sys@tonumber{\pgf@yc}} + \pgfkeysvalueof{/pgf/generic diode IEC/before background} + } + }% +}% + + +\pgfkeys{ + /pgf/generic circle IEC/before background/.initial=, + /pgf/generic diode IEC/before background/.initial=, +}% + + + + + + +\pgfdeclareshape{make contact IEC} +{% + \savedanchor\northeast{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=\pgf@xa% + \advance\pgf@x by .5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y=\pgf@ya% + \advance\pgf@y by\pgf@yb% + }% + \savedanchor\southwest{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=-.5\pgf@xa% + \advance\pgf@x by -.5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgf@y=-\pgf@ya% + }% + + \anchor{center}{\pgfpointorigin}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + + \anchorborder{% + \ifdim\pgf@y<0pt% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\southwest}% + \advance\pgf@y by-0.5pt% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\pgfqpoint{-\pgf@xa}{-\pgf@ya}}}% + \else% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\northeast}}% + \fi% + }% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xa=-\pgf@x \pgf@ya=0pt + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + }% +}% + + + + +\pgfdeclareshape{var make contact IEC} +{% + \savedanchor\northeast{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=\pgf@xa% + \advance\pgf@x by .5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y=\pgf@ya% + \advance\pgf@y by\pgf@yb% + }% + \savedanchor\southwest{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=-.5\pgf@xa% + \advance\pgf@x by -.5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgf@y=-\pgf@ya% + \pgf@xc=0.083333\pgf@x% + \advance\pgf@y by\pgf@xc% + }% + + \anchor{center}{\pgfpointorigin}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + + \anchorborder{% + \ifdim\pgf@y<0pt% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\southwest}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\pgfqpoint{-\pgf@xa}{-\pgf@ya}}}% + \else% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\northeast}}% + \fi% + }% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\northeast}{ + \pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xa=-\pgf@x \pgf@ya=0pt + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgf@xc=\pgf@xa + \pgfutil@tempdima=2\pgf@xb% + \pgfutil@tempdima=0.083333\pgfutil@tempdima% + \advance\pgf@xa by \pgfutil@tempdima + {\pgfpathcircle{\pgfqpoint{\pgf@xa}{0pt}}{\pgfutil@tempdima}} + \pgf@process{\pgfpointnormalised{\pgfpointdiff{\pgfqpoint{\pgf@xa}{0pt}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}}} + \pgf@xc=\pgf@x + \pgf@yc=\pgf@y + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{\pgf@xa}{0pt}}{% + \pgfpointscale{\pgfutil@tempdima}{\pgfqpoint{\pgf@xc}{\pgf@yc}}}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + }% +}% + + + +\pgfdeclareshape{break contact IEC} +{% + \savedanchor\northeast{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=\pgf@xa% + \advance\pgf@x by .5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y=\pgf@ya% + \advance\pgf@y by\pgf@yb% + }% + \savedanchor\southwest{% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x=-.5\pgf@xa% + \advance\pgf@x by -.5\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgf@y=-\pgf@ya% + }% + + \anchor{center}{\pgfpointorigin}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + + \anchorborder{% + \ifdim\pgf@y<0pt% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\southwest}% + \advance\pgf@y by-0.5pt% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\pgfqpoint{-\pgf@xa}{-\pgf@ya}}}% + \else% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{\pgfpointborderrectangle{\pgfqpoint{\pgf@xc}{\the\pgf@yc}}{\northeast}}% + \fi% + }% + + \backgroundpath{ + \pgf@process{\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + \pgf@xa=-\pgf@x \pgf@ya=0pt + \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + \pgf@xc=.2\pgf@xb + \advance\pgf@xc by-.2\pgf@xa + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{0pt}} + \advance\pgf@xb by-\pgf@xc + \pgfpathlineto{\pgfqpoint{\pgf@xb}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + }% +}% + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.ee.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.ee.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..d5bfe9410c933666def9d7bf1a72bd0c18abcae7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.ee.code.tex @@ -0,0 +1,146 @@ + + + + +\pgfdeclareshape{rectangle ee} +{% + \inheritsavedanchors[from=rectangle]% + \inheritanchorborder[from=rectangle]% + \inheritanchor[from=rectangle]{north}% + \inheritanchor[from=rectangle]{north west}% + \inheritanchor[from=rectangle]{north east}% + \inheritanchor[from=rectangle]{center}% + \inheritanchor[from=rectangle]{west}% + \inheritanchor[from=rectangle]{east}% + \inheritanchor[from=rectangle]{mid}% + \inheritanchor[from=rectangle]{mid west}% + \inheritanchor[from=rectangle]{mid east}% + \inheritanchor[from=rectangle]{base}% + \inheritanchor[from=rectangle]{base west}% + \inheritanchor[from=rectangle]{base east}% + \inheritanchor[from=rectangle]{south}% + \inheritanchor[from=rectangle]{south west}% + \inheritanchor[from=rectangle]{south east}% + \inheritbackgroundpath[from=rectangle]% + \anchor{input}{ + \pgf@process{\northeast}% + \pgf@ya=.5\pgf@y% + \pgf@process{\southwest}% + \pgf@y=.5\pgf@y% + \advance\pgf@y by \pgf@ya% + }% + \anchor{output}{% + \pgf@process{\southwest}% + \pgf@ya=.5\pgf@y% + \pgf@process{\northeast}% + \pgf@y=.5\pgf@y% + \advance\pgf@y by \pgf@ya% + }% +}% + +\pgfdeclareshape{circle ee} +{% + \inheritsavedanchors[from=circle]% + \inheritanchorborder[from=circle]% + \inheritanchor[from=circle]{north}% + \inheritanchor[from=circle]{north west}% + \inheritanchor[from=circle]{north east}% + \inheritanchor[from=circle]{center}% + \inheritanchor[from=circle]{west}% + \inheritanchor[from=circle]{east}% + \inheritanchor[from=circle]{mid}% + \inheritanchor[from=circle]{mid west}% + \inheritanchor[from=circle]{mid east}% + \inheritanchor[from=circle]{base}% + \inheritanchor[from=circle]{base west}% + \inheritanchor[from=circle]{base east}% + \inheritanchor[from=circle]{south}% + \inheritanchor[from=circle]{south west}% + \inheritanchor[from=circle]{south east}% + \inheritbackgroundpath[from=circle]% + \anchor{input}{\centerpoint\advance\pgf@x by-\radius}% + \anchor{output}{\centerpoint\advance\pgf@x by\radius}% +}% + + + + +\pgfdeclareshape{direction ee} +{% + \savedanchor\northeast{ + \pgf@x=0pt% + \pgfmathsetlength{\pgf@y}{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y=.5\pgf@y + }% + \savedanchor\southwest{ + \pgfarrowtotallength{\pgfkeysvalueof{/pgf/direction ee arrow}}% + \pgf@x=-\pgf@x% + \pgfmathsetlength{\pgf@y}{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y=-.5\pgf@y + }% + + \inheritanchor[from=rectangle ee]{center}% + \inheritanchor[from=rectangle ee]{north}% + \inheritanchor[from=rectangle ee]{south}% + \inheritanchor[from=rectangle ee]{east}% + \inheritanchor[from=rectangle ee]{west}% + \inheritanchor[from=rectangle ee]{north east}% + \inheritanchor[from=rectangle ee]{north west}% + \inheritanchor[from=rectangle ee]{south east}% + \inheritanchor[from=rectangle ee]{south west}% + \inheritanchor[from=rectangle ee]{input}% + \inheritanchor[from=rectangle ee]{output}% + \inheritanchorborder[from=rectangle ee]% + \nodeparts{}% + + \behindbackgroundpath{ + \pgf@process{\southwest} + \pgf@xa=\pgf@x + \pgf@process{\northeast} + \pgf@xb=\pgf@x + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{0pt}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{0pt}} + \pgfusepathqstroke + }% + + \beforebackgroundpath{ + { + \pgfsys@beginscope + \pgfarrowdraw{\pgfkeysvalueof{/pgf/direction ee arrow}}% + \pgfsys@endscope + } + }% +}% + +\pgfkeys{ + /pgf/direction ee arrow/.initial=direction ee, +}% + + + + +\pgfarrowsdeclare{direction ee}{direction ee} +{% + \pgfmathsetlength\pgfutil@tempdima{\pgfgetarrowoptions{direction ee}}% + \pgfutil@tempdima=.5\pgfutil@tempdima + \pgfarrowsleftextend{+-\pgfutil@tempdima} + \pgfarrowsrightextend{+\pgfutil@tempdima} +} +{ + \pgfmathsetlength\pgfutil@tempdima{\pgfgetarrowoptions{direction ee}}% + \pgfsetdash{}{+0pt} + \pgfsetroundjoin + \pgfpathmoveto{\pgfqpoint{-0.5\pgfutil@tempdima}{0.38268343237\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{0.5\pgfutil@tempdima}{0\pgfutil@tempdima}} + \pgfpathlineto{\pgfqpoint{-0.5\pgfutil@tempdima}{-0.38268343237\pgfutil@tempdima}} + \pgfpathclose + \pgfusepathqfillstroke +}% + +\pgfsetarrowoptions{direction ee}{4pt}% + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.IEC.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.IEC.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..309d72724a6bd41015474e34ef3cfeb98ae7fa5a --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.IEC.code.tex @@ -0,0 +1,686 @@ + +\usepgflibrary{shapes.gates.logic}% + +\pgfkeys{/pgf/.cd, + and gate IEC symbol/.initial=$\char`\&$, + nand gate IEC symbol/.initial=$\char`\&$, + or gate IEC symbol/.initial=$\geq1$, + nor gate IEC symbol/.initial=$\geq1$, + xor gate IEC symbol/.initial={$=1$}, + xnor gate IEC symbol/.initial={$=1$}, + not gate IEC symbol/.initial=1, + buffer gate IEC symbol/.initial=1, + logic gate IEC symbol align/.initial=top, + logic gate IEC symbol color/.initial=% +}% + +\pgfkeys{/pgf/logic gate IEC symbol align/.cd, + top/.code=\pgftransformyshift{\innerhalfheight}, + bottom/.code=\pgftransformyshift{-\innerhalfheight}, + left/.code=\pgftransformxshift{-\innerhalfwidth}, + right/.code=\pgftransformxshift{\innerhalfwidth}, +}% + +\def\pgf@lib@sh@logicgates@IEC@foregroundpath#1{% + \dimensions% + {% + \pgftransformshift{\centerpoint}% + \edef\pgf@lib@sh@temp{\pgfkeysvalueof{/pgf/logic gate IEC symbol align}}% + \edef\pgf@lib@sh@@temp{/pgf/logic gate IEC symbol align/.cd, \pgf@lib@sh@temp}% + \expandafter\pgfkeys\expandafter{\pgf@lib@sh@@temp}% + \expandafter\pgftext\expandafter[\pgf@lib@sh@temp]{% + \pgfkeysgetvalue{/pgf/logic gate IEC symbol color}{\pgf@lib@sh@temp}% + \ifx\pgf@lib@sh@temp\pgfutil@empty% + \else% + \expandafter\color\expandafter{\pgf@lib@sh@temp}% + \fi% + \pgfkeysvalueof{/pgf/#1 gate IEC symbol}% + }% + }% +}% + + +\def\pgf@lib@sh@logicgates@dimensions@IEC#1{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \setbox\pgf@hbox\hbox{% + \pgfinterruptpicture + {\pgfkeysvalueof{/pgf/#1 gate IEC symbol}}% + \endpgfinterruptpicture + }% + \pgf@xa.5\wd\pgf@hbox% + \pgf@ya.5\ht\pgf@hbox% + \advance\pgf@ya.5\dp\pgf@hbox% + \ifdim\pgf@x<\pgf@xa% + \pgf@x\pgf@xa% + \fi% + \ifdim\pgf@y<\pgf@ya% + \pgf@y\pgf@ya% + \fi% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \c@pgf@counta\pgf@lib@sh@logicgate@numinputs% + \advance\c@pgf@counta1\relax% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \pgf@yb2.0\pgf@yb% + \advance\pgf@yb\pgflinewidth% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/logic gate input sep}}% + \edef\inputsep{\the\pgf@yc}% + \addtosavedmacro\inputsep% + \ifdim\pgf@yb<\pgf@yc% + \pgf@yb\pgf@yc% + \fi% + \multiply\pgf@yb\c@pgf@counta% + \ifdim\pgf@y<.5\pgf@yb% + \pgf@y.5\pgf@yb% + \fi% + \pgf@xa\pgf@x% + \pgfmathaddtolength\pgf@xa{-\pgfkeysvalueof{/pgf/inner xsep}}% + \edef\innerhalfwidth{\the\pgf@xa}% + \addtosavedmacro\innerhalfwidth% + \pgf@ya\pgf@y% + \pgfmathaddtolength\pgf@ya{-\pgfkeysvalueof{/pgf/inner ysep}}% + \edef\innerhalfheight{\the\pgf@ya}% + \addtosavedmacro\innerhalfheight% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\halfwidth{\the\pgf@x}% + \edef\halfheight{\the\pgf@y}% + \addtosavedmacro\halfwidth% + \addtosavedmacro\halfheight% +}% + +\def\pgf@lib@sh@logicgate@IEC@inputanchor#1{% + \dimensions% + \centerpoint% + \advance\pgf@x-\halfwidth% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-#1\endcsname% + \advance\pgf@x-\invertedradius% + \advance\pgf@x-\outerinvertedradius% + \fi% + \pgfutil@tempdima\halfheight% + \multiply\pgfutil@tempdima2\relax% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \multiply\pgfutil@tempdima#1\relax% + \advance\pgf@y\halfheight% + \advance\pgf@y-\pgfutil@tempdima% +}% + + + +\pgfdeclareshape{and gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@and gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@and gate IEC@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@and gate IEC@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@IEC@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An and gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{and}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid west}{% + \dimensions% + \midpoint% + \advance\pgf@x-\halfwidth}% + \anchor{mid east}{% + \dimensions% + \midpoint% + \advance\pgf@x\halfwidth}% + \anchor{base}{\basepoint}% + \anchor{base west}{% + \dimensions% + \basepoint% + \advance\pgf@x-\halfwidth}% + \anchor{base east}{% + \dimensions% + \basepoint% + \advance\pgf@x\halfwidth}% + \anchor{north}{\dimensions\centerpoint\advance\pgf@y\halfheight}% + \anchor{south}{\dimensions\centerpoint\advance\pgf@y-\halfheight}% + \anchor{east}{\dimensions\centerpoint\advance\pgf@x\halfwidth}% + \anchor{west}{\dimensions\centerpoint\advance\pgf@x-\halfwidth}% + \anchor{north east}{\dimensions\centerpoint\advance\pgf@x\halfwidth\advance\pgf@y\halfheight}% + \anchor{north west}{\dimensions\centerpoint\advance\pgf@x-\halfwidth\advance\pgf@y\halfheight}% + \anchor{south east}{\dimensions\centerpoint\advance\pgf@x\halfwidth\advance\pgf@y-\halfheight}% + \anchor{south west}{\dimensions\centerpoint\advance\pgf@x-\halfwidth\advance\pgf@y-\halfheight}% + \anchor{output}{\dimensions\centerpoint\advance\pgf@x\halfwidth}% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \pgfmathaddtolength\pgf@xc{-\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@yc{-\pgfkeysvalueof{/pgf/outer xsep}}% + {% + \pgftransformshift{\centerpoint}% + \pgfpathrectangle{\pgfqpoint{-\pgf@xc}{-\pgf@yc}}% + {% + \pgf@xc2.0\pgf@xc% + \pgf@yc2.0\pgf@yc% + \pgfqpoint{\pgf@xc}{\pgf@yc}% + }% + \pgfpathclose% + \pgf@xc-\halfwidth% + \advance\pgf@xc-\invertedradius% + \pgf@yc\halfheight% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + }% + }% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{and}}% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \dimensions% + \pgfpointadd{\centerpoint}{\pgfpointborderrectangle{\externalpoint}{\pgfqpoint{\halfwidth}{\halfheight}}}% + }% +}% + + + + + +\pgfdeclareshape{nand gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@nand gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@nand gate IEC@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@nand gate IEC@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@IEC@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{A nand gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{nand}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \anchor{output}{% + \csname pgf@anchor@and gate IEC@east\endcsname% + \advance\pgf@x\invertedradius% + \advance\pgf@x\outerinvertedradius% + }% + \backgroundpath{% + \csname pgf@sh@bg@and gate IEC\endcsname% + \pgfpathcircle{% + \centerpoint% + \advance\pgf@x\halfwidth% + \advance\pgf@x\invertedradius% + }{+\invertedradius}% + }% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{nand}}% + \inheritanchorborder[from=and gate IEC]% +}% + + + + + +\pgfdeclareshape{or gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@or gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@or gate IEC@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@or gate IEC@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@IEC@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An or gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{or}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \inheritanchor[from=and gate IEC]{output}% + \inheritbackgroundpath[from=and gate IEC]% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{or}}% + \inheritanchorborder[from=and gate IEC]% +}% + + + + + +\pgfdeclareshape{nor gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@nor gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@nor gate IEC@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@nor gate IEC@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@IEC@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{A nor gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{nor}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \inheritanchor[from=nand gate IEC]{output}% + \inheritbackgroundpath[from=nand gate IEC]% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{nor}}% + \inheritanchorborder[from=and gate IEC]% +}% + + + + + +\pgfdeclareshape{xor gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@xor gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{2}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@xor gate IEC@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@xor gate IEC@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@IEC@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An xor gate must have two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{xor}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \inheritanchor[from=and gate IEC]{output}% + \inheritbackgroundpath[from=and gate IEC]% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{xor}}% + \inheritanchorborder[from=and gate IEC]% +}% + + + + + +\pgfdeclareshape{xnor gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@xnor gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@xnor gate IEC@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@xnor gate IEC@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@IEC@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{A xnor gate must have two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{xnor}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \inheritanchor[from=nand gate IEC]{output}% + \inheritbackgroundpath[from=nand gate IEC]% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{xnor}}% + \inheritanchorborder[from=and gate IEC]% +}% + + + + +\pgfdeclareshape{buffer gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@buffer gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1}% + \expandafter\gdef\csname pgf@anchor@buffer gate IEC@input\endcsname{% + \pgf@lib@sh@logicgate@IEC@inputanchor{1}% + }% + \ifnum\pgf@lib@sh@logicgate@numinputs=0\relax% + \pgferror{A buffer gate must have one inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{xor}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \inheritanchor[from=and gate IEC]{output}% + \inheritbackgroundpath[from=and gate IEC]% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{buffer}}% + \inheritanchorborder[from=and gate IEC]% +}% + + + + + +\pgfdeclareshape{not gate IEC}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@not gate IEC\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1}% + \pgfutil@ifundefined{pgf@anchor@not gate IEC@input}{% + \expandafter\gdef\csname pgf@anchor@not gate IEC@input\endcsname{% + \pgf@lib@sh@logicgate@IEC@inputanchor{1}% + }}{}% + \ifnum\pgf@lib@sh@logicgate@numinputs=0\relax% + \pgferror{A not gate must have one input}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{% + \pgf@lib@sh@logicgates@dimensions@IEC{not}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=and gate IEC]{center}% + \inheritanchor[from=and gate IEC]{mid}% + \inheritanchor[from=and gate IEC]{mid west}% + \inheritanchor[from=and gate IEC]{mid east}% + \inheritanchor[from=and gate IEC]{base}% + \inheritanchor[from=and gate IEC]{base west}% + \inheritanchor[from=and gate IEC]{base east}% + \inheritanchor[from=and gate IEC]{north}% + \inheritanchor[from=and gate IEC]{south}% + \inheritanchor[from=and gate IEC]{east}% + \inheritanchor[from=and gate IEC]{west}% + \inheritanchor[from=and gate IEC]{north east}% + \inheritanchor[from=and gate IEC]{north west}% + \inheritanchor[from=and gate IEC]{south east}% + \inheritanchor[from=and gate IEC]{south west}% + \inheritanchor[from=nand gate IEC]{output}% + \inheritbackgroundpath[from=nand gate IEC]% + \foregroundpath{\pgf@lib@sh@logicgates@IEC@foregroundpath{not}}% + \inheritanchorborder[from=and gate IEC]% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.US.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.US.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..bd3cabd66aaf4bd67d9b0f9f2d204b2605aaa6e5 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.US.code.tex @@ -0,0 +1,2378 @@ + +\usepgflibrary{shapes.gates.logic}% + + +\newif\ifpgfgateanchorsuseboundingrectangle% + + +\pgfkeys{ + /pgf/logic gate anchors use bounding box/.is if=pgfgateanchorsuseboundingrectangle,% +}% + +\def\pgf@lib@sh@logicgates@dimensions@orUS{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \c@pgf@counta\pgf@lib@sh@logicgate@numinputs% + \advance\c@pgf@counta1\relax% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@ya\pgflinewidth% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/logic gate input sep}}% + \pgf@yb.5\pgf@yb% + \ifdim\pgf@ya<\pgf@yb% + \pgf@ya\pgf@yb% + \fi% + \multiply\pgf@ya\c@pgf@counta% + \ifdim\pgf@y<\pgf@ya% + \pgf@y\pgf@ya% + \fi% + \ifdim\pgf@x>\pgf@y% + \pgf@y\pgf@x% + \else% + \pgf@x\pgf@y% + \fi% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \pgf@xb\pgf@x% + \advance\pgf@xb1.732051\pgf@y% + \ifdim\pgf@xb<\pgf@xa% + \pgf@xb\pgf@xa% + \pgf@x0.366025\pgf@xb% + \fi% + \ifdim\pgf@x>\pgf@y% + \pgf@y\pgf@x% + \else% + \pgf@x\pgf@y% + \fi% + \edef\halfside{\the\pgf@x}% + \addtosavedmacro\halfside% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\outerxsep{\the\pgf@xa}% + \edef\outerysep{\the\pgf@ya}% + \addtosavedmacro\outerxsep% + \addtosavedmacro\outerysep% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + \edef\halfwidth{\the\pgf@x}% + \edef\halfheight{\the\pgf@y}% + \addtosavedmacro\halfwidth% + \addtosavedmacro\halfheight% + \pgfextract@process\tipanchor{% + \advance\pgf@x-\pgf@xa% + \advance\pgf@y-\pgf@ya% + \pgf@x-.16666\pgf@x% + \pgf@yb2.0\pgf@y% + \advance\pgf@x.866025\pgf@yb% + \advance\pgf@x1.154701\pgf@xa% + \pgf@y0pt% + }% + \addtosavedmacro\tipanchor% +}% + + +\def\pgf@lib@sh@logicgates@dimensions@andUS{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \c@pgf@counta\pgf@lib@sh@logicgate@numinputs% + \advance\c@pgf@counta1\relax% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@ya\pgflinewidth% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/logic gate input sep}}% + \pgf@yb.5\pgf@yb% + \ifdim\pgf@ya<\pgf@yb% + \pgf@ya\pgf@yb% + \fi% + \multiply\pgf@ya\c@pgf@counta% + \ifdim\pgf@y<\pgf@ya% + \pgf@y\pgf@ya% + \fi% + \ifdim\pgf@x>\pgf@y% + \pgf@y\pgf@x% + \else% + \pgf@x\pgf@y% + \fi% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \pgf@xb2.5\pgf@x% + \ifdim\pgf@xb<\pgf@xa% + \pgf@xb\pgf@xa% + \pgf@x0.4\pgf@xb% + \fi% + \ifdim\pgf@x>\pgf@y% + \pgf@y\pgf@x% + \else% + \pgf@x\pgf@y% + \fi% + \edef\halfside{\the\pgf@x}% + \addtosavedmacro\halfside% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\outerxsep{\the\pgf@xa}% + \edef\outerysep{\the\pgf@ya}% + \addtosavedmacro\outerxsep% + \addtosavedmacro\outerysep% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + \edef\halfwidth{\the\pgf@x}% + \edef\halfheight{\the\pgf@y}% + \addtosavedmacro\halfwidth% + \addtosavedmacro\halfheight% +}% + + +\def\pgf@lib@sh@logicgate@AND@inputanchor#1{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-.166666\pgf@xa% + \advance\pgf@x-\halfwidth% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-#1\endcsname% + \advance\pgf@x-\invertedradius% + \advance\pgf@x-\outerinvertedradius% + \fi% + \pgfutil@tempdima\halfside% + \multiply\pgfutil@tempdima2\relax% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \multiply\pgfutil@tempdima#1\relax% + \advance\pgf@y\halfside% + \advance\pgf@y-\pgfutil@tempdima% +}% + + + + +\pgfdeclareshape{and gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@and gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@and gate US@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@and gate US@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@AND@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An and gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@andUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \csname pgf@anchor@and gate US@east\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{mid west}{% + \csname pgf@anchor@and gate US@west\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \csname pgf@anchor@and gate US@east\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \anchor{base west}{% + \csname pgf@anchor@and gate US@west\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \anchor{east}{% + \dimensions% + \pgf@xa\halfwidth% + \pgf@xb\pgf@xa% + \advance\pgf@xb-\outerxsep% + \centerpoint% + \advance\pgf@x.333333\pgf@xb% + \advance\pgf@x\pgf@xa% + }% + \anchor{output}{\csname pgf@anchor@and gate US@east\endcsname}% + \anchor{north east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@nand gate US@east\endcsname% + \advance\pgf@y\halfheight% + \else + \pgf@xa\halfwidth% + \pgf@ya\halfheight% + \pgf@xb\pgf@xa% + \advance\pgf@xb-\outerxsep% + \centerpoint% + \advance\pgf@x.333333\pgf@xb% + \advance\pgf@x.707106\pgf@xa% + \advance\pgf@y.707106\pgf@ya% + \fi% + }% + \anchor{south east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@nand gate US@east\endcsname% + \advance\pgf@y-\halfheight% + \else + \pgf@xa\halfwidth% + \pgf@ya\halfheight% + \pgf@xb\pgf@xa% + \advance\pgf@xb-\outerxsep% + \centerpoint% + \advance\pgf@x.333333\pgf@xb% + \advance\pgf@x.707106\pgf@xa% + \advance\pgf@y-.707106\pgf@ya% + \fi% + }% + \anchor{north}{% + \dimensions% + \centerpoint% + \advance\pgf@y\halfheight% + }% + \anchor{south}{% + \dimensions% + \centerpoint% + \advance\pgf@y-\halfheight% + }% + \anchor{south west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@y-\halfheight% + }% + \anchor{north west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@y\halfheight% + }% + \anchor{west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + }% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + \pgf@xb.333333\pgf@xc% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yc}}% + {% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{\pgf@yc}}% + \pgfpathclose% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@xa\halfside% + \pgf@x-1.16666\pgf@xa% + \advance\pgf@x-.5\pgflinewidth% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \pgfextract@process\externalpoint{\pgfpointadd{\centerpoint}{\externalpoint}}% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \dimensions% + \pgf@xb\halfside% + \pgf@xc1.66666\pgf@xb% + \advance\pgf@xc\outerxsep% + \pgf@yc\halfheight% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@and gate US@north west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\centerpoint\advance\pgf@x.333333\pgf@xb\advance\pgf@y\pgf@yc}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@x.333333\pgf@xb% + }% + {0}{90}{+\halfwidth and +\halfheight}% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\centerpoint\advance\pgf@x.333333\pgf@xb\advance\pgf@y\pgf@yc}% + {\centerpoint\advance\pgf@x-\pgf@xc\advance\pgf@y\pgf@yc}% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\centerpoint\advance\pgf@x.333333\pgf@xb\advance\pgf@y-\pgf@yc}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@x.333333\pgf@xb% + }% + {270}{360}{+\halfwidth and +\halfheight}% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@and gate US@south west\endcsname}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\centerpoint\advance\pgf@x.333333\pgf@xb\advance\pgf@y-\pgf@yc}% + {\csname pgf@anchor@and gate US@south west\endcsname}% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@and gate US@north west\endcsname}% + {\csname pgf@anchor@and gate US@south west\endcsname}% + \fi% + \fi% + \fi% + }% +}% + + + + + +\pgfdeclareshape{nand gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@nand gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@nand gate US@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@nand gate US@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@AND@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{A nand gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@andUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \inheritanchor[from=and gate US]{mid}% + \inheritanchor[from=and gate US]{mid east}% + \inheritanchor[from=and gate US]{mid west}% + \inheritanchor[from=and gate US]{base}% + \inheritanchor[from=and gate US]{base east}% + \inheritanchor[from=and gate US]{base west}% + \anchor{output}{% + \dimensions + \pgfpointadd{\centerpoint}{% + \pgf@xa\halfside% + \pgf@x1.33333\pgf@xa% + \advance\pgf@x\invertedradius% + \advance\pgf@x\outerinvertedradius% + \advance\pgf@x\outerxsep% + \pgf@y0pt% + }% + }% + \inheritanchor[from=and gate US]{east}% + \inheritanchor[from=and gate US]{north east}% + \inheritanchor[from=and gate US]{south east}% + \inheritanchor[from=and gate US]{north}% + \inheritanchor[from=and gate US]{south}% + \inheritanchor[from=and gate US]{south west}% + \inheritanchor[from=and gate US]{north west}% + \inheritanchor[from=and gate US]{west}% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + \pgf@xb.333333\pgf@xc% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{\pgf@xb}{\pgf@yc}}% + {% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{\pgf@yc}}% + \pgfpathclose% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@xa\halfside% + \pgf@x-1.166666\pgf@xa% + \advance\pgf@x-.5\pgflinewidth% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + {% + \pgfpathcircle{% + \pgf@x1.33333\pgf@xc% + \advance\pgf@x\outerinvertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + }% + }% + \inheritanchorborder[from=and gate US]% +}% + + +\def\pgf@lib@sh@logicgate@OR@inputanchor#1{% + \dimensions% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgfutil@tempdima\halfside% + \multiply\pgfutil@tempdima2\relax% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \multiply\pgfutil@tempdima#1\relax% + \pgf@yc\pgf@ya% + \advance\pgf@yc-\pgfutil@tempdima% + \pgf@xb\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@yb}}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@xc-1.166666\pgf@ya% + \advance\pgf@xc-.866025\pgf@xb% + \advance\pgf@xc\pgfmathresult\pgf@yb% + \advance\pgf@xc\halflinewidth% + \advance\pgf@xc-\outerxsep% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-#1\endcsname% + \advance\pgf@xc-\invertedradius% + \advance\pgf@xc-\outerinvertedradius% + \fi% + \centerpoint% + \advance\pgf@x\pgf@xc% + \advance\pgf@y\pgf@yc% +}% + + +\pgfdeclareshape{or gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@or gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@or gate US@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@or gate US@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@OR@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An or gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\halflinewidth{% + \pgf@x.5\pgflinewidth% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \csname pgf@anchor@or gate US@east\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{mid west}{% + \csname pgf@anchor@or gate US@north west\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \csname pgf@anchor@or gate US@east\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \anchor{base west}{% + \csname pgf@anchor@or gate US@north west\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \anchor{east}{% + \dimensions% + \pgfpointadd{\centerpoint}{\tipanchor}% + }% + \anchor{output}{\csname pgf@anchor@or gate US@east\endcsname}% + \anchor{north east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\halfheight% + \else% + \centerpoint% + \pgf@xa\halfwidth% + \pgf@ya\halfheight% + \pgf@xb\halfside% + \advance\pgf@x-.166666\pgf@xb% + \advance\pgf@xa\pgf@xb% + \advance\pgf@x.5\pgf@xa% + \advance\pgf@y-\pgf@xb% + \advance\pgf@ya\pgf@xb% + \advance\pgf@y.866025\pgf@ya% + \fi% + }% + \anchor{south east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y-\halfheight% + \else + \centerpoint% + \pgf@xa\halfwidth% + \pgf@ya\halfheight% + \pgf@xb\halfside% + \advance\pgf@x-.166666\pgf@xb% + \advance\pgf@xa\pgf@xb% + \advance\pgf@x.5\pgf@xa% + \advance\pgf@y\pgf@xb% + \advance\pgf@ya\pgf@xb% + \advance\pgf@y-.866025\pgf@ya% + \fi% + }% + \anchor{north}{% + \dimensions% + \centerpoint% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@y\halfheight% + \else% + \pgf@ya\halfheight% + \advance\pgf@y.993043\pgf@ya% + \fi% + }% + \anchor{south}{% + \dimensions% + \centerpoint% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@y-\halfheight% + \else% + \pgf@ya\halfheight% + \advance\pgf@y-.993043\pgf@ya% + \fi% + }% + \anchor{south west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \pgf@xa\outerxsep% + \advance\pgf@x-1.732050\pgf@xa% + \advance\pgf@y-\halfheight% + }% + \anchor{north west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \pgf@xa\outerxsep% + \advance\pgf@x-1.732050\pgf@xa% + \advance\pgf@y\halfheight% + }% + \anchor{west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + \else% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@x0.267949\pgf@xa% + \fi% + }% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-.16666\pgf@xc}{\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{30}{\the\pgf@yc}% + }% + \pgf@marshal% + } + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{-30}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \pgfpatharc{-30}{0}{+\pgf@yc}% + } + {% + \pgf@yc2.0\pgf@yc% + \pgfpatharc{0}{30}{+\pgf@yc}% + }% + \pgfpathclose% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgf@xa\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@yb}}% + \let\sineangle\pgfmathresult% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@x-1.166666\pgf@ya% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x\pgfmathresult\pgf@yb% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \pgfextract@process\externalpoint{\pgfpointadd{\centerpoint}{\externalpoint}}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \dimensions% + \pgf@xc\halfside% + \pgf@xc-.166666\pgf@xc% + \ifdim\pgf@xa<\pgf@xc% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@or gate US@north west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@or gate US@north\endcsname% + }% + {\csname pgf@anchor@or gate US@north west\endcsname}% + \else% + \pgfmathsubtract@{360}{\pgfmathresult}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@or gate US@south\endcsname% + }% + {\csname pgf@anchor@or gate US@south west\endcsname}% + \else% + \ifdim\pgf@ya>\pgf@yb% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \advance\pgf@yc-\outerxsep% + \pgfextract@process\point{% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.166666\pgf@xa% + \pgf@xa2.0\pgf@xa% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x-\outerxsep% + }% + {0}{90}{+\pgf@yc}% + }% + \else% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \advance\pgf@yc-\outerxsep% + \pgfextract@process\point{% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.166666\pgf@xa% + \pgf@xa2.0\pgf@xa% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x-\outerxsep% + }% + {270}{360}{+\pgf@yc}% + }% + \fi% + \fi% + \fi% + \else% + \ifdim\pgf@y=0pt\relax% + \csname pgf@anchor@and gate US@east\endcsname% + \else% + \pgf@xc\halfwidth% + \advance\pgf@xc\halfside% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \pgf@xb\halfside% + \pgf@xb-.166666\pgf@xb% + \ifdim\pgf@ya<0pt% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@y\halfside% + \advance\pgf@x\pgf@xb% + }% + {270}{330}{+\pgf@yc}% + \else% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@y-\halfside% + \advance\pgf@x\pgf@xb% + }% + {30}{90}{+\pgf@xc and +\pgf@yc}% + \fi% + \fi% + \fi% + }% +}% + + + + +\pgfdeclareshape{nor gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@nor gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@nor gate US@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@nor gate US@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@OR@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{A nor gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\halflinewidth{% + \pgf@x.5\pgflinewidth% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \inheritanchor[from=or gate US]{center}% + \inheritanchor[from=or gate US]{mid}% + \inheritanchor[from=or gate US]{mid east}% + \inheritanchor[from=or gate US]{mid west}% + \inheritanchor[from=or gate US]{base}% + \inheritanchor[from=or gate US]{base east}% + \inheritanchor[from=or gate US]{base west}% + \inheritanchor[from=or gate US]{east}% + \inheritanchor[from=or gate US]{north east}% + \inheritanchor[from=or gate US]{south east}% + \inheritanchor[from=or gate US]{north}% + \inheritanchor[from=or gate US]{south}% + \inheritanchor[from=or gate US]{south west}% + \inheritanchor[from=or gate US]{north west}% + \inheritanchor[from=or gate US]{west}% + \anchor{output}{% + \dimensions% + \centerpoint% + \pgf@xc\halfside% + \pgf@yc\pgf@xc% + \advance\pgf@x-.166666\pgf@xc% + \pgf@yc2.0\pgf@yc% + \advance\pgf@x.866025\pgf@yc% + \advance\pgf@x\outerinvertedradius% + \advance\pgf@x\invertedradius% + \advance\pgf@x\outerxsep% + }% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-.16666\pgf@xc}{\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{30}{\the\pgf@yc}% + }% + \pgf@marshal% + } + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{-30}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \pgfpatharc{-30}{0}{+\pgf@yc}% + } + {% + \pgf@yc2.0\pgf@yc% + \pgfpatharc{0}{30}{+\pgf@yc}% + }% + \pgfpathclose% + {% + \pgfpathcircle{% + \pgf@x-.166666\pgf@xc% + \pgf@yc2.0\pgf@yc% + \advance\pgf@x.866025\pgf@yc% + \advance\pgf@x\outerinvertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgf@xa\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@yb}}% + \let\sineangle\pgfmathresult% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@x-1.166666\pgf@ya% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x\pgfmathresult\pgf@yb% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + }% + }% + \inheritanchorborder[from=or gate US]% +}% + + + +\def\pgf@lib@sh@logicgate@XOR@inputanchor#1{% + \dimensions% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgfutil@tempdima\halfside% + \multiply\pgfutil@tempdima2\relax% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \multiply\pgfutil@tempdima#1\relax% + \pgf@yc\pgf@ya% + \advance\pgf@yc-\pgfutil@tempdima% + \pgf@xb\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@yb}}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@xc-1.166666\pgf@ya% + \advance\pgf@xc-.866025\pgf@xb% + \advance\pgf@xc\pgfmathresult\pgf@yb% + \advance\pgf@xc\halflinewidth% + \advance\pgf@xc-\outerxsep% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-#1\endcsname% + \advance\pgf@xc-\invertedradius% + \advance\pgf@xc-\outerinvertedradius% + \fi% + \centerpoint% + \advance\pgf@x\pgf@xc% + \advance\pgf@y\pgf@yc% + \pgf@xa\halfside% + \advance\pgf@x-.333333\pgf@xa% +}% + + + + + +\pgfdeclareshape{xor gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@xor gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{2}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@xor gate US@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@xor gate US@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@XOR@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An xor gate must have at two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\halflinewidth{% + \pgf@x.5\pgflinewidth% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \inheritanchor[from=or gate US]{mid east}% + \anchor{mid west}{% + \csname pgf@anchor@xor gate US@north west\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{base}{\basepoint}% + \inheritanchor[from=or gate US]{base east}% + \anchor{base west}{% + \csname pgf@anchor@xor gate US@north west\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \inheritanchor[from=or gate US]{base}% + \inheritanchor[from=or gate US]{output}% + \inheritanchor[from=or gate US]{east}% + \inheritanchor[from=or gate US]{north east}% + \inheritanchor[from=or gate US]{south east}% + \inheritanchor[from=or gate US]{north}% + \inheritanchor[from=or gate US]{south}% + \anchor{south west}{% + \dimensions% + \pgf@xa\halfside% + \pgf@xa-3.232051\pgf@xa% + \pgf@xb\halfside% + \pgf@xb2.0\pgf@xb% + \advance\pgf@xb-\halflinewidth% + \advance\pgf@xa.866025\pgf@xb% + \pgf@ya.5\pgf@xb% + \centerpoint% + \advance\pgf@x\pgf@xa% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@y-\halfheight% + \else% + \advance\pgf@y-\pgf@ya% + \fi% + }% + \anchor{north west}{% + \dimensions% + \pgf@xa\halfside% + \pgf@xa-3.232051\pgf@xa% + \pgf@xb\halfside% + \pgf@xb2.0\pgf@xb% + \advance\pgf@xb-\halflinewidth% + \advance\pgf@xa.866025\pgf@xb% + \pgf@ya.5\pgf@xb% + \centerpoint% + \advance\pgf@x\pgf@xa% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@y\halfheight% + \else% + \advance\pgf@y\pgf@ya% + \fi% + }% + \anchor{west}{% + \dimensions% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgf@xb\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{0}{\pgfmath@tonumber{\pgf@yb}}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@xc-1.166666\pgf@ya% + \advance\pgf@xc-.866025\pgf@xb% + \advance\pgf@xc\pgfmathresult\pgf@yb% + \advance\pgf@xc\halflinewidth% + \advance\pgf@xc-\outerxsep% + \centerpoint% + \advance\pgf@x\pgf@xc% + \pgf@xa\halfside% + \advance\pgf@x-.333333\pgf@xa% + \ifpgfgateanchorsuseboundingrectangle% + \pgf@xa2.0\pgf@xa% + \advance\pgf@x-0.133974\pgf@xa% + \fi% + }% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-.16666\pgf@xc}{\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{30}{\the\pgf@yc}% + }% + \pgf@marshal% + } + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{-30}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + {% + \pgf@yc2.66666\pgf@yc% + \pgfpatharc{-22}{0}{+1.166666\pgf@yc and +\pgf@yc}% + } + {% + \pgf@yc2.66666\pgf@yc% + \pgfpatharc{0}{22}{+1.166666\pgf@yc and +\pgf@yc}% + }% + \pgfpathclose% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgf@xa\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@yb}}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@x-1.5\pgf@ya% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x\pgfmathresult\pgf@yb% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + \pgf@xc\halfside% + \pgf@yc\halfside% + \pgfpathmoveto{\pgfqpoint{-1.5\pgf@xc}{-\pgf@yc}}% + \pgf@yc2.0\pgf@yc% + \pgfmathloop% + \ifnum\pgfmathcounter<61\relax% + {% + \pgfextract@process\point{% + \pgfpointadd{% + \pgf@x\halfside% + \pgf@x-3.232051\pgf@x% + \pgf@y0pt% + }{% + \pgfpointpolar{\pgfmathcounter-30}{+\pgf@yc}% + }% + }% + \pgfpathlineto{\point}% + \pgfpathmoveto{\point}% + } + \repeatpgfmathloop% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \pgfextract@process\externalpoint{\pgfpointadd{\centerpoint}{\externalpoint}}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \dimensions% + \pgf@xc\halfside% + \pgf@xc-.166666\pgf@xc% + \ifdim\pgf@xa<\pgf@xc% + \pgfmathanglebetweenpoints{\centerpoint}% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@xor gate US@north west\endcsname% + }% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@xor gate US@north\endcsname% + }% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@xor gate US@north west\endcsname% + }% + \else% + \pgfmathsubtract@{360}{\pgfmathresult}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@xor gate US@south\endcsname% + }% + {% + \pgfgateanchorsuseboundingrectangletrue% + \csname pgf@anchor@xor gate US@south west\endcsname% + }% + \else% + \ifdim\pgf@ya>\pgf@yb% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \advance\pgf@yc-\outerxsep% + \pgf@process{% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.166666\pgf@xa% + \pgf@xa2.0\pgf@xa% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@x-.166666\pgf@xa% + }% + {0}{90}{+\pgf@yc}% + }% + \else% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \advance\pgf@yc-\outerxsep% + \pgf@process{% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.166666\pgf@xa% + \pgf@xa2.0\pgf@xa% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@x-.166666\pgf@xa% + }% + {270}{360}{+\pgf@yc}% + }% + \fi% + \fi% + \fi% + \else% + \ifdim\pgf@y=0pt\relax% + \csname pgf@anchor@and gate US@east\endcsname% + \else% + \pgf@xc\halfwidth% + \advance\pgf@xc\halfside% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \pgf@xb\halfside% + \pgf@xb-.166666\pgf@xb% + \ifdim\pgf@ya<0pt% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@y\halfside% + \advance\pgf@x\pgf@xb% + }% + {270}{330}{+\pgf@yc}% + \else% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@y-\halfside% + \advance\pgf@x\pgf@xb% + }% + {30}{90}{+\pgf@xc and +\pgf@yc}% + \fi% + \fi% + \fi% + }% +}% + + + + +\pgfdeclareshape{xnor gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@xnor gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{2}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@xnor gate US@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@xnor gate US@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@XOR@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An xnor gate must have two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\halflinewidth{% + \pgf@x.5\pgflinewidth% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \inheritanchor[from=xor gate US]{mid east}% + \inheritanchor[from=xor gate US]{mid west}% + \anchor{base}{\basepoint}% + \inheritanchor[from=xor gate US]{base east}% + \inheritanchor[from=xor gate US]{base west}% + \inheritanchor[from=xor gate US]{base}% + \inheritanchor[from=nor gate US]{output}% + \inheritanchor[from=xor gate US]{east}% + \inheritanchor[from=xor gate US]{north east}% + \inheritanchor[from=xor gate US]{south east}% + \inheritanchor[from=xor gate US]{north}% + \inheritanchor[from=xor gate US]{south}% + \inheritanchor[from=xor gate US]{south west}% + \inheritanchor[from=xor gate US]{north west}% + \inheritanchor[from=xor gate US]{west}% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-.16666\pgf@xc}{\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{30}{\the\pgf@yc}% + }% + \pgf@marshal% + } + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{-30}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + {% + \pgf@yc2.66666\pgf@yc% + \pgfpatharc{-22}{0}{+1.166666\pgf@yc and +\pgf@yc}% + } + {% + \pgf@yc2.66666\pgf@yc% + \pgfpatharc{0}{22}{+1.166666\pgf@yc and +\pgf@yc}% + }% + \pgfpathclose% + {% + \pgfpathcircle{% + \pgf@x-.166666\pgf@xc% + \pgf@yc2.0\pgf@yc% + \advance\pgf@x.866025\pgf@yc% + \advance\pgf@x\outerinvertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@ya\halfside% + \pgf@yb2.0\pgf@ya% + \pgf@xa\pgf@yb% + \advance\pgf@yb-\halflinewidth% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@yb}}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@x-1.5\pgf@ya% + \advance\pgf@x-.866025\pgf@xa% + \advance\pgf@x\pgfmathresult\pgf@yb% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + \pgf@xc\halfside% + \pgf@yc\halfside% + \pgfpathmoveto{\pgfqpoint{-1.5\pgf@xc}{-\pgf@yc}}% + \pgf@yc2.0\pgf@yc% + \pgfmathloop% + \ifnum\pgfmathcounter<61\relax% + {% + \pgfextract@process\point{% + \pgfpointadd{% + \pgf@x\halfside% + \pgf@x-3.232051\pgf@x% + \pgf@y0pt% + }{% + \pgfpointpolar{\pgfmathcounter-30}{+\pgf@yc}% + }% + }% + \pgfpathlineto{\point}% + \pgfpathmoveto{\point}% + } + \repeatpgfmathloop% + }% + }% + \inheritanchorborder[from=xor gate US]% +}% + + + + + + +\pgfdeclareshape{not gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@not gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1}% + \ifnum\pgf@lib@sh@logicgate@numinputs=0\relax% + \pgferror{A not gate must have one input}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\halflinewidth{% + \pgf@x.5\pgflinewidth% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \midpoint% + \pgfutil@tempdima\pgf@y% + \csname pgf@anchor@not gate US@east\endcsname% + \pgf@y\pgfutil@tempdima% + }% + \anchor{mid west}{% + \dimensions% + \pgf@xc\halfside% + \pgf@xc-.833333\pgf@xc% + \advance\pgf@xc-\outerxsep% + \midpoint% + \advance\pgf@x\pgf@xc% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \basepoint% + \pgfutil@tempdima\pgf@y% + \csname pgf@anchor@not gate US@east\endcsname% + \pgf@y\pgfutil@tempdima% + }% + \anchor{base west}{% + \dimensions% + \pgf@xc\halfside% + \pgf@xc-.833333\pgf@xc% + \advance\pgf@xc-\outerxsep% + \basepoint% + \advance\pgf@x\pgf@xc% + }% + \inheritanchor[from=and gate US]{base}% + \anchor{output}{% + \dimensions% + \pgf@xc\halfside% + \centerpoint% + \advance\pgf@x-.166666\pgf@xc% + \pgf@xc2.0\pgf@xc% + \advance\pgf@x.866025\pgf@xc% + \advance\pgf@x\invertedradius% + \advance\pgf@x\outerinvertedradius% + \advance\pgf@x\outerxsep% + }% + \anchor{east}{% + \dimensions% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + }% + \anchor{north}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@north west\endcsname% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@y\pgf@ya% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@y1pt}% + {\csname pgf@anchor@not gate US@north west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \anchor{south}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@south west\endcsname% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@y\pgf@ya% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@y-1pt}% + {\csname pgf@anchor@not gate US@south west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \anchor{south east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@south west\endcsname% + \pgf@ya\pgf@y% + \pgf@process{% + \dimensions% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + }% + \pgf@y\pgf@ya% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@x1pt\advance\pgf@y-1pt}% + {\csname pgf@anchor@not gate US@south west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \anchor{north east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@north west\endcsname% + \pgf@ya\pgf@y% + \pgf@process{% + \dimensions% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + }% + \pgf@y\pgf@ya% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@x1pt\advance\pgf@y1pt}% + {\csname pgf@anchor@not gate US@north west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \anchor{south west}{% + \dimensions% + \pgf@xa\halfside% + \centerpoint% + \advance\pgf@x-.833333\pgf@xa + \advance\pgf@x-\outerxsep% + \advance\pgf@y-1.166666\pgf@xa% + \pgf@ya\outerysep% + \advance\pgf@y-1.565\pgf@ya% + }% + \anchor{north west}{% + \dimensions% + \pgf@xa\halfside% + \centerpoint% + \advance\pgf@x-.833333\pgf@xa + \advance\pgf@x-\outerxsep% + \advance\pgf@y1.166666\pgf@xa% + \pgf@ya\outerysep% + \advance\pgf@y1.565\pgf@ya% + }% + \anchor{input}{% + \dimensions% + \pgf@lib@sh@logicgate@AND@inputanchor{1}% + \pgf@xc\halfside% + \advance\pgf@x.333333\pgf@xc% + }% + \anchor{west}{% + \dimensions% + \pgf@xc\halfside% + \pgf@xc-.833333\pgf@xc% + \advance\pgf@xc-\outerxsep% + \centerpoint% + \advance\pgf@x\pgf@xc% + }% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\tipanchor}% + \pgfpathlineto{\pgfqpoint{-.833333\pgf@xc}{1.166666\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-.833333\pgf@xc}{-1.166666\pgf@yc}}% + \pgfpathlineto{\tipanchor}% + {% + \pgfpathcircle{% + \pgf@x-.166666\pgf@xc% + \pgf@yc2.0\pgf@yc% + \advance\pgf@x.866025\pgf@yc% + \advance\pgf@x\outerinvertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-1\endcsname% + {% + \pgfpathcircle{% + \pgf@xa\halfside% + \pgf@x-.833333\pgf@xa% + \advance\pgf@x-.5\pgflinewidth% + \advance\pgf@x-\invertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + \fi% + }% + }% + \anchorborder{% + \pgf@lib@gates@not@buffer@border{not gate US} + }% +}% + +\def\pgf@lib@gates@not@buffer@border#1{ + \pgfextract@process\externalpoint{}% + \pgfextract@process\externalpoint{\pgfpointadd{\centerpoint}{\externalpoint}}% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \ifx\pgfmathresult\pgf@lib@zero@text% + \csname pgf@anchor@#1@output\endcsname% + \else% + \ifx\pgfmathresult\pgf@lib@onehundredeighty@text% + \csname pgf@anchor@#1@input\endcsname% + \else% + \let\externalangle\pgfmathresult% + \dimensions% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@not gate US@north west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\csname pgf@anchor@not gate US@north west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@not gate US@south west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@not gate US@north west\endcsname}% + {\csname pgf@anchor@not gate US@south west\endcsname}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\csname pgf@anchor@not gate US@south west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + \fi% + \fi% + \fi% +}% + + +\def\pgf@lib@zero@text{0.0}% +\def\pgf@lib@onehundredeighty@text{180.0}% + + + + +\pgfdeclareshape{buffer gate US}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@buffer gate US\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1}% + \ifnum\pgf@lib@sh@logicgate@numinputs=0\relax% + \pgferror{A buffer gate must have one input}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\halflinewidth{% + \pgf@x.5\pgflinewidth% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \midpoint% + \pgfutil@tempdima\pgf@y% + \csname pgf@anchor@buffer gate US@east\endcsname% + \pgf@y\pgfutil@tempdima% + }% + \anchor{mid west}{% + \dimensions% + \pgf@xc\halfside% + \pgf@xc-.833333\pgf@xc% + \advance\pgf@xc-\outerxsep% + \midpoint% + \advance\pgf@x\pgf@xc% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \basepoint% + \pgfutil@tempdima\pgf@y% + \csname pgf@anchor@buffer gate US@east\endcsname% + \pgf@y\pgfutil@tempdima% + }% + \inheritanchor[from=not gate US]{base west}% + \inheritanchor[from=and gate US]{base}% + \anchor{output}{\csname pgf@anchor@buffer gate US@east\endcsname}% + \anchor{east}{% + \dimensions% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \anchor{north}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@north west\endcsname% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@y\pgf@ya% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@y1pt}% + {\csname pgf@anchor@buffer gate US@north west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \anchor{south}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@south west\endcsname% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@y\pgf@ya% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@y-1pt}% + {\csname pgf@anchor@not gate US@south west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \anchor{south east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@south west\endcsname% + \pgfutil@tempdima\pgf@y% + \csname pgf@anchor@buffer gate US@east\endcsname% + \pgf@y\pgfutil@tempdima% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@x1pt\advance\pgf@y-1pt}% + {\csname pgf@anchor@buffer gate US@south west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xc\outerxsep% + \advance\pgf@x2.350943\pgf@xc% + }% + }% + \fi% + }% + \anchor{north east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \csname pgf@anchor@not gate US@north west\endcsname% + \pgfutil@tempdima\pgf@y% + \csname pgf@anchor@buffer gate US@east\endcsname% + \pgf@y\pgfutil@tempdima% + \else% + \pgfpointintersectionoflines{\centerpoint}{\centerpoint\advance\pgf@x1pt\advance\pgf@y1pt}% + {\csname pgf@anchor@buffer gate US@north west\endcsname}% + {% + \pgfpointadd{\centerpoint}{% + \tipanchor% + \pgf@xa\outerxsep% + \advance\pgf@x2.350943\pgf@xa% + }% + }% + \fi% + }% + \inheritanchor[from=not gate US]{south west}% + \inheritanchor[from=not gate US]{north west}% + \inheritanchor[from=not gate US]{input}% + \inheritanchor[from=not gate US]{west}% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\tipanchor}% + \pgfpathlineto{\pgfqpoint{-.833333\pgf@xc}{1.166666\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-.833333\pgf@xc}{-1.166666\pgf@yc}}% + \pgfpathclose% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-1\endcsname% + {% + \pgfpathcircle{% + \pgf@xa\halfside% + \pgf@x-.833333\pgf@xa% + \advance\pgf@x-.5\pgflinewidth% + \advance\pgf@x-\invertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + \fi% + }% + }% + \anchorborder{% + \pgf@lib@gates@not@buffer@border{buffer gate US} + }% +}% + + + + + +\pgfdeclareshape{and gate CDH}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@and gate CDH\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@and gate CDH@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@and gate CDH@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@AND@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{An and gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \csname pgf@anchor@and gate CDH@east\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{mid west}{% + \csname pgf@anchor@and gate CDH@west\endcsname% + \pgf@xa\pgf@x% + \midpoint% + \pgf@x\pgf@xa}% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \csname pgf@anchor@and gate CDH@east\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \anchor{base west}{% + \csname pgf@anchor@and gate CDH@west\endcsname% + \pgf@xa\pgf@x% + \basepoint% + \pgf@x\pgf@xa}% + \anchor{east}{% + \dimensions% + \pgfpointadd{\centerpoint}{\tipanchor}% + }% + \anchor{output}{\csname pgf@anchor@and gate CDH@east\endcsname}% + \anchor{north east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\halfheight% + \else% + \centerpoint% + \pgf@xa\halfwidth% + \pgf@ya\halfheight% + \pgf@xb\halfside% + \advance\pgf@x-.166666\pgf@xb% + \advance\pgf@xa\pgf@xb% + \advance\pgf@x.5\pgf@xa% + \advance\pgf@y-\pgf@xb% + \advance\pgf@ya\pgf@xb% + \advance\pgf@y.866025\pgf@ya% + \fi% + }% + \anchor{south east}{% + \dimensions% + \ifpgfgateanchorsuseboundingrectangle% + \tipanchor% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y-\halfheight% + \else + \centerpoint% + \pgf@xa\halfwidth% + \pgf@ya\halfheight% + \pgf@xb\halfside% + \advance\pgf@x-.166666\pgf@xb% + \advance\pgf@xa\pgf@xb% + \advance\pgf@x.5\pgf@xa% + \advance\pgf@y\pgf@xb% + \advance\pgf@ya\pgf@xb% + \advance\pgf@y-.866025\pgf@ya% + \fi% + }% + \anchor{north}{% + \dimensions% + \centerpoint% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@y\halfheight% + \else% + \pgf@ya\halfheight% + \advance\pgf@y.993043\pgf@ya% + \fi% + }% + \anchor{south}{% + \dimensions% + \centerpoint% + \ifpgfgateanchorsuseboundingrectangle% + \advance\pgf@y-\halfheight% + \else% + \pgf@ya\halfheight% + \advance\pgf@y-.993043\pgf@ya% + \fi% + }% + \anchor{south west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@y-\halfheight% + }% + \anchor{north west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + \advance\pgf@y\halfheight% + }% + \anchor{west}{% + \dimensions% + \centerpoint% + \pgf@xa\halfside% + \advance\pgf@x-1.16666\pgf@xa% + \advance\pgf@x-\outerxsep% + }% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-.16666\pgf@xc}{\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{30}{\the\pgf@yc}% + }% + \pgf@marshal% + } + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{-30}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{\pgf@yc}}% + \pgfpathclose% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@xa\halfside% + \pgf@x-1.16666\pgf@xa% + \advance\pgf@x-.5\pgflinewidth% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \dimensions% + \pgf@xb\halfside% + \pgf@xb-.166666\pgf@xb% + \ifdim\pgf@xa<\pgf@xb% + \pgfpointadd{\centerpoint}{% + \pgfpointborderrectangle{\externalpoint}{% + \pgf@xc\halfside% + \pgf@xc.166666\pgf@xc% + \advance\pgf@xc\halfwidth% + \pgfqpoint{\pgf@xc}{\halfheight}% + }% + }% + \else% + \ifdim\pgf@y=0pt\relax% + \csname pgf@anchor@and gate CDH@east\endcsname% + \else% + \pgfextract@process\externalpoint{\pgfpointadd{\centerpoint}{\externalpoint}}% + \pgf@xc\halfwidth% + \advance\pgf@xc\halfside% + \pgf@yc\halfheight% + \advance\pgf@yc\halfside% + \ifdim\pgf@ya<0pt% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@y\halfside% + \advance\pgf@x\pgf@xb% + }% + {270}{330}{+\pgf@yc}% + \else% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \advance\pgf@y-\halfside% + \advance\pgf@x\pgf@xb% + }% + {30}{90}{+\pgf@xc and +\pgf@yc}% + \fi% + \fi% + \fi% + }% +}% + + +\pgfdeclareshape{nand gate CDH}{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@nand gate CDH\endcsname{% + \pgf@lib@sh@logicgate@parseinputs{1024}% + \pgfmathloop% + \ifnum\pgfmathcounter>\pgf@lib@sh@logicgate@numinputs% + \else% + \pgfutil@ifundefined{pgf@anchor@nand gate CDH@input \pgfmathcounter}{% + \expandafter\xdef\csname pgf@anchor@nand gate CDH@input \pgfmathcounter\endcsname{% + \noexpand\pgf@lib@sh@logicgate@AND@inputanchor{\pgfmathcounter}% + }% + }{}% + \repeatpgfmathloop% + \ifnum\pgf@lib@sh@logicgate@numinputs<2\relax% + \pgferror{A nand gate must have at least two inputs}% + \fi% + }% + \savedmacro\numinputs{\let\numinputs\pgf@lib@sh@logicgate@numinputs}% + \saveddimen\invertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + }% + \saveddimen\outerinvertedradius{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/logic gate inverted radius}}% + \advance\pgf@x.5\pgflinewidth% + }% + \savedmacro\dimensions{\pgf@lib@sh@logicgates@dimensions@orUS}% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \inheritanchor[from=and gate CDH]{mid east}% + \inheritanchor[from=and gate CDH]{mid west}% + \anchor{base}{\basepoint}% + \inheritanchor[from=and gate CDH]{base east}% + \inheritanchor[from=and gate CDH]{base west}% + \anchor{output}{% + \dimensions + \pgfpointadd{\centerpoint}{% + \pgf@xa\halfside% + \pgf@x-.166666\pgf@xa% + \pgf@xb2.0\pgf@xa% + \advance\pgf@x.866025\pgf@xb% + \advance\pgf@x\invertedradius% + \advance\pgf@x\outerinvertedradius% + \advance\pgf@x\outerxsep% + \pgf@y0pt% + }% + }% + \inheritanchor[from=and gate CDH]{east}% + \inheritanchor[from=and gate CDH]{north east}% + \inheritanchor[from=and gate CDH]{south east}% + \inheritanchor[from=and gate CDH]{north}% + \inheritanchor[from=and gate CDH]{south}% + \inheritanchor[from=and gate CDH]{south west}% + \inheritanchor[from=and gate CDH]{north west}% + \inheritanchor[from=and gate CDH]{west}% + \backgroundpath{% + \dimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \advance\pgf@xc-\outerxsep% + \advance\pgf@yc-\outerysep% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-.16666\pgf@xc}{\pgf@yc}}% + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{90}{30}{\the\pgf@yc}% + }% + \pgf@marshal% + } + {% + \pgf@yc2.0\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpatharc{-30}{-90}{\the\pgf@yc}% + }% + \pgf@marshal% + } + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{-\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-1.16666\pgf@xc}{\pgf@yc}}% + \pgfpathclose% + {% + \pgfpathcircle{% + \pgf@x-.166666\pgf@xc% + \pgf@yc2.0\pgf@yc% + \advance\pgf@x.866025\pgf@yc% + \advance\pgf@x\outerinvertedradius% + \pgf@y0pt% + }{+\invertedradius}% + }% + \pgfutil@tempdima2.0\pgf@yc% + \c@pgf@counta\numinputs% + \advance\c@pgf@counta1\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfmathloop% + \ifnum\pgfmathcounter>\numinputs% + \else% + \advance\pgf@yc-\pgfutil@tempdima% + \expandafter\ifx\expandafter\pgf@lib@sh@itext\csname input-\pgfmathcounter\endcsname% + {% + \pgfpathcircle{% + \pgf@xa\halfside% + \pgf@x-1.16666\pgf@xa% + \advance\pgf@x-.5\pgflinewidth% + \advance\pgf@x-\invertedradius% + \pgf@y\pgf@yc% + }{+\invertedradius}% + }% + \fi% + \repeatpgfmathloop% + }% + }% + \inheritanchorborder[from=and gate CDH]% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8e30fe2328ae70c028a1e04e1ca71ba4743440b5 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/circuits/pgflibraryshapes.gates.logic.code.tex @@ -0,0 +1,87 @@ + + +\pgfkeys{/pgf/.cd,% + logic gate input sep/.initial=0.125cm, + logic gate inputs/.initial={normal,normal},% + logic gate inverted radius/.initial=2pt, +}% + + +\expandafter\ifx\csname pgf@lib@sh@logicgate@parseinputs\endcsname\relax% +\def\pgf@lib@sh@logicgate@parseinputs#1{% + \edef\pgf@lib@sh@temp{\pgfkeysvalueof{/pgf/logic gate inputs}}% + \c@pgf@counta#1\relax% + \c@pgf@countb0\relax% + \expandafter\pgfutil@in@\expandafter,\expandafter{\pgf@lib@sh@temp}% + \ifpgfutil@in@% + \let\pgf@lib@sh@next\pgf@lib@sh@logicgate@parseinputs@long% + \else% + \let\pgf@lib@sh@next\pgf@lib@sh@logicgate@parseinputs@short% + \fi% + \pgf@lib@sh@next% +}% +\def\pgf@lib@sh@itext{i}% +\def\pgf@lib@sh@invertedtext{inverted}% +\def\pgf@lib@sh@atchar{@}% +\def\pgf@lib@sh@gobbletilat#1@{}% +\def\pgf@lib@sh@gobbletilatcomma#1@,{}% +\def\pgf@lib@sh@logicgate@parseinputs@short{% + \expandafter\pgf@lib@sh@logicgate@parseinputs@@short\pgf@lib@sh@temp @% +}% +\def\pgf@lib@sh@logicgate@parseinputs@@short#1{% + \def\pgf@lib@sh@tmp{#1}% + \ifx\pgf@lib@sh@tmp\pgf@lib@sh@atchar% + \edef\pgf@lib@sh@logicgate@numinputs{\the\c@pgf@countb}% + \let\pgf@lib@sh@next=\relax% + \else% + \ifnum\c@pgf@countb=\c@pgf@counta% + \edef\pgf@lib@sh@logicgate@numinputs{\the\c@pgf@countb}% + \let\pgf@lib@sh@next=\pgf@lib@sh@gobbletilat% + \else% + \advance\c@pgf@countb by1\relax% + \expandafter\ifx\pgf@lib@sh@itext#1% + \expandafter\pgf@sh@resavedmacro\expandafter{\csname input-\the\c@pgf@countb\endcsname}{% + \expandafter\def\csname input-\the\c@pgf@countb\endcsname{i}}% + \else% + \expandafter\pgf@sh@resavedmacro\expandafter{\csname input-\the\c@pgf@countb\endcsname}{% + \expandafter\def\csname input-\the\c@pgf@countb\endcsname{n}}% + \fi% + \let\pgf@lib@sh@next=\pgf@lib@sh@logicgate@parseinputs@@short% + \fi% + \fi% + \pgf@lib@sh@next% +}% + + +\def\pgf@lib@sh@logicgate@parseinputs@long{% + \expandafter\pgf@lib@sh@logicgate@parseinputs@@long\pgf@lib@sh@temp,@,% +}% +\def\pgf@lib@sh@logicgate@parseinputs@@long#1,{% + \def\pgf@lib@sh@tmp{#1}% + \ifx\pgf@lib@sh@tmp\pgf@lib@sh@atchar% + \edef\pgf@lib@sh@logicgate@numinputs{\the\c@pgf@countb}% + \let\pgf@lib@sh@next=\relax% + \else% + \ifnum\c@pgf@countb=\c@pgf@counta% + \edef\pgf@lib@sh@logicgate@numinputs{\the\c@pgf@countb}% + \let\pgf@lib@sh@next=\pgf@lib@sh@gobbletilatcomma% + \else% + \advance\c@pgf@countb by1\relax% + \def\pgf@lib@sh@temp{#1}% + \ifx\pgf@lib@sh@invertedtext\pgf@lib@sh@temp% + \expandafter\pgf@sh@resavedmacro\expandafter{\csname input-\the\c@pgf@countb\endcsname}{% + \expandafter\def\csname input-\the\c@pgf@countb\endcsname{i}}% + \else% + \expandafter\pgf@sh@resavedmacro\expandafter{\csname input-\the\c@pgf@countb\endcsname}{% + \expandafter\def\csname input-\the\c@pgf@countb\endcsname{n}}% + \fi% + \let\pgf@lib@sh@next=\pgf@lib@sh@logicgate@parseinputs@@@long% + \fi% + \fi% + \pgf@lib@sh@next% +}% +\def\pgf@lib@sh@logicgate@parseinputs@@@long{% + \pgfutil@ifnextchar x{\pgf@lib@sh@logicgate@parseinputs@@long}% + {\pgf@lib@sh@logicgate@parseinputs@@long}% +}% +\fi% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..cd8b4a68b59d8d7dbfe409df9634b3984656e773 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.arrows.code.tex @@ -0,0 +1,2200 @@ + +\ProvidesFileRCS{pgflibraryshapes.arrows.code.tex} + + + +\pgfkeys{/pgf/.cd, + single arrow tip angle/.initial=90, + single arrow head extend/.initial=.25cm, + single arrow head indent/.initial=0cm, +}% + +\pgfdeclareshape{single arrow}{% + \savedmacro\getsinglearrowpoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \edef\xoutersep{\the\pgf@x}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\youtersep{\the\pgf@y}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa.5\wd\pgfnodeparttextbox% + \advance\pgf@xa.5\pgflinewidth% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya.5\ht\pgfnodeparttextbox% + \advance\pgf@ya.5\dp\pgfnodeparttextbox% + \advance\pgf@ya.5\pgflinewidth% + \ifpgfshapeborderusesincircle% + \ifdim\pgf@xa<\pgf@ya% + \pgf@xa\pgf@ya% + \fi% + \pgf@xa1.41421\pgf@xa% + \pgf@ya\pgf@xa% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\xoutersep>\youtersep\relax% + \let\youtersep\xoutersep% + \else% + \let\xoutersep\youtersep% + \fi% + \else% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \pgfmathmod@{\rotate}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@x\pgf@xa% + \pgf@xa\pgf@ya% + \pgf@ya\pgf@x% + \let\pgfmathresult\xoutersep% + \let\xoutersep\youtersep% + \let\youtersep\pgfmathresult% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@x\pgf@xa% + \pgf@xa\pgf@ya% + \pgf@ya\pgf@x% + \let\pgfmathresult\xoutersep% + \let\xoutersep\youtersep% + \let\youtersep\pgfmathresult% + \fi% + \fi% + \fi% + \addtosavedmacro\rotate% + \pgfmathdivide{\pgfkeysvalueof{/pgf/single arrow tip angle}}{2}% + \let\halftipangle\pgfmathresult% + \pgfmathcosec@{\halftipangle}% + \let\cosechalftipangle\pgfmathresult% + \pgfmathcos@{\halftipangle}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfutil@tempdima\cosechalftipangle\pgfutil@tempdima% + \edef\cothalftipangle{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfmathreciprocal@{\pgfmathresult}% + \let\sechalftipangle\pgfmathresult% + \pgfmathsin@{\halftipangle}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfutil@tempdima\sechalftipangle\pgfutil@tempdima% + \edef\tanhalftipangle{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgf@xb\pgf@ya% + \pgf@xb\cothalftipangle\pgf@xb% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/single arrow head extend}}% + \pgf@yc\pgf@xc% + \advance\pgf@xc\pgf@ya% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@xc<.5\pgfutil@tempdimb% + \pgfutil@tempdimb.5\pgfutil@tempdimb% + \pgfmathdivide@{\pgfmath@tonumber{\pgfutil@tempdimb}}{\pgfmath@tonumber{\pgf@xc}}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgf@xc\pgfmathresult\pgf@xc% + \pgf@yc\pgfmathresult\pgf@yc% + \pgf@xb\pgfmathresult\pgf@xb% + \fi% + \advance\pgf@xc-\pgf@ya% + \pgf@xc\cothalftipangle\pgf@xc% + \pgf@xa2.0\pgf@xa% + \advance\pgf@xa\pgf@xb% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@xa<\pgfutil@tempdimb% + \pgf@xa\pgfutil@tempdimb% + \fi% + \advance\pgf@xa-\pgf@xb% + \pgf@xa.5\pgf@xa% + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/single arrow head indent}}% + \pgfsavepgf@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfsavepgf@process\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \pgfsavepgf@process\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \pgfsavepgf@process\arrowtip{% + \pgf@x\pgf@xa% + \advance\pgf@x\pgf@xb% + \pgf@y0pt\relax% + }% + \pgfsavepgf@process\beforearrowtip{% + \pgf@x\pgf@xa% + \advance\pgf@x-\pgf@xc% + \pgf@y\pgf@ya% + \advance\pgf@y\pgf@yc% + }% + \pgfsavepgf@process\beforearrowhead{% + \pgf@x\pgf@xa% + \advance\pgf@x-\pgf@xc% + \advance\pgf@x\pgfutil@tempdima% + \pgf@y\pgf@ya% + }% + \pgfsavepgf@process\afterarrowtail{% + \pgf@x-\pgf@xa% + \pgf@y\pgf@ya% + }% + \pgfsavepgf@process\arrowtipanchor{% + \pgfpointadd{\centerpoint}{\arrowtip}% + \pgf@xa\xoutersep\relax% + \advance\pgf@x\cosechalftipangle\pgf@xa% + }% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \edef\externalradius{\the\pgf@x}% + \addtosavedmacro\externalradius% + \pgfmathanglebetweenlines{\beforearrowtip}{\beforearrowhead}{\beforearrowtip}{\arrowtip}% + \pgf@xa\xoutersep\relax% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfutil@tempdima.5\pgfutil@tempdima% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgf@xa\pgfmathresult\pgf@xa% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima180pt\relax% + \advance\pgfutil@tempdima-\halftipangle pt\relax% + \pgfsavepgf@process\beforearrowtipanchor{% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgf@xa}% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@process{\pgfpointadd{\centerpoint}{\beforearrowtip}}% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + }% + \pgfmathanglebetweenpoints{\beforearrowhead}{\beforearrowtip}% + \pgfutil@tempdima-\pgfmathresult pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdima.5\pgfutil@tempdima% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgf@xa\xoutersep\relax% + \pgf@xa\pgfmathresult\pgf@xa% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima180pt\relax% + \pgfsavepgf@process\beforearrowheadanchor{% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgf@xa}% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@process{\pgfpointadd{\centerpoint}{\beforearrowhead}}% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + }% + \pgfsavepgf@process\afterarrowtailanchor{% + \pgfpointadd{\centerpoint}{\afterarrowtail}% + \advance\pgf@x-\xoutersep\relax% + \advance\pgf@y\youtersep\relax% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\beforearrowtipanchor}% + \let\center@angle@beforearrowtip\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\beforearrowheadanchor}% + \let\center@angle@beforearrowhead\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\afterarrowtailanchor}% + \let\center@angle@afterarrowtail\pgfmathresult% + \addtosavedmacro\center@angle@beforearrowtip% + \addtosavedmacro\center@angle@beforearrowhead% + \addtosavedmacro\center@angle@afterarrowtail% + \pgfmathanglebetweenpoints{\midpoint}{\beforearrowtipanchor}% + \let\mid@angle@beforearrowtip\pgfmathresult% + \pgfmathanglebetweenpoints{\midpoint}{\beforearrowheadanchor}% + \let\mid@angle@beforearrowhead\pgfmathresult% + \pgfmathanglebetweenpoints{\midpoint}{\afterarrowtailanchor}% + \let\mid@angle@afterarrowtail\pgfmathresult% + \addtosavedmacro\mid@angle@beforearrowtip% + \addtosavedmacro\mid@angle@beforearrowhead% + \addtosavedmacro\mid@angle@afterarrowtail% + \pgfmathanglebetweenpoints{\basepoint}{\beforearrowtipanchor}% + \let\base@angle@beforearrowtip\pgfmathresult% + \pgfmathanglebetweenpoints{\basepoint}{\beforearrowheadanchor}% + \let\base@angle@beforearrowhead\pgfmathresult% + \pgfmathanglebetweenpoints{\basepoint}{\afterarrowtailanchor}% + \let\base@angle@afterarrowtail\pgfmathresult% + \addtosavedmacro\base@angle@beforearrowtip% + \addtosavedmacro\base@angle@beforearrowhead% + \addtosavedmacro\base@angle@afterarrowtail% + \addtosavedmacro\arrowtipanchor% + \addtosavedmacro\beforearrowtipanchor% + \addtosavedmacro\beforearrowheadanchor% + \addtosavedmacro\afterarrowtailanchor% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \getsinglearrowpoints% + \let\pgf@singlearrow@referencepoint\midpoint% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{mid west}{% + \getsinglearrowpoints% + \let\pgf@singlearrow@referencepoint\midpoint% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \getsinglearrowpoints% + \let\pgf@singlearrow@referencepoint\basepoint% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{base west}{% + \getsinglearrowpoints% + \let\pgf@singlearrow@referencepoint\basepoint% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north east}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south east}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \anchor{south west}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{north west}{% + \getsinglearrowpoints% + \csname pgf@anchor@single arrow@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{before head}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{\beforearrowheadanchor}{\centerpoint}{\rotate}% + }% + \anchor{before tip}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{\beforearrowtipanchor}{\centerpoint}{\rotate}% + }% + \anchor{tip}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{\arrowtipanchor}{\centerpoint}{\rotate}% + }% + \anchor{after tip}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{after head}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{before tail}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\afterarrowtailanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{after tail}{% + \getsinglearrowpoints% + \pgfmathrotatepointaround{\afterarrowtailanchor}{\centerpoint}{\rotate}% + }% + \anchor{tail}{% + \getsinglearrowpoints% + \pgfpointlineattime{0.5}{% + \pgfmathrotatepointaround{\afterarrowtailanchor}{\centerpoint}{\rotate}% + }% + {% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\afterarrowtailanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + }% + \backgroundpath{% + {% + \pgftransformshift{\centerpoint}% + \pgftransformrotate{\rotate}% + \pgfpathmoveto{\arrowtip}% + \pgfpathlineto{\beforearrowtip}% + \pgfpathlineto{\beforearrowhead}% + \pgfpathlineto{\afterarrowtail}% + \pgfpathlineto{\afterarrowtail\pgf@y-\pgf@y}% + \pgfpathlineto{\beforearrowhead\pgf@y-\pgf@y}% + \pgfpathlineto{\beforearrowtip\pgf@y-\pgf@y}% + }% + \pgfpathclose% + }% + \anchorborder{% + \pgfsavepgf@process\externalpoint{}% + \getsinglearrowpoints% + \pgfutil@ifundefined{pgf@singlearrow@referencepoint}{\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@singlearrow@referencepoint}% + \pgfsavepgf@process\externalpoint{% + \externalpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \referencepoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya}% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \pgf@x\externalangle pt\relax% + \ifx\referencepoint\midpoint% + \pgf@xa\mid@angle@beforearrowtip pt\relax% + \pgf@xb\mid@angle@beforearrowhead pt\relax% + \pgf@xc\mid@angle@afterarrowtail pt\relax% + \else% + \ifx\referencepoint\basepoint% + \pgf@xa\base@angle@beforearrowtip pt\relax% + \pgf@xb\base@angle@beforearrowhead pt\relax% + \pgf@xc\base@angle@afterarrowtail pt\relax% + \else% + \pgf@xa\center@angle@beforearrowtip pt\relax% + \pgf@xb\center@angle@beforearrowhead pt\relax% + \pgf@xc\center@angle@afterarrowtail pt\relax% + \fi% + \fi% + \ifdim\pgf@x<\pgf@xa% + \let\firstpoint\arrowtipanchor% + \let\secondpoint\beforearrowtipanchor% + \else% + \ifdim\pgf@x<\pgf@xb% + \ifdim\pgf@xb<\pgf@xa% + \let\firstpoint\arrowtipanchor% + \let\secondpoint\beforearrowtipanchor% + \else% + \let\firstpoint\beforearrowheadanchor% + \let\secondpoint\beforearrowtipanchor% + \fi% + \else% + \ifdim\pgf@x<\pgf@xc% + \let\firstpoint\beforearrowheadanchor% + \let\secondpoint\afterarrowtailanchor% + \else% + \pgf@xc-\pgf@xc% + \advance\pgf@xc360pt\relax% + \ifdim\pgf@x<\pgf@xc% + \let\firstpoint\afterarrowtailanchor% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\afterarrowtailanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \else% + \pgf@xa-\pgf@xa% + \advance\pgf@xa360pt\relax% + \pgf@xb-\pgf@xb% + \advance\pgf@xb360pt\relax% + \ifdim\pgf@x<\pgf@xa% + \ifdim\pgf@x<\pgf@xb% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\afterarrowtailanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \else% + \ifdim\pgf@xb<\pgf@xa% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \else% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\arrowtipanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \fi% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \fi% + \else% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}% + }% + \let\secondpoint\arrowtipanchor% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgfsavepgf@process\firstpoint{% + \pgfmathrotatepointaround{\firstpoint}{\centerpoint}{\rotate}% + }% + \pgfsavepgf@process\secondpoint{% + \pgfmathrotatepointaround{\secondpoint}{\centerpoint}{\rotate}% + }% + \pgfpointintersectionoflines{\referencepoint}{\externalpoint}% + {\firstpoint}{\secondpoint}% + }% +}% + + + + + + + + +\pgfkeys{/pgf/.cd, + double arrow tip angle/.initial=90, + double arrow head extend/.initial=.25cm, + double arrow head indent/.initial=0cm, +}% + +\pgfdeclareshape{double arrow}{% + \savedmacro\getdoublearrowpoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \edef\xoutersep{\the\pgf@x}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\youtersep{\the\pgf@y}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa.5\wd\pgfnodeparttextbox% + \advance\pgf@xa.5\pgflinewidth% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya.5\ht\pgfnodeparttextbox% + \advance\pgf@ya.5\dp\pgfnodeparttextbox% + \advance\pgf@ya.5\pgflinewidth% + \ifpgfshapeborderusesincircle% + \ifdim\pgf@xa<\pgf@ya% + \pgf@xa\pgf@ya% + \fi% + \pgf@xa1.41421\pgf@xa% + \pgf@ya\pgf@xa% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\xoutersep>\youtersep\relax% + \let\youtersep\xoutersep% + \else% + \let\xoutersep\youtersep% + \fi% + \else% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}} + \pgfmathmod@{\rotate}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@x\pgf@xa% + \pgf@xa\pgf@ya% + \pgf@ya\pgf@x% + \let\pgfmathresult\xoutersep% + \let\xoutersep\youtersep% + \let\youtersep\pgfmathresult% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@x\pgf@xa% + \pgf@xa\pgf@ya% + \pgf@ya\pgf@x% + \let\pgfmathresult\xoutersep% + \let\xoutersep\youtersep% + \let\youtersep\pgfmathresult% + \fi% + \fi% + \fi% + \addtosavedmacro\rotate% + \pgfmathdivide{\pgfkeysvalueof{/pgf/double arrow tip angle}}{2}% + \let\halftipangle\pgfmathresult% + \pgfmathcosec@{\halftipangle}% + \let\cosechalftipangle\pgfmathresult% + \pgfmathcos@{\halftipangle}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfutil@tempdima\cosechalftipangle\pgfutil@tempdima% + \edef\cothalftipangle{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfmathreciprocal@{\pgfmathresult}% + \let\sechalftipangle\pgfmathresult% + \pgfmathsin@{\halftipangle}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfutil@tempdima\sechalftipangle\pgfutil@tempdima% + \edef\tanhalftipangle{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgf@xb\pgf@ya% + \pgf@xb\cothalftipangle\pgf@xb% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/double arrow head extend}}% + \pgf@yc\pgf@xc% + \advance\pgf@xc\pgf@ya% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@xc<.5\pgfutil@tempdimb% + \pgfutil@tempdimb.5\pgfutil@tempdimb% + \pgfmathdivide@{\pgfmath@tonumber{\pgfutil@tempdimb}}{\pgfmath@tonumber{\pgf@xc}}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgf@xc\pgfmathresult\pgf@xc% + \pgf@yc\pgfmathresult\pgf@yc% + \pgf@xb\pgfmathresult\pgf@xb% + \fi% + \advance\pgf@xc-\pgf@ya% + \pgf@xc\cothalftipangle\pgf@xc% + \advance\pgf@xa\pgf@xb% + \pgf@xa2.0\pgf@xa% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@xa<\pgfutil@tempdimb% + \pgf@xa\pgfutil@tempdimb% + \fi% + \pgf@xa.5\pgf@xa% + \advance\pgf@xa-\pgf@xb% + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/double arrow head indent}}% + \pgfsavepgf@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfsavepgf@process\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \pgfsavepgf@process\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \pgfsavepgf@process\arrowtip{% + \pgf@x\pgf@xa% + \advance\pgf@x\pgf@xb% + \pgf@y0pt\relax% + }% + \pgfsavepgf@process\beforearrowtip{% + \pgf@x\pgf@xa% + \advance\pgf@x-\pgf@xc% + \pgf@y\pgf@ya% + \advance\pgf@y\pgf@yc% + }% + \pgfsavepgf@process\beforearrowhead{% + \pgf@x\pgf@xa% + \advance\pgf@x-\pgf@xc% + \advance\pgf@x\pgfutil@tempdima% + \pgf@y\pgf@ya% + }% + \pgfsavepgf@process\arrowtipanchor{% + \pgfpointadd{\centerpoint}{\arrowtip}% + \pgf@xa\xoutersep\relax% + \advance\pgf@x\cosechalftipangle\pgf@xa% + }% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \edef\externalradius{\the\pgf@x}% + \addtosavedmacro\externalradius% + \pgfmathanglebetweenlines{\beforearrowtip}{\beforearrowhead}{\beforearrowtip}{\arrowtip}% + \pgf@xa\xoutersep\relax% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfutil@tempdima.5\pgfutil@tempdima% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgf@xa\pgfmathresult\pgf@xa% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima180pt\relax% + \advance\pgfutil@tempdima-\halftipangle pt\relax% + \pgfsavepgf@process\beforearrowtipanchor{% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgf@xa}% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@process{\pgfpointadd{\centerpoint}{\beforearrowtip}}% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + }% + \pgfmathanglebetweenpoints{\beforearrowhead}{\beforearrowtip}% + \pgfutil@tempdima-\pgfmathresult pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdima.5\pgfutil@tempdima% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgf@xa\xoutersep\relax% + \pgf@xa\pgfmathresult\pgf@xa% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima180pt\relax% + \pgfsavepgf@process\beforearrowheadanchor{% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgf@xa}% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@process{\pgfpointadd{\centerpoint}{\beforearrowhead}}% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\beforearrowtipanchor}% + \let\center@angle@beforearrowtip\pgfmathresult% + \addtosavedmacro\center@angle@beforearrowtip% + \pgfmathanglebetweenpoints{\midpoint}{\beforearrowtipanchor}% + \let\mid@angle@beforearrowtip\pgfmathresult% + \addtosavedmacro\mid@angle@beforearrowtip% + \pgfmathanglebetweenpoints{\basepoint}{\beforearrowtipanchor}% + \let\base@angle@beforearrowtip\pgfmathresult% + \addtosavedmacro\base@angle@beforearrowtip% + \addtosavedmacro\arrowtipanchor% + \addtosavedmacro\beforearrowtipanchor% + \addtosavedmacro\beforearrowheadanchor% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \getdoublearrowpoints% + \let\pgf@singlearrow@referencepoint\midpoint% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{mid west}{% + \getdoublearrowpoints% + \let\pgf@singlearrow@referencepoint\midpoint% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \getdoublearrowpoints% + \let\pgf@singlearrow@referencepoint\basepoint% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{base west}{% + \getdoublearrowpoints% + \let\pgf@singlearrow@referencepoint\basepoint% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north east}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south east}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \anchor{south west}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{north west}{% + \getdoublearrowpoints% + \csname pgf@anchor@double arrow@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{before head 1}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{\beforearrowheadanchor}{\centerpoint}{\rotate}% + }% + \anchor{before tip 1}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{\beforearrowtipanchor}{\centerpoint}{\rotate}% + }% + \anchor{tip 1}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{\arrowtipanchor}{\centerpoint}{\rotate}% + }% + \anchor{after tip 1}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{after head 1}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{before head 2}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{before tip 2}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{tip 2}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\arrowtipanchor}% + \pgf@x-\pgf@x% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{after tip 2}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@x-\pgf@x% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{after head 2}{% + \getdoublearrowpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@x-\pgf@x% + }{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \backgroundpath{% + {% + \pgftransformshift{\centerpoint}% + \pgftransformrotate{\rotate}% + \pgfpathmoveto{\arrowtip}% + \pgfpathlineto{\beforearrowtip}% + \pgfpathlineto{\beforearrowhead}% + \pgfpathlineto{\beforearrowhead\pgf@x-\pgf@x}% + \pgfpathlineto{\beforearrowtip\pgf@x-\pgf@x}% + \pgfpathlineto{\arrowtip\pgf@x-\pgf@x}% + \pgfpathlineto{\beforearrowtip\pgf@x-\pgf@x\pgf@y-\pgf@y}% + \pgfpathlineto{\beforearrowhead\pgf@x-\pgf@x\pgf@y-\pgf@y}% + \pgfpathlineto{\beforearrowhead\pgf@y-\pgf@y}% + \pgfpathlineto{\beforearrowtip\pgf@y-\pgf@y}% + }% + \pgfpathclose% + }% + \anchorborder{% + \pgfsavepgf@process\externalpoint{}% + \getdoublearrowpoints% + \pgfutil@ifundefined{pgf@singlearrow@referencepoint}{\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@singlearrow@referencepoint}% + \pgfsavepgf@process\externalpoint{% + \externalpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \referencepoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya}% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \pgf@x\externalangle pt\relax% + \ifx\referencepoint\midpoint% + \pgf@xa\mid@angle@beforearrowtip pt\relax% + \else% + \ifx\referencepoint\basepoint% + \pgf@xa\base@angle@beforearrowtip pt\relax% + \else% + \pgf@xa\center@angle@beforearrowtip pt\relax% + \fi% + \fi% + \ifdim\pgf@x<180pt\relax% + \ifdim\pgf@x<\pgf@xa% + \let\firstpoint\arrowtipanchor% + \let\secondpoint\beforearrowtipanchor% + \else% + \pgf@xa-\pgf@xa% + \advance\pgf@xa180pt\relax% + \ifdim\pgf@x<\pgf@xa% + \let\firstpoint\beforearrowheadanchor% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@x-\pgf@x + }{\centerpoint}}% + \else% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@x-\pgf@x + }{\centerpoint}}% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\arrowtipanchor}% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }{\centerpoint}}% + \fi% + \fi% + \else% + \pgf@xa-\pgf@xa% + \advance\pgf@xa360pt\relax% + \ifdim\pgf@x<\pgf@xa% + \pgf@xa-\pgf@xa% + \advance\pgf@xa540pt\relax% + \ifdim\pgf@x<\pgf@xa% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\arrowtipanchor}% + \pgf@x-\pgf@x% + }{\centerpoint}}% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowtipanchor}% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }{\centerpoint}}% + \else% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }{\centerpoint}}% + \pgfsavepgf@process\secondpoint{% + \pgfpointadd{% + \pgfpointdiff{\centerpoint}{\beforearrowheadanchor}% + \pgf@y-\pgf@y% + }{\centerpoint}}% + \fi% + \else% + \pgfsavepgf@process\firstpoint{% + \pgfpointadd{% + \pgfpointdiff{\beforearrowtipanchor}{\centerpoint}% + \pgf@x-\pgf@x% + }{\centerpoint}}% + \let\secondpoint\arrowtipanchor% + \fi% + \fi% + \pgfsavepgf@process\firstpoint{% + \pgfmathrotatepointaround{\firstpoint}{\centerpoint}{\rotate}% + }% + \pgfsavepgf@process\secondpoint{% + \pgfmathrotatepointaround{\secondpoint}{\centerpoint}{\rotate}% + }% + \pgfpointintersectionoflines{\referencepoint}{\externalpoint}% + {\firstpoint}{\secondpoint}% + }% +}% + + + + +\def\pgf@lib@arrowbox@parsearrowlength#1#2#3{% + \edef\pgf@lib@temp{#3}% + \edef\pgf@lib@marshal{% + \noexpand\pgfutil@in@{none}{\pgf@lib@temp}% + }% + \pgf@lib@marshal% + \ifpgfutil@in@% + #10pt\relax% + \else% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter#1\pgf@lib@temp\relax\pgfmath@% + \edef\pgf@lib@marshal{% + \noexpand\pgfutil@in@{from center}{\pgf@lib@temp}% + }% + \pgf@lib@marshal% + \ifpgfutil@in@% + \else% + \ifdim#1>0pt\relax% + \advance#1#2\relax% + \fi% + \fi% + \fi}% + +\def\pgf@lib@arrowbox@parsearrows#1{% + \pgfkeys{/pgf/.cd,% + arrow box west arrow=0pt, + arrow box east arrow=0pt, + arrow box south arrow=0pt, + arrow box north arrow=0pt + }% + \def\pgf@lib@arrowbox@extend{0pt}% + \edef\pgf@lib@temp{#1}% + \expandafter\pgf@lib@arrowbox@@parsearrows\pgf@lib@temp,\pgf@lib@arrowbox@parsearrows, +}% + + +\def\pgf@lib@arrowbox@@parsearrows#1,{% + \ifx\pgf@lib@arrowbox@parsearrows#1% + \let\pgflib@next\relax% + \else% + \pgfutil@in@:{#1}% + \ifpgfutil@in@% + \pgf@lib@arrowbox@getextend#1\pgf@lib% + \else% + \def\pgf@lib@arrowbox@direction{#1}% + \fi% + \edef\pgf@marshal{% + \noexpand\pgfkeys{/pgf/arrow box \pgf@lib@arrowbox@direction\space arrow=\pgf@lib@arrowbox@extend}% + }% + \pgf@marshal% + \let\pgflib@next\pgf@lib@arrowbox@@@parsearrows% + \fi% + \pgflib@next% +}% +\def\pgf@lib@arrowbox@@@parsearrows{% + \pgfutil@ifnextchar x{\relax\pgf@lib@arrowbox@@parsearrows}{\relax\pgf@lib@arrowbox@@parsearrows}% +}% + +\def\pgf@lib@arrowbox@getextend#1:#2\pgf@lib{% + \def\pgf@lib@arrowbox@direction{#1}% + \def\pgf@lib@arrowbox@extend{#2}% +}% + +\pgfkeys{/pgf/.cd, + arrow box west arrow/.initial=.5cm, + arrow box east arrow/.initial=.5cm, + arrow box south arrow/.initial=.5cm, + arrow box north arrow/.initial=.5cm, + arrow box shaft width/.initial=.125cm, + arrow box head extend/.initial=.125cm, + arrow box head indent/.initial=0cm, + arrow box tip angle/.initial=90, +}% + +\pgfdeclareshape{arrow box}{% + \saveddimen\shaftwidth{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/arrow box shaft width}}% + }% + \savedmacro\arrowboxpoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\halfboxwidth{\the\pgf@x}% + \edef\halfboxheight{\the\pgf@y}% + \pgfextract@process\arrowboxcorner{}% + \addtosavedmacro\arrowboxcorner% + \pgf@lib@arrowbox@parsearrowlength\pgf@x{\halfboxwidth}% + {\pgfkeysvalueof{/pgf/arrow box west arrow}}% + \edef\westextend{\the\pgf@x}% + \addtosavedmacro\westextend% + \pgf@lib@arrowbox@parsearrowlength\pgf@x{\halfboxwidth}% + {\pgfkeysvalueof{/pgf/arrow box east arrow}}% + \edef\eastextend{\the\pgf@x}% + \addtosavedmacro\eastextend% + \pgf@lib@arrowbox@parsearrowlength\pgf@x{\halfboxheight}% + {\pgfkeysvalueof{/pgf/arrow box north arrow}}% + \edef\northextend{\the\pgf@x}% + \addtosavedmacro\northextend% + \pgf@lib@arrowbox@parsearrowlength\pgf@x{\halfboxheight}% + {\pgfkeysvalueof{/pgf/arrow box south arrow}}% + \edef\southextend{\the\pgf@x}% + \addtosavedmacro\southextend% + }% + \saveddimen\arrowheadextend{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/arrow box head extend}}% + }% + \saveddimen\arrowheadindent{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/arrow box head indent}}% + }% + \savedmacro\arrowtipmiterangle{% + \pgfmathparse{\pgfkeysvalueof{/pgf/arrow box tip angle}}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\arrowtipmiterangle\pgfmathresult% + }% + \savedmacro\arrowheadangles{% + \pgfmathparse{\pgfkeysvalueof{/pgf/arrow box tip angle}}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\arrowtipmiterangle\pgfmathresult% + \addtosavedmacro\arrowtipmiterangle% + \pgfmathcosec@{\arrowtipmiterangle}% + \let\cosecarrowtipmiterangle\pgfmathresult% + \addtosavedmacro\cosecarrowtipmiterangle% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/arrow box head extend}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/arrow box head indent}}% + \ifdim\pgf@y=0pt\relax% + \def\pgfmathresult{90}% + \else% + \ifdim\pgf@y<0pt\relax% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \pgfmathatan@{\pgfmathresult}% + \pgfmathadd@{\pgfmathresult}{180}% + \else% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \pgfmathatan@{\pgfmathresult}% + \fi% + \fi% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\beforearrowheadmiterangle\pgfmathresult% + \addtosavedmacro\beforearrowheadmiterangle% + \pgfmathcosec@{\beforearrowheadmiterangle}% + \let\cosecbeforearrowheadmiterangle\pgfmathresult% + \addtosavedmacro\cosecbeforearrowheadmiterangle% + \pgfutil@tempdima-\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima90pt\relax% + \pgfutil@tempdimb\beforearrowheadmiterangle pt\relax% + \pgfutil@tempdimb2.0\pgfutil@tempdimb% + \advance\pgfutil@tempdimb-90pt\relax% + \advance\pgfutil@tempdima\pgfutil@tempdimb% + \divide\pgfutil@tempdima2\relax% + \edef\beforearrowtipmiterangle{\pgfmath@tonumber{\pgfutil@tempdima}}% + \addtosavedmacro\beforearrowtipmiterangle% + \pgfmathcosec@{\beforearrowtipmiterangle}% + \let\cosecbeforearrowtipmiterangle\pgfmathresult% + \addtosavedmacro\cosecbeforearrowtipmiterangle% + }% + \saveddimen\outerxsep{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + }% + \saveddimen\outerysep{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer ysep}}% + }% + \savedanchor\beforearrowtip{% + \pgfmathparse{\pgfkeysvalueof{/pgf/arrow box tip angle}}% + \pgfmathdivide@{\pgfmathresult}{2}% + \pgfmathcot@{\pgfmathresult}% + \let\cothalfangle\pgfmathresult% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/arrow box shaft width}}% + \pgf@y.5\pgf@y% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/arrow box head extend}}% + \pgf@y\pgf@y% + \pgf@x\cothalfangle\pgf@y% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \let\pgf@lib@shapes@arrowbox@referencepoint\midpoint% + \csname pgf@anchor@arrow box@border\endcsname{\pgfqpoint{\eastextend}{0pt}}% + \else% + \arrowboxcorner% + \pgf@xa\pgf@x% + \midpoint% + \advance\pgf@x\pgf@xa% + \fi% + }% + \anchor{mid west}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \let\pgf@lib@shapes@arrowbox@referencepoint\midpoint% + \csname pgf@anchor@arrow box@border\endcsname{\pgfqpoint{-\westextend}{0pt}}% + \else% + \arrowboxcorner% + \pgf@xa\pgf@x% + \midpoint% + \advance\pgf@x-\pgf@xa% + \fi% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \let\pgf@lib@shapes@arrowbox@referencepoint\basepoint% + \csname pgf@anchor@arrow box@border\endcsname{\pgfqpoint{\eastextend}{0pt}}% + \else% + \arrowboxcorner% + \pgf@xa\pgf@x% + \basepoint% + \advance\pgf@x\pgf@xa% + \fi% + }% + \anchor{base west}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \let\pgf@lib@shapes@arrowbox@referencepoint\basepoint% + \csname pgf@anchor@arrow box@border\endcsname{\pgfqpoint{-\westextend}{0pt}}% + \else% + \arrowboxcorner% + \pgf@xa\pgf@x% + \basepoint% + \advance\pgf@x-\pgf@xa% + \fi% + }% + \anchor{north}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \csname pgf@anchor@arrow box@north arrow tip\endcsname% + \else% + \pgfpointadd{\centerpoint}{\arrowboxcorner}% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@y\pgf@ya% + \fi% + }% + \anchor{south}{% + \arrowboxpoints% + \ifdim\southextend>0pt\relax% + \csname pgf@anchor@arrow box@south arrow tip\endcsname% + \else% + \pgfpointadd{\centerpoint}{\arrowboxcorner\pgf@y-\pgf@y}% + \pgf@ya\pgf@y% + \centerpoint% + \pgf@y\pgf@ya% + \fi% + }% + \anchor{east}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \csname pgf@anchor@arrow box@east arrow tip\endcsname% + \else% + \pgfpointadd{\centerpoint}{\arrowboxcorner}% + \pgf@xa\pgf@x% + \centerpoint% + \pgf@x\pgf@xa% + \fi% + }% + \anchor{west}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \csname pgf@anchor@arrow box@west arrow tip\endcsname% + \else% + \pgfpointadd{\centerpoint}{\arrowboxcorner\pgf@x-\pgf@x}% + \pgf@xa\pgf@x% + \centerpoint% + \pgf@x\pgf@xa% + \fi% + }% + \anchor{north east}{% + \arrowboxpoints% + \pgfpointadd{\centerpoint}{\arrowboxcorner}% + }% + \anchor{north west}{% + \arrowboxpoints% + \pgfpointadd{\centerpoint}{\arrowboxcorner\pgf@x-\pgf@x}% + }% + \anchor{south west}{% + \arrowboxpoints% + \pgfpointadd{\centerpoint}{\arrowboxcorner\pgf@x-\pgf@x\pgf@y-\pgf@y}% + }% + \anchor{south east}{% + \arrowboxpoints% + \pgfpointadd{\centerpoint}{\arrowboxcorner\pgf@y-\pgf@y}% + }% + \anchor{before east arrow}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + \advance\pgf@y\outerysep\relax% + }% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{before east arrow head}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + \advance\pgf@x\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + }% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{before east arrow tip}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + }% + }% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{east arrow tip}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \centerpoint% + \advance\pgf@x\eastextend\relax% + \pgf@xa\outerxsep\relax% + \pgfmathcosec@{\arrowtipmiterangle}% + \advance\pgf@x\pgfmathresult\pgf@xa% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{after east arrow tip}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + }% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{after east arrow head}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + \advance\pgf@x\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{after east arrow}{% + \arrowboxpoints% + \ifdim\eastextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + \advance\pgf@y\outerysep\relax% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{before west arrow}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@x-\pgf@x% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + \advance\pgf@y\outerysep\relax% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{before west arrow head}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\westextend\relax% + \advance\pgf@x\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{before west arrow tip}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\westextend\relax% + }% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{west arrow tip}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \centerpoint% + \advance\pgf@x-\westextend\relax% + \pgf@xa\outerxsep\relax% + \pgfmathcosec@{\arrowtipmiterangle}% + \advance\pgf@x-\pgfmathresult\pgf@xa% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{after west arrow tip}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\westextend\relax% + }% + \pgf@x-\pgf@x% + }% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{after west arrow head}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\westextend\relax% + \advance\pgf@x\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \pgf@x-\pgf@x% + }% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{after west arrow}{% + \arrowboxpoints% + \ifdim\westextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + \advance\pgf@y\outerysep\relax% + \pgf@x-\pgf@x% + }% + \else% + \csname pgf@anchor@arrow box@west\endcsname% + \fi% + }% + \anchor{before north arrow}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@x-\shaftwidth\relax% + \pgf@x.5\pgf@x% + \advance\pgf@x-\outerxsep\relax% + }% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{before north arrow head}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima270pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \advance\pgf@y\arrowheadindent\relax% + \pgf@x-\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + }% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{before north arrow tip}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-90pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y-\pgf@xa% + \advance\pgf@y\northextend\relax% + }% + \pgf@x-\pgf@x% + }% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{north arrow tip}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \centerpoint% + \advance\pgf@y\northextend\relax% + \pgf@ya\outerysep\relax% + \pgfmathcosec@{\arrowtipmiterangle}% + \advance\pgf@y\pgfmathresult\pgf@ya% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{after north arrow tip}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-90pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y-\pgf@xa% + \advance\pgf@y\northextend\relax% + }% + }% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{after north arrow head}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima270pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \advance\pgf@y\arrowheadindent\relax% + \pgf@x-\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + \pgf@x-\pgf@x% + }% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{after north arrow}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@x\shaftwidth\relax% + \pgf@x.5\pgf@x% + \advance\pgf@x\outerxsep\relax% + }% + \else% + \csname pgf@anchor@arrow box@north\endcsname% + \fi% + }% + \anchor{before south arrow}{% + \arrowboxpoints% + \ifdim\southextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@x\shaftwidth\relax% + \pgf@x.5\pgf@x% + \advance\pgf@x\outerxsep\relax% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@south\endcsname% + \fi% + }% + \anchor{before south arrow head}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima270pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \advance\pgf@y\arrowheadindent\relax% + \pgf@x-\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@south\endcsname% + \fi% + }% + \anchor{before south arrow tip}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-90pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y-\pgf@xa% + \advance\pgf@y\northextend\relax% + }% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@south\endcsname% + \fi% + }% + \anchor{south arrow tip}{% + \arrowboxpoints% + \ifdim\southextend>0pt\relax% + \centerpoint% + \advance\pgf@y-\southextend\relax% + \pgf@ya\outerysep\relax% + \pgfmathcosec@{\arrowtipmiterangle}% + \advance\pgf@y-\pgfmathresult\pgf@ya% + \else% + \csname pgf@anchor@arrow box@east\endcsname% + \fi% + }% + \anchor{after south arrow tip}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima\arrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima\beforearrowtipmiterangle pt\relax% + \advance\pgfutil@tempdima-90pt\relax% + \pgfutil@tempdimb\outerxsep\relax% + \pgfutil@tempdimb\cosecbeforearrowtipmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y-\pgf@xa% + \advance\pgf@y\northextend\relax% + }% + \pgf@x-\pgf@x% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@south\endcsname% + \fi% + }% + \anchor{after south arrow head}{% + \arrowboxpoints% + \ifdim\northextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointadd{% + \arrowheadangles% + \pgfutil@tempdima-\beforearrowheadmiterangle pt\relax% + \advance\pgfutil@tempdima270pt\relax% + \pgfutil@tempdimb\outerysep\relax% + \pgfutil@tempdimb\cosecbeforearrowheadmiterangle\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }% + {% + \beforearrowtip% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \advance\pgf@y\arrowheadindent\relax% + \pgf@x-\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@south\endcsname% + \fi% + }% + \anchor{after south arrow}{% + \arrowboxpoints% + \ifdim\southextend>0pt\relax% + \pgfpointadd{\centerpoint}{% + \arrowboxcorner% + \pgf@x-\shaftwidth\relax% + \pgf@x.5\pgf@x% + \advance\pgf@x-\outerxsep\relax% + \pgf@y-\pgf@y% + }% + \else% + \csname pgf@anchor@arrow box@south\endcsname% + \fi% + }% + \backgroundpath{% + \arrowboxpoints% + \pgfextract@process\arrowboxcorner{% + \arrowboxcorner% + \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}% + }% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\arrowboxcorner}% + \ifdim\eastextend>0pt\relax% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + \advance\pgf@x\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + }% + \pgfpathlineto{% + \pgf@x\eastextend\relax% + \pgf@y0pt\relax% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + \pgf@y-\pgf@y% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@x-\pgf@x% + \advance\pgf@x\eastextend\relax% + \advance\pgf@x\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y-.5\pgf@y% + }% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@y\shaftwidth\relax% + \pgf@y-.5\pgf@y% + }% + \fi% + \pgfpathlineto{\arrowboxcorner\pgf@y-\pgf@y}% + \ifdim\southextend>0pt\relax% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@x\shaftwidth\relax% + \pgf@x.5\pgf@x% + \pgf@y-\pgf@y% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@y\pgf@x% + \advance\pgf@y-\southextend\relax% + \advance\pgf@y-\arrowheadindent\relax% + \pgf@x\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@xa\pgf@y% + \pgf@y\pgf@x% + \advance\pgf@y-\southextend\relax% + \pgf@x\pgf@xa% + }% + \pgfpathlineto{% + \pgf@x0pt\relax% + \pgf@y-\southextend\relax% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@xa\pgf@y% + \pgf@y\pgf@x% + \advance\pgf@y-\southextend\relax% + \pgf@x-\pgf@xa% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@y\pgf@x% + \advance\pgf@y-\southextend\relax% + \advance\pgf@y-\arrowheadindent\relax% + \pgf@x\shaftwidth\relax% + \pgf@x-.5\pgf@x% + }% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@x\shaftwidth\relax% + \pgf@x-.5\pgf@x% + \pgf@y-\pgf@y% + }% + \fi% + \pgfpathlineto{\arrowboxcorner\pgf@x-\pgf@x\pgf@y-\pgf@y}% + \ifdim\westextend>0pt\relax% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@x-\pgf@x + \pgf@y\shaftwidth\relax% + \pgf@y-.5\pgf@y% + }% + \pgfpathlineto{% + \beforearrowtip% + \advance\pgf@x-\westextend\relax% + \advance\pgf@x-\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y-.5\pgf@y% + }% + \pgfpathlineto{% + \beforearrowtip% + \advance\pgf@x-\westextend\relax% + \pgf@y-\pgf@y% + }% + \pgfpathlineto{% + \pgf@x-\westextend\relax% + \pgf@y0pt\relax% + }% + \pgfpathlineto{% + \beforearrowtip% + \advance\pgf@x-\westextend\relax% + }% + \pgfpathlineto{% + \beforearrowtip% + \advance\pgf@x-\westextend\relax% + \advance\pgf@x-\arrowheadindent\relax% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@x-\pgf@x% + \pgf@y\shaftwidth\relax% + \pgf@y.5\pgf@y% + }% + \fi% + \pgfpathlineto{\arrowboxcorner\pgf@x-\pgf@x}% + \ifdim\northextend>0pt\relax% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@x\shaftwidth\relax% + \pgf@x-.5\pgf@x% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \advance\pgf@y\arrowheadindent\relax% + \pgf@x\shaftwidth\relax% + \pgf@x-.5\pgf@x% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@xa\pgf@y% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \pgf@x-\pgf@xa% + }% + \pgfpathlineto{% + \pgf@x0pt\relax% + \pgf@y\northextend\relax% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@xa\pgf@y% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \pgf@x\pgf@xa% + }% + \pgfpathlineto{% + \beforearrowtip% + \pgf@y-\pgf@x% + \advance\pgf@y\northextend\relax% + \advance\pgf@y\arrowheadindent\relax% + \pgf@x\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + \pgfpathlineto{% + \arrowboxcorner% + \pgf@x\shaftwidth\relax% + \pgf@x.5\pgf@x% + }% + \fi% + \pgfpathclose% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \pgfutil@ifundefined{pgf@lib@shapes@arrowbox@referencepoint}% + {\let\referencepoint\centerpoint}{\let\referencepoint\pgf@lib@shapes@arrowbox@referencepoint}% + \pgfextract@process\externalpoint{% + \pgfpointadd{\referencepoint}{\externalpoint}% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@north\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@north east\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before east arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{east arrow tip}% + \def\secondpoint{before east arrow tip}% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before east arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{before east arrow head}% + \def\secondpoint{before east arrow}% + \else% + \def\firstpoint{before east arrow}% + \def\secondpoint{north east}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after north arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after north arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{north east}% + \def\secondpoint{after north arrow}% + \else% + \def\firstpoint{after north arrow}% + \def\secondpoint{after north arrow head}% + \fi% + \else% + \def\firstpoint{after north arrow tip}% + \def\secondpoint{north arrow tip}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@north west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before north arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{north arrow tip}% + \def\secondpoint{before north arrow tip}% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before north arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{before north head}% + \def\secondpoint{before north arrow}% + \else% + \def\firstpoint{before north arrow}% + \def\secondpoint{north west}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after west arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after west arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{north west}% + \def\secondpoint{after west arrow}% + \else% + \def\firstpoint{after west arrow}% + \def\secondpoint{after west arrow head}% + \fi% + \else% + \def\firstpoint{after west arrow tip}% + \def\secondpoint{west arrow tip}% + \fi% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@south arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@south west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before west arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{west arrow tip}% + \def\secondpoint{before west arrow tip}% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before west arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{before west arrow head}% + \def\secondpoint{before west arrow}% + \else% + \def\firstpoint{before west arrow}% + \def\secondpoint{south west}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after south arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after south arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{south west}% + \def\secondpoint{after south arrow}% + \else% + \def\firstpoint{after south arrow}% + \def\secondpoint{after south arrow head}% + \fi% + \else% + \def\firstpoint{after south arrow tip}% + \def\secondpoint{south arrow tip}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@south east\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before south arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{south arrow tip}% + \def\secondpoint{before south arrow tip}% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@before south arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{before south arrow head}% + \def\secondpoint{before south arrow}% + \else% + \def\firstpoint{before south arrow}% + \def\secondpoint{south east}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after east arrow tip\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}% + {\csname pgf@anchor@arrow box@after east arrow\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \def\firstpoint{south east}% + \def\secondpoint{after east arrow}% + \else% + \def\firstpoint{after east arrow}% + \def\secondpoint{after east arrow head}% + \fi% + \else% + \def\firstpoint{after east arrow tip}% + \def\secondpoint{east arrow tip}% + \fi% + \fi% + \fi% + \fi% + \pgfpointintersectionoflines{\referencepoint}{\externalpoint}% + {\csname pgf@anchor@arrow box@\firstpoint\endcsname}% + {\csname pgf@anchor@arrow box@\secondpoint\endcsname}% + }% +}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e86b74f62a81431efc515dab432b3ae3bfb8cb56 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.callouts.code.tex @@ -0,0 +1,799 @@ + +\usepgflibrary{shapes.symbols}% + +\newif\ifpgf@lib@callout@absolutepointer +\pgfkeys{/pgf/.cd, + callout pointer arc/.initial=15, + callout pointer width/.initial=.25cm, + callout pointer start size/.initial=.2 of callout, + callout pointer end size/.initial=.1 of callout, + callout pointer segments/.initial=2, + callout absolute pointer/.code={\pgf@lib@callout@makeabsolutepointer{#1}}, + callout relative pointer/.code={\pgf@lib@callout@makerelativepointer{#1}}, + callout pointer shorten/.initial=0cm, +}% + + + +\def\pgf@lib@callout@makeabsolutepointer#1{% + \pgf@lib@callout@absolutepointertrue% + {% + \pgftransformshift{#1}% + \pgfmultipartnode{coordinate}{center}{pgf@lib@callout@pointer}{}% + }% +}% + +\def\pgf@lib@callout@makerelativepointer#1{% + \pgf@lib@callout@absolutepointerfalse% + \def\pgf@lib@callout@relativepointer{#1}% +}% +\pgfkeys{/pgf/callout relative pointer=\pgfpointpolar{300}{.5cm}}% + + +\pgfdeclareshape{ellipse callout}{% + \savedmacro\ellipsecalloutpoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x>\pgf@y% + \edef\outersep{\the\pgf@x}% + \else% + \edef\outersep{\the\pgf@y}% + \fi% + \addtosavedmacro\outersep% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgf@x1.4142136\pgf@x% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \pgf@y1.4142136\pgf@y% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \edef\xpathradius{\the\pgf@x}% + \edef\ypathradius{\the\pgf@y}% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \edef\xradius{\the\pgf@x}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\yradius{\the\pgf@y}% + \addtosavedmacro\xradius% + \addtosavedmacro\xpathradius% + \addtosavedmacro\yradius% + \addtosavedmacro\ypathradius% + \pgfmathsetmacro\pointerarc{\pgfkeysvalueof{/pgf/callout pointer arc}}% + \addtosavedmacro\pointerarc% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \ifpgf@lib@callout@absolutepointer% + \else% + \pgfextract@process\calloutpointer{% + \pgfextract@process\borderpoint{% + \expandafter\pgfpointborderellipse\expandafter{\pgf@lib@callout@relativepointer}{\pgfqpoint{\xpathradius}{\ypathradius}}% + }% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\borderpoint}% + \let\pointerangle\pgfmathresult% + \expandafter\pgf@process\expandafter{\pgf@lib@callout@relativepointer}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \edef\pointerradius{\pgfmathresult pt}% + \pgfpointadd{\borderpoint}{\pgfqpointpolar{\pointerangle}{\pointerradius}}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \addtosavedmacro\calloutpointer% + \pgf@lib@callouts@shortenpointer% + \pgf@lib@ellipsecallout@getpoints% + \addtosavedmacro\calloutpointeranchor% + \addtosavedmacro\beforecalloutangle% + \addtosavedmacro\aftercalloutangle% + \fi% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \ellipsecalloutpoints% + \pgfmathpointintersectionoflineandarc{\midpoint\advance\pgf@x\xradius}{\midpoint}% + {\centerpoint}{270}{450}{\xradius and \yradius}% + }% + \anchor{mid west}{% + \ellipsecalloutpoints% + \pgfmathpointintersectionoflineandarc{\midpoint\advance\pgf@x-\xradius}{\midpoint}% + {\centerpoint}{90}{270}{\xradius and \yradius}% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \ellipsecalloutpoints% + \pgfmathpointintersectionoflineandarc{\basepoint\advance\pgf@x\xradius}{\basepoint}% + {\centerpoint}{270}{450}{\xradius and \yradius}% + }% + \anchor{base west}{% + \ellipsecalloutpoints% + \pgfmathpointintersectionoflineandarc{\basepoint\advance\pgf@x-\xradius}{\basepoint}% + {\centerpoint}{90}{270}{\xradius and \yradius}% + }% + \anchor{north}{% + \ellipsecalloutpoints% + \centerpoint% + \advance\pgf@y\yradius\relax% + }% + \anchor{south}{% + \ellipsecalloutpoints% + \centerpoint% + \advance\pgf@y-\yradius\relax% + }% + \anchor{east}{% + \ellipsecalloutpoints% + \centerpoint% + \advance\pgf@x\xradius\relax% + }% + \anchor{west}{% + \ellipsecalloutpoints% + \centerpoint% + \advance\pgf@x-\xradius\relax% + }% + \anchor{north west}{% + \ellipsecalloutpoints% + \pgf@xa\xradius\relax% + \pgf@ya\yradius\relax% + \centerpoint% + \advance\pgf@y0.7071067\pgf@ya% + \advance\pgf@x-0.7071067\pgf@xa% + }% + \anchor{north east}{% + \ellipsecalloutpoints% + \pgf@xa\xradius\relax% + \pgf@ya\yradius\relax% + \centerpoint% + \advance\pgf@y0.7071067\pgf@ya% + \advance\pgf@x0.7071067\pgf@xa% + }% + \anchor{south west}{% + \ellipsecalloutpoints% + \pgf@xa\xradius\relax% + \pgf@ya\yradius\relax% + \centerpoint% + \advance\pgf@y-0.7071067\pgf@ya% + \advance\pgf@x-0.7071067\pgf@xa% + }% + \anchor{south east}{% + \ellipsecalloutpoints% + \pgf@xa\xradius\relax% + \pgf@ya\yradius\relax% + \centerpoint% + \advance\pgf@y-0.7071067\pgf@ya% + \advance\pgf@x0.7071067\pgf@xa% + }% + \anchor{pointer}{% + \ellipsecalloutpoints% + \calloutpointeranchor% + }% + \backgroundpath{% + \ellipsecalloutpoints% + \ifpgf@lib@callout@absolutepointer% + \pgfextract@process\calloutpointer{% + \pgfpointanchor{pgf@lib@callout@pointer}{center}% + }% + \pgf@lib@callouts@shortenpointer% + \pgf@lib@ellipsecallout@getpoints% + \calloutpointeranchor% + \ifx\pgf@node@name\pgfutil@empty% + \else% + \edef\pgf@sh@@temp{\noexpand\expandafter\noexpand\pgfutil@g@addto@macro\noexpand\csname pgf@sh@np@\pgf@node@name\noexpand\endcsname}% + \edef\pgf@sh@@@temp{% + \noexpand\def\noexpand\calloutpointeranchor{% + \noexpand\pgf@x\the\pgf@x% + \noexpand\pgf@y\the\pgf@y% + }% + }% + \expandafter\pgf@sh@@temp\expandafter{\pgf@sh@@@temp} + \fi% + \fi% + \pgfpathmoveto{\calloutpointer}% + \pgfpathlineto{\aftercalloutpointer}% + \ifdim\aftercalloutangle pt<\beforecalloutangle pt\relax% + \pgfpatharc{\aftercalloutangle}{\beforecalloutangle}{\xpathradius and \ypathradius}% + \else% + \pgfpatharc{\aftercalloutangle}{360}{\xpathradius and \ypathradius}% + \pgfpatharc{0}{\beforecalloutangle}{\xpathradius and \ypathradius}% + \fi% + \pgfpathclose% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \ellipsecalloutpoints% + \pgfpointadd{\pgfpointborderellipse{\externalpoint}{\pgfpoint{\xradius}{\yradius}}% + }{\centerpoint}% + }% +}% + +\def\pgf@lib@ellipsecallout@getpoints{% + \pgfextract@process\borderpoint{% + \pgfpointborderellipse{% + \centerpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \calloutpointer% + \advance\pgf@x-\pgf@xa% + \advance\pgf@y-\pgf@ya% + }{\pgfqpoint{\xpathradius}{\ypathradius}}% + }% + \pgfmathangleonellipse{\borderpoint}{\xpathradius and \ypathradius}% + \pgfutil@tempdima\pointerarc pt\relax% + \pgfutil@tempdimb\pgfmathresult pt\relax% + \advance\pgfutil@tempdimb-.5\pgfutil@tempdima% + \ifdim\pgfutil@tempdimb<0pt\relax% + \advance\pgfutil@tempdimb360pt\relax% + \fi% + \edef\beforecalloutangle{\pgfmath@tonumber{\pgfutil@tempdimb}}% + \advance\pgfutil@tempdimb\pgfutil@tempdima% + \ifdim\pgfutil@tempdimb<360pt\relax% + \else% + \advance\pgfutil@tempdimb-360pt\relax% + \fi% + \edef\aftercalloutangle{\pgfmath@tonumber{\pgfutil@tempdimb}}% + \pgfextract@process\beforecalloutpointer{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{\beforecalloutangle}{\xpathradius and \ypathradius}% + }% + }% + \pgfextract@process\aftercalloutpointer{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{\aftercalloutangle}{\xpathradius and \ypathradius}% + }% + }% + \pgf@lib@callouts@pointeranchor% +}% + + + +\pgfkeys{/pgf/callout pointer anchor aspect/.initial=1}% + +\def\pgf@lib@callouts@pointeranchor{% + \pgfutil@tempdimb\outersep\relax% + \pgfmathanglebetweenlines{\calloutpointer}{\aftercalloutpointer}{\calloutpointer}{\beforecalloutpointer}% + \pgfmathdivide@{\pgfmathresult}{2}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \pgfmathcosec@{\pgfmathresult}% + \pgfutil@tempdimb\pgfmathresult\pgfutil@tempdimb% + \pgfmathanglebetweenpoints{\calloutpointer}{\aftercalloutpointer}% + \advance\pgfutil@tempdima\pgfmathresult pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \pgfextract@process\calloutpointeranchor{% + \pgfpointadd{% + \pgfmathparse{\pgfkeysvalueof{/pgf/callout pointer anchor aspect}}% + \pgfutil@tempdimb\pgfmathresult\pgfutil@tempdimb% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + }{% + \calloutpointer% + }% + }% +}% + +\def\pgf@lib@callouts@shortenpointer{% + \pgfextract@process\calloutpointer{% + \pgfmathanglebetweenpoints{\calloutpointer}{\centerpoint}% + \let\angle\pgfmathresult% + \pgfmathsin@{\angle}% + \let\sinpointerangle\pgfmathresult% + \pgfmathcos@{\angle}% + \let\cospointerangle\pgfmathresult% + \pgfpointadd{\calloutpointer}{% + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/callout pointer shorten}}% + \pgf@x\cospointerangle\pgfutil@tempdima% + \pgf@y\sinpointerangle\pgfutil@tempdima% + }% + }% +}% + + +\pgfdeclareshape{rectangle callout}{% + \savedmacro\rectanglecalloutpoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \edef\xtemp{\the\pgf@x}% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \edef\ytemp{\the\pgf@y}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\xlength{\the\pgf@x}% + \edef\ylength{\the\pgf@y}% + \addtosavedmacro\xlength% + \addtosavedmacro\ylength% + \pgfmathsetlengthmacro\pointerwidth{\pgfkeysvalueof{/pgf/callout pointer width}}% + \addtosavedmacro\pointerwidth% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \ifpgf@lib@callout@absolutepointer% + \else% + \pgfextract@process\calloutpointer{% + \pgfextract@process\borderpoint{% + \expandafter\pgfpointborderrectangle\expandafter{\pgf@lib@callout@relativepointer}% + {\pgfqpoint{\xtemp}{\ytemp}}% + }% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\borderpoint}% + \let\pointerangle\pgfmathresult% + \expandafter\pgf@process\expandafter{\pgf@lib@callout@relativepointer}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \edef\pointerradius{\pgfmathresult pt}% + \pgfpointadd{\borderpoint}{\pgfqpointpolar{\pointerangle}{\pointerradius}}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgf@lib@callouts@shortenpointer% + \addtosavedmacro\calloutpointer% + \pgf@lib@rectanglecallout@pointer% + \addtosavedmacro\calloutpointeranchor% + \addtosavedmacro\beforecalloutpointer% + \addtosavedmacro\aftercalloutpointer% + \addtosavedmacro\firstpoint% + \addtosavedmacro\secondpoint% + \addtosavedmacro\thirdpoint% + \addtosavedmacro\fourthpoint% + \fi% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5em}% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \rectanglecalloutpoints% + \midpoint% + \advance\pgf@x\xlength\relax% + }% + \anchor{mid west}{% + \rectanglecalloutpoints% + \midpoint% + \advance\pgf@x-\xlength\relax% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \rectanglecalloutpoints% + \basepoint% + \advance\pgf@x\xlength\relax% + }% + \anchor{base west}{% + \rectanglecalloutpoints% + \basepoint% + \advance\pgf@x-\xlength\relax% + }% + \anchor{north}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@y\ylength\relax% + }% + \anchor{south}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@y-\ylength\relax% + }% + \anchor{east}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@x\xlength\relax% + }% + \anchor{west}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@x-\xlength\relax% + }% + \anchor{north east}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@x\xlength\relax% + \advance\pgf@y\ylength\relax% + }% + \anchor{south west}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@x-\xlength\relax% + \advance\pgf@y-\ylength\relax% + }% + \anchor{south east}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@x\xlength\relax% + \advance\pgf@y-\ylength\relax% + }% + \anchor{north west}{% + \rectanglecalloutpoints% + \centerpoint% + \advance\pgf@x-\xlength\relax% + \advance\pgf@y\ylength\relax% + }% + \anchor{pointer}{% + \rectanglecalloutpoints% + \calloutpointeranchor% + }% + \backgroundpath{% + \rectanglecalloutpoints% + \pgf@x\xlength\relax% + \pgf@y\ylength\relax% + \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\xtemp{\the\pgf@x}% + \edef\ytemp{\the\pgf@y}% + \ifpgf@lib@callout@absolutepointer% + \pgfextract@process\calloutpointer{% + \pgfpointanchor{pgf@lib@callout@pointer}{center}% + }% + \pgf@lib@callouts@shortenpointer% + \pgfmathsetlengthmacro\pointerwidth{\pgfkeysvalueof{/pgf/callout pointer width}}% + \pgf@lib@rectanglecallout@pointer% + \ifx\pgf@node@name\pgfutil@empty% + \else% + \edef\pgf@sh@@temp{\noexpand\expandafter\noexpand\pgfutil@g@addto@macro\noexpand\csname pgf@sh@np@\pgf@node@name\noexpand\endcsname}% + \edef\pgf@sh@@@temp{% + \noexpand\def\noexpand\calloutpointeranchor{% + \noexpand\pgf@x\the\pgf@x% + \noexpand\pgf@y\the\pgf@y% + }% + }% + \expandafter\pgf@sh@@temp\expandafter{\pgf@sh@@@temp}% + \fi% + \fi% + {% + \pgfsetcornersarced{\pgfqpoint{0pt}{0pt}}% + \pgfpathmoveto{\beforecalloutpointer}% + }% + \pgfpathlineto{\calloutpointer}% + {% + \pgfsetcornersarced{\pgfqpoint{0pt}{0pt}}% + \pgfpathlineto{\aftercalloutpointer}% + }% + {% + \pgftransformshift{\centerpoint}% + \pgfpathlineto{\firstpoint}% + \pgfpathlineto{\secondpoint}% + \pgfpathlineto{\thirdpoint}% + \pgfpathlineto{\fourthpoint}% + {% + \pgfsetcornersarced{\pgfqpoint{0pt}{0pt}}% + \pgfpathclose% + }% + } + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \rectanglecalloutpoints% + \pgfpointadd{\centerpoint}% + {% + \pgfpointborderrectangle{\pgfpointadd{\centerpoint}{\externalpoint}}% + {\pgfqpoint{\xlength}{\ylength}}% + }% + }% +}% + + + +\def\pgf@lib@rectanglecallout@pointer{% + \pgfextract@process\borderpoint{% + \pgfpointborderrectangle{% + \centerpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \calloutpointer% + \advance\pgf@x-\pgf@xa% + \advance\pgf@y-\pgf@ya% + }{\pgfqpoint{\xtemp}{\ytemp}}% + }% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\borderpoint}% + \let\borderangle\pgfmathresult% + \pgfutil@tempdima\pointerwidth\relax% + \pgf@xa\xtemp\relax% + \advance\pgf@xa-\pgfutil@tempdima% + \pgf@ya\ytemp\relax% + \advance\pgf@ya-\pgfutil@tempdima% + \pgf@process{% + \pgfutil@ifundefined{pgf@corner@arc}{\pgfpointorigin}{% + \expandafter\pgfqpoint\pgf@corner@arc}% + }% + \advance\pgf@xa-\pgf@x% + \advance\pgf@ya-\pgf@y% + \borderpoint% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@xc0pt\relax% + \pgf@yc0pt\relax% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\pgfqpoint{\xtemp}{\ytemp}}% + \ifdim\borderangle pt<\pgfmathresult pt\relax% + \pgf@yc.5\pgfutil@tempdima% + \ifdim\pgf@yb>\pgf@ya% + \pgf@yb\pgf@ya% + \fi% + \edef\firstpoint{\noexpand\pgfqpoint{\xtemp}{\ytemp}}% + \edef\secondpoint{\noexpand\pgfqpoint{-\xtemp}{\ytemp}}% + \edef\thirdpoint{\noexpand\pgfqpoint{-\xtemp}{-\ytemp}}% + \edef\fourthpoint{\noexpand\pgfqpoint{\xtemp}{-\ytemp}}% + \else% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\pgfqpoint{-\xtemp}{\ytemp}}% + \ifdim\borderangle pt<\pgfmathresult pt\relax% + \pgf@xc-.5\pgfutil@tempdima% + \ifdim\pgf@xb>\pgf@xa% + \pgf@xb\pgf@xa% + \else% + \ifdim\pgf@xb<-\pgf@xa% + \pgf@xb-\pgf@xa% + \fi% + \fi% + \edef\firstpoint{\noexpand\pgfqpoint{-\xtemp}{\ytemp}}% + \edef\secondpoint{\noexpand\pgfqpoint{-\xtemp}{-\ytemp}}% + \edef\thirdpoint{\noexpand\pgfqpoint{\xtemp}{-\ytemp}}% + \edef\fourthpoint{\noexpand\pgfqpoint{\xtemp}{\ytemp}}% + \else% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\pgfqpoint{-\xtemp}{-\ytemp}}% + \ifdim\borderangle pt<\pgfmathresult pt\relax% + \pgf@yc-.5\pgfutil@tempdima% + \ifdim\pgf@yb>\pgf@ya% + \pgf@yb\pgf@ya% + \else% + \ifdim\pgf@yb<-\pgf@ya% + \pgf@yb-\pgf@ya% + \fi% + \fi% + \edef\firstpoint{\noexpand\pgfqpoint{-\xtemp}{-\ytemp}}% + \edef\secondpoint{\noexpand\pgfqpoint{\xtemp}{-\ytemp}}% + \edef\thirdpoint{\noexpand\pgfqpoint{\xtemp}{\ytemp}}% + \edef\fourthpoint{\noexpand\pgfqpoint{-\xtemp}{\ytemp}}% + \else% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\pgfqpoint{\xtemp}{-\ytemp}}% + \ifdim\borderangle pt<\pgfmathresult pt\relax% + \pgf@xc.5\pgfutil@tempdima% + \ifdim\pgf@xb>\pgf@xa% + \pgf@xb\pgf@xa% + \else% + \ifdim\pgf@xb<-\pgf@xa% + \pgf@xb-\pgf@xa% + \fi% + \fi% + \edef\firstpoint{\noexpand\pgfqpoint{\xtemp}{-\ytemp}}% + \edef\secondpoint{\noexpand\pgfqpoint{\xtemp}{\ytemp}}% + \edef\thirdpoint{\noexpand\pgfqpoint{-\xtemp}{\ytemp}}% + \edef\fourthpoint{\noexpand\pgfqpoint{-\xtemp}{-\ytemp}}% + \else% + \pgf@yc.5\pgfutil@tempdima% + \ifdim\pgf@yb<-\pgf@ya% + \pgf@yb-\pgf@ya% + \fi% + \edef\firstpoint{\noexpand\pgfqpoint{\xtemp}{\ytemp}}% + \edef\secondpoint{\noexpand\pgfqpoint{-\xtemp}{\ytemp}}% + \edef\thirdpoint{\noexpand\pgfqpoint{-\xtemp}{-\ytemp}}% + \edef\fourthpoint{\noexpand\pgfqpoint{\xtemp}{-\ytemp}}% + \fi% + \fi% + \fi% + \fi% + \pgfextract@process\beforecalloutpointer{% + \centerpoint% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + \advance\pgf@x-\pgf@xc% + \advance\pgf@y-\pgf@yc% + }% + \pgfextract@process\aftercalloutpointer{% + \centerpoint% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + \advance\pgf@x\pgf@xc% + \advance\pgf@y\pgf@yc% + }% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x>\pgf@y% + \edef\outersep{\the\pgf@x}% + \else% + \edef\outersep{\the\pgf@y}% + \fi% + \pgf@lib@callouts@pointeranchor% +}% + + +\def\pgf@lib@callout@setpointersize#1{% + \edef\pgf@lib@callout@temp{#1}% + \edef\pgf@marshall{\noexpand\pgfutil@in@{of callout}{\pgf@lib@callout@temp}}% + \pgf@marshall% + \ifpgfutil@in@% + \expandafter\pgf@xa\expandafter\pgf@lib@callout@setpointerrelativesize% + \pgf@lib@callout@temp\pgf@lib@stop\pgf@x% + \expandafter\pgf@ya\expandafter\pgf@lib@callout@setpointerrelativesize% + \pgf@lib@callout@temp\pgf@lib@stop\pgf@y% + \else% + \edef\pgf@marshall{\noexpand\pgfutil@in@{and}{\pgf@lib@callout@temp}}% + \pgf@marshall% + \ifpgfutil@in@% + \expandafter\pgf@lib@callout@setpointerbothsizes\pgf@lib@callout@temp\pgf@lib@stop% + \else% + \pgfmathsetlength\pgf@xa{#1}% + \pgfmathsetlength\pgf@ya{#1}% + \fi% + \fi% +}% +\def\pgf@lib@callout@setpointerrelativesize#1of callout#2\pgf@lib@stop{#1}% +\def\pgf@lib@callout@setpointerbothsizes#1and#2\pgf@lib@stop{% + \pgfmathsetlength\pgf@xa{#2}% + \pgfmathsetlength\pgf@ya{#2}% +}% + +\pgfdeclareshape{cloud callout}{% + \savedanchor\calloutpointer{% + \pgfutil@ifundefined{pgf@sh@s@cloud}{% + \pgferror{I cannot find the cloud shape. Please load the `symbol shapes' library}}{}% + \pgf@sh@s@cloud% + \pgf@sh@savedmacros% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \ifpgf@lib@callout@absolutepointer% + \else% + \pgfextract@process\calloutpointer{% + \pgfextract@process\borderpoint{% + \expandafter\pgfpointborderellipse\expandafter{\pgf@lib@callout@relativepointer}% + {\pgfqpoint{\xouterradius}{\youterradius}}% + }% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\borderpoint}% + \let\pointerangle\pgfmathresult% + \expandafter\pgf@process\expandafter{\pgf@lib@callout@relativepointer}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \edef\pointerradius{\pgfmathresult pt}% + \pgfpointadd{\borderpoint}{\pgfqpointpolar{\pointerangle}{\pointerradius}}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgf@lib@callouts@shortenpointer% + \fi% + }% + \anchor{pointer}{% + \calloutpointer% + }% + \inheritsavedanchors[from=cloud]% + \inheritanchor[from=cloud]{center}% + \inheritanchor[from=cloud]{base}% + \inheritanchor[from=cloud]{mid}% + \inheritanchor[from=cloud]{north}% + \inheritanchor[from=cloud]{south}% + \inheritanchor[from=cloud]{east}% + \inheritanchor[from=cloud]{west}% + \inheritanchor[from=cloud]{north east}% + \inheritanchor[from=cloud]{south west}% + \inheritanchor[from=cloud]{south east}% + \inheritanchor[from=cloud]{north west}% + \inheritanchorborder[from=cloud]% + \backgroundpath{% + \pgf@sh@bg@cloud% + \ifpgf@lib@callout@absolutepointer% + \pgfextract@process\calloutpointer{% + \pgfpointanchor{pgf@lib@callout@pointer}{center}% + }% + \ifx\pgf@node@name\pgfutil@empty% + \else% + \edef\pgf@sh@@temp{\noexpand\expandafter\noexpand\pgfutil@g@addto@macro\noexpand\csname pgf@sh@np@\pgf@node@name\noexpand\endcsname}% + \edef\pgf@sh@@@temp{% + \noexpand\def\noexpand\calloutpointeranchor{% + \noexpand\pgf@x\the\pgf@x% + \noexpand\pgf@y\the\pgf@y% + }% + }% + \expandafter\pgf@sh@@temp\expandafter{\pgf@sh@@@temp} + \fi% + \fi% + \pgfextract@process\borderpoint{% + \pgfpointadd{% + \pgfpointborderellipse{\pgfpointdiff{\centerpoint}{\calloutpointer}}% + {\pgfqpoint{\xouterradius}{\youterradius}}% + }{\centerpoint}% + }% + \pgf@lib@callouts@shortenpointer% + \pgfmathanglebetweenpoints{\calloutpointer}{\centerpoint}% + \let\angle\pgfmathresult% + \pgfmathsin@{\angle}% + \let\sinpointerangle\pgfmathresult% + \pgfmathcos@{\angle}% + \let\cospointerangle\pgfmathresult% + \pgf@x\xouterradius\relax% + \pgf@x2.0\pgf@x% + \pgf@y\yinnerradius\relax% + \pgf@y2.0\pgf@y% + \pgf@lib@callout@setpointersize{\pgfkeysvalueof{/pgf/callout pointer start size}}% + \pgf@xb\pgf@xa% + \pgf@yb\pgf@ya% + \pgf@lib@callout@setpointersize{\pgfkeysvalueof{/pgf/callout pointer end size}}% + \advance\pgf@xb-\pgf@xa% + \advance\pgf@yb-\pgf@ya% + \pgfmathsetcount\c@pgf@counta{\pgfkeysvalueof{/pgf/callout pointer segments}}% + \divide\pgf@xb\c@pgf@counta% + \divide\pgf@yb\c@pgf@counta% + \pgf@process{\pgfpointdiff{\borderpoint}{\calloutpointer}}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \divide\pgfutil@tempdima\c@pgf@counta% + \pgfutil@tempdimb0pt\relax% + \pgfmathloop% + \ifnum\pgfmathcounter>\c@pgf@counta% + \else% + {% + \pgf@xa.5\pgf@xa% + \pgf@ya.5\pgf@ya% + \edef\tempxradius{\the\pgf@xa}% + \edef\tempyradius{\the\pgf@ya}% + \pgfpathellipse% + {% + \calloutpointer% + \advance\pgf@x\cospointerangle\pgfutil@tempdimb% + \advance\pgf@y\sinpointerangle\pgfutil@tempdimb% + }% + {\pgfqpoint{\tempxradius}{0pt}}{\pgfqpoint{0pt}{\tempyradius}}% + }% + \advance\pgf@xa\pgf@xb% + \advance\pgf@ya\pgf@yb% + \advance\pgfutil@tempdimb\pgfutil@tempdima% + \repeatpgfmathloop% + }% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@cloud callout\endcsname{% + \c@pgf@counta\puffs\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>0\relax% + \pgfutil@ifundefined{pgf@anchor@cloud callout@puff\space\the\c@pgf@counta}{% + \expandafter\xdef\csname pgf@anchor@cloud callout@puff\space\the\c@pgf@counta\endcsname{% + \noexpand\pgf@sh@@cloudpuffanchor{\the\c@pgf@counta}% + }% + }{\c@pgf@counta0\relax}% + \advance\c@pgf@counta-1\relax% + \repeatpgfmathloop% + }% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f7d4010816656e85969debfb1f841cb8fcc78371 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.code.tex @@ -0,0 +1,10 @@ + +\ProvidesFileRCS{pgflibraryshapes.code.tex} + + +\usepgflibrary{shapes.geometric}% +\usepgflibrary{shapes.misc}% +\usepgflibrary{shapes.symbols}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..9af39951211107b88ec6a69ae93cdc74ab15ff22 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.geometric.code.tex @@ -0,0 +1,3521 @@ + +\ProvidesFileRCS{pgflibraryshapes.geometric.code.tex} + +\pgfdeclareshape{ellipse} +{% + \savedanchor\centerpoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgf@y=.5\ht\pgfnodeparttextbox% + \advance\pgf@y by-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\radius{% + \pgf@y=.5\ht\pgfnodeparttextbox% + \advance\pgf@y by.5\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y by\pgf@yb% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x by\pgf@xb% + \pgf@x=1.4142136\pgf@x% + \pgf@y=1.4142136\pgf@y% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@yc% + \pgf@y=.5\pgf@yc% + \fi% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<.5\pgf@xc% + \pgf@x=.5\pgf@xc% + \fi% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \advance\pgf@x by\pgf@xb% + \advance\pgf@y by\pgf@yb% + }% + + \anchor{center}{\centerpoint}% + \anchor{mid}{\centerpoint\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base}{\centerpoint\pgf@y=0pt}% + \anchor{north} + { + \pgf@process{\radius} + \pgf@ya=\pgf@y% + \pgf@process{\centerpoint} + \advance\pgf@y by\pgf@ya + }% + \anchor{south} + { + \pgf@process{\radius} + \pgf@ya=\pgf@y% + \pgf@process{\centerpoint} + \advance\pgf@y by-\pgf@ya + }% + \anchor{west} + { + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@process{\centerpoint} + \advance\pgf@x by-\pgf@xa + }% + \anchor{mid west} + {% + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@process{\centerpoint} + \advance\pgf@x by-\pgf@xa% + \pgfmathsetlength\pgf@y{.5ex} + }% + \anchor{base west} + {% + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@process{\centerpoint} + \advance\pgf@x by-\pgf@xa% + \pgf@y=0pt + }% + \anchor{north west} + { + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\centerpoint} + \advance\pgf@x by-0.707107\pgf@xa + \advance\pgf@y by0.707107\pgf@ya + }% + \anchor{south west} + { + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\centerpoint} + \advance\pgf@x by-0.707107\pgf@xa + \advance\pgf@y by-0.707107\pgf@ya + }% + \anchor{east} + {% + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@process{\centerpoint} + \advance\pgf@x by\pgf@xa + }% + \anchor{mid east} + {% + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@process{\centerpoint} + \advance\pgf@x by\pgf@xa% + \pgfmathsetlength\pgf@y{.5ex} + }% + \anchor{base east} + {% + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@process{\centerpoint} + \advance\pgf@x by\pgf@xa% + \pgf@y=0pt + }% + \anchor{north east} + { + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\centerpoint} + \advance\pgf@x by0.707107\pgf@xa + \advance\pgf@y by0.707107\pgf@ya + }% + \anchor{south east} + { + \pgf@process{\radius} + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\centerpoint} + \advance\pgf@x by0.707107\pgf@xa + \advance\pgf@y by-0.707107\pgf@ya + }% + \anchorborder{% + \edef\pgf@marshal{% + \noexpand\pgfpointborderellipse + {\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + {\noexpand\radius}% + }% + \pgf@marshal% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \centerpoint% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + }% + + \backgroundpath + { + \pgf@process{\radius}% + \pgfutil@tempdima=\pgf@x% + \pgfutil@tempdimb=\pgf@y% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \advance\pgfutil@tempdima by-\pgf@xb% + \advance\pgfutil@tempdimb by-\pgf@yb% + \pgfpathellipse{\centerpoint}{\pgfqpoint{\pgfutil@tempdima}{0pt}}{\pgfqpoint{0pt}{\pgfutil@tempdimb}}% + }% +}% + + + + + +\pgfkeys{/pgf/.cd, + aspect/.code={\pgfsetshapeaspect{#1}},% + shape aspect/.initial=1,% + shape aspect/.code={% + \pgfkeys{/pgf/aspect={#1}}% + \pgfkeyssetvalue{/pgf/shape aspect}{#1} + }% +}% + + +\def\pgfsetshapeaspect#1{% + \def\pgfshapeaspect{#1}% + \pgfutil@tempdima=#1pt% + \pgfutil@tempdima=.125\pgfutil@tempdima% + \c@pgf@counta=\pgfutil@tempdima\relax% + \pgfutil@tempdima=8192pt% + \divide\pgfutil@tempdima by\c@pgf@counta% + \edef\pgfshapeaspectinverse{\pgf@sys@tonumber{\pgfutil@tempdima}}% +}% + +\pgfsetshapeaspect{1}% + +\pgfdeclareshape{diamond} +{% + \savedanchor\outernortheast{% + \pgf@xa=.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa by\pgf@xc% + \pgf@ya=.5\ht\pgfnodeparttextbox% + \advance\pgf@ya by.5\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya by\pgf@yc% + \pgf@x=\pgf@xa% + \advance\pgf@x by\pgfshapeaspect\pgf@ya% + \pgf@y=\pgfshapeaspectinverse\pgf@xa% + \advance\pgf@y by\pgf@ya% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@xb=.5\pgf@xb% + \ifdim\pgf@x<\pgf@xb% + \pgf@x=\pgf@xb% + \fi% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@yb=.5\pgf@yb% + \ifdim\pgf@y<\pgf@yb% + \pgf@y=\pgf@yb% + \fi% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \advance\pgf@x by\pgf@xa% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \advance\pgf@y by\pgf@ya% + }% + \savedanchor\text{% + \pgf@x=-.5\wd\pgfnodeparttextbox% + \pgf@y=-.5\ht\pgfnodeparttextbox% + \advance\pgf@y by.5\dp\pgfnodeparttextbox% + }% + + \anchor{text}{\text}% + \anchor{center}{\pgfpointorigin}% + \anchor{mid}{% + \pgf@process{\text}% + \pgf@x=0pt% + \pgfmathsetlength\pgf@ya{.5ex}% + \advance\pgf@y by\pgf@ya% + }% + \anchor{base}{\pgf@process{\text}\pgf@x=0pt}% + \anchor{north}{\pgf@process{\outernortheast}\pgf@x=0pt}% + \anchor{south}{\pgf@process{\outernortheast}\pgf@x=0pt\pgf@y=-\pgf@y}% + \anchor{west}{\pgf@process{\outernortheast}\pgf@x=-\pgf@x\pgf@y=0pt}% + \anchor{north west}{\pgf@process{\outernortheast}\pgf@x=-.5\pgf@x\pgf@y=.5\pgf@y}% + \anchor{south west}{\pgf@process{\outernortheast}\pgf@x=-.5\pgf@x\pgf@y=-.5\pgf@y}% + \anchor{east}{\pgf@process{\outernortheast}\pgf@y=0pt}% + \anchor{north east}{\pgf@process{\outernortheast}\pgf@x=.5\pgf@x\pgf@y=.5\pgf@y}% + \anchor{south east}{\pgf@process{\outernortheast}\pgf@x=.5\pgf@x\pgf@y=-.5\pgf@y}% + \anchorborder{% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\outernortheast}% + \ifdim\pgf@xa>0pt% + \else% + \pgf@x=-\pgf@x% + \fi% + \ifdim\pgf@ya>0pt% + \else% + \pgf@y=-\pgf@y% + \fi% + \edef\pgf@marshal{% + \noexpand\pgfpointintersectionoflines + {\noexpand\pgfpointorigin} + {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}} + {\noexpand\pgfqpoint{\the\pgf@x}{0pt}} + {\noexpand\pgfqpoint{0pt}{\the\pgf@y}}% + }% + \pgf@process{\pgf@marshal}% + }% + + \backgroundpath{ + \pgf@process{\outernortheast}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/outer ysep}}% + \advance\pgf@xc by-1.414213\pgf@xa% + \advance\pgf@yc by-1.414213\pgf@ya% + \pgfpathmoveto{\pgfqpoint{\pgf@xc}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{\pgf@yc}}% + \pgfpathlineto{\pgfqpoint{-\pgf@xc}{0pt}}% + \pgfpathlineto{\pgfqpoint{0pt}{-\pgf@yc}}% + \pgfpathclose% + }% +}% + + + + + + +\newif\ifpgf@lib@shapes@starouterradiususesratio +\pgf@lib@shapes@starouterradiususesratiotrue + + +\pgfkeys{/pgf/.cd, + star points/.initial=5, + star point height/.initial=.5cm, + star point height/.code={% + \def\pgf@lib@temp{#1}% + \pgfkeyslet{/pgf/star point height}{\pgf@lib@temp}% + \pgf@lib@shapes@starouterradiususesratiofalse% + }, + star point ratio/.initial=1.5, + star point ratio/.code={% + \def\pgf@lib@temp{#1}% + \pgfkeyslet{/pgf/star point ratio}{\pgf@lib@temp}% + \pgf@lib@shapes@starouterradiususesratiotrue% + },% + star rotate/.style={/pgf/shape border rotate={#1}},% +}% + + +\pgfdeclareshape{star}{% + \savedmacro\totalstarpoints{% + \pgfmathsetcounter{pgf@counta}{\pgfkeysvalueof{/pgf/star points}}% + \multiply\c@pgf@counta2\relax% + \edef\totalstarpoints{\the\c@pgf@counta}% + }% + \savedmacro\anglestep{% + \pgfmathdivide{180}{\pgfkeysvalueof{/pgf/star points}}% + \let\anglestep\pgfmathresult% + }% + \savedmacro\calculateradii{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifdim\pgf@y>\pgf@x% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \edef\innerradius{\the\pgf@x}% + \ifpgf@lib@shapes@starouterradiususesratio% + \pgfmathparse{\pgfkeysvalueof{/pgf/star point ratio}}% + \expandafter\pgf@x\pgfmathresult\pgf@x% + \else% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/star point height}}% + \fi% + \pgf@xc\pgf@x% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@ya>\pgf@xa% + \pgf@xa\pgf@ya% + \fi% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \edef\outerradius{\the\pgf@x}% + \ifdim\pgf@x>\pgf@xc% + \ifpgf@lib@shapes@starouterradiususesratio% + \pgfmathreciprocal{\pgfkeysvalueof{/pgf/star point ratio}}% + \pgf@xa\pgfmathresult\pgf@x\relax% + \edef\innerradius{\the\pgf@xa}% + \else% + \pgf@xa\pgf@x\relax% + \pgfmathaddtolength\pgf@xa{-\pgfkeysvalueof{/pgf/star point height}}% + \edef\innerradius{\the\pgf@xa}% + \fi% + \fi% + \edef\outerradius{\the\pgf@x}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@ya>\pgf@xa% + \pgf@xa\pgf@ya% + \fi + \pgfmathdivide{180}{\pgfkeysvalueof{/pgf/star points}}% + \let\angletofirstpoint\pgfmathresult% + \pgfmathmultiply@{\angletofirstpoint}{2}% + \let\angletosecondpoint\pgfmathresult% + \pgfmathanglebetweenlines% + {\pgfqpointpolar{\angletofirstpoint}{\outerradius}}% + {\pgfqpointpolar{\angletosecondpoint}{\innerradius}}% + {\pgfqpointpolar{\angletofirstpoint}{\outerradius}}% + {\pgfqpointpolar{0}{\innerradius}}% + \pgfmathdivide@{\pgfmathresult}{2}% + \pgfmathcosec@{\pgfmathresult}% + \pgf@x\outerradius\relax% + \advance\pgf@x\pgfmathresult\pgf@xa% + \edef\anchorouterradius{\the\pgf@x}% + \pgfmathanglebetweenlines% + {\pgfqpointpolar{\angletofirstpoint}{\innerradius}}% + {\pgfqpointpolar{0}{\outerradius}}% + {\pgfqpointpolar{\angletofirstpoint}{\innerradius}}% + {\pgfqpointpolar{\angletosecondpoint}{\outerradius}}% + \pgfmathdivide@{\pgfmathresult}{2}% + \pgfmathcosec@{\pgfmathresult}% + \pgf@x\innerradius\relax% + \advance\pgf@x\pgfmathresult\pgf@xa% + \edef\anchorinnerradius{\the\pgf@x}% + \addtosavedmacro{\innerradius}% + \addtosavedmacro{\outerradius}% + \addtosavedmacro{\anchorinnerradius}% + \addtosavedmacro{\anchorouterradius}% + }% + \savedmacro\startangle{% + \pgfmathadd{90}{\pgfkeysvalueof{/pgf/shape border rotate}}% + \let\startangle\pgfmathresult% + }% + \savedanchor{\centerpoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor{\midpoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\centerpoint\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base}{\centerpoint\pgf@y=0pt}% + \anchor{north}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{0pt}{\anchorouterradius}}}% + \anchor{south}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{0pt}{-\anchorouterradius}}}% + \anchor{east}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{\anchorouterradius}{0pt}}}% + \anchor{west}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{-\anchorouterradius}{0pt}}}% + \anchor{north east}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{\anchorouterradius}{\anchorouterradius}}}% + \anchor{north west}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{-\anchorouterradius}{\anchorouterradius}}}% + \anchor{south east}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{\anchorouterradius}{-\anchorouterradius}}}% + \anchor{south west}{% + \calculateradii% + \csname pgf@anchor@star@border\endcsname{\pgfqpoint{-\anchorouterradius}{-\anchorouterradius}}}% + \backgroundpath{% + \calculateradii% + \let\angle\startangle% + \pgfpathmoveto{\pgfpointadd{\centerpoint}{\pgfqpointpolar{\startangle}{\outerradius}}}% + \pgfmathloop% + \pgfmathadd@{\angle}{\anglestep}% + \let\angle\pgfmathresult% + \ifnum\pgfmathcounter=\totalstarpoints% + \pgfpathclose% + \else% + \ifodd\pgfmathcounter + \pgfpathlineto{\pgfpointadd{\centerpoint}{\pgfqpointpolar{\angle}{\innerradius}}}% + \else% + \pgfpathlineto{\pgfpointadd{\centerpoint}{\pgfqpointpolar{\angle}{\outerradius}}}% + \fi% + \repeatpgfmathloop% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \centerpoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + \pgfmathsubtract@{\pgfmathresult}{\startangle}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \pgfmathdivide@{\pgfmathresult}{\anglestep}% + \pgfmathfloor@{\pgfmathresult}% + \afterassignment\pgfmath@gobbletilpgfmath@ + \c@pgf@counta\pgfmathresult\relax\pgfmath@ + \pgfmathmultiply@{\pgfmathresult}{\anglestep}% + \pgfmathadd@{\pgfmathresult}{\startangle}% + \let\firstangle\pgfmathresult% + \pgfmathadd@{\pgfmathresult}{\anglestep}% + \let\secondangle\pgfmathresult% + \calculateradii% + \ifodd\c@pgf@counta + \pgfpointintersectionoflines{\centerpoint}{\pgfpoint{+\externalx}{+\externaly}}% + {% + \pgfpointadd{\centerpoint}% + {\pgfqpointpolar{+\firstangle}{+\anchorinnerradius}}% + }% + {% + \pgfpointadd{\centerpoint}% + {\pgfqpointpolar{+\secondangle}{+\anchorouterradius}}% + }% + \else% + \pgfpointintersectionoflines{\centerpoint}{\pgfpoint{+\externalx}{+\externaly}}% + {% + \pgfpointadd{\centerpoint}% + {\pgfqpointpolar{+\firstangle}{+\anchorouterradius}}% + }% + {% + \pgfpointadd{\centerpoint}% + {\pgfqpointpolar{+\secondangle}{+\anchorinnerradius}}% + }% + \fi% + }% + \pgfutil@g@addto@macro\pgf@sh@s@star{% + \c@pgf@counta\totalstarpoints\relax% + \divide\c@pgf@counta2\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>0\relax% + \c@pgf@countb\c@pgf@counta\relax% + \advance\c@pgf@countb-1\relax% + \pgfutil@ifundefined{pgf@anchor@star@inner point\space\the\c@pgf@counta}{% + \expandafter\xdef\csname pgf@anchor@star@inner point\space\the\c@pgf@counta\endcsname{% + \noexpand\calculateradii% + \noexpand\pgfmathmultiply@{\the\c@pgf@countb}{\noexpand\anglestep}% + \noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{2}% + \noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\anglestep}% + \noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}% + \noexpand\let\noexpand\angle\noexpand\pgfmathresult% + \noexpand\pgfpointadd{\noexpand\centerpoint}% + {\noexpand\pgfqpointpolar{\noexpand\angle}{\noexpand\anchorinnerradius}}% + }% + \expandafter\xdef\csname pgf@anchor@star@outer point\space\the\c@pgf@counta\endcsname{% + \noexpand\calculateradii% + \noexpand\pgfmathmultiply@{\the\c@pgf@countb}{\noexpand\anglestep}% + \noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{2}% + \noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}% + \noexpand\let\noexpand\angle\noexpand\pgfmathresult% + \noexpand\pgfpointadd{\noexpand\centerpoint}% + {\noexpand\pgfqpointpolar{\noexpand\angle}{\noexpand\anchorouterradius}}% + }% + }{\c@pgf@counta0\relax}% + \advance\c@pgf@counta-1\relax% + \repeatpgfmathloop% + }% +}% + + + + +\pgfkeys{/pgf/.cd, + regular polygon sides/.initial=5, + regular polygon rotate/.style={/pgf/shape border rotate={#1}}% +}% + + +\pgfdeclareshape{regular polygon}{% + \savedmacro\sides{% + \pgfmathtruncatemacro\sides{\pgfkeysvalueof{/pgf/regular polygon sides}}% + }% + \savedmacro\anglestep{% + \pgfmathdivide{360}{\pgfkeysvalueof{/pgf/regular polygon sides}}% + \let\anglestep\pgfmathresult% + }% + \savedmacro\calculateradii{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifdim\pgf@y>\pgf@x% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \pgfmathdivide{180}{\pgfkeysvalueof{/pgf/regular polygon sides}}% + \pgfmathsec@{\pgfmathresult}% + \pgf@x\pgfmathresult\pgf@x% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@ya>\pgf@xa% + \pgf@xa\pgf@ya% + \fi% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \edef\radius{\the\pgf@x}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@ya>\pgf@xa% + \pgf@xa\pgf@ya% + \fi + \pgfmathdivide{180}{\pgfkeysvalueof{/pgf/regular polygon sides}}% + \pgfmathsubtract@{90}{\pgfmathresult}% + \pgfmathcosec@{\pgfmathresult}% + \advance\pgf@x\pgfmathresult\pgf@xa% + \edef\anchorradius{\the\pgf@x}% + \addtosavedmacro{\radius}% + \addtosavedmacro{\anchorradius}% + }% + \savedmacro\startangle{% + \pgfmathdivide{360}{\pgfkeysvalueof{/pgf/regular polygon sides}}% + \let\anglestep\pgfmathresult% + \pgfmathtruncatemacro\sides{\pgfkeysvalueof{/pgf/regular polygon sides}}% + \expandafter\ifodd\sides\relax% + \edef\pgfmathresult{90}% + \else% + \pgfmathdivide@{\anglestep}{2}% + \pgfmathsubtract@{90}{\pgfmathresult}% + \fi% + \pgfmathadd{\pgfmathresult}{\pgfkeysvalueof{/pgf/shape border rotate}}% + \let\startangle\pgfmathresult% + }% + \savedanchor{\centerpoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor{\midpoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{base}{\centerpoint\pgf@y=0pt}% + \anchor{north}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{0pt}{\anchorradius}}}% + \anchor{south}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{0pt}{-\anchorradius}}}% + \anchor{east}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{\anchorradius}{0pt}}}% + \anchor{west}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{-\anchorradius}{0pt}}}% + \anchor{north east}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{\anchorradius}{\anchorradius}}}% + \anchor{north west}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{-\anchorradius}{\anchorradius}}}% + \anchor{south east}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{\anchorradius}{-\anchorradius}}}% + \anchor{south west}{% + \calculateradii% + \csname pgf@anchor@regular polygon@border\endcsname{\pgfqpoint{-\anchorradius}{-\anchorradius}}}% + \backgroundpath{% + \calculateradii% + \pgfpathmoveto{% + \pgfpointadd{\centerpoint}{\pgfqpointpolar{\startangle}{\radius}}% + }% + \let\angle\startangle% + \pgfmathloop% + \ifnum\pgfmathcounter=\sides\relax% + \pgfpathclose% + \else% + \pgfmathadd@{\angle}{\anglestep}% + \let\angle\pgfmathresult% + \pgfpathlineto{% + \pgfpointadd{\centerpoint}{\pgfqpointpolar{\angle}{\radius}}% + }% + \repeatpgfmathloop% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \centerpoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + \pgfmathsubtract@{\pgfmathresult}{\startangle}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \pgfmathdivide@{\pgfmathresult}{\anglestep}% + \pgfmathfloor@{\pgfmathresult}% + \pgfmathmultiply@{\pgfmathresult}{\anglestep}% + \pgfmathadd@{\pgfmathresult}{\startangle}% + \let\firstangle\pgfmathresult% + \pgfmathadd@{\pgfmathresult}{\anglestep}% + \let\secondangle\pgfmathresult% + \calculateradii% + \pgfpointintersectionoflines{\centerpoint}{\pgfpoint{+\externalx}{+\externaly}}% + {% + \pgfpointadd{\centerpoint}% + {\pgfqpointpolar{+\firstangle}{+\anchorradius}}% + }% + {% + \pgfpointadd{\centerpoint}% + {\pgfqpointpolar{+\secondangle}{+\anchorradius}}% + }% + }% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@regular polygon\endcsname{% + \c@pgf@counta\sides\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>0\relax% + \pgfutil@ifundefined{pgf@anchor@regular polygon@corner\space\the\c@pgf@counta}{% + \expandafter\xdef\csname pgf@anchor@regular polygon@corner\space\the\c@pgf@counta\endcsname{% + \noexpand\calculateradii% + \noexpand\pgfmathsubtract@{\the\c@pgf@counta}{1}% + \noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{\noexpand\anglestep}% + \noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}% + \noexpand\let\noexpand\angle\noexpand\pgfmathresult% + \noexpand\pgfpointadd{\noexpand\centerpoint}% + {\noexpand\pgfqpointpolar{\noexpand\angle}{\noexpand\anchorradius}}% + }% + \expandafter\xdef\csname pgf@anchor@regular polygon@side\space\the\c@pgf@counta\endcsname{% + \noexpand\calculateradii% + \noexpand\pgfmathsubtract@{\the\c@pgf@counta}{1}% + \noexpand\pgfmathmultiply@{\noexpand\pgfmathresult}{\noexpand\anglestep}% + \noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\startangle}% + \noexpand\let\noexpand\firstangle\noexpand\pgfmathresult% + \noexpand\pgfmathadd@{\noexpand\pgfmathresult}{\noexpand\anglestep}% + \noexpand\let\noexpand\secondangle\noexpand\pgfmathresult% + \noexpand\pgfpointlineattime{0.5}% + {\noexpand\pgfpointadd{\noexpand\centerpoint}% + {\noexpand\pgfqpointpolar{\noexpand\firstangle}{\noexpand\anchorradius}}}% + {\noexpand\pgfpointadd{\noexpand\centerpoint}% + {\noexpand\pgfqpointpolar{\noexpand\secondangle}{\noexpand\anchorradius}}}% + }% + }{\c@pgf@counta0\relax}% + \advance\c@pgf@counta-1\relax% + \repeatpgfmathloop% + }% +}% + + + + +\pgfkeys{/pgf/.cd, + trapezium left angle/.initial=60, + trapezium right angle/.initial=60, + trapezium angle/.style={ + /pgf/trapezium left angle={#1}, + /pgf/trapezium right angle={#1} + },% + trapezium stretches/.is if=pgf@lib@sh@trapeziumstretches,% + trapezium stretches body/.is if=pgf@lib@sh@trapeziumstretchesbody,% +}% + +\newif\ifpgf@lib@sh@trapeziumstretchesbody +\newif\ifpgf@lib@sh@trapeziumstretches + + +\pgfdeclareshape{trapezium}{% + \savedmacro\installtrapeziumparameters{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \pgf@y\pgf@x% + \else% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \fi% + \fi% + \fi% + \pgfmathmod{\pgfkeysvalueof{/pgf/trapezium left angle}}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\leftangle\pgfmathresult% + \ifdim\leftangle pt=0pt\relax% + \def\pgfmathresult{0}% + \else% + \pgfmathcot@{\leftangle}% + \fi% + \pgf@xa2\pgf@y% + \pgf@xa\pgfmathresult\pgf@xa% + \pgfmathmod{\pgfkeysvalueof{/pgf/trapezium right angle}}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\rightangle\pgfmathresult% + \ifdim\rightangle pt=0pt\relax% + \def\pgfmathresult{0}% + \else% + \pgfmathcot@{\rightangle}% + \fi% + \pgf@xb2\pgf@y% + \pgf@xb\pgfmathresult\pgf@xb% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@ya% + \ifpgf@lib@sh@trapeziumstretches% + \pgf@y.5\pgf@ya% + \else% + \ifpgf@lib@sh@trapeziumstretchesbody% + \pgf@y.5\pgf@ya% + \else% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}% + \pgf@yb.5\pgf@ya% + \pgf@yb\pgfmathresult\pgf@yb% + \pgf@y.5\pgf@ya% + \pgf@x\pgfmath@tonumber{\pgf@yb}\pgf@x% + \pgf@xa\pgfmath@tonumber{\pgf@yb}\pgf@xa% + \pgf@xb\pgfmath@tonumber{\pgf@yb}\pgf@xb% + \fi% + \fi% + \fi% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@xc2\pgf@x% + \ifdim\pgf@xa<0pt\relax% + \advance\pgf@xc-\pgf@xa% + \else% + \advance\pgf@xc\pgf@xa% + \fi% + \ifdim\pgf@xb<0pt\relax% + \advance\pgf@xc-\pgf@xb% + \else% + \advance\pgf@xc\pgf@xb% + \fi% + \ifdim\pgf@xc<\pgf@ya% + \ifpgf@lib@sh@trapeziumstretchesbody% + \pgf@xc-\pgf@xc% + \advance\pgf@xc\pgf@ya% + \advance\pgf@x.5\pgf@xc% + \else% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@xc}}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgf@x\pgfmath@tonumber{\pgf@ya}\pgf@x% + \pgf@xa\pgfmath@tonumber{\pgf@ya}\pgf@xa% + \pgf@xb\pgfmath@tonumber{\pgf@ya}\pgf@xb% + \ifpgf@lib@sh@trapeziumstretches% + \else% + \pgf@y\pgfmath@tonumber{\pgf@ya}\pgf@y% + \fi% + \fi% + \fi% + \edef\halfheight{\the\pgf@y}% + \edef\halfwidth{\the\pgf@x}% + \edef\leftextension{\the\pgf@xa}% + \edef\rightextension{\the\pgf@xb}% + \pgf@xc2\pgf@x% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@y>\pgf@x% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \advance\pgf@xc2.0\pgf@x% + \pgf@yc\halfheight\relax% + \multiply\pgf@yc2\relax% + \advance\pgf@yc2.0\pgf@x% + \ifdim\pgf@xc<\pgf@yc% + \edef\externalradius{\the\pgf@yc}% + \else% + \edef\externalradius{\the\pgf@xc}% + \fi% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfextract@process\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \pgfextract@process\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \pgfextract@process\lowerleftpoint{% + \centerpoint% + \advance\pgf@x-\halfwidth\relax% + \ifdim\leftextension>0pt\relax% + \advance\pgf@x-\leftextension\relax% + \fi% + \advance\pgf@y-\halfheight\relax% + }% + \pgfextract@process\upperleftpoint{% + \centerpoint% + \advance\pgf@x-\halfwidth\relax% + \ifdim\leftextension<0pt\relax% + \advance\pgf@x\leftextension\relax% + \fi% + \advance\pgf@y\halfheight\relax% + }% + \pgfextract@process\upperrightpoint{% + \centerpoint% + \advance\pgf@x\halfwidth\relax% + \ifdim\rightextension<0pt\relax% + \advance\pgf@x-\rightextension\relax% + \fi% + \advance\pgf@y\halfheight\relax% + }% + \pgfextract@process\lowerrightpoint{% + \centerpoint% + \advance\pgf@x\halfwidth\relax% + \ifdim\rightextension>0pt\relax% + \advance\pgf@x\rightextension\relax% + \fi% + \advance\pgf@y-\halfheight\relax% + }% + \pgfextract@process\lowerleftmiter{% + \pgfmathanglebetweenlines{\lowerleftpoint}{\lowerrightpoint}{\lowerleftpoint}{\upperleftpoint}% + \pgfmathmultiply@{\pgfmathresult}{.5}% + \pgfmathtan@{\pgfmathresult}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@x-\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y-\outersep\relax% + }% + \pgfextract@process\upperleftmiter{% + \pgfmathanglebetweenlines{\upperleftpoint}{\lowerleftpoint}{\upperleftpoint}{\upperrightpoint}% + \pgfmathmultiply@{\pgfmathresult}{.5}% + \pgfmathtan@{\pgfmathresult}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@x-\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y\outersep\relax% + }% + \pgfextract@process\upperrightmiter{% + \pgfmathanglebetweenlines{\upperrightpoint}{\upperleftpoint}{\upperrightpoint}{\lowerrightpoint}% + \pgfmathmultiply@{\pgfmathresult}{.5}% + \pgfmathtan@{\pgfmathresult}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@x\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y\outersep\relax% + }% + \pgfextract@process\lowerrightmiter{% + \pgfmathanglebetweenlines{\lowerrightpoint}{\upperrightpoint}{\lowerrightpoint}{\lowerleftpoint}% + \pgfmathmultiply@{\pgfmathresult}{.5}% + \pgfmathtan@{\pgfmathresult}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@x\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y-\outersep\relax% + }% + \pgfextract@process\lowerleftborderpoint{% + \pgfpointadd{\lowerleftpoint}{\lowerleftmiter}% + }% + \pgfextract@process\upperleftborderpoint{% + \pgfpointadd{\upperleftpoint}{\upperleftmiter}% + }% + \pgfextract@process\upperrightborderpoint{% + \pgfpointadd{\upperrightpoint}{\upperrightmiter}% + }% + \pgfextract@process\lowerrightborderpoint{% + \pgfpointadd{\lowerrightpoint}{\lowerrightmiter}% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\lowerleftborderpoint}% + \let\angletolowerleft\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\upperleftborderpoint}% + \let\angletoupperleft\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\upperrightborderpoint}% + \let\angletoupperright\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\lowerrightborderpoint}% + \let\angletolowerright\pgfmathresult% + \pgfextract@process\rotatedbasepoint{% + \pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\lowerleftborderpoint}% + \let\baseangletolowerleft\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\upperleftborderpoint}% + \let\baseangletoupperleft\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\upperrightborderpoint}% + \let\baseangletoupperright\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\lowerrightborderpoint}% + \let\baseangletolowerright\pgfmathresult% + \pgfextract@process\rotatedmidpoint{% + \pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\lowerleftborderpoint}% + \let\midangletolowerleft\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\upperleftborderpoint}% + \let\midangletoupperleft\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\upperrightborderpoint}% + \let\midangletoupperright\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\lowerrightborderpoint}% + \let\midangletolowerright\pgfmathresult% + \pgfextract@process\lowerleftborderpoint{% + \pgfmathrotatepointaround% + {\lowerleftborderpoint}% + {\centerpoint}% + {\rotate}% + }% + \pgfextract@process\upperleftborderpoint{% + \pgfmathrotatepointaround% + {\upperleftborderpoint}% + {\centerpoint}% + {\rotate}% + }% + \pgfextract@process\upperrightborderpoint{% + \pgfmathrotatepointaround% + {\upperrightborderpoint}% + {\centerpoint}% + {\rotate}% + }% + \pgfextract@process\lowerrightborderpoint{% + \pgfmathrotatepointaround% + {\lowerrightborderpoint}% + {\centerpoint}% + {\rotate}% + }% + \pgfextract@process\lowerleftpoint{% + \pgfmathrotatepointaround{\lowerleftpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\upperleftpoint{% + \pgfmathrotatepointaround{\upperleftpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\upperrightpoint{% + \pgfmathrotatepointaround{\upperrightpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\lowerrightpoint{% + \pgfmathrotatepointaround{\lowerrightpoint}{\centerpoint}{\rotate}% + }% + \addtosavedmacro{\lowerleftpoint}% + \addtosavedmacro{\upperleftpoint}% + \addtosavedmacro{\upperrightpoint}% + \addtosavedmacro{\lowerrightpoint}% + \addtosavedmacro{\lowerleftborderpoint}% + \addtosavedmacro{\upperleftborderpoint}% + \addtosavedmacro{\upperrightborderpoint}% + \addtosavedmacro{\lowerrightborderpoint}% + \addtosavedmacro{\angletolowerleft}% + \addtosavedmacro{\angletoupperleft}% + \addtosavedmacro{\angletoupperright}% + \addtosavedmacro{\angletolowerright}% + \addtosavedmacro{\baseangletolowerleft}% + \addtosavedmacro{\baseangletoupperleft}% + \addtosavedmacro{\baseangletoupperright}% + \addtosavedmacro{\baseangletolowerright}% + \addtosavedmacro{\midangletolowerleft}% + \addtosavedmacro{\midangletoupperleft}% + \addtosavedmacro{\midangletoupperright}% + \addtosavedmacro{\midangletolowerright}% + \addtosavedmacro{\rotate}% + \addtosavedmacro{\externalradius}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \installtrapeziumparameters% + \let\pgf@trapeziumanchorborderreferencepoint\basepoint% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{base west}{% + \installtrapeziumparameters% + \let\pgf@trapeziumanchorborderreferencepoint\basepoint% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \installtrapeziumparameters% + \let\pgf@trapeziumanchorborderreferencepoint\midpoint% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{mid west}{% + \installtrapeziumparameters% + \let\pgf@trapeziumanchorborderreferencepoint\midpoint% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north east}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south west}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{south east}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \anchor{north west}{% + \installtrapeziumparameters% + \csname pgf@anchor@trapezium@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{bottom left corner}{% + \installtrapeziumparameters% + \lowerleftborderpoint% + }% + \anchor{top left corner}{% + \installtrapeziumparameters% + \upperleftborderpoint% + }% + \anchor{top right corner}{% + \installtrapeziumparameters% + \upperrightborderpoint% + }% + \anchor{bottom right corner}{% + \installtrapeziumparameters% + \lowerrightborderpoint% + }% + \anchor{left side}{% + \installtrapeziumparameters% + \pgfpointlineattime{0.5}{\lowerleftborderpoint}{\upperleftborderpoint}% + }% + \anchor{right side}{% + \installtrapeziumparameters% + \pgfpointlineattime{0.5}{\lowerrightborderpoint}{\upperrightborderpoint}% + }% + \anchor{top side}{% + \installtrapeziumparameters% + \pgfpointlineattime{0.5}{\upperleftborderpoint}{\upperrightborderpoint}% + }% + \anchor{bottom side}{% + \installtrapeziumparameters% + \pgfpointlineattime{0.5}{\lowerleftborderpoint}{\lowerrightborderpoint}% + }% + \backgroundpath{% + \installtrapeziumparameters% + \pgfpathmoveto{\lowerleftpoint}% + \pgfpathlineto{\upperleftpoint}% + \pgfpathlineto{\upperrightpoint}% + \pgfpathlineto{\lowerrightpoint}% + \pgfpathclose% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \pgfutil@ifundefined{pgf@trapeziumanchorborderreferencepoint}% + {\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@trapeziumanchorborderreferencepoint}% + \referencepoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \installtrapeziumparameters% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \ifx\referencepoint\basepoint% + \let\angletoupperright\baseangletoupperright% + \let\angletoupperleft\baseangletoupperleft% + \let\angletolowerright\baseangletolowerright% + \let\angletolowerleft\baseangletolowerleft% + \else% + \ifx\referencepoint\midpoint% + \let\angletoupperright\midangletoupperright% + \let\angletoupperleft\midangletoupperleft% + \let\angletolowerright\midangletolowerright% + \let\angletolowerleft\midangletolowerleft% + \fi\fi% + \ifdim\externalangle pt<\angletoupperright pt\relax% + \let\firstpoint\upperrightborderpoint% + \let\secondpoint\lowerrightborderpoint% + \else% + \ifdim\externalangle pt<\angletoupperleft pt\relax% + \let\firstpoint\upperleftborderpoint% + \let\secondpoint\upperrightborderpoint% + \else% + \ifdim\externalangle pt<\angletolowerleft pt\relax% + \let\firstpoint\upperleftborderpoint% + \let\secondpoint\lowerleftborderpoint% + \else% + \ifdim\externalangle pt<\angletolowerright pt\relax% + \let\firstpoint\lowerleftborderpoint% + \let\secondpoint\lowerrightborderpoint% + \else% + \let\firstpoint\upperrightborderpoint% + \let\secondpoint\lowerrightborderpoint% + \fi% + \fi% + \fi% + \fi% + \pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + {\firstpoint}{\secondpoint}% + }% +}% + + + + +\pgfdeclareshape{semicircle}{% + \savedmacro\installsemicircleparameters{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x+.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y+.5\ht\pgfnodeparttextbox% + \advance\pgf@y+.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \edef\halfheight{\the\pgf@x}% + \advance\pgf@x\pgf@x% + \else% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \fi% + \fi% + \advance\pgf@y\pgf@y% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \pgf@x\pgfmathresult pt\relax% + \pgf@y.5\pgf@y% + \edef\halfheight{\the\pgf@y}% + \fi% + \edef\defaultradius{\the\pgf@x}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<\pgf@ya% + \pgf@x\pgf@ya% + \fi% + \edef\semicircleradius{\the\pgf@x}% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y+-.5\dp\pgfnodeparttextbox% + }% + \pgfextract@process\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \pgfextract@process\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \pgfextract@process\semicirclecenterpoint{% + \centerpoint% + \pgf@ya\semicircleradius\relax% + \advance\pgf@ya-\defaultradius\relax% + \pgf@ya.4\pgf@ya% + \advance\pgf@y-\pgf@ya% + \pgf@ya\halfheight\relax% + \advance\pgf@y-\pgf@ya% + }% + \pgf@x\semicircleradius\relax% + \advance\pgf@x\outersep\relax% + \edef\semicircleradius{\the\pgf@x}% + \pgfpointdiff{\centerpoint}{\semicirclecenterpoint}% + \ifdim\pgf@y<0pt\pgf@y-\pgf@y\fi% + \edef\centerpointdiff{\the\pgf@y}% + \pgfextract@process\arcstartborder{% + \semicirclecenterpoint% + \advance\pgf@x\semicircleradius\relax% + }% + \pgfextract@process\arcendborder{% + \semicirclecenterpoint% + \advance\pgf@x-\semicircleradius\relax% + }% + \pgfextract@process\arcstartcorner{% + \arcstartborder% + \advance\pgf@y-\outersep\relax% + }% + \pgfextract@process\arcendcorner{% + \arcendborder% + \advance\pgf@y-\outersep\relax% + } + \pgfmathanglebetweenpoints{\centerpoint}{\arcstartborder}% + \let\angletoarcstartborder\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcendborder}% + \let\angletoarcendborder\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcstartcorner}% + \let\angletoarcstartcorner\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcendcorner}% + \let\angletoarcendcorner\pgfmathresult% + \pgfextract@process\rotatedbasepoint{% + \pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcstartborder}% + \let\baseangletoarcstartborder\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcendborder}% + \let\baseangletoarcendborder\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcstartcorner}% + \let\baseangletoarcstartcorner\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\arcendcorner}% + \let\baseangletoarcendcorner\pgfmathresult% + \pgfextract@process\rotatedmidpoint{% + \pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcstartborder}% + \let\midangletoarcstartborder\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcendborder}% + \let\midangletoarcendborder\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcstartcorner}% + \let\midangletoarcstartcorner\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\arcendcorner}% + \let\midangletoarcendcorner\pgfmathresult% + \pgfextract@process\semicirclecenterpoint{% + \pgfmathrotatepointaround{\semicirclecenterpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcstartborder{% + \pgfmathrotatepointaround{\arcstartborder}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcendborder{% + \pgfmathrotatepointaround{\arcendborder}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcstartcorner{% + \pgfmathrotatepointaround{\arcstartcorner}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcendcorner{% + \pgfmathrotatepointaround{\arcendcorner}{\centerpoint}{\rotate}% + }% + \pgfpointdiff{\basepoint}{\semicirclecenterpoint}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \edef\basesemicirclecenterdiff{\pgfmathresult pt}% + \pgfpointdiff{\midpoint}{\semicirclecenterpoint}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \edef\midsemicirclecenterdiff{\pgfmathresult pt}% + \addtosavedmacro{\rotate}% + \addtosavedmacro{\outersep}% + \addtosavedmacro{\semicircleradius}% + \addtosavedmacro{\arcstartborder}% + \addtosavedmacro{\arcendborder}% + \addtosavedmacro{\arcstartcorner}% + \addtosavedmacro{\arcendcorner}% + \addtosavedmacro{\semicirclecenterpoint}% + \addtosavedmacro{\angletoarcstartborder}% + \addtosavedmacro{\angletoarcendborder}% + \addtosavedmacro{\angletoarcstartcorner}% + \addtosavedmacro{\angletoarcendcorner}% + \addtosavedmacro{\centerpointdiff}% + \addtosavedmacro{\basesemicirclecenterdiff}% + \addtosavedmacro{\midsemicirclecenterdiff}% + \addtosavedmacro{\baseangletoarcstartborder}% + \addtosavedmacro{\baseangletoarcendborder}% + \addtosavedmacro{\baseangletoarcstartcorner}% + \addtosavedmacro{\baseangletoarcendcorner}% + \addtosavedmacro{\midangletoarcstartborder}% + \addtosavedmacro{\midangletoarcendborder}% + \addtosavedmacro{\midangletoarcstartcorner}% + \addtosavedmacro{\midangletoarcendcorner}% + }% + \savedanchor{\centerpoint}{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+.5\ht\pgfnodeparttextbox}% + \pgfmathaddtolength\pgf@y{-.5\dp\pgfnodeparttextbox}% + }% + \savedanchor{\basepoint}{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgf@y0pt\relax% + }% + \savedanchor{\midpoint}{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{base west}{% + \installsemicircleparameters% + \let\pgf@semicirclereferencepoint\basepoint% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{-\semicircleradius}{0pt}}% + }% + \anchor{base east}{% + \installsemicircleparameters% + \let\pgf@semicirclereferencepoint\basepoint% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{\semicircleradius}{0pt}}% + }% + \anchor{mid}{\midpoint}% + \anchor{mid west}{% + \installsemicircleparameters% + \let\pgf@semicirclereferencepoint\midpoint% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{-\semicircleradius}{0pt}}% + }% + \anchor{mid east}{% + \installsemicircleparameters% + \let\pgf@semicirclereferencepoint\midpoint% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpoint{\semicircleradius}{0pt}}% + }% + \anchor{apex}{% + \installsemicircleparameters% + \pgfmathadd@{\rotate}{90}% + \let\angle\pgfmathresult% + \pgfpointadd{\semicirclecenterpoint}{\pgfqpointpolar{\angle}{\semicircleradius}}% + }% + \anchor{arc start}{% + \installsemicircleparameters% + \arcstartcorner% + }% + \anchor{arc end}{% + \installsemicircleparameters% + \arcendcorner% + }% + \anchor{chord center}{% + \installsemicircleparameters% + \pgfpointlineattime{0.5}{\arcstartcorner}{\arcendcorner}% + }% + \anchor{north}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{90}{\semicircleradius}}% + }% + \anchor{south}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{270}{\semicircleradius}}% + }% + \anchor{east}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{0}{\semicircleradius}}% + }% + \anchor{west}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{180}{\semicircleradius}}% + }% + \anchor{north west}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{135}{\semicircleradius}}% + }% + \anchor{south west}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{225}{\semicircleradius}}% + }% + \anchor{north east}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{45}{\semicircleradius}}% + }% + \anchor{south east}{% + \installsemicircleparameters% + \csname pgf@anchor@semicircle@border\endcsname{\pgfqpointpolar{315}{\semicircleradius}}% + }% + \backgroundpath{% + \installsemicircleparameters% + \pgf@x\semicircleradius\relax% + \advance\pgf@x-\outersep\relax% + \edef\semicircleradius{\the\pgf@x}% + \pgfpathmoveto{\pgfpointadd{\semicirclecenterpoint}{\pgfqpointpolar{\rotate}{\semicircleradius}}}% + {% + \pgftransformrotate{\rotate}% + \pgfpatharc{0}{180}{\semicircleradius}% + \pgfpathclose% + }% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \pgfutil@ifundefined{pgf@semicirclereferencepoint}% + {\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@semicirclereferencepoint}% + \referencepoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \installsemicircleparameters% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + \let\externalangle\pgfmathresult% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\angle\pgfmathresult% + \ifx\referencepoint\basepoint% + \let\angletoarcstartborder\baseangletoarcstartborder% + \let\angletoarcendborder\baseangletoarcendborder% + \let\angletoarcstartcorner\baseangletoarcstartcorner% + \let\angletoarcendcorner\baseangletoarcendcorner% + \let\centerpointdiff\basesemicirclecenterdiff% + \else% + \ifx\referencepoint\midpoint% + \let\angletoarcstartborder\midangletoarcstartborder% + \let\angletoarcendborder\midangletoarcendborder% + \let\angletoarcstartcorner\midangletoarcstartcorner% + \let\angletoarcendcorner\midangletoarcendcorner% + \let\centerpointdiff\midsemicirclecenterdiff% + \fi\fi% + \ifdim\angle pt>\angletoarcstartborder pt\relax% + \let\firstpoint\pgfutil@empty% + \let\secondpoint\pgfutil@empty% + \else% + \ifdim\angle pt>\angletoarcstartcorner pt\relax% + \let\firstpoint\arcstartcorner% + \let\secondpoint\arcstartborder% + \else% + \ifdim\angle pt>\angletoarcendcorner pt\relax% + \let\firstpoint\arcendcorner% + \let\secondpoint\arcstartcorner% + \else% + \ifdim\angle pt>\angletoarcendborder pt\relax% + \let\firstpoint\arcendborder% + \let\secondpoint\arcendcorner% + \else% + \let\firstpoint\pgfutil@empty% + \let\secondpoint\pgfutil@empty% + \fi% + \fi% + \fi% + \fi% + \ifx\firstpoint\pgfutil@empty + \pgfmathanglebetweenlines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + {\semicirclecenterpoint}{\referencepoint}% + \pgfmathsin@{\pgfmathresult}% + \let\sineangle\pgfmathresult% + \pgf@x\semicircleradius\relax% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@x}}% + \let\reciprocalradius\pgfmathresult% + \pgf@x\centerpointdiff\relax% + \pgf@x\sineangle\pgf@x% + \pgf@x\reciprocalradius\pgf@x% + \pgfmathasin@{\pgfmath@tonumber{\pgf@x}}% + \pgf@x\pgfmathresult pt\relax% + \advance\pgf@x\externalangle pt\relax% + \edef\angle{\pgfmath@tonumber{\pgf@x}}% + \pgfpointadd{\semicirclecenterpoint}{\pgfqpointpolar{\angle}{\semicircleradius}}% + \else% + \pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + {\firstpoint}{\secondpoint}% + \fi% + }% +}% + + +\pgfkeys{/pgf/.cd, + isosceles triangle apex angle/.initial=45, + isosceles triangle stretches/.is if=pgf@lib@sh@isosceslestrianglestretches +}% +\newif\ifpgf@lib@sh@isosceslestrianglestretches + +\pgfdeclareshape{isosceles triangle}{% + \savedmacro\trianglepoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/isosceles triangle apex angle}}% + \divide\pgf@x2\relax% + \edef\halfapexangle{\pgfmath@tonumber{\pgf@x}}% + \addtosavedmacro\halfapexangle% + \pgfmathtan@{\halfapexangle}% + \let\tanhalfapexangle\pgfmathresult% + \pgfmathcot@{\halfapexangle}% + \let\cothalfapexangle\pgfmathresult% + \pgfmathsin@{\halfapexangle}% + \let\sinhalfapexangle\pgfmathresult% + \pgfmathreciprocal@{\pgfmathresult}% + \let\cosechalfapexangle\pgfmathresult% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \else% + \pgf@y\pgf@x% + \fi% + \pgf@x1.414213\pgf@x% + \pgf@y1.414213\pgf@y% + \pgf@xa\pgf@x% + \advance\pgf@xa\cosechalfapexangle\pgf@x% + \pgf@ya\tanhalfapexangle\pgf@xa% + \else% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \pgfmathsetcount\c@pgf@counta{+\pgfmathresult}% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xa% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xa% + \fi% + \fi% + \pgf@xa2.0\pgf@x% + \pgf@ya\tanhalfapexangle\pgf@xa% + \advance\pgf@xa\cothalfapexangle\pgf@y% + \advance\pgf@ya\pgf@y% + \fi% + \addtosavedmacro\rotate% + \ifdim\pgf@xa=0pt\relax% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum height}}% + \fi% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@ya<.5\pgf@yb% + \ifpgf@lib@sh@isosceslestrianglestretches% + \pgf@ya.5\pgf@yb% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@ya}}{\pgfmath@tonumber{\pgf@xa}}% + \pgfmathatan@{\pgfmathresult}% + \let\halfapexangle\pgfmathresult% + \else% + \pgf@ya.5\pgf@yb% + \pgf@xa\cothalfapexangle\pgf@ya% + \fi% + \fi% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@xa<\pgf@xb% + \ifpgf@lib@sh@isosceslestrianglestretches% + \pgf@xa\pgf@xb% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@ya}}{\pgfmath@tonumber{\pgf@xa}}% + \pgfmathatan@{\pgfmathresult}% + \let\halfapexangle\pgfmathresult% + \else% + \pgf@xa\pgf@xb% + \pgf@ya\tanhalfapexangle\pgf@xa% + \fi% + \fi% + \ifpgfshapeborderusesincircle% + \pgf@xc\pgf@xa% + \pgfmathsin@{\halfapexangle}% + \pgf@xc\pgfmathresult\pgf@xc% + \pgf@yc1pt\relax% + \advance\pgf@yc\pgfmathresult pt\relax% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@xc}}{\pgfmath@tonumber{\pgf@yc}} + \pgfutil@tempdima\pgfmathresult pt\relax% + \else% + \pgf@xc\pgf@ya% + \advance\pgf@xc-\pgf@y% + \pgfmathcos@{\halfapexangle}% + \pgf@xc\pgfmathresult\pgf@xc% + \pgfmathsin@{\halfapexangle}% + \advance\pgf@xc-\pgfmathresult\pgf@x% + \advance\pgf@xc-\pgfmathresult\pgf@x% + \pgf@yc\pgfmathresult pt\relax% + \advance\pgf@yc1pt\relax% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@xc}}{\pgfmath@tonumber{\pgf@yc}}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \advance\pgfutil@tempdima\pgf@x% + \fi% + \pgfextract@process\apex{% + \pgf@y0pt% + \pgf@x\pgf@xa% + \advance\pgf@x-\pgfutil@tempdima% + }% + \addtosavedmacro\apex% + \pgfextract@process\lowerleft{% + \pgf@y\pgf@ya% + \pgf@x-\pgfutil@tempdima% + }% + \addtosavedmacro\lowerleft% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \pgf@xb\pgf@yb% + \fi% + \pgfextract@process\apexanchor{% + \apex% + \advance\pgf@x\cosechalfapexangle\pgf@xb% + }% + \addtosavedmacro\apexanchor% + \pgf@yc-\halfapexangle pt\relax% + \advance\pgf@yc90pt\relax% + \divide\pgf@yc2\relax% + \pgfmathcot@{\pgfmath@tonumber{\pgf@yc}}% + \pgfextract@process\lowerleftanchor{% + \lowerleft% + \advance\pgf@y\pgfmathresult\pgf@xb% + \advance\pgf@x-\pgf@xb% + }% + \addtosavedmacro\lowerleftanchor% + \pgfextract@process\lowerrightanchor{% + \lowerleftanchor% + \pgf@y-\pgf@y% + }% + \addtosavedmacro\lowerrightanchor% + }% + \anchor{apex}{% + \trianglepoints% + \pgfpointadd{\centerpoint}{% + \pgfmathrotatepointaround{\apexanchor}{\pgfpointorigin}{\rotate}% + }% + }% + \anchor{left corner}{% + \trianglepoints% + \pgfpointadd{\centerpoint}{% + \pgfmathrotatepointaround{\lowerleftanchor}{\pgfpointorigin}{\rotate}% + }% + }% + \anchor{right corner}{% + \trianglepoints% + \pgfpointadd{\centerpoint}{% + \pgfmathrotatepointaround{\lowerrightanchor}{\pgfpointorigin}{\rotate}% + }% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid west}{% + \trianglepoints% + \let\pgf@isoscelestriangle@referencepoint\midpoint% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{0pt}}% + }% + \anchor{mid east}{% + \trianglepoints% + \let\pgf@isoscelestriangle@referencepoint\midpoint% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{0pt}}% + }% + \anchor{base}{\basepoint}% + \anchor{base west}{% + \trianglepoints% + \let\pgf@isoscelestriangle@referencepoint\basepoint% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{0pt}}% + }% + \anchor{base east}{% + \trianglepoints% + \let\pgf@isoscelestriangle@referencepoint\basepoint% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{0pt}}% + }% + \anchor{north}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{0pt}{1pt}}% + }% + \anchor{south}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{0pt}{-1pt}}% + }% + \anchor{east}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{0pt}}% + }% + \anchor{west}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{0pt}}% + }% + \anchor{north east}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{1pt}}% + }% + \anchor{south west}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{-1pt}}% + }% + \anchor{south east}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{1pt}{-1pt}}% + }% + \anchor{north west}{% + \trianglepoints% + \csname pgf@anchor@isosceles triangle@border\endcsname{\pgfqpoint{-1pt}{1pt}}% + }% + \anchor{left side}{% + \trianglepoints% + \pgfmathrotatepointaround{% + \pgfpointadd{\pgfpointlineattime{0.5}{\lowerleftanchor}{\apexanchor}}{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{right side}{% + \trianglepoints% + \pgfmathrotatepointaround{% + \pgfpointadd{\pgfpointlineattime{0.5}{\lowerrightanchor}{\apexanchor}}{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{lower side}{% + \trianglepoints% + \pgfmathrotatepointaround{% + \pgfpointadd{\pgfpointlineattime{0.5}{\lowerleftanchor}{\lowerrightanchor}}{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \backgroundpath{% + \trianglepoints% + {% + \pgftransformshift{\centerpoint}% + \pgftransformrotate{\rotate}% + \pgfpathmoveto{\apex}% + \pgfpathlineto{\lowerleft}% + \pgfpathlineto{\lowerleft\pgf@y-\pgf@y}% + \pgfpathclose% + }% + }% + \anchorborder{% + \pgfutil@ifundefined{pgf@isoscelestriangle@referencepoint}{\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@isoscelestriangle@referencepoint}% + \pgfextract@process\externalpoint{% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \referencepoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \trianglepoints% + \pgfmathanglebetweenpoints{\referencepoint}{\externalpoint}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \pgfmathmod@{\pgfmathresult}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\centerpoint}{\lowerrightanchor}}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\centerpoint}{\lowerleftanchor}}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\centerpoint}{\apexanchor}}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \let\firstpoint\apexanchor% + \let\secondpoint\lowerleftanchor% + \else% + \let\firstpoint\apexanchor% + \let\secondpoint\lowerrightanchor% + \fi% + \else% + \let\firstpoint\lowerleftanchor% + \let\secondpoint\lowerrightanchor% + \fi% + \else% + \let\firstpoint\lowerrightanchor% + \let\secondpoint\apexanchor% + \fi% + \pgfpointintersectionoflines{\referencepoint}{\externalpoint}% + {\pgfmathrotatepointaround{\pgfpointadd{\centerpoint}{\firstpoint}}{\centerpoint}{\rotate}}% + {\pgfmathrotatepointaround{\pgfpointadd{\centerpoint}{\secondpoint}}{\centerpoint}{\rotate}}% + }% +}% + + + + +\pgfkeys{/pgf/.cd, + kite upper vertex angle/.initial=120, + kite lower vertex angle/.initial=60, + kite vertex angles/.code={% + \pgfutil@in@{and}{#1}% + \ifpgfutil@in@% + \def\pgf@marshal##1and##2\@@{% + \pgfkeys{/pgf/kite upper vertex angle={##1}}% + \pgfkeys{/pgf/kite lower vertex angle={##2}}% + }% + \expandafter\pgf@marshal#1\@@% + \else% + \pgfkeys{/pgf/kite upper vertex angle={#1}}% + \pgfkeys{/pgf/kite lower vertex angle={#1}}% + \fi% + }% +}% + +\pgfdeclareshape{kite}{% + \savedmacro\installkiteparameters{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfextract@process\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \pgfextract@process\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \pgfmathdivide{\pgfkeysvalueof{/pgf/kite upper vertex angle}}{2}% + \let\halfuppervertexangle\pgfmathresult% + \pgfmathdivide{\pgfkeysvalueof{/pgf/kite lower vertex angle}}{2}% + \let\halflowervertexangle\pgfmathresult% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \pgfmathsin@{\halfuppervertexangle}% + \let\sinehalfuppervertexangle\pgfmathresult% + \pgfmathreciprocal@{\pgfmathresult}% + \let\cosechalfuppervertexangle\pgfmathresult% + \pgf@ya\pgfmathresult\pgf@x% + \pgfmathsin@{\halflowervertexangle}% + \let\sinehalflowervertexangle\pgfmathresult% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@yb\pgfmathresult\pgf@x% + \pgf@yc\pgf@x% + \pgfmathadd@{\halfuppervertexangle}{\halflowervertexangle}% + \pgfmathcosec@{\pgfmathresult}% + \pgf@yc\pgfmathresult\pgf@yc% + \pgfmathadd@{\sinehalfuppervertexangle}{\sinehalflowervertexangle}% + \pgf@yc\pgfmathresult\pgf@yc% + \pgfmathcos@{\halfuppervertexangle}% + \pgf@yc\pgfmathresult\pgf@yc% + \pgf@yc-\cosechalfuppervertexangle\pgf@yc% + \advance\pgf@yc\cosechalfuppervertexangle\pgf@x% + \edef\deltay{\the\pgf@yc}% + \advance\pgf@ya-\pgf@yc% + \advance\pgf@yb\pgf@yc% + \pgfmathtan@{\halfuppervertexangle}% + \pgf@xa\pgfmathresult\pgf@ya% + \else% + \multiply\pgf@x2\relax% + \multiply\pgf@y2\relax% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \fi% + \fi% + \pgfmathadd@{\halfuppervertexangle}{\halflowervertexangle}% + \pgfmathsin@{\pgfmathresult}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@ya\pgfmathresult\pgf@y% + \pgfmathcos@{\halfuppervertexangle}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgfmathsin@{\halflowervertexangle}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgf@yb\pgf@y% + \advance\pgf@yb-\pgf@ya% + \pgf@yc.5\pgf@y% + \advance\pgf@yc-\pgf@ya% + \edef\deltay{\the\pgf@yc}% + \pgfmathtan@{\halfuppervertexangle}% + \pgf@xa.5\pgf@x% + \advance\pgf@xa\pgfmathresult\pgf@ya% + \pgf@xb.5\pgf@x% + \pgfmathreciprocal@{\pgfmathresult}% + \advance\pgf@ya\pgfmathresult\pgf@xb% + \pgfmathtan@{\halflowervertexangle}% + \pgfmathreciprocal@{\pgfmathresult}% + \advance\pgf@yb\pgfmathresult\pgf@xb% + \fi% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/minimum height}}% + \pgf@y\pgf@ya% + \advance\pgf@y\pgf@yb% + \ifdim\pgf@y<\pgf@yc% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@y}}% + \pgf@yc\pgfmathresult\pgf@yc% + \pgf@xa\pgfmath@tonumber{\pgf@yc}\pgf@xa% + \pgf@ya\pgfmath@tonumber{\pgf@yc}\pgf@ya% + \pgf@yb\pgfmath@tonumber{\pgf@yc}\pgf@yb% + \fi% + \pgf@x2.0\pgf@xa% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<\pgf@xc% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@x}}% + \pgf@xc\pgfmathresult\pgf@xc% + \pgf@xa\pgfmath@tonumber{\pgf@xc}\pgf@xa% + \pgf@ya\pgfmath@tonumber{\pgf@xc}\pgf@ya% + \pgf@yb\pgfmath@tonumber{\pgf@xc}\pgf@yb% + \fi% + \edef\kitehalfwidth{\the\pgf@xa}% + \edef\kiteheight{\the\pgf@ya}% + \edef\kitedepth{\the\pgf@yb}% + \pgfextract@process\toppoint{% + \centerpoint% + \advance\pgf@y\deltay\relax% + \advance\pgf@y\kiteheight% + }% + \pgfextract@process\bottompoint{% + \centerpoint% + \advance\pgf@y\deltay\relax% + \advance\pgf@y-\kitedepth% + }% + \pgfextract@process\leftpoint{% + \centerpoint% + \advance\pgf@y\deltay\relax% + \advance\pgf@x-\kitehalfwidth% + }% + \pgfextract@process\rightpoint{% + \centerpoint% + \advance\pgf@y\deltay\relax% + \advance\pgf@x\kitehalfwidth% + }% + \pgfmathsin@{\halfuppervertexangle}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@y\outersep\relax% + \pgf@y\pgfmathresult\pgf@y% + \edef\topmiter{\the\pgf@y}% + \pgfmathsin@{\halflowervertexangle}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@y\outersep\relax% + \pgf@y\pgfmathresult\pgf@y% + \edef\bottommiter{\the\pgf@y}% + \pgfmathsubtract@{180}{\halflowervertexangle}% + \pgfmathsubtract@{\pgfmathresult}{\halfuppervertexangle}% + \pgfmathdivide@{\pgfmathresult}{2}% + \pgfmathsin@{\pgfmathresult}% + \pgfmathreciprocal@{\pgfmathresult}% + \pgf@xa\outersep\relax% + \pgf@xa\pgfmathresult\pgf@xa% + \pgfmathsubtract@{\halfuppervertexangle}{\halflowervertexangle}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\angle\pgfmathresult% + \pgfextract@process\rightmiter{% + \pgfqpointpolar{\angle}{\the\pgf@xa}% + }% + \pgfmathsubtract@{180}{\angle}% + \let\angle\pgfmathresult% + \pgfextract@process\leftmiter{% + \pgfqpointpolar{\angle}{\the\pgf@xa}% + }% + \pgfextract@process\topborderpoint{% + \toppoint% + \advance\pgf@y\topmiter\relax% + }% + \pgfextract@process\bottomborderpoint{% + \bottompoint% + \advance\pgf@y-\bottommiter\relax% + }% + \pgfextract@process\leftborderpoint{% + \leftpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \leftmiter% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\rightborderpoint{% + \rightpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \rightmiter% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\topborderpoint}% + \let\angletotoppoint\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\leftborderpoint}% + \let\angletoleftpoint\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\bottomborderpoint}% + \let\angletobottompoint\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\rightborderpoint}% + \let\angletorightpoint\pgfmathresult% + \pgfextract@process\rotatedbasepoint{% + \pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\topborderpoint}% + \let\baseangletotoppoint\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\leftborderpoint}% + \let\baseangletoleftpoint\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\bottomborderpoint}% + \let\baseangletobottompoint\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\rightborderpoint}% + \let\baseangletorightpoint\pgfmathresult% + \pgfextract@process\rotatedmidpoint{% + \pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\topborderpoint}% + \let\midangletotoppoint\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\leftborderpoint}% + \let\midangletoleftpoint\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\bottomborderpoint}% + \let\midangletobottompoint\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\rightborderpoint}% + \let\midangletorightpoint\pgfmathresult% + \pgfextractx\pgf@xa{\pgfpointdiff{\leftborderpoint}{\rightborderpoint}}% + \ifdim\pgf@xa<0pt\relax% + \pgf@xa-\pgf@xa% + \fi% + \pgfextracty\pgf@ya{\pgfpointdiff{\topborderpoint}{\bottomborderpoint}}% + \ifdim\pgf@ya<0pt\relax% + \pgf@ya-\pgf@ya% + \fi% + \ifdim\pgf@ya>\pgf@xa% + \edef\externalradius{\the\pgf@ya}% + \else% + \edef\externalradius{\the\pgf@xa}% + \fi% + \pgfextract@process\toppoint{% + \pgfmathrotatepointaround{\toppoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\bottompoint{% + \pgfmathrotatepointaround{\bottompoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\leftpoint{% + \pgfmathrotatepointaround{\leftpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\rightpoint{% + \pgfmathrotatepointaround{\rightpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\topborderpoint{% + \pgfmathrotatepointaround{\topborderpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\bottomborderpoint{% + \pgfmathrotatepointaround{\bottomborderpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\leftborderpoint{% + \pgfmathrotatepointaround{\leftborderpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\rightborderpoint{% + \pgfmathrotatepointaround{\rightborderpoint}{\centerpoint}{\rotate}% + }% + \addtosavedmacro{\rotate}% + \addtosavedmacro{\externalradius}% + \addtosavedmacro\toppoint% + \addtosavedmacro\bottompoint% + \addtosavedmacro\leftpoint% + \addtosavedmacro\rightpoint% + \addtosavedmacro\topborderpoint% + \addtosavedmacro\bottomborderpoint% + \addtosavedmacro\leftborderpoint% + \addtosavedmacro\rightborderpoint% + \addtosavedmacro\angletotoppoint% + \addtosavedmacro\angletobottompoint% + \addtosavedmacro\angletoleftpoint% + \addtosavedmacro\angletorightpoint% + \addtosavedmacro\baseangletotoppoint% + \addtosavedmacro\baseangletobottompoint% + \addtosavedmacro\baseangletoleftpoint% + \addtosavedmacro\baseangletorightpoint% + \addtosavedmacro\midangletotoppoint% + \addtosavedmacro\midangletobottompoint% + \addtosavedmacro\midangletoleftpoint% + \addtosavedmacro\midangletorightpoint% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{base west}{% + \installkiteparameters% + \let\pgf@kiteanchorborderreferencepoint\basepoint% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{base east}{% + \installkiteparameters% + \let\pgf@kiteanchorborderreferencepoint\basepoint% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{mid}{\midpoint}% + \anchor{mid west}{% + \installkiteparameters% + \let\pgf@kiteanchorborderreferencepoint\midpoint% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{mid east}{% + \installkiteparameters% + \let\pgf@kiteanchorborderreferencepoint\midpoint% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{north}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north east}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south west}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{south east}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \anchor{north west}{% + \installkiteparameters% + \csname pgf@anchor@kite@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{upper vertex}{% + \installkiteparameters% + \topborderpoint}% + \anchor{lower vertex}{% + \installkiteparameters% + \bottomborderpoint}% + \anchor{left vertex}{% + \installkiteparameters% + \leftborderpoint}% + \anchor{right vertex}{% + \installkiteparameters% + \rightborderpoint}% + \anchor{upper left side}{% + \installkiteparameters% + \pgfpointlineattime{0.5}{\topborderpoint}{\leftborderpoint}}% + \anchor{lower left side}{% + \installkiteparameters% + \pgfpointlineattime{0.5}{\bottomborderpoint}{\leftborderpoint}}% + \anchor{upper right side}{% + \installkiteparameters% + \pgfpointlineattime{0.5}{\topborderpoint}{\rightborderpoint}}% + \anchor{lower right side}{% + \installkiteparameters% + \pgfpointlineattime{0.5}{\bottomborderpoint}{\rightborderpoint}}% + \backgroundpath{% + \installkiteparameters% + \pgfpathmoveto{\toppoint}% + \pgfpathlineto{\leftpoint}% + \pgfpathlineto{\bottompoint}% + \pgfpathlineto{\rightpoint}% + \pgfpathclose% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \pgfutil@ifundefined{pgf@kiteanchorborderreferencepoint}% + {\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@kiteanchorborderreferencepoint}% + \referencepoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \installkiteparameters% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \ifx\referencepoint\basepoint% + \let\angletotoppoint\baseangletotoppoint% + \let\angletobottompoint\baseangletobottompoint% + \let\angletoleftpoint\baseangletoleftpoint% + \let\angletorightpoint\baseangletorightpoint% + \else% + \ifx\referencepoint\midpoint% + \let\angletotoppoint\midangletotoppoint% + \let\angletobottompoint\midangletobottompoint% + \let\angletoleftpoint\midangletoleftpoint% + \let\angletorightpoint\midangletorightpoint% + \fi\fi% + \ifdim\angletorightpoint pt<\angletotoppoint pt\relax% + \ifdim\externalangle pt<\angletorightpoint pt\relax% + \let\firstpoint\rightborderpoint% + \let\secondpoint\bottomborderpoint% + \else% + \ifdim\externalangle pt<\angletotoppoint pt\relax% + \let\firstpoint\rightborderpoint% + \let\secondpoint\topborderpoint% + \else% + \ifdim\externalangle pt<\angletoleftpoint pt\relax% + \let\firstpoint\topborderpoint% + \let\secondpoint\leftborderpoint% + \else% + \ifdim\externalangle pt<\angletobottompoint pt\relax% + \let\firstpoint\leftborderpoint% + \let\secondpoint\bottomborderpoint% + \else% + \let\firstpoint\rightborderpoint% + \let\secondpoint\bottomborderpoint% + \fi% + \fi% + \fi% + \fi% + \else% + \ifdim\externalangle pt<\angletotoppoint pt\relax% + \let\firstpoint\rightborderpoint% + \let\secondpoint\topborderpoint% + \else% + \ifdim\externalangle pt<\angletoleftpoint pt\relax% + \let\firstpoint\leftborderpoint% + \let\secondpoint\topborderpoint% + \else% + \ifdim\externalangle pt<\angletobottompoint pt\relax% + \let\firstpoint\bottomborderpoint% + \let\secondpoint\leftborderpoint% + \else% + \ifdim\externalangle pt<\angletorightpoint pt\relax% + \let\firstpoint\rightborderpoint% + \let\secondpoint\bottomborderpoint% + \else% + \let\firstpoint\rightborderpoint% + \let\secondpoint\topborderpoint% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + {\firstpoint}{\secondpoint}% + }% +}% + + + + + +\pgfkeys{/pgf/.cd, + dart tip angle/.initial=45, + dart tail angle/.initial=135, +}% + +\pgfdeclareshape{dart}{% + \savedmacro\installdartparameters{% + \pgfmathdivide{\pgfkeysvalueof{/pgf/dart tip angle}}{2}% + \let\halftipangle\pgfmathresult% + \pgfmathdivide{\pgfkeysvalueof{/pgf/dart tail angle}}{2}% + \let\halftailangle\pgfmathresult% + \pgfmathcot@{\halftipangle}% + \let\cothalftipangle\pgfmathresult% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfextract@process\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \pgfextract@process\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \pgf@xa\cothalftipangle\pgf@x% + \advance\pgf@xa\pgf@x% + \else% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \fi% + \fi% + \pgf@xa\cothalftipangle\pgf@y% + \advance\pgf@xa2.0\pgf@x% + \fi% + \pgfmathsubtract@{\halftailangle}{\halftipangle}% + \pgfmathcosec@{\pgfmathresult}% + \pgf@ya\pgfmathresult\pgf@xa% + \pgfmathsin@{\halftipangle}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgfmathcos@{\halftipangle}% + \pgf@ya\pgfmathresult\pgf@ya% + \pgf@xb\cothalftipangle\pgf@ya% + \pgf@xc-\pgf@xa% + \advance\pgf@xc\pgf@xb% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@xb<\pgf@y% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@xb}}% + \pgf@y\pgfmathresult\pgf@y% + \pgf@xa\pgfmath@tonumber{\pgf@y}\pgf@xa% + \pgf@xc\pgfmath@tonumber{\pgf@y}\pgf@xc% + \pgf@ya\pgfmath@tonumber{\pgf@y}\pgf@ya% + \pgf@x\pgfmath@tonumber{\pgf@y}\pgf@x% + \fi% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@y.5\pgf@y% + \ifdim\pgf@ya<\pgf@y% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@ya}}% + \pgf@ya\pgf@y% + \pgf@y\pgfmathresult\pgf@y% + \pgf@xa\pgfmath@tonumber{\pgf@y}\pgf@xa% + \pgf@xc\pgfmath@tonumber{\pgf@y}\pgf@xc% + \pgf@x\pgfmath@tonumber{\pgf@y}\pgf@x% + \fi% + \edef\dartlength{\the\pgf@xa}% + \edef\deltax{\the\pgf@x}% + \edef\taillength{\the\pgf@xc}% + \edef\halftailseparation{\the\pgf@ya} + \pgfextract@process\tippoint{% + \centerpoint% + \advance\pgf@x\dartlength\relax% + \advance\pgf@x-\deltax\relax% + }% + \pgfextract@process\tailcenterpoint{% + \centerpoint% + \advance\pgf@x-\deltax\relax% + }% + \pgfextract@process\lefttailpoint{% + \centerpoint% + \advance\pgf@x-\deltax\relax% + \advance\pgf@x-\taillength\relax% + \advance\pgf@y\halftailseparation\relax% + }% + \pgfextract@process\righttailpoint{% + \centerpoint% + \advance\pgf@x-\deltax\relax% + \advance\pgf@x-\taillength\relax% + \advance\pgf@y-\halftailseparation\relax% + }% + \pgfextract@process\tipmiter{% + \pgfmathcosec@{\halftipangle}% + \pgf@x\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y0pt\relax% + }% + \pgfextract@process\tailcentermiter{% + \pgfmathcosec@{\halftailangle}% + \pgf@x-\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y0pt\relax% + }% + \pgfmathsubtract@{\halftailangle}{\halftipangle}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\angle\pgfmathresult% + \pgfmathcosec@{\pgfmathresult}% + \pgf@x\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \pgfmathadd@{\angle}{90}% + \pgfmathsubtract{\pgfmathresult}{\halftailangle}% + \pgfmathsincos@{\pgfmathresult}% + \pgf@ya\pgfmathresultx\pgf@x% + \pgf@xa\pgfmathresulty\pgf@x% + \pgfextract@process\lefttailmiter{% + \pgf@x-\pgf@xa% + \pgf@y\pgf@ya% + }% + \pgfextract@process\righttailmiter{% + \pgf@x-\pgf@xa% + \pgf@y-\pgf@ya% + }% + \pgfextract@process\tipborderpoint{% + \pgfpointadd{\tippoint}{\tipmiter} + }% + \pgfextract@process\tailcenterborderpoint{% + \pgfpointadd{\tailcenterpoint}{\tailcentermiter}% + }% + \pgfextract@process\lefttailborderpoint{% + \pgfpointadd{\lefttailpoint}{\lefttailmiter}% + }% + \pgfextract@process\righttailborderpoint{% + \pgfpointadd{\righttailpoint}{\righttailmiter}% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\tipborderpoint}% + \let\angletotip\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\tailcenterborderpoint}% + \let\angletotailcenter\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\lefttailborderpoint}% + \let\angletolefttail\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\righttailborderpoint}% + \let\angletorighttail\pgfmathresult% + \pgfextract@process\rotatedbasepoint{% + \pgfmathrotatepointaround{\basepoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\tipborderpoint}% + \let\baseangletotip\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\tailcenterborderpoint}% + \let\baseangletotailcenter\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\lefttailborderpoint}% + \let\baseangletolefttail\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedbasepoint}{\righttailborderpoint}% + \let\baseangletorighttail\pgfmathresult% + \pgfextract@process\rotatedmidpoint{% + \pgfmathrotatepointaround{\midpoint}{\centerpoint}{-\rotate}% + }% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\tipborderpoint}% + \let\midangletotip\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\tailcenterborderpoint}% + \let\midangletotailcenter\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\lefttailborderpoint}% + \let\midangletolefttail\pgfmathresult% + \pgfmathanglebetweenpoints{\rotatedmidpoint}{\righttailborderpoint}% + \let\midangletorighttail\pgfmathresult% + \pgfextract@process\tippoint{% + \pgfmathrotatepointaround{\tippoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\tailcenterpoint{% + \pgfmathrotatepointaround{\tailcenterpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\lefttailpoint{% + \pgfmathrotatepointaround{\lefttailpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\righttailpoint{% + \pgfmathrotatepointaround{\righttailpoint}{\centerpoint}{\rotate}% + }% + \pgfextractx\pgf@xa{\pgfpointdiff{\lefttailborderpoint}{\tipborderpoint}}% + \pgfextracty\pgf@ya{\pgfpointdiff{\lefttailborderpoint}{\righttailborderpoint}}% + \ifdim\pgf@xa<0pt\relax% + \pgf@xa-\pgf@xa% + \fi% + \ifdim\pgf@ya<0pt\relax% + \pgf@ya-\pgf@ya% + \fi% + \ifdim\pgf@xa>\pgf@ya% + \edef\externalradius{\the\pgf@xa}% + \else% + \edef\externalradius{\the\pgf@ya}% + \fi% + \pgfextract@process\tipborderpoint{% + \pgfmathrotatepointaround{\tipborderpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\tailcenterborderpoint{% + \pgfmathrotatepointaround{\tailcenterborderpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\lefttailborderpoint{% + \pgfmathrotatepointaround{\lefttailborderpoint}{\centerpoint}{\rotate}% + }% + \pgfextract@process\righttailborderpoint{% + \pgfmathrotatepointaround{\righttailborderpoint}{\centerpoint}{\rotate}% + }% + \addtosavedmacro{\rotate}% + \addtosavedmacro{\externalradius}% + \addtosavedmacro{\tippoint}% + \addtosavedmacro{\tailcenterpoint}% + \addtosavedmacro{\lefttailpoint}% + \addtosavedmacro{\righttailpoint}% + \addtosavedmacro{\tipborderpoint}% + \addtosavedmacro{\tailcenterborderpoint}% + \addtosavedmacro{\lefttailborderpoint}% + \addtosavedmacro{\righttailborderpoint}% + \addtosavedmacro{\angletotip}% + \addtosavedmacro{\angletotailcenter}% + \addtosavedmacro{\angletolefttail}% + \addtosavedmacro{\angletorighttail}% + \addtosavedmacro{\baseangletotip}% + \addtosavedmacro{\baseangletotailcenter}% + \addtosavedmacro{\baseangletolefttail}% + \addtosavedmacro{\baseangletorighttail}% + \addtosavedmacro{\midangletotip}% + \addtosavedmacro{\midangletotailcenter}% + \addtosavedmacro{\midangletolefttail}% + \addtosavedmacro{\midangletorighttail}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{base west}{% + \installdartparameters% + \let\pgf@dartanchorborderreferencepoint\basepoint% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{base east}{% + \installdartparameters% + \let\pgf@dartanchorborderreferencepoint\basepoint% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{mid}{\midpoint}% + \anchor{mid west}{% + \installdartparameters% + \let\pgf@dartanchorborderreferencepoint\midpoint% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{mid east}{% + \installdartparameters% + \let\pgf@dartanchorborderreferencepoint\midpoint% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{north}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north east}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south west}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{south east}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \anchor{north west}{% + \installdartparameters% + \csname pgf@anchor@dart@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{tip}{% + \installdartparameters% + \tipborderpoint}% + \anchor{left tail}{% + \installdartparameters% + \lefttailborderpoint}% + \anchor{right tail}{% + \installdartparameters% + \righttailborderpoint}% + \anchor{tail center}{% + \installdartparameters% + \tailcenterborderpoint}% + \anchor{left side}{% + \installdartparameters% + \pgfpointlineattime{0.5}{\tipborderpoint}{\lefttailborderpoint}}% + \anchor{right side}{% + \installdartparameters% + \pgfpointlineattime{0.5}{\tipborderpoint}{\righttailborderpoint}}% + \backgroundpath{% + \installdartparameters% + \pgfpathmoveto{\tippoint}% + \pgfpathlineto{\lefttailpoint}% + \pgfpathlineto{\tailcenterpoint}% + \pgfpathlineto{\righttailpoint}% + \pgfpathclose% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \pgfutil@ifundefined{pgf@dartanchorborderreferencepoint}% + {\let\referencepoint\centerpoint}% + {\let\referencepoint\pgf@dartanchorborderreferencepoint}% + \referencepoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \installdartparameters% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \ifx\referencepoint\basepoint% + \let\angletotip\baseangletotip% + \let\angletotailcenter\baseangletotailcenter% + \let\angletolefttail\baseangletolefttail% + \let\angletorighttail\baseangletorighttail% + \else% + \ifx\referencepoint\midpoint% + \let\angletotip\midangletotip% + \let\angletotailcenter\midangletotailcenter% + \let\angletolefttail\midangletolefttail% + \let\angletorighttail\midangletorighttail% + \fi\fi% + \ifdim\externalangle pt<\angletotip pt\relax% + \let\firstpoint\tipborderpoint% + \let\secondpoint\righttailborderpoint% + \else% + \ifdim\externalangle pt<\angletolefttail pt\relax% + \let\firstpoint\lefttailborderpoint% + \let\secondpoint\tipborderpoint% + \else% + \ifdim\externalangle pt<\angletotailcenter pt\relax% + \let\firstpoint\lefttailborderpoint% + \let\secondpoint\tailcenterborderpoint% + \else% + \ifdim\externalangle pt<\angletorighttail pt\relax% + \let\firstpoint\righttailborderpoint% + \let\secondpoint\tailcenterborderpoint% + \else% + \let\firstpoint\tipborderpoint% + \let\secondpoint\righttailborderpoint% + \fi% + \fi% + \fi% + \fi% + \pgfpointintersectionoflines{\referencepoint}{\pgfqpoint{\externalx}{\externaly}}% + {\firstpoint}{\secondpoint}% + }% +}% + + + +\pgfkeys{/pgf/circular sector angle/.initial=60}% + +\pgfdeclareshape{circular sector}{% + \savedmacro\installcircularsectorparameters{% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \pgfmathmod{\pgfkeysvalueof{/pgf/circular sector angle}}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\angle\pgfmathresult% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\halfangle\pgfmathresult% + \pgfmathsin@{\halfangle}% + \let\sinehalfangle\pgfmathresult% + \pgfmathreciprocal@{\pgfmathresult}% + \let\cosechalfangle\pgfmathresult% + \pgfmathabs@{\halfangle}% + \pgfmathcos@{\pgfmathresult}% + \let\coshalfangle\pgfmathresult% + \pgf@x\pgfmathresult pt\relax% + \pgf@x\cosechalfangle\pgf@x% + \edef\cothalfangle{\pgfmath@tonumber{\pgf@x}}% + \pgf@x\outersep\relax% + \pgf@x\cosechalfangle\pgf@x% + \edef\centermiter{\the\pgf@x}% + \pgfmathsubtract@{180}{\halfangle}% + \let\startangle\pgfmathresult% + \pgfmathadd@{180}{\halfangle}% + \let\endangle\pgfmathresult% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \pgf@xa\cosechalfangle\pgf@x% + \pgf@xb\pgf@xa% + \advance\pgf@xa\pgf@x% + \else% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \fi% + \fi% + \pgf@xa\cosechalfangle\pgf@y% + \pgf@xa\coshalfangle\pgf@xa% + \advance\pgf@xa\pgf@x% + \pgf@xb\pgf@xa% + \advance\pgf@xa\pgf@x% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@y}}% + \pgf@xa\pgfmathresult pt\relax% + \fi% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/minimum width}}% + \pgf@x.5\pgf@x% + \pgfmathsec@{\halfangle}% + \pgf@xc\pgfmathresult\pgf@xb% + \ifdim\pgf@xc<0pt\relax% + \pgf@xc-\pgf@xc% + \fi% + \ifdim\pgf@xc<\pgf@x% + \pgfmathreciprocal{\pgfmath@tonumber{\pgf@xc}}% + \pgf@xc\pgfmathresult\pgf@x% + \pgf@xa\pgfmath@tonumber{\pgf@xc}\pgf@xa% + \pgf@xb\pgfmath@tonumber{\pgf@xc}\pgf@xb% + \fi% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@xa<\pgf@y% + \pgfmathreciprocal{\pgfmath@tonumber{\pgf@xa}}% + \pgf@xc\pgfmathresult\pgf@y% + \pgf@xa\pgf@y% + \pgf@xb\pgfmath@tonumber{\pgf@xc}\pgf@xb% + \fi% + \edef\centeroffset{\the\pgf@xb}% + \edef\radius{\the\pgf@xa}% + \advance\pgf@xa\outersep\relax% + \edef\borderradius{\the\pgf@xa}% + \pgf@x\outersep\relax% + \pgf@x\cosechalfangle\pgf@x% + \pgf@x\coshalfangle\pgf@x% + \advance\pgf@xa\pgf@x% + \edef\cornerradius{\the\pgf@xa}% + \pgfextract@process\sectorcenter{% + \centerpoint% + \advance\pgf@x\centeroffset% + }% + \pgfextract@process\arcstart{% + \pgfqpointpolar{\startangle}{\radius}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \sectorcenter% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\sectorcenterborder{% + \sectorcenter% + \advance\pgf@x\centermiter\relax% + }% + \pgfextract@process\arcstartborder{% + \pgfqpointpolar{\startangle}{\borderradius}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \sectorcenter% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\arcendborder{% + \pgfqpointpolar{\endangle}{\borderradius}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \sectorcenter% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\arcstartcorner{% + \pgfqpointpolar{\startangle}{\cornerradius}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \sectorcenterborder% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\arcendcorner{% + \pgfqpointpolar{\endangle}{\cornerradius}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \sectorcenterborder% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\sectorcenterborder}% + \let\angletosectorcenterborder\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcstartborder}% + \let\angletoarcstartborder\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcendborder}% + \let\angletoarcendborder\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcstartcorner}% + \let\angletoarcstartcorner\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\arcendcorner}% + \let\angletoarcendcorner\pgfmathresult% + \pgfextract@process\sectorcenter{% + \pgfmathrotatepointaround{\sectorcenter}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcstart{% + \pgfmathrotatepointaround{\arcstart}{\centerpoint}{\rotate}% + }% + \pgfextract@process\sectorcenterborder{% + \pgfmathrotatepointaround{\sectorcenterborder}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcstartborder{% + \pgfmathrotatepointaround{\arcstartborder}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcendborder{% + \pgfmathrotatepointaround{\arcendborder}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcstartcorner{% + \pgfmathrotatepointaround{\arcstartcorner}{\centerpoint}{\rotate}% + }% + \pgfextract@process\arcendcorner{% + \pgfmathrotatepointaround{\arcendcorner}{\centerpoint}{\rotate}% + }% + \pgfmathadd@{\startangle}{\rotate}% + \let\startangle\pgfmathresult% + \pgfmathadd@{\endangle}{\rotate}% + \let\endangle\pgfmathresult% + \addtosavedmacro{\rotate}% + \addtosavedmacro{\centeroffset}% + \addtosavedmacro{\radius}% + \addtosavedmacro{\borderradius}% + \addtosavedmacro{\cornerradius}% + \addtosavedmacro{\endangle}% + \addtosavedmacro{\startangle}% + \addtosavedmacro{\sectorcenter}% + \addtosavedmacro{\arcstart}% + \addtosavedmacro{\sectorcenterborder}% + \addtosavedmacro{\arcstartborder}% + \addtosavedmacro{\arcendborder}% + \addtosavedmacro{\arcstartcorner}% + \addtosavedmacro{\arcendcorner}% + \addtosavedmacro{\angletosectorcenterborder}% + \addtosavedmacro{\angletoarcstartborder}% + \addtosavedmacro{\angletoarcendborder}% + \addtosavedmacro{\angletoarcstartcorner}% + \addtosavedmacro{\angletoarcendcorner}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{mid}{\midpoint}% + \anchor{arc start}{% + \installcircularsectorparameters% + \arcstartcorner% + }% + \anchor{arc end}{% + \installcircularsectorparameters% + \arcendcorner% + }% + \anchor{sector center}{% + \installcircularsectorparameters% + \sectorcenterborder% + }% + \anchor{arc center}{% + \installcircularsectorparameters% + \pgfmathadd@{\rotate}{180}% + \let\angle\pgfmathresult% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpointpolar{\angle}{\cornerradius}}% + }% + \anchor{north}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{0pt}{\cornerradius}}% + }% + \anchor{south}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{0pt}{-\cornerradius}}% + }% + \anchor{east}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{\cornerradius}{0pt}}% + }% + \anchor{west}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{-\cornerradius}{0pt}}% + }% + \anchor{north west}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{-\cornerradius}{\cornerradius}}% + }% + \anchor{south west}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{-\cornerradius}{-\cornerradius}}% + }% + \anchor{north east}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{\cornerradius}{\cornerradius}}% + }% + \anchor{south east}{% + \installcircularsectorparameters% + \csname pgf@anchor@circular sector@border\endcsname{\pgfqpoint{\cornerradius}{-\cornerradius}}% + }% + \backgroundpath{% + \installcircularsectorparameters% + \pgfpathmoveto{\sectorcenter}% + \pgfpathlineto{\arcstart}% + \ifdim\endangle pt>360pt\relax% + \ifdim\startangle pt>360pt\relax% + \pgfpatharc{\startangle}{\endangle}{\radius}% + \else% + \pgfpatharc{\startangle}{360}{\radius}% + \pgfpatharc{0}{\endangle}{\radius}% + \fi% + \else% + \pgfpatharc{\startangle}{\endangle}{\radius}% + \fi% + \pgfpathclose% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \centerpoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \installcircularsectorparameters% + \pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + \let\externalangle\pgfmathresult% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\angle\pgfmathresult% + \ifdim\angle pt>\angletoarcendcorner pt\relax% + \let\firstpoint\arcendcorner% + \let\secondpoint\sectorcenterborder% + \else% + \ifdim\angle pt>\angletoarcendborder pt\relax% + \let\firstpoint\arcendborder% + \let\secondpoint\arcendcorner% + \else% + \ifdim\angle pt>\angletoarcstartborder pt\relax% + \let\firstpoint\pgfutil@empty% + \let\secondpoint\pgfutil@empty% + \else% + \ifdim\angle pt>\angletoarcstartcorner pt\relax% + \let\firstpoint\arcstartborder + \let\secondpoint\arcstartcorner + \else% + \let\firstpoint\sectorcenterborder% + \let\secondpoint\arcstartcorner% + \fi% + \fi% + \fi% + \fi% + \ifx\firstpoint\pgfutil@empty + \pgfmathanglebetweenlines{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + {\sectorcenter}{\centerpoint}% + \pgfmathsin@{\pgfmathresult}% + \let\sineangle\pgfmathresult% + \pgf@x\borderradius\relax% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@x}}% + \let\reciprocalradius\pgfmathresult% + \pgf@x\centeroffset\relax% + \pgf@x\sineangle\pgf@x% + \pgf@x\reciprocalradius\pgf@x% + \pgfmathasin@{\pgfmath@tonumber{\pgf@x}}% + \pgf@x\pgfmathresult pt\relax% + \advance\pgf@x\externalangle pt\relax% + \edef\angle{\pgfmath@tonumber{\pgf@x}}% + \pgfpointadd{\sectorcenter}{\pgfqpointpolar{\angle}{\borderradius}}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + {\firstpoint}{\secondpoint}% + \fi% + }% +}% + + + + +\newif\ifpgfcylinderusescustomfill +\pgfkeys{/pgf/.cd, + cylinder uses custom fill/.is if=pgfcylinderusescustomfill, + cylinder end fill/.initial=white, + cylinder body fill/.initial=white, +}% + + +\pgfdeclareshape{cylinder}{% + \savedmacro\getcylinderpoints{% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/inner xsep}}% + \pgf@x\pgf@xc% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgf@y\pgf@yc% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \ifpgfshapeborderusesincircle% + \pgfmathsetmacro\rotate{\pgfkeysvalueof{/pgf/shape border rotate}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \else% + \pgf@y\pgf@x% + \fi% + \pgf@x1.414213\pgf@x% + \pgf@y1.414213\pgf@y% + \else% + \pgfmathmod{\pgfkeysvalueof{/pgf/shape border rotate}}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \pgfmathsetcount\c@pgf@counta{+\pgfmathresult}% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \edef\rotate{\the\c@pgf@counta}% + \ifnum\c@pgf@counta=90\relax% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xa% + \pgf@yc\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xa\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xa% + \pgf@yc\pgf@xc% + \fi% + \fi% + \fi% + \addtosavedmacro\rotate% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfutil@tempdima\pgfshapeaspect\pgf@ya% + \pgfutil@tempdimb\pgf@ya% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgfutil@tempdimb<.5\pgf@xc\relax% + \pgfutil@tempdimb.5\pgf@xc% + \pgf@ya\pgfutil@tempdimb% + \fi% + \pgf@yb\pgfutil@tempdimb% + \advance\pgf@yb-\pgf@yc% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yb}}{\pgfmath@tonumber{\pgfutil@tempdimb}}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \let\angle\pgfmathresult% + \pgf@xb\pgfmathresult\pgfutil@tempdima% + \pgf@x.5\pgflinewidth% + \advance\pgf@x2.0\pgf@xa% + \advance\pgf@x3.0\pgfutil@tempdima% + \advance\pgf@x-\pgf@xb% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<\pgf@xc% + \advance\pgf@xc-\pgf@x% + \advance\pgf@xa.5\pgf@xc% + \fi% + \pgf@x\pgfutil@tempdima\relax% + \pgf@y\pgfutil@tempdimb\relax% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xc>\pgf@yc% + \advance\pgf@x\pgf@xc% + \advance\pgf@y\pgf@xc% + \edef\outersep{\the\pgf@xc}% + \else% + \advance\pgf@x\pgf@yc% + \advance\pgf@y\pgf@yc% + \edef\outersep{\the\pgf@yc}% + \fi% + \edef\xradius{\the\pgf@x}% + \edef\yradius{\the\pgf@y}% + \addtosavedmacro\xradius% + \addtosavedmacro\yradius% + \addtosavedmacro\outersep% + \pgfextract@process\cylindercenter{% + \pgf@x\pgfutil@tempdima% + \advance\pgf@x.5\pgflinewidth% + \advance\pgf@x\pgf@xb% + \pgf@x.5\pgf@x% + \pgf@y0pt% + }% + \addtosavedmacro\cylindercenter% + \pgfextract@process\beforetop{% + \pgf@x\pgf@xa% + \advance\pgf@x\pgfutil@tempdima% + \advance\pgf@x.5\pgflinewidth% + \pgf@y\pgf@ya% + }% + \pgfextract@process\afterbottom{% + \pgf@x-\pgf@xa% + \advance\pgf@x\pgf@xb% + \pgf@y\pgf@ya% + }% + \addtosavedmacro\beforetop% + \addtosavedmacro\afterbottom% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/outer ysep}}% + \pgfextract@process\beforetopanchor{% + \beforetop% + \advance\pgf@y\pgf@yc% + }% + \pgfextract@process\afterbottomanchor{% + \afterbottom% + \advance\pgf@y\pgf@yc% + }% + \addtosavedmacro\beforetopanchor% + \addtosavedmacro\afterbottomanchor% + \beforetopanchor% + \advance\pgf@x\xradius\relax% + \ifdim\pgf@x>\pgf@y% + \edef\externalradius{\the\pgf@x}% + \else% + \edef\externalradius{\the\pgf@y}% + \fi% + \addtosavedmacro\externalradius% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{shape center}{% + \getcylinderpoints% + \pgfmathrotatepointaround{\pgfpointadd{\cylindercenter}{\centerpoint}}% + {\centerpoint}{\rotate}% + }% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \getcylinderpoints% + \let\pgf@cylinder@referencepoint\midpoint% + \pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{mid west}{% + \getcylinderpoints% + \let\pgf@cylinder@referencepoint\midpoint% + \pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \getcylinderpoints% + \let\pgf@cylinder@referencepoint\basepoint% + \pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{base west}{% + \getcylinderpoints% + \let\pgf@cylinder@referencepoint\basepoint% + \pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north east}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south west}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{south east}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \anchor{north west}{% + \getcylinderpoints% + \pgf@anchor@cylinder@border{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{before top}{% + \getcylinderpoints% + \pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor}{\centerpoint}}{\centerpoint}{\rotate}% + }% + \anchor{top}{% + \getcylinderpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \beforetop% + \pgf@y0pt\relax% + \advance\pgf@x\xradius\relax% + }{\centerpoint}}{\centerpoint}{\rotate}% + }% + \anchor{after top}{% + \getcylinderpoints% + \pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor\pgf@y-\pgf@y}{\centerpoint}}{\centerpoint}{\rotate}% + }% + \anchor{before bottom}{% + \getcylinderpoints% + \pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor\pgf@y-\pgf@y}{\centerpoint}}{\centerpoint}{\rotate}% + }% + \anchor{bottom}{% + \getcylinderpoints% + \pgfmathrotatepointaround{% + \pgfpointadd{% + \afterbottom% + \pgf@y0pt\relax% + \advance\pgf@x-\xradius\relax% + }{\centerpoint}}{\centerpoint}{\rotate}% + }% + \anchor{after bottom}{% + \getcylinderpoints% + \pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor}{\centerpoint}}{\centerpoint}{\rotate}% + }% + \backgroundpath{% + \getcylinderpoints% + {% + \pgf@x\xradius\relax% + \advance\pgf@x-\outersep\relax% + \edef\xradius{\the\pgf@x}% + \pgf@y\yradius\relax% + \advance\pgf@y-\outersep\relax% + \edef\yradius{\the\pgf@y}% + \pgftransformshift{\centerpoint}% + \pgftransformrotate{\rotate}% + \pgfpathmoveto{\afterbottom}% + \pgfpatharc{90}{270}{\xradius and \yradius}% + \pgfpathlineto{\beforetop\pgf@y-\pgf@y}% + \pgfpatharc{-90}{90}{\xradius and \yradius}% + \pgfpathclose% + \pgfpathmoveto{\beforetop}% + \pgfpatharc{90}{270}{\xradius and \yradius}% + }% + }% + \behindbackgroundpath{% + \ifpgfcylinderusescustomfill% + \getcylinderpoints% + \pgf@x\xradius\relax% + \advance\pgf@x-\outersep\relax% + \edef\xradius{\the\pgf@x}% + \pgf@y\yradius\relax% + \advance\pgf@y-\outersep\relax% + \edef\yradius{\the\pgf@y}% + {% + \pgftransformshift{\centerpoint}% + \pgftransformrotate{\rotate}% + \pgfpathmoveto{\afterbottom}% + \pgfpatharc{90}{270}{\xradius and \yradius}% + \pgfpathlineto{\beforetop\pgf@y-\pgf@y}% + \pgfpatharc{270}{90}{\xradius and \yradius}% + \pgfpathclose% + \expandafter\pgfsetfillcolor\expandafter{\pgfkeysvalueof{/pgf/cylinder body fill}}% + \pgfusepath{fill}% + \pgfpathmoveto{\beforetop}% + \pgfpatharc{90}{-270}{\xradius and \yradius}% + \pgfpathclose + \expandafter\pgfsetfillcolor\expandafter{\pgfkeysvalueof{/pgf/cylinder end fill}}% + \pgfusepath{fill}% + }% + \fi% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \getcylinderpoints% + \pgfutil@ifundefined{pgf@cylinder@referencepoint}{\let\referencepoint\centerpoint}{% + \let\referencepoint\pgf@cylinder@referencepoint}% + \pgfextract@process\externalpoint{% + \externalpoint% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \referencepoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\afterbottomanchor}{\centerpoint}}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\beforetopanchor}{\centerpoint}}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathrotatepointaround{% + \pgfmathpointintersectionoflineandarc% + {\pgfmathrotatepointaround{\externalpoint}{\centerpoint}{-\rotate}}% + {\pgfmathrotatepointaround{\referencepoint}{\centerpoint}{-\rotate}}% + {% + \beforetop% + \pgf@xa\pgf@x% + \centerpoint% + \advance\pgf@x\pgf@xa% + }% + {0}{90}{\xradius and \yradius}% + }{\centerpoint}{\rotate}% + \else% + \pgfpointintersectionoflines{% + \pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor}{\centerpoint}}% + {\centerpoint}{\rotate}}{% + \pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor}{\centerpoint}}% + {\centerpoint}{\rotate}}% + {\referencepoint}{\externalpoint}% + \fi% + \else% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\afterbottomanchor\pgf@y-\pgf@y}{\centerpoint}}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\referencepoint}{\pgfpointadd{\beforetopanchor\pgf@y-\pgf@y}{\centerpoint}}% + \ifdim\externalangle pt>\pgfmathresult pt\relax% + \pgfmathrotatepointaround{% + \pgfmathpointintersectionoflineandarc% + {\pgfmathrotatepointaround{\externalpoint}{\centerpoint}{-\rotate}}% + {\pgfmathrotatepointaround{\referencepoint}{\centerpoint}{-\rotate}}% + {% + \beforetop% + \pgf@xa\pgf@x% + \centerpoint + \advance\pgf@x\pgf@xa% + }% + {270}{360}{\xradius and \yradius}% + }{\centerpoint}{\rotate}% + \else% + \pgfpointintersectionoflines{% + \pgfmathrotatepointaround{\pgfpointadd{\afterbottomanchor\pgf@y-\pgf@y}{\centerpoint}}% + {\centerpoint}{\rotate}}{% + \pgfmathrotatepointaround{\pgfpointadd{\beforetopanchor\pgf@y-\pgf@y}{\centerpoint}}% + {\centerpoint}{\rotate}}% + {\referencepoint}{\externalpoint}% + \fi% + \else% + \pgfmathrotatepointaround{% + \pgfmathpointintersectionoflineandarc% + {\pgfmathrotatepointaround{\externalpoint}{\centerpoint}{-\rotate}}% + {\pgfmathrotatepointaround{\referencepoint}{\centerpoint}{-\rotate}}% + {% + \afterbottom% + \pgf@xa\pgf@x% + \centerpoint + \advance\pgf@x\pgf@xa% + }% + {90}{270}{\xradius and \yradius}% + }{\centerpoint}{\rotate}% + \fi% + \fi% + }% +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e3a5f1a6686e8af4c9ec3e2a4c5ee53f325957df --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.misc.code.tex @@ -0,0 +1,1045 @@ + +\ProvidesFileRCS{pgflibraryshapes.misc.code.tex} + + +\pgfdeclareshape{cross out} +{% + \inheritsavedanchors[from=rectangle]% + \inheritanchorborder[from=rectangle]% + \inheritanchor[from=rectangle]{north}% + \inheritanchor[from=rectangle]{north west}% + \inheritanchor[from=rectangle]{north east}% + \inheritanchor[from=rectangle]{center}% + \inheritanchor[from=rectangle]{west}% + \inheritanchor[from=rectangle]{east}% + \inheritanchor[from=rectangle]{mid}% + \inheritanchor[from=rectangle]{mid west}% + \inheritanchor[from=rectangle]{mid east}% + \inheritanchor[from=rectangle]{base}% + \inheritanchor[from=rectangle]{base west}% + \inheritanchor[from=rectangle]{base east}% + \inheritanchor[from=rectangle]{south}% + \inheritanchor[from=rectangle]{south west}% + \inheritanchor[from=rectangle]{south east}% + \foregroundpath{ + \southwest \pgf@xa=\pgf@x \pgf@ya=\pgf@y + \northeast \pgf@xb=\pgf@x \pgf@yb=\pgf@y + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@ya}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@yb}} + \pgfpathmoveto{\pgfqpoint{\pgf@xa}{\pgf@yb}} + \pgfpathlineto{\pgfqpoint{\pgf@xb}{\pgf@ya}} + \pgfsetarrowsstart{} + \pgfsetarrowsend{} + }% +}% + + +\pgfdeclareshape{strike out} +{% + \inheritsavedanchors[from=rectangle]% + \inheritanchorborder[from=rectangle]% + \inheritanchor[from=rectangle]{north}% + \inheritanchor[from=rectangle]{north west}% + \inheritanchor[from=rectangle]{north east}% + \inheritanchor[from=rectangle]{center}% + \inheritanchor[from=rectangle]{west}% + \inheritanchor[from=rectangle]{east}% + \inheritanchor[from=rectangle]{mid}% + \inheritanchor[from=rectangle]{mid west}% + \inheritanchor[from=rectangle]{mid east}% + \inheritanchor[from=rectangle]{base}% + \inheritanchor[from=rectangle]{base west}% + \inheritanchor[from=rectangle]{base east}% + \inheritanchor[from=rectangle]{south}% + \inheritanchor[from=rectangle]{south west}% + \inheritanchor[from=rectangle]{south east}% + \foregroundpath{ + \pgfpathmoveto{\southwest} + \pgfpathlineto{\northeast} + \pgfsetarrowsstart{} + \pgfsetarrowsend{} + }% +}% + + + + +\pgfkeys{/pgf/.cd, + rounded rectangle west arc/.initial=convex, + rounded rectangle east arc/.initial=convex, + rounded rectangle left arc/.style={/pgf/rounded rectangle west arc={#1}},% + rounded rectangle right arc/.style={/pgf/rounded rectangle east arc={#1}},% + rounded rectangle arc length/.initial=180% +}% + +\def\pgf@lib@sh@misc@rr@text@concave{concave}% +\def\pgf@lib@sh@misc@rr@text@convex{convex}% + +\pgfdeclareshape{rounded rectangle}{% + \savedmacro\westarc{% + \edef\westarc{\pgfkeysvalueof{/pgf/rounded rectangle west arc}}% + }% + \savedmacro\eastarc{% + \edef\eastarc{\pgfkeysvalueof{/pgf/rounded rectangle east arc}}% + }% + \savedmacro\roundedrectanglepoints{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/rounded rectangle arc length}}% + \pgf@x=.5\pgf@x% + \edef\halfarcangle{\pgfmath@tonumber{\pgf@x}}% + \addtosavedmacro\halfarcangle% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \edef\innerxsep{\the\pgf@x}% + \pgf@xa=0.5\wd\pgfnodeparttextbox% + \edef\halftextwidth{\the\pgf@xa}% + \addtosavedmacro\halftextwidth% + \advance\pgf@x by\pgf@xa% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \edef\innerysep{\the\pgf@y}% + \pgf@ya=.5\ht\pgfnodeparttextbox% + \advance\pgf@ya by.5\dp\pgfnodeparttextbox% + \edef\halftextheight{\the\pgf@ya}% + \addtosavedmacro\halftextheight% + \advance\pgf@y by\pgf@ya% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<.5\pgf@yb% + \pgf@y=.5\pgf@yb% + \fi% + \edef\halfheight{\the\pgf@y}% + \addtosavedmacro\halfheight% + \pgfmathcosec@{\halfarcangle}% + \pgf@ya=\pgfmathresult\pgf@y% + \edef\radius{\the\pgf@ya}% + \addtosavedmacro\radius% + \pgfmathcos@{\halfarcangle}% + \pgf@xa=\pgf@ya% + \advance\pgf@xa by-\pgfmathresult\pgf@ya% + \pgfmathdivide{\halftextheight}{\radius}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathcos@{\pgfmathresult}% + \pgf@xb=\pgf@ya% + \advance\pgf@xb by-\pgfmathresult\pgf@ya% + \edef\westarc{\pgfkeysvalueof{/pgf/rounded rectangle west arc}}% + \edef\eastarc{\pgfkeysvalueof{/pgf/rounded rectangle east arc}}% + \pgfutil@tempdima=2.0\pgf@x% + \ifx\westarc\pgf@lib@sh@misc@rr@text@concave% + \advance\pgfutil@tempdima by\pgf@xa% + \else% + \ifx\westarc\pgf@lib@sh@misc@rr@text@convex% + \advance\pgfutil@tempdima by\pgf@xb% + \fi% + \fi% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@concave% + \advance\pgfutil@tempdima by\pgf@xa% + \else% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \advance\pgfutil@tempdima by\pgf@xb% + \fi% + \fi% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgfutil@tempdima<\pgfutil@tempdimb% + \advance\pgfutil@tempdimb by-\pgfutil@tempdima% + \divide\pgfutil@tempdimb by2\relax% + \edef\xoffset{\the\pgfutil@tempdimb}% + \else% + \let\xoffset=\innerxsep% + \fi% + \pgf@x=\halftextwidth\relax% + \advance\pgf@x by\xoffset\relax% + \pgf@xc=\pgf@ya% + \advance\pgf@xc by-\pgf@xb% + \ifdim\pgf@xc>\pgf@x\relax% + \advance\pgf@xc by-\pgf@x% + \advance\pgf@xc by\xoffset\relax% + \edef\xoffset{\the\pgf@xc}% + \fi% + \addtosavedmacro\xoffset% + \pgf@x=\halftextwidth\relax% + \advance\pgf@x by\xoffset\relax% + \edef\halfwidth{\the\pgf@x}% + \addtosavedmacro\halfwidth% + \edef\arcwidth{\the\pgf@xa}% + \addtosavedmacro\arcwidth% + \edef\chordwidth{\the\pgf@xb}% + \addtosavedmacro\chordwidth% + \pgfmathsetlengthmacro\outerxsep{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlengthmacro\outerysep{\pgfkeysvalueof{/pgf/outer ysep}}% + \addtosavedmacro\outerxsep% + \addtosavedmacro\outerysep% + \ifdim\halfarcangle pt=90pt\relax% + \def\concavexshift{0pt}% + \else% + \pgfmathsubtract@{90}{\halfarcangle}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\angletemp=\pgfmathresult% + \pgf@x=\outerxsep\relax% + \pgfmathcosec@{\angletemp}% + \pgf@x=\pgfmathresult\pgf@x% + \pgfmathcos@{\angletemp}% + \pgf@x=\pgfmathresult\pgf@x% + \edef\concavexshift{\the\pgf@x}% + \fi% + \addtosavedmacro\concavexshift% + \ifdim\halfarcangle pt=90pt\relax% + \def\convexxshift{0pt}% + \else% + \pgfmathadd@{90}{\halfarcangle}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\angletemp=\pgfmathresult% + \pgf@x=\outerxsep\relax% + \pgfmathcosec@{\angletemp}% + \pgf@x=\pgfmathresult\pgf@x% + \pgfmathcos@{\angletemp}% + \pgf@x=\pgfmathresult\pgf@x% + \edef\convexxshift{\the\pgf@x}% + \fi% + \addtosavedmacro\convexxshift% + }% + \saveddimen\halflinewidth{\pgf@x.5\pgflinewidth}% + \savedanchor\centerpoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgf@y=.5\ht\pgfnodeparttextbox% + \advance\pgf@y by-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgf@y=0pt\relax% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid west}{% + \csname pgf@anchor@rounded rectangle@west\endcsname% + \pgf@xc=\pgf@x% + \midpoint% + \pgf@x=\pgf@xc% + }% + \anchor{mid east}{% + \csname pgf@anchor@rounded rectangle@east\endcsname% + \pgf@xc=\pgf@x% + \midpoint% + \pgf@x=\pgf@xc% + }% + \anchor{base}{\basepoint}% + \anchor{base west}{% + \csname pgf@anchor@rounded rectangle@west\endcsname% + \pgf@xc=\pgf@x% + \basepoint% + \pgf@x=\pgf@xc% + }% + \anchor{base east}{% + \csname pgf@anchor@rounded rectangle@east\endcsname% + \pgf@xc=\pgf@x% + \basepoint% + \pgf@x=\pgf@xc% + }% + \anchor{north}{% + \roundedrectanglepoints% + \pgfpointadd{\centerpoint}{\pgfpoint{+0pt}{\halfheight+\outerysep}}% + }% + \anchor{south}{% + \roundedrectanglepoints% + \pgfpointadd{\centerpoint}{\pgfpoint{+0pt}{-\halfheight-\outerysep}}% + }% + \anchor{west}{% + \roundedrectanglepoints% + \pgfpointadd{\centerpoint}{% + \ifx\westarc\pgf@lib@sh@misc@rr@text@concave% + \pgfpoint{-\halfwidth-\arcwidth-\concavexshift}{+0pt}% + \else% + \ifx\westarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpoint{-\halfwidth-\chordwidth-\outerxsep}{+0pt}% + \else% + \pgfpoint{-\halfwidth-\outerxsep}{+0pt}% + \fi% + \fi% + }% + }% + \anchor{north west}{% + \roundedrectanglepoints% + \ifx\westarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpointadd{\centerpoint}{\pgfpoint{-\halfwidth-\chordwidth+\arcwidth-\convexxshift}{+0pt}}% + \else% + \csname pgf@anchor@rounded rectangle@west\endcsname% + \fi% + \pgf@xc=\pgf@x% + \csname pgf@anchor@rounded rectangle@north\endcsname% + \pgf@x=\pgf@xc% + }% + \anchor{south west}{% + \roundedrectanglepoints% + \ifx\westarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpointadd{\centerpoint}{\pgfpoint{-\halfwidth-\chordwidth+\arcwidth-\convexxshift}{+0pt}}% + \else% + \csname pgf@anchor@rounded rectangle@west\endcsname% + \fi% + \pgf@xc=\pgf@x% + \csname pgf@anchor@rounded rectangle@south\endcsname% + \pgf@x=\pgf@xc% + }% + \anchor{east}{% + \roundedrectanglepoints% + \pgfpointadd{\centerpoint}{% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@concave% + \pgfpoint{\halfwidth+\arcwidth+\concavexshift}{+0pt}% + \else% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpoint{\halfwidth+\chordwidth+\outerxsep}{+0pt}% + \else% + \pgfpoint{\halfwidth+\outerxsep}{+0pt}% + \fi% + \fi% + }% + }% + \anchor{north east}{% + \roundedrectanglepoints% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpointadd{\centerpoint}{\pgfpoint{\halfwidth+\chordwidth-\arcwidth+\convexxshift}{+0pt}}% + \else% + \csname pgf@anchor@rounded rectangle@east\endcsname% + \fi% + \pgf@xc=\pgf@x% + \csname pgf@anchor@rounded rectangle@north\endcsname% + \pgf@x=\pgf@xc% + }% + \anchor{south east}{% + \roundedrectanglepoints% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpointadd{\centerpoint}{\pgfpoint{\halfwidth+\chordwidth-\arcwidth+\convexxshift}{+0pt}}% + \else% + \csname pgf@anchor@rounded rectangle@east\endcsname% + \fi% + \pgf@xc=\pgf@x% + \csname pgf@anchor@rounded rectangle@south\endcsname% + \pgf@x=\pgf@xc% + }% + \backgroundpath{% + {% + \roundedrectanglepoints% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfpoint{0pt}{\halfheight}}% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@concave% + \pgfpathlineto{\pgfpoint{\halfwidth+\arcwidth}{+\halfheight}}% + \pgfpatharc{180-\halfarcangle}{180+\halfarcangle}{+\radius}% + \else% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpathlineto{\pgfpoint{\halfwidth+\chordwidth-\arcwidth}{+\halfheight}}% + \pgfpatharc{+\halfarcangle}{+-\halfarcangle}{+\radius}% + \else% + \pgfpathlineto{\pgfqpoint{\halfwidth}{\halfheight}}% + \pgfpathlineto{\pgfqpoint{\halfwidth}{-\halfheight}}% + \fi% + \fi% + \ifx\westarc\pgf@lib@sh@misc@rr@text@concave% + \pgfpathlineto{\pgfpoint{-\halfwidth-\arcwidth}{+-\halfheight}}% + \pgfpatharc{+-\halfarcangle}{+\halfarcangle}{+\radius}% + \else% + \ifx\westarc\pgf@lib@sh@misc@rr@text@convex% + \pgfpathlineto{\pgfpoint{-\halfwidth-\chordwidth+\arcwidth}{+-\halfheight}}% + \pgfpatharc{180+\halfarcangle}{180-\halfarcangle}{+\radius}% + \else% + \pgfpathlineto{\pgfqpoint{-\halfwidth}{-\halfheight}}% + \pgfpathlineto{\pgfqpoint{-\halfwidth}{\halfheight}}% + \fi% + \fi% + \pgfpathclose% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{% + \pgfextract@process\externalpoint{}% + \pgfpointadd{\centerpoint}{\externalpoint}% + }% + \roundedrectanglepoints% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle=\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@rounded rectangle@north west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@rounded rectangle@north east\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \pgfextract@process\arccenter{% + \pgfpointadd{\centerpoint}{\pgfpoint{\halfwidth+\chordwidth-\radius}{+0pt}}% + }% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {\arccenter}{0}{\halfarcangle}{\radius+\outerxsep and \radius+\outerysep}% + \else% + \pgfpointintersectionoflines% + {\csname pgf@anchor@rounded rectangle@north east\endcsname}% + {\csname pgf@anchor@rounded rectangle@south east\endcsname}% + {\externalpoint}{\centerpoint}% + \fi% + \else% + \pgfpointintersectionoflines% + {\csname pgf@anchor@rounded rectangle@north east\endcsname}% + {\csname pgf@anchor@rounded rectangle@north west\endcsname}% + {\externalpoint}{\centerpoint}% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@rounded rectangle@south west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \ifx\westarc\pgf@lib@sh@misc@rr@text@convex% + \pgfextract@process\arccenter{% + \pgfpointadd{\centerpoint}{\pgfpoint{-\halfwidth-\chordwidth+\radius}{+0pt}}% + }% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {\arccenter}{180-\halfarcangle}{180+\halfarcangle}{\radius+\outerxsep and \radius+\outerysep}% + \else% + \pgfpointintersectionoflines% + {\csname pgf@anchor@rounded rectangle@north west\endcsname}% + {\csname pgf@anchor@rounded rectangle@south west\endcsname}% + {\externalpoint}{\centerpoint}% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@rounded rectangle@south east\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines% + {\csname pgf@anchor@rounded rectangle@south east\endcsname}% + {\csname pgf@anchor@rounded rectangle@south west\endcsname}% + {\externalpoint}{\centerpoint}% + \else% + \ifx\eastarc\pgf@lib@sh@misc@rr@text@convex% + \pgfextract@process\arccenter{% + \pgfpointadd{\centerpoint}{\pgfpoint{\halfwidth+\chordwidth-\radius}{+0pt}}% + }% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {\arccenter}{360-\halfarcangle}{360}{\radius+\outerxsep and \radius+\outerysep}% + \else% + \pgfpointintersectionoflines% + {\csname pgf@anchor@rounded rectangle@north east\endcsname}% + {\csname pgf@anchor@rounded rectangle@south east\endcsname}% + {\externalpoint}{\centerpoint}% + \fi% + \fi% + \fi% + \fi% + }% +}% + + + + +\pgfkeys{/pgf/chamfered rectangle corners/.store in=\pgf@lib@sh@misc@cr@corners}% +\pgfkeys{/tikz/chamfered rectangle corners/.store in=\pgf@lib@sh@misc@cr@corners}% + +\def\pgf@lib@sh@misc@cr@chamferall{chamfer all}% +\def\pgf@lib@sh@misc@cr@chamfer{chamfer}% +\let\pgf@lib@sh@misc@cr@corners\pgf@lib@sh@misc@cr@chamferall + + +\def\pgf@lib@sh@misc@cr@getcorners{% + \let\northeastcorner\pgfutil@empty% + \let\southeastcorner\pgfutil@empty% + \let\southwestcorner\pgfutil@empty% + \let\northwestcorner\pgfutil@empty% + \expandafter\pgfutil@in@\expandafter{\pgf@lib@sh@misc@cr@corners}{chamfer all}% + \ifpgfutil@in@% + \let\northeastcorner\pgf@lib@sh@misc@cr@round% + \let\southeastcorner\pgf@lib@sh@misc@cr@round% + \let\southwestcorner\pgf@lib@sh@misc@cr@round% + \let\northwestcorner\pgf@lib@sh@misc@cr@round% + \let\pgf@next\relax% + \else% + \let\pgf@next\pgf@lib@sh@misc@cr@parsecorners% + \fi% + \pgf@next}% + +\def\pgf@lib@sh@misc@cr@parsecorners{% + \expandafter\pgf@@chamferedrectangle@parsecorners\pgf@lib@sh@misc@cr@corners,\pgf@stop,% +}% + +\def\pgf@@chamferedrectangle@parsecorners#1,{% + \ifx#1\pgf@stop% + \let\pgf@next\relax% + \else% + \pgfutil@in@{@#1@}{@north east@@top left@}% + \ifpgfutil@in@% + \let\northeastcorner\pgf@lib@sh@misc@cr@chamfer% + \else% + \pgfutil@in@{@#1@}{@south east@@bottom right@}% + \ifpgfutil@in@% + \let\southeastcorner\pgf@lib@sh@misc@cr@chamfer% + \else% + \pgfutil@in@{@#1@}{@south west@@bottom left@}% + \ifpgfutil@in@% + \let\southwestcorner\pgf@lib@sh@misc@cr@chamfer% + \else% + \pgfutil@in@{@#1@}{@north west@@top right@}% + \ifpgfutil@in@% + \let\northwestcorner\pgf@lib@sh@misc@cr@round% + \fi% + \fi% + \fi% + \fi% + \let\pgf@next\pgf@@@chamferedrectangle@parsecorners% + \fi% + \pgf@next% +}% +\def\pgf@@@chamferedrectangle@parsecorners{% + \pgfutil@ifnextchar x{\pgf@@chamferedrectangle@parsecorners}{\pgf@@chamferedrectangle@parsecorners}% +}% + +\pgfkeys{/pgf/.cd, + chamfered rectangle angle/.initial=45,% + chamfered rectangle xsep/.initial=.666ex,% + chamfered rectangle ysep/.initial=.666ex% +}% + \pgfkeys{/pgf/chamfered rectangle sep/.style={% + /pgf/chamfered rectangle xsep={#1},/pgf/chamfered rectangle ysep={#1}}% +}% + + + + +\pgfdeclareshape{chamfered rectangle}{% + \savedmacro\getchamferedrectanglepoints{% + \pgf@lib@sh@misc@cr@getcorners% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya.5\ht\pgfnodeparttextbox% + \advance\pgf@ya.5\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/chamfered rectangle angle}}% + \ifdim\pgfutil@tempdima<89pt\relax% + \ifdim\pgfutil@tempdima<1pt\relax% + \pgfutil@tempdima1pt\relax% + \fi% + \else% + \pgfutil@tempdima89pt\relax% + \fi% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima90pt\relax% + \pgfmathtan@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \let\tanangle\pgfmathresult% + \pgfmathcot@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \let\cotangle\pgfmathresult% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/chamfered rectangle xsep}}% + \pgf@yc\tanangle\pgf@xb% + \ifdim\pgf@yc>\pgf@ya% + \pgf@yc\pgf@ya% + \pgf@xb\cotangle\pgf@yc% + \fi% + \pgfmathcot@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/chamfered rectangle ysep}}% + \pgf@xc\cotangle\pgf@yb% + \ifdim\pgf@xc>\pgf@xa% + \pgf@xc\pgf@xa% + \pgf@yb\tanangle\pgf@xc% + \fi% + \pgfutil@tempdima\pgf@xa% + \advance\pgfutil@tempdima\pgf@xb% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgfutil@tempdima<.5\pgfutil@tempdimb% + \pgf@xa.5\pgfutil@tempdimb% + \advance\pgf@xa-\pgf@xb% + \fi% + \pgfutil@tempdima\pgf@ya% + \advance\pgfutil@tempdima\pgf@yb% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgfutil@tempdima<.5\pgfutil@tempdimb% + \pgf@ya.5\pgfutil@tempdimb% + \advance\pgf@ya-\pgf@yb% + \fi% + \pgfextract@process\centerpoint{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+.5\ht\pgfnodeparttextbox}% + \pgfmathaddtolength\pgf@y{+-.5\dp\pgfnodeparttextbox}% + }% + \pgfextract@process\beforenortheast{% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@ya% + \advance\pgf@y-\pgf@yc% + }% + \pgfextract@process\northeast{% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + \ifx\northeastcorner\pgfutil@empty% + \advance\pgf@x\pgf@xb% + \advance\pgf@y\pgf@yb% + \fi% + }% + \pgfextract@process\afternortheast{% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@x-\pgf@xc% + \advance\pgf@y\pgf@ya% + \advance\pgf@y\pgf@yb% + }% + \pgfextract@process\northwest{% + \centerpoint% + \advance\pgf@x-\pgf@xa% + \advance\pgf@y\pgf@ya% + \ifx\northwestcorner\pgfutil@empty% + \advance\pgf@x-\pgf@xb% + \advance\pgf@y\pgf@yb% + \fi% + }% + \pgfextract@process\beforesouthwest{% + \centerpoint% + \advance\pgf@x-\pgf@xa% + \advance\pgf@x-\pgf@xb% + \advance\pgf@y-\pgf@ya% + \advance\pgf@y\pgf@yc% + }% + \pgfextract@process\southwest{% + \centerpoint% + \advance\pgf@x-\pgf@xa% + \advance\pgf@y-\pgf@ya% + \ifx\southwestcorner\pgfutil@empty% + \advance\pgf@x-\pgf@xb% + \advance\pgf@y-\pgf@yb% + \fi% + }% + \pgfextract@process\aftersouthwest{% + \centerpoint% + \advance\pgf@x-\pgf@xa% + \advance\pgf@x\pgf@xc% + \advance\pgf@y-\pgf@ya% + \advance\pgf@y-\pgf@yb% + }% + \pgfextract@process\southeast{% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y-\pgf@ya% + \ifx\southeastcorner\pgfutil@empty% + \advance\pgf@x\pgf@xb% + \advance\pgf@y-\pgf@yb% + \fi% + }% + \pgfmathanglebetweenlines{\beforenortheast}{\afternortheast}{\beforenortheast}% + {\beforesouthwest\pgf@ya\pgf@y\beforenortheast\pgf@y\pgf@ya}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \ifdim\pgfutil@tempdima>180pt\relax% + \advance\pgfutil@tempdima-180pt\relax% + \fi% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/outer xsep}}% + \ifdim\pgfutil@tempdima<90pt\relax% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfutil@tempdimb\pgfmathresult\pgfutil@tempdimb% + \pgfutil@tempdima0pt\relax% + \else% + \pgfutil@tempdima.5\pgfutil@tempdima% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfutil@tempdimb\pgfmathresult\pgfutil@tempdimb% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima90pt\relax% + \fi% + \pgfextract@process\before@ne@anchor{% + \beforenortheast% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima180pt\relax% + \pgfextract@process\before@sw@anchor{% + \beforesouthwest% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfqpointpolar{-\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenlines{\afternortheast}{\aftersouthwest\pgf@xa\pgf@x\afternortheast\pgf@x\pgf@xa}% + {\afternortheast}{\beforenortheast}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \ifdim\pgfutil@tempdima>270pt\relax% + \advance\pgfutil@tempdima-270pt\relax% + \fi% + \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgfutil@tempdima<90pt\relax% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfutil@tempdimb\pgfmathresult\pgfutil@tempdimb% + \pgfutil@tempdima90pt\relax% + \else% + \pgfutil@tempdima.5\pgfutil@tempdima% + \pgfmathcosec@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfutil@tempdimb\pgfmathresult\pgfutil@tempdimb% + \fi% + \pgfextract@process\after@ne@anchor{% + \afternortheast% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfqpointpolar{\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfutil@tempdima-\pgfutil@tempdima% + \advance\pgfutil@tempdima180pt\relax% + \pgfextract@process\after@sw@anchor{% + \aftersouthwest + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfqpointpolar{-\pgfmath@tonumber{\pgfutil@tempdima}}{\the\pgfutil@tempdimb}% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \addtosavedmacro\before@ne@anchor% + \addtosavedmacro\after@ne@anchor% + \addtosavedmacro\before@sw@anchor% + \addtosavedmacro\after@sw@anchor% + \pgfextract@process\ne@anchor{% + \ifx\northeastcorner\pgfutil@empty% + \northeast% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \else% + \pgfpointlineattime{0.5}{\before@ne@anchor}{\after@ne@anchor}% + \fi% + }% + \pgfextract@process\nw@anchor{% + \ifx\northwestcorner\pgfutil@empty% + \northwest% + \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \else% + \pgfpointlineattime{0.5}{% + \before@ne@anchor% + \pgf@ya\pgf@y + \before@sw@anchor% + \pgf@y\pgf@ya% + }{% + \after@ne@anchor% + \pgf@ya\pgf@y + \after@sw@anchor% + \pgf@y\pgf@ya% + }% + \fi% + }% + \pgfextract@process\sw@anchor{% + \ifx\southwestcorner\pgfutil@empty% + \southwest% + \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}% + \else% + \pgfpointlineattime{0.5}{\before@sw@anchor}{\after@sw@anchor}% + \fi% + }% + \pgfextract@process\se@anchor{% + \ifx\southeastcorner\pgfutil@empty% + \southeast% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}% + \else% + \pgfpointlineattime{0.5}{% + \before@ne@anchor% + \pgf@xa\pgf@x + \before@sw@anchor% + \pgf@x\pgf@xa% + }{% + \after@ne@anchor% + \pgf@xa\pgf@x + \after@sw@anchor% + \pgf@x\pgf@xa% + }% + \fi% + }% + \addtosavedmacro\ne@anchor% + \addtosavedmacro\nw@anchor% + \addtosavedmacro\sw@anchor% + \addtosavedmacro\se@anchor% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \getchamferedrectanglepoints% + \midpoint% + \pgf@ya\pgf@y% + \pgf@process{% + \before@sw@anchor% + \pgf@ya\pgf@y% + \before@ne@anchor% + \pgf@y\pgf@ya% + }% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\after@sw@anchor\pgf@ya\pgf@y\after@ne@anchor\pgf@y\pgf@ya}% + \else% + \pgf@process{\before@ne@anchor}% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor}% + \else% + \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor}% + {\after@ne@anchor}% + \fi% + \fi% + }% + \anchor{mid west}{% + \getchamferedrectanglepoints% + \midpoint% + \pgf@ya\pgf@y% + \pgf@process{\before@sw@anchor}% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor}{\after@sw@anchor}% + \else% + \pgf@process{\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor}% + \else% + \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\after@ne@anchor\pgf@ya\pgf@y\after@sw@anchor\pgf@y\pgf@ya}% + \fi% + \fi% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \getchamferedrectanglepoints% + \basepoint% + \pgf@ya\pgf@y% + \pgf@process{% + \before@sw@anchor% + \pgf@ya\pgf@y% + \before@ne@anchor% + \pgf@y\pgf@ya% + }% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\after@sw@anchor\pgf@ya\pgf@y\after@ne@anchor\pgf@y\pgf@ya}% + \else% + \pgf@process{\before@ne@anchor}% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor}% + \else% + \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor}% + {\after@ne@anchor}% + \fi% + \fi% + }% + \anchor{base west}{% + \getchamferedrectanglepoints% + \basepoint% + \pgf@ya\pgf@y% + \pgf@process{\before@sw@anchor}% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor}{\after@sw@anchor}% + \else% + \pgf@process{\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + \ifdim\pgf@ya<\pgf@y% + \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@sw@anchor}% + \else% + \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + {\after@ne@anchor\pgf@ya\pgf@y\after@sw@anchor\pgf@y\pgf@ya}% + \fi% + \fi% + }% + \anchor{before north east}{\getchamferedrectanglepoints\before@ne@anchor}% + \anchor{north east}{\getchamferedrectanglepoints\ne@anchor}% + \anchor{after north east}{\getchamferedrectanglepoints\after@ne@anchor}% + \anchor{north}{% + \getchamferedrectanglepoints% + \centerpoint% + \pgf@xa\pgf@x% + \after@ne@anchor% + \pgf@x\pgf@xa}% + \anchor{before north west}{% + \getchamferedrectanglepoints% + \after@sw@anchor% + \pgf@xa\pgf@x% + \after@ne@anchor% + \pgf@x\pgf@xa}% + \anchor{north west}{\getchamferedrectanglepoints\nw@anchor}% + \anchor{after north west}{% + \getchamferedrectanglepoints% + \before@sw@anchor% + \pgf@xa\pgf@x% + \before@ne@anchor% + \pgf@x\pgf@xa}% + \anchor{west}{% + \getchamferedrectanglepoints% + \centerpoint% + \pgf@ya\pgf@y% + \before@sw@anchor% + \pgf@y\pgf@ya}% + \anchor{before south west}{\getchamferedrectanglepoints\before@sw@anchor}% + \anchor{south west}{\getchamferedrectanglepoints\sw@anchor}% + \anchor{after south west}{\getchamferedrectanglepoints\after@sw@anchor}% + \anchor{south}{% + \getchamferedrectanglepoints% + \centerpoint% + \pgf@xa\pgf@x% + \after@sw@anchor% + \pgf@x\pgf@xa}% + \anchor{before south east}{% + \getchamferedrectanglepoints% + \after@sw@anchor% + \pgf@ya\pgf@y% + \after@ne@anchor% + \pgf@y\pgf@ya}% + \anchor{south east}{\getchamferedrectanglepoints\se@anchor}% + \anchor{after south east}{% + \getchamferedrectanglepoints% + \before@sw@anchor% + \pgf@ya\pgf@y% + \before@ne@anchor% + \pgf@y\pgf@ya}% + \anchor{east}{% + \getchamferedrectanglepoints% + \centerpoint% + \pgf@ya\pgf@y% + \before@ne@anchor% + \pgf@y\pgf@ya}% + \backgroundpath{% + \pgfpathmoveto{\beforenortheast}% + \pgfpathlineto{\northeast}% + \pgfpathlineto{\afternortheast}% + \pgfpathlineto{\aftersouthwest\pgf@xa\pgf@x\afternortheast\pgf@x\pgf@xa}% + \pgfpathlineto{\northwest}% + \pgfpathlineto{\beforesouthwest\pgf@xa\pgf@x\beforenortheast\pgf@x\pgf@xa}% + \pgfpathlineto{\beforesouthwest}% + \pgfpathlineto{\southwest}% + \pgfpathlineto{\aftersouthwest}% + \pgfpathlineto{\aftersouthwest\pgf@ya\pgf@y\afternortheast\pgf@y\pgf@ya}% + \pgfpathlineto{\southeast}% + \pgfpathlineto{\beforesouthwest\pgf@ya\pgf@y\beforenortheast\pgf@y\pgf@ya}% + \pgfpathclose% + }% + \anchorborder{% + \pgfextract@process\externalpoint{% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \getchamferedrectanglepoints% + \pgfmathanglebetweenpoints{\centerpoint}{\centerpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\centerpoint\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\ne@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\before@ne@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\centerpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}{\before@ne@anchor}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\before@ne@anchor}{\ne@anchor}% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\after@ne@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\ne@anchor}{\after@ne@anchor}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\after@ne@anchor}{\centerpoint\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\nw@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\centerpoint\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}% + {\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}% + {\nw@anchor}% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\nw@anchor}{\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}% + {\before@sw@anchor\pgf@xa\pgf@x\centerpoint\pgf@x\pgf@xa}% + \fi% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\centerpoint\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\sw@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\before@sw@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\before@sw@anchor\pgf@xa\pgf@x\centerpoint\pgf@x\pgf@xa}% + {\before@sw@anchor}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\before@sw@anchor}{\sw@anchor}% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\after@sw@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\sw@anchor}{\after@sw@anchor}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\after@sw@anchor}{\centerpoint\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\se@anchor}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}% + {\centerpoint\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}{\se@anchor} + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\se@anchor}{\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}% + \else% + \pgfpointintersectionoflines{\centerpoint}{\externalpoint}% + {\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}% + {\centerpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}% + \fi% + \fi% + \fi% + \fi% + }% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..43d3246a34dbcc5aa6107fa84dfa1b4f8d8c150c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.multipart.code.tex @@ -0,0 +1,1206 @@ + +\ProvidesFileRCS{pgflibraryshapes.multipart.code.tex} + +\newbox\pgfnodepartlowerbox + + +\pgfdeclareshape{circle split} +{% + \nodeparts{text,lower}% + + \savedanchor\centerpoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgfmathsetlength{\pgf@y}{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgf@y=-\pgf@y% + \advance\pgf@y by-\dp\pgfnodeparttextbox% + \advance\pgf@y by-.5\pgflinewidth% + }% + \savedanchor\loweranchor{% + \pgf@x=-.5\wd\pgfnodepartlowerbox% + \advance\pgf@x by.5\wd\pgfnodeparttextbox% + \pgfmathsetlength{\pgf@y}{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgf@y=-2\pgf@y% + \advance\pgf@y by-\ht\pgfnodepartlowerbox% + \advance\pgf@y by-.5\pgflinewidth% + \advance\pgf@y by-\dp\pgfnodeparttextbox% + \advance\pgf@y by-.5\pgflinewidth% + }% + + \saveddimen\radius{% + \pgf@ya=.5\ht\pgfnodeparttextbox% + \advance\pgf@ya by.5\dp\pgfnodeparttextbox% + \pgf@yb=.5\ht\pgfnodepartlowerbox% + \advance\pgf@yb by.5\dp\pgfnodepartlowerbox% + \ifdim\pgf@ya>\pgf@yb\relax% + \pgf@ya2.0\pgf@ya\relax% + \else% + \pgf@ya2.0\pgf@yb\relax% + \fi% + \advance\pgf@ya by.5\pgflinewidth% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya by2\pgf@yb% + \pgf@xa=.5\wd\pgfnodeparttextbox% + \ifdim\pgf@xa<.5\wd\pgfnodepartlowerbox% + \pgf@xa=.5\wd\pgfnodepartlowerbox% + \fi% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa by\pgf@xb% + \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgf@xa}{\pgf@ya}}}% + \ifdim\pgf@x>\pgf@y% + \c@pgf@counta=\pgf@x% + \ifnum\c@pgf@counta=0\relax% + \else% + \divide\c@pgf@counta by 255\relax% + \pgf@xa=16\pgf@xa\relax% + \divide\pgf@xa by\c@pgf@counta% + \pgf@xa=16\pgf@xa\relax% + \fi% + \else% + \c@pgf@counta=\pgf@y% + \ifnum\c@pgf@counta=0\relax% + \else% + \divide\c@pgf@counta by 255\relax% + \pgf@ya=16\pgf@ya\relax% + \divide\pgf@ya by\c@pgf@counta% + \pgf@xa=16\pgf@ya\relax% + \fi% + \fi% + \pgf@x=\pgf@xa% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<.5\pgf@xb% + \pgf@x=.5\pgf@xb% + \fi% + \ifdim\pgf@x<.5\pgf@yb% + \pgf@x=.5\pgf@yb% + \fi% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgf@x by\pgf@yb% + \else% + \advance\pgf@x by\pgf@xb% + \fi% + }% + + \inheritanchorborder[from=circle]% + \inheritanchor[from=circle]{north}% + \inheritanchor[from=circle]{north west}% + \inheritanchor[from=circle]{north east}% + \inheritanchor[from=circle]{center}% + \inheritanchor[from=circle]{west}% + \inheritanchor[from=circle]{east}% + \inheritanchor[from=circle]{mid}% + \inheritanchor[from=circle]{mid west}% + \inheritanchor[from=circle]{mid east}% + \inheritanchor[from=circle]{base}% + \inheritanchor[from=circle]{base west}% + \inheritanchor[from=circle]{base east}% + \inheritanchor[from=circle]{south}% + \inheritanchor[from=circle]{south west}% + \inheritanchor[from=circle]{south east}% + \anchor{lower}{\loweranchor}% + + \inheritbackgroundpath[from=circle]% + \beforebackgroundpath{ + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgfutil@tempdima by-\pgf@yb% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \advance\pgfutil@tempdima by-.5\pgflinewidth% + \pgfsetshortenstart{0pt}% + \pgfsetshortenend{0pt}% + \pgfsetarrows{-}% + \pgfpathmoveto{\pgfpointadd{\centerpoint}{\pgfqpoint{-1\pgfutil@tempdima}{0pt}}}% + \pgfpathlineto{\pgfpointadd{\centerpoint}{\pgfqpoint{\pgfutil@tempdima}{0pt}}}% + \pgfusepath{stroke}% + }% +}% + + + +\pgfdeclareshape{circle solidus}{% + \nodeparts{text,lower}% + \savedanchor\centerpoint{% + \pgf@x=0.5\wd\pgfnodeparttextbox% + \advance\pgf@x by0.5\dp\pgfnodeparttextbox% + \advance\pgf@x by0.5\ht\pgfnodeparttextbox% + \pgf@y=-\pgf@x% + \advance\pgf@y by\ht\pgfnodeparttextbox% + \advance\pgf@x by0.3536\pgflinewidth% + \advance\pgf@y by-0.3536\pgflinewidth% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x by\pgf@xa% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y by-\pgf@ya% + }% + \savedanchor\loweranchor{% + \pgf@x=0.5\wd\pgfnodeparttextbox% + \advance\pgf@x by0.5\dp\pgfnodeparttextbox% + \advance\pgf@x by0.5\ht\pgfnodeparttextbox% + \pgf@y=-\pgf@x% + \advance\pgf@y by\ht\pgfnodeparttextbox% + \advance\pgf@x by0.5\ht\pgfnodepartlowerbox% + \advance\pgf@x by0.5\dp\pgfnodepartlowerbox% + \advance\pgf@x by-0.5\wd\pgfnodepartlowerbox% + \advance\pgf@y by-0.5\ht\pgfnodepartlowerbox% + \advance\pgf@y by0.5\dp\pgfnodepartlowerbox% + \advance\pgf@y by-0.5\wd\pgfnodepartlowerbox% + \advance\pgf@x by0.7071\pgflinewidth% + \advance\pgf@y by-0.7071\pgflinewidth% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x by2\pgf@xa% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y by-2\pgf@ya% + }% + \saveddimen\radius{% + \pgf@x=\ht\pgfnodeparttextbox% + \advance\pgf@x by\dp\pgfnodeparttextbox% + \advance\pgf@x by\wd\pgfnodeparttextbox% + \pgf@y=\ht\pgfnodepartlowerbox% + \advance\pgf@y by\dp\pgfnodepartlowerbox% + \advance\pgf@y by\wd\pgfnodepartlowerbox% + \ifdim\pgf@x<\pgf@y% + \pgf@x=\pgf@y% + \fi% + \pgf@x=0.7071\pgf@x% + \advance\pgf@x by0.5\pgflinewidth% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/inner xsep}}% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgfmathaddtolength{\pgf@x}{veclen(2\pgf@xa,2\pgf@ya)}% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x=.5\pgf@xa% + \fi% + \ifdim\pgf@x<.5\pgf@ya% + \pgf@x=.5\pgf@ya% + \fi% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xa<\pgf@ya% + \advance\pgf@x by\pgf@ya% + \else% + \advance\pgf@x by\pgf@xa% + \fi% + }% + \inheritanchorborder[from=circle]% + \inheritanchor[from=circle]{north}% + \inheritanchor[from=circle]{north west}% + \inheritanchor[from=circle]{north east}% + \inheritanchor[from=circle]{center}% + \inheritanchor[from=circle]{west}% + \inheritanchor[from=circle]{east}% + \inheritanchor[from=circle]{mid}% + \inheritanchor[from=circle]{mid west}% + \inheritanchor[from=circle]{mid east}% + \inheritanchor[from=circle]{base}% + \inheritanchor[from=circle]{base west}% + \inheritanchor[from=circle]{base east}% + \inheritanchor[from=circle]{south}% + \inheritanchor[from=circle]{south west}% + \inheritanchor[from=circle]{south east}% + \anchor{lower}{\loweranchor}% + \inheritbackgroundpath[from=circle]% + \beforebackgroundpath{% + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xa}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@ya}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xa<\pgf@ya% + \advance\pgfutil@tempdima by-\pgf@ya% + \else% + \advance\pgfutil@tempdima by-\pgf@xa% + \fi% + \advance\pgfutil@tempdima by-.5\pgflinewidth% + \pgfsetshortenstart{0pt}% + \pgfsetshortenend{0pt}% + \pgfsetarrows{-}% + \pgfpathmoveto{\pgfpointadd{\centerpoint}{\pgfqpoint{-0.437\pgfutil@tempdima}{-0.437\pgfutil@tempdima}}}% + \pgfpathlineto{\pgfpointadd{\centerpoint}{\pgfqpoint{0.437\pgfutil@tempdima}{0.437\pgfutil@tempdima}}}% + \pgfusepath{stroke}% + }% +}% + + +\def\pgf@lib@sh@newbox{\csname newbox\endcsname}% + +\def\pgf@lib@sh@toalpha#1{% + \ifcase#1\relax% + \or one\or two\or three\or four\or five\or six\or seven\or eight\or nine\or ten% + \or eleven\or twelve\or thirteen\or fourteen\or fifteen% + \or sixteen\or seventeen\or eighteen\or nineteen\or twenty% + \else% + twenty% + \fi% +}% + + +\def\pgf@lib@sh@getalpha#1#2{\expandafter\edef\expandafter#1\expandafter{\pgf@lib@sh@toalpha{#2}}}% + +\newbox\pgfnodeparttwobox +\newbox\pgfnodepartthreebox +\newbox\pgfnodepartfourbox + +\let\pgfnodepartonebox=\pgfnodeparttextbox +\let\pgfnodepartsecondbox=\pgfnodeparttwobox +\let\pgfnodepartthirdbox=\pgfnodepartthreebox +\let\pgfnodepartfourthbox=\pgfnodepartfourbox + +\def\pgf@lib@sh@allocateboxes#1{% + \c@pgf@counta=#1\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>4\relax% + \pgfutil@ifundefined{pgfnodepart\pgf@lib@sh@toalpha{\c@pgf@counta}box}% + {% + \expandafter\pgf@lib@sh@newbox\csname pgfnodepart\pgf@lib@sh@toalpha{\c@pgf@counta}box\endcsname% + }% + {}% + \advance\c@pgf@counta by-1\relax% + \repeatpgfmathloop% +}% + +\def\pgf@lib@sh@rs@lefttext{left}% +\def\pgf@lib@sh@rs@righttext{right}% +\def\pgf@lib@sh@rs@centertext{center}% +\def\pgf@lib@sh@rs@bottomtext{bottom}% +\def\pgf@lib@sh@rs@toptext{top}% +\def\pgf@lib@sh@rs@basetext{base}% +\def\pgf@lib@sh@rs@nonetext{none}% + + +\newif\ifpgfrectanglesplithorizontal +\newif\ifpgfrectanglesplitdrawsplits\pgfrectanglesplitdrawsplitstrue +\newif\ifpgfrectanglesplitignoreemptyparts +\newif\ifpgfrectanglesplitusecustomfill + +\let\pgf@lib@sh@rs@every@emptypart=\pgfutil@empty +\let\pgf@lib@sh@rs@every@part=\pgfutil@empty +\def\pgf@lib@sh@rs@list@fill{none}% + +\pgfkeys{/pgf/.cd, + rectangle split parts/.initial=4, + rectangle split part align/.initial=center, + rectangle split horizontal/.is if=pgfrectanglesplithorizontal, + rectangle split ignore empty parts/.is if=pgfrectanglesplitignoreemptyparts, + rectangle split empty part width/.code={% + \pgfmathsetlength\pgf@x{#1} + \edef\pgf@lib@sh@rs@temp{\noexpand\vrule width\the\pgf@x height0ptdepth0pt\relax}% + \def\pgf@lib@sh@rs@@temp{\def\pgf@lib@sh@rs@every@emptypart}% + \expandafter\expandafter\expandafter\pgf@lib@sh@rs@@temp\expandafter\expandafter\expandafter{% + \expandafter\pgf@lib@sh@rs@every@emptypart\pgf@lib@sh@rs@temp}% + },% + rectangle split empty part width=1ex, + rectangle split empty part height/.code={% + \pgfmathsetlength\pgf@x{#1} + \edef\pgf@lib@sh@rs@temp{\noexpand\vrule width0ptheight\the\pgf@x depth0pt\relax}% + \def\pgf@lib@sh@rs@@temp{\def\pgf@lib@sh@rs@every@emptypart}% + \expandafter\expandafter\expandafter\pgf@lib@sh@rs@@temp\expandafter\expandafter\expandafter{% + \expandafter\pgf@lib@sh@rs@every@emptypart\pgf@lib@sh@rs@temp}% + },% + rectangle split empty part height=1ex, + rectangle split empty part depth/.code={% + \pgfmathsetlength\pgf@x{#1} + \edef\pgf@lib@sh@rs@temp{\noexpand\vrule width0ptheight0ptdepth\the\pgf@x\relax}% + \def\pgf@lib@sh@rs@@temp{\def\pgf@lib@sh@rs@every@emptypart}% + \expandafter\expandafter\expandafter\pgf@lib@sh@rs@@temp\expandafter\expandafter\expandafter{% + \expandafter\pgf@lib@sh@rs@every@emptypart\pgf@lib@sh@rs@temp}% + },% + rectangle split empty part depth=0ex, + rectangle split every empty part/.store in=\pgf@lib@sh@rs@every@emptypart, + rectangle split part fill/.code=\def\pgf@lib@sh@rs@list@fill{#1}\pgfrectanglesplitusecustomfilltrue, + rectangle split uses custom fill/.is if=pgfrectanglesplitusecustomfill, + rectangle split draw splits/.is if=pgfrectanglesplitdrawsplits, + rectangle split allocate boxes/.code=\pgf@lib@sh@allocateboxes{#1}, +}% + + +\def\pgf@lib@sh@rs@process@list#1#2{% + \c@pgf@counta=1\relax% + \c@pgf@countb=#2\relax% + \edef\pgf@lib@sh@rs@temp{#1}% + \expandafter\pgf@lib@sh@rs@@process@list\pgf@lib@sh@rs@temp,\pgf@stop, +}% + +\def\pgf@lib@sh@rs@@process@list{% + \pgfutil@ifnextchar x{\pgf@lib@sh@rs@@@process@list}% + {\pgf@lib@sh@rs@@@process@list} +}% + +\def\pgf@lib@sh@rs@@@process@list#1,{% + \ifx#1\pgf@stop% + \let\pgf@next\pgf@lib@sh@rs@@@@process@list% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\c@pgf@counta}% + \def\pgf@lib@sh@rs@lastalign{#1}% + \pgfutil@namedef{pgf@lib@sh@rs@\pgf@lib@sh@toalpha{\c@pgf@counta}@item}{#1}% + \let\pgf@next\pgf@lib@sh@rs@@process@list% + \advance\c@pgf@counta by1\relax% + \fi% + \pgf@next}% + +\def\pgf@lib@sh@rs@@@@process@list{% + \pgfmathloop% + \ifnum\c@pgf@counta>\c@pgf@countb% + \else% + \expandafter\edef\csname pgf@lib@sh@rs@\pgf@lib@sh@toalpha{\c@pgf@counta}@item\endcsname% + {\pgf@lib@sh@rs@lastalign}% + \advance\c@pgf@counta by1\relax% + \repeatpgfmathloop% +}% + +\pgf@lib@sh@allocateboxes{20}% + +\pgfdeclareshape{rectangle split}{% + \savedmacro\rectanglesplitparameters{% + \pgfmathsetcount\c@pgf@counta{\pgfkeysvalueof{/pgf/rectangle split parts}}% + \edef\parts{\the\c@pgf@counta}% + \addtosavedmacro\parts% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \edef\innerxsep{\the\pgf@x}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \edef\innerysep{\the\pgf@y}% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \edef\outerxsep{\the\pgf@x}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \edef\outerysep{\the\pgf@y}% + \addtosavedmacro\outerxsep% + \addtosavedmacro\outerysep% + \pgf@x=0pt\relax% + \pgf@y=0pt\relax% + \pgfutil@tempdima=0pt\relax% + \pgfutil@tempdimb=0pt\relax% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \expandafter\let\expandafter\pgf@lib@sh@box\expandafter=% + \csname pgfnodepart\pgf@lib@sh@rs@number box\endcsname% + \pgf@xa=\wd\pgf@lib@sh@box% + \pgf@ya=\ht\pgf@lib@sh@box% + \pgf@yb=\dp\pgf@lib@sh@box% + \expandafter\def\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname{\relax}% + \ifdim\pgf@xa=0pt\relax% + \ifdim\pgf@ya=0pt\relax% + \ifdim\pgf@yb=0pt\relax% + \ifpgfrectanglesplitignoreemptyparts% + \expandafter\let\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname=\pgfutil@empty% + \else% + \setbox\pgf@lib@sh@box=\hbox{{\pgf@lib@sh@rs@every@emptypart}}% + \pgf@xa=\wd\pgf@lib@sh@box% + \pgf@ya=\ht\pgf@lib@sh@box% + \pgf@yb=\dp\pgf@lib@sh@box% + \fi% + \fi% + \fi% + \fi% + \expandafter\edef\csname pgf@lib@sh@rs@width@\pgf@lib@sh@rs@number\endcsname{\the\pgf@xa}% + \expandafter\edef\csname pgf@lib@sh@rs@height@\pgf@lib@sh@rs@number\endcsname{\the\pgf@ya}% + \expandafter\edef\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@number\endcsname{\the\pgf@yb}% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname% + \ifdim\pgf@xa>\pgf@x% + \pgf@x=\pgf@xa% + \fi% + \ifdim\pgf@ya>\pgfutil@tempdima% + \pgfutil@tempdima=\pgf@ya% + \fi% + \ifdim\pgf@yb>\pgfutil@tempdimb% + \pgfutil@tempdimb=\pgf@yb% + \fi% + \pgf@yc=\pgfutil@tempdima% + \advance\pgf@yc by\pgfutil@tempdimb% + \ifdim\pgf@yc>\pgf@y% + \pgf@y=\pgf@yc% + \fi% + \repeatpgfmathloop% + \edef\pgf@lib@sh@rs@max@width{\the\pgf@x}% + \edef\pgf@lib@sh@rs@max@totalheight{\the\pgf@y}% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/minimum width}}% + \advance\pgf@x by-\innerxsep\relax% + \advance\pgf@x by-\innerxsep\relax% + \pgf@xa=\pgf@x% + \advance\pgf@xa by-\pgf@lib@sh@rs@max@width\relax% + \ifdim\pgf@xa>0pt\relax% + \edef\pgf@lib@sh@rs@max@width{\the\pgf@x}% + \fi% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum height}}% + \advance\pgf@y by-\innerysep\relax% + \advance\pgf@y by-\innerysep\relax% + \pgf@ya=\pgf@y% + \advance\pgf@ya by-\pgf@lib@sh@rs@max@totalheight\relax% + \ifdim\pgf@ya>0pt\relax% + \edef\pgf@lib@sh@rs@max@totalheight{\the\pgf@y}% + \fi% + \pgf@lib@sh@rs@process@list{\pgfkeysvalueof{/pgf/rectangle split part align}}{\parts}% + \ifpgfrectanglesplithorizontal% + \pgf@x=0pt\relax% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \expandafter\let\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname=\pgfutil@empty% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \ifpgfrectanglesplitignoreemptyparts% + \expandafter\let\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname=% + \pgf@lib@sh@rs@lastanchor% + \fi% + \fi% + \expandafter\ifx\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname% + \pgf@lib@sh@rs@bottomtext% + \pgf@y=\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@number\endcsname\relax% + \else% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname% + \pgf@lib@sh@rs@toptext% + \pgf@y=-\csname pgf@lib@sh@rs@height@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@y by\pgf@lib@sh@rs@max@totalheight\relax% + \else% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname% + \pgf@lib@sh@rs@basetext% + \pgf@y=\pgf@lib@sh@rs@max@totalheight\relax% + \advance\pgf@y by-\pgfutil@tempdima% + \advance\pgf@y by\pgfutil@tempdimb% + \divide\pgf@y by2\relax% + \else% + \pgf@y=\pgf@lib@sh@rs@max@totalheight\relax% + \advance\pgf@y by-\csname pgf@lib@sh@rs@height@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@y by\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@number\endcsname\relax% + \divide\pgf@y by2\relax% + \fi% + \fi% + \fi% + \ifnum\pgfmathcounter=1\relax% + \edef\pgf@lib@sh@rs@yoffset{\the\pgf@y}% + \pgf@y=0pt\relax% + \pgfextract@process\pgf@lib@sh@rs@anchor@one{}% + \addtosavedmacro\pgf@lib@sh@rs@anchor@one% + \let\pgf@lib@sh@rs@lastanchor=\pgf@lib@sh@rs@anchor@one% + \let\pgf@lib@sh@rs@lastnumber=\pgf@lib@sh@rs@number% + \else + \advance\pgf@y by-\pgf@lib@sh@rs@yoffset\relax% + \advance\pgf@x by\csname pgf@lib@sh@rs@width@\pgf@lib@sh@rs@lastnumber\endcsname\relax% + \advance\pgf@x by\innerxsep\relax% + \advance\pgf@x by\pgflinewidth% + \advance\pgf@x by\innerxsep\relax% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname{}% + \expandafter\let\expandafter\pgf@lib@sh@rs@lastanchor\expandafter=% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \let\pgf@lib@sh@rs@lastnumber=\pgf@lib@sh@rs@number% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \fi% + \fi% + \repeatpgfmathloop% + \pgfextract@process\northeast{% + \pgf@lib@sh@rs@lastanchor% + \advance\pgf@x by\csname pgf@lib@sh@rs@width@\pgf@lib@sh@rs@lastnumber\endcsname\relax% + \advance\pgf@x by\innerxsep\relax% + \advance\pgf@x by\outerxsep\relax% + \pgf@y=\pgf@lib@sh@rs@max@totalheight\relax% + \advance\pgf@y by-\pgf@lib@sh@rs@yoffset\relax% + \advance\pgf@y by\innerysep\relax% + \advance\pgf@y by\outerysep\relax% + }% + \addtosavedmacro\northeast% + \pgfextract@process\southwest{% + \pgf@lib@sh@rs@anchor@one% + \advance\pgf@x by-\innerxsep\relax% + \advance\pgf@x by-\outerxsep\relax% + \pgf@y=-\pgf@lib@sh@rs@yoffset\relax% + \advance\pgf@y by-\innerysep\relax% + \advance\pgf@y by-\outerysep\relax% + }% + \addtosavedmacro\southwest% + \pgfextract@process\centerpoint{% + \pgfpointadd{\southwest}{\northeast}% + \divide\pgf@x by2\relax% + \divide\pgf@y by2\relax% + }% + \addtosavedmacro\centerpoint% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \else% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \pgf@xa=\pgf@x% + \pgf@xb=\csname pgf@lib@sh@rs@width@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@xa by0.5\pgf@xb% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @south\endcsname{% + \southwest% + \pgf@x=\pgf@xa% + }% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @north\endcsname{% + \northeast% + \pgf@x=\pgf@xa% + }% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @north\endcsname% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @south\endcsname% + \ifnum\pgfmathcounter=\parts% + \else% + \advance\pgf@xa by0.5\pgf@xb% + \advance\pgf@xa by\innerxsep\relax% + \advance\pgf@xa by.5\pgflinewidth% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@south\endcsname{% + \southwest% + \pgf@x=\pgf@xa% + }% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@north\endcsname{% + \northeast% + \pgf@x=\pgf@xa% + }% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split\endcsname{% + \centerpoint% + \pgf@x=\pgf@xa% + }% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@north\endcsname% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@south\endcsname% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split\endcsname% + \fi% + \fi% + \repeatpgfmathloop% + \else% + \pgf@y=0pt\relax% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \expandafter\let\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname=\pgfutil@empty% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \ifpgfrectanglesplitignoreemptyparts% + \expandafter\let\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname=% + \pgf@lib@sh@rs@lastanchor% + \fi% + \fi% + \expandafter\ifx\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname% + \pgf@lib@sh@rs@lefttext% + \pgf@x=0pt\relax% + \else% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname% + \pgf@lib@sh@rs@righttext% + \pgf@x=-\csname pgf@lib@sh@rs@width@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@x by\pgf@lib@sh@rs@max@width\relax% + \else% + \pgf@x=-\csname pgf@lib@sh@rs@width@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@x by\pgf@lib@sh@rs@max@width\relax% + \divide\pgf@x by2\relax% + \fi% + \fi% + \ifnum\pgfmathcounter=1\relax% + \edef\pgf@lib@sh@rs@xoffset{\the\pgf@x}% + \pgf@x=0pt\relax% + \pgfextract@process\pgf@lib@sh@rs@anchor@one{}% + \addtosavedmacro\pgf@lib@sh@rs@anchor@one% + \let\pgf@lib@sh@rs@lastanchor=\pgf@lib@sh@rs@anchor@one% + \let\pgf@lib@sh@rs@lastnumber=\pgf@lib@sh@rs@number% + \else + \advance\pgf@x by-\pgf@lib@sh@rs@xoffset\relax% + \advance\pgf@y by-\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@lastnumber\endcsname\relax% + \advance\pgf@y by-\innerysep\relax% + \advance\pgf@y by-\pgflinewidth% + \advance\pgf@y by-\innerysep\relax% + \advance\pgf@y by-\csname pgf@lib@sh@rs@height@\pgf@lib@sh@rs@number\endcsname\relax% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname{}% + \expandafter\let\expandafter\pgf@lib@sh@rs@lastanchor\expandafter=% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \let\pgf@lib@sh@rs@lastnumber=\pgf@lib@sh@rs@number% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \fi% + \fi% + \repeatpgfmathloop% + \pgfextract@process\northeast{% + \pgf@x=\pgf@lib@sh@rs@max@width\relax% + \advance\pgf@x by-\pgf@lib@sh@rs@xoffset\relax% + \advance\pgf@x by\innerxsep\relax% + \advance\pgf@x by\outerxsep\relax% + \pgf@y=\pgf@lib@sh@rs@height@one\relax% + \advance\pgf@y by\innerysep\relax% + \advance\pgf@y by\outerysep\relax% + \advance\pgf@y by.5\pgflinewidth% + }% + \addtosavedmacro\northeast% + \pgfextract@process\southwest{% + \pgf@lib@sh@rs@lastanchor% + \pgf@x=-\pgf@lib@sh@rs@xoffset\relax% + \advance\pgf@x by-\innerxsep\relax% + \advance\pgf@x by-\outerxsep\relax% + \advance\pgf@y by-\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@lastnumber\endcsname\relax% + \advance\pgf@y by-\innerysep\relax% + \advance\pgf@y by-\outerysep\relax% + \advance\pgf@y by-.5\pgflinewidth% + }% + \addtosavedmacro\southwest% + \pgfextract@process\centerpoint{% + \pgfpointadd{\southwest}{\northeast}% + \divide\pgf@x by2\relax% + \divide\pgf@y by2\relax% + }% + \addtosavedmacro\centerpoint% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \else% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \pgf@ya=\csname pgf@lib@sh@rs@height@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@y by0.5\pgf@ya% + \pgf@ya=\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@y by-0.5\pgf@ya% + \pgf@ya=\pgf@y% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @west\endcsname{% + \southwest% + \pgf@y=\pgf@ya% + }% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @east\endcsname{% + \northeast% + \pgf@y=\pgf@ya% + }% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @east\endcsname% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @west\endcsname% + \ifnum\pgfmathcounter=\parts% + \else% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number\endcsname% + \pgf@ya=\pgf@y% + \advance\pgf@ya by-\csname pgf@lib@sh@rs@depth@\pgf@lib@sh@rs@number\endcsname\relax% + \advance\pgf@ya by-\innerysep\relax% + \advance\pgf@ya by-.5\pgflinewidth% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@west\endcsname{% + \southwest% + \pgf@y=\pgf@ya% + }% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@east\endcsname{% + \northeast% + \pgf@y=\pgf@ya% + }% + \expandafter\pgfextract@process\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split\endcsname{% + \centerpoint% + \pgf@y=\pgf@ya% + }% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@east\endcsname% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@west\endcsname% + \expandafter\addtosavedmacro\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split\endcsname% + \fi% + \fi% + \repeatpgfmathloop% + \fi% + }% + \savedanchor\basepoint{% + \pgf@x=0.5\wd\pgfnodeparttextbox% + \pgf@y=0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x=0.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \anchor{center}{% + \rectanglesplitparameters% + \centerpoint% + }% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \rectanglesplitparameters% + \northeast% + \pgf@y=0pt\relax% + }% + \anchor{base west}{% + \rectanglesplitparameters% + \southwest% + \pgf@y=0pt\relax% + }% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \rectanglesplitparameters% + \northeast% + \pgf@xa=\pgf@x% + \midpoint% + \pgf@x=\pgf@xa% + }% + \anchor{mid west}{% + \rectanglesplitparameters% + \southwest% + \pgf@xa=\pgf@x% + \midpoint% + \pgf@x=\pgf@xa% + }% + \anchor{north}{% + \rectanglesplitparameters% + \centerpoint% + \pgf@xa=\pgf@x% + \northeast% + \pgf@x=\pgf@xa% + }% + \anchor{south}{% + \rectanglesplitparameters% + \centerpoint% + \pgf@xa=\pgf@x% + \southwest% + \pgf@x=\pgf@xa% + }% + \anchor{east}{% + \rectanglesplitparameters% + \centerpoint% + \pgf@ya=\pgf@y% + \northeast% + \pgf@y=\pgf@ya% + }% + \anchor{west}{% + \rectanglesplitparameters% + \centerpoint% + \pgf@ya=\pgf@y% + \southwest% + \pgf@y=\pgf@ya% + }% + \anchor{north east}{% + \rectanglesplitparameters% + \northeast% + }% + \anchor{north west}{% + \rectanglesplitparameters% + \northeast% + \pgf@ya=\pgf@y% + \southwest% + \pgf@y=\pgf@ya% + }% + \anchor{south west}{% + \rectanglesplitparameters% + \southwest% + }% + \anchor{south east}{% + \rectanglesplitparameters% + \southwest% + \pgf@ya=\pgf@y% + \northeast% + \pgf@y=\pgf@ya% + }% + \behindbackgroundpath{% + \ifpgfrectanglesplitusecustomfill% + \pgf@lib@sh@rs@process@list{\pgf@lib@sh@rs@list@fill}{\parts}% + {% + \ifpgfrectanglesplithorizontal% + \expandafter\let\expandafter\pgf@lib@sh@rs@fill@bottomleft\expandafter=% + \csname pgf@anchor@rectangle split@south west\endcsname% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \ifnum\pgfmathcounter=\parts% + \expandafter\let\expandafter\pgf@lib@sh@rs@fill@topright\expandafter=% + \csname pgf@anchor@rectangle split@north east\endcsname% + \else% + \expandafter\let\expandafter\pgf@lib@sh@rs@fill@topright\expandafter=% + \csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@number\space split north\endcsname% + \fi% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \else% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname\pgf@lib@sh@rs@nonetext% + \else% + \pgfextract@process\pgf@lib@sh@rs@fill@bottomleft{% + \pgf@lib@sh@rs@fill@bottomleft% + \advance\pgf@y by\outerysep\relax% + \ifnum\pgfmathcounter=1\relax% + \advance\pgf@x by\outerxsep\relax% + \fi% + }% + \pgfextract@process\pgf@lib@sh@rs@fill@topright{% + \pgf@lib@sh@rs@fill@topright% + \advance\pgf@y by-\outerysep\relax% + \ifnum\pgfmathcounter=\parts\relax% + \advance\pgf@x by-\outerxsep\relax% + \fi% + }% + \ifnum\pgfmathcounter>1\relax% + \begingroup\pgfsetcornersarced{\pgfpointorigin}% + \fi% + \pgfpathmoveto{% + \pgf@lib@sh@rs@fill@topright% + \pgf@xa=\pgf@x% + \pgf@lib@sh@rs@fill@bottomleft% + \pgf@x=\pgf@xa% + }% + \pgfpathlineto{\pgf@lib@sh@rs@fill@bottomleft}% + \pgfpathlineto{% + \pgf@lib@sh@rs@fill@bottomleft% + \pgf@xa=\pgf@x% + \pgf@lib@sh@rs@fill@topright% + \pgf@x=\pgf@xa% + }% + \ifnum\pgfmathcounter>1\relax% + \endgroup% + \fi% + \ifnum\pgfmathcounter<\parts% + \begingroup\pgfsetcornersarced{\pgfpointorigin}% + \fi% + \pgfpathlineto{\pgf@lib@sh@rs@fill@topright}% + \pgfpathclose% + \ifnum\pgfmathcounter<\parts% + \endgroup% + \fi% + \pgfsetfillcolor{\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname}% + \pgfusepath{fill}% + \fi% + \fi% + \pgfextract@process\pgf@lib@sh@rs@fill@bottomleft{% + \pgf@lib@sh@rs@fill@bottomleft% + \pgf@ya=\pgf@y% + \pgf@lib@sh@rs@fill@topright% + \pgf@y=\pgf@ya% + \advance\pgf@y by-\outerysep% + }% + \repeatpgfmathloop% + \else% + \expandafter\let\expandafter\pgf@lib@sh@rs@fill@topright\expandafter=% + \csname pgf@anchor@rectangle split@north east\endcsname% + \pgfmathloop% + \ifnum\pgfmathcounter>\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \ifnum\pgfmathcounter=\parts% + \expandafter\let\expandafter\pgf@lib@sh@rs@fill@bottomleft\expandafter=% + \csname pgf@anchor@rectangle split@south west\endcsname% + \else% + \expandafter\let\expandafter\pgf@lib@sh@rs@fill@bottomleft\expandafter=% + \csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@number\space split west\endcsname% + \fi% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \else% + \expandafter\ifx\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname\pgf@lib@sh@rs@nonetext% + \else% + \pgfextract@process\pgf@lib@sh@rs@fill@bottomleft{% + \pgf@lib@sh@rs@fill@bottomleft% + \advance\pgf@x by\outerxsep\relax% + \ifnum\parts=1\relax% + \advance\pgf@y by\outerysep\relax% + \else% + \ifnum\pgfmathcounter=\parts + \advance\pgf@y by\outerysep\relax% + \fi% + \fi% + }% + \pgfextract@process\pgf@lib@sh@rs@fill@topright{% + \pgf@lib@sh@rs@fill@topright% + \advance\pgf@x by-\outerxsep\relax% + \ifnum\parts=1\relax% + \advance\pgf@y by-\outerysep\relax% + \else% + \ifnum\pgfmathcounter=1\relax% + \advance\pgf@y by-\outerysep\relax% + \fi% + \fi% + }% + \pgfpathmoveto{\pgf@lib@sh@rs@fill@bottomleft}% + \ifnum\pgfmathcounter>1\relax% + \begingroup\pgfsetcornersarced{\pgfpointorigin}% + \fi% + \pgfpathlineto{% + \pgf@lib@sh@rs@fill@bottomleft% + \pgf@xa=\pgf@x% + \pgf@lib@sh@rs@fill@topright% + \pgf@x=\pgf@xa% + }% + \pgfpathlineto{\pgf@lib@sh@rs@fill@topright}% + \ifnum\pgfmathcounter>1\relax% + \endgroup% + \fi% + \ifnum\pgfmathcounter<\parts% + \begingroup\pgfsetcornersarced{\pgfpointorigin}% + \fi% + \pgfpathlineto{% + \pgf@lib@sh@rs@fill@topright% + \pgf@xa=\pgf@x% + \pgf@lib@sh@rs@fill@bottomleft% + \pgf@x=\pgf@xa% + }% + \pgfpathclose% + \ifnum\pgfmathcounter<\parts% + \endgroup% + \fi% + \pgfsetfillcolor{\csname pgf@lib@sh@rs@\pgf@lib@sh@rs@number @item\endcsname}% + \pgfusepath{fill}% + \fi% + \fi% + \pgfextract@process\pgf@lib@sh@rs@fill@topright{% + \pgf@lib@sh@rs@fill@topright% + \pgf@xa=\pgf@x% + \pgf@lib@sh@rs@fill@bottomleft% + \pgf@x=\pgf@xa% + \advance\pgf@x by\outerxsep\relax% + }% + \repeatpgfmathloop% + \fi% + }% + \fi% + }% + \backgroundpath{% + \begingroup% + \pgfextract@process\southwest{% + \southwest% + \advance\pgf@x by\outerxsep\relax% + \advance\pgf@y by\outerysep\relax% + }% + \pgfextract@process\northeast{% + \northeast% + \advance\pgf@x by-\outerxsep\relax% + \advance\pgf@y by-\outerysep\relax% + }% + \pgfpathrectangle{\southwest}{\pgfpointdiff{\southwest}{\northeast}}% + \endgroup% + \ifpgfrectanglesplitdrawsplits% + \pgfmathloop% + \ifnum\pgfmathcounter=\parts% + \else% + \pgf@lib@sh@getalpha\pgf@lib@sh@rs@number{\pgfmathcounter}% + \expandafter\ifx\csname pgf@lib@sh@rs@empty@\pgf@lib@sh@rs@number\endcsname\pgfutil@empty% + \else% + \pgfpathmoveto{% + \ifpgfrectanglesplithorizontal% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@north\endcsname% + \advance\pgf@y by-\outerysep\relax% + \else% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@east\endcsname% + \advance\pgf@x by-\outerxsep\relax% + \fi% + }% + \pgfpathlineto{% + \ifpgfrectanglesplithorizontal% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@south\endcsname% + \advance\pgf@y by\outerysep\relax% + \else% + \csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@number @split@west\endcsname% + \advance\pgf@x by\outerxsep\relax% + \fi% + }% + \fi% + \repeatpgfmathloop% + \fi% + }% + \anchorborder{% + \pgfutil@tempdima\pgf@x% + \pgfutil@tempdimb\pgf@y% + \rectanglesplitparameters% + \pgfpointdiff{\southwest}{\northeast}% + \pgf@x.5\pgf@x% + \pgf@y.5\pgf@y% + \edef\pgf@marshall{% + \noexpand\pgfpointborderrectangle{% + \noexpand\pgfqpoint{\the\pgfutil@tempdima}{\the\pgfutil@tempdimb}% + }% + {% + \noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}% + }% + }% + \pgf@marshall% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@rectangle split\endcsname{% + \let\pgf@lib@sh@rs@temp=\pgfutil@empty% + \pgfmathloop% + \ifnum\pgfmathcounter=\parts% + \expandafter\edef\csname pgf@sh@boxes@rectangle split\endcsname% + {\pgf@lib@sh@rs@temp\pgf@lib@sh@toalpha{\pgfmathcounter}}% + \else% + \edef\pgf@lib@sh@rs@temp{\pgf@lib@sh@rs@temp\pgf@lib@sh@toalpha{\pgfmathcounter},}% + \repeatpgfmathloop% + }% +}% + +\pgfutil@for\pgf@lib@sh@rs@temp:={one,two,three,four,five,six,seven,eight,nine,ten,eleven,twelve,thirteen,fourteen,fifteen,sixteen,seventeen,eighteen,nineteen,twenty}\do{% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp}{\noexpand\pgf@lib@sh@rs@anchor@one}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space split\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split}% + {\noexpand\centerpoint}% + {\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space split north\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@north}% + {\noexpand\csname pgf@anchor@rectangle split@north\noexpand\endcsname}% + {\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@north\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space split south\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@south}% + {\noexpand\csname pgf@anchor@rectangle split@south\noexpand\endcsname}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@south\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space north\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @north}% + {\noexpand\csname pgf@anchor@rectangle split@north\noexpand\endcsname}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @north\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space south\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @south}% + {\noexpand\csname pgf@anchor@rectangle split@south\noexpand\endcsname}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @south\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space split east\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@east}% + {\noexpand\csname pgf@anchor@rectangle split@east\noexpand\endcsname}% + {\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@east\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space split west\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@west}% + {\noexpand\csname pgf@anchor@rectangle split@west\noexpand\endcsname}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @split@west\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space east\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @east}% + {\noexpand\csname pgf@anchor@rectangle split@east\noexpand\endcsname}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @east\noexpand\endcsname}% + }% + \expandafter\xdef\csname pgf@anchor@rectangle split@\pgf@lib@sh@rs@temp\space west\endcsname{% + \noexpand\rectanglesplitparameters% + \noexpand\pgfutil@ifundefined{pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @west}% + {\noexpand\csname pgf@anchor@rectangle split@west\noexpand\endcsname}% + {\noexpand\csname pgf@lib@sh@rs@anchor@\pgf@lib@sh@rs@temp @west\noexpand\endcsname}% + }% +}% + + +\pgfutil@namelet{pgf@anchor@rectangle split@text east}{pgf@anchor@rectangle split@one east}% +\pgfutil@namelet{pgf@anchor@rectangle split@text west}{pgf@anchor@rectangle split@one west}% +\pgfutil@namelet{pgf@anchor@rectangle split@text split}{pgf@anchor@rectangle split@one split}% +\pgfutil@namelet{pgf@anchor@rectangle split@text split east}{pgf@anchor@rectangle split@one split east}% +\pgfutil@namelet{pgf@anchor@rectangle split@text split west}{pgf@anchor@rectangle split@one split west}% + +\pgfutil@namelet{pgf@anchor@rectangle split@second}{pgf@anchor@rectangle split@two}% +\pgfutil@namelet{pgf@anchor@rectangle split@second east}{pgf@anchor@rectangle split@two east}% +\pgfutil@namelet{pgf@anchor@rectangle split@second west}{pgf@anchor@rectangle split@two west}% +\pgfutil@namelet{pgf@anchor@rectangle split@second split}{pgf@anchor@rectangle split@two split}% +\pgfutil@namelet{pgf@anchor@rectangle split@second split east}{pgf@anchor@rectangle split@two split east}% +\pgfutil@namelet{pgf@anchor@rectangle split@second split west}{pgf@anchor@rectangle split@two split west}% + +\pgfutil@namelet{pgf@anchor@rectangle split@third}{pgf@anchor@rectangle split@three}% +\pgfutil@namelet{pgf@anchor@rectangle split@third east}{pgf@anchor@rectangle split@three east}% +\pgfutil@namelet{pgf@anchor@rectangle split@third west}{pgf@anchor@rectangle split@three west}% +\pgfutil@namelet{pgf@anchor@rectangle split@third split}{pgf@anchor@rectangle split@three split}% +\pgfutil@namelet{pgf@anchor@rectangle split@third split east}{pgf@anchor@rectangle split@three split east}% +\pgfutil@namelet{pgf@anchor@rectangle split@third split west}{pgf@anchor@rectangle split@three split west}% + +\pgfutil@namelet{pgf@anchor@rectangle split@fourth}{pgf@anchor@rectangle split@four}% +\pgfutil@namelet{pgf@anchor@rectangle split@fourth east}{pgf@anchor@rectangle split@four east}% +\pgfutil@namelet{pgf@anchor@rectangle split@fourth west}{pgf@anchor@rectangle split@four west}% +\pgfutil@namelet{pgf@anchor@rectangle split@fourth split}{pgf@anchor@rectangle split@four split}% +\pgfutil@namelet{pgf@anchor@rectangle split@fourth split east}{pgf@anchor@rectangle split@four split east}% +\pgfutil@namelet{pgf@anchor@rectangle split@fourth split west}{pgf@anchor@rectangle split@four split west}% + + + + +\pgfdeclareshape{ellipse split}{% + \nodeparts{text,lower}% + \savedanchor\radii{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgf@y2.0\pgf@y% + \advance\pgf@y.5\pgflinewidth% + \pgf@xa.5\wd\pgfnodeparttextbox% + \pgf@xb.5\wd\pgfnodepartlowerbox% + \advance\pgf@xa\pgf@x% + \advance\pgf@xb\pgf@x% + \pgf@ya\ht\pgfnodeparttextbox% + \advance\pgf@ya\dp\pgfnodeparttextbox% + \pgf@yb\ht\pgfnodepartlowerbox% + \advance\pgf@yb\dp\pgfnodepartlowerbox% + \advance\pgf@ya\pgf@y% + \advance\pgf@yb\pgf@y% + \ifdim\pgf@xa>\pgf@xb% + \pgf@x1.414213\pgf@xa% + \else% + \pgf@x1.414213\pgf@xb% + \fi% + \ifdim\pgf@ya>\pgf@yb% + \pgf@y1.414213\pgf@ya% + \else% + \pgf@y1.414213\pgf@yb% + \fi% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + }% + \savedanchor\lower{% + \pgf@x-.5\wd\pgfnodepartlowerbox% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \pgf@y-2.0\pgf@y% + \advance\pgf@y-\pgflinewidth% + \advance\pgf@y-\dp\pgfnodeparttextbox% + \advance\pgf@y-\ht\pgfnodepartlowerbox% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{-\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y-\dp\pgfnodeparttextbox% + \advance\pgf@y-.5\pgflinewidth% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt\relax% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{lower}{\lower}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{\radii\pgf@xa\pgf@x\midpoint\advance\pgf@x\pgf@xa}% + \anchor{mid west}{\radii\pgf@xa\pgf@x\midpoint\advance\pgf@x-\pgf@xa}% + \anchor{base}{\basepoint}% + \anchor{base east}{\radii\pgf@xa\pgf@x\basepoint\advance\pgf@x\pgf@xa}% + \anchor{base west}{\radii\pgf@xa\pgf@x\basepoint\advance\pgf@x-\pgf@xa}% + \anchor{north}{\pgfpointadd{\centerpoint}{\radii\pgf@x0pt}}% + \anchor{south}{\pgfpointadd{\centerpoint}{\radii\pgf@x0pt\pgf@y-\pgf@y}}% + \anchor{east}{\pgfpointadd{\centerpoint}{\radii\pgf@y0pt}}% + \anchor{west}{\pgfpointadd{\centerpoint}{\radii\pgf@x-\pgf@x\pgf@y0pt}}% + \anchor{north west}{\pgfpointadd{\centerpoint}{\radii\pgf@x-0.707106\pgf@x\pgf@y0.707106\pgf@y}}% + \anchor{south west}{\pgfpointadd{\centerpoint}{\radii\pgf@x-0.707106\pgf@x\pgf@y-0.707106\pgf@y}}% + \anchor{north east}{\pgfpointadd{\centerpoint}{\radii\pgf@x0.707106\pgf@x\pgf@y0.707106\pgf@y}}% + \anchor{south east}{\pgfpointadd{\centerpoint}{\radii\pgf@x0.707106\pgf@x\pgf@y-0.707106\pgf@y}}% + \backgroundpath{% + \radii% + \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}% + \pgfutil@tempdima\pgf@x% + \pgfutil@tempdimb\pgf@y% + \pgfpathellipse{\centerpoint}{\pgfqpoint{\the\pgfutil@tempdima}{0pt}}{\pgfqpoint{0pt}{\the\pgfutil@tempdimb}}% + \pgfpathmoveto{\centerpoint\advance\pgf@x-\pgfutil@tempdima}% + \pgfpathlineto{\centerpoint\advance\pgf@x\pgfutil@tempdima}% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \radii% + \edef\pgf@marshal{% + \noexpand\pgfpointadd{\noexpand\pgfpointborderellipse{\noexpand\externalpoint}% + {\noexpand\pgfpoint{\the\pgf@x}{\the\pgf@y}}}{\noexpand\centerpoint}% + }% + \pgf@marshal% + }% +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..7509deaaec8188281e008e5806b9ec3ca97904e5 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/libraries/shapes/pgflibraryshapes.symbols.code.tex @@ -0,0 +1,2259 @@ + +\ProvidesFileRCS{pgflibraryshapes.symbols.code.tex} + +\pgfdeclareshape{forbidden sign} +{% + \inheritsavedanchors[from=circle]% + \inheritanchorborder[from=circle]% + \inheritanchor[from=circle]{north}% + \inheritanchor[from=circle]{north west}% + \inheritanchor[from=circle]{north east}% + \inheritanchor[from=circle]{center}% + \inheritanchor[from=circle]{west}% + \inheritanchor[from=circle]{east}% + \inheritanchor[from=circle]{mid}% + \inheritanchor[from=circle]{mid west}% + \inheritanchor[from=circle]{mid east}% + \inheritanchor[from=circle]{base}% + \inheritanchor[from=circle]{base west}% + \inheritanchor[from=circle]{base east}% + \inheritanchor[from=circle]{south}% + \inheritanchor[from=circle]{south west}% + \inheritanchor[from=circle]{south east}% + \inheritbackgroundpath[from=circle]% + \foregroundpath{ + \centerpoint% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgfutil@tempdima by-\pgf@yb% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{-0.707107\pgfutil@tempdima}{-0.707107\pgfutil@tempdima}}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{0.707107\pgfutil@tempdima}{0.707107\pgfutil@tempdima}}} + \pgfsetarrowsstart{} + \pgfsetarrowsend{} + }% +}% + + +\pgfdeclareshape{correct forbidden sign} +{% + \inheritsavedanchors[from=circle]% + \inheritanchorborder[from=circle]% + \inheritanchor[from=circle]{north}% + \inheritanchor[from=circle]{north west}% + \inheritanchor[from=circle]{north east}% + \inheritanchor[from=circle]{center}% + \inheritanchor[from=circle]{west}% + \inheritanchor[from=circle]{east}% + \inheritanchor[from=circle]{mid}% + \inheritanchor[from=circle]{mid west}% + \inheritanchor[from=circle]{mid east}% + \inheritanchor[from=circle]{base}% + \inheritanchor[from=circle]{base west}% + \inheritanchor[from=circle]{base east}% + \inheritanchor[from=circle]{south}% + \inheritanchor[from=circle]{south west}% + \inheritanchor[from=circle]{south east}% + \inheritbackgroundpath[from=circle]% + \foregroundpath{ + \centerpoint% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgfutil@tempdima by-\pgf@yb% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{0.707107\pgfutil@tempdima}{-0.707107\pgfutil@tempdima}}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{-0.707107\pgfutil@tempdima}{0.707107\pgfutil@tempdima}}} + \pgfsetarrowsstart{} + \pgfsetarrowsend{} + }% +}% + + + + + +\pgfkeys{/pgf/random starburst/% + .code={% + \ifx\pgfkeysnovalue#1% + \pgfmathgeneratepseudorandomnumber% + \else% + \pgfmathtruncatemacro\pgfmathresult{#1}% + \fi% + \pgfkeyslet{/pgf/random starburst}{\pgfmathresult}% + }% +}% +\pgfkeys{/pgf/random starburst=100}% + +\pgfkeys{/pgf/starburst point height/.value required}% +\pgfkeys{/pgf/starburst point height/.code={% + \pgfmathparse{#1}% + \edef\pgfmathresult{\pgfmathresult pt}% + \pgfkeyslet{/pgf/starburst point height}{\pgfmathresult}% + }% +}% +\pgfkeys{/pgf/starburst point height=.5cm}% + +\pgfkeys{/pgf/starburst points/.value required}% +\pgfkeys{/pgf/starburst points/.code={% + \pgfmathtruncatemacro\pgfmathresult{#1}% + \pgfkeyslet{/pgf/starburst points}{\pgfmathresult}% + }% +}% +\pgfkeys{/pgf/starburst points=17}% + +\pgfdeclareshape{starburst}{% + \savedmacro\anglestep{% + \pgfmathdivide@{180}{\pgfkeysvalueof{/pgf/starburst points}}% + \let\anglestep\pgfmathresult% + }% + \savedmacro\calculatestarburstpoints{% + \pgfmathdivide@{180}{\pgfkeysvalueof{/pgf/starburst points}}% + \let\anglestep\pgfmathresult% + \pgfmathsetcounter{pgf@counta}{\pgfkeysvalueof{/pgf/starburst points}}% + \multiply\c@pgf@counta2\relax% + \edef\totalpoints{\the\c@pgf@counta}% + \addtosavedmacro{\totalpoints}% + \pgfextract@process\centerpoint{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+.5\ht\pgfnodeparttextbox}% + \pgfmathaddtolength\pgf@y{+-.5\dp\pgfnodeparttextbox}% + }% + \pgfmathsetlength\pgf@x{+\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{+\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \pgfmathsetlength\pgf@x{+\pgfkeysvalueof{/pgf/inner xsep}}% + \pgfmathaddtolength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+\pgfkeysvalueof{/pgf/inner ysep}}% + \pgfmathaddtolength\pgf@y{+.5\ht\pgfnodeparttextbox}% + \pgfmathaddtolength\pgf@y{+.5\dp\pgfnodeparttextbox}% + \ifpgfshapeborderusesincircle% + \pgfkeysgetvalue{/pgf/shape border rotate}{\rotate}% + \ifdim\pgf@y>\pgf@x% + \pgf@x\pgf@y% + \fi% + \pgf@x1.41421\pgf@x% + \pgf@y\pgf@x% + \else% + \pgfkeysgetvalue{/pgf/shape border rotate}{\rotate}% + \pgfmathmod@{\rotate}{360}% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgf@counta\pgfmathresult\relax\pgfmath@% + \advance\c@pgf@counta45\relax% + \divide\c@pgf@counta90\relax% + \multiply\c@pgf@counta90\relax% + \ifnum\c@pgf@counta<0\relax% + \advance\c@pgf@counta360\relax% + \fi% + \ifnum\c@pgf@counta=90\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \else% + \ifnum\c@pgf@counta=270\relax% + \pgf@xc\pgf@x% + \pgf@x\pgf@y% + \pgf@y\pgf@xc% + \fi% + \fi% + \edef\rotate{\the\c@pgf@counta}% + \pgf@x=1.41421\pgf@x% + \pgf@y=1.41421\pgf@y% + \fi% + \addtosavedmacro{\rotate}% + \pgf@xa\pgf@x% + \pgfmathsetlength\pgf@xb{+\pgfkeysvalueof{/pgf/starburst point height}}% + \advance\pgf@xa\pgf@xb% + \pgfmathsetlength\pgf@xc{+\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@xa<.5\pgf@xc% + \pgf@x.5\pgf@xc% + \advance\pgf@x-\pgf@xb% + \fi% + \pgf@ya\pgf@y% + \pgfmathsetlength\pgf@yb{+\pgfkeysvalueof{/pgf/starburst point height}}% + \advance\pgf@ya\pgf@yb% + \pgfmathsetlength\pgf@yc{+\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@ya<.5\pgf@yc% + \pgf@y.5\pgf@yc% + \advance\pgf@y-\pgf@yb% + \fi% + \edef\xinnerradius{\the\pgf@x}% + \edef\yinnerradius{\the\pgf@y}% + \addtosavedmacro{\xinnerradius}% + \addtosavedmacro{\yinnerradius}% + \ifdim\pgf@y>\pgf@x% + \pgf@x\pgf@y% + \fi% + \pgfmathaddtolength\pgf@x{+\pgfkeysvalueof{/pgf/starburst point height}}% + \edef\externalradius{\the\pgf@x}% + \addtosavedmacro{\externalradius}% + \pgfmathsetseed{\pgfkeysvalueof{/pgf/random starburst}}% + \def\angle{90}% + \c@pgf@counta1\relax% + \c@pgf@countb0\relax% + \c@pgf@countc\totalpoints\relax% + \advance\c@pgf@countc2\relax% + \edef\looppoints{\the\c@pgf@countc}% + \let\secondpoint\pgfutil@empty% + \let\thirdpoint\pgfutil@empty% + \pgfmathloop% + \let\firstpoint\secondpoint% + \let\secondpoint\thirdpoint% + \ifnum\pgfmathcounter>\looppoints% + \else% + \ifnum\pgfmathcounter>\totalpoints% + \expandafter\let\expandafter\thirdpoint\csname point@\the\c@pgf@counta @\endcsname% + \else% + \ifodd\pgfmathcounter% + \ifnum\pgfkeysvalueof{/pgf/random starburst}=0\relax% + \pgf@xa\pgfkeysvalueof{/pgf/starburst point height}\relax% + \else% + \pgf@x\pgfkeysvalueof{/pgf/starburst point height}\relax% + \pgf@xa.75\pgf@x% + \pgf@xb.25\pgf@x% + \pgfmathrnd% + \pgf@xa\pgfmathresult\pgf@xa% + \advance\pgf@xa\pgf@xb% + \fi% + \pgf@x\xinnerradius\relax% + \advance\pgf@x\pgf@xa% + \pgf@y\yinnerradius\relax% + \advance\pgf@y\pgf@xa% + \expandafter\pgfextract@process\csname point@\the\c@pgf@counta @\endcsname{% + \pgfpointpolar{\angle}{\the\pgf@x and \the\pgf@y}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \else% + \expandafter\pgfextract@process\csname point@\the\c@pgf@counta @\endcsname{% + \pgfpointpolar{\angle}{\xinnerradius and \yinnerradius}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \fi% + \expandafter\let\expandafter\thirdpoint\csname point@\the\c@pgf@counta @\endcsname% + \expandafter\addtosavedmacro\expandafter{\csname point@\the\c@pgf@counta @\endcsname}% + \fi% + \ifx\firstpoint\pgfutil@empty% + \else% + \pgfmathanglebetweenlines{\secondpoint}{\thirdpoint}{\secondpoint}{\firstpoint}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\defaultmiterangle\pgfmathresult% + \pgfmathcosec@{\pgfmathresult}% + \pgf@x\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \edef\miterlength{\the\pgf@x}% + \pgfmathanglebetweenlines{\firstpoint}{\secondpoint}{\firstpoint}{\thirdpoint}% + \pgfmathadd@{\pgfmathresult}{\defaultmiterangle}% + \pgfmathsubtract@{180}{\pgfmathresult}% + \let\angletemp\pgfmathresult% + \pgfmathanglebetweenpoints{\firstpoint}{\thirdpoint}% + \pgfmathsubtract@{180}{\pgfmathresult}% + \pgfmathsubtract@{\angletemp}{\pgfmathresult}% + \edef\miterangle{\pgfmathresult}% + \pgfextract@process\borderpoint{% + \secondpoint% + \pgf@xa\pgf@x + \pgf@ya\pgf@y% + \pgfpointpolar{\miterangle}{\miterlength}% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\borderpoint}% + \expandafter\edef\csname angletoborderpoint@\the\c@pgf@countb @\endcsname{\pgfmathresult}% + \expandafter\addtosavedmacro\expandafter{\csname angletoborderpoint@\the\c@pgf@countb @\endcsname}% + \expandafter\pgfextract@process\csname borderpoint@\the\c@pgf@countb @\endcsname{% + \pgfmathrotatepointaround{\borderpoint}{\centerpoint}{\rotate}% + }% + \expandafter\addtosavedmacro\expandafter{\csname borderpoint@\the\c@pgf@countb @\endcsname}% + \c@pgf@countc\c@pgf@countb% + \advance\c@pgf@countc1\relax% + \divide\c@pgf@countc2\relax% + \ifodd\c@pgf@countb\relax% + \pgfutil@ifundefined{pgf@anchor@starburst@outer point\space\the\c@pgf@countc}{% + \expandafter\xdef\csname pgf@anchor@starburst@outer point\space\the\c@pgf@countc\endcsname{% + \noexpand\calculatestarburstpoints% + \noexpand\csname borderpoint@\the\c@pgf@countb @\noexpand\endcsname% + }% + }{}% + \else% + \pgfutil@ifundefined{pgf@anchor@starburst@inner point\space\the\c@pgf@countc}{% + \expandafter\xdef\csname pgf@anchor@starburst@inner point\space\the\c@pgf@countc\endcsname{% + \noexpand\calculatestarburstpoints% + \noexpand\csname borderpoint@\the\c@pgf@countb @\noexpand\endcsname% + }% + }{}% + \fi% + \fi% + \pgfmathadd@{\angle}{\anglestep}% + \pgfmathmod@{\pgfmathresult}{360}% + \let\angle\pgfmathresult% + \advance\c@pgf@counta1\relax% + \ifnum\c@pgf@counta>\totalpoints% + \c@pgf@counta1\relax% + \fi% + \advance\c@pgf@countb1\relax% + \ifnum\c@pgf@countb>\totalpoints% + \c@pgf@countb1\relax% + \fi% + \repeatpgfmathloop% + }% + \savedanchor\centerpoint{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+.5\ht\pgfnodeparttextbox}% + \pgfmathaddtolength\pgf@y{+-.5\dp\pgfnodeparttextbox}% + }% + \savedanchor\midpoint{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \savedanchor\basepoint{% + \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}% + \pgf@y0pt\relax% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{mid}{\midpoint}% + \anchor{north}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{0pt}{\externalradius}}% + }% + \anchor{south}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{0pt}{-\externalradius}}% + }% + \anchor{east}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{\externalradius}{0pt}}% + }% + \anchor{west}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{-\externalradius}{0pt}}% + }% + \anchor{north west}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{-\externalradius}{\externalradius}}% + }% + \anchor{south west}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{-\externalradius}{-\externalradius}}% + }% + \anchor{north east}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{\externalradius}{\externalradius}}% + }% + \anchor{south east}{% + \calculatestarburstpoints% + \csname pgf@anchor@starburst@border\endcsname{\pgfqpoint{\externalradius}{-\externalradius}}% + }% + \backgroundpath{% + \calculatestarburstpoints% + \pgfmathloop% + \ifnum\pgfmathcounter>\totalpoints% + \else% + \ifnum\pgfmathcounter=1\relax% + \let\starburstaction\pgfpathmoveto% + \else% + \let\starburstaction\pgfpathlineto% + \fi% + \starburstaction{% + \csname point@\pgfmathcounter @\endcsname} + \repeatpgfmathloop% + \pgfpathclose% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \centerpoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \calculatestarburstpoints% + \pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + \pgfmathsubtract@{\pgfmathresult}{\rotate}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\externalangle\pgfmathresult% + \ifdim\externalangle pt<90pt\relax% + \c@pgf@counta0\relax% + \c@pgf@countb\totalpoints\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>0\relax% + \else% + \ifdim\csname angletoborderpoint@\the\c@pgf@countb @\endcsname pt>90pt\relax% + \c@pgf@counta\c@pgf@countb% + \else% + \ifdim\externalangle pt>\csname angletoborderpoint@\the\c@pgf@countb @\endcsname pt\relax% + \c@pgf@counta\c@pgf@countb% + \fi% + \fi% + \advance\c@pgf@countb-1\relax% + \repeatpgfmathloop% + \edef\first{\the\c@pgf@counta}% + \advance\c@pgf@counta1\relax% + \ifnum\c@pgf@counta>\totalpoints\relax% + \c@pgf@counta1\relax% + \fi% + \edef\second{\the\c@pgf@counta}% + \else% + \c@pgf@counta0\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>0\relax% + \else% + \ifdim\csname angletoborderpoint@\pgfmathcounter @\endcsname pt<90pt\relax% + \c@pgf@counta\pgfmathcounter% + \else% + \ifdim\externalangle pt<\csname angletoborderpoint@\pgfmathcounter @\endcsname pt\relax% + \c@pgf@counta\pgfmathcounter% + \fi% + \fi% + \repeatpgfmathloop% + \edef\first{\the\c@pgf@counta}% + \advance\c@pgf@counta-1\relax% + \ifnum\c@pgf@counta=0\relax% + \c@pgf@counta\totalpoints\relax% + \fi% + \edef\second{\the\c@pgf@counta}% + \fi% + \pgfpointintersectionoflines{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + {\csname borderpoint@\first @\endcsname}{\csname borderpoint@\second @\endcsname}% + }% +}% + + + + + +\newif\ifpgfcloudanchorsuseellipse% +\newif\ifpgfcloudignoresaspect% +\pgfcloudignoresaspectfalse% +\pgfkeys{/pgf/.cd, + cloud puffs/.initial=10, + cloud puff arc/.initial=150, + cloud ignores aspect/.is if=pgfcloudignoresaspect, + cloud anchors use ellipse/.is if=pgfcloudanchorsuseellipse, +}% + + +\pgfkeys{/pgf/.cd, + aspect/.code={\pgfsetshapeaspect{#1}},% + shape aspect/.initial=1,% + shape aspect/.code={% + \pgfkeys{/pgf/aspect={#1}}% + \pgfkeyssetvalue{/pgf/shape aspect}{#1} + }% +}% + +\def\pgfsetshapeaspect#1{% + \def\pgfshapeaspect{#1}% + \pgfutil@tempdima=#1pt% + \pgfutil@tempdima=.125\pgfutil@tempdima% + \c@pgf@counta=\pgfutil@tempdima\relax% + \pgfutil@tempdima=8192pt% + \divide\pgfutil@tempdima by\c@pgf@counta% + \edef\pgfshapeaspectinverse{\pgf@sys@tonumber{\pgfutil@tempdima}}% +}% + +\pgfsetshapeaspect{1}% + + +\pgfdeclareshape{cloud}{% + \savedmacro\getradii{% + \pgfmathtruncatemacro\puffs{\pgfkeysvalueof{/pgf/cloud puffs}}% + \addtosavedmacro\puffs% + \pgfmathdivide{360}{\pgfkeysvalueof{/pgf/cloud puffs}}% + \let\anglestep\pgfmathresult% + \addtosavedmacro\anglestep% + \pgfmathsetmacro\arc{\pgfkeysvalueof{/pgf/cloud puff arc}}% + \addtosavedmacro\arc% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgf@x1.4142135\pgf@x% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \pgf@y1.4142135\pgf@y% + \ifpgfcloudignoresaspect% + \pgf@xc\pgf@x% + \pgf@yc\pgf@y% + \else% + \pgf@xc\pgfshapeaspect\pgf@y% + \ifdim\pgf@xc<\pgf@x% + \pgf@xc\pgf@x% + \fi% + \pgf@yc\pgfshapeaspectinverse\pgf@xc% + \ifdim\pgf@yc<\pgf@y% + \pgf@yc\pgf@y% + \pgf@xc\pgfshapeaspect\pgf@y% + \fi% + \fi% + \edef\xinnerradius{\the\pgf@xc}% + \edef\yinnerradius{\the\pgf@yc}% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x<\pgf@y% + \pgf@x\pgf@y% + \fi% + \edef\outersep{\the\pgf@x}% + \addtosavedmacro\outersep% + \pgfmathsubtract{180}{\arc}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\tempangle\pgfmathresult% + \pgfmathsec@{\pgfmathresult}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\arcradiusquotient\pgfmathresult% + \addtosavedmacro\arcradiusquotient% + \pgfmathsin@{\tempangle}% + \pgfmathsubtract@{1}{\pgfmathresult}% + \pgfmathmultiply@{\pgfmathresult}{\arcradiusquotient}% + \let\archeightquotient\pgfmathresult% + \addtosavedmacro\archeightquotient% + \pgfmathdivide{\arc}{2}% + \let\halfarcangle\pgfmathresult% + \pgfmathcos@{\pgfmathresult}% + \pgfmathsubtract@{1}{\pgfmathresult}% + \let\pgf@temp\pgfmathresult% + \pgfmathsin@{\halfarcangle}% + \pgfmathdivide@{\pgf@temp}{\pgfmathresult}% + \let\pgf@temp\pgfmathresult% + \pgfmathdivide@{\anglestep}{2}% + \pgfmathsin@{\pgfmathresult}% + \pgfmathmultiply@{\pgfmathresult}{\pgf@temp}% + \let\k\pgfmathresult% + \pgfmathdivide@{\anglestep}{2}% + \pgfmathcos@{\pgfmathresult}% + \let\coshalfanglestep\pgfmathresult% + \pgf@x\xinnerradius\relax% + \pgf@y\yinnerradius\relax% + \pgf@xa\coshalfanglestep\pgf@x% + \advance\pgf@xa\k\pgf@y% + \pgf@ya\coshalfanglestep\pgf@y% + \advance\pgf@ya\k\pgf@x% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@ya<.5\pgf@yb% + \pgf@ya.5\pgf@yb% + \fi% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@xa<.5\pgf@xb% + \pgf@xa.5\pgf@xb% + \fi% + \edef\xouterradius{\the\pgf@xa}% + \addtosavedmacro\xouterradius% + \edef\youterradius{\the\pgf@ya}% + \addtosavedmacro\youterradius% + \pgf@xc\k pt\relax% + \pgf@xc-\k\pgf@xc% + \pgf@yc\coshalfanglestep pt\relax% + \pgf@yc\coshalfanglestep\pgf@yc% + \advance\pgf@xc\pgf@yc\relax% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgf@xc}}% + \pgf@x\coshalfanglestep\pgf@xa% + \advance\pgf@x-\k\pgf@ya% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y\coshalfanglestep\pgf@ya% + \advance\pgf@y-\k\pgf@xa% + \pgf@y\pgfmathresult\pgf@y% + \edef\xinnerradius{\the\pgf@x}% + \edef\yinnerradius{\the\pgf@y}% + \addtosavedmacro\xinnerradius% + \addtosavedmacro\yinnerradius% + \pgfmathdivide@{\arc}{4}% + \let\quarterarc\pgfmathresult% + \pgfmathsubtract@{180}{\arc}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\halfcomplementarc\pgfmathresult% + \addtosavedmacro\arc% + \addtosavedmacro\quarterarc% + \addtosavedmacro\halfcomplementarc% + \pgfmathsec@{\halfcomplementarc}% + \let\sechalfcomplementarc\pgfmathresult% + \pgfmathsin@{\halfcomplementarc}% + \let\sinhalfcomplementarc\pgfmathresult% + \addtosavedmacro\sechalfcomplementarc% + \addtosavedmacro\sinhalfcomplementarc% + \pgfmathsin@{\quarterarc}% + \let\sinquarterarc\pgfmathresult% + \pgfmathcos@{\quarterarc}% + \let\cosquarterarc\pgfmathresult% + \pgfmathreciprocal@{\cosquarterarc}% + \pgfmathmultiply@{\pgfmathresult}{\sinquarterarc}% + \let\tanquarterarc\pgfmathresult% + \addtosavedmacro\sinquarterarc% + \addtosavedmacro\cosquarterarc% + \addtosavedmacro\tanquarterarc% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{base}{\basepoint}% + \anchor{north}{% + \getradii% + \csname pgf@anchor@cloud@border\endcsname{\pgfqpoint{0pt}{\youterradius}}% + }% + \anchor{south}{% + \getradii% + \csname pgf@anchor@cloud@border\endcsname{\pgfqpoint{0pt}{-\youterradius}}% + }% + \anchor{east}{% + \getradii% + \csname pgf@anchor@cloud@border\endcsname{\pgfqpoint{\xouterradius}{0pt}}% + }% + \anchor{west}{% + \getradii% + \csname pgf@anchor@cloud@border\endcsname{\pgfqpoint{-\xouterradius}{0pt}}% + }% + \anchor{north west}{% + \getradii% + \pgfextract@process\pgf@sh{% + \pgf@x\xouterradius\relax% + \pgf@x-0.707106\pgf@x% + \pgf@y\youterradius\relax% + \pgf@y0.707106\pgf@y% + }% + \csname pgf@anchor@cloud@border\endcsname{\pgf@sh}% + }% + \anchor{north east}{% + \getradii% + \pgfextract@process\pgf@sh{% + \pgf@x\xouterradius\relax% + \pgf@x0.707106\pgf@x% + \pgf@y\youterradius\relax% + \pgf@y0.707106\pgf@y% + }% + \csname pgf@anchor@cloud@border\endcsname{\pgf@sh}% + }% + \anchor{south west}{% + \getradii% + \pgfextract@process\pgf@sh{% + \pgf@x\xouterradius\relax% + \pgf@x-0.707106\pgf@x% + \pgf@y\youterradius\relax% + \pgf@y-0.707106\pgf@y% + }% + \csname pgf@anchor@cloud@border\endcsname{\pgf@sh}% + }% + \anchor{south east}{% + \getradii% + \pgfextract@process\pgf@sh{% + \pgf@x\xouterradius\relax% + \pgf@x0.707106\pgf@x% + \pgf@y\youterradius\relax% + \pgf@y-0.707106\pgf@y% + }% + \csname pgf@anchor@cloud@border\endcsname{\pgf@sh}% + }% + \backgroundpath{% + {% + \getradii% + \pgfmathdivide@{\anglestep}{2}% + \pgfmathsubtract@{90}{\pgfmathresult}% + \let\angle\pgfmathresult% + \pgfextract@process\arcfirstpoint{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{+\angle}{+\xinnerradius and +\yinnerradius}% + }% + }% + \pgfpathmoveto{\arcfirstpoint}% + \let\arcendpoint\arcfirstpoint% + \pgfmathloop% + \ifnum\pgfmathcounter>\puffs\relax% + \else + \let\arcstartpoint\arcendpoint% + \ifnum\pgfmathcounter=\puffs\relax% + \let\arcendpoint\arcfirstpoint% + \else% + \pgfmathadd@{\angle}{\anglestep}% + \let\angle\pgfmathresult% + \pgfextract@process\arcendpoint{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{+\angle}{+\xinnerradius and +\yinnerradius}% + }% + }% + \fi% + \pgf@sh@getcloudpuffparameters% + \pgfmathsubtract@{90}{\quarterarc}% + \pgfmathadd@{\pgfmathresult}{\arcslope}% + \let\arcrotate\pgfmathresult% + \pgfmathsin@{\arcrotate}% + \let\sinarcrotate\pgfmathresult% + \pgfmathcos@{\arcrotate}% + \let\cosarcrotate\pgfmathresult% + \pgf@x\arcradius\relax% + \pgf@x\tanquarterarc\pgf@x% + \edef\controlscale{\pgfmath@tonumber{\pgf@x}}% + \pgfextract@process\controlone{% + \pgf@x0.55228475pt\relax% + \pgf@x\sinquarterarc\pgf@x% + \pgf@y0.55228475pt\relax% + \pgf@y\cosquarterarc\pgf@y% + \pgf@x\controlscale\pgf@x% + \pgf@y\controlscale\pgf@y% + \pgf@xa\cosarcrotate\pgf@x% + \advance\pgf@xa-\sinarcrotate\pgf@y% + \pgf@ya\cosarcrotate\pgf@y% + \advance\pgf@ya\sinarcrotate\pgf@x% + \arcstartpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\arcmidpoint{% + \pgfextract@process\arcmidpoint{% + \pgf@x-\halfchordlength\relax% + \pgf@y\segmentheight\relax% + }% + \pgfpointadd{\arcstartpoint}{% + \pgfmathrotatepointaround{\arcmidpoint}{\pgfpointorigin}{\arcslope}% + }% + }% + \pgfextract@process\controltwo{% + \pgf@x0.55228475pt\relax% + \pgf@x\sinquarterarc\pgf@x% + \pgf@y-0.55228475pt\relax% + \pgf@y\cosquarterarc\pgf@y% + \pgf@x\controlscale\pgf@x% + \pgf@y\controlscale\pgf@y% + \pgf@xa\cosarcrotate\pgf@x% + \advance\pgf@xa-\sinarcrotate\pgf@y% + \pgf@ya\cosarcrotate\pgf@y% + \advance\pgf@ya\sinarcrotate\pgf@x% + \arcmidpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + {% + \pgfsetcornersarced{\pgfpointorigin}% + \pgfpathcurveto{\controlone}{\controltwo}{\arcmidpoint}% + }% + \pgfmathadd@{\quarterarc}{90}% + \pgfmathadd@{\pgfmathresult}{\arcslope}% + \let\arcrotate\pgfmathresult% + \pgfmathsin@{\arcrotate}% + \let\sinarcrotate\pgfmathresult% + \pgfmathcos@{\arcrotate}% + \let\cosarcrotate\pgfmathresult% + \pgfextract@process\controlone{% + \pgf@x0.55228475pt\relax% + \pgf@x\sinquarterarc\pgf@x% + \pgf@y0.55228475pt\relax% + \pgf@y\cosquarterarc\pgf@y% + \pgf@x\controlscale\pgf@x% + \pgf@y\controlscale\pgf@y% + \pgf@xa\cosarcrotate\pgf@x% + \advance\pgf@xa-\sinarcrotate\pgf@y% + \pgf@ya\cosarcrotate\pgf@y% + \advance\pgf@ya\sinarcrotate\pgf@x% + \arcmidpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfextract@process\controltwo{% + \pgf@x0.55228475pt\relax% + \pgf@x\sinquarterarc\pgf@x% + \pgf@y-0.55228475pt\relax% + \pgf@y\cosquarterarc\pgf@y% + \pgf@x\controlscale\pgf@x% + \pgf@y\controlscale\pgf@y% + \pgf@xa\cosarcrotate\pgf@x% + \advance\pgf@xa-\sinarcrotate\pgf@y% + \pgf@ya\cosarcrotate\pgf@y% + \advance\pgf@ya\sinarcrotate\pgf@x% + \arcendpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfpathcurveto{\controlone}{\controltwo}{\arcendpoint}% + \repeatpgfmathloop% + \pgfpathclose% + }% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \getradii% + \ifpgfcloudanchorsuseellipse% + \pgfpointadd{\centerpoint}{% + \pgfpointborderellipse{% + \pgfpoint{\externalx}{\externaly} + }{% + \pgfpoint{\xouterradius}{\youterradius} + }% + }% + \else% + \pgfextract@process\externalpoint{% + \centerpoint% + \advance\pgf@x\externalx\relax% + \advance\pgf@y\externaly\relax% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \pgfmathdivide@{\anglestep}{2}% + \let\halfanglestep\pgfmathresult% + \pgfmathsubtract@{90}{\halfanglestep}% + \let\endangle\pgfmathresult% + \pgfmathloop% + \pgfmathsubtract@{\endangle}{\anglestep}% + \ifdim\pgfmathresult pt<-\anglestep pt\relax% + \else% + \let\endangle\pgfmathresult% + \repeatpgfmathloop% + \def\angle{0}% + \let\lastangle\angle% + \pgfmathloop% + \pgfmathadd@{\endangle}{\anglestep}% + \let\endangle\pgfmathresult% + \pgfextract@process\miterpoint{% + \pgfextract@process\secondpoint{% + \pgfpointpolar{+\endangle}{+\xinnerradius and +\yinnerradius}% + }% + \pgfmathadd@{\endangle}{\anglestep}% + \let\angletemp\pgfmathresult% + \pgfextract@process\thirdpoint{% + \pgfpointpolar{+\angletemp}{+\xinnerradius and +\yinnerradius}% + }% + \pgfmathsubtract@{\endangle}{\anglestep}% + \let\angletemp\pgfmathresult% + \pgfextract@process\firstpoint{% + \pgfpointpolar{+\angletemp}{+\xinnerradius and +\yinnerradius}% + }% + \pgfmathanglebetweenpoints{\firstpoint}{\secondpoint}% + \let\anglealpha\pgfmathresult% + \pgfmathanglebetweenpoints{\secondpoint}{\thirdpoint}% + \let\anglebeta\pgfmathresult% + \pgfmathsubtract@{\anglebeta}{\anglealpha}% + \pgfmathdivide@{\pgfmathresult}{2}% + \pgfmathadd@{\pgfmathresult}{\halfcomplementarc}% + \pgfmathcosec@{\pgfmathresult}% + \pgf@x\outersep\relax% + \pgf@x\pgfmathresult\pgf@x% + \edef\miterradius{\the\pgf@x}% + \pgfmathadd@{\anglealpha}{\anglebeta}% + \pgfmathsubtract@{\pgfmathresult}{180}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\miterangle\pgfmathresult% + \pgfpointadd{\secondpoint}{% + \pgfqpointpolar{\miterangle}{\miterradius}% + }% + }% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\miterpoint}% + \let\angle\pgfmathresult% + \ifdim\angle pt<\lastangle pt\relax% + \pgfmathadd@{\angle}{360}% + \let\angle\pgfmathresult% + \fi% + \let\lastangle\angle% + \ifdim\externalangle pt>\angle pt\relax% + \repeatpgfmathloop% + \pgfmathmod@{\endangle}{360}% + \let\endangle\pgfmathresult% + \pgfmathsubtract@{\endangle}{\anglestep}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\startangle\pgfmathresult% + \pgfextract@process\arcstartpoint{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{+\startangle}{+\xinnerradius and +\yinnerradius}% + }% + }% + \pgfextract@process\arcendpoint{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{+\endangle}{+\xinnerradius and +\yinnerradius}% + }% + }% + \pgf@sh@getcloudpuffparameters% + \ifdim\endangle pt<\startangle pt\relax% + \pgfmathadd@{\externalangle}{180}% + \pgfmathmod@{\pgfmathresult}{360}% + \let\x\pgfmathresult% + \else% + \let\x\externalangle% + \fi% + \let\s\halfcomplementarc% + \pgfmathadd@{\s}{\arc}% + \let\e\pgfmathresult% + \pgfmathadd@{\e}{\s}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\n\pgfmathresult% + \def\m{360}% + \pgfmathloop% + \pgfmathadd@{\e}{\s}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\p\pgfmathresult% + \ifdim\p pt=\s pt\relax% + \else% + \pgfmathadd@{\p}{\arcslope}% + \let\a\pgfmathresult% + \pgfextract@process\arcpoint{% + \pgfpointadd{\circlecenterpoint}{% + \pgfqpointpolar{\a}{\outerarcradius}% + }% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\arcpoint}% + \ifdim\endangle pt<\startangle pt\relax% + \pgfmathadd@{\pgfmathresult}{180}% + \pgfmathmod@{\pgfmathresult}{360}% + \fi% + \let\q\pgfmathresult% + \ifdim\x pt=\q pt% + \pgfmathbreakloop% + \else + \ifdim\x pt<\q pt\relax% + \let\e\p% + \else% + \let\s\p% + \fi% + \fi% + \pgfmathsubtract@{\x}{\q}% + \pgfmathabs@{\pgfmathresult}% + \ifdim\pgfmathresult pt<\m pt\relax% + \let\m\pgfmathresult% + \let\n\p% + \fi% + \repeatpgfmathloop% + \pgfmathadd@{\n}{\arcslope}% + \let\anchorangle\pgfmathresult% + \pgfpointadd{\circlecenterpoint}{% + \pgfqpointpolar{\anchorangle}{\outerarcradius}% + }% + \fi% + }% + \pgfutil@g@addto@macro\pgf@sh@s@cloud{% + \c@pgf@counta\puffs\relax% + \pgfmathloop% + \ifnum\c@pgf@counta>0\relax% + \pgfutil@ifundefined{pgf@anchor@cloud@puff\space\the\c@pgf@counta}{% + \expandafter\xdef\csname pgf@anchor@cloud@puff\space\the\c@pgf@counta\endcsname{% + \noexpand\pgf@sh@@cloudpuffanchor{\the\c@pgf@counta}% + }% + }{\c@pgf@counta0\relax}% + \advance\c@pgf@counta-1\relax% + \repeatpgfmathloop% + }% +}% + +\def\pgf@sh@@cloudpuffanchor#1{% + \getradii% + \pgfmathdivide@{\anglestep}{2}% + \let\halfanglestep\pgfmathresult% + \c@pgf@counta#1\relax% + \advance\c@pgf@counta-1\relax% + \pgfmathmultiply@{\anglestep}{\the\c@pgf@counta}% + \pgfmathadd@{\pgfmathresult}{90}% + \pgfmathsubtract@{\pgfmathresult}{\halfanglestep}% + \let\angle\pgfmathresult% + \pgfextract@process\arcstartpoint{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{+\angle}{+\xinnerradius and +\yinnerradius}% + }% + }% + \pgfmathadd@{\angle}{\anglestep}% + \let\angle\pgfmathresult% + \pgfextract@process\arcendpoint{% + \pgfpointadd{\centerpoint}{% + \pgfpointpolar{+\angle}{+\xinnerradius and +\yinnerradius}% + }% + }% + \pgf@sh@getcloudpuffparameters% + \pgfmathadd@{\arcslope}{90}% + \let\anchorangle\pgfmathresult% + \pgfpointadd{\circlecenterpoint}{% + \pgfqpointpolar{\anchorangle}{\outerarcradius}% + }% +}% + +\def\pgf@sh@getcloudpuffparameters{% + \pgfmathanglebetweenpoints{\arcendpoint}{\arcstartpoint}% + \let\arcslope\pgfmathresult% + \pgfpointdiff{\arcendpoint}{\arcstartpoint}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}} + \pgf@x\pgfmathresult pt\relax% + \pgf@xa.5\pgf@x% + \edef\halfchordlength{\the\pgf@xa}% + \pgf@x\arcradiusquotient\pgf@x% + \edef\arcradius{\the\pgf@x}% + \pgf@xa\outersep\relax% + \advance\pgf@xa\pgf@x% + \edef\outerarcradius{\the\pgf@xa}% + \pgf@y-\sinhalfcomplementarc\pgf@x% + \advance\pgf@y\pgf@x% + \edef\segmentheight{\the\pgf@y}% + \pgfextract@process\circlecenterpoint{% + \pgfextract@process\circlecenterpoint{% + \pgf@x-\halfchordlength\relax% + \pgf@y\segmentheight\relax% + \advance\pgf@y-\arcradius + }% + \pgfpointadd{\arcstartpoint}{% + \pgfmathrotatepointaround{\circlecenterpoint}{\pgfpointorigin}{\arcslope}% + }% + }% +}% + + + + + +\def\pgf@lib@sh@signal@nowhere{nowhere}% +\def\pgf@lib@sh@signal@from{from}% +\def\pgf@lib@sh@signal@to{to}% + +\def\pgf@lib@sh@signal@parsedirection#1#2{% + \let\pgf@lib@sh@signal@direction=#2% + \edef\pgf@lib@sh@temp{#1}% + \expandafter\pgf@lib@sh@signal@@parsedirection\pgf@lib@sh@temp\pgf@stop}% + +\def\pgf@lib@sh@signal@@parsedirection#1\pgf@stop{% + \pgfutil@in@{and}{#1}% + \ifpgfutil@in@% + \pgf@lib@sh@signal@@@parsedirection#1\pgf@lib% + \else% + \pgf@lib@sh@signal@@@parsedirection#1 and #1\pgf@lib% + \fi +}% +\def\pgf@lib@sh@signal@@@parsedirection#1 and #2\pgf@lib{% + \pgfutil@in@{nowhere}{#1}% + \ifpgfutil@in@ + \else% + \pgf@lib@sh@signal@@@@parsedirection{#1}% + \pgf@lib@sh@signal@@@@parsedirection{#2}% + \fi% +}% +\def\pgf@lib@sh@signal@@@@parsedirection#1{% + \pgfutil@in@{ #1 }{ east right }% + \ifpgfutil@in@% + \let\pgf@lib@sh@signal@east=\pgf@lib@sh@signal@direction% + \let\pgf@lib@sh@signal@north=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@south=\pgf@lib@sh@signal@nowhere% + \fi% + \pgfutil@in@{ #1 }{ left west }% + \ifpgfutil@in@% + \let\pgf@lib@sh@signal@west=\pgf@lib@sh@signal@direction% + \let\pgf@lib@sh@signal@north=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@south=\pgf@lib@sh@signal@nowhere% + \fi% + \pgfutil@in@{ #1 }{ above up north }% + \ifpgfutil@in@% + \let\pgf@lib@sh@signal@north=\pgf@lib@sh@signal@direction% + \let\pgf@lib@sh@signal@east=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@west=\pgf@lib@sh@signal@nowhere% + \fi% + \pgfutil@in@{ #1 }{ below down south }% + \ifpgfutil@in@% + \let\pgf@lib@sh@signal@south=\pgf@lib@sh@signal@direction% + \let\pgf@lib@sh@signal@east=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@west=\pgf@lib@sh@signal@nowhere% + \fi% +}% + + +\pgfkeys{/pgf/.cd, + signal pointer angle/.initial=90, + signal to/.initial=east, + signal from/.initial=nowhere, +}% + +\pgfdeclareshape{signal}{% + \savedmacro\installsignalparameters{% + \let\pgf@lib@sh@signal@north=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@south=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@east=\pgf@lib@sh@signal@nowhere% + \let\pgf@lib@sh@signal@west=\pgf@lib@sh@signal@nowhere% + \pgf@lib@sh@signal@parsedirection{\pgfkeysvalueof{/pgf/signal from}}{\pgf@lib@sh@signal@from}% + \pgf@lib@sh@signal@parsedirection{\pgfkeysvalueof{/pgf/signal to}}{\pgf@lib@sh@signal@to}% + \pgfextract@process\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \pgfmathsetmacro\pointerangle{\pgfkeysvalueof{/pgf/signal pointer angle}}% + \pgfmathdivide@{\pointerangle}{2}% + \let\halfpointerangle=\pgfmathresult% + \pgfmathcosec@{\halfpointerangle}% + \let\cosechalfpointerangle=\pgfmathresult% + \pgfmathdivide@{\halfpointerangle}{2}% + \let\quarterpointerangle=\pgfmathresult% + \pgfmathcosec@{\quarterpointerangle}% + \let\cosecquarterpointerangle=\pgfmathresult% + \pgfmathsec@{\quarterpointerangle}% + \let\secquarterpointerangle=\pgfmathresult% + \pgfmathsubtract@{90}{\quarterpointerangle}% + \let\complementquarterpointerangle\pgfmathresult% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@x>\pgf@y% + \pgf@y\pgf@x% + \fi% + \pgf@yc=\pgf@y% + \pgf@x=\cosechalfpointerangle\pgf@y% + \edef\pointerapexmiter{\the\pgf@x}% + \pgf@x=\secquarterpointerangle\pgf@y% + \edef\tocornermiter{\the\pgf@x}% + \pgf@x=\cosecquarterpointerangle\pgf@y + \edef\fromcornermiter{\the\pgf@x}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya.5\ht\pgfnodeparttextbox% + \advance\pgf@ya.5\dp\pgfnodeparttextbox% + \pgfmathsubtract@{90}{\halfpointerangle}% + \pgfmathtan@{\pgfmathresult}% + \pgf@xb=\pgfmathresult\pgf@ya% + \pgf@yb=\pgfmathresult\pgf@xa% + \pgfutil@tempdima=2.0\pgf@ya% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by\pgf@yb% + \fi% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by\pgf@yb% + \fi% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgfutil@tempdima<\pgf@y% + \pgfutil@tempdima=\pgf@y% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by-\pgf@yb% + \fi% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by-\pgf@yb% + \fi% + \pgf@ya=0.5\pgfutil@tempdima% + \pgfmathsubtract@{90}{\halfpointerangle}% + \pgfmathtan@{\pgfmathresult}% + \pgf@xb=\pgfmathresult\pgf@ya% + \fi% + \pgfutil@tempdima=2.0\pgf@xa% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by\pgf@xb% + \fi% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by\pgf@xb% + \fi% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgfutil@tempdima<\pgf@x% + \pgfutil@tempdima=\pgf@x% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@nowhere% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \pgf@xa=0.5\pgfutil@tempdima% + \pgfmathsubtract@{90}{\halfpointerangle}% + \pgfmathtan@{\pgfmathresult}% + \pgf@yb=\pgfmathresult\pgf@xa% + \fi% + \pgfextract@process\north{% + \centerpoint% + \advance\pgf@y\pgf@ya% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@to% + \advance\pgf@y\pgf@yb% + \fi% + }% + \pgfextract@process\south{% + \centerpoint% + \advance\pgf@y-\pgf@ya% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@to% + \advance\pgf@y-\pgf@yb% + \fi% + }% + \pgfextract@process\east{% + \centerpoint% + \advance\pgf@x\pgf@xa% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@to% + \advance\pgf@x\pgf@xb% + \fi% + }% + \pgfextract@process\west{% + \centerpoint% + \advance\pgf@x-\pgf@xa% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@to% + \advance\pgf@x-\pgf@xb% + \fi% + }% + \pgfextract@process\northeast{% + \centerpoint% + \advance\pgf@y\pgf@ya% + \advance\pgf@x\pgf@xa% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@from% + \advance\pgf@y\pgf@yb% + \fi% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@from% + \advance\pgf@x\pgf@xb% + \fi% + }% + \pgfextract@process\southeast{% + \centerpoint% + \advance\pgf@y-\pgf@ya% + \advance\pgf@x\pgf@xa% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@from% + \advance\pgf@y-\pgf@yb% + \fi% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@from% + \advance\pgf@x\pgf@xb% + \fi% + }% + \pgfextract@process\southwest{% + \centerpoint% + \advance\pgf@y-\pgf@ya% + \advance\pgf@x-\pgf@xa% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@from% + \advance\pgf@y-\pgf@yb% + \fi% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@from% + \advance\pgf@x-\pgf@xb% + \fi% + }% + \pgfextract@process\northwest{% + \centerpoint% + \advance\pgf@y\pgf@ya% + \advance\pgf@x-\pgf@xa% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@from% + \advance\pgf@y\pgf@yb% + \fi% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@from% + \advance\pgf@x-\pgf@xb% + \fi% + }% + \addtosavedmacro{\north}% + \addtosavedmacro{\south}% + \addtosavedmacro{\east}% + \addtosavedmacro{\west}% + \addtosavedmacro{\northeast}% + \addtosavedmacro{\southwest}% + \addtosavedmacro{\southeast}% + \addtosavedmacro{\northwest}% + \pgfextract@process\northmiter{% + \pgf@x0pt% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@nowhere% + \pgf@y\pgf@yc% + \else% + \pgf@y\pointerapexmiter\relax% + \fi% + }% + \pgfextract@process\southmiter{% + \pgf@x0pt% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@nowhere% + \pgf@y-\pgf@yc% + \else% + \pgf@y-\pointerapexmiter\relax% + \fi% + }% + \pgfextract@process\eastmiter{% + \pgf@y0pt% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@nowhere% + \pgf@x\pgf@yc% + \else% + \pgf@x\pointerapexmiter\relax% + \fi% + }% + \pgfextract@process\westmiter{% + \pgf@y0pt% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@nowhere% + \pgf@x-\pgf@yc% + \else% + \pgf@x-\pointerapexmiter\relax% + \fi% + }% + \pgfextract@process\northeastmiter{% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@nowhere% + \pgf@x\pgf@yc + \pgf@y\pgf@yc% + \else + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@from% + \pgfqpointpolar{\quarterpointerangle}{\fromcornermiter} + \else% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@to% + \pgfqpointpolar{\complementquarterpointerangle}{\tocornermiter}% + \fi% + \fi% + \fi% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@from% + \pgfqpointpolar{\complementquarterpointerangle}{\fromcornermiter}% + \else% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@to% + \pgfqpointpolar{\quarterpointerangle}{\tocornermiter}% + \fi% + \fi% + }% + \pgfextract@process\southeastmiter{% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@nowhere% + \pgf@x\pgf@yc% + \pgf@y\pgf@yc% + \else + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@from% + \pgfqpointpolar{-\quarterpointerangle}{\fromcornermiter} + \else% + \ifx\pgf@lib@sh@signal@east\pgf@lib@sh@signal@to% + \pgfqpointpolar{-\complementquarterpointerangle}{\tocornermiter}% + \fi% + \fi% + \fi% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@from% + \pgfqpointpolar{-\complementquarterpointerangle}{\fromcornermiter} + \else% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@to% + \pgfqpointpolar{-\quarterpointerangle}{\tocornermiter}% + \fi% + \fi% + }% + \pgfextract@process\southwestmiter{% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@nowhere% + \pgf@x-\pgf@yc + \pgf@y-\pgf@yc% + \else + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@from% + \pgfmathadd@{\quarterpointerangle}{180}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\fromcornermiter} + \else% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@to% + \pgfmathadd@{\complementquarterpointerangle}{180}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\tocornermiter}% + \fi% + \fi% + \fi% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@from% + \pgfmathadd@{\complementquarterpointerangle}{180}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\fromcornermiter}% + \else% + \ifx\pgf@lib@sh@signal@south\pgf@lib@sh@signal@to% + \pgfmathadd@{\quarterpointerangle}{180}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\tocornermiter}% + \fi% + \fi% + }% + \pgfextract@process\northwestmiter{% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@nowhere% + \pgf@x-\pgf@yc% + \pgf@y\pgf@yc% + \else + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@from% + \pgfmathsubtract@{180}{\quarterpointerangle}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\fromcornermiter} + \else% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@to% + \pgfmathsubtract@{180}{\complementquarterpointerangle}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\tocornermiter}% + \fi% + \fi% + \fi% + \ifx\pgf@lib@sh@signal@north\pgf@lib@sh@signal@from% + \pgfmathsubtract@{180}{\complementquarterpointerangle}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\fromcornermiter}% + \else% + \ifx\pgf@lib@sh@signal@west\pgf@lib@sh@signal@to% + \pgfmathsubtract@{180}{\quarterpointerangle}% + \expandafter\pgfqpointpolar\expandafter{\pgfmathresult}{\tocornermiter}% + \fi% + \fi% + }% + \addtosavedmacro{\northmiter}% + \addtosavedmacro{\southmiter}% + \addtosavedmacro{\eastmiter}% + \addtosavedmacro{\westmiter}% + \addtosavedmacro{\northeastmiter}% + \addtosavedmacro{\southeastmiter}% + \addtosavedmacro{\southwestmiter}% + \addtosavedmacro{\northwestmiter}% + \pgfextract@process\anchornorth{% + \pgfpointadd{\north}{\northmiter}% + }% + \pgfextract@process\anchorsouth{% + \pgfpointadd{\south}{\southmiter}% + }% + \pgfextract@process\anchoreast{% + \pgfpointadd{\east}{\eastmiter}% + }% + \pgfextract@process\anchorwest{% + \pgfpointadd{\west}{\westmiter}% + }% + \pgfextract@process\anchornortheast{% + \pgfpointadd{\northeast}{\northeastmiter}% + }% + \pgfextract@process\anchorsoutheast{% + \pgfpointadd{\southeast}{\southeastmiter}% + }% + \pgfextract@process\anchorsouthwest{% + \pgfpointadd{\southwest}{\southwestmiter}% + }% + \pgfextract@process\anchornorthwest{% + \pgfpointadd{\northwest}{\northwestmiter}% + }% + \addtosavedmacro{\anchornorth}% + \addtosavedmacro{\anchorsouth}% + \addtosavedmacro{\anchoreast}% + \addtosavedmacro{\anchorwest}% + \addtosavedmacro{\anchornortheast}% + \addtosavedmacro{\anchorsouthwest}% + \addtosavedmacro{\anchorsoutheast}% + \addtosavedmacro{\anchornorthwest}% + }% + \savedanchor\centerpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor\basepoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \savedanchor\midpoint{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+.5ex}% + }% + \anchor{center}{\centerpoint}% + \anchor{base}{\basepoint}% + \anchor{base east}{% + \installsignalparameters% + \anchoreast% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \anchorsoutheast% + \ifdim\pgf@xa>\pgf@x% + \pgfutil@tempdima\pgf@xa% + \else% + \pgfutil@tempdima\pgf@x% + \fi% + \pgfextract@process\externalpoint{% + \basepoint% + \pgf@x\pgfutil@tempdima% + } + \basepoint% + \let\firstpoint\anchoreast% + \ifdim\pgf@y<\pgf@ya% + \let\secondpoint\anchorsoutheast% + \else% + \let\secondpoint\anchornortheast% + \fi% + \pgfpointintersectionoflines{\basepoint}{\externalpoint}% + {\firstpoint}{\secondpoint}% + }% + \anchor{base west}{% + \installsignalparameters% + \anchorwest% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \anchorsouthwest% + \ifdim\pgf@xa<\pgf@x% + \pgfutil@tempdima\pgf@xa% + \else% + \pgfutil@tempdima\pgf@x% + \fi% + \pgfextract@process\externalpoint{% + \basepoint% + \pgf@x\pgfutil@tempdima% + } + \basepoint% + \let\firstpoint\anchorwest% + \ifdim\pgf@y<\pgf@ya% + \let\secondpoint\anchorsouthwest% + \else% + \let\secondpoint\anchornorthwest% + \fi% + \pgfpointintersectionoflines{\basepoint}{\externalpoint}% + {\firstpoint}{\secondpoint}% + }% + \anchor{mid}{\midpoint}% + \anchor{mid east}{% + \installsignalparameters% + \anchoreast% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \anchorsoutheast% + \ifdim\pgf@xa>\pgf@x% + \pgfutil@tempdima\pgf@xa% + \else% + \pgfutil@tempdima\pgf@x% + \fi% + \pgfextract@process\externalpoint{% + \midpoint% + \pgf@x\pgfutil@tempdima% + } + \midpoint% + \let\firstpoint\anchoreast% + \ifdim\pgf@y<\pgf@ya% + \let\secondpoint\anchorsoutheast% + \else% + \let\secondpoint\anchornortheast% + \fi% + \pgfpointintersectionoflines{\midpoint}{\externalpoint}% + {\firstpoint}{\secondpoint}% + }% + \anchor{mid west}{% + \installsignalparameters% + \anchorwest% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \anchorsouthwest% + \ifdim\pgf@xa<\pgf@x% + \pgfutil@tempdima\pgf@xa% + \else% + \pgfutil@tempdima\pgf@x% + \fi% + \pgfextract@process\externalpoint{% + \midpoint% + \pgf@x\pgfutil@tempdima% + } + \midpoint% + \let\firstpoint\anchorwest% + \ifdim\pgf@y<\pgf@ya% + \let\secondpoint\anchorsouthwest% + \else% + \let\secondpoint\anchornorthwest% + \fi% + \pgfpointintersectionoflines{\midpoint}{\externalpoint}% + {\firstpoint}{\secondpoint}% + }% + \anchor{north}{\installsignalparameters\anchornorth}% + \anchor{south}{\installsignalparameters\anchorsouth}% + \anchor{east}{\installsignalparameters\anchoreast}% + \anchor{west}{\installsignalparameters\anchorwest}% + \anchor{north east}{\installsignalparameters\anchornortheast}% + \anchor{south east}{\installsignalparameters\anchorsoutheast}% + \anchor{south west}{\installsignalparameters\anchorsouthwest}% + \anchor{north west}{\installsignalparameters\anchornorthwest}% + \backgroundpath{% + \installsignalparameters% + \pgfpathmoveto{\north}% + \pgfpathlineto{\northeast}% + \pgfpathlineto{\east}% + \pgfpathlineto{\southeast}% + \pgfpathlineto{\south}% + \pgfpathlineto{\southwest}% + \pgfpathlineto{\west}% + \pgfpathlineto{\northwest}% + \pgfpathclose% + }% + \anchorborder{% + \edef\externalx{\the\pgf@x}% + \edef\externaly{\the\pgf@y}% + \centerpoint% + \pgf@xa\externalx\relax% + \pgf@ya\externaly\relax% + \advance\pgf@xa\pgf@x% + \advance\pgf@ya\pgf@y% + \edef\externalx{\the\pgf@xa}% + \edef\externaly{\the\pgf@ya}% + \installsignalparameters% + \pgfmathanglebetweenpoints{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + \let\externalangle\pgfmathresult% + \pgfmathanglebetweenpoints{\centerpoint}{\anchorwest}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\anchornorth}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\anchornortheast}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \let\firstpoint\anchoreast% + \let\secondpoint\anchornortheast% + \else% + \let\secondpoint\anchornortheast% + \let\firstpoint\anchornorth% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\anchornorthwest}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \let\firstpoint\anchornorth% + \let\secondpoint\anchornorthwest% + \else% + \let\secondpoint\anchornorthwest% + \let\firstpoint\anchorwest% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\anchorsouth}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \pgfmathanglebetweenpoints{\centerpoint}{\anchorsouthwest}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \let\firstpoint\anchorwest% + \let\secondpoint\anchorsouthwest% + \else% + \let\secondpoint\anchorsouthwest% + \let\firstpoint\anchorsouth% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\anchorsoutheast}% + \ifdim\externalangle pt<\pgfmathresult pt\relax% + \let\firstpoint\anchorsouth% + \let\secondpoint\anchorsoutheast% + \else% + \let\secondpoint\anchorsoutheast% + \let\firstpoint\anchoreast% + \fi% + \fi% + \fi% + \pgfpointintersectionoflines{\centerpoint}{\pgfqpoint{\externalx}{\externaly}}% + {\firstpoint}{\secondpoint}% + }% +}% + + + + + + +\pgfkeys{/pgf/.cd, + tape bend top/.initial=in and out, + tape bend bottom/.initial=in and out, + tape bend/.style={/pgf/tape bend top={#1}, /pgf/tape bend bottom={#1}}, + tape bend height/.initial=5pt, +}% + +\def\pgf@lib@sh@inandouttext{in and out}% +\def\pgf@lib@sh@outandintext{out and in}% +\def\pgf@lib@sh@nonetext{none}% + +\pgfdeclareshape{tape}{% + \savedmacro\tapedimensions{% + \pgfmathsetlength\pgf@x{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y.5\dp\pgfnodeparttextbox% + \pgfmathsetlengthmacro\outerxsep{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlengthmacro\outerysep{\pgfkeysvalueof{/pgf/outer ysep}}% + \addtosavedmacro\outerxsep% + \addtosavedmacro\outerysep% + \pgfmathsetlength\pgfutil@tempdima{\pgfkeysvalueof{/pgf/tape bend height}}% + \pgfutil@tempdima.5\pgfutil@tempdima% + \edef\halfbendheight{\the\pgfutil@tempdima}% + \addtosavedmacro\halfbendheight% + \pgfkeysgetvalue{/pgf/tape bend top}{\topbendstyle}% + \pgfkeysgetvalue{/pgf/tape bend bottom}{\bottombendstyle}% + \addtosavedmacro\topbendstyle% + \addtosavedmacro\bottombendstyle% + \ifx\topbendstyle\pgf@lib@sh@nonetext% + \else% + \advance\pgf@y\pgfutil@tempdima% + \fi% + \ifx\bottombendstyle\pgf@lib@sh@none% + \else% + \advance\pgf@y\pgfutil@tempdima% + \fi% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<.5\pgf@xa% + \pgf@x.5\pgf@xa% + \fi% + \ifdim\pgf@y<.5\pgf@ya% + \pgf@y.5\pgf@ya% + \fi% + \ifx\topbendstyle\pgf@lib@sh@nonetext% + \else% + \advance\pgf@y-\pgfutil@tempdima% + \fi% + \ifx\bottombendstyle\pgf@lib@sh@nonetext% + \else% + \advance\pgf@y-\pgfutil@tempdima% + \fi% + \pgfutil@tempdima3.414213\pgfutil@tempdima% + \edef\bendyradius{\the\pgfutil@tempdima}% + \addtosavedmacro\bendyradius% + \advance\pgfutil@tempdima\outerysep% + \edef\outerbendyradius{\the\pgfutil@tempdima}% + \addtosavedmacro\outerbendyradius% + \advance\pgfutil@tempdima-\outerysep% + \advance\pgfutil@tempdima-\outerysep% + \edef\innerbendyradius{\the\pgfutil@tempdima}% + \addtosavedmacro\innerbendyradius% + \pgfutil@tempdima0.707106\pgf@x% + \edef\bendxradius{\the\pgfutil@tempdima}% + \addtosavedmacro\bendxradius% + \advance\pgfutil@tempdima\outerxsep% + \edef\outerbendxradius{\the\pgfutil@tempdima}% + \addtosavedmacro\outerbendxradius% + \advance\pgfutil@tempdima-\outerxsep% + \advance\pgfutil@tempdima-\outerxsep% + \edef\innerbendxradius{\the\pgfutil@tempdima}% + \addtosavedmacro\innerbendxradius% + \edef\halfwidth{\the\pgf@x}% + \edef\halfheight{\the\pgf@y}% + \addtosavedmacro\halfwidth% + \addtosavedmacro\halfheight% + \advance\pgf@x\outerxsep% + \edef\outerhalfwidth{\the\pgf@x}% + \addtosavedmacro\outerhalfwidth% + \pgf@xc\bendxradius% + \pgf@yc\bendyradius% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@yc}}{\pgfmath@tonumber{\pgf@xc}}% + \pgfmathatan{\pgfmathresult}% + \pgf@xc\pgfmathresult pt\relax% + \pgf@xc.5\pgf@xc% + \edef\halfangle{\pgfmath@tonumber{\pgf@xc}}% + \addtosavedmacro\halfangle% + \pgf@xc45pt\relax% + \advance\pgf@xc-\halfangle pt% + \pgfmathcot@{\pgfmath@tonumber{\pgf@xc}}% + \let\cothalfanglein\pgfmathresult% + \addtosavedmacro\cothalfanglein% + \pgf@xc90pt\relax% + \advance\pgf@xc-\halfangle pt% + \pgfmathcot@{\pgfmath@tonumber{\pgf@xc}}% + \let\cothalfangleout\pgfmathresult% + \addtosavedmacro\cothalfangleout% + }% + \savedanchor{\centerpoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y.5\ht\pgfnodeparttextbox% + \advance\pgf@y-.5\dp\pgfnodeparttextbox% + }% + \savedanchor{\midpoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@y{+0.5ex}% + }% + \savedanchor{\basepoint}{% + \pgf@x.5\wd\pgfnodeparttextbox% + \pgf@y0pt% + }% + \anchor{center}{\centerpoint}% + \anchor{mid}{\midpoint}% + \anchor{mid east}{\tapedimensions\midpoint\advance\pgf@x\outerhalfwidth}% + \anchor{mid west}{\tapedimensions\midpoint\advance\pgf@x-\outerhalfwidth}% + \anchor{base}{\basepoint}% + \anchor{base east}{\tapedimensions\basepoint\advance\pgf@x\outerhalfwidth}% + \anchor{base west}{\tapedimensions\basepoint\advance\pgf@x-\outerhalfwidth}% + \anchor{north}{% + \csname pgf@anchor@tape@north east\endcsname% + \pgf@ya\pgf@y% + \csname pgf@anchor@tape@north west\endcsname% + \advance\pgf@ya\pgf@y% + \centerpoint% + \pgf@y.5\pgf@ya% + }% + \anchor{south}{% + \csname pgf@anchor@tape@south east\endcsname% + \pgf@ya\pgf@y% + \csname pgf@anchor@tape@south west\endcsname% + \advance\pgf@ya\pgf@y% + \centerpoint% + \pgf@y.5\pgf@ya% + }% + \anchor{east}{% + \tapedimensions% + \centerpoint% + \advance\pgf@x\outerhalfwidth% + }% + \anchor{west}{% + \tapedimensions% + \centerpoint% + \advance\pgf@x-\outerhalfwidth% + }% + \anchor{north east}{% + \tapedimensions% + \centerpoint% + \advance\pgf@x\outerhalfwidth% + \advance\pgf@y\halfheight% + \pgf@yc\outerysep% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \advance\pgf@y\halfbendheight% + \advance\pgf@y\cothalfangleout\pgf@yc% + \else% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \advance\pgf@y\halfbendheight% + \advance\pgf@y\cothalfanglein\pgf@yc% + \else% + \advance\pgf@y\pgf@yc% + \fi% + \fi% + }% + \anchor{north west}{% + \tapedimensions% + \centerpoint% + \advance\pgf@x-\outerhalfwidth% + \advance\pgf@y\halfheight% + \pgf@yc\outerysep% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \advance\pgf@y\halfbendheight% + \advance\pgf@y\cothalfanglein\pgf@yc% + \else% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \advance\pgf@y\halfbendheight% + \advance\pgf@y\cothalfangleout\pgf@yc% + \else% + \advance\pgf@y\pgf@yc% + \fi% + \fi% + }% + \anchor{south east}{% + \tapedimensions% + \centerpoint% + \advance\pgf@x\outerhalfwidth% + \advance\pgf@y-\halfheight% + \pgf@yc\outerysep% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \advance\pgf@y-\halfbendheight% + \advance\pgf@y-\cothalfangleout\pgf@yc% + \else% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \advance\pgf@y-\halfbendheight% + \advance\pgf@y-\cothalfanglein\pgf@yc% + \else% + \advance\pgf@y-\pgf@yc% + \fi% + \fi% + }% + \anchor{south west}{% + \tapedimensions% + \centerpoint% + \advance\pgf@x-\outerhalfwidth% + \advance\pgf@y-\halfheight% + \pgf@yc\outerysep% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \advance\pgf@y-\halfbendheight% + \advance\pgf@y-\cothalfanglein\pgf@yc% + \else% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \advance\pgf@y-\halfbendheight% + \advance\pgf@y-\cothalfangleout\pgf@yc% + \else% + \advance\pgf@y-\pgf@yc% + \fi% + \fi% + }% + \backgroundpath{% + \tapedimensions% + \pgf@xc\halfwidth% + \pgf@yc\halfheight% + \pgf@xc\bendxradius% + \pgf@yc\bendyradius% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfqpoint{-\halfwidth}{0pt}}% + \pgfpathlineto{\pgfqpoint{-\halfwidth}{\halfheight}}% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \pgfpathlineto{\pgf@x-\halfwidth\pgf@y\halfheight\advance\pgf@y\halfbendheight}% + \pgfpatharc{225}{315}{\bendxradius and \bendyradius}% + \pgfpatharc{135}{45}{\bendxradius and \bendyradius}% + \else% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \pgfpathlineto{\pgf@x-\halfwidth\pgf@y\halfheight\advance\pgf@y\halfbendheight}% + \pgfpatharc{135}{45}{\bendxradius and \bendyradius}% + \pgfpatharc{225}{315}{\bendxradius and \bendyradius}% + \else% + \pgfpathlineto{\pgfqpoint{\halfwidth}{\halfheight}}% + \fi% + \fi% + \pgfpathlineto{\pgfqpoint{\halfwidth}{-\halfheight}}% + \ifx\bottombendstyle\pgf@lib@sh@inandouttext% + \pgfpathlineto{\pgf@x\halfwidth\pgf@y-\halfheight\advance\pgf@y-\halfbendheight}% + \pgfpatharc{45}{135}{\bendxradius and \bendyradius}% + \pgfpatharc{315}{225}{\bendxradius and \bendyradius}% + \else% + \ifx\bottombendstyle\pgf@lib@sh@outandintext% + \pgfpathlineto{\pgf@x\halfwidth\pgf@y-\halfheight\advance\pgf@y-\halfbendheight}% + \pgfpatharc{315}{225}{\bendxradius and \bendyradius}% + \pgfpatharc{45}{135}{\bendxradius and \bendyradius}% + \else% + \pgfpathlineto{\pgfqpoint{-\halfwidth}{-\halfheight}}% + \fi% + \fi% + \pgfpathclose% + }% + }% + \anchorborder{% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfextract@process\externalpoint{% + \centerpoint% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% + \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}% + \let\externalangle\pgfmathresult% + \tapedimensions% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@tape@north west\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt% + \ifdim\externalangle pt<90pt% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@tape@north east\endcsname}% + \ifdim\externalangle pt<\pgfmathresult pt% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@north east\endcsname}% + {\csname pgf@anchor@tape@south east\endcsname}% + \else% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x.5\pgf@xc% + \advance\pgf@y\halfheight% + \advance\pgf@y\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y-.707106\pgf@yc% + }% + {5}{175}{\outerbendxradius and \outerbendyradius}% + \else% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x.5\pgf@xc% + \advance\pgf@y\halfheight% + \advance\pgf@y\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y.707106\pgf@yc% + }% + {185}{355}{\innerbendxradius and \innerbendyradius}% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@north east\endcsname}% + {\csname pgf@anchor@tape@north west\endcsname}% + \fi% + \fi% + \fi% + \else% + \ifx\topbendstyle\pgf@lib@sh@inandouttext% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x-.5\pgf@xc% + \advance\pgf@y\halfheight% + \advance\pgf@y\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y.707106\pgf@yc% + }% + {185}{355}{\innerbendxradius and \innerbendyradius}% + \else% + \ifx\topbendstyle\pgf@lib@sh@outandintext% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x-.5\pgf@xc% + \advance\pgf@y\halfheight% + \advance\pgf@y\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y-.707106\pgf@yc% + }% + {5}{175}{\outerbendxradius and \outerbendyradius}% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@north east\endcsname}% + {\csname pgf@anchor@tape@north west\endcsname}% + \fi% + \fi% + \fi% + \else% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@tape@south west\endcsname}% + \ifdim\externalangle pt>\pgfmathresult pt% + \ifdim\externalangle pt>270pt% + \pgfmathanglebetweenpoints{\centerpoint}{\csname pgf@anchor@tape@south east\endcsname}% + \ifdim\externalangle pt>\pgfmathresult pt% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@north east\endcsname}% + {\csname pgf@anchor@tape@south east\endcsname}% + \else% + \ifx\bottombendstyle\pgf@lib@sh@inandouttext% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x.5\pgf@xc% + \advance\pgf@y-\halfheight% + \advance\pgf@y-\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y-.707106\pgf@yc% + }% + {5}{175}{\innerbendxradius and \innerbendyradius}% + \else% + \ifx\bottombendstyle\pgf@lib@sh@outandintext% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x.5\pgf@xc% + \advance\pgf@y-\halfheight% + \advance\pgf@y-\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y.707106\pgf@yc% + }% + {185}{355}{\outerbendxradius and \outerbendyradius}% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@south east\endcsname}% + {\csname pgf@anchor@tape@south west\endcsname}% + \fi% + \fi% + \fi% + \else% + \ifx\bottombendstyle\pgf@lib@sh@inandouttext% + \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x-.5\pgf@xc% + \advance\pgf@y-\halfheight% + \advance\pgf@y-\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y.707106\pgf@yc% + }% + {185}{355}{\outerbendxradius and \outerbendyradius}% + \else% + \ifx\bottombendstyle\pgf@lib@sh@outandintext% + \pgfmathpointintersectionoflineandarc{\centerpoint}{\externalpoint}% + {% + \centerpoint% + \pgf@xc\halfwidth% + \advance\pgf@x-.5\pgf@xc% + \advance\pgf@y-\halfheight% + \advance\pgf@y-\halfbendheight% + \pgf@yc\bendyradius% + \advance\pgf@y-.707106\pgf@yc% + }% + {5}{175}{\innerbendxradius and \innerbendyradius}% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@south east\endcsname}% + {\csname pgf@anchor@tape@south west\endcsname}% + \fi% + \fi% + \fi% + \else% + \pgfpointintersectionoflines{\externalpoint}{\centerpoint}% + {\csname pgf@anchor@tape@north west\endcsname}% + {\csname pgf@anchor@tape@south west\endcsname}% + \fi% + \fi% + }% +}% + + + + + +\pgfkeys{/pgf/.cd, + magnifying glass handle angle/.initial=-45, + magnifying glass handle aspect/.initial=1.5, +}% + +\pgfdeclareshape{magnifying glass} +{% + \inheritsavedanchors[from=circle]% + \inheritanchorborder[from=circle]% + \inheritanchor[from=circle]{north}% + \inheritanchor[from=circle]{north west}% + \inheritanchor[from=circle]{north east}% + \inheritanchor[from=circle]{center}% + \inheritanchor[from=circle]{west}% + \inheritanchor[from=circle]{east}% + \inheritanchor[from=circle]{mid}% + \inheritanchor[from=circle]{mid west}% + \inheritanchor[from=circle]{mid east}% + \inheritanchor[from=circle]{base}% + \inheritanchor[from=circle]{base west}% + \inheritanchor[from=circle]{base east}% + \inheritanchor[from=circle]{south}% + \inheritanchor[from=circle]{south west}% + \inheritanchor[from=circle]{south east}% + \inheritbackgroundpath[from=circle]% + \foregroundpath{ + \centerpoint% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgfutil@tempdima by-\pgf@yb% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \pgfpathmoveto{\pgfpointadd{\pgfqpoint{\pgf@xc}{\pgf@yc}} + {\pgfpointpolar{\pgfkeysvalueof{/pgf/magnifying glass handle angle}}{\pgfutil@tempdima}}} + \pgfpathlineto{\pgfpointadd{\pgfqpoint{\pgf@xc}{\pgf@yc}} + {\pgfpointpolar{\pgfkeysvalueof{/pgf/magnifying glass handle angle}}{\pgfutil@tempdima+\pgfutil@tempdima*(\pgfkeysvalueof{/pgf/magnifying glass handle aspect})}}} + \pgfsetarrowsstart{} + \pgfsetarrowsend{} + }% +}% + + +\pgfkeys{% + /pgf/magnetic tape tail/.initial=0.15, + /pgf/magnetic tape tail extend/.initial=0cm, +}% +\pgfdeclareshape{magnetic tape}{% + \nodeparts{text}% + \savedmacro\installparameters{% + \pgf@x=0.5\wd\pgfnodeparttextbox% + \pgf@y=0.5\ht\pgfnodeparttextbox% + \advance\pgf@y by-0.5\dp\pgfnodeparttextbox% + \edef\centerpoint{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@x=\wd\pgfnodeparttextbox% + \pgf@y=\ht\pgfnodeparttextbox% + \advance\pgf@y by\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/inner xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@x by2.0\pgf@xa% + \advance\pgf@y by2.0\pgf@ya% + \ifdim\pgf@y>\pgf@x% + \pgf@x=\pgf@y% + \fi% + \pgf@x=1.414213\pgf@x% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<\pgf@xa% + \pgf@x=\pgf@xa% + \fi% + \ifdim\pgf@x<\pgf@ya% + \pgf@x=\pgf@ya% + \fi% + \pgf@x=0.5\pgf@x% + \edef\radius{\the\pgf@x}% + \pgfmathparse{max(\pgfkeysvalueof{/pgf/magnetic tape tail extend},0)}% + \edef\tailextend{\pgfmathresult pt}% + \pgfmathparse{min(max(\pgfkeysvalueof{/pgf/magnetic tape tail},0),1)}% + \pgf@xa=\pgfmathresult\pgf@x% + \edef\tailheight{\the\pgf@xa}% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xa<\pgf@ya% + \pgf@xa=\pgf@ya% + \fi% + \edef\outersep{\the\pgf@xa}% + \pgfmathparse{\outersep+\radius}% + \edef\outerradius{\pgfmathresult pt}% + \pgfmathparse{(\radius-\tailheight)/\radius}% + \pgfmathasin@{\pgfmathresult}% + \pgfmathadd@{-\pgfmathresult}{360}% + \let\tailangle=\pgfmathresult% + \pgfmathparse{\outerradius/(\outerradius+\tailextend)}% + \pgfmathatan@{\pgfmathresult}% + \pgfmathadd@{-\pgfmathresult}{360}% + \let\tailbottomangle=\pgfmathresult% + \pgfmathparse{(\outerradius-\outersep-\tailheight-\outersep)/(\outerradius+\tailextend)}% + \pgfmathatan@{\pgfmathresult}% + \pgfmathadd@{-\pgfmathresult}{360}% + \let\tailtopangle=\pgfmathresult% + \addtosavedmacro\radius% + \addtosavedmacro\outerradius% + \addtosavedmacro\outersep% + \addtosavedmacro\tailheight% + \addtosavedmacro\tailextend + \addtosavedmacro\tailangle% + \addtosavedmacro\tailtopangle% + \addtosavedmacro\tailbottomangle% + \addtosavedmacro\centerpoint% + }% + \savedanchor{\base}{\pgfqpoint{0.5\wd\pgfnodeparttextbox}{0pt}}% + \savedanchor{\mid}{\pgfqpoint{0.5\wd\pgfnodeparttextbox}{0pt}\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{center}{\installparameters\centerpoint}% + \anchor{base}{\base}% + \anchor{mid}{\mid}% + \anchor{base west}{\installparameters\pgfpointadd{\base}{\pgfqpoint{-\outerradius}{0pt}}}% + \anchor{base east}{\installparameters\pgfpointadd{\base}{\pgfqpoint{\outerradius}{0pt}}}% + \anchor{mid west}{\installparameters\pgfpointadd{\mid}{\pgfqpoint{-\outerradius}{0pt}}}% + \anchor{mid east}{\installparameters\pgfpointadd{\mid}{\pgfqpoint{\outerradius}{0pt}}}% + \anchor{north}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpoint{0pt}{\outerradius}}}% + \anchor{north east}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpointpolar{45}{\outerradius}}}% + \anchor{south}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpoint{0pt}{-\outerradius}}}% + \anchor{south east}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpoint{\outerradius}{-\outerradius}}}% + \anchor{east}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpoint{\outerradius}{0pt}}}% + \anchor{south west}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpointpolar{225}{\outerradius}}}% + \anchor{west}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpoint{-\outerradius}{0pt}}}% + \anchor{north west}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfqpointpolar{135}{\outerradius}}}% + \anchor{tail east}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfpoint{\radius+\tailextend+\outersep}{-\outerradius+\outersep+\tailheight/2}}}% + \anchor{tail south east}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfpoint{\radius+\tailextend+\outersep}{-\outerradius}}}% + \anchor{tail north east}{\installparameters% + \pgfpointadd{\centerpoint}{\pgfpoint{\radius+\tailextend+\outersep}{-\outerradius+\outersep+\tailheight+\outersep}}}% + \backgroundpath{ + \installparameters% + {% + \pgftransformshift{\centerpoint}% + \pgfpathmoveto{\pgfpointpolar{\tailangle}{\radius}}% + \pgfpatharc{\tailangle}{360}{\radius}% + \pgfpatharc{0}{270}{\radius}% + \pgfpathlineto{\pgfpoint{\radius+\tailextend}{-\radius}}% + \pgfpathlineto{\pgfpoint{\radius+\tailextend}{-\radius+\tailheight}}% + \pgfpathclose% + }% + }% + \anchorborder{% + \pgfextract@process\externalpoint{}% + \installparameters% + \pgfmathanglebetweenpoints{\pgfpointorigin}{\externalpoint} + \ifdim\pgfmathresult pt<270pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointborderellipse% + {\externalpoint}% + {\pgfqpoint{\outerradius}{\outerradius}}% + }% + \else% + \ifdim\pgfmathresult pt<\tailbottomangle pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointintersectionoflines% + {\externalpoint}{\pgfpointorigin}% + {\pgfqpoint{0pt}{-\outerradius}}{\pgfqpoint{\outerradius}{-\outerradius}}% + }% + \else% + \ifdim\pgfmathresult pt<\tailtopangle pt\relax% + \pgfpointadd{\centerpoint}{% + \pgfpointintersectionoflines% + {\externalpoint}{\pgfpointorigin}% + {\pgfqpoint{\outerradius}{\outerradius}}{\pgfqpoint{\outerradius}{-\outerradius}}% + }% + \else% + \pgfpointadd{\centerpoint}{% + \pgfpointborderellipse% + {\externalpoint}% + {\pgfqpoint{\outerradius}{\outerradius}}% + }% + \fi% + \fi% + \fi% + }% +}% + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfint.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfint.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..0562146de73644d7a6765b5014ccb7bad4a8d0c4 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfint.code.tex @@ -0,0 +1,94 @@ + + +\ifx\pgfintloaded\pgfutil@undefined + \let\pgfintloaded=\relax +\else + \expandafter\endinput +\fi + + + +\def\pgfinteval#1{\number\numexpr#1\relax} + +\def\pgfintabs#1{\number\expandafter\pgfint@abs\number\numexpr#1\relax} +\def\pgfint@abs#1{\ifx-#1\else\expandafter#1\fi} + +\def\pgfintmax#1#2{% + \number\expandafter\pgfint@minmax + \number\numexpr#1\expandafter;% + \number\numexpr#2;% + > +} +\def\pgfintmin#1#2{% + \number\expandafter\pgfint@minmax + \number\numexpr#1\expandafter;% + \number\numexpr#2;% + < +} +\def\pgfint@minmax#1;#2;#3{% + \ifnum#1#3#2 + #1% + \else + #2% + \fi +} + +\def\pgfintdivtruncate#1#2{% + \number\numexpr\expandafter\pgfint@divtruncate + \number\numexpr#1\expandafter;% + \number\numexpr#2;% + \relax +} +\def\pgfint@divtruncate#1#2;#3#4;{% + \ifx0#1 + 0% + \else + (#1#2% + \ifx-#1 +\else-\fi + (\ifx-#3 -\fi#3#4-1)/2% + )% + \fi + /#3#4% +} + +\def\pgfintdivfloor#1#2{% + \number\numexpr\expandafter\pgfint@divfloor + \number\numexpr#1\expandafter;% + \number\numexpr#2;% + \relax +} +\def\pgfint@divfloor#1#2;#3#4;{% + \ifx0#1 + 0% + \else + \ifnum + 0\ifx-#1\ifx#3-\else1\fi\fi + 0\ifx-#3\ifx#1-\else1\fi\fi + >0 + \pgfint@@divfloor#1#2;#3#4;-+% + \else + \pgfint@@divfloor#1#2;#3#4;+-% + \fi + \fi + /#3#4% +} +\def\pgfint@@divfloor#1#2;#3#4;#5#6{% + (#1#2% + \ifx-#1 #5\else#6\fi + (\ifx-#3 -\fi#3#4#61)/2% + )% +} + +\def\pgfintdivround#1#2{\number\numexpr(#1)/(#2)\relax} + +\def\pgfintmod#1#2{% + \number\numexpr\expandafter\pgfint@mod% + \number\numexpr#1\expandafter;% + \number\numexpr#2;% + \relax +} +\def\pgfint@mod#1;#2;{#1-(\pgfint@divfloor#1;#2;)*#2} + +\def\pgfintset#1#2{#1 \numexpr#2\relax} + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmath.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmath.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ca11896e2fd1e67d11473210615e17189afdea12 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmath.code.tex @@ -0,0 +1,27 @@ + + +\ifx\pgfmathloaded\pgfutil@undefined + \let\pgfmathloaded=\relax +\else + \expandafter\endinput +\fi + +\ifx\pgfkeysloaded\pgfutil@undefined + \input pgfkeys.code.tex +\fi + +\input pgfmathutil.code.tex +\input pgfmathparser.code.tex +\input pgfmathfunctions.code.tex +\input pgfmathfunctions.basic.code.tex +\input pgfmathfunctions.trigonometric.code.tex +\input pgfmathfunctions.random.code.tex +\input pgfmathfunctions.comparison.code.tex +\input pgfmathfunctions.base.code.tex +\input pgfmathfunctions.round.code.tex +\input pgfmathfunctions.misc.code.tex +\input pgfmathfunctions.integerarithmetics.code.tex +\input pgfmathcalc.code.tex +\input pgfmathfloat.code.tex + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathcalc.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathcalc.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..dbbf3bae40e35b77649468126110e6b1013f4ba9 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathcalc.code.tex @@ -0,0 +1,353 @@ + + + +\def\pgfmathsetlength#1#2{% + \expandafter\pgfmath@onquick#2\pgfmath@% + {% + \begingroup% + \pgfmath@selectfont% + #1#2\unskip% + \expandafter\endgroup% + \expandafter#1\the#1\relax% + }% + {% + \pgfmathparse{#2}% + \ifpgfmathmathunitsdeclared% + #1\pgfmathresult mu\relax% + \else% + #1\pgfmathresult pt\relax% + \fi% + }% + \ignorespaces% +} + +\def\pgfmathaddtolength#1#2{% + \expandafter\pgfmath@onquick#2\pgfmath@% + {% + \begingroup% + \pgfmath@selectfont% + \advance#1#2\unskip% + \expandafter% + \endgroup% + \expandafter#1\the#1\relax% + }% + {% + \pgfmathparse{#2}% + \ifpgfmathmathunitsdeclared% + \advance#1\pgfmathresult mu\relax% + \else% + \advance#1\pgfmathresult pt\relax% + \fi% + }% + \ignorespaces% +} + +\def\pgfmathsetcount#1#2{% + \expandafter\pgfmath@onquick#2\pgfmath@% + {% + \afterassignment\pgfmath@gobbletilpgfmath@% + #1#2\relax\pgfmath@% + }% + {% + \pgfmathparse{#2}% + \afterassignment\pgfmath@gobbletilpgfmath@% + #1\pgfmathresult\relax\pgfmath@% + }% + \ignorespaces% +} + +\def\pgfmathaddtocount#1#2{% + \expandafter\pgfmath@onquick#2\pgfmath@% + {% + \edef\pgfmath@addtocounttemp{\the#1}% + \afterassignment\pgfmath@gobbletilpgfmath@% + #1#2\relax\pgfmath@% + \advance#1\pgfmath@addtocounttemp\relax% + }% + {% + \edef\pgfmath@addtocounttemp{\the#1}% + \pgfmathparse{#2}% + \afterassignment\pgfmath@gobbletilpgfmath@% + #1\pgfmathresult\relax\pgfmath@% + \advance#1\pgfmath@addtocounttemp\relax% + }% + \ignorespaces% +} + +\def\pgfmathnewcounter#1{% + \expandafter\ifx\csname c@#1\endcsname\relax% + \def\pgfmath@marshal{\csname newcount\endcsname}% + \expandafter\pgfmath@marshal\csname c@#1\endcsname% + \expandafter\def\csname the#1\endcsname{\expandafter\the\csname c@#1\endcsname}% + \fi% +} + +\def\pgfmathsetcounter#1#2{% + \expandafter\pgfmathsetcount\csname c@#1\endcsname{#2}% +} + +\def\pgfmathaddtocounter#1#2{% + \expandafter\pgfmathaddtocount\csname c@#1\endcsname{#2}% +} + +\def\pgfmath@pgftext{pgf} +\def\pgfmath@tikztext{tikz} +\def\pgfmathmakecounterglobal#1{% + \pgfmath@ifundefined{c@#1}{}{% + \expandafter\pgfmath@in@\expandafter{\pgfmath@pgftext}{#1}% + \ifpgfmath@in@% + \else% + \expandafter\pgfmath@in@\expandafter{\pgfmath@tikztext}{#1}% + \ifpgfmath@in@% + \else% + \expandafter\global\csname c@#1\endcsname\csname c@#1\endcsname\relax% + \fi% + \fi% + }% +} + +\def\pgfmathsetmacro#1#2{% + \begingroup% + \pgfmathparse{#2}% + \let#1=\pgfmathresult + \pgfmath@smuggleone{#1}% + \endgroup% +} + +\def\pgfmathsetlengthmacro#1#2{% + \begingroup% + \pgfmathsetlength\pgfmath@x{#2}% + \edef#1{\the\pgfmath@x}% + \pgfmath@smuggleone{#1}% + \endgroup% +} + +\def\pgfmathtruncatemacro#1#2{% + \begingroup% + \pgfmathsetcount\c@pgfmath@counta{#2}% + \edef#1{\the\c@pgfmath@counta}% + \pgfmath@smuggleone{#1}% + \endgroup% +} + + +\def\pgfmath@onquick{% + \futurelet\pgfmath@next% + \pgfmath@@onquick} +\def\pgfmath@@onquick#1\pgfmath@{% + \ifx\pgfmath@next+% + \let\pgfmath@next=\pgfmath@firstoftwo% + \else% + \let\pgfmath@next=\pgfmath@secondoftwo% + \fi% + \pgfmath@next% +} + + +\def\pgfmathanglebetweenpoints#1#2{% + \begingroup% + \pgf@process{\pgfpointdiff{#1}{#2}}% + \edef\pgf@marshall{\expandafter\noexpand\csname pgfmathatan2@\endcsname{\expandafter\Pgf@geT\the\pgf@y}{\expandafter\Pgf@geT\the\pgf@x}}% + \pgf@marshall% + \ifdim\pgfmathresult pt<0pt% + \pgfmathparse{\pgfmathresult+360}% + \fi% + \expandafter% + \endgroup\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult}% +} + +\def\pgfmathrotatepointaround#1#2#3{% + \pgf@process{% + \pgf@process{#1}% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + \pgf@process{#2}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgf@xb\pgf@x% + \pgf@yb\pgf@y% + \pgf@x=\pgf@xc% + \pgf@y=\pgf@yc% + \advance\pgf@x-\pgf@xa% + \advance\pgf@y-\pgf@ya% + \pgfmathsetmacro\angle{#3}% + \pgfmathsin@{\angle}% + \let\sineangle\pgfmathresult% + \pgfmathcos@{\angle}% + \let\cosineangle\pgfmathresult% + \pgf@xa\cosineangle\pgf@x% + \advance\pgf@xa-\sineangle\pgf@y% + \pgf@ya\sineangle\pgf@x% + \advance\pgf@ya\cosineangle\pgf@y% + \pgf@x\pgf@xb% + \pgf@y\pgf@yb% + \advance\pgf@x\pgf@xa% + \advance\pgf@y\pgf@ya% + }% +} + +\def\pgfmathanglebetweenlines#1#2#3#4{% + \begingroup% + \pgfmathanglebetweenpoints{#1}{#2}% + \let\firstangle\pgfmathresult% + \pgfmathanglebetweenpoints{#3}{#4}% + \let\secondangle\pgfmathresult% + \ifdim\firstangle pt>\secondangle pt\relax% + \pgfmathadd@{\secondangle}{360}% + \let\secondangle\pgfmathresult% + \fi% + \pgfmathsubtract@{\secondangle}{\firstangle}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\def\pgfmathreflectpointalongaxis#1#2#3{% + \pgf@process{% + \pgfmathanglebetweenpoints{#2}{#1}% + \pgfmath@tempdima\pgfmathresult pt\relax% + \pgfmathparse{#3}% + \advance\pgfmath@tempdima-\pgfmathresult pt\relax% + \pgfmath@tempdima-2.0\pgfmath@tempdima% + \pgfmathrotatepointaround{#1}{#2}{\pgfmath@tonumber{\pgfmath@tempdima}}% + }% +} + + + +\def\pgfmathpointintersectionoflineandarc#1#2#3#4#5#6{% + \pgf@process{% + \pgfmathanglebetweenpoints{#2}{#1}% + \let\x\pgfmathresult% + \pgfmath@in@{and }{#6}% + \ifpgfmath@in@% + \pgf@polar@#6\@@% + \else% + \pgf@polar@#6 and #6\@@% + \fi% + \edef\xarcradius{\the\pgf@x}% + \edef\yarcradius{\the\pgf@y}% + \pgfmathsetmacro\s{#4}% + \pgfmathsetmacro\e{#5}% + \pgfmathmod@{\s}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\ss\pgfmathresult% + \pgfmathmod@{\e}{360}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathadd@{\pgfmathresult}{360}% + \fi% + \let\ee\pgfmathresult% + \ifdim\ee pt<\ss pt\relax% + \pgfmathadd@{\x}{180}% + \pgfmathmod@{\pgfmathresult}{360}% + \let\x\pgfmathresult% + \fi% + \def\m{360}% + \pgfmathadd@{\s}{\e}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\n\pgfmathresult% + \pgfmathloop% + \pgfmathadd@{\s}{\e}% + \pgfmathdivide@{\pgfmathresult}{2}% + \let\p\pgfmathresult% + \ifdim\p pt=\s pt\relax% + \else% + \pgfmathanglebetweenpoints{#2}{% + \pgfpointadd{#3}{% + \pgf@x\xarcradius\relax% + \pgfmathcos@{\p}% + \pgf@x\pgfmathresult\pgf@x% + \pgf@y\yarcradius\relax% + \pgfmathsin@{\p}% + \pgf@y\pgfmathresult\pgf@y% + }% + }% + \ifdim\ee pt<\ss pt\relax% + \pgfmathadd@{\pgfmathresult}{180}% + \pgfmathmod@{\pgfmathresult}{360}% + \fi% + \let\q\pgfmathresult% + \ifdim\x pt>335pt\relax% + \ifdim\q pt<45pt\relax% + \pgfmathadd@{\q}{360}% + \let\q\pgfmathresult% + \fi% + \fi% + \ifdim\x pt=\q pt% + \pgfmathbreakloop% + \else + \ifdim\x pt<\q pt\relax% + \let\e\p% + \else% + \let\s\p% + \fi% + \fi% + \pgfmathsubtract@{\x}{\q}% + \pgfmathabs@{\pgfmathresult}% + \ifdim\pgfmathresult pt<\m pt\relax% + \let\m\pgfmathresult% + \let\n\p% + \fi% + \repeatpgfmathloop% + \pgfpointadd{#3}{\pgfpointpolar{\n}{\xarcradius and \yarcradius}}% + }% +} + +\def\pgfmathangleonellipse#1#2{% + \begingroup% + \pgfmath@in@{and }{#2}% + \ifpgfmath@in@% + \pgf@polar@#2\@@% + \else% + \pgf@polar@#2 and #2\@@% + \fi% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgf@process{#1}% + \ifdim\pgf@x=0pt\relax% + \pgfutil@tempdima1pt\relax% + \else% + \pgfutil@tempdima\pgf@x% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgfutil@tempdima}}% + \pgfutil@tempdima\pgfmathresult pt\relax% + \fi% + \ifdim\pgf@y=0pt\relax% + \pgfutil@tempdima1pt\relax% + \else% + \pgfmathdivide@{\pgfmath@tonumber{\pgf@y}}{\pgfmath@tonumber{\pgf@ya}}% + \pgfutil@tempdima\pgfmathresult\pgfutil@tempdima% + \pgfmathatan@{\pgfmath@tonumber{\pgfutil@tempdima}}% + \fi% + \pgfutil@tempdima\pgfmathresult pt\relax% + \ifdim\pgfutil@tempdima<0pt\relax% + \advance\pgfutil@tempdima360pt\relax% + \fi% + \ifdim\pgf@x<0pt\relax% + \ifdim\pgf@y=0pt\relax% + \pgfutil@tempdima180pt\relax% + \else% + \ifdim\pgf@y<0pt\relax% + \advance\pgfutil@tempdima180pt\relax% + \else% + \advance\pgfutil@tempdima-180pt\relax% + \fi% + \fi% + \else% + \ifdim\pgf@x=0pt\relax% + \ifdim\pgf@y<0pt\relax% + \pgfutil@tempdima270pt\relax% + \else% + \pgfutil@tempdima90pt\relax% + \fi% + \else% + \ifdim\pgf@y=0pt\relax% + \pgfutil@tempdima0pt\relax% + \fi% + \fi% + \fi% + \pgfmath@returnone\pgfutil@tempdima% + \endgroup% +} + + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfloat.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfloat.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..abec5f7cad737d7a495a8b951d0e3f730682e879 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfloat.code.tex @@ -0,0 +1,2156 @@ + + +\pgfkeys{ + /pgf/compat/number printer/.is choice, + /pgf/compat/number printer/2.10/.code={% + \def\pgfmathprintnumber@begingroup{\bgroup}% + \def\pgfmathprintnumber@endgroup{\egroup}% + }, + /pgf/compat/number printer/next after 2.10/.code={% + \def\pgfmathprintnumber@begingroup{\begingroup}% + \def\pgfmathprintnumber@endgroup{\endgroup}% + }, + /pgf/compat/number printer/next after 2.10,% +} + + +\newif\ifpgfmathfloatcomparison +\newif\ifpgfmathfloatroundhasperiod +\newif\ifpgfmathprintnumberskipzeroperiod + + +\toksdef\pgfmathfloat@tmptoks=1 +\newif\ifpgfmathfloat@fixed@digits@after@period +\newif\ifpgfmathfloatroundmayneedrenormalize +\toksdef\pgfmathfloat@a@Mtok=0 + +\let\pgfmathfloat@a@S=\c@pgf@counta +\let\pgfmathfloat@a@M=\pgf@xa +\let\pgfmathfloat@a@E=\c@pgf@countb +\let\pgfmathfloat@b@S=\c@pgf@countc +\let\pgfmathfloat@b@M=\pgf@xb +\let\pgfmathfloat@b@E=\c@pgf@countd + +\def\pgfmathfloat@round@precision{2} + +\def\pgfmathfloat@round@precision@orig{\pgfmathfloat@round@precision}% + +\gdef\pgfmathfloat@glob@TMP{} + + +\def\pgfmathfloatparsenumber#1{% + \begingroup + \edef\pgfmathresult{#1}% + \expandafter\pgfflt@impl\pgfmathresult\pgfflt@EOI + \ifpgfmathfloatparsenumberpendingperiod + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.0}% + \fi + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\let\pgfmathfloatqparsenumber=\pgfmathfloatparsenumber + +\def\pgfmathfloattoregisters#1#2#3#4{% + \expandafter\pgfmathfloat@decompose#1\relax{#2}{#3}{#4}% +} + +\def\pgfmathfloattoregisterstok#1#2#3#4{% + \expandafter\pgfmathfloat@decompose@tok#1\relax{#2}{#3}{#4}% +} + +\def\pgfmathfloatgetflags#1#2{% + \expandafter\pgfmathfloat@decompose@F#1\relax{#2}% +} +\def\pgfmathfloatgetflagstomacro#1#2{% + \expandafter\pgfmathfloat@decompose@Fmacro#1\relax{#2}% +}% + +\def\pgfmathfloatgetmantissa#1#2{% + \expandafter\pgfmathfloat@decompose@M#1\relax{#2}% +} +\let\pgfmathfloatgetmantisse=\pgfmathfloatgetmantissa +\def\pgfmathfloatgetmantissatok#1#2{% + \expandafter\pgfmathfloat@decompose@Mtok#1\relax{#2}% +} +\let\pgfmathfloatgetmantissetok=\pgfmathfloatgetmantissatok +\def\pgfmathfloatgetexponent#1#2{% + \expandafter\pgfmathfloat@decompose@E#1\relax{#2}% +} + + +\def\pgfmathfloat@to@FMeE@style#1{\expandafter\pgfmathfloat@to@FMeE@style@#1\relax\relax}% +\def\pgfmathfloat@to@FMeE@style@#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@to@FMeE@style@@% + \else + \expandafter\pgfmathfloat@to@FMeE@style@error% + \fi + #1#2% +}% +\def\pgfmathfloat@to@FMeE@style@@#1Y#2e#3]\relax\relax{\def\pgfmathresult{#1#2e#3}}% +\def\pgfmathfloat@to@FMeE@style@error#1\relax\relax{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{% + \noexpand\pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + }% + \endgroup + \pgfmathfloat@decompose@TMP +}% + + +\def\pgfmathfloat@decompose#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@% + \else + \expandafter\pgfmathfloat@decompose@error% + \fi + #1#2% +} +\def\pgfmathfloat@decompose@#1Y#2e#3]\relax#4#5#6{% + #4=#1\relax + #5=#2pt % + #6=#3\relax% +} + +\def\pgfmathfloat@decompose@tok#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@tok@% + \else + \expandafter\pgfmathfloat@decompose@tok@error% + \fi + #1#2% +}% +\def\pgfmathfloat@decompose@tok@#1Y#2e#3]\relax#4#5#6{% + #4=#1\relax + #5={#2}% + #6=#3\relax% +} +\def\pgfmathfloat@decompose@F#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@F@% + \else + \expandafter\pgfmathfloat@decompose@F@error% + \fi + #1#2% +}% +\def\pgfmathfloat@decompose@Fmacro#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@Fmacro@% + \else + \expandafter\pgfmathfloat@decompose@F@error% + \fi + #1#2% +}% +\def\pgfmathfloat@decompose@M#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@M@% + \else + \expandafter\pgfmathfloat@decompose@M@error% + \fi + #1#2% +}% +\def\pgfmathfloat@decompose@E#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@E@% + \else + \expandafter\pgfmathfloat@decompose@E@error% + \fi + #1#2% +}% +\def\pgfmathfloat@decompose@Mtok#1#2{% + \ifx#2Y% + \expandafter\pgfmathfloat@decompose@Mtok@% + \else + \expandafter\pgfmathfloat@decompose@Mtok@error% + \fi + #1#2% +}% +\def\pgfmathfloat@decompose@F@#1Y#2e#3]\relax#4{#4=#1\relax}% +\def\pgfmathfloat@decompose@Fmacro@#1Y#2e#3]\relax#4{\def#4{#1}}% +\def\pgfmathfloat@decompose@M@#1Y#2e#3]\relax#4{#4=#2pt}% +\def\pgfmathfloat@decompose@Mtok@#1Y#2e#3]\relax#4{#4={#2}}% +\def\pgfmathfloat@decompose@E@#1Y#2e#3]\relax#4{#4=#3\relax}% + +\def\pgfmathfloat@decompose@error#1\relax#2#3#4{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{% + \noexpand#2=\the\pgfmathfloat@a@S\space + \noexpand#3=\the\pgfmathfloat@a@Mtok pt + \noexpand#4=\the\pgfmathfloat@a@E\space + }% + \endgroup + \pgfmathfloat@decompose@TMP +}% +\def\pgfmathfloat@decompose@tok@error#1\relax#2#3#4{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{% + \noexpand#2=\the\pgfmathfloat@a@S\space + \noexpand#3={\the\pgfmathfloat@a@Mtok}% + \noexpand#4=\the\pgfmathfloat@a@E\space + }% + \endgroup + \pgfmathfloat@decompose@TMP +}% +\def\pgfmathfloat@decompose@F@error#1\relax#2{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{\noexpand#2=\the\pgfmathfloat@a@S\space}% + \endgroup + \pgfmathfloat@decompose@TMP +}% +\def\pgfmathfloat@decompose@M@error#1\relax#2{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{\noexpand#2=\the\pgfmathfloat@a@Mtok pt }% + \endgroup + \pgfmathfloat@decompose@TMP +}% +\def\pgfmathfloat@decompose@Mtok@error#1\relax#2{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{\noexpand#2={\the\pgfmathfloat@a@Mtok}}% + \endgroup + \pgfmathfloat@decompose@TMP +}% +\def\pgfmathfloat@decompose@E@error#1\relax#2{% + \begingroup + \pgfmathfloatparsenumber@handleerror{wrong lowlevel format}{#1}{#1}% + \xdef\pgfmathfloat@decompose@TMP{\noexpand#2=\the\pgfmathfloat@a@E\space}% + \endgroup + \pgfmathfloat@decompose@TMP +}% +\def\pgfmathfloattomacro#1#2#3#4{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \xdef\pgfmathfloat@glob@TMP{% + \noexpand\def\noexpand#2{\the\pgfmathfloat@a@S}% + \noexpand\def\noexpand#3{\the\pgfmathfloat@a@Mtok}% + \noexpand\def\noexpand#4{\the\pgfmathfloat@a@E}% + }% + \endgroup + \pgfmathfloat@glob@TMP +} + + +\def\pgfmathfloatcreate#1#2#3{% + \edef\pgfmathresult{#1Y#2e#3]}% +}% +\def\pgfmathfloat@POSTFLAGSCHAR{Y} + + + +\def\pgfmathfloattofixed@#1{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S + \def\pgfmathresult{0.0}% + \or + \expandafter\pgfmathfloattofixed@impl\the\pgfmathfloat@a@Mtok\relax + \or + \expandafter\pgfmathfloattofixed@impl\the\pgfmathfloat@a@Mtok\relax + \pgfmathfloat@a@Mtok=\expandafter{\pgfmathresult}% + \edef\pgfmathresult{-\the\pgfmathfloat@a@Mtok}% + \or\def\pgfmathresult{nan}% + \or\def\pgfmathresult{inf}% + \or\def\pgfmathresult{-inf}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +} +\let\pgfmathfloattofixed=\pgfmathfloattofixed@ + +\def\pgfmathfloattoint#1{% + \pgfmathfloattofixed{#1}% + \expandafter\pgfmathfloattoint@@\pgfmathresult\relax +}% +\def\pgfmathfloattoint@@#1.#2\relax{% + \def\pgfmathresult{#1}% +}% + +\def\pgfmathfloattosci@#1{% + \begingroup + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifcase\pgfmathfloat@a@S + \def\pgfmathresult{0.0e0}% + \or + \edef\pgfmathresult{\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}% + \or + \edef\pgfmathresult{-\the\pgfmathfloat@a@Mtok e\the\pgfmathfloat@a@E}% + \or\def\pgfmathresult{nan}% + \or\def\pgfmathresult{inf}% + \or\def\pgfmathresult{-inf}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\let\pgfmathfloattosci=\pgfmathfloattosci@ + +\def\pgfmathfloatvalueof#1{\expandafter\pgfmathfloatvalueof@@#1@@}% + +\def\pgfmathfloatvalueof@@#1#2{% + \if#2Y% + \expandafter\pgfmathfloatvalueof@@@\expandafter#1\expandafter#2% + \else + \expandafter\pgfmathfloatvalueof@abort\expandafter#1\expandafter#2% + \fi +} +\def\pgfmathfloatvalueof@@@#1Y#2e#3]@@{% + \ifcase#1 % + 0.0e0% + \or + #2e#3% + \or + -#2e#3% + \or nan% + \or inf% + \or -inf% + \fi +}% +\def\pgfmathfloatvalueof@abort#1@@{#1}% + + + +\def\pgfmathroundto#1{% + \pgfmathfloatroundhasperiodtrue + \begingroup + \pgfmathfloat@fixed@digits@after@periodfalse + \pgfmathroundto@impl{#1}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + + +\def\pgfmathroundtozerofill#1{% + \pgfmathfloatroundhasperiodtrue + \begingroup + \pgfmathfloat@fixed@digits@after@periodtrue + \pgfmathroundto@impl{#1}% + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\def\pgfmathprintnumber@fixed@styleDEFAULT#1#2#3e#4\relax{% + \begingroup + \pgfkeysgetvalue{/pgf/number format/set decimal separator}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP + \pgfkeysgetvalue{/pgf/number format/@dec sep mark}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK + \pgfkeysgetvalue{/pgf/number format/set thousands separator}\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP + \c@pgf@counta=#4\relax % + \ifnum#2=0 + \c@pgf@counta=0 + \fi + \def\pgfmathresult{}% + \ifpgfmathfloatroundhasperiod + \expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@period#1\pgfmathfloat@EOI + \else + \expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI% + \begingroup + \toks0=\expandafter{\pgfmathresult}% + \toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }% + \endgroup + \let\pgfmathresult=\pgfmathfloat@glob@TMP + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +} +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@period#1.#2\pgfmathfloat@EOI{% + \ifpgfmathprintnumberskipzeroperiod + \def\pgfmathfloat@loc@TMPb{#1}% + \ifx\pgfmathfloatparsenumber@tok@ZERO\pgfmathfloat@loc@TMPb + \else + \def\pgfmathfloat@loc@TMPc{-0}% + \ifx\pgfmathfloat@loc@TMPc\pgfmathfloat@loc@TMPb + \def\pgfmathresult{-}% + \else + \def\pgfmathfloat@loc@TMPc{+0}% + \ifx\pgfmathfloat@loc@TMPc\pgfmathfloat@loc@TMPb + \def\pgfmathresult{+}% + \else + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI + \fi + \fi + \fi + \else + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI + \fi + \ifpgfmathprintnumber@thousand@sep@in@fractional + \let\pgfmathresultfractional\pgfutil@empty% + \pgfmathprintnumber@thousand@sep@in@fractional#2MMMM\@@ + \else + \def\pgfmathresultfractional{#2}% + \fi + \begingroup + \toks0=\expandafter{\pgfmathresult}% + \toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}% + \toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP}% + \toks3=\expandafter{\pgfmathresultfractional}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 \the\toks3 }% + \endgroup + \let\pgfmathresult=\pgfmathfloat@glob@TMP +}% + +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod{% + \ifx\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP\pgfutil@empty + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}% + \else + \ifnum\c@pgf@counta<0\relax % + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}% + \else + \ifnum\c@pgf@counta<\pgfkeysvalueof{/pgf/number format/min exponent for 1000 sep}\relax + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall}% + \else + \advance\c@pgf@counta by1 % + \c@pgf@countb=\c@pgf@counta + \divide\c@pgf@countb by3 % + \c@pgf@countc=\c@pgf@countb + \multiply\c@pgf@countc by3 + \advance\c@pgf@counta by-\c@pgf@countc% + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printsign + }% + \fi + \fi + \fi + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT +} +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printsign#1{% + \def\pgfmathfloat@loc@TMPb{#1}% + \ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@MINUS + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}% + \let\pgfmathfloat@loc@TMPb=\pgfutil@empty + \else + \ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@PLUS + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}% + \let\pgfmathfloat@loc@TMPb=\pgfutil@empty + \else + \ifpgfmathprintnumber@showpositive + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult +}% + \fi + \fi + \fi + \ifnum\c@pgf@counta>0 % + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits\pgfmathfloat@loc@TMPb + }% + \else + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird\pgfmathfloat@loc@TMPb + }% + \fi + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT +} +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printtrailingdigits#1#2{% + \ifcase\c@pgf@counta % + \or + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}% + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird#2% + }% + \or + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1#2}% + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird% + }% + \fi + \ifnum\c@pgf@countb>0\relax % + \begingroup + \toks0=\expandafter{\pgfmathresult}% + \toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }% + \endgroup + \let\pgfmathresult=\pgfmathfloat@glob@TMP + \fi + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT +} +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird#1#2#3{% + \ifnum\c@pgf@countb>0\relax + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1#2#3}% + \advance\c@pgf@countb by-1 + \ifnum\c@pgf@countb>0\relax + \begingroup + \toks0=\expandafter{\pgfmathresult}% + \toks1=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }% + \endgroup + \let\pgfmathresult=\pgfmathfloat@glob@TMP + \fi + \def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT{% + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@counteverythird% + }% + \else + \let\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT=\relax + \fi + \pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@NEXT +} + +\def\pgfmathprintnumber@thousand@sep@in@fractional#1#2#3#4{% + \if#4M% + \def\pgfmathprint@next{\pgfmathprintnumber@thousand@sep@in@fractional@finish#1#2#3#4}% + \else + \begingroup + \toks0=\expandafter{\pgfmathresultfractional}% + \toks1={#1#2#3}% + \toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@THOUSAND@SEP}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }% + \endgroup + \let\pgfmathresultfractional=\pgfmathfloat@glob@TMP + \def\pgfmathprint@next{\pgfmathprintnumber@thousand@sep@in@fractional#4}% + \fi + \pgfmathprint@next +}% +\def\pgfmathprintnumber@thousand@sep@in@fractional@finish#1M{% + \expandafter\def\expandafter\pgfmathresultfractional\expandafter{\pgfmathresultfractional #1}% + \pgfmathprintnumber@thousand@sep@in@fractional@finish@ +}% +\def\pgfmathprintnumber@thousand@sep@in@fractional@finish@#1\@@{}% + +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall#1{% + \def\pgfmathfloat@loc@TMPb{#1}% + \let\pgfmathfloat@loc@TMPc=\pgfutil@empty + \ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@MINUS + \else + \ifx\pgfmathfloat@loc@TMPb\pgfmathfloatparsenumber@tok@PLUS + \else + \ifpgfmathprintnumber@showpositive + \def\pgfmathfloat@loc@TMPc{+}% + \fi + \fi + \fi + \expandafter\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall@\pgfmathfloat@loc@TMPc#1% +} +\def\pgfmathprintnumber@fixed@styleDEFAULT@impl@noperiod@printall@#1\pgfmathfloat@EOI\pgfmathfloat@EOI\pgfmathfloat@EOI{% + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult #1}% +}% + +\def\pgfmathprintnumber@fixed@stylePERIOD#1#2#3e#4\relax{% + \def\pgfmathresult{#1}% +} + +\def\pgfmathprintnumber@fixed@styleCOMMA#1#2#3e#4\relax{% + \ifpgfmathfloatroundhasperiod + \expandafter\pgfmathprintnumber@fixed@styleCOMMA@impl#1\pgfmathfloat@EOI + \else + \def\pgfmathresult{#1}% + \fi +} +\def\pgfmathprintnumber@fixed@styleCOMMA@impl#1.#2\pgfmathfloat@EOI{\def\pgfmathresult{#1{,}#2}} + + +\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT + + +\def\pgfmathfloatround#1{% + \pgfmathfloatroundhasperiodtrue + \begingroup + \pgfmathfloat@fixed@digits@after@periodfalse + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \pgfmathfloatround@impl + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\def\pgfmathfloatroundzerofill#1{% + \pgfmathfloatroundhasperiodtrue + \begingroup + \pgfmathfloat@fixed@digits@after@periodtrue + \expandafter\pgfmathfloat@decompose@tok#1\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \pgfmathfloatround@impl + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\newif\ifpgfmathfloatround@allow@empty@mantissa +\def\pgfmathfloatround@mantissa@ONE{1pt }% + +\def\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax#4#5#6{% + \pgfkeysgetvalue{/pgf/number format/@sci exponent mark}\pgfmathfloatrounddisplaystyle@e@mark + \ifcase#1\relax + \pgfmathprintnumber@fixed@style{#2}#1#2e0\relax% + \expandafter\pgfmathfloatrounddisplaystyle@shared@impl@\expandafter{\pgfmathresult}{#4#6}% + \or + \def\pgfmathfloat@loc@TMPa{1}% + \ifpgfmathfloatround@allow@empty@mantissa + \else + \ifdim#2pt=\pgfmathfloatround@mantissa@ONE + \def\pgfmathfloat@loc@TMPa{0}% + \fi + \fi + \if1\pgfmathfloat@loc@TMPa + \pgfmathprintnumber@fixed@style{#2}#1#2e0\relax% + \expandafter\pgfmathfloatrounddisplaystyle@shared@impl@\expandafter{\pgfmathresult}{#4#6}% + \else + \def\pgfmathfloat@loc@TMPa{0}% + \pgfmathfloatrounddisplaystyle@shared@impl@{#5}{#6}% + \fi + \or + \def\pgfmathfloat@loc@TMPa{1}% + \ifpgfmathfloatround@allow@empty@mantissa + \else + \ifdim#2pt=\pgfmathfloatround@mantissa@ONE + \def\pgfmathfloat@loc@TMPa{0}% + \fi + \fi + \if1\pgfmathfloat@loc@TMPa + \pgfmathprintnumber@fixed@style{-#2}#1#2e0\relax% + \expandafter\pgfmathfloatrounddisplaystyle@shared@impl@\expandafter{\pgfmathresult}{#4#6}% + \else + \def\pgfmathfloat@loc@TMPa{0}% + \pgfmathfloatrounddisplaystyle@shared@impl@{-#5}{#6}% + \fi + \or + \pgfmathfloatrounddisplaystyle@shared@impl@@{\hbox{NaN}}{}% + \or + \ifpgfmathprintnumber@showpositive + \pgfmathfloatrounddisplaystyle@shared@impl@@{+\infty}{}% + \else + \pgfmathfloatrounddisplaystyle@shared@impl@@{\infty}{}% + \fi + \or + \pgfmathfloatrounddisplaystyle@shared@impl@@{-\infty}{}% + \fi +} + +\def\pgfmathfloatrounddisplaystyle@shared@impl@#1#2{% + \pgfmathprintnumber@begingroup + \toks0={#1}% + \toks1=\expandafter{\pgfmathfloatrounddisplaystyle@e@mark #2}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 }% + \pgfmathprintnumber@endgroup + \let\pgfmathresult=\pgfmathfloat@glob@TMP +}% +\def\pgfmathfloatrounddisplaystyle@shared@impl@@#1#2{% + \pgfmathprintnumber@begingroup + \toks0={#1}% + \toks1=\expandafter{\pgfmathfloatrounddisplaystyle@e@mark #2}% + \pgfkeysgetvalue{/pgf/number format/@dec sep mark}\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK + \toks2=\expandafter{\pgfmathprintnumber@fixed@styleDEFAULT@DEC@SEP@MARK}% + \xdef\pgfmathfloat@glob@TMP{\the\toks0 \the\toks1 \the\toks2 }% + \pgfmathprintnumber@endgroup + \let\pgfmathresult=\pgfmathfloat@glob@TMP +} + +\def\pgfmathfloatrounddisplaystyle@std#1#2e#3\relax{% + \pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{\cdot}{}{10^{#3}}% +} +\def\pgfmathfloatrounddisplaystyle@subscript#1#2e#3\relax{% + \pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}{_{#3}}% +} +\def\pgfmathfloatrounddisplaystyle@superscript#1#2e#3\relax{% + \pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}{^{#3}}% +} +\def\pgfmathfloatrounddisplaystyle@e#1#2e#3\relax{% + \ifnum#3<0\relax + \pgfmathprintnumber@begingroup + \count0=#3\relax + \multiply\count0 by-1 + \xdef\pgfmathfloat@glob@TMP{e{-}\the\count0}% + \pgfmathprintnumber@endgroup% + \let\pgfmathresult=\pgfmathfloat@glob@TMP + \else + \def\pgfmathresult{e{+}#3}% + \fi + \def\pgfmathfloat@loc@TMPb{\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}}% + \expandafter\pgfmathfloat@loc@TMPb\expandafter{\pgfmathresult}% +} +\def\pgfmathfloatrounddisplaystyle@E#1#2e#3\relax{% + \ifnum#3<0\relax + \pgfmathprintnumber@begingroup + \count0=#3\relax + \multiply\count0 by-1 + \xdef\pgfmathfloat@glob@TMP{E{-}\the\count0}% + \pgfmathprintnumber@endgroup% + \let\pgfmathresult=\pgfmathfloat@glob@TMP + \else + \def\pgfmathresult{E{+}#3}% + \fi + \def\pgfmathfloat@loc@TMPb{\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\relax{}{1}}% + \expandafter\pgfmathfloat@loc@TMPb\expandafter{\pgfmathresult}% +} + +\def\pgfmathfloatrounddisplaystyle@generic#1#2e#3\relax{% + \begingroup + \pgfkeysvalueof {/pgf/number format/sci generic/@/.@cmd}{#3}{#1}{#2}\pgfeov + \pgfkeysgetvalue{/pgf/number format/sci generic/mantissa sep}\pgfmathdisplay@aftermantissa + \pgfkeysgetvalue{/pgf/number format/sci generic/empty mantissa sep}\pgfmathdisplay@nomantissa + \pgfkeysgetvalue{/pgf/number format/sci generic/exponent}\pgfmathdisplay@e + \toks0=\expandafter{\pgfmathdisplay@aftermantissa}% + \toks1=\expandafter{\pgfmathdisplay@nomantissa}% + \toks2=\expandafter{\pgfmathdisplay@e}% + \xdef\pgfmathfloat@glob@TMP{\noexpand\pgfmathfloatrounddisplaystyle@shared@impl#1#2e#3\noexpand\relax{\the\toks0}{\the\toks1}{\the\toks2}}% + \endgroup + \pgfmathfloat@glob@TMP +} + +\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std +\newif\ifpgfmathfloat@usezerofill@sci +\newif\ifpgfmathfloat@usezerofill@fixed +\newif\ifpgfmathprintnumber@assumemathmode +\newif\ifpgfmathprintnumber@showpositive +\newif\ifpgfmathprintnumber@frac@warn +\newif\ifpgfmathprintnumber@frac@whole +\newif\ifpgfmathparsenumber@comma@as@period + +\long\def\pgfmathfloatfrac@verbatim#1#2{#1/#2}% + +\let\pgfmathround@@orig=\pgfmathround@ + +\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{2}% + +\newif\ifpgfmathprintnumber@thousand@sep@in@fractional +\pgfkeys{% + /pgf/number format/.is family, + /pgf/number format, + fixed/.code= \pgfmath@set@number@printer{pgfmathprintnumber@FIXED}, + sci/.code= \pgfmath@set@number@printer{pgfmathprintnumber@SCI}, + std/.code= {\pgfmath@set@number@printer{pgfmathprintnumber@STD}\pgfmathprintnumber@STD@setparam{#1}}, + std/.default=,% + relative round mode/.is choice, + relative round mode/fixed/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{1}}, + relative round mode/mantissa/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{0}}, + relative round mode/compatible/.code={\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed{2}}, + relative/.code={% + \pgfmath@set@number@printer{pgfmathprintnumber@RELATIVE}% + \pgfmathround@@orig{#1}% + \expandafter\pgfmathfloattoint@@\pgfmathresult\relax + \let\pgfmathprintnumber@RELATIVE@param=\pgfmathresult + },% + relative/.value required, + relative*/.style={/pgf/number format/relative={#1},/pgf/number format/relative round mode=fixed}, + every relative/.style=std, + relative style/.style={/pgf/number format/every relative/.append style={#1}}, + fixed relative/.code= \pgfmath@set@number@printer{pgfmathprintnumber@FIXED@RELATIVE}, + int detect/.code= \pgfmath@set@number@printer{pgfmathprintnumber@INT@DETECT}, + int trunc/.code= \pgfmath@set@number@printer{pgfmathprintnumber@INT@TRUNC}, + frac/.code= \pgfmath@set@number@printer{pgfmathprintnumber@frac},% + frac TeX/.initial=\frac, + frac whole format/.code={\def\pgfmathresult{#1}}, + frac denom/.initial=, + frac whole/.is if=pgfmathprintnumber@frac@whole, + frac whole=true, + frac shift/.initial=4, + frac warning/.is if=pgfmathprintnumber@frac@warn, + frac warning=true, + assume math mode/.is if=pgfmathprintnumber@assumemathmode, + assume math mode/.default=true, + fixed zerofill/.is if= pgfmathfloat@usezerofill@fixed, + fixed zerofill/.default=true, + sci zerofill/.is if= pgfmathfloat@usezerofill@sci, + sci zerofill/.default=true, + zerofill/.style= {/pgf/number format/fixed zerofill={#1},/pgf/number format/sci zerofill={#1}}, + zerofill/.default= true, + precision/.store in= \pgfmathfloat@round@precision, + sci precision/.code={% + \edef\pgfmathfloat@loc@TMPa{#1}% + \ifx\pgfmathfloat@loc@TMPa\pgfutil@empty + \def\pgfmathprintnumber@sci@precision{\pgfmathfloat@round@precision}% + \else + \let\pgfmathprintnumber@sci@precision=\pgfmathfloat@loc@TMPa + \fi + },% + sci precision/.default=, + sci precision=, + fixed default/.code= {\let\pgfmathprintnumber@fixed@style=\pgfmathprintnumber@fixed@styleDEFAULT}, + set decimal separator/.initial=, + dec sep/.style={/pgf/number format/set decimal separator={#1}}, + @dec sep mark/.initial=, + @sci exponent mark/.initial=, + set thousands separator/.initial=, + 1000 sep in fractionals/.is if=pgfmathprintnumber@thousand@sep@in@fractional, + 1000 sep in fractionals/.default=true, + 1000 sep/.style={/pgf/number format/set thousands separator={#1}}, + min exponent for 1000 sep/.initial=0, + use period/.style= {/pgf/number format/set decimal separator={.},/pgf/number format/set thousands separator={{{,}}}}, + use comma/.style= {/pgf/number format/set decimal separator={{{,}}},/pgf/number format/set thousands separator={.}}, + showpos/.is if=pgfmathprintnumber@showpositive, + showpos/.default=true, + print sign/.is if=pgfmathprintnumber@showpositive, + print sign/.default=true, + read comma as period/.is if=pgfmathparsenumber@comma@as@period, + read comma as period/.default=true, + skip 0./.is if=pgfmathprintnumberskipzeroperiod, + skip 0./.default=true, + skip 0.= false, + use period, + sci 10^e/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std}, + sci 10e/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@std}, + sci e/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@e}, + sci E/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@E}, + sci subscript/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@subscript}, + sci superscript/.code= {\let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@superscript}, + sci generic/.code= {% + \let\pgfmathfloatrounddisplaystyle=\pgfmathfloatrounddisplaystyle@generic + \pgfkeysdefargs{/pgf/number format/sci generic/@}% + {##1##2##3}% + {\pgfqkeys{/pgf/number format/sci generic}{#1}}% + }, + sci generic/mantissa sep/.initial=,% + sci generic/empty mantissa sep/.initial=,% + sci generic/mantisse sep/.style={/pgf/number format/sci generic/mantissa sep={#1}},% + sci generic/empty mantisse sep/.style={/pgf/number format/sci generic/empty mantissa sep={#1}},% + sci generic/exponent/.initial=,% + sci generic/.value required, + verbatim/.code={% + \pgfqkeys{/pgf/number format}{% + sci generic={mantissa sep=,exponent={e##1}}, + 1000 sep=, + skip 0.=false, + print sign=false, + dec sep=., + assume math mode, + frac TeX=\pgfmathfloatfrac@verbatim, + frac whole format/.code={\def\pgfmathresult{##1 }}, + @dec sep mark=, + @sci exponent mark=, + }% + }, + retain unit mantissa/.is if=pgfmathfloatround@allow@empty@mantissa, + retain unit mantissa/.default=true, + retain unit mantissa=true, + implementation/.code={\def\pgfmathprintnumber@protected{#1}}, +} + + + +\def\pgfmathprintnumber@STD#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@STD@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@STD@setparam#1{% + \edef\pgfmathfloat@loc@TMPb{#1}% + \ifx\pgfmathfloat@loc@TMPb\pgfutil@empty + \def\pgfmathprintnumber@STD@getlowerbound{% + \c@pgf@counta=\pgfmathfloat@round@precision@orig\relax + \divide\c@pgf@counta by-2\relax + }% + \def\pgfmathprintnumber@STD@upperbound{4}% + \else + \expandafter\pgfutil@in@\expandafter:\expandafter{\pgfmathfloat@loc@TMPb}% + \ifpgfutil@in@ + \def\pgfmathfloat@loc@TMPa##1:##2\relax{% + \edef\pgfmathprintnumber@STD@getlowerbound{% + \noexpand\c@pgf@counta=##1\space + }% + \edef\pgfmathprintnumber@STD@upperbound{##2}% + }% + \expandafter\pgfmathfloat@loc@TMPa\pgfmathfloat@loc@TMPb\relax + \else + \def\pgfmathprintnumber@STD@upperbound{4}% + \edef\pgfmathprintnumber@STD@getlowerbound{% + \noexpand\c@pgf@counta=\pgfmathfloat@loc@TMPb\space + }% + \fi + \fi +}% + +\def\pgfmathprintnumber@STD@issci#1#2e#3\relax{% + \expandafter\ifnum#1<3 + \expandafter\ifnum#3>\pgfmathprintnumber@STD@upperbound\relax + \pgfmathprintnumber@SCI@issci#1#2e#3\relax% + \else + \begingroup + \pgfmathprintnumber@STD@getlowerbound + \ifnum#3<\c@pgf@counta + \pgfmathprintnumber@SCI@issci#1#2e#3\relax% + \else + \pgfmathprintnumber@FIXED@issci#1#2e#3\relax% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup + \fi + \else% + \pgfmathfloatrounddisplaystyle#1#2e#3\relax% + \fi +} + +\def\pgfmathprintnumber@RELATIVE#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@RELATIVE@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn{% + \pgf@typeout{! Package pgf warning: the use of /pgf/number format/relative is discouraged (buggy). Please use 'relative*' instead or type \string\pgfkeys{/pgf/number format/relative round mode=fixed} into your preamble.}% + \global\let\pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn=\relax +} + +\def\pgfmathprintnumber@RELATIVE@issci#1#2e#3\relax{% + \begingroup + \c@pgf@counta=#3\relax + \advance\c@pgf@counta by-\pgfmathprintnumber@RELATIVE@param\relax + \pgfmathfloatcreate{#1}{#2}{\the\c@pgf@counta}% + \if0\pgfmathprintnumber@RELATIVE@choice@roundtofixed + \def\b@round@fixed{0}% + \else + \if1\pgfmathprintnumber@RELATIVE@choice@roundtofixed + \def\b@round@fixed{1}% + \else + \pgfmathprintnumber@RELATIVE@choice@roundtofixed@warn + \ifnum\c@pgf@counta>0 + \def\b@round@fixed{0}% + \else + \def\b@round@fixed{1}% + \fi + \fi + \fi + \if1\b@round@fixed + \pgfmathfloattofixed\pgfmathresult + \expandafter\pgfmathroundto\expandafter{\pgfmathresult}% + \pgfmathfloatparsenumber{\pgfmathresult}% + \pgfmathfloatroundhasperiodtrue% + \else + \expandafter\pgfmathfloatround\expandafter{\pgfmathresult}% + \fi + \pgfmathfloattoregisterstok\pgfmathresult\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifnum\pgfmathfloat@a@S=0 + \pgfmathfloat@a@E=\pgfmathfloat@a@S % + \else + \advance\pgfmathfloat@a@E by+\pgfmathprintnumber@RELATIVE@param\relax + \fi + \edef\pgfmathresultX{% + \the\pgfmathfloat@a@S + \the\pgfmathfloat@a@Mtok + \ifpgfmathfloatroundhasperiod\else.0\fi + e\the\pgfmathfloat@a@E}% + \pgfqkeys{/pgf/number format}{/pgf/number format/every relative, + fixed zerofill=false,% + sci zerofill=false}% + \ifx\pgfmathprintnumber@issci\pgfmathprintnumber@RELATIVE@issci + \pgfmath@error{The '/pgf/number format/every relative' style should set a valid display style}{}% + \fi + \let\pgfmathfloat@round@precision@orig=\pgfmathfloat@round@precision + \def\pgfmathfloat@round@precision{9999}% + \expandafter\pgfmathprintnumber@issci\pgfmathresultX\relax% + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\def\pgfmathprintnumber@FIXED@RELATIVE#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@FIXED@RELATIVE@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@FIXED@RELATIVE@issci#1#2e#3\relax{% + \begingroup + \pgfmathfloatcreate{#1}{#2}{#3}% + \c@pgf@counta=\pgfmathfloat@round@precision\relax + \advance\c@pgf@counta by-1 + \edef\pgfmathfloat@round@precision{\the\c@pgf@counta}% + \pgfmathfloatround{\pgfmathresult}% + \pgfmathfloattoregisterstok\pgfmathresult\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \ifnum\pgfmathfloat@a@S=0 + \pgfmathfloat@a@E=\pgfmathfloat@a@S % + \fi + \edef\pgfmathresultX{% + \the\pgfmathfloat@a@S + \the\pgfmathfloat@a@Mtok + \ifpgfmathfloatroundhasperiod\else.0\fi + e\the\pgfmathfloat@a@E}% + \let\pgfmathfloat@round@precision@orig=\pgfmathfloat@round@precision + \pgfmathfloat@usezerofill@fixedfalse + \def\pgfmathfloat@round@precision{9999}% + \expandafter\pgfmathprintnumber@FIXED@issci\pgfmathresultX\relax% + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\def\pgfmathprintnumber@frac#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloatgetfrac{\pgfmathresult}% + \expandafter\pgfmathprintnumber@frac@formatresult\pgfmathresult +} +\def\pgfmathprintnumber@frac@issci#1#2e#3\relax{% + \pgfmathfloatcreate{#1}{#2}{#3}% + \pgfmathfloatgetfrac{\pgfmathresult}% + \expandafter\pgfmathprintnumber@frac@formatresult\pgfmathresult +} +\def\pgfmathprintnumber@frac@formatresult#1#2#3{% + \begingroup + \pgfkeysgetvalue{/pgf/number format/frac TeX}\pgfmathresult + \toks0=\expandafter{\pgfmathresult}% + \def\pgfmathfloat@loc@TMPa{#1}% + \ifx\pgfmathfloat@loc@TMPa\pgfutil@empty + \ifpgfmathprintnumber@showpositive + \def\pgfmathfloat@loc@TMPa{+}% + \fi + \else + \ifx\pgfmathfloat@loc@TMPa-% + \else + \ifx\pgfmathfloat@loc@TMPa+% + \else + \ifpgfmathprintnumber@showpositive + \edef\pgfmathfloat@loc@TMPa{+\pgfmathfloat@loc@TMPa}% + \fi + \def\pgfmathfloat@loc@TMPb{\pgfkeysvalueof{/pgf/number format/frac whole format/.@cmd}}% + \expandafter\pgfmathfloat@loc@TMPb\pgfmathfloat@loc@TMPa\pgfeov + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \fi + \fi + \fi + \toks1=\expandafter{\pgfmathfloat@loc@TMPa}% + \edef\pgfmathresult{% + \the\toks1 \ifnum#2=0 \else\the\toks0 {#2}{#3}\fi% + }% + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfmathfloatgetfrac#1{% + \pgfutil@ifundefined{pgfmathfloatmultiply@}{% + \pgfmath@error{Sorry, the number format 'frac' requires '\string\usetikzlibrary{fpu}' (and, optionally, \string\usepackage{fp}) in order to work correctly}{}% + \edef\pgfmathresult{{#1}{0}{1}}% + }{% + \pgfmathfloatgetfrac@{#1}% + }% +}% +\def\pgfmathfloatgetfrac@#1{% + \begingroup + \edef\pgfmathfloat@arg{#1}% + \expandafter\pgfmathfloat@decompose@tok\pgfmathfloat@arg\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \def\pgfmathfloat@loc@TMPa{0}% + \ifcase\pgfmathfloat@a@S + \def\pgfmathresult{{0}{0}{1}}% + \or% + \pgfmathfloat@a@S=1 + \def\pgfmathfloat@loc@TMPa{1}% + \or% + \pgfmathfloat@a@S=-1 + \def\pgfmathfloat@loc@TMPa{1}% + \or + \edef\pgfmathresult{{}{NaN}{1}}% + \or + \edef\pgfmathresult{{}{\infty}{1}}% + \or + \edef\pgfmathresult{{-}{\infty}{1}}% + \fi + \if1\pgfmathfloat@loc@TMPa + \ifnum\pgfmathfloat@a@E<0 + \def\pgfmathfloat@wholenumber{}% + \else + \pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \pgfmathfloattofixed\pgfmathresult% + \def\pgfmathfloat@loc@TMPa##1.##2\relax{% + \def\pgfmathfloat@wholenumber{##1}% + \pgfmathfloatparsenumber{0.##2}% + }% + \expandafter\pgfmathfloat@loc@TMPa\pgfmathresult\relax + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@b@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \fi + \def\pgfmathfloat@loc@TMPa##1.##2\relax{% + \def\pgfmathfloat@mantissa@first{##1}% + \def\pgfmathfloat@mantissa@ltone{0.##2}% + }% + \expandafter\pgfmathfloat@loc@TMPa\the\pgfmathfloat@a@Mtok\relax + \def\pgfmathfloat@loc@@to@int##1.##2\relax##3{% + ##3=##1 + \ifdim0.##2pt>0.5pt + \advance##3 by1 + \fi + }% + \let\pgfmathresultnumerator=\pgfmathfloat@b@S + \let\pgfmathresultdenom=\pgfmathfloat@b@E + \pgfkeysgetvalue{/pgf/number format/frac denom}\pgfmath@target@denominator + \ifx\pgfmath@target@denominator\pgfutil@empty + \pgfmathfloat@a@E=-\pgfmathfloat@a@E + \ifdim\pgfmathfloat@mantissa@ltone pt=0pt + \def\pgfmathfloat@factor{1}% + \edef\pgfmathfloat@scaled@numerator{\the\pgfmathfloat@a@Mtok}% + \else + \pgfutil@ifundefined{FPdiv}{% + \pgfmathfloatparsenumber{\pgfmathfloat@mantissa@ltone}% + \pgfmathfloatreciprocal@{\pgfmathresult}% + }{% + \FPmessagesfalse% + \FPdebugfalse% + \FPdiv\pgfmathresult{1}{\pgfmathfloat@mantissa@ltone}% + \pgfmathfloatparsenumber{\pgfmathresult}% + }% + \let\pgfmathfloat@inv=\pgfmathresult + \pgfmathfloatcreate{1}{1.0}{\pgfkeysvalueof{/pgf/number format/frac shift}}% + \let\pgfmathfloat@scalebaseten=\pgfmathresult + \pgfmathfloatmultiply@{\pgfmathfloat@inv}{\pgfmathfloat@scalebaseten}% + \let\pgfmathfloat@factor=\pgfmathresult + \expandafter\pgfmathfloatparsenumber\expandafter{\the\pgfmathfloat@a@Mtok}% + \let\pgfmathfloat@loc@TMPa=\pgfmathresult + \pgfmathfloatmultiply@{\pgfmathfloat@factor}{\pgfmathfloat@loc@TMPa}% + \pgfmathfloattofixed\pgfmathresult + \let\pgfmathfloat@scaled@numerator=\pgfmathresult + \pgfmathfloattofixed\pgfmathfloat@factor + \expandafter\pgfmathfloat@loc@@to@int\pgfmathresult\relax{\pgfmathfloat@b@S}% + \edef\pgfmathfloat@factor{\the\pgfmathfloat@b@S}% + \fi + \pgfmathresultdenom=\pgfmathfloat@factor\relax + \pgfmathfloat@multiply@ten@to@the@E\pgfmathresultdenom + \expandafter\pgfmathfloat@loc@@to@int\pgfmathfloat@scaled@numerator\relax{\pgfmathresultnumerator}% + \pgfmathgreatestcommondivisor{\pgfmathresultnumerator}{\pgfmathresultdenom}% + \divide\pgfmathresultnumerator by\pgfmathresult\relax + \divide\pgfmathresultdenom by\pgfmathresult\relax + \ifpgfmathprintnumber@frac@warn + \ifnum\pgfmathresultdenom>1000 + \pgfutil@ifundefined{FPdiv}{% + \pgfmathfloattosci@\pgfmathfloat@arg + \pgf@typeout{! Package pgf /pgf/number format/frac warning=true: /pgf/number format/frac of `\pgfmathresult' = \the\pgfmathresultnumerator\space / \the\pgfmathresultdenom\space might be large due to instabilities. Try \string\usepackage{fp} to improve accuracy.}% + }{}% + \fi + \fi + \else + \pgfmathresultdenom=\pgfmath@target@denominator\relax + \pgfmathfloatcreate{1}{\the\pgfmathfloat@a@Mtok}{\the\pgfmathfloat@a@E}% + \pgfmathfloattofixed\pgfmathresult + \pgf@xa=\pgfmathresult pt + \multiply\pgf@xa by\pgfmathresultdenom + \edef\pgfmathfloat@scaled@numerator{\pgfmath@tonumber\pgf@xa}% + \expandafter\pgfmathfloat@loc@@to@int\pgfmathfloat@scaled@numerator\relax{\pgfmathresultnumerator}% + \fi + \ifpgfmathprintnumber@frac@whole + \else + \ifx\pgfmathfloat@wholenumber\pgfutil@empty + \else + \count0=\pgfmathfloat@wholenumber\relax + \multiply\count0 by\pgfmathresultdenom + \advance\pgfmathresultnumerator by\count0 + \def\pgfmathfloat@wholenumber{}% + \fi + \fi + \ifnum\pgfmathfloat@a@S<0 + \edef\pgfmathresult{{-\pgfmathfloat@wholenumber}{\the\pgfmathresultnumerator}{\the\pgfmathresultdenom}}% + \else + \edef\pgfmathresult{{\pgfmathfloat@wholenumber}{\the\pgfmathresultnumerator}{\the\pgfmathresultdenom}}% + \fi + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% +\def\pgfmathfloat@gobble@until@relax#1\relax{} + +\def\pgfmathgreatestcommondivisor#1#2{% + \begingroup + \count0=#1\relax + \count1=#2\relax + \ifnum\count0=0 + \edef\pgfmathresult{\the\count1}% + \else + \pgfmathgreatestcommondivisor@loop + \edef\pgfmathresult{\the\count0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +} +\def\pgfmathgreatestcommondivisor@loop{% + \ifnum\count1=0 + \else + \ifnum\count0>\count1 + \advance\count0 by-\count1 + \else + \advance\count1 by-\count0 + \fi + \expandafter\pgfmathgreatestcommondivisor@loop + \fi +}% + +\def\pgfmathfloat@multiply@ten@to@the@E#1{% + \ifnum\pgfmathfloat@a@E>0 + \multiply#1 by10 + \advance\pgfmathfloat@a@E by-1 + \def\pgfmathfloat@multiply@ten@to@the@E@next{\pgfmathfloat@multiply@ten@to@the@E{#1}}% + \else + \let\pgfmathfloat@multiply@ten@to@the@E@next=\relax% + \fi + \pgfmathfloat@multiply@ten@to@the@E@next +}% + +\def\pgfmathprintnumber@INT@TRUNC#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@INT@TRUNC@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@INT@TRUNC@impl#1.#2\relax#3#4e#5\relax{% + \pgfmathfloatroundhasperiodfalse + \pgfmathprintnumber@fixed@style{#1}#3#4e#5\relax% +} +\def\pgfmathprintnumber@INT@TRUNC@issci#1#2e#3\relax{% + \ifnum#1<3\relax + \pgfmathfloatcreate{#1}{#2}{#3}% + \pgfmathfloattofixed{\pgfmathresult}% + \expandafter\pgfmathprintnumber@INT@TRUNC@impl\pgfmathresult\relax#1#2e#3\relax + \else + \pgfmathfloatrounddisplaystyle#1#2e#3\relax% + \fi +} + +\def\pgfmathifisint#1#2#3{% + \gdef\pgfmathfloatisint@@{0}% + \begingroup + \pgfmathfloatparsenumber{#1}% + \let\pgfretval\pgfmathresult + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathfloatisint@\pgfmathresult\relax + \pgfmath@smuggleone\pgfretval + \endgroup + \if1\pgfmathfloatisint@@ #2\else #3\fi +}% +\def\pgfmathfloatisint@#1#2e#3\relax{% + \ifnum#1<3\relax + \pgfmathfloatcreate{#1}{#2}{#3}% + \pgfmathfloattofixed{\pgfmathresult}% + \def\pgfmathfloat@round@precision{6}% + \expandafter\pgfmathroundto\expandafter{\pgfmathresult}% + \ifpgfmathfloatroundhasperiod + \else + \let\pgfretval\pgfmathresult% + \gdef\pgfmathfloatisint@@{1}% + \fi + \fi +} + +\def\pgfmathprintnumber@INT@DETECT#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@INT@DETECT@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@INT@DETECT@issci#1#2e#3\relax{% + \begingroup + \ifnum#1<3\relax + \pgfmathfloatcreate{#1}{#2}{#3}% + \pgfmathfloattofixed{\pgfmathresult}% + \let\pgfmathfloat@round@precision@=\pgfmathfloat@round@precision + \def\pgfmathfloat@round@precision{6}% + \expandafter\pgfmathroundto\expandafter{\pgfmathresult}% + \let\pgfmathfloat@round@precision=\pgfmathfloat@round@precision@ + \ifpgfmathfloatroundhasperiod + \pgfmathprintnumber@SCI@issci#1#2e#3\relax + \else + \expandafter\pgfmathprintnumber@fixed@style\expandafter{\pgfmathresult}#1#2e#3\relax + \fi + \else + \pgfmathfloatrounddisplaystyle#1#2e#3\relax% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\def\pgfmathprintnumber@FIXED#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@FIXED@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@FIXED@issci#1#2e#3\relax{% + \begingroup + \ifnum#1<3 + \pgfmathfloatcreate{#1}{#2}{#3}% + \pgfmathfloattofixed{\pgfmathresult}% + \ifpgfmathfloat@usezerofill@fixed + \expandafter\pgfmathroundtozerofill\expandafter{\pgfmathresult}% + \else + \expandafter\pgfmathroundto\expandafter{\pgfmathresult}% + \fi + \ifpgfmathfloatroundmayneedrenormalize + \pgfmathfloat@a@E=#3\relax + \advance\pgfmathfloat@a@E by1 + \edef\pgfmathfloat@loc@TMPb{\noexpand\pgfmathprintnumber@fixed@style{\pgfmathresult}#1#2e\the\pgfmathfloat@a@E}% + \pgfmathfloat@loc@TMPb\relax% + \else + \expandafter\pgfmathprintnumber@fixed@style\expandafter{\pgfmathresult}#1#2e#3\relax% + \fi + \else% + \pgfmathfloatrounddisplaystyle#1#2e#3\relax% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + + +\def\pgfmathprintnumber@SCI#1{% + \pgfmathfloatparsenumber{#1}% + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathprintnumber@SCI@issci\pgfmathresult\relax +} + +\def\pgfmathprintnumber@SCI@issci#1#2e#3\relax{% + \begingroup + \pgfmathfloatcreate{#1}{#2}{#3}% + \edef\pgfmathfloat@round@precision{\pgfmathprintnumber@sci@precision}% + \ifpgfmathfloat@usezerofill@sci + \pgfmathfloatroundzerofill{\pgfmathresult}% + \else + \pgfmathfloatround{\pgfmathresult}% + \fi + \pgfmathfloat@to@FMeE@style\pgfmathresult + \expandafter\pgfmathfloatrounddisplaystyle\pgfmathresult\relax + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\pgfutil@protected\def\pgfmathprintnumber{% + \pgfutil@ifnextchar[% + {\pgfmathprintnumber@OPT}% + {\pgfmathprintnumber@noopt}% +} + +\def\pgfmathprintnumber@noopt#1{% + \pgfmathprintnumber@{#1}% + \ifpgfmathprintnumber@assumemathmode + \pgfmathresult + \else + \pgfutilensuremath{\pgfmathresult}% + \fi +}% +\def\pgfmathprintnumber@OPT[#1]#2{% + \begingroup + \pgfqkeys{/pgf/number format}{#1}% + \pgfmathprintnumber@{#2}% + \ifpgfmathprintnumber@assumemathmode + \pgfmathresult + \else + \pgfutilensuremath{\pgfmathresult}% + \fi + \endgroup +}% + +\def\pgfmathprintnumberto{% + \pgfutil@ifnextchar[% + {\pgfmathprintnumberto@OPT}% + {\pgfmathprintnumberto@noopt}% +} + +\def\pgfmathprintnumberto@noopt#1#2{% + \begingroup + \pgfmathprintnumber@{#1}% + \ifpgfmathprintnumber@assumemathmode + \global\let\pgfmathfloat@glob@TMP=\pgfmathresult + \else + \toks0=\expandafter{\pgfmathresult}% + \xdef\pgfmathfloat@glob@TMP{\noexpand\pgfutilensuremath{\the\toks0 }}% + \fi + \endgroup + \let#2=\pgfmathfloat@glob@TMP +}% +\def\pgfmathprintnumberto@OPT[#1]#2#3{% + \begingroup + \pgfqkeys{/pgf/number format}{#1}% + \pgfmathprintnumber@{#2}% + \ifpgfmathprintnumber@assumemathmode + \global\let\pgfmathfloat@glob@TMP=\pgfmathresult + \else + \toks0=\expandafter{\pgfmathresult}% + \xdef\pgfmathfloat@glob@TMP{\noexpand\pgfutilensuremath{\the\toks0 }}% + \fi + \endgroup + \let#3=\pgfmathfloat@glob@TMP +}% + + +\def\pgfmath@set@number@printer#1{% + \expandafter\let\expandafter\pgfmathprintnumber@\csname #1\endcsname + \expandafter\let\expandafter\pgfmathprintnumber@issci\csname #1@issci\endcsname +} + +\pgfkeys{/pgf/number format/std} + + +\def\pgfmathfloat@EOI{\pgfmathfloat@EOI}% + +\let\c@pgfmathroundto@prec=\pgfmathfloat@b@S% +\let\c@pgfmathroundto@offsetbehindperiod=\pgfmathfloat@b@E +\newcount\c@pgfmathroundto@lastzeros + +\newif\ifpgfmathround@impl@PREPERIOD@is@negative@zero + +\def\pgfmathroundto@impl#1{% + \edef\pgfmathround@input{#1}% + \global\pgfmathfloatroundmayneedrenormalizefalse + \pgfmathfloat@tmptoks={}% + \let\pgfmathround@next=\pgfutil@empty + \let\pgfmathround@cur=\pgfutil@empty + \let\pgfmathresult=\pgfutil@empty + \expandafter\c@pgfmathroundto@prec\pgfmathfloat@round@precision\relax + \c@pgfmathroundto@lastzeros=0 + \c@pgfmathroundto@offsetbehindperiod=-1 % + \pgfmathround@impl@PREPERIOD@is@negative@zerotrue + \expandafter\pgfmathroundto@impl@ITERATE@NODOT@firstcall\pgfmathround@input\pgfmathfloat@EOI +} + + +\def\pgfmathroundto@impl@discard@period#1.#2\pgfmathfloat@EOI{% + \pgfmathfloatroundhasperiodfalse + \aftergroup\pgfmathfloatroundhasperiodfalse + \def\pgfmathresult{#1}% +} + +\def\pgfmathroundto@impl@gobble@rest@and@start#1\pgfmathfloat@EOI{% + \pgfmathroundto@impl@start +} +\def\pgfmathroundto@impl@gobble@and@start\pgfmathfloat@EOI{% + \pgfmathroundto@impl@start +} +\def\pgfmathroundto@impl@gobble\pgfmathfloat@EOI{}% +\def\pgfmathroundto@impl@gobble@rest#1\pgfmathfloat@EOI{}% + +\def\pgfmathroundto@impl@start{% + \ifx\pgfmathround@next\pgfutil@empty + \ifnum\c@pgfmathroundto@offsetbehindperiod<0 + \ifpgfmathfloat@fixed@digits@after@period + \ifnum\c@pgfmathroundto@prec=0\relax + \pgfmathfloatroundhasperiodfalse + \aftergroup\pgfmathfloatroundhasperiodfalse + \edef\pgfmathresult{\pgfmathround@input}% + \else + \pgfmathfloat@tmptoks=\expandafter{\pgfmathround@input.}% + \c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec + \pgfmathroundto@impl@append@zeros + \edef\pgfmathresult{\the\pgfmathfloat@tmptoks}% + \fi + \else + \pgfmathfloatroundhasperiodfalse + \aftergroup\pgfmathfloatroundhasperiodfalse + \edef\pgfmathresult{\pgfmathround@input}% + \fi + \else + \pgfmathroundto@impl@finish@with@truncation + \fi + \else + \expandafter\ifnum\pgfmathround@next<5\relax + \pgfmathroundto@impl@finish@with@truncation + \else + \multiply\c@pgfmathroundto@offsetbehindperiod by-1 + \expandafter\pgfmathroundto@impl@ADD@ONE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI + \fi + \fi +} + +\def\pgfmathroundto@impl@finish@with@truncation{% + \ifpgfmathfloat@fixed@digits@after@period + \expandafter\pgfmathroundto@impl@REVERSE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI + \ifnum\c@pgfmathroundto@lastzeros=\c@pgfmathroundto@offsetbehindperiod + \ifpgfmathround@impl@PREPERIOD@is@negative@zero + \expandafter\pgfmathroundto@impl@discard@minus\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI + \fi + \fi + \ifnum\c@pgfmathroundto@prec=0\relax + \expandafter\pgfmathroundto@impl@discard@period\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI + \else + \advance\c@pgfmathroundto@prec by-\c@pgfmathroundto@offsetbehindperiod + \c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec + \pgfmathroundto@impl@append@zeros + \edef\pgfmathresult{\the\pgfmathfloat@tmptoks}% + \fi + \else + \pgfmathroundto@impl@discard@suffix@zeros + \fi +} + +\def\pgfmathroundto@impl@discard@minus-#1\pgfmathfloat@EOI{\pgfmathfloat@tmptoks={#1}}% + +\def\pgfmathroundto@impl@append@zeros{% + \ifnum\c@pgfmathroundto@offsetbehindperiod>0 + \pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}% + \advance\c@pgfmathroundto@offsetbehindperiod by-1 + \pgfmathroundto@impl@append@zeros + \fi +} + +\def\pgfmathroundto@impl@ADD@ONE{% + \pgfmathfloat@tmptoks={}% + \pgfmathroundto@impl@ADD@ONE@ITERATE +} +\def\pgfmathroundto@impl@ADD@ONE@ITERATE{% + \pgfutil@ifnextchar\pgfmathfloat@EOI{% + \global\pgfmathfloatroundmayneedrenormalizetrue + \edef\pgfmathresult{1\the\pgfmathfloat@tmptoks}% + \pgfmathroundto@impl@gobble + }{% + \pgfutil@ifnextchar.{% + \ifnum\c@pgfmathroundto@prec=0 + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot}% + \else + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@NEXT@COLLECT}% + \fi + \pgfmathround@nextcmd + }{% + \pgfutil@ifnextchar+{% + \global\pgfmathfloatroundmayneedrenormalizetrue + \edef\pgfmathresult{1\the\pgfmathfloat@tmptoks}% + \pgfmathroundto@impl@gobble@rest + }{% + \pgfutil@ifnextchar-{% + \global\pgfmathfloatroundmayneedrenormalizetrue + \edef\pgfmathresult{-1\the\pgfmathfloat@tmptoks}% + \pgfmathroundto@impl@gobble@rest + }{% + \pgfmathroundto@impl@ADD@ONE@NEXT + }% + }% + }% + }% +} + +\def\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot.{% + \pgfmathfloatroundhasperiodfalse + \aftergroup\pgfmathfloatroundhasperiodfalse + \pgfmathroundto@impl@ADD@ONE@ITERATE +} + +\def\pgfmathroundto@impl@ADD@ONE@NEXT@COLLECT#1{% + \pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}% + \pgfmathroundto@impl@ADD@ONE@ITERATE +} +\def\pgfmathroundto@impl@ADD@ONE@NEXT#1{% + \ifnum#1=9 + \ifnum\c@pgfmathroundto@offsetbehindperiod<0 + \ifpgfmathfloat@fixed@digits@after@period + \pgfmathfloat@tmptoks=\expandafter{\expandafter0\the\pgfmathfloat@tmptoks}% + \else + \fi + \else + \pgfmathfloat@tmptoks=\expandafter{\expandafter0\the\pgfmathfloat@tmptoks}% + \fi + \advance\c@pgfmathroundto@offsetbehindperiod by1 + \ifnum\c@pgfmathroundto@offsetbehindperiod=0 + \ifpgfmathfloat@fixed@digits@after@period + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE}% + \else + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE@gobble@dot}% + \fi + \else + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ADD@ONE@ITERATE}% + \fi + \else + \c@pgfmathroundto@lastzeros=#1 + \advance\c@pgfmathroundto@lastzeros by1 + \edef\pgfmathresult{\the\c@pgfmathroundto@lastzeros\the\pgfmathfloat@tmptoks}% + \pgfmathfloat@tmptoks=\expandafter{\pgfmathresult}% + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@REVERSE@ITERATE}% + \fi + \pgfmathround@nextcmd +} + + +\def\pgfmathroundto@impl@discard@suffix@zeros{% + \ifnum\c@pgfmathroundto@lastzeros=\c@pgfmathroundto@offsetbehindperiod + \ifpgfmathround@impl@PREPERIOD@is@negative@zero + \pgfmathfloatroundhasperiodfalse + \aftergroup\pgfmathfloatroundhasperiodfalse + \def\pgfmathresult{0}% + \else + \expandafter\pgfmathroundto@impl@discard@period\pgfmathround@input\pgfmathfloat@EOI + \fi + \else + \ifnum\c@pgfmathroundto@lastzeros=0 + \expandafter\pgfmathroundto@impl@REVERSE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI + \else + \expandafter\pgfmathroundto@impl@discard@suffix@zeros@ITERATE\the\pgfmathfloat@tmptoks\pgfmathfloat@EOI + \fi + \fi +} + +\def\pgfmathroundto@impl@discard@suffix@zeros@ITERATE#1{% + \advance\c@pgfmathroundto@lastzeros by-1 + \ifnum\c@pgfmathroundto@lastzeros=0 + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@REVERSE}% + \else + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@discard@suffix@zeros@ITERATE}% + \fi + \pgfmathround@nextcmd +} + +\def\pgfmathroundto@impl@REVERSE{% + \pgfmathfloat@tmptoks={}% + \pgfmathroundto@impl@REVERSE@ITERATE +} + +\def\pgfmathroundto@impl@REVERSE@ITERATE{% + \pgfutil@ifnextchar\pgfmathfloat@EOI{% + \edef\pgfmathresult{\the\pgfmathfloat@tmptoks}% + \pgfmathroundto@impl@gobble + }{% + \pgfmathroundto@impl@REVERSE@NEXT + }% +} + +\def\pgfmathroundto@impl@REVERSE@NEXT#1{% + \pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}% + \pgfmathroundto@impl@REVERSE@ITERATE +} + +\def\pgfmathroundto@impl@BEGIN@DOT.{% + \pgfmathfloat@tmptoks=\expandafter{\expandafter.\the\pgfmathfloat@tmptoks}% + \c@pgfmathroundto@offsetbehindperiod=0 + \pgfmathroundto@impl@ITERATE@DOT +} +\def\pgfmathroundto@impl@ITERATE@DOT{% + \pgfutil@ifnextchar\pgfmathfloat@EOI{% + \pgfmathroundto@impl@gobble@and@start + }{% + \pgfmathroundto@impl@NEXT@DOT + }% +} +\def\pgfmathroundto@impl@NEXT@DOT#1{% + \ifnum\c@pgfmathroundto@offsetbehindperiod=\c@pgfmathroundto@prec + \def\pgfmathround@next{#1}% + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@gobble@rest@and@start}% + \else + \advance\c@pgfmathroundto@offsetbehindperiod by1 + \ifnum#1=0 + \advance\c@pgfmathroundto@lastzeros by1 + \else + \c@pgfmathroundto@lastzeros=0 + \fi + \pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}% + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@DOT}% + \fi + \pgfmathround@nextcmd +}% + +\def\pgfmathroundto@impl@ITERATE@NODOT@firstcall#1{% + \def\pgfmathround@cur{#1}% + \ifx\pgfmathround@cur\pgfmathfloat@EOI + \pgfmathround@impl@PREPERIOD@is@negative@zerofalse + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@start}% + \else + \ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@PERIOD + \pgfmathround@impl@PREPERIOD@is@negative@zerofalse + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@BEGIN@DOT.}% + \else + \ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@MINUS + \else + \pgfmathround@impl@PREPERIOD@is@negative@zerofalse + \fi + \pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}% + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@NODOT}% + \fi + \fi + \pgfmathround@nextcmd +} + +\def\pgfmathroundto@impl@ITERATE@NODOT#1{% + \def\pgfmathround@cur{#1}% + \ifx\pgfmathround@cur\pgfmathfloat@EOI + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@start}% + \else + \ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@PERIOD + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@BEGIN@DOT.}% + \else + \ifx\pgfmathround@cur\pgfmathfloatparsenumber@tok@ZERO + \else + \pgfmathround@impl@PREPERIOD@is@negative@zerofalse + \fi + \pgfmathfloat@tmptoks=\expandafter{\expandafter#1\the\pgfmathfloat@tmptoks}% + \def\pgfmathround@nextcmd{\pgfmathroundto@impl@ITERATE@NODOT}% + \fi + \fi + \pgfmathround@nextcmd +} + + + +\def\pgfmathfloatround@impl{% + \expandafter\pgfmathroundto@impl\expandafter{\the\pgfmathfloat@a@Mtok}% + \ifpgfmathfloatroundmayneedrenormalize + \ifpgfmathfloatroundhasperiod + \expandafter\pgfmathfloatround@impl@renormalize\pgfmathresult\pgfmathfloat@EOI% + \else + \expandafter\pgfmathfloatround@impl@renormalize\pgfmathresult.\pgfmathfloat@EOI% + \fi + \advance\pgfmathfloat@a@E by1 + \fi + \pgfmathfloatcreate{\the\pgfmathfloat@a@S}{\pgfmathresult}{\the\pgfmathfloat@a@E}% +} + +\def\pgfmathfloatround@impl@renormalize#1#2.#3\pgfmathfloat@EOI{% + \pgfmathroundto@impl{#1.#2#3}% +} + + + + + +\def\pgfmathfloattofixed@impl#1.#2\relax{% + \ifnum\pgfmathfloat@a@E<0 + \ifcase-\pgfmathfloat@a@E + \or% + \pgfmathfloat@a@Mtok={0.}% + \or% + \pgfmathfloat@a@Mtok={0.0}% + \or% + \pgfmathfloat@a@Mtok={0.00}% + \or% + \pgfmathfloat@a@Mtok={0.000}% + \or% + \pgfmathfloat@a@Mtok={0.0000}% + \or% + \pgfmathfloat@a@Mtok={0.00000}% + \or% + \pgfmathfloat@a@Mtok={0.000000}% + \or% + \pgfmathfloat@a@Mtok={0.0000000}% + \or% + \pgfmathfloat@a@Mtok={0.00000000}% + \or% + \pgfmathfloat@a@Mtok={0.000000000}% + \else% + \pgfmathfloat@a@Mtok={0.0000000000}% + \advance\pgfmathfloat@a@E by10 + \pgfutil@loop + \ifnum\pgfmathfloat@a@E<-1 + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok 0}% + \advance\pgfmathfloat@a@E by1 + \pgfutil@repeat + \fi + \def\pgfmathfloat@loc@TMPb{#2}% + \def\pgfmathfloat@loc@TMPc{0}% + \ifx\pgfmathfloat@loc@TMPb\pgfmathfloat@loc@TMPc + \edef\pgfmathresult{\the\pgfmathfloat@a@Mtok #1}% + \else + \edef\pgfmathresult{\the\pgfmathfloat@a@Mtok #1#2}% + \fi + \else + \pgfmathfloat@a@Mtok{#1}% + \pgfmathfloattofixed@impl@pos#2000000000\pgfmathfloat@EOI + \edef\pgfmathresult{\the\pgfmathfloat@a@Mtok}% + \fi +} + +\def\pgfmathfloattofixed@impl@pos#1#2#3#4#5#6#7#8#9\pgfmathfloat@EOI{% + \ifcase\pgfmathfloat@a@E + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok .#1#2#3#4#5#6#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1.#2#3#4#5#6#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2.#3#4#5#6#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3.#4#5#6#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4.#5#6#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5.#6#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6.#7#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6#7.#8#9}% + \or% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6#7#8.#9}% + \else% + \pgfmathfloat@a@Mtok\expandafter{\the\pgfmathfloat@a@Mtok #1#2#3#4#5#6#7#8}% + \advance\pgfmathfloat@a@E by-8 + \pgfmathfloattofixed@impl@collectmantissa#9\count\pgfmathfloat@a@E + \fi +}% + +\def\pgfmathfloattofixed@impl@collectmantissa#1#2\count#3{% + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok #1}% + \advance\pgfmathfloat@a@E by-1% + \def\pgfmathfloat@loc@TMPb{#2}% + \ifx\pgfmathfloat@loc@TMPb\pgfutil@empty + \pgfutil@loop + \ifnum\pgfmathfloat@a@E>0% + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok 0}% + \advance\pgfmathfloat@a@E by-1% + \pgfutil@repeat + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok .0}% + \else + \ifnum\pgfmathfloat@a@E=0 + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok .#2}% + \else + \pgfmathfloattofixed@impl@collectmantissa#2\count#3% + \fi + \fi +} + + + +\def\pgfmathfloatparsenumber@tok@ZERO{0} +\def\pgfmathfloatparsenumber@tok@PLUS{+} +\def\pgfmathfloatparsenumber@tok@MINUS{-} +\def\pgfmathfloatparsenumber@tok@PERIOD{.} + +\newif\ifpgfmathfloatparsenumberpendingperiod + +\def\pgfflt@EOI{p@EOI}% +\def\pgfflt@EOI@unexpanded{\pgfflt@EOI}% + +\def\pgfflt@impl#1{% + \pgfmathfloatparsenumberpendingperiodfalse + \pgfmathfloat@tmptoks={}% + \pgfmathfloat@a@E=0 + \expandafter\ifx\csname pgfflt@#1\endcsname\relax + \pgfmathfloat@a@S=1 + \expandafter\pgfflt@init\expandafter#1% + \else + \expandafter\expandafter\csname pgfflt@#1\endcsname + \fi +} +\expandafter\def\csname pgfflt@+\endcsname{% + \pgfmathfloat@a@S=1 % + \pgfflt@init}% +\expandafter\def\csname pgfflt@-\endcsname{% + \pgfmathfloat@a@S=2 % + \pgfflt@init}% +\expandafter\def\csname pgfflt@\pgfflt@EOI\endcsname{% + \pgfmathfloatparsenumber@handleerror{empty number}{}{}}% + +\pgfkeys{ + /pgf/fpu/handlers/empty number/.style 2 args={% + /pgf/fpu/handlers/invalid number={#1}{#2}% + }, + /pgf/fpu/empty number is zero/.style={% + /pgf/fpu/handlers/empty number/.code 2 args={% + \pgfmathfloatcreate{0}{0.0}{0}% + }% + },% + /pgf/fpu/handlers/invalid separator/.code 2 args={% + \pgfmath@error{Could not parse input '#1' as a floating point number, sorry. The unreadable part was near the decimal separator '#2'. Do you need the option 'read comma as period'?}{}% + }, + /pgf/fpu/handlers/invalid number/.code 2 args={% + \pgfmath@error{Could not parse input '#1' as a floating point number, sorry. The unreadable part was near '#2'.}{}% + }, + /pgf/fpu/handlers/wrong lowlevel format/.code 2 args={% + \pgfmath@error{Sorry, an internal routine of the floating point unit got an ill-formatted floating point number `#1'. The unreadable part was near '#2'.}{}% + \let\pgfmathresult=\pgfutil@empty + }, +} + +\def\pgfmathfloatparsenumber@handleerror#1#2#3{% + \let\pgfmathresult=\pgfutil@empty + \pgfmathfloatparsenumberpendingperiodfalse + \pgfkeys{/pgf/fpu/handlers/#1={#2}{#3}}% + \ifx\pgfmathresult\pgfutil@empty + \pgfmathfloat@a@S=3 + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0 + \else + \expandafter\pgfmathfloat@decompose@tok\pgfmathresult\relax\pgfmathfloat@a@S\pgfmathfloat@a@Mtok\pgfmathfloat@a@E + \fi +} +\def\pgfflt@error#1\pgfflt@EOI{% + \begingroup + \pgfmathfloat@a@Mtok={#1}% + \xdef\pgfmathfloat@glob@TMP{% + \noexpand\pgfmathfloatparsenumber@handleerror + {invalid number}{\pgfmathresult}{\the\pgfmathfloat@a@Mtok}}% + \endgroup + \pgfmathfloat@glob@TMP +}% + + + +\def\pgfflt@init#1{% + \expandafter\ifx\csname pgffltA@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltA@#1\endcsname + \fi} +\expandafter\def\csname pgffltA@0\endcsname{\pgfflt@leadingzero}% +\expandafter\def\csname pgffltA@1\endcsname{\pgfflt@nonzerodigit1}% +\expandafter\def\csname pgffltA@2\endcsname{\pgfflt@nonzerodigit2}% +\expandafter\def\csname pgffltA@3\endcsname{\pgfflt@nonzerodigit3}% +\expandafter\def\csname pgffltA@4\endcsname{\pgfflt@nonzerodigit4}% +\expandafter\def\csname pgffltA@5\endcsname{\pgfflt@nonzerodigit5}% +\expandafter\def\csname pgffltA@6\endcsname{\pgfflt@nonzerodigit6}% +\expandafter\def\csname pgffltA@7\endcsname{\pgfflt@nonzerodigit7}% +\expandafter\def\csname pgffltA@8\endcsname{\pgfflt@nonzerodigit8}% +\expandafter\def\csname pgffltA@9\endcsname{\pgfflt@nonzerodigit9}% +\def\pgfflt@nonzerodigit#1{% + \pgfmathfloat@a@Mtok={#1}% + \pgfmathfloatparsenumberpendingperiodtrue + \pgfflt@positiveexp}% +\expandafter\def\csname pgffltA@n\endcsname{\pgfflt@readnan}% +\expandafter\def\csname pgffltA@N\endcsname{\pgfflt@readnan}% +\expandafter\def\csname pgffltA@i\endcsname{\pgfflt@readinf}% +\expandafter\def\csname pgffltA@I\endcsname{\pgfflt@readinf}% +\expandafter\def\csname pgffltA@.\endcsname{% + \pgfmathfloat@a@E=-1 + \pgfflt@leadingzero@foundperiod}% +\expandafter\def\csname pgffltA@,\endcsname{% + \pgfmathfloat@frenchinput{% + \pgfmathfloat@a@E=-1 + \pgfflt@leadingzero@foundperiod + }% +}% + +\def\pgfmathfloat@frenchinput#1{% + \ifpgfmathparsenumber@comma@as@period + \def\pgf@marshal{#1}% + \expandafter\pgf@marshal + \else + \expandafter\pgfflt@error@separator\expandafter,% + \fi +}% +\def\pgfflt@error@separator#1\pgfflt@EOI{% + \begingroup + \pgfmathfloat@a@Mtok={#1}% + \xdef\pgfmathfloat@glob@TMP{% + \noexpand\pgfmathfloatparsenumber@handleerror + {invalid separator}{\pgfmathresult}{\the\pgfmathfloat@a@Mtok}}% + \endgroup + \pgfmathfloat@glob@TMP +}% + +\def\pgfflt@finish#1\pgfflt@EOI{} + +\def\pgfflt@readnan #1#2{% + \def\pgfflt@readnan@ok{1}% + \if#1a\else\if#1A\else\def\pgfflt@readnan@ok{0}\fi\fi + \if#2n\else\if#2N\else\def\pgfflt@readnan@ok{0}\fi\fi + \if\pgfflt@readnan@ok1% + \pgfmathfloat@a@S=3\relax% + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0% + \expandafter\pgfflt@finish + \else + \def\pgfflt@readnan@{\pgfflt@error #1#2}% + \expandafter\pgfflt@readnan@ + \fi +} +\def\pgfflt@readinf #1#2{% + \def\pgfflt@readinf@ok{1}% + \if#1n\else\if#1N\else\def\pgfflt@readinf@ok{0}\fi\fi + \if#2f\else\if#2F\else\def\pgfflt@readinf@ok{0}\fi\fi + \if\pgfflt@readinf@ok1% + \ifnum\pgfmathfloat@a@S=1 % + \pgfmathfloat@a@S=4 % + \pgfmathfloat@a@Mtok={0.0}% + \else + \pgfmathfloat@a@S=5 % + \pgfmathfloat@a@Mtok={0.0}% + \fi + \pgfmathfloat@a@E=0 % + \expandafter\pgfflt@finish + \else + \def\pgfflt@readinf@{\pgfflt@error #1#2}% + \expandafter\pgfflt@readinf@ + \fi +} +\def\pgfflt@leadingzero#1{% + \expandafter\ifx\csname pgffltB@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltB@#1\endcsname + \fi} +\expandafter\def\csname pgffltB@0\endcsname{\pgfflt@leadingzero}% +\expandafter\def\csname pgffltB@1\endcsname{\pgfmathfloat@a@Mtok={1}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@2\endcsname{\pgfmathfloat@a@Mtok={2}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@3\endcsname{\pgfmathfloat@a@Mtok={3}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@4\endcsname{\pgfmathfloat@a@Mtok={4}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@5\endcsname{\pgfmathfloat@a@Mtok={5}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@6\endcsname{\pgfmathfloat@a@Mtok={6}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@7\endcsname{\pgfmathfloat@a@Mtok={7}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@8\endcsname{\pgfmathfloat@a@Mtok={8}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@9\endcsname{\pgfmathfloat@a@Mtok={9}\pgfmathfloatparsenumberpendingperiodtrue \pgfflt@positiveexp} +\expandafter\def\csname pgffltB@\pgfmathfloat@POSTFLAGSCHAR\endcsname{\pgfmathfloat@a@Mtok={0}\pgfflt@readlowlevelfloat}% +\expandafter\def\csname pgffltB@.\endcsname{% + \pgfmathfloat@a@E=-1 + \pgfflt@leadingzero@foundperiod}% +\expandafter\def\csname pgffltB@,\endcsname{% + \pgfmathfloat@frenchinput{% + \pgfmathfloat@a@E=-1 + \pgfflt@leadingzero@foundperiod + }% +}% +\expandafter\def\csname pgffltB@e\endcsname{% + \pgfmathfloat@a@S=0\relax% + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0% + \pgfflt@readexponent}% +\let\pgffltB@E=\pgffltB@e +\expandafter\def\csname pgffltB@\pgfflt@EOI\endcsname{% + \pgfmathfloat@a@S=0\relax% + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0}% + +\def\pgfflt@leadingzero@foundperiod#1{% + \expandafter\ifx\csname pgffltC@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltC@#1\endcsname + \fi} +\expandafter\def\csname pgffltC@0\endcsname{% + \advance\pgfmathfloat@a@E by-1 + \pgfflt@leadingzero@foundperiod}% +\expandafter\def\csname pgffltC@1\endcsname{\pgfmathfloat@a@Mtok={1}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@2\endcsname{\pgfmathfloat@a@Mtok={2}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@3\endcsname{\pgfmathfloat@a@Mtok={3}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@4\endcsname{\pgfmathfloat@a@Mtok={4}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@5\endcsname{\pgfmathfloat@a@Mtok={5}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@6\endcsname{\pgfmathfloat@a@Mtok={6}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@7\endcsname{\pgfmathfloat@a@Mtok={7}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@8\endcsname{\pgfmathfloat@a@Mtok={8}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@9\endcsname{\pgfmathfloat@a@Mtok={9}\pgfmathfloatparsenumberpendingperiodtrue\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltC@e\endcsname{% + \pgfmathfloat@a@S=0\relax% + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0% + \pgfflt@readexponent}% +\let\pgffltC@E=\pgffltC@e +\expandafter\def\csname pgffltC@\pgfflt@EOI\endcsname{% + \pgfmathfloat@a@S=0\relax% + \pgfmathfloat@a@Mtok={0.0}% + \pgfmathfloat@a@E=0}% + + +\def\pgfflt@positiveexp#1{% + \expandafter\ifx\csname pgffltD@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltD@#1\endcsname + \fi} +\expandafter\def\csname pgffltD@0\endcsname{% + \advance\pgfmathfloat@a@E by1 + \pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}% + \pgfflt@pendingzeros@positiveexp}% +\expandafter\def\csname pgffltD@1\endcsname{\pgffltD@nonzerodigit1}% +\expandafter\def\csname pgffltD@2\endcsname{\pgffltD@nonzerodigit2}% +\expandafter\def\csname pgffltD@3\endcsname{\pgffltD@nonzerodigit3}% +\expandafter\def\csname pgffltD@4\endcsname{\pgffltD@nonzerodigit4}% +\expandafter\def\csname pgffltD@5\endcsname{\pgffltD@nonzerodigit5}% +\expandafter\def\csname pgffltD@6\endcsname{\pgffltD@nonzerodigit6}% +\expandafter\def\csname pgffltD@7\endcsname{\pgffltD@nonzerodigit7}% +\expandafter\def\csname pgffltD@8\endcsname{\pgffltD@nonzerodigit8}% +\expandafter\def\csname pgffltD@9\endcsname{\pgffltD@nonzerodigit9}% +\expandafter\def\csname pgffltD@\pgfmathfloat@POSTFLAGSCHAR\endcsname{\pgfflt@readlowlevelfloat}% +\expandafter\def\csname pgffltD@.\endcsname{\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltD@,\endcsname{\pgfmathfloat@frenchinput{\pgfflt@finish@number@after@period}}% +\expandafter\def\csname pgffltD@e\endcsname{\pgfflt@readexponent}% +\let\pgffltD@E=\pgffltD@e +\expandafter\def\csname pgffltD@\pgfflt@EOI\endcsname{}% +\def\pgffltD@nonzerodigit#1{% + \advance\pgfmathfloat@a@E by1 + \ifpgfmathfloatparsenumberpendingperiod + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}% + \pgfmathfloatparsenumberpendingperiodfalse + \fi + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}% + \pgfflt@positiveexp}% + +\def\pgfflt@readlowlevelfloat#1e#2]\pgfflt@EOI{% + \pgfmathfloatparsenumberpendingperiodfalse + \pgfmathfloat@a@S=\the\pgfmathfloat@a@Mtok\relax + \pgfmathfloat@a@Mtok={#1}% + \pgfmathfloat@a@E=#2 +}% + +\def\pgfflt@readexponent#1\pgfflt@EOI{% + \afterassignment\pgfflt@readexponent@ + \pgfmathfloat@b@E=#1 \pgfflt@EOI% +} +\def\pgfflt@readexponent@#1{% + \advance\pgfmathfloat@a@E by\pgfmathfloat@b@E\relax + \def\pgfmathfloat@loc@TMPb{#1}% + \ifx\pgfmathfloat@loc@TMPb\pgfflt@EOI@unexpanded + \else + \def\pgfmathfloat@loc@TMPb{\pgfflt@error#1}% + \expandafter\pgfmathfloat@loc@TMPb + \fi +} + +\def\pgfflt@pendingzeros@positiveexp#1{% + \expandafter\ifx\csname pgffltE@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltE@#1\endcsname + \fi} +\expandafter\def\csname pgffltE@0\endcsname{% + \pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}% + \advance\pgfmathfloat@a@E by1 + \pgfflt@pendingzeros@positiveexp}% +\expandafter\def\csname pgffltE@1\endcsname{\pgffltE@nonzerodigit1}% +\expandafter\def\csname pgffltE@2\endcsname{\pgffltE@nonzerodigit2}% +\expandafter\def\csname pgffltE@3\endcsname{\pgffltE@nonzerodigit3}% +\expandafter\def\csname pgffltE@4\endcsname{\pgffltE@nonzerodigit4}% +\expandafter\def\csname pgffltE@5\endcsname{\pgffltE@nonzerodigit5}% +\expandafter\def\csname pgffltE@6\endcsname{\pgffltE@nonzerodigit6}% +\expandafter\def\csname pgffltE@7\endcsname{\pgffltE@nonzerodigit7}% +\expandafter\def\csname pgffltE@8\endcsname{\pgffltE@nonzerodigit8}% +\expandafter\def\csname pgffltE@9\endcsname{\pgffltE@nonzerodigit9}% +\expandafter\def\csname pgffltE@.\endcsname{\pgfflt@finish@number@after@period}% +\expandafter\def\csname pgffltE@,\endcsname{\pgfmathfloat@frenchinput{\pgfflt@finish@number@after@period}}% +\def\pgffltE@e{\pgfflt@readexponent}% +\let\pgffltE@E=\pgffltE@e +\expandafter\def\csname pgffltE@\pgfflt@EOI\endcsname{}% +\def\pgffltE@nonzerodigit#1{% + \advance\pgfmathfloat@a@E by1 + \ifpgfmathfloatparsenumberpendingperiod + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}% + \pgfmathfloatparsenumberpendingperiodfalse + \fi + \pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}% + \pgfmathfloat@tmptoks={}% + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}% + \pgfflt@positiveexp}% + +\def\pgfflt@finish@number@after@period#1{% + \expandafter\ifx\csname pgffltF@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltF@#1\endcsname + \fi} +\expandafter\def\csname pgffltF@0\endcsname{% + \pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}% + \pgfflt@pendingzeros}% +\expandafter\def\csname pgffltF@1\endcsname{\pgffltF@nonzerodigit1}% +\expandafter\def\csname pgffltF@2\endcsname{\pgffltF@nonzerodigit2}% +\expandafter\def\csname pgffltF@3\endcsname{\pgffltF@nonzerodigit3}% +\expandafter\def\csname pgffltF@4\endcsname{\pgffltF@nonzerodigit4}% +\expandafter\def\csname pgffltF@5\endcsname{\pgffltF@nonzerodigit5}% +\expandafter\def\csname pgffltF@6\endcsname{\pgffltF@nonzerodigit6}% +\expandafter\def\csname pgffltF@7\endcsname{\pgffltF@nonzerodigit7}% +\expandafter\def\csname pgffltF@8\endcsname{\pgffltF@nonzerodigit8}% +\expandafter\def\csname pgffltF@9\endcsname{\pgffltF@nonzerodigit9}% +\def\pgffltF@e{\pgfflt@readexponent}% +\let\pgffltF@E=\pgffltF@e +\expandafter\def\csname pgffltF@\pgfflt@EOI\endcsname{}% +\def\pgffltF@nonzerodigit#1{% + \ifpgfmathfloatparsenumberpendingperiod + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}% + \pgfmathfloatparsenumberpendingperiodfalse + \fi + \pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}% + \pgfmathfloat@tmptoks={}% + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}% + \pgfflt@finish@number@after@period}% + + +\def\pgfflt@pendingzeros#1{% + \expandafter\ifx\csname pgffltG@#1\endcsname\relax + \expandafter\pgfflt@error\expandafter#1% + \else + \expandafter\expandafter\csname pgffltG@#1\endcsname + \fi} +\expandafter\def\csname pgffltG@0\endcsname{% + \pgfmathfloat@tmptoks=\expandafter{\the\pgfmathfloat@tmptoks0}% + \pgfflt@pendingzeros}% +\expandafter\def\csname pgffltG@1\endcsname{\pgffltG@nonzerodigit1}% +\expandafter\def\csname pgffltG@2\endcsname{\pgffltG@nonzerodigit2}% +\expandafter\def\csname pgffltG@3\endcsname{\pgffltG@nonzerodigit3}% +\expandafter\def\csname pgffltG@4\endcsname{\pgffltG@nonzerodigit4}% +\expandafter\def\csname pgffltG@5\endcsname{\pgffltG@nonzerodigit5}% +\expandafter\def\csname pgffltG@6\endcsname{\pgffltG@nonzerodigit6}% +\expandafter\def\csname pgffltG@7\endcsname{\pgffltG@nonzerodigit7}% +\expandafter\def\csname pgffltG@8\endcsname{\pgffltG@nonzerodigit8}% +\expandafter\def\csname pgffltG@9\endcsname{\pgffltG@nonzerodigit9}% +\def\pgffltG@e{\pgfflt@readexponent}% +\let\pgffltG@E=\pgffltG@e +\expandafter\def\csname pgffltG@\pgfflt@EOI\endcsname{}% +\def\pgffltG@nonzerodigit#1{% + \ifpgfmathfloatparsenumberpendingperiod + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok.}% + \pgfmathfloatparsenumberpendingperiodfalse + \fi + \pgfmathfloat@a@Mtok=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfmathfloat@a@Mtok\the\pgfmathfloat@tmptoks}% + \pgfmathfloat@tmptoks={}% + \pgfmathfloat@a@Mtok=\expandafter{\the\pgfmathfloat@a@Mtok#1}% + \pgfflt@finish@number@after@period}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.base.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.base.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8fb945b74d100dd15e088c35f1e8d3f1effec25e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.base.code.tex @@ -0,0 +1,211 @@ + +\pgfmathdeclarefunction{bin}{1}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@% + \c@pgfmath@counta=#1\relax\pgfmath@% + \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{2}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} +\pgfmathdeclarefunction{hex}{1}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@% + \c@pgfmath@counta=#1\relax\pgfmath@% + \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{16}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{Hex}{1}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@% + \c@pgfmath@counta=#1\relax\pgfmath@% + \expandafter\pgfmathbasetoBase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{16}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{oct}{1}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@% + \c@pgfmath@counta=#1\relax\pgfmath@% + \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\the\c@pgfmath@counta}{10}{8}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + + +\def\pgfmathbasetodec#1#2#3{% + \pgfmath@checknumber{#2}% + \pgfmath@checkbase{#3}% + \def\pgfmath@base{#3}% + \def\pgfmath@base@macro{#1}% + \c@pgfmath@counta=1\relax% + \let\pgfmath@reversed=\pgfmath@empty% + \expandafter\pgfmathbasetodec@#2\pgfmath@base@stop} + +\def\pgfmathbasetodec@#1{% + \ifx#1\pgfmath@base@stop% + \c@pgfmath@countb=0% + \divide\c@pgfmath@counta by\pgfmath@base\relax% + \expandafter\pgfmathbasetodec@@% + \else% + \edef\pgfmath@reversed{\pgfmath@reversed#1}% + \expandafter\multiply\expandafter\c@pgfmath@counta\pgfmath@base\relax% + \expandafter\pgfmathbasetodec@% + \fi} + +\def\pgfmathbasetodec@@{\expandafter\pgfmathbasetodec@@@\pgfmath@reversed\pgfmathbasetodec} + +\def\pgfmathbasetodec@@@#1{% + \ifx\pgfmathbasetodec#1\relax% + \expandafter\edef\pgfmath@base@macro{\the\c@pgfmath@countb}% + \let\pgfmath@next=\pgfmathbasetodec@@@@% + \else% + \chardef\pgfmath@charnum`#1\relax% + \c@pgfmath@countc=\pgfmath@charnum\relax% + \ifnum\c@pgfmath@countc>96\relax% + \advance\c@pgfmath@countc by-87\relax% + \else + \ifnum\c@pgfmath@countc>64\relax% + \advance\c@pgfmath@countc by-55\relax% + \else + \advance\c@pgfmath@countc by-48\relax% + \fi% + \fi% + \ifnum\c@pgfmath@countc<\pgfmath@base\relax% + \multiply\c@pgfmath@countc by\c@pgfmath@counta% + \advance\c@pgfmath@countb by\c@pgfmath@countc% + \divide\c@pgfmath@counta by\pgfmath@base\relax% + \let\pgfmath@next\pgfmathbasetodec@@@% + \else + \pgfmath@error{Digit `#1' invalid for base \pgfmath@base}{}% + \let\pgfmath@next=\relax% + \fi% + \fi% + \pgfmath@next} +\def\pgfmathbasetodec@@@@{% + \expandafter\pgfmath@ensurenumberlength\expandafter{\pgfmath@base@macro}% +} + +\def\pgfmathdectobase#1#2#3{% + \pgfmath@checknumber{#2}% + \pgfmath@checkbase{#3}% + \c@pgfmath@counta=#2\relax% + \let#1=\pgfmath@empty% + \pgfmathloop + \ifnum\c@pgfmath@counta>0\relax% + \c@pgfmath@countb=\c@pgfmath@counta% + \divide\c@pgfmath@countb by#3\relax% + \multiply\c@pgfmath@countb by-#3\relax% + \advance\c@pgfmath@countb by\c@pgfmath@counta% + \edef#1{\csname pgfmath@lowercase digit@\the\c@pgfmath@countb\endcsname#1}% + \divide\c@pgfmath@counta by#3\relax% + \repeatpgfmathloop% + \pgfmath@ensurenumberlength{#1}} + +\def\pgfmathdectoBase#1#2#3{% + \pgfmath@checkbase{#3}% + \pgfmath@checknumber{#2}% + \c@pgfmath@counta=#2\relax% + \let#1=\pgfmath@empty% + \pgfmathloop + \ifnum\c@pgfmath@counta>0\relax% + \c@pgfmath@countb=\c@pgfmath@counta% + \divide\c@pgfmath@countb by#3\relax% + \multiply\c@pgfmath@countb by-#3\relax% + \advance\c@pgfmath@countb by\c@pgfmath@counta% + \edef#1{\csname pgfmath@uppercase digit@\the\c@pgfmath@countb\endcsname#1}% + \divide\c@pgfmath@counta by#3\relax% + \repeatpgfmathloop% + \pgfmath@ensurenumberlength{#1}} + +\def\pgfmath@base@digits@create{% + \def\pgfmath@base@digit@style{lowercase digit}% + \c@pgfmath@counta=0\relax% + \pgfmath@base@digits@create@0123456789abcdefghijklmnopqrstuvwxyz\pgfmath@base@digits@create% + \def\pgfmath@base@digit@style{uppercase digit}% + \c@pgfmath@counta=0\relax% + \pgfmath@base@digits@create@0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ\pgfmath@base@digits@create} + +\def\pgfmath@base@digits@create@#1{% + \ifx\pgfmath@base@digits@create#1\relax% + \else% + \expandafter\pgfmath@def\expandafter{\pgfmath@base@digit@style}{\the\c@pgfmath@counta}{#1}% + \advance\c@pgfmath@counta by1\relax% + \expandafter\pgfmath@base@digits@create@% + \fi} +\pgfmath@base@digits@create + +\def\pgfmathbasetobase#1#2#3#4{% + \pgfmathbasetodec{\pgfmath@base@temp}{#2}{#3}% + \pgfmathdectobase{#1}{\pgfmath@base@temp}{#4}% +} + +\def\pgfmathbasetoBase#1#2#3#4{% + \pgfmathbasetodec{\pgfmath@base@temp}{#2}{#3}% + \pgfmathdectoBase{#1}{\pgfmath@base@temp}{#4}% +} + +\def\pgfmath@checkbase#1{% + \ifnum#1<2\relax% + \pgfmath@error{Cannot process numbers in base `#1'.}{}% + \else% + \ifnum#1>36\relax% + \pgfmath@error{Cannot process numbers in base `#1'.}{}% + \fi% + \fi} + +\def\pgfmath@checknumber#1{% + \expandafter\pgfmath@checknumber@#1\pgfmath@} +\def\pgfmath@checknumber@#1#2\pgfmath@{% + \ifx#1-% + \pgfmath@error{Cannot process negative numbers.}{}% + \fi} + +\def\pgfmath@ensurenumberlength#1{% + \def\pgfmath@base@tempa{#1}% + \expandafter\c@pgfmath@counta\pgfmath@basenumberlength\relax% + \expandafter\pgfmath@ensurenumberlength@#1\pgfmath@ensurenumberlength} +\def\pgfmath@ensurenumberlength@#1{% + \ifx\pgfmath@ensurenumberlength#1\relax% + \expandafter\pgfmath@ensurenumberlength@@% + \else% + \advance\c@pgfmath@counta by-1\relax% + \expandafter\pgfmath@ensurenumberlength@ + \fi} + +\def\pgfmath@ensurenumberlength@@{% + \edef\pgfmath@base@tempb{\pgfmath@base@tempa}% + \pgfmath@ensurenumberlength@@@} +\def\pgfmath@ensurenumberlength@@@{% + \ifnum\c@pgfmath@counta>0\relax% + \advance\c@pgfmath@counta by-1\relax% + \edef\pgfmath@base@tempb{0\pgfmath@base@tempb}% + \expandafter\pgfmath@ensurenumberlength@@@% + \fi% + \expandafter\edef\pgfmath@base@tempa{\pgfmath@base@tempb}} + +\def\pgfmathsetbasenumberlength#1{\def\pgfmath@basenumberlength{#1}} +\pgfmathsetbasenumberlength{1}% + +\def\pgfmathtodigitlist#1#2{% + \def\pgfmath@temp{#1}% + \let\pgfmath@digitlist=\pgfutil@empty% + \edef\pgfmath@@tmp{#2}% + \expandafter\pgfmath@todigitlist\pgfmath@@tmp @% +} +\def\pgfmath@base@atchar{@} +\def\pgfmath@todigitlist#1{% + \def\pgfmath@digit{#1}% + \ifx\pgfmath@digit\pgfmath@base@atchar% + \expandafter\let\pgfmath@temp=\pgfmath@digitlist% + \else% + \ifx\pgfmath@digitlist\pgfutil@empty% + \edef\pgfmath@digitlist{#1}% + \else% + \edef\pgfmath@digitlist{\pgfmath@digitlist,#1}% + \fi% + \expandafter\pgfmath@todigitlist% + \fi% +} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f4bdd66875e0ef196152ce416ddf322c3274c97c --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.basic.code.tex @@ -0,0 +1,726 @@ + + +\pgfmathdeclarefunction{add}{2}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \pgfmath@y=#2pt\relax% + \advance\pgfmath@x by\pgfmath@y% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + + +\pgfmathdeclarefunction{subtract}{2}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \pgfmath@y=#2pt\relax% + \advance\pgfmath@x by-\pgfmath@y% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{neg}{1}{% + \begingroup% + \pgfmath@x=-#1pt\relax% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} +\def\pgfmath@operation@neg@precedence{500} + +\pgfmathdeclarefunction{multiply}{2}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \pgfmath@y=#2pt\relax% + \pgfmath@x=\pgfmath@tonumber{\pgfmath@y}\pgfmath@x% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\newif\ifpgfmath@divide@period + +\pgfmathdeclarefunction{divide}{2}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \pgfmath@y=#2pt\relax% + \let\pgfmath@sign=\pgfmath@empty% + \ifdim0pt=\pgfmath@y% + \pgfmath@error{You've asked me to divide `#1' by `#2', % + but I cannot divide any number by `#2'}{}% + \fi% + \afterassignment\pgfmath@xa% + \c@pgfmath@counta\the\pgfmath@y\relax% + \ifdim0pt=\pgfmath@xa% + \divide\pgfmath@x by\c@pgfmath@counta% + \else% + \ifdim0pt>\pgfmath@x% + \def\pgfmath@sign{-}% + \pgfmath@x=-\pgfmath@x% + \fi% + \ifdim0pt>\pgfmath@y% + \expandafter\def\expandafter\pgfmath@sign\expandafter{\pgfmath@sign-}% + \pgfmath@y=-\pgfmath@y% + \fi% + \ifdim1pt>\pgfmath@y% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}% + \pgfmath@x=\pgfmath@sign\pgfmathresult\pgfmath@x% + \else% + \def\pgfmathresult{0}% + \pgfmath@divide@periodtrue% + \c@pgfmath@counta=0\relax% + \pgfmathdivide@@% + \pgfmath@x=\pgfmath@sign\pgfmathresult pt\relax% + \fi% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\def\pgfmath@small@number{0.00002} + +\def\pgfmathdivide@@{% + \let\pgfmath@next=\relax% + \ifdim\pgfmath@small@number pt<\pgfmath@x% + \ifdim\pgfmath@small@number pt<\pgfmath@y% + \ifdim\pgfmath@y>\pgfmath@x% + \ifpgfmath@divide@period% + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult.}% + \pgfmath@divide@periodfalse% + \fi% + \pgfmathdivide@dimenbyten\pgfmath@y% + \ifdim\pgfmath@y>\pgfmath@x% + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmathresult0}% + \fi% + \else% + \c@pgfmath@counta=\pgfmath@x% + \c@pgfmath@countb=\pgfmath@y% + \divide\c@pgfmath@counta by\c@pgfmath@countb% + \pgfmath@ya=\c@pgfmath@counta\pgfmath@y% + \advance\pgfmath@x by-\pgfmath@ya% + \def\pgfmath@next{% + \toks0=\expandafter{\pgfmathresult}% + \edef\pgfmathresult{\the\toks0 \the\c@pgfmath@counta}% + }% + \ifpgfmath@divide@period + \else + \ifnum\c@pgfmath@counta>9 % + \expandafter\pgfmathdivide@advance@last@digit\pgfmathresult CCCCC\@@ + \advance\c@pgfmath@counta by-10 % + \ifnum\c@pgfmath@counta=0 + \let\pgfmath@next=\relax + \fi + \fi + \fi + \pgfmath@next + \fi% + \let\pgfmath@next=\pgfmathdivide@@% + \fi% + \fi% + \pgfmath@next% +} + +\def\pgfmathdivide@advance@last@digit#1.#2#3#4#5#6#7\@@{% + \pgfmath@ya=\pgfmathresult pt % + \if#2C% + \pgfmath@xa=1pt % + \else + \if#3C% + \pgfmath@xa=0.1pt % + \else + \if#4C% + \pgfmath@xa=0.01pt % + \else + \if#5C% + \pgfmath@xa=0.001pt % + \else + \if#6C% + \pgfmath@xa=0.0001pt % + \else + \pgfmath@xa=0.00001pt % + \fi + \fi + \fi + \fi + \fi + \advance\pgfmath@ya by\pgfmath@xa + \edef\pgfmathresult{\pgfmath@tonumber@notrailingzero\pgfmath@ya}% +}% + +{ +\catcode`\p=12 +\catcode`\t=12 +\gdef\Pgf@geT@NO@TRAILING@ZERO#1.#2pt{% + #1.% + \ifnum#2=0 \else #2\fi +} +} +\def\pgfmath@tonumber@notrailingzero#1{\expandafter\Pgf@geT@NO@TRAILING@ZERO\the#1} + + +\def\pgfmathdivide@dimenbyten#1{% + \edef\pgfmath@temp{\pgfmath@tonumber{#1}}% + \expandafter\pgfmathdivide@@dimenbyten\pgfmath@temp\@@#1\@@} +\def\pgfmathdivide@@dimenbyten#1.#2\@@#3\@@{% + \pgfmath@tempcnta=#1\relax% + \divide\pgfmath@tempcnta by10\relax% + \pgfmath@tempcntb=\pgfmath@tempcnta% + \multiply\pgfmath@tempcnta by-10\relax% + \advance\pgfmath@tempcnta by#1\relax% + #3=\the\pgfmath@tempcntb.\the\pgfmath@tempcnta#2pt\relax% +} + + +\pgfmathdeclarefunction{reciprocal}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \ifdim\pgfmath@x=0pt\relax% + \pgfmath@error{You asked me to calculate `1/#1', but I cannot divide any number by zero}{}% + \fi% + \edef\pgfmath@reciprocaltemp{\pgfmath@tonumber{\pgfmath@x}}% + \expandafter\pgfmathreciprocal@@\pgfmath@reciprocaltemp0000000\pgfmath@} +\def\pgfmathreciprocal@@#1.#2#3#4#5#6#7\pgfmath@{% + \c@pgfmath@counta#2#3#4#5#6\relax% + \ifnum\c@pgfmath@counta=0\relax% + \pgfmath@x1pt\relax% + \divide\pgfmath@x#1\relax% + \else% + \ifnum#1>100\relax% + \c@pgfmath@counta#1#2#3#4\relax% + \c@pgfmath@countb1000000000\relax% + \divide\c@pgfmath@countb\c@pgfmath@counta% + \c@pgfmath@counta\c@pgfmath@countb% + \divide\c@pgfmath@counta10000\relax% + \pgfmath@x\c@pgfmath@counta pt\relax% + \multiply\c@pgfmath@counta-10000\relax% + \advance\c@pgfmath@countb\c@pgfmath@counta% + \pgfmath@y\c@pgfmath@countb pt\relax% + \divide\pgfmath@y1000000\relax% + \advance\pgfmath@x\pgfmath@y% + \else% + \c@pgfmath@counta#1#2#3#4#5#6\relax% + \c@pgfmath@countb1000000000\relax% + \divide\c@pgfmath@countb\c@pgfmath@counta% + \c@pgfmath@counta\c@pgfmath@countb% + \divide\c@pgfmath@counta10000\relax% + \pgfmath@x\c@pgfmath@counta pt\relax% + \multiply\c@pgfmath@counta-10000\relax% + \advance\c@pgfmath@countb\c@pgfmath@counta% + \pgfmath@y\c@pgfmath@countb pt\relax% + \pgfmath@y.1\pgfmath@y% + \pgfmath@y.1\pgfmath@y% + \pgfmath@y.1\pgfmath@y% + \pgfmath@y.1\pgfmath@y% + \advance\pgfmath@x\pgfmath@y% + \fi% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{div}{2}{% + \begingroup% + \pgfmathdivide@{#1}{#2}% + \ifdim\pgfmathresult pt<0pt\relax% + \pgfmathceil@{\pgfmathresult}% + \else% + \pgfmathfloor@{\pgfmathresult}% + \fi% + \afterassignment\pgfmath@gobbletilpgfmath@% + \c@pgfmath@counta=\pgfmathresult\relax\pgfmath@% + \edef\pgfmathresult{\the\c@pgfmath@counta}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{mod}{2}{% + \begingroup% + \pgfmath@xa#1pt% + \pgfmath@xb#2pt% + \pgfmath@x\pgfmath@xa% + \c@pgfmath@counta\pgfmath@xa% + \c@pgfmath@countb\pgfmath@xb% + \divide\c@pgfmath@counta\c@pgfmath@countb% + \multiply\pgfmath@xb\c@pgfmath@counta% + \advance\pgfmath@x-\pgfmath@xb% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{Mod}{2}{% + \begingroup% + \pgfmathmod@{#1}{#2}% + \pgfmath@x=\pgfmathresult pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \advance\pgfmath@x by#2pt\relax% + \fi% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{abs}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{sign}{1}{% + \begingroup + \ifdim#1pt>0sp % + \def\pgfmathresult{1}% + \else + \ifdim#1pt=0sp % + \def\pgfmathresult{0}% + \else + \def\pgfmathresult{-1}% + \fi + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +} + +\pgfmathdeclarefunction{e}{0}{\def\pgfmathresult{2.718281828}} + +\pgfmathdeclarefunction{ln}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \ifdim\pgfmath@x>0pt\else% + \pgfmath@error{I cannot calculate the logarithm of `#1'}{}% + \fi% + \c@pgfmath@counta=0\relax% + \ifdim\pgfmath@x>2pt\relax% + \ifdim\pgfmath@x<128pt\relax% + \ifdim\pgfmath@x<8pt\relax% + \ifdim\pgfmath@x<4pt\relax% + \divide\pgfmath@x by2\relax% + \c@pgfmath@counta=1\relax% + \else% + \divide\pgfmath@x by4\relax% + \c@pgfmath@counta=2\relax% + \fi% + \else% + \ifdim\pgfmath@x<32pt\relax% + \ifdim\pgfmath@x<16pt\relax% + \divide\pgfmath@x by8\relax% + \c@pgfmath@counta=3\relax% + \else% + \divide\pgfmath@x by16\relax% + \c@pgfmath@counta=4\relax% + \fi% + \else% + \ifdim\pgfmath@x<64pt\relax% + \divide\pgfmath@x by32\relax% + \c@pgfmath@counta=5\relax% + \else% + \divide\pgfmath@x by64\relax% + \c@pgfmath@counta=6\relax% + \fi% + \fi% + \fi% + \else% + \ifdim\pgfmath@x<2048pt\relax% + \ifdim\pgfmath@x<512pt\relax% + \ifdim\pgfmath@x<256pt\relax% + \divide\pgfmath@x by128\relax% + \c@pgfmath@counta=7\relax% + \else% + \divide\pgfmath@x by256\relax% + \c@pgfmath@counta=8\relax% + \fi% + \else% + \ifdim\pgfmath@x<1024pt\relax% + \divide\pgfmath@x by512\relax% + \c@pgfmath@counta=9\relax% + \else% + \divide\pgfmath@x by1024\relax% + \c@pgfmath@counta=10\relax% + \fi% + \fi% + \else% + \ifdim\pgfmath@x<8192pt\relax% + \ifdim\pgfmath@x<4096pt\relax% + \divide\pgfmath@x by2048\relax% + \c@pgfmath@counta=11\relax% + \else% + \divide\pgfmath@x by4096\relax% + \c@pgfmath@counta =12\relax% + \fi% + \else% + \divide\pgfmath@x by8192\relax% + \c@pgfmath@counta=13\relax% + \fi% + \fi% + \fi% + \else% + \ifdim\pgfmath@x<1pt\relax% + \ifdim\pgfmath@x>0.0078125pt\relax% + \ifdim\pgfmath@x>0.125pt\relax% + \ifdim\pgfmath@x>0.5pt\relax% + \multiply\pgfmath@x by2\relax% + \c@pgfmath@counta=-1\relax% + \else% + \multiply\pgfmath@x by4\relax% + \c@pgfmath@counta=-2\relax% + \fi% + \else% + \ifdim\pgfmath@x>0.03125pt\relax% + \ifdim\pgfmath@x>0.0625pt\relax% + \multiply\pgfmath@x by8\relax% + \c@pgfmath@counta=-3\relax% + \else% + \multiply\pgfmath@x by16\relax% + \c@pgfmath@counta=-4\relax% + \fi% + \else% + \ifdim\pgfmath@x>0.015625pt\relax% + \multiply\pgfmath@x by32\relax% + \c@pgfmath@counta=-5\relax% + \else% + \multiply\pgfmath@x by64\relax% + \c@pgfmath@counta=-6\relax% + \fi% + \fi% + \fi% + \else% + \ifdim\pgfmath@x>0.00048828125pt\relax% + \ifdim\pgfmath@x>0.001953125pt\relax% + \ifdim\pgfmath@x>0.00390625pt\relax% + \multiply\pgfmath@x by128\relax% + \c@pgfmath@counta=-7\relax% + \else% + \multiply\pgfmath@x by256\relax% + \c@pgfmath@counta=-8\relax% + \fi% + \else% + \ifdim\pgfmath@x>0.0009765625pt\relax% + \multiply\pgfmath@x by512\relax% + \c@pgfmath@counta=-9\relax% + \else% + \multiply\pgfmath@x by1024\relax% + \c@pgfmath@counta=-10\relax% + \fi% + \fi% + \else% + \ifdim\pgfmath@x>0.0001220703125pt\relax% + \ifdim\pgfmath@x>0.0002441406256pt\relax% + \multiply\pgfmath@x by2048\relax% + \c@pgfmath@counta=-11\relax% + \else% + \multiply\pgfmath@x by4096\relax% + \c@pgfmath@counta=-12\relax% + \fi% + \else% + \multiply\pgfmath@x by8192\relax% + \c@pgfmath@counta=-13\relax% + \fi% + \fi% + \fi% + \fi% + \fi% + \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@x=0.04300521312\pgfmath@x% + \advance\pgfmath@x by-.4025153233pt\relax% + \pgfmath@x=\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x by1.589480044pt\relax% + \pgfmath@x=\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x by-3.489886985pt\relax% + \pgfmath@x=\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x by5.047861502pt\relax% + \pgfmath@x=\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x by-2.787927935pt\relax% + \advance\pgfmath@x by\c@pgfmath@counta pt\relax% + \pgfmath@x=0.6931471806\pgfmath@x% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{log2}{1}{% + \begingroup% + \pgfmathln@{#1}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmath@x=1.442695041\pgfmath@x% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{log10}{1}{% + \begingroup% + \pgfmathln@{#1}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmath@x=0.43429441\pgfmath@x% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\expandafter\let\expandafter\pgfmathlogtwo\csname pgfmathlog2\endcsname +\expandafter\let\expandafter\pgfmathlogtwo@\csname pgfmathlog2@\endcsname +\expandafter\let\expandafter\pgfmathlogten\csname pgfmathlog10\endcsname +\expandafter\let\expandafter\pgfmathlogten@\csname pgfmathlog10@\endcsname + +\pgfmathdeclarefunction{exp}{1}{% + \begingroup + \pgfmath@xc=#1pt\relax + \pgfmath@yc=#1pt\relax + \ifdim\pgfmath@xc<-9pt + \pgfmath@x=1sp\relax + \else + \ifdim\pgfmath@xc<0pt + \pgfmath@xc=-\pgfmath@xc + \fi + \pgfmath@x=1pt\relax + \pgfmath@xa=1pt\relax + \pgfmath@xb=\pgfmath@x + \pgfmathloop% + \divide\pgfmath@xa by\pgfmathcounter + \pgfmath@xa=\pgfmath@tonumber\pgfmath@xc\pgfmath@xa% + \advance\pgfmath@x by\pgfmath@xa + \ifdim\pgfmath@x=\pgfmath@xb + \else + \pgfmath@xb=\pgfmath@x + \repeatpgfmathloop% + \ifdim\pgfmath@yc<0pt + \pgfmathreciprocal@{\pgfmath@tonumber\pgfmath@x}% + \pgfmath@x=\pgfmathresult pt\relax + \fi + \fi + \pgfmath@returnone\pgfmath@x% + \endgroup +} + +\pgfmathdeclarefunction{sqrt}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@error{I cannot calculate the square-root of the negative number `#1'}{}% + \else% + \ifdim\pgfmath@x<10pt\relax% + \def\pgfmath@zeros{0}% + \def\pgfmath@targetiterations{1}% + \else% + \ifdim\pgfmath@x<100pt\relax% + \def\pgfmath@zeros{}% + \def\pgfmath@targetiterations{1}% + \else% + \ifdim\pgfmath@x<1000pt\relax% + \def\pgfmath@zeros{0}% + \def\pgfmath@targetiterations{2}% + \else% + \ifdim\pgfmath@x<10000pt\relax% + \def\pgfmath@zeros{}% + \def\pgfmath@targetiterations{2}% + \else% + \def\pgfmath@zeros{0}% + \def\pgfmath@targetiterations{3}% + \fi\fi\fi\fi\fi% + \edef\pgfmath@temp{\pgfmath@zeros\pgfmath@tonumber{\pgfmath@x}}% + \expandafter\pgfmath@sqrt@\pgfmath@temp\pgfmath@% +} +\def\pgfmath@sqrt@#1.#2\pgfmath@{\pgfmath@@sqrt@#1#2\pgfmath@empty\pgfmath@empty\pgfmath@} + +\def\pgfmath@@sqrt@#1#2{% + \c@pgfmath@countb=#1#2\relax% + \ifnum\c@pgfmath@countb>35\relax% + \ifnum\c@pgfmath@countb>63\relax% + \ifnum\c@pgfmath@countb>80\relax% + \c@pgfmath@counta=9\relax% + \else% + \c@pgfmath@counta=8\relax% + \fi% + \else% + \ifnum\c@pgfmath@countb>48\relax% + \c@pgfmath@counta=7\relax% + \else% + \c@pgfmath@counta=6\relax% + \fi% + \fi% + \else% + \ifnum\c@pgfmath@countb>15\relax% + \ifnum\c@pgfmath@countb>24\relax% + \c@pgfmath@counta5\relax% + \else% + \c@pgfmath@counta=4\relax% + \fi% + \else% + \ifnum\c@pgfmath@countb>3\relax% + \ifnum\c@pgfmath@countb>8\relax% + \c@pgfmath@counta=3\relax% + \else% + \c@pgfmath@counta=2\relax% + \fi% + \else% + \ifnum\c@pgfmath@countb>0\relax% + \c@pgfmath@counta=1\relax% + \else% + \c@pgfmath@counta=0\relax% + \fi% + \fi% + \fi% + \fi% + \edef\pgfmath@root{\the\c@pgfmath@counta}% + \edef\pgfmath@rootspecial{\the\c@pgfmath@counta}% + \multiply\c@pgfmath@counta by-\c@pgfmath@counta\relax% + \advance\c@pgfmath@counta by#1#2\relax% + \edef\pgfmath@remainder{\the\c@pgfmath@counta}% + \pgfmath@@@sqrt@% +} + +\def\pgfmath@@@sqrt@#1#2{% + \ifx\pgfmath@empty#1% + \edef\pgfmath@remainder{\pgfmath@remainder00}% + \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}% + \else% + \ifx\pgfmath@empty#2% + \edef\pgfmath@remainder{\pgfmath@remainder#10}% + \def\pgfmath@tokens{\pgfmath@empty\pgfmath@empty}% + \else% + \edef\pgfmath@remainder{\pgfmath@remainder#1#2}% + \def\pgfmath@tokens{}% + \fi\fi% + \c@pgfmath@counta=\pgfmath@rootspecial\relax% + \multiply\c@pgfmath@counta by20\relax% + \c@pgfmath@countb=\c@pgfmath@counta% + \multiply\c@pgfmath@countb by6\relax% + \advance\c@pgfmath@countb by36\relax% + \c@pgfmath@countc=\c@pgfmath@counta% + \multiply\c@pgfmath@countc by2\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \advance\c@pgfmath@countb by-\c@pgfmath@countc% + \advance\c@pgfmath@countb by-20\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \advance\c@pgfmath@countb by-\c@pgfmath@countc% + \advance\c@pgfmath@countb by-12\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \advance\c@pgfmath@countb by-\c@pgfmath@counta% + \advance\c@pgfmath@countb by-3\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \def\pgfmath@digit{0}% + \else% + \def\pgfmath@digit{1}% + \fi% + \else% + \advance\c@pgfmath@countb by\c@pgfmath@counta% + \advance\c@pgfmath@countb by5\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \def\pgfmath@digit{2}% + \else% + \def\pgfmath@digit{3}% + \fi% + \fi% + \else% + \advance\c@pgfmath@countb by\c@pgfmath@counta% + \advance\c@pgfmath@countb by9\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \def\pgfmath@digit{4}% + \else% + \def\pgfmath@digit{5}% + \fi% + \fi% + \else% + \advance\c@pgfmath@countb by\c@pgfmath@countc% + \advance\c@pgfmath@countb by28\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \advance\c@pgfmath@countb by-\c@pgfmath@counta% + \advance\c@pgfmath@countb by-15\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \def\pgfmath@digit{6}% + \else% + \def\pgfmath@digit{7}% + \fi% + \else% + \advance\c@pgfmath@countb by\c@pgfmath@counta% + \advance\c@pgfmath@countb by17\relax% + \ifnum\c@pgfmath@countb>\pgfmath@remainder\relax% + \def\pgfmath@digit{8}% + \else% + \def\pgfmath@digit{9}% + \fi% + \fi% + \fi% + \edef\pgfmath@rootspecial{\pgfmath@rootspecial\pgfmath@digit}% + \advance\c@pgfmath@counta by\pgfmath@digit\relax% + \multiply\c@pgfmath@counta by-\pgfmath@digit\relax% + \advance\c@pgfmath@counta by\pgfmath@remainder\relax% + \edef\pgfmath@remainder{\the\c@pgfmath@counta}% + \c@pgfmath@counta=\pgfmath@targetiterations\relax% + \advance\c@pgfmath@counta by-1\relax% + \edef\pgfmath@targetiterations{\the\c@pgfmath@counta}% + \ifnum\c@pgfmath@counta=0\relax% + \edef\pgfmath@root{\pgfmath@root.\pgfmath@digit}% + \else% + \edef\pgfmath@root{\pgfmath@root\pgfmath@digit}% + \fi% + \ifnum\c@pgfmath@counta=-4\relax% + \let\pgfmath@next\pgfmath@sqrt@end% + \else% + \let\pgfmath@next\pgfmath@@@sqrt@% + \fi% + \expandafter\pgfmath@next\pgfmath@tokens% +} + +\def\pgfmath@sqrt@end#1\pgfmath@{% + \edef\pgfmathresult{\pgfmath@root}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup} + +\pgfmathdeclarefunction{pow}{2}{% + \begingroup% + \pgfmath@xa=#1pt% + \pgfmath@xb=#2pt% + \ifdim\pgfmath@xa=0pt\relax% + \ifdim\pgfmath@xb=0pt\relax% + \pgfmath@x=1pt\relax% + \else% + \pgfmath@x=0pt\relax% + \fi% + \else% + \afterassignment\pgfmath@x% + \expandafter\c@pgfmath@counta\the\pgfmath@xb\relax% + \ifnum\c@pgfmath@counta<0\relax% + \c@pgfmath@counta=-\c@pgfmath@counta% + \pgfmathreciprocal@{#1}% + \pgfmath@xa=\pgfmathresult pt\relax% + \fi + \ifdim\pgfmath@x=0pt\relax% + \pgfmath@x=1pt\relax% + \pgfmathloop% + \ifnum\c@pgfmath@counta>0\relax% + \ifodd\c@pgfmath@counta% + \pgfmath@x=\pgfmath@tonumber{\pgfmath@x}\pgfmath@xa% + \fi + \ifnum\c@pgfmath@counta>1\relax% + \pgfmath@xa=\pgfmath@tonumber{\pgfmath@xa}\pgfmath@xa% + \fi% + \divide\c@pgfmath@counta by2\relax% + \repeatpgfmathloop% + \else% + \pgfmathln@{#1}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmath@x=\pgfmath@tonumber{\pgfmath@xb}\pgfmath@x% + \pgfmathexp@{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@x=\pgfmathresult pt\relax% + \fi% + \fi + \pgfmath@returnone\pgf@x% + \endgroup% +} + +\pgfmathdeclarefunction{factorial}{1}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@% + \c@pgfmath@counta=#1\relax\pgfmath@% + \pgfmath@x=1pt\relax% + \pgfmathloop% + \ifnum\c@pgfmath@counta<2\relax% + \else% + \multiply\pgfmath@x by\c@pgfmath@counta% + \advance\c@pgfmath@counta by-1\relax% + \repeatpgfmathloop% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..08d0b00c7d7966072c28863ff009ae77ad342da1 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.code.tex @@ -0,0 +1,235 @@ + +\def\pgfmathdeclarefunction{\pgfmath@ifnextchar*\pgfmathdeclarefunction@force\pgfmathdeclarefunction@check} +\def\pgfmathdeclarefunction@check#1{% + \expandafter\ifx\csname pgfmath@function@#1\endcsname\relax\else% + \pgfmath@error{The function `#1' already exists}{}% + \fi% + \pgfmath@declarefunction{#1}% +} +\def\pgfmathdeclarefunction@force*{\pgfmath@declarefunction}% + +\def\pgfmathredeclarefunction#1#2{% + \expandafter\ifx\csname pgfmath@function@#1\endcsname\relax% + \pgfmath@error{The function `#1' does not exist}{}% + \else% + \edef\pgf@marshal{\noexpand\pgfmathdeclarefunction*{#1}{\csname pgfmath@operation@#1@arity\endcsname}}% + \pgf@marshal{#2}% + \fi% +} + +\def\pgfmath@declarefunction#1#2{% + \pgfmath@namedef{pgfmath@function@#1}{#1}% + \pgfmath@namedef{pgfmath@operation@#1@type}{function}% + \pgfmath@namedef{pgfmath@operation@#1@arity}{#2}% + \pgfmath@namedef{pgfmath@operation@#1@infix}{#1}% + \pgfmath@namedef{pgfmath@operation@#1@precedence}{1000}% + \expandafter\ifx\csname pgfmath@operation@#1@arity\endcsname\pgfmath@dots% + \pgfmath@namedef{pgfmath@operation@#1@arity}{1}% + \else% + \ifnum\csname pgfmath@operation@#1@arity\endcsname>9\relax% + \pgfmath@namedef{pgfmath@operation@#1@arity}{1}% + \fi% + \fi% + \edef\pgfmath@marshal{% + \noexpand\pgfmath@@declarefunction% + {\expandafter\noexpand\csname pgfmath#1\endcsname}% + {\expandafter\noexpand\csname pgfmath#1@\endcsname}% + {\csname pgfmath@operation@#1@arity\endcsname}% + }% + \pgfkeysvalueof{/pgf/declare function/execute at begin function}% + \pgfmath@marshal% +} + +\def\pgfmath@@declarefunction#1#2#3#4{% + \pgfkeysvalueof{/pgf/declare function/execute at end function}% + \ifcase#3\relax% + \def#1{#2}% + \def\pgfmath@@head{\def#2}% + \or + \def#1##1{\pgfmathparse{##1}\expandafter#2\expandafter{\pgfmathresult}}% + \def\pgfmath@@head{\def#2####1}% + \else% + \pgfmath@toks={}% + \pgfmathloop% + \ifnum\pgfmathcounter>#3\relax% + \else% + \expandafter\pgfmath@addto@toks\expandafter{\pgfmath@char@hash}% + \expandafter\pgfmath@addto@toks\expandafter{\pgfmathcounter}% + \repeatpgfmathloop% + \edef\pgfmath@head{\noexpand\def\noexpand#1\the\pgfmath@toks}% + \edef\pgfmath@@head{\noexpand\def\noexpand#2\the\pgfmath@toks}% + \pgfmath@toks={}% + \def\pgfmath@arguments{}% + \pgfmathloop% + \ifnum\pgfmathcounter>#3\relax% + \else% + \pgfmath@addto@toks{\pgfmathparse}% + \expandafter\expandafter\expandafter\pgfmath@addto@toks% + \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter% + {\expandafter\pgfmath@char@hash\pgfmathcounter}}% + \pgfmath@addto@toks{\let}% + \expandafter\pgfmath@addto@toks\expandafter{% + \csname pgfmath@argument@\pgfmathcounter\endcsname=\pgfmathresult}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgfmath@arguments\expandafter\expandafter\expandafter{\expandafter% + \pgfmath@arguments\expandafter{\csname pgfmath@argument@\pgfmathcounter\endcsname}}% + \repeatpgfmathloop% + \expandafter\pgfmath@addto@toks\expandafter{\expandafter#2\pgfmath@arguments}% + \edef\pgfmath@body{{\the\pgfmath@toks}}% + \expandafter\pgfmath@head\pgfmath@body% + \fi% + \pgfmath@@head{#4}% +} + +\def\pgfmath@addto@toks#1{% + \edef\pgfmath@toks@expanded{\the\pgfmath@toks}% + \expandafter\pgfmath@toks\expandafter{\pgfmath@toks@expanded#1}} + +\pgfkeys{% + /pgf/declare function/.code={% + \pgfmath@local@functions#1@=@;% + }, + /pgf/declare function/execute at begin function/.initial={}, + /pgf/declare function/execute at end function/.initial={}, + /pgf/declare function/ignore spaces/.is choice, + /pgf/declare function/ignore spaces/.default=true, + /pgf/declare function/ignore spaces/true/.style={% + /pgf/declare function/execute at begin function={% + \begingroup + \catcode`\^^I=9\relax + \catcode`\ =9\relax + \catcode`\~=10\relax + \endlinechar=`\ \relax + }, + /pgf/declare function/execute at end function={% + \endgroup + }, + }, + /pgf/declare function/ignore spaces/false/.style={% + /pgf/declare function/execute at begin function={}, + /pgf/declare function/execute at end function={}, + }, +} + +\def\pgfmath@local@gobbleone#1{} +\def\pgfmath@local@at{@}% + +\def\pgfmath@local@functions{% + \pgfutil@ifnextchar x{\pgfmath@local@@functions}{\pgfmath@local@@functions}% +} + +\def\pgfmath@local@@functions#1=#2;{% + \def\pgfmath@local@temp{#1}% + \ifx\pgfmath@local@temp\pgfmath@local@at% + \let\pgfmath@local@next=\relax% + \else% + \pgfmath@local@function#1=#2;% + \let\pgfmath@local@next=\pgfmath@local@functions% + \fi% + \pgfmath@local@next% +} + +\def\pgfmath@local@function{% + \let\pgfmath@local@name=\pgfutil@empty% + \let\pgfmath@local@args=\pgfutil@empty% + \let\pgfmath@local@body=\pgfutil@empty% + \pgfmath@local@@function} + +\def\pgfmath@local@@function#1{% + \if#1=% + \let\pgfmath@local@next=\pgfmath@local@function@body% + \else% + \if#1(% + \let\pgfmath@local@next=\pgfmath@local@function@args% + \else% + \expandafter\def\expandafter\pgfmath@local@name\expandafter{\pgfmath@local@name#1}% + \let\pgfmath@local@next=\pgfmath@local@@function% + \fi% + \fi% + \pgfmath@local@next% +} + +\def\pgfmath@local@function@args#1){% + \def\pgfmath@local@args{#1}% + \pgfmath@local@@function} + +\def\pgfmath@local@function@body#1;{% + \def\pgfmath@local@body{#1}% + \begingroup% + \c@pgf@counta=0\relax% + \ifx\pgfmath@local@args\pgfmath@empty% + \expandafter\pgfmath@toks\expandafter=\expandafter{\pgfmath@local@body}% + \else% + \pgfmath@toks={}% + \expandafter\pgfmath@local@function@@body\pgfmath@local@args,,% + \fi% + \xdef\pgfmath@local@temp{% + \noexpand\pgfmathnotifynewdeclarefunction{\pgfmath@local@name}{\the\c@pgf@counta}% + {\the\pgfmath@toks}% + }% + \endgroup% + \pgfmath@local@temp% +} + +\def\pgfmathnotifynewdeclarefunction#1#2#3{% + \pgfmathdeclarefunction{#1}{#2}{\pgfmathparse{#3}}% +}% + +\def\pgfmath@local@function@@body#1,{% + \def\pgfmath@local@test{#1}% + \ifx\pgfmath@local@test\pgfutil@empty% + \let\pgfmath@local@next=\relax% + \else% + \edef\pgfmath@local@var@string{@\expandafter\pgfmath@local@gobbleone\string#1}% + \advance\c@pgf@counta by1\relax% + \expandafter\expandafter\expandafter\pgfmath@toks\expandafter\expandafter\expandafter=% + \expandafter\expandafter\expandafter{\expandafter\pgfmath@char@hash\the\c@pgf@counta}% + \edef#1{\the\pgfmath@toks}% + \pgfmath@toks={}% + \expandafter\pgfmath@local@function@@@body\pgfmath@local@body @% + \edef\pgfmath@local@body{\the\pgfmath@toks}% + \let\pgfmath@local@next=\pgfmath@local@function@@body% + \fi% + \pgfmath@local@next% +} + +\def\pgfmath@local@function@@@body{% + \pgfutil@ifnextchar\bgroup{\pgfmath@local@function@@@body@bgroup}% + {\pgfmath@local@function@@@body@nobgroup}}% + +\def\pgfmath@local@function@@@body@bgroup#1{% + \begingroup% + \pgfmath@toks={}% + \pgfmath@local@function@@@body#1 @% + \xdef\pgfmath@local@temp{{\the\pgfmath@toks}}% + \endgroup% + \expandafter\pgfmath@addto@toks\expandafter{\pgfmath@local@temp}% + \pgfmath@local@function@@@body% +} + +\def\pgfmath@local@function@@@body@nobgroup#1{% + \ifx#1@% + \let\pgfmath@local@next=\relax% + \else% + \let\pgfmath@local@next=\pgfmath@local@function@@@body% + \edef\pgfmath@local@var@@string{@\expandafter\pgfmath@local@gobbleone\string#1}% + \ifx\pgfmath@local@var@@string\pgfmath@local@var@string% + \expandafter\pgfmath@addto@toks\expandafter{#1}% + \else% + \edef\pgfmath@local@temp{\the\pgfmath@toks}% + \pgfmath@toks={#1}% + \edef\pgfmath@local@@temp{\the\pgfmath@toks}% + \expandafter\pgfmath@toks\expandafter=\expandafter{\pgfmath@local@temp}% + \expandafter\pgfmath@addto@toks\expandafter{\pgfmath@local@@temp}% + \fi% + \fi% + \pgfmath@local@next% +} + +\def\pgfmathdeclarepseudoconstant#1#2{% + \pgfmathdeclarefunction*{#1}{0}{#2}% +}% +\def\pgfmathredeclarepseudoconstant#1#2{% + \pgfmathredeclarefunction{#1}{#2}% +}% + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..717c5412b6c9a559627f8e25f964886f6f9117a6 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.comparison.code.tex @@ -0,0 +1,148 @@ + + +\pgfmathdeclarefunction{greater}{2}{% + \begingroup% + \ifdim#1pt>#2pt\relax% + \def\pgfmathresult{1}% + \else% + \def\pgfmathresult{0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} +\let\pgfmathgreaterthan=\pgfmathgreater + +\pgfmathdeclarefunction{less}{2}{% + \begingroup% + \ifdim#1pt<#2pt\relax% + \def\pgfmathresult{1}% + \else% + \def\pgfmathresult{0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} +\let\pgfmathlessthan=\pgfmathless + +\pgfmathdeclarefunction{equal}{2}{% + \begingroup% + \ifdim#1pt=#2pt\relax% + \def\pgfmathresult{1}% + \else% + \def\pgfmathresult{0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} +\let\pgfmathequalto=\pgfmathequal + + +\newif\ifpgfmathcomparison +\pgfmathdeclarefunction{approxequalto}{2}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \pgfmath@y=#2pt\relax% + \advance\pgfmath@x by-\pgfmath@y% + \ifdim\pgfmath@x<0pt\relax% + \multiply\pgfmath@x by-1\relax% + \fi + \ifdim\pgfmath@x<0.0001pt\relax% + \def\pgfmathresult{1.0}% + \global\pgfmathcomparisontrue% + \else% + \def\pgfmathresult{0.0}% + \global\pgfmathcomparisonfalse% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + + + +\pgfmathdeclarefunction{ifthenelse}{3}{% + \begingroup% + \ifdim#1pt=0.0pt\relax% + \expandafter\def\expandafter\pgfmathresult\expandafter{#3}% + \else% + \expandafter\def\expandafter\pgfmathresult\expandafter{#2}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{notequal}{2}{% + \begingroup% + \ifdim#1pt=#2pt\relax% + \def\pgfmathresult{0}% + \else% + \def\pgfmathresult{1}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{notless}{2}{% + \begingroup% + \ifdim#1pt<#2pt\relax% + \def\pgfmathresult{0}% + \else% + \def\pgfmathresult{1}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{notgreater}{2}{% + \begingroup% + \ifdim#1pt>#2pt\relax% + \def\pgfmathresult{0}% + \else% + \def\pgfmathresult{1}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{and}{2}{% + \begingroup% + \def\pgfmathresult{1}% + \ifdim#1pt=0pt\relax% + \def\pgfmathresult{0}% + \else% + \ifdim#2pt=0pt\relax% + \def\pgfmathresult{0}% + \fi% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{or}{2}{% + \begingroup% + \def\pgfmathresult{0}% + \ifdim#1pt=0pt\relax% + \ifdim#2pt=0pt\relax% + \else% + \def\pgfmathresult{1}% + \fi% + \else% + \def\pgfmathresult{1}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{not}{1}{% + \begingroup% + \ifdim#1pt=0pt\relax% + \def\pgfmathresult{1}% + \else% + \def\pgfmathresult{0}% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{true}{0}{\def\pgfmathresult{1}} + +\pgfmathdeclarefunction{false}{0}{\def\pgfmathresult{0}} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..56eca18d07fe29b82e1391d63688aa8c6f2f7f43 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.integerarithmetics.code.tex @@ -0,0 +1,112 @@ + +\pgfmathdeclarefunction{gcd}{2}{% + \begingroup + \pgfmathcontinuelooptrue + \pgfmath@xa=#1pt + \pgfmath@xb=#2pt + \ifdim\pgfmath@xa=0pt\relax + \pgfmathcontinueloopfalse + \pgfmath@xa=\pgfmath@xb + \fi + \ifdim\pgfmath@xb=0pt\relax + \pgfmathcontinueloopfalse + \pgfmath@xb=\pgfmath@xa + \fi + \ifdim\pgfmath@xa<0pt\relax + \pgfmath@xa=-\pgfmath@xa + \fi + \ifdim\pgfmath@xb<0pt\relax + \pgfmath@xb=-\pgfmath@xb + \fi + \loop + \ifpgfmathcontinueloop + \ifdim\pgfmath@xa=\pgfmath@xb + \pgfmathcontinueloopfalse + \else + \ifdim\pgfmath@xa>\pgfmath@xb + \advance\pgfmath@xa by-\pgfmath@xb + \else + \advance\pgfmath@xb by-\pgfmath@xa + \fi + \fi + \repeat + \pgfmathparse{int(\pgfmath@xa)}% + \pgfmath@smuggleone\pgfmathresult + \endgroup} + +\newif\ifpgfmath@isprime@unknown +\newif\ifpgfmath@isprime + +\pgfmathdeclarefunction{isprime}{1}{% + \begingroup + \pgfmath@isprime@unknowntrue + \pgfmathsetcount\c@pgfmath@counta{abs(int(#1))}% + \ifcase\c@pgfmath@counta\relax + \pgfmath@isprimefalse + \pgfmath@isprime@unknownfalse + \or + \pgfmath@isprimefalse + \pgfmath@isprime@unknownfalse + \or + \pgfmath@isprimetrue + \pgfmath@isprime@unknownfalse + \or + \pgfmath@isprimetrue + \pgfmath@isprime@unknownfalse + \else + \ifodd\c@pgfmath@counta\relax + \else + \pgfmath@isprimefalse + \pgfmath@isprime@unknownfalse + \fi + \fi + \ifpgfmath@isprime@unknown + \c@pgfmath@countd=3 + \pgfmath@isprimetrue + \pgfmathloop + \c@pgfmath@countb=\c@pgfmath@counta + \divide\c@pgfmath@countb by\c@pgfmath@countd + \ifnum\c@pgfmath@countb>\c@pgfmath@countd + \pgfmath@isprime@unknowntrue + \else + \pgfmath@isprime@unknownfalse + \fi + \multiply\c@pgfmath@countb by\c@pgfmath@countd + \ifnum\c@pgfmath@countb=\c@pgfmath@counta + \global\pgfmath@isprimefalse + \pgfmath@isprime@unknownfalse + \fi + \ifpgfmath@isprime@unknown\advance\c@pgfmath@countd by 2 + \repeatpgfmathloop + \fi + \ifpgfmath@isprime + \def\pgfmathresult{1}% + \else + \def\pgfmathresult{0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup} + +\pgfmathdeclarefunction{isodd}{1}{% + \begingroup + \pgfmathsetcount\c@pgfmath@counta{abs(int(#1))}% + \ifodd\c@pgfmath@counta + \def\pgfmathresult{1}% + \else + \def\pgfmathresult{0}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup} + +\pgfmathdeclarefunction{iseven}{1}{% + \begingroup + \pgfmathsetcount\c@pgfmath@counta{abs(int(#1))}% + \ifodd\c@pgfmath@counta + \def\pgfmathresult{0}% + \else + \def\pgfmathresult{1}% + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup} + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..89ce863a178d51d6acd4db105a8a0cead7991a6e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.misc.code.tex @@ -0,0 +1,292 @@ + + +\pgfmathdeclarefunction{veclen}{2}{% + \begingroup% + \pgfmath@x#1pt\relax% + \pgfmath@y#2pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \ifdim\pgfmath@y<0pt\relax% + \pgfmath@y-\pgfmath@y% + \fi% + \ifdim\pgfmath@x=0pt\relax% + \pgfmath@x\pgfmath@y% + \else% + \ifdim\pgfmath@y=0pt\relax% + \else% + \ifdim\pgfmath@x>\pgfmath@y% + \pgfmath@xa\pgfmath@x% + \pgfmath@x\pgfmath@y% + \pgfmath@y\pgfmath@xa% + \fi% + \ifdim\pgfmath@y>10000pt\relax% + \c@pgfmath@counta1500\relax% + \else% + \ifdim\pgfmath@y>1000pt\relax% + \c@pgfmath@counta150\relax% + \else% + \ifdim\pgfmath@y>100pt\relax% + \c@pgfmath@counta50\relax% + \else% + \c@pgfmath@counta1\relax% + \fi% + \fi% + \fi% + \divide\pgfmath@x\c@pgfmath@counta\relax% + \divide\pgfmath@y\c@pgfmath@counta\relax% + \pgfmathreciprocal@{\pgfmath@tonumber{\pgfmath@y}}% + \pgfmath@x\pgfmathresult\pgfmath@x% + \pgfmath@xa\pgfmath@tonumber{\pgfmath@x}\pgfmath@x% + \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@xa}}% + \pgfmath@x-0.01019210944\pgfmath@xa% + \advance\pgfmath@x0.04453994279pt\relax% + \pgfmath@x\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x-0.1195159052pt\relax% + \pgfmath@x\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x0.4993615349pt\relax% + \pgfmath@x\pgfmath@temp\pgfmath@x% + \advance\pgfmath@x1.000012594pt\relax% + \ifdim\pgfmath@y<0pt\relax% + \pgfmath@y-\pgfmath@y% + \fi% + \pgfmath@x\pgfmath@tonumber{\pgfmath@y}\pgfmath@x% + \multiply\pgfmath@x\c@pgfmath@counta\relax% + \fi% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{cosh}{1}{% + \begingroup + \edef\pgfmath@arg{#1}% + \pgfmathexp@{\pgfmath@arg}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmathexp@{-\pgfmath@arg}% + \advance\pgfmath@x by\pgfmathresult pt\relax% + \divide\pgfmath@x by2\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup} + +\pgfmathdeclarefunction{sinh}{1}{% + \begingroup + \edef\pgfmath@arg{#1}% + \pgfmathexp@{\pgfmath@arg}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmathexp@{-\pgfmath@arg}% + \advance\pgfmath@x by-\pgfmathresult pt\relax% + \divide\pgfmath@x by2\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup +}% + +\pgfmathdeclarefunction{tanh}{1}{% + \begingroup + \edef\pgfmath@arg{#1}% + \pgfmathsinh@{\pgfmath@arg}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmathcosh@{\pgfmath@arg}% + \pgfmath@y=\pgfmathresult pt\relax% + \pgfmathdivide@{\pgfmath@tonumber{\pgfmath@x}}{\pgfmath@tonumber{\pgfmath@y}}% + \pgfmath@x=\pgfmathresult pt\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup +}% + +\def\pgfmathscientific#1#2{% + \begingroup% + \edef\pgfmath@sci@exponent{#2}% + \pgfmath@x#1pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \edef\pgfmath@sci@sign{-}% + \expandafter\edef\expandafter\pgfmath@temp\expandafter{\expandafter\pgfmath@gobbleone#1}% + \else% + \edef\pgfmath@sci@sign{+}% + \edef\pgfmath@temp{#1}% + \fi% + \expandafter\pgfmath@in@\expandafter.\expandafter{#1}% + \ifpgfmath@in@% + \else% + \edef\pgfmath@temp{\pgfmath@temp.0}% + \fi% + \expandafter\pgfmath@scientific@@\pgfmath@temp00000000000\pgfmath@} + +\def\pgfmath@scientific@@#1.#2#3#4#5#6{% + \edef\pgfmath@sci@int{#1}% + \edef\pgfmath@sci@mantissaA{#2#3#4#5#6}% + \pgfmath@scientific@@@} + +\def\pgfmath@scientific@@@#1#2#3#4#5#6\pgfmath@{% + \edef\pgfmath@sci@mantissaB{#1#2#3#4#5}% + \c@pgfmath@counta\pgfmath@sci@exponent\relax% + \ifnum\c@pgfmath@counta<-4\relax% + \pgfmath@x0pt\relax% + \else% + \c@pgfmath@countb\c@pgfmath@counta% + \ifnum\c@pgfmath@counta<0\relax% + \c@pgfmath@counta-\c@pgfmath@counta% + \fi% + \pgfmathpow@{10}{\the\c@pgfmath@counta}% + \afterassignment\pgfmath@gobbletilpgfmath@ + \c@pgfmath@countc\pgfmathresult\relax\pgfmath@ + \edef\pgfmath@sci@factor{\the\c@pgfmath@countc}% + \ifnum\c@pgfmath@countb<0\relax% + \pgfmath@x\pgfmath@sci@int.\pgfmath@sci@mantissaA pt\relax% + \divide\pgfmath@x\pgfmath@sci@factor\relax% + \else% + \c@pgfmath@counta\pgfmath@sci@int% + \c@pgfmath@countb\pgfmath@sci@mantissaA% + \multiply\c@pgfmath@counta\pgfmath@sci@factor\relax% + \multiply\c@pgfmath@countb\pgfmath@sci@factor\relax% + \c@pgfmath@countc\c@pgfmath@countb% + \divide\c@pgfmath@countb100000\relax% + \advance\c@pgfmath@counta\c@pgfmath@countb% + \multiply\c@pgfmath@countb100000\relax% + \advance\c@pgfmath@countc-\c@pgfmath@countb% + \c@pgfmath@countb\pgfmath@sci@mantissaB\relax% + \multiply\c@pgfmath@countb\pgfmath@sci@factor\relax% + \divide\c@pgfmath@countb100000\relax% + \advance\c@pgfmath@countc\c@pgfmath@countb% + \advance\c@pgfmath@countc100000\relax% + \edef\pgfmath@sci@result{\pgfmath@sci@sign\the\c@pgfmath@counta.\expandafter\pgfmath@gobbleone\the\c@pgfmath@countc pt}% + \pgfmath@x\pgfmath@sci@result\relax% + \fi\fi% + \pgfmath@returnone\pgfmath@x% + \endgroup} + + + +\pgfmathdeclarefunction{width}{1}{% + \begingroup% + \setbox\pgfmath@box=\hbox{{\pgfmath@selectfont{#1}}}% + \pgfmath@x=\wd\pgfmath@box% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + + +\pgfmathdeclarefunction{height}{1}{% + \begingroup% + \setbox\pgfmath@box=\hbox{{\pgfmath@selectfont{#1}}}% + \pgfmath@x=\ht\pgfmath@box% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + +\pgfmathdeclarefunction{depth}{1}{% + \begingroup% + \setbox\pgfmath@box=\hbox{{\pgfmath@selectfont{#1}}}% + \pgfmath@x=\dp\pgfmath@box% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} + + +\pgfmathdeclarefunction{array}{2}{% + \begingroup% + \afterassignment\pgfmath@gobbletilpgfmath@\pgfmath@count=#2\relax\pgfmath@% + \expandafter\pgfmatharray@@#1\pgfmath@stop% +} + +\def\pgfmath@token@stop{\pgfmath@stop}% +\def\pgfmatharray@@#1{% + \def\pgfmath@temp{#1}% + \advance\pgfmath@count by-1\relax% + \ifx\pgfmath@temp\pgfmath@token@stop% + \pgfmath@error{Array index out of bounds.}{}% + \def\pgfmathresult{0}% + \pgfmath@smuggleone\pgfmathresult\endgroup% + \let\pgfmath@next=\relax% + \else% + \ifnum\pgfmath@count=-1\relax% + \def\pgfmathresult{#1}% + \let\pgfmath@next=\pgfmatharray@@@% + \else% + \let\pgfmath@next=\pgfmatharray@@% + \fi% + \fi% + \pgfmath@next} + +\def\pgfmatharray@@@#1\pgfmath@stop{% + \pgfmath@smuggleone\pgfmathresult\endgroup% +} + +\pgfmathdeclarefunction{dim}{1}{% + \begingroup + \pgfmath@count=0\relax + \expandafter\pgfmath@dim@i\pgfutil@firstofone#1{\pgfmath@token@stop}% + \edef\pgfmathresult{\the\pgfmath@count}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup} + +\def\pgfmath@dim@i#1#{% + \pgfutil@ifempty{#1}{}{\advance\pgfmath@count by 1}% + \pgfmath@dim@ii{#1}} + +\def\pgfmath@dim@ii#1#2{% + \ifx\pgfmath@token@stop#2% + \else + \advance\pgfmath@count by 1\relax + \expandafter\pgfmath@dim@i + \fi} + + +\pgfmathdeclarefunction{max}{...}{% + \begingroup% + \pgfmath@x=-16383pt\relax% + \pgfmathmax@@#1{}} + +\def\pgfmathmax@@#1{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \let\pgfmath@next=\pgfmathmax@@@% + \else% + \ifdim#1pt>\pgfmath@x% + \pgfmath@x=#1pt\relax% + \fi% + \let\pgfmath@next=\pgfmathmax@@% + \fi% + \pgfmath@next} + +\def\pgfmathmax@@@{\pgfmath@returnone\pgfmath@x\endgroup}% + +\def\pgfmathmax#1#2{% + \pgfmathparse{#1,#2}% + \expandafter\pgfmathmax@\expandafter{\pgfmathresult}% +} + +\pgfmathdeclarefunction{min}{...}{% + \begingroup% + \pgfmath@x=16383pt\relax% + \pgfmathmin@@#1{}} + +\def\pgfmathmin@@#1{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \let\pgfmath@next=\pgfmathmin@@@% + \else% + \ifdim#1pt<\pgfmath@x% + \pgfmath@x=#1pt\relax% + \fi% + \let\pgfmath@next=\pgfmathmin@@% + \fi% + \pgfmath@next} + +\def\pgfmathmin@@@{\pgfmath@returnone\pgfmath@x\endgroup}% + +\def\pgfmathmin#1#2{% + \pgfmathparse{#1,#2}% + \expandafter\pgfmathmin@\expandafter{\pgfmathresult}% +} + + + +\pgfmathdeclarefunction{scalar}{1}{% + \def\pgfmathresult{#1}% + \global\pgfmathunitsdeclaredfalse% +} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.random.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.random.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3898e99b826ad1af20cb9b5ca8d29b1416897492 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.random.code.tex @@ -0,0 +1,168 @@ + + +\def\pgfmath@rnd@m{2147483647}% + +\begingroup +\c@pgfmath@counta=\time% +\multiply\c@pgfmath@counta by\year% +\ifnum\c@pgfmath@counta=0 + \c@pgfmath@counta=1 +\fi +\xdef\pgfmath@rnd@z{\the\c@pgfmath@counta}% +\endgroup + +\def\pgfmathsetseed#1{% + \pgfmathparse{#1}\expandafter\pgfmath@setseed\pgfmathresult.0\pgfmath@stop +}% +\def\pgfmath@setseed#1.#2\pgfmath@stop{\def\pgfmath@rnd@z{#1}}% + +\def\pgfmath@rnd@a{69621} +\def\pgfmath@rnd@r{23902} +\def\pgfmath@rnd@q{30845} + +\def\pgfmathgeneratepseudorandomnumber{% + \begingroup% + \c@pgfmath@counta=\pgfmath@rnd@z% + \c@pgfmath@countb=\pgfmath@rnd@z% + \c@pgfmath@countc=\pgfmath@rnd@q% + \divide\c@pgfmath@counta by\c@pgfmath@countc% + \multiply\c@pgfmath@counta by-\c@pgfmath@countc% + \advance\c@pgfmath@counta by\c@pgfmath@countb + \c@pgfmath@countc=\pgfmath@rnd@a% + \multiply\c@pgfmath@counta by\c@pgfmath@countc% + \c@pgfmath@countc=\pgfmath@rnd@q% + \divide\c@pgfmath@countb by\c@pgfmath@countc% + \c@pgfmath@countc=\pgfmath@rnd@r% + \multiply\c@pgfmath@countb by\c@pgfmath@countc% + \advance\c@pgfmath@counta by-\c@pgfmath@countb% + \ifnum\c@pgfmath@counta<0\relax% + \c@pgfmath@countb=\pgfmath@rnd@m% + \advance\c@pgfmath@counta by\c@pgfmath@countb% + \fi% + \xdef\pgfmath@rnd@z{\the\c@pgfmath@counta}% + \endgroup% + \edef\pgfmathresult{\pgfmath@rnd@z}% +} + +\pgfmathdeclarefunction{rnd}{0}{% + \begingroup% + \pgfmathgeneratepseudorandomnumber% + \c@pgfmath@counta\pgfmathresult% + \c@pgfmath@countb\c@pgfmath@counta% + \divide\c@pgfmath@countb100001\relax% + \multiply\c@pgfmath@countb-100001\relax% + \advance\c@pgfmath@countb\c@pgfmath@counta% + \advance\c@pgfmath@countb1000000\relax% + \expandafter\pgfmathrnd@@\the\c@pgfmath@countb\pgfmath@% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\def\pgfmathrnd@@#1#2#3\pgfmath@{% + \edef\pgfmath@temp{#2.#3}% + \pgfmath@x=\pgfmath@temp pt\relax% +}% + +\pgfmathdeclarefunction{rand}{0}{% + \begingroup% + \pgfmathgeneratepseudorandomnumber% + \c@pgfmath@counta\pgfmathresult% + \c@pgfmath@countb\c@pgfmath@counta% + \divide\c@pgfmath@countb200001\relax% + \multiply\c@pgfmath@countb-200001\relax% + \advance\c@pgfmath@countb\c@pgfmath@counta% + \advance\c@pgfmath@countb-100000\relax% + \ifnum\c@pgfmath@countb<0\relax% + \advance\c@pgfmath@countb-1000000\relax% + \else% + \advance\c@pgfmath@countb1000000\relax% + \fi% + \expandafter\pgfmathrand@@\the\c@pgfmath@countb\pgfmath@% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\def\pgfmathrand@@#1#2#3#4\pgfmath@{% + \ifx#1-% + \edef\pgfmath@temp{-#3.#4}% + \else% + \edef\pgfmath@temp{#2.#3#4}% + \fi% + \pgfmath@x=\pgfmath@temp pt\relax% +}% + +\pgfmathdeclarefunction{random}{...}{% + \begingroup% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \pgfmathrnd@% + \else% + \expandafter\pgfmathrandom@@#1\pgfmath@stop% + \fi% + \pgfmath@smuggleone\pgfmathresult% + \endgroup} + +\def\pgfmathrandom@@{\futurelet\pgfmath@token\pgfmathrandom@@@} +\def\pgfmathrandom@@@{% + \ifx\pgfmath@token\bgroup% + \expandafter\pgfmath@random@@@@% + \else% + \expandafter\pgfmath@random@@@@@% + \fi% +} +\def\pgfmath@random@@@@@#1\pgfmath@stop{% + \pgfmathrandominteger\pgfmathresult{1}{#1}% +} +\def\pgfmath@random@@@@#1#2\pgfmath@stop{% + \pgfmathrandominteger\pgfmathresult{#1}{#2}% +} + +\def\pgfmathrandominteger#1#2#3{% + \begingroup% + \pgfmathsetcount\c@pgfmath@counta{#2}% + \pgfmathsetcount\c@pgfmath@countb{#3}% + \c@pgfmath@countc\c@pgfmath@countb% + \ifnum\c@pgfmath@counta>\c@pgfmath@countb\relax% + \c@pgfmath@countc\c@pgfmath@counta% + \c@pgfmath@counta\c@pgfmath@countb% + \c@pgfmath@countb\c@pgfmath@countc% + \fi% + \c@pgfmath@countd\c@pgfmath@counta + \advance\c@pgfmath@countc1\relax% + \advance\c@pgfmath@countc-\c@pgfmath@counta% + \pgfmathgeneratepseudorandomnumber% + \c@pgfmath@counta\pgfmathresult\relax% + \c@pgfmath@countb\c@pgfmath@counta% + \divide\c@pgfmath@countb\c@pgfmath@countc% + \multiply\c@pgfmath@countb-\c@pgfmath@countc% + \advance\c@pgfmath@counta\c@pgfmath@countb% + \advance\c@pgfmath@counta\c@pgfmath@countd + \edef\pgfmathresult{\the\c@pgfmath@counta}% + \pgfmath@smuggleone{\pgfmathresult}% + \endgroup% + \edef#1{\pgfmathresult}% +} + +\def\pgfmathdeclarerandomlist#1#2{% + \def\pgfmath@randomlistname{#1}% + \begingroup% + \c@pgfmath@counta=1\relax% + \def\pgfmath@empty{pgfmath@empty}% + \expandafter\pgfmath@scanrandomlist#2{pgfmath@empty}} +\def\pgfmath@scanrandomlist#1{% + \def\pgfmath@scanneditem{#1}% + \ifx\pgfmath@scanneditem\pgfmath@empty% + \advance\c@pgfmath@counta-1\relax% + \expandafter\xdef\csname pgfmath@randomlist@\pgfmath@randomlistname\endcsname{\the\c@pgfmath@counta}% + \endgroup% + \else% + \expandafter\gdef\csname pgfmath@randomlist@\pgfmath@randomlistname @\the\c@pgfmath@counta\endcsname{#1}% + \advance\c@pgfmath@counta1\relax% + \expandafter\pgfmath@scanrandomlist% + \fi} + +\def\pgfmathrandomitem#1#2{% + \pgfmath@ifundefined{pgfmath@randomlist@#2}{\pgfmath@error{Unknown random list `#2'}{}}{% + \edef\pgfmath@randomlistlength{\csname pgfmath@randomlist@#2\endcsname}% + \pgfmathrandominteger{\pgfmath@randomtemp}{1}{\pgfmath@randomlistlength}% + \expandafter\def\expandafter#1\expandafter{\csname pgfmath@randomlist@#2@\pgfmath@randomtemp\endcsname}}} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.round.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.round.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..ac3db56976080428c15f00add47e74cae35da702 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.round.code.tex @@ -0,0 +1,99 @@ + + +\pgfmathdeclarefunction{round}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \afterassignment\pgfmath@xa% + \expandafter\c@pgfmath@counta\the\pgfmath@x\relax% + \pgfmath@xb\pgfmath@x% + \ifdim\pgfmath@xb<0pt\relax% + \ifdim\pgfmath@xa<0.5pt\relax% + \else% + \advance\c@pgfmath@counta-1\relax% + \fi% + \else% + \ifdim\pgfmath@xa<0.5pt\relax% + \else% + \advance\c@pgfmath@counta1\relax% + \fi% + \fi% + \pgfmath@returnone\the\c@pgfmath@counta pt% + \endgroup% +}% + +\pgfmathdeclarefunction{floor}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \afterassignment\pgfmathfloor@collect@remainder% + \expandafter\c@pgfmath@counta\the\pgfmath@x\pgfmath@% + \expandafter\pgfmath@x#1pt\relax% + \ifdim\pgfmath@x<0pt\relax% + \ifdim\pgfmathfloor@remainder>0pt + \advance\c@pgfmath@counta by -1\relax% + \else + \fi + \fi% + \pgfmath@x\c@pgfmath@counta pt\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\def\pgfmathfloor@collect@remainder#1\pgfmath@{% + \def\pgfmathfloor@remainder{#1}% + \ifx\pgfmathfloor@remainder\pgfutil@empty + \def\pgfmathfloor@remainder{0}% + \fi +}% + +\pgfmathdeclarefunction{ceil}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% + \pgfmath@y\pgfmath@x% + \advance\pgfmath@y-\c@pgfmath@counta pt\relax% + \pgfmath@x\c@pgfmath@counta pt\relax% + \ifdim\pgfmath@y>0pt\relax% + \advance\pgfmath@x1pt\relax% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\pgfmathdeclarefunction{int}{1}{% + \begingroup% + \expandafter\pgfmathint@@#1.\pgfmath@stop + \pgfmath@smuggleone\pgfmathresult% + \endgroup} + +\def\pgfmathint@@#1.#2\pgfmath@stop{% + \def\pgfmath@temp{#1}% + \ifx\pgfmath@temp\pgfmath@empty% + \def\pgfmathresult{0}% + \else% + \pgfmath@in@{#1}{+-+0-0}% + \ifpgfmath@in@ + \def\pgfmathresult{0}% + \else% + \def\pgfmathresult{#1}% + \fi% + \fi} + +\pgfmathdeclarefunction{frac}{1}{% + \begingroup% + \expandafter\pgfmathfrac@@#1.\pgfmath@stop% + \pgfmath@smuggleone\pgfmathresult% + \endgroup} + +\def\pgfmathfrac@@#1.{% + \pgfmath@ifnextchar\pgfmath@stop{\def\pgfmathresult{0.0}\pgfmath@gobbleone}{\pgfmathfrac@@@}% +} +\def\pgfmathfrac@@@#1.\pgfmath@stop{\def\pgfmathresult{0.#1}} + +\pgfmathdeclarefunction{real}{1}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmath@smuggleone\pgfmathresult% + \endgroup% +} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a8e2fa5efcd42a5773e11a0337ad8300fc06c2bf --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathfunctions.trigonometric.code.tex @@ -0,0 +1,1463 @@ + + +\pgfmathdeclarefunction{pi}{0}{\def\pgfmathresult{3.141592654}} + +\pgfkeys{ + /pgf/trig format/.is choice, + /pgf/trig format/deg/.code={\def\pgfmath@trig@format@choice{0}}, + /pgf/trig format/rad/.code={\def\pgfmath@trig@format@choice{1}}, + /pgf/trig format/deg, +} + +\def\pgfmathiftrigonometricusesdeg#1#2{% + \if0\pgfmath@trig@format@choice + #1% + \else + #2% + \fi +}% + +\pgfmathdeclarefunction{radians}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@x57.29577\pgfmath@x\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\pgfmathdeclarefunction{deg}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@scale@rad@to@deg\pgfmath@x + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\def\pgfmath@scale@rad@to@deg#1{% + #1=57.29577#1\relax% +}% + +\pgfmathdeclarefunction{rad}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@scale@deg@to@rad\pgfmath@x + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + +\def\pgfmath@scale@deg@to@rad#1{% + #1=3.14159#1% + \divide#1180\relax% +}% + +\pgfmathdeclarefunction{sin}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \if1\pgfmath@trig@format@choice + \pgfmath@scale@rad@to@deg\pgfmath@x + \fi + \advance\pgfmath@x-90pt\relax% + \afterassignment\pgfmath@gobbletilpgfmath@ + \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@ + \divide\c@pgfmath@counta360\relax% + \multiply\c@pgfmath@counta-360\relax% + \advance\pgfmath@x\c@pgfmath@counta pt\relax% + \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi% + \ifdim\pgfmath@x<180pt\relax% + \else + \pgfmath@x-\pgfmath@x% + \advance\pgfmath@x360pt\relax% + \fi% + \afterassignment\pgfmath@xa% + \expandafter\c@pgfmath@counta\the\pgfmath@x\relax% + \ifdim\pgfmath@xa=0pt% + \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt\relax% + \else% + \pgfmath@x-\pgfmath@xa% + \advance\pgfmath@x1pt\relax% + \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x% + \advance\c@pgfmath@counta1\relax% + \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi% + \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup +} + +\pgfmathdeclarefunction{cos}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \if1\pgfmath@trig@format@choice + \pgfmath@scale@rad@to@deg\pgfmath@x + \fi + \afterassignment\pgfmath@gobbletilpgfmath@% + \expandafter\c@pgfmath@counta\the\pgfmath@x\relax\pgfmath@% + \divide\c@pgfmath@counta360\relax% + \multiply\c@pgfmath@counta-360\relax% + \advance\pgfmath@x\c@pgfmath@counta pt\relax% + \ifdim\pgfmath@x<0pt\relax\pgfmath@x-\pgfmath@x\fi% + \ifdim\pgfmath@x<180pt\relax% + \else% + \pgfmath@x-\pgfmath@x% + \advance\pgfmath@x360pt\relax% + \fi% + \afterassignment\pgfmath@xa% + \expandafter\c@pgfmath@counta\the\pgfmath@x\relax% + \ifdim\pgfmath@xa=0pt% + \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname pt% + \else% + \pgfmath@x-\pgfmath@xa% + \advance\pgfmath@x1pt\relax% + \expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@x% + \advance\c@pgfmath@counta1\relax% + \ifnum\c@pgfmath@counta=181\relax\c@pgfmath@counta179\relax\fi% + \expandafter\advance\expandafter\pgfmath@x\csname pgfmath@cos@\the\c@pgfmath@counta\endcsname\pgfmath@xa% + \fi% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\def\pgfmathsincos#1{% + \pgfmathparse{#1}% + \expandafter\pgfmathsincos@\expandafter{\pgfmathresult}} +\def\pgfmathsincos@#1{% + \edef\pgfmath@temparg{#1}% + \pgfmathsin@{\pgfmath@temparg}\edef\pgfmathresulty{\pgfmathresult}% + \pgfmathcos@{\pgfmath@temparg}\edef\pgfmathresultx{\pgfmathresult}% +} + +\pgfmathdeclarefunction{tan}{1}{% + \begingroup% + \edef\pgfmath@temparg{#1}% + \pgfmathcos@{\pgfmath@temparg}% + \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}% + \edef\pgfmath@tantemp{\pgfmathresult}% + \pgfmathsin@{\pgfmath@temparg}% + \pgfmath@x\pgfmathresult pt\relax% + \pgfmath@x\pgfmath@tantemp\pgfmath@x% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{cosec}{1}{% + \expandafter\pgfmathsin@\expandafter{#1}% + \pgfmathreciprocal@{\pgfmathresult}% +} + +\pgfmathdeclarefunction{sec}{1}{% + \expandafter\pgfmathcos@\expandafter{#1}% + \pgfmathreciprocal@{\pgfmathresult}% +} + +\pgfmathdeclarefunction{cot}{1}{% + \begingroup% + \edef\pgfmath@temparg{#1}% + \pgfmathsin@{\pgfmath@temparg}% + \expandafter\pgfmathreciprocal@\expandafter{\pgfmathresult}% + \edef\pgfmath@tantemp{\pgfmathresult}% + \pgfmathcos@{\pgfmath@temparg}% + \pgfmath@x\pgfmathresult pt\relax% + \pgfmath@x\pgfmath@tantemp\pgfmath@x% + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\def\pgfmath@multiply@thousand#1.#2#3#4#5\relax{% + \edef\pgfmathresult{#1#2#3#4.#5}% +}% + +\pgfmathdeclarefunction{asin}{1}{% + \begingroup% + \pgfmath@x=#1pt % + \pgfmath@xa\pgfmath@x% + \edef\pgf@temp{\pgfmath@tonumber\pgfmath@x}% + \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax + \pgfmath@x=\pgfmathresult pt % + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}% + \pgfmath@x=-\pgfmath@x + \advance\pgfmath@x90pt\relax% + \ifdim\pgfmath@xa<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \if1\pgfmath@trig@format@choice + \pgfmath@scale@deg@to@rad\pgfmath@x + \fi + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\def\pgfmath@table@lookup#1#2#3{% + \pgfmath@x=#1\relax + \expandafter\pgfmath@table@lookup@\the\pgfmath@x\relax{#2}{#3}% +} +\def\pgfmath@table@lookup@#1.#2\relax#3#4{% + \edef\pgf@temp{\Pgf@geT#2}% + \pgfmath@x=\csname #3#1\endcsname pt % + \c@pgfmath@countc=#1 % + \advance\c@pgfmath@countc by1 % + \ifnum\c@pgfmath@countc<#4 % + \pgfmath@ya=\csname #3\the\c@pgfmath@countc\endcsname pt % + \advance\pgfmath@ya by-\pgfmath@x % + \advance\pgfmath@x by0.\pgf@temp\pgfmath@ya + \fi +}% + +\pgfmathdeclarefunction{acos}{1}{% + \begingroup% + \pgfmath@x#1pt\relax% + \pgfmath@xa\pgfmath@x% + \edef\pgf@temp{\pgfmath@tonumber\pgfmath@x}% + \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax + \pgfmath@x=\pgfmathresult pt % + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \pgfmath@table@lookup{\pgfmath@x}{pgfmath@acos@}{1001}% + \ifdim\pgfmath@xa<0pt\relax% + \pgfmath@x-\pgfmath@x% + \advance\pgfmath@x by180pt\relax% + \fi% + \if1\pgfmath@trig@format@choice + \pgfmath@scale@deg@to@rad\pgfmath@x + \fi + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{atan}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@xa\pgfmath@x% + \ifdim\pgfmath@x<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \pgfmath@xb\pgfmath@x% + \ifdim\pgfmath@x>1pt\relax% + \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}% + \pgfmathreciprocal@{\pgfmath@temp}% + \pgfmath@x\pgfmathresult pt\relax% + \fi% + \edef\pgf@temp{\pgfmath@tonumber\pgfmath@x}% + \expandafter\pgfmath@multiply@thousand\pgf@temp 000\relax + \pgfmath@x=\pgfmathresult pt % + \pgfmath@table@lookup{\pgfmath@x}{pgfmath@atan@}{1001}% + \ifdim\pgfmath@xb>1pt\relax% + \pgfmath@x=-\pgfmath@x% + \advance\pgfmath@x90pt% + \fi% + \ifdim\pgfmath@xa<0pt\relax% + \pgfmath@x-\pgfmath@x% + \fi% + \if1\pgfmath@trig@format@choice + \pgfmath@scale@deg@to@rad\pgfmath@x + \fi + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\pgfmathdeclarefunction{atan2}{2}{% + \begingroup% + \let\pgfmath@trig@format@choice@@=\pgfmath@trig@format@choice + \def\pgfmath@trig@format@choice{0}% + \pgfmath@y=#1pt\relax% + \ifdim\pgfmath@y<0pt\relax% + \pgfmath@y=-\pgfmath@y% + \fi% + \ifdim\pgfmath@y<0.001pt\relax% + \ifdim#2pt<0pt\relax% + \pgfmath@x=+180pt\relax% + \else% + \ifdim#2pt>0pt\relax% + \pgfmath@x=0pt\relax% + \else% + \ifdim#1pt<0pt% + \pgfmath@x=-90pt\relax% + \else% + \pgfmath@x=90pt\relax% + \fi% + \fi% + \fi% + \else% + \pgfmathabs@{#1}\let\pgfmath@tempa\pgfmathresult% + \pgfmathabs@{#2}\let\pgfmath@tempb\pgfmathresult% + \ifdim\pgfmath@tempa pt>\pgfmath@tempb pt% + \pgfmathdivide@{#2}{\pgfmath@tempa}% + \expandafter\pgfmathatan@\expandafter{\pgfmathresult}% + \pgfmath@x=90pt% + \advance\pgfmath@x by-\pgfmathresult pt\relax% + \else% + \pgfmathdivide@{\pgfmath@tempa}{#2}% + \expandafter\pgfmathatan@\expandafter{\pgfmathresult}% + \pgfmath@x=\pgfmathresult pt\relax% + \ifdim#2pt<0pt% + \advance\pgfmath@x by180pt\relax% + \fi% + \fi% + \ifdim#1pt<0pt\relax% + \pgfmath@x=-\pgfmath@x% + \fi% + \fi% + \if1\pgfmath@trig@format@choice@@ + \pgfmath@scale@deg@to@rad\pgfmath@x + \fi + \pgfmath@returnone\pgfmath@x% + \endgroup% +} + +\expandafter\let\expandafter\pgfmathatantwo\csname pgfmathatan2\endcsname +\expandafter\let\expandafter\pgfmathatantwo@\csname pgfmathatan2@\endcsname + +\def\pgfmath@def#1#2#3{\expandafter\def\csname pgfmath@#1@#2\endcsname{#3}} +\pgfmath@def{cos}{0}{1.00000} \pgfmath@def{cos}{1}{0.99985} +\pgfmath@def{cos}{2}{0.99939} \pgfmath@def{cos}{3}{0.99863} +\pgfmath@def{cos}{4}{0.99756} \pgfmath@def{cos}{5}{0.99619} +\pgfmath@def{cos}{6}{0.99452} \pgfmath@def{cos}{7}{0.99255} +\pgfmath@def{cos}{8}{0.99027} \pgfmath@def{cos}{9}{0.98769} +\pgfmath@def{cos}{10}{0.98481} \pgfmath@def{cos}{11}{0.98163} +\pgfmath@def{cos}{12}{0.97815} \pgfmath@def{cos}{13}{0.97437} +\pgfmath@def{cos}{14}{0.97030} \pgfmath@def{cos}{15}{0.96593} +\pgfmath@def{cos}{16}{0.96126} \pgfmath@def{cos}{17}{0.95630} +\pgfmath@def{cos}{18}{0.95106} \pgfmath@def{cos}{19}{0.94552} +\pgfmath@def{cos}{20}{0.93969} \pgfmath@def{cos}{21}{0.93358} +\pgfmath@def{cos}{22}{0.92718} \pgfmath@def{cos}{23}{0.92050} +\pgfmath@def{cos}{24}{0.91355} \pgfmath@def{cos}{25}{0.90631} +\pgfmath@def{cos}{26}{0.89879} \pgfmath@def{cos}{27}{0.89101} +\pgfmath@def{cos}{28}{0.88295} \pgfmath@def{cos}{29}{0.87462} +\pgfmath@def{cos}{30}{0.86603} \pgfmath@def{cos}{31}{0.85717} +\pgfmath@def{cos}{32}{0.84805} \pgfmath@def{cos}{33}{0.83867} +\pgfmath@def{cos}{34}{0.82904} \pgfmath@def{cos}{35}{0.81915} +\pgfmath@def{cos}{36}{0.80902} \pgfmath@def{cos}{37}{0.79864} +\pgfmath@def{cos}{38}{0.78801} \pgfmath@def{cos}{39}{0.77715} +\pgfmath@def{cos}{40}{0.76604} \pgfmath@def{cos}{41}{0.75471} +\pgfmath@def{cos}{42}{0.74314} \pgfmath@def{cos}{43}{0.73135} +\pgfmath@def{cos}{44}{0.71934} \pgfmath@def{cos}{45}{0.70711} +\pgfmath@def{cos}{46}{0.69466} \pgfmath@def{cos}{47}{0.68200} +\pgfmath@def{cos}{48}{0.66913} \pgfmath@def{cos}{49}{0.65606} +\pgfmath@def{cos}{50}{0.64279} \pgfmath@def{cos}{51}{0.62932} +\pgfmath@def{cos}{52}{0.61566} \pgfmath@def{cos}{53}{0.60182} +\pgfmath@def{cos}{54}{0.58779} \pgfmath@def{cos}{55}{0.57358} +\pgfmath@def{cos}{56}{0.55919} \pgfmath@def{cos}{57}{0.54464} +\pgfmath@def{cos}{58}{0.52992} \pgfmath@def{cos}{59}{0.51504} +\pgfmath@def{cos}{60}{0.50000} \pgfmath@def{cos}{61}{0.48481} +\pgfmath@def{cos}{62}{0.46947} \pgfmath@def{cos}{63}{0.45399} +\pgfmath@def{cos}{64}{0.43837} \pgfmath@def{cos}{65}{0.42262} +\pgfmath@def{cos}{66}{0.40674} \pgfmath@def{cos}{67}{0.39073} +\pgfmath@def{cos}{68}{0.37461} \pgfmath@def{cos}{69}{0.35837} +\pgfmath@def{cos}{70}{0.34202} \pgfmath@def{cos}{71}{0.32557} +\pgfmath@def{cos}{72}{0.30902} \pgfmath@def{cos}{73}{0.29237} +\pgfmath@def{cos}{74}{0.27564} \pgfmath@def{cos}{75}{0.25882} +\pgfmath@def{cos}{76}{0.24192} \pgfmath@def{cos}{77}{0.22495} +\pgfmath@def{cos}{78}{0.20791} \pgfmath@def{cos}{79}{0.19081} +\pgfmath@def{cos}{80}{0.17365} \pgfmath@def{cos}{81}{0.15643} +\pgfmath@def{cos}{82}{0.13917} \pgfmath@def{cos}{83}{0.12187} +\pgfmath@def{cos}{84}{0.10453} \pgfmath@def{cos}{85}{0.08716} +\pgfmath@def{cos}{86}{0.06976} \pgfmath@def{cos}{87}{0.05234} +\pgfmath@def{cos}{88}{0.03490} \pgfmath@def{cos}{89}{0.01745} +\pgfmath@def{cos}{90}{0.00000} \pgfmath@def{cos}{91}{-0.01745} +\pgfmath@def{cos}{92}{-0.03490} \pgfmath@def{cos}{93}{-0.05234} +\pgfmath@def{cos}{94}{-0.06976} \pgfmath@def{cos}{95}{-0.08716} +\pgfmath@def{cos}{96}{-0.10453} \pgfmath@def{cos}{97}{-0.12187} +\pgfmath@def{cos}{98}{-0.13917} \pgfmath@def{cos}{99}{-0.15643} +\pgfmath@def{cos}{100}{-0.17365} \pgfmath@def{cos}{101}{-0.19081} +\pgfmath@def{cos}{102}{-0.20791} \pgfmath@def{cos}{103}{-0.22495} +\pgfmath@def{cos}{104}{-0.24192} \pgfmath@def{cos}{105}{-0.25882} +\pgfmath@def{cos}{106}{-0.27564} \pgfmath@def{cos}{107}{-0.29237} +\pgfmath@def{cos}{108}{-0.30902} \pgfmath@def{cos}{109}{-0.32557} +\pgfmath@def{cos}{110}{-0.34202} \pgfmath@def{cos}{111}{-0.35837} +\pgfmath@def{cos}{112}{-0.37461} \pgfmath@def{cos}{113}{-0.39073} +\pgfmath@def{cos}{114}{-0.40674} \pgfmath@def{cos}{115}{-0.42262} +\pgfmath@def{cos}{116}{-0.43837} \pgfmath@def{cos}{117}{-0.45399} +\pgfmath@def{cos}{118}{-0.46947} \pgfmath@def{cos}{119}{-0.48481} +\pgfmath@def{cos}{120}{-0.50000} \pgfmath@def{cos}{121}{-0.51504} +\pgfmath@def{cos}{122}{-0.52992} \pgfmath@def{cos}{123}{-0.54464} +\pgfmath@def{cos}{124}{-0.55919} \pgfmath@def{cos}{125}{-0.57358} +\pgfmath@def{cos}{126}{-0.58779} \pgfmath@def{cos}{127}{-0.60182} +\pgfmath@def{cos}{128}{-0.61566} \pgfmath@def{cos}{129}{-0.62932} +\pgfmath@def{cos}{130}{-0.64279} \pgfmath@def{cos}{131}{-0.65606} +\pgfmath@def{cos}{132}{-0.66913} \pgfmath@def{cos}{133}{-0.68200} +\pgfmath@def{cos}{134}{-0.69466} \pgfmath@def{cos}{135}{-0.70711} +\pgfmath@def{cos}{136}{-0.71934} \pgfmath@def{cos}{137}{-0.73135} +\pgfmath@def{cos}{138}{-0.74314} \pgfmath@def{cos}{139}{-0.75471} +\pgfmath@def{cos}{140}{-0.76604} \pgfmath@def{cos}{141}{-0.77715} +\pgfmath@def{cos}{142}{-0.78801} \pgfmath@def{cos}{143}{-0.79864} +\pgfmath@def{cos}{144}{-0.80902} \pgfmath@def{cos}{145}{-0.81915} +\pgfmath@def{cos}{146}{-0.82904} \pgfmath@def{cos}{147}{-0.83867} +\pgfmath@def{cos}{148}{-0.84805} \pgfmath@def{cos}{149}{-0.85717} +\pgfmath@def{cos}{150}{-0.86603} \pgfmath@def{cos}{151}{-0.87462} +\pgfmath@def{cos}{152}{-0.88295} \pgfmath@def{cos}{153}{-0.89101} +\pgfmath@def{cos}{154}{-0.89879} \pgfmath@def{cos}{155}{-0.90631} +\pgfmath@def{cos}{156}{-0.91355} \pgfmath@def{cos}{157}{-0.92050} +\pgfmath@def{cos}{158}{-0.92718} \pgfmath@def{cos}{159}{-0.93358} +\pgfmath@def{cos}{160}{-0.93969} \pgfmath@def{cos}{161}{-0.94552} +\pgfmath@def{cos}{162}{-0.95106} \pgfmath@def{cos}{163}{-0.95630} +\pgfmath@def{cos}{164}{-0.96126} \pgfmath@def{cos}{165}{-0.96593} +\pgfmath@def{cos}{166}{-0.97030} \pgfmath@def{cos}{167}{-0.97437} +\pgfmath@def{cos}{168}{-0.97815} \pgfmath@def{cos}{169}{-0.98163} +\pgfmath@def{cos}{170}{-0.98481} \pgfmath@def{cos}{171}{-0.98769} +\pgfmath@def{cos}{172}{-0.99027} \pgfmath@def{cos}{173}{-0.99255} +\pgfmath@def{cos}{174}{-0.99452} \pgfmath@def{cos}{175}{-0.99619} +\pgfmath@def{cos}{176}{-0.99756} \pgfmath@def{cos}{177}{-0.99863} +\pgfmath@def{cos}{178}{-0.99939} \pgfmath@def{cos}{179}{-0.99985} +\pgfmath@def{cos}{180}{-1.00000} \pgfmath@def{cos}{181}{-0.99985} + +\pgfmath@def{cosfrac}{0}{1.00000} \pgfmath@def{cosfrac}{1}{0.99995} +\pgfmath@def{cosfrac}{2}{0.99980} \pgfmath@def{cosfrac}{3}{0.99955} +\pgfmath@def{cosfrac}{4}{0.99920} \pgfmath@def{cosfrac}{5}{0.99875} +\pgfmath@def{cosfrac}{6}{0.99820} \pgfmath@def{cosfrac}{7}{0.99755} +\pgfmath@def{cosfrac}{8}{0.99681} \pgfmath@def{cosfrac}{9}{0.99597} +\pgfmath@def{cosfrac}{10}{0.99503} 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+\pgfmath@def{acos}{824}{34.51276} \pgfmath@def{acos}{825}{34.41150} +\pgfmath@def{acos}{826}{34.30999} \pgfmath@def{acos}{827}{34.20821} +\pgfmath@def{acos}{828}{34.10616} \pgfmath@def{acos}{829}{34.00385} +\pgfmath@def{acos}{830}{33.90126} \pgfmath@def{acos}{831}{33.79840} +\pgfmath@def{acos}{832}{33.69526} \pgfmath@def{acos}{833}{33.59184} +\pgfmath@def{acos}{834}{33.48814} \pgfmath@def{acos}{835}{33.38416} +\pgfmath@def{acos}{836}{33.27989} \pgfmath@def{acos}{837}{33.17533} +\pgfmath@def{acos}{838}{33.07047} \pgfmath@def{acos}{839}{32.96532} +\pgfmath@def{acos}{840}{32.85988} \pgfmath@def{acos}{841}{32.75413} +\pgfmath@def{acos}{842}{32.64807} \pgfmath@def{acos}{843}{32.54171} +\pgfmath@def{acos}{844}{32.43504} \pgfmath@def{acos}{845}{32.32806} +\pgfmath@def{acos}{846}{32.22076} \pgfmath@def{acos}{847}{32.11314} +\pgfmath@def{acos}{848}{32.00520} \pgfmath@def{acos}{849}{31.89693} +\pgfmath@def{acos}{850}{31.78833} \pgfmath@def{acos}{851}{31.67939} +\pgfmath@def{acos}{852}{31.57012} \pgfmath@def{acos}{853}{31.46051} +\pgfmath@def{acos}{854}{31.35056} \pgfmath@def{acos}{855}{31.24026} +\pgfmath@def{acos}{856}{31.12961} \pgfmath@def{acos}{857}{31.01860} +\pgfmath@def{acos}{858}{30.90724} \pgfmath@def{acos}{859}{30.79551} +\pgfmath@def{acos}{860}{30.68341} \pgfmath@def{acos}{861}{30.57095} +\pgfmath@def{acos}{862}{30.45811} \pgfmath@def{acos}{863}{30.34489} +\pgfmath@def{acos}{864}{30.23128} \pgfmath@def{acos}{865}{30.11729} +\pgfmath@def{acos}{866}{30.00291} \pgfmath@def{acos}{867}{29.88813} +\pgfmath@def{acos}{868}{29.77294} \pgfmath@def{acos}{869}{29.65736} +\pgfmath@def{acos}{870}{29.54136} \pgfmath@def{acos}{871}{29.42494} +\pgfmath@def{acos}{872}{29.30810} \pgfmath@def{acos}{873}{29.19084} +\pgfmath@def{acos}{874}{29.07315} \pgfmath@def{acos}{875}{28.95502} +\pgfmath@def{acos}{876}{28.83645} \pgfmath@def{acos}{877}{28.71743} +\pgfmath@def{acos}{878}{28.59796} \pgfmath@def{acos}{879}{28.47803} +\pgfmath@def{acos}{880}{28.35763} \pgfmath@def{acos}{881}{28.23677} +\pgfmath@def{acos}{882}{28.11542} \pgfmath@def{acos}{883}{27.99360} +\pgfmath@def{acos}{884}{27.87128} \pgfmath@def{acos}{885}{27.74847} +\pgfmath@def{acos}{886}{27.62516} \pgfmath@def{acos}{887}{27.50134} +\pgfmath@def{acos}{888}{27.37700} \pgfmath@def{acos}{889}{27.25214} +\pgfmath@def{acos}{890}{27.12675} \pgfmath@def{acos}{891}{27.00082} +\pgfmath@def{acos}{892}{26.87434} \pgfmath@def{acos}{893}{26.74731} +\pgfmath@def{acos}{894}{26.61973} \pgfmath@def{acos}{895}{26.49157} +\pgfmath@def{acos}{896}{26.36283} \pgfmath@def{acos}{897}{26.23351} +\pgfmath@def{acos}{898}{26.10359} \pgfmath@def{acos}{899}{25.97306} +\pgfmath@def{acos}{900}{25.84193} \pgfmath@def{acos}{901}{25.71017} +\pgfmath@def{acos}{902}{25.57778} \pgfmath@def{acos}{903}{25.44475} +\pgfmath@def{acos}{904}{25.31106} \pgfmath@def{acos}{905}{25.17671} +\pgfmath@def{acos}{906}{25.04169} \pgfmath@def{acos}{907}{24.90598} +\pgfmath@def{acos}{908}{24.76958} \pgfmath@def{acos}{909}{24.63247} +\pgfmath@def{acos}{910}{24.49464} \pgfmath@def{acos}{911}{24.35608} +\pgfmath@def{acos}{912}{24.21678} \pgfmath@def{acos}{913}{24.07672} +\pgfmath@def{acos}{914}{23.93588} \pgfmath@def{acos}{915}{23.79427} +\pgfmath@def{acos}{916}{23.65185} \pgfmath@def{acos}{917}{23.50863} +\pgfmath@def{acos}{918}{23.36457} \pgfmath@def{acos}{919}{23.21967} +\pgfmath@def{acos}{920}{23.07391} \pgfmath@def{acos}{921}{22.92728} +\pgfmath@def{acos}{922}{22.77975} \pgfmath@def{acos}{923}{22.63132} +\pgfmath@def{acos}{924}{22.48195} \pgfmath@def{acos}{925}{22.33164} +\pgfmath@def{acos}{926}{22.18036} \pgfmath@def{acos}{927}{22.02810} +\pgfmath@def{acos}{928}{21.87483} \pgfmath@def{acos}{929}{21.72053} +\pgfmath@def{acos}{930}{21.56518} \pgfmath@def{acos}{931}{21.40876} +\pgfmath@def{acos}{932}{21.25124} \pgfmath@def{acos}{933}{21.09260} +\pgfmath@def{acos}{934}{20.93281} \pgfmath@def{acos}{935}{20.77185} +\pgfmath@def{acos}{936}{20.60969} \pgfmath@def{acos}{937}{20.44630} +\pgfmath@def{acos}{938}{20.28165} \pgfmath@def{acos}{939}{20.11570} +\pgfmath@def{acos}{940}{19.94844} \pgfmath@def{acos}{941}{19.77982} +\pgfmath@def{acos}{942}{19.60981} \pgfmath@def{acos}{943}{19.43837} +\pgfmath@def{acos}{944}{19.26546} \pgfmath@def{acos}{945}{19.09105} +\pgfmath@def{acos}{946}{18.91509} \pgfmath@def{acos}{947}{18.73754} +\pgfmath@def{acos}{948}{18.55835} \pgfmath@def{acos}{949}{18.37748} +\pgfmath@def{acos}{950}{18.19487} \pgfmath@def{acos}{951}{18.01047} +\pgfmath@def{acos}{952}{17.82423} \pgfmath@def{acos}{953}{17.63609} +\pgfmath@def{acos}{954}{17.44598} \pgfmath@def{acos}{955}{17.25385} +\pgfmath@def{acos}{956}{17.05962} \pgfmath@def{acos}{957}{16.86322} +\pgfmath@def{acos}{958}{16.66457} \pgfmath@def{acos}{959}{16.46359} +\pgfmath@def{acos}{960}{16.26020} \pgfmath@def{acos}{961}{16.05430} +\pgfmath@def{acos}{962}{15.84580} \pgfmath@def{acos}{963}{15.63459} +\pgfmath@def{acos}{964}{15.42057} \pgfmath@def{acos}{965}{15.20360} +\pgfmath@def{acos}{966}{14.98357} \pgfmath@def{acos}{967}{14.76033} +\pgfmath@def{acos}{968}{14.53374} \pgfmath@def{acos}{969}{14.30364} +\pgfmath@def{acos}{970}{14.06986} \pgfmath@def{acos}{971}{13.83221} +\pgfmath@def{acos}{972}{13.59049} \pgfmath@def{acos}{973}{13.34447} +\pgfmath@def{acos}{974}{13.09392} \pgfmath@def{acos}{975}{12.83856} +\pgfmath@def{acos}{976}{12.57811} \pgfmath@def{acos}{977}{12.31225} +\pgfmath@def{acos}{978}{12.04060} \pgfmath@def{acos}{979}{11.76278} +\pgfmath@def{acos}{980}{11.47834} \pgfmath@def{acos}{981}{11.18676} +\pgfmath@def{acos}{982}{10.88748} \pgfmath@def{acos}{983}{10.57984} +\pgfmath@def{acos}{984}{10.26309} \pgfmath@def{acos}{985}{9.93636} +\pgfmath@def{acos}{986}{9.59863} \pgfmath@def{acos}{987}{9.24870} +\pgfmath@def{acos}{988}{8.88512} \pgfmath@def{acos}{989}{8.50614} +\pgfmath@def{acos}{990}{8.10961} \pgfmath@def{acos}{991}{7.69281} +\pgfmath@def{acos}{992}{7.25224} \pgfmath@def{acos}{993}{6.78328} +\pgfmath@def{acos}{994}{6.27958} \pgfmath@def{acos}{995}{5.73196} +\pgfmath@def{acos}{996}{5.12640} \pgfmath@def{acos}{997}{4.43922} +\pgfmath@def{acos}{998}{3.62430} \pgfmath@def{acos}{999}{2.56255} +\pgfmath@def{acos}{1000}{0.00000} + + + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathode.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathode.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..526573a3263c00988c3a5ed147683b50bdaf4087 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathode.code.tex @@ -0,0 +1,100 @@ +\def\pgfmathode@stopadd{\pgfmathode@stopadd} + +\def\pgfmathode@addindextofunc[#1]#2{% + \begingroup + \gdef\pgfmathode@func{}% + \pgfmathode@addindextofunc@i[#1]#2\pgfmathode@stopadd} + +\def\pgfmathode@addindextofunc@i[#1]#2#3{% + \ifx#1#2 + \expandafter\gdef\expandafter\pgfmathode@func\expandafter{% + \pgfmathode@func #2[\pgfmathode@timeindex]}% + \else + \expandafter\gdef\expandafter\pgfmathode@func\expandafter{% + \pgfmathode@func #2}% + \fi + \ifx#3\pgfmathode@stopadd + \expandafter\gdef\expandafter\pgfmathode@func\expandafter{% + \expandafter{\pgfmathode@func}}% + \let\next\endgroup + \else + \def\next{\pgfmathode@addindextofunc@i[#1]#3}% + \fi + \next} + + + +\def\pgfmathode@generic@init@RK{% + \begingroup + \gdef#1{{#3}}% + \pgfmathode@addindextofunc[#1]#2% + \pgfmathsetmacro\pgfmathode@Sol@t{#1[0][0]}% + \pgfmathsetmacro\pgfmathode@Deltat{(#4-\pgfmathode@Sol@t)/#5}% + \pgfmathsetmacro\pgfmathode@dimfunc{dim(#3)-1}% + \pgfmathsetmacro\pgfmathode@numstep{#5-1}} + +\def\pgfmathodeRKI#1#2#3#4#5{% + \pgfmathode@generic@init@RK + \foreach \pgfmathode@timeindex in {0,...,\pgfmathode@numstep} {% + \message{Step \pgfmathode@timeindex...}% + \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {% + \pgfmathparse{% + \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+ + #1[\pgfmathode@timeindex][\pgfmathode@funcindex]}% + \expandafter\xdef\csname pgfmathode@Sol@\pgfmathode@funcindex + \endcsname{\pgfmathresult}% + } + \pgfmathparse{\pgfmathode@Sol@t+\pgfmathode@Deltat}% + \xdef\pgfmathode@Sol@t{\pgfmathresult}% + \xdef\pgfmathode@temp{}% + \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {% + \ifx\pgfmathode@temp\pgfutil@empty + \xdef\pgfmathode@temp{% + \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}% + \else + \xdef\pgfmathode@temp{% + \pgfmathode@temp, + \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}% + \fi} + \xdef#1{% + {\expandafter\pgfutil@firstofone#1,% + {\pgfmathode@Sol@t,\pgfmathode@temp}}}% + } + \endgroup} + +\def\pgfmathodeRKIV#1#2#3#4#5{% + \pgfmathode@generic@init@RK + \foreach \pgfmathode@timeindex in {0,...,\pgfmathode@numstep} {% + \message{Step \pgfmathode@timeindex...}% + \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {% + \pgfmathparse{% + \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+ + #1[\pgfmathode@timeindex][\pgfmathode@funcindex]}% + \expandafter\xdef\csname pgfmathode@RKIV@1@\pgfmathode@funcindex + \endcsname{\pgfmathresult}% + \pgfmathparse{% + \pgfmathode@Deltat*(\pgfmathode@func[\pgfmathode@funcindex-1])+ + #1[\pgfmathode@timeindex][\pgfmathode@funcindex]}% + \expandafter\xdef\csname pgfmathode@RKIV@1@\pgfmathode@funcindex + \endcsname{\pgfmathresult}% + } + \pgfmathparse{\pgfmathode@Sol@t+\pgfmathode@Deltat}% + \xdef\pgfmathode@Sol@t{\pgfmathresult}% + \xdef\pgfmathode@temp{}% + \foreach \pgfmathode@funcindex in {1,...,\pgfmathode@dimfunc} {% + \ifx\pgfmathode@temp\pgfutil@empty + \xdef\pgfmathode@temp{% + \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}% + \else + \xdef\pgfmathode@temp{% + \pgfmathode@temp, + \csname pgfmathode@Sol@\pgfmathode@funcindex\endcsname}% + \fi} + \xdef#1{% + {\expandafter\pgfutil@firstofone#1,% + {\pgfmathode@Sol@t,\pgfmathode@temp}}}% + } + \endgroup} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathparser.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathparser.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..20a5e6c8a7ded81b01fcdaf03c5640be8cca15e7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathparser.code.tex @@ -0,0 +1,859 @@ + +\newdimen\pgfmath@dimen +\newcount\pgfmath@count +\newbox\pgfmath@box +\newtoks\pgfmath@toks + +\newif\ifpgfmath@quickparse +\newif\ifpgfmathfloat +\newif\ifpgfmathunitsdeclared +\newif\ifpgfmathmathunitsdeclared +\newif\ifpgfmathignoreunitscale + +\let\pgfmath@protected@edef=\edef +\ifcsname protected@edef\endcsname + \let\pgfmath@protected@edef=\protected@edef +\fi + +\def\pgfmathprint#1{\pgfmathparse{#1}\pgfmathresult} + +\def\pgfmathparse{% + \begingroup + \pgfmath@catcodes + \pgfmath@quickparsefalse + \ifpgfmathfloat + \let\pgfmath@parse@next=\pgfmathfloatparsenumber + \else + \let\pgfmath@parse@next=\pgfmathparse@ + \fi + \pgfmath@parse@next} + +\begingroup + \lccode`\~=`\" + \lowercase{\endgroup + \def\pgfmath@catcodes{% + \catcode`\==12 % + \catcode`\,=12 % + \catcode`\|=12 % + \catcode`\&=12 % + \let~\pgfmath@char@quote + }}% + +\def\pgfmathqparse{% + \begingroup + \pgfmath@catcodes + \pgfmath@quickparsetrue + \pgfmathparse@} + +\def\pgfmathparse@#1{% + \global\pgfmathunitsdeclaredfalse + \global\pgfmathmathunitsdeclaredfalse + \pgfmath@protected@edef\pgfmath@expression{#1}% + \expandafter\pgfmathparse@trynumber@loop\pgfmath@expression\pgfmath@parse@stop +} + +\def\pgfmath@parse@stop{\pgfmath@parse@stop}% + +\def\pgfmathparse@trynumber@token{numeric} +\begingroup +\def\\{\global\let\pgf@let@space@token= } \\ % +\endgroup + +\def\pgfmathparse@trynumber@loop{% + \futurelet\pgfmath@token@let\pgfmathparse@trynumber@loop@ +}% +\def\pgfmathparse@trynumber@loop@#1{% + \ifx\pgfmath@token@let\pgf@let@space@token + \def\pgfmath@parse@next{\pgfmathparse@@#1}% + \else + \ifx\pgfmath@token@let\bgroup% + \let\pgfmath@parse@next=\pgfmathparse@@ + \else + \ifx\pgfmath@token@let\pgfmath@parse@stop + \let\pgfmath@parse@next=\pgfmathparse@expression@is@number + \else + \expandafter\ifx\csname pgfmath@token@\pgfmathparse@trynumber@token @\string#1\endcsname\relax% + \let\pgfmath@parse@next=\pgfmathparse@@ + \else + \let\pgfmath@parse@next=\pgfmathparse@trynumber@loop + \fi + \fi + \fi + \fi + \pgfmath@parse@next +}% + +\def\pgfmathparse@expression@is@number{% + \let\pgfmathresult=\pgfmath@expression + \pgfmath@smuggleone\pgfmathresult% + \endgroup + \ignorespaces +}% +\def\pgfmathparse@@#1\pgfmath@parse@stop{% + \let\real=\pgfmath@calc@real + \let\minof=\pgfmath@calc@minof + \let\maxof=\pgfmath@calc@maxof + \let\ratio=\pgfmath@calc@ratio + \let\widthof=\pgfmath@calc@widthof + \let\heightof=\pgfmath@calc@heightof + \let\depthof=\pgfmath@calc@depthof + \pgfmath@selectfont + \pgfmath@stack@operation={{}{}{}}% + \pgfmath@stack@operand={{}{}{}}% + \let\pgfmath@stack@operation@top=\pgfmath@stack@empty + \let\pgfmath@stack@operand@top=\pgfmath@stack@empty + \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmath@expression}% + \expandafter\pgfmath@parse@@operand\pgfmath@bgroup@stripped @@@@\pgfmath@parse@stop% +} + +\def\pgfmath@parse@end#1\pgfmath@parse@stop{% + \pgfmathpostparse + \pgfmath@smuggleone\pgfmathresult% + \endgroup + \ignorespaces} + +\let\pgfmathpostparse=\relax + +\def\pgfmathscaleresult{% + \ifpgfmathunitsdeclared + \else + \ifpgfmathignoreunitscale + \else + \afterassignment\pgfmath@gobbletilpgfmath@% + \pgfmath@x\pgfmathresultunitscale pt\relax\pgfmath@% + \expandafter\pgfmath@x\pgfmathresult\pgfmath@x% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@x}}% + \fi + \fi +} + +\def\pgfmathsetresultunitscale#1{\def\pgfmathresultunitscale{#1}} + +\def\pgfmathresultunitscale{1} + + +\def\pgfmathifexpression#1#2#3{% + \pgfmathparse{#1}% + \pgfmath@iftrue{#2}{#3}% +}% +\def\pgfmath@iftrue{% + \ifdim\pgfmathresult pt=1.0pt % + \let\pgfmath@next=\pgfutil@firstoftwo + \else + \let\pgfmath@next=\pgfutil@secondoftwo + \fi + \pgfmath@next% +}% + +\def\pgfmath@calc@real#1{#1} +\def\pgfmath@calc@minof#1#2{min(#1,#2)} +\def\pgfmath@calc@maxof#1#2{max(#1,#2)} +\def\pgfmath@calc@ratio#1#2{#1/#2} +\def\pgfmath@calc@widthof#1{width("#1")} +\def\pgfmath@calc@heightof#1{height("#1")} +\def\pgfmath@calc@depthof#1{depth("#1")} + +\def\pgfmath@bgroup{\string\pgfmath@bgroup} +\def\pgfmath@egroup{\string\pgfmath@egroup} +\def\pgfmath@egroup@token{\pgfmath@egroup} + +\def\pgfmath@text@@{@} +\def\pgfmath@text@operator{operator} +\def\pgfmath@text@function{function} +\def\pgfmath@dots{...} +\def\pgfmath@char@zero{0} +\def\pgfmath@char@quote{"} +\def\pgfmath@char@exclamation{!} +\def\pgfmath@char@plus{+} +\def\pgfmath@char@minus{-} +\def\pgfmath@char@period{.} +\def\pgfmath@char@leftangle{<} +\def\pgfmath@char@leftbracket{[} +\pgfmath@toks={#} +\edef\pgfmath@char@hash{\the\pgfmath@toks} + +\def\pgfmath@tokens@make#1#2{% + \def\pgfmath@prefix{#1}% + \expandafter\pgfmath@tokens@@make#2{}} + +\def\pgfmath@tokens@@make#1{% + \def\pgfmath@token{#1}% + \ifx\pgfmath@token\pgfmath@empty + \else + \pgfmath@namedef{pgfmath@token@\pgfmath@prefix @\string#1}{#1}% + \expandafter\pgfmath@tokens@@make% + \fi} + +\pgfmath@tokens@make{box}{\wd\ht\dp} +\ifx\dimexpr\@undefined\else % + \pgfmath@tokens@make{dimexpr}{\dimexpr\glueexpr} +\fi +\pgfmath@tokens@make{unit}{{bp}{cc}{cm}{dd}{em}{ex}{in}{mm}{pc}{pt}{sp}} +\ifx\pdftexversion\@undefined\else % + \pgfmath@tokens@make{unit}{{nc}{nd}{px}} +\fi +\ifx\directlua\@undefined\else % + \pgfmath@tokens@make{unit}{{nc}{nd}{px}} +\fi +\ifx\kanjiskip\@undefined\else % + \pgfmath@tokens@make{unit}{{H}{Q}{zh}{zw}} +\fi +\pgfmath@tokens@make{mathunit}{{mu}} +\pgfmath@tokens@make{numeric}{.0123456789} +\pgfmath@tokens@make{number}{0123456789} +\pgfmath@tokens@make{functional}{_abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ} +\pgfmath@tokens@make{exponent}{eE} +\pgfmath@tokens@make{group}{{()}{[]}{\pgfmath@bgroup\pgfmath@egroup}} +\pgfmath@tokens@make{specials}{@)]\pgfmath@egroup} +\pgfmath@tokens@make{hexadecimal}{0123456789ABCDEFabcdef} +\pgfmath@tokens@make{octal}{01234567} +\pgfmath@tokens@make{binary}{01} + +\pgfmath@namedef{pgfmath@base@0x}{16} +\pgfmath@namedef{pgfmath@base@0X}{16} +\pgfmath@namedef{pgfmath@base@0b}{2} +\pgfmath@namedef{pgfmath@base@0B}{2} + +\newif\ifpgfmath@dimen@ +\def\pgfmath@dimen@#1{% + \begingroup + \afterassignment\pgfmath@dimen@@% + #1=0.0pt\relax\pgfmath@} +\def\pgfmath@dimen@@#1#2\pgfmath@{% + \endgroup + \ifx#1.% + \pgfmath@dimen@false + \else + \pgfmath@dimen@true + \fi} + +\def\pgfmath@parse@ifbgroup#1#2{% + \let\pgfmath@parse@bgroup@after=#1% + \let\pgfmath@parse@nobgroup@after=#2% + \futurelet\pgfmath@token@let% + \pgfmath@parse@@ifbgroup} + +\def\pgfmath@parse@@ifbgroup{% + \ifx\pgfmath@token@let\bgroup + \let\pgfmath@parse@next=\pgfmath@parse@@@ifbgroup + \else + \ifx\pgfmath@token@let\pgfmath@sptoken + \let\pgfmath@parse@next=\pgfmath@parse@@@@ifbgroup + \else + \let\pgfmath@parse@next=\pgfmath@parse@nobgroup@after + \fi + \fi + \pgfmath@parse@next} + +\newif\ifpgfmath@octalparsing +\pgfmath@octalparsingtrue + +\def\pgfmath@parse@@@ifbgroup#1{% + \pgfmath@parse@bgroup@after\pgfmath@bgroup#1\pgfmath@egroup} + +{ +\def\:{\pgfmath@parse@@@@ifbgroup} +\expandafter\gdef\: {\futurelet\pgfmath@token@let\pgfmath@parse@@ifbgroup} +} + +\def\pgfmath@parse@operand{% + \expandafter\pgfmath@parse@@operand\pgfmath@token@next} + +\def\pgfmath@parse@@operand{% + \pgfmath@parse@ifbgroup{\pgfmath@parse@@operand}{\pgfmath@parse@@operand@}} + +\def\pgfmath@parse@@operand@#1{% + \def\pgfmath@token{#1}% + \ifx\pgfmath@token\pgfmath@char@plus + \let\pgfmath@parse@next=\pgfmath@parse@@operand% + \else + \ifx\pgfmath@token\pgfmath@char@minus + \pgfmath@stack@push@operation{neg}% + \let\pgfmath@parse@next=\pgfmath@parse@@operand + \else + \expandafter\ifx\csname pgfmath@operation@\expandafter\string\pgfmath@token @prefix\endcsname\pgfmath@token + \let\pgfmath@parse@next=\pgfmath@parse@prefix@operator + \else + \ifpgfmath@quickparse + \let\pgfmath@parse@next=\pgfmath@qparse@operand + \else + \let\pgfmath@number=\pgfmath@empty + \expandafter\ifx\csname pgfmath@token@functional@\string#1\endcsname\relax% + \let\pgfmath@base=\pgfmath@empty% + \let\pgfmath@token@next=\pgfmath@token% + \if#10% + \ifpgfmath@octalparsing% + \def\pgfmath@base{8}% + \fi% + \fi% + \let\pgfmath@parse@next=\pgfmath@parse@number% + \else% + \let\pgfmath@function=\pgfmath@token% + \let\pgfmath@parse@next=\pgfmath@parse@function% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgfmath@parse@next% +} + +\def\pgfmath@parse@prefix@operator{% + \ifx\pgfmath@token\pgfmath@char@quote% + \let\pgfmath@parse@next=\pgfmath@parse@operand@quote% + \else% + \ifx\pgfmath@token\pgfmath@char@exclamation% + \pgfmath@stack@push@operation{not}% + \let\pgfmath@parse@next=\pgfmath@parse@@operand% + \else% + \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@token}% + \let\pgfmath@parse@next=\pgfmath@parse@@operand% + \fi% + \fi% + \pgfmath@parse@next% +}% + + +\def\pgfmath@parse@operand@quote#1"{% + \def\pgfmathresult{#1}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +} + +\def\pgfmath@qparse@operand{% + \afterassignment\pgfmath@qparse@@operand% + \pgfmath@dimen\pgfmath@token} +\def\pgfmath@qparse@@operand{% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +} + +\def\pgfmath@parse@number{\pgfmath@parse@ifbgroup{\pgfmath@parse@number}{\pgfmath@parse@number@}} +\def\pgfmath@parse@number@#1{% + \let\pgfmath@token=\pgfmath@token@next% + \def\pgfmath@token@next{#1}% + \pgfmath@parse@@number} + +\def\pgfmath@parse@@number{% + \ifx\pgfmath@token\pgfmath@egroup@token% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmath@number}% + \let\pgfmath@parse@next=\pgfmath@parse@@@operator% + \else% + \expandafter\ifcat\pgfmath@token\relax% + \expandafter\ifx\csname pgfmath@token@dimexpr@\expandafter\string\pgfmath@token\endcsname\relax% + \expandafter\ifx\pgfmath@token\numexpr% + \let\pgfmath@parse@next=\pgfmath@parse@numexpr% + \else% + \expandafter\ifx\pgfmath@token\muexpr% + \let\pgfmath@parse@next=\pgfmath@parse@muexpr% + \else% + \expandafter\ifx\csname pgfmath@token@box@\expandafter\string\pgfmath@token\endcsname\relax% + \expandafter\pgfmath@dimen@\pgfmath@token% + \ifpgfmath@dimen@% + \global\pgfmathunitsdeclaredtrue% + \pgfmath@dimen=\pgfmath@number\pgfmath@token% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@operator% + \else% + \pgfmath@count=\pgfmath@token% + \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}% + \expandafter\ifcat\pgfmath@token@next\relax% + \let\pgfmath@parse@next=\pgfmath@parse@number% + \else% + \let\pgfmathresult=\pgfmath@number% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@operator% + \fi% + \fi% + \else% + \global\pgfmathunitsdeclaredtrue% + \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@@operator% + \fi% + \fi% + \fi% + \else% + \global\pgfmathunitsdeclaredtrue% + \let\pgfmath@parse@next=\pgfmath@parse@dimexpr% + \fi% + \else% + \expandafter\ifx\csname pgfmath@token@numeric@\expandafter\string\pgfmath@token\endcsname\relax% + \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax% + \expandafter\ifx\csname pgfmath@token@unit@\pgfmath@token\endcsname\relax% + \expandafter\ifx\csname pgfmath@token@exponent@\pgfmath@token\endcsname\relax% + \expandafter\ifx\csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname\relax% + \expandafter\ifx\csname pgfmath@token@mathunit@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax% + \ifx\pgfmath@base\pgfmath@empty% + \let\pgfmathresult=\pgfmath@number% + \else% + \ifx\pgfmath@number\pgfmath@char@zero% + \let\pgfmathresult=\pgfmath@number% + \else% + \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{8}{10}% + \fi% + \fi% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@@@operator% + \else% + \global\pgfmathunitsdeclaredtrue% + \global\pgfmathmathunitsdeclaredtrue% + \pgfmath@dimen=\pgfmath@number pt\relax% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@@operator% + \fi% + \else% + \expandafter\let\expandafter\pgfmath@base\expandafter=% + \csname pgfmath@base@\pgfmath@number\pgfmath@token\endcsname% + \let\pgfmath@parse@next=\pgfmath@parse@base% + \fi% + \else% + \let\pgfmath@parse@next=\pgfmath@parse@exponent% + \fi% + \else% + \global\pgfmathunitsdeclaredtrue% + \pgfmath@dimen=\pgfmath@number\pgfmath@token\relax% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@@operator% + \fi% + \else% + \global\pgfmathunitsdeclaredtrue% + \pgfmath@dimen=\pgfmath@number\pgfmath@token\pgfmath@token@next\relax% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@@operator% + \fi% + \else% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfmath@number% + \expandafter\expandafter\expandafter{\expandafter\pgfmath@number\pgfmath@token}% + \ifx\pgfmath@token\pgfmath@char@period% + \let\pgfmath@base=\pgfmath@empty% + \fi% + \let\pgfmath@parse@next=\pgfmath@parse@number% + \fi% + \fi% + \fi% + \pgfmath@parse@next% +} + + +\def\pgfmath@parse@dimexpr{% + \afterassignment\pgfmath@parse@dimexpr@% + \expandafter\expandafter\expandafter\pgfmath@dimen\expandafter\pgfmath@token\pgfmath@token@next% +} +\def\pgfmath@parse@dimexpr@{% + \edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@dimen}}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +} + + +\def\pgfmath@parse@muexpr{% + \begingroup% + \afterassignment\pgfmath@parse@muexpr@% + \expandafter\expandafter\expandafter\muskip\expandafter\expandafter\expandafter0\expandafter\pgfmath@token\expandafter\pgfmath@token@next% +} +\def\pgfmath@parse@muexpr@{% + \expandafter\endgroup% + \expandafter\edef\expandafter\pgfmathresult\expandafter{\expandafter\pgfMATH@STRIPMU\the\muskip0}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +} + +{ +\catcode`\m=12 +\catcode`\u=12 +\gdef\pgfMATH@STRIPMU#1mu{#1} +} + + +\def\pgfmath@parse@numexpr{% + \afterassignment\pgfmath@parse@numexpr@% + \expandafter\expandafter\expandafter\pgfmath@count\expandafter\pgfmath@token\pgfmath@token@next% +} +\def\pgfmath@parse@numexpr@#1{% + \expandafter\def\expandafter\pgfmath@number\expandafter{\the\pgfmath@count}% + \def\pgfmath@token@next{#1}% + \expandafter\ifcat\pgfmath@token@next\relax% + \let\pgfmath@parse@next=\pgfmath@parse@number% + \else% + \let\pgfmathresult=\pgfmath@number% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@operator% + \fi% + \pgfmath@parse@next% +} + + +\def\pgfmath@parse@exponent{% + \afterassignment\pgfmath@parse@@exponent% + \pgfmath@count\pgfmath@token@next} +\def\pgfmath@parse@@exponent{% + \pgfmathscientific{\pgfmath@number}{\the\pgfmath@count}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \pgfmath@parse@@operator% +} + +\def\pgfmath@parse@base{% + \ifnum\pgfmath@base=2\relax% + \let\pgfmath@parse@next=\pgfmath@parse@binary% + \else% + \ifnum\pgfmath@base=16\relax% + \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal% + \else% + \pgfmath@error{Unexpected numerical base `\pgfmath@base'}{}% + \def\pgfmathresult{0}% + \let\pgfmath@parse@next=\pgfmath@parse@end% + \fi% + \fi% + \let\pgfmath@number=\pgfmath@empty% + \expandafter\pgfmath@parse@next\pgfmath@token@next% +} + +\def\pgfmath@parse@binary#1{% + \expandafter\ifx\csname pgfmath@token@binary@#1\endcsname\relax% + \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{2}{10}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \def\pgfmath@token@next{#1}% + \let\pgfmath@parse@next=\pgfmath@parse@operator% + \else% + \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}% + \let\pgfmath@parse@next=\pgfmath@parse@binary% + \fi% + \pgfmath@parse@next% +} + +\def\pgfmath@parse@hexadecimal#1{% + \expandafter\ifx\csname pgfmath@token@hexadecimal@#1\endcsname\relax% + \expandafter\pgfmathbasetobase\expandafter\pgfmathresult\expandafter{\pgfmath@number}{16}{10}% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \def\pgfmath@token@next{#1}% + \let\pgfmath@parse@next=\pgfmath@parse@operator% + \else% + \expandafter\def\expandafter\pgfmath@number\expandafter{\pgfmath@number#1}% + \let\pgfmath@parse@next=\pgfmath@parse@hexadecimal% + \fi% + \pgfmath@parse@next% +} + +\def\pgfmath@parse@function{\pgfmath@parse@ifbgroup{\pgfmath@parse@function}{\pgfmath@parse@@function}} +\def\pgfmath@parse@function@{\futurelet\pgfmath@token@let\pgfmath@parse@@function} +\def\pgfmath@parse@@function{% + \ifx\pgfmath@token@let\pgfmath@sptoken% + \let\pgfmath@token=\pgfmath@empty% + \let\pgfmath@parse@next=\pgfmath@parse@@@@function% + \else% + \let\pgfmath@parse@next=\pgfmath@parse@@@function% + \fi% + \pgfmath@parse@next} + +\def\pgfmath@parse@@@function#1{% + \expandafter\ifx\csname pgfmath@token@functional@\expandafter\string#1\endcsname\relax% + \expandafter\ifx\csname pgfmath@token@number@\expandafter\string#1\endcsname\relax% + \def\pgfmath@token{#1}% + \let\pgfmath@parse@next=\pgfmath@parse@@@@function% + \else% + \expandafter\def\expandafter\pgfmath@function\expandafter{\pgfmath@function#1}% + \let\pgfmath@parse@next=\pgfmath@parse@function@% + \fi% + \else% + \edef\pgfmath@function{\pgfmath@function#1}% + \let\pgfmath@parse@next=\pgfmath@parse@function@% + \fi% + \pgfmath@parse@next} + +\def\pgfmath@parse@@@@function{% + \expandafter\ifx\csname pgfmath@function@\pgfmath@function\endcsname\relax% + \pgfmath@error{Unknown function `\pgfmath@function'}{}% + \def\pgfmathresult{0}% + \let\pgfmath@parse@next=\pgfmath@parse@end% + \else% + \expandafter\ifnum\csname pgfmath@operation@\pgfmath@function @arity\endcsname=0\relax% + \csname pgfmath\pgfmath@function @\endcsname% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \let\pgfmath@parse@next=\pgfmath@parse@@operator% + \else% + \expandafter\pgfmath@stack@push@operation\expandafter{\pgfmath@function}% + \let\pgfmath@parse@next=\pgfmath@parse@@operand% + \fi% + \fi% + \expandafter\pgfmath@parse@next\pgfmath@token} + +\def\pgfmath@parse@operator{\pgfmath@parse@ifbgroup{\pgfmath@parse@operator}{\pgfmath@parse@operator@}}% +\def\pgfmath@parse@operator@#1{% + \let\pgfmath@token=\pgfmath@token@next% + \def\pgfmath@token@next{#1}% + \pgfmath@parse@@@operator} + +\def\pgfmath@parse@@operator{\pgfmath@parse@ifbgroup{\pgfmath@parse@@operator}{\pgfmath@parse@@operator@}}% +\def\pgfmath@parse@@operator@#1{% + \def\pgfmath@token{#1}% + \pgfmath@parse@ifbgroup{\pgfmath@parse@@operator@@}{\pgfmath@parse@@operator@@}}% +\def\pgfmath@parse@@operator@@#1{% + \def\pgfmath@token@next{#1}% + \pgfmath@parse@@@operator} + +\def\pgfmath@parse@@@operator{% + \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\expandafter\string\pgfmath@token@next\endcsname\relax% + \expandafter\ifx\csname pgfmath@operator@\pgfmath@token\endcsname\relax% + \pgfmath@error{Unknown operator `\pgfmath@token' or `\pgfmath@token\pgfmath@token@next'}{}% + \def\pgfmathresult{0}% + \let\pgfmath@parse@next=\pgfmath@parse@end% + \else% + \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}% + \ifx\pgfmath@token\pgfmath@text@@% + \let\pgfmath@parse@next=\pgfmath@parse@end% + \else% + \expandafter\ifx\csname pgfmath@operation@\pgfmath@token @postfix\endcsname\pgfmath@token% + \ifx\pgfmath@token@next\pgfmath@char@leftbracket% + \let\pgfmath@parse@next=\pgfmath@parse@operand% + \else% + \let\pgfmath@parse@next=\pgfmath@parse@operator% + \fi% + \else% + \let\pgfmath@parse@next=\pgfmath@parse@operand% + \fi% + \fi% + \fi% + \else% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgfmath@token\expandafter\expandafter\expandafter% + {\expandafter\pgfmath@token\pgfmath@token@next}% + \expandafter\pgfmath@operation@process\expandafter{\pgfmath@token}% + \let\pgfmath@parse@next=\pgfmath@parse@@operand% + \fi% + \pgfmath@parse@next% +} + + +\def\pgfmath@operation@process#1{% + \def\pgfmath@operator{#1}% + \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty% + \else% + \pgfmath@operation@@process% + \fi% + \expandafter\ifx\csname pgfmath@token@specials@#1\endcsname\relax% + \pgfmath@stack@push@operation{#1}% + \fi% +} + +\def\pgfmath@operation@@process{% + \ifx\pgfmath@stack@operation@top\pgfmath@stack@empty% + \let\pgfmath@parse@next=\relax% + \else% + \ifnum\csname pgfmath@operation@\pgfmath@operator @precedence\endcsname>% + \csname pgfmath@operation@\pgfmath@stack@operation@top @precedence\endcsname\relax% + \let\pgfmath@parse@next=\relax% + \else% + \let\pgfmath@stack@operation@last=\pgfmath@stack@operation@top% + \expandafter\ifx\csname pgfmath@operator@\pgfmath@stack@operation@top\endcsname\relax% + \pgfmath@function@@@process% + \else% + \pgfmath@operator@@@process% + \fi% + \expandafter\pgfmath@stack@push@operand\expandafter{\pgfmathresult}% + \expandafter\ifx\csname pgfmath@token@group@\pgfmath@stack@operation@last\pgfmath@operator\endcsname\relax% + \let\pgfmath@parse@next=\pgfmath@operation@@process% + \else% + \let\pgfmath@parse@next=\relax% + \fi% + \fi% + \fi% + \pgfmath@parse@next% +} + +\def\pgfmath@operator@@@process{% + \pgfmath@stack@pop@operation\pgfmath@@operator% + \pgfmath@stack@pop@operand\pgfmath@operand@a% + \ifcase\csname pgfmath@operation@\pgfmath@@operator @arity\endcsname\relax% + \or% + \pgfmath@operator@@@@process{\pgfmath@operand@a}% + \or% + \pgfmath@stack@pop@operand\pgfmath@operand@b% + \pgfmath@operator@@@@process{\pgfmath@operand@b}{\pgfmath@operand@a}% + \or% + \pgfmath@stack@pop@operand\pgfmath@operand@b% + \expandafter\pgfmath@operator@@@@process\expandafter% + {\expandafter\pgfmath@operand@b\expandafter}\pgfmath@operand@a% + \else% + \fi% +} + +\def\pgfmath@operator@@@@process{% + \csname pgfmath% + \csname pgfmath@operation@\pgfmath@@operator @name\endcsname% + @\endcsname} + +\def\pgfmath@function@@@process{% + \ifnum\csname pgfmath@operation@\pgfmath@stack@operation@top @arity\endcsname>0\relax% + \pgfmath@stack@pop@operation\pgfmath@@function% + \pgfmath@stack@pop@operand\pgfmath@@operand% + \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>1\relax% + \ifnum\csname pgfmath@operation@\pgfmath@@function @arity\endcsname>9\relax% + \csname pgfmath\pgfmath@@function @\endcsname{\pgfmath@@operand}% + \else% + \expandafter\pgfmath@function@@@@process\pgfmath@@operand% + \fi + \else% + \expandafter\pgfmath@function@@@@process\expandafter{\pgfmath@@operand}% + \fi% + \fi% +} + +\def\pgfmath@function@@@@process{\csname pgfmath\pgfmath@@function @\endcsname} + +\newtoks\pgfmath@stack@operand +\newtoks\pgfmath@stack@operation +\let\pgfmath@stack@empty=\pgfmath@empty + +\def\pgfmath@stack@push#1#2{% + \def\pgfmath@stack@top{#2}% + \expandafter\expandafter\expandafter#1% + \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter% + {\expandafter\pgfmath@stack@top\expandafter}\the#1}}% + +\def\pgfmath@stack@pop#1#2{\expandafter\pgfmath@stack@@pop\the#1\pgfmath@stack@stop{#1}{#2}} +\def\pgfmath@stack@@pop#1#2#3\pgfmath@stack@stop#4#5{\def#5{#1}#4={{#2}#3}\def\pgfmath@stack@top{#2}} + +\def\pgfmath@stack@push@operation#1{% + \pgfmath@stack@push\pgfmath@stack@operation{#1}% + \let\pgfmath@stack@operation@top=\pgfmath@stack@top} + +\def\pgfmath@stack@pop@operation#1{% + \pgfmath@stack@pop\pgfmath@stack@operation{#1}% + \let\pgfmath@stack@operation@top=\pgfmath@stack@top} + +\def\pgfmath@stack@push@operand#1{% + \pgfmath@stack@push\pgfmath@stack@operand{#1}% + \let\pgfmath@stack@operand@top=\pgfmath@stack@top} + +\def\pgfmath@stack@pop@operand#1{% + \pgfmath@stack@pop\pgfmath@stack@operand{#1}% + \let\pgfmath@stack@operand@top=\pgfmath@stack@top} + + +\def\pgfmathdeclareoperator#1#2#3#4#5{% + \ifx\pgfmath@operatorlist\pgfutil@empty + \edef\pgfmath@operatorlist{{\string#1}}% + \else + \edef\pgfmath@operatorlist{\pgfmath@operatorlist,{\string#1}}% + \fi + \pgfmath@namedef{pgfmath@operator@\string#1}{#1}% + \pgfmath@namedef{pgfmath@operation@\string#1@name}{#2}% + \pgfmath@namedef{pgfmath@operation@\string#1@arity}{#3}% + \pgfmath@namedef{pgfmath@operation@\string#1@#4}{#1}% + \pgfmath@namedef{pgfmath@operation@\string#1@precedence}{#5}% +} + +\def\pgfmath@operatorlist{} + +\pgfmathdeclareoperator{+}{add} {2}{infix}{500} +\pgfmathdeclareoperator{-}{subtract}{2}{infix}{500} +\pgfmathdeclareoperator{*}{multiply}{2}{infix}{700} +\pgfmathdeclareoperator{/}{divide} {2}{infix}{700} +\pgfmathdeclareoperator{^}{pow} {2}{infix}{900} + +\pgfmathdeclareoperator{<} {} {1}{prefix} {1} + +\pgfmathdeclareoperator{>} {greater} {2}{infix} {250} +\pgfmathdeclareoperator{<} {less} {2}{infix} {250} +\pgfmathdeclareoperator{==}{equal} {2}{infix} {250} +\pgfmathdeclareoperator{>=}{notless} {2}{infix} {250} +\pgfmathdeclareoperator{<=}{notgreater}{2}{infix} {250} +\pgfmathdeclareoperator{&&}{and} {2}{infix} {200} +\pgfmathdeclareoperator{||}{or} {2}{infix} {200} +\pgfmathdeclareoperator{!=}{notequal} {2}{infix} {250} +\pgfmathdeclareoperator{!} {not} {1}{prefix}{975} +\pgfmathdeclareoperator{?} {ifthenelse}{3}{infix} {100} +\pgfmathdeclareoperator{:} {@@collect} {2}{infix}{101} + +\pgfmathdeclareoperator{!}{factorial}{1}{postfix}{800}% +\pgfmathdeclareoperator{r}{deg} {1}{postfix}{600} + +\pgfmathdeclareoperator{,}{@collect} {2}{infix} {10} +\pgfmathdeclareoperator{[}{@startindex}{2}{prefix} {7} +\pgfmathdeclareoperator{]}{@endindex} {0}{postfix}{6} +\pgfmathdeclareoperator{(}{@startgroup}{1}{prefix} {5} +\pgfmathdeclareoperator{)}{@endgroup} {0}{postfix}{4} + +\pgfmathdeclareoperator{\pgfmath@bgroup}{@startarray}{1}{prefix} {3} +\pgfmathdeclareoperator{\pgfmath@egroup}{@endarray} {1}{postfix}{2}% + +\pgfmathdeclareoperator{"}{}{1}{prefix}{1} +\pgfmathdeclareoperator{@}{}{0}{postfix}{0} + + +\def\pgfmath@startgroup@#1{\pgfmath@protected@edef\pgfmathresult{#1}} +\def\pgfmath@endgroup@{}% + +\def\pgfmath@startindex@#1#2{% + \expandafter\pgfmatharray@#1{#2}% + \expandafter\pgfmath@bgroup@strip\expandafter{\pgfmathresult}% + \ifx\pgfmath@token@let\bgroup% + \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmathresult}}% + \fi} +\def\pgfmath@endindex@{}% + +\def\pgfmath@startarray@#1{\expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{#1}}} +\def\pgfmath@endarray@#1{\expandafter\def\expandafter\pgfmathresult\expandafter{#1}}% + + +\def\pgfmath@@collect@#1#2{% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgfmathresult\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter% + {\expandafter#1\expandafter}\expandafter{#2}}% +} +\def\pgfmath@collect@#1#2{% + \expandafter\def\expandafter\pgfmath@collect@original\expandafter{#1}% + \expandafter\pgfmath@bgroup@strip\expandafter{#1}% + \ifx\pgfmath@token@let\bgroup% + \ifx\pgfmath@collect@original\pgfmath@bgroup@stripped% + \expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}% + \else% + \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}% + \fi% + \else% + \expandafter\def\expandafter\pgfmathresult\expandafter{\expandafter{\pgfmath@bgroup@stripped}}% + \fi% + \expandafter\pgfmath@bgroup@strip\expandafter{#2}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgfmathresult\expandafter\expandafter\expandafter% + {\expandafter\pgfmathresult\expandafter{\pgfmath@bgroup@stripped}}% +} + +\def\pgfmath@bgroup@strip#1{% + \def\pgfmath@bgroup@strip@last{#1}% + \pgfmath@bgroup@@strip{#1}\pgfmath@\pgfmath@@\pgfmath@@@} + +\def\pgfmath@bgroup@strip@#1{% + \def\pgfmath@bgroup@strip@last{#1}% + \pgfmath@bgroup@@strip#1\pgfmath@\pgfmath@@\pgfmath@@@} + +\def\pgfmath@bgroup@pgfmath@{\pgfmath@} + +\def\pgfmath@bgroup@@strip{% + \futurelet\pgfmath@token@let\pgfmath@bgroup@@@strip} + +\def\pgfmath@bgroup@@@strip#1#2#3\pgfmath@@@{% + \ifx\pgfmath@token@let\bgroup + \def\pgfmath@bgroup@test{#2}% + \ifx\pgfmath@bgroup@test\pgfmath@bgroup@pgfmath@ + \def\pgfmath@next{\pgfmath@bgroup@strip@{#1}}% + \else + \let\pgfmath@bgroup@stripped=\pgfmath@bgroup@strip@last + \let\pgfmath@next=\relax + \fi + \else + \pgfmath@bgroup@@@@strip#1#2#3% + \let\pgfmath@next=\relax + \fi + \pgfmath@next} + +\def\pgfmath@bgroup@@@@strip#1\pgfmath@\pgfmath@@{% + \def\pgfmath@bgroup@stripped{#1}} + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathutil.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathutil.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..77d9e65d46cbdc0a0ed54d63bb92f9aecfe570fd --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/math/pgfmathutil.code.tex @@ -0,0 +1,209 @@ + + +\def\pgfmathincluded{} + +\def\pgfmath@grabv#1#2#3#4#5#6#7\pgfmath@grabv{#2#3#4#5\ifx#6!!\fi} +\def\pgfmath@ifskip@extract#1{\expandafter\pgfmath@grabv\meaning#1!!!!!!\pgfmath@grabv} +\def\pgfmath@iftoks@extract#1{\expandafter\pgfmath@grabv\meaning#1!!!!!!\pgfmath@grabv} + +\def\pgfmath@grabvi#1#2#3#4#5#6#7#8\pgfmath@grabvi{#2#3#4#5#6\ifx#7!!\fi} +\def\pgfmath@ifdimen@extract#1{\expandafter\pgfmath@grabvi\meaning#1!!!!!!\pgfmath@grabvi} +\def\pgfmath@ifcount@extract#1{\expandafter\pgfmath@grabvi\meaning#1!!!!!!\pgfmath@grabvi} + +\def\pgfmath@grabvii#1#2#3#4#5#6#7#8#9\pgfmath@grabvii{#2#3#4#5#6#7\ifx#8!!\fi} +\def\pgfmath@ifmuskip@extract#1{\expandafter\pgfmath@grabvii\meaning#1!!!!!!\pgfmath@grabvii} + +\def\pgfmath@ifregister@unguarded#1#2{% + \expandafter\ifx\csname\csname pgfmath@if#1@extract\endcsname{#2}\expandafter\endcsname\csname #1\endcsname + \expandafter\pgfutil@firstoftwo + \else + \expandafter\pgfutil@secondoftwo + \fi} + +\def\pgfmath@ifregister#1#2{% + \pgfutil@IfUndefined{pgfmath@if#1@extract}% + {\errmessage{Package PGF Math Error: Cannot test for #1 register}}% + {\pgfutil@IfUndefined{\csname pgfmath@if#1@extract\endcsname{#2}}% + {\pgfutil@secondoftwo}}% + {\pgfmath@ifregister@unguarded{#1}{#2}}} + +\def\pgfmath@ensureregister#1#2{% + \pgfmath@ifregister{#1}{#2}% + {}% + {\csname new#1\endcsname#2}% +} + +\pgfmath@ensureregister{dimen}{\pgf@x} +\pgfmath@ensureregister{dimen}{\pgf@xa} +\pgfmath@ensureregister{dimen}{\pgf@xb} +\pgfmath@ensureregister{dimen}{\pgf@xc} + +\pgfmath@ensureregister{dimen}{\pgf@y} +\pgfmath@ensureregister{dimen}{\pgf@ya} +\pgfmath@ensureregister{dimen}{\pgf@yb} +\pgfmath@ensureregister{dimen}{\pgf@yc} + +\pgfmath@ensureregister{dimen}{\pgfutil@tempdima} +\pgfmath@ensureregister{dimen}{\pgfutil@tempdimb} + +\pgfmath@ensureregister{count}{\c@pgf@counta} +\pgfmath@ensureregister{count}{\c@pgf@countb} +\pgfmath@ensureregister{count}{\c@pgf@countc} +\pgfmath@ensureregister{count}{\c@pgf@countd} + +\pgfmath@ensureregister{count}{\pgfutil@tempcnta} +\pgfmath@ensureregister{count}{\pgfutil@tempcntb} + +\let\pgfmath@x\pgf@x +\let\pgfmath@xa\pgf@xa +\let\pgfmath@xb\pgf@xb +\let\pgfmath@xc\pgf@xc + +\let\pgfmath@y\pgf@y +\let\pgfmath@ya\pgf@ya +\let\pgfmath@yb\pgf@yb +\let\pgfmath@yc\pgf@yc + +\let\pgfmath@tempdima\pgfutil@tempdima +\let\pgfmath@tempdimb\pgfutil@tempdimb + +\let\c@pgfmath@counta\c@pgf@counta +\let\c@pgfmath@countb\c@pgf@countb +\let\c@pgfmath@countc\c@pgf@countc +\let\c@pgfmath@countd\c@pgf@countd + +\let\pgfmath@tempcnta\pgfutil@tempcnta +\let\pgfmath@tempcntb\pgfutil@tempcntb + + +\ifx\pgfutil@ifnextchar\pgfmath@undefined% + \long\def\pgfmath@ifnextchar#1#2#3{% + \let\pgfmath@reserved@d#1% + \def\pgfmath@reserved@a{#2}% + \def\pgfmath@reserved@b{#3}% + \futurelet\pgfmath@let@token\pgfmath@ifnch} + \def\pgfmath@ifnch{% + \ifx\pgfmath@let@token\pgfmath@sptoken% + \let\pgfmath@reserved@c\pgfmath@xifnch% + \else% + \ifx\pgfmath@let@token\pgfmath@reserved@d% + \let\pgfmath@reserved@c\pgfmath@reserved@a% + \else% + \let\pgfmath@reserved@c\pgfmath@reserved@b% + \fi% + \fi% + \pgfmath@reserved@c} + {% + \def\:{\global\let\pgfmath@sptoken= } \: + \def\:{\pgfmath@xifnch} \expandafter\gdef\: {\futurelet\pgfmath@let@token\pgfmath@ifnch} + }% +\else% + \let\pgfmath@ifnextchar\pgfutil@ifnextchar% + {% + \def\:{\global\let\pgfmath@sptoken= } \: + }% +\fi% + +\ifx\pgfutil@ifundefined\pgfmath@undefined% + \long\def\pgfmath@ifundefined#1{% + \expandafter\ifx\csname#1\endcsname\relax% + \expandafter\pgfmath@firstoftwo% + \else% + \expandafter\pgfmath@secondoftwo% + \fi}% +\else% + \let\pgfmath@ifundefined\pgfutil@ifundefined% +\fi% + +\ifx\pgfutil@selectfont\pgfmath@undefined% + \ifx\selectfont\pgfmath@undefined% + \let\pgfmath@selectfont\rm% + \else% + \let\pgfmath@selectfont\selectfont% + \fi% +\else% + \let\pgfmath@selectfont\pgfutil@selectfont% +\fi% + +\newif\ifpgfmath@in@ +\def\pgfmath@in@#1#2{% + \def\pgfmath@in@@##1#1##2##3\pgfmath@in@@{% + \ifx\pgfmath@in@##2\pgfmath@in@false\else\pgfmath@in@true\fi}% + \pgfmath@in@@#2#1\pgfmath@in@\pgfmath@in@@} + + +\ifx\pgf@sys@tonumber\pgfmath@undefined% + {\catcode`\p=12\catcode`\t=12\gdef\Pgf@geT#1pt{#1}} + \def\pgfmath@tonumber#1{\expandafter\Pgf@geT\the#1} +\else% + \let\pgfmath@tonumber\pgf@sys@tonumber% +\fi% + + +\ifx\PackageWarning\pgfmath@undefined + \def\pgfmath@PackageWarning#1#2{\immediate\write-1{Package #1: Warning! #2.}}% +\else% + \let\pgfmath@PackageWarning\PackageWarning% +\fi% +\ifx\PackageError\pgfmath@undefined + \def\pgfmath@PackageError#1#2#3{\errmessage{Package #1 Error: #2.}}% +\else% + \let\pgfmath@PackageError\PackageError% +\fi% + +\def\pgfmath@error#1#2{% + \pgfmath@PackageError{PGF Math}{% + #1% + \pgfutil@ifundefined{pgfmath@expression}{}{ (in '\pgfmath@expression')}% + }{#2}% +} +\def\pgfmath@warning#1{% + \pgfmath@PackageWarning{PGF Math}{% + #1% + \pgfutil@ifundefined{pgfmath@expression}{}{ (in '\pgfmath@expression')}% + }% +} + +{\catcode`\p=12\catcode`\t=12\gdef\PgfmaTh@PT{pt}} +\edef\pgfmath@pt{\PgfmaTh@PT}% + +\def\pgfmath@empty{} + +\def\pgfmath@firstoftwo#1#2{#1} +\def\pgfmath@secondoftwo#1#2{#2} + +\def\pgfmath@gobbletilpgfmath@#1\pgfmath@{} +\def\pgfmath@gobbleone#1{}% + + +\def\pgfmath@namedef#1{\expandafter\def\csname#1\endcsname} +\def\pgfmath@nameedef#1{\expandafter\edef\csname#1\endcsname} + +\newif\ifpgfmathcontinueloop +\def\pgfmathloop#1\repeatpgfmathloop{% + \def\pgfmathcounter{1}% + \def\pgfmath@iterate{% + #1\relax% + {% + \c@pgfmath@counta\pgfmathcounter% + \advance\c@pgfmath@counta1\relax% + \xdef\pgfmathloop@temp{\the\c@pgfmath@counta}% + }% + \edef\pgfmathcounter{\pgfmathloop@temp}% + \expandafter\pgfmath@iterate\fi}% + \pgfmath@iterate\let\pgfmath@iterate\relax} +\let\repeatpgfmathloop\fi +\def\pgfmathbreakloop{\let\pgfmath@iterate\relax}% + +\def\pgfmath@returnone#1\endgroup{% + \pgfmath@x#1% + \edef\pgfmath@temp{\pgfmath@tonumber{\pgfmath@x}}% + \expandafter\endgroup\expandafter\def\expandafter\pgfmathresult\expandafter{\pgfmath@temp}% +} + +\let\pgfmathreturn=\pgfmath@returnone + +\def\pgfmath@smuggleone#1\endgroup{% + \expandafter\endgroup\expandafter\def\expandafter#1\expandafter{#1}} + +\let\pgfmathsmuggle=\pgfmath@smuggleone diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleanimations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleanimations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..be168566a348a2f20bedfa5867aed769d93c47eb --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleanimations.code.tex @@ -0,0 +1,808 @@ + +\ProvidesFileRCS{pgfmoduleanimations.code.tex} + + + +\input pgfsysanimations.code.tex + + + +\def\pgfanimateattribute#1#2{% + \pgfanimateattributecode{#1}{\pgfkeys{/pgf/animation/.cd,#2}}% +}% + + + +\def\pgfanimateattributecode#1#2{% + {% + \pgfkeys{/pgf/@animation attributes/.cd,#1}% + #2% + \csname pgf@animation@check@\pgf@animation@attribute\endcsname% + \pgfsysanimate{\pgf@animation@attribute}% + }% +}% + + + + +\def\pgfsnapshot#1{\pgfparsetime{#1}\expandafter\pgfsysanimsnapshot\expandafter{\pgftimeresult}}% +\def\pgfsnapshotafter#1{\pgfparsetime{#1}\expandafter\pgfsysanimsnapshotafter\expandafter{\pgftimeresult}}% + + + +\pgfkeys{/pgf/@animation attributes/.cd, + visible/.code=\pgf@animate@attr{visibility}{mapped}\def\pgf@anim@map@true{visible}\def\pgf@anim@map@false{hidden}, + stage/.code=\pgf@animate@attr{visibility}{mapped}\def\pgf@anim@map@true{visible}\def\pgf@anim@map@false{hidden}\pgfsysanimkeybase\pgfsysanimvaltext{hidden}, + opacity/.code=\pgf@animate@attr{opacity}{scalar}, + fill opacity/.code=\pgf@animate@attr{fillopacity}{scalar}, + draw opacity/.code=\pgf@animate@attr{strokeopacity}{scalar}, + stroke opacity/.style=draw opacity, + line width/.code=\pgf@animate@attr{linewidth}{dimension}, + fill/.code=\pgf@animate@attr{fillcolor}{color}, + draw/.code=\pgf@animate@attr{strokecolor}{color}, + color/.code=\pgf@animate@attr{color}{color}, + stroke/.style=draw, + motion/.code=\pgf@animate@attr{motion}{scalar}, + translate/.code=\pgf@animate@attr{translate}{point}, + scale/.code=\pgf@animate@attr{scale}{scaling}, + rotate/.code=\pgf@animate@attr{rotate}{scalar}, + xskew/.code=\pgf@animate@attr{skewx}{scalar}, + yskew/.code=\pgf@animate@attr{skewy}{scalar}, + skew x/.style=xskew, + skew y/.style=yskew, + path/.code=\pgf@animate@attr{path}{path}, + softpath/.code=\pgf@animate@attr{path}{softpath}, + view/.code=\pgf@animate@attr{viewbox}{viewbox}, + dash/.code=\pgf@animate@attr{dash}{dash}, + none/.code=\pgf@animate@attr{none}{none}, +}% + +\def\pgf@animate@attr#1#2{% + \def\pgf@animation@attribute{#1}% + \expandafter\let\expandafter\pgfanim@type@parser\csname pgfanim@parse@type@#2\endcsname% +}% + + + + +\def\pgfparsetime#1{% + \begingroup% + \pgfmathdeclareoperator{s}{@seconds}{1}{postfix}{600}% + \pgfmathdeclareoperator{m}{m@encountered}{1}{postfix}{600}% + \pgfmathdeclareoperator{i}{i@encountered}{1}{postfix}{600}% + \pgfmathdeclareoperator{n}{@minutes}{1}{postfix}{600}% + \pgfmathdeclareoperator{h}{@hours}{1}{postfix}{600}% + \pgfmathdeclareoperator{:}{time@colon}{2}{infix}{50}% + \pgfmath@octalparsingfalse% + \pgfmathparse{#1}% + \expandafter\endgroup% + \expandafter\def\expandafter\pgftimeresult\expandafter{\pgfmathresult}% +}% + +\newif\ifpgfanim@m@encountered +\newif\ifpgfanim@i@encountered +\pgfmathdeclarefunction{@seconds}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \ifpgfanim@m@encountered% + \divide\pgfmath@x by1000\relax% + \fi% + \global\pgfanim@m@encounteredfalse% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% +\pgfmathdeclarefunction{m@encountered}{1}{% + \global\pgfanim@m@encounteredtrue% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% +\pgfmathdeclarefunction{i@encountered}{1}{% + \ifpgfanim@m@encountered% + \global\pgfanim@m@encounteredfalse% + \global\pgfanim@i@encounteredtrue% + \else% + \pgfmath@error{Unexpected i}{}% + \fi% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% +\pgfmathdeclarefunction{@minutes}{1}{% + \ifpgfanim@i@encountered% + \global\pgfanim@i@encounteredfalse% + \else% + \pgfmath@error{Unexpected n}{}% + \fi% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@x60\pgfmath@x\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% +\pgfmathdeclarefunction{@hours}{1}{% + \begingroup% + \expandafter\pgfmath@x#1pt\relax% + \pgfmath@x3600\pgfmath@x\relax% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% +\pgfmathdeclarefunction{time@colon}{2}{% + \begingroup% + \pgfmath@x=#1pt\relax% + \pgfmath@x=60\pgfmath@x\relax% + \pgfmath@y=#2pt\relax% + \advance\pgfmath@x by\pgfmath@y% + \pgfmath@returnone\pgfmath@x% + \endgroup% +}% + + + + +\def\pgfanimationset{\pgfqkeys{/pgf/animation}}% + + + +\pgfanimationset{ + whom/.code={% + \pgf@anim@decomp{#1}% + \pgfidrefnextuse\pgf@anim@id\pgf@anim@id@name% + \expandafter\expandafter\expandafter\pgfsysanimkeywhom\expandafter\expandafter\expandafter{\expandafter\pgf@anim@id\expandafter}\expandafter{\pgf@anim@type}% + \let\pgf@anim@whom@id\pgf@anim@id% + \let\pgf@anim@whom@type\pgf@anim@type% + } +}% + +\def\pgf@anim@decomp#1{% + \edef\pgf@temp{#1}% + \expandafter\pgfutil@in@\expandafter.\expandafter{\pgf@temp}% + \ifpgfutil@in@% + \expandafter\pgf@anim@decomp@\pgf@temp\pgf@stop% + \else% + \expandafter\pgf@anim@decomp@\pgf@temp.\pgf@stop% + \fi% +}% +\def\pgf@anim@decomp@#1.#2\pgf@stop{% + \def\pgf@anim@id@name{#1}% + \def\pgf@anim@type{#2}% +}% + + + +\pgfanimationset{ + name/.code=\pgfuseid{#1}, +}% + + + + + +\pgfanimationset{ + restart/.is choice, + restart/.default=true, + restart/true/.code=\pgfsysanimkeyrestartalways, + restart/false/.code=\pgfsysanimkeyrestartnever, + restart/never/.code=\pgfsysanimkeyrestartnever, + restart/when not active/.code=\pgfsysanimkeyrestartwhennotactive, +}% + + + +\pgfanimationset{ + repeats/.code={% + \pgfutil@in@{accumulating\pgf@stop}{#1\pgf@stop}% + \ifpgfutil@in@% + \pgfsysanimkeyaccumulate% + \pgfanim@parse@acc#1\pgf@stop% + \else% + \pgfsysanimkeynoaccumulate% + \pgfanim@parse@noacc{#1}% + \fi% + }, + repeats/.default=, + repeat/.style={repeats={#1}}, + repeat/.default=, +}% +\def\pgfanim@parse@acc#1accumulating\pgf@stop{% + \pgfanim@parse@noacc{#1}% +}% +\def\pgfanim@parse@noacc#1{% + \pgfutil@in@{\pgf@stop for}{\pgf@stop#1}% + \ifpgfutil@in@% + \pgfanim@parse@for#1\pgf@stop% + \else% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty% + \pgfsysanimkeyrepeatindefinite% + \else% + \pgfmathparse{#1}% + \expandafter\pgfsysanimkeyrepeat\expandafter{\pgfmathresult}% + \fi% + \fi% +}% +\def\pgfanim@parse@for for#1\pgf@stop{\pgfparsetime{#1}\expandafter\pgfsysanimkeyrepeatdur\expandafter{\pgftimeresult}}% + + + + + + +\pgfanimationset{ + begin/.code=\pgfparsetime{#1}\expandafter\pgfsysanimkeyoffset\expandafter{\pgftimeresult}{begin}, + end/.code=\pgfparsetime{#1}\expandafter\pgfsysanimkeyoffset\expandafter{\pgftimeresult}{end}, +}% + + + + +\pgfanimationset{ + begin on/.code={\pgfanim@make@event{#1}{begin}},% + end on/.code={\pgfanim@make@event{#1}{end}}, +}% + +\def\pgfanim@make@event#1#2{% + \let\pgfanim@event@event\pgfutil@empty% + \let\pgf@anim@id\pgfutil@empty% + \let\pgf@anim@type\pgfutil@empty% + \let\pgfanim@event@key\pgfutil@empty% + \let\pgfanim@event@repeat\pgfutil@empty% + \let\pgfanim@event@delay\pgfutil@empty% + \pgfkeys{/pgf/animation/events/.cd,#1}% + \ifx\pgfanim@event@key\pgfutil@empty% + \ifx\pgfanim@event@repeat\pgfutil@empty% + \ifx\pgfanim@event@event\pgfutil@empty% + \pgferror{No event specified}% + \else% + \pgfsysanimkeyevent{\pgf@anim@id}{\pgf@anim@type}{\pgfanim@event@event}{\pgfanim@event@delay}{#2}% + \fi% + \else% + \pgfsysanimkeyrepeatevent{\pgf@anim@id}{\pgf@anim@type}{\pgfanim@event@repeat}{\pgfanim@event@delay}{#2}% + \fi% + \else% + \pgfsysanimkeyaccesskey{\pgfanim@event@key}{\pgfanim@event@delay}{#2}% + \fi% +}% + +\pgfkeys{/pgf/animation/events/.cd, + event/.store in=\pgfanim@event@event, + of/.code={% + \pgf@anim@decomp{#1}% + \pgfidrefprevuse\pgf@anim@id\pgf@anim@id@name% + \ifx\pgf@anim@id\pgfutil@empty% + \pgferror{Unknown object/node name '\pgf@anim@id@name'. Did you + mean 'of next=\pgf@anim@id@name'?}% + \fi% + }, + of next/.code={% + \pgf@anim@decomp{#1}% + \pgfidrefnextuse\pgf@anim@id\pgf@anim@id@name% + }, + of id/.code=\def\pgf@anim@id{#1}, + key/.store in=\pgfanim@event@key, + repeat/.code=\pgfmathparse{#1}\let\pgfanim@event@repeat\pgfmathresult, + delay/.code=\pgfparsetime{#1}\let\pgfanim@event@delay\pgftimeresult, + click/.style={event=click}, + focus in/.style={event=focusin}, + focus out/.style={event=focusout}, + mouse down/.style={event=mousedown}, + mouse up/.style={event=mouseup}, + mouse over/.style={event=mouseover}, + mouse move/.style={event=mousemove}, + mouse out/.style={event=mouseout}, + begin/.style={event=begin}, + end/.style={event=end}, +}% + + + +\pgfanimationset{ + begin snapshot/.code= + \pgfparsetime{#1}\expandafter\pgfsysanimkeysnapshotstart\expandafter{\pgftimeresult} +}% + + + +\pgfanimationset{ + origin/.code={% + \pgf@process{#1}% + \edef\pgf@marshal{% + \noexpand\pgfsysanimkeycanvastransform% + {\noexpand\pgftransformshift{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}{\noexpand\pgflowlevelsynccm}}% + {\noexpand\pgftransforminvert\noexpand\pgflowlevelsynccm}% + \noexpand\pgf@anim@save@transform{\noexpand\pgftransformshift{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + }% + \pgf@marshal% + }, +}% + +\pgfsysanimkeycanvastransform{{\pgflowlevelsynccm}}{\pgftransforminvert\pgflowlevelsynccm}% + + + + +\pgfanimationset{ + transform/.code={% + \pgfsysanimkeycanvastransform{#1{\pgflowlevelsynccm}}{\pgftransforminvert\pgflowlevelsynccm}% + \pgf@anim@save@transform{#1}% + }, +}% + + + + +\pgfanimationset{ + along/.code=% + {% + \pgfsyssoftpath@getcurrentpath\pgfanim@save@path% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + #1% + \pgfsyssoftpath@getcurrentpath\pgfanim@the@path% + \global\let\pgfanim@the@path\pgfanim@the@path% + \pgfsyssoftpath@setcurrentpath\pgfanim@save@path% + }% + \expandafter\pgf@anim@protocol@path@size\pgfanim@the@path\pgf@stop% + \expandafter\pgfsysanimkeymovealong\expandafter{\pgfanim@the@path}% +}% + + + +\pgfanimationset{ + along softpath/.code=% + \pgf@anim@protocol@path@size#1\pgf@stop% + \pgfsysanimkeymovealong{#1}% +}% + + +\def\pgf@anim@protocol@path@size{% + \pgfutil@ifnextchar\pgf@stop\pgfutil@gobble\pgf@anim@protocol@path@size@% +}% +\def\pgf@anim@protocol@path@size@#1#2#3{% + \pgf@protocolanimsizes@direct{#2}{#3}% + \pgf@anim@protocol@path@size% +}% + + + +\pgfanimationset{ + rotate along/.is choice, + rotate along/.default=true, + rotate along/true/.code=\pgfsysanimkeyrotatealong, + rotate along/false/.code=\pgfsysanimkeynorotatealong, +}% + + + + +\pgfanimationset{entry/.code 2 args=\pgf@anim@entry{#1}{#2}}% +\def\pgf@anim@entry#1#2{% + \pgf@anim@entry@giventrue% + \pgfparsetime{#1}% + \edef\pgf@marshal{\noexpand\pgfsysanimkeytime{\pgftimeresult}\pgf@anim@entry@spline\pgf@anim@exit@spline}% + \pgf@marshal% + \def\pgf@temp{#2}% + \ifx\pgf@temp\pgf@special@current@text% + \pgfsysanimvalcurrent% + \else% + \pgfanim@type@parser{#2}% + \fi% +}% +\def\pgf@special@current@text{current value}% +\newif\ifpgf@anim@entry@given + + + +\pgfanimationset{base/.code=\pgf@anim@base{#1}}% +\def\pgf@anim@base#1{% + \pgfsysanimkeybase% + \pgfanim@type@parser{#1}% +}% + + + +\pgfanimationset{ + freeze at end/.is choice, + freeze at end/.default=true, + freeze at end/true/.code=\pgfsysanimkeyfreezeatend, + freeze at end/false/.code=\pgfsysanimkeyremoveatend, +}% + + + + +\pgfanimationset{ + entry control/.code 2 args={% + \pgfmathsetmacro\pgf@temp@t{#1}% + \pgfmathsetmacro\pgf@temp@a{#2}% + \edef\pgf@anim@entry@spline{{\pgf@temp@t}{\pgf@temp@a}}% + }, + exit control/.code 2 args={% + \pgfmathsetmacro\pgf@temp@t{#1}% + \pgfmathsetmacro\pgf@temp@a{#2}% + \edef\pgf@anim@exit@spline{{\pgf@temp@t}{\pgf@temp@a}}% + }, + stay/.code=\let\pgf@anim@exit@spline\pgfsys@stay@text,% + jump/.code=\let\pgf@anim@entry@spline\pgfsys@jump@text,% + linear/.style={entry control={1}{1},exit control={0}{0}}, +}% +\def\pgf@anim@entry@spline@base{{1}{1}}% +\def\pgf@anim@exit@spline@base{{0}{0}}% + +\def\pgf@anim@reset@linear{\let\pgf@anim@entry@spline\pgf@anim@entry@spline@base\let\pgf@anim@exit@spline\pgf@anim@exit@spline@base}% +\pgf@anim@reset@linear + + + + +\pgfanimationset{ + shorten /.code={% + \ifpgf@anim@entry@given% + \pgferror{You must specify shorten < prior to the path entries}% + \else% + \pgfmathsetmacro\pgf@anim@marker@extra@shorten@end{#1}% + \edef\pgf@anim@marker@extra@shorten@end{\pgf@anim@marker@extra@shorten@end pt}% + \fi% + }, +}% +\def\pgf@anim@marker@extra@shorten@start{0pt}% +\def\pgf@anim@marker@extra@shorten@end{0pt}% +\def\pgf@anim@marker@shorten@start{0pt}% +\def\pgf@anim@marker@shorten@end{0pt}% + + +\pgfanimationset{ + arrows/.code={% + \ifpgf@anim@entry@given% + \pgferror{You must specify animation arrows prior to the path entries}% + \else% + \pgf@anim@parser@arrows#1\pgf@stop% + \fi% + }, +}% + +\def\pgf@anim@parser@arrows#1-#2\pgf@stop{% + \pgf@anim@prepare@arrow@start{#1}% + \pgf@anim@prepare@arrow@end{#2}% + \expandafter\expandafter\expandafter\pgfsysanimkeytipmarkers\expandafter\expandafter\expandafter{\expandafter\pgf@anim@marker@id@start\expandafter}\expandafter{\pgf@anim@marker@id@end}% +}% + +\def\pgf@anim@prepare@arrow@start#1{% + \def\pgf@anim@temp{#1}% + \ifx\pgf@anim@temp\pgfutil@empty% + \let\pgf@anim@marker@id@start\pgfutil@empty% + \def\pgf@anim@marker@shorten@start{0pt}% + \else% + {% + \pgfsetarrowsstart{#1}% + \pgf@anim@prep@marker@arrow\pgf@start@tip@sequence\pgf@anim@marker@id\pgf@anim@marker@shorten% + \global\let\pgf@anim@marker@id@start\pgf@anim@marker@id% + \global\let\pgf@anim@temp\pgf@anim@marker@shorten% + }% + \let\pgf@anim@marker@shorten@start\pgf@anim@temp% + \fi% +}% + +\def\pgf@anim@prepare@arrow@end#1{% + \def\pgf@anim@temp{#1}% + \ifx\pgf@anim@temp\pgfutil@empty% + \let\pgf@anim@marker@id@end\pgfutil@empty% + \def\pgf@anim@marker@shorten@end{0pt}% + \else% + {% + \pgfsetarrowsend{#1}% + \pgf@anim@prep@marker@arrow\pgf@end@tip@sequence\pgf@anim@marker@id\pgf@anim@marker@shorten% + \global\let\pgf@anim@marker@id@end\pgf@anim@marker@id% + }% + \let\pgf@anim@marker@shorten@end\pgf@anim@marker@shorten% + \fi% +}% + + + +\def\pgf@anim@prep@marker@arrow#1#2#3{% + {% + \let\pgf@arrow@handle\pgf@anim@marker@id@test% + \let\pgf@arrow@handle@dot\relax% + \global\let\pgf@anim@marker@id@list\pgfutil@empty% + #1% + }% + \expandafter\let\expandafter#2\csname pgfanim@marker@cache@\pgf@anim@marker@id@list\endcsname% + \expandafter\let\expandafter#3\csname pgfanim@marker@cachel@\pgf@anim@marker@id@list\endcsname% + \ifx#2\relax% + \pgf@relevantforpicturesizefalse% + \pgfinterruptpath% + \pgf@arrow@compute@shortening{#1}% + \xdef#3{\the\pgf@xa}% + {% + \let\pgf@arrow@handle\pgf@anim@drawer@marker + \let\pgf@arrow@handle@dot\relax% + \pgfsys@marker@declare#2{% + \pgftransformxshift{-\pgf@xb}% + \pgftransformxshift{\pgf@xa}% + #1% + }% + }% + \endpgfinterruptpath% + \expandafter\global\expandafter\let\csname pgfanim@marker@cache@\pgf@anim@marker@id@list\endcsname#2% + \expandafter\global\expandafter\let\csname pgfanim@marker@cachel@\pgf@anim@marker@id@list\endcsname#3% + \fi% +}% + +\def\pgf@anim@marker@id@test#1#2{% + \pgfarrows@getid{#1}{#2}% + \expandafter\expandafter\expandafter\pgf@arrow@drawer@shift\csname pgf@ar@ends@\pgf@arrow@id\endcsname% + \xdef\pgf@anim@marker@id@list{\pgf@anim@marker@id@list:\pgf@arrow@id\ifpgfarrowswap s\else n\fi\pgfarrows@slant w\the\pgf@xc}% +}% + +\def\pgf@anim@drawer@marker#1#2{% + {% + \pgfarrows@getid{#1}{#2}% + \expandafter\expandafter\expandafter\pgf@arrow@drawer@shift\csname pgf@ar@ends@\pgf@arrow@id\endcsname% + \ifdim\pgfarrows@slant pt=0pt% + \else% + \pgftransformxslant{\pgfarrows@slant}% + \fi% + \ifpgfarrowswap% + \pgftransformyscale{-1}% + \fi% + {% + \csname pgf@ar@saves@\pgf@arrow@id\endcsname% + \pgfsys@beginscope% + \pgf@arrows@color@setup% + \pgflowlevelsynccm\csname pgf@ar@cache@\pgf@arrow@id\endcsname% + \pgfsys@endscope% + }% + \expandafter}% + \expandafter\pgftransformxshift\expandafter{\the\pgf@xc}% +}% + + + + + + + + + + + +\def\pgfanim@parse@type@none#1{% + \pgfsysanimvalnone% +}% + + +\def\pgfanim@parse@type@scalar#1{% + \pgfmathparse{#1}% + \expandafter\pgfsysanimvalscalar\expandafter{\pgfmathresult}% +}% + + + +\def\pgfanim@parse@type@dimension#1{% + \pgfmathparse{#1}% + \expandafter\pgfsysanimvaldimension\expandafter{\pgfmathresult pt}% +}% + + + + +\def\pgfanim@parse@type@mapped#1{% + {% + \expandafter\let\expandafter\pgf@temp\csname pgf@anim@map@#1\endcsname\relax% + \ifx\pgf@temp\relax% + \pgferror{Value '#1' not allowed for an animation for this attribute}% + \let\pgf@temp\pgfutil@empty% + \fi% + \expandafter}% + \expandafter\pgfsysanimvaltext\expandafter{\pgf@temp}% +}% + + + +\def\pgfanim@parse@type@color#1{% + \pgfsysanimvalcolor{#1}% +}% + + + +\def\pgfanim@parse@type@path#1{% + {% + \pgfsyssoftpath@getcurrentpath\pgfanim@save@path% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% + #1% + \pgfsyssoftpath@getcurrentpath\pgfanim@the@path% + \pgfprocessround{\pgfanim@the@path}{\pgfanim@the@path}% + \global\let\pgfanim@the@path\pgfanim@the@path% + \pgfsyssoftpath@setcurrentpath\pgfanim@save@path% + }% + \expandafter\pgfanim@parse@type@softpath\expandafter{\pgfanim@the@path}% +}% + + + +\def\pgfanim@parse@type@softpath#1{% + {% + \def\pgf@anim@path{#1}% + \pgf@worryfalse% + \pgf@xb=\pgf@anim@marker@extra@shorten@start% + \advance\pgf@xb by\pgf@anim@marker@shorten@start% + \pgf@xc=\pgf@anim@marker@extra@shorten@end% + \advance\pgf@xc by\pgf@anim@marker@shorten@end% + \ifdim\pgf@xb=0pt\else\pgf@worrytrue\fi% + \ifdim\pgf@xc=0pt\else\pgf@worrytrue\fi% + \ifpgf@worry% + \edef\pgf@path@shortening@distance@end{\the\pgf@xc}% + \edef\pgf@path@shortening@distance@start{\the\pgf@xb}% + \pgf@anim@shorten@path% + \fi% + \expandafter}% + \expandafter\pgfsysanimvalpath\expandafter{\pgf@anim@path}% +}% + + +\def\pgf@anim@shorten@path{% + \pgf@precise@shorteningfalse% + \let\pgf@path@shortening@distance\pgf@path@shortening@distance@end% + \pgfprocesssplitpath{\pgf@anim@path}% + \pgfprocesssplitsubpath{\pgfprocessresultpathsuffix}% + \expandafter\pgf@parse@end\pgfprocessresultsubpathsuffix\pgf@stop\pgf@stop\pgf@stop% + \pgf@prep@end% + \ifdim\pgf@path@shortening@distance=0pt\else\pgf@do@shorten@end\fi% + \let\pgf@path@shortening@distance\pgf@path@shortening@distance@start% + \expandafter\pgf@parse@start\pgfprocessresultpathsuffix\pgf@stop\pgf@stop\pgf@stop% + \pgf@prep@start% + \ifdim\pgf@path@shortening@distance=0pt\else\pgf@do@shorten@start\fi% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@anim@path% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathprefix\pgfprocessresultpathsuffix}% +}% + + + + +\def\pgfanim@parse@type@point#1{% + \pgf@process{#1}% + \pgf@protocolanimsizes\pgf@x\pgf@y% + \expandafter\expandafter\expandafter\pgfsysanimvaltranslate\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgf@x\expandafter}\expandafter{\the\pgf@y}% +}% + + + +\def\pgfanim@parse@type@scaling#1{% + \pgfutil@in@{,}{#1}% + \ifpgfutil@in@% + \pgfanim@unpack@comma#1\pgf@stop% + \else% + \pgfmathparse{#1}% + \expandafter\pgfsysanimvalscale\expandafter{\pgfmathresult}{\pgfmathresult}% + \fi% +}% +\def\pgfanim@unpack@comma#1,#2\pgf@stop{% + \pgfmathsetmacro{\pgf@anim@temp@x}{#1}% + \pgfmathsetmacro{\pgf@anim@temp@y}{#2}% + \expandafter\expandafter\expandafter\pgfsysanimvalscale\expandafter\expandafter\expandafter{\expandafter\pgf@anim@temp@x\expandafter}\expandafter{\pgf@anim@temp@y}% +}% + + + + +\def\pgfanim@parse@type@viewbox#1{% + {% + \pgfanim@unpack@viewbox#1% + \xdef\pgf@anim@caller{\noexpand\pgfsysanimvalviewbox{\the\pgf@x}{\the\pgf@y}{\the\pgf@xa}{\the\pgf@ya}}% + }% + \pgf@anim@caller% +}% +\def\pgfanim@unpack@viewbox#1#2{% + \pgfpointtransformed{#2}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfpointtransformed{#1}% + \ifdim\pgf@xa<\pgf@x% + \pgf@xb=\pgf@x% + \pgf@x=\pgf@xa% + \pgf@xa=\pgf@xb% + \fi% + \ifdim\pgf@ya<\pgf@y% + \pgf@yb=\pgf@y% + \pgf@y=\pgf@ya% + \pgf@ya=\pgf@yb% + \fi% +}% + + + + + +\def\pgfanim@parse@type@dash#1{\pgfanim@parse@type@dash@#1}% +\def\pgfanim@parse@type@dash@#1#2{% + \def\pgf@temp{}% + \def\pgf@next{\pgf@strip}% + \pgf@strip#1{pgf@stop}% + \expandafter\pgfsysanimvaldash\expandafter{\pgf@temp}{#2}% +}% + + + + + + +\def\pgf@protocolanimsizes#1#2{% + \edef\pgf@temp{\noexpand\pgf@anim@handle@point{\the#1}{\the#2}}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@protocolanim@list\expandafter\expandafter\expandafter{\expandafter\pgf@protocolanim@list\pgf@temp}% +}% +\def\pgf@protocolanimsizes@direct#1#2{% + \expandafter\def\expandafter\pgf@protocolanim@list\expandafter{\pgf@protocolanim@list\pgf@anim@handle@point{#1}{#2}}% +}% +\let\pgf@protocolanim@list\pgfutil@empty + +\def\pgf@animation@check@translate{% + \ifx\pgf@protocolanim@list\pgfutil@empty% + \else% + \expandafter\expandafter\expandafter\pgf@animation@check@translate@\expandafter\expandafter\expandafter{\expandafter\pgf@protocolanim@list\expandafter}\expandafter{\pgf@anim@saved@transform}% + \fi% +}% +\let\pgf@animation@check@motion\pgf@animation@check@translate + +\def\pgf@animation@check@translate@#1#2{% + \pgfsys@attach@to@id\pgf@anim@whom@id\pgf@anim@whom@type{% + \pgf@size@hookedtrue% + {% + #2% + \pgf@pt@x0pt% + \pgf@pt@y0pt% + \pgf@picmaxx=-16000pt\relax% + \pgf@picminx=16000pt\relax% + \pgf@picmaxy=-16000pt\relax% + \pgf@picminy=16000pt\relax% + #1% + \edef\pgf@temp{{\the\pgf@picminx}{\the\pgf@picminy}{\the\pgf@picmaxx}{\the\pgf@picmaxy}}% + \expandafter% + }\expandafter% + \def\expandafter\pgf@temp\expandafter{\pgf@temp}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@path@size@hook\expandafter\expandafter\expandafter{% + \expandafter\pgf@path@size@hook\expandafter\pgf@anim@bb\pgf@temp}% + }{}% +}% +\def\pgf@anim@handle@point#1#2{% + \pgf@x#1\pgf@y#2% + \pgf@pos@transform\pgf@x\pgf@y% + \ifdim\pgf@x<\pgf@picminx\pgf@picminx\pgf@x\fi% + \ifdim\pgf@x>\pgf@picmaxx\pgf@picmaxx\pgf@x\fi% + \ifdim\pgf@y<\pgf@picminy\pgf@picminy\pgf@y\fi% + \ifdim\pgf@y>\pgf@picmaxy\pgf@picmaxy\pgf@y\fi% +}% + +\newdimen\pgf@anim@dim + +\def\pgf@anim@bb#1#2#3#4{% + \pgf@anim@dim\pgf@size@hook@x% + \advance\pgf@anim@dim by#1\relax% + \ifdim\pgf@anim@dim<\pgf@picminx\global\pgf@picminx\pgf@anim@dim\fi% + \pgf@anim@dim\pgf@size@hook@x% + \advance\pgf@anim@dim by#3\relax% + \ifdim\pgf@anim@dim>\pgf@picmaxx\global\pgf@picmaxx\pgf@anim@dim\fi% + \pgf@anim@dim\pgf@size@hook@y% + \advance\pgf@anim@dim by#2\relax% + \ifdim\pgf@anim@dim<\pgf@picminy\global\pgf@picminy\pgf@anim@dim\fi% + \pgf@anim@dim\pgf@size@hook@y% + \advance\pgf@anim@dim by#4\relax% + \ifdim\pgf@anim@dim>\pgf@picmaxy\global\pgf@picmaxy\pgf@anim@dim\fi% +}% + +\def\pgf@anim@save@transform#1{% + \def\pgf@anim@saved@transform{#1}% +}% +\let\pgf@anim@saved@transform\pgfutil@empty% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulebending.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulebending.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..2540b49ac11bb967e64051300f9d064dd9b2a4bc --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulebending.code.tex @@ -0,0 +1,305 @@ + +\ProvidesFileRCS{pgfmodulebending.code.tex} + + + +\usepgfmodule{nonlineartransformations}% +\usepgflibrary{curvilinear}% + + + +\pgfkeys{ + /pgf/arrow keys/flex/.code=\pgfarrowsaddtooptions{\pgf@arrows@the@rigidity#1pt\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@flex}, + /pgf/arrow keys/flex/.default=1, + /pgf/arrow keys/flex'/.code=\pgfarrowsaddtooptions{\pgf@arrows@the@rigidity#1pt\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@flex@prime}, + /pgf/arrow keys/flex'/.default=1, + /pgf/arrow + keys/bend/.code=\pgfarrowsaddtooptions{\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@bend}, +}% + + +\def\pgf@arrow@mode@is@flex{1}% +\def\pgf@arrow@mode@is@flex@prime{2}% +\def\pgf@arrow@mode@is@bend{3}% + +\newdimen\pgf@arrows@the@rigidity + + + +\def\pgf@prep@curveend{ + \pgftransformreset% + \pgfsetcurvilinearbeziercurve{\pgfpointlastonpath}{\pgfpointsecondlastonpath}{\pgfpointthirdlastonpath}{\pgfpointfourthlastonpath} +}% + + +\def\pgf@do@shorten@curvedend{% + \expandafter\expandafter\expandafter\pgf@do@shorten@curvedend@unpack\expandafter\pgfpointfourthlastonpath\pgfpointthirdlastonpath% +}% +\def\pgf@do@shorten@curvedend@unpack\pgfqpoint#1#2\pgfqpoint#3#4{% + \pgf@process{\pgfcurvilineardistancetotime{\pgf@path@shortening@distance}}% + \pgfpointcurveattime{\pgf@x}{\pgfpointlastonpath}{\pgfpointsecondlastonpath}{\pgfpointthirdlastonpath}{\pgfpointfourthlastonpath}% + \pgf@xb#3% + \pgf@yb#4% + \pgf@xb\pgf@time@t\pgf@xb% + \pgf@yb\pgf@time@t\pgf@yb% + \advance\pgf@xb by\pgf@time@s\pgf@xc% + \advance\pgf@yb by\pgf@time@s\pgf@yc% + \edef\pgfprocessresultsubpathsuffix{% + \expandafter\noexpand\pgfsubpathfourthlasttoken{#1}{#2}% + \noexpand\pgfsyssoftpath@curvetosupportatoken{\the\pgf@xb}{\the\pgf@yb}% + \noexpand\pgfsyssoftpath@curvetosupportbtoken{\the\pgf@xa}{\the\pgf@ya}% + \noexpand\pgfsyssoftpath@curvetotoken{\the\pgf@x}{\the\pgf@y}}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultsubpathprefix\pgfprocessresultsubpathsuffix}% +}% + + +\def\pgf@do@draw@curvedend{% + \pgf@do@draw@curved\pgf@end@tip@sequence% +}% + +\def\pgf@do@draw@curved#1{% + {% + \pgftransformreset% + \pgf@xb\pgf@arrow@tip@total@length% + \let\pgf@arrow@handle\pgf@draw@curved% + \let\pgf@arrow@handle@dot\relax% + #1% + }% +}% + +\def\pgf@draw@curved#1#2{% + {% + \pgfarrows@getid{#1}{#2}% + \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid@shift\csname pgf@ar@ends@\pgf@arrow@id\endcsname% + \expandafter\let\expandafter\pgf@arrow@bending@mode\csname pgf@ar@bending@mode@#1\endcsname% + \ifx\pgf@arrow@bending@mode\pgfutil@empty\let\pgf@arrow@flex@mode\pgf@arrow@mode@is@flex\fi% + {% + \csname pgf@ar@saves@\pgf@arrow@id\endcsname% + \ifcase\pgf@arrow@flex@mode\relax% + \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid\csname pgf@ar@visual@\pgf@arrow@id\endcsname% + \or% + \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid\csname pgf@ar@visual@\pgf@arrow@id\endcsname% + \or% + \expandafter\expandafter\expandafter\pgf@arrow@drawer@rigid\csname pgf@ar@ends@\pgf@arrow@id\endcsname% + \or% + \pgf@arrow@drawer@bend% + \fi% + }% + \expandafter}% + \expandafter\pgf@xb\the\pgf@xb% +}% +\def\pgf@falsetext{false}% + +\def\pgf@arrow@drawer@rigid@shift#1#2#3{% + \advance\pgf@xb by#2% + \pgf@xa\pgf@xb% + \pgf@x#1% + \advance\pgf@x by\pgfarrowsep% + \advance\pgf@xb by-\pgf@x% +}% + + +\def\pgf@arrow@drawer@bend{% + \pgftransformnonlinear{\pgf@arrow@bending@mode{\pgf@x}{\pgf@y}} + \pgftransformscale{-1}% + \pgftransformxshift{-\pgf@xa}% + \ifdim\pgfarrows@slant pt=0pt% + \else% + \pgftransformxslant{\pgfarrows@slant}% + \fi% + \ifpgfarrowswap% + \pgftransformyscale{-1}% + \fi% + {% + \pgf@relevantforpicturesizefalse% + \pgfscope% + \pgf@arrows@color@setup% + \csname pgf@ar@inst@code@\pgf@arrow@id\endcsname% + \endpgfscope% + }% + \pgf@arrows@bending@hull% +}% + +\def\pgf@arrow@drawer@rigid#1#2#3{% + \pgf@x#1% + \pgf@y#2% + \advance\pgf@y by-\pgf@x% + \pgf@y\pgf@sys@tonumber\pgf@arrows@the@rigidity\pgf@y% + \advance\pgf@y by\pgf@x% + \ifdim\pgf@x=\pgf@y% + \pgf@bending@do@tangent% + \else% + \pgf@bending@do@flex% + \fi% + \pgf@xc#1% + \pgf@xc-\pgf@xc% + \pgftransformxshift{+\pgf@xc}% + \ifdim\pgfarrows@slant pt=0pt% + \else% + \pgftransformxslant{\pgfarrows@slant}% + \fi% + \ifpgfarrowswap% + \pgftransformyscale{-1}% + \fi% + \pgfscope% + \pgf@arrows@color@setup% + \pgflowlevelsynccm\csname pgf@ar@cache@\pgf@arrow@id\endcsname% + \endpgfscope% + \pgf@arrows@rigid@hull% +}% + +\def\pgf@bending@do@tangent{% + \pgf@xb\pgf@xa% + \advance\pgf@xb by-\pgf@x% + \pgfcurvilineardistancetotime{\pgf@xb}% + \pgf@xb\pgf@x% + \ifdim\pgf@xb=0pt% + \pgf@bending@possible@degenerate% + \else% + \pgf@bending@do@tangent@normal% + \fi% + \pgf@ya-\pgf@y% + \pgfsettransformentries% + {\pgf@sys@tonumber\pgf@x}{\pgf@sys@tonumber\pgf@y}% + {\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@x}{\pgf@xc}{\pgf@yc}% +}% + +\def\pgf@bending@do@tangent@normal{% + \pgfpointcurveattime{\pgf@xb}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}% + \pgf@xc\pgf@x% + \pgf@yc\pgf@y% + \advance\pgf@xb by-\pgf@xa% + \advance\pgf@yb by-\pgf@ya% + \pgf@process{\pgfpointnormalised{\pgf@x=\pgf@xb\pgf@y=\pgf@yb}} +}% + +\def\pgf@bending@possible@degenerate{% + \ifx\pgf@curvilinear@line@a\pgf@curvilinear@line@b% + \ifx\pgf@curvilinear@line@a\pgf@curvilinear@line@c% + \let\pgf@ref\pgf@curvilinear@line@d% + \else + \let\pgf@ref\pgf@curvilinear@line@c% + \fi% + \pgf@process{\pgf@curvilinear@line@a}% + \pgf@xc\pgf@x% + \pgf@yc\pgf@y% + \pgf@process{\pgf@ref}% + \advance\pgf@x by-\pgf@xc + \advance\pgf@y by-\pgf@yc + \pgf@process{\pgfpointnormalised{}} + \pgf@x-\pgf@x + \pgf@y-\pgf@y + \else% + \pgf@bending@do@tangent@normal% + \fi% +}% + +\def\pgf@bending@do@flex{ + \pgf@xb\pgf@xa% + \pgf@xc\pgf@xa% + \advance\pgf@xc by-\pgf@x% + \advance\pgf@xb by-\pgf@y% + \pgfcurvilineardistancetotime{\pgf@xc}% + \pgf@xc\pgf@x% + \pgfcurvilineardistancetotime{\pgf@xb}% + \pgf@xb\pgf@x% + \pgf@process{\pgfpointcurveattime{\pgf@xc}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}}% + \pgf@xc\pgf@x\pgf@yc\pgf@y% + \pgf@process{\pgfpointcurveattime{\pgf@xb}{\pgf@curvilinear@line@a}{\pgf@curvilinear@line@b}{\pgf@curvilinear@line@c}{\pgf@curvilinear@line@d}}% + \pgf@xb\pgf@x\pgf@yb\pgf@y% + \pgftransformarrow{\pgfqpoint{\pgf@xb}{\pgf@yb}}{\pgfqpoint{\pgf@xc}{\pgf@yc}}% +}% + + + + + + + +\def\pgf@arrows@bending@hull{% + \ifpgf@relevantforpicturesize% + \expandafter\let\expandafter\pgf@temp\csname pgf@ar@hull@\pgf@arrow@id\endcsname% + \ifx\pgf@temp\pgfutil@empty\else% + \let\pgf@arrow@hull@point\pgf@arrow@bending@hull@point@first% + \pgf@temp% + \pgf@arrow@bending@update@bb% + \fi% + \fi% +}% + +\def\pgf@arrow@bending@hull@point@first#1#2{% + \pgfpointtransformednonlinear{\pgfqpoint{#1}{#2}}% + \pgf@xa\pgf@x\pgf@xb\pgf@x% + \pgf@ya\pgf@y\pgf@yb\pgf@y% + \let\pgf@arrow@hull@point\pgf@arrow@bending@hull@point@other% +}% +\def\pgf@arrow@bending@hull@point@other#1#2{% + \pgfpointtransformednonlinear{\pgfqpoint{#1}{#2}}% + \ifdim\pgf@x<\pgf@xa\pgf@xa\pgf@x\else\ifdim\pgf@x>\pgf@xb\pgf@xb\pgf@x\fi\fi% + \ifdim\pgf@y<\pgf@ya\pgf@ya\pgf@y\else\ifdim\pgf@y>\pgf@yb\pgf@yb\pgf@y\fi\fi% +}% + +\def\pgf@arrow@bending@update@bb{% + \ifdim\pgf@picmaxx=-16000pt\relax% + \global\pgf@picminx\pgf@xa% + \global\pgf@picmaxx\pgf@xb% + \global\pgf@picminy\pgf@ya% + \global\pgf@picmaxy\pgf@yb% + \else% + \ifdim\pgf@xa<\pgf@picminx\global\pgf@picminx\pgf@xa\fi% + \ifdim\pgf@ya<\pgf@picminy\global\pgf@picminy\pgf@ya\fi% + \ifdim\pgf@xb>\pgf@picmaxx\global\pgf@picmaxx\pgf@xb\fi% + \ifdim\pgf@yb>\pgf@picmaxy\global\pgf@picmaxy\pgf@yb\fi% + \fi% +}% + + + + + + + +\def\pgf@prep@curvedstart{ + \pgftransformreset% + \pgfsetcurvilinearbeziercurve{\pgfpointfirstonpath}{\pgfpointsecondonpath}{\pgfpointthirdonpath}{\pgfpointfourthonpath}% +}% + + +\def\pgf@do@shorten@curvedstart{% + \expandafter\expandafter\expandafter\pgf@do@shorten@curvedstart@unpack\expandafter\pgfpointthirdonpath\pgfpointfourthonpath% +}% +\def\pgf@do@shorten@curvedstart@unpack\pgfqpoint#1#2\pgfqpoint#3#4{% + \pgf@process{\pgfcurvilineardistancetotime{\pgf@path@shortening@distance}}% + \pgfpointcurveattime{\pgf@x}{\pgfpointfirstonpath}{\pgfpointsecondonpath}{\pgfpointthirdonpath}{\pgfpointfourthonpath}% + \pgf@xb#1% + \pgf@yb#2% + \pgf@xb\pgf@time@t\pgf@xb% + \pgf@yb\pgf@time@t\pgf@yb% + \advance\pgf@xb by\pgf@time@s\pgf@xc% + \advance\pgf@yb by\pgf@time@s\pgf@yc% + \edef\pgfpointfirstonpath{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \edef\pgfpointsecondonpath{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \edef\pgfprocessresultpathsuffix{% + \noexpand\pgfsyssoftpath@movetotoken{\the\pgf@x}{\the\pgf@y}% + \noexpand\pgfsyssoftpath@curvetosupportatoken{\the\pgf@xa}{\the\pgf@ya}% + \noexpand\pgfsyssoftpath@curvetosupportbtoken{\the\pgf@xb}{\the\pgf@yb}% + \noexpand\pgfsyssoftpath@curvetotoken{#3}{#4}% + } + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgfprocessresultpathsuffix% + \expandafter\expandafter\expandafter{\expandafter\pgfprocessresultpathsuffix\pgfsubpathend}% +}% + + + +\def\pgf@do@draw@curvedstart{% + \pgf@do@draw@curved\pgf@start@tip@sequence% +}% + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduledatavisualization.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduledatavisualization.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..b6f8594daa780323b7c0aa0713091645d5ba979d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduledatavisualization.code.tex @@ -0,0 +1,1909 @@ + +\ProvidesFileRCS{pgfmoduledatavisualization.code.tex} + +\usepgfmodule{oo,shapes}% +\usepgflibrary{fpu}% + + + + +\pgfooclass{data visualization} +{% + + + \attribute before survey;% + \attribute at start survey;% + \attribute at end survey;% + \attribute after survey;% + \attribute before visualization;% + \attribute at start visualization;% + \attribute at end visualization;% + \attribute after visualization;% + + + \attribute survey count=1;% + + \attribute number of surveys=1;% + + + \attribute data;% + + + \attribute prepare datapoint signal;% + \attribute map datapoint signal;% + \attribute transform datapoint signal;% + \attribute visualize datapoint signal;% + \attribute finish datapoint signal;% + \attribute survey datapoint signal;% + \attribute phase signal;% + \attribute path signal;% + \attribute direction signal;% + \attribute style signal;% + + + \method data visualization() { + \pgfoonew{prepare datapoint signal}=new signal()% + \pgfoonew{map datapoint signal}=new signal()% + \pgfoonew{transform datapoint signal}=new signal()% + \pgfoonew{visualize datapoint signal}=new signal()% + \pgfoonew{finish datapoint signal}=new signal()% + \pgfoonew{survey datapoint signal}=new signal()% + \pgfoonew{phase signal}=new signal()% + \pgfoonew{path signal}=new signal()% + \pgfoonew{direction signal}=new signal()% + \pgfoonew{style signal}=new signal()% + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeyslet{/pgf/data visualization/obj}\pgf@dv@me + }% + + \def\pgfdvbeforesurvey{1}% + \def\pgfdvbeginsurvey{2}% + \def\pgfdvendsurvey{3}% + \def\pgfdvaftersurvey{4}% + \def\pgfdvbeforevisualization{5}% + \def\pgfdvbeginvisualization{6}% + \def\pgfdvendvisualization{7}% + \def\pgfdvaftervisualization{8}% + + \def\pgfdvpathmovetotoken{5}% + \def\pgfdvpathlinetotoken{6}% + \def\pgfdvdirectionfromtoken{7}% + \def\pgfdvdirectiontotoken{8}% + \def\pgfdvdirectionattoken{9}% + + \method connect(#1,#2,#3) { + \pgfoovalueof{#3}.connect(#1,#2) + }% + + \method add data(#1) { + \pgf@dv@stripped@add#1\pgf@stop + }% + \def\pgf@dv@stripped@add#1\pgf@stop{% + \pgfooappend{data}{#1}% + }% + + + \method before survey(#1) { + \pgfooappend{before survey}{#1} + }% + \method at start survey(#1) { + \pgfooappend{at start survey}{#1} + }% + \method before visualization(#1) { + \pgfooappend{before visualization}{#1} + }% + \method at start visualization(#1) { + \pgfooappend{at start visualization}{#1} + }% + + \method at end survey(#1) { + \pgfooprefix{at end survey}{#1} + }% + \method after survey(#1) { + \pgfooprefix{after survey}{#1} + }% + \method at end visualization(#1) { + \pgfooprefix{at end visualization}{#1} + }% + \method after visualization(#1) { + \pgfooprefix{after visualization}{#1} + }% + + + \method prepare signal macros() { + \pgfooget{prepare datapoint signal}\pgf@signalpreparedatapoint + \pgfooget{map datapoint signal}\pgf@signalmapdatapoint + \pgfooget{transform datapoint signal}\pgf@signaltransformdatapoint + \pgfooget{visualize datapoint signal}\pgf@signalvisualizedatapoint + \pgfooget{finish datapoint signal}\pgf@signalfinishdatapoint + \pgfooget{survey datapoint signal}\pgf@signalsurveydatapoint + \pgfooget{phase signal}\pgf@signalphase + \pgfooget{path signal}\pgf@signalpath + \pgfooget{direction signal}\pgf@signaldirection + \pgfooget{style signal}\pgf@signalstyle + }% + + + \method survey() { + \let\pgfdatapoint=\pgfdatapoint@surveyphase% + \pgfoothis.prepare signal macros() + \pgfooset{survey count}{1} + \pgfutil@loop + \pgf@signalphase.emit(\pgfdvbeforesurvey) + \pgfoovalueof{before survey}% + \pgf@signalphase.emit(\pgfdvbeginsurvey) + \pgfoovalueof{at start survey} + \pgfoovalueof{data}% + \pgfoovalueof{at end survey} + \pgf@signalphase.emit(\pgfdvendsurvey)% + \pgfoovalueof{after survey} + \pgf@signalphase.emit(\pgfdvaftersurvey) + \c@pgf@counta=\pgfoovalueof{survey count}\relax + \c@pgf@countb=\pgfoovalueof{number of surveys}\relax + \ifnum\c@pgf@counta<\c@pgf@countb + \advance\c@pgf@counta by1\relax + \pgfooeset{survey count}{\the\c@pgf@counta} + \pgfutil@repeat + }% + + \method get survey count(#1) { + \pgfooget{survey count}{#1} + }% + + \method do an additional survey() { + \c@pgf@counta=\pgfoovalueof{number of surveys}\relax + \advance\c@pgf@counta by1\relax + \pgfooeset{number of surveys}{\the\c@pgf@counta} + }% + + \method visualize() { + \let\pgfdatapoint=\pgfdatapoint@visualizationphase% + \pgfoothis.prepare signal macros() + \pgf@signalphase.emit(\pgfdvbeforevisualization)% + \pgfoovalueof{before visualization} + \pgf@signalphase.emit(\pgfdvbeginvisualization)% + \pgfoovalueof{at start visualization} + \pgfoovalueof{data}% + \pgfoovalueof{at end visualization} + \pgf@signalphase.emit(\pgfdvendvisualization)% + \pgfoovalueof{after visualization} + \pgf@signalphase.emit(\pgfdvaftervisualization)% + }% +}% + + +\pgfkeys{/data point/.unknown/.code={% + \pgfkeyssetvalue{/data point/\pgfkeyscurrentname}{#1} + }, +}% + + + + + +\def\pgfdatapoint@surveyphase{% + \pgf@signalpreparedatapoint.emit()% + \pgf@signalmapdatapoint.emit()% + \pgf@signalsurveydatapoint.emit()% +}% + +\def\pgfdatapoint@visualizationphase{% + \pgf@signalpreparedatapoint.emit()% + \pgfdvmapdatapointtocanvas% + \pgfkeysifdefined{/data point/name} + {% + \pgfcoordinate{\pgfkeysvalueof{/data point/name}}{\pgfpointdvdatapoint}% + }{}% + \pgf@signalvisualizedatapoint.emit()% + \pgf@signalfinishdatapoint.emit()% +}% + + + + +\def\pgfdvmapdatapointtocanvas{% + {% + \pgfpointdvlocaldatapoint + \expandafter% + }% + \edef\pgf@marshal{% + \noexpand\pgfkeyssetvalue{/data point/canvas x}{\the\pgf@x} + \noexpand\pgfkeyssetvalue{/data point/canvas y}{\the\pgf@y} + }% + \pgf@marshal% +}% + + +\def\pgfpointdvdatapoint{% + \pgfqpoint{\pgfkeysvalueof{/data point/canvas x}}{\pgfkeysvalueof{/data point/canvas y}}% +}% + +\def\pgfpointdvlocaldatapoint{% + {% + \pgf@signalmapdatapoint.emit()% + \pgftransformreset% + \pgf@signaltransformdatapoint.emit()% + \pgfpointtransformed{\pgfpointorigin}% + }% +}% + + + + +\newif\ifpgfdvhandled + +\def\pgfdv@generic#1#2#3{% + {% + \pgfdvhandledfalse% + \pgf@signalmapdatapoint.emit()% + #1.emit(#2)% + \ifpgfdvhandled% + \else% + \pgf@process{% + \pgftransformreset% + \pgf@signaltransformdatapoint.emit()% + \pgfpointtransformed{\pgfpointorigin}% + }% + #3{}% + \fi% + }% +}% + + +\def\pgfpathdvmoveto{% + \pgfdv@generic{\pgf@signalpath}{\pgfdvpathmovetotoken}{\pgfpathmoveto} +}% + + +\def\pgfpathdvlineto{% + \pgfdv@generic{\pgf@signalpath}{\pgfdvpathlinetotoken}{\pgfpathlineto} +}% + + + + +\def\pgfpointdvdirection#1#2{% + { + { + #1 + \pgfdv@generic{\pgf@signaldirection}{\pgfdvdirectionfromtoken}{\xdef\pgf@dv@from{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}} + } + { + #2 + \pgfdv@generic{\pgf@signaldirection}{\pgfdvdirectiontotoken}{\xdef\pgf@dv@to{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}} + } + {\pgfdv@generic{\pgf@signaldirection}{\pgfdvdirectionattoken}{% + \pgf@process{ + \pgfpointnormalised{% + \pgfpointdiff{\pgf@dv@from}{\pgf@dv@to} + } + }}} + } +}% + + + + + + + + + +\def\pgfdata{\pgfutil@ifnextchar[{\pgf@datagroup@data@opt}{\pgf@datagroup@data@opt[]}}% +\def\pgf@datagroup@data@opt[#1]{% + \begingroup% + \pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}% + \pgfkeysgetvalue{/pgf/data/continue code}\pgf@dv@cont@code% + \global\let\pgf@dv@cont@code\pgf@dv@cont@code% + \pgfkeysgetvalue{/pgf/data/use group}\pgf@dv@use@group% + \ifx\pgf@dv@use@group\pgfutil@empty% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data(\pgf@do@data{#1})}% + \expandafter\pgf@datagroup@data@opt@cont% + \else% + \expandafter\ifx\csname pgf@dv@group@@\pgf@dv@use@group\endcsname\relax% + \pgferror{Undefined data group '\pgf@dv@use@group'}% + \else% + {% + \pgfkeys{/pgf/data/define group/.code=}% + \csname pgf@dv@group@@\pgf@dv@use@group\endcsname% + }% + \fi% + \endgroup% + \expandafter\pgf@dv@cont@code% + \fi% +}% +\def\pgf@datagroup@data@opt@cont{% + \pgfkeysgetvalue{/pgf/data/format}\pgf@dv@format% + \expandafter\let\expandafter\pgf@dv@format@catcodes\csname pgfdv@format@\pgf@dv@format @catcodes\endcsname% + \ifx\pgf@dv@format@catcodes\relax + \pgferror{Unknown data format '\pgf@dv@format'}% + \else% + \pgfkeysgetvalue{/pgf/data/read from file}\pgf@dv@source% + \ifx\pgf@dv@source\pgfutil@empty% + \let\pgf@next\pgf@datagroup@grab@inline% + \else% + \let\pgf@next\pgf@datagroup@grab@external% + \fi% + \pgf@next% +}% + +\def\pgf@datagroup@grab@inline{% + \pgfutil@ifnextchar\bgroup{% + \begingroup% + \catcode`\^^M=\active% + \pgf@dv@format@catcodes% + \pgf@datagroup@grab@@inline}% + {\pgferror{Opening brace expected}}% +}% +\def\pgf@datagroup@grab@external{% + \fi% + \endgroup% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{{\pgf@datagroup@do@external}}})}% + \pgf@dv@cont@code% +}% + +\def\pgf@dv@do@adddata#1{% + \pgfkeysgetvalue{/pgf/data/store in group}\pgf@dv@temp% + \ifx\pgf@dv@temp\pgfutil@empty% + #1% + \else% + \expandafter\pgfutil@g@addto@macro\csname pgf@dv@group@@\pgf@dv@temp\endcsname{#1}% + \fi% +}% + +{\catcode`\^=7 \catcode`\^^M=13 + \gdef\pgf@datagroup@grab@@inline#1{% + \endgroup% + \pgf@dv@do@adddata{\pgfkeysvalueof{/pgf/data visualization/obj}.add data({{{\pgf@datagroup@do@inline#1^^M\pgf@@eol}}})}% + \fi% + \endgroup% + \pgf@dv@cont@code% + }% +}% +\def\pgf@@eol{\pgf@eol}% + +\def\pgf@do@data#1#2{% + \begingroup% + \pgfkeys{/pgf/data/.cd,/pgf/every data/.try,#1}% + \pgfkeysgetvalue{/pgf/data/format}\pgf@dv@format% + \expandafter\let\expandafter\pgf@dv@format@line\csname pgfdv@format@\pgf@dv@format @line\endcsname% + \expandafter\let\expandafter\pgf@dv@format@emptyline\csname pgfdv@format@\pgf@dv@format @empty\endcsname% + \csname pgfdv@format@\pgfkeysvalueof{/pgf/data/format}@startup\endcsname% + #2% + \csname pgfdv@format@\pgfkeysvalueof{/pgf/data/format}@end\endcsname% + \endgroup% +}% + + + +\def\pgf@datagroup@do@external{% + \csname pgfdv@format@\pgfkeysvalueof{/pgf/data/format}@catcodes\endcsname% + \immediate\openin\r@pgf@reada=\pgfkeysvalueof{/pgf/data/read from file} % + \ifeof\r@pgf@reada\relax + \pgferror{Data file '\pgfkeysvalueof{/pgf/data/read from file}' not found}% + \else + \pgf@datagroup@readline% + \fi + \immediate\closein\r@pgf@reada% +}% + +\def\pgf@partext{\par}% +\def\pgf@datagroup@readline{% + \endlinechar=-1 % + \immediate\read\r@pgf@reada to \pgf@temp% + \ifx\pgf@temp\pgf@partext% + \pgf@dv@format@emptyline% + \else% + \ifx\pgf@temp\pgfutil@empty% + \pgf@dv@format@emptyline% + \else% + \expandafter\pgf@dv@format@line\pgf@temp\pgfeol% + \fi% + \fi% + \ifeof\r@pgf@reada\else\expandafter\pgf@datagroup@readline\fi% +}% + + + +\def\pgf@datagroup@do@inline{% + \pgf@dv@handle@line% +}% + +{\catcode`\^=7 \catcode`\^^M=13 +\gdef\pgf@dv@handle@line{% + \pgfutil@ifnextchar^^M{\pgf@dv@format@emptyline\expandafter\pgf@dv@handle@line\pgfutil@gobble}% + {\pgfutil@ifnextchar\pgf@@eol{\pgfutil@gobble}{\pgf@dv@handle@nonemptyline}}% +}% +\gdef\pgf@dv@handle@nonemptyline#1^^M{% + \pgf@dv@format@line#1\pgfeol% + \pgf@dv@handle@line% +}% +}% + +\pgfkeys{ + /pgf/data/data visualization obj/.initial=\undefined, + /pgf/data/format/.initial=table,% + /pgf/data/read from file/.initial=, + /pgf/data/inline/.style={read from file=}, + /pgf/data/continue code/.initial=, + /pgf/data/store in group/.initial=, + /pgf/data/new group/.code={\expandafter\global\expandafter\let\csname pgf@dv@group@@#1\endcsname\pgfutil@empty}, + /pgf/data/use group/.initial=, +}% + + + + + + + +\def\pgfdeclaredataformat#1#2#3#4#5#6#7{% + \expandafter\def\csname pgfdv@format@#1@catcodes\endcsname{#2}% + \expandafter\def\csname pgfdv@format@#1@startup\endcsname{#3}% + \expandafter\def\csname pgfdv@format@#1@line\endcsname#4\pgfeol{#5}% + \expandafter\def\csname pgfdv@format@#1@empty\endcsname{#6}% + \expandafter\def\csname pgfdv@format@#1@end\endcsname{#7}% +}% + + + + + +\pgfdeclaredataformat{TeX code}{}{}{#1}{#1 }{}{}% + + + + +\pgfdeclaredataformat{named}{}{}{#1}{\pgf@dv@parse@named#1,\pgf@stop}{}{}% +\def\pgf@dv@parse@named{% + \pgfutil@ifnextchar\pgf@stop{\pgfdatapoint\pgfutil@gobble}{\pgf@dv@parse@named@} +}% +\def\pgf@dv@parse@named@#1=#2,#3\pgf@stop{% + \foreach \pgf@dv@temp in {#2} {% + \def\pgf@dv@tempb{/data point/#1=}% + \expandafter\expandafter\expandafter\pgfkeys% + \expandafter\expandafter\expandafter{\expandafter\pgf@dv@tempb\pgf@dv@temp}% + \pgf@dv@parse@named#3\pgf@stop% + } +}% + + + + + + +\pgfdeclaredataformat{table} +{} % +{ + \pgfkeysgetvalue{/pgf/data/headline}\pgf@dv@headline + \pgfkeysgetvalue{/pgf/data/separator}\pgf@dv@separator + \ifx\pgf@dv@separator\pgfutil@empty + \let\pgf@dv@separator\space + \fi + \ifx\pgf@dv@separator\pgf@dv@spacetext + \let\pgf@dv@separator\space + \fi + \expandafter\def\expandafter\pgf@dv@till@separator% + \expandafter##\expandafter1\pgf@dv@separator{\pgf@dv@table@handle{##1}} + \expandafter\def\expandafter\pgf@dv@till@separator@head% + \expandafter##\expandafter1\pgf@dv@separator{\pgf@dv@head@handle{##1}} + \ifx\pgf@dv@headline\pgfutil@empty + \pgfdv@firstlinetrue + \else + \pgfdv@firstlinefalse + \expandafter\pgf@dv@parse@headline\expandafter{\pgf@dv@headline} + \fi +} +{#1} % +{ + \ifpgfdv@firstline + \pgfdv@firstlinefalse + \pgf@dv@parse@headline{#1} + \else + { + \c@pgf@counta=0\relax% + \def\pgf@marshal{\pgf@dv@parse@table#1} + \expandafter\expandafter\expandafter\pgf@marshal% + \expandafter\pgf@dv@separator\expandafter\pgfeol\pgf@dv@separator + \pgfdatapoint + } + \fi +} +{}% +{}% + +\newif\ifpgfdv@firstline + +\pgfkeys{ + /pgf/data/separator/.initial={,}, + /pgf/data/headline/.initial= +}% +\def\pgf@dv@spacetext{\space}% + +\def\pgf@dv@parse@table{% + \pgfutil@ifnextchar"% + {\pgferror{csv with quotes not yet implemented}} + {\pgf@dv@till@separator} +}% +\def\pgf@dv@table@handle#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfeoltext% + \let\pgf@next=\relax% + \else% + \advance\c@pgf@counta by1\relax% + \pgfkeysgetvalue{/pgf/data/table/attribute \the\c@pgf@counta}\pgf@dv@target + \ifx\pgf@dv@target\relax% + \edef\pgf@dv@target{attribute \the\c@pgf@counta} + \pgfkeyslet{/pgf/data/table/attribute \the\c@pgf@counta}\pgf@dv@target + \fi + \pgfkeyssetvalue{/data point/\pgf@dv@target}{#1} + \let\pgf@next=\pgf@dv@parse@table% + \fi% + \pgf@next% +}% + + + +\def\pgf@dv@parse@headline#1{ + \c@pgf@counta=0\relax% + \def\pgf@marshal{\pgf@dv@doparse@headline#1} + \expandafter\expandafter\expandafter\pgf@marshal% + \expandafter\pgf@dv@separator\expandafter\pgfeol\pgf@dv@separator +}% + +\def\pgf@dv@doparse@headline{% + \pgfutil@ifnextchar"% + {\pgferror{csv with quotes not yet implemented}} + {\pgf@dv@till@separator@head} +}% +\def\pgf@dv@head@handle#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfeoltext% + \let\pgf@next=\relax% + \else% + \advance\c@pgf@counta by1\relax% + \pgfkeyssetvalue{/pgf/data/table/attribute \the\c@pgf@counta}{#1} + \let\pgf@next=\pgf@dv@doparse@headline% + \fi% + \pgf@next% +}% + +\def\pgfeoltext{\pgfeol}% + + + + + + + +\def\pgfdvmathenter#1#2{% + \expandafter\pgfdvmathenter@check\expandafter#1#2\pgfdvmath@end% +}% +\def\pgfdvmathenter@check#1{% + \pgfutil@ifnextchar @{\pgfdvmath@internal#1}{% + \pgfutil@ifnextchar ({\pgfdvmath@expression#1}{% + \pgfutil@ifnextchar !{\pgfdvmath@execute#1}{\pgfdvmath@normal#1}}}% +}% + +\def\pgfdvmath@internal#1@#2\pgfdvmath@end{% + \def#1{#2}% +}% +\def\pgfdvmath@expression#1(#2)#3\pgfdvmath@end{% + \pgfmathparse{#2}% + \pgfmathfloatparsenumber{\pgfmathresult}% + \let#1=\pgfmathresult% +}% +\def\pgfdvmath@execute#1!#2\pgfdvmath@end{% + #2% + \let#1=\pgfdvmathvalue% +}% +\def\pgfdvmath@normal#1#2\pgfdvmath@end{% + \pgfmathfloatparsenumber{#2}% + \let#1=\pgfmathresult% +}% + + + + +\def\pgfdvmathexitbyprinting#1{% + \pgfmathprintnumber{#1}% +}% + + + + +\def\pgfdvmathexitbyscientificformat#1#2{% + \edef#1{\pgfmathfloatvalueof#2}% +}% + + + + +\def\pgfdvmathexitbyserializing#1#2{% + \edef#1{@#2}% +}% + + + + + + +\def\pgfdvmathadd#1#2#3{% + \pgfmathfloatadd{#2}{#3}% + \let#1=\pgfmathresult% +}% +\def\pgfdvmathsub#1#2#3{% + \pgfmathfloatsubtract{#2}{#3}% + \let#1=\pgfmathresult% +}% +\def\pgfdvmathmul#1#2#3{% + \pgfmathfloatmultiply{#2}{#3}% + \let#1=\pgfmathresult% +}% +\def\pgfdvmathdiv#1#2#3{% + \pgfmathfloatdivide{#2}{#3}% + \let#1=\pgfmathresult% +}% + + +\def\pgfdvmathmulfixed#1#2#3{% + \pgfmathfloatmultiplyfixed{#2}{#3}% + \let#1=\pgfmathresult% +}% + + + + +\def\pgfdvmathln#1#2{% + \pgfmathfloatln{#2}% + \let#1=\pgfmathresult% +}% + +\def\pgfdvmathlog#1#2{% + \pgfmathfloatln{#2}% + \pgfmathfloatmultiply{\pgfmathresult}{\pgfdvmathalwaysloge}% + \let#1=\pgfmathresult% +}% + +\def\pgfdvmathexp#1#2{% + \pgfmathfloatexp{#2}% + \let#1=\pgfmathresult% +}% + +\def\pgfdvmathpowten#1#2{% + \pgfmathfloattofixed{#2}% + \let\pgf@dv@temp=\pgfmathresult% + \pgfmathround{\pgf@dv@temp}% + \let\pgf@dv@temp@round=\pgfmathresult% + \pgf@x=\pgf@dv@temp@round pt% + \pgf@x=-\pgf@x% + \advance\pgf@x by\pgf@dv@temp pt\relax% + \ifdim\pgf@x>0.0002pt% + \pgfmathfloatmultiply{#2}{\pgfdvmathalwayslnten}% + \pgfmathfloatexp{\pgfmathresult}% + \else + \ifdim\pgf@x<-0.0002pt% + \pgfmathfloatmultiply{#2}{\pgfdvmathalwayslnten}% + \pgfmathfloatexp{\pgfmathresult}% + \else + \pgf@x=\pgf@dv@temp@round sp% + \c@pgf@counta=\pgf@x% + \pgfmathfloatcreate{1}{1.0}{\the\c@pgf@counta}% + \fi + \fi + \let#1=\pgfmathresult% +}% + + + +\def\pgfdvmathfloor#1#2{% + \pgfmathifisint{#2}{% + \let#1=#2% + }{% + \pgfmathfloatgetflags#2\c@pgf@counta% + \ifcase\c@pgf@counta + \let#1=\pgfdvmathalwayszero% + \or + \pgfmathfloatfloor{#2}% + \let#1=\pgfmathresult% + \or + \pgfmathfloatsubtract{\pgfdvmathalwaysone}{#2}% + \pgfmathfloatfloor{\pgfmathresult}% + \pgfmathfloatsubtract{\pgfdvmathalwayszero}{\pgfmathresult}% + \let#1=\pgfmathresult% + \or\let#1=#2% + \or\let#1=#2% + \or\let#1=#2% + \fi% + }% +}% + + + +\def\pgfdvmathunaryop#1#2#3{% + \csname pgfmathfloat#2\endcsname{#3}% + \let#1=\pgfmathresult% +}% + + + +\def\pgfdvmathbinop#1#2#3#4{% + \csname pgfmathfloat#2\endcsname{#3}{#4}% + \let#1=\pgfmathresult% +}% + + + + +\def\pgfdvmathifless#1#2#3#4{% + \pgfmathfloatlessthan{#1}{#2}% + \ifpgfmathfloatcomparison#3\else#4\fi% +}% + + + + + + + +\pgfooclass{linear transformer} +{% + + + \attribute attribute;% + + \attribute origin = \pgfpointorigin;% + + \attribute unit vector;% + + + \method linear transformer(#1,#2) { + \pgfooset{attribute}{#1} + \pgf@process{#2} + \edef\pgf@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgfoolet{unit vector}\pgf@temp% + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,transform,transform datapoint signal) + }% + + \method set origin(#1) { + \pgf@process{#1} + \edef\pgf@temp{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgfoolet{origin}\pgf@temp% + }% + + \method transform() { + \pgfkeysgetvalue{/data point/\pgfoovalueof{attribute}}\pgf@dv@val% + \ifx\pgf@dv@val\pgfutil@empty% + \else% + \ifx\pgf@dv@val\relax% + \else% + \pgfdvmathenter{\pgf@dv@math@var}{\pgf@dv@val}% + \pgfdvmathexitbyscientificformat{\pgf@dv@val}{\pgf@dv@math@var}% + \pgftransformshift{\pgfoovalueof{origin}}% + \pgfmathfloatgetexponent\pgf@dv@math@var\c@pgf@counta% + \ifnum\c@pgf@counta<-3\relax% + \else% + \pgftransformshift{\pgfpointscale{\pgf@dv@val}{\pgfoovalueof{unit vector}}}% + \fi% + \fi% + \fi% + }% +}% + + + +\pgfooclass{interval mapper} +{% + + + \attribute in;% + + \attribute out;% + + \attribute trans;% + + \attribute out min;% + + \attribute out min;% + + \attribute trans in min;% + + \attribute scale;% + + + \method interval mapper(#1,#2,#3) { + \pgfooset{in}{#1} + \pgfooset{out}{#2} + \def\pgf@temp{#3}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgfooset{trans}{% + #3% + }% + \fi% + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,map,map datapoint signal) + }% + + \method set interval values(#1,#2,#3,#4) { + {% + \pgfdvmathenter{\pgf@in@interval@min}{#1} + \pgfdvmathenter{\pgf@in@interval@max}{#2} + \pgfdvmathenter{\pgf@out@interval@min}{#3} + \pgfdvmathenter{\pgf@out@interval@max}{#4} + \pgfoolet{out min}{\pgf@out@interval@min} + \pgfoolet{out max}{\pgf@out@interval@max} + \pgfdvmathifless{\pgf@in@interval@min}{\pgf@in@interval@max}{% + \pgfdvmathsub{\pgf@out@diff}{\pgf@out@interval@max}{\pgf@out@interval@min} + \let\pgfvalue=\pgf@in@interval@min + \pgfoovalueof{trans} + \let\pgf@in@interval@min@transformed=\pgfvalue + \pgfoolet{trans in min}{\pgf@in@interval@min@transformed}% + \let\pgfvalue=\pgf@in@interval@max + \pgfoovalueof{trans} + \let\pgf@in@interval@max@transformed=\pgfvalue + \pgfdvmathsub{\pgf@diff@in@transformed}{\pgf@in@interval@max@transformed}{\pgf@in@interval@min@transformed} + \pgfdvmathdiv{\pgf@scale}{\pgf@out@diff}{\pgf@diff@in@transformed}% + \pgfoolet{scale}{\pgf@scale}% + }{% + \pgfoolet{scale}\pgf@dv@no@scale% + }% + }% + }% + \def\pgf@dv@no@scale{noscale}% + + \method map() { + \pgfooget{scale}\pgf@dv@scale + \ifx\pgf@dv@scale\pgfutil@empty% + \else% + \pgfkeysgetvalue{/data point/\pgfoovalueof{in}/is min or max}\pgf@dv@is% + \ifx\pgf@dv@is\pgf@min@text% + \pgf@dv@set@out@min% + \else% + \ifx\pgf@dv@is\pgf@max@text% + \pgf@dv@set@out@max% + \else% + \ifx\pgf@dv@scale\pgf@dv@no@scale% + \pgf@dv@mapper@goto@mid% + \else% + \pgfkeysgetvalue{/data point/\pgfoovalueof{in}/const}\pgf@dv@external@value% + \ifx\pgf@dv@external@value\relax% + \pgfkeysgetvalue{/data point/\pgfoovalueof{in}}\pgf@dv@external@value% + \fi% + \ifx\pgf@dv@external@value\pgfutil@empty% + \pgf@dv@mapper@pos@check% + \else% + \ifx\pgf@dv@external@value\relax% + \pgf@dv@mapper@pos@check% + \else% + \pgfdvmathenter{\pgfvalue}{\pgf@dv@external@value}% + \pgf@dv@mapper@trans + \fi% + \fi% + \fi% + \fi% + \fi% + \fi% + }% + + \def\pgf@dv@set@out@min{% + \pgfkeyslet{/data point/\pgfoovalueof{out}/is min or max}\pgf@min@text% + \pgfooget{out min}{\pgf@minmax@temp}% + \pgf@dv@set@out@now% + }% + \def\pgf@dv@set@out@max{% + \pgfkeyslet{/data point/\pgfoovalueof{out}/is min or max}\pgf@max@text% + \pgfooget{out max}{\pgf@minmax@temp}% + \pgf@dv@set@out@now% + }% + \def\pgf@dv@set@out@now{% + \pgfkeysgetvalue{/data point/\pgfoovalueof{out}/offset}\pgf@dv@external@offset% + \ifx\pgf@dv@external@offset\relax\else% + \ifx\pgf@dv@external@offset\pgfutil@empty\else% + \pgfdvmathenter{\pgfvalue}{\pgf@minmax@temp}% + \pgfdvmathenter{\pgf@dv@offset}{\pgf@dv@external@offset}% + \pgfdvmathadd{\pgfvalue}{\pgfvalue}{\pgf@dv@offset} + \pgfdvmathexitbyserializing{\pgf@minmax@temp}{\pgfvalue}% + \fi + \fi + \pgfkeyslet{/data point/\pgfoovalueof{out}}\pgf@minmax@temp% + }% + + \def\pgf@dv@mapper@trans{ + \pgfooget{trans in min}{\pgf@dv@trans@in@min}% + \pgfooget{scale}{\pgf@dv@scale}% + \pgfooget{out min}{\pgf@dv@out@min}% + \pgfoovalueof{trans}% + \pgfdvmathsub{\pgfvalue}{\pgfvalue}{\pgf@dv@trans@in@min}% + \pgfdvmathmul{\pgfvalue}{\pgfvalue}{\pgf@dv@scale}% + \pgfdvmathadd{\pgfvalue}{\pgfvalue}{\pgf@dv@out@min}% + \pgfkeysgetvalue{/data point/\pgfoovalueof{out}/offset}\pgf@dv@external@offset% + \ifx\pgf@dv@external@offset\relax\else% + \ifx\pgf@dv@external@offset\pgfutil@empty\else% + \pgfdvmathenter{\pgf@dv@offset}{\pgf@dv@external@offset}% + \pgfdvmathadd{\pgfvalue}{\pgfvalue}{\pgf@dv@offset} + \fi + \fi + \pgfdvmathexitbyserializing{\pgf@temp}{\pgfvalue}% + \pgfkeyslet{/data point/\pgfoovalueof{out}}\pgf@temp% + }% + + \def\pgf@dv@mapper@pos@check{% + \pgfkeysgetvalue{/data point/\pgfoovalueof{in}/out pos}\pgf@dv@pos@value% + \ifx\pgf@dv@pos@value\relax\else\if\pgf@dv@pos@value\pgfutil@empty\else% + \pgfmathsetmacro{\pgf@dv@pos@num}{\pgf@dv@pos@value}% + \pgfmathsetmacro{\pgf@dv@pos@num@prime}{1-\pgf@dv@pos@num}% + \pgfooget{out min}{\pgf@out@interval@min} + \pgfooget{out max}{\pgf@out@interval@max} + \pgfdvmathmulfixed{\pgf@out@interval@min}{\pgf@out@interval@min}{\pgf@dv@pos@num@prime} + \pgfdvmathmulfixed{\pgf@out@interval@max}{\pgf@out@interval@max}{\pgf@dv@pos@num} + \pgfdvmathadd{\pgf@out@val}{\pgf@out@interval@min}{\pgf@out@interval@max}% + \pgfdvmathexitbyserializing{\pgf@temp}{\pgf@out@val}% + \pgfkeyslet{/data point/\pgfoovalueof{out}}\pgf@temp% + \fi\fi% + }% + + \def\pgf@dv@mapper@goto@mid{% + \pgfooget{out min}{\pgf@out@interval@min} + \pgfooget{out max}{\pgf@out@interval@max} + \pgfdvmathmulfixed{\pgf@out@interval@min}{\pgf@out@interval@min}{.5} + \pgfdvmathmulfixed{\pgf@out@interval@max}{\pgf@out@interval@max}{.5} + \pgfdvmathadd{\pgf@out@val}{\pgf@out@interval@min}{\pgf@out@interval@max}% + \pgfdvmathexitbyserializing{\pgf@temp}{\pgf@out@val}% + \pgfkeyslet{/data point/\pgfoovalueof{out}}\pgf@temp% + }% +}% + + + + + +\newif\ifpgf@dvignore + +\pgfooclass{scaling mapper} +{% + + \attribute in;% + + \attribute out;% + + \attribute in range obj;% + + \attribute scaling spec;% + + \attribute spec maps min;% + + \attribute spec maps max;% + + \attribute function;% + + \attribute interval mapper;% + + \attribute range surveyor;% + + + \method scaling mapper(#1,#2,#3,#4) { + \pgfooset{in}{#1} + \pgfooset{out}{#2} + \pgfooset{scaling spec}{#3} + \pgfooset{function}{#4} + \pgfoonew \pgf@dv@in@range@obj=new interval(,) + \pgfoolet{in range obj}\pgf@dv@in@range@obj + \pgfoonew \pgf@dv@range@obj=new range surveyor(#1,\pgf@dv@in@range@obj) + \pgf@dv@range@obj.default connects() + \pgfoolet{range surveyor}\pgf@dv@range@obj + \pgfoonew{interval mapper}=new interval mapper(#1,#2,#4) + \pgfoovalueof{interval mapper}.default connects() + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,phase,phase signal) + }% + + \method get in range interval() { + \pgfooget{in range obj}\pgfdvinrangeinterval + }% + + + \method get out() { + \pgfooget{out}\pgfdvout + }% + + \method get function(#1) { + \pgfooget{function}#1 + }% + + \method include in value(#1) { + \pgfoovalueof{range surveyor}.include attribute value({#1}) + }% + + + \method set in to(#1) {% + \edef\pgf@temp{#1}% + \ifx\pgf@temp\pgf@min@text% + \pgf@dv@lib@set@mm% + \let\pgf@dv@value\pgfdvmin% + \pgfoovalueof{spec maps min}{\pgfkeyslet{/data point/\pgfoovalueof{in}/is min or max}\pgf@min@text}{}% + \else% + \ifx\pgf@temp\pgf@max@text% + \pgf@dv@lib@set@mm% + \let\pgf@dv@value\pgfdvmax% + \pgfoovalueof{spec maps min}{\pgfkeyslet{/data point/\pgfoovalueof{in}/is min or max}\pgf@max@text}{}% + \else% + \pgfdvmathenter{\pgf@dv@value}{\pgf@temp}% + \fi% + \fi% + \pgfdvmathexitbyserializing{\pgf@dv@serial}{\pgf@dv@value}% + \pgfkeyslet{/data point/\pgfoovalueof{in}}\pgf@dv@serial% + }% + \def\pgf@dv@lib@set@mm{ + \pgfooget{in range obj}\pgfdvinrangeinterval + \pgfdvinrangeinterval.get min and max()% + }% + + + \method phase(#1) { + \ifx#1\pgfdvendsurvey + \pgfoovalueof{in range obj}.get min and max() + \ifx\pgfdvmin\pgfutil@empty% + \else% + \pgfooget{scaling spec}\pgf@temp% + \expandafter\pgf@lib@dv@parse@scaling\pgf@temp\pgf@stop% + \pgfoovalueof{interval mapper}.set interval values(% + \pgf@lib@dv@min,\pgf@lib@dv@max,% + \pgf@lib@dv@min@at,\pgf@lib@dv@max@at) + \fi + \fi + }% + + + \def\pgf@lib@dv@parse@scaling#1 at#2and #3 at#4\pgf@stop{% + \def\pgf@lib@dv@min{#1}% + \pgfdvmathenter{\pgf@lib@dv@min@at@mv}{#2} + \def\pgf@lib@dv@max{#3}% + \pgfdvmathenter{\pgf@lib@dv@max@at@mv}{#4} + \ifx\pgf@lib@dv@min\pgf@min@text% + \let\pgf@lib@dv@min@mv\pgfdvmin + \pgfoolet{spec maps min}\pgfutil@firstoftwo% + \else + \pgfdvmathenter{\pgf@lib@dv@min@mv}{\pgf@lib@dv@min} + \pgfoolet{spec maps min}\pgfutil@secondoftwo% + \fi + \ifx\pgf@lib@dv@max\pgf@max@text% + \let\pgf@lib@dv@max@mv\pgfdvmax + \pgfoolet{spec maps max}\pgfutil@firstoftwo% + \else + \pgfdvmathenter{\pgf@lib@dv@max@mv}{\pgf@lib@dv@max} + \pgfoolet{spec maps max}\pgfutil@secondoftwo% + \fi + \pgfdvmathexitbyserializing{\pgf@lib@dv@min}{\pgf@lib@dv@min@mv} + \pgfdvmathexitbyserializing{\pgf@lib@dv@min@at}{\pgf@lib@dv@min@at@mv} + \pgfdvmathexitbyserializing{\pgf@lib@dv@max}{\pgf@lib@dv@max@mv} + \pgfdvmathexitbyserializing{\pgf@lib@dv@max@at}{\pgf@lib@dv@max@at@mv} + }% + \def\pgf@min@text{min}% + \def\pgf@max@text{max}% +}% + + + + + + +\pgfooclass{range surveyor} +{% + + \attribute attribute;% + + \attribute interval obj;% + + + \method range surveyor(#1,#2) { + \pgfooset{attribute}{#1} + \pgfoolet{interval obj}#2 + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,survey,survey datapoint signal) + }% + + \method include attribute value(#1) { + \pgf@dv@assign@val@stripped#1\pgf@stop% + \pgfoovalueof{interval obj}.adjust(\pgf@dv@range@surv) + }% + \def\pgf@dv@assign@val@stripped#1\pgf@stop{% + \def\pgf@dv@val{#1} + }% + + \method survey() { + \let\pgfdvsub\pgf@dv@range@surv@sub + \pgfdvsub{}% + \pgfkeysvalueof{/data point/\pgfoovalueof{attribute}/sub attributes} + }% + + \def\pgf@dv@range@surv@sub#1{ + \pgfkeysgetvalue{/data point/\pgfoovalueof{attribute}#1}\pgf@dv@val% + \ifx\pgf@dv@val\relax% + \else% + \edef\pgf@dv@val{\pgf@dv@val}% + \ifx\pgf@dv@val\pgfutil@empty% + \else% + \pgfoovalueof{interval obj}.adjust(\pgf@dv@range@surv)% + \fi% + \fi% + }% + + \def\pgf@dv@range@surv{% + \pgfdvmathenter{\pgf@dv@value}{\pgf@dv@val}% + \ifx\pgfdvmin\pgfutil@empty% + \let\pgfdvmin\pgf@dv@value% + \else% + \pgfdvmathifless{\pgf@dv@value}{\pgfdvmin}{\let\pgfdvmin\pgf@dv@value}{}% + \fi% + \ifx\pgfdvmax\pgfutil@empty% + \let\pgfdvmax\pgf@dv@value% + \else% + \pgfdvmathifless{\pgfdvmax}{\pgf@dv@value}{\let\pgfdvmax\pgf@dv@value}{}% + \fi% + }% +}% + + + + +\usepgflibrary{plothandlers}% + + + +\pgfooclass{plot handler visualizer} +{% + + \attribute handlers;% + + \attribute name;% + + \attribute filter=\pgfdvnamedvisualizerfilter;% + + \attribute positions;% + + \attribute cache;% + + \attribute projection code;% + + \method plot handler visualizer(#1,#2) { + \pgfooset{name}{#1} + \pgfooset{handlers}{#2} + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,protocol,visualize datapoint signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,phase,phase signal) + }% + + \method set filter(#1) { + \pgfooset{filter}{#1} + }% + + \method set projection code(#1) { + \pgfooset{projection code}{#1} + }% + + \method protocol() { + \pgfdvfilterpassedtrue + \pgfoovalueof{filter} + \ifpgfdvfilterpassed% + \pgf@dv@line@cache@it + \fi% + }% + + \def\pgf@dv@line@cache@it{ + \pgfooget{cache}\pgf@dv@cache + \pgfkeysgetvalue{/data point/outlier}\pgf@temp% + \ifx\pgf@temp\pgfutil@empty + {% + \pgfoovalueof{projection code} + \xdef\pgf@dv@add{\noexpand\pgf@dv@ph{\pgfkeysvalueof{/data + point/canvas x}}{\pgfkeysvalueof{/data point/canvas y}}}% + } + \else% + \gdef\pgf@dv@add{\pgf@dv@outliner}% + \fi% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@dv@cache% + \expandafter\expandafter\expandafter{\expandafter\pgf@dv@cache\pgf@dv@add}% + \global\advance\pgf@lib@dv@cache@count by1\relax% + \ifnum\pgf@lib@dv@cache@count=100\relax% + \global\pgf@lib@dv@cache@count=0\relax% + \pgfooget{positions}\pgf@dv@temp + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@dv@temp% + \expandafter\expandafter\expandafter{\expandafter\pgf@dv@temp\pgf@dv@cache}% + \pgfoolet{positions}\pgf@dv@temp + \let\pgf@dv@cache\pgfutil@empty + \fi + \pgfoolet{cache}\pgf@dv@cache + }% + + \method phase(#1) {% + \ifx#1\pgfdvendvisualization% + \pgfoothis.render()% + \fi% + }% + + \method render() { + \pgfscope + \pgfooget{handlers}\tikz@dv@temp@list + \foreach\tikz@dv@temp in\tikz@dv@temp@list{ + \ifx\tikz@dv@temp\pgfutil@empty + \else + \pgfkeysvalueof{/data point/\pgfoovalueof{name}/execute at begin} + \tikz@dv@temp + \pgfdvnewstreamtrue + \pgfoovalueof{positions} + \pgfoovalueof{cache} + \ifpgfdvnewstream\else\pgfplotstreamend\fi + \pgfkeysvalueof{/data point/\pgfoovalueof{name}/execute at end} + \fi + } + \endpgfscope + \pgfoolet{positions}\pgfutil@empty + \pgfoolet{cache}\pgfutil@empty + }% + + \def\pgf@dv@ph#1#2{\ifpgfdvnewstream\pgfplotstreamstart\pgfdvnewstreamfalse\fi\pgfplotstreampoint{\pgfqpoint{#1}{#2}}}% + \def\pgf@dv@outliner{\ifpgfdvnewstream\else\pgfplotstreamend\pgfdvnewstreamtrue\fi}% +}% + +\newif\ifpgfdvnewstream +\newcount\pgf@lib@dv@cache@count + +\pgfkeys{% + /data point/outlier/.initial=, + /data point/outlier/.default=true, +}% + + + +\def\pgfdvvisualizerfilter#1{% + \pgfkeysgetvalue{/data point/set}\pgf@dv@visualizer% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgf@dv@visualizer% + \else + \pgfdvfilterpassedfalse + \fi% +}% + + + + +\def\pgfdvnamedvisualizerfilter{% + \pgfkeysgetvalue{/data point/set}\pgf@dv@visualizer% + \pgfooget{name}\pgf@temp% + \ifx\pgf@temp\pgf@dv@visualizer% + \else + \pgfdvfilterpassedfalse + \fi% +}% + + + +\pgfooclass{rectangle visualizer} +{% + + + \attribute name;% + + \attribute a1;% + \attribute a2;% + + + \method rectangle visualizer(#1) { + \pgfooset{name}{#1} + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,visualize,visualize datapoint signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,phase,phase signal) + }% + + \method phase(#1) {% + \ifx#1\pgfdvbeginsurvey% + \pgfooeset{a1}{/data point/\pgfkeysvalueof{/data point/\pgfoovalueof{name}/attribute 1}} + \pgfooeset{a2}{/data point/\pgfkeysvalueof{/data point/\pgfoovalueof{name}/attribute 2}} + \pgfkeyssetvalue{\pgfoovalueof{a1}/sub attributes}{\pgfdvsub{/min}\pgfdvsub{/max}} + \pgfkeyssetvalue{\pgfoovalueof{a2}/sub attributes}{\pgfdvsub{/min}\pgfdvsub{/max}} + \fi% + }% + + \method visualize() { + { + \pgfkeysgetvalue{/data point/set}\pgf@dv@visualizer% + \pgfooget{name}\pgf@temp% + \ifx\pgf@temp\pgf@dv@visualizer% + \pgf@dv@rect@do + \fi + } + }% + + \def\pgf@dv@rect@do{ + \pgfkeysgetvalue{\pgfoovalueof{a1}/min}\pgf@dv@amin + \ifx\pgf@dv@amin\relax\else\ifx\pgf@dv@amin\pgfutil@empty\else + \pgfkeysgetvalue{\pgfoovalueof{a1}/max}\pgf@dv@amax + \ifx\pgf@dv@amax\relax\else\ifx\pgf@dv@amax\pgfutil@empty\else + \pgfkeysgetvalue{\pgfoovalueof{a2}/min}\pgf@dv@bmin + \ifx\pgf@dv@bmin\relax\else\ifx\pgf@dv@bmin\pgfutil@empty\else + \pgfkeysgetvalue{\pgfoovalueof{a2}/max}\pgf@dv@bmax + \ifx\pgf@dv@bmax\relax\else\ifx\pgf@dv@bmax\pgfutil@empty\else + \pgfkeysvalueof{/data point/\pgfoovalueof{name}/execute at begin} + \pgfkeyssetvalue{\pgfoovalueof{a1}}{\pgf@dv@amin} + \pgfkeyssetvalue{\pgfoovalueof{a2}}{\pgf@dv@bmin} + \pgfpathdvmoveto + \pgfkeyssetvalue{\pgfoovalueof{a2}}{\pgf@dv@bmax} + \pgfpathdvlineto + \pgfkeyssetvalue{\pgfoovalueof{a1}}{\pgf@dv@amax} + \pgfpathdvlineto + \pgfkeyssetvalue{\pgfoovalueof{a2}}{\pgf@dv@bmin} + \pgfpathdvlineto + \pgfkeyssetvalue{\pgfoovalueof{a1}}{\pgf@dv@amin} + \pgfpathdvlineto + \pgfpathclose + \pgfkeysvalueof{/data point/\pgfoovalueof{name}/execute at end} + \fi\fi + \fi\fi + \fi\fi + \fi\fi + }% +}% + +\newcount\pgf@lib@dv@cache@count + + + + +\pgfooclass{label visualizer} +{% + + \attribute attribute;% + + \attribute filter;% + + \attribute threshold;% + + \attribute before canvas position=;% + + \attribute canvas position=;% + + \attribute code;% + + + \method label visualizer(#1,#2,#3,#4) { + \pgfooset{attribute}{#1} + \expandafter\pgfdvmathenter\expandafter{\expandafter\pgf@temp\expandafter}\expandafter{#2} + \pgfoolet{threshold}\pgf@temp + \pgfooset{code}{#3} + \pgfooset{filter}{#4} + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,test,visualize datapoint signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,phase,phase signal) + }% + + \method test() { + \pgfdvfilterpassedtrue + \pgfoovalueof{filter} + \ifpgfdvfilterpassed% + \pgfooget{attribute}\pgf@dv@attribute + \ifx\pgf@dv@attribute\pgfutil@empty% + \else% + \pgf@dv@label@vis@record + \fi% + \fi% + }% + + \def\pgf@dv@label@vis@record{ + \edef\pgf@dv@pos{% + \noexpand\pgfqpoint% + {\pgfkeysvalueof{/data point/canvas x}}% + {\pgfkeysvalueof{/data point/canvas y}}}% + \pgfooget{canvas position}\pgf@dv@temp% + \pgfoolet{before canvas position}\pgf@dv@temp% + \pgfoolet{canvas position}\pgf@dv@pos% + \pgfooget{threshold}\pgf@dv@thres% + \ifx\pgf@dv@thres\pgfutil@empty% + \else% + \pgfkeysgetvalue{/data point/\pgfoovalueof{attribute}}\pgf@dv@val + \ifx\pgf@dv@val\relax% + \else\ifx\pgf@dv@val\pgfutil@empty% + \else% + \pgfdvmathenter{\pgf@dv@value}{\pgf@dv@val}% + \pgfooget{threshold}{\pgf@dv@thres} + \pgfdvmathifless{\pgf@dv@value}{\pgf@dv@thres}{}{% + \pgfoolet{attribute}\pgfutil@empty% + }% + \fi\fi% + \fi% + }% + + \method phase(#1) {% + \ifx#1\pgfdvendvisualization% + \scope + \pgfcoordinate{label visualizer coordinate}{\pgfoovalueof{canvas position}} + \pgfcoordinate{label visualizer coordinate'}{\pgfoovalueof{before canvas position}} + \pgfoovalueof{code} + \endscope + \fi% + }% +}% + + + +\pgfooclass{style attribute} +{% + + \attribute attribute;% + + \attribute style sheet name;% + + \method style attribute(#1,#2) { + \pgfooset{attribute}{#1} + \pgfooset{style sheet name}{#2} + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,invoke style,style signal) + }% + + \method invoke style() { + \pgfooget{attribute}\pgf@dv@temp + \pgfkeysgetvalue{\pgf@dv@temp}\pgf@dv@temp@val + \ifx\pgf@dv@temp@val\pgfutil@empty% + \else\ifx\pgf@dv@temp@val\relax% + \else% + \pgfkeysifdefined{\pgf@dv@temp/\pgf@dv@temp@val}{\pgfkeysgetvalue{\pgf@dv@temp/\pgf@dv@temp@val}\pgf@dv@temp@val}{}% + \edef\pgf@temp{/pgf/data visualization/style sheets/\pgfoovalueof{style sheet name}} + \pgfkeysifassignable{\pgf@temp/\pgf@dv@temp@val}{% + \pgfkeysalso{\pgf@temp/\pgf@dv@temp@val}}{% + \pgfkeysalso{\pgf@temp/default style/.expand once=\pgf@dv@temp@val} + } + \fi\fi% + }% +}% + + + +\def\pgfdvdeclarestylesheet#1#2{ + \pgfkeys{/pgf/data visualization/style sheets/#1/.cd,#2} +}% + + + + + + + + + + +\pgfooclass{legend} +{% + + + \attribute entries;% + + \attribute columns or rows;% + + \attribute ideal;% + + \attribute max;% + + \attribute strategy;% + + \attribute number of entries=0;% + + + \method legend(#1,#2,#3,#4) { + \pgfooset{columns or rows}{#1} + \pgfooset{ideal}{#2} + \pgfooset{max}{#3} + \pgfooset{strategy}{#4} + }% + + \method default connects() { + }% + + \method add entry(#1) { + \pgfooappend{entries}{{#1}} + \c@pgf@counta=\pgfoovalueof{number of entries}\relax% + \advance\c@pgf@counta by1\relax% + \pgfooeset{number of entries}{\the\c@pgf@counta} + }% + + \method get arrangement(#1) { + { + \ifnum\pgfoovalueof{number of entries}>\pgfoovalueof{ideal}\relax% + \c@pgf@counta=\pgfoovalueof{ideal}\relax% + \multiply\c@pgf@counta by\pgfoovalueof{max}\relax% + \ifnum\c@pgf@counta>\pgfoovalueof{number of entries}\relax + \c@pgf@counta=\pgfoovalueof{ideal}\relax% + \c@pgf@countb=\pgfoovalueof{number of entries}\relax + \advance\c@pgf@countb by-1\relax + \divide\c@pgf@countb by\c@pgf@counta\relax% + \advance\c@pgf@countb by1\relax% + \else + \c@pgf@countb=\pgfoovalueof{max}\relax% + \c@pgf@counta=\pgfoovalueof{number of entries}\relax + \advance\c@pgf@counta by-1\relax + \divide\c@pgf@counta by\c@pgf@countb\relax% + \advance\c@pgf@counta by1\relax% + \fi + \else + \c@pgf@counta=\pgfoovalueof{number of entries}\relax% + \c@pgf@countb=1\relax% + \fi% + \pgfooget{columns or rows}\pgf@temp + \ifx\pgf@temp\pgf@dv@columnstext% + \c@pgf@countc=\c@pgf@counta\relax + \c@pgf@counta=\c@pgf@countb\relax + \c@pgf@countb=\c@pgf@countc\relax + \fi + \csname pgf@dv@legend@init@\pgfoovalueof{strategy}\endcsname + \expandafter\let\expandafter\pgf@dv@updater\csname pgf@dv@legend@update@\pgfoovalueof{strategy}\endcsname + \pgfooget{entries}\pgf@temp + \expandafter\pgf@dv@legend@arrange\pgf@temp\pgf@stop + \edef\pgf@dv@row@list{1,...,\the\c@pgf@counta} + \edef\pgf@dv@column@list{1,...,\the\c@pgf@countb} + \global\let\pgf@dv@matrix\pgfutil@empty + \foreach \pgf@dv@row in \pgf@dv@row@list + { + \global\let\pgf@dv@matrix@row\pgf@dv@first@mark + \foreach \pgf@dv@column in \pgf@dv@column@list + { + \expandafter\let\expandafter\pgf@temp\csname pgf@dv@legend@entry@\pgf@dv@row @\pgf@dv@column\endcsname + \ifx\pgf@temp\relax + \let\pgf@temp\pgfutil@empty + \fi + \ifx\pgf@dv@matrix@row\pgf@dv@first@mark + \global\let\pgf@dv@matrix@row\pgf@temp + \else + \expandafter\pgfutil@g@addto@macro\expandafter\pgf@dv@matrix@row\expandafter{\expandafter\pgfdvnextcell\pgf@temp} + \fi + } + \pgfutil@g@addto@macro\pgf@dv@matrix@row{\pgfdvendrow} + \expandafter\pgfutil@g@addto@macro\expandafter\pgf@dv@matrix\expandafter{\pgf@dv@matrix@row} + } + \global\let\pgf@dv@matrix@row\relax + } + \let#1\pgf@dv@matrix + \global\let\pgf@dv@matrix\relax + }% + + \def\pgf@dv@first@mark{\pgf@dv@first@mark}% + + \def\pgf@dv@legend@arrange{% + \pgfutil@ifnextchar\pgf@stop{\pgfutil@gobble}{\pgf@dv@legend@handle@entry} + }% + + \def\pgf@dv@legend@handle@entry#1{ + \expandafter\def\csname pgf@dv@legend@entry@\the\c@pgf@countc @\the\c@pgf@countd\endcsname{#1}% + \pgf@dv@updater% + \pgf@dv@legend@arrange% + }% + + \expandafter\def\csname pgf@dv@legend@init@down then right\endcsname{% + \c@pgf@countc=1\relax% + \c@pgf@countd=1\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@down then right\endcsname{% + \advance\c@pgf@countc by1\relax + \ifnum\c@pgf@countc>\c@pgf@counta\relax% + \c@pgf@countc=1\relax% + \advance\c@pgf@countd by1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@right then down\endcsname{% + \c@pgf@countc=1\relax% + \c@pgf@countd=1\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@right then down\endcsname{% + \advance\c@pgf@countd by1\relax + \ifnum\c@pgf@countd>\c@pgf@countb\relax% + \c@pgf@countd=1\relax% + \advance\c@pgf@countc by1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@up then right\endcsname{% + \c@pgf@countc=\c@pgf@counta\relax% + \c@pgf@countd=1\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@up then right\endcsname{% + \advance\c@pgf@countc by-1\relax + \ifnum\c@pgf@countc=0\relax% + \c@pgf@countc=\c@pgf@counta\relax% + \advance\c@pgf@countd by1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@right then up\endcsname{% + \c@pgf@countc=\c@pgf@counta\relax% + \c@pgf@countd=1\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@right then up\endcsname{% + \advance\c@pgf@countd by1\relax + \ifnum\c@pgf@countd>\c@pgf@countb\relax% + \c@pgf@countd=1\relax% + \advance\c@pgf@countc by-1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@left then up\endcsname{% + \c@pgf@countc=\c@pgf@counta\relax% + \c@pgf@countd=\c@pgf@countb\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@left then up\endcsname{% + \advance\c@pgf@countd by-1\relax + \ifnum\c@pgf@countd=0\relax% + \c@pgf@countd=\c@pgf@countb\relax% + \advance\c@pgf@countc by-1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@up then left\endcsname{% + \c@pgf@countc=\c@pgf@counta\relax% + \c@pgf@countd=\c@pgf@countb\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@up then left\endcsname{% + \advance\c@pgf@countc by-1\relax + \ifnum\c@pgf@countc=0\relax% + \c@pgf@countc=\c@pgf@counta\relax% + \advance\c@pgf@countd by-1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@left then down\endcsname{% + \c@pgf@countc=1\relax% + \c@pgf@countd=\c@pgf@countb\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@left then down\endcsname{% + \advance\c@pgf@countd by-1\relax + \ifnum\c@pgf@countd=0\relax% + \c@pgf@countd=\c@pgf@countb\relax% + \advance\c@pgf@countc by1\relax% + \fi% + }% + + \expandafter\def\csname pgf@dv@legend@init@down then left\endcsname{% + \c@pgf@countc=1\relax% + \c@pgf@countd=\c@pgf@countb\relax% + }% + + \expandafter\def\csname pgf@dv@legend@update@down then left\endcsname{% + \advance\c@pgf@countc by1\relax + \ifnum\c@pgf@countc>\c@pgf@countb\relax% + \c@pgf@countc=1\relax% + \advance\c@pgf@countd by-1\relax% + \fi% + }% + + \def\pgf@dv@columnstext{columns}% +}% + + + + +\pgfooclass{interval} +{% + + \attribute min;% + + \attribute max;% + + \method interval(#1,#2) { + \pgfooset{min}{#1} + \pgfooset{max}{#2} + }% + + \method default connects() { + }% + + \method set min(#1) { + \pgfooset{min}{#1} + }% + \method set max(#1) { + \pgfooset{max}{#1} + }% + \method let min(#1) { + \pgfoolet{min}{#1} + }% + \method let max(#1) { + \pgfoolet{max}{#1} + }% + + \method get min and max() { + \pgfooget{min}\pgfdvmin + \pgfooget{max}\pgfdvmax + }% + + \method adjust(#1) { + {% + \pgfooget{min}\pgfdvmin + \pgfooget{max}\pgfdvmax + #1% + \pgfoolet{min}\pgfdvmin + \pgfoolet{max}\pgfdvmax + }% + }% +}% + + + +\pgfooclass{count} +{% + + + \attribute attribute;% + + \attribute val=0;% + + \attribute max=0;% + + \attribute step=1;% + + \attribute start val=0;% + + \attribute filter=;% + + + \method count(#1) { + \pgfooset{attribute}{#1} + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,apply,prepare datapoint signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,phase,phase signal) + }% + + \method get max(#1) { + \pgfooget{max}{#1} + }% + + \method set value(#1) { + \pgfooset{val}{#1} + \pgfkeyssetvalue{/data point/\pgfoovalueof{attribute}}{#1}% + }% + + \method set start value(#1) { + \pgfooset{start val}{#1} + \pgfooset{max}{#1} + }% + + \method set filter(#1) { + \pgfooset{filter}{#1} + }% + + \method set step(#1) { + \pgfooset{step}{#1} + }% + + \method apply() { + \pgfdvfilterpassedtrue% + \pgfoovalueof{filter}% + \ifpgfdvfilterpassed% + \pgfmathparse{\pgfoovalueof{val}+\pgfoovalueof{step}}% + \pgfoolet{val}\pgfmathresult% + \pgfkeyslet{/data point/\pgfoovalueof{attribute}}\pgfmathresult% + \ifdim\pgfmathresult pt>\pgfoovalueof{max}pt\relax% + \pgfoolet{max}\pgfmathresult% + \fi% + \pgfooget{max}\pgfmathresult% + \pgfkeyslet{/data point/\pgfoovalueof{attribute}/max}\pgfmathresult% + \fi% + }% + + \method phase(#1) { + \ifx#1\pgfdvbeginsurvey + \pgfooeset{val}{\pgfoovalueof{start val}} + \else \ifx#1\pgfdvbeginvisualization + \pgfooeset{val}{\pgfoovalueof{start val}} + \fi\fi + }% +}% + +\newif\ifpgfdvfilterpassed + + + + +\pgfooclass{accumulator} +{% + + \attribute attribute;% + + \attribute sum;% + + \method accumulator(#1) { + \pgfooset{attribute}{#1} + \pgfoothis.reset() + }% + + \method default connects() { + \pgfoothis.get handle(\pgf@dv@me) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,apply,prepare datapoint signal) + \pgfkeysvalueof{/pgf/data visualization/obj}.connect(\pgf@dv@me,phase,phase signal) + }% + + \method apply() {% + \pgfkeysgetvalue{/data point/\pgfoovalueof{attribute}/sum}\pgf@temp% + \pgfkeyslet{/data point/\pgfoovalueof{attribute}/prev sum}\pgf@temp% + \pgfkeysgetvalue{/data point/\pgfoovalueof{attribute}}{\pgf@temp@b}% + \pgfdvmathenter{\pgf@dv@new@val}{\pgf@temp@b}% + \pgfooget{sum}\pgf@dv@sum% + \pgfdvmathadd{\pgf@dv@sum}{\pgf@dv@new@val}{\pgf@dv@sum}% + \pgfoolet{sum}\pgf@dv@sum + \pgfdvmathexitbyscientificformat{\pgf@dv@serial@sum}{\pgf@dv@sum} + \pgfkeyslet{/data point/\pgfoovalueof{attribute}/sum}\pgf@dv@serial@sum + }% + + \method reset() { + \pgfdvmathenter{\pgf@dv@temp}{0} + \pgfoolet{sum}{\pgf@dv@temp} + \pgfdvmathexitbyserializing{\pgf@dv@zero}{\pgf@dv@temp} + \pgfkeyslet{/data point/\pgfoovalueof{attribute}/prev sum}{\pgf@dv@zero} + \pgfkeyslet{/data point/\pgfoovalueof{attribute}/sum}{\pgf@dv@zero} + }% + + \method phase(#1) { + \ifx#1\pgfdvbeginsurvey + \pgfoothis.reset() + \else \ifx#1\pgfdvbeginvisualization + \pgfoothis.reset() + \fi\fi + }% +}% + + + + + + + + +\pgfkeys{% + /data point/always true/.initial=true, + /data point/always false/.initial=false, + /data point/always 0/.initial=0, + /data point/always 1/.initial=1, + /data point/always empty/.initial=, + /data point/always pgfusepath stroke/.initial=\pgfusepath{stroke}, +}% + +\pgfdvmathenter{\pgfdvmathalwaysloge}{0.434294481903252}% +\pgfdvmathenter{\pgfdvmathalwayslnten}{2.302585092994046}% +\pgfdvmathenter{\pgfdvmathalwayszero}{0}% +\pgfdvmathenter{\pgfdvmathalwaysone}{1}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduledecorations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduledecorations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..490e160f02285c12bd3912ca8064466c86ea477b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduledecorations.code.tex @@ -0,0 +1,1449 @@ + + + + + +\def\pgfgetpath#1{\pgfsyssoftpath@getcurrentpath{#1}}% +\def\pgfsetpath#1{\pgfsyssoftpath@setcurrentpath{#1}}% + + +\newdimen\pgfdecoratedcompleteddistance +\newdimen\pgfdecoratedremainingdistance +\newdimen\pgfdecoratedinputsegmentcompleteddistance +\newdimen\pgfdecoratedinputsegmentremainingdistance +\newdimen\pgf@decorate@distancetomove + +\newcount\pgf@decorate@repeatstate + + + +\newdimen\pgfdecorationsegmentamplitude +\newdimen\pgfdecorationsegmentlength +\pgfdecorationsegmentamplitude2.5pt +\pgfdecorationsegmentlength10pt +\def\pgfdecorationsegmentangle{45}% +\def\pgfdecorationsegmentaspect{0.5}% +\def\pgfmetadecorationsegmentamplitude{2.5pt}% +\def\pgfmetadecorationsegmentlength{1cm}% + +\pgfkeys{% + /pgf/decoration/.code={\pgfkeys{/pgf/decoration/.cd,#1}}, + /pgf/decoration/.cd, + amplitude/.code={\pgfmathsetlength\pgfdecorationsegmentamplitude{#1}}, + meta-amplitude/.store in=\pgfmetadecorationsegmentamplitude, + segment length/.code={\pgfmathsetlength\pgfdecorationsegmentlength{#1}}, + meta-segment length/.store in=\pgfmetadecorationsegmentlength, + angle/.code={\pgfmathparse{#1}\let\pgfdecorationsegmentangle\pgfmathresult}, + aspect/.code={\pgfmathparse{#1}\let\pgfdecorationsegmentaspect\pgfmathresult}, + start radius/.initial=2.5pt, + end radius/.initial=2.5pt, + radius/.style={start radius={#1},end radius={#1}}, + path has corners/.is if=pgfdecoratepathhascorners, + reverse path/.is if=pgf@decorate@inputsegmentobjects@reverse, +}% +\newif\ifpgfdecoratepathhascorners +\newif\ifpgf@decorate@inputsegmentobjects@reverse + + +\long\def\pgfdeclaredecoration#1#2#3{% + \let\pgf@mod@dec@next=\pgf@mod@dec@firstofone% + \pgfifmetadecoration{#1}{% + \pgferror{You cannot declare a decoration of the same + name as a meta-decoration}% + \let\pgf@mod@dec@next=\pgfutil@gobble% + }{}% + \pgf@mod@dec@next + {% + \def\pgf@decorate@name{#1}% + \pgfutil@namedef{pgf@decorate@@#1@initial}{#2}% + \let\pgf@orig@state\state% + \let\state\pgf@decorate@state + #3% + \let\state\pgf@orig@state% + }% +}% + +\def\pgf@decorate@state#1{\pgfutil@ifnextchar[{\pgf@decorate@@start#1}{\pgf@decorate@@start#1[]}}% +\def\pgf@decorate@@start#1[#2]#3{% + \pgfutil@namedef{pgf@decorate@@\pgf@decorate@name @#1@options}{#2}% + \pgfutil@namedef{pgf@decorate@@\pgf@decorate@name @#1@code}{#3}% +}% +\long\def\pgf@mod@dec@firstofone#1{#1}% + + + +\def\pgfifdecoration#1#2#3{\pgfutil@ifundefined{pgf@decorate@@#1@initial}{#3}{#2}}% + + + + +\long\def\pgfdeclaremetadecoration#1#2#3{% + \let\pgf@mod@dec@next=\pgf@mod@dec@firstofone% + \pgfifdecoration{#1}{% + \pgferror{You cannot declare a meta-decoration of the + same name as a decoration}% + \let\pgf@mod@dec@next=\pgfutil@gobble% + }{}% + \pgf@mod@dec@next{% + \def\pgf@metadecoration@name{#1}% + \pgfutil@namedef{pgf@metadecoration@@#1@initial}{#2}% + \let\pgf@orig@state\state% + \let\state\pgf@metadecoration@state + #3% + \let\state\pgf@orig@state% + }% +}% + +\def\pgf@metadecoration@state#1{\pgfutil@ifnextchar[{\pgf@metadecoration@@state#1}{\pgf@metadecoration@@state#1[]}}% +\def\pgf@metadecoration@@state#1[#2]#3{% + \pgfutil@namedef{pgf@metadecoration@@\pgf@metadecoration@name @#1@options}{#2}% + \pgfutil@namedef{pgf@metadecoration@@\pgf@metadecoration@name @#1@code}{#3}% +}% + + + +\def\pgfifmetadecoration#1#2#3{\pgfutil@ifundefined{pgf@metadecoration@@#1@initial}{#3}{#2}}% + + + + + +\let\pgfdecoratebeforecode\pgfutil@empty +\let\pgfdecorateaftercode\pgfutil@empty + +\long\def\pgfdecoratepath#1#2{% + \pgfdecoration{{#1}{\pgfdecoratedpathlength}{\pgfdecoratebeforecode}{\pgfdecorateaftercode}}% + #2% + \endpgfdecoration}% + + + + +\def\pgfdecoratecurrentpath#1{% + \pgfgetpath\pgf@decorate@currentpath% + \pgfsetpath\pgfutil@empty% + \pgfdecoration{{#1}{\pgfdecoratedpathlength}{\pgfdecoratebeforecode}{\pgfdecorateaftercode}}% + \pgfsetpath\pgf@decorate@currentpath% + \endpgfdecoration}% + + + + +\def\pgfdecoration#1{% + \begingroup% + \def\pgf@decorate@decorationlist{#1}% + \pgf@decoration@env% +}% + +\def\endpgfdecoration{% + \pgf@decoration@endenv% + \ifx\pgfdecoratedpath\pgfutil@empty% + \else% + \pgf@decorate@for\pgf@temp:=\pgf@decorate@decorationlist\do{% + \ifx\pgf@temp\pgfutil@empty% + \else% + \expandafter\pgf@decorate@invoke\expandafter{\pgf@temp}% + \fi% + }% + \fi% + \pgfgetpath\pgfdecorationpath% + \global\let\pgf@decorate@decorationpathtemp\pgfdecorationpath% + \global\let\pgf@decorate@decoratedpathtemp\pgfdecoratedpath% + \global\let\pgf@decorate@existingpathtemp\pgfdecorateexistingpath% + \global\let\pgfpoint@decorated@pathlasttemp\pgfpoint@decorated@pathlast% + \endgroup% + \pgfutil@ifnextchar\@checkend{\aftergroup\pgf@decorate@installmacrosatend}% + {\pgf@decorate@installmacrosatend}% +}% + + + +\def\pgfmetadecoration#1{% + \begingroup% + \let\decoration\pgf@metadecoration@decoration% + \let\beforedecoration\pgf@metadecoration@beforedecoration% + \let\afterdecoration\pgf@metadecoration@afterdecoration% + \def\pgf@metadecoration@name{#1}% + \pgf@decoration@env% +}% + +\def\endpgfmetadecoration{% + \pgf@decoration@endenv% + \ifx\pgfdecoratedpath\pgfutil@empty% + \else% + \let\pgfmetadecoratedpathlength\pgf@decorate@totalpathlength% + \def\pgfmetadecoratedinputsegmentremainingdistance{\pgfdecoratedremainingdistance}% + \def\pgfmetadecoratedinputsegmentcompleteddistance{\pgfdecoratedcompleteddistance}% + \expandafter\let\expandafter\pgf@metadecoration@current@state% + \csname pgf@metadecoration@@\pgf@metadecoration@name @initial\endcsname% + \pgf@metadecoration@run% + \let\pgf@decorate@tempname\pgfutil@empty% + \let\pgf@decorate@tempbefore\pgfutil@empty% + \let\pgf@decorate@tempafter\pgfutil@empty% + \csname pgf@metadecoration@@\pgf@metadecoration@name @\pgf@metadecoration@current@state @code\endcsname% + \ifx\pgf@decorate@tempname\pgfutil@empty% + \def\pgf@decorate@tempname{moveto} + \fi% + \pgf@decorate@invoke{% + {\pgf@decorate@tempname}{\pgfdecoratedremainingdistance}% + {\pgf@decorate@tempbefore}{\pgf@decorate@tempafter}% + }% + \fi% + \pgfgetpath\pgfdecorationpath% + \global\let\pgf@decorate@decorationpathtemp\pgfdecorationpath% + \global\let\pgf@decorate@decoratedpathtemp\pgfdecoratedpath% + \global\let\pgf@decorate@existingpathtemp\pgfdecorateexistingpath% + \global\let\pgfpoint@decorated@pathlasttemp\pgfpoint@decorated@pathlast% + \endgroup% + \pgfutil@ifnextchar\@checkend{\aftergroup\pgf@decorate@installmacrosatend}% + {\pgf@decorate@installmacrosatend}% +}% + + + + + + +\def\pgf@decoration@env{% + \pgfgetpath\pgfdecorateexistingpath% + \pgfsetpath\pgfutil@empty% + \let\pgfdecorationpath\pgfutil@empty% + \let\pgfdecoratedpath\pgfutil@empty% + \let\pgfpoint@decorated@pathlast\pgfpointorigin% + \edef\pgfpoint@decorate@existingpathlast{\pgf@x\the\pgf@path@lastx\pgf@y\the\pgf@path@lasty}% + \bgroup% +}% + +\def\pgf@decorate@path@check@moveto#1{% + \expandafter\pgf@decorate@path@@check@moveto#1\pgf@decorate@stop\pgf@decorate@@stop}% + +\def\pgf@decorate@token@stop{\pgf@decorate@stop}% +\def\pgf@decorate@path@@check@moveto#1#2#3#4\pgf@decorate@@stop#5#6{% + \def\pgf@decorate@temp{#4}% + \pgf@x=#2\relax% + \pgf@y=#3\relax% + \ifx\pgf@decorate@temp\pgf@decorate@token@stop% + #5% + \else% + #6% + \fi% +}% + +\def\pgf@decoration@endenv{% + \egroup% + \pgftransformreset% + \pgfgetpath\pgfdecoratedpath% + \pgfsetpath\pgfdecorateexistingpath% + \ifx\pgfdecoratedpath\pgfutil@empty% + \pgferror{I cannot decorate an empty path}% + \else% + \pgf@decorate@path@check@moveto\pgfdecoratedpath{% + \advance\pgf@x by0.0001pt\relax% + \edef\pgfdecoratedpath{% + \expandafter\noexpand\pgfdecoratedpath% + \noexpand\pgfsyssoftpath@linetotoken{\the\pgf@x}{\the\pgf@y}% + }% + }% + {}% + \pgfprocessround{\pgfdecoratedpath}{\pgfdecoratedpath}% + \pgf@decorate@parsesoftpath{\pgfdecoratedpath}{\pgf@decorate@inputsegmentobjects}% + \pgfkeys{/pgf/every decoration/.try}% + \ifpgf@decorate@inputsegmentobjects@reverse% + \pgf@decorate@inputsegmentobjects@reverse{\pgf@decorate@inputsegmentobjects}{\pgf@decorate@inputsegmentobjects}% + \fi% + \let\pgf@decorated@remainingdistance\pgf@decorate@totalpathlength% + \let\pgfpoint@decorated@totalpathfirst\pgfpoint@decorated@firstparsed% + \let\pgfpoint@decorated@totalpathlast\pgfpoint@decorate@lastnonmovetoparsed% + \let\pgfpoint@decorated@pathfirst\pgfpoint@decorated@totalpathfirst + \let\pgfpoint@decorated@pathlast\pgfpoint@decorated@totalpathlast% + \let\pgf@decorate@currentinputsegmentobjects\pgf@decorate@inputsegmentobjects% + \let\pgf@decorate@transformtoinputsegment\pgfutil@empty% + \pgf@decorate@getnextinputsegmentobject\pgf@decorate@nextinputsegmentobject% + \pgf@decorate@processnextinputsegmentobject% + \pgf@decorate@distancetomove0pt\relax% + \fi% +}% + + + + +\def\pgf@decorate@installmacrosatend{% + \let\pgfdecorationpath\pgf@decorate@decorationpathtemp% + \let\pgfdecoratedpath\pgf@decorate@decoratedpathtemp% + \let\pgfdecorateexistingpath\pgf@decorate@existingpathtemp% + \let\pgfpoint@decorated@pathlast\pgfpoint@decorated@pathlasttemp% +}% + +\let\pgfdecorationpath\pgfutil@empty +\let\pgfdecoratedpath\pgfutil@empty +\let\pgfdecorateexisitingpath\pgfutil@empty + +\let\pgfpoint@decorated@pathlast\pgfpointorigin + + + +\def\pgf@decorate@for#1:=#2\do#3{% + \def\pgf@decorate@for@var{#1}% + \def\pgf@decorate@for@action{#3}% + \expandafter\pgf@decorate@@for#2,\pgf@stop,}% + +\def\pgf@decorate@@for#1,{% + \ifx#1\pgf@stop% + \expandafter\let\pgf@decorate@for@var\pgfutil@empty% + \else% + \expandafter\def\pgf@decorate@for@var{#1}% + \pgf@decorate@for@action% + \expandafter\pgf@decorate@@for% + \fi% +}% + + +\def\pgf@decorate@invoke#1{% + \pgf@decorate@@invoke#1\pgf@decorate@invoke\pgf@decorate@invoke\pgf@decorate@invoke\pgf@stop}% + +\def\pgf@decorate@@invoke#1#2#3#4#5\pgf@stop{% + \pgfutil@ifundefined{pgf@decorate@@#1@initial}% + {% + \pgferror{Unknown decoration `#1'}% + }% + {% + \def\pgf@decorate@name{#1}% + \ifx\pgf@decorate@invoke#3% + \let\pgf@decorate@beforecode\pgfutil@empty% + \else% + \def\pgf@decorate@beforecode{#3}% + \fi% + \ifx\pgf@decorate@invoke#4% + \let\pgf@decorate@aftercode\pgfutil@empty% + \else% + \def\pgf@decorate@aftercode{#4}% + \fi% + \pgfdecoratedremainingdistance\pgf@decorated@remainingdistance\relax% + \let\pgfdecoratedpathlength\pgf@decorate@totalpathlength% + \pgfmathsetlength\pgf@xa{#2}% + \ifdim\pgf@xa>\pgf@decorated@remainingdistance\relax% + \pgf@xa\pgf@decorated@remainingdistance\relax% + \fi% + \edef\pgf@decorate@currentpathlength{\the\pgf@xa}% + \pgf@xa-\pgf@decorate@currentpathlength\relax% + \advance\pgf@xa\pgf@decorated@remainingdistance\relax% + \edef\pgf@decorated@remainingdistance{\the\pgf@xa}% + \let\pgfdecoratedpathlength\pgf@decorate@currentpathlength% + \pgfdecoratedremainingdistance\pgfdecoratedpathlength\relax% + \pgfdecoratedcompleteddistance0pt\relax% + \pgf@decorate@beforecode% + \expandafter\let\expandafter\pgf@decorate@current@state% + \csname pgf@decorate@@\pgf@decorate@name @initial\endcsname% + \pgf@decorate@run% + \ifdim\pgf@decorated@remainingdistance<1pt\relax% + \let\pgfpoint@decorated@pathlast\pgfpoint@decorated@totalpathlast% + \else% + {% + \pgf@decorate@movealonginputsegment{\the\pgfdecoratedremainingdistance}% + \pgf@decorate@transformtoinputsegment% + \pgfpointorigin% + \pgf@pos@transform@glob% + \global\pgf@x\pgf@x% + \global\pgf@y\pgf@y% + }% + \edef\pgfpoint@decorated@pathlast{\pgf@x\the\pgf@x\pgf@y\the\pgf@y}% + \fi% + {% + \pgftransformreset% + \pgf@decorate@transformtoinputsegment% + \pgf@decorate@additionaltransform% + \csname pgf@decorate@@\pgf@decorate@name @final@code\endcsname% + }% + \pgf@decorate@movealonginputsegment{\the\pgfdecoratedremainingdistance}% + \pgf@decorate@aftercode% + \let\pgf@decorate@additionaltransform\pgfutil@empty% + \let\pgf@decorate@inputsegmentobjects\pgf@decorate@inputsegmentobjects@aftersplit% + \let\pgfpoint@decorated@pathfirst\pgfpoint@decorated@pathlast% + }% +}% + + + +\let\pgf@decorate@transformtoinputsegment\pgfutil@empty% +\let\pgf@decorate@additionaltransform\pgfutil@empty% + + +\def\pgfpointdecoratedpathfirst{% + {% + \pgftransforminvert% + \pgfpoint@decorated@pathfirst% + \pgf@pos@transform@glob% + \global\pgf@x\pgf@x% + \global\pgf@y\pgf@y% + }% +}% + +\def\pgfpointdecoratedpathlast{% + {% + \pgftransforminvert% + \pgfpoint@decorated@pathlast% + \pgf@pos@transform@glob% + \global\pgf@x\pgf@x% + \global\pgf@y\pgf@y% + }% +}% + +\def\pgfpointdecoratedinputsegmentfirst{% + {% + \pgftransforminvert% + \pgf@decorate@inputsegment@first% + \pgf@pos@transform@glob% + \global\pgf@x\pgf@x% + \global\pgf@y\pgf@y% + }% +}% + +\def\pgfpointdecoratedinputsegmentlast{% + {% + \pgftransforminvert% + \pgf@decorate@inputsegment@last% + \pgf@pos@transform@glob% + \global\pgf@x\pgf@x% + \global\pgf@y\pgf@y% + }% +}% + + +\def\pgf@final@text{final}% + +\def\pgf@decorate@run{% + \let\pgf@decorate@next\pgf@decorate@do@state% + \ifx\pgf@decorate@current@state\pgf@final@text% + \let\pgf@decorate@next\relax% + \fi% + \pgf@decorate@next% +}% + +\def\pgf@decorate@do@state{% + \let\pgf@decorate@next\relax% + \let\pgf@decorate@next@state\pgf@decorate@current@state% + \let\pgf@decorate@persistent@pre=\relax% + \let\pgf@decorate@persistent@post=\relax% + \expandafter\expandafter\expandafter\pgf@decorate@setter + \expandafter\expandafter\expandafter{\csname pgf@decorate@@\pgf@decorate@name @\pgf@decorate@current@state @options\endcsname}% + \ifx\pgf@decorate@next\relax% + \let\pgf@decorate@next\pgf@decorate@do@code% + \fi% + \pgf@decorate@next% +}% + +\def\pgf@decorate@setter{\pgfqkeys{/pgf/decoration automaton}}% + +\pgf@decorate@repeatstate-1\relax + +\def\pgf@decorate@do@code{% + \pgf@decorate@persistent@pre% + {% + \pgftransformreset% + \pgf@decorate@transformtoinputsegment% + \pgf@decorate@additionaltransform% + \csname pgf@decorate@@\pgf@decorate@name @\pgf@decorate@current@state @code\endcsname% + }% + \pgf@decorate@persistent@post% + \pgf@decorate@movealongpath{\pgf@decorate@width}% + \ifnum\pgf@decorate@repeatstate>0\relax% + \advance\pgf@decorate@repeatstate-1\relax% + \else% + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@current@state\pgf@decorate@next@state% + \fi% + \pgf@decorate@run% +}% + +\pgfkeys{ + /pgf/decoration automaton/width/.code=\def\pgf@decorate@width{#1}\pgf@decorate@switch@if#1 to final\pgf@stop,% + /pgf/decoration automaton/switch if less than/.code=\pgf@decorate@switch@if#1\pgf@stop,% + /pgf/decoration automaton/switch if input segment less than/.code=\pgf@decorate@switch@ifinputsegment#1\pgf@stop,% + /pgf/decoration automaton/next state/.store in=\pgf@decorate@next@state,% + /pgf/decoration automaton/persistent precomputation/.store in=\pgf@decorate@persistent@pre,% + /pgf/decoration automaton/persistent postcomputation/.store in=\pgf@decorate@persistent@post,% + /pgf/decoration automaton/repeat state/.code={% + \ifnum\pgf@decorate@repeatstate=-1\relax% + \pgfmathsetcount\pgf@decorate@repeatstate{#1}% + \fi% + },% + /pgf/decoration automaton/if input segment is closepath/.code={% + \ifpgf@decorate@is@closepath@% + \pgfkeysalso{#1}% + \fi% + }, + /pgf/decoration automaton/auto end on length/.code=\pgf@decorate@auto@end{#1}, + /pgf/decoration automaton/auto corner on length/.code=\pgf@decorate@auto@corner{#1}, +}% + +\def\pgf@decorate@auto@end#1{% + \ifx\pgf@decorate@next\relax% + \pgfmathsetlength\pgf@x{#1}% + \ifpgf@decorate@is@closepath@% + \ifdim\pgfdecoratedremainingdistance>\pgf@x% + \ifdim\pgfdecoratedinputsegmentremainingdistance>\pgf@x% + \else% + \pgfpathclose% + \pgf@decorate@movealongpath{\pgfdecoratedinputsegmentremainingdistance}% + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \fi% + \else% + \pgfpathclose% + \def\pgf@decorate@current@state{final}% + \def\pgf@decorate@width{\pgfdecoratedremainingdistance} + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \fi% + \else% + \ifdim\pgfdecoratedremainingdistance>\pgf@x% + \else% + {% + \pgftransformreset% + \pgf@decorate@transformtoinputsegment% + \pgf@decorate@additionaltransform% + \pgfpathlineto{\pgfpoint{\pgfdecoratedremainingdistance}{0pt}} + }% + \def\pgf@decorate@current@state{final}% + \def\pgf@decorate@width{\pgfdecoratedremainingdistance} + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \fi% + \fi% + \fi% +}% + +\def\pgf@decorate@auto@corner#1{% + \ifpgfdecoratepathhascorners% + \ifx\pgf@decorate@next\relax% + \pgfmathsetlength\pgf@x{#1}% + \ifdim\pgfdecoratedinputsegmentremainingdistance>\pgf@x% + \else% + {% + \pgftransformreset% + \pgf@decorate@transformtoinputsegment% + \pgf@decorate@additionaltransform% + \pgfpathlineto{\pgfqpoint{\pgfdecoratedinputsegmentremainingdistance}{0pt}} + }% + \pgf@decorate@movealongpath{\pgfdecoratedinputsegmentremainingdistance}% + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \fi% + \fi% + \fi% +}% + +\def\pgf@decorate@switch@if#1to #2\pgf@stop{% + \ifx\pgf@decorate@next\relax% + \ifdim\pgfdecoratedremainingdistance=0pt\relax% + \def\pgf@decorate@current@state{#2}% + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \else% + \pgfmathsetlength\pgf@x{#1}% + \ifdim\pgfdecoratedremainingdistance<\pgf@x% + \def\pgf@decorate@current@state{#2}% + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \fi% + \fi% + \fi% +}% + +\def\pgf@decorate@switch@ifinputsegment#1to #2\pgf@stop{% + \ifx\pgf@decorate@next\relax% + \pgfmathsetlength\pgf@x{#1}% + \ifdim\pgfdecoratedinputsegmentremainingdistance<\pgf@x% + \def\pgf@decorate@current@state{#2}% + \pgf@decorate@repeatstate-1\relax% + \let\pgf@decorate@next\pgf@decorate@run% + \fi% + \fi% +}% + + + + +\def\pgfsetdecorationsegmenttransformation#1{\def\pgf@decorate@additionaltransform{#1}}% +\let\pgf@decorate@additionaltransform\pgfutil@empty% + + + + +\def\pgf@metadecoration@decoration#1{% + \edef\pgf@decorate@tempname{#1}% +}% +\def\pgf@metadecoration@beforedecoration#1{% + \def\pgf@decorate@tempbefore{#1}% +}% +\def\pgf@metadecoration@afterdecoration#1{% + \def\pgf@decorate@tempafter{#1}% +}% + + +\def\pgf@final@text{final}% + +\def\pgf@metadecoration@run{% + \let\pgf@metadecoration@next\pgf@metadecoration@do@state% + \ifx\pgf@metadecoration@current@state\pgf@final@text% + \let\pgf@metadecoration@next\relax% + \fi% + \pgf@metadecoration@next% +}% + +\def\pgf@metadecoration@do@state{% + \let\pgf@metadecoration@next\relax% + \let\pgf@metadecoration@next@state\pgf@metadecoration@current@state% + \let\pgfmetadecoratedremainingdistance\pgf@decorated@remainingdistance% + \pgf@x-\pgfmetadecoratedremainingdistance\relax% + \advance\pgf@x\pgf@decorate@totalpathlength\relax% + \edef\pgfmetadecoratedcompleteddistance{\the\pgf@x}% + \expandafter\expandafter\expandafter\pgf@metadecoration@setter + \expandafter\expandafter\expandafter{\csname pgf@metadecoration@@\pgf@metadecoration@name @\pgf@metadecoration@current@state @options\endcsname}% + \ifx\pgf@metadecoration@next\relax% + \let\pgf@metadecoration@next\pgf@metadecoration@do@code% + \fi% + \pgf@metadecoration@next% +}% + +\def\pgf@metadecoration@do@code{% + \let\pgf@decorate@tempname\pgfutil@empty% + \let\pgf@decorate@tempbefore\pgfutil@empty% + \let\pgf@decorate@tempafter\pgfutil@empty% + \let\pgfpointmetadecoratedpathfirst\pgfpointdecoratedpathfirst% + \let\pgfpointmetadecoratedpathlast\pgfpointdecoratedpathlast% + \csname pgf@metadecoration@@\pgf@metadecoration@name @\pgf@metadecoration@current@state @code\endcsname% + \ifx\pgf@decorate@tempname\pgfutil@empty% + \def\pgf@decorate@tempname{moveto} + \fi% + \pgf@decorate@invoke{% + {\pgf@decorate@tempname}{\pgf@metadecoration@width}% + {\pgf@decorate@tempbefore}{\pgf@decorate@tempafter}% + }% + \let\pgf@metadecoration@current@state\pgf@metadecoration@next@state% + \pgf@metadecoration@run% +}% + +\def\pgf@metadecoration@setter{\pgfqkeys{/pgf/meta-decoration automaton}}% + +\pgfkeys{ + /pgf/meta-decoration automaton/width/.code=\def\pgf@metadecoration@width{#1}\pgf@metadecoration@switch@if#1 to final\pgf@stop,% + /pgf/meta-decoration automaton/switch if less than/.code=\pgf@metadecoration@switch@if#1\pgf@stop,% + /pgf/meta-decoration automaton/switch if input segment less than/.code=\pgf@metadecoration@switch@ifinputsegment#1\pgf@stop,% + /pgf/meta-decoration automaton/next state/.store in=\pgf@metadecoration@next@state,% +}% + +\def\pgf@metadecoration@switch@if#1to #2\pgf@stop{% + \ifx\pgf@metadecoration@next\relax% + \pgfmathsetlength\pgf@x{#1}% + \ifdim\pgf@decorated@remainingdistance<\pgf@x% + \def\pgf@metadecoration@current@state{#2}% + \let\pgf@metadecoration@next\pgf@metadecoration@run% + \fi% + \fi% +}% + +\def\pgf@metadecoration@switch@ifinputsegment#1to #2\pgf@stop{% + \ifx\pgf@metadecoration@next\relax% + \pgfmathsetlength\pgf@x{#1}% + \ifdim\pgfdecoratedinputsegmentremainingdistance<\pgf@x% + \def\pgf@metadecoration@current@state{#2}% + \let\pgf@metadecoration@next\pgf@metadecoration@run% + \fi% + \fi% +}% + + + +\def\pgf@decorate@movealongpath#1{% + \pgfmathsetlength\pgf@decorate@distancetomove{#1}% + \advance\pgfdecoratedcompleteddistance\pgf@decorate@distancetomove% + \advance\pgfdecoratedremainingdistance-\pgf@decorate@distancetomove% + \pgf@decorate@@movealongpath% +}% +\def\pgf@decorate@@movealongpath{% + \advance\pgfdecoratedinputsegmentcompleteddistance\pgf@decorate@distancetomove% + \advance\pgfdecoratedinputsegmentremainingdistance-\pgf@decorate@distancetomove% + \ifdim\pgfdecoratedinputsegmentremainingdistance>0pt\relax% + \let\pgf@next\pgf@decorate@@@movealongpath% + \else% + \pgf@decorate@distancetomove-\pgfdecoratedinputsegmentremainingdistance% + \pgf@decorate@processnextinputsegmentobject% + \ifx\pgf@decorate@currentinputsegmentobjects\pgfutil@empty% + \pgfdecoratedremainingdistance0pt\relax% + \let\pgf@next\relax% + \else% + \let\pgf@next\pgf@decorate@@movealongpath% + \fi% + \fi% + \pgf@next% +}% + +\def\pgf@decorate@@@movealongpath{% + \pgf@decorate@movealonginputsegment{\the\pgf@decorate@distancetomove}% + \pgf@decorate@distancetomove0pt\relax% + \ifdim\pgf@decorate@inputsegmenttime pt>1pt\relax% + \let\pgf@decorate@inputsegmenttimetemp\pgf@decorate@inputsegmenttime% + \pgf@decorate@processnextinputsegmentobject% + \pgf@x\pgf@decorate@inputsegmenttimetemp pt\relax% + \advance\pgf@x-1pt\relax% + \edef\pgf@decorate@inputsegmenttime{\pgfmath@tonumber{\pgf@x}}% + \ifx\pgf@decorate@currentinputsegmentobjects\pgfutil@empty% + \pgfdecoratedremainingdistance0pt\relax% + \fi% + \fi% +}% + +\def\pgf@decorate@getnextinputsegmentobject#1{% + \ifx\pgf@decorate@currentinputsegmentobjects\pgfutil@empty% + \let\pgf@next\relax% + \else% + \def\pgf@decorate@temp{#1}% + \let\pgf@next\pgf@decorate@@getnextinputsegmentobject% + \fi% + \pgf@next% +}% +\def\pgf@decorate@@getnextinputsegmentobject{% + \expandafter\pgf@decorate@@@getnextinputsegmentobject\pgf@decorate@currentinputsegmentobjects\pgf@stop}% +\def\pgf@decorate@@@getnextinputsegmentobject#1#2\pgf@stop{% + \expandafter\def\pgf@decorate@temp{#1}% + \def\pgf@decorate@currentinputsegmentobjects{#2}}% + +\def\pgf@decorate@processnextinputsegmentobject{% + \let\pgfdecorationpreviousinputsegment\pgfdecoratecurrentinputsegment% + \let\pgf@decorate@currentinputsegmentobject\pgf@decorate@nextinputsegmentobject% + \pgf@decorate@getnextinputsegmentobject\pgf@decorate@nextinputsegmentobject% + \pgf@decorate@is@closepath@false% + \pgf@decorate@currentinputsegmentobject% + \ifx\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentmoveto% + \pgfpathmoveto{\pgf@decorate@inputsegment@first}% + \let\pgfdecorationpreviousinputsegment\pgfdecorationcurrentinputsegment% + \let\pgf@decorate@currentinputsegmentobject\pgf@decorate@nextinputsegmentobject% + \pgf@decorate@getnextinputsegmentobject\pgf@decorate@nextinputsegmentobject% + \pgf@decorate@is@closepath@false% + \pgf@decorate@currentinputsegmentobject% + \fi% + \ifdim\pgfdecoratedinputsegmentlength=0pt\relax% + \def\pgfdecoratedinputsegmentlength{0.05pt}% + \fi% + \pgfdecoratedinputsegmentremainingdistance\pgfdecoratedinputsegmentlength\relax% + \pgfdecoratedinputsegmentcompleteddistance0pt\relax% + \def\pgf@decorate@inputsegmenttime{0}% + \ifx\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentcurveto% + \pgfmathanglebetweenpoints{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@supporta}% + \let\pgfdecoratedangle\pgfmathresult% + \let\pgfdecoratedinputsegmentstartangle\pgfmathresult% + \pgfmathanglebetweenpoints{\pgf@decorate@inputsegment@supportb}{\pgf@decorate@inputsegment@last}% + \let\pgfdecoratedinputsegmentendangle\pgfmathresult% + \else% + \pgfmathanglebetweenpoints{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@last}% + \let\pgfdecoratedangle\pgfmathresult% + \let\pgfdecoratedinputsegmentstartangle\pgfmathresult% + \let\pgfdecoratedinputsegmentendangle\pgfmathresult% + \fi% + \begingroup% + \pgf@decorate@nextinputsegmentobject% + \global\let\pgf@decorate@temp\pgfdecorationcurrentinputsegment% + \ifx\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentmoveto% + \expandafter\pgf@decorate@currentinputsegmentobject% + \fi% + \ifx\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentcurveto% + \pgfmathanglebetweenpoints{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@supporta}% + \else% + \pgfmathanglebetweenpoints{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@last}% + \fi% + \pgf@x-\pgfdecoratedangle pt\relax% + \advance\pgf@x\pgfmathresult pt\relax% + \edef\pgfdecoratedangletonextinputsegment{\the\pgf@x}% + \pgfmath@smuggleone\pgfdecoratedangletonextinputsegment% + \endgroup% + \let\pgfdecorationnextinputsegmentobject\pgf@decorate@temp% +}% + + + +\newif\ifpgf@decorate@is@closepath@% + +\def\pgfdecorationinputsegmentmoveto{moveto}% +\def\pgfdecorationinputsegmentlineto{lineto}% +\def\pgfdecorationinputsegmentcurveto{curveto}% +\def\pgfdecorationinputsegmentclosepath{closepath}% +\def\pgfdecorationinputsegmentlast{last}% + +\def\pgf@decorate@inputsegmentobject@moveto#1{% + \def\pgf@decorate@inputsegment@first{#1}% + \def\pgf@decorate@inputsegment@supporta{#1}% + \def\pgf@decorate@inputsegment@supportb{#1}% + \def\pgf@decorate@inputsegment@last{#1}% + \edef\pgf@decorate@lastmoveto{#1}% + \def\pgfdecoratedinputsegmentlength{0pt}% + \let\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentmoveto% +}% + +\def\pgf@decorate@inputsegmentobject@lineto#1#2#3{% + \def\pgfdecoratedinputsegmentlength{#1}% + \def\pgf@decorate@inputsegment@first{#2}% + \def\pgf@decorate@inputsegment@last{#3}% + \pgfpointdiff{#2}{#3}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfextract@process\pgf@decorate@inputsegment@supporta{% + \pgf@process{#2}% + \advance\pgf@x0.333333\pgf@xa% + \advance\pgf@y0.333333\pgf@ya% + }% + \pgfextract@process\pgf@decorate@inputsegment@supportb{% + \pgf@process{#2}% + \advance\pgf@x0.666666\pgf@xa% + \advance\pgf@y0.666666\pgf@ya% + }% + \let\pgf@decorate@movealonginputsegment\pgf@decorate@movealonginputsegment@line% + \let\pgf@decorate@transformtoinputsegment\pgf@decorate@transformtoinputsegment@line% + \let\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentlineto% +}% + +\def\pgf@decorate@inputsegmentobject@curveto#1#2#3#4#5{% + \def\pgfdecoratedinputsegmentlength{#1}% + \def\pgf@decorate@inputsegment@first{#2}% + \def\pgf@decorate@inputsegment@supporta{#3}% + \def\pgf@decorate@inputsegment@supportb{#4}% + \def\pgf@decorate@inputsegment@last{#5}% + \let\pgf@decorate@movealonginputsegment\pgf@decorate@movealonginputsegment@curve% + \let\pgf@decorate@transformtoinputsegment\pgf@decorate@transformtoinputsegment@curve% + \let\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentcurveto% +}% + +\def\pgf@decorate@inputsegmentobject@closepath#1#2#3{% + \pgf@decorate@is@closepath@true% + \def\pgfdecoratedinputsegmentlength{#1}% + \def\pgf@decorate@inputsegment@first{#2}% + \def\pgf@decorate@inputsegment@last{#3}% + \pgfpointdiff{#2}{#3}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgfextract@process\pgf@decorate@inputsegment@supporta{% + \pgf@process{#2}% + \advance\pgf@x0.333333\pgf@xa% + \advance\pgf@y0.333333\pgf@ya% + }% + \pgfextract@process\pgf@decorate@inputsegment@supportb{% + \pgf@process{#2}% + \advance\pgf@x0.666666\pgf@xa% + \advance\pgf@y0.666666\pgf@ya% + }% + \let\pgf@decorate@movealonginputsegment\pgf@decorate@movealonginputsegment@line% + \let\pgf@decorate@transformtoinputsegment\pgf@decorate@transformtoinputsegment@line% + \let\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentclosepath% +}% + + +\def\pgf@decorate@inputsegmentobject@endofinputsegments{% + \let\pgfdecorationcurrentinputsegment\pgfdecorationinputsegmentlast% +}% + + + + +\def\pgf@decorate@movealonginputsegment@line#1{}% + +\def\pgf@decorate@movealonginputsegment@curve#1{% + \ifdim#1=0pt\relax% + \else% + \pgfpointcurveattime{\pgf@decorate@inputsegmenttime}% + {\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@supporta}% + {\pgf@decorate@inputsegment@supportb}{\pgf@decorate@inputsegment@last}% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \pgf@xb\pgf@decorate@inputsegmenttime pt\relax% + \ifdim\pgf@decorate@currentpathlength<128pt\relax% + \pgf@yb.03125pt\relax% + \else% + \ifdim\pgf@decorate@currentpathlength<512pt\relax% + \pgf@yb.015625pt\relax% + \else% + \ifdim\pgf@decorate@currentpathlength<2048pt\relax% + \pgf@yb.00390625pt\relax% + \else% + \pgf@yb.0009765625pt\relax% + \fi% + \fi% + \fi% + \c@pgf@counta1\relax% + \pgfutil@tempdima0pt\relax% + \pgfmathloop% + \advance\pgf@xb\c@pgf@counta\pgf@yb% + \edef\pgf@decorate@temp{% + \pgf@xa\the\pgf@xa% + \pgf@xb\the\pgf@xb% + \pgf@ya\the\pgf@ya% + \pgf@yb\the\pgf@yb% + }% + \pgfpoint@decorate@curveattime{\pgfmath@tonumber{\pgf@xb}}% + {\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@supporta}% + {\pgf@decorate@inputsegment@supportb}{\pgf@decorate@inputsegment@last}% + \pgf@decorate@temp% + \pgf@xc\pgf@xa% + \pgf@yc\pgf@ya% + \pgf@xa\pgf@x% + \pgf@ya\pgf@y% + \advance\pgf@x-\pgf@xc% + \advance\pgf@y-\pgf@yc% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \pgfutil@tempdimb\pgfmathresult pt\relax% + \advance\pgfutil@tempdima\c@pgf@counta\pgfutil@tempdimb% + \ifnum\c@pgf@counta>0\relax% + \ifdim\pgfutil@tempdima>#1\relax% + \c@pgf@counta-\c@pgf@counta% + \pgf@yb.5\pgf@yb% + \fi% + \else% + \ifdim\pgfutil@tempdima<#1\relax% + \c@pgf@counta-\c@pgf@counta% + \pgf@yb.5\pgf@yb% + \fi% + \fi% + \ifdim\pgf@yb=0pt\relax% + \else% + \repeatpgfmathloop% + \edef\pgf@decorate@inputsegmenttime{\pgfmath@tonumber{\pgf@xb}}% + \pgfpointcurveattime{\pgf@decorate@inputsegmenttime}% + {\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@supporta}% + {\pgf@decorate@inputsegment@supportb}{\pgf@decorate@inputsegment@last}% + \edef\pgf@marshal{% + \noexpand\pgfmathanglebetweenpoints% + {\pgf@x\the\pgf@xb\pgf@y\the\pgf@yb}% + {\pgf@x\the\pgf@xa\pgf@y\the\pgf@ya}% + }% + \pgf@marshal% + \let\pgfdecoratedangle\pgfmathresult% + \fi% +}% + +\def\pgfpoint@decorate@curveattime#1#2#3#4#5{% + \edef\pgf@time@s{#1}% + \pgf@x-\pgf@time@s pt\relax% + \advance\pgf@x1pt\relax% + \edef\pgf@time@t{\pgf@sys@tonumber{\pgf@x}}% + #5\relax% + \pgf@xc=\pgf@x% + \pgf@yc=\pgf@y% + #4\relax% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + #3\relax% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + #2\relax% + \pgf@x=\pgf@time@t\pgf@x\advance\pgf@x by\pgf@time@s\pgf@xa% + \pgf@y=\pgf@time@t\pgf@y\advance\pgf@y by\pgf@time@s\pgf@ya% + \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb% + \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb% + \pgf@xb=\pgf@time@t\pgf@xb\advance\pgf@xb by\pgf@time@s\pgf@xc% + \pgf@yb=\pgf@time@t\pgf@yb\advance\pgf@yb by\pgf@time@s\pgf@yc% + \pgf@x=\pgf@time@t\pgf@x\advance\pgf@x by\pgf@time@s\pgf@xa% + \pgf@y=\pgf@time@t\pgf@y\advance\pgf@y by\pgf@time@s\pgf@ya% + \pgf@xa=\pgf@time@t\pgf@xa\advance\pgf@xa by\pgf@time@s\pgf@xb% + \pgf@ya=\pgf@time@t\pgf@ya\advance\pgf@ya by\pgf@time@s\pgf@yb% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgf@x=\pgf@time@t\pgf@x\advance\pgf@x by\pgf@time@s\pgf@xa% + \pgf@y=\pgf@time@t\pgf@y\advance\pgf@y by\pgf@time@s\pgf@ya% +}% + + +\def\pgf@decorate@transformtoinputsegment@line{% + \pgftransformshift{% + \pgfpointlineatdistance{\pgfdecoratedinputsegmentcompleteddistance}{\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@last} + }% + \pgftransformrotate{\pgfdecoratedangle}% +}% + +\def\pgf@decorate@transformtoinputsegment@curve{% + \pgfslopedattimetrue% + \pgfallowupsidedownattimetrue% + \pgftransformcurveattime{\pgf@decorate@inputsegmenttime}% + {\pgf@decorate@inputsegment@first}{\pgf@decorate@inputsegment@supporta}% + {\pgf@decorate@inputsegment@supportb}{\pgf@decorate@inputsegment@last}% +}% + + + + + + +\def\pgf@decorate@parsesoftpath#1#2{% + \def\pgf@decorate@inputsegmentobjectsmacro{#2}% + \let\pgf@decorate@inputsegmentobjects\pgfutil@empty% + \pgfutil@tempdima0pt\relax% + \let\pgfpoint@decorate@lastparsed\pgfpoint@decorate@existingpathlast% + \let\pgfpoint@decorate@lastnonmovetoparsed\pgfpoint@origin% + \let\pgf@decorate@queueinputsegmentobject\pgfutil@empty% + \let\pgfpoint@decorated@firstparsed\pgfutil@empty% + \expandafter\pgf@decorate@@parsesoftpath#1\pgf@stop% +}% + +\def\pgf@decorate@@parsesoftpath#1{% + \ifx#1\pgf@stop% + \let\pgf@decorate@queueinputsegmentobject\pgfutil@empty% + \pgf@decorate@addtoinputsegmentobjects{\pgf@decorate@inputsegmentobject@endofinputsegments}% + \pgf@decorate@addtoinputsegmentobjects{\pgf@decorate@inputsegmentobject@endofinputsegments}% + \expandafter\let\pgf@decorate@inputsegmentobjectsmacro\pgf@decorate@inputsegmentobjects% + \edef\pgf@decorate@totalpathlength{\the\pgfutil@tempdima}% + \let\pgf@next\relax% + \else% + \ifx#1\pgfsyssoftpath@movetotoken% + \let\pgf@next\pgf@decorate@parsemoveto% + \else% + \ifx#1\pgfsyssoftpath@linetotoken% + \let\pgf@next\pgf@decorate@parselineto% + \else% + \ifx#1\pgfsyssoftpath@curvetosupportatoken% + \let\pgf@next\pgf@decorate@parsecurveto% + \else% + \ifx#1\pgfsyssoftpath@closepathtoken% + \let\pgf@next\pgf@decorate@parseclosepath% + \else% + \ifx#1\pgfsyssoftpath@rectcornertoken% + \let\pgf@next\pgf@decorate@parserect% + \else% + \pgferror{Unrecognised soft path token `#1'}% + \fi% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgf@next}% + + +\def\pgf@decorate@addtoinputsegmentobjects#1{% + \ifx\pgf@decorate@queueinputsegmentobject\pgfutil@empty% + \else% + \let\pgf@decorate@temp\pgf@decorate@queueinputsegmentobject% + \let\pgf@decorate@queueinputsegmentobject\pgfutil@empty% + \expandafter\pgf@decorate@addtoinputsegmentobjects\expandafter{\pgf@decorate@temp}% + \fi% + \ifx\pgfpoint@decorated@firstparsed\pgfutil@empty% + #1% + \let\pgfpoint@decorated@firstparsed\pgf@decorate@inputsegment@first% + \fi% + \expandafter\def\expandafter\pgf@decorate@inputsegmentobjects\expandafter% + {\pgf@decorate@inputsegmentobjects{#1}}% +}% + +\def\pgf@decorate@parsemoveto#1#2{% + \def\pgf@decorate@queueinputsegmentobject{\pgf@decorate@inputsegmentobject@moveto{\pgf@x#1\pgf@y#2}}% + \def\pgfpoint@decorate@lastparsed{\pgf@x#1\pgf@y#2}% + \pgf@decorate@@parsesoftpath% +}% + +\def\pgf@decorate@parselineto#1#2{% + \pgf@decorate@linelength{\pgfpoint@decorate@lastparsed}{\pgf@x#1\pgf@y#2}% + \advance\pgfutil@tempdima\pgfmathresult pt\relax% + \edef\pgf@decorate@temp{% + \noexpand\pgf@decorate@inputsegmentobject@lineto{\pgfmathresult pt}{\pgfpoint@decorate@lastparsed}{\pgf@x#1\pgf@y#2}% + }% + \edef\pgfpoint@decorate@lastparsed{\pgf@x#1\pgf@y#2}% + \let\pgfpoint@decorate@lastnonmovetoparsed\pgfpoint@decorate@lastparsed% + \expandafter\pgf@decorate@addtoinputsegmentobjects\expandafter{\pgf@decorate@temp}% + \pgf@decorate@@parsesoftpath% +}% + +\def\pgf@decorate@parsecurveto#1#2\pgfsyssoftpath@curvetosupportbtoken#3#4\pgfsyssoftpath@curvetotoken#5#6{% + \pgf@decorate@curvelength{\pgfpoint@decorate@lastparsed}{\pgf@x#1\pgf@y#2}{\pgf@x#3\pgf@y#4}{\pgf@x#5\pgf@y#6}% + \advance\pgfutil@tempdima\pgfmathresult pt\relax% + \edef\pgf@decorate@temp{% + \noexpand\pgf@decorate@inputsegmentobject@curveto{\pgfmathresult pt}{\pgfpoint@decorate@lastparsed}% + {\pgf@x#1\pgf@y#2}{\pgf@x#3\pgf@y#4}{\pgf@x#5\pgf@y#6}% + }% + \expandafter\pgf@decorate@addtoinputsegmentobjects\expandafter{\pgf@decorate@temp}% + \edef\pgfpoint@decorate@lastparsed{\pgf@x#5\pgf@y#6}% + \let\pgfpoint@decorate@lastnonmovetoparsed\pgfpoint@decorate@lastparsed% + \pgf@decorate@@parsesoftpath% +}% + + +\def\pgf@decorate@parseclosepath#1#2{% + \pgf@decorate@linelength{\pgfpoint@decorate@lastparsed}{\pgf@x#1\pgf@y#2}% + \advance\pgfutil@tempdima\pgfmathresult pt\relax% + \edef\pgf@decorate@temp{% + \noexpand\pgf@decorate@inputsegmentobject@closepath{\pgfmathresult pt}{\pgfpoint@decorate@lastparsed}{\pgf@x#1\pgf@y#2}% + }% + \expandafter\pgf@decorate@addtoinputsegmentobjects\expandafter{\pgf@decorate@temp}% + \edef\pgfpoint@decorate@lastparsed{\pgf@x#1\pgf@y#2}% + \let\pgfpoint@decorate@lastnonmovetoparsed\pgfpoint@decorate@lastparsed% + \pgf@decorate@@parsesoftpath% +}% + +\newif\ifpgfdecoraterectangleclockwise +\def\pgf@decorate@parserect#1#2\pgfsyssoftpath@rectsizetoken#3#4{% + \let\pgf@decorate@orig@@parsesoftpath\pgf@decorate@@parsesoftpath% + \let\pgf@decorate@@parsesoftpath\relax% + \pgf@decorate@parsemoveto{#1}{#2}% + \pgf@xa#1\relax% + \pgf@ya#2\relax% + \ifpgfdecoraterectangleclockwise% + \advance\pgf@ya#4% + \pgf@yb\pgf@ya% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parselineto\pgf@temp% + \advance\pgf@xa#3% + \pgf@xb\pgf@xa% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parselineto\pgf@temp% + \advance\pgf@ya-#4% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parselineto\pgf@temp% + \advance\pgf@xa-#3% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parseclosepath\pgf@temp% + \else% + \advance\pgf@xa#3% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \pgf@xb\pgf@xa% + \expandafter\pgf@decorate@parselineto\pgf@temp% + \advance\pgf@ya#4% + \pgf@yb\pgf@ya% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parselineto\pgf@temp% + \advance\pgf@xa-#3% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parselineto\pgf@temp% + \advance\pgf@ya-#4% + \edef\pgf@temp{{\the\pgf@xa}{\the\pgf@ya}}% + \expandafter\pgf@decorate@parseclosepath\pgf@temp% + \fi% + \let\pgf@decorate@@parsesoftpath\pgf@decorate@orig@@parsesoftpath% + \edef\pgf@marshal{\noexpand\pgf@decorate@parsemoveto{\the\pgf@xb}{\the\pgf@yb}}% + \pgf@marshal% +}% + + + + +\def\pgf@decorate@linelength#1#2{% + \pgf@process{\pgfpointdiff{#1}{#2}}% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% +}% + +\newif\ifpgf@decorate@subdivide +\def\pgf@decorate@curvelength#1#2#3#4{% + \begingroup% + \pgf@decorate@recursive@subdividecurve@left{#1}{#2}{#3}{#4}% + \pgfutil@tempdimb\pgfmathresult pt\relax% + \pgf@decorate@recursive@subdividecurve@right{#1}{#2}{#3}{#4}% + \advance\pgfutil@tempdimb\pgfmathresult pt\relax% + \pgfmath@returnone\pgfutil@tempdimb% + \endgroup% +}% + +\def\pgf@decorate@@curvelength#1#2#3#4{% + \begingroup% + \pgf@decorate@curvecordlength{#1}{#2}{#3}{#4}% + \ifpgf@decorate@subdivide% + \pgf@decorate@recursive@subdividecurve@left{#1}{#2}{#3}{#4}% + \pgfutil@tempdimb\pgfmathresult pt\relax% + \pgf@decorate@recursive@subdividecurve@right{#1}{#2}{#3}{#4}% + \advance\pgfutil@tempdimb\pgfmathresult pt\relax% + \expandafter\pgfmath@returnone\expandafter\pgfutil@tempdimb% + \else% + \expandafter\pgfmath@returnone\expandafter\pgfmathresult\expandafter p\expandafter t\expandafter% + \fi% + \endgroup% +}% + +\def\pgf@decorate@curvelength@tolerance{1pt}% + +\def\pgf@decorate@curvecordlength#1#2#3#4{% + #4\relax% + \pgf@xa\pgf@x\pgf@ya\pgf@y% + #1\relax% + \advance\pgf@xa-\pgf@x% + \advance\pgf@ya-\pgf@y% + \ifdim\pgf@xa<0pt\relax\pgf@xa-\pgf@xa\fi% + \ifdim\pgf@ya<0pt\relax\pgf@ya-\pgf@ya\fi% + \pgf@decorate@subdividetrue% + \ifdim\pgf@xa<\pgf@decorate@curvelength@tolerance\relax% + \ifdim\pgf@ya<\pgf@decorate@curvelength@tolerance\relax% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@xa}}{\pgfmath@tonumber{\pgf@ya}}% + \pgf@decorate@subdividefalse% + \fi% + \fi% +}% + +\def\pgf@decorate@recursive@subdividecurve@left#1#2#3#4{% + {% + #1\relax% + \pgfutil@tempdima\pgf@x% + \pgfutil@tempdimb\pgf@y% + \pgf@xa.5\pgf@x\pgf@ya.5\pgf@y% + \pgf@xb.25\pgf@x\pgf@yb.25\pgf@y% + \pgf@xc.125\pgf@x\pgf@yc.125\pgf@y% + #2\relax% + \advance\pgf@xa.5\pgf@x\advance\pgf@ya.5\pgf@y% + \advance\pgf@xb.5\pgf@x\advance\pgf@yb.5\pgf@y% + \advance\pgf@xc.375\pgf@x\advance\pgf@yc.375\pgf@y% + #3\relax% + \advance\pgf@xb.25\pgf@x\advance\pgf@yb.25\pgf@y% + \advance\pgf@xc.375\pgf@x\advance\pgf@yc.375\pgf@y% + #4\relax% + \advance\pgf@xc.125\pgf@x\advance\pgf@yc.125\pgf@y% + \xdef\pgf@marshal{% + \noexpand\pgf@decorate@@curvelength% + {\pgf@x\the\pgfutil@tempdima\pgf@y\the\pgfutil@tempdimb}% + {\pgf@x\the\pgf@xa\pgf@y\the\pgf@ya}{\pgf@x\the\pgf@xb\pgf@y\the\pgf@yb} + {\pgf@x\the\pgf@xc\pgf@y\the\pgf@yc}% + }% + }% + \pgf@marshal% +}% + +\def\pgf@decorate@recursive@subdividecurve@right#1#2#3#4{% + {% + #1\relax% + \pgfutil@tempdima.125\pgf@x\pgfutil@tempdimb.125\pgf@y% + #2\relax% + \advance\pgfutil@tempdima.375\pgf@x\advance\pgfutil@tempdimb.375\pgf@y% + \pgf@xa.25\pgf@x\pgf@ya.25\pgf@y% + #3\relax% + \advance\pgfutil@tempdima.375\pgf@x\advance\pgfutil@tempdimb.375\pgf@y% + \advance\pgf@xa.5\pgf@x\advance\pgf@ya.5\pgf@y% + \pgf@xb.5\pgf@x\pgf@yb.5\pgf@y% + #4\relax% + \advance\pgfutil@tempdima.125\pgf@x\advance\pgfutil@tempdimb.125\pgf@y% + \advance\pgf@xa.25\pgf@x\advance\pgf@ya.25\pgf@y% + \advance\pgf@xb.5\pgf@x\advance\pgf@yb.5\pgf@y% + \pgf@xc\pgf@x\pgf@yc\pgf@y% + \xdef\pgf@marshal{% + \noexpand\pgf@decorate@@curvelength% + {\pgf@x\the\pgfutil@tempdima\pgf@y\the\pgfutil@tempdimb}% + {\pgf@x\the\pgf@xa\pgf@y\the\pgf@ya}{\pgf@x\the\pgf@xb\pgf@y\the\pgf@yb} + {\pgf@x\the\pgf@xc\pgf@y\the\pgf@yc}% + }% + }% + \pgf@marshal% +}% + + +\def\pgf@decorate@inputsegmentobjects@reverse#1#2{% + \def\pgf@decorate@path@storein{#2}% + \def\pgf@decorate@inputsegments@@temp{}% + \expandafter\pgf@decorate@inputsegments@@reverse@pass@first#1\pgf@stop}% + +\def\pgf@decorate@inputsegments@@reverse@pass@first#1#2\pgf@stop{% + \def\pgf@decorate@temp{#1}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgf@decorate@inputsegments@@temp\expandafter\expandafter\expandafter% + {\expandafter\pgf@decorate@temp\pgf@decorate@inputsegments@@temp}% + \def\pgf@decorate@test{#2} + \ifx\pgf@decorate@test\pgfutil@empty% + \def\pgf@decorate@next{% + \expandafter\pgf@decorate@inputsegmentobjects@reverse@pass@second\pgf@decorate@inputsegments@@temp\pgf@stop% + }% + \else% + \def\pgf@decorate@next{\pgf@decorate@inputsegments@@reverse@pass@first#2\pgf@stop}% + \fi% + \pgf@decorate@next% +}% +\def\pgf@decorate@inputsegmentobjects@reverse@pass@second#1#2#3\pgf@stop{% + \def\pgf@decorate@inputsegments@temp{#3}% + \def\pgf@decorate@inputsegments@@temp{}% + \let\pgf@decorate@current@inputsegmentobject=\pgfutil@empty + \let\pgf@decorate@last@object=\pgfutil@empty + \pgf@decorate@inputsegmentobjects@reverse@moveto@waitingtrue% + \pgf@decorate@inputsegmentobjects@reverse@closepath@waitingfalse% + \expandafter\pgf@decorate@path@@reverse@pass@second\pgf@decorate@inputsegments@temp\pgf@stop}% + + +\def\pgf@decorate@path@@reverse@pass@second#1{% + \ifx#1\pgf@stop% + \expandafter\def\expandafter\pgf@decorate@inputsegments@@temp\expandafter{% + \pgf@decorate@inputsegments@@temp% + {\pgf@decorate@inputsegmentobject@endofinputsegments}% + {\pgf@decorate@inputsegmentobject@endofinputsegments} + }% + \expandafter\let\pgf@decorate@path@storein=\pgf@decorate@inputsegments@@temp% + \let\pgf@decorate@next=\relax% + \else% + \ifx#1\pgf@decorate@inputsegmentobject@moveto% + \let\pgf@decorate@next=\pgf@decorate@inputsegmentobjects@reverse@moveto% + \else% + \ifx#1\pgf@decorate@inputsegmentobject@lineto% + \let\pgf@decorate@next=\pgf@decorate@inputsegmentobjects@reverse@lineto% + \else% + \ifx#1\pgf@decorate@inputsegmentobject@curveto% + \let\pgf@decorate@next=\pgf@decorate@inputsegmentobjects@reverse@curveto% + \else% + \ifx#1\pgf@decorate@inputsegmentobject@closepath% + \let\pgf@decorate@next=\pgf@decorate@inputsegmentobjects@reverse@closepath% + \else% + \fi% + \fi% + \fi% + \fi% + \fi% + \pgf@decorate@next% +}% + +\newif\ifpgf@decorate@inputsegmentobjects@reverse@moveto@waiting + +\def\pgf@decorate@inputsegmentobjects@reverse@moveto#1{% + \ifpgf@decorate@inputsegmentobjects@reverse@closepath@waiting% + \edef\pgf@decorate@current@inputsegmentobject{% + {\noexpand\pgf@decorate@inputsegmentobject@closepath% + {\pgf@decorate@reverse@closepath@length}% + {\pgf@decorate@last}% + {#1}% + }% + }% + \pgf@decorate@inputsegmentobjects@reverse@closepath@waitingfalse% + \else% + \let\pgf@decorate@current@inputsegmentobject=\pgfutil@empty% + \fi% + \pgf@decorate@inputsegmentobjects@reverse@moveto@waitingtrue% + \pgf@decorate@path@@@reverse@pass@second% +}% + +\newif\ifpgf@decorate@inputsegmentobjects@reverse@closepath@waiting + +\def\pgf@decorate@inputsegmentobjects@reverse@closepath#1#2#3{% + \pgf@decorate@inputsegmentobjects@reverse@closepath@waitingtrue% + \def\pgf@decorate@reverse@closepath@length{#1}% + \def\pgf@decorate@current@inputsegmentobject{}% + \pgf@decorate@inputsegmentobjects@reverse@lineto{#1}{#2}{#3}% +}% + +\def\pgf@decorate@inputsegmentobjects@reverse@lineto#1#2#3#4{% + \ifpgf@decorate@inputsegmentobjects@reverse@moveto@waiting% + \def\pgf@decorate@current@inputsegmentobject{{\pgf@decorate@inputsegmentobject@moveto{#3}}}% + \pgf@decorate@inputsegmentobjects@reverse@moveto@waitingfalse% + \else% + \let\pgf@decorate@current@inputsegmentobject=\pgfutil@empty% + \fi% + \def\pgf@decorate@append@inputsegmentobject{{\pgf@decorate@inputsegmentobject@lineto{#1}{#3}{#2}}}% + \ifx#4\pgf@decorate@inputsegmentobject@moveto% + \ifpgf@decorate@inputsegmentobjects@reverse@closepath@waiting% + \def\pgf@decorate@append@inputsegmentobject{{\pgf@decorate@inputsegmentobject@closepath{#1}{#3}{#2}}}% + \pgf@decorate@inputsegmentobjects@reverse@closepath@waitingfalse% + \else% + \def\pgf@decorate@append@inputsegmentobject{{\pgf@decorate@inputsegmentobject@lineto{#1}{#3}{#2}}}% + \fi% + \fi% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgf@decorate@current@inputsegmentobject\expandafter\expandafter\expandafter% + {\expandafter\pgf@decorate@current@inputsegmentobject\pgf@decorate@append@inputsegmentobject} + \def\pgf@decorate@last{#2}% + \pgf@decorate@path@@@reverse@pass@second#4% +}% + +\def\pgf@decorate@inputsegmentobjects@reverse@curveto#1#2#3#4#5{% + \ifpgf@decorate@inputsegmentobjects@reverse@moveto@waiting% + \def\pgf@decorate@current@inputsegmentobject{% + {\pgf@decorate@inputsegmentobject@moveto{#5}}% + {\pgf@decorate@inputsegmentobject@curveto{#1}{#5}{#4}{#3}{#2}}% + }% + \pgf@decorate@inputsegmentobjects@reverse@moveto@waitingfalse% + \else% + \def\pgf@decorate@current@inputsegmentobject{{\pgf@decorate@inputsegmentobject@curveto{#1}{#5}{#4}{#3}{#2}}}% + \fi% + \def\pgf@decorate@last{#2}% + \pgf@decorate@path@@@reverse@pass@second% +}% + +\def\pgf@decorate@path@@@reverse@pass@second{% + \ifx\pgf@decorate@current@inputsegmentobject\pgfutil@empty% + \else% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + \pgf@decorate@inputsegments@@temp\expandafter\expandafter\expandafter% + {\expandafter\pgf@decorate@inputsegments@@temp\pgf@decorate@current@inputsegmentobject}% + \fi% + \pgf@decorate@path@@reverse@pass@second% +}% + + + + + +\let\startpgfdecoration=\pgfdecoration +\let\stoppgfdecoration=\endpgfdecoration + +\let\startpgfmetadecoration=\pgfmetadecoration +\let\stoppgfmetadecoration=\endpgfmetadecoration + + + + + + +\pgfdeclaredecoration{lineto}{initial}{% + \state{initial}[switch if input segment less than=\pgfdecoratedremainingdistance to input segment, + width=\pgfdecoratedremainingdistance] + { + }% + \state{input segment}[width=\pgfdecoratedinputsegmentlength,next state=initial] + { + \pgfpathlineto{\pgfpointdecoratedinputsegmentlast} + }% + + \state{final}{\pgfpathlineto{\pgfpointdecoratedpathlast}}% +}% + +\pgfdeclaredecoration{moveto}{initial}{% + \state{initial}[width=\pgfdecoratedremainingdistance]{}% + \state{final}{\pgfpathmoveto{\pgfpointdecoratedpathlast}}% +}% + + +\pgfdeclaredecoration{curveto}{initial}{% + \state{initial}[width=\pgfdecoratedinputsegmentlength/100] + { + \pgfpathlineto{\pgfpointorigin} + }% + \state{final}{\pgfpathlineto{\pgfpointdecoratedpathlast}}% +}% + + + + + +\let\pgfsnakeremainingdistance=\pgfdecoratedremainingdistance +\let\pgfsnakecompleteddistance=\pgfdecoratedcompleteddistance +\def\pgfsnakeangle{\pgfdecoratedangle}% +\let\pgfdeclaresnake=\pgfdeclaredecoration +\let\pgfsetsnakesegmenttransformation=\pgfsetdecorationsegmenttransformation +\def\pgfpathsnakesto#1#2{% + \edef\pgf@temp{#1}% + \expandafter\pgfdecoration\expandafter{\pgf@temp}% + \pgfpathlineto{#2}% + \endpgfdecoration% +}% +\def\pgfpathsnaketo#1#2{\pgfpathsnakesto{{#1}{\pgfsnakeremainingdistance}}{#2}}% +\def\pgfpathsnakealongvector#1#2#3{% + \pgf@process{#3}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgfmathparse{#2}% + \pgf@xa=\pgfmathresult\pgf@xa% + \pgf@ya=\pgfmathresult\pgf@ya% + \advance\pgf@xa by\pgf@path@lastx% + \advance\pgf@ya by\pgf@path@lasty% + \edef\pgf@snake@lib@temp{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \pgfpathsnaketo{#1}{\pgf@snake@lib@temp}% +}% + +\let\pgfsnakesegmentamplitude=\pgfdecorationsegmentamplitude +\let\pgfsnakesegmentlength=\pgfdecorationsegmentlength +\def\pgfsnakesegmentangle{\pgfdecorationsegmentangle}% +\def\pgfsnakesegmentobjectlength{\pgfkeysvalueof{/pgf/decoration/shape start width}}% +\def\pgfsnakesegmentaspect{\pgfdecorationsegmentaspect}% + +\pgfset{% + /pgf/segment amplitude/.style={/pgf/decoration={amplitude={#1},shape height={2*(#1)}}}, + /pgf/segment length/.style={/pgf/decoration={segment length={#1}}}, + /pgf/segment angle/.style={/pgf/decoration={angle={#1}}}, + /pgf/segment aspect/.style={/pgf/decoration={aspect={#1}}}, + /pgf/segment object length/.style={/pgf/decoration={shape width={#1},radius={#1}}}}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulematrix.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulematrix.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..b1f5aa62f0d2986a17b0d63e858b05012906f101 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulematrix.code.tex @@ -0,0 +1,422 @@ + +\ProvidesFileRCS{pgfmodulematrix.code.tex} + +\usepgfmodule{shapes}% + +\newif\ifpgfmatrix +\newif\ifpgf@matrix@correct@call + +\newif\ifpgf@matrix@fixed + +\newcount\pgfmatrixcurrentrow + +\newcount\pgfmatrixcurrentcolumn +\newcount\pgf@matrix@numberofcolumns + +\let\pgf@matrix@cell=\pgfnodeparttextbox % +\let\pgf@matrix@box=\pgf@matrix@cell % + +\long\def\pgfmatrixbeforeassemblenode#1{% + \long\def\pgf@matrix@before@assemnble@node{#1}} +\pgfmatrixbeforeassemblenode{} + + +\def\pgfsetmatrixrowsep#1{\def\pgfmatrixrowsep{#1}}% +\def\pgfsetmatrixcolumnsep#1{\def\pgfmatrixcolumnsep{#1}}% + +\def\pgfmatrixrowsep{0pt}% +\def\pgfmatrixcolumnsep{0pt}% + + + + +\def\pgfmatrix#1#2#3#4#5#6{% + \ifpgfmatrix% + \pgferror{You cannot nest pgfmatrix environments, yet} + \fi% + \bgroup% + \everycr{}% + #6% + \def\pgf@matrix@par@shape{#1}% + \def\pgf@matrix@par@anchor{#2}% + \def\pgf@matrix@par@name{#3}% + \def\pgf@matrix@par@usage{#4}% + \def\pgf@matrix@par@shift{#5}% + \ifx\pgf@matrix@par@name\pgfutil@empty% + \def\pgf@matrix@par@name{pgf@matrix@internal}% + \fi% + \pgfmatrixcurrentrow=0\relax% + \pgfmatrixcurrentcolumn=0\relax% + \pgf@matrix@numberofcolumns=0\relax% + \let\\=\pgfmatrixendrow% + \tabskip=0pt% + \offinterlineskip% + \pgfmatrixtrue% + \let\pgf@matrix@node@list=\pgfutil@empty% + \expandafter\let\csname pgf@matrix@column@finish@1\endcsname=\pgfutil@empty% + \let\pgf@matrix@row@finish=\pgfutil@empty% + \afterassignment\pgf@matrix@cont\let\pgf@next=% +}% +\def\pgf@matrix@cont{% + \setbox\pgf@matrix@box=\hbox\bgroup\vbox\bgroup% + \halign\bgroup% + \pgf@matrix@init@row% + \pgf@matrix@step@column% + {% + \pgf@matrix@startcell% + ##% + \pgf@matrix@endcell% + }% + &% + ##\pgf@matrix@padding&&% + \pgf@matrix@step@column% + {% + \pgf@matrix@startcell% + ##% + \pgf@matrix@endcell% + }&% + ##\pgf@matrix@padding% + \cr% +}% + +\def\pgf@end@matrix{% + \egroup\egroup% + \egroup% + \pgf@matrix@before@assemnble@node + \ifx\pgf@matrix@node@list\pgfutil@empty% + \else% + \pgf@matrix@compute@origin% + \pgf@matrix@shift@nodes@initial% + \fi% + \pgftransformresetnontranslations% + \pgftransformshift{\pgf@process{\pgftransformreset\pgf@matrix@par@shift\pgf@x=-\pgf@x\pgf@y=-\pgf@y}}% + \pgfmultipartnode{\pgf@matrix@par@shape}{\pgf@matrix@par@anchor}{\pgf@matrix@par@name}{\pgf@matrix@par@usage}% + \ifx\pgf@matrix@node@list\pgfutil@empty% + \else% + {% + \pgftransformreset% + \pgf@process{\pgfpointanchor{\pgf@matrix@par@name}{text}}% + \xdef\pgf@matrix@offset{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + \pgf@matrix@shift@nodes@secondary{\pgf@matrix@offset}% + }% + \fi% +}% + + + + + +\def\pgfmatrixnextcell{% + \let\pgf@matrix@signal@cell@end=\pgf@matrix@signal@cell@end% + \pgfutil@ifnextchar[{\pgf@matrix@cell@cont}{\pgf@matrix@cell@cont[0pt]}}% + +\def\pgf@matrix@cell@cont[#1]{% + \xdef\pgf@matrix@last@nextcell@options{#1}% + &\pgf@matrix@correct@calltrue&% +}% + + +\def\pgf@matrix@fixed@text{between origins}% +\def\pgf@matrix@natural@text{between borders}% + +\def\pgf@matrix@addtolength#1#2{\edef\pgf@temp{#2}\expandafter\pgf@matrix@addtolength@\expandafter#1#2,\pgf@stop}% +\def\pgf@matrix@addtolength@#1#2,#3\pgf@stop{% + \pgfkeys@spdef\pgf@temp{#2}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \ifx\pgf@temp\pgf@matrix@fixed@text% + \global\pgf@matrix@fixedtrue% + \else% + \ifx\pgf@temp\pgf@matrix@natural@text% + \global\pgf@matrix@fixedfalse% + \else% + \pgfmathaddtolength{#1}{#2}% + \fi% + \fi% + \fi% + \def\pgf@temp{#3}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \pgf@matrix@addtolength@#1#3\pgf@stop% + \fi% +}% + + + + +\def\pgf@matrix@init@row{% + \relax% + \global\advance\pgfmatrixcurrentrow by 1\relax% + \global\pgfmatrixcurrentcolumn=0\relax% + \expandafter\gdef\csname pgf@matrix@maxy\the\pgfmatrixcurrentrow\endcsname{0pt}% + \expandafter\gdef\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname{0pt}% +}% + + + + +\def\pgf@matrix@step@column{% + \relax% + \global\advance\pgfmatrixcurrentcolumn by1\relax% +}% + + + + +\def\pgf@matrix@startcell{% + \let\pgf@nodecallback=\pgf@matrix@nodecallback% + \pgfinterruptboundingbox% + \pgftransformreset% + \setbox\pgf@matrix@cell=\hbox\bgroup\bgroup% + \pgf@relevantforpicturesizetrue + \pgfsys@beginpicture% + \normalbaselines% + \pgfutil@ifnextchar\let% + {% + \afterassignment\pgf@matrix@empty@check\let\pgf@matrix@temp=% + }% + {% + \pgf@matrix@empty@cell@false% + \pgfmatrixbegincode% + }% +}% + +\def\pgf@matrix@empty@check{\futurelet\pgf@matrix@check@token\pgf@matrix@empty@check@cont}% +\def\pgf@matrix@empty@check@cont{% + \ifx\pgf@matrix@check@token\pgf@matrix@signal@cell@end% + \pgf@matrix@empty@cell@true% + \expandafter% + \pgfmatrixemptycode% + \expandafter% + \let% + \else% + \pgf@matrix@empty@cell@false% + \expandafter% + \pgfmatrixbegincode% + \expandafter + \let% + \fi% +}% + +\newif\ifpgf@matrix@empty@cell@ + + + +\def\pgf@matrix@endcell{% + \ifpgf@matrix@empty@cell@% + \else% + \expandafter\expandafter\expandafter\pgfmatrixendcode% + \expandafter\ifpgf@matrix@last@cell@in@row\expandafter\pgf@matrix@last@cell@in@rowtrue\expandafter\fi% + \fi% + \pgfsys@endpicture% + \ifnum\pgfmatrixcurrentcolumn<\pgf@matrix@numberofcolumns% + \else% + \ifpgf@matrix@last@cell@in@row\else% + {% + \global\pgf@matrix@fixedfalse% + \pgf@x=0pt% + \pgf@matrix@addtolength{\pgf@x}{\pgfmatrixcolumnsep}% + \pgf@matrix@addtolength{\pgf@x}{\pgf@matrix@last@nextcell@options}% + \ifpgf@matrix@fixed% + \expandafter\pgfutil@g@addto@macro\csname pgf@matrix@column@finish@\the\pgfmatrixcurrentcolumn\endcsname% + {\global\pgf@picmaxx=0pt}% + \fi% + \advance\pgfmatrixcurrentcolumn by1\relax % + \expandafter\xdef\csname pgf@matrix@column@sep@\the\pgfmatrixcurrentcolumn\endcsname{\the\pgf@x}% + \ifpgf@matrix@fixed% + \expandafter\gdef\csname pgf@matrix@column@finish@\the\pgfmatrixcurrentcolumn\endcsname{\global\pgf@picminx=0pt}% + \else% + \expandafter\global\expandafter\let\csname pgf@matrix@column@finish@\the\pgfmatrixcurrentcolumn\endcsname=\pgfutil@empty% + \fi% + }% + \fi\fi% + \ifdim\pgf@picmaxx=-16000pt\relax% + \global\pgf@picmaxx=0pt\relax% + \global\pgf@picminx=0pt\relax% + \global\pgf@picmaxy=0pt\relax% + \global\pgf@picminy=0pt\relax% + \fi% + \csname pgf@matrix@column@finish@\the\pgfmatrixcurrentcolumn\endcsname% + \pgf@matrix@row@finish% + \egroup\egroup% + \ifnum\pgfmatrixcurrentcolumn>1\relax% + \pgf@y=\csname pgf@matrix@column@sep@\the\pgfmatrixcurrentcolumn\endcsname\relax% + \advance\pgf@picminx by-\pgf@y% + \fi% + \ifdim\pgf@picmaxy>\csname pgf@matrix@maxy\the\pgfmatrixcurrentrow\endcsname% + \expandafter\xdef\csname pgf@matrix@maxy\the\pgfmatrixcurrentrow\endcsname{\the\pgf@picmaxy}% + \fi% + \ifdim\pgf@picminy<\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname% + \expandafter\xdef\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname{\the\pgf@picminy}% + \fi% + \ht\pgf@matrix@cell=\pgf@picmaxy% + \dp\pgf@matrix@cell=-\pgf@picminy% + \ifnum\pgfmatrixcurrentcolumn>\pgf@matrix@numberofcolumns\relax% + \expandafter\xdef\csname pgf@matrix@maxx\the\pgfmatrixcurrentcolumn\endcsname{\the\pgf@picmaxx}% + \expandafter\xdef\csname pgf@matrix@minx\the\pgfmatrixcurrentcolumn\endcsname{\the\pgf@picminx}% + \global\pgf@matrix@numberofcolumns=\pgfmatrixcurrentcolumn\relax% + \else% + \ifdim\pgf@picmaxx>\csname pgf@matrix@maxx\the\pgfmatrixcurrentcolumn\endcsname% + \expandafter\xdef\csname pgf@matrix@maxx\the\pgfmatrixcurrentcolumn\endcsname{\the\pgf@picmaxx}% + \fi% + \ifdim\pgf@picminx<\csname pgf@matrix@minx\the\pgfmatrixcurrentcolumn\endcsname% + \expandafter\xdef\csname pgf@matrix@minx\the\pgfmatrixcurrentcolumn\endcsname{\the\pgf@picminx}% + \fi% + \fi% + \xdef\pgf@matrix@paddingskip{\the\pgf@picmaxx}% + \hfil\hskip-\pgf@picminx% + \wd\pgf@matrix@cell=0pt% + \box\pgf@matrix@cell% + \endpgfinterruptboundingbox% +}% + +\let\pgfmatrixbegincode=\relax +\let\pgfmatrixendcode=\relax +\let\pgfmatrixemptycode=\relax + + + +\def\pgf@matrix@nodecallback#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \xdef\pgf@matrix@node@list{\pgf@matrix@node@list,{#1}}% + \expandafter\xdef\csname pgf@matrix@node@location@#1\endcsname{{\the\pgfmatrixcurrentrow}{\the\pgfmatrixcurrentcolumn}}% + \fi% +}% + + + + +\def\pgf@matrix@padding{% + \ifpgf@matrix@correct@call% + \else% + \pgferror{Single ampersand used with wrong catcode}% + \fi% + \hskip\pgf@matrix@paddingskip\hfil% +}% + + + + +\def\pgf@matrix@compute@origin{% + {% + \ifnum\pgfmatrixcurrentrow>0\relax% + \expandafter\gdef\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname{0pt}% + \fi + \c@pgf@counta=\pgfmatrixcurrentrow\relax% + \loop% + \ifnum\c@pgf@counta>1\relax% + \pgf@y=\csname pgf@matrix@miny\the\c@pgf@counta\endcsname\relax% + \advance\pgf@y by\csname pgf@matrix@maxy\the\c@pgf@counta\endcsname\relax + \advance\c@pgf@counta by-1\relax% + \pgf@ya=\csname pgf@matrix@miny\the\c@pgf@counta\endcsname\relax% + \advance\pgf@y by-\pgf@ya\relax% + \expandafter\xdef\csname pgf@matrix@miny\the\c@pgf@counta\endcsname{\the\pgf@y}% + \repeat% + }% + {% + \ifnum\pgf@matrix@numberofcolumns>0\relax% + \pgf@x=\csname pgf@matrix@minx1\endcsname\relax% + \pgf@x=-\pgf@x% + \expandafter\xdef\csname pgf@matrix@minx1\endcsname{\the\pgf@x}% + \fi + \c@pgf@counta=1\relax% + \loop% + \ifnum\c@pgf@counta<\pgf@matrix@numberofcolumns\relax% + \pgf@x=\csname pgf@matrix@minx\the\c@pgf@counta\endcsname\relax% + \advance\pgf@x by\csname pgf@matrix@maxx\the\c@pgf@counta\endcsname\relax% + \advance\c@pgf@counta by1\relax% + \pgf@xa=\csname pgf@matrix@minx\the\c@pgf@counta\endcsname\relax% + \advance\pgf@x by-\pgf@xa\relax% + \expandafter\xdef\csname pgf@matrix@minx\the\c@pgf@counta\endcsname{\the\pgf@x}% + \repeat% + }% +}% + + + + +\def\pgf@matrix@shift@nodes@initial{% + {% + \pgfutil@for\pgf@matrix@node@name:=\pgf@matrix@node@list\do{% + \ifx\pgf@matrix@node@name\pgfutil@empty% + \else% + \expandafter\ifx\csname pgf@matrix@node@visited@\pgf@matrix@node@name\endcsname\relax% + \pgf@shift@node{\pgf@matrix@node@name}{% + \pgf@x=\csname pgf@matrix@minx% + \expandafter\expandafter\expandafter\pgfutil@secondoftwo\csname pgf@matrix@node@location@\pgf@matrix@node@name\endcsname\endcsname% + \pgf@y=\csname pgf@matrix@miny% + \expandafter\expandafter\expandafter\pgfutil@firstoftwo\csname pgf@matrix@node@location@\pgf@matrix@node@name\endcsname\endcsname% + }% + \expandafter\let\csname pgf@matrix@node@visited@\pgf@matrix@node@name\endcsname=\pgfutil@empty% + \fi% + \fi% + }% + }% +}% + + + +\def\pgf@matrix@shift@nodes@secondary#1{% + \pgfutil@for\pgf@matrix@node@name:=\pgf@matrix@node@list\do{% + \ifx\pgf@matrix@node@name\pgfutil@empty% + \else% + \expandafter\ifx\csname pgf@matrix@node@visited@\pgf@matrix@node@name\endcsname\relax% + \pgf@shift@node{\pgf@matrix@node@name}{#1}% + \expandafter\let\csname pgf@matrix@node@visited@\pgf@matrix@node@name\endcsname=\pgfutil@empty% + \fi% + \fi% + }% +}% + + +\def\pgfmatrixendrow{% + \let\pgf@matrix@signal@cell@end=\pgf@matrix@signal@cell@end + \pgf@matrix@last@cell@in@rowtrue% + \xdef\pgf@matrix@rowsep{\pgfmatrixrowsep}% + &\pgf@matrix@correct@calltrue% + \global\pgf@matrix@fixedfalse% + \pgf@y=0pt% + \pgf@matrix@addtolength\pgf@y{\pgf@matrix@rowsep}% + \pgfutil@ifnextchar[{\pgfmatrixendrow@skip}{\pgf@matrix@finish@line}% +}% +\newif\ifpgf@matrix@last@cell@in@row + +\def\pgf@matrix@signal@cell@end{\pgf@matrix@signal@cell@end}% + +\def\pgfmatrixendrow@skip[#1]{% + \pgf@matrix@addtolength\pgf@y{#1}% + \pgf@matrix@finish@line% +}% + +\def\pgf@matrix@finish@line{% + \global\pgf@y=\pgf@y% + \pgf@ya=-\pgf@y% + \global\advance\pgf@ya by\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname% + \expandafter\xdef\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname{\the\pgf@ya}% + \pgfutil@ifnextchar\egroup{\cr\pgf@end@matrix}{\pgf@matrix@no@eom@found}% +}% + +\def\pgf@matrix@eom@found{% + \cr% + \pgf@end@matrix% +}% + +\def\pgf@matrix@no@eom@found{% + \cr% + \noalign{\vskip\pgf@y% + \ifpgf@matrix@fixed% + \vskip\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname% + \vskip\pgf@y% + \pgf@y=-\pgf@y% + \expandafter\xdef\csname pgf@matrix@miny\the\pgfmatrixcurrentrow\endcsname{\the\pgf@y}% + \gdef\pgf@matrix@row@finish{\global\pgf@picmaxy=0pt}% + \else% + \global\let\pgf@matrix@row@finish=\pgfutil@empty% + \fi% + }% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulenonlineartransformations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulenonlineartransformations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..4193386aac9d5736d3d414fe54fbdd215f8fe3b4 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulenonlineartransformations.code.tex @@ -0,0 +1,232 @@ + +\ProvidesFileRCS{pgfmodulenonlineartransformations.code.tex} + + + + + + + +\def\pgfpointtransformednonlinear#1{% + \pgf@process{% + #1% + \pgf@pos@transform@glob% + \pgf@nlt@list% + } +}% + + + + + +\def\pgfapproximatenonlineartranslation{% + \ifx\pgf@nlt@list\pgfutil@empty% + \else% + \pgfpointtransformednonlinear{\pgfpointorigin}% + \pgf@pt@x=\pgf@x% + \pgf@pt@y=\pgf@y% + \let\pgf@nlt@list\pgfutil@empty% + \let\pgf@nlt@moveto\pgf@lt@moveto% + \let\pgf@nlt@lineto\pgf@lt@lineto% + \let\pgf@nlt@curveto\pgf@lt@curveto% + \let\pgf@nlt@closepath\pgf@lt@closepath% + \fi% +}% + + + + +\def\pgfapproximatenonlineartransformation{% + \ifx\pgf@nlt@list\pgfutil@empty% + \else% + \pgfpointtransformednonlinear{\pgfpoint{1pt}{0pt}}% + \pgf@xa\pgf@x + \pgf@ya\pgf@y + \pgfpointtransformednonlinear{\pgfpoint{0pt}{1pt}}% + \pgf@xb\pgf@x + \pgf@yb\pgf@y + \pgfpointtransformednonlinear{\pgfpointorigin}% + \advance\pgf@xa by-\pgf@x + \advance\pgf@xb by-\pgf@x + \advance\pgf@ya by-\pgf@y + \advance\pgf@yb by-\pgf@y + \pgfsettransformentries{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@xb}{\pgf@sys@tonumber\pgf@yb}{\pgf@x}{\pgf@y}% + \let\pgf@nlt@list\pgfutil@empty% + \let\pgf@nlt@moveto\pgf@lt@moveto% + \let\pgf@nlt@lineto\pgf@lt@lineto% + \let\pgf@nlt@curveto\pgf@lt@curveto% + \let\pgf@nlt@closepath\pgf@lt@closepath% + \fi% +}% + + + + +\def\pgftransformnonlinear#1{% + \expandafter\def\expandafter\pgf@nlt@list\expandafter{\pgf@nlt@list#1}% + \let\pgf@nlt@moveto\pgf@nlt@moveto@nlt + \let\pgf@nlt@lineto\pgf@nlt@lineto@nlt + \let\pgf@nlt@curveto\pgf@nlt@curveto@nlt + \let\pgf@nlt@closepath\pgf@nlt@closepath@nlt +}% + +\def\pgf@nlt@moveto@nlt#1#2{% + {% + \pgfutil@tempdima#1% + \pgfutil@tempdimb#2% + \pgf@x\pgfutil@tempdima% + \pgf@y\pgfutil@tempdimb% + \xdef\pgf@nlt@last@moveto@orig{{\the\pgf@x}{\the\pgf@y}}% + \pgf@nlt@list% + \xdef\pgf@nlt@last@moveto@trans{{\the\pgf@x}{\the\pgf@y}}% + \xdef\pgf@nlt@last@moveto@xaxis{{\the\pgf@xa}{\the\pgf@ya}}% + \xdef\pgf@nlt@last@moveto@yaxis{{\the\pgf@xb}{\the\pgf@yb}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \pgfsyssoftpath@moveto{\the\pgf@x}{\the\pgf@y}% + \global\let\pgf@nlt@last@coord@orig\pgf@nlt@last@moveto@orig% + \global\let\pgf@nlt@last@coord@trans\pgf@nlt@last@moveto@trans% + \global\let\pgf@nlt@last@coord@xaxis\pgf@nlt@last@moveto@xaxis% + \global\let\pgf@nlt@last@coord@yaxis\pgf@nlt@last@moveto@yaxis% + }% +}% + + +\def\pgf@nlt@lineto@nlt#1#2{% + {% + \edef\pgf@temp{\pgf@xc\the#1\pgf@yc\the#2}% + \pgf@temp% + \expandafter\pgfqpoint\pgf@nlt@last@coord@orig% + \expandafter\pgf@nlt@set@temps\pgf@nlt@last@coord@trans% + \pgf@xa\pgf@x\advance\pgf@xa by-\pgf@xc% + \pgf@ya\pgf@y\advance\pgf@ya by-\pgf@yc% + \pgfutil@tempswafalse% + \ifdim\pgf@xa<0.1pt\relax\ifdim\pgf@xa>-0.1pt\relax\ifdim\pgf@ya<0.1pt\relax\ifdim\pgf@ya>-0.1pt\relax\pgfutil@tempswatrue\fi\fi\fi\fi% + \ifpgfutil@tempswa% + \pgf@x\pgf@xc\pgf@y\pgf@yc% + \xdef\pgf@nlt@last@coord@orig{{\the\pgf@x}{\the\pgf@y}}% + \pgf@process{\pgf@nlt@list}% + \xdef\pgf@nlt@last@coord@trans{{\the\pgf@x}{\the\pgf@y}}% + \xdef\pgf@nlt@last@coord@xaxis{{\the\pgf@xa}{\the\pgf@ya}}% + \xdef\pgf@nlt@last@coord@yaxis{{\the\pgf@xb}{\the\pgf@yb}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y}% + \pgfsyssoftpath@lineto{\the\pgf@x}{\the\pgf@y}% + \else% + \pgf@xb=.333333\pgf@x% + \advance\pgf@xb by.666666\pgf@xc% + \pgf@yb=.333333\pgf@y% + \advance\pgf@yb by.666666\pgf@yc% + \pgf@xa=.333333\pgf@xc% + \advance\pgf@xa by.666666\pgf@x% + \pgf@ya=.333333\pgf@yc% + \advance\pgf@ya by.666666\pgf@y% + \pgf@nlt@inner@curve% + \fi% + }% +}% + +\def\pgf@nlt@set@temps#1#2{% + \pgfutil@tempdima#1\pgfutil@tempdimb#2% +}% + +\def\pgf@nlt@curveto@nlt#1#2#3#4#5#6{% + {% + \edef\pgf@temp{\pgf@xa\the#1\pgf@ya\the#2\pgf@xb\the#3\pgf@yb\the#4\pgf@xc\the#5\pgf@yc\the#6}% + \pgf@temp% + \pgf@nlt@inner@curve% + }% +}% + +\newdimen\pgftransformnonlinearflatness +\pgftransformnonlinearflatness=5pt +\def\pgfsettransformnonlinearflatness#1{\pgfmathsetlength\pgftransformnonlinearflatness{#1}}% + + + +\def\pgf@nlt@inner@curve{% + \expandafter\pgfqpoint\pgf@nlt@last@coord@orig% + \pgfutil@tempdima\pgf@xa\advance\pgfutil@tempdima by-\pgf@xb + \pgfutil@tempdimb\pgf@ya\advance\pgfutil@tempdimb by-\pgf@yb + \begingroup + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \advance\pgf@xb by-\pgf@xc% + \advance\pgf@yb by-\pgf@yc% + \pgfutil@tempswafalse + \ifdim\pgfutil@tempdima>\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgfutil@tempdima<-\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgfutil@tempdimb>\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgfutil@tempdimb<-\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@xa>\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@xa<-\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@ya>\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@ya<-\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@xb>\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@xb<-\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@yb>\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifdim\pgf@yb<-\pgftransformnonlinearflatness\pgfutil@tempswatrue\fi% + \ifpgfutil@tempswa% + \endgroup% + {% + \edef\pgf@orig@xya{\pgf@xa\the\pgf@xa\pgf@ya\the\pgf@ya} + \edef\pgf@orig@xyb{\pgf@xb\the\pgf@xb\pgf@yb\the\pgf@yb} + \edef\pgf@orig@xyc{\pgf@xc\the\pgf@xc\pgf@yc\the\pgf@yc} + \pgfpointcurveattime{.5}% + {\expandafter\pgfqpoint\pgf@nlt@last@coord@orig}% + {\pgf@x\pgf@xa\pgf@y\pgf@ya}% + {\pgf@x\pgf@xb\pgf@y\pgf@yb}% + {\pgf@x\pgf@xc\pgf@y\pgf@yc}% + {% + \pgf@xc\pgf@x\pgf@yc\pgf@y + \expandafter\pgfqpoint\pgf@nlt@last@coord@orig% + \pgf@orig@xya% + \pgf@xa\pgf@time@s\pgf@xa\advance\pgf@xa by\pgf@time@t\pgf@x% + \pgf@ya\pgf@time@s\pgf@ya\advance\pgf@ya by\pgf@time@t\pgf@y% + \pgf@nlt@inner@curve% + }% + {% + \pgf@orig@xyb% + \pgf@orig@xyc% + \pgf@xb\pgf@time@t\pgf@xb\advance\pgf@xb by\pgf@time@s\pgf@xc% + \pgf@yb\pgf@time@t\pgf@yb\advance\pgf@yb by\pgf@time@s\pgf@yc% + \pgf@nlt@inner@curve% + }% + }% + \else% + \endgroup% + \pgf@nlt@do@inner@curve% + \fi% +}% + +\def\pgf@nlt@do@inner@curve{% + \pgf@process{\pgf@x\pgf@xa\pgf@y\pgf@ya\pgf@nlt@list}% + \pgf@xa\pgf@x\pgf@ya\pgf@y% + \pgf@process{\pgf@x\pgf@xb\pgf@y\pgf@yb\pgf@nlt@list}% + \pgf@xb\pgf@x\pgf@yb\pgf@y% + \xdef\pgf@nlt@last@coord@orig{{\the\pgf@xc}{\the\pgf@yc}}% + \pgf@process{\pgf@x\pgf@xc\pgf@y\pgf@yc\pgf@nlt@list}% + \pgf@xc\pgf@x\pgf@yc\pgf@y% + \xdef\pgf@nlt@last@coord@trans{{\the\pgf@xc}{\the\pgf@yc}}% + \pgf@protocolsizes{\pgf@xa}{\pgf@ya}% + \pgf@protocolsizes{\pgf@xb}{\pgf@yb}% + \pgf@protocolsizes{\pgf@xc}{\pgf@yc}% + \pgfsyssoftpath@curveto{\the\pgf@xa}{\the\pgf@ya}{\the\pgf@xb}{\the\pgf@yb}{\the\pgf@xc}{\the\pgf@yc}% +}% + + +\def\pgf@nlt@closepath@nlt{% + {% + \expandafter\pgfqpoint\pgf@nlt@last@moveto@orig% + \expandafter\pgf@nlt@set@temps\pgf@nlt@last@coord@orig% + \advance\pgfutil@tempdima by-\pgf@x% + \advance\pgfutil@tempdimb by-\pgf@y% + \pgfutil@tempswatrue% + \ifdim\pgfutil@tempdima<0.01pt\relax\ifdim\pgfutil@tempdima>-0.01pt\relax\ifdim\pgfutil@tempdimb<0.01pt\relax\ifdim\pgfutil@tempdimb>-0.01pt\relax\pgfutil@tempswafalse\fi\fi\fi\fi% + \ifpgfutil@tempswa% + \pgf@nlt@lineto@nlt{\pgf@x}{\pgf@y}% + \fi% + \pgfsyssoftpath@closepath% + }% +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleoo.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleoo.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..67e93cd2a6d45d022641862f0afc2fd66ae51db0 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleoo.code.tex @@ -0,0 +1,530 @@ + + + + + + + + + + +\def\pgfooclass{% + \pgfutil@ifnextchar ({% + \pgfooclass@ + }{% + \pgfooclass@() + }% +}% +\long\def\pgfooclass@(#1)#2#3{% + \def\pgfoo@classname{#2}% + \expandafter\ifx\csname pgfooY\pgfoo@classname.@pgfooinit\endcsname\relax\else + \pgferror{class #2 is already defined}% + \fi + \pgfoo@ciii{#2}{#1}% + \expandafter\let\csname pgfooY#2@pgfoo@mro\endcsname\pgfoo@mro + \let\pgfoo@origmethod=\method% + \let\pgfoo@origattribute=\attribute% + \let\method=\pgfoo@declaremethod% + \let\attribute=\pgfoo@declareattribute% + \let\pgfoo@attributes=\pgfutil@empty% + \let\pgfoo@methods=\pgfutil@empty% + #3% + \def\pgfoo@temp@baseclasses{#1}% + \pgfoo@inherit@methods + \pgfoo@inherit@attributes + \expandafter\let\csname pgfooY\pgfoo@classname.get handle\endcsname\pgfoo@obj% + \expandafter\let\csname pgfooY\pgfoo@classname.get id\endcsname\pgfoo@id% + \expandafter\let\expandafter\pgfoo@init\csname pgfooY\pgfoo@classname.init\endcsname + \expandafter\let\csname pgfooY\pgfoo@classname.\pgfoo@classname\endcsname\pgfoo@init + \let\method=\pgfoo@origmethod% + \let\attribute=\pgfoo@origattribute% +}% + +\def\pgfoo@emptyinit(){}% +\def\pgfoo@escapeif#1#2\fi{\fi#1}% + + + +\def\pgfoo@ciii#1#2{% + \def\pgfoo@seq{[#1,].}% + \pgfutil@for\pgfoo@baseclass:={#2}\do{% + \edef\pgfoo@baseclass@mro{\csname pgfooY\pgfoo@baseclass @pgfoo@mro\endcsname}% + \expandafter\ifx\expandafter\relax\pgfoo@baseclass@mro\relax\else + \edef\pgfoo@seq{\pgfoo@seq[\pgfoo@baseclass@mro,].}% + \fi + }% + \ifx\relax#2\relax\else + \edef\pgfoo@seq{\pgfoo@seq[#2,].}% + \fi + \edef\pgfoo@temp{()(\pgfoo@seq)}% + \expandafter\pgfoo@ciii@merge\pgfoo@temp +}% + +\def\pgfoo@ciii@merge(#1)(#2){% + \ifx\relax#2\relax + \pgfoo@ciii@done(#1)% + \else\pgfoo@escapeif{% + \pgfoo@ciii@merge@A(#1)(#2)% + }\fi% +}% +\def\pgfoo@ciii@merge@A(#1)(#2.#3){% + \ifx\relax#3\relax % + \pgfoo@ciii@mergeA@done(#1)(#2)% + \else\pgfoo@escapeif{% + \pgfoo@ciii@merge@checkHead(#1)()(#2)()(#3)% + }\fi +}% + +\def\pgfoo@ciii@mergeA@done(#1)([#2]){% + \pgfoo@ciii@done(#1#2)% +}% + +\def\pgfoo@ciii@merge@checkHead(#1)(#2)([#3,#4])(#5)(#6){% + \pgfutil@in@{[#3,}{#2}% + \ifpgfutil@in@\pgfoo@escapeif{% + \pgfoo@ciii@clean\pgfoo@ciii@merge@checkHead@P{(#1)(#2[#3,#4].)(#5#6)}% + }\else\pgfoo@escapeif{% + \ifx\relax#6\relax\pgfoo@escapeif{% + \pgfoo@ciii@goodHeadFound(#1)(#3)(#2[#4].#5)% + }\else\pgfoo@escapeif{% + \pgfoo@ciii@merge@checkHead@A(#1)(#2)([#3,#4])(#5)(#6)% + }\fi + }\fi +}% +\def\pgfoo@ciii@merge@checkHead@A(#1)(#2)([#3,#4])(#5)(#6.#7){% + \pgfoo@ciii@merge@checkHead@B(#1)(#2)([#3,#4])(#5)(#6)(#7)% +}% +\def\pgfoo@ciii@merge@checkHead@B(#1)(#2)([#3,#4])(#5)([#6,#7])(#8){% + \pgfutil@in@{,#3,}{,#7}% + \ifpgfutil@in@\pgfoo@escapeif{% + \pgfoo@ciii@clean\pgfoo@ciii@merge@checkHead@P{(#1)(#2[#3,#4].)(#5[#6,#7].#8)}% + }\else\pgfoo@escapeif{% + \ifx\relax#8\relax\pgfoo@escapeif{% + \pgfoo@ciii@goodHeadFound(#1)(#3)(#2[#4].#5[#6,#7].)% + }\else\pgfoo@escapeif{% + \pgfoo@ciii@clean\pgfoo@ciii@merge@checkHead{(#1)(#2)([#3,#4])(#5[#6,#7].)(#8)}% + }\fi + }\fi +}% + +\def\pgfoo@ciii@goodHeadFound(#1)(#2)(#3){% + \pgfutil@in@{,#2,}{#3}% + \ifpgfutil@in@\pgfoo@escapeif{% + \def\pgfoo@ciii@removeGoodHead(##1)(##2)(##3,#2,##4){% + \pgfoo@ciii@goodHeadFound(##1)(##2)(##3,##4)}% + \pgfoo@ciii@removeGoodHead(#1)(#2)(#3)% + }\else\pgfoo@escapeif{% + \pgfutil@in@{[#2,}{#3}% + \ifpgfutil@in@\pgfoo@escapeif{% + \def\pgfoo@ciii@removeGoodHead(##1)(##2)(##3[#2,##4){% + \pgfoo@ciii@goodHeadFound(##1)(##2)(##3[##4)}% + \pgfoo@ciii@removeGoodHead(#1)(#2)(#3)% + }\else\pgfoo@escapeif{% + \pgfoo@ciii@clean\pgfoo@ciii@merge{(#1#2,)(#3)}% + }\fi + }\fi +}% + +\def\pgfoo@ciii@merge@checkHead@P(#1)(#2)(#3){% + \if\relax#3\relax % + \pgferror{Bad MRO: There is no good (monotonic etc.) + Method Resolution Order for your class hierarchy}% + \else\pgfoo@escapeif{% + \pgfoo@ciii@merge@checkHead@Q(#1)(#2)(#3)% + }\fi +}% +\def\pgfoo@ciii@merge@checkHead@Q(#1)(#2)(#3.#4){% + \pgfoo@ciii@merge@checkHead(#1)(#2)(#3)()(#4)% +}% + +\def\pgfoo@ciii@clean#1#2{% + \pgfutil@in@{[].}{#2}% + \ifpgfutil@in@\pgfoo@escapeif{% + \pgfoo@ciii@clean@dot#1#2\pgfoo@ciii@clean@END + }\else\pgfoo@escapeif{% + #1#2% + }\fi +}% +\def\pgfoo@ciii@clean@dot#1#2[].#3\pgfoo@ciii@clean@END{% + \pgfoo@ciii@clean#1{#2#3}% +}% + +\def\pgfoo@ciii@done(#1,){% + \def\pgfoo@mro{#1}% +}% + + + + +\long\def\pgfoo@declaremethod#1(#2)#3{% + \def\pgfoo@method{#1}% + \ifx\pgfoo@classname\pgfoo@method + \def\pgfoo@method{init}% + \fi + \expandafter\long\expandafter\def\csname pgfooY\pgfoo@classname.\pgfoo@method\endcsname(#2){#3}% + \edef\pgfoo@methods{\pgfoo@methods,\pgfoo@method}% +}% + +\def\pgfoo@inherit@methods{% + \expandafter\ifx\expandafter\relax\pgfoo@temp@baseclasses\relax + \expandafter\ifx\csname pgfooY\pgfoo@classname.init\endcsname\relax + \expandafter\let\csname pgfooY\pgfoo@classname.init\endcsname\pgfoo@emptyinit% + \edef\pgfoo@methods{,init\pgfoo@methods}% + \fi + \fi + \if\relax\pgfoo@methods\relax\else + \edef\pgfoo@methods{\expandafter\pgfutil@gobble\pgfoo@methods}% + \fi + \expandafter\let\csname pgfooY\pgfoo@classname @pgfoo@methods\endcsname\pgfoo@methods + \expandafter\let\expandafter\pgfoo@mro\csname pgfooY\pgfoo@classname @pgfoo@mro\endcsname + \pgfutil@for\pgfoo@baseclass:=\pgfoo@mro\do{% + \ifx\pgfoo@baseclass\pgfoo@classname % + \else\pgfoo@escapeif{% + \expandafter\let\expandafter\pgfoo@methods\csname pgfooY\pgfoo@baseclass @pgfoo@methods\endcsname + \pgfutil@for\pgfoo@method:=\pgfoo@methods\do{% + \expandafter\ifx\csname pgfooY\pgfoo@classname.\pgfoo@method\endcsname\relax + \edef\pgfoo@temp{\noexpand\let + \expandafter\noexpand\csname pgfooY\pgfoo@classname.\pgfoo@method\endcsname + \expandafter\noexpand\csname pgfooY\pgfoo@baseclass.\pgfoo@method\endcsname}% + \pgfoo@temp + \fi + }% + }\fi + }% +}% + +\def\pgfoosuper(#1,#2).#3({% + #2.get id(\pgfoo@temp@id)% + \edef\pgfoo@classname{\csname pgfooX\pgfoo@temp@id @class\endcsname}% + \def\pgfoo@super@A##1,#1,##2.##3({% + \pgfoo@super@B##2.##3(% + }% + \expandafter\let\expandafter\pgfoo@mro\csname pgfooY\pgfoo@classname @pgfoo@mro\endcsname + \expandafter\pgfoo@super@A\expandafter,\pgfoo@mro,.#3(% +}% +\def\pgfoo@super@B#1,#2.#3({% + \expandafter\ifx\csname pgfooY#1.#3\endcsname\relax + \pgfoo@escapeif{\pgfoo@super@B#2.#3(}% + \else + \pgfoo@escapeif{\expandafter\pgfoo@caller\pgfoo@temp@id.#1.#3(}% + \fi +}% + + + + +\def\pgfoo@declareattribute#1;{% + \pgfutil@in@{ =}{#1}% + \ifpgfutil@in@% + \pgfoo@declareunpackspace#1;% + \else% + \pgfutil@in@={#1}% + \ifpgfutil@in@% + \pgfoo@declareunpack#1;% + \else% + \pgfoo@declareattribute@\let{#1}\pgfutil@empty + \fi% + \fi% +}% +\def\pgfoo@declareunpack#1=#2;{\pgfoo@declareattribute@\def{#1}{{#2}}}% +\def\pgfoo@declareunpackspace#1 =#2;{\pgfoo@declareattribute@\def{#1}{{#2}}}% + +\def\pgfoo@declareattribute@#1#2#3{% + \expandafter#1\csname pgfooY\pgfoo@classname @#2\endcsname#3% + \expandafter\def\expandafter\pgfoo@attributes\expandafter{\pgfoo@attributes,#2}% +}% + +\def\pgfoo@inherit@attributes{% + \if\relax\pgfoo@attributes\relax\else + \edef\pgfoo@attributes{\expandafter\pgfutil@gobble\pgfoo@attributes}% + \fi + \expandafter\let\csname pgfooY\pgfoo@classname.@pgfoo@attributes\endcsname\pgfoo@attributes% + \expandafter\let\expandafter\pgfoo@mro\csname pgfooY\pgfoo@classname @pgfoo@mro\endcsname + \def\pgfoo@allattributes{}% + \pgfutil@for\pgfoo@baseclass:=\pgfoo@mro\do{% + \expandafter\let\expandafter\pgfoo@attributes\csname pgfooY\pgfoo@baseclass.@pgfoo@attributes\endcsname + \pgfutil@for\pgfoo@attribute:=\pgfoo@attributes\do{% + \edef\pgfoo@temp{{,\pgfoo@attribute=}{\pgfoo@allattributes,}}% + \expandafter\pgfutil@in@\pgfoo@temp + \ifpgfutil@in@\else % + \edef\pgfoo@allattributes{\pgfoo@allattributes,\pgfoo@attribute=\pgfoo@baseclass}% + \fi + }% + }% + \if\relax\pgfoo@allattributes\relax\else + \edef\pgfoo@allattributes{\expandafter\pgfutil@gobble\pgfoo@allattributes}% + \fi + \def\pgfoo@process@attributes{}% + \pgfutil@for\pgfoo@attributeclass:=\pgfoo@allattributes\do{% + \expandafter\pgfoo@inherit@attributes@appendattribute\pgfoo@attributeclass.% + }% + \expandafter\let\csname pgfooY\pgfoo@classname .@pgfoo@process@attributes\endcsname\pgfoo@process@attributes +}% + + +\def\pgfoo@inherit@attributes@appendattribute#1=#2.{% + \def\pgfoo@tempA{\pgfoo@attribute@op{#1}}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfoo@tempB\expandafter\expandafter\expandafter{\expandafter\pgfoo@tempA\csname pgfooY#2@#1\endcsname}% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfoo@process@attributes\expandafter\expandafter\expandafter{\expandafter\pgfoo@process@attributes\pgfoo@tempB}% +}% + +\def\pgfoo@gc@attribute#1#2{\pgfoolet{#1}\relax}% + + +\newcount\pgfoo@objectcount +\newcount\pgfoothis@count + + +\def\pgfoovalueof#1{% + \csname pgfooX\the\pgfoothis@count @#1\endcsname% +}% + + + +\def\pgfooget#1#2{% + \expandafter\let\expandafter#2\csname pgfooX\the\pgfoothis@count @#1\endcsname% +}% + + + +\long\def\pgfooset#1#2{% + \expandafter\gdef\csname pgfooX\the\pgfoothis@count @#1\endcsname{#2}% +}% + + + +\long\def\pgfooeset#1#2{% + \expandafter\xdef\csname pgfooX\the\pgfoothis@count @#1\endcsname{#2}% +}% + + + +\def\pgfoolet#1#2{% + \expandafter\global\expandafter\let\csname pgfooX\the\pgfoothis@count @#1\endcsname#2% +}% + + + +\def\pgfooappend#1#2{% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@oo@temp\expandafter\expandafter\expandafter{\csname pgfooX\the\pgfoothis@count @#1\endcsname#2}% + \expandafter\global\expandafter\let\csname pgfooX\the\pgfoothis@count @#1\endcsname\pgf@oo@temp% +}% + + + +\def\pgfooprefix#1#2{% + \pgfooget{#1}\pgf@oo@temp% + \def\pgf@oo@@temp{#2}% + \expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\pgf@oo@temp% + \expandafter\expandafter\expandafter{\expandafter\pgf@oo@@temp\pgf@oo@temp}% + \pgfoolet{#1}\pgf@oo@temp% +}% + + + +\newtoks\pgfoo@toks + +\def\pgfoo@collect@args{% + \pgfutil@ifnextchar\bgroup\pgfoo@collect@args@group\pgfoo@collect@args@nogroup% +}% +\def\pgfoo@collect@args@nogroup#1){% + \pgfoo@toks{#1}% + \pgfoo@continue% +}% +\def\pgfoo@collect@args@group#1{% + \pgfutil@ifnextchar){\pgfoo@toks{{#1}}\expandafter\pgfoo@continue\pgfutil@gobble}{\pgfoo@collect@args@nogroup{#1}}% +}% + + + +\def\pgfoonew{% + \pgfutil@ifnextchar n{% + \pgfoo@new\pgfoo@dummy=% + }{% + \pgfutil@ifnextchar\bgroup{% + \pgfoo@new@attribute% + }{% + \pgfoo@new% + }% + }% +}% +\def\pgfoo@new#1={% + \def\pgfutil@reserved@a{#1}% + \let\pgfutil@next\pgfoo@@new + \futurelet\pgfutil@let@token\pgfutil@ignorespaces}% +\def\pgfoo@@new new #1({% + \expandafter\ifx\csname pgfooY#1.get id\endcsname\relax% + \pgferror{Unknown class '#1'}% + \else% + \expandafter\pgfoo@new@create\pgfutil@reserved@a{#1}% + {% + \pgfoothis@count\pgfoo@objectcount% + \let\pgfoo@attribute@op\pgfoolet + \csname pgfooY#1.@pgfoo@process@attributes\endcsname% + }% + \let\pgfoo@continue=\pgf@oo@new@cont% + \expandafter\pgfoo@collect@args% + \fi% +}% + +\def\pgf@oo@new@cont{% + \expandafter\pgfoolastobj\expandafter.\expandafter i\expandafter n\expandafter i\expandafter t\expandafter(\the\pgfoo@toks)% + \aftergroup\pgfoogc% +}% + +\def\pgfoo@new@attribute#1={% + \def\pgfutil@reserved@a{#1}% + \let\pgfutil@next\pgfoo@@new@attribute + \futurelet\pgfutil@let@token\pgfutil@ignorespaces}% +\def\pgfoo@@new@attribute new #1({% + \expandafter\ifx\csname pgfooY#1.get id\endcsname\relax% + \pgferror{Unknown class '#1'}% + \else% + \pgfoo@new@create\pgfoo@temp{#1}% + {% + \pgfoothis@count\pgfoo@objectcount% + \let\pgfoo@attribute@op\pgfoolet% + \csname pgfooY#1.@pgfoo@process@attributes\endcsname% + }% + \expandafter\pgfoolet\expandafter{\pgfutil@reserved@a}\pgfoo@temp% + \let\pgfoo@continue=\pgf@oo@new@cont% + \expandafter\pgfoo@collect@args% + \fi% +}% + +\def\pgfoo@new@create#1#2{% + \advance\pgfoo@objectcount by 1\relax% + \edef\pgfoolastobj{\noexpand\pgfoo@caller{\the\pgfoo@objectcount}}% + \expandafter\gdef\csname pgfooX\the\pgfoo@objectcount @class\endcsname{#2}% + \let#1\pgfoolastobj% +}% + +\def\pgfoo@caller#1.#2({% + \expandafter\let\expandafter\pgfoo@caller@temp\csname pgfooY\csname pgfooX#1@class\endcsname.#2\endcsname% + \ifx\pgfoo@caller@temp\relax% + \expandafter\let\expandafter\pgfoo@caller@temp\csname pgfooY#2\endcsname% + \ifx\pgfoo@caller@temp\relax% + \pgferror{Object #1 has no method '#2'}% + \fi% + \fi% + \def\pgf@marshal{% + \pgfoothis@count=#1\relax% + }% + \let\pgfoo@continue\pgfoo@caller@cont% + \pgfoo@collect@args% +}% +\def\pgfoo@caller@cont{% + \edef\pgf@marshal{% + \pgf@marshal% + \noexpand\pgfoo@caller@temp(\the\pgfoo@toks)% + }% + \expandafter\pgf@marshal\expandafter\pgfoothis@count\the\pgfoothis@count\relax% +}% +\let\pgfoo@orig@caller=\pgfoo@caller + + +\def\pgfoothis.#1({% + \expandafter\let\expandafter\pgfoo@caller@temp\csname pgfooY\csname pgfooX\the\pgfoothis@count @class\endcsname.#1\endcsname% + \ifx\pgfoo@caller@temp\relax% + \expandafter\let\expandafter\pgfoo@caller@temp\csname pgfooY#1\endcsname% + \fi% + \let\pgfoo@continue\pgfoothis@cont% + \pgfoo@collect@args% +}% +\def\pgfoothis@cont{% + \expandafter\pgfoo@caller@temp\expandafter(\the\pgfoo@toks)% +}% + + + + +\def\pgfoo@id(#1){% + \edef#1{\the\pgfoothis@count}% +}% + + +\def\pgfooobj#1{% + \pgfoo@caller{#1}% +}% + + + +\def\pgfoo@obj(#1){% + \edef#1{\noexpand\pgfoo@caller{\the\pgfoothis@count}}% +}% + + + + +\def\pgfoogc{% + {% + \pgfoothis@count\pgfoo@objectcount% + \let\pgfoo@next=\pgfoo@dogc% + \pgfoo@next% + }% +}% +\def\pgfoo@dogc{% + \advance\pgfoothis@count by 1\relax% + \expandafter\ifx\csname pgfooX\the\pgfoothis@count @class\endcsname\relax% + \let\pgfoo@next=\relax% + \else% + \let\pgfoo@attribute@op\pgfoo@gc@attribute + \csname pgfooY\csname pgfooX\the\pgfoothis@count @class\endcsname.@pgfoo@process@attributes\endcsname% + \expandafter\global\expandafter\let\csname pgfooX\the\pgfoothis@count @class\endcsname\relax% + \fi% + \pgfoo@next% +}% + + + + +\pgfooclass{object}{% + \method copy(#1) {% + \edef\pgfoo@temp@classname{\csname pgfooX\the\pgfoothis@count @class\endcsname}% + \expandafter\pgfoo@new@create\expandafter#1\expandafter{\pgfoo@temp@classname}% + \def\pgfoo@copy@attributes##1##2{% + \pgfooget{##1}\pgfoo@attrvalue + \expandafter\let\csname pgfooX\the\pgfoo@objectcount @##1\endcsname\pgfoo@attrvalue + }% + \let\pgfoo@attribute@op\pgfoo@copy@attributes + \csname pgfooY\pgfoo@temp@classname .@pgfoo@process@attributes\endcsname + \aftergroup\pgfoogc% + }% +}% + + + +\pgfooclass{signal} +{% + + \attribute emitter;% + + \method signal() {}% + + \method connect(#1,#2) {% + {% + #1.get id(\pgf@tempid)% + \pgfooget{emitter}\pgf@temp% + \let\pgfoo@signal@call=\relax% + \edef\pgf@temp{\pgf@temp\pgfoo@signal@call{\pgf@tempid}{#2}}% + \pgfoolet{emitter}\pgf@temp% + }% + }% + + \def\pgfoo@signal@call#1#2{% + \def\pgf@temp{\pgfooobj{#1}.#2}% + \expandafter\pgf@temp\expandafter(\pgfoo@signal@args)% + }% + + \method emit(#1) {% + \def\pgfoo@signal@args{#1}% + \pgfoovalueof{emitter} + }% +}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleparser.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleparser.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..500c3fe3f5c2a3cd55fc45b57d656bdac8764975 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleparser.code.tex @@ -0,0 +1,658 @@ + +\ProvidesFileRCS{pgfmoduleparser.code.tex} + + +\long\def\pgfparserset#1% + {% + \pgfqkeys{/pgfparser}{#1}% + } +\pgfparserset + {% + ,silent/.is if=\pgfparser@ifname{every parser silent}% + ,status/.is if=\pgfparser@ifname{pgfparser status}% + } + +\long\def\pgfparser@fi@Bn\fi#1{\fi} +\long\def\pgfparser@fi@Bg\fi#1#2{\fi} +\long\def\pgfparser@fi@BTb\fi#1#2#3{\fi#2} +\long\def\pgfparser@fi@BTc\fi#1#2#3{\fi#3} + +\long\def\pgfparserifmark#1% + {% + \ifx\pgfparser@mark#1% + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + } +\pgfutil@protected\long\def\pgfparser@oarg@oarg#1% + {% + \pgfutil@ifnextchar[{\pgfparser@oarg@oarg@{#1}}{#1{\pgfparser@mark}}% + } +\long\def\pgfparser@oarg@oarg@#1[#2]% + {% + #1{#2}% + } +\pgfutil@protected\long\def\pgfparser@oarg@Oarg#1#2% + {% + \pgfutil@ifnextchar[{\pgfparser@oarg@oarg@{#2}}{#2{#1}}% + } +\pgfutil@protected\long\def\pgfparser@oarg@darg#1#2#3% + {% + \long\def\pgfparser@oarg@darg@##1#1##2#2{##1{##2}}% + \pgfutil@ifnextchar#1{\pgfparser@oarg@darg@{#3}}{#3{\pgfparser@mark}}% + } +\pgfutil@protected\long\def\pgfparser@oarg@Darg#1#2#3#4% + {% + \long\def\pgfparser@oarg@darg@##1#1##2#2{##1{##2}}% + \pgfutil@ifnextchar#1{\pgfparser@oarg@darg@{#4}}{#4{#3}}% + } +\pgfutil@protected\long\def\pgfparser@oarg@targ@#1% + {% + \def\pgfparser@oarg@targ@next{#1}% + \afterassignment\pgfparser@oarg@targ@next + \let\pgfparser@ignored@token=% + } +\pgfutil@protected\long\def\pgfparser@oarg@targ#1#2% + {% + \pgfutil@ifnextchar#1% + {\pgfparser@oarg@targ@{#2{\pgfparser@mark}}}{#2{\pgfparser@stop}}% + } + +\pgfutil@protected\def\pgfparser@msg#1% + {% + \immediate\write0{(pgfparser) #1}% + } +\pgfutil@protected\def\pgfparser@status@start#1% + {% + \pgfparser@if{pgfparser status}{\pgfparser@msg{parser '#1' started}}{}% + } +\pgfutil@protected\def\pgfparser@status@state#1% + {% + \pgfparser@if{pgfparser status} + {\pgfparser@msg{|= switched to state '#1'}} + {}% + } +\pgfutil@protected\def\pgfparser@status@rule + {% + \pgfparser@if{pgfparser status} + {\pgfparser@msg{| \space|= rule '\meaning\pgfparsertoken' executed}} + {}% + } +\pgfutil@protected\def\pgfparser@status@rule@all + {% + \pgfparser@if{pgfparser status} + {% + \pgfparser@msg + {| \space|= (all) rule '\meaning\pgfparsertoken' executed}% + } + {}% + } +\pgfutil@protected\def\pgfparser@status@rule@undefined + {% + \pgfparser@if{pgfparser status} + {% + \pgfparser@msg + {| \space|= unknown for '\meaning\pgfparsertoken' executed}% + } + {}% + } +\pgfutil@protected\def\pgfparser@status@rule@undefined@all + {% + \pgfparser@if{pgfparser status} + {% + \pgfparser@msg + {| \space|= (all) unknown for '\meaning\pgfparsertoken' executed}% + } + {}% + } + +\begingroup +\lccode`\P=`\P \lccode`\G=`\G \lccode`\F=`\F +\lccode`\:=`\X \lccode`\;=`\r \lccode`\A=`\- +\lowercase + {% + \endgroup + \def\pgfparser@mark{APGFparse;:mark-}% + \def\pgfparser@stop{APGFparse;:stop-}% + }% +\def\pgfparser@final{final} +\def\pgfparser@noarg{noarg} +\def\pgfparser@blankspace{blank space} + +\newcount\pgfparserdef@arg@count + +\def\pgfparser@name#1% + {% + pgfparser #1% + } +\def\pgfparser@rule#1% + {% + \pgfparser@current\space #1\space \meaning\pgfparsertoken + } +\def\pgfparser@type#1% + {% + \pgfparser@rule{#1} type% + } +\def\pgfparser@code#1% + {% + \pgfparser@rule{#1} code% + } +\def\pgfparser@undefined#1% + {% + \pgfparser@current\space #1\space unknown% + } +\def\pgfparser@ifname#1% + {% + pgfparserconditional #1% + } + +\def\pgfparser@if#1% + {% + \pgfutil@ifundefined{if\pgfparser@ifname{#1}} + {% + \pgferror{Undefined conditional '#1'. Falling back to false}% + \iffalse + } + {\csname if\pgfparser@ifname{#1}\endcsname}% + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + } +\def\pgfparser@newif#1% + {% + \csname newif\expandafter\endcsname + \csname if\pgfparser@ifname{#1}\endcsname + } +\pgfparser@newif{every parser silent} +\pgfparser@newif{pgfparserdef abort} +\pgfparser@newif{pgfparser status} + +\pgfutil@protected\def\pgfparserdef#1#2% + {% + \def\pgfparserdef@twoargs{{#1}{#2}}% + \pgfparserdef@a + } +\pgfutil@protected\def\pgfparserdef@a + {% + \futurelet\pgfparserdef@arg\pgfparserdef@b + } +\def\pgfparserdef@b + {% + \ifx\pgfparserdef@arg\pgfutil@sptoken + \pgfparserdef@gobble@space + \fi + \pgfparserdef@c + } +\pgfutil@protected\def\pgfparserdef@gobble@space\fi#1% + {% + \fi + \afterassignment\pgfparserdef@a + \let\pgfparser@ignored@token= % + } +\pgfutil@protected\def\pgfparserdef@c#1% + {% + \ifx\pgfparserdef@arg\bgroup + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + {% + \def\pgfparserdef@arg{#1}% + \ifx\pgfparser@blankspace\pgfparserdef@arg + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + {\expandafter\pgfparserdef@d\pgfparserdef@twoargs{blank space \space}} + {\expandafter\pgfparserdef@d\pgfparserdef@twoargs{#1}}% + } + {% + \expandafter\pgfparserdef@d\pgfparserdef@twoargs + {\meaning\pgfparserdef@arg}% + }% + } +\long\def\pgfparserdef@d#1#2#3% + {% + \pgfparser@oarg@Oarg{}{\pgfparserdef@e{#1}{#2}{#3}}% + } +\pgfutil@protected\long\def\pgfparserdef@e#1#2#3#4#5% + {% + \pgfparser@initiate@parser{#1}% + \csname\pgfparser@ifname{pgfparserdef abort}false\endcsname + \pgfparserdef@arg@count=0 + \pgfparserdef@argcount#4\pgfparser@mark + \ifnum\pgfparserdef@arg@count>9 + \pgferror + {% + Too many arguments for parser rule. A maximum of 9 parameters is + supported.% + }% + \csname\pgfparser@ifname{pgfparserdef abort}true\endcsname + \fi + \pgfparser@if{pgfparserdef abort}{} + {% + \ifnum\pgfparserdef@arg@count=0 + \pgfutil@namedef{\pgfparser@name{#1} #2 #3 type}{noarg}% + \pgfutil@namedef{\pgfparser@name{#1} #2 #3 code}% + {#5\pgfparser@getnexttoken}% + \else + \pgfutil@namedef{\pgfparser@name{#1} #2 #3 type}{#4}% + \expandafter\pgfparserdef@argstring@def\the\pgfparserdef@arg@count + \pgfutil@namedef{\pgfparser@name{#1} #2 #3 code\expandafter}% + \pgfparserdef@argstring##1##2##3##4##5##6##7##8##9% + {#5\pgfparser@getnexttoken}% + \fi + }% + } +\def\pgfparserdef@argstring@def#1% + {% + \def\pgfparserdef@argstring##1#1##2##{##1#1}% + } +\def\pgfparserdef@argcount#1% + {% + \ifx\pgfparser@mark#1% + \pgfparser@fi@Bg + \fi + \pgfutil@firstofone + {% + \pgfutil@IfUndefined{pgfparserdef@argcount@#1} + {% + \pgferror{Unknown argument type '#1'. Aborting rule definition}% + \pgfparserdef@argcount@abort + } + {\csname pgfparserdef@argcount@#1\endcsname}% + }% + } +\pgfutil@protected\long\def\pgfparserdef@argcount@abort#1\pgfparser@mark + {% + \csname\pgfparser@ifname{pgfparserdef abort}true\endcsname + } +\def\pgfparserdef@argcount@m + {% + \advance\pgfparserdef@arg@count1 + \pgfparserdef@argcount + } +\let\pgfparserdef@argcount@o\pgfparserdef@argcount@m +\def\pgfparserdef@argcount@O#1% + {% + \advance\pgfparserdef@arg@count1 + \pgfparserdef@argcount + } +\let\pgfparserdef@argcount@r\pgfparserdef@argcount@O +\let\pgfparserdef@argcount@t\pgfparserdef@argcount@O +\def\pgfparserdef@argcount@d#1#2% + {% + \advance\pgfparserdef@arg@count1 + \pgfparserdef@argcount + } +\def\pgfparserdef@argcount@D#1#2#3% + {% + \advance\pgfparserdef@arg@count1 + \pgfparserdef@argcount + } + +\pgfutil@protected\def\pgfparser@initiate@parser#1% + {% + \pgfutil@IfUndefined{if\pgfparser@ifname{#1 silent}}% + {% + \pgfutil@namedef + {\pgfparser@name{#1} all blank space \space\space type}{noarg}% + \pgfutil@namedef + {\pgfparser@name{#1} all blank space \space\space code}% + {\pgfparser@getnexttoken}% + \pgfparser@newif{#1 silent}% + \pgfparserset + {% + #1/silent/.is if=\pgfparser@ifname{#1 silent}% + }% + } + {}% + } + +\pgfutil@protected\def\pgfparserlet#1#2% + {% + \def\pgfparserlet@parser@a{#1}% + \def\pgfparserlet@state@a{#2}% + \pgfparserlet@a + } +\pgfutil@protected\def\pgfparserlet@a + {% + \futurelet\pgfparserlet@arga\pgfparserlet@b + } +\def\pgfparserlet@b + {% + \ifx\pgfparserlet@arga\pgfutil@sptoken + \pgfparserlet@gobble@space\pgfparserlet@a + \fi + \pgfparserlet@c + } +\pgfutil@protected\def\pgfparserlet@gobble@space#1\fi#2% + {% + \fi + \afterassignment#1% + \let\pgfparser@ignored@token= % + } +\pgfutil@protected\def\pgfparserlet@c#1% + {% + \ifx\pgfparserlet@arga\bgroup + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + {% + \def\pgfparserlet@arga{#1}% + \ifx\pgfparser@blankspace\pgfparserlet@arga + \def\pgfparserlet@arga{blank space \space}% + \fi + } + {\edef\pgfparserlet@arga{\meaning\pgfparserlet@arga}}% + \pgfparser@oarg@oarg\pgfparserlet@d + } +\pgfutil@protected\def\pgfparserlet@d#1% + {% + \pgfparserifmark{#1} + {% + \let\pgfparserlet@parser@b\pgfparserlet@parser@a + \let\pgfparserlet@state@b\pgfparserlet@state@a + \pgfparserlet@f + } + {\pgfparser@oarg@oarg{\pgfparserlet@e{#1}}}% + } +\pgfutil@protected\def\pgfparserlet@e#1#2% + {% + \pgfparserifmark{#2} + {% + \let\pgfparserlet@parser@b\pgfparserlet@parser@a + \def\pgfparserlet@state@b{#1}% + } + {% + \def\pgfparserlet@parser@b{#1}% + \def\pgfparserlet@state@b{#2}% + } + \pgfparserlet@f + } +\pgfutil@protected\def\pgfparserlet@f + {% + \futurelet\pgfparserlet@argb\pgfparserlet@g + } +\def\pgfparserlet@g + {% + \ifx\pgfparserlet@argb\pgfutil@sptoken + \pgfparserlet@gobble@space\pgfparserlet@f + \fi + \pgfparserlet@h + } +\pgfutil@protected\def\pgfparserlet@h#1% + {% + \ifx\pgfparserlet@argb\bgroup + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + {% + \def\pgfparserlet@argb{#1}% + \ifx\pgfparser@blankspace\pgfparserlet@argb + \def\pgfparserlet@argb{blank space \space}% + \fi + } + {\edef\pgfparserlet@argb{\meaning\pgfparserlet@argb}}% + \pgfparserlet@i + \pgfparserlet@parser@a + \pgfparserlet@state@a + \pgfparserlet@arga + \pgfparserlet@parser@b + \pgfparserlet@state@b + \pgfparserlet@argb + } +\def\pgfparserlet@i#1#2#3#4#5#6% + {% + \pgfutil@IfUndefined{\pgfparser@name{#4} #5 #6 type} + {% + \pgferror + {% + There is no rule defined for parser '#4' in state '#5' for '#6'. + Aborting \string\pgfparserlet + }% + } + {% + \pgfparser@initiate@parser{#1}% + \pgfparserlet@let{#1}{#2}{#3}{#4}{#5}{#6}{type}% + \pgfparserlet@let{#1}{#2}{#3}{#4}{#5}{#6}{code}% + }% + } +\def\pgfparserlet@let#1#2#3#4#5#6#7% + {% + \expandafter\let\csname\pgfparser@name{#1} #2 #3 #7\expandafter\endcsname + \csname\pgfparser@name{#4} #5 #6 #7\endcsname + } + +\pgfutil@protected\long\def\pgfparserdefunknown#1#2#3% + {% + \pgfparser@initiate@parser{#1}% + \pgfutil@namedef{\pgfparser@name{#1} #2 unknown}{#3}% + } +\pgfutil@protected\long\def\pgfparserdeffinal#1#2% + {% + \pgfutil@namedef{\pgfparser@name{#1} final action}{#2}% + } +\pgfutil@protected\def\pgfparserswitch#1% + {% + \pgfparser@status@state{#1}% + \def\pgfparserstate{#1}% + } +\pgfutil@protected\def\pgfparserparse#1% + {% + \pgfutil@IfUndefined{if\pgfparser@ifname{#1 silent}} + {\pgferror{No parser named '#1' defined}} + {% + \edef\pgfparser@current{\pgfparser@name{#1}}% + \def\pgfparser@usersname{#1}% + \pgfparser@status@start{#1}% + \pgfparserswitch{initial}% + \pgfparser@getnexttoken + }% + } +\pgfutil@protected\def\pgfparser@getnexttoken + {% + \ifx\pgfparserstate\pgfparser@final + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + {% + \pgfutil@IfUndefined{\pgfparser@current\space final action} + {} + {\csname \pgfparser@current\space final action\endcsname}% + } + {\futurelet\pgfparsertoken\pgfparser@getnexttoken@a}% + } +\pgfutil@protected\def\pgfparser@getnexttoken@a + {% + \edef\pgfparser@tokencategory{\pgfparser@extractmeaning\pgfparsertoken}% + \pgfparser@getnexttoken@ifcategory\pgfparser@category@i\bgroup + {% + \pgfparser@getnexttoken@ifcategory\pgfparser@category@ii\egroup + {% + \pgfparser@getnexttoken@ifcategory\pgfparser@category@x{ }% + {% + \pgfparser@getnexttoken@ifcategory\pgfparser@category@vi{####}% + {\pgfparser@getnexttoken@defchar}% + }% + }% + }% + } +\begingroup +\def\pgfparser@extractmeaning#1% + {% + \endgroup + \def\pgfparser@extractmeaning##1% + {\expandafter\pgfparser@extractmeaning@\meaning##1#1#1\pgfparser@mark}% + \def\pgfparser@extractmeaning@##1#1##2#1##3\pgfparser@mark{##1#1##2}% + } +\catcode`\ =12\pgfparser@extractmeaning{ } % +\edef\pgfparser@category@i{\pgfparser@extractmeaning\bgroup} +\edef\pgfparser@category@ii{\pgfparser@extractmeaning\egroup} +\edef\pgfparser@category@vi{\pgfparser@extractmeaning#} +\edef\pgfparser@category@x{\pgfparser@extractmeaning\pgfutil@sptoken} +\pgfutil@protected\def\pgfparser@getnexttoken@ifcategory#1#2% + {% + \ifx\pgfparser@tokencategory#1% + \def\pgfparserletter{#2}% + \pgfparser@getnexttoken@gobble + \fi + \pgfutil@firstofone + } +\pgfutil@protected\def\pgfparser@getnexttoken@gobble\fi#1#2% + {% + \fi + \afterassignment\pgfparser@getnexttoken@b + \let\pgfparser@ignored@token= % + } +\pgfutil@protected\long\def\pgfparser@getnexttoken@defchar#1% + {% + \def\pgfparserletter{#1}% + \pgfparser@getnexttoken@b + } +\pgfutil@protected\def\pgfparser@getnexttoken@b + {% + \pgfutil@IfUndefined{\pgfparser@type{\pgfparserstate}} + {% + \pgfutil@IfUndefined{\pgfparser@type{all}} + {% + \pgfparser@if{every parser silent}{} + {% + \pgfparser@if{\pgfparser@usersname\space silent}{} + {% + \pgferror + {% + No rule for parser '\pgfparser@usersname' in state + '\pgfparserstate' for '\meaning\pgfparsertoken'. + Ignoring token% + }% + }% + }% + \pgfutil@IfUndefined{\pgfparser@undefined{\pgfparserstate}} + {% + \pgfutil@IfUndefined{\pgfparser@undefined{all}} + {} + {% + \pgfparser@status@rule@undefined@all + \csname\pgfparser@undefined{all}\endcsname + }% + } + {% + \pgfparser@status@rule@undefined + \csname\pgfparser@undefined{\pgfparserstate}\endcsname + }% + \pgfparser@getnexttoken + } + {% + \pgfparser@status@rule@all + \pgfparser@handle{all}% + }% + } + {% + \pgfparser@status@rule + \pgfparser@handle{\pgfparserstate}% + }% + } + +\pgfutil@protected\def\pgfparser@handle#1% + {% + \expandafter\ifx\csname\pgfparser@type{#1}\endcsname\pgfparser@noarg + \pgfparser@fi@BTb + \fi + \pgfutil@secondoftwo + {\csname\pgfparser@code{#1}\endcsname} + {\pgfparser@handle@args{#1}}% + } +\pgfutil@protected\def\pgfparser@handle@args#1% + {% + \def\pgfparser@stateorall{#1}% + \expandafter\expandafter\expandafter\pgfparser@handle@args@a + \csname\pgfparser@type{#1}\endcsname\pgfparser@mark\pgfparser@stop + } +\def\pgfparser@handle@args@a + {% + \pgfparser@handle@args@b{}% + } +\pgfutil@protected\long\def\pgfparser@handle@args@b#1#2#3\pgfparser@stop + {% + \pgfparserifmark{#2} + {\csname\pgfparser@code{\pgfparser@stateorall}\endcsname#1} + {% + \pgfutil@IfUndefined{pgfparser@handle@args@#2} + {\pgferror{Unknown argument type '#2'}} + {\csname pgfparser@handle@args@#2\endcsname{#1}{#3}}% + }% + } +\long\def\pgfparser@handle@args@c#1#2% + {% + \pgfparserifmark{#2} + {\csname\pgfparser@code{\pgfparser@stateorall}\endcsname#1} + {\pgfparser@handle@args@b{#1}#2\pgfparser@stop}% + } +\long\def\pgfparser@handle@args@m#1#2#3% + {% + \pgfparser@handle@args@c{#1{#3}}{#2}% + } +\pgfutil@protected\long\def\pgfparser@handle@args@o#1#2% + {% + \pgfparser@oarg@oarg{\pgfparser@handle@args@m{#1}{#2}}% + } +\long\def\pgfparser@handle@args@O#1#2% + {% + \pgfparser@handle@args@O@{#1}#2\pgfparser@stop + } +\pgfutil@protected\long\def\pgfparser@handle@args@O@#1#2#3\pgfparser@stop + {% + \pgfparser@oarg@Oarg{#2}{\pgfparser@handle@args@m{#1}{#3}}% + } +\long\def\pgfparser@handle@args@d#1#2% + {% + \pgfparser@handle@args@d@{#1}#2\pgfparser@stop + } +\pgfutil@protected\long\def\pgfparser@handle@args@d@#1#2#3#4\pgfparser@stop + {% + \pgfparser@oarg@darg{#2}{#3}{\pgfparser@handle@args@m{#1}{#4}}% + } +\long\def\pgfparser@handle@args@D#1#2% + {% + \pgfparser@handle@args@D@{#1}#2\pgfparser@stop + } +\pgfutil@protected\long\def\pgfparser@handle@args@D@#1#2#3#4#5\pgfparser@stop + {% + \pgfparser@oarg@Darg{#2}{#3}{#4}{\pgfparser@handle@args@m{#1}{#5}}% + } +\long\def\pgfparser@handle@args@r#1#2% + {% + \pgfparser@handle@args@r@a{#1}#2\pgfparser@stop + } +\pgfutil@protected\long\def\pgfparser@handle@args@r@a#1#2#3\pgfparser@stop + {% + \def\pgfparser@handle@args@r@b##1#2% + {\pgfparser@handle@args@c{#1{##1}}{#3}}% + \pgfparser@handle@args@r@b + } +\long\def\pgfparser@handle@args@t#1#2% + {% + \pgfparser@handle@args@t@{#1}#2\pgfparser@stop + } +\pgfutil@protected\long\def\pgfparser@handle@args@t@#1#2#3\pgfparser@stop + {% + \pgfparser@oarg@targ{#2}{\pgfparser@handle@args@m{#1}{#3}}% + } + +\pgfutil@protected\long\def\pgfparserreinsert#1% + {% + \ifx\pgfparser@getnexttoken#1% + \pgfparser@fi@BTb + \fi + \@secondoftwo + {\expandafter\pgfparser@getnexttoken\pgfparserletter} + {% + \pgferror + {% + Misuse of \string\pgfparserreinsert\space detected. You should only + use it at the the end of an action code% + }% + #1% + }% + } + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleplot.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleplot.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e4fc5c36163036d0a57231d2ebc4d08f5d314d6d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleplot.code.tex @@ -0,0 +1,338 @@ + +\ProvidesFileRCS{pgfmoduleplot.code.tex} + + + + +\def\pgfplotstreamstart{\pgf@plotstreamstart}% +\def\pgfplotstreampoint#1{\gdef\pgfplotlastpoint{#1}\pgf@plotstreampoint{#1}}% +\def\pgfplotstreampointoutlier#1{\pgfplot@outliers{}{\pgf@plotstreamjump}{\pgfplotstreampoint{#1}}}% +\def\pgfplotstreampointundefined{\pgfplot@outliers{}{\pgf@plotstreamjump}{}}% +\def\pgfplotstreamnewdataset{\pgfplot@outliers{}{\pgf@plotstreamjump}{}}% +\def\pgfplotstreamspecial{\pgf@plotstreamspecial}% +\def\pgfplotstreamend{\pgf@plotstreamend}% + +\def\pgfplot@ignorer#1#2#3{#1}% +\def\pgfplot@jumper#1#2#3{#2}% +\def\pgfplot@plotter#1#2#3{#3}% + +\let\pgfplot@outliers\pgfplot@jumper +\let\pgfplot@undefined\pgfplot@jumper +\let\pgfplot@newdata\pgfplot@jumper + +\pgfset{ + handle outlier points in plots/.is choice, + handle outlier points in plots/ignore/.code=\let\pgfplot@outliers\pgfplot@ignorer, + handle outlier points in plots/jump/.code=\let\pgfplot@outliers\pgfplot@jumper, + handle outlier points in plots/plot/.code=\let\pgfplot@outliers\pgfplot@plotter, + handle undefined points in plots/.is choice, + handle undefined points in plots/ignore/.code=\let\pgfplot@undefined\pgfplot@ignorer, + handle undefined points in plots/jump/.code=\let\pgfplot@undefined\pgfplot@jumper, + handle new data sets in plots/.is choice, + handle new data sets in plots/ignore/.code=\let\pgfplot@newdata\pgfplot@ignorer, + handle new data sets in plots/jump/.code=\let\pgfplot@newdata\pgfplot@jumper, +}% + + + +\def\pgfdeclareplothandler#1#2#3{% + \def#1#2{% + \pgfkeys{% + /pgf/plots/@handler options/.cd, + start=\relax, + end macro=\relax, + point macro=\pgfutil@gobble, + jump macro=\relax, + special macro=\pgfutil@gobble,% + #3% + }% + }% +}% + +\pgfkeys{% + /pgf/plots/@handler options/.cd, + start/.code=% + \gdef\pgf@plotstreamstart{% + \global\pgf@plot@startedfalse% + \global\let\pgf@plotstreamend\pgf@plotstreamend@init% + \global\let\pgf@plotstreampoint\pgf@plotstreampoint@init% + \global\let\pgf@plotstreamjump\pgf@plotstreamjump@init% + \global\let\pgf@plotstreamspecial\pgf@plotstreamspecial@init% + #1% + },% + start macro/.code=% + \gdef\pgf@plotstreamstart{% + \global\pgf@plot@startedfalse% + \global\let\pgf@plotstreamend\pgf@plotstreamend@init% + \global\let\pgf@plotstreampoint\pgf@plotstreampoint@init% + \global\let\pgf@plotstreamjump\pgf@plotstreamjump@init% + \global\let\pgf@plotstreamspecial\pgf@plotstreamspecial@init% + #1% + },% + end/.code=\gdef\pgf@plotstreamend@init{#1}, + end macro/.code=\global\let\pgf@plotstreamend@init#1, + point/.code=\gdef\pgf@plotstreampoint@init##1{#1}, + point macro/.code=\global\let\pgf@plotstreampoint@init#1, + jump/.code=\gdef\pgf@plotstreamjump@init{#1}, + jump macro/.code=\global\let\pgf@plotstreamjump@init#1, + special/.code=\gdef\pgf@plotstreamspecial@init##1{#1}, + special macro/.code=\global\let\pgf@plotstreamspecial@init#1, +}% + +\newif\ifpgf@plot@started + + + + + +\def\pgfsetlinetofirstplotpoint{\let\pgf@plot@first@action=\pgfpathlineto}% + + + +\def\pgfsetmovetofirstplotpoint{\let\pgf@plot@first@action=\pgfpathmoveto}% + +\let\pgf@plot@first@action=\pgfpathmoveto + + + + + + + +\pgfdeclareplothandler{\pgfplothandlerlineto}{}{ + point macro=\pgf@plot@line@handler, + jump=\global\let\pgf@plotstreampoint\pgf@plot@line@handler@move% +}% + +\def\pgf@plot@line@handler#1{% + \pgf@plot@first@action{#1}% + \global\let\pgf@plotstreampoint=\pgfpathlineto% +}% + +\def\pgf@plot@line@handler@move#1{% + \pgfpathmoveto{#1}% + \global\let\pgf@plotstreampoint=\pgfpathlineto% +}% + + + + +\pgfdeclareplothandler{\pgfplothandlerpolygon}{}{% + point macro=\pgf@plot@line@handler@close, + jump macro=\pgf@plot@next@close@and@moveto, + end macro=\pgf@plot@polygon@stop +}% + +\def\pgf@plot@line@handler@close#1{% + \pgfpathmoveto{#1}% + \global\pgf@plot@startedtrue% + \global\let\pgf@plotstreampoint=\pgfpathlineto% +}% + +\def\pgf@plot@polygon@stop{% + \ifpgf@plot@started% + \pgfpathclose% + \fi% + \global\pgf@plot@startedfalse% +}% + +\def\pgf@plot@next@close@and@moveto{% + \ifpgf@plot@started% + \pgfpathclose% + \fi% + \global\let\pgf@plotstreampoint\pgf@plot@line@handler@close% +}% + + + + + + + + +\pgfdeclareplothandler{\pgfplothandlerdiscard}{}{}% + + + + +\pgfdeclareplothandler{\pgfplothandlerrecord}{#1}{% + start=\gdef#1{\pgfplotstreamstart}, + point=\expandafter\gdef\expandafter#1\expandafter{#1\pgfplotstreampoint{##1}}, + jump=\expandafter\gdef\expandafter#1\expandafter{#1\pgf@plotstreamjump}, + special=\expandafter\gdef\expandafter#1\expandafter{#1\pgfplotstreamspecial{##1}}, + end=\expandafter\gdef\expandafter#1\expandafter{#1\pgfplotstreamend}, +}% + + + + +\def\pgfplotxyfile#1{% + \begingroup% + \def\b@pgfplotsxyfile@scanning@for@first{1}% + \pgfplotstreamstart% + \openin\r@pgf@reada=#1 + \ifeof\r@pgf@reada + \pgfwarning{Plot data file `#1' not found.} + \else + \catcode`\#=14 + \catcode`\^^M=5 + \pgf@readxyfile% + \fi + \pgfplotstreamend% + \endgroup% +}% + +\let\pgf@savedpar=\par +\def\pgf@partext{\par}% +\def\pgf@readxyfile{% + \pgfutil@read\r@pgf@reada to \pgf@temp% + \let\par=\pgf@savedpar% + \edef\pgf@temp{\pgf@temp}% + \ifx\pgf@temp\pgfutil@empty% + \if1\b@pgfplotsxyfile@scanning@for@first + \else + \ifeof\r@pgf@reada\else\pgfplotstreamnewdataset\fi% + \fi + \else\ifx\pgf@temp\pgf@partext% + \if1\b@pgfplotsxyfile@scanning@for@first + \else + \ifeof\r@pgf@reada\else\pgfplotstreamnewdataset\fi% + \fi + \else% + \expandafter\pgf@parsexyline\pgf@temp\pgf@stop% + \fi\fi% + \ifeof\r@pgf@reada\else\expandafter\pgf@readxyfile\fi% +}% + +\def\pgf@parsexyline#1 #2 #3\pgf@stop{% + \def\b@pgfplotsxyfile@scanning@for@first{0}% + \edef\pgf@xyline@flag@val{#3}% + \ifx\pgf@xyline@flag@val\pgf@xyline@flag@undef% + \pgfplotstreampointundefined% + \else\ifx\pgf@xyline@flag@val\pgf@xyline@flag@out% + \pgfplotstreampointoutlier{\pgfpointxy{#1}{#2}}% + \else% + \pgfplotstreampoint{\pgfpointxy{#1}{#2}}% + \fi\fi% +}% + +\edef\pgf@xyline@flag@out{o\space}% +\edef\pgf@xyline@flag@undef{u\space}% + + + + + +\def\pgfplotxyzfile#1{% + \begingroup% + \pgfplotstreamstart% + \openin\r@pgf@reada=#1 + \ifeof\r@pgf@reada + \pgfwarning{Plot data file `#1' not found.} + \else + \catcode`\#=14 + \catcode`\^^M=5 + \pgf@readxyzfile% + \fi + \pgfplotstreamend% + \endgroup% +}% + +\def\pgf@readxyzfile{% + \pgfutil@read\r@pgf@reada to \pgf@temp% + \ifx\pgf@temp\pgfutil@empty% + \if1\b@pgfplotsxyfile@scanning@for@first + \else + \ifeof\r@pgf@reada\else\pgfplotstreamnewdataset\fi% + \fi + \else\ifx\pgf@temp\pgf@partext% + \if1\b@pgfplotsxyfile@scanning@for@first + \else + \ifeof\r@pgf@reada\else\pgfplotstreamnewdataset\fi% + \fi + \else% + \expandafter\pgf@parsexyzline\pgf@temp\pgf@stop% + \fi\fi% + \ifeof\r@pgf@reada\else\expandafter\pgf@readxyzfile\fi% +}% + +\def\pgf@parsexyzline#1 #2 #3 #4\pgf@stop{% + \def\b@pgfplotsxyfile@scanning@for@first{0}% + \edef\pgf@xyline@flag@val{#4}% + \ifx\pgf@xyline@flag@val\pgf@xyline@flag@undef% + \pgfplotstreampointundefined% + \else\ifx\pgf@xyline@flag@val\pgf@xyline@flag@out% + \pgfplotstreampointoutlier{\pgfpointxyz{#1}{#2}{#3}}% + \else% + \pgfplotstreampoint{\pgfpointxyz{#1}{#2}{#3}}% + \fi\fi% +}% + + + + + +{% + \catcode`\%=12 + \catcode`\"=12 + \xdef\pgf@gnuplot@head{set table \noexpand\pgf@plottablefile@quoted; set format "%.5f"} +}% + +\let\pgf@plotwrite=\w@pgf@writea +\newif\ifpgf@resample@plot + +\pgfkeys{% + /pgf/plot/gnuplot call/.initial={gnuplot}}% + +\def\pgfplotgnuplot{\pgfutil@ifnextchar[{\pgf@plotgnuplot}{\pgf@plotgnuplot[\jobname]}}% +\def\pgf@plotgnuplot[#1]#2{% + \pgf@resample@plottrue% + \pgfutilpreparefilename{#1.gnuplot}% + \let\pgf@plotgnuplotfile=\pgfretval + \pgfutilpreparefilename{#1.table}% + \let\pgf@plottablefile=\pgfretval + \let\pgf@plottablefile@quoted=\pgfretvalquoted + \openin\pgfutil@inputcheck=\pgf@plotgnuplotfile\relax + \ifeof\pgfutil@inputcheck% + \else% + \pgfutil@read\pgfutil@inputcheck to\pgf@temp% + \pgfutil@read\pgfutil@inputcheck to\pgf@plot@line% + \closein\pgfutil@inputcheck + \edef\pgf@plot@code{#2\space}% + \ifx\pgf@plot@code\pgf@plot@line% + \openin\pgfutil@inputcheck=\pgfretval\relax + \ifeof\pgfutil@inputcheck% + \else% + \closein\pgfutil@inputcheck + \pgf@resample@plotfalse% + \fi% + \fi% + \fi + \ifpgf@resample@plot% + \immediate\openout\pgf@plotwrite=\pgf@plotgnuplotfile\relax + \immediate\pgfutil@write\pgf@plotwrite{\pgf@gnuplot@head}% + \immediate\pgfutil@write\pgf@plotwrite{#2}% + \immediate\closeout\pgf@plotwrite% + \pgfutil@shellescape{% + \pgfkeysvalueof{/pgf/plot/gnuplot call} \pgf@plotgnuplotfile}% + \fi% + \pgfplotxyfile{\pgf@plottablefile}% +}% + + + +\def\pgfplotfunction#1#2#3{% + \pgfplotstreamstart% + \foreach#1in{#2}% + {% + \pgf@process{#3}% + \edef\pgf@marshal{\noexpand\pgfplotstreampoint{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}}% + \pgf@marshal% + } + \pgfplotstreamend% +}% + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleshapes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleshapes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..a176f5a88a8a4dbaad1c0d200a1314b2a7e48f72 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmoduleshapes.code.tex @@ -0,0 +1,925 @@ + +\ProvidesFileRCS{pgfmoduleshapes.code.tex} + + + +\newbox\pgfnodeparttextbox + + + +\def\pgfmultipartnode#1#2#3#4{% + \pgfutil@ifundefined{pgf@sh@s@#1}% + {\pgferror{Unknown shape ``#1''}}% + {% + {% + \ifpgflatenodepositioning% + \pgfsys@beginscope% + \fi% + \pgf@outer@adjust@hook% + \let\pgf@sh@savedmacros=\pgfutil@empty% + \let\pgf@sh@savedpoints=\pgfutil@empty% + \def\pgf@sm@shape@name{#1}% + \csname pgf@sh@s@#1\endcsname% + \pgf@sh@savedpoints% + \pgf@sh@savedmacros% + \pgftransformshift{% + \pgf@sh@reanchor{#1}{#2}% + \pgf@x=-\pgf@x% + \pgf@y=-\pgf@y% + }% + \expandafter\pgfsavepgf@process\csname pgf@sh@sa@#3\endcsname{% + \pgf@sh@reanchor{#1}{#2}% + }% + \edef\pgf@node@name{#3}% + \ifpgflatenodepositioning% + \pgf@shapes@late@pos@begin% + \fi% + \ifx\pgf@node@name\pgfutil@empty% + \else% + \expandafter\xdef\csname pgf@sh@ns@\pgf@node@name\endcsname{#1}% + \edef\pgf@sh@@temp{\noexpand\gdef\expandafter\noexpand\csname pgf@sh@np@\pgf@node@name\endcsname}% + \expandafter\pgf@sh@@temp\expandafter{\pgf@sh@savedpoints}% + \edef\pgf@sh@@temp{\noexpand\gdef\expandafter\noexpand\csname pgf@sh@ma@\pgf@node@name\endcsname}% + \expandafter\pgf@sh@@temp\expandafter{\pgf@sh@savedmacros}% + \pgfgettransform\pgf@temp% + \expandafter\xdef\csname pgf@sh@nt@\pgf@node@name\endcsname{\pgf@temp}% + \expandafter\xdef\csname pgf@sh@pi@\pgf@node@name\endcsname{\pgfpictureid}% + \fi% + \pgfutil@ifundefined{pgf@sh@bbg@#1}{} + {{\pgfusetype{.behind background}\pgfidscope\pgfscope\csname pgf@sh@bbg@#1\endcsname\endpgfscope\endpgfidscope}}% + \pgfutil@ifundefined{pgf@sh@bg@#1}{% + \global\let\pgfpositionnodelaterpath\pgfutil@empty% + }% + {\pgfpushtype% + \pgfusetype{.background}\csname pgf@sh@bg@#1\endcsname% + \ifpgflatenodepositioning% + \pgfsyssoftpath@getcurrentpath\pgfpositionnodelaterpath% + \pgfprocessround{\pgfpositionnodelaterpath}{\pgfpositionnodelaterpath}% + \global\let\pgfpositionnodelaterpath\pgfpositionnodelaterpath% + \fi% + #4\pgfpoptype}% + \pgfutil@ifundefined{pgf@sh@fbg@#1}{} + {{\pgfusetype{.before background}\pgfidscope\pgfscope\csname pgf@sh@fbg@#1\endcsname\endpgfscope\endpgfidscope}}% + {% + \expandafter\pgfutil@for\expandafter\pgf@shape@com\expandafter:\expandafter=\csname pgf@sh@boxes@#1\endcsname\do{% + {% + \pgfusetype{.\pgf@shape@com}% + \pgftransformshift{\pgf@sh@reanchor{#1}{\pgf@shape@com}}% + \pgfapproximatenonlineartransformation% + \expandafter\pgfqboxsynced\expandafter{\csname pgfnodepart\pgf@shape@com box\endcsname}% + }% + }% + }% + \pgfutil@ifundefined{pgf@sh@bfg@#1}{}% + {{\pgfusetype{.behind foreground}\pgfidscope\pgfscope\csname pgf@sh@bfg@#1\endcsname\endpgfscope\endpgfidscope}}% + \pgfutil@ifundefined{pgf@sh@fg@#1}{}% + {\pgfpushtype\pgfusetype{.foreground}\csname pgf@sh@fg@#1\endcsname#4\pgfpoptype}% + \pgfutil@ifundefined{pgf@sh@ffg@#1}{}% + {{\pgfusetype{.before foreground}\pgfidscope\pgfscope\csname pgf@sh@ffg@#1\endcsname\endpgfscope\endpgfidscope}}% + \ifpgflatenodepositioning% + \pgf@shapes@late@pos@end% + \pgfsys@endscope% + \else% + \expandafter\pgf@nodecallback\expandafter{\pgf@node@name}% + \fi% + }% + }% +}% +\let\pgf@outer@adjust@hook\relax + +\def\pgf@shapes@late@pos@begin{% + \edef\pgf@node@name{not yet positionedPGFINTERNAL\pgf@node@name}% + \pgfinterruptboundingbox% + \pgf@relevantforpicturesizetrue% + \setbox\pgfpositionnodelaterbox=\hbox% + \bgroup% + \pgfsys@beginscope% +}% + +\def\pgf@shapes@late@pos@end{% + \pgfsys@endscope% + \egroup% + \ifdim\pgf@picminx>\pgf@picmaxx\relax% + \def\pgfpositionnodelaterminx{0.0pt}% + \let\pgfpositionnodelaterminy\pgfpositionnodelaterminx% + \let\pgfpositionnodelatermaxx\pgfpositionnodelaterminx% + \let\pgfpositionnodelatermaxy\pgfpositionnodelaterminx% + \else% + \edef\pgfpositionnodelaterminx{\the\pgf@picminx}% + \edef\pgfpositionnodelaterminy{\the\pgf@picminy}% + \edef\pgfpositionnodelatermaxx{\the\pgf@picmaxx}% + \edef\pgfpositionnodelatermaxy{\the\pgf@picmaxy}% + \fi% + \let\pgfpositionnodelatername=\pgf@node@name% + \pgf@positionnodelater@macro% + \endpgfinterruptboundingbox% +}% + +\def\pgf@shift@node#1#2{% + {% + \pgfsettransform{\csname pgf@sh@nt@#1\endcsname}% + \pgf@process{#2}% + \advance\pgf@pt@x by\pgf@x% + \advance\pgf@pt@y by\pgf@y% + \pgfgettransform{\pgf@temp}% + \expandafter\xdef\csname pgf@sh@nt@#1\endcsname{\pgf@temp}% + }% +}% + + + + +\def\pgfnode#1#2#3#4#5{% + {% + \setbox\pgfnodeparttextbox=\hbox% + {% + \pgfinterruptpicture% + {#3}% + \endpgfinterruptpicture% + }% + \pgfmultipartnode{#1}{#2}{#4}{#5}% + } +}% + + + + +\def\pgfpositionnodelater#1{% + \let\pgf@positionnodelater@macro=#1% + \ifx\pgf@positionnodelater@macro\relax% + \pgflatenodepositioningfalse% + \else% + \pgflatenodepositioningtrue% + \fi% +}% +\newif\ifpgflatenodepositioning +\pgfpositionnodelater{\relax}% +\def\pgfpositionnodelaterbox{0}% + + + + + +\def\pgfpositionnodenow#1{% + \pgfinterruptpath% + {% + \pgfpointtransformed{#1}% + \edef\pgf@temp@shift{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}} + \pgftransformreset% + \pgftransformshift{\pgf@temp@shift}% + \pgfsys@pictureboxsynced\pgfpositionnodelaterbox% + \pgf@shift@node{\pgfpositionnodelatername}{\pgf@temp@shift}% + \pgfpointtransformed{\pgfqpoint{\pgfpositionnodelaterminx}{\pgfpositionnodelaterminy}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y} + \pgfpointtransformed{\pgfqpoint{\pgfpositionnodelatermaxx}{\pgfpositionnodelatermaxy}}% + \pgf@protocolsizes{\pgf@x}{\pgf@y} + \expandafter\pgfpositionnodenow@rename\pgfpositionnodelatername\relax% + }% + {% + \csname pgf@lns@\pgfpositionnodelatername\endcsname% + \expandafter\global\expandafter\let\csname pgf@lns@\pgfpositionnodelatername\endcsname\relax% + }% + \endpgfinterruptpath% +}% + +\def\pgfpositionnodenow@rename not yet positionedPGFINTERNAL#1\relax{% + \pgfnoderename{#1}{not yet positionedPGFINTERNAL#1} +}% + + + +\def\pgffakenode#1{% + \edef\pgf@temp{\ifpgflatenodepositioning not yet positionedPGFINTERNAL\fi#1}% + \expandafter\gdef\csname pgf@sh@ns@\pgf@temp\endcsname{coordinate}% + \expandafter\gdef\csname pgf@sh@np@\pgf@temp\endcsname{\def\centerpoint{\pgfpointorigin}}% + \expandafter\gdef\csname pgf@sh@nt@\pgf@temp\endcsname{{1}{0}{0}{1}{0pt}{0pt}}% + \expandafter\global\expandafter\let\csname pgf@sh@ma@\pgf@temp\endcsname\pgfutil@empty% + \expandafter\xdef\csname pgf@sh@pi@\pgf@temp\endcsname{\pgfpictureid}% +}% + + + + +\def\pgfnodepostsetupcode#1#2{% + \ifpgflatenodepositioning% + \expandafter\ifx\csname pgf@lns@not yet positionedPGFINTERNAL#1\endcsname\relax% + \expandafter\gdef\csname pgf@lns@not yet positionedPGFINTERNAL#1\endcsname{#2}% + \else% + \expandafter\pgfutil@g@addto@macro\csname pgf@lns@not yet positionedPGFINTERNAL#1\endcsname{#2}% + \fi% + \fi% +}% + + + + +\def\pgfnodealias#1#2{% + \pgf@node@gnamelet{pgf@sh@ns@#1}{pgf@sh@ns@#2}% + \pgf@node@gnamelet{pgf@sh@np@#1}{pgf@sh@np@#2}% + \pgf@node@gnamelet{pgf@sh@nt@#1}{pgf@sh@nt@#2}% + \pgf@node@gnamelet{pgf@sh@pi@#1}{pgf@sh@pi@#2}% + \pgf@node@gnamelet{pgf@sh@ma@#1}{pgf@sh@ma@#2}% + \pgf@nodecallback{#1}% +}% +\def\pgf@node@gnamelet#1#2{% + \expandafter\let\expandafter\pgf@temp\csname #2\endcsname% + \expandafter\global\expandafter\let\csname #1\endcsname=\pgf@temp% +}% + + +\def\pgfnoderename#1#2{% + \pgfnodealias{#1}{#2}% + \expandafter\global\expandafter\let\csname pgf@sh@ns@#2\endcsname\relax + \expandafter\global\expandafter\let\csname pgf@sh@np@#2\endcsname\relax + \expandafter\global\expandafter\let\csname pgf@sh@nt@#2\endcsname\relax + \expandafter\global\expandafter\let\csname pgf@sh@pi@#2\endcsname\relax + \expandafter\global\expandafter\let\csname pgf@sh@ma@#2\endcsname\relax +}% + + + + + +\def\pgfcoordinate#1#2{% + \edef\pgf@temp{#1}% + \ifx\pgf@temp\pgfutil@empty% + \else% + \ifpgflatenodepositioning% + {\pgftransformshift{#2}\pgfnode{coordinate}{center}{}{#1}{}}% + \else% + \pgf@process{\pgfpointtransformed{#2}}% + \expandafter\gdef\csname pgf@sh@ns@#1\endcsname{coordinate}% + \expandafter\xdef\csname pgf@sh@np@#1\endcsname{% + \noexpand\def\noexpand\centerpoint{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + } + \expandafter\gdef\csname pgf@sh@nt@#1\endcsname{{1}{0}{0}{1}{0pt}{0pt}}% + \expandafter\global\expandafter\let\csname pgf@sh@ma@#1\endcsname\pgfutil@empty% + \expandafter\xdef\csname pgf@sh@pi@#1\endcsname{\pgfpictureid}% + \fi% + \fi% +}% + +\def\pgf@sh@redeferredanchor#1#2{% + \expandafter\gdef\csname pgf@anchor@\pgf@sm@shape@name @#1\endcsname{#2}}% + + + + + + +\def\pgf@sh@resavedanchor#1#2{% + \pgf@process{#2}% + \edef\pgf@sh@marshal{% + \noexpand\pgfutil@g@addto@macro\noexpand\pgf@sh@savedpoints{% + \noexpand\def\noexpand#1{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + }}% + \pgf@sh@marshal% +}% + + +\def\pgf@sh@resaveddimen#1#2{% + {#2\global\pgf@x=\pgf@x}% + \edef\pgf@sh@marshal{% + \noexpand\pgfutil@g@addto@macro\noexpand\pgf@sh@savedpoints{% + \noexpand\def\noexpand#1{\the\pgf@x}% + }}% + \pgf@sh@marshal% +}% + +\def\pgf@sh@resavedmacro#1#2{% + \let#1\pgfutil@empty% + \def\addtosavedmacro##1{% + \expandafter\def\expandafter\pgf@sh@addtomacro@temp\expandafter{#1\noexpand\def\noexpand##1{##1}}% + {\expandafter\pgfutil@toks@\expandafter{\pgf@sh@addtomacro@temp}\expandafter}% + \expandafter\def\expandafter#1\expandafter{\the\pgfutil@toks@}% + }% + #2\relax% + \edef\pgf@sh@marshal{% + \noexpand\pgfutil@g@addto@macro\noexpand\pgf@sh@savedmacros{% + \noexpand\def\noexpand#1{#1}% + }}% + \pgf@sh@marshal% +}% + +\def\pgf@sh@reanchor#1#2{% + \pgfutil@ifundefined{pgf@anchor@#1@#2}% + {% + \pgfutil@ifundefined{pgf@anchor@generic@#2}{% + \pgfmathsetcounter{pgf@counta}{#2}% + \csname pgf@anchor@#1@border\endcsname{\pgfqpointpolar{\the\c@pgf@counta}{1pt}}% + }{% + \csname pgf@anchor@generic@#2\endcsname{#1}% + }% + }% + {\csname pgf@anchor@#1@#2\endcsname}% +}% + +\def\pgfdeclaregenericanchor#1#2{% + \expandafter\def\csname pgf@anchor@generic@#1\endcsname##1{#2}% +}% + + + +\def\pgfpointanchor#1#2{% + \pgfutil@ifundefined{pgf@sh@ns@#1} + {\pgfutil@ifundefined{pgf@sh@ns@not yet positionedPGFINTERNAL#1}{% + \pgferror{No shape named `#1' is known}}{ + }% + \pgfpointorigin}% + {% + \pgf@process{% + \edef\pgfreferencednodename{#1}% + \csname pgf@sh@ma@#1\endcsname% + \csname pgf@sh@np@#1\endcsname + \pgf@sh@reanchor{\csname pgf@sh@ns@#1\endcsname}{#2}% + {% + \pgfsettransform{\csname pgf@sh@nt@#1\endcsname}% + \pgf@pos@transform@glob% + }% + \pgf@shape@interpictureshift{#1}% + \pgftransforminvert% + \pgf@pos@transform@glob% + }% + }% +}% + +\def\pgf@shape@interpictureshift#1{% + \expandafter\ifx\csname pgf@sh@pi@#1\endcsname\pgfpictureid% + \else% + \pgfsys@getposition{\csname pgf@sh@pi@#1\endcsname}\pgf@shape@original@pos% + \pgfsys@getposition{\pgfpictureid}\pgf@shape@current@pos% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointorigin\pgf@shape@current@pos}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@process{\pgfpointorigin\pgf@shape@original@pos}% + \advance\pgf@xa by\pgf@x% + \advance\pgf@ya by\pgf@y% + \pgf@x=\pgf@xa% + \pgf@y=\pgf@ya% + \fi% +}% + + + + +\def\pgfpointshapeborder#1#2{% + \pgfutil@ifundefined{pgf@sh@ns@#1} + {\pgferror{No shape named `#1' is known}% + \pgfpointorigin}% + {% + \pgf@process{% + \edef\pgfreferencednodename{#1}% + \csname pgf@sh@ma@#1\endcsname% + \csname pgf@sh@np@#1\endcsname% + {% + \pgf@process{\pgfpointtransformed{#2}}% + \pgfsettransform{\csname pgf@sh@nt@#1\endcsname}% + \pgftransforminvert% + \pgf@pos@transform@glob% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\csname pgf@anchor@\csname pgf@sh@ns@#1\endcsname @center\endcsname}% + \pgf@process{\pgf@shape@interpictureshift{#1}}% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgf@xb=10pt + \ifdim\pgf@xa<1pt\ifdim\pgf@xa>-1pt + \pgf@xb=10\pgf@xa + \fi\fi + \pgf@yb=10pt + \ifdim\pgf@ya<1pt\ifdim\pgf@ya>-1pt + \pgf@yb=10\pgf@ya + \fi\fi + \ifdim\dimexpr\expandafter\Pgf@geT\the\pgf@xb\pgf@xb + +\expandafter\Pgf@geT\the\pgf@yb\pgf@yb\relax<0.04pt + \expandafter\pgfutil@firstoftwo + \else + \expandafter\pgfutil@secondoftwo + \fi + {% + \pgfwarning + {Returning node center instead of a point on node border. Did you + specify a point identical to the center of node + ``\pgfreferencednodename''?}% + \pgf@sh@reanchor{\csname pgf@sh@ns@#1\endcsname}{center}% + } + {% + \csname pgf@anchor@\csname pgf@sh@ns@#1\endcsname @border\endcsname + {\pgfqpoint{\pgf@xa}{\pgf@ya}}% + }% + \pgfsettransform{\csname pgf@sh@nt@#1\endcsname}% + \pgf@pos@transform@glob% + \global\pgf@x=\pgf@x% + \global\pgf@y=\pgf@y% + }% + \pgf@shape@interpictureshift{#1}% + \pgftransforminvert% + \pgf@pos@transform@glob% + }% + }% +}% + + + +\def\pgfgetnodeparts#1#2{% + \expandafter\let\expandafter#1\csname pgf@sh@boxes@#2\endcsname% +}% + + + +\long\def\pgfdeclareshape#1#2{% + {% + \def\pgf@sm@shape@name{#1}% + \let\savedanchor=\pgf@sh@savedanchor + \let\saveddimen=\pgf@sh@saveddimen + \let\savedmacro=\pgf@sh@savedmacro% + \let\deferredanchor=\pgf@sh@deferredanchor% + \let\anchor=\pgf@sh@anchor + \let\anchorborder=\pgf@sh@anchorborder + \let\behindbackgroundpath=\pgf@sh@behindbgpath + \let\backgroundpath=\pgf@sh@bgpath + \let\beforebackgroundpath=\pgf@sh@beforebgpath + \let\behindforegroundpath=\pgf@sh@behindfgpath + \let\foregroundpath=\pgf@sh@fgpath + \let\beforeforegroundpath=\pgf@sh@beforefgpath + \let\nodeparts=\pgf@sh@boxes + \let\inheritsavedanchors=\pgf@sh@inheritsavedanchors + \let\inheritanchor=\pgf@sh@inheritanchor + \let\inheritanchorborder=\pgf@sh@inheritanchorborder + \let\inheritbehindbackgroundpath=\pgf@sh@inheritbehindbgpath + \let\inheritbackgroundpath=\pgf@sh@inheritbgpath + \let\inheritbeforebackgroundpath=\pgf@sh@inheritbeforebgpath + \let\inheritbehindforegroundpath=\pgf@sh@inheritbehindfgpath + \let\inheritforegroundpath=\pgf@sh@inheritfgpath + \let\inheritbeforeforegroundpath=\pgf@sh@inheritbeforefgpath + \let\inheritnodeparts=\pgf@sh@inheritboxes + \anchorborder{\csname pgf@anchor@#1@center\endcsname}% + \anchor{text}{\pgfpointorigin}% + \nodeparts{text}% + \expandafter\global\expandafter\let\csname pgf@sh@s@\pgf@sm@shape@name\endcsname=\pgfutil@empty% + #2% + }% +}% + +\def\pgf@sh@savedanchor#1#2{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@\pgf@sm@shape@name\endcsname{\pgf@sh@resavedanchor{#1}{#2}}}% +\def\pgf@sh@saveddimen#1#2{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@\pgf@sm@shape@name\endcsname{\pgf@sh@resaveddimen{#1}{#2}}}% + \def\pgf@sh@savedmacro#1#2{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@\pgf@sm@shape@name\endcsname{\pgf@sh@resavedmacro{#1}{#2}}}% +\def\pgf@sh@anchor#1#2{\expandafter\gdef\csname pgf@anchor@\pgf@sm@shape@name @#1\endcsname{#2}}% +\def\pgf@sh@deferredanchor#1#2{% + \expandafter\pgfutil@g@addto@macro + \csname pgf@sh@s@\pgf@sm@shape@name\endcsname{\pgf@sh@redeferredanchor{#1}{#2}}}% +\def\pgf@sh@anchorborder#1{\expandafter\gdef\csname pgf@anchor@\pgf@sm@shape@name @border\endcsname##1{\pgf@process{##1}#1}}% +\long\def\pgf@sh@behindbgpath#1{\expandafter\gdef\csname pgf@sh@bbg@\pgf@sm@shape@name\endcsname{#1}}% +\long\def\pgf@sh@bgpath#1{\expandafter\gdef\csname pgf@sh@bg@\pgf@sm@shape@name\endcsname{#1}}% +\long\def\pgf@sh@beforebgpath#1{\expandafter\gdef\csname pgf@sh@fbg@\pgf@sm@shape@name\endcsname{#1}}% +\long\def\pgf@sh@behindfgpath#1{\expandafter\gdef\csname pgf@sh@bfg@\pgf@sm@shape@name\endcsname{#1}}% +\long\def\pgf@sh@fgpath#1{\expandafter\gdef\csname pgf@sh@fg@\pgf@sm@shape@name\endcsname{#1}}% +\long\def\pgf@sh@beforefgpath#1{\expandafter\gdef\csname pgf@sh@ffg@\pgf@sm@shape@name\endcsname{#1}}% +\def\pgf@sh@boxes#1{\expandafter\gdef\csname pgf@sh@boxes@\pgf@sm@shape@name\endcsname{#1}}% + +\def\pgf@sh@inheritsavedanchors[from=#1]{% + \expandafter\pgfutil@g@addto@macro\csname pgf@sh@s@\pgf@sm@shape@name\endcsname{\csname pgf@sh@s@#1\endcsname}}% + +\def\pgf@sh@inheritanchor[from=#1]#2{% + \edef\pgf@marshal{\global\let\expandafter\noexpand\csname + pgf@anchor@\pgf@sm@shape@name @#2\endcsname=\expandafter\noexpand\csname + pgf@anchor@#1@#2\endcsname}% + \pgf@marshal% +}% +\def\pgf@sh@inheritanchorborder[from=#1]{% + \edef\pgf@marshal{\global\let\expandafter\noexpand\csname + pgf@anchor@\pgf@sm@shape@name @border\endcsname=\expandafter\noexpand\csname + pgf@anchor@#1@border\endcsname}% + \pgf@marshal% +}% +\def\pgf@sh@inheritor#1#2{% + \edef\pgf@marshal{\global\let\expandafter\noexpand\csname + pgf@sh@#1@\pgf@sm@shape@name\endcsname=\expandafter\noexpand\csname + pgf@sh@#1@#2\endcsname}% + \pgf@marshal% +}% +\def\pgf@sh@inheritbehindbgpath[from=#1]{\pgf@sh@inheritor{bbg}{#1}}% +\def\pgf@sh@inheritbgpath[from=#1]{\pgf@sh@inheritor{bg}{#1}}% +\def\pgf@sh@inheritbeforebgpath[from=#1]{\pgf@sh@inheritor{fbg}{#1}}% +\def\pgf@sh@inheritbehindfgpath[from=#1]{\pgf@sh@inheritor{bfg}{#1}}% +\def\pgf@sh@inheritfgpath[from=#1]{\pgf@sh@inheritor{fg}{#1}}% +\def\pgf@sh@inheritbeforefgpath[from=#1]{\pgf@sh@inheritor{ffg}{#1}}% +\def\pgf@sh@inheritboxes[from=#1]{\pgf@sh@inheritor{boxes}{#1}}% + + + + +\pgfdeclareshape{coordinate} +{% + \savedanchor\centerpoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgf@y=.5\ht\pgfnodeparttextbox% + \advance\pgf@y by -.5\dp\pgfnodeparttextbox% + }% + + \anchor{center}{\centerpoint}% + \anchor{north}{\centerpoint}% + \anchor{north west}{\centerpoint}% + \anchor{north east}{\centerpoint}% + \anchor{west}{\centerpoint}% + \anchor{east}{\centerpoint}% + \anchor{mid}{\centerpoint}% + \anchor{mid west}{\centerpoint}% + \anchor{mid east}{\centerpoint}% + \anchor{base}{\centerpoint}% + \anchor{base west}{\centerpoint}% + \anchor{base east}{\centerpoint}% + \anchor{south}{\centerpoint}% + \anchor{south west}{\centerpoint}% + \anchor{south east}{\centerpoint}% + \anchorborder{\centerpoint}% + + \nodeparts{}% +}% + + + +\pgfset{ + inner xsep/.initial =.3333em, + inner ysep/.initial =.3333em, + inner sep/.style ={/pgf/inner xsep={#1},/pgf/inner ysep={#1}}, + outer xsep/.initial =.5\pgflinewidth, + outer ysep/.initial =.5\pgflinewidth, + outer sep/.code =\pgf@handle@outer@sep{#1}, + minimum width/.initial =1pt, + minimum height/.initial =1pt, + minimum size/.style ={/pgf/minimum width={#1},/pgf/minimum height={#1}}, +}% + + + +\def\pgf@handle@outer@sep#1{% + \def\pgf@temp{#1}% + \ifx\pgf@temp\pgf@auto@text% + \def\pgf@outer@adjust@hook{% + \pgftransformationadjustments% + \pgfkeyssetvalue{/pgf/outer xsep}{.5\pgflinewidth*\pgfhorizontaltransformationadjustment}% + \pgfkeyssetvalue{/pgf/outer ysep}{.5\pgflinewidth*\pgfverticaltransformationadjustment}% + \pgf@outer@auto@adjust@hook% + }% + \else% + \pgfkeyssetvalue{/pgf/outer xsep}{#1}% + \pgfkeyssetvalue{/pgf/outer ysep}{#1}% + \fi% +}% +\def\pgf@auto@text{auto}% + +\let\pgf@outer@auto@adjust@hook\relax + + + +\newif\ifpgfshapeborderusesincircle +\pgfkeys{/pgf/shape border uses incircle/.is if=pgfshapeborderusesincircle}% +\pgfkeys{/pgf/shape border rotate/.initial=0}% + + +\pgfdeclareshape{rectangle} +{% + \savedanchor\northeast{% + \pgf@x=\the\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x by 2\pgf@xc% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<\pgf@xb% + \pgf@x=\pgf@xb% + \fi% + \pgf@x=.5\pgf@x% + \advance\pgf@x by.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \advance\pgf@x by\pgf@xa% + \pgf@y=\ht\pgfnodeparttextbox% + \advance\pgf@y by\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y by 2\pgf@yc% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<\pgf@yb% + \pgf@y=\pgf@yb% + \fi% + \pgf@y=.5\pgf@y% + \advance\pgf@y by-.5\dp\pgfnodeparttextbox% + \advance\pgf@y by.5\ht\pgfnodeparttextbox% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \advance\pgf@y by\pgf@ya% + }% + + \savedanchor\southwest{% + \pgf@x=\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xc{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@x by 2\pgf@xc% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/minimum width}}% + \ifdim\pgf@x<\pgf@xb% + \pgf@x=\pgf@xb% + \fi% + \pgf@x=-.5\pgf@x% + \advance\pgf@x by.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/outer xsep}}% + \advance\pgf@x by-\pgf@xa% + \pgf@y=\ht\pgfnodeparttextbox% + \advance\pgf@y by\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@yc{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@y by 2\pgf@yc% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@y<\pgf@yb% + \pgf@y=\pgf@yb% + \fi% + \pgf@y=-.5\pgf@y% + \advance\pgf@y by-.5\dp\pgfnodeparttextbox% + \advance\pgf@y by.5\ht\pgfnodeparttextbox% + \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/outer ysep}}% + \advance\pgf@y by-\pgf@ya% + }% + + \anchor{center}{ + \pgf@process{\northeast}% + \pgf@xa=.5\pgf@x% + \pgf@ya=.5\pgf@y% + \pgf@process{\southwest}% + \pgf@x=.5\pgf@x% + \pgf@y=.5\pgf@y% + \advance\pgf@x by \pgf@xa% + \advance\pgf@y by \pgf@ya% + }% + \anchor{mid}{\pgf@anchor@rectangle@center\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base}{\pgf@anchor@rectangle@center\pgf@y=0pt}% + \anchor{north}{ + \pgf@process{\southwest}% + \pgf@xa=.5\pgf@x% + \pgf@process{\northeast}% + \pgf@x=.5\pgf@x% + \advance\pgf@x by \pgf@xa% + }% + \anchor{south}{ + \pgf@process{\northeast}% + \pgf@xa=.5\pgf@x% + \pgf@process{\southwest}% + \pgf@x=.5\pgf@x% + \advance\pgf@x by \pgf@xa% + }% + \anchor{west}{ + \pgf@process{\northeast}% + \pgf@ya=.5\pgf@y% + \pgf@process{\southwest}% + \pgf@y=.5\pgf@y% + \advance\pgf@y by \pgf@ya% + }% + \anchor{mid west}{\southwest\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base west}{\southwest\pgf@y=0pt}% + \anchor{north west}{ + \southwest + \pgf@xa=\pgf@x + \northeast + \pgf@x=\pgf@xa}% + \anchor{south west}{\southwest}% + \anchor{east}{% + \pgf@process{\southwest}% + \pgf@ya=.5\pgf@y% + \pgf@process{\northeast}% + \pgf@y=.5\pgf@y% + \advance\pgf@y by \pgf@ya% + }% + \anchor{mid east}{\northeast\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base east}{\northeast\pgf@y=0pt}% + \anchor{north east}{\northeast}% + \anchor{south east}{ + \northeast + \pgf@xa=\pgf@x + \southwest + \pgf@x=\pgf@xa + }% + \anchorborder{% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \southwest% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \northeast% + \advance\pgf@x by-\pgf@xa% + \advance\pgf@y by-\pgf@ya% + \pgf@xc=.5\pgf@x% + \pgf@yc=.5\pgf@y% + \advance\pgf@xa by\pgf@xc% + \advance\pgf@ya by\pgf@yc% + \edef\pgf@marshal{% + \noexpand\pgfpointborderrectangle + {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}} + {\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}% + }% + \pgf@process{\pgf@marshal}% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + }% + + \backgroundpath{ + \pgfpathrectanglecorners + {\pgfpointadd{\southwest}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}} + {\pgfpointadd{\northeast}{\pgfpointscale{-1}{\pgfpoint{\pgfkeysvalueof{/pgf/outer xsep}}{\pgfkeysvalueof{/pgf/outer ysep}}}}} + }% +}% + + +\expandafter\def\csname pgf@sh@ns@current subpath start\endcsname{coordinate}% +\expandafter\def\csname pgf@sh@np@current subpath start\endcsname{% + \def\centerpoint{\expandafter\pgfqpoint\pgfsyssoftpath@lastmoveto}% +}% +\expandafter\def\csname pgf@sh@nt@current subpath start\endcsname{{1}{0}{0}{1}{0pt}{0pt}}% +\expandafter\def\csname pgf@sh@pi@current subpath start\endcsname{\pgfpictureid}% + + + +\expandafter\def\csname pgf@sh@ns@current bounding box\endcsname{rectangle}% +\expandafter\def\csname pgf@sh@np@current bounding box\endcsname{% + \def\southwest{\pgfqpoint{\pgf@picminx}{\pgf@picminy}}% + \def\northeast{\pgfqpoint{\pgf@picmaxx}{\pgf@picmaxy}}% +}% +\expandafter\def\csname pgf@sh@nt@current bounding box\endcsname{{1}{0}{0}{1}{0pt}{0pt}}% +\expandafter\def\csname pgf@sh@pi@current bounding box\endcsname{\pgfpictureid}% + + +\expandafter\def\csname pgf@sh@ns@current path bounding box\endcsname{rectangle}% +\expandafter\def\csname pgf@sh@np@current path bounding box\endcsname{% + \def\southwest{\pgfqpoint{\pgf@pathminx}{\pgf@pathminy}}% + \def\northeast{\pgfqpoint{\pgf@pathmaxx}{\pgf@pathmaxy}}% +}% +\expandafter\def\csname pgf@sh@nt@current path bounding box\endcsname{{1}{0}{0}{1}{0pt}{0pt}}% +\expandafter\def\csname pgf@sh@pi@current path bounding box\endcsname{\pgfpictureid}% + + +\expandafter\def\csname pgf@sh@ns@current page\endcsname{rectangle}% +\expandafter\def\csname pgf@sh@np@current page\endcsname{% + \def\southwest{\pgfpointorigin}% + \def\northeast{\pgfpoint{\pgfsys@thepagewidth}{\pgfsys@thepageheight}}% +}% +\expandafter\def\csname pgf@sh@nt@current page\endcsname{{1}{0}{0}{1}{0pt}{0pt}}% +\expandafter\def\csname pgf@sh@pi@current page\endcsname{pgfpageorigin}% + + +\pgfkeys{/pgf/local bounding box/.code={% + \expandafter\gdef\csname pgf@sh@ns@#1\endcsname{rectangle} + \expandafter\gdef\csname pgf@sh@np@#1\endcsname{% + \def\southwest{\pgfqpoint{\csname pgf@lbb@minx@#1\endcsname}{\csname pgf@lbb@miny@#1\endcsname}}% + \def\northeast{\pgfqpoint{\csname pgf@lbb@maxx@#1\endcsname}{\csname pgf@lbb@maxy@#1\endcsname}}% + } + \expandafter\gdef\csname pgf@sh@nt@#1\endcsname{{1}{0}{0}{1}{0pt}{0pt}} + \expandafter\gdef\csname pgf@sh@pi@#1\endcsname{\pgfpictureid} + \expandafter\gdef\csname pgf@lbb@maxx@#1\endcsname{-16000pt}% + \expandafter\gdef\csname pgf@lbb@minx@#1\endcsname{16000pt}% + \expandafter\gdef\csname pgf@lbb@maxy@#1\endcsname{-16000pt}% + \expandafter\gdef\csname pgf@lbb@miny@#1\endcsname{16000pt}% + \pgf@size@hookedtrue% + \expandafter\def\expandafter\pgf@path@size@hook\expandafter{\pgf@path@size@hook\pgf@lbb@do{#1}} + }, + /pgf/freeze local bounding box/.code={% + {% + \csname pgf@sh@np@#1\endcsname% + \southwest% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \northeast% + \expandafter\xdef\csname pgf@sh@np@#1\endcsname{% + \noexpand\def\noexpand\southwest{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}% + \noexpand\def\noexpand\northeast{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}% + }% + }% + }, +}% +\def\pgf@lbb@do#1{% + \ifdim\pgf@size@hook@x<\csname pgf@lbb@minx@#1\endcsname\expandafter\xdef\csname pgf@lbb@minx@#1\endcsname{\the\pgf@size@hook@x}\fi% + \ifdim\pgf@size@hook@x>\csname pgf@lbb@maxx@#1\endcsname\expandafter\xdef\csname pgf@lbb@maxx@#1\endcsname{\the\pgf@size@hook@x}\fi% + \ifdim\pgf@size@hook@y<\csname pgf@lbb@miny@#1\endcsname\expandafter\xdef\csname pgf@lbb@miny@#1\endcsname{\the\pgf@size@hook@y}\fi% + \ifdim\pgf@size@hook@y>\csname pgf@lbb@maxy@#1\endcsname\expandafter\xdef\csname pgf@lbb@maxy@#1\endcsname{\the\pgf@size@hook@y}\fi% +}% + + +\pgfdeclareshape{circle} +{% + \savedanchor\centerpoint{% + \pgf@x=.5\wd\pgfnodeparttextbox% + \pgf@y=.5\ht\pgfnodeparttextbox% + \advance\pgf@y by-.5\dp\pgfnodeparttextbox% + }% + + \saveddimen\radius{% + \pgf@ya=.5\ht\pgfnodeparttextbox% + \advance\pgf@ya by.5\dp\pgfnodeparttextbox% + \pgfmathsetlength\pgf@yb{\pgfkeysvalueof{/pgf/inner ysep}}% + \advance\pgf@ya by\pgf@yb% + \pgf@xa=.5\wd\pgfnodeparttextbox% + \pgfmathsetlength\pgf@xb{\pgfkeysvalueof{/pgf/inner xsep}}% + \advance\pgf@xa by\pgf@xb% + \pgf@process{\pgfpointnormalised{\pgfqpoint{\pgf@xa}{\pgf@ya}}}% + \ifdim\pgf@x>\pgf@y% + \c@pgf@counta=\pgf@x% + \ifnum\c@pgf@counta=0\relax% + \else% + \divide\c@pgf@counta by 255\relax% + \pgf@xa=16\pgf@xa\relax% + \divide\pgf@xa by\c@pgf@counta% + \pgf@xa=16\pgf@xa\relax% + \fi% + \else% + \c@pgf@counta=\pgf@y% + \ifnum\c@pgf@counta=0\relax% + \else% + \divide\c@pgf@counta by 255\relax% + \pgf@ya=16\pgf@ya\relax% + \divide\pgf@ya by\c@pgf@counta% + \pgf@xa=16\pgf@ya\relax% + \fi% + \fi% + \pgf@x=\pgf@xa% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/minimum width}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/minimum height}}% + \ifdim\pgf@x<.5\pgf@xb% + \pgf@x=.5\pgf@xb% + \fi% + \ifdim\pgf@x<.5\pgf@yb% + \pgf@x=.5\pgf@yb% + \fi% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgf@x by\pgf@yb% + \else% + \advance\pgf@x by\pgf@xb% + \fi% + }% + + \anchor{center}{\centerpoint}% + \anchor{mid}{\centerpoint\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base}{\centerpoint\pgf@y=0pt}% + \anchor{north}{\centerpoint\advance\pgf@y by\radius}% + \anchor{south}{\centerpoint\advance\pgf@y by-\radius}% + \anchor{west}{\centerpoint\advance\pgf@x by-\radius}% + \anchor{east}{\centerpoint\advance\pgf@x by\radius}% + \anchor{mid west}{\centerpoint\advance\pgf@x by-\radius\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{mid east}{\centerpoint\advance\pgf@x by\radius\pgfmathsetlength\pgf@y{.5ex}}% + \anchor{base west}{\centerpoint\advance\pgf@x by-\radius\pgf@y=0pt}% + \anchor{base east}{\centerpoint\advance\pgf@x by\radius\pgf@y=0pt}% + \anchor{north west}{ + \centerpoint + \pgf@xa=\radius + \advance\pgf@x by-0.707107\pgf@xa + \advance\pgf@y by0.707107\pgf@xa + }% + \anchor{south west}{ + \centerpoint + \pgf@xa=\radius + \advance\pgf@x by-0.707107\pgf@xa + \advance\pgf@y by-0.707107\pgf@xa + }% + \anchor{north east}{ + \centerpoint + \pgf@xa=\radius + \advance\pgf@x by0.707107\pgf@xa + \advance\pgf@y by0.707107\pgf@xa + }% + \anchor{south east}{ + \centerpoint + \pgf@xa=\radius + \advance\pgf@x by0.707107\pgf@xa + \advance\pgf@y by-0.707107\pgf@xa + }% + \anchorborder{% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \edef\pgf@marshal{% + \noexpand\pgfpointborderellipse + {\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}} + {\noexpand\pgfqpoint{\radius}{\radius}}% + }% + \pgf@marshal% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \centerpoint% + \advance\pgf@x by\pgf@xa% + \advance\pgf@y by\pgf@ya% + }% + + \backgroundpath{% + \pgfutil@tempdima=\radius% + \pgfmathsetlength{\pgf@xb}{\pgfkeysvalueof{/pgf/outer xsep}}% + \pgfmathsetlength{\pgf@yb}{\pgfkeysvalueof{/pgf/outer ysep}}% + \ifdim\pgf@xb<\pgf@yb% + \advance\pgfutil@tempdima by-\pgf@yb% + \else% + \advance\pgfutil@tempdima by-\pgf@xb% + \fi% + \pgfpathcircle{\centerpoint}{\pgfutil@tempdima}% + }% +}% + + + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulesnakes.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulesnakes.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..40550f0c4785bece78a243abc4ff5029c7dace9b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulesnakes.code.tex @@ -0,0 +1,190 @@ + +\ProvidesFileRCS{pgfmodulesnakes.code.tex} + +\pgfwarning{Snakes have been superseded by decorations. Use the module decorations instead of snakes} + +\usepgfmodule{decorations}% + +\endinput + + + +\newdimen\pgfsnakeremainingdistance +\newdimen\pgfsnakecompleteddistance + + + +\long\def\pgfdeclaresnake#1#2#3{% + \def\pgf@snake@name{#1}% + \pgfutil@namedef{pgf@snake@@#1@initial}{#2}% + \let\pgf@orig@state=\state% + \let\state=\pgf@snake@state + #3 + \let\state=\pgf@orig@state% +}% + + + +\def\pgfsetsnakesegmenttransformation#1{\def\pgf@snakeadditionaltransform{#1}}% +\pgfsetsnakesegmenttransformation{}% + + + +\def\pgf@snake@state#1{\pgfutil@ifnextchar[{\pgf@@snake@start#1}{\pgf@@snake@start#1[]}}% +\def\pgf@@snake@start#1[#2]#3{% + \pgfutil@namedef{pgf@snake@@\pgf@snake@name @#1@options}{#2}% + \pgfutil@namedef{pgf@snake@@\pgf@snake@name @#1@code}{#3}% +}% + + + + +\def\pgfpathsnakesto#1#2{% + \begingroup% + \pgfpointtransformed{#2}% + \advance\pgf@x by-\pgf@path@lastx% + \advance\pgf@y by-\pgf@path@lasty% + \edef\pgf@marshal{% + \noexpand\pgfmathanglebetweenpoints{\noexpand\pgfpointorigin}{% + \noexpand\pgf@x\the\pgf@x\noexpand\pgf@y\the\pgf@y}% + }% + \pgf@marshal% + \let\pgfsnakeangle\pgfmathresult% + \pgfmathveclen@{\pgfmath@tonumber{\pgf@x}}{\pgfmath@tonumber{\pgf@y}}% + \pgfsnakeremainingdistance\pgfmathresult pt\relax% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@process{\pgfpointnormalised{}}% + \edef\pgf@list{#1}% + \pgfsnakecompleteddistance=0pt% + \pgf@xb=\pgf@x% + \pgf@yb=\pgf@y% + \pgfutil@for\pgf@temp:=\pgf@list\do{% + \ifx\pgf@temp\pgfutil@empty% + \else% + \expandafter\pgf@snake@invoke\pgf@temp% + \fi% + }% + \endgroup% +}% + +\def\pgf@snake@invoke#1#2{% + \pgfmathsetlength\pgf@xa{#2}% + {% + \edef\pgf@marshal{\noexpand\pgfpathsnakealongvector{#1}{\the\pgf@xa}{\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}}% + \pgf@marshal% + }% + \advance\pgfsnakecompleteddistance by\pgf@xa% + \advance\pgfsnakeremainingdistance by-\pgf@xa% +}% + + +\def\pgfpathsnaketo#1#2{\pgfpathsnakesto{{#1}{\pgfsnakeremainingdistance}}{#2}}% + + + + +\def\pgfpathsnakealongvector#1#2#3{% + \pgfutil@ifundefined{pgf@snake@@#1@initial}{\pgferror{Undefined snake ``#1''}} + { + \begingroup% + \pgftransformreset% + \pgf@pt@x=\pgf@path@lastx% + \pgf@pt@y=\pgf@path@lasty% + \pgf@process{#3}% + \pgf@xa=\pgf@x% + \pgf@ya=\pgf@y% + \pgf@xb=-\pgf@y% + \pgf@yb=\pgf@x% + \pgftransformcm + {\pgf@sys@tonumber{\pgf@xa}}{\pgf@sys@tonumber{\pgf@ya}} + {\pgf@sys@tonumber{\pgf@xb}}{\pgf@sys@tonumber{\pgf@yb}} + {\pgfpointorigin}% + \expandafter\let\expandafter\pgf@snake@current@state\expandafter=\csname pgf@snake@@#1@initial\endcsname% + \def\pgf@snake@name{#1}% + \pgfsnakecompleteddistance=0pt% + \pgfmathsetlength\pgfsnakeremainingdistance{#2}% + \pgf@snake@run% + {% + \pgftransformxshift{\pgfsnakecompleteddistance}% + \pgf@snakeadditionaltransform% + \csname pgf@snake@@#1@final@code\endcsname% + }% + \endgroup% + }% +}% + +\def\pgf@final@text{final}% + +\def\pgf@snake@run{% + \let\pgf@snake@next=\pgf@snake@do@state% + \ifx\pgf@snake@current@state\pgf@final@text% + \let\pgf@snake@next=\relax% + \fi% + \pgf@snake@next% +}% + +\def\pgf@snake@do@state{% + \let\pgf@snake@next=\relax% + \let\pgf@snake@next@state=\pgf@snake@current@state% + \expandafter\expandafter\expandafter\pgf@snakes@setter + \expandafter\expandafter\expandafter{\csname pgf@snake@@\pgf@snake@name @\pgf@snake@current@state @options\endcsname}% + \ifx\pgf@snake@next\relax% + \let\pgf@snake@next=\pgf@snake@do@code% + \fi% + \pgf@snake@next% +}% +\def\pgf@snakes@setter{% + \pgfqkeys{/pgf/snakes}% +}% + +\def\pgf@snake@do@code{% + {% + \pgftransformxshift{\pgfsnakecompleteddistance}% + \pgf@snakeadditionaltransform% + \csname pgf@snake@@\pgf@snake@name @\pgf@snake@current@state @code\endcsname% + }% + \pgfmathsetlength{\pgf@xa}{\pgf@snake@width}% + \advance\pgfsnakeremainingdistance by-\pgf@xa% + \advance\pgfsnakecompleteddistance by\pgf@xa% + \let\pgf@snake@current@state=\pgf@snake@next@state% + \pgf@snake@run% +}% + +\pgfkeys{ + /pgf/snakes/width/.code=\def\pgf@snake@width{#1}\pgf@snake@switch@if#1 to final\pgf@stop,% + /pgf/snakes/switch if less than/.code=\pgf@snake@switch@if#1\pgf@stop,% + /pgf/snakes/next state/.store in=\pgf@snake@next@state% +}% + +\def\pgf@snake@switch@if#1to #2\pgf@stop{% + \ifx\pgf@snake@next\relax% + \pgfmathsetlength\pgf@x{#1}% + \ifdim\pgfsnakeremainingdistance<\pgf@x% + \def\pgf@snake@current@state{#2}% + \let\pgf@snake@next=\pgf@snake@run% + \fi% + \fi% +}% + + + + +\pgfdeclaresnake{lineto}{final} +{% + \state{final} + { \pgfpathlineto{\pgfqpoint{\pgfsnakeremainingdistance}{0pt}} } +}% + + + + +\pgfdeclaresnake{moveto}{final} +{% + \state{final} + { \pgfpathmoveto{\pgfqpoint{\pgfsnakeremainingdistance}{0pt}} } +}% + + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulesorting.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulesorting.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..3009ec5c4a6fbfed0878311a7d34bf674bc21d01 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/modules/pgfmodulesorting.code.tex @@ -0,0 +1,37 @@ + +\ProvidesFileRCS{pgfmodulesorting.code.tex} + + + +\newcount\pgfsortingbuckets + + +\def\pgfsortinginit#1{ + \pgfsortingbuckets#1\relax% + \c@pgf@counta=0\relax + \pgfutil@loop + \ifnum\c@pgf@counta<\c@pgf@countb\relax% + \expandafter\global\expandafter\let\csname pgf@sort@\the\c@pgf@counta\endcsname\pgfutil@empty% + \advance\c@pgf@counta by1\relax% + \pgfutil@repeat +}% + +\def\pgfsortinginsert#1#2{ + \expandafter\let\expandafter\pgf@temp\csname pgf@lib@sort@#1\endcsname% + \expandafter\def\expandafter\pgf@temp\expandafter{\pgf@temp#2}% + \expandafter\global\expandafter\let\csname pgf@lib@sort@\the\c@pgf@counta\endcsname\pgf@temp% +}% + + +\def\pgfsortingexecute{ + \c@pgf@countb=\pgfoovalueof{buckets}\relax + \c@pgf@counta=0\relax + \pgfutil@loop + \ifnum\c@pgf@counta<\c@pgf@countb\relax% + \csname pgf@lib@sort@\the\c@pgf@counta\endcsname% + \advance\c@pgf@counta by1\relax% + \pgfutil@repeat +}% + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/pgf.revision.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/pgf.revision.tex new file mode 100644 index 0000000000000000000000000000000000000000..12b28e20457e0223f434063a15b5180396cdc03e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/pgf.revision.tex @@ -0,0 +1,4 @@ +\def\pgfrevision{3.1.10} +\def\pgfversion{3.1.10} +\def\pgfrevisiondate{2023-01-15} +\def\pgfversiondate{2023-01-15} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsys.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsys.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..d3c11e9b7eae00f623ba92184fc78bb6dcdd9968 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsys.code.tex @@ -0,0 +1,805 @@ + +\ProvidesPackageRCS{pgfsys.code.tex} + + +\ifdefined\pgfkeysloaded\else + \input pgfkeys.code.tex +\fi + +\pgfkeys{/pgf/.is family} +\def\pgfset{\pgfqkeys{/pgf}} + +\newif\ifpgfpicture + + +{\catcode`\p=12\catcode`\t=12\gdef\Pgf@geT#1pt{#1}} + +\def\pgf@sys@tonumber#1{\expandafter\Pgf@geT\the#1} + +\def\pgf@sys@bp@correct#1{#1=0.99627#1} + +\def\pgf@sys@bp#1{% + {% + \pgf@x=#1\relax% + \pgf@x=0.99627\pgf@x% + \edef\temp{\expandafter\Pgf@geT\the\pgf@x\space}% + \pgfutil@toks@\expandafter\expandafter\expandafter{\expandafter\pgfsysprotocol@currentprotocol\temp}% + \xdef\pgfsysprotocol@currentprotocol{\the\pgfutil@toks@}% + }% +} +\def\pgf@sys@pt#1{% + {% + \pgf@x=#1\relax% + \edef\temp{\expandafter\Pgf@geT\the\pgf@x\space}% + \pgfutil@toks@\expandafter\expandafter\expandafter{\expandafter\pgfsysprotocol@currentprotocol\temp}% + \xdef\pgfsysprotocol@currentprotocol{\the\pgfutil@toks@}% + }% +} + + +\newdimen\pgf@x +\newdimen\pgf@y +\newdimen\pgf@xa +\newdimen\pgf@ya +\newdimen\pgf@xb +\newdimen\pgf@yb +\newdimen\pgf@xc +\newdimen\pgf@yc +\newdimen\pgf@xd +\newdimen\pgf@yd + +\newwrite\w@pgf@writea +\newread\r@pgf@reada +\let\pgfutil@inputcheck=\r@pgf@reada + +\newcount\c@pgf@counta +\newcount\c@pgf@countb +\newcount\c@pgf@countc +\newcount\c@pgf@countd + +\newtoks\t@pgf@toka +\newtoks\t@pgf@tokb +\newtoks\t@pgf@tokc + +\let\pgfmath@x\pgf@x +\let\pgfmath@xa\pgf@xa +\let\pgfmath@xb\pgf@xb +\let\pgfmath@xc\pgf@xc + +\let\pgfmath@y\pgf@y +\let\pgfmath@ya\pgf@ya +\let\pgfmath@yb\pgf@yb +\let\pgfmath@yc\pgf@yc + +\let\c@pgfmath@counta\c@pgf@counta +\let\c@pgfmath@countb\c@pgf@countb +\let\c@pgfmath@countc\c@pgf@countc +\let\c@pgfmath@countd\c@pgf@countd + + + + + + +\def\pgf@sys@fail#1{% + \expandafter\ifx\csname pgf@sys@fail@#1\endcsname\pgfutil@empty% + \else% + \expandafter\global\expandafter\let\csname pgf@sys@fail@#1\endcsname=\pgfutil@empty% + \pgfwarning{Your graphic driver \pgfsysdriver\space does not support #1. This warning is given only once}% + \fi% +} + + + + +\def\pgfsys@invoke{\pgf@sys@fail{invoking specials}} + +\def\pgfsys@outerinvoke{\pgfsys@invoke} + + + + +\def\pgfsys@moveto#1#2{\pgf@sys@fail{path constructions}} + +\def\pgfsys@lineto#1#2{\pgf@sys@fail{path constructions}} + +\def\pgfsys@curveto#1#2#3#4#5#6{\pgf@sys@fail{path constructions}} + +\def\pgfsys@rect#1#2#3#4{\pgf@sys@fail{path constructions}} + +\def\pgfsys@closepath{\pgf@sys@fail{path constructions}} + + + + + + + +\def\pgfsys@stroke{\pgf@sys@fail{path usage}} + +\def\pgfsys@fill{\pgf@sys@fail{path usage}} + +\def\pgfsys@fillstroke{\pgf@sys@fail{path usage}} + +\def\pgfsys@clipnext{\pgf@sys@fail{path usage}} + +\def\pgfsys@discardpath{\pgf@sys@fail{path usage}} + +\def\pgfsys@closestroke{\pgfsys@closepath\pgfsys@stroke} + +\newif\ifpgfsys@eorule + + + + +\def\pgfsys@setlinewidth#1{\pgf@sys@fail{setting the line width}} + +\def\pgfsys@buttcap{\pgf@sys@fail{setting the line cap}} + +\def\pgfsys@roundcap{\pgf@sys@fail{setting the line cap}} + +\def\pgfsys@rectcap{\pgf@sys@fail{setting the line cap}} + +\def\pgfsys@miterjoin{\pgf@sys@fail{setting the line join}} + +\def\pgfsys@setmiterlimit#1{\pgf@sys@fail{setting the line cap}} + +\def\pgfsys@roundjoin{\pgf@sys@fail{setting the line cap}} + +\def\pgfsys@beveljoin{\pgf@sys@fail{setting the line cap}} + +\def\pgfsys@setdash#1#2{\pgf@sys@fail{setting the dashing pattern}} + + + + + + +\def\pgfsys@color@rgb@stroke#1#2#3{\pgf@sys@fail{color}} + +\def\pgfsys@color@rgb@fill#1#2#3{\pgf@sys@fail{color}} + +\def\pgfsys@color@rgb#1#2#3{\pgfsys@color@rgb@stroke{#1}{#2}{#3}\pgfsys@color@rgb@fill{#1}{#2}{#3}} + +\def\pgfsys@color@cmyk@stroke#1#2#3#4{\pgf@sys@fail{color}} + +\def\pgfsys@color@cmyk@fill#1#2#3#4{\pgf@sys@fail{color}} + +\def\pgfsys@color@cmyk#1#2#3#4{\pgfsys@color@cmyk@stroke{#1}{#2}{#3}{#4}\pgfsys@color@cmyk@fill{#1}{#2}{#3}{#4}} + +\def\pgfsys@color@cmy@stroke#1#2#3{\pgf@sys@fail{color}} + +\def\pgfsys@color@cmy@fill#1#2#3{\pgf@sys@fail{color}} + +\def\pgfsys@color@cmy#1#2#3{\pgfsys@color@cmy@stroke{#1}{#2}{#3}\pgfsys@color@cmy@fill{#1}{#2}{#3}} + +\def\pgfsys@color@gray@stroke#1{\pgf@sys@fail{color}} + +\def\pgfsys@color@gray@fill#1{\pgf@sys@fail{color}} + +\def\pgfsys@color@gray#1{\pgfsys@color@gray@stroke{#1}\pgfsys@color@gray@fill{#1}} + +\newif\ifpgfsys@color@reset@inorder +\pgfsys@color@reset@inordertrue + + +\def\pgfsys@color@reset{} + +\def\pgfsys@color@unstacked#1{} + +\def\pgfsys@text@to@black@hook{} + + + + +\def\pgfsys@transformcm#1#2#3#4#5#6{\pgf@sys@fail{transformations}} + +\def\pgfsys@transformshift#1#2{\pgfsys@transformcm{1}{0}{0}{1}{#1}{#2}} + +\def\pgfsys@transformxyscale#1#2{\pgfsys@transformcm{#1}{0}{0}{#2}{0bp}{0bp}} + +\def\pgfsys@viewboxmeet#1#2#3#4#5#6#7#8{\pgfsys@beginscope\pgf@sys@default@viewbox@impl{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}{<}} + +\def\pgfsys@viewboxslice#1#2#3#4#5#6#7#8{\pgfsys@beginscope\pgf@sys@default@viewbox@impl{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}{>}} + +\def\pgfsys@endviewbox{\pgfsys@endscope} + + +\def\pgf@sys@default@viewbox@impl#1#2#3#4#5#6#7#8#9{{% + \pgf@x#1% + \pgf@y#2% + \pgf@xa#3% + \pgf@ya#4% + \advance\pgf@xa by-\pgf@x% + \advance\pgf@ya by-\pgf@y% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@ya}% + \let\aspectr\pgfmathresult% + \pgf@xb#5% + \pgf@yb#6% + \pgf@xc#7% + \pgf@yc#8% + \advance\pgf@xc by-\pgf@xb% + \advance\pgf@yc by-\pgf@yb% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@xc}{\pgf@sys@tonumber\pgf@yc}% + \let\aspects\pgfmathresult% + \ifdim\aspectr pt#9\aspects pt% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@xc}% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@yc}% + \fi% + \advance\pgf@x by.5\pgf@xa% + \advance\pgf@xb by.5\pgf@xc% + \advance\pgf@y by.5\pgf@ya% + \advance\pgf@yb by.5\pgf@yc% + \pgfsys@transformcm{\pgfmathresult}{0}{0}{\pgfmathresult}{\pgf@x}{\pgf@y}% + \pgfsys@transformcm{1}{0}{0}{1}{-\pgf@xb}{-\pgf@yb}% + }% +} + + + + + +\def\pgfsys@beginscope{\pgf@sys@fail{scoping}} + +\def\pgfsys@endscope{\pgf@sys@fail{scoping}} + +\def\pgfsys@begin@idscope{% + \begingroup% + \edef\pgf@sys@cacheref{\pgfsys@id@refcurrent}% + \expandafter\let\expandafter\pgfsys@beg@save\csname pgf@sys@att@beg@\pgf@sys@cacheref\endcsname% + \expandafter\let\expandafter\pgfsys@end@save\csname pgf@sys@att@end@\pgf@sys@cacheref\endcsname% + \ifx\pgfsys@beg@save\relax% + \ifx\pgfsys@end@save\relax% + \else% + \pgfsys@call@save% + \fi% + \else% + \pgfsys@call@save% + \fi% + \pgfsys@invalidate@currentid% + \begingroup% +} + +\def\pgfsys@call@save{% + \pgfsys@beginscope% + \pgfsys@beg@save% + \expandafter\global\expandafter\let\csname pgf@sys@att@beg@\pgfsys@id@refcurrent\endcsname\relax% + \expandafter\global\expandafter\let\csname pgf@sys@att@end@\pgfsys@id@refcurrent\endcsname\relax% +} + +\def\pgfsys@end@idscope{ + \endgroup% + \ifx\pgfsys@beg@save\relax% + \ifx\pgfsys@end@save\relax% + \else% + \pgfsys@call@end% + \fi% + \else% + \pgfsys@call@end% + \fi% + \endgroup +} + +\def\pgfsys@call@end{% + \pgfsys@end@save% + \pgfsys@endscope% +} + + +\def\pgfsys@begin@text{} + +\def\pgfsys@end@text{} + + + + +\newcount\pgf@sys@id@count + +\def\pgfsys@new@id#1{% + \edef#1{pgf\the\pgf@sys@id@count}% + \global\advance\pgf@sys@id@count by1\relax% +} + +\def\pgfsys@use@id#1{% + \edef\pgf@sys@id@current@id{#1}% + \let\pgfsys@current@type\pgfutil@empty% +} +\let\pgf@sys@id@current@id\pgfutil@empty + +\def\pgfsys@clear@id{% + \let\pgf@sys@id@current@id\pgfutil@empty% +} + +\def\pgfsys@use@type#1{% + \edef\pgfsys@current@type{#1}% + \pgfsys@register@type\pgfsys@current@type% +} +\let\pgfsys@current@type\pgfutil@empty + +\def\pgfsys@append@type#1{% + \ifx\pgfsys@current@type\pgfutil@empty% + \pgfsys@use@type{#1}% + \else% + \pgfsys@use@type{\pgfsys@current@type.#1}% + \fi% +} + +\def\pgfsys@register@type#1{% + \expandafter\let\expandafter\pgf@sys@temp\csname pgf@sys@reg@type@#1\endcsname% + \ifx\pgf@sys@temp\relax% + {% + \c@pgf@counta\pgf@sys@type@count\relax% + \global\advance\c@pgf@counta by1\relax% + \edef\pgf@sys@type@count{\the\c@pgf@counta}% + \expandafter\xdef\csname pgf@sys@reg@type@#1\endcsname{y\the\c@pgf@counta}% + }% + \fi% +} +\def\pgf@sys@reg@type@{} +\def\pgf@sys@reg@type@background{b} +\def\pgf@sys@reg@type@path{p} +\def\pgf@sys@reg@type@text{t} +\expandafter\def\csname pgf@sys@reg@type@background.path\endcsname{bp} +\def\pgf@sys@type@count{0} + +\def\pgfsys@push@type{% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgf@sys@typestack% + \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfsys@current@type% + \expandafter\expandafter\expandafter{\expandafter\pgfsys@current@type\expandafter}% + \expandafter\def\expandafter\pgf@sys@typestack\expandafter{\pgf@sys@typestack}}% +} +\let\pgf@sys@typestack\pgfutil@empty + +\def\pgfsys@pop@type{\pgf@sys@typestack} + +\def\pgfsys@id@ref#1#2{#1\csname pgf@sys@reg@type@#2\endcsname} + +\def\pgfsys@id@refcurrent{\pgfsys@id@ref{\pgf@sys@id@current@id}{\pgfsys@current@type}} + +\def\pgfsys@invalidate@currentid{% + \expandafter\global\expandafter\let\csname pgf@sys@id@keylist@\pgfsys@id@refcurrent\endcsname\pgfutil@empty% +} + +\def\pgfsys@attach@to@id#1#2#3#4{% + \pgfsys@register@type{#2}% + \expandafter\def\expandafter\pgf@sys@tempbeg\expandafter{\csname pgf@sys@att@beg@\pgfsys@id@ref{#1}{#2}\endcsname}% + \expandafter\def\expandafter\pgf@sys@tempend\expandafter{\csname pgf@sys@att@end@\pgfsys@id@ref{#1}{#2}\endcsname}% + \expandafter\ifx\pgf@sys@tempbeg\relax% + \expandafter\let\pgf@sys@tempbeg\pgfutil@empty% + \fi% + \expandafter\ifx\pgf@sys@tempend\relax% + \expandafter\let\pgf@sys@tempend\pgfutil@empty% + \fi% + \expandafter\let\expandafter\pgf@sys@tempbeg@cont\pgf@sys@tempbeg% + \expandafter\let\expandafter\pgf@sys@tempend@cont\pgf@sys@tempend% + \expandafter\expandafter\expandafter\gdef\expandafter\pgf@sys@tempbeg\expandafter{\pgf@sys@tempbeg@cont#3}% + \def\pgf@sys@temp{#4}% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef\expandafter\expandafter\expandafter\pgf@sys@tempend\expandafter\expandafter\expandafter{\expandafter\pgf@sys@temp\pgf@sys@tempend@cont}% +} + +\def\pgfsys@if@fresh@id#1#2#3#4{% + \edef\pgf@sys@temp{#1}% + \ifx\pgf@sys@temp\pgfutil@empty% + #4% + \else% + \pgfsys@register@type{#2}% + \expandafter\ifx\csname pgf@sys@id@keylist@\pgfsys@id@ref{#1}{#2}\endcsname\pgfutil@empty% + #4% + \else% + #3% + \fi% + \fi% +} + +\def\pgfsys@if@fresh@currentid#1#2{% + \ifx\pgf@sys@id@current@id\pgfutil@empty% + #2% + \else% + \expandafter\ifx\csname pgf@sys@id@keylist@\pgfsys@id@refcurrent\endcsname\pgfutil@empty% + #2% + \else% + #1% + \fi% + \fi% +} + + + + + +\def\pgfsys@imagesuffixlist{} + + + + +\def\pgfsys@opacity#1{\pgfsys@stroke@opacity{#1}\pgfsys@fill@opacity{#1}} + +\def\pgfsys@stroke@opacity#1{\pgf@sys@fail{opacity}} + +\def\pgfsys@fill@opacity#1{\pgf@sys@fail{opacity}} + +\def\pgfsys@transparencygroupfrombox#1{\pgf@sys@fail{transparency groups}} + +\newif\ifpgfsys@transparency@group@isolated +\newif\ifpgfsys@transparency@group@knockout + + +\def\pgfsys@blend@mode#1{\pgf@sys@fail{blend mode}} + + +\def\pgfsys@definemask{\pgf@sys@fail{image masks}} + +\def\pgfsys@fadingfrombox#1#2{\pgf@sys@fail{fadings}} + +\def\pgfsys@usefading#1#2#3#4#5#6#7{\pgf@sys@fail{fadings}} + +\def\pgfsys@clipfading{} + + + +\def\pgfsys@horishading#1#2#3{\pgf@sys@fail{shadings}\pgf@sys@noshading{#1}} + +\def\pgfsys@vertshading#1#2#3{\pgf@sys@fail{shadings}\pgf@sys@noshading{#1}} + +\def\pgfsys@radialshading#1#2#3{\pgf@sys@fail{shadings}\pgf@sys@noshading{#1}} + +\def\pgfsys@functionalshading#1#2#3#4{\pgf@sys@fail{shadings (functional)}\pgf@sys@noshading{#1}} + +\def\pgf@sys@noshading#1{\expandafter\global\expandafter\let\csname @pgfshading#1!\endcsname=\pgfutil@empty} + + + + + +\def\pgfsys@declarepattern#1#2#3#4#5#6#7#8#9{\pgf@sys@fail{patterns}} + +\def\pgfsys@setpatternuncolored#1#2#3#4{\pgf@sys@fail{patterns}} + +\def\pgfsys@setpatterncolored#1{\pgf@sys@fail{patterns}} + + + + + + + +\newif\ifpgfsysanimationsupported + + +\def\pgfsys@animate#1{\pgf@sys@fail{animations}} + + + + + +\def\pgfsys@animation@restart@always{} + +\def\pgfsys@animation@restart@never{} + +\def\pgfsys@animation@restart@whennotactive{} + +\def\pgfsys@animation@repeat#1{} + +\def\pgfsys@animation@repeat@indefinite{} + +\def\pgfsys@animation@repeat@dur#1{} + +\def\pgfsys@animation@freezeatend{} + +\def\pgfsys@animation@removeatend{} + +\def\pgfsys@animation@time#1#2#3#4#5{} + +\def\pgfsys@stay@text{{stay}{0}} +\def\pgfsys@jump@text{{jump}{1}} + +\def\pgfsys@animation@base{} + +\def\pgfsys@animation@offset#1#2{} + +\def\pgfsys@animation@syncbegin#1#2#3#4{} + +\def\pgfsys@animation@syncend#1#2#3#4{} + +\def\pgfsys@animation@event#1#2#3#4#5{} + +\def\pgfsys@animation@repeat@event#1#2#3#4#5{} + +\def\pgfsys@animation@accesskey#1#2#3{} + +\def\pgf@sys@begin@text{begin} + + + +\def\pgfsys@animation@accumulate{} + +\def\pgfsys@animation@noaccumulate{} + + + +\def\pgfsys@animation@whom#1#2{} + + + +\def\pgfsys@animation@rotatealong{} + +\def\pgfsys@animation@norotatealong{} + +\def\pgfsys@animation@movealong#1{} + +\def\pgfsys@animation@tip@markers#1#2{} + +\def\pgfsys@animation@canvas@transform#1#2{} + + + + +\def\pgfsys@animation@val@current{} + +\def\pgfsys@animation@val@text#1{} + +\def\pgfsys@animation@val@scalar#1{} + +\def\pgfsys@animation@val@dimension#1{} + +\def\pgfsys@animation@val@color@rgb#1#2#3{} + +\def\pgfsys@animation@val@color@cmyk#1#2#3#4{} + +\def\pgfsys@animation@val@color@cmy#1#2#3{} + +\def\pgfsys@animation@val@color@gray#1{} + +\def\pgfsys@animation@val@path#1{} + +\def\pgfsys@animation@val@translate#1#2{} + +\def\pgfsys@animation@val@scale#1#2{} + +\def\pgfsys@animation@val@viewbox#1#2#3#4{} + +\def\pgfsys@animation@val@dash#1#2{} + + + + +\def\pgfsys@marker@declare#1#2{% + {% + \pgfpicturetrue% + \pgfsysprotocol@getcurrentprotocol\pgfsys@marker@temp% + \pgfsysprotocol@setcurrentprotocol\pgfutil@empty% + \pgfsysprotocol@bufferedtrue% + \pgfsys@beginscope% + #2% + \pgfsys@endscope% + \xdef#1{\the\pgf@sys@id@count}% + \expandafter\expandafter\expandafter\global\expandafter\pgfsysprotocol@getcurrentprotocol\csname pgf@sys@marker@prot@#1\endcsname% + \pgfsys@marker@declare@% + \pgfsysprotocol@setcurrentprotocol\pgfsys@marker@temp% + \global\advance\pgf@sys@id@count by1\relax% + }% +} +\let\pgfsys@marker@declare@\relax + +\def\pgfsys@marker@use#1{% + \pgfsysprotocol@literal{\csname pgf@sys@marker@prot@#1\endcsname}% +} + + + + + + + +\def\pgfsys@rdf@about#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@content#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@datatype#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@href#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@inlist{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@prefix#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@property#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@rel#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@resource#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@rev#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@src#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@typeof#1{\pgf@sys@fail{rdf}} + +\def\pgfsys@rdf@vocab#1{\pgf@sys@fail{rdf}} + + + + +\def\pgfsys@papersize#1#2{\pgf@sys@fail{papersize}} + +\def\pgfsys@global@papersize#1#2{\pgfsys@papersize{#1}{#2}} + +\def\pgfsys@prepare@papersize#1#2{\pgfsys@papersize{#1}{#2}} + +\ifx\paperheight\@undefined + \def\pgfsys@thepageheight{\the\vsize} % + \def\pgfsys@thepagewidth{\the\hsize} +\else + \def\pgfsys@thepageheight{\paperheight} + \def\pgfsys@thepagewidth{\paperwidth} +\fi + + + +\def\pgfsys@markposition#1{\pgf@sys@fail{marking the current position}} + + +\def\pgfsys@getposition#1#2{\let#2=\relax} + + + + + +\def\pgfsys@shadingoutsidepgfpicture#1{% + #1% +} + + +\def\pgfsys@shadinginsidepgfpicture#1{% + \pgf@makehbox{#1}% + \setbox\pgf@hbox=\hbox{\hskip-.5\wd\pgf@hbox\lower.5\ht\pgf@hbox\hbox{\box\pgf@hbox}}% + \pgfqbox{\pgf@hbox}% +} + + +\def\pgfsys@hbox#1{% + \pgfsys@begin@idscope% + \pgfsys@beginscope% + \setbox#1=\hbox{\box#1}% + \wd#1=0pt% + \ht#1=0pt% + \dp#1=0pt% + \box#1% + \pgfsys@endscope% + \pgfsys@end@idscope% +} + +\def\pgfsys@hboxsynced#1{% + \pgfsys@beginscope\pgflowlevelsynccm\pgfsys@hbox#1\pgfsys@endscope% +}% + +\def\pgfsys@pictureboxsynced#1{% + {% + \setbox0=\hbox{\pgfsys@beginpicture\box#1\pgfsys@endpicture}% + \pgfsys@hboxsynced0% + }% +} + +\def\pgfsys@beginpicture{} + +\def\pgfsys@endpicture{} + +\def\pgfsys@typesetpicturebox#1{% + \pgf@ya=\pgf@shift@baseline\relax% + \advance\pgf@ya by-\pgf@picminy\relax% + \advance\pgf@picmaxy by-\pgf@picminy\relax% + \advance\pgf@picmaxx by-\pgf@picminx\relax% + \setbox#1=\hbox{\hskip-\pgf@picminx\lower\pgf@picminy\box#1}% + \ht#1=\pgf@picmaxy% + \wd#1=\pgf@picmaxx% + \dp#1=0pt% + \leavevmode% + \pgf@xa=\pgf@trimleft@final\relax \ifdim\pgf@xa=0pt \else\kern\pgf@xa\fi + \raise-\pgf@ya\box#1% + \pgf@xa=\pgf@trimright@final\relax \ifdim\pgf@xa=0pt \else\kern\pgf@xa\fi +} + +\def\pgfsys@beginpurepicture{\pgfsys@beginpicture} + +\def\pgfsys@endpurepicture{\pgfsys@endpicture} + +\def\pgfsys@defineimage{% + \ifx\pgf@imagewidth\pgfutil@empty\else\edef\pgf@imagewidth{width=\pgf@imagewidth,}\fi% + \ifx\pgf@imageheight\pgfutil@empty\else\edef\pgf@imageheight{height=\pgf@imageheight,}\fi% + \ifx\pgf@imagepage\pgfutil@empty\else\edef\pgf@imagepage{page=\pgf@imagepage,}\fi% + \edef\pgf@image{\noexpand\includegraphics[\pgf@imageheight\pgf@imagewidth]{\pgf@filename}}% +} + + +\def\pgfsys@defobject#1#2#3#4{% + \pgfsysprotocol@getcurrentprotocol\pgfsys@temp% + {% + \pgfpicturetrue% + \pgfsysprotocol@setcurrentprotocol\pgfutil@empty% + \pgfsysprotocol@bufferedtrue% + \pgfsys@beginscope% + #4% + \pgfsys@endscope% + \pgfsysprotocol@getcurrentprotocol\pgfsys@@temp% + \expandafter\global\expandafter\let\csname #1\endcsname=\pgfsys@@temp% + }% + \pgfsysprotocol@setcurrentprotocol\pgfsys@temp% +} + + +\def\pgfsys@useobject#1#2{% + \pgfsysprotocol@getcurrentprotocol\pgfsys@temp% + {% + \pgfsysprotocol@setcurrentprotocol\pgfutil@empty% + \pgfsysprotocol@bufferedfalse% + #2% + \expandafter\pgfsysprotocol@setcurrentprotocol\csname #1\endcsname% + \pgfsysprotocol@invokecurrentprotocol% + }% + \pgfsysprotocol@setcurrentprotocol\pgfsys@temp% +} + + +\def\pgfsys@begininvisible{\pgfsys@transformcm{1}{0}{0}{1}{2000bp}{2000bp}} + +\def\pgfsys@endinvisible{\pgfsys@transformcm{1}{0}{0}{1}{-2000bp}{-2000bp}} + +\def\pgfsys@begininvisiblescope{\pgfsys@beginscope\pgfsys@begininvisible} + +\def\pgfsys@endinvisiblescope{\pgfsys@endinvisible\pgfsys@endscope} + + +\def\pgfsys@atbegindocument{} + + +\ifdefined\pdfstrcmp + \let\pgfsys@strcmp\pdfstrcmp +\else\ifdefined\strcmp + \let\pgfsys@strcmp\strcmp +\else\ifdefined\directlua + \directlua{ + local lft = lua.get_functions_table() + lft[\string#lft+1] = function() + local lhs = token.scan_string() + local rhs = token.scan_string() + if lhs < rhs then + tex.sprint(-2, "-1") + elseif lhs == rhs then + tex.sprint(-2, "0") + else + tex.sprint(-2, "1") + end + end + token.set_lua("pgfsys@strcmp", \string#lft, "global") + } +\else + \def\pgfsys@strcmp#1#2{\pgf@sys@fail{string comparison}}% +\fi\fi\fi + + + +\ifx\pgfsysdriver\@undefined + \pgfutil@guessdriver +\fi + +\input pgf.cfg + +\immediate\write-1{Driver file for pgf: \pgfsysdriver} +\pgfutil@InputIfFileExists{\pgfsysdriver}{}{% + \pgferror{Driver file ``\pgfsysdriver'' not found.}} + + + +\AtBeginDocument{ + \pgfsys@atbegindocument + \let\pgfsys@atbegindocument=\pgfutil@empty +} + + + + +\pgfutil@aux@read@hook + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsysanimations.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsysanimations.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..c6ad7d6cd4f5766303ed2c06361b6e9b266c6997 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsysanimations.code.tex @@ -0,0 +1,1568 @@ + + + +\ifx\pgfsysanimationsloaded\pgfutil@undefined + \let\pgfsysanimationsloaded=\relax +\else + \expandafter\endinput +\fi + + +\usepgfmodule{decorations} + + + + + +\def\pgfsysanimsnapshot#1{% + \def\pgfsysanim@snaptime{#1}% + \pgfsysanim@snap@firsttrue% + \pgfsysanim@is@snaptrue% +} +\def\pgfsysanimsnapshotafter#1{% + \def\pgfsysanim@snaptime{#1}% + \pgfsysanim@snap@firstfalse% + \pgfsysanim@is@snaptrue% +} +\newif\ifpgfsysanim@is@snap +\newif\ifpgfsysanim@snap@first + + + + +\def\pgfsysanimate#1{% + \csname pgfsysanim@checks@#1\endcsname% + \ifpgfsysanim@is@snap% + \pgfsysanim@do@snap{#1}% + \else% + \pgfsys@animate{#1}% + \fi% +} + +\def\pgfsysanim@do@snap#1{% + {% + \expandafter\ifx\csname pgfsysanim@prep@attr@#1\endcsname\pgfutil@undefined% + \else% + \pgfsysanim@compute@interval% + \let\pgfsysanim@code@begin\relax% + \let\pgfsysanim@code@end\pgfutil@empty% + \csname pgfsysanim@prep@attr@#1\endcsname% + \ifx\pgfsysanim@code@begin\relax% + \else% + \expandafter\expandafter\expandafter\pgfsysanim@call@attacher% + \expandafter\expandafter\expandafter{\expandafter\pgfsysanim@code@begin\expandafter}\expandafter{\pgfsysanim@code@end}{}% + \fi% + \fi% + }% +} +\def\pgfsysanim@call@attacher{\pgfsys@attach@to@id{\pgfsysanim@whom@id}{\pgfsysanim@whom@type}} + + +\def\pgfsysanim@checks@path{% + \expandafter\global\expandafter\let\csname pgfsysanim@path@is@animated@\pgfsysanim@whom@id @\pgfsysanim@whom@type\endcsname\pgfutil@empty% +} + + + +\def\pgfsysanimkeyrestartalways{\pgfsys@animation@restart@always} +\def\pgfsysanimkeyrestartnever{\pgfsys@animation@restart@never} +\def\pgfsysanimkeyrestartwhennotactive{\pgfsys@animation@restart@whennotactive} + + + + +\def\pgfsysanimkeyrepeat#1{% + \pgfsys@animation@repeat{#1}% + \let\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@normal% + {% + \pgf@x#1pt\relax% + \expandafter}% + \expandafter\def\expandafter\pgfsysanim@snap@repeat@arg\expandafter{\the\pgf@x}% +} +\def\pgfsysanimkeyrepeatindefinite{% + \pgfsys@animation@repeat@indefinite% + \let\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@indefinite% + \let\pgfsysanim@snap@repeat@arg\pgfutil@empty% +} +\def\pgfsysanimkeyrepeatdur#1{% + \pgfsys@animation@repeat@dur{#1}% + \let\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@dur% + {% + \pgf@x#1pt\relax% + \expandafter}% + \expandafter\def\expandafter\pgfsysanim@snap@repeat@arg\expandafter{\the\pgf@x}% +} +\def\pgfsysanim@snap@repeat@none{n}% +\def\pgfsysanim@snap@repeat@normal{m}% +\def\pgfsysanim@snap@repeat@indefinite{i}% +\def\pgfsysanim@snap@repeat@dur{d}% +\let\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@none +\let\pgfsysanim@snap@repeat@arg\pgfutil@empty + + + + +\def\pgfsysanimkeyfreezeatend{\pgfsys@animation@freezeatend\pgfsysanim@freezeatendtrue} +\def\pgfsysanimkeyremoveatend{\pgfsys@animation@removeatend\pgfsysanim@freezeatendfalse} +\newif\ifpgfsysanim@freezeatend + + + + +\def\pgfsysanimkeytime#1#2#3#4#5{% + \pgfsys@animation@time{#1}{#2}{#3}{#4}{#5}% + \def\pgfsysanim@time{{#1}{#2}{#3}{#4}{#5}}% +} + + + +\def\pgfsysanimkeybase{% + \pgfsys@animation@base% + \let\pgfsysanim@time\pgfsysanim@base@text% +} +\def\pgfsysanim@base@text{base}% + + +\def\pgfsysanimkeysnapshotstart#1{% + \def\pgfsysanim@snapshotstart{#1}% +} +\def\pgfsysanim@snapshotstart{0} + + + +\def\pgfsysanimkeyoffset#1#2{% + \pgfsys@animation@offset{#1}{#2}% +} + + + +\def\pgfsysanimkeysyncbegin#1#2#3#4{% + \pgfsys@animation@syncbegin{#1}{#2}{#3}{#4}% +} + +\def\pgfsysanimkeysyncend#1#2#3#4{% + \pgfsys@animation@syncend{#1}{#2}{#3}{#4}% +} + + + +\def\pgfsysanimkeyevent#1#2#3#4#5{% + \pgfsys@animation@event{#1}{#2}{#3}{#4}{#5}% +} + + + +\def\pgfsysanimkeyrepeatevent#1#2#3#4#5{% + \pgfsys@animation@repeat@event{#1}{#2}{#3}{#4}{#5}% +} + + + + +\def\pgfsysanimkeyaccesskey#1#2#3{% + \pgfsys@animation@accesskey{#1}{#2}{#3}% +} + + + + + +\def\pgfsysanimkeyaccumulate{\pgfsys@animation@accumulate\pgfsysanim@accumulatetrue} +\def\pgfsysanimkeynoaccumulate{\pgfsys@animation@noaccumulate\pgfsysanim@accumulatefalse} +\newif\ifpgfsysanim@accumulate + + + + + +\def\pgfsysanimkeywhom#1#2{% + \pgfsys@register@type{#2}% + \pgfsys@animation@whom{#1}{#2}% + \def\pgfsysanim@whom@id{#1}% + \def\pgfsysanim@whom@type{#2}% +} + + + + + + +\def\pgfsysanimkeyrotatealong{\pgfsys@animation@rotatealong\pgfsysanim@rotatealongtrue} +\def\pgfsysanimkeynorotatealong{\pgfsys@animation@norotatealong\pgfsysanim@rotatealongfalse} +\newif\ifpgfsysanim@rotatealong + + + +\def\pgfsysanimkeymovealong#1{% + \pgfsys@animation@movealong{#1}% + \def\pgfsysanim@snap@movealong{#1}% +} + + + + + +\def\pgfsysanimkeytipmarkers#1#2{% + \pgfsys@animation@tip@markers{#1}{#2}% + \def\pgfsysanim@snap@tip@start{#1}% + \def\pgfsysanim@snap@tip@end{#2}% +} +\let\pgfsysanim@snap@tip@start\pgfutil@empty% +\let\pgfsysanim@snap@tip@end\pgfutil@empty% + + + +\def\pgfsysanimkeycanvastransform#1#2{% + \pgfsys@animation@canvas@transform{#1}{#2}% + \def\pgfsysanim@snap@canvas@transform@pre{#1}% + \def\pgfsysanim@snap@canvas@transform@post{#2}% +} +\let\pgfsysanim@snap@canvas@transform@pre\relax +\let\pgfsysanim@snap@canvas@transform@post\relax + + + + +\def\pgfsysanimvalcurrent{% + \pgfsys@animation@val@current% + \ifpgfsysanim@is@snap% + \pgferror{You may not use "current value" with an animation snapshot}% + \fi% +} + + + +\def\pgfsysanimvalnone{% +} + + + + +\def\pgfsysanimvaltext#1{% + \pgfsys@animation@val@text{#1}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{#1}% + \fi% +} + + + + + +\def\pgfsysanimvalscalar#1{% + \pgfsys@animation@val@scalar{#1}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{#1}% + \fi% +} + + + + +\def\pgfsysanimvaldimension#1{% + \pgfsys@animation@val@dimension{#1}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{#1}% + \fi% +} + + + + +\def\pgfsysanimvalcolor#1{% + \pgfutil@colorlet{pgf@anim@temp}{#1}% + \pgfutil@ifundefined{applycolormixins}{}{\applycolormixins{pgf@anim@temp}}% + \expandafter\let\expandafter\pgf@sys@temp\csname\string\color@pgf@anim@temp\endcsname + \expandafter\pgfanim@parse@type@color@\pgf@sys@temp% +} +\def\pgfanim@parse@type@color@#1#2#3#4#5{% + \expandafter\ifx\csname pgfsysanimvalcolor#4\endcsname\relax% + \pgferror{Unsupported color model `#4'}% + \else% + \edef\pgf@sys@colmarshal{\expandafter\noexpand\csname pgfsysanimvalcolor#4\endcsname}% + \pgf@sys@uncomma#5,,% + \pgf@sys@colmarshal% + \fi% +} + +\def\pgf@sys@uncomma#1,{% + \def\pgf@sys@coltest{#1}% + \ifx\pgf@sys@coltest\pgfutil@empty% + \else% + \expandafter\def\expandafter\pgf@sys@colmarshal\expandafter{\pgf@sys@colmarshal{#1}}% + \expandafter\pgf@sys@uncomma% + \fi% +} + + + + + +\def\pgfsysanimvalcolorrgb#1#2#3{% + \pgfsys@animation@val@color@rgb{#1}{#2}{#3}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{{#1}{#2}{#3}}% + \fi% +} + + + + +\def\pgfsysanimvalcolorcmyk#1#2#3#4{% + \pgfsys@animation@val@color@cmyk{#1}{#2}{#3}{#4}% + \ifpgfsysanim@is@snap% + {% + \pgf@xa=1pt% + \advance\pgf@xa by-#1pt% + \advance\pgf@xa by-#4pt\relax% + \ifdim\pgf@xa<0pt\pgf@xa0pt\fi% + \pgf@xb=1pt% + \advance\pgf@xb by-#1pt% + \advance\pgf@xb by-#4pt\relax% + \ifdim\pgf@xb<0pt\pgf@xb0pt\fi% + \pgf@xc=1pt% + \advance\pgf@xc by-#1pt% + \advance\pgf@xc by-#4pt\relax% + \ifdim\pgf@xc<0pt\pgf@xc0pt\fi% + \edef\pgfsys@temp{{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@xb}{\pgf@sys@tonumber\pgf@xc}}% + \expandafter}% + \expandafter\pgfsysanim@esnap@record\expandafter{\pgfsys@temp}% + \fi% +} + + + +\def\pgfsysanimvalcolorcmy#1#2#3{% + \pgfsys@animation@val@color@cmy{#1}{#2}{#3}% + \ifpgfsysanim@is@snap% + {% + \pgf@xa=1pt% + \advance\pgf@xa by-#1pt% + \pgf@xb=1pt% + \advance\pgf@xb by-#1pt% + \pgf@xc=1pt% + \advance\pgf@xc by-#1pt% + \edef\pgfsys@temp{{\pgf@sys@tonumber\pgf@xa}{\pgf@sys@tonumber\pgf@xb}{\pgf@sys@tonumber\pgf@xc}}% + \expandafter}% + \expandafter\pgfsysanim@esnap@record\expandafter{\pgfsys@temp}% + \fi% +} + + + + +\def\pgfsysanimvalcolorgray#1{% + \pgfsys@animation@val@color@gray{#1}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{{#1}{#1}{#1}}% + \fi% +} + + + + +\def\pgfsysanimvalpath#1{% + \pgfsys@animation@val@path{#1}% + \ifpgfsysanim@is@snap% + \pgfsysanim@snap@record{#1}% + \fi% +} + + + +\def\pgfsysanimvaltranslate#1#2{% + \pgfsys@animation@val@translate{#1}{#2}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{{#1}{#2}}% + \fi% +} + + + + +\def\pgfsysanimvalscale#1#2{% + \pgfsys@animation@val@scale{#1}{#2}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{{#1}{#2}}% + \fi% +} + + + + +\def\pgfsysanimvalviewbox#1#2#3#4{% + \pgfsys@animation@val@viewbox{#1}{#2}{#3}{#4}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{{#1}{#2}{#3}{#4}}% + \fi% +} + + + + + +\def\pgfsysanimvaldash#1#2{% + \pgfsys@animation@val@dash{#1}{#2}% + \ifpgfsysanim@is@snap% + \pgfsysanim@esnap@record{{#1}{#2}}% + \fi% +} + + + + + + +\def\pgfsysanim@esnap@record#1{% + \edef\pgfsysanim@temp{#1}% + \expandafter\pgfsysanim@snap@record\expandafter{\pgfsysanim@temp}% +} +\def\pgfsysanim@snap@record#1{% + \ifx\pgfsysanim@time\pgfsysanim@base@text% + \def\pgfsysanim@base@value{#1}% + \else% + \advance\pgfsysanim@snap@count by1\relax% + \expandafter\def\expandafter\pgfsysanim@temp\expandafter{\pgfsysanim@time{#1}}% + \expandafter\let\csname pgfsysanim@snap@\the\pgfsysanim@snap@count\endcsname\pgfsysanim@temp% + \fi% +} +\newcount\pgfsysanim@snap@count +\let\pgfsysanim@base@value\pgfutil@empty% + + +\def\pgfsysanim@compute@interval{% + \let\pgfsysanim@prev@val\relax% + \let\pgfsysanim@prev@time\relax% + \let\pgfsysanim@prev@spline\pgfsysanim@default@spline% + \let\pgfsysanim@next@val\relax% + \let\pgfsysanim@next@time\relax% + \let\pgfsysanim@next@spline\pgfsysanim@default@spline% + \let\pgfsysanim@first@time\relax% + \let\pgfsysanim@last@time\relax% + \let\pgfsysanim@last@val\relax% + \ifnum\pgfsysanim@snap@count>0\relax% + \pgf@xc\pgfsysanim@snaptime pt\relax% + \pgf@x\pgfsysanim@snapshotstart pt\relax% + \advance\pgf@xc-\pgf@x\relax% + \pgfsysanim@compute@start@end% + \pgfsysanim@compute@value% + \fi% + \pgfsysanim@valid@snapshot@timefalse% + \ifx\pgfsysanim@prev@time\relax% + \else\ifx\pgfsysanim@next@time\relax% + \else\pgfsysanim@valid@snapshot@timetrue% + \fi\fi% + \ifpgfsysanim@valid@snapshot@time% + \else% + \ifx\pgfsysanim@base@value\pgfutil@empty% + \else% + \let\pgfsysanim@prev@val\pgfsysanim@base@value% + \def\pgfsysanim@prev@time{0}% + \let\pgfsysanim@prev@spline\pgfsysanim@default@spline% + \let\pgfsysanim@next@val\pgfsysanim@base@value% + \let\pgfsysanim@next@time\pgfsysanim@prev@time% + \let\pgfsysanim@next@spline\pgfsysanim@default@spline% + \def\pgfsysanim@first@time{-16382}% + \let\pgfsysanim@last@time\pgfsysanim@prev@time% + \let\pgfsysanim@last@val\pgfsysanim@base@value% + \def\pgfsysanim@frac@a{1}% + \def\pgfsysanim@frac@b{0}% + \pgfsysanim@valid@snapshot@timetrue% + \fi% + \fi% +} +\newif\ifpgfsysanim@cont% +\newif\ifpgfsysanim@valid@snapshot@time +\def\pgfsysanim@default@spline{{0}{0}{1}{1}} + +\def\pgfsysanim@compute@start@end{% + \expandafter\expandafter\expandafter\pgfsysanim@compute@start\csname pgfsysanim@snap@1\endcsname% + \expandafter\expandafter\expandafter\pgfsysanim@compute@end\csname pgfsysanim@snap@\the\pgfsysanim@snap@count\endcsname% +} +\def\pgfsysanim@compute@start#1#2#3#4#5#6{% + \def\pgfsysanim@first@time{#1}% +} +\def\pgfsysanim@compute@end#1#2#3#4#5#6{% + \def\pgfsysanim@last@time{#1}% + \def\pgfsysanim@last@val{#6}% +} + + +\def\pgfsysanim@compute@value{% + \ifdim\pgf@xc<\pgfsysanim@first@time pt\relax% + \else% + \ifx\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@none% + \pgfsysanim@handle@repeat@none% + \else\ifx\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@normal% + \pgfsysanim@handle@repeat@normal% + \else\ifx\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@indefinite% + \pgfsysanim@handle@repeat@indefinite% + \else\ifx\pgfsysanim@snap@repeat@kind\pgfsysanim@snap@repeat@dur% + \pgfsysanim@handle@repeat@dur% + \fi\fi\fi\fi% + \fi% +} + +\def\pgfsysanim@handle@repeat@none{% + \ifdim\pgf@xc<\pgfsysanim@last@time pt\relax% + \pgfsysanim@compute@time% + \else% + \ifdim\pgf@xc=\pgfsysanim@last@time pt\relax% + \ifpgfsysanim@snap@first% + \pgfsysanim@compute@time% + \else% + \ifpgfsysanim@freezeatend% + \let\pgfsysanim@prev@val\pgfsysanim@last@val% + \let\pgfsysanim@prev@time\pgfsysanim@last@time% + \let\pgfsysanim@next@val\pgfsysanim@last@val% + \let\pgfsysanim@next@time\pgfsysanim@last@time% + \fi% + \fi% + \else% + \ifpgfsysanim@freezeatend% + \let\pgfsysanim@prev@val\pgfsysanim@last@val% + \let\pgfsysanim@prev@time\pgfsysanim@last@time% + \let\pgfsysanim@next@val\pgfsysanim@last@val% + \let\pgfsysanim@next@time\pgfsysanim@last@time% + \fi% + \fi% + \fi% +} + + +\def\pgfsysanim@handle@repeat@indefinite{% + \ifdim\pgf@xc<\pgfsysanim@last@time pt\relax% + \pgfsysanim@compute@time% + \else% + \pgf@xa=\pgfsysanim@last@time pt% + \pgf@xb=\pgfsysanim@first@time pt% + \advance\pgf@xa by-\pgf@xb% + \pgf@ya\pgf@xc% + \advance\pgf@ya by-\pgf@xb% + \ifdim\pgf@xa<0.01pt\relax% + \def\pgfmathresult{1.0}% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@xa}% + \fi% + \pgf@x\pgfmathresult pt\relax% + \expandafter\pgfsysanim@splitter\the\pgf@x% + \pgf@xc=\pgfsysanim@repeat@frac\pgf@xa% + \advance\pgf@xc by\pgf@xb% + \pgfsysanim@compute@time% + \fi% +} +{\catcode`\p=12\catcode`\t=12\gdef\Pgfsysanim@sPliTTer#1.#2pt{\Pgfsysanim@seTTer{#1}{#2}}} +\let\pgfsysanim@splitter\Pgfsysanim@sPliTTer +\def\Pgfsysanim@seTTer#1#2{% + \def\pgfsysanim@repeat@decimal{#1}% + \def\pgfsysanim@repeat@frac{.#2}% + \ifdim\pgfsysanim@repeat@frac pt=0pt% + \c@pgf@counta\pgfsysanim@repeat@decimal% + \advance\c@pgf@counta by-1\relax% + \edef\pgfsysanim@repeat@decimal{\the\c@pgf@counta}% + \def\pgfsysanim@repeat@frac{1}% + \fi% +} +\def\pgfsysanim@repeat@decimal{0}% + + +\def\pgfsysanim@handle@repeat@normal{% + \pgf@xa=\pgfsysanim@last@time pt% + \pgf@xb=\pgfsysanim@first@time pt% + \advance\pgf@xa by-\pgf@xb% + \pgf@ya\pgf@xc% + \advance\pgf@ya by-\pgf@xb% + \ifdim\pgf@xa<0.01pt\relax% + \def\pgfmathresult{1.0}% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@xa}% + \fi% + \pgf@x\pgfmathresult pt\relax% + \expandafter\pgfsysanim@splitter\the\pgf@x% + \ifdim\pgfmathresult pt<\pgfsysanim@snap@repeat@arg\relax% + \pgf@xc=\pgfsysanim@repeat@frac\pgf@xa% + \advance\pgf@xc by\pgf@xb% + \pgfsysanim@compute@time% + \else% + \ifpgfsysanim@freezeatend% + \expandafter\pgfsysanim@splitter\pgfsysanim@snap@repeat@arg% + \pgf@xc=\pgfsysanim@repeat@frac\pgf@xa% + \advance\pgf@xc by\pgf@xb% + \pgfsysanim@compute@time% + \else% + \ifdim\pgfmathresult pt=\pgfsysanim@snap@repeat@arg\relax% + \ifpgfsysanim@snap@first% + \expandafter\pgfsysanim@splitter\pgfsysanim@snap@repeat@arg% + \pgf@xc=\pgfsysanim@repeat@frac\pgf@xa% + \advance\pgf@xc by\pgf@xb% + \pgfsysanim@compute@time% + \fi% + \fi% + \fi% + \fi% +} + +\def\pgfsysanim@handle@repeat@dur{% + \pgf@yb=\pgfsysanim@first@time pt% + \advance\pgf@yb by\pgfsysanim@snap@repeat@arg\relax% + \ifdim\pgf@xc<\pgf@yb% + \pgf@xa=\pgfsysanim@last@time pt% + \pgf@xb=\pgfsysanim@first@time pt% + \advance\pgf@xa by-\pgf@xb% + \pgf@ya\pgf@xc% + \advance\pgf@ya by-\pgf@xb% + \ifdim\pgf@xa<0.01pt\relax% + \def\pgfmathresult{1.0}% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\pgf@ya}{\pgf@sys@tonumber\pgf@xa}% + \fi% + \pgf@x\pgfmathresult pt\relax% + \expandafter\pgfsysanim@splitter\the\pgf@x% + \pgf@xc=\pgfsysanim@repeat@frac\pgf@xa% + \advance\pgf@xc by\pgf@xb% + \pgfsysanim@compute@time% + \else% + \ifpgfsysanim@freezeatend% + \pgfsysanim@handle@repeat@dur@freeze% + \else% + \ifdim\pgf@xc=\pgf@yb% + \ifpgfsysanim@snap@first% + \pgfsysanim@handle@repeat@dur@freeze% + \fi% + \fi% + \fi% + \fi% +} + +\def\pgfsysanim@handle@repeat@dur@freeze{% + \pgf@xa=\pgfsysanim@last@time pt% + \pgf@xb=\pgfsysanim@first@time pt% + \advance\pgf@xa by-\pgf@xb% + \ifdim\pgf@xa<0.01pt\relax% + \def\pgfmathresult{1.0}% + \else% + \pgfmathdivide@{\pgf@sys@tonumber\dimexpr\pgfsysanim@snap@repeat@arg}{\pgf@sys@tonumber\pgf@xa}% + \fi% + \pgf@x\pgfmathresult pt\relax% + \expandafter\pgfsysanim@splitter\the\pgf@x% + \pgf@xc=\pgfsysanim@repeat@frac\pgf@xa% + \advance\pgf@xc by\pgf@xb% + \pgfsysanim@compute@time% +} + + + + + +\def\pgfsysanim@compute@time{% + \pgfutil@tempcnta=1\relax% + \pgfsysanim@conttrue% + \pgfutil@loop% + \ifnum\pgfutil@tempcnta>\pgfsysanim@snap@count% + \pgfsysanim@contfalse% + \else% + \expandafter\let\expandafter\pgfsys@temp\csname pgfsysanim@snap@\the\pgfutil@tempcnta\endcsname% + \expandafter\pgfsysanim@test@time\pgfsys@temp% + \fi% + \ifpgfsysanim@cont% + \advance\pgfutil@tempcnta by1\relax% + \pgfutil@repeat% +} + + +\def\pgfsysanim@test@time#1#2#3#4#5#6{% + \ifdim#1pt<\pgf@xc% + \def\pgfsysanim@prev@val{#6}% + \def\pgfsysanim@prev@time{#1}% + \def\pgfsysanim@prev@spline{{#2}{#3}{#4}{#5}}% + \else% + \ifdim#1pt=\pgf@xc% + \ifpgfsysanim@snap@first% + \ifx\pgfsysanim@next@val\relax% + \def\pgfsysanim@prev@val{#6}% + \def\pgfsysanim@prev@time{#1}% + \def\pgfsysanim@prev@spline{{#2}{#3}{#4}{#5}}% + \let\pgfsysanim@next@val\pgfsysanim@prev@val% + \let\pgfsysanim@next@time\pgfsysanim@prev@time% + \let\pgfsysanim@next@spline\pgfsysanim@prev@spline% + \pgfsysanim@contfalse% + \fi + \else% + \def\pgfsysanim@prev@val{#6}% + \def\pgfsysanim@prev@time{#1}% + \def\pgfsysanim@prev@spline{{#2}{#3}{#4}{#5}}% + \let\pgfsysanim@next@val\pgfsysanim@prev@val% + \let\pgfsysanim@next@time\pgfsysanim@prev@time% + \let\pgfsysanim@next@spline\pgfsysanim@prev@spline% + \fi% + \else% + \ifx\pgfsysanim@next@val\relax% + \def\pgfsysanim@next@val{#6}% + \def\pgfsysanim@next@time{#1}% + \def\pgfsysanim@next@spline{{#2}{#3}{#4}{#5}}% + \else% + \pgfsysanim@contfalse% + \fi% + \fi% + \fi% +} + +\let\pgfsysanim@prev@val\relax% +\let\pgfsysanim@prev@time\relax% +\let\pgfsysanim@next@val\relax% +\let\pgfsysanim@next@time\relax% + +\def\pgfsysanim@attach#1#2#3{% + \expandafter\pgfsysanim@prep@beg\expandafter{\pgfsysanim@first@time}{#2}{#3}% + \expandafter\def\expandafter\pgfsysanim@code@main\expandafter{\csname pgfsysanim@main@of@\pgfsysanim@whom@id @\pgfsysanim@whom@type @#1\endcsname}% + \expandafter\ifx\pgfsysanim@code@main\relax% + \edef\pgfsysanim@code@begin{% + \let\noexpand\pgfsysanim@c@begin\noexpand\pgfutil@empty% + \let\noexpand\pgfsysanim@c@end\noexpand\pgfutil@empty% + \pgfsysanim@lasttime-16383pt\relax% + \expandafter\noexpand\pgfsysanim@code@main% + \global\let\expandafter\noexpand\pgfsysanim@code@main\relax% + \noexpand\pgfsysanim@c@begin% + }% + \let\pgfsysanim@code@end\pgfsysanim@code@closer% + \expandafter\global\expandafter\let\pgfsysanim@code@main\pgfutil@empty% + \else% + \let\pgfsysanim@code@begin\relax% + \let\pgfsysanim@code@end\relax% + \fi% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\def% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\pgfsysanim@new@main% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{\expandafter\pgfsysanim@code@main\pgfsysanim@add@main} + \expandafter\global\expandafter\let\pgfsysanim@code@main\pgfsysanim@new@main% +} +\def\pgfsysanim@code@closer{\pgfsysanim@c@end} + +\def\pgfsysanim@prep@beg#1#2#3{% + \edef\pgfsysanim@add@main{% + \noexpand\ifdim\pgfsysanim@lasttime>#1pt% + \noexpand\else% + \pgfsysanim@lasttime#1pt% + \def\noexpand\pgfsysanim@c@begin{#2}% + \def\noexpand\pgfsysanim@c@end{#3}% + \noexpand\fi% + } +} + +\def\pgfsysanim@prep@beg@special#1#2{% + \def\pgfsysanim@add@main{% + \ifdim\pgfsysanim@lasttime>#1pt% + \else% + \pgfsysanim@lasttime#1pt% + \def\pgfsysanim@c@begin{#2}% + \fi% + } +} + + + +\def\pgfsysanim@attach@special#1#2{% + \expandafter\expandafter\expandafter\pgfsysanim@prep@beg@special\expandafter\expandafter\expandafter{\expandafter\pgfsysanim@first@time\expandafter}\expandafter{#2}% + \ifx#1\relax% + \def#1{% + \pgfsysanim@lasttime-16383pt\relax% + \let\pgfsysanim@c@begin\pgfutil@empty% + }% + \fi% + \expandafter\expandafter\expandafter\gdef\expandafter\expandafter\expandafter#1\expandafter\expandafter\expandafter{\expandafter#1\pgfsysanim@add@main}% +} + + + +\newdimen\pgfsysanim@lasttime + + +\def\pgfsysanim@add@trans{% + \ifx\pgfsysanim@snap@canvas@transform@pre\relax% + \else% + \ifx\pgfsysanim@code@begin\relax% + \let\pgfsysanim@code@begin\pgfutil@empty% + \fi% + \pgfsysanim@add@trans@% + \fi% +} +\def\pgfsysanim@add@trans@{% + \toks0\expandafter{\pgfsysanim@snap@canvas@transform@pre}% + \toks1\expandafter{\pgfsysanim@code@begin}% + \toks2\expandafter{\pgfsysanim@snap@canvas@transform@post}% + \edef\pgfsysanim@code@begin{{\the\toks0 \the\toks1 \the\toks2}}% +} + + +\def\pgfsysanim@prep@attr@opacity{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scalar% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{1}% + \pgfsysanim@attach{opacity}{\noexpand\pgfsys@opacity{\pgfsysanim@x@val}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@fillopacity{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scalar% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{1}% + \pgfsysanim@attach{fillopacity}{\noexpand\pgfsys@fill@opacity{\pgfsysanim@x@val}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@strokeopacity{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scalar% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{1}% + \pgfsysanim@attach{strokeopacity}{\noexpand\pgfsys@stroke@opacity{\pgfsysanim@x@val}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@visibility{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@text% + \ifx\pgfsysanim@text@val\pgf@hidden@text% + \pgfsysanim@attach{visibility}{\noexpand\pgfsys@begininvisiblescope}{\noexpand\pgfsys@endinvisiblescope}% + \else% + \pgfsysanim@attach{visibility}{}{}% + \fi% + \fi% +} +\def\pgf@hidden@text{hidden} + +\def\pgfsysanim@prep@attr@linewidth{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@dimension% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{16382}% + \pgfsysanim@attach{linewidth}{\noexpand\pgfsys@setlinewidth{\pgfsysanim@x@val pt}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@dash{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@dash% + \pgfsysanim@attach{dash}{\noexpand\pgfsys@setdash{\pgfsysanim@dash@vals}{\pgfsysanim@x@val pt}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@translate{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@translate% + \edef\pgfsysanim@code@begin{\noexpand\pgfsys@transformshift{\pgfsysanim@x@val pt}{\pgfsysanim@y@val pt}}% + \fi% + \pgfsysanim@add@trans% +} + + +\def\pgfsysanim@prep@attr@scale{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scale% + \edef\pgfsysanim@code@begin{\noexpand\pgfsys@transformxyscale{\pgfsysanim@x@val}{\pgfsysanim@y@val}}% + \fi% + \pgfsysanim@add@trans% +} + +\def\pgfsysanim@prep@attr@rotate{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scalar% + {% + \pgfmathsin@{\pgfsysanim@x@val}% + \let\pgftransform@sin=\pgfmathresult% + \pgfmathcos@{\pgfsysanim@x@val}% + \let\pgftransform@cos=\pgfmathresult% + \pgf@x=\pgftransform@sin pt% + \pgf@xa=-\pgf@x% + \edef\pgfsysanim@code@begin{\noexpand\pgfsys@transformcm{\pgftransform@cos}{\pgftransform@sin}{\pgf@sys@tonumber{\pgf@xa}}{\pgftransform@cos}{0pt}{0pt}}% + \expandafter}% + \expandafter\def\expandafter\pgfsysanim@code@begin\expandafter{\pgfsysanim@code@begin}% + \fi% + \pgfsysanim@add@trans% +} + +\def\pgfsysanim@prep@attr@skewx{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scalar% + {% + \pgfmathtan@{\pgfsysanim@x@val}% + \edef\pgfsysanim@code@begin{\noexpand\pgfsys@transformcm{1}{0}{\pgfmathresult}{1}{0pt}{0pt}}% + \expandafter}% + \expandafter\def\expandafter\pgfsysanim@code@begin\expandafter{\pgfsysanim@code@begin}% + \fi% + \pgfsysanim@add@trans% +} + +\def\pgfsysanim@prep@attr@skewy{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@scalar% + {% + \pgfmathtan@{\pgfsysanim@x@val}% + \edef\pgfsysanim@code@begin{\noexpand\pgfsys@transformcm{1}{\pgfmathresult}{0}{1}{0pt}{0pt}}% + \expandafter}% + \expandafter\def\expandafter\pgfsysanim@code@begin\expandafter{\pgfsysanim@code@begin}% + \fi% + \pgfsysanim@add@trans% +} + +\def\pgfsysanim@prep@attr@motion{% + \ifx\pgfsysanim@base@value\pgfutil@empty% + \else% + \pgferror{You may not provide a base value for a motion}% + \let\pgfsysanim@base@value\pgfutil@empty% + \fi% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@motion% + \expandafter\pgfsysanim@prep@attr@motion@\pgfsysanim@motion@trans% + \fi% + \pgfsysanim@add@trans% +} +\def\pgfsysanim@prep@attr@motion@#1#2#3#4#5#6{% + \ifpgfsysanim@rotatealong% + \def\pgfsysanim@code@begin{\pgfsys@transformcm{#1}{#2}{#3}{#4}{#5}{#6}}% + \else% + \def\pgfsysanim@code@begin{\pgfsys@transformshift{#5}{#6}}% + \fi% +} + + +\def\pgfsysanim@prep@attr@strokecolor{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@color% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{1}% + \pgfsysanim@cap@scalar{\pgfsysanim@y@val}{0}{1}% + \pgfsysanim@cap@scalar{\pgfsysanim@z@val}{0}{1}% + \pgfsysanim@attach{strokecolor}{\noexpand\pgfsys@color@rgb@stroke{\pgfsysanim@x@val}{\pgfsysanim@y@val}{\pgfsysanim@z@val}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@fillcolor{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@color% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{1}% + \pgfsysanim@cap@scalar{\pgfsysanim@y@val}{0}{1}% + \pgfsysanim@cap@scalar{\pgfsysanim@z@val}{0}{1}% + \pgfsysanim@attach{fillcolor}{\noexpand\pgfsys@color@rgb@fill{\pgfsysanim@x@val}{\pgfsysanim@y@val}{\pgfsysanim@z@val}}{}% + \fi% +} + +\def\pgfsysanim@prep@attr@color{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@color% + \pgfsysanim@cap@scalar{\pgfsysanim@x@val}{0}{1}% + \pgfsysanim@cap@scalar{\pgfsysanim@y@val}{0}{1}% + \pgfsysanim@cap@scalar{\pgfsysanim@z@val}{0}{1}% + \pgfsysanim@attach{color}{\noexpand\pgfsys@color@rgb{\pgfsysanim@x@val}{\pgfsysanim@y@val}{\pgfsysanim@z@val}}{}% + \fi% +} + +\newif\ifpgfsys@animation@view@hooked + +\def\pgfsysanim@prep@attr@viewbox{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@viewbox% + \pgfsys@attach@to@id{\pgfsysanim@whom@id}{}{% + \ifpgfsys@animation@view@hooked% + \else% + \let\pgfsys@viewboxmeet@orig\pgfsys@viewboxmeet% + \let\pgfsys@viewboxmeet\pgfsysanim@hooked@viewboxmeet% + \let\pgfsys@viewboxslice@orig\pgfsys@viewboxslice% + \let\pgfsys@viewboxslice\pgfsysanim@hooked@viewboxslice% + \pgfsys@animation@view@hookedtrue% + \fi% + }{}{}% + \edef\pgfsysanim@temp{{\pgfsysanim@x@val}{\pgfsysanim@y@val}{\pgfsysanim@z@val}{\pgfsysanim@w@val}}% + \expandafter\pgfsysanim@attach@special\csname pgfsysanim@hook@for@\pgfsys@id@ref{\pgfsysanim@whom@id}{\pgfsysanim@whom@type}\endcsname\pgfsysanim@temp% + \fi% +} +\def\pgfsysanim@hooked@viewboxmeet#1#2#3#4#5#6#7#8{% + \expandafter\ifx\csname pgfsysanim@hook@for@\pgfsys@id@refcurrent\endcsname\relax% + \pgfsys@viewboxmeet@orig{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \else% + \csname pgfsysanim@hook@for@\pgfsys@id@refcurrent\endcsname% + \ifx\pgfsysanim@c@begin\pgfutil@empty% + \else% + \expandafter\pgfsysanim@hooked@viewboxmeet@\pgfsysanim@c@begin{#1}{#2}{#3}{#4}% + \fi% + \expandafter\global\expandafter\let\csname pgfsysanim@hook@for@\pgfsys@id@refcurrent\endcsname\relax% + \fi% +} +\def\pgfsysanim@hooked@viewboxmeet@#1#2#3#4#5#6#7#8{% + \pgfsys@viewboxmeet@orig{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% +} +\def\pgfsysanim@hooked@viewboxslice#1#2#3#4#5#6#7#8{% + \expandafter\ifx\csname pgfsysanim@hook@for@\pgfsys@id@refcurrent\endcsname\relax% + \pgfsys@viewboxslice@orig{#1}{#2}{#3}{#4}{#5}{#6}{#7}{#8}% + \else% + \csname pgfsysanim@hook@for@\pgfsys@id@refcurrent\endcsname% + \expandafter\pgfsysanim@hooked@viewboxslice@\pgfsysanim@c@begin{#1}{#2}{#3}{#4}% + \expandafter\global\expandafter\let\csname pgfsysanim@hook@for@\pgfsys@id@refcurrent\endcsname\relax% + \fi% +} +\def\pgfsysanim@hooked@viewboxslice@#1#2#3#4#5#6#7#8{% + \pgfsys@viewboxslice@orig{#5}{#6}{#7}{#8}{#1}{#2}{#3}{#4}% +} + + +\newif\ifpgfsys@animation@path@hooked + +\def\pgfsysanim@prep@attr@path{% + \ifpgfsysanim@valid@snapshot@time% + \pgfsysanim@comp@path% + \pgfsys@attach@to@id{\pgfsysanim@whom@id}{}{% + \ifpgfsys@animation@path@hooked% + \else% + \let\pgfsys@discardpath@orig\pgfsys@discardpath% + \let\pgfsys@stroke@orig\pgfsys@stroke% + \let\pgfsys@fill@orig\pgfsys@fill% + \let\pgfsys@fillstroke@orig\pgfsys@fillstroke% + \let\pgfsys@closestroke@orig\pgfsys@closestroke% + \let\pgfsys@discardpath\pgfsys@discardpath@hook% + \let\pgfsys@stroke\pgfsys@stroke@hook% + \let\pgfsys@fill\pgfsys@fill@hook% + \let\pgfsys@fillstroke\pgfsys@fillstroke@hook% + \let\pgfsys@closestroke\pgfsys@closestroke@hook% + \pgfsys@animation@path@hookedtrue% + \fi% + }{}{}% + \expandafter\pgfsysanim@attach@special\csname pgfsysanim@phook@for@\pgfsys@id@ref{\pgfsysanim@whom@id}{\pgfsysanim@whom@type}\endcsname\pgfsysanim@path@all% + \fi% +} +\def\pgfsys@stroke@hook{\pgfsysanim@with@tipstrue\pgfsysanim@path@hooks\pgfsys@stroke@orig} +\def\pgfsys@fill@hook{\pgfsysanim@with@tipsfalse\pgfsysanim@path@hooks\pgfsys@fill@orig} +\def\pgfsys@fillstroke@hook{\pgfsysanim@with@tipstrue\pgfsysanim@path@hooks\pgfsys@fillstroke@orig} +\def\pgfsys@closestroke@hook{\pgfsysanim@with@tipsfalse\pgfsysanim@path@hooks\pgfsys@closestroke@orig} +\def\pgfsys@discardpath@hook{\pgfsysanim@with@tipsfalse\pgfsysanim@path@hooks\pgfsys@discardpath@orig} + +\newif\ifpgfsysanim@with@tips + +\def\pgfsysanim@path@hooks#1{% + {% + \expandafter\ifx\csname pgfsysanim@phook@for@\pgfsys@id@refcurrent\endcsname\relax% + #1% + \else% + \pgfsys@discardpath@orig% + \csname pgfsysanim@phook@for@\pgfsys@id@refcurrent\endcsname% + \pgfsysanim@c@begin% + \pgfsysanim@path@val% + #1% + \ifpgfsysanim@with@tips% + \ifx\pgfsysanim@path@val\pgfutil@empty\else% + \pgfsysanim@prepare@end@of@path% + \begingroup% + \pgfsysanim@prepare@start@of@path% + \pgfsysanim@add@marker@at@start% + \endgroup% + \pgfsysanim@add@marker@at@end% + \fi% + \fi% + \expandafter\global\expandafter\let\csname pgfsysanim@phook@for@\pgfsys@id@refcurrent\endcsname\relax% + \fi% + }% +} + + +\def\pgfsysanim@prepare@start@of@path{% + \ifx\pgfsysanim@snap@tip@start\pgfutil@empty\else + \ifx\pgfprocessresultpathsuffix\relax% + \pgfprocesssplitpath{\pgf@arrowpath}% + \fi% + \expandafter\pgf@parse@start\pgfprocessresultpathsuffix\pgf@stop\pgf@stop\pgf@stop% + \pgf@prep@start% + \fi% +} +\def\pgfsysanim@add@marker@at@start{% + \ifx\pgfsysanim@snap@tip@start\pgfutil@empty\else + {% + \pgftransformreset% + \pgftransformarrow{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgfsys@beginscope% + \pgflowlevelsynccm% + \pgfsys@marker@use{\pgfsysanim@snap@tip@start}% + \pgfsys@endscope% + }% + \fi% +} + + +\def\pgfsysanim@prepare@end@of@path{% + \let\pgfprocessresultpathsuffix\relax% + \let\pgfprocessresultsubpathsuffix\relax% + \pgf@precise@shorteningfalse% + \edef\pgf@path@shortening@distance{0pt}% + \ifx\pgfsysanim@snap@tip@end\pgfutil@empty\else + \pgfprocesssplitpath{\pgfsysanim@path@val}% + \pgfprocesssplitsubpath{\pgfprocessresultpathsuffix}% + \expandafter\pgf@parse@end\pgfprocessresultsubpathsuffix\pgf@stop\pgf@stop\pgf@stop% + \pgf@prep@end% + \fi% +} +\def\pgfsysanim@add@marker@at@end{% + \ifx\pgfsysanim@snap@tip@end\pgfutil@empty\else + {% + \pgftransformreset% + \pgftransformarrow{\pgfqpoint{\pgf@xc}{\pgf@yc}}{\pgfqpoint{\pgf@xb}{\pgf@yb}}% + \pgfsys@beginscope% + \pgflowlevelsynccm% + \pgfsys@marker@use{\pgfsysanim@snap@tip@end}% + \pgfsys@endscope% + }% + \fi% +} + + + + + +\def\pgfsysanim@comp@scalar{% + \pgfsysanim@compute@fractions% + \pgfsysanim@mix@scalar% + \ifpgfsysanim@accumulate% + \ifnum\pgfsysanim@repeat@decimal=0\else% + \let\pgfsysanim@frac@b\pgfsysanim@one% + \let\pgfsysanim@prev@val\pgfsysanim@x@val% + \let\pgfsysanim@frac@a\pgfsysanim@repeat@decimal% + \let\pgfsysanim@next@val\pgfsysanim@last@val% + \pgfsysanim@mix@scalar% + \fi% + \fi% +} +\def\pgfsysanim@one{1} + +\def\pgfsysanim@mix@scalar{% + \pgf@x\pgfsysanim@prev@val pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y\pgfsysanim@next@val pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% +} +\def\pgfsysanim@cap@scalar#1#2#3{% + \ifdim#1 pt<#2 pt% + \def#1{#2}% + \else\ifdim#1 pt>#3 pt% + \def#1{#3}% + \fi\fi% +} + + + +\def\pgfsysanim@comp@scale{% + \pgfsysanim@compute@fractions% + \expandafter\expandafter\expandafter\pgfsysanim@mix@scale\expandafter\pgfsysanim@prev@val\pgfsysanim@next@val% + \ifpgfsysanim@accumulate% + \ifnum\pgfsysanim@repeat@decimal=0\else% + \let\pgfsysanim@frac@b\pgfsysanim@one% + \let\pgfsysanim@frac@a\pgfsysanim@repeat@decimal% + \expandafter\pgfsysanim@mix@scale\expandafter\pgfsysanim@x@val\expandafter\pgfsysanim@y@val\pgfsysanim@last@val% + \fi% + \fi% +} +\def\pgfsysanim@mix@scale#1#2#3#4{% + \pgf@x#1pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#3pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% + \pgf@x#2pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#4pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@y@val{\pgf@sys@tonumber\pgf@x}% +} + + + +\def\pgfsysanim@comp@dimension{% + \pgfsysanim@compute@fractions% + \pgfsysanim@mix@dimension% + \ifpgfsysanim@accumulate% + \ifnum\pgfsysanim@repeat@decimal=0\else% + \let\pgfsysanim@frac@b\pgfsysanim@one% + \def\pgfsysanim@prev@val{\pgfsysanim@x@val pt}% + \let\pgfsysanim@frac@a\pgfsysanim@repeat@decimal% + \let\pgfsysanim@next@val\pgfsysanim@last@val% + \pgfsysanim@mix@dimension% + \fi% + \fi% +} +\def\pgfsysanim@mix@dimension{% + \pgf@x\pgfsysanim@prev@val% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y\pgfsysanim@next@val% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% +} + + + + +\def\pgfsysanim@comp@translate{% + \pgfsysanim@compute@fractions% + \expandafter\expandafter\expandafter\pgfsysanim@mix@translate\expandafter\pgfsysanim@prev@val\pgfsysanim@next@val% + \ifpgfsysanim@accumulate% + \ifnum\pgfsysanim@repeat@decimal=0\else% + \let\pgfsysanim@frac@b\pgfsysanim@one% + \let\pgfsysanim@frac@a\pgfsysanim@repeat@decimal% + \edef\pgfsysanim@prev@val{{\pgfsysanim@x@val pt}{\pgfsysanim@y@val pt}} + \expandafter\expandafter\expandafter\pgfsysanim@mix@translate\expandafter\pgfsysanim@prev@val\pgfsysanim@last@val% + \fi% + \fi% +} +\def\pgfsysanim@mix@translate#1#2#3#4{% + \pgf@x#1% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#3% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% + \pgf@x#2% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#4% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@y@val{\pgf@sys@tonumber\pgf@x}% +} + + + + +\def\pgfsysanim@comp@color{% + \pgfsysanim@compute@fractions% + \expandafter\expandafter\expandafter\pgfsysanim@mix@color\expandafter\pgfsysanim@prev@val\pgfsysanim@next@val% + \ifpgfsysanim@accumulate% + \ifnum\pgfsysanim@repeat@decimal=0\else% + \let\pgfsysanim@frac@b\pgfsysanim@one% + \let\pgfsysanim@frac@a\pgfsysanim@repeat@decimal% + \expandafter\pgfsysanim@mix@color\expandafter\pgfsysanim@x@val\expandafter\pgfsysanim@y@val\expandafter\pgfsysanim@z@val\pgfsysanim@last@val% + \fi% + \fi% +} +\def\pgfsysanim@mix@color#1#2#3#4#5#6{% + \pgf@x#1pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#4pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% + \pgf@x#2pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#5pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@y@val{\pgf@sys@tonumber\pgf@x}% + \pgf@x#3pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#6pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@z@val{\pgf@sys@tonumber\pgf@x}% +} + + + +\def\pgfsysanim@comp@text{% + \let\pgfsysanim@text@val\pgfsysanim@prev@val% +} + + + + +\def\pgfsysanim@comp@dash{% + \pgfsysanim@compute@fractions% + \expandafter\expandafter\expandafter\pgfsysanim@mix@dash\expandafter\pgfsysanim@prev@val\pgfsysanim@next@val% + \ifpgfsysanim@accumulate% + \ifnum\pgfsysanim@repeat@decimal=0\else% + \let\pgfsysanim@frac@b\pgfsysanim@one% + \let\pgfsysanim@frac@a\pgfsysanim@repeat@decimal% + \edef\pgfsysanim@prev@val{{\pgfsysanim@dash@vals}{\pgfsysanim@x@val pt}}% + \expandafter\expandafter\expandafter\pgfsysanim@mix@dash\expandafter\pgfsysanim@prev@val\pgfsysanim@last@val% + \fi% + \fi% +} +\def\pgfsysanim@mix@dash#1#2#3#4{% + \pgf@x#2\relax% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#4\relax% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% + \let\pgfsysanim@dash@vals\pgfutil@empty% + \pgfsysanim@parse@dash#1,\pgf@stop#3,\pgf@stop% +} +\def\pgfsysanim@parse@dash{\pgfutil@ifnextchar\pgf@stop\pgfsysanim@parse@dash@done\pgfsysanim@parse@dash@first} +\def\pgfsysanim@parse@dash@done\pgf@stop\pgf@stop{}% +\def\pgfsysanim@parse@dash@first#1,#2\pgf@stop#3\pgf@stop{% + \pgf@x#1\relax% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgfsysanim@parse@dash@second#3\pgf@stop{#2}% +} +\def\pgfsysanim@parse@dash@second#1,#2\pgf@stop#3{% + \pgf@y#1\relax% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \def\pgfsys@temp{#2}% + \edef\pgfsysanim@dash@vals{\pgfsysanim@dash@vals\the\pgf@x\ifx\pgfsys@temp\pgfutil@empty\else,\fi}% + \pgfsysanim@parse@dash#3\pgf@stop#2\pgf@stop% +} + + + + + +\def\pgfsysanim@comp@viewbox{% + \pgfsysanim@compute@fractions% + \expandafter\expandafter\expandafter\pgfsysanim@mix@viewbox\expandafter\pgfsysanim@prev@val\pgfsysanim@next@val% + \ifpgfsysanim@accumulate% + \pgferror{viewbox animations cannot accumulate / add}% + \fi% +} +\def\pgfsysanim@mix@viewbox#1#2#3#4#5#6#7#8{% + \pgf@x#1% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#5% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\the\pgf@x}% + \pgf@x#2% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#6% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@y@val{\the\pgf@x}% + \pgf@x#3% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#7% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@z@val{\the\pgf@x}% + \pgf@x#4% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#8% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@w@val{\the\pgf@x}% +} + + + + + +\def\pgfsysanim@comp@path{% + \pgfsysanim@compute@fractions% + \edef\pgfsysanim@path@tips{% + \def\noexpand\pgfsysanim@snap@tip@start{\pgfsysanim@snap@tip@start}% + \def\noexpand\pgfsysanim@snap@tip@end{\pgfsysanim@snap@tip@end}% + }% + \let\pgfsysanim@path@val\pgfutil@empty% + \expandafter\expandafter\expandafter\pgfsysanim@parse@path\expandafter\pgfsysanim@prev@val\expandafter\pgf@stop\expandafter\relax\pgfsysanim@next@val\pgf@stop\relax% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfsysanim@path@all\expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfsysanim@path@val\expandafter\expandafter\expandafter{\expandafter\pgfsysanim@path@val\expandafter}\pgfsysanim@path@tips}% + \ifpgfsysanim@accumulate% + \pgferror{path animations cannot accumulate / add}% + \fi% +} +\def\pgfsysanim@parse@path{\pgfutil@ifnextchar\pgf@stop\pgfsysanim@parse@path@done\pgfsysanim@parse@path@first} +\def\pgfsysanim@parse@path@done\pgf@stop\relax\pgf@stop\relax{}% +\def\pgfsysanim@parse@path@first{\pgfutil@ifnextchar\bgroup\pgfsysanim@parse@path@first@num\pgfsysanim@parse@path@token} +\def\pgfsysanim@parse@path@token#1#2\relax#3#4\relax{% + \expandafter\def\expandafter\pgfsysanim@path@val\expandafter{\pgfsysanim@path@val#1}% + \pgfsysanim@parse@path#2\relax#4\relax% +} +\def\pgfsysanim@parse@path@first@num#1#2\relax#3#4\relax{% + \pgf@x#1% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y#3% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\pgfsysanim@path@val\expandafter\expandafter\expandafter{\expandafter\pgfsysanim@path@val\expandafter{\the\pgf@x}}% + \pgfsysanim@parse@path#2\relax#4\relax% +} + + + + +\def\pgfsysanim@comp@motion{% + \pgfsysanim@compute@fractions% + \pgf@x\pgfsysanim@prev@val pt% + \pgf@x\pgfsysanim@frac@b\pgf@x% + \pgf@y\pgfsysanim@next@val pt% + \advance\pgf@x by\pgfsysanim@frac@a\pgf@y% + \edef\pgfsysanim@x@val{\pgf@sys@tonumber\pgf@x}% + \ifdim\pgfsysanim@x@val pt=1pt% + \def\pgfsysanim@x@val{0.9999}% + \fi% + \pgf@relevantforpicturesizefalse% + \pgfdecoratepath{pgfsysanim@motion}{% + \pgfsyssoftpath@setcurrentpath\pgfsysanim@snap@movealong% + }% + \ifpgfsysanim@accumulate% + \pgferror{motion animations cannot accumulate / add}% + \fi% +} +\pgfdeclaredecoration{pgfsysanim@motion}{s}{% + \state{s}[width=\pgfsysanim@x@val\pgfdecoratedremainingdistance,next state=final]{}% + \state{final}{\pgfgettransform\pgfsysanim@motion@trans\global\let\pgfsysanim@motion@trans\pgfsysanim@motion@trans}% +} + + + + + + + +\def\pgfsysanim@compute@fractions{% + \ifdim\pgf@xc=\pgfsysanim@prev@time pt% + \def\pgfsysanim@frac@a{0}% + \def\pgfsysanim@frac@b{1}% + \else% + \pgfmathsubtract@{\pgfsysanim@next@time}{\pgfsysanim@prev@time}% + \ifdim\pgfmathresult pt<0.01pt% + \def\pgfsysanim@frac@a{0}% + \def\pgfsysanim@frac@b{1}% + \else% + \let\pgfsysanim@divby\pgfmathresult% + \pgfmathsubtract@{\pgf@sys@tonumber\pgf@xc}{\pgfsysanim@prev@time}% + \pgfmathdivide@{\pgfmathresult}{\pgfsysanim@divby}% + \ifdim\pgfmathresult pt<0pt\def\pgfmathresult{0}\fi% + \ifdim\pgfmathresult pt>1pt\def\pgfmathresult{1}\fi% + \let\pgfsysanim@frac@a\pgfmathresult% + \pgfmathsubtract@{1}{\pgfmathresult}% + \let\pgfsysanim@frac@b\pgfmathresult% + \fi% + \fi% + \ifdim\pgfsysanim@frac@a pt=0pt% + \else\ifdim\pgfsysanim@frac@b pt=0pt% + \else% + \expandafter\expandafter\expandafter\pgfsysanim@apply@spline\expandafter\pgfsysanim@prev@spline\pgfsysanim@next@spline% + \fi\fi% +} + + +\def\pgfsysanim@apply@spline#1#2#3#4#5#6#7#8{% + \edef\pgfsys@temp{#3,#5,#4,#6}% + \ifx\pgfsys@temp\pgfsysanim@id@spline% + \else% + \def\pgfsysanim@prev@out@time{{#3}{#4}}% + \def\pgfsysanim@next@in@time{{#5}{#6}}% + \ifx\pgfsysanim@prev@out@time\pgfsys@stay@text% + \pgfsysanim@jump@splines% + \else\ifx\pgfsysanim@next@in@time\pgfsys@jump@text% + \pgfsysanim@jump@splines% + \else% + \pgf@xa#3pt% + \pgf@xb#5pt% + \let\pgfsysanim@t\pgfsysanim@frac@a% + \let\pgfsysanim@s\pgfsysanim@frac@b% + \pgfsysanim@eval@spline% + \edef\pgfsysanim@ft{\the\pgf@x}% + \pgf@x\pgfsysanim@t pt% + \advance\pgf@x by256sp% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@t{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@s{\pgf@sys@tonumber\pgf@y}% + \pgfsysanim@eval@spline% + \advance\pgf@x by-\pgfsysanim@ft% + \pgf@x256\pgf@x% + \pgf@ya\pgfsysanim@ft% + \advance\pgf@ya by-\pgfsysanim@frac@a pt% + \pgf@yb\pgf@x + \pgfmathreciprocal@{\pgf@sys@tonumber\pgf@yb}% + \ifdim\pgfmathresult pt>2.5pt% + \def\pgfmathresult{2.5}% + \fi% + \ifdim\pgfmathresult pt<-2.5pt% + \def\pgfmathresult{-2.5}% + \fi% + \pgf@x\pgfsysanim@t pt% + \advance\pgf@x by-\pgfmathresult\pgf@ya% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@t{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@s{\pgf@sys@tonumber\pgf@y}% + \pgfsysanim@eval@spline% + \edef\pgfsysanim@ft{\the\pgf@x}% + \pgf@x\pgfsysanim@t pt% + \advance\pgf@x by256sp% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@t{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@s{\pgf@sys@tonumber\pgf@y}% + \pgfsysanim@eval@spline% + \advance\pgf@x by-\pgfsysanim@ft% + \pgf@x256\pgf@x% + \pgf@ya\pgfsysanim@ft% + \advance\pgf@ya by-\pgfsysanim@frac@a pt% + \pgf@yb\pgf@x + \pgfmathreciprocal@{\pgf@sys@tonumber\pgf@yb}% + \ifdim\pgfmathresult pt>2.5pt% + \def\pgfmathresult{2.5}% + \fi% + \ifdim\pgfmathresult pt<-2.5pt% + \def\pgfmathresult{-2.5}% + \fi% + \pgf@x\pgfsysanim@t pt% + \advance\pgf@x by-\pgfmathresult\pgf@ya% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@t{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@s{\pgf@sys@tonumber\pgf@y}% + \pgfsysanim@eval@spline% + \edef\pgfsysanim@ft{\the\pgf@x}% + \pgf@x\pgfsysanim@t pt% + \advance\pgf@x by256sp% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@t{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@s{\pgf@sys@tonumber\pgf@y}% + \pgfsysanim@eval@spline% + \advance\pgf@x by-\pgfsysanim@ft% + \pgf@x256\pgf@x% + \pgf@ya\pgfsysanim@ft% + \advance\pgf@ya by-\pgfsysanim@frac@a pt% + \pgf@yb\pgf@x + \pgfmathreciprocal@{\pgf@sys@tonumber\pgf@yb}% + \ifdim\pgfmathresult pt>2.5pt% + \def\pgfmathresult{2.5}% + \fi% + \ifdim\pgfmathresult pt<-2.5pt% + \def\pgfmathresult{-2.5}% + \fi% + \pgf@x\pgfsysanim@t pt% + \advance\pgf@x by-\pgfmathresult\pgf@ya% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@t{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@s{\pgf@sys@tonumber\pgf@y}% + \pgf@xa#4pt% + \pgf@xb#6pt% + \pgfsysanim@eval@spline% + \pgf@y1pt% + \advance\pgf@y by-\pgf@x% + \edef\pgfsysanim@frac@a{\pgf@sys@tonumber\pgf@x}% + \edef\pgfsysanim@frac@b{\pgf@sys@tonumber\pgf@y}% + \fi\fi% + \fi% +} +\def\pgfsysanim@id@spline{0,1,0,1} + +\def\pgfsysanim@eval@spline{% + \pgf@ya\pgfsysanim@t\pgf@xa% + \pgf@yb\pgfsysanim@t\pgf@xb% + \advance\pgf@yb by\pgfsysanim@s\pgf@xa% + \pgf@yc\pgfsysanim@t pt% + \advance\pgf@yc by\pgfsysanim@s\pgf@xb% + \pgf@y\pgfsysanim@t\pgf@yb% + \advance\pgf@y by\pgfsysanim@s\pgf@ya% + \pgf@xc\pgfsysanim@t\pgf@yc% + \advance\pgf@xc by\pgfsysanim@s\pgf@yb% + \pgf@x\pgfsysanim@t\pgf@xc% + \advance\pgf@x by\pgfsysanim@s\pgf@y% +} + +\def\pgfsysanim@jump@splines{% + \ifx\pgfsysanim@prev@out@time\pgfsys@stay@text% + \ifx\pgfsysanim@next@in@time\pgfsys@jump@text% + \ifdim\pgfsysanim@frac@a pt<0.5pt% + \def\pgfsysanim@frac@a{0}% + \def\pgfsysanim@frac@b{1}% + \else% + \def\pgfsysanim@frac@a{1}% + \def\pgfsysanim@frac@b{0}% + \fi% + \else% + \def\pgfsysanim@frac@a{0}% + \def\pgfsysanim@frac@b{1}% + \fi% + \else + \def\pgfsysanim@frac@a{1}% + \def\pgfsysanim@frac@b{0}% + \fi% +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..0bd2f66f377fe54fdbe02002c7d38f34cae78bf4 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsysprotocol.code.tex @@ -0,0 +1,48 @@ + +\ProvidesFileRCS{pgfsysprotocol.code.tex} + + + + + + +\let\pgfsysprotocol@currentprotocol=\pgfutil@empty +\newif\ifpgfsysprotocol@buffered + + +\def\pgfsysprotocol@literalbuffered#1{% + \edef\pgfsysprotocol@temp{{#1\space}}% + \expandafter\pgfutil@g@addto@macro\expandafter\pgfsysprotocol@currentprotocol\pgfsysprotocol@temp% +} + +\def\pgfsysprotocol@literal#1{% + \pgfsysprotocol@literalbuffered{#1}% + \ifpgfsysprotocol@buffered% + \else% + \pgfsysprotocol@flushcurrentprotocol% + \fi% +} + +\def\pgfsysprotocol@getcurrentprotocol#1{% + \let#1=\pgfsysprotocol@currentprotocol% +} + +\def\pgfsysprotocol@setcurrentprotocol#1{% + \global\let\pgfsysprotocol@currentprotocol=#1% +} + + +\def\pgfsysprotocol@invokecurrentprotocol{% + \ifx\pgfsysprotocol@currentprotocol\pgfutil@empty% + \else% + \expandafter\pgfsys@invoke\expandafter{\pgfsysprotocol@currentprotocol}% + \fi% +} + +\def\pgfsysprotocol@flushcurrentprotocol{% + \pgfsysprotocol@invokecurrentprotocol% + \pgfsysprotocol@setcurrentprotocol\pgfutil@empty% +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..8fadadb709e253162747d9b83c04a3380c7beb2d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/systemlayer/pgfsyssoftpath.code.tex @@ -0,0 +1,141 @@ + +\ProvidesFileRCS{pgfsyssoftpath.code.tex} + + + + + + + +\let\pgfsyssoftpath@thepath=\pgfutil@empty +\let\pgfsyssoftpath@bigbuffer=\pgfutil@empty +\let\pgfsyssoftpath@smallbuffer=\pgfutil@empty +\newcount\pgfsyssoftpath@smallbuffer@items +\newcount\pgfsyssoftpath@bigbuffer@items + +\def\pgfsyssoftpath@flushbuffers{% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\pgfsyssoftpath@thepath% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{% + \expandafter\expandafter\expandafter\pgfsyssoftpath@thepath% + \expandafter\pgfsyssoftpath@bigbuffer\pgfsyssoftpath@smallbuffer}% + \global\let\pgfsyssoftpath@smallbuffer=\pgfutil@empty + \global\let\pgfsyssoftpath@bigbuffer=\pgfutil@empty + \global\pgfsyssoftpath@bigbuffer@items0\relax% + \global\pgfsyssoftpath@smallbuffer@items0\relax% +} + +\def\pgfsyssoftpath@getcurrentpath#1{% + \pgfsyssoftpath@flushbuffers% + \let#1=\pgfsyssoftpath@thepath% +} + +\def\pgfsyssoftpath@setcurrentpath#1{% + \global\let\pgfsyssoftpath@thepath=#1% + \global\let\pgfsyssoftpath@smallbuffer=\pgfutil@empty + \global\let\pgfsyssoftpath@bigbuffer=\pgfutil@empty + \global\pgfsyssoftpath@bigbuffer@items0\relax% + \global\pgfsyssoftpath@smallbuffer@items0\relax% +} + + +\def\pgfsyssoftpath@invokecurrentpath{% + \pgfsyssoftpath@thepath% + \pgfsyssoftpath@bigbuffer% + \pgfsyssoftpath@smallbuffer% +} + +\def\pgfsyssoftpath@flushcurrentpath{% + \pgfsyssoftpath@invokecurrentpath% + \pgfsyssoftpath@setcurrentpath\pgfutil@empty% +} + +\def\pgfsyssoftpath@addtocurrentpath#1{% + \global\advance\pgfsyssoftpath@smallbuffer@items by1\relax% + \ifnum\pgfsyssoftpath@smallbuffer@items<40\relax% + \expandafter\gdef\expandafter\pgfsyssoftpath@smallbuffer\expandafter{\pgfsyssoftpath@smallbuffer#1}% + \else% + \pgfsyssoftpath@smalloverflow{#1}% + \fi% +} +\def\pgfsyssoftpath@smalloverflow#1{% + \global\advance\pgfsyssoftpath@bigbuffer@items by1\relax% + \ifnum\pgfsyssoftpath@bigbuffer@items<30\relax% + \expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\pgfsyssoftpath@bigbuffer% + \expandafter\expandafter\expandafter{\expandafter\pgfsyssoftpath@bigbuffer\pgfsyssoftpath@smallbuffer#1}% + \global\let\pgfsyssoftpath@smallbuffer=\pgfutil@empty% + \global\pgfsyssoftpath@smallbuffer@items0\relax% + \else% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\pgfsyssoftpath@thepath% + \expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter{% + \expandafter\expandafter\expandafter\pgfsyssoftpath@thepath + \expandafter\pgfsyssoftpath@bigbuffer\pgfsyssoftpath@smallbuffer#1}% + \global\let\pgfsyssoftpath@smallbuffer=\pgfutil@empty + \global\let\pgfsyssoftpath@bigbuffer=\pgfutil@empty + \global\pgfsyssoftpath@bigbuffer@items0\relax% + \global\pgfsyssoftpath@smallbuffer@items0\relax% + \fi% +} + + + +\def\pgfsyssoftpath@lastmoveto{{0pt}{0pt}} + +\newif\ifpgfsyssoftpathmovetorelevant +\pgfsyssoftpathmovetorelevanttrue + +\def\pgfsyssoftpath@moveto#1#2{% + \edef\pgfsyssoftpath@coord{{#1}{#2}}% + \expandafter\pgfsyssoftpath@addtocurrentpath\expandafter{\expandafter\pgfsyssoftpath@movetotoken\pgfsyssoftpath@coord}% + \ifpgfsyssoftpathmovetorelevant% + \global\let\pgfsyssoftpath@lastmoveto\pgfsyssoftpath@coord% + \fi% +} + +\def\pgfsyssoftpath@lineto#1#2{% + \edef\pgfsyssoftpath@coord{{#1}{#2}}% + \expandafter\pgfsyssoftpath@addtocurrentpath\expandafter{\expandafter\pgfsyssoftpath@linetotoken\pgfsyssoftpath@coord}% +} + + +\def\pgfsyssoftpath@curveto#1#2#3#4#5#6{% + \edef\pgfsyssoftpath@temp{{% + \noexpand\pgfsyssoftpath@curvetosupportatoken{#1}{#2}% + \noexpand\pgfsyssoftpath@curvetosupportbtoken{#3}{#4}% + \noexpand\pgfsyssoftpath@curvetotoken{#5}{#6}% + }}% + \expandafter\pgfsyssoftpath@addtocurrentpath\pgfsyssoftpath@temp% +} + + +\def\pgfsyssoftpath@rect#1#2#3#4{% + \edef\pgfsyssoftpath@temp{{% + \noexpand\pgfsyssoftpath@rectcornertoken{#1}{#2}% + \noexpand\pgfsyssoftpath@rectsizetoken{#3}{#4}% + }}% + \expandafter\pgfsyssoftpath@addtocurrentpath\pgfsyssoftpath@temp% +} + +\def\pgfsyssoftpath@closepath{% + \expandafter\pgfsyssoftpath@addtocurrentpath\expandafter{\expandafter\pgfsyssoftpath@closepathtoken\pgfsyssoftpath@lastmoveto}% +} + +\def\pgfsyssoftpath@specialround#1#2{% + \edef\pgfsyssoftpath@temp{{#1}{#2}}% + \expandafter\pgfsyssoftpath@addtocurrentpath\expandafter{\expandafter\pgfsyssoftpath@specialroundtoken\pgfsyssoftpath@temp}% +} + +\def\pgfsyssoftpath@movetotoken#1#2{\pgfsys@moveto{#1}{#2}} +\def\pgfsyssoftpath@linetotoken#1#2{\pgfsys@lineto{#1}{#2}} +\def\pgfsyssoftpath@rectcornertoken#1#2#3#4#5{\pgfsys@rect{#1}{#2}{#4}{#5}} % +\def\pgfsyssoftpath@curvetosupportatoken#1#2#3#4#5#6#7#8{\pgfsys@curveto{#1}{#2}{#4}{#5}{#7}{#8}} +\def\pgfsyssoftpath@closepathtoken#1#2{\pgfsys@closepath} +\let\pgfsyssoftpath@specialroundtoken=\pgfutil@gobbletwo +\def\pgfsyssoftpath@curvetosupportbtoken#1#2{curvetotokenb} % +\def\pgfsyssoftpath@curvetotoken#1#2{curvetotoken}% + + +\endinput + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfcalendar.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfcalendar.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..bb5d1fe6e252dd93fecd96cf1f7eed41cc4b1eb8 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfcalendar.code.tex @@ -0,0 +1,462 @@ + +\ProvidesFileRCS{pgfcalendar.code.tex} + +\ifdefined\pgfintloaded\else + \input pgfint.code.tex +\fi + + +\ifx\translate\@undefined + \def\translate#1{#1} +\fi + + +\ifx\usedictionary\@undefined +\else + \usedictionary{translator-months-dictionary} +\fi + + + + + +\long\def\pgfcalendar#1#2#3#4{% + \begingroup% + \let\ifdate=\pgfcalendar@local@ifdate% + \def\pgfcalendarprefix{#1}% + \pgfcalendardatetojulian{#2}{\pgfcalendarcurrentjulian}% + \edef\pgfcalendarbeginjulian{\the\pgfcalendarcurrentjulian}% + \edef\pgfcalendarbeginiso{#2}% + \pgfcalendardatetojulian{#3}{\pgfutil@tempcnta}% + \edef\pgfcalendarendjulian{\the\pgfutil@tempcnta}% + \advance\pgfutil@tempcnta by1\relax% + \edef\pgfcalendarendjulianplus{\the\pgfutil@tempcnta}% + \edef\pgfcalendarendiso{#3}% + \loop% + \ifnum\pgfcalendarcurrentjulian<\pgfcalendarendjulianplus\relax% + \pgfcalendarjuliantodate{\pgfcalendarcurrentjulian}% + {\pgfcalendarcurrentyear}{\pgfcalendarcurrentmonth}{\pgfcalendarcurrentday}% + \pgfcalendarjuliantoweekday{\pgfcalendarcurrentjulian}{\pgfutil@tempcntb}% + \edef\pgfcalendarcurrentweekday{\the\pgfutil@tempcntb}% + #4% + \advance\pgfcalendarcurrentjulian by1\relax% + \repeat% + \endgroup% +} + +\newcount\pgfcalendarcurrentjulian + +\def\pgfcalendar@local@ifdate{% + \let\pgfcalendarifdatejulian=\pgfcalendarcurrentjulian% + \let\pgfcalendarifdateyear=\pgfcalendarcurrentyear% + \let\pgfcalendarifdatemonth=\pgfcalendarcurrentmonth% + \let\pgfcalendarifdateday=\pgfcalendarcurrentday% + \let\pgfcalendarifdateweekday=\pgfcalendarcurrentweekday% + \pgfcalendar@launch@ifdate% +} + + + + +\def\pgfcalendarifdate#1#2#3#4{% + \pgfcalendardatetojulian{#1}{\pgfutil@tempcnta}% + \pgfcalendarjuliantodate{\pgfutil@tempcnta} + {\pgfcalendarifdateyear}{\pgfcalendarifdatemonth}{\pgfcalendarifdateday}% + \edef\pgfcalendarifdatejulian{\the\pgfutil@tempcnta}% + \pgfcalendarjuliantoweekday{\pgfutil@tempcnta}{\pgfutil@tempcntb}% + \edef\pgfcalendarifdateweekday{\the\pgfutil@tempcntb}% + \pgfcalendar@launch@ifdate{#2}{#3}{#4}% +} + + +\long\def\pgfcalendar@launch@ifdate#1{% + \pgfcalendarmatchesfalse% + \pgfqkeys{/pgf/calendar}{#1}% + \ifpgfcalendarmatches% + \expandafter\pgfutil@firstoftwo + \else% + \expandafter\pgfutil@secondoftwo + \fi% +} + +\newif\ifpgfcalendarmatches + + + +\pgfkeys{/pgf/calendar/all/.code=\pgfcalendarmatchestrue} + +\pgfkeys{/pgf/calendar/Monday/.code={\ifnum\pgfcalendarifdateweekday=0\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/Tuesday/.code={\ifnum\pgfcalendarifdateweekday=1\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/Wednesday/.code={\ifnum\pgfcalendarifdateweekday=2\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/Thursday/.code={\ifnum\pgfcalendarifdateweekday=3\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/Friday/.code={\ifnum\pgfcalendarifdateweekday=4\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/Saturday/.code={\ifnum\pgfcalendarifdateweekday=5\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/Sunday/.code={\ifnum\pgfcalendarifdateweekday=6\relax\pgfcalendarmatchestrue\fi}} + +\pgfkeys{/pgf/calendar/workday/.code={\ifnum\pgfcalendarifdateweekday<5\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/weekend/.code={\ifnum\pgfcalendarifdateweekday>4\relax\pgfcalendarmatchestrue\fi}} + +\pgfkeys{/pgf/calendar/equals/.cd,.value required,.code={% + \pgfcalendar@special@datetojulian{#1}% + \ifnum\pgfcalendarifdatejulian=\pgfutil@tempcnta\relax% + \pgfcalendarmatchestrue% + \fi}% +} + +\pgfkeys{/pgf/calendar/day of month/.cd,.value required,.code={\ifnum#1=\pgfcalendarifdateday\relax\pgfcalendarmatchestrue\fi}} +\pgfkeys{/pgf/calendar/end of month/.cd,.default=1,.code={% + \ifpgfcalendarmatches% + \else% + {% + \pgfutil@tempcnta=\pgfcalendarifdatejulian\relax% + \advance\pgfutil@tempcnta by#1\relax% + \pgfcalendarjuliantodate{\pgfutil@tempcnta}{\pgf@dummy}{\pgf@dummy}{\pgf@cal@temp}% + \global\let\pgf@cal@temp=\pgf@cal@temp% + }% + \ifnum\pgf@cal@temp=1\relax\pgfcalendarmatchestrue\fi% + \fi}% +} + +\pgfkeys{/pgf/calendar/at least/.cd,.value required,.code={% + \pgfcalendar@special@datetojulian{#1}% + \ifnum\pgfcalendarifdatejulian<\pgfutil@tempcnta\relax% + \else% + \pgfcalendarmatchestrue% + \fi% +}} + +\pgfkeys{/pgf/calendar/at most/.cd,.value required,.code={% + \pgfcalendar@special@datetojulian{#1}% + \ifnum\pgfcalendarifdatejulian>\pgfutil@tempcnta\relax% + \else% + \pgfcalendarmatchestrue% + \fi% +}} + +\pgfkeys{/pgf/calendar/between/.cd,.value required,.code args={#1and#2}{% + \pgfcalendar@special@datetojulian{#1}% + \ifnum\pgfcalendarifdatejulian<\pgfutil@tempcnta\relax% + \else% + \pgfcalendar@special@datetojulian{#2}% + \ifnum\pgfcalendarifdatejulian>\pgfutil@tempcnta\relax% + \else% + \pgfcalendarmatchestrue% + \fi% + \fi% +}} + +\def\pgfcalendar@special@datetojulian#1{% + \edef\pgf@temp{#1}% + \expandafter\pgfcalendar@special@split@test\pgf@temp-\relax{#1}% +} + +\def\pgfcalendar@special@split@test#1-#2-#3\relax#4{% + \def\pgf@temp{#3}% + \ifx\pgf@temp\pgfutil@empty% + \def\pgf@temp{\pgfcalendarifdateyear-#1-#2}% + \else% + \def\pgf@temp{#4}% + \fi% + \pgfcalendardatetojulian{\pgf@temp}{\pgfutil@tempcnta}% +} + + + +\def\pgfcalendarsuggestedname{% + \ifx\pgfcalendarprefix\pgfutil@empty\else\pgfcalendarprefix-% + \pgfcalendarcurrentyear-\pgfcalendarcurrentmonth-\pgfcalendarcurrentday\fi% +} + + + + + + + +\def\pgfcalendardatetojulian#1#2{\edef\pgf@temp{#1}\expandafter\pgfcalendar@datetojulian\pgf@temp+/{#2}} +\def\pgfcalendar@datetojulian#1-#2-#3+#4/#5{% + {% + \count1=#1\relax% + \count2=#2\relax% + \edef\pgf@temp{#3}% + \ifx\pgf@temp\pgfcalendar@last@text% + \advance\count2 by1\relax% + \count3=1\relax% + \else% + \count3=#3\relax% + \fi% + \edef\pgf@@temp{#4}% + \ifx\pgf@@temp\pgfutil@empty% + \count8=0\relax% + \else% + \pgfcalendar@unpack#4% + \fi% + \ifnum\count2<3\relax% + \count4=1\relax% + \else% + \count4=0\relax% + \fi% + \count5=\count1\relax% + \advance\count5 by 4800\relax% + \advance\count5 by-\count4\relax% + \count6=\count2\relax% + \count0=\count4\relax% + \multiply\count0 by12\relax + \advance\count6 by\count0\relax% + \advance\count6 by-3\relax% + \count7=\count3\relax% + \count0=\count6\relax% + \multiply\count0 by 153\relax% + \advance\count0 by 2\relax% + \divide\count0 by 5\relax% + \advance\count7 by \count0\relax% + \count0=\count5% + \multiply\count0by365\relax% + \advance\count7 by\count0\relax% + \count0=\count5\relax% + \divide\count0 by 4\relax% + \advance\count7 by\count0% + \count0=\count5\relax% + \divide\count0 by 100\relax% + \advance\count7 by-\count0\relax% + \count0=\count5\relax% + \divide\count0 by 400\relax% + \advance\count7 by\count0% + \advance\count7 by-32045\relax% + \ifx\pgf@temp\pgfcalendar@last@text% + \advance\count7by-1\relax% + \fi% + \advance\count7by\count8\relax% + \expandafter% + }% + \expandafter#5\the\count7\relax% +} +\def\pgfcalendar@last@text{last} +\def\pgfcalendar@unpack#1+{% + \count8=#1\relax% +} + + +\def\pgfcalendarjuliantodate#1#2#3#4{% + {% + \count1=#1\relax% + \count2=\count1\relax% + \advance\count2 by 32044\relax% + \count3=\count2\relax% + \divide\count3 by 146097\relax% + \count4=\count3\relax% + \multiply\count4 by-146097\relax% + \advance\count4 by\count2\relax% + \count5=\count4\relax% + \divide\count5 by36524\relax% + \advance\count5 by1\relax% + \multiply\count5 by3\relax% + \divide\count5 by4\relax% + \count6=\count4\relax% + \count0=\count5\relax% + \multiply\count0 by-36524\relax% + \advance\count6 by\count0\relax% + \count7=\count6\relax% + \divide\count7 by1461\relax% + \count8=\count7\relax% + \multiply\count8 by-1461\relax% + \advance\count8 by\count6\relax% + \count9=\count8\relax% + \divide\count9 by 365\relax% + \advance\count9 by 1\relax% + \multiply\count9 by3\relax% + \divide\count9 by4\relax% + \count10=\count8\relax% + \count0=\count9\relax% + \multiply\count0 by-365\relax% + \advance\count10 by\count0\relax% + \count11=\count3\relax% + \multiply\count11 by400\relax% + \count0=\count5\relax% + \multiply\count0 by100\relax% + \advance\count11 by\count0\relax% + \count0=\count7\relax% + \multiply\count0 by4\relax% + \advance\count11 by\count0\relax% + \advance\count11 by\count9\relax% + \count12=\count10\relax% + \multiply\count12 by5\relax% + \advance\count12 by 308\relax% + \divide\count12 by 153\relax% + \advance\count12 by -2\relax% + \count13=\count12\relax% + \advance\count13 by 4\relax% + \multiply\count13 by153\relax% + \divide\count13 by5\relax% + \count13=-\count13\relax% + \advance\count13 by 122\relax% + \advance\count13 by \count10\relax% + \count14=\count12\relax% + \advance\count14 by 2\relax% + \divide\count14 by12\relax% + \advance\count14 by\count11\relax% + \advance\count14 by-4800\relax% + \count15=\count12\relax% + \advance\count15 by2\relax% + \count0=\count15\relax% + \divide\count0 by12\relax% + \multiply\count0 by12\relax% + \advance\count15 by-\count0\relax% + \advance\count15 by1\relax% + \count16=\count13% + \advance\count16by 1\relax% + \xdef\pgf@temp@year{\the\count14}% + \xdef\pgf@temp@month{\ifnum\count15<10 0\fi\the\count15}% + \xdef\pgf@temp@day{\ifnum\count16<10 0\fi\the\count16}% + }% + \let#2=\pgf@temp@year% + \let#3=\pgf@temp@month% + \let#4=\pgf@temp@day% +} + + + + +\def\pgfcalendarjuliantoweekday#1#2{% + {% + \pgfutil@tempcnta=#1\relax% + #2=\pgfutil@tempcnta% + \divide#2by7\relax% + \multiply#2by-7\relax% + \advance#2by\pgfutil@tempcnta\relax% + \expandafter% + }% + \expandafter#2\the#2\relax% +} + + + + +\def\pgfcalendarweekdayname#1{% + \pgfutil@translate{\ifcase#1Monday\or Tuesday\or Wednesday\or Thursday\or Friday\or Saturday\or Sunday\fi}% +} + +\def\pgfcalendarweekdayshortname#1{% + \pgfutil@translate{\ifcase#1Mon\or Tue\or Wed\or Thu\or Fri\or Sat\or Sun\fi}% +} + + + +\def\pgfcalendarmonthname#1{% + \pgfutil@translate{\ifcase#1\or January\or February\or March\or April\or + May\or June\or July\or August\or September\or October\or + November\or December\fi}% +} + +\def\pgfcalendarmonthshortname#1{% + \pgfutil@translate{\ifcase#1\or Jan\or Feb\or Mar\or Apr\or + May\or Jun\or Jul\or Aug\or Sep\or Oct\or + Nov\or Dec\fi}% +} + + + + + + + +\def\pgfcalendarshorthand#1#2{\csname pgfcalendar@shorthand@#1#2\endcsname} +\expandafter\def\csname pgfcalendar@shorthand@d-\endcsname{% + {\pgfutil@tempcnta=\pgfcalendarcurrentday\relax\the\pgfutil@tempcnta}} +\expandafter\def\csname pgfcalendar@shorthand@d=\endcsname{% + {\pgfutil@tempcnta=\pgfcalendarcurrentday\relax\ifnum\pgfutil@tempcnta<10\relax\setbox0=\hbox{1}\kern\wd0\relax\fi\the\pgfutil@tempcnta}} +\expandafter\def\csname pgfcalendar@shorthand@d0\endcsname{% + \pgfcalendarcurrentday} +\expandafter\def\csname pgfcalendar@shorthand@m-\endcsname{% + {\pgfutil@tempcnta=\pgfcalendarcurrentmonth\relax\the\pgfutil@tempcnta}} +\expandafter\def\csname pgfcalendar@shorthand@m=\endcsname{% + {\pgfutil@tempcnta=\pgfcalendarcurrentmonth\relax\ifnum\pgfutil@tempcnta<10\relax\setbox0=\hbox{1}\kern\wd0\relax\fi\the\pgfutil@tempcnta}} +\expandafter\def\csname pgfcalendar@shorthand@m0\endcsname{% + \pgfcalendarcurrentmonth} +\expandafter\def\csname pgfcalendar@shorthand@y-\endcsname{% + \pgfcalendarcurrentyear} +\expandafter\def\csname pgfcalendar@shorthand@y=\endcsname{% + \pgfcalendarcurrentyear} +\expandafter\def\csname pgfcalendar@shorthand@y0\endcsname{% + \pgfcalendarcurrentyear} +\expandafter\def\csname pgfcalendar@shorthand@w.\endcsname{% + \pgfcalendarweekdayshortname{\pgfcalendarcurrentweekday}} +\expandafter\def\csname pgfcalendar@shorthand@wt\endcsname{% + \pgfcalendarweekdayname{\pgfcalendarcurrentweekday}} +\expandafter\def\csname pgfcalendar@shorthand@m.\endcsname{% + \pgfcalendarmonthshortname{\pgfcalendarcurrentmonth}} +\expandafter\def\csname pgfcalendar@shorthand@mt\endcsname{% + \pgfcalendarmonthname{\pgfcalendarcurrentmonth}} + + + +\newcount\pgf@cal@easter@Y +\newcount\pgf@cal@easter@G +\newcount\pgf@cal@easter@C +\newcount\pgf@cal@easter@X +\newcount\pgf@cal@easter@Z +\newcount\pgf@cal@easter@D +\newcount\pgf@cal@easter@E +\newcount\pgf@cal@easter@N +\newcount\pgf@cal@easter@M +\newcount\pgf@cal@easter@julianday + +\pgfutil@protected\def\pgfcalendareastersunday#1#2{% + \pgfintset\pgf@cal@easter@Y{#1}% + \pgfintset\pgf@cal@easter@G{% + \pgfintmod{\pgf@cal@easter@Y}{19}+1 + }% + \pgfintset\pgf@cal@easter@C{% + \pgfintdivfloor{\pgf@cal@easter@Y}{100}+1 + }% + \pgfintset\pgf@cal@easter@X{% + \pgfintdivfloor{3*\pgf@cal@easter@C}{4}-12 + }% + \pgfintset\pgf@cal@easter@Z{% + \pgfintdivfloor{8*\pgf@cal@easter@C+5}{25}-5 + }% + \pgfintset\pgf@cal@easter@D{% + \pgfintdivfloor{5*\pgf@cal@easter@Y}{4}-\pgf@cal@easter@X-10 + }% + \pgfintset\pgf@cal@easter@E{% + \pgfintmod{11*\pgf@cal@easter@G+20+\pgf@cal@easter@Z-\pgf@cal@easter@X}{30} + }% + \ifnum\pgf@cal@easter@E<0 + \pgfintset\pgf@cal@easter@E{\pgf@cal@easter@E+30}% + \fi + \ifnum\pgf@cal@easter@E=25 + \ifnum\pgf@cal@easter@G>11 + \pgfintset\pgf@cal@easter@E{\pgf@cal@easter@E+1}% + \fi + \else + \ifnum\pgf@cal@easter@E=24 + \pgfintset\pgf@cal@easter@E{\pgf@cal@easter@E+1}% + \fi + \fi + \pgfintset\pgf@cal@easter@N{44-\pgf@cal@easter@E}% + \ifnum\pgf@cal@easter@N<21 + \pgfintset\pgf@cal@easter@N{\pgf@cal@easter@N+30}% + \fi + \pgfintset\pgf@cal@easter@N{% + \pgf@cal@easter@N+7-\pgfintmod{\pgf@cal@easter@D+\pgf@cal@easter@N}{7} + }% + \ifnum\pgf@cal@easter@N>31 + \pgfintset\pgf@cal@easter@N{\pgf@cal@easter@N-31}% + \pgfintset\pgf@cal@easter@M{4}% + \else + \pgfintset\pgf@cal@easter@M{3}% + \fi + \pgfcalendardatetojulian + {\pgf@cal@easter@Y-\pgf@cal@easter@M-\pgf@cal@easter@N}% + {#2}% +} + +\pgfkeys{/pgf/calendar/Easter/.cd,.default=0,.code={% + \pgfcalendareastersunday{\pgfcalendarifdateyear}{\pgf@cal@easter@julianday}% + \ifnum\pgfcalendarifdatejulian=\pgfinteval{\pgf@cal@easter@julianday+#1} + \expandafter\pgfcalendarmatchestrue + \fi}% +} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfexternal.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfexternal.tex new file mode 100644 index 0000000000000000000000000000000000000000..c64db3be4c902efac44327dd9d6899c19e666c79 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfexternal.tex @@ -0,0 +1,3 @@ + + +\long\def\beginpgfgraphicnamed#1#2\endpgfgraphicnamed{\includegraphics{#1}} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfexternalwithdepth.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfexternalwithdepth.tex new file mode 100644 index 0000000000000000000000000000000000000000..d42d509dcbc2037693bd95865d1d708995ee335d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfexternalwithdepth.tex @@ -0,0 +1,14 @@ + + +\long\def\beginpgfgraphicnamed#1#2\endpgfgraphicnamed{% + \begingroup + \setbox1=\hbox{\includegraphics{#1}}% + \openin1=#1.dpth + \ifeof1 \box1 + \else + \read1 to\pgfincludeexternalgraphicsdp \closein1 + \dimen0=\pgfincludeexternalgraphicsdp\relax + \hbox{\lower\dimen0 \box1 }% + \fi + \endgroup +} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgffor.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgffor.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..fceb8347975ef7797956c8ff4c19121413631596 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgffor.code.tex @@ -0,0 +1,720 @@ + +\ProvidesPackageRCS{pgffor.code.tex} + +\ifdefined\pgfmathloaded\else + \input pgfmath.code.tex +\fi + +\newdimen\pgffor@iter +\newdimen\pgffor@skip +\newif\ifpgffor@continue + + +\def\pgffor@reset@hooks{% + \let\pgffor@beginhook=\relax% + \let\pgffor@endhook=\relax% + \let\pgffor@afterhook=\relax% +} +\pgffor@reset@hooks + + +\newtoks\pgffor@stack +\pgffor@stack={{}{}{}} + +\def\pgffor@stackpush#1{% + \def\pgffor@stacktemp{#1}% + \expandafter\expandafter\expandafter\pgffor@stack\expandafter\expandafter\expandafter=% + \expandafter\expandafter\expandafter{\expandafter\expandafter\expandafter% + {\expandafter\pgffor@stacktemp\expandafter}\the\pgffor@stack}% +} + +\def\pgffor@stackpop{\expandafter\pgffor@@stackpop\the\pgffor@stack\pgffor@stackstop} +\def\pgffor@@stackpop#1#2\pgffor@stackstop{\pgffor@stack{#2}#1} + +\def\pgffor@emptyvalues{, \pgffor@stop,}% + +\def\pgffor@foreach{% + \pgffor@atbeginforeach% + \let\pgffor@assign@before@code=\pgfutil@empty% + \let\pgffor@assign@after@code=\pgfutil@empty% + \let\pgffor@assign@once@code=\pgfutil@empty% + \let\pgffor@remember@code=\pgfutil@empty% + \let\pgffor@remember@once@code=\pgfutil@empty% + \pgffor@alphabeticsequencefalse% + \pgffor@contextfalse% + \let\pgffor@var=\pgfutil@empty + \pgffor@vars% +} + +\let\foreach=\pgffor@foreach + +\def\pgffor@vars{% + \pgfutil@ifnextchar i{\pgffor@@vars@end}{% + \pgfutil@ifnextchar[{\pgffor@@vars@opt}{% + \pgfutil@ifnextchar/{\pgffor@@vars@slash@gobble}{% + \pgffor@@vars}}}}% + +\def\pgffor@@vars@end in{\pgfutil@ifnextchar\bgroup{\pgffor@normal@list}{\pgffor@macro@list}} +\def\pgffor@@vars@opt[#1]{\pgfkeys{/pgf/foreach/.cd,#1}\pgffor@vars} +\def\pgffor@@vars#1{\pgffor@var@add#1\pgffor@stop\pgffor@vars} +\def\pgffor@@vars@slash@gobble/{\pgffor@@vars} + +\def\pgffor@var@add#1#2\pgffor@stop{% + \ifx\pgffor@var\pgfutil@empty% + \def\pgffor@var{#1}% + \def\pgffor@mainvar{#1}% + \else% + \expandafter\def\expandafter\pgffor@var\expandafter{\pgffor@var/#1}% + \fi% +} + +\def\pgffor@expand@list@true{\let\pgffor@expand@list\edef} +\def\pgffor@expand@list@false{\let\pgffor@expand@list\def} +\def\pgffor@macro@list#1{% + \expandafter\pgffor@normal@list\expandafter{#1}} +\def\pgffor@normal@list#1{% + \pgffor@expand@list\pgffor@values{#1}% + \expandafter\def\expandafter\pgffor@values\expandafter{\pgffor@values, \pgffor@stop,}% + \ifx\pgffor@values\pgffor@emptyvalues + \def\pgffor@values{\pgffor@stop,}% + \fi% + \let\pgffor@body=\pgfutil@empty% + \global\pgffor@continuetrue% + \pgffor@collectbody} +\def\pgffor@collectbody{% + \pgfutil@ifnextchar\foreach{\pgffor@collectforeach}{% + \pgfutil@ifnextchar\bgroup{\pgffor@collectargument}{\pgffor@collectsemicolon}}% +} + +\def\pgffor@collectforeach\foreach#1in{% + \pgfutil@ifnextchar\bgroup{\pgffor@collectforeach@normal{#1}}{\pgffor@collectforeach@macro{#1}}} +\def\pgffor@collectforeach@macro#1#2{% + \expandafter\long\expandafter\def\expandafter\pgffor@body\expandafter{\pgffor@body\foreach#1in#2}% + \pgffor@collectbody% +} +\def\pgffor@collectforeach@normal#1#2{% + \expandafter\long\expandafter\def\expandafter\pgffor@body\expandafter{\pgffor@body\foreach#1in{#2}}% + \pgffor@collectbody% +} +\long\def\pgffor@collectargument#1{% + \expandafter\pgfutil@in@\expandafter\foreach\expandafter{\pgffor@body}% + \ifpgfutil@in@% + \expandafter\long\expandafter\def\expandafter\pgffor@body\expandafter% + {\pgffor@body{#1}}% + \else% + \expandafter\long\expandafter\def\expandafter\pgffor@body\expandafter% + {\pgffor@body#1}% + \fi% + \pgffor@iterate% +} + +\def\pgffor@collectsemicolon{% + \let\pgffor@next=\pgffor@collectnormalsemicolon% + \ifnum\the\catcode`\;=\active\relax% + \let\pgffor@next=\pgffor@collectactivesemicolon% + \fi% + \pgffor@next% +} + +\def\pgffor@collectnormalsemicolon#1;{% + \expandafter\long\expandafter\def\expandafter\pgffor@body\expandafter{\pgffor@body#1;}% + \pgffor@iterate% +} + +{ + \catcode`\;=\active + + \gdef\pgffor@collectactivesemicolon#1;{% + \expandafter\long\expandafter\def\expandafter\pgffor@body\expandafter{\pgffor@body#1;}% + \pgffor@iterate% + } +} + +\def\pgffor@iterate{% + \let\pgffor@last=\pgfutil@empty% + \let\pgffor@prevlast=\pgfutil@empty% + \let\pgffor@dotsend=\pgfutil@empty% + \let\pgffor@dots@pre=\pgfutil@empty% + \let\pgffor@dots@post=\pgfutil@empty% + \expandafter\pgffor@scan\pgffor@values} + +\def\pgffor@stop{\pgffor@stop}% +\def\pgffor@dots{...}% + +\def\pgffor@scan{\pgfutil@ifnextchar({\pgffor@scanround}{\pgffor@scanone}} +\def\pgffor@scanround(#1)#2,{\def\pgffor@value{(#1)#2}\pgffor@scanned} +\def\pgffor@scanone#1,{\def\pgffor@value{#1}\pgffor@scanned} + + +\newif\ifpgffor@dots@in@ +\def\pgffor@dots@in@#1...#2#3\pgffor@stop{% + \ifx\pgffor@dots@@#2% + \pgffor@dots@in@false% + \else% + \pgffor@dots@in@true% + \fi% +} + +\def\pgffor@dots@@{\pgffor@dots@@} + +\def\pgffor@scanned{% + \ifx\pgffor@value\pgffor@stop% + \let\pgffor@next=\pgffor@after% + \else% + \expandafter\pgffor@dots@in@\pgffor@value\pgffor@dots@...\pgffor@dots@@\pgffor@stop% + \ifpgffor@dots@in@% + \let\pgffor@next=\pgffor@handledots% + \else% + \let\pgffor@next=\pgffor@handlevalue% + \fi% + \ifpgffor@continue% + \else% + \let\pgffor@next=\pgffor@scan% + \fi% + \fi% + \pgffor@next} + + +\def\pgffor@after{% + \global\pgffor@continuetrue% + \pgffor@atendforeach% + \pgffor@afterhook} + +\def\pgffor@handlevalue{% + \let\pgffor@prevlast=\pgffor@last% + \let\pgffor@last=\pgffor@value% + \pgffor@invokebody% + \pgffor@scan% +} + + +\def\pgffor@invokebody{% + \pgffor@begingroup% + \expandafter\pgfutil@in@\expandafter/\expandafter{\pgffor@var}% + \ifpgfutil@in@% + \expandafter\def\expandafter\pgffor@valuerest\expandafter{\pgffor@value//\relax}% + \expandafter\pgffor@multiassign\pgffor@var/\pgffor@stop/\pgffor@stop/\relax% + \else% + \expandafter\expandafter\expandafter\def\expandafter\pgffor@var\expandafter{\pgffor@value}% + \fi% + \ifx\pgffor@assign@once@code\pgfutil@empty% + \else% + \pgffor@assign@once@code% + \fi% + \ifx\pgffor@assign@before@code\pgfutil@empty% + \else% + \pgffor@assign@before@code% + \fi% + \expandafter\expandafter\expandafter\pgffor@reset@hooks\expandafter\pgffor@beginhook\expandafter\pgffor@body\pgffor@endhook% + \ifx\pgffor@assign@after@code\pgfutil@empty% + \else% + \pgffor@assign@after@code% + \fi% + \pgffor@endgroup% +} + + +\def\pgffor@multiassign#1/#2/\relax{% + \def\pgffor@currentvar{#1}% + \def\pgffor@rest{#2}% + \ifx\pgffor@currentvar\pgffor@stop% + \let\pgffor@next=\relax% + \else% + \let\pgffor@next=\pgffor@multiassignrest% + \fi% + \pgffor@next% +} + +\def\pgffor@multiassignrest{\expandafter\pgffor@multiassignfinal\pgffor@valuerest} +\def\pgffor@multiassignfinal#1/#2/\relax{% + \def\pgffor@temp{#1}% + \ifx\pgffor@currentvar\pgffor@mainvar% + \ifpgffor@alphabeticsequence% + \pgffor@makealphabetic\pgffor@temp% + \fi% + \fi% + \def\pgffor@test{#2}% + \ifx\pgffor@test\pgfutil@empty% + \expandafter\def\expandafter\pgffor@valuerest\expandafter{\pgffor@temp//\relax}% + \else% + \def\pgffor@valuerest{#2/\relax}% + \fi% + \expandafter\expandafter\expandafter\def\expandafter\pgffor@currentvar\expandafter{\pgffor@temp}% + \expandafter\pgffor@multiassign\pgffor@rest/\relax% +} + +\def\pgffor@gobblespaces#1{\pgfutil@ifnextchar x{#1}{#1}} + +\def\pgffor@handledots{% + \pgffor@gobblespaces{\expandafter\pgffor@@handledots\pgffor@value\pgffor@@stop}% +} + +\newif\ifpgffor@context + +\def\pgffor@@handledots#1...#2\pgffor@@stop{% + \def\pgffor@dots@pre{#1}% + \def\pgffor@dots@post{#2}% + \def\pgffor@dots@stripcontext#1##1#2\pgffor@@stop{\def\pgffor@dotsvalue{##1}}% + \pgffor@contexttrue% + \ifx\pgffor@dots@pre\pgfutil@empty% + \ifx\pgffor@dots@post\pgfutil@empty% + \pgffor@contextfalse% + \def\pgffor@dots@stripcontext##1\pgffor@@stop{\def\pgffor@dotsvalue{##1}}% + \fi% + \fi% + \pgffor@gobblespaces{\pgffor@dotsscanend}% +} + +\def\pgffor@dots@value@process#1{% + \expandafter\pgffor@dots@stripcontext#1\pgffor@@stop% + \expandafter\pgffor@dots@charcheck\pgffor@dotsvalue\pgffor@@stop% + \ifpgffor@alphabeticsequence + \else + \ifpgffor@assign@parse + \begingroup + \pgfkeys{/pgf/fpu/false/.try}% + \pgfmathparse{\pgffor@dotsvalue}% + \pgfmath@smuggleone\pgfmathresult + \endgroup + \let\pgffor@dotsvalue=\pgfmathresult + \fi + \fi + \let#1=\pgffor@dotsvalue% +} + +\def\pgffor@dotsscanend#1,{% + \pgffor@alphabeticsequencefalse% + \def\pgffor@dotsend{#1}% + \pgffor@dots@value@process{\pgffor@dotsend}% + \pgffor@dots@value@process{\pgffor@last}% + \ifx\pgffor@prevlast\pgfutil@empty% + \ifdim\pgffor@dotsend pt>\pgffor@last pt% + \pgffor@skip=1pt% + \else% + \pgffor@skip=-1pt% + \fi% + \else% + \pgffor@dots@value@process{\pgffor@prevlast}% + \pgffor@skip=\pgffor@last pt% + \pgffor@iter=\pgffor@prevlast pt% + \advance\pgffor@skip by-\pgffor@iter% + \fi% + \pgffor@iter=\pgffor@last pt% + \pgffor@loop% +} + +\def\pgffor@loop{% + \advance\pgffor@iter by\pgffor@skip% + \let\pgffor@next=\pgffor@doloop% + \ifdim\pgffor@skip<0pt% + \ifdim\pgffor@iter<\pgffor@dotsend pt% + \let\pgffor@next=\pgffor@endloop% + \fi% + \else% + \ifdim\pgffor@iter>\pgffor@dotsend pt% + \let\pgffor@next=\pgffor@endloop% + \fi% + \fi% + \ifpgffor@continue% + \else% + \let\pgffor@next=\pgffor@endloop% + \fi% + \pgffor@next% +} + +\def\pgffor@endloop{% + \pgffor@alphabeticsequencefalse% + \pgffor@scan% +} + +{\catcode`\p=12\catcode`\t=12\gdef\Pgffor@geT#1pt{#1}} + +\def\pgffor@doloop{% + \pgffor@begingroup + \edef\pgffor@temp{\expandafter\Pgffor@geT\the\pgffor@iter}% + \edef\pgffor@incheck{{.0/}{\pgffor@temp/}}% + \expandafter\pgfutil@in@\pgffor@incheck% + \ifpgfutil@in@% + \expandafter\pgffor@strip\pgffor@temp% + \fi% + \expandafter\pgfutil@in@\expandafter/\expandafter{\pgffor@var}% + \ifpgfutil@in@% + \expandafter\def\expandafter\pgffor@valuerest\expandafter{\pgffor@temp//\relax}% + \expandafter\pgffor@multiassign\pgffor@var/\pgffor@stop/\pgffor@stop/\relax% + \else% + \ifpgffor@alphabeticsequence% + \pgffor@makealphabetic\pgffor@temp% + \expandafter\let\pgffor@var=\pgffor@temp% + \else% + \expandafter\expandafter\expandafter\def\expandafter\pgffor@var\expandafter{\pgffor@temp}% + \fi% + \fi% + \ifpgffor@context% + \let\pgffor@temp=\pgffor@dots@pre% + \expandafter\pgfutil@append@macrotomacro\expandafter% + {\expandafter\pgffor@temp\expandafter}\expandafter{\pgffor@var}% + \expandafter\pgfutil@append@macrotomacro\expandafter% + {\expandafter\pgffor@temp\expandafter}\expandafter{\pgffor@dots@post}% + \expandafter\let\pgffor@var=\pgffor@temp% + \fi% + \ifx\pgffor@assign@before@code\pgfutil@empty% + \else% + \pgffor@assign@before@code% + \fi% + \expandafter\expandafter\expandafter\pgffor@reset@hooks\expandafter\pgffor@beginhook\expandafter\pgffor@body\pgffor@endhook% + \ifx\pgffor@assign@after@code\pgfutil@empty% + \else% + \pgffor@assign@after@code% + \fi% + \pgffor@endgroup% + \pgffor@loop% +} + +\def\pgffor@strip#1.0{\def\pgffor@temp{#1}} + +\def\breakforeach{\global\pgffor@continuefalse} + +\def\pgffor@gobbletil@pgffor@@stop#1\pgffor@@stop{} + + +\newif\ifpgffor@registeriscount + +\def\pgffor@ifcsregister#1{% + \expandafter\pgffor@@ifcsregister\meaning#1\pgffor@stop} + +\def\pgffor@@ifcsregister#1#2#3#4#5\pgffor@stop{% + \if#1m% + \pgffor@registeriscountfalse% + \let\pgffor@csnext=\pgfutil@secondoftwo% + \else% + \if#1u% + \let\pgffor@csnext=\pgfutil@secondoftwo% + \pgffor@registeriscountfalse% + \else% + \let\pgffor@csnext=\pgfutil@firstoftwo% + \if#4u% + \pgffor@registeriscounttrue% + \else% + \pgffor@registeriscountfalse% + \let\pgffor@csnext=\pgfutil@firstoftwo% + \fi% + \fi% + \fi% + \pgffor@csnext} + +\newif\ifpgffor@alphabeticsequence + +\def\pgffor@dots@charcheck#1\pgffor@@stop{% + \edef\pgffor@dots@charcheck@temp{#1}% + \expandafter\expandafter\expandafter\pgffor@@dotscharcheck\expandafter\meaning\pgffor@dots@charcheck@temp\pgffor@@stop% +} +\def\pgffor@@dotscharcheck#1#2\pgffor@@stop{% + \if#1t% + \afterassignment\pgffor@gobbletil@pgffor@@stop% + \expandafter\chardef\expandafter\pgffor@char\expandafter=\expandafter`\pgffor@dots@charcheck@temp\relax\pgffor@@stop% + \edef\pgffor@char{\the\pgffor@char}% + \ifnum\pgffor@char>64\relax% + \ifnum\pgffor@char<91\relax% + \let\pgffor@dotsvalue=\pgffor@char% + \pgffor@alphabeticsequencetrue% + \else% + \ifnum\pgffor@char>96\relax% + \ifnum\pgffor@char<123\relax% + \let\pgffor@dotsvalue=\pgffor@char% + \pgffor@alphabeticsequencetrue% + \fi% + \fi% + \fi% + \fi% + \fi% +} + +\def\pgffor@makealphabetic#1{% + \pgfutil@tempcnta=#1\relax% + \ifnum\pgfutil@tempcnta>95\relax% + \advance\pgfutil@tempcnta by-96\relax% + \edef#1{\pgffor@alpha\pgfutil@tempcnta}% + \else% + \advance\pgfutil@tempcnta by-64 % + \edef#1{\pgffor@Alpha\pgfutil@tempcnta}% + \fi% +} + +\def\pgffor@Alpha#1{% + \ifcase#1\relax\or A\or B\or C\or D\or E\or F\or G\or H\or I\or J\or K\or L\or M% + \or N\or O\or P\or Q\or R\or S\or T\or U\or V\or W\or X\or Y\or Z\else?\fi% +} + +\def\pgffor@alpha#1{% + \ifcase#1\relax\or a\or b\or c\or d\or e\or f\or g\or h\or i\or j\or k\or l\or m% + \or n\or o\or p\or q\or r\or s\or t\or u\or v\or w\or x\or y\or z\else?\fi% +} + +\newtoks\pgffor@toks + +\def\pgffor@addcstotoks#1{% + \expandafter\def\expandafter\pgffor@tokstemp\expandafter{\expandafter\def\expandafter#1\expandafter{#1}}% + \pgffor@@addcstotoks} + +\def\pgffor@addregtotoks#1{% + \expandafter\def\expandafter\pgffor@tokstemp\expandafter{\expandafter#1\expandafter=\the#1}% + \pgffor@@addcstotoks} + +\def\pgffor@addiftotoks#1{% + \begingroup% + \escapechar=-1\relax% + \expandafter\pgffor@@addiftotoks\string#1\pgffor@stop} +\def\pgffor@@addiftotoks#1#2#3#4\pgffor@stop{% + \endgroup + \csname if#3#4\endcsname% + \expandafter\def\expandafter\pgffor@tokstemp\expandafter{\csname#3#4true\endcsname}% + \else% + \expandafter\def\expandafter\pgffor@tokstemp\expandafter{\csname#3#4false\endcsname}% + \fi% + \pgffor@@addcstotoks% +} + +\def\pgffor@@addcstotoks{% + \expandafter\expandafter\expandafter\pgffor@toks\expandafter\expandafter\expandafter=% + \expandafter\expandafter\expandafter{\expandafter\pgffor@tokstemp\the\pgffor@toks}% +} + + +\def\pgffor@atbeginforeach{% + \begingroup% +} + +\def\pgffor@atendforeach{% + \global\edef\pgffor@remember@expanded{\pgffor@remember@code}% + \ifx\pgffor@remember@expanded\pgfutil@empty% + \else% + \pgffor@remember@expanded% + \global\let\pgffor@remember@expanded=\pgfutil@empty% + \fi% + \endgroup% +} +\def\pgffor@default@begingroup{% + \begingroup% +} + +\let\pgffor@remember@once@expanded=\pgfutil@empty +\let\pgffor@remember@expanded=\pgfutil@empty + +\def\pgffor@default@endgroup{% + \ifx\pgffor@remember@once@code\pgfutil@empty + \else + \xdef\pgffor@remember@once@expanded{\pgffor@remember@once@code}% + \fi + \ifx\pgffor@remember@code\pgfutil@empty + \else + \xdef\pgffor@remember@expanded{\pgffor@remember@code}% + \fi + \endgroup + \ifx\pgffor@remember@once@expanded\pgfutil@empty + \else + \pgffor@remember@once@expanded% + \global\let\pgffor@remember@once@expanded=\pgfutil@empty + \fi + \ifx\pgffor@assign@once@code\pgfutil@empty + \else + \global\let\pgffor@assign@once@code=\pgfutil@empty + \fi + \ifx\pgffor@remember@expanded\pgfutil@empty + \else + \pgffor@remember@expanded% + \global\let\pgffor@remember@expanded=\pgfutil@empty + \fi +} + +\let\pgffor@begingroup=\pgffor@default@begingroup +\let\pgffor@endgroup=\pgffor@default@endgroup + + +\def\pgffor@stack@begingroup{% + \pgffor@toks={}% + \pgffor@addcstotoks{\pgffor@mainvar}% + \pgffor@addcstotoks{\pgffor@var}% + \pgffor@addcstotoks{\pgffor@body}% + \pgffor@addcstotoks{\pgffor@last}% + \pgffor@addcstotoks{\pgffor@prevlast}% + \pgffor@addcstotoks{\pgffor@dotsend}% + \pgffor@addcstotoks{\pgffor@assign@before@code}% + \pgffor@addcstotoks{\pgffor@assign@after@code}% + \pgffor@addcstotoks{\pgffor@remember@code}% + \pgffor@addcstotoks{\pgffor@remember@once@code}% + \pgffor@addcstotoks{\pgffor@dots@pre}% + \pgffor@addcstotoks{\pgffor@dots@post}% + \pgffor@addregtotoks{\pgffor@iter}% + \pgffor@addregtotoks{\pgffor@skip}% + \pgffor@addiftotoks{\ifpgffor@alphabeticsequence}% + \pgffor@addiftotoks{\ifpgffor@context}% + \expandafter\pgffor@stackpush\expandafter{\the\pgffor@toks}% +} + +\def\pgffor@stack@endgroup{\pgffor@stackpop} + + +\newif\ifpgffor@assign@evaluate +\newif\ifpgffor@assign@once +\newif\ifpgffor@assign@parse + +\pgfkeys{/pgf/foreach/.cd, + var/.code=\pgffor@var@add#1\pgffor@stop, + scope iterations/.code={ + \csname if#1\endcsname% + \let\pgffor@begingroup=\pgffor@default@begingroup% + \let\pgffor@endgroup=\pgffor@default@endgroup% + \else% + \let\pgffor@begingroup=\pgffor@stack@begingroup% + \let\pgffor@endgroup=\pgffor@stack@endgroup% + \fi% + }, + evaluate/.code=\pgffor@assign@evaluatetrue\pgffor@assign@oncefalse\pgffor@assign@parse{#1},% + assign/.code=\pgffor@assign@evaluatefalse\pgffor@assign@oncefalse\pgffor@assign@parse{#1},% + evaluate once/.code=\pgffor@assign@evaluatetrue\pgffor@assign@oncetrue\pgffor@assign@parse{#1},% + assign once/.code=\pgffor@assign@evaluatefalse\pgffor@assign@oncetrue\pgffor@assign@parse{#1},% + remember/.code=\pgffor@remember@parse{#1},% + count/.code=\pgffor@count@parse#1\pgffor@stop, + parse/.is if=pgffor@assign@parse, + parse/.default=false, + expand list/.is if=pgffor@expand@list@, + expand list/.default=true, + expand list=false, +} + +\def\pgffor@assign@parse#1{% + \pgfutil@in@;{#1}% + \ifpgfutil@in@% + \else% + \pgfutil@in@={#1}% + \fi% + \ifpgfutil@in@% + \pgffor@assign@@parse#1;\pgffor@stop;% + \else% + \pgffor@assign@parse@old#1\pgffor@stop% + \fi% +} + +\def\pgffor@stop{\pgffor@stop} +\def\pgffor@assign@@parse#1;{% + \def\pgffor@test{#1}% + \ifx\pgffor@test\pgffor@stop% + \let\pgffor@next=\relax% + \else% + \let\pgffor@next=\pgffor@assign@@parse% + \ifx\pgffor@test\pgfutil@empty% + \else% + \pgfutil@in@={#1}% + \ifpgfutil@in@% + \pgffor@assign@@@parse#1\pgffor@stop% + \else% + \pgffor@assign@@@parse#1=#1\pgffor@stop% + \fi% + \fi% + \fi% + \pgffor@next} + +\def\pgffor@assign@@@parse#1=#2\pgffor@stop{% + \ifpgffor@assign@evaluate% + \ifpgffor@assign@once% + \pgfutil@append@tomacro{\pgffor@assign@once@code}{\pgfmathparse{#2}\let#1=\pgfmathresult}% + \pgfutil@append@tomacro{\pgffor@remember@once@code}{\noexpand\def\noexpand#1{#2}}% + \else + \pgfutil@append@tomacro{\pgffor@assign@before@code}{\pgfmathparse{#2}\let#1=\pgfmathresult}% + \fi% + \else% + \ifpgffor@assign@once% + \pgfutil@append@tomacro{\pgffor@assign@once@code}{\def#1{#2}}% + \pgfutil@append@tomacro{\pgffor@remember@once@code}{\noexpand\def\noexpand#1{#2}}% + \else + \pgfutil@append@tomacro{\pgffor@assign@before@code}{\def#1{#2}}% + \fi% + \fi% +} + +\def\pgffor@assign@parse@old#1#2\pgffor@stop{% + \pgffor@assign@@parse@old#2\pgffor@stop as#1using #1\pgffor@@stop} + +\def\pgffor@assign@@parse@old#1as#2#3\pgffor@@stop{% + \pgffor@assign@@@parse@old{#2}#1#3\pgffor@stop\pgffor@@stop} + +\def\pgffor@assign@@@parse@old#1#2using #3\pgffor@stop#4\pgffor@@stop{% + \pgffor@assign@@@parse#1=#3\pgffor@stop} + + + +\def\pgffor@remember@parse#1{% + \pgfutil@in@ a{#1}% + \ifpgfutil@in@% + \pgffor@remember@parse@old#1\pgffor@stop% + \else% + \pgffor@remember@@parse#1;\pgffor@stop;% + \fi% +} + +\def\pgffor@remember@@parse#1;{% + \def\pgffor@test{#1}% + \ifx\pgffor@test\pgffor@stop% + \let\pgffor@next=\relax% + \else% + \let\pgffor@next=\pgffor@remember@@parse% + \ifx\pgffor@test\pgfutil@empty% + \else% + \pgfutil@in@={#1}% + \ifpgfutil@in@% + \pgffor@remember@@@parse#1\pgffor@stop% + \else% + \pgffor@ifcsregister{#1}{% + \pgfutil@append@tomacro{\pgffor@remember@code}{\noexpand#1=\the#1\noexpand\relax}% + }% + {% + \pgfutil@append@tomacro{\pgffor@remember@code}{\noexpand\def\noexpand#1{#1}}% + }% + \fi% + \fi% + \fi% + \pgffor@next% +} + +\def\pgffor@remember@@@parse#1=#2\pgffor@stop{% + \pgffor@ifcsregister{#2}{% + \pgfutil@append@tomacro{\pgffor@assign@after@code}{\expandafter\def\expandafter#1\expandafter{\the#2}}% + \pgfutil@append@tomacro{\pgffor@remember@code}{\noexpand\def\noexpand#1{#1}}% + }% + {% + \pgfutil@append@tomacro{\pgffor@assign@after@code}{\expandafter\def\expandafter#1\expandafter{#2}}% + \pgfutil@append@tomacro{\pgffor@remember@code}{\noexpand\def\noexpand#1{#1}}% + }% +} + +\def\pgffor@remember@parse@old#1#2\pgffor@stop{% + \pgffor@remember@@parse@old#1#2\pgffor@stop as#1(initially 0)\pgffor@@stop} + +\def\pgffor@remember@@parse@old#1#2as#3#4\pgffor@@stop{% + \pgffor@remember@@@parse@old{#1}{#3}#2#4\pgffor@stop\pgffor@@stop} + +\def\pgffor@remember@@@parse@old#1#2#3(initially #4)#5\pgffor@stop#6\pgffor@@stop{% + \pgfutil@append@tomacro{\pgffor@assign@after@code}{\edef#2{#1}}% + \pgfutil@append@tomacro{\pgffor@remember@code}{\noexpand\def\noexpand#2{#2}}% + \pgfutil@append@tomacro{\pgffor@assign@once@code}{\def#2{#4}}% +} + +\def\pgffor@count@parse#1#2\pgffor@stop{% + \pgffor@count@@parse#1#2\pgffor@stop from 1\pgffor@stop\pgffor@@stop} + +\def\pgffor@count@@parse#1#2from#3\pgffor@stop#4\pgffor@@stop{% + \pgfutil@append@tomacro\pgffor@remember@code{\noexpand\def\noexpand#1{#1}}% + \pgfutil@append@tomacro\pgffor@assign@before@code{\pgfmathparse{int(#1+1)}\let#1=\pgfmathresult}% + \pgfmathparse{int(#3-1)}\let#1=\pgfmathresult% +} + + +\def\pgfutil@append@macrotomacro#1#2{% + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter% + #1\expandafter\expandafter\expandafter{\expandafter#1#2}} + +\def\pgfutil@append@tomacro#1#2{% + \expandafter\def\expandafter#1\expandafter{#1#2}} + + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfkeys.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfkeys.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..fd8d0de64e777f559b1911a1208f4efe604ecdf3 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfkeys.code.tex @@ -0,0 +1,873 @@ + + + + +\ifx\pgfkeysloaded\undefined + \let\pgfkeysloaded=\relax +\else + \expandafter\endinput +\fi + + +\def\pgfkeys@empty{} +\long\def\pgfkeys@firstoftwo#1#2{#1} +\long\def\pgfkeys@secondoftwo#1#2{#2} +\long\def\pgfkeys@ifcsname#1{% + \ifcsname#1\endcsname + \expandafter\pgfkeys@firstoftwo + \else + \expandafter\pgfkeys@secondoftwo + \fi +} + + +\ifx\PackageError\undefined + \def\pgfkeys@error#1{\errmessage{Package pgfkeys Error: #1}}% +\else + \def\pgfkeys@error#1{\PackageError{pgfkeys}{#1}{}}% +\fi + +\ifx\eTeXrevision\undefined% + \pgfkeys@error{PGF requires etex in extended mode}% + \csname @@end\expandafter\endcsname\expandafter\end% +\fi + +\ifnum\eTeXversion<2 + \pgfkeys@error{PGF requires etex version 2}% + \csname @@end\expandafter\endcsname\expandafter\end% +\fi + + +\ifx\contextversion\undefined + \let\pgfkeys@expanded \expanded + \let\pgfkeys@unexpanded \unexpanded +\else + \let\pgfkeys@expanded \normalexpanded + \let\pgfkeys@unexpanded \normalunexpanded +\fi + +\begingroup + \edef\pgfkeys@tmpa{\string\expanded} + \edef\pgfkeys@tmpb{\meaning\pgfkeys@expanded} + \expandafter +\endgroup +\ifx\pgfkeys@tmpa\pgfkeys@tmpb +\else + \pgfkeys@error{PGF requires the \noexpand\expanded primitive} + \csname @@end\expandafter\endcsname\expandafter\end% +\fi + + + +\long\def\pgfkeyssetvalue#1#2{% + \pgfkeys@temptoks{#2}\expandafter\edef\csname pgfk@#1\endcsname{\the\pgfkeys@temptoks}% +} + +\long\def\pgfkeyssetevalue#1#2{% + \expandafter\edef\csname pgfk@#1\endcsname + {\pgfkeys@unexpanded\expandafter{\pgfkeys@expanded{#2}}}% +} + + +\long\def\pgfkeysaddvalue#1#2#3{% + {% + \toks0{#2}% + \pgfkeysifdefined{#1} + {\pgfkeys@temptoks\expandafter\expandafter\expandafter{\csname pgfk@#1\endcsname}}% + {\pgfkeys@temptoks{}}% + \toks1{#3}% + \xdef\pgfkeys@global@temp{\the\toks0 \the\pgfkeys@temptoks \the\toks1}% + }% + \pgfkeyslet{#1}\pgfkeys@global@temp% +} + + + + +\long\def\pgfkeyslet#1#2{% + \expandafter\let\csname pgfk@#1\endcsname#2% +} + + + +\long\def\pgfkeysgetvalue#1#2{% + \pgfkeys@ifcsname{pgfk@#1}% + {\expandafter\let\expandafter#2\csname pgfk@#1\endcsname}% + {\let#2\relax}} + + + + +\let\pgfkeys@relax\relax +\long\def\pgfkeysvalueof#1{\csname\pgfkeys@ifcsname{pgfk@#1}{pgfk@#1}{pgfkeys@relax}\endcsname} + + + + +\long\def\pgfkeysifdefined#1{% + \ifcsname pgfk@#1\endcsname + \expandafter\pgfkeys@firstoftwo + \else + \expandafter\pgfkeys@secondoftwo + \fi +} + +\long\def\pgfkeysifassignable#1#2#3{% + \pgfkeysifdefined{#1}% + {#2} + {\pgfkeysifdefined{#1/.@cmd}% + {#2}% + {#3}}% +}% + + + + +\newtoks\pgfkeys@pathtoks +\def\pgfkeyscurrentpath{\the\pgfkeys@pathtoks} +\newtoks\pgfkeys@temptoks + +\def\pgfkeys@root{/} +\let\pgfkeysdefaultpath\pgfkeys@root + +\def\pgfkeys{\expandafter\pgfkeys@@set\expandafter{\pgfkeysdefaultpath}}% +\long\def\pgfkeys@@set#1#2{% + \let\pgfkeysdefaultpath\pgfkeys@root% + \pgfkeys@parse#2,\pgfkeys@mainstop% + \def\pgfkeysdefaultpath{#1}} + +\def\pgfkeys@parse{\futurelet\pgfkeys@possiblerelax\pgfkeys@parse@main} +\def\pgfkeys@parse@main{% + \ifx\pgfkeys@possiblerelax\pgfkeys@mainstop% + \expandafter\pgfkeys@cleanup% + \else% + \expandafter\pgfkeys@normal% + \fi% +} +\newif\ifpgfkeys@syntax@handlers +\def\pgfkeys@normal{% + \ifpgfkeys@syntax@handlers% + \expandafter\pgfkeys@syntax@handlers% + \else% + \expandafter\pgfkeys@@normal% + \fi% +} +\def\pgfkeys@syntax@handlers{\pgf@keys@utilifnextchar\relax\pgfkeys@syntax@@handlers\pgfkeys@syntax@@handlers}% +\def\pgfkeys@syntax@@handlers{\futurelet\pgfkeys@first@char\pgfkeys@syntax@handlers@test} +\def\pgfkeys@syntax@handlers@test{% + \pgfkeysgetvalue{/handlers/first char syntax/\meaning\pgfkeys@first@char}\pgfkeys@the@handler% + \ifx\pgfkeys@the@handler\relax% + \expandafter\pgfkeys@@normal% + \else% + \expandafter\pgfkeys@use@handler% + \fi% +} +\long\def\pgfkeys@use@handler#1,{% + \pgfkeys@the@handler{#1}% + \pgfkeys@parse% +} + +\long\def\pgfkeys@@normal#1,{% + \pgfkeys@unpack#1=\pgfkeysnovalue=\pgfkeys@stop% + \pgfkeys@parse% +} +\def\pgfkeys@cleanup\pgfkeys@mainstop{} + +\def\pgfkeys@mainstop{\pgfkeys@mainstop} % +\def\pgfkeys@novalue{} +\def\pgfkeysnovalue{\pgfkeys@novalue} % +\def\pgfkeysnovalue@text{\pgfkeysnovalue} +\def\pgfkeysvaluerequired{\pgfkeysvaluerequired} % + +\long\def\pgfkeys@unpack#1=#2=#3\pgfkeys@stop{% + \pgfkeys@spdef\pgfkeyscurrentkey{#1}% + \edef\pgfkeyscurrentkey{\pgfkeyscurrentkey}% + \ifx\pgfkeyscurrentkey\pgfkeys@empty% + \else% + \pgfkeys@add@path@as@needed% + \pgfkeys@spdef\pgfkeyscurrentvalue{#2}% + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \pgfkeysifdefined{\pgfkeyscurrentkey/.@def}% + {\pgfkeysgetvalue{\pgfkeyscurrentkey/.@def}{\pgfkeyscurrentvalue}} + {}% + \fi% + \ifx\pgfkeyscurrentvalue\pgfkeysvaluerequired% + \def\pgf@marshal{\pgfkeysvalueof{/errors/value required/.@cmd}}% + \expandafter\pgf@marshal\expandafter{\pgfkeyscurrentkey}{}\pgfeov% + \else% + \pgfkeys@case@one% + \fi% + \fi} + +\def\pgfkeys@case@one{% + \pgfkeysifdefined{\pgfkeyscurrentkey/.@cmd}% + {\pgfkeysgetvalue{\pgfkeyscurrentkey/.@cmd}{\pgfkeys@code}% + \ifx\pgfkeys@code\relax\expandafter\pgfkeys@firstoftwo\else\expandafter\pgfkeys@secondoftwo\fi + {\pgfkeys@unknown}% + {\expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov}} + {\pgfkeys@case@two}% +} + +\def\pgfkeys@case@two{% + \pgfkeysifdefined{\pgfkeyscurrentkey}% + {\pgfkeys@case@two@extern}% + {\pgfkeys@case@three}% +} + +\def\pgfkeys@case@two@extern{% + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \pgfkeysvalueof{\pgfkeyscurrentkey}% + \else% + \pgfkeyslet{\pgfkeyscurrentkey}\pgfkeyscurrentvalue% + \fi% +} + + +\def\pgfkeys@case@three{% + \pgfkeys@split@path% + \pgfkeysifdefined{/handlers/\pgfkeyscurrentname/.@cmd}% + {\pgfkeysgetvalue{/handlers/\pgfkeyscurrentname/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov} + {\pgfkeys@unknown}% +} +\let\pgfkeys@case@three@handleall=\pgfkeys@case@three +\def\pgfkeys@case@three@handle@restricted{% + \pgfkeys@split@path% + \pgfkeysifdefined{/handlers/\pgfkeyscurrentname/.@cmd}{% + \pgfkeys@ifexecutehandler{% + \pgfkeysgetvalue{/handlers/\pgfkeyscurrentname/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov + }{% + \let\pgfkeys@tempa=\pgfkeyscurrentkey + \let\pgfkeys@tempb=\pgfkeyscurrentname + \edef\pgfkeyscurrentkey{\pgfkeyscurrentpath}% + \pgfkeys@split@path% + \let\pgfkeyscurrentkey=\pgfkeys@tempa + \edef\pgfkeyscurrentname{\pgfkeyscurrentname/\pgfkeys@tempb}% + \pgfkeys@unknown + }% + }{% + \pgfkeys@unknown + }% +} + +\def\pgfkeys@ifexecutehandler#1#2{#1}% +\let\pgfkeys@ifexecutehandler@handleall=\pgfkeys@ifexecutehandler +\def\pgfkeys@ifexecutehandler@handleonlyexisting#1#2{% + \pgfkeys@ifcsname{pgfk@excpt@\pgfkeyscurrentname}{% + #1% + }{% + \pgfkeysifdefined{\pgfkeyscurrentpath}{#1}{% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}{#1}{#2}% + }{}% + }% +}% +\def\pgfkeys@ifexecutehandler@handlefullorexisting#1#2{% + \ifpgfkeysaddeddefaultpath + \pgfkeys@ifcsname{pgfk@excpt@\pgfkeyscurrentname}{% + #1% + }{% + \pgfkeysifdefined{\pgfkeyscurrentpath}{% + #1% + }{% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}{% + #1% + }{% + #2% + }% + }% + }% + \else + #1% + \fi +}% +\def\pgfkeysaddhandleonlyexistingexception#1{\expandafter\def\csname pgfk@excpt@#1\endcsname{1}}% + +\def\pgfkeys@unknown{% + \pgfkeysifdefined{\pgfkeyscurrentpath/.unknown/.@cmd}% + {% + \pgfkeysgetvalue{\pgfkeyscurrentpath/.unknown/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov} + {% + \pgfkeysgetvalue{/handlers/.unknown/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov% + }% +} + + +\long\def\pgfkey@argumentisspace#1{% + \long\def\pgfkeys@spdef##1##2{% + \futurelet\pgfkeys@possiblespace\pgfkeys@sp@a##2\pgfkeys@stop\pgfkeys@stop#1\pgfkeys@stop\relax##1}% + \def\pgfkeys@sp@a{% + \ifx\pgfkeys@possiblespace\pgfkeys@sptoken% + \expandafter\pgfkeys@sp@b% + \else% + \expandafter\pgfkeys@sp@b\expandafter#1% + \fi}% + \long\def\pgfkeys@sp@b#1##1 \pgfkeys@stop{\pgfkeys@sp@c##1}% +} +\pgfkey@argumentisspace{ } +\long\def\pgfkeys@sp@c#1\pgfkeys@stop#2\relax#3{\pgfkeys@temptoks{#1}\edef#3{\the\pgfkeys@temptoks}} +{\def\:{\global\let\pgfkeys@sptoken= } \: } + + + +\def\pgfkeys@add@path@as@needed{% + \expandafter\futurelet\expandafter\pgfkeys@possibleslash\expandafter\pgfkeys@check@slash\pgfkeyscurrentkey\relax% +} +\newif\ifpgfkeysaddeddefaultpath +\def\pgfkeys@check@slash{% + \ifx\pgfkeys@possibleslash/% + \expandafter\pgfkeys@nevermind% + \else% + \expandafter\pgfkeys@addpath% + \fi% +} + +\def\pgfkeys@nevermind#1\relax{% + \pgfkeysaddeddefaultpathfalse + \let\pgfkeyscurrentkeyRAW\pgfkeyscurrentkey +} +\def\pgfkeys@addpath#1\relax{% + \pgfkeysaddeddefaultpathtrue + \def\pgfkeyscurrentkeyRAW{#1}% + \edef\pgfkeyscurrentkey{\pgfkeysdefaultpath#1}% +} + + +\def\pgfkeys@split@path{% + \pgfkeys@pathtoks{}% + \expandafter\pgfkeys@splitter\pgfkeyscurrentkey//% +} +\def\pgfkeys@splitter#1/#2/{% + \def\pgfkeys@temp{#2}% + \ifx\pgfkeys@temp\pgfkeys@empty% + \def\pgfkeyscurrentname{#1}% + \expandafter\pgfkeys@gobbletoslash% + \else% + \expandafter\pgfkeys@pathtoks\expandafter{\the\pgfkeys@pathtoks#1/}% + \fi% + \pgfkeys@splitter#2/% +} +\def\pgfkeys@gobbletoslash\pgfkeys@splitter/{% + \if\relax\detokenize\expandafter{\the\pgfkeys@pathtoks}\relax\else + \expandafter\pgfkeys@remove@slash\the\pgfkeys@pathtoks\relax + \fi +}% +\def\pgfkeys@remove@slash#1/\relax{\pgfkeys@pathtoks{#1}} + + + + +\def\pgfqkeys{\expandafter\pgfkeys@@qset\expandafter{\pgfkeysdefaultpath}}% +\long\def\pgfkeys@@qset#1#2#3{\def\pgfkeysdefaultpath{#2/}\pgfkeys@parse#3,\pgfkeys@mainstop\def\pgfkeysdefaultpath{#1}} + + + +\long\def\pgfkeysalso#1{\pgfkeys@parse#1,\pgfkeys@mainstop} + + + + +\long\def\pgfqkeysalso#1#2{\def\pgfkeysdefaultpath{#1/}\pgfkeys@parse#2,\pgfkeys@mainstop} + + + + + + +\long\def\pgfkeysdef#1#2{% + \long\def\pgfkeys@temp##1\pgfeov{#2}% + \pgfkeyslet{#1/.@cmd}{\pgfkeys@temp}% + \pgfkeyssetvalue{#1/.@body}{#2}% +} +\long\def\pgfkeysedef#1#2{% + \long\edef\pgfkeys@temp##1\pgfeov{#2}% + \pgfkeyslet{#1/.@cmd}{\pgfkeys@temp}% + \pgfkeyssetevalue{#1/.@body}{#2}% +} + + + +\long\def\pgfkeysdefargs#1#2#3{% + \long\def\pgfkeys@temp#2\pgfeov{#3}% + \pgfkeyslet{#1/.@cmd}{\pgfkeys@temp}% + \pgfkeyssetvalue{#1/.@args}{#2\pgfeov}% + \pgfkeyssetvalue{#1/.@body}{#3}% +} + +\long\def\pgfkeysedefargs#1#2#3{% + \long\edef\pgfkeys@temp#2\pgfeov{#3}% + \pgfkeyslet{#1/.@cmd}{\pgfkeys@temp}% + \pgfkeyssetvalue{#1/.@args}{#2\pgfeov}% + \pgfkeyssetevalue{#1/.@body}{#3}% +} + +\long\def\pgfkeysdefnargs#1#2#3{\pgfkeysdefnargs@{#1}{#2}{#3}{\def}{\pgfkeyssetvalue}}% +\long\def\pgfkeysedefnargs#1#2#3{\pgfkeysdefnargs@{#1}{#2}{#3}{\edef}{\pgfkeyssetevalue}}% +\long\def\pgfkeysdefnargs@#1#2#3#4#5{% + \ifcase#2\relax + \pgfkeyssetvalue{#1/.@args}{}% + \or + \pgfkeyssetvalue{#1/.@args}{##1}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3##4}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3##4##5}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3##4##5##6}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3##4##5##6##7}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3##4##5##6##7##8}% + \or + \pgfkeyssetvalue{#1/.@args}{##1##2##3##4##5##6##7##8##9}% + \else + \pgfkeys@error{\string\pgfkeysdefnargs: expected <= 9 arguments, got #2}% + \fi + \pgfkeysgetvalue{#1/.@args}\pgfkeys@tempargs + \def\pgfkeys@temp{\expandafter\long\expandafter#4\csname pgfk@#1/.@@body\endcsname}% + \expandafter\pgfkeys@temp\pgfkeys@tempargs{#3}% + \edef\pgfkeys@tempargs{\noexpand\pgfkeysvalueof{#1/.@@body}}% + \def\pgfkeys@temp{\pgfkeysdef{#1}}% + \ifnum#2=1\relax + \expandafter\pgfkeys@temp\expandafter{\pgfkeys@tempargs{##1}}% + \else + \expandafter\pgfkeys@temp\expandafter{\pgfkeys@tempargs##1}% + \fi + #5{#1/.@body}{#3}% +} + + +\pgfkeysdef{/handlers/.code}{\pgfkeysdef{\pgfkeyscurrentpath}{#1}} +\pgfkeysdef{/handlers/.code 2 args}{\pgfkeysdefargs{\pgfkeyscurrentpath}{##1##2}{#1}} +\pgfkeysdef{/handlers/.ecode}{\pgfkeysedef{\pgfkeyscurrentpath}{#1}} +\pgfkeysdef{/handlers/.ecode 2 args}{\pgfkeysedefargs{\pgfkeyscurrentpath}{##1##2}{#1}} +\pgfkeysdefnargs{/handlers/.code args}{2}{\pgfkeysdefargs{\pgfkeyscurrentpath}{#1}{#2}} +\pgfkeysdefnargs{/handlers/.ecode args}{2}{\pgfkeysedefargs{\pgfkeyscurrentpath}{#1}{#2}} +\pgfkeysdefnargs{/handlers/.code n args}{2}{\pgfkeysdefnargs{\pgfkeyscurrentpath}{#1}{#2}} +\pgfkeysdefnargs{/handlers/.ecode n args}{2}{\pgfkeysedefnargs{\pgfkeyscurrentpath}{#1}{#2}} + + +\pgfkeys{/handlers/.add code/.code 2 args=% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@args}% + {% + \pgfkeysaddvalue{\pgfkeyscurrentpath/.@body}{#1}{#2}% + {% + \pgfkeysgetvalue{\pgfkeyscurrentpath/.@args}{\pgfkeys@tempargs}% + \pgfkeysgetvalue{\pgfkeyscurrentpath/.@body}{\pgfkeys@tempbody}% + \def\pgfkeys@marshal{\expandafter\long\expandafter\gdef\expandafter\pgfkeys@global@temp\pgfkeys@tempargs}% + \expandafter\pgfkeys@marshal\expandafter{\pgfkeys@tempbody}% + }% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@@body}{% + \pgfkeyslet{\pgfkeyscurrentpath/.@@body}{\pgfkeys@global@temp}% + }{% + \pgfkeyslet{\pgfkeyscurrentpath/.@cmd}{\pgfkeys@global@temp}% + }% + }% + {% + \edef\pgf@expanded@path{\pgfkeyscurrentpath}% + {% + \toks0{#1}% + \pgfkeysifdefined{\pgf@expanded@path/.@cmd}% + {\expandafter\expandafter\expandafter\pgfkeys@temptoks\expandafter\expandafter\expandafter{\csname pgfk@\pgf@expanded@path/.@body\endcsname}}% + {\expandafter\pgfkeys@temptoks\expandafter{\expandafter\pgfkeyssetvalue\expandafter{\pgf@expanded@path}{##1}}}% + \toks1{#2}% + \xdef\pgfkeys@global@temp{\the\toks0 \the\pgfkeys@temptoks \the\toks1 }% + }% + \def\pgf@temp{\pgfkeyssetvalue{\pgf@expanded@path/.@body}}% + \expandafter\pgf@temp\expandafter{\pgfkeys@global@temp}% + \expandafter\long\expandafter\def\expandafter\pgfkeys@temp\expandafter##\expandafter1\expandafter\pgfeov\expandafter{\pgfkeys@global@temp}% + \pgfkeyslet{\pgf@expanded@path/.@cmd}\pgfkeys@temp% + }% +} +\pgfkeys{/handlers/.prefix code/.code=\pgfkeys{\pgfkeyscurrentpath/.add code={#1}{}}}% +\pgfkeys{/handlers/.append code/.code=\pgfkeys{\pgfkeyscurrentpath/.add code={}{#1}}}% + + + +\pgfkeys{/handlers/.style/.code=\pgfkeys{\pgfkeyscurrentpath/.code=\pgfkeysalso{#1}}} +\pgfkeys{/handlers/.estyle/.code=\pgfkeys{\pgfkeyscurrentpath/.ecode=\noexpand\pgfkeysalso{#1}}} +\pgfkeys{/handlers/.style args/.code 2 args=\pgfkeys{\pgfkeyscurrentpath/.code args={#1}{\pgfkeysalso{#2}}}} +\pgfkeys{/handlers/.estyle args/.code 2 args=\pgfkeys{\pgfkeyscurrentpath/.ecode args={#1}{\noexpand\pgfkeysalso{#2}}}} +\pgfkeys{/handlers/.style 2 args/.code=\pgfkeys{\pgfkeyscurrentpath/.code 2 args=\pgfkeysalso{#1}}} +\pgfkeys{/handlers/.style n args/.code 2 args=\pgfkeys{\pgfkeyscurrentpath/.code n args={#1}{\pgfkeysalso{#2}}}} + + +\pgfkeys{/handlers/.add style/.code 2 args=\pgfkeys{\pgfkeyscurrentpath/.add code={\pgfkeysalso{#1}}{\pgfkeysalso{#2}}}}% +\pgfkeys{/handlers/.prefix style/.code=\pgfkeys{\pgfkeyscurrentpath/.add code={\pgfkeysalso{#1}}{}}}% +\pgfkeys{/handlers/.append style/.code=\pgfkeys{\pgfkeyscurrentpath/.add code={}{\pgfkeysalso{#1}}}}% + + + +\pgfkeys{/handlers/.initial/.code=\pgfkeyssetvalue{\pgfkeyscurrentpath}{#1}} +\pgfkeys{/handlers/.add/.code 2 args=\pgfkeysaddvalue{\pgfkeyscurrentpath}{#1}{#2}} +\pgfkeys{/handlers/.prefix/.code=\pgfkeysaddvalue{\pgfkeyscurrentpath}{#1}{}} +\pgfkeys{/handlers/.append/.code=\pgfkeysaddvalue{\pgfkeyscurrentpath}{}{#1}} +\pgfkeys{/handlers/.get/.code=\pgfkeysgetvalue{\pgfkeyscurrentpath}{#1}} +\pgfkeys{/handlers/.link/.code=\pgfkeyssetvalue{\pgfkeyscurrentpath}{\pgfkeysvalueof{#1}}} + + + +\pgfkeys{/handlers/.default/.code=\pgfkeyssetvalue{\pgfkeyscurrentpath/.@def}{#1}} +\pgfkeys{/handlers/.value required/.code=\pgfkeyssetvalue{\pgfkeyscurrentpath/.@def}{\pgfkeysvaluerequired}} +\pgfkeys{/handlers/.value forbidden/.code=\pgfkeys{\pgfkeyscurrentpath/.add code=% +{% + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \else% + \def\pgf@marshal{\pgfkeysvalueof{/errors/value forbidden/.@cmd}}% + \expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\pgfkeyscurrentkey\expandafter}\expandafter{\pgfkeyscurrentvalue}\pgfeov% + \fi% +}{}}} + + + +\pgfkeys{/handlers/.store in/.code=\pgfkeysalso{\pgfkeyscurrentpath/.code=\def#1{##1}}} +\pgfkeys{/handlers/.estore in/.code=\pgfkeysalso{\pgfkeyscurrentpath/.code=\edef#1{##1}}} + +\pgfkeys{/handlers/.is if/.code=\pgfkeysalso{% + \pgfkeyscurrentpath/.code=\pgfkeys@handle@boolean{#1}{##1}, + \pgfkeyscurrentpath/.default=true% + }% +} +\def\pgfkeys@handle@boolean#1#2{% + \pgfkeys@ifcsname{#1#2}{% + \csname#1#2\endcsname% + }{% + \def\pgf@marshal{\pgfkeysvalueof{/errors/boolean expected/.@cmd}}% + \expandafter\pgf@marshal\expandafter{\pgfkeyscurrentkey}{#2}\pgfeov% + }% +} + +\pgfkeys{/handlers/.is choice/.code=% + \pgfkeys{% + \pgfkeyscurrentpath/.cd,% + .code=\def\pgfkeys@was@choice{##1}\expandafter\pgfkeysalso\expandafter{\pgfkeyscurrentkey/##1}, + .unknown/.code={% + \def\pgf@marshal{\pgfkeysvalueof{/errors/unknown choice value/.@cmd}}% + {\expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@pathtoks\expandafter}\expandafter{\pgfkeys@was@choice}\pgfeov}% + }% + }% +} + + + +\pgfkeys{/handlers/.list/.code=% + {% + \ifx\foreach\@undefined% + \pgfkeys@error{You need to load the pgffor package to use the .list key syntax.}% + \fi% + \def\pgf@keys@temp{}% + \foreach \pgf@keys@key in{#1}% + {\expandafter\expandafter\expandafter\gdef% + \expandafter\expandafter\expandafter\pgf@keys@temp% + \expandafter\expandafter\expandafter{\expandafter\pgf@keys@temp\expandafter{\pgf@keys@key}}}% + \edef\pgf@keys@list@path{\pgfkeyscurrentpath}% + \expandafter\expandafter\expandafter\pgf@keys@do@list% + \expandafter\expandafter\expandafter{\expandafter\pgf@keys@list@path\expandafter}\pgf@keys@temp\pgf@stop% + }% +} +\def\pgf@keys@do@list#1{\pgf@keys@utilifnextchar\bgroup{\pgf@keys@do@list@item{#1}}\pgf@keys@gobble} +\def\pgf@keys@do@list@item#1#2{\pgfkeysalso{#1={#2}}\pgf@keys@do@list{#1}} + + + +\pgfkeys{/handlers/.forward to/.code=% + \pgfkeys{\pgfkeyscurrentpath/.add code={}{\pgfkeys{#1={##1}}}} +} + + + +\pgfkeys{/handlers/.show value/.code=\pgfkeysgetvalue{\pgfkeyscurrentpath}{\pgfkeysshower}\show\pgfkeysshower} % +\pgfkeys{/handlers/.show code/.code=\pgfkeysgetvalue{\pgfkeyscurrentpath/.@cmd}{\pgfkeysshower}\show\pgfkeysshower} % + + +\pgfkeys{/handlers/first char syntax/.is if=pgfkeys@syntax@handlers} + + +\def\pgfkeys@searchalso@prepare@unknown@handler#1{% + \global\def\pgfkeys@global@temp##1\pgfeov{}% + \pgfkeys@searchalso@parse#1,\pgfkeys@mainstop + {% + \toks0=\expandafter{\pgfkeys@global@temp##1\pgfeov}% + \toks1={% + \pgfkeysgetvalue{/handlers/.unknown/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeys@searchalso@temp@value\pgfeov + }% + \xdef\pgfkeys@global@temp{% + \noexpand\def\noexpand\pgfkeys@searchalso@temp@value{####1}% + \noexpand\ifpgfkeysaddeddefaultpath + \noexpand\expandafter\noexpand\pgfkeys@firstoftwo + \noexpand\else + \noexpand\expandafter\noexpand\pgfkeys@secondoftwo + \noexpand\fi{% + \noexpand\pgfkeyssuccessfalse + \noexpand\let\noexpand\pgfkeys@searchalso@name=\noexpand\pgfkeyscurrentkeyRAW + \the\toks0 % + }{% + \the\toks1 % + }% + }% + \expandafter\gdef\expandafter\pgfkeys@global@temp\expandafter##\expandafter1\expandafter\pgfeov\expandafter{\pgfkeys@global@temp}% + }% +}% + +\def\pgfkeys@searchalso@parse{\futurelet\pgfkeys@possiblerelax\pgfkeys@searchalso@parse@main} +\def\pgfkeys@searchalso@parse@main{% + \ifx\pgfkeys@possiblerelax\pgfkeys@mainstop% + \expandafter\pgfkeys@cleanup% + \else% + \expandafter\pgfkeys@searchalso@appendentry% + \fi% +} +\def\pgfkeys@searchalso@appendentry#1,#2{% + \def\pgfkeys@searchalso@nexttok{#2}% + \pgfkeys@spdef\pgfkeys@temp{#1}% + {% + \toks0=\expandafter{\pgfkeys@global@temp##1\pgfeov}% + \toks1=\expandafter{\pgfkeys@temp}% + \xdef\pgfkeys@global@temp{% + \the\toks0 % + \noexpand\ifpgfkeyssuccess\noexpand\else + \noexpand\pgfqkeys{\the\toks1 }{\noexpand\pgfkeys@searchalso@name + \ifx\pgfkeys@searchalso@nexttok\pgfkeys@mainstop\else/.try\fi /.expand once=\noexpand\pgfkeys@searchalso@temp@value}% + \noexpand\fi}% + \expandafter\gdef\expandafter\pgfkeys@global@temp\expandafter##\expandafter1\expandafter\pgfeov\expandafter{\pgfkeys@global@temp}% + }% + \pgfkeys@searchalso@parse#2% +} +\pgfkeys{% + /handlers/.is family/.code=\pgfkeys{\pgfkeyscurrentpath/.ecode=\edef\noexpand\pgfkeysdefaultpath{\pgfkeyscurrentpath/}},% + /handlers/.cd/.code=\edef\pgfkeysdefaultpath{\pgfkeyscurrentpath/},% + /handlers/.search also/.code={% + \pgfkeys@searchalso@prepare@unknown@handler{#1}% + \pgfkeyslet{\pgfkeyscurrentpath/.unknown/.@cmd}{\pgfkeys@global@temp}% + } +}% + + + +\pgfkeys{/handlers/.expand once/.code=\expandafter\pgfkeys@exp@call\expandafter{#1}} +\pgfkeys{/handlers/.expand twice/.code=\expandafter\expandafter\expandafter\pgfkeys@exp@call\expandafter\expandafter\expandafter{#1}} +\pgfkeys{/handlers/.expanded/.code=\edef\pgfkeys@temp{#1}\expandafter\pgfkeys@exp@call\expandafter{\pgfkeys@temp}} + +\long\def\pgfkeys@exp@call#1{\pgfkeysalso{\pgfkeyscurrentpath={#1}}} + +\def\pgfkeys@mathparse{% + \pgfkeys@ifcsname{pgfmathparse}{% + \pgfmathparse + }{% + \pgfkeys@error{You have to load `pgfmath' to use \string\pgfmathparse}% + \def\pgfmathresult + }% +} +\pgfkeys{/handlers/.evaluated/.code=\pgfkeys@mathparse{#1}\expandafter\pgfkeys@exp@call\expandafter{\pgfmathresult}} + + +\newif\ifpgfkeyssuccess +\pgfkeys{/handlers/.try/.code=\pgfkeys@try} +\pgfkeys{/handlers/.retry/.code=\ifpgfkeyssuccess\else\pgfkeys@try\fi} +\def\pgfkeys@try{% + \edef\pgfkeyscurrentkey{\pgfkeyscurrentpath}% + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@def}% + {\pgfkeysgetvalue{\pgfkeyscurrentpath/.@def}{\pgfkeyscurrentvalue}} + {}% + \fi% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}% + {% + \pgfkeysgetvalue{\pgfkeyscurrentpath/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov% + \pgfkeyssuccesstrue% + }% + {% + \pgfkeysifdefined{\pgfkeyscurrentpath}% + {% + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \pgfkeysvalueof{\pgfkeyscurrentpath}% + \else% + \pgfkeyslet{\pgfkeyscurrentpath}\pgfkeyscurrentvalue% + \fi% + \pgfkeyssuccesstrue% + }% + {% + \pgfkeys@split@path% + \pgfkeysifdefined{/handlers/\pgfkeyscurrentname/.@cmd}{% + \pgfkeys@ifexecutehandler{% + \pgfkeysgetvalue{/handlers/\pgfkeyscurrentname/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov + \pgfkeyssuccesstrue% + }{% + \pgfkeyssuccessfalse + }% + }{% + \pgfkeyssuccessfalse + }% + }% + }% +} + + +\pgfkeys{/utils/exec/.code={#1}} % + + + +\pgfkeys{ + /errors/boolean expected/.code 2 args=% + {% + \toks1={#1}% + \toks2={#2}% + \pgfkeys@error{% + Boolean parameter of key '\the\toks1' must be 'true' or 'false', not + '\the\toks2'. I am going to ignore it% + }% + }, + /errors/value required/.code 2 args=% + {% + \toks1={#1}% + \pgfkeys@error{% + The key '\the\toks1' requires a value. I am going to ignore this + key% + }% + }, + /errors/value forbidden/.code 2 args=% + {% + \toks1={#1}% + \toks2={#2}% + \pgfkeys@error{% + You may not specify a value for the key '\the\toks1'. I am going to ignore + the value '\the\toks2' that you provided% + }% + }, + /errors/unknown choice value/.code 2 args=% + {% + \toks1={#1}% + \toks2={#2}% + \pgfkeys@error{% + Choice '\the\toks2' unknown in choice key '\the\toks1'. I am + going to ignore this key% + }% + }, + /errors/unknown key/.code 2 args=% + {% + \toks1={#1}% + \toks2={#2}% + \def\pgf@temp{#2}% + \pgfkeys@error{% + I do not know the key '\the\toks1'\ifx\pgf@temp\pgfkeysnovalue@text\space\else, to which you passed + '\the\toks2', \fi and I am going to ignore it. Perhaps you + misspelled it% + }% + } +} + +\pgfkeys{/handlers/.unknown/.code=% + {% + \def\pgf@marshal{\pgfkeysvalueof{/errors/unknown key/.@cmd}}% + {\expandafter\expandafter\expandafter\pgf@marshal\expandafter\expandafter\expandafter{\expandafter\pgfkeyscurrentkey\expandafter}\expandafter{\pgfkeyscurrentvalue}\pgfeov}% + }% +} + +\pgfkeys{ + /handler config/.is choice, + /handler config/all/.code={% + \let\pgfkeys@case@three=\pgfkeys@case@three@handleall + \let\pgfkeys@ifexecutehandler=\pgfkeys@ifexecutehandler@handleall + }, + /handler config/only existing/.code={% + \let\pgfkeys@case@three=\pgfkeys@case@three@handle@restricted + \let\pgfkeys@ifexecutehandler=\pgfkeys@ifexecutehandler@handleonlyexisting + }, + /handler config/full or existing/.code={% + \let\pgfkeys@case@three=\pgfkeys@case@three@handle@restricted + \let\pgfkeys@ifexecutehandler=\pgfkeys@ifexecutehandler@handlefullorexisting + }, + /handler config/only existing/add exception/.code={\pgfkeysaddhandleonlyexistingexception{#1}}, +}% +\pgfkeysaddhandleonlyexistingexception{.cd}% +\pgfkeysaddhandleonlyexistingexception{.try}% +\pgfkeysaddhandleonlyexistingexception{.retry}% +\pgfkeysaddhandleonlyexistingexception{.lastretry}% +\pgfkeysaddhandleonlyexistingexception{.unknown}% +\pgfkeysaddhandleonlyexistingexception{.expand once}% +\pgfkeysaddhandleonlyexistingexception{.expand twice}% +\pgfkeysaddhandleonlyexistingexception{.expanded}% + + +\def\pgf@keys@gobble#1{} +\long\def\pgf@keys@utilifnextchar#1#2#3{% + \let\pgf@keys@utilreserved@d=#1% + \def\pgf@keys@utilreserved@a{#2}% + \def\pgf@keys@utilreserved@b{#3}% + \futurelet\pgf@keys@utillet@token\pgf@keys@utilifnch} +\def\pgf@keys@utilifnch{% + \ifx\pgf@keys@utillet@token\pgf@keys@utilsptoken + \let\pgf@keys@utilreserved@c\pgf@keys@utilxifnch + \else + \ifx\pgf@keys@utillet@token\pgf@keys@utilreserved@d + \let\pgf@keys@utilreserved@c\pgf@keys@utilreserved@a + \else + \let\pgf@keys@utilreserved@c\pgf@keys@utilreserved@b + \fi + \fi + \pgf@keys@utilreserved@c} +{% + \def\:{\global\let\pgf@keys@utilsptoken= } \: + \def\:{\pgf@keys@utilxifnch} \expandafter\gdef\: {\futurelet\pgf@keys@utillet@token\pgf@keys@utilifnch} +} + +\chardef\pgfkeys@inputcheck0 +\def\pgfkeys@IfFileExists#1{% + \openin\pgfkeys@inputcheck=#1 + \ifeof\pgfkeys@inputcheck + \expandafter\closein\expandafter\pgfkeys@inputcheck + \expandafter\pgfkeys@secondoftwo + \else + \expandafter\closein\expandafter\pgfkeys@inputcheck + \expandafter\pgfkeys@firstoftwo + \fi +} + +\def\usepgfkeyslibrary{\pgf@keys@utilifnextchar[{\pgfkeys@@uselibrary}{\pgfkeys@uselibrary}} +\def\pgfkeys@@uselibrary[#1]{\pgfkeys@uselibrary{#1}} +\def\pgfkeys@uselibrary#1{\pgfkeys@uselibrary@parse#1,\pgfkeys@mainstop} +\def\pgfkeys@uselibrary@parse{% + \pgf@keys@utilifnextchar\pgfkeys@mainstop{\pgfkeys@cleanup}{\pgfkeys@uselibrary@normal}% +}% +\def\pgfkeys@uselibrary@normal#1,{% + \pgfkeys@uselibrary@load{#1}% + \pgfkeys@uselibrary@parse +} +\def\pgfkeys@uselibrary@load#1{% + \expandafter\pgfkeys@spdef\expandafter\pgf@temp\expandafter{#1}% + \ifx\pgf@temp\pgfkeys@empty\expandafter\pgfkeys@firstoftwo\else\expandafter\pgfkeys@secondoftwo\fi{}{% + \pgfkeys@ifcsname{pgfkeys@library@\pgf@temp @loaded}{}{% + \expandafter\let\csname pgfkeys@library@\pgf@temp @loaded\endcsname=\pgfkeys@empty + \expandafter\edef\csname pgfkeys@library@#1@atcode\endcsname{\the\catcode`\@}% + \expandafter\edef\csname pgfkeys@library@#1@barcode\endcsname{\the\catcode`\|}% + \expandafter\edef\csname pgfkeys@library@#1@dollarcode\endcsname{\the\catcode`\$}% + \catcode`\@=11 + \catcode`\|=12 + \catcode`\$=3 + \pgfkeys@IfFileExists{pgfkeyslibrary\pgf@temp.code.tex}{% + \input pgfkeyslibrary\pgf@temp.code.tex + }{% + \pgfkeys@error{I did not find the pgfkeys library '\pgf@temp'. I looked for the + file named pgfkeyslibrary\pgf@temp.code.tex, but could not find it in the + current texmf trees.}% + }% + \catcode`\@=\csname pgfkeys@library@#1@atcode\endcsname + \catcode`\|=\csname pgfkeys@library@#1@barcode\endcsname + \catcode`\$=\csname pgfkeys@library@#1@dollarcode\endcsname + }% + }% +} + +\let\pgfkeys@library@filtered@loaded\pgfkeys@empty +\input pgfkeyslibraryfiltered.code.tex + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..e6c357b885922534418600735ae7030100671e81 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfkeyslibraryfiltered.code.tex @@ -0,0 +1,571 @@ + + + +\let\pgfkeys@orig@case@one=\pgfkeys@case@one +\let\pgfkeys@orig@@set=\pgfkeys@@set +\let\pgfkeys@orig@@qset=\pgfkeys@@qset +\let\pgfkeys@orig@try=\pgfkeys@try +\let\pgfkeys@orig@unknown=\pgfkeys@unknown + +\newif\ifpgfkeysfilteringisactive +\newif\ifpgfkeysfiltercontinue +\let\pgfkeys@key@predicate=\pgfkeys@empty +\let\pgfkeys@filtered@handler=\pgfkeys@empty +\newtoks\pgfkeys@tmptoks + +\def\pgfkeysfiltered{% + \expandafter\pgfkeysfiltered@@install\expandafter{\pgfkeysdefaultpath}% +} + +\long\def\pgfkeysfiltered@@install#1#2{% + \pgfkeys@install@filter@and@invoke{% + \let\pgfkeysdefaultpath\pgfkeys@root% + \pgfkeys@parse#2,\pgfkeys@mainstop% + \def\pgfkeysdefaultpath{#1}% + }% +} + +\long\def\pgfkeysalsofrom#1{% + \expandafter\pgfkeysalso\expandafter{#1}% +} + +\long\def\pgfkeysalsofilteredfrom#1{% + \expandafter\pgfkeysalsofiltered\expandafter{#1}% +} + +\long\def\pgfkeysalsofiltered#1{% + \pgfkeys@install@filter@and@invoke{\pgfkeysalso{#1}}% +}% + +\long\def\pgfqkeysfiltered#1{% + \expandafter\pgfqkeysfiltered@@install\expandafter{\pgfkeysdefaultpath}{#1}% +} + +\long\def\pgfqkeysfiltered@@install#1#2#3{% + \pgfkeys@install@filter@and@invoke{% + \def\pgfkeysdefaultpath{#2/}\pgfkeys@parse#3,\pgfkeys@mainstop\def\pgfkeysdefaultpath{#1}% + }% +} + + + +\def\pgfkeysactivatefamily#1{% + \pgfkeysiffamilydefined + {#1}% + {\csname pgfk@#1/familyactivetrue\endcsname}% + {\pgfkeysvalueof{/errors/family unknown/.@cmd}{#1}\pgfeov}% +} + +\def\pgfkeysdeactivatefamily#1{% + \pgfkeysiffamilydefined + {#1}% + {\csname pgfk@#1/familyactivefalse\endcsname}% + {\pgfkeysvalueof{/errors/family unknown/.@cmd}{#1}\pgfeov}% +} + +\def\pgfkeysactivatefamilies#1#2{% + \pgfkeyssavekeyfilterstateto\pgfkeys@cur@state + \expandafter\pgfkeysactivatefamilies@impl\expandafter{\pgfkeys@cur@state}{#1}{#2}% +} +\def\pgfkeysactivatefamilies@impl#1#2#3{% + \pgfkeysinstallkeyfilter{/pgf/key filters/false}{}% + \let#3=\pgfkeys@empty% + \def\pgfkeys@filtered@handler{\pgfkeys@family@activate@handler{#3}}% + \pgfkeysalsofiltered{#2}% + #1% +} + +\def\pgfkeys@family@activate@handler#1{% + \pgfkeysactivatefamily{\pgfkeyscurrentkey}% + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter#1\expandafter\pgfkeysdeactivatefamily\expandafter{\pgfkeyscurrentkey}}% + \edef#1{\the\pgfkeys@tmptoks}% +} + +\long\def\pgfkeysiffamilydefined#1#2#3{\ifcsname ifpgfk@#1/familyactive\endcsname#2\else#3\fi} + +\def\pgfkeysisfamilyactive#1{% + \pgfkeysiffamilydefined{#1}{% + \expandafter\let\expandafter\ifpgfkeysfiltercontinue\csname ifpgfk@#1/familyactive\endcsname + }{% + \pgfkeysvalueof{/errors/family unknown/.@cmd}{#1}\pgfeov% + \expandafter\expandafter\expandafter\let\csname ifpgfkeysfiltercontinue\endcsname\csname iffalse\endcsname + }% +}% + +\def\pgfkeysgetfamily#1#2{% + \pgfkeysifdefined{#1/family}{\pgfkeysgetvalue{#1/family}{#2}\pgfkeyssuccesstrue}{\pgfkeyssuccessfalse}% +} + +\def\pgfkeyssetfamily#1#2{% + \pgfkeysiffamilydefined{#2}{% + \pgfkeyssetvalue{#1/family}{#2}% + }{% + \pgfkeysalso{/errors/family unknown={#2}}% + }% +}% + + +\long\def\pgfkeys@cur@is@descendant@of@errors{% + \expandafter\pgfkeys@cur@is@descendant@of@errors@impl\pgfkeyscurrentkey/errors\pgf@@eov +}% +\long\def\pgfkeys@cur@is@descendant@of@errors@impl#1/errors#2\pgf@@eov{% + \def\pgfkeyspred@TMP{#1}% + \ifx\pgfkeyspred@TMP\pgfkeys@empty + \pgfkeysfiltercontinuetrue + \else + \pgfkeysfiltercontinuefalse + \fi +}% + +\def\pgfkeysinterruptkeyfilter{% + \ifpgfkeysfilteringisactive + \let\pgfkeys@case@one=\pgfkeys@orig@case@one + \let\pgfkeys@try=\pgfkeys@orig@try + \let\pgfkeys@unknown=\pgfkeys@orig@unknown + \fi +} + +\def\endpgfkeysinterruptkeyfilter{% + \ifpgfkeysfilteringisactive + \let\pgfkeys@case@one=\pgfkeys@case@one@filtered + \let\pgfkeys@try=\pgfkeys@try@filtered + \let\pgfkeys@unknown=\pgfkeys@unknown@filtered + \fi +} + +\def\pgfkeysactivatefamiliesandfilteroptions#1#2{% + \pgfkeysactivatefamilies{#1}{\pgfkeys@family@deactivation}% + \pgfkeysfiltered{#2}% + \pgfkeys@family@deactivation +} + +\def\pgfqkeysactivatefamiliesandfilteroptions#1#2#3{% + \pgfkeysactivatefamilies{#1}{\pgfkeys@family@deactivation}% + \pgfqkeysfiltered{#2}{#3}% + \pgfkeys@family@deactivation +} + +\def\pgfkeyssplitpath{\pgfkeys@split@path}% + + +\def\pgfkeysactivatesinglefamilyandfilteroptions#1#2{% + \pgfkeysactivatefamily{#1}% + \pgfkeysfiltered{#2}% + \pgfkeysdeactivatefamily{#1}% +} + +\def\pgfqkeysactivatesinglefamilyandfilteroptions#1#2#3{% + \pgfkeysactivatefamily{#1}% + \pgfqkeysfiltered{#2}{#3}% + \pgfkeysdeactivatefamily{#1}% +} + +\def\pgfkeysinstallkeyfilter#1#2{% + \pgfkeysifdefined{#1/.@cmd}{% + \edef\pgfkeyscurrentkeyfilter{#1}% + \def\pgfkeyscurrentkeyfilterargs{#2}% + \pgfkeysgetvalue{#1/.@cmd}{\pgfkeys@key@predicate@}% + \def\pgfkeys@key@predicate{\pgfkeys@key@predicate@#2\pgfeov}% + }{% + \pgfkeysvalueof{/errors/no such key filter/.@cmd}{#1}{#2}\pgfeov% + }% +} + +\def\pgfkeysinstallkeyfilterhandler#1#2{% + \pgfkeysifdefined{#1/.@cmd}{% + \edef\pgfkeyscurrentkeyfilterhandler{#1}% + \def\pgfkeyscurrentkeyfilterhandlerargs{#2}% + \pgfkeysgetvalue{#1/.@cmd}{\pgfkeys@filtered@handler@}% + \def\pgfkeys@filtered@handler{\pgfkeys@filtered@handler@#2\pgfeov}% + }{% + \pgfkeysvalueof{/errors/no such key filter handler/.@cmd}{#1}{#2}\pgfeov% + }% +} + +\def\pgfkeyssavekeyfilterstateto#1{% + \pgfkeys@tmptoks={\pgfkeysinstallkeyfilter}% + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilter}}% + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilterargs}\pgfkeysinstallkeyfilterhandler}% + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilterhandler}}% + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\the\expandafter\pgfkeys@tmptoks\expandafter{\pgfkeyscurrentkeyfilterhandlerargs}}% + \edef#1{% + \the\pgfkeys@tmptoks + }% +} + + +\pgfkeys{% + /errors/family unknown/.code=\pgfkeys@error{% + Sorry, I do not know family '#1' and can't work with any assoicated family handling. Perhaps you misspelled it?}, + /errors/no such key filter/.code 2 args=\pgfkeys@error{Sorry, there is no such key filter '#1'.}, + /errors/no such key filter handler/.code 2 args=\pgfkeys@error{Sorry, there is no such key filter handler '#1'.}, + /handlers/.is family/.append code={% + \edef\pgfkeyspred@TMP{pgfk@\pgfkeyscurrentpath/familyactive}% + \expandafter\pgfkeys@non@outer@newif\expandafter{\pgfkeyspred@TMP}% + \edef\pgfkeyspred@TMP{\pgfkeyscurrentpath/.belongs to family=\pgfkeyscurrentpath}% + \expandafter\pgfkeysalso\expandafter{\pgfkeyspred@TMP}% + },% + /handlers/.activate family/.code=\pgfkeysactivatefamily{\pgfkeyscurrentpath}, + /handlers/.deactivate family/.code=\pgfkeysdeactivatefamily{\pgfkeyscurrentpath}, + /handlers/.belongs to family/.code={\pgfkeyssetfamily{\pgfkeyscurrentpath}{#1}},% + /handlers/.lastretry/.code={% + \ifpgfkeyssuccess\else + \pgfkeys@try + \ifpgfkeyssuccess\else + \pgfkeys@split@path% + \pgfkeys@unknown + \fi + \fi + }, + /handlers/.install key filter/.code={% + \pgfkeysinstallkeyfilter{\pgfkeyscurrentpath}{#1}% + },% + /handlers/.install key filter handler/.code={% + \pgfkeysinstallkeyfilterhandler{\pgfkeyscurrentpath}{#1}% + },% + /pgf/key filter handlers/append filtered to/.code={% + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter\pgfkeyscurrentkeyRAW\expandafter=\expandafter{\pgfkeyscurrentvalue}}% + \ifx#1\pgfkeys@empty + \else + \pgfkeys@tmptoks=\expandafter\expandafter\expandafter{\expandafter#1\expandafter,\the\pgfkeys@tmptoks}% + \fi + \edef#1{\the\pgfkeys@tmptoks}% + },% + /pgf/key filter handlers/ignore/.code={}, + /pgf/key filter handlers/ignore/.install key filter handler, + /pgf/key filter handlers/log/.code={% + \pgf@typeout{LOG: the option '\pgfkeyscurrentkey' (was originally '\pgfkeyscurrentkeyRAW') (case \pgfkeyscasenumber) has not been processed due to pgfkeysfiltered.}% + }, + /pgf/key filters/active families/.code={% + \if\pgfkeyscasenumber0% + \pgfkeysfiltercontinuetrue + \else + \if\pgfkeyscasenumber3% + \pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP + \else + \pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP + \fi + \ifpgfkeyssuccess + \pgfkeysisfamilyactive{\pgfkeyspred@TMP}% + \else% + \pgfkeysfiltercontinuefalse + \fi + \fi + },% + /pgf/key filters/active families or no family/.code 2 args={% + \if\pgfkeyscasenumber0% + \pgfkeysevalkeyfilterwith{#2}% + \else + \if\pgfkeyscasenumber3% + \pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP + \else + \pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP + \fi + \ifpgfkeyssuccess + \pgfkeysisfamilyactive{\pgfkeyspred@TMP}% + \else% + \pgfkeysevalkeyfilterwith{#1}% + \fi + \fi + }, + /pgf/key filters/active families or no family DEBUG/.code 2 args={% + \if\pgfkeyscasenumber0% + \pgf@typeout{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) invoking unknown handler '#2']}% + \pgfkeysevalkeyfilterwith{#2}% + \else + \if\pgfkeyscasenumber3% + \pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP + \else + \pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP + \fi + \ifpgfkeyssuccess + \pgfkeysisfamilyactive{\pgfkeyspred@TMP}% + \ifpgfkeysfiltercontinue + \pgf@typeout{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) family is ACTIVE]}% + \else + \pgf@typeout{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) family is NOT active.]}% + \fi + \else% + \pgf@typeout{[pgfkeyshasactivefamilyornofamily(\pgfkeyscurrentkey, \pgfkeyscasenumber) invoking has-no-family-handler '#1']}% + \pgfkeysevalkeyfilterwith{#1}% + \fi + \fi + }, + /pgf/key filters/active families and known/.code={% + \if\pgfkeyscasenumber0% + \pgfkeysfiltercontinuefalse + \else + \if\pgfkeyscasenumber3% + \pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP + \else + \pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP + \fi + \ifpgfkeyssuccess + \pgfkeysisfamilyactive{\pgfkeyspred@TMP}% + \else% + \pgfkeysfiltercontinuefalse + \fi + \fi + }, + /pgf/key filters/active families or descendants of/.code={% + \if\pgfkeyscasenumber0% + \pgfkeysfiltercontinuefalse + \else + \if\pgfkeyscasenumber3% + \pgfkeysgetfamily\pgfkeyscurrentpath\pgfkeyspred@TMP + \else + \pgfkeysgetfamily\pgfkeyscurrentkey\pgfkeyspred@TMP + \fi + \ifpgfkeyssuccess + \pgfkeysisfamilyactive{\pgfkeyspred@TMP}% + \else% + \def\pgfkeysisdescendantof@impl##1#1##2\pgf@@eov{% + \def\pgfkeyspred@TMP{##1}% + \ifx\pgfkeyspred@TMP\pgfkeys@empty + \pgfkeysfiltercontinuetrue + \else + \pgfkeysfiltercontinuefalse + \fi + }% + \expandafter\pgfkeysisdescendantof@impl\pgfkeyscurrentkey#1\pgf@@eov + \fi + \fi + }, + /pgf/key filters/is descendant of/.code={% + \if\pgfkeyscasenumber0% + \pgfkeysfiltercontinuetrue + \else + \def\pgfkeysisdescendantof@impl##1#1##2\pgf@@eov{% + \def\pgfkeyspred@TMP{##1}% + \ifx\pgfkeyspred@TMP\pgfkeys@empty + \pgfkeysfiltercontinuetrue + \else + \pgfkeysfiltercontinuefalse + \fi + }% + \expandafter\pgfkeysisdescendantof@impl\pgfkeyscurrentkey#1\pgf@@eov + \fi + },% + /pgf/key filters/equals/.code={% + \if\pgfkeyscasenumber0% + \pgfkeysfiltercontinuetrue + \else + \def\pgfkeyspred@TMP{#1}% + \ifx\pgfkeyscurrentkey\pgfkeyspred@TMP + \pgfkeysfiltercontinuetrue + \else + \pgfkeysfiltercontinuefalse + \fi + \fi + },% + /pgf/key filters/not/.code={% + \pgfkeysevalkeyfilterwith{#1}% + \ifpgfkeysfiltercontinue + \pgfkeysfiltercontinuefalse + \else + \pgfkeysfiltercontinuetrue + \fi + },% + /pgf/key filters/and/.code 2 args={% + \pgfkeysevalkeyfilterwith{#1}% + \ifpgfkeysfiltercontinue + \pgfkeysevalkeyfilterwith{#2}% + \fi + },% + /pgf/key filters/or/.code 2 args={% + \pgfkeysevalkeyfilterwith{#1}% + \ifpgfkeysfiltercontinue + \else + \pgfkeysevalkeyfilterwith{#2}% + \fi + },% + /pgf/key filters/true/.code={\pgfkeysfiltercontinuetrue},% + /pgf/key filters/true/.install key filter, + /pgf/key filters/false/.code={% + \pgfkeysfiltercontinuefalse + },% + /pgf/key filters/defined/.code={% + \if\pgfkeyscasenumber0% + \pgfkeysfiltercontinuefalse + \else + \pgfkeysfiltercontinuetrue + \fi + }, +}% + + + +\def\pgfkeys@case@one@filtered{% + \pgfkeys@cur@is@descendant@of@errors + \ifpgfkeysfiltercontinue + \pgfkeys@orig@case@one + \else + \pgfkeysfiltercontinuetrue + \pgfkeysifdefined{\pgfkeyscurrentkey/.@cmd}{% + \def\pgfkeyscasenumber{1}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \pgfkeysgetvalue{\pgfkeyscurrentkey/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov + \else + \pgfkeys@filtered@handler% + \fi + }{% + \pgfkeysifdefined{\pgfkeyscurrentkey}{% + \def\pgfkeyscasenumber{2}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \pgfkeys@case@two@extern + \else + \pgfkeys@filtered@handler% + \fi + }{% + \pgfkeys@split@path + \pgfkeysifdefined{/handlers/\pgfkeyscurrentname/.@cmd}{% + \pgfkeys@ifexecutehandler{% + \def\pgfkeyscasenumber{3}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \pgfkeysgetvalue{/handlers/\pgfkeyscurrentname/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov + \else + \pgfkeys@filtered@handler% + \fi + }{% + \pgfkeys@unknown + }% + }{% + \pgfkeys@unknown + }% + }% + }% + \fi +}% + +\def\pgfkeys@unknown@filtered{% + \def\pgfkeyscasenumber{0}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \pgfkeys@orig@unknown + \else + \pgfkeys@filtered@handler% + \fi +} + +\def\pgfkeys@try@filtered{% + \ifpgfkeysfiltercontinue + \pgfkeys@orig@try + \else + \pgfkeysfiltercontinuetrue + \edef\pgfkeyscurrentkey{\pgfkeyscurrentpath}% + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@def}% + {\pgfkeysgetvalue{\pgfkeyscurrentpath/.@def}{\pgfkeyscurrentvalue}} + {}% + \fi% + \pgfkeysifdefined{\pgfkeyscurrentpath/.@cmd}% + {% + \def\pgfkeyscasenumber{1}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \pgfkeysgetvalue{\pgfkeyscurrentkey/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov% + \else + \pgfkeys@filtered@handler% + \fi + \pgfkeyssuccesstrue% + }% + {% + \pgfkeysifdefined{\pgfkeyscurrentpath}% + {% + \def\pgfkeyscasenumber{2}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \ifx\pgfkeyscurrentvalue\pgfkeysnovalue@text% + \pgfkeysvalueof{\pgfkeyscurrentpath}% + \else% + \pgfkeyslet{\pgfkeyscurrentpath}\pgfkeyscurrentvalue% + \fi% + \else + \pgfkeys@filtered@handler% + \fi + \pgfkeyssuccesstrue% + }% + {% + \pgfkeys@split@path% + \pgfkeysifdefined{/handlers/\pgfkeyscurrentname/.@cmd}{% + \pgfkeys@ifexecutehandler{% + \def\pgfkeyscasenumber{3}% + \pgfkeys@key@predicate% + \ifpgfkeysfiltercontinue + \pgfkeysgetvalue{/handlers/\pgfkeyscurrentname/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyscurrentvalue\pgfeov + \else + \pgfkeys@filtered@handler% + \fi + \pgfkeyssuccesstrue% + }{% + \pgfkeyssuccessfalse + }% + }{% + \pgfkeyssuccessfalse + }% + }% + }% + \fi +} + + +\long\def\pgfkeys@install@filter@and@invoke#1{% + \ifpgfkeysfilteringisactive + \pgfkeys@error{Sorry, nested calls to key filtering routines are not allowed. (reason: It is not possible to properly restore the previous filtering state after returning from the nested call)}% + \fi + \pgfkeysfilteringisactivetrue + \let\pgfkeys@case@one=\pgfkeys@case@one@filtered + \let\pgfkeys@try=\pgfkeys@try@filtered + \let\pgfkeys@unknown=\pgfkeys@unknown@filtered + #1% + \let\pgfkeys@case@one=\pgfkeys@orig@case@one + \let\pgfkeys@try=\pgfkeys@orig@try + \let\pgfkeys@unknown=\pgfkeys@orig@unknown + \pgfkeysfilteringisactivefalse +} + + + + +\long\def\pgfkeysevalkeyfilterwith#1{% + \pgfkeys@eval@key@filter@subroutine@unpack#1=\pgfkeysnovalue=\pgfkeys@stop +}% +\long\def\pgfkeys@eval@key@filter@subroutine@unpack#1=#2=#3\pgfkeys@stop{% + \pgfkeys@spdef\pgfkeyspred@TMP{#1}% + \edef\pgfkeyspred@TMP{\pgfkeyspred@TMP}% + \pgfkeys@spdef\pgfkeyspred@TMPB{#2}% + \ifx\pgfkeyspred@TMPB\pgfkeysnovalue@text% + \pgfkeysifdefined{\pgfkeyspred@TMP/.@def}% + {\pgfkeysgetvalue{\pgfkeyspred@TMP/.@def}{\pgfkeyspred@TMPB}} + {}% + \fi% + \ifx\pgfkeyspred@TMPB\pgfkeysvaluerequired% + \pgfkeysvalueof{/errors/value required/.@cmd}\pgfkeyspred@TMP\pgfkeyspred@TMPB\pgfeov% + \else% + \pgfkeysifdefined{\pgfkeyspred@TMP/.@cmd}{% + \pgfkeysgetvalue{\pgfkeyspred@TMP/.@cmd}{\pgfkeys@code}% + \expandafter\pgfkeys@code\pgfkeyspred@TMPB\pgfeov + }{% + \pgfkeysvalueof{/errors/no such key filter/.@cmd}\pgfkeyspred@TMP\pgfkeyspred@TMPB\pgfeov% + }% + \fi% +} + + +\def\pgfkeys@non@outer@newif@#1#2{% + \expandafter\edef\csname #2true\endcsname{\noexpand\let\noexpand#1=\noexpand\iftrue}% + \expandafter\edef\csname #2false\endcsname{\noexpand\let\noexpand#1=\noexpand\iffalse}% + \csname #2false\endcsname +}% + +\def\pgfkeys@non@outer@newif#1{% + \expandafter\pgfkeys@non@outer@newif@\csname if#1\endcsname{#1}% +} +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfrcs.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfrcs.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..f4a390b828c2f79eecd0b9ce6f5a0636fe4f3700 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfrcs.code.tex @@ -0,0 +1,121 @@ + +\ifx\eTeXrevision\undefined% + \pgfutil@packageerror{PGF}{PGF requires etex in extended mode}{}% + \csname @@end\expandafter\endcsname\expandafter\end% +\fi + +\ifnum\eTeXversion<2 + \pgfutil@packageerror{PGF}{PGF requires etex version 2}{}% + \csname @@end\expandafter\endcsname\expandafter\end% +\fi + + +\pgfutil@IfFileExists{pgf.revision.tex}{\input pgf.revision.tex } {% + \def\pgfrevision{0.0}% + \def\pgfversion{0.0}% + \def\pgfversiondate{2014-07-01}% + \def\pgfrevisiondate{2014-07-01}% +} + +\begingroup +\catcode`\"=12 +\pgfutil@IfUndefined{directlua}{}{% + \directlua{pgf = {}; pgf.pgfversion = "\pgfversion"}% +}% +\endgroup + +\let\pgftypesetversion=\pgfrevision + + +\ifx\pgfrcsloaded\undefined +\def\pgfrcsloaded{} + +\edef\pgfrcsatcode{\the\catcode`\@} +\catcode`\@=11 + +\def\ProvidesFileRCS{% + \let\pgfrcs@final=\ProvidesFileRCS@ + \pgfrcs@parseinput +} +\def\ProvidesFileRCS@#1{% + \ProvidesFile{#1}[\pgfversiondate\space v\pgfversion\space(\pgfrevision)]% +} + +\def\pgf@remove@ext#1.#2\relax{% + \def\pgfretval{#1}% +}% + +\def\ProvidesPackageRCS{% + \let\pgfrcs@final=\ProvidesPackageRCS@ + \pgfrcs@parseinput +} +\def\ProvidesPackageRCS@#1{% + \pgf@remove@ext#1.\relax + \edef\pgfrcs@marshal{{\pgfretval}[\pgfversiondate\space v\pgfversion\space(\pgfrevision)]}% + \expandafter\ProvidesPackage\pgfrcs@marshal +} + +\def\ProvidesClassRCS{% + \let\pgfrcs@final=\ProvidesClassRCS@ + \pgfrcs@parseinput +} +\def\ProvidesClassRCS@#1{% + \pgf@remove@ext#1.\relax + \edef\pgfrcs@marshal{{\pgfretval}[\pgfversiondate\space v\pgfversion\space(\pgfrevision)]}% + \expandafter\ProvidesClass\pgfrcs@marshal +} + +\def\pgfrcs@parseinput@bracket{[}% +\def\pgfrcs@parseinput@dollarsign{$}% + +\def\pgfrcs@parseinput#1{% + \def\pgfrcs@parseinput@{#1}% + \ifx\pgfrcs@parseinput@\pgfrcs@parseinput@bracket% + \let\next=\pgfrcs@parseinput@opt + \else + \ifx\pgfrcs@parseinput@\pgfrcs@parseinput@dollarsign + \let\next\pgfrcs@parseinput@dollar + \else + \def\next{\pgfrcs@final{#1}}% + \fi + \fi + \next +} +\def\pgfrcs@parseinput@opt#1] ${% + \pgfrcs@parseinput@dollar +}% +\def\pgfrcs@parseinput@dollar#1${% + \pgf@parseid $#1$% + \edef\pgfrcs@parseinput@{\pgf@rcsfile.\pgf@rcssuffix}% + \expandafter\pgfrcs@final\expandafter{\pgfrcs@parseinput@}% +}% +\def\pgf@parseid $#1: #2.#3,v #4 #5/#6/#7 #8${% + \pgf@parsercsfile$#2/$ + \def\pgf@rcssuffix{#3} + \def\pgf@rcsrevision{#4} + \def\pgf@rcsdate{#5/#6/#7} +} +\def\pgf@parsercsfile$#1/#2${ + \def\pgf@temp{#2} + \ifx\pgf@temp\pgfutil@empty + \def\pgf@rcsfile{#1} + \else + \pgf@parsercsfile$#2$ + \fi} + + +\ifx\ProvidesPackage\@undefined + \def\ProvidesPackage#1[#2]{\wlog{Loading package #1 version #2.}} +\fi + +\ifx\ProvidesFile\@undefined + \def\ProvidesFile#1[#2]{\wlog{Loading file #1 version #2.}} +\fi + +\ProvidesPackageRCS{pgfrcs.code.tex} + +\catcode`\@=\pgfrcsatcode + +\fi + + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfutil-common-lists.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfutil-common-lists.tex new file mode 100644 index 0000000000000000000000000000000000000000..7776abe78a7b397bcccbc8dac2a53c8523057a5e --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfutil-common-lists.tex @@ -0,0 +1,129 @@ + + +\pgfutil@packagewarning + {pgfutil-common-lists}% + {This package is deprecated and will be removed by the end of 2022} + +\def\pgfapplistnewempty#1{% + \expandafter\let\csname pgfapp@#1\endcsname=\pgfutil@empty + \expandafter\let\csname pgfapp@#1@smallbuf\endcsname=\pgfutil@empty + \expandafter\let\csname pgfapp@#1@bigbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfapp@#1@smallbuf@c\endcsname{0}% + \expandafter\def\csname pgfapp@#1@bigbuf@c\endcsname{0}% +}% + +\long\def\pgfapplistpushback#1\to#2{% + \begingroup + \c@pgf@counta=\csname pgfapp@#2@smallbuf@c\endcsname\relax + \advance\c@pgf@counta by1 + \xdef\pgf@glob@TMPa{\the\c@pgf@counta}% + \endgroup + \expandafter\let\csname pgfapp@#2@smallbuf@c\endcsname=\pgf@glob@TMPa + \ifnum\csname pgfapp@#2@smallbuf@c\endcsname<40 + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfapp@#2@smallbuf\endcsname#1}% + \expandafter\edef\csname pgfapp@#2@smallbuf\endcsname{\the\t@pgf@toka}% + \else + \pgfapplistpushback@smallbufoverfl{#1}{#2}% + \fi +}% +\long\def\pgfapplistpushback@smallbufoverfl#1#2{% + \begingroup + \c@pgf@counta=\csname pgfapp@#2@bigbuf@c\endcsname\relax + \advance\c@pgf@counta by1 + \xdef\pgf@glob@TMPa{\the\c@pgf@counta}% + \endgroup + \expandafter\let\csname pgfapp@#2@bigbuf@c\endcsname=\pgf@glob@TMPa + \ifnum\csname pgfapp@#2@bigbuf@c\endcsname<30 + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfapp@#2@bigbuf\endcsname}% + \t@pgf@tokb=\expandafter\expandafter\expandafter{\csname pgfapp@#2@smallbuf\endcsname#1}% + \expandafter\edef\csname pgfapp@#2@bigbuf\endcsname{\the\t@pgf@toka\the\t@pgf@tokb}% + \expandafter\let\csname pgfapp@#2@smallbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfapp@#2@smallbuf@c\endcsname{0}% + \else% + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfapp@#2\endcsname}% + \t@pgf@tokb=\expandafter\expandafter\expandafter{\csname pgfapp@#2@bigbuf\endcsname}% + \t@pgf@tokc=\expandafter\expandafter\expandafter{\csname pgfapp@#2@smallbuf\endcsname#1}% + \expandafter\edef\csname pgfapp@#2\endcsname{\the\t@pgf@toka\the\t@pgf@tokb\the\t@pgf@tokc}% + \expandafter\let\csname pgfapp@#2@smallbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfapp@#2@smallbuf@c\endcsname{0}% + \expandafter\let\csname pgfapp@#2@bigbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfapp@#2@bigbuf@c\endcsname{0}% + \fi% +}% +\def\pgfapplist@flushbuffers#1{% + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfapp@#1\endcsname}% + \t@pgf@tokb=\expandafter\expandafter\expandafter{\csname pgfapp@#1@bigbuf\endcsname}% + \t@pgf@tokc=\expandafter\expandafter\expandafter{\csname pgfapp@#1@smallbuf\endcsname}% + \expandafter\edef\csname pgfapp@#1\endcsname{\the\t@pgf@toka\the\t@pgf@tokb\the\t@pgf@tokc}% + \expandafter\let\csname pgfapp@#1@smallbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfapp@#1@smallbuf@c\endcsname{0}% + \expandafter\let\csname pgfapp@#1@bigbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfapp@#1@bigbuf@c\endcsname{0}% +}% + +\def\pgfapplistlet#1=#2{% + \pgfapplist@flushbuffers{#2}% + \expandafter\let\expandafter#1\csname pgfapp@#2\endcsname +}% + + + + +\def\pgfprependlistnewempty#1{% + \expandafter\let\csname pgfpPRP@#1\endcsname=\pgfutil@empty + \expandafter\let\csname pgfpPRP@#1@smallbuf\endcsname=\pgfutil@empty + \expandafter\let\csname pgfpPRP@#1@bigbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfpPRP@#1@smallbuf@c\endcsname{0}% + \expandafter\def\csname pgfpPRP@#1@bigbuf@c\endcsname{0}% +}% + +\long\def\pgfprependlistpushfront#1\to#2{% + \begingroup + \c@pgf@counta=\csname pgfpPRP@#2@smallbuf@c\endcsname\relax + \advance\c@pgf@counta by1 + \xdef\pgf@glob@TMPa{\the\c@pgf@counta}% + \endgroup + \expandafter\let\csname pgfpPRP@#2@smallbuf@c\endcsname=\pgf@glob@TMPa + \ifnum\csname pgfpPRP@#2@smallbuf@c\endcsname<40 + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfpPRP@#2@smallbuf\endcsname}% + \t@pgf@tokb={#1}% + \expandafter\edef\csname pgfpPRP@#2@smallbuf\endcsname{\the\t@pgf@tokb\the\t@pgf@toka}% + \else + \pgfprependlistpushfront@smallbufoverfl{#1}{#2}% + \fi +}% +\long\def\pgfprependlistpushfront@smallbufoverfl#1#2{% + \begingroup + \c@pgf@counta=\csname pgfpPRP@#2@bigbuf@c\endcsname\relax + \advance\c@pgf@counta by1 + \xdef\pgf@glob@TMPa{\the\c@pgf@counta}% + \endgroup + \expandafter\let\csname pgfpPRP@#2@bigbuf@c\endcsname=\pgf@glob@TMPa + \ifnum\csname pgfpPRP@#2@bigbuf@c\endcsname<30 + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfpPRP@#2@bigbuf\endcsname}% + \t@pgf@tokb=\expandafter\expandafter\expandafter{\csname pgfpPRP@#2@smallbuf\endcsname}% + \t@pgf@tokc={#1}% + \expandafter\edef\csname pgfpPRP@#2@bigbuf\endcsname{\the\t@pgf@tokc\the\t@pgf@tokb\the\t@pgf@toka}% + \expandafter\let\csname pgfpPRP@#2@smallbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfpPRP@#2@smallbuf@c\endcsname{0}% + \else% + \pgfprependlist@flushbuffers{#2}% + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfpPRP@#2\endcsname}% + \t@pgf@tokb={#1}% + \expandafter\edef\csname pgfpPRP@#2\endcsname{\the\t@pgf@tokb\the\t@pgf@toka}% + \fi% +}% +\def\pgfprependlist@flushbuffers#1{% + \t@pgf@toka=\expandafter\expandafter\expandafter{\csname pgfpPRP@#1\endcsname}% + \t@pgf@tokb=\expandafter\expandafter\expandafter{\csname pgfpPRP@#1@bigbuf\endcsname}% + \t@pgf@tokc=\expandafter\expandafter\expandafter{\csname pgfpPRP@#1@smallbuf\endcsname}% + \expandafter\edef\csname pgfpPRP@#1\endcsname{\the\t@pgf@tokc\the\t@pgf@tokb\the\t@pgf@toka}% + \expandafter\let\csname pgfpPRP@#1@smallbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfpPRP@#1@smallbuf@c\endcsname{0}% + \expandafter\let\csname pgfpPRP@#1@bigbuf\endcsname=\pgfutil@empty + \expandafter\def\csname pgfpPRP@#1@bigbuf@c\endcsname{0}% +}% +\def\pgfprependlistlet#1=#2{% + \pgfprependlist@flushbuffers{#2}% + \expandafter\let\expandafter#1\csname pgfpPRP@#2\endcsname +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfutil-common.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfutil-common.tex new file mode 100644 index 0000000000000000000000000000000000000000..4ed7e7b5016d6446913e213b2cc86b64c0510a0d --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/generic/pgf/utilities/pgfutil-common.tex @@ -0,0 +1,623 @@ + + + + + +\catcode`\@=11\relax + + +\newif\ifpgfutil@format@is@latex +\newif\ifpgfutil@format@is@plain +\newif\ifpgfutil@format@is@context + + +\let\pgfutil@exp\romannumeral +\chardef\pgfutil@exp@end=0 + + +\catcode`\Q=3 +\def\pgfutil@trimspaces#1{% + \romannumeral-`0\pgfutil@trimspaces@\noexpand#1Q Q} +\def\pgfutil@trimspaces@#1 Q{\pgfutil@trimspaces@@#1Q} +\def\pgfutil@trimspaces@@#1Q#2{#1} +\catcode`\Q=11 + +\long\def\pgfutil@ifx#1#2{% + \ifx#1#2% + \expandafter\pgfutil@firstoftwo + \else + \expandafter\pgfutil@secondoftwo + \fi} + +\long\def\pgfutil@ifstrequal#1#2{% + \ifnum\pgfsys@strcmp{\pgfutil@unexpanded{#1}}{\pgfutil@unexpanded{#2}}=0 + \expandafter\pgfutil@firstoftwo + \else + \expandafter\pgfutil@secondoftwo + \fi +} + +\def\pgfutil@ifxempty{\pgfutil@ifx\pgfutil@empty} + +\long\def\pgfutil@ifempty#1{% + \if\relax\detokenize{#1}\relax + \expandafter\pgfutil@firstoftwo + \else + \expandafter\pgfutil@secondoftwo + \fi} + +\def\pgfutil@ifundefined#1{% + \expandafter\pgfutil@ifx\csname#1\endcsname\relax} + +\def\pgfutil@IfUndefined#1{% + \ifcsname#1\endcsname + \expandafter\pgfutil@secondoftwo + \else + \expandafter\pgfutil@firstoftwo + \fi +} + +\long\def\pgfutil@firstofone#1{#1} +\long\def\pgfutil@firstoftwo#1#2{#1} +\long\def\pgfutil@secondoftwo#1#2{#2} +\def\pgfutil@empty{} +\long\def\pgfutil@gobble@until@relax#1\relax{} +\long\def\pgfutil@gobble#1{} +\long\def\pgfutil@gobbletwo#1#2{} +\def\pgfutil@namedef#1{\expandafter\def\csname #1\endcsname} +\def\pgfutil@namelet#1{\expandafter\pgfutil@@namelet\csname#1\endcsname} +\def\pgfutil@@namelet#1#2{\expandafter\let\expandafter#1\csname#2\endcsname} +\long\def\pgfutil@g@addto@macro#1#2{% + \begingroup + \pgfutil@toks@\expandafter{#1#2}% + \xdef#1{\the\pgfutil@toks@}% + \endgroup} +\newif\ifpgfutil@tempswa +\newif\ifpgfutil@tempswb + + +\let\pgfutil@pushmacro@string\pgfutil@empty + +\def\pgfutil@pushmacro#1{% + \xdef\pgfutil@pushmacro@string{\string#1}% + \ifcsname pgfutil@pushedmacro@\pgfutil@pushmacro@string\endcsname\else + \csname newcount\expandafter\endcsname\csname pgfutil@pushedmacro@\pgfutil@pushmacro@string\endcsname + \fi + \global\advance\csname pgfutil@pushedmacro@\pgfutil@pushmacro@string\endcsname 1\relax + \global\expandafter\let\csname\the\csname pgfutil@pushedmacro@\pgfutil@pushmacro@string\endcsname\pgfutil@pushmacro@string\endcsname#1% +} + +\def\pgfutil@popmacro#1{% + \xdef\pgfutil@pushmacro@string{\string#1}% + \expandafter\let\expandafter#1\csname\the\csname pgfutil@pushedmacro@\pgfutil@pushmacro@string\endcsname\pgfutil@pushmacro@string\endcsname + \global\advance\csname pgfutil@pushedmacro@\pgfutil@pushmacro@string\endcsname -1\relax +} + + +\long\def\pgfutil@ifnextchar#1#2#3{% + \let\pgfutil@reserved@d=#1% + \def\pgfutil@reserved@a{#2}% + \def\pgfutil@reserved@b{#3}% + \futurelet\pgfutil@let@token\pgfutil@ifnch} +\def\pgfutil@ifnch{% + \ifx\pgfutil@let@token\pgfutil@sptoken + \let\pgfutil@reserved@c\pgfutil@xifnch + \else + \ifx\pgfutil@let@token\pgfutil@reserved@d + \let\pgfutil@reserved@c\pgfutil@reserved@a + \else + \let\pgfutil@reserved@c\pgfutil@reserved@b + \fi + \fi + \pgfutil@reserved@c} +{% + \def\:{\global\let\pgfutil@sptoken= } \: + \def\:{\pgfutil@xifnch} \expandafter\gdef\: {\futurelet\pgfutil@let@token\pgfutil@ifnch} +} + + +\def\pgfutil@ignorespaces + {\ifx\pgfutil@let@token\pgfutil@sptoken + \expandafter\pgfutil@ignorespaces@helper + \else + \expandafter\pgfutil@next + \fi} + +{ + \def\:{\pgfutil@ignorespaces@helper} + \expandafter\gdef\: {\futurelet\pgfutil@let@token\pgfutil@ignorespaces} +} + + +\newif\ifpgfutil@in@ + +\def\pgfutil@in@#1#2{% + \def\pgfutil@in@@##1#1##2##3\pgfutil@in@@{% + \ifx\pgfutil@in@##2\pgfutil@in@false\else\pgfutil@in@true\fi}% + \pgfutil@in@@#2#1\pgfutil@in@\pgfutil@in@@} + + + +\def\pgfutil@nnil{\pgfutil@nil} +\def\pgfutil@fornoop#1\@@#2#3{} +\long\def\pgfutil@for#1:=#2\do#3{% + \expandafter\def\expandafter\pgfutil@fortmp\expandafter{#2}% + \ifx\pgfutil@fortmp\pgfutil@empty \else + \expandafter\pgfutil@forloop#2,\pgfutil@nil,\pgfutil@nil\@@#1{#3}\fi} +\long\def\pgfutil@forloop#1,#2,#3\@@#4#5{\def#4{#1}\ifx #4\pgfutil@nnil \else + #5\def#4{#2}\ifx #4\pgfutil@nnil \else#5\pgfutil@iforloop #3\@@#4{#5}\fi\fi} +\long\def\pgfutil@iforloop#1,#2\@@#3#4{\def#3{#1}\ifx #3\pgfutil@nnil + \expandafter\pgfutil@fornoop \else + #4\relax\expandafter\pgfutil@iforloop\fi#2\@@#3{#4}} +\def\pgfutil@tfor#1:={\pgfutil@tf@r#1 } +\long\def\pgfutil@tf@r#1#2\do#3{\def\pgfutil@fortmp{#2}\ifx\pgfutil@fortmp\pgfutil@space\else + \pgfutil@tforloop#2\pgfutil@nil\pgfutil@nil\@@#1{#3}\fi} +\long\def\pgfutil@tforloop#1#2\@@#3#4{\def#3{#1}\ifx #3\pgfutil@nnil + \expandafter\pgfutil@fornoop \else + #4\relax\expandafter\pgfutil@tforloop\fi#2\@@#3{#4}} + +\def\pgfutil@space{ } + + +\chardef\pgfutil@inputcheck0 +\def\pgfutil@IfFileExists#1#2#3{% + \openin\pgfutil@inputcheck=#1 % + \ifeof\pgfutil@inputcheck + #3\relax + \else + #2\relax + \fi + \closein\pgfutil@inputcheck} + +\def\pgfutil@InputIfFileExists#1#2#3{\pgfutil@IfFileExists{#1}{\input #1\relax#2}{#3}}% + + + +\def\pgfutil@loop#1\pgfutil@repeat{\def\pgfutil@body{#1}\pgfutil@iterate} +\def\pgfutil@iterate{\pgfutil@body \let\pgfutil@next\pgfutil@iterate \else\let\pgfutil@next\relax\fi \pgfutil@next} +\let\pgfutil@repeat=\fi % + + +\let\pgfutil@scan@mark\relax +\let\pgfutil@scan@stop\relax + +\long\def\pgfutil@switch#1#2#3#4#5{% + \pgfutil@exp + \pgfutil@switch@@{#1}% + {#2}#3% + {#2}{}% + \pgfutil@scan@mark{#4}% + \pgfutil@scan@mark{#5}% + \pgfutil@scan@stop +} +\long\def\pgfutil@switch@@#1#2#3#4{% + #1{#2}{#3}% + {\pgfutil@switch@end{#4}}% + {\pgfutil@switch@@{#1}{#2}}% +} +\long\def\pgfutil@switch@end#1#2#3\pgfutil@scan@mark#4#5\pgfutil@scan@stop{\pgfutil@exp@end#1#4} + + +\let\pgfutil@aux@read@hook=\relax + + + +\newtoks\pgfutil@everybye + + + + +\def\pgfutil@addpdfresource@extgs#1{\pgf@sys@addpdfresource@extgs@plain{#1}} +\def\pgfutil@addpdfresource@colorspaces#1{\pgf@sys@addpdfresource@colorspaces@plain{#1}} +\def\pgfutil@addpdfresource@patterns#1{\pgf@sys@addpdfresource@patterns@plain{#1}} +\def\pgfutil@setuppdfresources{\pgf@sys@setuppdfresources@plain} + + + +\let\pgfutil@insertatbegincurrentpage=\relax + + + +\def\pgfutil@raggedright{\rightskip\z@ plus2em \spaceskip.3333em \xspaceskip.5em\relax} +\def\pgfutil@raggedleft{\leftskip\z@ plus2em \rightskip\z@ \spaceskip.3333em \xspaceskip.5em\parfillskip0pt\relax} + + +\def\pgfutil@packageerror#1#2#3{\errhelp{#3}\errmessage{Package #1 Error: #2}} +\def\pgfutil@packagewarning#1#2{\immediate\write17{Package #1: Warning! #2.}} +\def\pgferror#1{\pgfutil@packageerror{pgf}{#1}{}} +\def\pgfwarning#1{\pgfutil@packagewarning{pgf}{#1}} + + + + + +\def\usepgflibrary{\pgfutil@ifnextchar[{\use@pgflibrary}{\use@@pgflibrary}}% +\def\use@pgflibrary[#1]{\use@@pgflibrary{#1}} +\def\use@@pgflibrary#1{% + \edef\pgf@list{#1}% + \pgfutil@for\pgf@temp:=\pgf@list\do{% + \expandafter\pgfkeys@spdef\expandafter\pgf@temp\expandafter{\pgf@temp}% + \ifx\pgf@temp\pgfutil@empty + \else + \expandafter\ifx\csname pgf@library@\pgf@temp @loaded\endcsname\relax% + \expandafter\let\csname pgf@library@\pgf@temp @loaded\endcsname=\pgfutil@empty% + \expandafter\edef\csname pgf@library@#1@atcode\endcsname{\the\catcode`\@} + \expandafter\edef\csname pgf@library@#1@barcode\endcsname{\the\catcode`\|} + \expandafter\edef\csname pgf@library@#1@dollarcode\endcsname{\the\catcode`\$} + \catcode`\@=11 + \catcode`\|=12 + \catcode`\$=3 + \pgfutil@InputIfFileExists{pgflibrary\pgf@temp.code.tex}{}{% + \pgferror{I did not find the pgf library + '\pgf@temp'. I looked for the file named + pgflibrary\pgf@temp.code.tex, but could not find it in + the current texmf trees.} + }% + \catcode`\@=\csname pgf@library@#1@atcode\endcsname + \catcode`\|=\csname pgf@library@#1@barcode\endcsname + \catcode`\$=\csname pgf@library@#1@dollarcode\endcsname + \fi% + \fi + }% +} + + + +\def\usepgfmodule{\pgfutil@ifnextchar[{\use@pgfmodule}{\use@@pgfmodule}}% +\def\use@pgfmodule[#1]{\use@@pgfmodule{#1}} +\def\use@@pgfmodule#1{% + \edef\pgf@list{#1}% + \pgfutil@for\pgf@temp:=\pgf@list\do{% + \expandafter\ifx\csname pgf@module@\pgf@temp @loaded\endcsname\relax% + \expandafter\let\csname pgf@module@\pgf@temp @loaded\endcsname=\pgfutil@empty% + \expandafter\edef\csname pgf@module@#1@atcode\endcsname{\the\catcode`\@} + \expandafter\edef\csname pgf@module@#1@barcode\endcsname{\the\catcode`\|} + \expandafter\edef\csname pgf@module@#1@dollarcode\endcsname{\the\catcode`\$} + \catcode`\@=11 + \catcode`\|=12 + \catcode`\$=3 + \input pgfmodule\pgf@temp.code.tex + \catcode`\@=\csname pgf@module@#1@atcode\endcsname + \catcode`\|=\csname pgf@module@#1@barcode\endcsname + \catcode`\$=\csname pgf@module@#1@dollarcode\endcsname + \fi% + }% +} + +\def\pgfutilensuremath#1{% + \ifmmode#1\else$#1$\fi +} + + + +\begingroup + \catcode`\"=12 + \edef\pgf@loc@TMPa{"}% + \gdef\pgfutilpreparefilename#1{% + \begingroup + \ifnum\the\catcode`\"=13 + \pgfutilconvertdcolon + \fi + \xdef\pgf@temp{#1}% + \endgroup + \expandafter\pgfutil@in@\expandafter"\expandafter{\pgf@temp}% + \ifpgfutil@in@ + \def\pgf@loc@TMPa{\pgfutilstrreplace{"}{}}% + \expandafter\pgf@loc@TMPa\expandafter{\pgf@temp}% + \edef\pgfretval{"\pgfretval"}% + \let\pgfretvalquoted=\pgfretval + \else + \let\pgfretval=\pgf@temp + \edef\pgfretvalquoted{"\pgfretval"}% + \fi + }% + \catcode`\"=13 + \xdef\pgfutilconvertdcolon{% + \noexpand\def\noexpand"{\pgf@loc@TMPa}% + }% +\endgroup + +\def\pgfutil@command@to@string#1#2{% + \expandafter\pgfutil@command@to@string@@\meaning#1\pgfutil@EOI{#2}% +}% +\xdef\pgfutil@glob@TMPa{\meaning\pgfutil@empty}% +\expandafter\def\expandafter\pgfutil@command@to@string@@\pgfutil@glob@TMPa#1\pgfutil@EOI#2{% + \def#2{#1}% +}% +\begingroup +\catcode`\|=0 +\catcode`\\=12 +|gdef|pgfutil@backslash@as@other{\}% +|endgroup + +\def\pgfutilifcontainsmacro#1#2#3{% + \def\pgf@marshal{#1}% + \pgfutil@command@to@string\pgf@marshal\pgf@marshal + \edef\pgf@marshal{\noexpand\pgfutil@in@{\pgfutil@backslash@as@other}{\pgf@marshal}}% + \pgf@marshal + \ifpgfutil@in@ + \def\pgf@marshal{#2}% + \else + \def\pgf@marshal{#3}% + \fi + \pgf@marshal +}% + +\def\pgfutilifstartswith#1#2#3#4{% + \def\pgfutilifstartswith@ ##1#1##2\pgf@EOI{% + \def\pgfutil@tmp{##1}% + \ifx\pgfutil@tmp\pgfutil@empty + \def\pgfutil@tmp#1####1\pgf@EOI{% + \def\pgfretval{####1}% + }% + \pgfutil@tmp#2\pgf@EOI% + #3\relax% + \else + #4\relax% + \fi + }% + \pgfutilifstartswith@#2--#1\pgf@EOI% +}% + +\long\def\pgfutilstrreplace#1#2#3{% + \def\pgfretval{}% + \long\def\pgfutil@search@and@replace@@##1#1##2\pgf@EOI{% + \expandafter\def\expandafter\pgfretval\expandafter{\pgfretval ##1#2}% + \pgfutil@search@and@replace@loop{#1}{##2}% + }% + \pgfutil@search@and@replace@loop{#1}{#3}% +} +\long\def\pgfutil@search@and@replace@loop#1#2{% + \pgfutil@in@{#1}{#2}% + \ifpgfutil@in@ + \def\pgf@loc@TMPa{\pgfutil@search@and@replace@@ #2\pgf@EOI}% + \else + \expandafter\def\expandafter\pgfretval\expandafter{\pgfretval #2}% + \let\pgf@loc@TMPa=\relax + \fi + \pgf@loc@TMPa +}% + +\def\pgfutilsolvetwotwoleq#1#2{% + \begingroup + \dimendef\aa=0 + \dimendef\ab=1 + \dimendef\ba=2 + \dimendef\bb=3 + \dimendef\ra=4 + \dimendef\rb=5 + \dimendef\tmpa=6 + \dimendef\tmpb=7 + \edef\pgf@temp{#1}% + \expandafter\pgfutilsolvetwotwoleq@A\pgf@temp + \edef\pgf@temp{#2}% + \expandafter\pgfutilsolvetwotwoleq@r\pgf@temp + \pgfutilsolvetwotwoleq@ifislarger\aa\ba{% + \def\Pa{a}% + \def\Pb{b}% + }{% + \def\Pa{b}% + \def\Pb{a}% + }% + \tmpa=\csname m\Pa a\endcsname pt % + \ifdim\tmpa<0pt \tmpa=-\tmpa\fi + \ifdim\tmpa<0.0001pt + \let\pgfmathresult=\pgfutil@empty + \else + \pgfmathreciprocal@ + {\csname m\Pa a\endcsname}% + \let\pivot=\pgfmathresult + \csname \Pb a\endcsname=\pivot\csname \Pb a\endcsname + \edef\factor{\expandafter\pgf@sys@tonumber\csname \Pb a\endcsname}% + \tmpa=-\factor\csname \Pa b\endcsname + \advance\csname \Pb b\endcsname by\tmpa + \tmpa=-\factor\csname r\Pa\endcsname + \advance\csname r\Pb\endcsname by\tmpa + \tmpa=\csname \Pb b\endcsname% + \ifdim\tmpa<0pt \tmpa=-\tmpa\fi + \ifdim\tmpa<0.0001pt + \let\pgfmathresult=\pgfutil@empty + \else + \pgfmathdivide@ + {\expandafter\pgf@sys@tonumber\csname r\Pb\endcsname} + {\expandafter\pgf@sys@tonumber\csname \Pb b\endcsname}% + \expandafter\let\csname pgfmathresult\Pb\endcsname=\pgfmathresult + \tmpa=\csname pgfmathresult\Pb\endcsname\csname \Pa b\endcsname + \advance\csname r\Pa\endcsname by-\tmpa + \tmpa=\pivot\csname r\Pa\endcsname + \expandafter\edef\csname pgfmathresult\Pa\endcsname{\pgf@sys@tonumber\tmpa}% + \edef\pgfmathresult{% + {\csname pgfmathresult\Pa\endcsname}% + {\csname pgfmathresult\Pb\endcsname}% + }% + \fi + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + +\def\pgfutilsolvetwotwoleq@ifislarger#1#2#3#4{% + \tmpa=#1 + \ifdim\tmpa<0pt + \multiply\tmpa by-1 + \fi + \tmpb=#2 + \ifdim\tmpb<0pt + \multiply\tmpb by-1 + \fi + \ifdim\tmpa>\tmpb + #3% + \else + #4% + \fi +}% + +\def\pgfutilsolvetwotwoleqfloat@ifislarger#1#2#3#4{% + \pgfmathfloatabs@{#1}\let\tmpa=\pgfmathresult + \pgfmathfloatabs@{#2}\let\tmpb=\pgfmathresult + \pgfmathfloatlessthan@{\tmpb}{\tmpa}% + \ifpgfmathfloatcomparison + #3% + \else + #4% + \fi +}% +\def\pgfutilsolvetwotwoleq@A#1#2#3#4{% + \def\maa{#1}\def\mab{#2}% + \def\mba{#3}\def\mbb{#3}% + \aa=#1pt \ab=#2pt + \ba=#3pt \bb=#4pt +} +\def\pgfutilsolvetwotwoleq@r#1#2{% + \ra=#1pt \rb=#2pt +}% +\def\pgfutilsolvetwotwoleqfloat@A#1#2#3#4{% + \pgfmathfloatparsenumber{#1}\let\maa=\pgfmathresult + \pgfmathfloatparsenumber{#2}\let\mab=\pgfmathresult + \pgfmathfloatparsenumber{#3}\let\mba=\pgfmathresult + \pgfmathfloatparsenumber{#4}\let\mbb=\pgfmathresult +} +\def\pgfutilsolvetwotwoleqfloat@r#1#2{% + \pgfmathfloatparsenumber{#1}\let\ra=\pgfmathresult + \pgfmathfloatparsenumber{#2}\let\rb=\pgfmathresult +}% + +\def\pgfutilsolvetwotwoleqfloat#1#2{% + \begingroup + \pgfmathfloatcreate{1}{1.0}{-4}% + \let\thresh=\pgfmathresult + \edef\pgf@temp{#1}% + \expandafter\pgfutilsolvetwotwoleqfloat@A\pgf@temp + \edef\pgf@temp{#2}% + \expandafter\pgfutilsolvetwotwoleqfloat@r\pgf@temp + \pgfutilsolvetwotwoleqfloat@ifislarger\maa\mba{% + \def\Pa{a}% + \def\Pb{b}% + }{% + \def\Pa{b}% + \def\Pb{a}% + }% + \expandafter\pgfmathfloatabs@\expandafter{\csname m\Pa a\endcsname}% + \let\tmpa=\pgfmathresult + \pgfmathfloatlessthan@{\tmpa}{\thresh}% + \ifpgfmathfloatcomparison + \let\pgfmathresult=\pgfutil@empty + \else + \expandafter\pgfmathfloatreciprocal@\expandafter{\csname m\Pa a\endcsname}% + \let\pivot=\pgfmathresult + \expandafter\pgfmathfloatmultiply@\expandafter{\csname m\Pb a\endcsname}{\pivot}% + \let\factor=\pgfmathresult + \expandafter\let\csname m\Pb a\endcsname=\factor + \expandafter\pgfmathfloatmultiply@\expandafter{\csname m\Pa b\endcsname}{\factor}% + \let\tmpa=\pgfmathresult + \expandafter\pgfmathfloatsubtract@\expandafter{\csname m\Pb b\endcsname}{\tmpa}% + \expandafter\let\csname m\Pb b\endcsname=\pgfmathresult + \expandafter\pgfmathfloatmultiply@\expandafter{\csname r\Pa\endcsname}{\factor}% + \let\tmpa=\pgfmathresult + \expandafter\pgfmathfloatsubtract@\expandafter{\csname r\Pb\endcsname}{\tmpa}% + \expandafter\let\csname r\Pb\endcsname=\pgfmathresult + \expandafter\pgfmathfloatabs@\expandafter{\csname m\Pb b\endcsname}% + \let\tmpa=\pgfmathresult + \pgfmathfloatlessthan@{\tmpa}{\thresh}% + \ifpgfmathfloatcomparison + \let\pgfmathresult=\pgfutil@empty + \else + \edef\pgf@marshal{% + \noexpand\pgfmathfloatdivide@ + {\csname r\Pb\endcsname} + {\csname m\Pb b\endcsname}% + }% + \pgf@marshal + \expandafter\let\csname pgfmathresult\Pb\endcsname=\pgfmathresult + \let\tmpa=\pgfmathresult + \expandafter\pgfmathfloatmultiply@\expandafter{\csname m\Pa b\endcsname}{\tmpa}% + \let\tmpa=\pgfmathresult + \expandafter\pgfmathfloatsubtract@\expandafter{\csname r\Pa\endcsname}{\tmpa}% + \expandafter\let\csname r\Pa\endcsname=\pgfmathresult + \expandafter\pgfmathfloatmultiply@\expandafter{\csname r\Pa\endcsname}{\pivot}% + \expandafter\let\csname pgfmathresult\Pa\endcsname=\pgfmathresult + \edef\pgfmathresult{% + {\csname pgfmathresult\Pa\endcsname}% + {\csname pgfmathresult\Pb\endcsname}% + }% + \expandafter\pgfutilsolvetwotwoleqfloat@to@pgf@range\pgfmathresult + \fi + \fi + \pgfmath@smuggleone\pgfmathresult + \endgroup +}% + + +\def\pgfutilsolvetwotwoleqfloat@to@pgf@range#1#2{% + \pgfmathfloatcreate{1}{1.6}{4}\let\pgfutilsolvetwotwoleqfloat@to@pgf@range@max=\pgfmathresult + \pgfmathfloatabs@{#1}% + \expandafter\pgfmathfloatlessthan@\expandafter{\pgfmathresult}{\pgfutilsolvetwotwoleqfloat@to@pgf@range@max}% + \ifpgfmathfloatcomparison + \pgfmathfloatabs@{#2}% + \expandafter\pgfmathfloatlessthan@\expandafter{\pgfmathresult}{\pgfutilsolvetwotwoleqfloat@to@pgf@range@max}% + \ifpgfmathfloatcomparison + \pgfmathfloattofixed{#1}\let\tmpa=\pgfmathresult + \pgfmathfloattofixed{#2}% + \edef\pgfmathresult{{\tmpa}{\pgfmathresult}}% + \else + \let\pgfmathresult=\pgfutil@empty + \fi + \else + \let\pgfmathresult=\pgfutil@empty + \fi +}% + +\let\pgfutil@write=\write +\let\pgfutil@read=\read + +\let\pgfutil@protect\relax + +\def\pgfutil@check@rerun#1#2{} + +\newdimen\pgfutil@tempdima +\newdimen\pgfutil@tempdimb + + +\let\pgfutil@ifluatex\iffalse +\begingroup\expandafter\expandafter\expandafter\endgroup +\expandafter\ifx\csname directlua\endcsname\relax +\else + \expandafter\let\csname pgfutil@ifluatex\expandafter\endcsname + \csname iftrue\endcsname +\fi + +\pgfutil@ifluatex + \let\pgfutil@directlua\directlua + \pgfutil@directlua{% + tex.enableprimitives('pgfutil@',{'luaescapestring'})} +\else + \def\pgfutil@directlua#1{} + \def\pgfutil@luaescapestring#1{} +\fi + + +\def\pgfutil@shellescape@lua@eightseven#1{% + \pgfutil@directlua{os.execute("\pgfutil@luaescapestring{#1}")}% +}% +\def\pgfutil@shellescape#1{% + \immediate\write18{#1}% +}% +\pgfutil@IfUndefined{directlua}{% +}{% + \pgfutil@IfUndefined{lastsavedimageresourcepages}{% + }{% + \let\pgfutil@shellescape=\pgfutil@shellescape@lua@eightseven + }% +}% + + +\def\pgfutil@advancestringcounter#1{% + \begingroup + \c@pgf@counta=#1\relax + \advance\c@pgf@counta by1 + \edef#1{\the\c@pgf@counta}% + \pgfmath@smuggleone#1% + \endgroup +}% + +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual-en-macros.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual-en-macros.tex new file mode 100644 index 0000000000000000000000000000000000000000..3e61cac99549a466b5f09c7258122713fa440ff7 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual-en-macros.tex @@ -0,0 +1,1834 @@ + + + +\newcount\pgfmanualtargetcount + +\colorlet{examplefill}{yellow!80!black} +\definecolor{graphicbackground}{rgb}{0.96,0.96,0.8} +\definecolor{codebackground}{rgb}{0.9,0.9,1} +\definecolor{animationgraphicbackground}{rgb}{0.96,0.96,0.8} + +\newenvironment{pgfmanualentry}{\list{}{\leftmargin=2em\itemindent-\leftmargin\def\makelabel##1{\hss##1}}}{\endlist} +\newcounter{pgfmanualentry} +\newcommand\pgfmanualentryheadline[1]{% + \itemsep=0pt\parskip=0pt{\raggedright\item\refstepcounter{pgfmanualentry}\strut{#1}\par}\topsep=0pt} +\newcommand\pgfmanualbody{\parskip3pt} + +\let\origtexttt=\texttt +\def\texttt#1{{\def\textunderscore{\char`\_}\def\textbraceleft{\char`\{}\def\textbraceright{\char`\}}\origtexttt{#1}}} +\def\exclamationmarktext{!} +\def\atmarktext{@} + +{ + \catcode`\|=12 + \gdef\pgfmanualnormalbar{|} + \catcode`\|=13 + \AtBeginDocument{\gdef|{\ifmmode\pgfmanualnormalbar\else\expandafter\verb\expandafter|\fi}} +} + + + +\newenvironment{pgflayout}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \texttt{\string\pgfpagesuselayout\char`\{\declare{#1}\char`\}}\oarg{options}% + } + \index{#1@\protect\texttt{#1} layout}% + \index{Page layouts!#1@\protect\texttt{#1}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{sysanimateattribute}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \texttt{\string\pgfsysanimate\char`\{\declare{#1}\char`\}}% + } + \index{#1@\protect\texttt{#1} system layer animation attribute}% + \index{Animation attributes (system layer)!#1@\protect\texttt{#1}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{animateattribute}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \texttt{\string\pgfanimateattribute\char`\{\declare{#1}\char`\}\marg{options}}% + } + \index{#1@\protect\texttt{#1} basic layer animation attribute}% + \index{Animation attributes (basic layer)!#1@\protect\texttt{#1}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{tikzanimateattribute}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \foreach \attr in{#1} {\expandafter\pgfmanualpdflabel\expandafter{\attr}{}}% + \textbf{Animation attribute} \foreach \attr[count=\i] + in{#1}{{\ifnum\i>1 \textbf,\fi} \texttt{:\declare{\attr}}}% + } + \foreach\attr in{#1}{% + \edef\indexcall{% + \noexpand\index{\attr@\noexpand\protect\noexpand\texttt{\attr} animation attribute}% + \noexpand\index{Animation attributes!\attr@\noexpand\protect\noexpand\texttt{\attr}}% + }% + \indexcall% + }% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{command}[1]{ + \begin{pgfmanualentry} + \extractcommand#1\@@ + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\makeatletter + +\def\includeluadocumentationof#1{ + \directlua{require 'pgf.manual.DocumentParser'} + \directlua{pgf.manual.DocumentParser.include '#1'} +} + +\newenvironment{luageneric}[4]{ + \pgfmanualentry + \pgfmanualentryheadline{#4 \texttt{#1\declare{#2}}#3} + \index{#2@\protect\texttt{#2} (Lua)}% + \def\temp{#1} + \ifx\temp\pgfutil@empty\else + \index{#1@\protect\texttt{#1}!#2@\protect\texttt{#2} (Lua)}% + \fi + \pgfmanualbody +}{\endpgfmanualentry} + +\newenvironment{luatable}[3]{ + \medskip + \luageneric{#1}{#2}{ (declared in \texttt{#3})}{\textbf{Lua table}} +}{\endluageneric} + +\newenvironment{luafield}[1]{ + \pgfmanualentry + \pgfmanualentryheadline{Field \texttt{\declare{#1}}} + \pgfmanualbody +}{\endpgfmanualentry} + + +\newenvironment{lualibrary}[1]{ + \pgfmanualentry + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Graph Drawing Library} \texttt{\declare{#1}}% + } + \index{#1@\protect\texttt{#1} graph drawing library}% + \index{Libraries!#1@\protect\texttt{#1}}% + \index{Graph drawing libraries!#1@\protect\texttt{#1}}% + \vskip.25em + {\ttfamily\char`\\usegdlibrary\char`\{\declare{#1}\char`\}\space\space \char`\%\space\space \LaTeX\space and plain \TeX}\\ + {\ttfamily\char`\\usegdlibrary[\declare{#1}]\space \char`\%\space\space Con\TeX t}\smallskip\par + \pgfmanualbody +}{\endpgfmanualentry} + +\newenvironment{luadeclare}[4]{ + \pgfmanualentry + \def\manual@temp@default{#3}% + \def\manual@temp@initial{#4}% + \def\manual@temp@{#3#4}% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + {\ttfamily/graph + drawing/\declare{#1}\opt{=}}\opt{#2}\hfill% + \ifx\manual@temp@\pgfutil@empty\else% + (\ifx\manual@temp@default\pgfutil@empty\else% + default {\ttfamily #3}\ifx\manual@temp@initial\pgfutil@empty\else, \fi% + \fi% + \ifx\manual@temp@initial\pgfutil@empty\else% + initially {\ttfamily #4}% + \fi% + )\fi% + }% + \index{#1@\protect\texttt{#1} key}% + \pgfmanualbody + \gdef\myname{#1}% +}{\endpgfmanualentry} + +\newenvironment{luadeclarestyle}[4]{ + \pgfmanualentry + \def\manual@temp@para{#2}% + \def\manual@temp@default{#3}% + \def\manual@temp@initial{#4}% + \def\manual@temp@{#3#4}% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + {\ttfamily/graph drawing/\declare{#1}}\ifx\manual@temp@para\pgfutil@empty\else\opt{\texttt=}\opt{#2}\fi\hfill% + (style\ifx\manual@temp@\pgfutil@empty\else, % + \ifx\manual@temp@default\pgfutil@empty\else% + default {\ttfamily #3}\ifx\manual@temp@initial\pgfutil@empty\else, \fi% + \fi% + \ifx\manual@temp@initial\pgfutil@empty\else% + initially {\ttfamily #4}% + \fi% + \fi)% + }% + \index{#1@\protect\texttt{#1} key}% + \pgfmanualbody% + \gdef\myname{#1}% +}{\endpgfmanualentry} + +\newenvironment{luanamespace}[2]{ + \luageneric{#1}{#2}{}{\textbf{Lua namespace}} +}{\endluageneric} + +\newenvironment{luafiledescription}[1]{}{} + +\newenvironment{luacommand}[4]{ + \hypertarget{pgf/lua/#1}{\luageneric{#2}{#3}{\texttt{(#4)}}{\texttt{function}}} +}{\endluageneric} + +\newenvironment{luaparameters}{\par\emph{Parameters:}% + \parametercount=0\relax% + \let\item=\parameteritem% + \let\list=\restorelist% +} +{\par +} + +\newenvironment{luareturns}{\par\emph{Returns:}% + \parametercount=0\relax% + \let\item=\parameteritem% + \let\list=\restorelist% +} +{\par +} + +\newcount\parametercount + +\newenvironment{parameterdescription}{\unskip% + \parametercount=0\relax% + \let\item=\parameteritem% + \let\list=\restorelist% +} +{\par +} +\let\saveditemcommand=\item +\let\savedlistcommand=\list +\def\denselist#1#2{\savedlistcommand{#1}{#2}\parskip0pt\itemsep0pt} +\def\restorelist{\let\item=\saveditemcommand\denselist} +\def\parameteritem{\pgfutil@ifnextchar[\parameteritem@{}}% +\def\parameteritem@[#1]{\advance\parametercount by1\relax\hskip0.15em plus 1em\emph{\the\parametercount.}\kern1ex\def\test{#1}\ifx\test\pgfutil@empty\else#1\kern.5em\fi} + +\newenvironment{commandlist}[1]{% + \begin{pgfmanualentry} + \foreach \xx in {#1} {% + \expandafter\extractcommand\xx\@@ + }% + \pgfmanualbody +}{% + \end{pgfmanualentry} +}% + +\newenvironment{internallist}[2][register]{% + \begin{pgfmanualentry} + \foreach \xx in {#2} {% + \expandafter\extractinternalcommand\expandafter{\xx}{#1}% + }% + \pgfmanualbody +}{% + \end{pgfmanualentry} +}% +\def\extractinternalcommand#1#2{% + \removeats{#1}% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{\textbackslash\strippedat}{}% + Internal #2 \declare{\texttt{\string#1}}}% + \index{Internals!\strippedat @\protect\myprintocmmand{\strippedat}}% + \index{\strippedat @\protect\myprintocmmand{\strippedat}}% +} + +\def\mvar#1{{\ifmmode\textrm{\textit{#1}}\else\rmfamily\textit{#1}\fi}} + +\makeatletter + +\def\extractmathfunctionname#1{\extractmathfunctionname@#1(,)\tmpa\tmpb} +\def\extractmathfunctionname@#1(#2)#3\tmpb{\def\mathname{#1}} + +\makeatother + +\newenvironment{math-function}[1]{ + \def\mathdefaultname{#1} + \extractmathfunctionname{#1} + \edef\mathurl{{math:\mathname}}\expandafter\hypertarget\expandafter{\mathurl}{}% + \begin{pgfmanualentry} + \pgfmanualentryheadline{\texttt{#1}}% + \index{\mathname @\protect\texttt{\mathname} math function}% + \index{Math functions!\mathname @\protect\texttt{\mathname}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\pgfmanualemptytext{} +\def\pgfmanualvbarvbar{\char`\|\char`\|} + +\newenvironment{math-operator}[4][]{% + \begin{pgfmanualentry} + \csname math#3operator\endcsname{#2}{#4} + \def\mathtest{#4}% + \ifx\mathtest\pgfmanualemptytext% + \def\mathtype{(#3 operator)} + \else% + \def\mathtype{(#3 operator; uses the \texttt{#4} function)} + \fi% + \pgfmanualentryheadline{\mathexample\hfill\mathtype}% + \def\mathtest{#1}% + \ifx\mathtest\pgfmanualemptytext% + \index{#2@\protect\texttt{#2} #3 math operator}% + \index{Math operators!#2@\protect\texttt{#2}}% + \fi% + \pgfmanualbody +} +{\end{pgfmanualentry}} + +\newenvironment{math-operators}[5][]{% + \begin{pgfmanualentry} + \csname math#4operator\endcsname{#2}{#3} + \def\mathtest{#5}% + \ifx\mathtest\pgfmanualemptytext% + \def\mathtype{(#4 operators)} + \else% + \def\mathtype{(#4 operators; use the \texttt{#5} function)} + \fi% + \pgfmanualentryheadline{\mathexample\hfill\mathtype}% + \def\mathtest{#1}% + \ifx\mathtest\pgfmanualemptytext% + \index{#2#3@\protect\texttt{#2\protect\ #3} #4 math operators}% + \index{Math operators!#2#3@\protect\texttt{#2\protect\ #3}}% + \fi% + \pgfmanualbody +} +{\end{pgfmanualentry}} + +\def\mathinfixoperator#1#2{% + \def\mathoperator{\texttt{#1}}% + \def\mathexample{\mvar{x}\space\texttt{#1}\space\mvar{y}}% +} + +\def\mathprefixoperator#1#2{% + \def\mathoperator{\texttt{#1}}% + \def\mathexample{\texttt{#1}\mvar{x}}% +} + +\def\mathpostfixoperator#1#2{% + \def\mathoperator{\texttt{#1}} + \def\mathexample{\mvar{x}\texttt{#1}}% +} + +\def\mathgroupoperator#1#2{% + \def\mathoperator{\texttt{#1\ #2}}% + \def\mathexample{\texttt{#1}\mvar{x}\texttt{#2}}% +} + +\expandafter\let\csname matharray accessoperator\endcsname=\mathgroupoperator +\expandafter\let\csname matharrayoperator\endcsname=\mathgroupoperator + +\def\mathconditionaloperator#1#2{% + \def\mathoperator{#1\space#2} + \def\mathexample{\mvar{x}\ \texttt{#1}\ \mvar{y}\ {\texttt{#2}}\ \mvar{z}} +} + +\newcommand\mathcommand[1][\mathdefaultname]{% + \expandafter\makemathcommand#1(\empty)\stop% + \expandafter\extractcommand\mathcommandname\@@% + \medskip +} +\makeatletter + +\def\makemathcommand#1(#2)#3\stop{% + \expandafter\def\expandafter\mathcommandname\expandafter{\csname pgfmath#1\endcsname}% + \ifx#2\empty% + \else% + \@makemathcommand#2,\stop, + \fi} +\def\@makemathcommand#1,{% + \ifx#1\stop% + \else% + \expandafter\def\expandafter\mathcommandname\expandafter{\mathcommandname{\ttfamily\char`\{#1\char`\}}}% + \expandafter\@makemathcommand% + \fi} +\makeatother + +\def\calcname{\textsc{calc}} + +\newenvironment{math-keyword}[1]{ + \extracttikzmathkeyword#1@ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\texttt{\color{red}\mathname}\mathrest}% + \index{\mathname @\protect\texttt{\mathname} tikz math function}% + \index{TikZ math functions!\mathname @\protect\texttt{\mathname}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\extracttikzmathkeyword#1#2@{% + \def\mathname{#1}% + \def\mathrest{#2}% +} + + + +\def\extractcommand#1#2\@@{% + \removeats{#1}% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{\textbackslash\strippedat}{}% + \declare{\expandafter\texttt\expandafter{\string#1}}#2% + }% + \index{\strippedat @\protect\myprintocmmand{\strippedat}} +} + +\def\luaextractcommand#1#2\relax{% + \declare{\texttt{\string#1}}#2\par% +} + + +\renewenvironment{environment}[1]{ + \begin{pgfmanualentry} + \extractenvironement#1\@@ + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\extractenvironement#1#2\@@{% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + {\ttfamily\char`\\begin\char`\{\declare{#1}\char`\}}#2% + }% + \pgfmanualentryheadline{{\ttfamily\ \ }\meta{environment contents}}% + \pgfmanualentryheadline{{\ttfamily\char`\\end\char`\{\declare{#1}\char`\}}}% + \index{#1@\protect\texttt{#1} environment}% + \index{Environments!#1@\protect\texttt{#1}} +} + + +\newenvironment{plainenvironment}[1]{ + \begin{pgfmanualentry} + \extractplainenvironement#1\@@ + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\extractplainenvironement#1#2\@@{% + \pgfmanualentryheadline{{\ttfamily\declare{\char`\\#1}}#2}% + \pgfmanualentryheadline{{\ttfamily\ \ }\meta{environment contents}}% + \pgfmanualentryheadline{{\ttfamily\declare{\char`\\end#1}}}% + \index{#1@\protect\texttt{#1} environment}% + \index{Environments!#1@\protect\texttt{#1}}% +} + + +\newenvironment{contextenvironment}[1]{ + \begin{pgfmanualentry} + \extractcontextenvironement#1\@@ + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\extractcontextenvironement#1#2\@@{% + \pgfmanualentryheadline{{\ttfamily\declare{\char`\\start#1}}#2}% + \pgfmanualentryheadline{{\ttfamily\ \ }\meta{environment contents}}% + \pgfmanualentryheadline{{\ttfamily\declare{\char`\\stop#1}}}% + \index{#1@\protect\texttt{#1} environment}% + \index{Environments!#1@\protect\texttt{#1}}} + + +\newenvironment{shape}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Shape} {\ttfamily\declare{#1}}% + }% + \index{#1@\protect\texttt{#1} shape}% + \index{Shapes!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{pictype}[2]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Pic type} {\ttfamily\declare{#1}#2}% + }% + \index{#1@\protect\texttt{#1} pic type}% + \index{Pic Types!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{shading}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Shading} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} shading}% + \index{Shadings!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{graph}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Graph} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} graph}% + \index{Graphs!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{gdalgorithm}[2]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Layout} {\ttfamily/graph drawing/\declare{#1}\opt{=}}\opt{\meta{options}}}% + \index{#1@\protect\texttt{#1} layout}% + \index{Layouts!#1@\protect\texttt{#1}}% + \foreach \algo in {#2} + {\edef\marshal{\noexpand\index{#2@\noexpand\protect\noexpand\texttt{#2} algorithm}}\marshal}% + \index{Graph drawing layouts!#1@\protect\texttt{#1}} + \item{\small alias {\ttfamily/tikz/#1}}\par + \item{\small alias {\ttfamily/tikz/graphs/#1}}\par + \item{\small Employs {\ttfamily algorithm=#2}}\par + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{dataformat}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Format} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} format}% + \index{Formats!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{stylesheet}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Style sheet} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} style sheet}% + \index{Style sheets!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{handler}[1]{ + \begin{pgfmanualentry} + \extracthandler#1\@nil% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\gobble#1{} +\def\extracthandler#1#2\@nil{% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{/handlers/#1}{}% + \textbf{Key handler} \meta{key}{\ttfamily/\declare{#1}}#2}% + \index{\gobble#1@\protect\texttt{#1} handler}% + \index{Key handlers!#1@\protect\texttt{#1}} +} + + +\makeatletter + + +\newenvironment{stylekey}[1]{ + \begin{pgfmanualentry} + \def\extrakeytext{style, } + \extractkey#1\@nil% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\choicesep{$\vert$}% +\def\choicearg#1{\texttt{#1}} + +\newif\iffirstchoice + +\newcommand\mchoice[1]{% + \begingroup + \firstchoicetrue + \foreach \mchoice@ in {#1} {% + \iffirstchoice + \global\firstchoicefalse + \else + \choicesep + \fi + \choicearg{\mchoice@}% + }% + \endgroup +}% + +\newenvironment{key}[1]{ + \begin{pgfmanualentry} + \def\extrakeytext{} + \extractkey#1\@nil% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\insertpathifneeded#1#2{% + \def\insertpathifneeded@@{#2}% + \ifx\insertpathifneeded@@\empty + \def\mykey{#1}% + \else + \insertpathifneeded@#2\@nil + \ifpgfutil@in@ + \def\mykey{#2/#1}% + \else + \def\mykey{#1}% + \fi + \fi +}% +\def\insertpathifneeded@#1#2\@nil{% + \def\insertpathifneeded@@{#1}% + \def\insertpathifneeded@@@{/}% + \ifx\insertpathifneeded@@\insertpathifneeded@@@ + \pgfutil@in@true + \else + \pgfutil@in@false + \fi +}% + +\newenvironment{keylist}[2][]{% + \begin{pgfmanualentry} + \def\extrakeytext{}% + \foreach \xx in {#2} {% + \expandafter\insertpathifneeded\expandafter{\xx}{#1}% + \expandafter\extractkey\mykey\@nil% + }% + \pgfmanualbody +}{% + \end{pgfmanualentry} +}% + +\def\extractkey#1\@nil{% + \pgfutil@in@={#1}% + \ifpgfutil@in@% + \extractkeyequal#1\@nil + \else% + \pgfutil@in@{(initial}{#1}% + \ifpgfutil@in@% + \extractequalinitial#1\@nil% + \else + \pgfmanualentryheadline{% + \def\mykey{#1}% + \def\mypath{}% + \gdef\myname{}% + \firsttimetrue% + \pgfmanualdecomposecount=0\relax% + \decompose#1/\nil% + {\ttfamily\declare{#1}}\hfill(\extrakeytext no value)}% + \fi + \fi% +} + +\def\extractkeyequal#1=#2\@nil{% + \pgfutil@in@{(default}{#2}% + \ifpgfutil@in@% + \extractdefault{#1}#2\@nil% + \else% + \pgfutil@in@{(initial}{#2}% + \ifpgfutil@in@% + \extractinitial{#1}#2\@nil% + \else + \pgfmanualentryheadline{% + \def\mykey{#1}% + \def\mypath{}% + \gdef\myname{}% + \firsttimetrue% + \pgfmanualdecomposecount=0\relax% + \decompose#1/\nil% + {\ttfamily\declare{#1}=}#2\hfill(\extrakeytext no default)}% + \fi% + \fi% +} + +\def\extractdefault#1#2(default #3)\@nil{% + \pgfmanualentryheadline{% + \def\mykey{#1}% + \def\mypath{}% + \gdef\myname{}% + \firsttimetrue% + \pgfmanualdecomposecount=0\relax% + \decompose#1/\nil% + {\ttfamily\declare{#1}\opt{=}}\opt{#2}\hfill (\extrakeytext default {\ttfamily#3})}% +} + +\def\extractinitial#1#2(initially #3)\@nil{% + \pgfmanualentryheadline{% + \def\mykey{#1}% + \def\mypath{}% + \gdef\myname{}% + \firsttimetrue% + \pgfmanualdecomposecount=0\relax% + \decompose#1/\nil% + {\ttfamily\declare{#1}=}#2\hfill (\extrakeytext no default, initially {\ttfamily#3})}% +} + +\def\extractequalinitial#1 (initially #2)\@nil{% + \pgfmanualentryheadline{% + \def\mykey{#1}% + \def\mypath{}% + \gdef\myname{}% + \firsttimetrue% + \pgfmanualdecomposecount=0\relax% + \decompose#1/\nil% + {\ttfamily\declare{#1}}\hfill (\extrakeytext initially {\ttfamily#2})}% +} + +\def\keyalias#1{\vspace{-3pt}\item{\small alias {\ttfamily/#1/\myname}}\vspace{-2pt}\par + \pgfmanualpdflabel{/#1/\myname}{}% +} + +\newif\iffirsttime +\newcount\pgfmanualdecomposecount + +\makeatother + +\def\decompose/#1/#2\nil{% + \def\test{#2}% + \ifx\test\empty% + \index{#1@\protect\texttt{#1} key}% + \index{\mypath#1@\protect\texttt{#1}}% + \gdef\myname{#1}% + \pgfmanualpdflabel{#1}{} + \else% + \advance\pgfmanualdecomposecount by1\relax% + \ifnum\pgfmanualdecomposecount>2\relax% + \decomposetoodeep#1/#2\nil% + \else% + \iffirsttime% + \begingroup% + \def\hyperlabelwithoutslash##1/\nil{% + \pgfmanualpdflabel{##1}{}% + }% + \hyperlabelwithoutslash/#1/#2\nil% + \endgroup% + \def\mypath{#1@\protect\texttt{/#1/}!}% + \firsttimefalse% + \else% + \expandafter\def\expandafter\mypath\expandafter{\mypath#1@\protect\texttt{#1/}!}% + \fi% + \def\firsttime{}% + \decompose/#2\nil% + \fi% + \fi% +} + +\def\decomposetoodeep#1/#2/\nil{% + \index{#1/#2@\protect\texttt{#1/#2} key}% + \index{\mypath#1/#2@\protect\texttt{#1/#2}}% + \decomposefindlast/#1/#2/\nil% +} +\makeatletter +\def\decomposefindlast/#1/#2\nil{% + \def\test{#2}% + \ifx\test\pgfutil@empty% + \gdef\myname{#1}% + \else% + \decomposefindlast/#2\nil% + \fi% +} +\makeatother +\def\indexkey#1{% + \def\mypath{}% + \decompose#1/\nil% +} + +\newenvironment{predefinedmethod}[1]{ + \begin{pgfmanualentry} + \extractpredefinedmethod#1\@nil + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} +\def\extractpredefinedmethod#1(#2)\@nil{% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + Method \declare{\ttfamily #1}\texttt(#2\texttt) \hfill(predefined for all classes)} + \index{#1@\protect\texttt{#1} method}% + \index{Methods!#1@\protect\texttt{#1}} +} + + +\newenvironment{ooclass}[1]{ + \begin{pgfmanualentry} + \def\currentclass{#1} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Class} \declare{\texttt{#1}}} + \index{#1@\protect\texttt{#1} class}% + \index{Class #1@Class \protect\texttt{#1}}% + \index{Classes!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{method}[1]{ + \begin{pgfmanualentry} + \extractmethod#1\@nil + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} +\def\extractmethod#1(#2)\@nil{% + \def\test{#1} + \ifx\test\currentclass + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + Constructor \declare{\ttfamily #1}\texttt(#2\texttt)} + \else + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + Method \declare{\ttfamily #1}\texttt(#2\texttt)} + \fi + \index{#1@\protect\texttt{#1} method}% + \index{Methods!#1@\protect\texttt{#1}} + \index{Class \currentclass!#1@\protect\texttt{#1}}% +} + +\newenvironment{classattribute}[1]{ + \begin{pgfmanualentry} + \extractattribute#1\@nil + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} +\def\extractattribute#1=#2;\@nil{% + \def\test{#2}% + \ifx\test\@empty + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + Private attribute \declare{\ttfamily #1} \hfill (initially empty)} + \else + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + Private attribute \declare{\ttfamily #1} \hfill (initially {\ttfamily #2})} + \fi + \index{#1@\protect\texttt{#1} attribute}% + \index{Attributes!#1@\protect\texttt{#1}} + \index{Class \currentclass!#1@\protect\texttt{#1}}% +} + + + +\newenvironment{predefinednode}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Predefined node} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} node}% + \index{Predefined node!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{coordinatesystem}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{Coordinate system} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} coordinate system}% + \index{Coordinate systems!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{snake}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\textbf{Snake} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} snake}% + \index{Snakes!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{decoration}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\textbf{Decoration} {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} decoration}% + \index{Decorations!#1@\protect\texttt{#1}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\def\pgfmanualbar{\char`\|} +\makeatletter +\newenvironment{pathoperation}[3][]{ + \begin{pgfmanualentry} + \def\pgfmanualtest{#1}% + \pgfmanualentryheadline{% + \ifx\pgfmanualtest\@empty% + \pgfmanualpdflabel{#2}{}% + \fi% + \textcolor{gray}{{\ttfamily\char`\\path}\ + \ \dots} + \declare{\texttt{\noligs{#2}}}#3\ \textcolor{gray}{\dots\texttt{;}}}% + \ifx\pgfmanualtest\@empty% + \index{#2@\protect\texttt{#2} path operation}% + \index{Path operations!#2@\protect\texttt{#2}}% + \fi% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} +\newenvironment{datavisualizationoperation}[3][]{ + \begin{pgfmanualentry} + \def\pgfmanualtest{#1}% + \pgfmanualentryheadline{% + \ifx\pgfmanualtest\@empty% + \pgfmanualpdflabel{#2}{}% + \fi% + \textcolor{gray}{{\ttfamily\char`\\datavisualization}\ + \ \dots} + \declare{\texttt{\noligs{#2}}}#3\ \textcolor{gray}{\dots\texttt{;}}}% + \ifx\pgfmanualtest\@empty% + \index{#2@\protect\texttt{#2} (data visualization)}% + \index{Data visualization!#2@\protect\texttt{#2}}% + \fi% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} +\makeatother + +\def\doublebs{\texttt{\char`\\\char`\\}} + + +\newenvironment{package}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + {\ttfamily\char`\\usepackage\char`\{\declare{#1}\char`\}\space\space \char`\%\space\space \LaTeX}} + \index{#1@\protect\texttt{#1} package}% + \index{Packages and files!#1@\protect\texttt{#1}}% + \pgfmanualentryheadline{{\ttfamily\char`\\input \declare{#1}.tex\space\space\space \char`\%\space\space plain \TeX}} + \pgfmanualentryheadline{{\ttfamily\char`\\usemodule[\declare{#1}]\space\space \char`\%\space\space Con\TeX t}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{pgfmodule}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + {\ttfamily\char`\\usepgfmodule\char`\{\declare{#1}\char`\}\space\space\space + \char`\%\space\space \LaTeX\space and plain \TeX\space and pure pgf}} + \index{#1@\protect\texttt{#1} module}% + \index{Modules!#1@\protect\texttt{#1}}% + \pgfmanualentryheadline{{\ttfamily\char`\\usepgfmodule[\declare{#1}]\space\space \char`\%\space\space Con\TeX t\space and pure pgf}} + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{pgflibrary}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{\tikzname\ Library} \texttt{\declare{#1}}} + \index{#1@\protect\texttt{#1} library}% + \index{Libraries!#1@\protect\texttt{#1}}% + \vskip.25em% + {{\ttfamily\char`\\usepgflibrary\char`\{\declare{#1}\char`\}\space\space\space + \char`\%\space\space \LaTeX\space and plain \TeX\space and pure pgf}}\\ + {{\ttfamily\char`\\usepgflibrary[\declare{#1}]\space\space \char`\%\space\space Con\TeX t\space and pure pgf}}\\ + {{\ttfamily\char`\\usetikzlibrary\char`\{\declare{#1}\char`\}\space\space + \char`\%\space\space \LaTeX\space and plain \TeX\space when using \tikzname}}\\ + {{\ttfamily\char`\\usetikzlibrary[\declare{#1}]\space + \char`\%\space\space Con\TeX t\space when using \tikzname}}\\[.5em] + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{purepgflibrary}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{{\small PGF} Library} \texttt{\declare{#1}}} + \index{#1@\protect\texttt{#1} library}% + \index{Libraries!#1@\protect\texttt{#1}}% + \vskip.25em% + {{\ttfamily\char`\\usepgflibrary\char`\{\declare{#1}\char`\}\space\space\space + \char`\%\space\space \LaTeX\space and plain \TeX}}\\ + {{\ttfamily\char`\\usepgflibrary[\declare{#1}]\space\space \char`\%\space\space Con\TeX t}}\\[.5em] + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{tikzlibrary}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{\tikzname\ Library} \texttt{\declare{#1}}} + \index{#1@\protect\texttt{#1} library}% + \index{Libraries!#1@\protect\texttt{#1}}% + \vskip.25em% + {{\ttfamily\char`\\usetikzlibrary\char`\{\declare{#1}\char`\}\space\space \char`\%\space\space \LaTeX\space and plain \TeX}}\\ + {{\ttfamily\char`\\usetikzlibrary[\declare{#1}]\space \char`\%\space\space Con\TeX t}}\\[.5em] + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\newenvironment{pgfkeyslibrary}[1]{% + \begin{pgfmanualentry}% + \pgfmanualentryheadline{% + \pgfmanualpdflabel{#1}{}% + \textbf{pgfkeys Library} \texttt{\declare{#1}}}% + \index{#1@\protect\texttt{#1} pgfkeys library}% + \index{pgfkeys Libraries!#1@\protect\texttt{#1}}% + \vskip.25em + {{\ttfamily\char`\\usepgfkeyslibrary\char`\{\declare{#1}\char`\}\space\space \char`\%\space\space \LaTeX\space and plain \TeX}}\\ + {{\ttfamily\char`\\usepgfkeyslibrary[\declare{#1}]\space \char`\%\space\space Con\TeX t}}\\[.5em]% + \pgfmanualbody +}% +{% + \end{pgfmanualentry}% +} + + +\newenvironment{filedescription}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{File {\ttfamily\declare{#1}}}% + \index{#1@\protect\texttt{#1} file}% + \index{Packages and files!#1@\protect\texttt{#1}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + +\newenvironment{packageoption}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{{\ttfamily\char`\\usepackage[\declare{#1}]\char`\{pgf\char`\}}} + \index{#1@\protect\texttt{#1} package option}% + \index{Package options for \textsc{pgf}!#1@\protect\texttt{#1}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + + + +\newcommand\opt[1]{{\color{black!50!green}#1}} +\newcommand\ooarg[1]{{\ttfamily[}\meta{#1}{\ttfamily]}} + +\def\opt{\afterassignment\pgfmanualopt\let\next=} +\def\pgfmanualopt{\ifx\next\bgroup\bgroup\color{black!50!green}\else{\color{black!50!green}\next}\fi} + + + +\def\beamer{\textsc{beamer}} +\def\pdf{\textsc{pdf}} +\def\eps{\texttt{eps}} +\def\pgfname{\textsc{pgf}} +\def\tikzname{Ti\emph{k}Z} +\def\pstricks{\textsc{pstricks}} +\def\prosper{\textsc{prosper}} +\def\seminar{\textsc{seminar}} +\def\texpower{\textsc{texpower}} +\def\foils{\textsc{foils}} + +{ + \makeatletter + \global\let\myempty=\@empty + \global\let\mygobble=\@gobble + \catcode`\@=12 + \gdef\getridofats#1@#2\relax{% + \def\getridtest{#2}% + \ifx\getridtest\myempty% + \expandafter\def\expandafter\strippedat\expandafter{\strippedat#1} + \else% + \expandafter\def\expandafter\strippedat\expandafter{\strippedat#1\protect\printanat} + \getridofats#2\relax% + \fi% + } + + \gdef\removeats#1{% + \let\strippedat\myempty% + \edef\strippedtext{\stripcommand#1}% + \expandafter\getridofats\strippedtext @\relax% + } + + \gdef\stripcommand#1{\expandafter\mygobble\string#1} +} + +\def\printanat{\char`\@} + +\def\declare{\afterassignment\pgfmanualdeclare\let\next=} +\def\pgfmanualdeclare{\ifx\next\bgroup\bgroup\color{red!75!black}\else{\color{red!75!black}\next}\fi} + + +\let\textoken=\command +\let\endtextoken=\endcommand + +\def\myprintocmmand#1{\texttt{\char`\\#1}} + +\def\example{\par\smallskip\noindent\textit{Example: }} +\def\themeauthor{\par\smallskip\noindent\textit{Theme author: }} + + +\def\indexoption#1{% + \index{#1@\protect\texttt{#1} option}% + \index{Graphic options and styles!#1@\protect\texttt{#1}}% +} + +\def\itemcalendaroption#1{\item \declare{\texttt{#1}}% + \index{#1@\protect\texttt{#1} date test}% + \index{Date tests!#1@\protect\texttt{#1}}% +} + + + +\def\class#1{\list{}{\leftmargin=2em\itemindent-\leftmargin\def\makelabel##1{\hss##1}}% +\extractclass#1@\par\topsep=0pt} +\def\endclass{\endlist} +\def\extractclass#1#2@{% +\item{{{\ttfamily\char`\\documentclass}#2{\ttfamily\char`\{\declare{#1}\char`\}}}}% + \index{#1@\protect\texttt{#1} class}% + \index{Classes!#1@\protect\texttt{#1}}} + +\def\partname{Part} + +\makeatletter +\def\index@prologue{\section*{Index}\addcontentsline{toc}{section}{Index} + This index only contains automatically generated entries. A good + index should also contain carefully selected keywords. This index is + not a good index. + \bigskip +} +\c@IndexColumns=2 + \def\theindex{\@restonecoltrue + \columnseprule \z@ \columnsep 29\p@ + \twocolumn[\index@prologue]% + \parindent -30pt + \columnsep 15pt + \parskip 0pt plus 1pt + \leftskip 30pt + \rightskip 0pt plus 2cm + \small + \def\@idxitem{\par}% + \let\item\@idxitem \ignorespaces} + \def\endtheindex{\onecolumn} +\def\noindexing{\let\index=\@gobble} + + +\newenvironment{arrowtipsimple}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\textbf{Arrow Tip Kind} {\ttfamily#1}} + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \def\currentarrowtype{#1} + \pgfmanualbody} +{ + \end{pgfmanualentry} +} + +\newenvironment{arrowtip}[4]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\textbf{Arrow Tip Kind} {\ttfamily#1}} + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \pgfmanualbody + \def\currentarrowtype{#1} + \begin{minipage}[t]{10.25cm} + #2 + \end{minipage}\hskip5mm\begin{minipage}[t]{4.75cm} + \leavevmode\vskip-2em + \tikz{ + \draw [black!50,line width=5mm,-{#1[#3,color=black]}] (-4,0) -- (0,0); + \foreach \action in {#4} + { \expandafter\processaction\action\relax } + } + \end{minipage}\par\smallskip + } +{ + \end{pgfmanualentry} +} + +\newenvironment{arrowcap}[5]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\textbf{Arrow Tip Kind} {\ttfamily#1}} + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \pgfmanualbody + \def\currentarrowtype{#1} + \begin{minipage}[t]{10.25cm} + #2 + \end{minipage}\hskip5mm\begin{minipage}[t]{4.75cm} + \leavevmode\vskip-2em + \tikz{ + \path [tips, line width=10mm,-{#1[#3,color=black]}] (-4,0) -- (0,0); + \draw [line width=10mm,black!50] (-3,0) -- (#5,0); + \foreach \action in {#4} + { \expandafter\processaction\action\relax } + } + \end{minipage}\par\smallskip + } +{ + \end{pgfmanualentry} +} + +\newenvironment{pattern}[1]{ + \begin{pgfmanualentry} + \pgfmanualentryheadline{\textbf{Pattern} {\ttfamily#1}} + \index{#1@\protect\texttt{#1} pattern}% + \index{Patterns!#1@\protect\texttt{#1}}% + \pgfmanualbody +} +{ + \end{pgfmanualentry} +} + +\def\processaction#1=#2\relax{ + \expandafter\let\expandafter\pgf@temp\csname manual@action@#1\endcsname + \ifx\pgf@temp\relax\else + \pgf@temp#2/0/\relax + \fi +} +\def\manual@action@length#1/#2/#3\relax{% + \draw [red,|<->|,semithick,xshift=#2] ([yshift=4pt]current bounding + box.north -| -#1,0) coordinate (last length) -- node + [above=-2pt] {|length|} ++(#1,0); +} +\def\manual@action@width#1/#2/#3\relax{% + \draw [overlay, red,|<->|,semithick] (.5,-#1/2) -- node [below,sloped] {|width|} (.5,#1/2); +} +\def\manual@action@inset#1/#2/#3\relax{% + \draw [red,|<->|,semithick,xshift=#2] ([yshift=-4pt]current bounding + box.south -| last length) -- node [below] {|inset|} ++(#1,0); +} + +\newenvironment{arrowexamples} +{\begin{tabbing} + \hbox to \dimexpr\linewidth-5.5cm\relax{\emph{Appearance of the below at line width} \hfil} \= + \hbox to 1.9cm{\emph{0.4pt}\hfil} \= \hbox to 2cm{\emph{0.8pt}\hfil} \= \emph{1.6pt} \\ + } +{\end{tabbing}\vskip-1em} + +\newenvironment{arrowcapexamples} +{\begin{tabbing} + \hbox to \dimexpr\linewidth-5.5cm\relax{\emph{Appearance of the below at line width} \hfil} \= + \hbox to 1.9cm{\emph{1ex}\hfil} \= \hbox to 2cm{\emph{1em}\hfil} \\ + } +{\end{tabbing}\vskip-1em} + +\def\arrowcapexample#1[#2]{\def\temp{#1}\ifx\temp\pgfutil@empty\arrowcapexample@\currentarrowtype[{#2}]\else\arrowcapexample@#1[{#2}]\fi} +\def\arrowcapexample@#1[#2]{% + {\sfcode`\.1000\small\texttt{#1[#2]}} \> + \kern-.5ex\tikz [baseline,>={#1[#2]}] \draw [line + width=1ex,->] (0,.5ex) -- (2em,.5ex); \> + \kern-.5em\tikz [baseline,>={#1[#2]}] \draw [line + width=1em,->] (0,.5ex) -- (2em,.5ex); \\ +} + +\def\arrowexample#1[#2]{\def\temp{#1}\ifx\temp\pgfutil@empty\arrowexample@\currentarrowtype[{#2}]\else\arrowexample@#1[{#2}]\fi} +\def\arrowexample@#1[#2]{% + {\sfcode`\.1000\small\texttt{#1[#2]}} \> + \tikz [baseline,>={#1[#2]}] \draw [line + width=0.4pt,->] (0,.5ex) -- (2em,.5ex); thin \> + \tikz [baseline,>={#1[#2]}] \draw [line + width=0.8pt,->] (0,.5ex) -- (2em,.5ex); \textbf{thick} \> + \tikz [baseline,>={#1[#2]}] \draw [line + width=1.6pt,->] (0,.5ex) -- (3em,.5ex); \\ +} +\def\arrowexampledup[#1]{\arrowexample[{#1] \currentarrowtype[}]} +\def\arrowexampledupdot[#1]{\arrowexample[{#1] . \currentarrowtype[}]} + +\def\arrowexampledouble#1[#2]{\def\temp{#1}\ifx\temp\pgfutil@empty\arrowexampledouble@\currentarrowtype[{#2}]\else\arrowexampledouble@#1[{#2}]\fi} +\def\arrowexampledouble@#1[#2]{% + {\sfcode`\.1000\small\texttt{#1[#2]} on double line} \> + \tikz [baseline,>={#1[#2]}] + \draw [double equal sign distance,line width=0.4pt,->] (0,.5ex) -- (2em,.5ex); thin \> + \tikz [baseline,>={#1[#2]}] + \draw [double equal sign distance,line width=0.8pt,->] (0,.5ex) -- (2em,.5ex); \textbf{thick} \> + \tikz [baseline,>={#1[#2]}] + \draw [double equal sign distance, line width=1.6pt,->] (0,.5ex) -- (3em,.5ex); \\ +} + + + +\newcommand\symarrow[1]{% + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \texttt{#1}& yields thick + \begin{tikzpicture}[arrows={#1-#1},thick,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} and thin + \begin{tikzpicture}[arrows={#1-#1},thin,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} +} +\newcommand\symarrowdouble[1]{% + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \texttt{#1}& yields thick + \begin{tikzpicture}[arrows={#1-#1},thick,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} + and thin + \begin{tikzpicture}[arrows={#1-#1},thin,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture}, double + \begin{tikzpicture}[arrows={#1-#1},thick,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw[double,double equal sign distance] (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} and + \begin{tikzpicture}[arrows={#1-#1},thin,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw[double,double equal sign distance] (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} +} + +\newcommand\sarrow[2]{% + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \index{#2@\protect\texttt{#2} arrow tip}% + \index{Arrow tips!#2@\protect\texttt{#2}}% + \texttt{#1-#2}& yields thick + \begin{tikzpicture}[arrows={#1-#2},thick,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} and thin + \begin{tikzpicture}[arrows={#1-#2},thin,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} +} + +\newcommand\sarrowdouble[2]{% + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \index{#2@\protect\texttt{#2} arrow tip}% + \index{Arrow tips!#2@\protect\texttt{#2}}% + \texttt{#1-#2}& yields thick + \begin{tikzpicture}[arrows={#1-#2},thick,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} and thin + \begin{tikzpicture}[arrows={#1-#2},thin,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture}, double + \begin{tikzpicture}[arrows={#1-#2},thick,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw[double,double equal sign distance] (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} and + \begin{tikzpicture}[arrows={#1-#2},thin,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.1cm,2ex); + \fill [black!15] (1cm,-.5ex) rectangle (1.1cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw[double,double equal sign distance] (0pt,.5ex) -- (1cm,.5ex); + \end{tikzpicture} +} + +\newcommand\carrow[1]{% + \index{#1@\protect\texttt{#1} arrow tip}% + \index{Arrow tips!#1@\protect\texttt{#1}}% + \texttt{#1}& yields for line width 1ex + \begin{tikzpicture}[arrows={#1-#1},line width=1ex,baseline] + \useasboundingbox (-1mm,-0.5ex) rectangle (1.6cm,2ex); + \fill [black!15] (1.5cm,-.5ex) rectangle (1.6cm,1.5ex) (-1mm,-.5ex) rectangle (0mm,1.5ex) ; + \draw (0pt,.5ex) -- (1.5cm,.5ex); + \end{tikzpicture} +} +\def\myvbar{\char`\|} +\newcommand\plotmarkentry[1]{% + \index{#1@\protect\texttt{#1} plot mark}% + \index{Plot marks!#1@\protect\texttt{#1}} + \texttt{\char`\\pgfuseplotmark\char`\{\declare{\noligs{#1}}\char`\}} & + \tikz\draw[color=black!25] plot[mark=#1,mark options={fill=examplefill,draw=black}] coordinates{(0,0) (.5,0.2) (1,0) (1.5,0.2)};\\ +} +\newcommand\plotmarkentrytikz[1]{% + \index{#1@\protect\texttt{#1} plot mark}% + \index{Plot marks!#1@\protect\texttt{#1}} + \texttt{mark=\declare{\noligs{#1}}} & \tikz\draw[color=black!25] + plot[mark=#1,mark options={fill=examplefill,draw=black}] + coordinates {(0,0) (.5,0.2) (1,0) (1.5,0.2)};\\ +} + + + +\ifx\scantokens\@undefined + \PackageError{pgfmanual-macros}{You need to use extended latex + (elatex) or (pdfelatex) to process this document}{} +\fi + +\begingroup +\catcode`|=0 +\catcode`[= 1 +\catcode`]=2 +\catcode`\{=12 +\catcode `\}=12 +\catcode`\\=12 |gdef|find@example#1\end{codeexample}[|endofcodeexample[#1]] +|endgroup + +\begingroup +\catcode`\^=7 +\catcode`\^^M=13 +\catcode`\^^I=13 +\catcode`\ =13% +\gdef\returntospace{\catcode`\ =13\def {\space}\catcode`\^^I=13\def^^I{\space}} +\gdef\showreturn{\show^^M} +\endgroup + +\begingroup +\catcode`\%=13 +\catcode`\^^M=13 +\gdef\commenthandler{\catcode`\%=13\def%{\@gobble@till@return}} +\gdef\@gobble@till@return#1^^M{} +\gdef\@gobble@till@return@ignore#1^^M{\ignorespaces} +\gdef\typesetcomment{\catcode`\%=13\def%{\@typeset@till@return}} +\gdef\@typeset@till@return#1^^M{{\def%{\char`\%}\textsl{\char`\%#1}}\par} +\endgroup + +{ +\catcode`\^^I=13 +\gdef\codeexample@tabinit@replacementchars@{% + \begingroup + \count0=\pgfkeysvalueof{/codeexample/tabsize}\relax + \toks0={}% + \loop + \ifnum\count0>0 + \advance\count0 by-1 + \toks0=\expandafter{\the\toks0\ }% + \repeat + \xdef\codeexample@tabinit@replacementchars@@{\the\toks0}% + \endgroup + \let^^I=\codeexample@tabinit@replacementchars@@ +}% +\gdef\codeexample@tabinit@catcode@{\catcode`\^^I=13}% +}% + +\def\codeexample@tabinit{% + \ifnum\pgfkeysvalueof{/codeexample/tabsize}=0\relax + \let\codeexample@tabinit@replacementchars=\relax + \let\codeexample@tabinit@catcode=\relax + \else + \let\codeexample@tabinit@catcode=\codeexample@tabinit@catcode@ + \let\codeexample@tabinit@replacementchars=\codeexample@tabinit@replacementchars@ + \fi +} + +\newif\ifpgfmanualtikzsyntaxhilighting + +\pgfqkeys{/codeexample}{% + width/.code= {\setlength\codeexamplewidth{#1}}, + graphic/.code= {\colorlet{graphicbackground}{#1}}, + code/.code= {\colorlet{codebackground}{#1}}, + execute code/.is if=code@execute, + hidden/.is if=code@hidden, + code only/.code= {\code@executefalse}, + setup code/.code= {\pgfmanual@setup@codetrue\code@executefalse}, + multipage/.code= {\code@executefalse\pgfmanual@multipage@codetrue}, + pre/.store in=\code@pre, + post/.store in=\code@post, + typeset listing/.code= {#1}, + render instead/.store in=\code@render, + vbox/.code= {\def\code@pre{\vbox\bgroup\setlength{\hsize}{\linewidth-6pt}}\def\code@post{\egroup}}, + ignorespaces/.code= {\let\@gobble@till@return=\@gobble@till@return@ignore}, + leave comments/.code= {\def\code@catcode@hook{\catcode`\%=12}\let\commenthandler=\relax\let\typesetcomment=\relax}, + tabsize/.initial=0,% + every codeexample/.style={width=4cm+7pt, tikz syntax=true}, + from file/.code={\codeexamplefromfiletrue\def\codeexamplesource{#1}}, + tikz syntax/.is if=pgfmanualtikzsyntaxhilighting, + animation list/.store in=\code@animation@list, + animation pre/.store in=\code@animation@pre, + animation post/.store in=\code@animation@post, + animation scale/.store in=\pgfmanualanimscale, + animation bb/.style={ + animation pre={ + \tikzset{ + every picture/.style={ + execute at begin picture={ + \useasboundingbox[clip] #1;} + } + } + } + }, + preamble/.store in=\code@preamble, +} + +\def\pgfmanualanimscale{.5} + +\newread\examplesource + + + +\def\opensource#1{ + \immediate\openin\examplesource=#1 +} +\def\do@codeexamplefromfile{% + \immediate\openin\examplesource\expandafter{\codeexamplesource}% + \def\examplelines{}% + \readexamplelines + \closein\examplesource + \expandafter\endofcodeexample\expandafter{\examplelines}% +} + +\def\readexamplelines{ + \ifeof\examplesource% + \else + \immediate\read\examplesource to \exampleline + \expandafter\expandafter\expandafter\def\expandafter\expandafter\expandafter\examplelines\expandafter\expandafter\expandafter{\expandafter\examplelines\exampleline} + \expandafter\readexamplelines% + \fi +} + +\let\code@animation@pre\pgfutil@empty +\let\code@animation@post\pgfutil@empty +\let\code@animation@list\pgfutil@empty + +\let\code@pre\pgfutil@empty +\let\code@post\pgfutil@empty +\let\code@render\pgfutil@empty +\let\code@preamble\pgfutil@empty +\def\code@catcode@hook{} + +\newif\ifpgfmanual@multipage@code +\newif\ifpgfmanual@setup@code +\newif\ifcodeexamplefromfile +\newdimen\codeexamplewidth +\newif\ifcode@execute +\newif\ifcode@hidden +\newbox\codeexamplebox +\def\codeexample[#1]{% + \global\let\pgfmanual@do@this\relax% + \aftergroup\pgfmanual@do@this% + \begingroup% + \code@executetrue + \pgfqkeys{/codeexample}{every codeexample,#1}% + \pgfmanualswitchoncolors% + \ifcodeexamplefromfile\begingroup\fi + \codeexample@tabinit% + \parindent0pt + \begingroup% + \par% + \ifcode@hidden\else + \medskip% + \fi + \let\do\@makeother% + \dospecials% + \obeylines% + \@vobeyspaces% + \catcode`\%=13% + \catcode`\^^M=13% + \code@catcode@hook% + \codeexample@tabinit@catcode + \relax% + \ifcodeexamplefromfile% + \expandafter\do@codeexamplefromfile% + \else% + \expandafter\find@example% + \fi} +\def\endofcodeexample#1{% + \endgroup% + \ifpgfmanual@setup@code% + \gdef\pgfmanual@do@this{% + {% + \returntospace% + \commenthandler% + \obeylines% + \xdef\code@temp{#1}% + }% + \edef\pgfmanualmcatcode{\the\catcode`\^^M}% + \catcode`\^^M=9\relax% + \expandafter\scantokens\expandafter{\code@temp}% + \catcode`\^^M=\pgfmanualmcatcode% + }% + \fi% + \ifcode@hidden\else + \ifcode@execute% + \setbox\codeexamplebox=\hbox{% + \ifx\code@render\pgfutil@empty% + {% + {% + \returntospace% + \commenthandler% + \obeylines% + \xdef\code@temp{#1}% + }% + \catcode`\^^M=9% + \colorbox{graphicbackground}{\color{black}\ignorespaces% + \code@pre\expandafter\scantokens\expandafter{\code@temp\ignorespaces}\code@post\ignorespaces}% + }% + \else% + \global\let\code@temp\code@render% + \colorbox{graphicbackground}{\color{black}\ignorespaces% + \code@render}% + \fi% + }% + \ifx\code@animation@list\pgfutil@empty% + \else% + \setbox\codeexampleboxanim=\vbox{% + \rightskip0pt\leftskip0pt plus1filll% + \ifdim\wd\codeexamplebox>\codeexamplewidth% + \else% + \hsize\codeexamplewidth% + \advance\hsize by2cm% + \fi% + \leavevmode\catcode`\^^M=9% + \foreach \pgfmanualtime/\pgfmanualtimehow in\code@animation@list{% + \setbox\codeexampleboxanim=\hbox{\colorbox{animationgraphicbackground}{% + \tikzset{make snapshot of=\pgfmanualtime}% + \scalebox{\pgfmanualanimscale}{\color{black}\ignorespaces% + \code@animation@pre\expandafter\scantokens\expandafter{\code@temp\ignorespaces}\code@animation@post\ignorespaces}% + }}% + \space\raise4pt\hbox to0pt{\vrule width0pt height1em\hbox + to\wd\codeexampleboxanim{\hfil\scriptsize$t{=}\pgfmanualtimehow \mathrm s$\hfil}\hss}% + \lower\ht\codeexampleboxanim\box\codeexampleboxanim\hfil\penalty0\hskip0ptplus-1fil% + }% + }% + \setbox\codeexampleboxanim=\hbox{\hbox{}\hskip-2cm\box\codeexampleboxanim}% + \fi% + \ifdim\wd\codeexamplebox>\codeexamplewidth% + \def\code@start{\par}% + \def\code@flushstart{}\def\code@flushend{}% + \def\code@mid{\parskip2pt\par\noindent}% + \def\code@width{\linewidth-6pt}% + \def\code@end{}% + \else% + \def\code@start{% + \linewidth=\textwidth% + \parshape \@ne 0pt \linewidth + \leavevmode% + \hbox\bgroup}% + \def\code@flushstart{\hfill}% + \def\code@flushend{\hbox{}}% + \def\code@mid{\hskip6pt}% + \def\code@width{\linewidth-12pt-\codeexamplewidth}% + \def\code@end{\egroup}% + \fi% + \code@start% + \noindent% + \begin{minipage}[t]{\codeexamplewidth}\raggedright + \hrule width0pt% + \footnotesize\vskip-1em% + \code@flushstart\box\codeexamplebox\code@flushend% + \vskip0pt% + \leavevmode% + \box\codeexampleboxanim% + \vskip-1ex + \leavevmode% + \end{minipage}% + \else% + \def\code@mid{\par} + \def\code@width{\linewidth-6pt} + \def\code@end{} + \fi% + \code@mid% + \ifpgfmanual@multipage@code% + {% + \pgfkeysvalueof{/codeexample/prettyprint/base color}% + \pgfmanualdolisting{#1}% + }% + \else% + \colorbox{codebackground}{% + \pgfkeysvalueof{/codeexample/prettyprint/base color}% + \begin{minipage}[t]{\code@width}% + \pgfmanualdolisting{#1}% + \end{minipage}}% + \fi% + \code@end% + \par% + \medskip + \fi + \endcodeexample\endgroup% +} + +\def\endcodeexample{\endgroup} +\newbox\codeexampleboxanim + +\def\pgfmanualdolisting#1{% + {% + \let\do\@makeother + \dospecials + \frenchspacing\@vobeyspaces + \normalfont\ttfamily\footnotesize + \typesetcomment% + \codeexample@tabinit@replacementchars + \@tempswafalse + \def\par{% + \if@tempswa + \leavevmode \null \@@par\penalty\interlinepenalty + \else + \@tempswatrue + \ifhmode\@@par\penalty\interlinepenalty\fi + \fi}% + \obeylines + \everypar \expandafter{\the\everypar \unpenalty}% + \ifx\code@preamble\pgfutil@empty\else + \pgfutil@tempdima=\hsize + \vbox{\hsize=\pgfutil@tempdima + \raggedright\scriptsize\detokenize\expandafter{\code@preamble}}% + \fi + \pgfkeysvalueof{/codeexample/typeset listing/.@cmd}{#1}\pgfeov + }% +} + +\makeatother + +\usepackage{pgfmanual} + + + + +\newdimen\pgfmanualcslinkpreskip + +\pgfkeys{ + /codeexample/syntax hilighting/.style={ + /codeexample/prettyprint/key name/.code={\textcolor{keycolor}{\pgfmanualpdfref{##1}{\noligs{##1}}}}, + /codeexample/prettyprint/key name with handler/.code 2 args={\textcolor{keycolor}{\pgfmanualpdfref{##1}{\noligs{##1}}}/\textcolor{blue!70!black}{\pgfmanualpdfref{/handlers/##2}{\noligs{##2}}}}, + /codeexample/prettyprint/key value display only/.code={\textcolor{keycolor}{{\itshape{\let\pgfmanualwordstartup\relax\pgfmanualprettyprintcode{##1}}}}}, + /codeexample/prettyprint/cs/.code={\textcolor{cscolor}{\pgfmanualcslinkpreskip4.25pt\pgfmanualpdfref{##1}{\noligs{##1}}}}, + /codeexample/prettyprint/cs with args/.code 2 args={\textcolor{black}{\pgfmanualcslinkpreskip4.25pt\pgfmanualpdfref{##1}{\noligs{##1}}}\{\textcolor{black}{\pgfmanualprettyprintcode{##2}}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/pgfkeys/.initial=1, + /codeexample/prettyprint/cs/pgfkeys/.code 2 args={\textcolor{black}{\pgfmanualcslinkpreskip4.25pt\pgfmanualpdfref{##1}{\noligs{##1}}}\{\textcolor{black}{\pgfmanualprettyprintpgfkeys{##2}}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/begin/.initial=1, + /codeexample/prettyprint/cs/begin/.code 2 args={\textcolor{black}{##1}\{\textcolor{cscolor}{\pgfmanualpdfref{##2}{\noligs{##2}}}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/end/.initial=1, + /codeexample/prettyprint/cs/end/.code 2 args={\textcolor{black}{##1}\{\textcolor{cscolor}{\pgfmanualpdfref{##2}{\noligs{##2}}}\pgfmanualclosebrace}, + /codeexample/prettyprint/word/.code={\pgfmanualwordstartup{\begingroup\pgfkeyssetvalue{/pdflinks/search key prefixes in}{}\pgfmanualpdfref{##1}{\noligs{##1}}\endgroup}}, + /codeexample/prettyprint/point/.code={\textcolor{pointcolor}{\noligs{##1}}},% + /codeexample/prettyprint/point with cs/.code 2 args={\textcolor{pointcolor}{(\pgfmanualpdfref{##1}{\noligs{##1}}:\noligs{##2}}},% + /codeexample/prettyprint/comment font=\itshape, + /codeexample/prettyprint/base color/.initial=\color{basecolor}, + /pdflinks/render hyperlink/.code={% + {\setbox0=\hbox{##1}% + \rlap{{\color{linkcolor}\dimen0\wd0\advance\dimen0by-\pgfmanualcslinkpreskip\hskip\pgfmanualcslinkpreskip\vrule width\dimen0 height-1pt depth1.6pt}}% + \box0% + }% + } + },/codeexample/syntax hilighting +} + +\colorlet{keycolor}{black} +\colorlet{cscolor}{black} +\colorlet{pointcolor}{black} +\colorlet{basecolor}{black} +\colorlet{linkcolor}{black!8} + +\def\pgfmanualswitchoncolors{% + \colorlet{keycolor}{green!50!black}% + \colorlet{cscolor}{blue!70!black} + \colorlet{pointcolor}{violet} + \colorlet{basecolor}{black!55} + \colorlet{linkcolor}{white} +} + +\makeatletter + +\def\pgfmanualwordstartup{\textcolor{black}} + +\def\noligs#1{\pgfmanualnoligs#1\kern0pt--\pgf@stop}% +\def\pgfmanualnoligs#1--{% + \pgfutil@ifnextchar\pgf@stop{#1\pgfutil@gobble}{#1-\kern0pt-\kern0pt\pgfmanualnoligs}% +} +\makeatother + + diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..337e84a2a2ba23662c9be52d73362fd3eda7d8f1 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.code.tex @@ -0,0 +1,21 @@ + +\input pgfmanual.prettyprinter.code.tex +\input pgfmanual.pdflinks.code.tex + + +\def\pgfmanual@warning#1{\pgf@typeout{! Package pgfmanual Warning: #1}}% + + +\pgfkeys{ + /pdflinks/codeexample links=true, + /codeexample/prettyprint/cs arguments/tikzset/.initial=1, + /codeexample/prettyprint/cs/tikzset/.code 2 args={\pgfmanualpdfref{#1}{#1}\{\pgfmanualprettyprintpgfkeys{#2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/usetikzlibrary/.initial=1, + /codeexample/prettyprint/cs/usetikzlibrary/.code 2 args={\pgfmanualpdfref{#1}{#1}\{\pgfmanualpdfref{#2}{#2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/usepgflibrary/.initial=1, + /codeexample/prettyprint/cs/usepgflibrary/.code 2 args={\pgfmanualpdfref{#1}{#1}\{\pgfmanualpdfref{#2}{#2}\pgfmanualclosebrace}, + /pdflinks/search key prefixes in={/tikz/,/pgf/}, + /pdflinks/internal link prefix=pgf, + /pdflinks/warnings=false, + /pdflinks/show labels=false, +}% diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.pdflinks.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.pdflinks.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..55a9fbed4c8ffc5dfae370bf9c72df572a664fa6 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.pdflinks.code.tex @@ -0,0 +1,285 @@ + + +\newif\ifpgfmanualpdfwarnings +\pgfmanualpdfwarningstrue + +\newif\ifpgfmanualshowlabels + +\pgfkeys{% + /codeexample/prettyprint/cs arguments/pgfkeys/.initial=1, + /codeexample/prettyprint/cs/pgfkeys/.code 2 args={\pgfmanualpdfref{#1}{#1}\{\pgfmanualprettyprintpgfkeys{#2}\pgfmanualclosebrace}, + /codeexample/prettyprint/autolinks/.style={% + /codeexample/prettyprint/key name/.code={\pgfmanualpdfref{##1}{##1}}, + /codeexample/prettyprint/key name with handler/.code 2 args={\pgfmanualpdfref{##1}{##1}/\pgfmanualpdfref{/handlers/##2}{##2}}, + /codeexample/prettyprint/key value display only/.code={\pgfmanualprettyprintcode{##1}}, + /codeexample/prettyprint/cs/.code={\pgfmanualpdfref{##1}{##1}}, + /codeexample/prettyprint/cs with args/.code 2 args={\pgfmanualpdfref{##1}{##1}\{\pgfmanualprettyprintcode{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/pgfkeys/.initial=1, + /codeexample/prettyprint/cs/pgfkeys/.code 2 args={\pgfmanualpdfref{##1}{##1}\{\pgfmanualprettyprintpgfkeys{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/begin/.initial=1, + /codeexample/prettyprint/cs/begin/.code 2 args={##1\{\pgfmanualpdfref{##2}{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/end/.initial=1, + /codeexample/prettyprint/cs/end/.code 2 args={##1\{\pgfmanualpdfref{##2}{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/word/.code={\begingroup\pgfkeyssetvalue{/pdflinks/search key prefixes in}{}\pgfmanualpdfref{##1}{##1}\endgroup}, + /codeexample/prettyprint/point/.code={##1},% + /codeexample/prettyprint/point with cs/.code 2 args={(\pgfmanualpdfref{##1}{##1}:##2},% + },% + /codeexample/prettyprint/autolinks, +}% + +\pgfkeys{ + /pdflinks/codeexample links/.is if=pgfmanualprettyenabled, + /pdflinks/codeexample links/.default=true, + /pdflinks/render hyperlink/.code={#1}, + /pdflinks/search key prefixes in/.initial={/tikz/,/pgf/}, + /pdflinks/warnings/.is if=pgfmanualpdfwarnings, + /pdflinks/warnings/.default=true, + /pdflinks/show labels/.is if=pgfmanualshowlabels, + /pdflinks/show labels/.default=true, + /pdflinks/show labels=false, + /pdflinks/show labels code/.code={ + \hbox to 0pt{% + \vbox to 0pt{\hsize=0pt + \vskip-\baselineskip + \hbox to \hsize{% + \hss + {\footnotesize\ttfamily\textcolor{red}{#1}}% + \hss + }% + \vss + }% + \vbox to 0pt{\hsize=0pt + \vss + \hbox to \hsize{% + \hss + {\footnotesize\ttfamily\textcolor{red}{$\vert$}}% + \hss + }% + }% + \vsize=0pt + }% + }, + /pdflinks/internal link prefix/.initial=pgf, +} + +\begingroup + \catcode`\_=12 + \gdef\pgfmanualpdf@underscore{_}% + \catcode`\ =13\relax\gdef\pgfmanualpdf@install@active@space{\def {\space}}% +\endgroup + +\gdef\pgfmanualpdf@installreplacements{% + \def\marg##1{{##1}}% + \def\oarg##1{[##1]}% + \def\meta##1{meta(##1)}% + \def\x{x}% + \def\textbackslash{back/}% + \def\\{\textbackslash}% + \def\space{:}% + \edef\ {\space}% + \edef\SPACE{\` \relax}% + \ifnum\the\catcode`\ =13 % + \pgfmanualpdf@install@active@space + \fi + \edef\#{}% + \def\printanat{@}% + \def\protect{}% + \def\textasciicircum{o}% + \def\_{\pgfmanualpdf@underscore}% + \expandafter\edef\pgfmanual@verb@activebar{\pgfmanual@verb@bar}% +}% + +\def\pgfmanualpdflabel{\pgfutil@ifnextchar[{\pgfmanualpdflabel@opt}{\pgfmanualpdflabel@opt[]}}% +\def\pgfmanualpdflabel@opt[#1]#2#3{% + \begingroup + \def\pgfmanualpdf@catcode{#1}% + \pgfmanualpdf@catcode + \pgfmanualpdflabel@generate{#2}{#3}% + \pgfutil@in@\x{#2}% + \ifpgfutil@in@ + \def\x{y}% + \pgfmanualpdflabel@generate{#2}{#3}% + \def\x{z}% + \pgfmanualpdflabel@generate{#2}{#3}% + \fi + \endgroup +}% +\def\pgfmanualpdflabel@generate#1#2{% + \pgfmanual@handlespeciallabeltokens@in{#1}% + \def\pgfmanualpdflabel@generateone{0}% + \pgfutil@ifundefined{pgfd@lbl@\pgfmanualpdflabel@@}{% + \def\pgfmanualpdflabel@generateone{1}% + }{% + \if\csname pgfd@lbl@\pgfmanualpdflabel@@\endcsname a% + \def\pgfmanualpdflabel@generateone{1}% + \else + \fi + }% + \if\pgfmanualpdflabel@generateone1% + \ifpgfmanualshowlabels + \pgfkeysvalueof{/pdflinks/show labels code/.@cmd}{\pgfmanualpdflabel@@}\pgfeov + \fi + \if@filesw + \ifx\pgfmanualpdf@catcode\pgfutil@empty + \else + \toks0=\expandafter{\pgfmanualpdf@catcode}% + \immediate\write\@auxout{% + \noexpand\begingroup + \the\toks0 + }% + \fi + \immediate\write\@auxout{% + \noexpand\expandafter\noexpand\gdef + \noexpand\csname pgfd@lbl@\pgfmanualpdflabel@@\noexpand\endcsname{a}% + }% + \ifx\pgfmanualpdf@catcode\pgfutil@empty + \else + \immediate\write\@auxout{\noexpand\endgroup}% + \fi + \fi + \expandafter\gdef\csname pgfd@lbl@\pgfmanualpdflabel@@\endcsname{w}% + \edef\pgfmanualpdflabel@@{\pgfkeysvalueof{/pdflinks/internal link prefix}.\pgfmanualpdflabel@@}% + \ifvmode% + \expandafter\hypertarget\expandafter{\pgfmanualpdflabel@@}{#2}% + \else% + {\setbox0=\hbox{\raise1em\hbox{\expandafter\hypertarget\expandafter{\pgfmanualpdflabel@@}{}}}\ht0=0pt\box0}#2% + \fi% + \else + #2% + \fi +}% + +\def\pgfmanualpdfref#1#2{% + \begingroup + \pgfmanual@handlespeciallabeltokens@in{#1}% + \ifcsname pgfd@lbl@\pgfmanualpdflabel@@\endcsname + \else + \global\let\pgfmanual@glob=\pgfmanualpdflabel@@ + \def\pgfmanual@tempa{\foreach \prefix in }% + \pgfkeysgetvalue{/pdflinks/search key prefixes in}\pgfmanual@tempb + \expandafter\pgfmanual@tempa\expandafter{\pgfmanual@tempb}{% + \edef\pgfmanualpdflabel@@{\prefix\pgfmanualpdflabel@@}% + \expandafter\pgfmanual@handlespeciallabeltokens@in\expandafter{\pgfmanualpdflabel@@}% + \ifcsname pgfd@lbl@\pgfmanualpdflabel@@\endcsname + \xdef\pgfmanual@glob{\pgfmanualpdflabel@@}% + \breakforeach + \fi + }% + \let\pgfmanualpdflabel@@=\pgfmanual@glob + \ifcsname pgfd@lbl@\pgfmanualpdflabel@@\endcsname + \else + \ifpgfmanualpdfwarnings + \begingroup + \toks0={#1}% + \pgfmanual@warning{pgfmanualpdfref{\the\toks0 }: target label does not exist.}% + \endgroup + \fi + #2% + \let\pgfmanualpdflabel@@=\pgfutil@empty + \fi + \fi + \ifx\pgfmanualpdflabel@@\pgfutil@empty + \else + \expandafter\pgfmanualpdfref@\expandafter{\pgfmanualpdflabel@@}{#2}% + \fi + \endgroup +}% +\def\pgfmanualpdfref@#1#2{% + \pgfkeysgetvalue{/pdflinks/internal link prefix}\pgfmanual@temp + \expandafter\hyperlink\expandafter{\pgfmanual@temp.#1}{\pgfkeysvalueof{/pdflinks/render hyperlink/.@cmd}{#2}\pgfeov}% + \ifpgfmanualshowlabels + \pgfkeysvalueof{/pdflinks/show labels code/.@cmd}{#1}\pgfeov + \fi +}% + +\def\pgfmanual@handlespeciallabeltokens@in#1{% + \begingroup + \pgfmanualpdf@installreplacements + \expandafter\pgfutil@in@\pgfmanual@pretty@backslash{#1}% + \ifpgfutil@in@ + \pgfmanualpdfref@substitute@backslash#1\relax + \else + \edef\pgfmanualpdflabel@@{#1}% + \fi + \def\pgfmanual@tmp{\pgfutilstrreplace{ }{\space}}% + \expandafter\pgfmanual@tmp\expandafter{\pgfmanualpdflabel@@}% + \edef\pgfmanualpdflabel@@{\pgfretval}% + \pgfmath@smuggleone\pgfmanualpdflabel@@ + \endgroup +}% + +\expandafter\def\expandafter\pgfmanualpdfref@substitute@backslash\expandafter#\expandafter1\pgfmanual@pretty@backslash#2\relax{% + \edef\pgfmanualpdflabel@@{#1\textbackslash #2}% +}% + +\def\declareandlabel{% + \begingroup + \pgfmanual@verb@preparecatcodes@ + \def\pgfmanualprettyprinterhandlecollectedargs##1{% + \pgfmanualpdflabel##1{\texttt{\declare##1}}% + \endgroup + }% + \pgfmanualprettyprintercollectargcount1{\relax}% +} + +\def\verbpdfref{% + \begingroup + \pgfmanual@verb@preparecatcodes@ + \def\pgfmanualprettyprinterhandlecollectedargs##1{% + \pgfmanualpdfref##1{\texttt{##1}}% + \endgroup + }% + \pgfmanualprettyprintercollectargcount1{\relax}% +} + +{ + \catcode`\|=12 + \gdef\pgfmanual@verb@bar{|}% + \catcode`\|=13 + \gdef\pgfmanual@verb@activebar{|}% +} +\def\pgfmanual@verb{% + \begingroup + \pgfmanual@verb@preparecatcodes@ + \toksdef\t@pgfmanual@verb=0 + \t@pgfmanual@verb={}% + \pgfmanual@verb@collect +} +\def\pgfmanual@verb@collect#1{% + \def\pgfmanual@temp{#1}% + \ifx\pgfmanual@temp\pgfmanual@verb@bar + \edef\pgfmanual@verb@collect@next{% + \noexpand\endgroup + \noexpand\texttt{\noexpand\pgfmanualprettyprintpgfkeys{\the\t@pgfmanual@verb}}% + }% + \else + \ifx\pgfmanual@temp\pgfmanual@verb@activebar + \edef\pgfmanual@verb@collect@next{% + \noexpand\endgroup + \noexpand\texttt{\the\t@pgfmanual@verb}% + }% + \else + \t@pgfmanual@verb=\expandafter{\the\t@pgfmanual@verb #1}% + \let\pgfmanual@verb@collect@next=\pgfmanual@verb@collect + \fi + \fi + \pgfmanual@verb@collect@next +}% + +\AtBeginDocument{% + \ifpgfmanualprettyenabled + \catcode`\|=13 + \expandafter\let\pgfmanual@verb@activebar=\pgfmanual@verb + \fi +}% + +\def\pgfmanual@verb@preparecatcodes@{% + \let\do\@makeother% + \dospecials% + \catcode`\%=12 % + \catcode`\ =13 + \catcode`\^^I=13 + \expandafter\def\pgfmanual@pretty@activespace{\space}% + \expandafter\def\pgfmanual@pretty@activetab{\space\space\space\space}% +}% +\endinput diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.prettyprinter.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.prettyprinter.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..6429f148f1de849112da6ca5208f7945f0c9c59b --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/doc/pgfmanual.prettyprinter.code.tex @@ -0,0 +1,719 @@ + + +\pgfkeys{% + /codeexample/typeset listing/.code= {\pgfmanualprettyprintcode{#1}}, + /codeexample/prettyprint/key name/.code={#1}, + /codeexample/prettyprint/key name with handler/.code 2 args={#1/#2}, + /codeexample/prettyprint/key value/.code 2 args={% + \pgfkeysifdefined{/codeexample/prettyprint/key value/#1}{% + \pgfkeysalso{/codeexample/prettyprint/key value/#1={#1}{#2}}% + }{% + \pgfkeysalso{/codeexample/prettyprint/key value with style detection={#1}{#2}}% + }% + }, + /codeexample/prettyprint/key value with style detection/.code 2 args={% + \pgfutil@in@{style}{#1}% + \ifpgfutil@in@ + \pgfmanualprettyprintpgfkeys{#2}% + \else + \pgfkeysalso{/codeexample/prettyprint/key value display only={#2}}% + \fi + },% + /codeexample/prettyprint/key value display only/.code={#1}, + /codeexample/prettyprint/word/.code={#1}, + /codeexample/prettyprint/if space is word delim/.code 2 args={% + #1% + },% + /codeexample/prettyprint/if is word delim/.code args={#1#2#3}{% + \edef\pgfmanual@check{,;().;\pgfmanual@pretty@lbrace\pgfmanual@pretty@rbrace}% + \def\pgfmanual@check@{\pgfutil@in@{#1}}% + \expandafter\pgfmanual@check@\expandafter{\pgfmanual@check}% + \ifpgfutil@in@ #2\else #3\fi + },% + /codeexample/prettyprint/cs/.code={#1}, + /codeexample/prettyprint/cs with args/.code 2 args={#1\{#2\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/pgfkeys/.initial=1, + /codeexample/prettyprint/cs/pgfkeys/.code 2 args={#1\{\pgfmanualprettyprintpgfkeys{#2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/begin/.initial=1, + /codeexample/prettyprint/cs/begin/.code 2 args={#1\{#2\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/end/.initial=1, + /codeexample/prettyprint/cs/end/.code 2 args={#1\{#2\pgfmanualclosebrace}, + /codeexample/prettyprint/point/.code={#1},% + /codeexample/prettyprint/point with cs/.code 2 args={(#1:#2},% + /codeexample/prettyprint/comment font/.initial=,% + /codeexample/prettyprint/colored/.style={% + /codeexample/prettyprint/key name/.code={\textcolor{red!75!black}{##1}}, + /codeexample/prettyprint/key name with handler/.code 2 args={\textcolor{red!75!black}{##1}/\textcolor{red!90!black}{##2}}, + /codeexample/prettyprint/key value display only/.code={\textcolor{yellow}{##1}}, + /codeexample/prettyprint/cs/.code={\textcolor{green}{##1}}, + /codeexample/prettyprint/cs with args/.code 2 args={\textcolor{green}{##1}\{\textcolor{orange}{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/pgfkeys/.initial=1, + /codeexample/prettyprint/cs/pgfkeys/.code 2 args={\textcolor{green}{##1}\{\pgfmanualprettyprintpgfkeys{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/begin/.initial=1, + /codeexample/prettyprint/cs/begin/.code 2 args={\textcolor{green}{##1}\{\textcolor{orange}{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/cs arguments/end/.initial=1, + /codeexample/prettyprint/cs/end/.code 2 args={\textcolor{green}{##1}\{\textcolor{orange}{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/word/.code={\textcolor{brown}{##1}}, + /codeexample/prettyprint/point/.code={\textcolor{red}{##1}},% + /codeexample/prettyprint/point with cs/.code 2 args={(\textcolor{green}{##1}:\textcolor{red}{##2}},% + },% + /codeexample/prettyprint/colored and verbose/.style={% + /codeexample/prettyprint/colored, + /codeexample/prettyprint/key name/.code={\message{[key name=##1]}\textcolor{red!75!black}{##1}}, + /codeexample/prettyprint/key name with handler/.code 2 args={\message{[key name with handler=##1/##2]}\textcolor{red!75!black}{##1}/\textcolor{red!90!black}{##2}}, + /codeexample/prettyprint/key value display only/.code={\def\temp{##1}\message{[key value=\meaning\temp]}\textcolor{yellow}{##1}}, + /codeexample/prettyprint/cs/.code={\message{[cs=##1]}\textcolor{green}{##1}}, + /codeexample/prettyprint/cs with args/.code 2 args={\def\temp{##2}\message{[cs with args={##1}{\meaning\temp}]}\textcolor{green}{##1}\{\textcolor{orange}{##2}\pgfmanualclosebrace}, + /codeexample/prettyprint/word/.code={\message{[word=##1]}\textcolor{brown}{##1}}, + /codeexample/prettyprint/point/.code={\message{[point=##1]}\textcolor{red}{##1}},% + /codeexample/prettyprint/point with cs/.code 2 args={\message{[point with cs={##1}{##2}]}(\textcolor{green}{##1}:\textcolor{red}{##2}},% + },% +}% + +\newif\ifpgfmanualprettyenabled +\pgfmanualprettyenabledtrue + +\def\pgfmanualclosebrace{% + \ifpgfmanualprettyprinterarghasunmatchedbraces + \else + \}% + \fi +}% + + +\long\def\pgfmanualprettyprintcode#1{% + \ifpgfmanualprettyenabled + \begingroup + \pgfmanualprettyprintstyles + \pgfmanual@pretty@mainloop#1\pgfmanual@EOI + \endgroup + \else + #1% + \fi +}% + +\def\pgfmanualprettyprintstyles{% + \def\{{\pgfmanual@pretty@lbrace}% + \def\}{\pgfmanual@pretty@rbrace}% + \pgfmanual@pretty@installcommenthandler + \let\pgfmanualprettyprintstyles=\relax +}% + + +\newif\ifpgfmanualprettycommentactive + +\def\pgfmanual@pretty@installcommenthandler{% + \expandafter\def\pgfmanual@pretty@activepercent{% + \begingroup% + \pgfmanualprettycommentactivetrue + \expandafter\let\pgfmanual@pretty@activenl=\pgfmanual@pretty@recoveraftercomment + \expandafter\def\pgfmanual@pretty@activepercent{\%}% + \pgfkeysvalueof{/codeexample/prettyprint/comment font}% + \%% + }% +}% +\def\pgfmanual@pretty@recoveraftercomment{% + \endgroup + \pgfmanual@pretty@activenl +}% + +\def\pgfmanual@EOI{\pgfmanual@EOI}% + +{ + \catcode`\[=0 + \catcode`\\=12 + [gdef[pgfmanual@pretty@backslash{\}% +} +\begingroup + \catcode`\:=12 + \catcode`\(=12 + \catcode`\)=12 + \gdef\pgfmanual@pretty@colon{:}% + \gdef\pgfmanual@pretty@lroundbrace{(}% + \gdef\pgfmanual@pretty@rroundbrace{)}% + \catcode`\[=1 + \catcode`\]=2 + \catcode`\{=12 + \catcode`\}=12 + \gdef\pgfmanual@pretty@lbrace[{]% + \gdef\pgfmanual@pretty@rbrace[}]% + \catcode`\{=1 + \catcode`\}=2 + \catcode`\[=12 + \catcode`\]=12 + \catcode`\,=12 + \catcode`\ =10\relax\gdef\pgfmanual@pretty@space{ }% + \gdef\pgfmanual@pretty@lbracket{[}% + \gdef\pgfmanual@pretty@rbracket{]}% + \gdef\pgfmanual@pretty@comma{,}% + \catcode`\==12 + \gdef\pgfmanual@pretty@eq{=}% +\endgroup +\begingroup + \catcode`\%=12 + \gdef\pgfmanual@pretty@percent{%} + \catcode`\%=13 + \gdef\pgfmanual@pretty@activepercent{%} + \catcode`\^^M=13 + \gdef\pgfmanual@pretty@activenl{^^M}\endgroup +\begingroup +\catcode`\^^I=13\relax\gdef\pgfmanual@pretty@activetab{^^I}% +\catcode`\ =13\relax\gdef\pgfmanual@pretty@activespace{ }\endgroup + +\def\pgfmanual@pretty@mainloop{% + \def\pgfmanual@pretty@mainloop@currentword{}% + \pgfmanual@pretty@mainloop@ +}% +\long\def\pgfmanual@pretty@mainloop@#1{% + \def\pgfmanual@loc@TMPa{#1}% + \let\pgfmanual@pretty@mainloop@NEXT=\pgfmanual@pretty@mainloop@ + \ifx\pgfmanual@loc@TMPa\pgfmanual@EOI + \pgfmanual@pretty@mainloop@finishword + \let\pgfmanual@pretty@mainloop@NEXT=\relax + \else + \ifpgfmanualprettycommentactive + #1\kern0pt% + \else + \ifx\pgfmanual@loc@TMPa\pgfmanual@pretty@lbracket% + \pgfmanual@pretty@mainloop@finishword + \let\pgfmanual@pretty@mainloop@NEXT=\pgfmanual@pretty@pgfkeys + \else + \ifx\pgfmanual@loc@TMPa\pgfmanual@pretty@backslash + \pgfmanual@pretty@mainloop@finishword + \let\pgfmanual@loc@TMPa=\pgfutil@empty + \let\pgfmanual@pretty@mainloop@NEXT=\pgfmanual@pretty@collectcs@loop + \else + \ifx\pgfmanual@loc@TMPa\pgfmanual@pretty@lroundbrace% + \pgfmanual@pretty@mainloop@finishword + \let\pgfmanual@pretty@mainloop@NEXT=\pgfmanual@pretty@collectpoint + \else + \def\pgfmanual@isspace{0}% + \ifnum13=\catcode`#1 + \def\pgfmanual@isspace{1}% + \else + \ifnum10=\catcode`#1 + \def\pgfmanual@isspace{1}% + \fi + \fi + \if\pgfmanual@isspace1% + \pgfkeysvalueof{/codeexample/prettyprint/if space is word delim/.@cmd}{% + \pgfmanual@pretty@mainloop@finishword + #1% + }{% + \expandafter\def\expandafter\pgfmanual@pretty@mainloop@currentword\expandafter{\pgfmanual@pretty@mainloop@currentword #1}% + }% + \else + \pgfkeysvalueof{/codeexample/prettyprint/if is word delim/.@cmd}{#1}{% + \pgfmanual@pretty@mainloop@finishword + #1% + }{% + \expandafter\def\expandafter\pgfmanual@pretty@mainloop@currentword\expandafter{\pgfmanual@pretty@mainloop@currentword #1}% + }\pgfeov% + \fi + \fi + \fi + \fi + \fi + \fi + \pgfmanual@pretty@mainloop@NEXT +}% + +\def\pgfmanual@pretty@mainloop@finishword{% + \ifx\pgfmanual@pretty@mainloop@currentword\pgfutil@empty + \else + \def\pgfmanual@loc@TMPa{\pgfkeysvalueof{/codeexample/prettyprint/word/.@cmd}}% + \expandafter\pgfmanual@loc@TMPa\pgfmanual@pretty@mainloop@currentword\pgfeov + \let\pgfmanual@pretty@mainloop@currentword=\pgfutil@empty + \fi +}% + +\def\pgfmanual@pretty@collectpoint{% + \let\pgfmanualprettyprinterhandlecollectedargsVtwo=\pgfmanual@pretty@collectargs@finish@collectpoint + \expandafter\pgfmanualprettyprintercollectupto\pgfmanual@pretty@rroundbrace + {\afterpgfmanual@pretty@collectpoint}% +} + +{ +\catcode`\:=12 +\gdef\pgfmanual@pretty@collectargs@finish@collectpoint#1#2{% + \expandafter\pgfutil@in@\pgfmanual@pretty@colon{#1}% + \ifpgfutil@in@ + \def\pgfmanual@pretty@collectpoint@getcoordsystem##1:##2\relax{% + \begingroup + \pgfmanual@pretty@restorespaces + \xdef\pgfmanual@pretty@glob@TMPa{##1}% + \endgroup + \pgfkeysifdefined{/codeexample/prettyprint/point with cs/\pgfmanual@pretty@glob@TMPa/.@cmd}{% + \def\pgfmanual@loc@TMPb{\pgfkeysvalueof{/codeexample/prettyprint/point with cs/\pgfmanual@pretty@glob@TMPa/.@cmd}}% + }{% + \def\pgfmanual@loc@TMPb{\pgfkeysvalueof{/codeexample/prettyprint/point with cs/.@cmd}}% + }% + \expandafter\def\expandafter\pgfmanual@loc@TMPa\expandafter{\expandafter{\pgfmanual@pretty@glob@TMPa}{##2}}% + \expandafter\pgfmanual@loc@TMPb\pgfmanual@loc@TMPa\pgfeov + }% + \if1#2% + \pgfmanual@pretty@collectpoint@getcoordsystem#1)\relax + \else + \pgfmanual@pretty@collectpoint@getcoordsystem#1\relax + \fi + \else + \def\pgfmanual@loc@TMPb{\pgfkeysvalueof{/codeexample/prettyprint/point/.@cmd}}% + \if1#2% + \pgfmanual@loc@TMPb(#1)\pgfeov + \else + \pgfmanual@loc@TMPb(#1\pgfeov + \fi + \fi +}% +} +\def\afterpgfmanual@pretty@collectpoint{\pgfmanual@pretty@mainloop}% + +\def\pgfmanual@pretty@collectcs@loop#1{% + \let\pgfmanual@pretty@collectcs@loop@NEXT=\pgfmanual@pretty@collectcs@loop + \def\pgfmanual@loc@TMPb{#1}% + \ifx\pgfmanual@loc@TMPb\pgfmanual@EOI + \def\pgfmanual@pretty@collectcs@loop@NEXT{\pgfmanual@pretty@collectcs@loop@END #1}% + \else + \ifnum\lccode`#1=0 + \ifx\pgfmanual@loc@TMPb\pgfmanual@attext% + \edef\pgfmanual@loc@TMPa{\pgfmanual@loc@TMPa #1}% + \else + \def\pgfmanual@pretty@collectcs@loop@NEXT{\pgfmanual@pretty@collectcs@loop@END #1}% + \fi + \else + \edef\pgfmanual@loc@TMPa{\pgfmanual@loc@TMPa #1}% + \fi + \fi + \pgfmanual@pretty@collectcs@loop@NEXT +}% +\def\afterpgfmanual@pretty@cs{\pgfmanual@pretty@mainloop}% +\def\pgfmanual@attext{@} + +\def\pgfmanual@pretty@collectcs@loop@END{% + \pgfkeysifdefined{/codeexample/prettyprint/cs arguments/\pgfmanual@loc@TMPa}{% + \let\pgfmanualprettyprinterhandlecollectedargs=\pgfmanual@pretty@collectargs@finish@cs + \def\pgfmanual@pretty@collectcs@loop@END@next{% + \pgfmanualprettyprintercollectargcount + {\pgfkeysvalueof{/codeexample/prettyprint/cs arguments/\pgfmanual@loc@TMPa}}% + {\afterpgfmanual@pretty@cs}% + }% + }{% + \edef\pgfmanual@loc@TMPa{\pgfmanual@pretty@backslash \pgfmanual@loc@TMPa}% + \def\pgfmanual@loc@TMPb{\pgfkeysvalueof{/codeexample/prettyprint/cs/.@cmd}}% + \expandafter\pgfmanual@loc@TMPb\pgfmanual@loc@TMPa\pgfeov + \let\pgfmanual@pretty@collectcs@loop@END@next=\afterpgfmanual@pretty@cs + }% + \pgfmanual@pretty@collectcs@loop@END@next +}% + +\newif\ifpgfmanualprettyprinterarghasunmatchedbraces + +\def\pgfmanualprettyprintercollectargcount#1#2{% + \pgfmanualprettyprinterarghasunmatchedbracesfalse + \begingroup + \edef\pgfmanual@loc@csargcount{#1}% + \toksdef\t@afterpgfmanualprettyprinterhandlecollected=10 + \t@afterpgfmanualprettyprinterhandlecollected={#2}% + \let\c@pgfmanual@pretty@openbracecount=\c@pgf@counta + \let\c@pgfmanual@pretty@curargcount=\c@pgf@countb + \c@pgfmanual@pretty@openbracecount=0 + \c@pgfmanual@pretty@curargcount=0 + \toksdef\t@pgfmanual@currentarg=0 + \toksdef\t@pgfmanual@allargs=1 + \t@pgfmanual@currentarg={}% + \t@pgfmanual@allargs={}% + \pgfmanual@pretty@collectargs@loop +}% + +\def\pgfmanual@pretty@collectargs@loop#1{% + \let\pgfmanual@pretty@collectargs@loop@NEXT=\pgfmanual@pretty@collectargs@loop + \def\pgfmanual@loc@TMPc{#1}% + \ifx\pgfmanual@loc@TMPc\pgfmanual@EOI + \ifnum\c@pgfmanual@pretty@openbracecount>0 + \ifpgfmanualpdfwarnings + \pgfplots@warning{The pretty printer did not found the closing curly brace!? This will potentially lead to display errors}% + \fi + \fi + \edef\pgfmanual@pretty@collectargs@loop@NEXT{% + \noexpand\endgroup + \ifnum\c@pgfmanual@pretty@openbracecount>0 + \noexpand\pgfmanualprettyprinterarghasunmatchedbracestrue + \fi + \noexpand\def\noexpand\pgfmanualprettyprinternumcollectedargs{\the\c@pgfmanual@pretty@curargcount}% + \noexpand\pgfmanualprettyprinterhandlecollectedargs{\the\t@pgfmanual@allargs\the\t@pgfmanual@currentarg}% + \the\t@afterpgfmanualprettyprinterhandlecollected + \noexpand\pgfmanual@EOI% + }% + \else + \ifpgfmanualprettycommentactive + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@activenl + \pgfmanualprettycommentactivefalse + \fi + \else + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@activepercent + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \pgfmanualprettycommentactivetrue + \else + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@lbrace + \advance\c@pgfmanual@pretty@openbracecount by1 + \ifnum\c@pgfmanual@pretty@openbracecount>1 + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \fi + \else + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@rbrace + \advance\c@pgfmanual@pretty@openbracecount by-1 + \ifnum\c@pgfmanual@pretty@openbracecount=0 + \edef\pgfmanual@loc@TMPc{\the\t@pgfmanual@allargs{\the\t@pgfmanual@currentarg}}% + \t@pgfmanual@allargs=\expandafter{\pgfmanual@loc@TMPc}% + \t@pgfmanual@currentarg={}% + \advance\c@pgfmanual@pretty@curargcount by1 + \ifnum\c@pgfmanual@pretty@curargcount=\pgfmanual@loc@csargcount\relax + \edef\pgfmanual@pretty@collectargs@loop@NEXT{% + \noexpand\endgroup + \noexpand\def\noexpand\pgfmanualprettyprinternumcollectedargs{\the\c@pgfmanual@pretty@curargcount}% + \noexpand\pgfmanualprettyprinterhandlecollectedargs{\the\t@pgfmanual@allargs}% + \the\t@afterpgfmanualprettyprinterhandlecollected + }% + \fi + \else + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \fi + \else + \ifnum13=\catcode`#1 + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \else + \ifnum10=\catcode`#1 + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \else + \ifnum\c@pgfmanual@pretty@openbracecount=0 + \ifpgfmanualpdfwarnings + \begingroup + \toks4{#1}% + \pgfplots@warning{The pretty printer did not find the expected \pgfmanual@loc@csargcount\space arguments (only token \the\toks4 )}% + \endgroup + \fi + \edef\pgfmanual@pretty@collectargs@loop@NEXT{% + \noexpand\endgroup + \noexpand\def\noexpand\pgfmanualprettyprinternumcollectedargs{\the\c@pgfmanual@pretty@curargcount}% + \noexpand\pgfmanualprettyprinterhandlecollectedargs{\the\t@pgfmanual@allargs\the\t@pgfmanual@currentarg}% + \the\t@afterpgfmanualprettyprinterhandlecollected + \noexpand#1% + }% + \else + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \fi + \fi + \fi + \fi + \fi + \fi + \fi + \fi + \pgfmanual@pretty@collectargs@loop@NEXT +}% + +\newif\ifpgfmanualprettyprinterfoundterminator + +\def\pgfmanualprettyprinterhandlecollectedargsVtwo@default#1#2{% + \if1#2% + \pgfmanualprettyprinterfoundterminatortrue + \else + \pgfmanualprettyprinterfoundterminatorfalse + \fi + \pgfmanualprettyprinterhandlecollectedargs{#1}% +}% +\def\pgfmanualprettyprintercollectupto@restore@callback{% + \let\pgfmanualprettyprinterhandlecollectedargsVtwo=\pgfmanualprettyprinterhandlecollectedargsVtwo@default +}% +\pgfmanualprettyprintercollectupto@restore@callback + +\def\pgfmanualprettyprintercollectupto#1#2{% + \pgfmanualprettyprinterarghasunmatchedbracesfalse + \def\pgfmanualprettyprinterterminator{}% + \begingroup + \def\pgfmanual@loc@delimittokens{#1}% + \toksdef\t@afterpgfmanualprettyprinterhandlecollected=10 + \t@afterpgfmanualprettyprinterhandlecollected={#2}% + \let\c@pgfmanual@pretty@openbracecount=\c@pgf@counta + \c@pgfmanual@pretty@openbracecount=0 + \toksdef\t@pgfmanual@currentarg=0 + \t@pgfmanual@currentarg={}% + \pgfmanual@pretty@collectupto@loop +}% + +\def\pgfmanualprettyprinterterminator{} + +\def\pgfmanual@pretty@collectupto@loop#1{% + \let\pgfmanual@pretty@collectupto@loop@NEXT=\pgfmanual@pretty@collectupto@loop + \def\pgfmanual@loc@TMPc{#1}% + \ifx\pgfmanual@loc@TMPc\pgfmanual@EOI + \edef\pgfmanual@pretty@collectupto@loop@NEXT{% + \noexpand\endgroup + \ifnum\c@pgfmanual@pretty@openbracecount>0 + \noexpand\pgfmanualprettyprinterarghasunmatchedbracestrue + \fi + \noexpand\pgfmanualprettyprinterhandlecollectedargsVtwo{\the\t@pgfmanual@currentarg}{0}% + \noexpand\pgfmanualprettyprintercollectupto@restore@callback + \the\t@afterpgfmanualprettyprinterhandlecollected + \noexpand\pgfmanual@EOI% + }% + \else + \ifpgfmanualprettycommentactive + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@activenl + \pgfmanualprettycommentactivefalse + \fi + \else + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@activepercent + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \pgfmanualprettycommentactivetrue + \else + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@lbrace + \advance\c@pgfmanual@pretty@openbracecount by1 + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \else + \ifx\pgfmanual@loc@TMPc\pgfmanual@pretty@rbrace + \advance\c@pgfmanual@pretty@openbracecount by-1 + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \else + \expandafter\expandafter\expandafter\pgfutil@in@\expandafter\pgfmanual@loc@TMPc\expandafter{\pgfmanual@loc@delimittokens}% + \ifpgfutil@in@ + \ifnum\c@pgfmanual@pretty@openbracecount=0 + \edef\pgfmanual@pretty@collectupto@loop@NEXT{% + \noexpand\endgroup + \noexpand\def\noexpand\pgfmanualprettyprinterterminator{\pgfmanual@loc@TMPc}% + \noexpand\pgfmanualprettyprinterhandlecollectedargsVtwo{\the\t@pgfmanual@currentarg}{1}% + \noexpand\pgfmanualprettyprintercollectupto@restore@callback + \the\t@afterpgfmanualprettyprinterhandlecollected + }% + \else + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \fi + \else + \t@pgfmanual@currentarg=\expandafter{\the\t@pgfmanual@currentarg#1}% + \fi + \fi + \fi + \fi + \fi + \fi + \pgfmanual@pretty@collectupto@loop@NEXT +}% + +\def\pgfmanual@pretty@collectargs@finish@cs#1{% + \def\pgfmanual@pretty@collectargs@finish@cs@hasargs{1}% + \ifnum\pgfmanualprettyprinternumcollectedargs=0 + \ifpgfmanualprettyprinterarghasunmatchedbraces + \else + \def\pgfmanual@pretty@collectargs@finish@cs@hasargs{0}% + \fi + \fi + \if\pgfmanual@pretty@collectargs@finish@cs@hasargs1% + \pgfkeysifdefined{/codeexample/prettyprint/cs/\pgfmanual@loc@TMPa/.@cmd}{% + \edef\pgfmanual@loc@TMPb{\noexpand\pgfkeysvalueof{/codeexample/prettyprint/cs/\pgfmanual@loc@TMPa/.@cmd}}% + }{% + \edef\pgfmanual@loc@TMPb{\noexpand\pgfkeysvalueof{/codeexample/prettyprint/cs with args/.@cmd}}% + }% + \edef\pgfmanual@loc@TMPa{{\pgfmanual@pretty@backslash\pgfmanual@loc@TMPa}}% + \expandafter\pgfmanual@loc@TMPb\pgfmanual@loc@TMPa #1\pgfeov + \else + \edef\pgfmanual@loc@TMPa{{\pgfmanual@pretty@backslash\pgfmanual@loc@TMPa}}% + \edef\pgfmanual@loc@TMPb{\noexpand\pgfkeysvalueof{/codeexample/prettyprint/cs/.@cmd}}% + \expandafter\pgfmanual@loc@TMPb\pgfmanual@loc@TMPa\pgfeov + #1\relax% + \fi +}% + +\long\def\pgfmanualprettyprintpgfkeys#1{% + \ifpgfmanualprettyenabled + \begingroup + \pgfmanualprettyprintstyles + \pgfmanual@pretty@pgfkeys@loop#1\pgfmanual@EOI + \endgroup + \else + #1% + \fi +} + +\def\pgfmanual@pretty@pgfkeys{% + \let\pgfmanualprettyprinterhandlecollectedargsVtwo=\pgfmanual@pretty@pgfkeys@start + \pgfmanualprettyprintercollectupto]{\pgfmanual@pretty@mainloop}% +}% +\long\def\pgfmanual@pretty@pgfkeys@start#1#2{% + [% + \pgfmanual@pretty@pgfkeys@loop#1\pgfmanual@EOI + \if1#2% + ]% + \fi +}% +\long\def\pgfmanual@pretty@pgfkeys@loop#1{% + \def\pgfmanual@loc@TMPa{#1}% + \ifx\pgfmanual@loc@TMPa\pgfmanual@EOI + \def\pgfmanual@pretty@pgfkeys@loop@NEXT{\relax}% + \else + \def\pgfmanual@pretty@pgfkeys@loop@NEXT{\pgfmanual@pretty@pgfkeys@loop}% + \ifpgfmanualprettycommentactive + #1\kern0pt% + \else + \ifnum13=\catcode`#1 + #1% + \else + \ifx\pgfmanual@loc@TMPa\pgfmanual@pretty@comma% + ,% + \else + \ifnum10=\catcode`#1 + #1% + \else + \ifx\pgfmanual@loc@TMPa\pgfmanual@pretty@lbrace + #1% + \else + \ifx\pgfmanual@loc@TMPa\pgfmanual@pretty@rbrace + #1% + \else + \toks0={}% + \def\pgfmanual@pretty@pgfkeys@loop@NEXT{\pgfmanual@pretty@pgfkeys@collectkey #1}% + \fi + \fi + \fi + \fi + \fi + \fi + \fi + \pgfmanual@pretty@pgfkeys@loop@NEXT +}% +\def\pgfmanual@pretty@pgfkeys@collectkey#1{% + \def\pgfmanual@loc@TMPb{#1}% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\pgfmanual@pretty@pgfkeys@collectkey}% + \ifx\pgfmanual@loc@TMPb\pgfmanual@EOI + \edef\pgfmanual@loc@TMPb{\the\toks0 }% + \ifx\pgfmanual@loc@TMPb\pgfutil@empty + \else + \expandafter\pgfmanual@pretty@pgfkeys@processkey\expandafter{\the\toks0 }% + \fi + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\relax}% + \else + \ifx\pgfmanual@loc@TMPb\pgfmanual@pretty@eq + \expandafter\pgfmanual@pretty@pgfkeys@processkey\expandafter{\the\toks0 }% + #1% + \toks0={}% + \def\pgfmanual@pretty@pgfkeys@collectvalue@hasconsumedspaces{0}% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\pgfmanual@pretty@pgfkeys@collectvalue}% + \else + \ifx\pgfmanual@loc@TMPb\pgfmanual@pretty@comma + \expandafter\pgfmanual@pretty@pgfkeys@processkey\expandafter{\the\toks0 }% + #1% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\pgfmanual@pretty@pgfkeys@loop}% + \else + \ifx\pgfmanual@loc@TMPb\pgfmanual@pretty@activenl + \expandafter\pgfmanual@pretty@pgfkeys@processkey\expandafter{\the\toks0 }% + #1% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\pgfmanual@pretty@pgfkeys@loop}% + \else + \ifx\pgfmanual@loc@TMPb\pgfmanual@pretty@backslash + \edef\pgfmanual@loc@TMPb{\the\toks0 }% + \ifx\pgfmanual@loc@TMPb\pgfutil@empty + \else + \expandafter\pgfmanual@pretty@pgfkeys@processkey\expandafter{\the\toks0 }% + \fi + \begingroup + \let\pgfmanual@loc@TMPa=\pgfutil@empty + \def\afterpgfmanual@pretty@cs{% + \endgroup + \pgfmanual@pretty@pgfkeys@loop + }% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\pgfmanual@pretty@collectcs@loop}% + \else + \ifx\pgfmanual@loc@TMPb\pgfmanual@pretty@lbrace + \def\pgfmanualprettyprinterhandlecollectedargs##1{% + \toks1={##1}% + \edef\pgfmanual@loc@TMPc{% + \the\toks0 \pgfmanual@pretty@lbrace \the\toks1 + \ifpgfmanualprettyprinterarghasunmatchedbraces + \else + \pgfmanual@pretty@rbrace + \fi + }% + \toks0=\expandafter{\pgfmanual@loc@TMPc}% + }% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{% + \pgfmanualprettyprintercollectargcount{1}{\pgfmanual@pretty@pgfkeys@collectkey}% + #1% + }% + \else + \ifx\pgfmanual@loc@TMPb\pgfmanual@pretty@rbrace + \expandafter\pgfmanual@pretty@pgfkeys@processkey\expandafter{\the\toks0 }% + #1% + \def\pgfmanual@pretty@pgfkeys@collectkey@next{\pgfmanual@pretty@pgfkeys@loop}% + \else + \toks0=\expandafter{\the\toks0 #1}% + \fi + \fi + \fi + \fi + \fi + \fi + \fi + \pgfmanual@pretty@pgfkeys@collectkey@next +}% +\def\pgfmanual@pretty@pgfkeys@collectvalue#1{% + \def\pgfmanual@loc@TMPb{#1}% + \let\pgfmanual@pretty@pgfkeys@collectvalue@next=\pgfmanual@pretty@pgfkeys@collectvalue + \ifx\pgfmanual@loc@TMPb\pgfmanual@EOI + \let\pgfmanual@pretty@pgfkeys@collectvalue@next=\relax + \else + \def\pgfmanual@pretty@isconsumed{0}% + \if\pgfmanual@pretty@pgfkeys@collectvalue@hasconsumedspaces0% + \ifnum13=\catcode`#1 + #1% + \def\pgfmanual@pretty@isconsumed{1}% + \else + \ifnum10=\catcode`#1 + \def\pgfmanual@pretty@isconsumed{1}% + #1% + \fi + \fi + \fi + \if\pgfmanual@pretty@isconsumed0% + \def\pgfmanualprettyprinterhandlecollectedargsVtwo##1##2{\pgfmanual@pretty@pgfkeys@processvalue{##1}}% + \def\pgfmanual@pretty@pgfkeys@collectvalue@next{% + \pgfmanualprettyprintercollectupto{,]}{\afterpgfmanual@pretty@collectargs@finish@value}#1% + }% + \fi + \fi + \pgfmanual@pretty@pgfkeys@collectvalue@next +}% +\def\afterpgfmanual@pretty@collectargs@finish@value{% + \expandafter\pgfmanual@pretty@pgfkeys@loop\pgfmanualprettyprinterterminator% +}% + +{\catcode`\^^M=13 \catcode`\ =13\relax\catcode`\%=13\relax\gdef\pgfmanual@pretty@restorespaces{\def%{\pgfmanual@pretty@percent}\def^^M{\pgfmanual@pretty@space}\def {\pgfmanual@pretty@space}}} + +\def\pgfmanual@pretty@pgfkeys@processkey#1{% + \begingroup + \pgfmanual@pretty@restorespaces + \xdef\pgfmanual@pretty@pgfkeys@collectkey@keyname{#1}% + \endgroup + \def\pgfmanual@loc@TMPa{\pgfutil@in@{/.}}% + \expandafter\pgfmanual@loc@TMPa\expandafter{\pgfmanual@pretty@pgfkeys@collectkey@keyname}% + \ifpgfutil@in@ + \def\pgfmanual@pretty@splitit##1/.##2\relax{% + \def\pgfmanual@loc@TMPb{{##1}{.##2}}% + }% + \expandafter\pgfmanual@pretty@splitit\pgfmanual@pretty@pgfkeys@collectkey@keyname\relax + \def\pgfmanual@loc@TMPa{\pgfkeysvalueof{/codeexample/prettyprint/key name with handler/.@cmd}}% + \expandafter\pgfmanual@loc@TMPa\pgfmanual@loc@TMPb\pgfeov + \else + \def\pgfmanual@loc@TMPa{\pgfkeysvalueof{/codeexample/prettyprint/key name/.@cmd}}% + \expandafter\pgfmanual@loc@TMPa\pgfmanual@pretty@pgfkeys@collectkey@keyname\pgfeov + \fi +} +\def\pgfmanual@pretty@pgfkeys@processvalue#1{% + \pgfkeysifdefined{/codeexample/prettyprint/key value/\pgfmanual@pretty@pgfkeys@collectkey@keyname/.@cmd}{% + \edef\pgfmanual@loc@TMPb{\noexpand\pgfkeysvalueof{/codeexample/prettyprint/key value/\pgfmanual@pretty@pgfkeys@collectkey@keyname/.@cmd}}% + }{% + \edef\pgfmanual@loc@TMPb{\noexpand\pgfkeysvalueof{/codeexample/prettyprint/key value/.@cmd}}% + }% + \edef\pgfmanual@loc@TMPa{{\pgfmanual@pretty@pgfkeys@collectkey@keyname}}% + \expandafter\pgfmanual@loc@TMPb\pgfmanual@loc@TMPa{#1}\pgfeov +} diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/frontendlayer/libraries/tikzlibraryexternal.code.tex b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/frontendlayer/libraries/tikzlibraryexternal.code.tex new file mode 100644 index 0000000000000000000000000000000000000000..bd5bfd9755112c8c690df3348a6774bf8cc646ab --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/build/tools/tex/latex/pgf/frontendlayer/libraries/tikzlibraryexternal.code.tex @@ -0,0 +1,63 @@ + +\usepackage{pdftexcmds} +\pgfutil@IfFileExists{atveryend.sty}{% + \usepackage{atveryend}% +}{% + \message{! Package tikz Warning: \string\usepackage{atveryend} impossible. Automatic resolving of references within external files impossible.}% +}% + +\input tikzexternalshared.code.tex + +\pgfutil@IfUndefined{pdf@mdfivesum}{}{% + \let\tikzexternal@mdfivesum=\pdf@mdfivesum +}% + +\def\tikzexternal@TEXDIALECT@begpicture{\begin{tikzpicture}} +\def\tikzexternal@TEXDIALECT@endpicture{\end{tikzpicture}}% + +\def\tikzexternal@TEXDIALECT@collectpicture#1{% + \begingroup + \t@tikzexternal@tmpa={}% + \tikzexternal@laTeX@collect@until@end@tikzpicture{#1}% +} + +\long\def\tikzexternal@laTeX@collect@until@end@tikzpicture#1#2\end#3{% + \def\tikzexternal@laTeX@collect@until@end@tikzpicture@{#3}% + \ifx\tikzexternal@laTeX@collect@until@end@tikzpicture@\tikzexternal@laTeX@collect@until@end@tikzpicturetikzpicturestring + \t@tikzexternal@tmpa=\expandafter{\the\t@tikzexternal@tmpa #2}% + \edef\tikzexternal@TEXDIALECT@collectpicture@next{% + \noexpand\endgroup + \noexpand#1{\the\t@tikzexternal@tmpa}% + }% + \t@tikzexternal@tmpa={}% + \else + \t@tikzexternal@tmpa=\expandafter{\the\t@tikzexternal@tmpa #2\end{#3}}% + \def\tikzexternal@TEXDIALECT@collectpicture@next{% + \tikzexternal@laTeX@collect@until@end@tikzpicture{#1}}% + \fi + \tikzexternal@TEXDIALECT@collectpicture@next +}% +\def\tikzexternal@laTeX@collect@until@end@tikzpicturetikzpicturestring{tikzpicture}% + +\def\tikzexternal@handle@landscape{% + \ltx@ifpackageloaded{pdflscape}{% + \tikzset{ + external/.cd, + optimize command away=\landscape, + optimize command away=\endlandscape + }% + }{% + }% +}% + +\let\tikzexternal@currname\@currname +\def\@currname{tikzlibraryexternal} + +\AtBeginDocument{% + \pgfutil@ifundefined{tikzexternalrealjob}{% + \global\let\tikzexternalrealjob=\jobname + }{}% + \tikzexternal@handle@landscape +}% + +\let\@currname\tikzexternal@currname diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf new file mode 100644 index 0000000000000000000000000000000000000000..095d0f30fe95139dde3cd000969189351a3c0867 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b1bb20744f2bfa517cf927d9b7f48cfb2ca923ab73fd7fc5cbad077af30aa548 +size 775445 diff --git a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/verification/rows.txt b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/verification/rows.txt new file mode 100644 index 0000000000000000000000000000000000000000..eb01ff68d5554a223e77b6c30cc12f9794766d85 --- /dev/null +++ b/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/verification/rows.txt @@ -0,0 +1,20 @@ +0 7181518 05:-849651 07:-2958744 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08:10575875 14:-252576 17:-8002616 18:22592844 28:7370640 + 32:289294 35:1400647 37:1987740 38:4030699 42:-1731401 43:-1034062 46:-1106371 + 47:-1257051 48:1461735 53:1408149 55:1136847 58:1878501 61:-2838516 63:-734099 + 64:1062416 65:11745 67:611312 72:-480776 73:20459 74:316925 76:37092 +7 1441784 07:3441286 08:-6097155 37:-1002399 47:-251321 58:1143225 66:-17397 71:-1007464 + 73:-662286 76:-344621 78:-1115284 diff --git a/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/README.md b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/README.md new file mode 100644 index 0000000000000000000000000000000000000000..08ed04d75bb95983f25daad7f6a8fc6dee9bf0c1 --- /dev/null +++ b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/README.md @@ -0,0 +1,17 @@ +# [Uniformization of complete Kähler manifolds with positive bisectional curvature](paper.pdf) + +OpenAI +September 23, 2026 + +## Citation + +```bibtex +@misc{OAI:Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026, + author = {{OpenAI}}, + title = {{Uniformization of complete K{\"a}hler manifolds with positive bisectional curvature}}, + howpublished = {OpenAI Math Release preprint + \href{https://github.com/openai/math/blob/main/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/paper.pdf}{OAI:Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026}}, + year = {2026} +} +``` + diff --git a/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/bibliography.tex b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/bibliography.tex new file mode 100644 index 0000000000000000000000000000000000000000..3cb1b2a2af3dcfcb2a0903f8401decf1f0fc16fa --- /dev/null +++ b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/bibliography.tex @@ -0,0 +1,424 @@ +\begin{thebibliography}{99} + +\bibitem{Aleksandrov1939} +A.~D.~Aleksandrov, +\emph{Almost everywhere existence of the second differential of a convex +function and some properties of convex surfaces connected with it}, +Uchenye Zapiski Leningradskogo Gosudarstvennogo Universiteta, +no.~37, Seriya Matematicheskikh Nauk \textbf{6} (1939), 3--35 (Russian). + +\bibitem{AndersenVolume1990} +E.~Anders\'en, +\emph{Volume-preserving automorphisms of $\mathbb C^n$}, +Complex Variables Theory Appl. \textbf{14} (1990), nos.~1--4, 223--235. +\href{https://doi.org/10.1080/17476939008814422} +{doi:10.1080/17476939008814422}. + +\bibitem{BeraVerma2024} +S.~Bera and K.~Verma, +\emph{Uniform non-autonomous basins of attraction}, +Invent. 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Stud., vol.~102, +Princeton University Press, Princeton, NJ, and University of Tokyo Press, +Tokyo, 1982, pp.~3--71. +\href{https://doi.org/10.1515/9781400881918-002} +{doi:10.1515/9781400881918-002} (digital reprint). + +\end{thebibliography} diff --git a/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/main.tex b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/main.tex new file mode 100644 index 0000000000000000000000000000000000000000..43c43eeb814a88120b7ebc590bd7ce6825e609e2 --- /dev/null +++ b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/main.tex @@ -0,0 +1,101 @@ +\documentclass[11pt]{article} +\usepackage[T1]{fontenc} +\usepackage[utf8]{inputenc} +\usepackage{lmodern} +\usepackage[margin=1in]{geometry} +\usepackage{amsmath,amssymb,amsthm,mathtools,mathrsfs} +\usepackage{microtype,enumitem,booktabs} +\input{glyphtounicode} +\pdfgentounicode=1 +\input{unicode-map} +\usepackage[unicode,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref} +\usepackage{bookmark} +\hypersetup{ + pdftitle={Uniformization of complete Kähler manifolds with positive bisectional curvature}, + pdfauthor={OpenAI}, + pdfsubject={Yau's uniformization conjecture}, + pdfkeywords={Kähler manifolds, bisectional curvature, uniformization, Ricci flow, holomorphic discs} +} +\newtheorem{theorem}{Theorem}[section] +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem{proposition}[theorem]{Proposition} +\newtheorem{corollary}[theorem]{Corollary} +\theoremstyle{definition} +\newtheorem{definition}[theorem]{Definition} +\theoremstyle{remark} +\newtheorem{remark}[theorem]{Remark} +\newcommand{\C}{\mathbb C} +\newcommand{\R}{\mathbb R} +\newcommand{\N}{\mathbb N} +\newcommand{\dd}{\partial\bar\partial} +\newcommand{\ddbar}{\sqrt{-1}\partial\bar\partial} +\newcommand{\dbar}{\bar\partial} +\newcommand{\eps}{\varepsilon} +\DeclareMathOperator{\Ric}{Ric} +\DeclareMathOperator{\Rm}{Rm} +\DeclareMathOperator{\tr}{tr} +\DeclareMathOperator{\Id}{Id} +\DeclareMathOperator{\diag}{diag} +\DeclareMathOperator{\rank}{rank} +\DeclareMathOperator{\Span}{span} +\DeclareMathOperator{\supp}{supp} +\DeclareMathOperator{\Vol}{Vol} +\DeclareMathOperator{\dist}{dist} +\DeclareMathOperator{\Gr}{Gr} +\DeclareMathOperator{\Schur}{Schur} +\DeclareMathOperator{\osc}{osc} +\DeclareMathOperator{\Lip}{Lip} +\DeclareMathOperator{\Aut}{Aut} +\newcommand{\norm}[1]{\lVert#1\rVert} +\newcommand{\abs}[1]{\lvert#1\rvert} +\numberwithin{equation}{section} +\allowdisplaybreaks[1] +\setlist[itemize]{topsep=4pt,itemsep=2pt,parsep=0pt} +\setlist[enumerate]{topsep=4pt,itemsep=2pt,parsep=0pt} +\title{Uniformization of complete K\"ahler manifolds\protect\\ +with positive bisectional curvature} +\author{OpenAI} +\date{September 23, 2026} +\makeatletter +\renewcommand{\@maketitle}{% + \begin{center} + {\LARGE\bfseries\@title\par}\vspace{0.75em} + {\large\@author\par}\vspace{0.35em} + {\@date\par} + \end{center}\vspace{0.5em}} +\makeatother +\usepackage{accsupp} +\newcommand{\MathActualText}[2]{% + \BeginAccSupp{method=hex,unicode,space=false,pdfliteral=direct,ActualText=#1}% + #2% + \EndAccSupp{pdfliteral=direct}% +} +\let\OriginalMapsto\mapsto +\let\OriginalLongmapsto\longmapsto +\renewcommand{\mapsto}{\mathrel{\MathActualText{21A6}{\OriginalMapsto}}} +\renewcommand{\longmapsto}{\mathrel{\MathActualText{27FC}{{\let\longrightarrow\OriginalLongrightarrow\OriginalLongmapsto}}}} +\let\OriginalLongrightarrow\longrightarrow +\let\OriginalCapitalLongrightarrow\Longrightarrow +\renewcommand{\longrightarrow}{\mathrel{\MathActualText{27F6}{\OriginalLongrightarrow}}} +\renewcommand{\Longrightarrow}{\mathrel{\MathActualText{27F9}{\OriginalCapitalLongrightarrow}}} +\newcommand{\boldone}{\mathord{\MathActualText{D835DFCF}{\mathbf1}}} +\begin{document} +\maketitle +\begin{abstract} +We prove that every complete connected noncompact K\"ahler manifold with +strictly positive holomorphic bisectional curvature is biholomorphic to +complex Euclidean space. This resolves Yau's uniformization conjecture +positively in every complex dimension. +\end{abstract} +\tableofcontents +\input{sections/introduction} +\input{sections/preliminaries} +\input{sections/flow} +\input{sections/discs} +\input{sections/variation} +\input{sections/ellipsoids} +\input{sections/charts} +\input{sections/dynamics} +\input{sections/uniformization} +\input{bibliography} +\end{document} diff --git a/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/sections/charts.tex b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/sections/charts.tex new file mode 100644 index 0000000000000000000000000000000000000000..5711b9b59bf57cc575d5783b4839f42e00eff0d1 --- /dev/null +++ b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/sections/charts.tex @@ -0,0 +1,1070 @@ +\section{Harnack inequalities and shrinking holomorphic charts} +\label{sec:charts} + +The joint positivity of the cotangent norm will now give an exhausting +system of inverse charts with quantitative transition estimates. +We first prove positive-time completeness and construct uniform local +charts. These charts may have several sheets, so continuing their +inverse germs across compact sets also requires a topological step: +we will contract loops before constructing single-valued inverse branches. +For the quantitative estimates, volume loss must force contraction in +every direction, with an exponent common to all compact sets. +The local chart and path-lifting constructions have antecedents in Chau--Tam +\cite[Section~2]{ChauTamSimply}\cite[Sections~2--3]{ChauTamStein}. +Throughout this Section, a metric on a cotangent space is the Hermitian +dual metric, including the transpose in its matrix representation. + +\subsection{From joint positivity to completeness} + +The differential Harnack inequalities for K\"ahler--Ricci flow have +their classical antecedent in Cao's work \cite{CaoHarnack}. +Here we derive the needed inequalities from joint positivity before +using them to prove completeness of the evolving metric. + +\begin{proposition}\label{prop:harnack-completeness} +The flow of Theorem~\ref{thm:localized-flow} has nonnegative holomorphic +bisectional curvature and is complete at every positive time. Its +Ricci tensor is positive definite. Writing $A=\Ric(h_t)$ and +$R=\tr_{h_t}A$, one has, in fixed holomorphic coordinates, +\begin{align} + A_t+A h_t^{-1}A+t^{-1}A&\ge0, + \label{chart:matrix-harnack}\\ + R_t+t^{-1}R+2\operatorname{Re}\partial_XR+A(X,\overline X)&\ge0 + \qquad(X\in T^{1,0}M). + \label{chart:scalar-harnack} +\end{align} +In particular $h_{t'}\le h_t$ for $t'\ge t$, $R(o,t)\le C$ for +$t\ge0$, and +\begin{equation}\label{chart:integrated-harnack} + R(x,t)\le R(y,t')\frac{t'}t + \exp\!\left(\frac{C\dist_{h_t}(x,y)^2}{t'-t}\right) + \qquad(00$. +\end{proposition} + +\begin{proof} +By Theorem~\ref{thm:joint-positivity}, the dual squared norm of the +tangent metric pulled back to $(x,w)$, where $t=e^{w+\bar w}$, is +plurisubharmonic. Completing the square in the free first derivative +of a cotangent section identifies this assertion with Griffiths +nonnegativity of the pulled-back tangent metric. At a spatially +K\"ahler-normal point its curvature blocks are +\[ + \Theta_{i\bar j\,\alpha\bar\beta} + =\Rm_{i\bar j\alpha\bar\beta},\qquad + \Theta_{w\bar j\,\alpha\bar\beta} + =t\nabla_{\bar j}A_{\alpha\bar\beta},\qquad + \Theta_{w\bar w}=tA+t^2(A_t+A h_t^{-1}A). +\] +The spatial block gives nonnegative bisectional curvature and hence +$A\ge0$ and metric monotonicity. The last block gives +\eqref{chart:matrix-harnack}. Trace the curvature in its fiber +indices and evaluate on the spacetime direction $(X,t^{-1})$. +The identities +\[ + \tr_{h_t}A_t=R_t-|A|_{h_t}^2, + \qquad \tr_{h_t}(A h_t^{-1}A)=|A|_{h_t}^2, + \qquad \tr_{h_t}\nabla_X A=\partial_XR +\] +give \eqref{chart:scalar-harnack}. + +At a fixed point choose a moving unitary frame satisfying +$E_t=\tfrac12 A^{\#}E$, where $A^{\#}=h_t^{-1}A$. +Differentiation shows that +\[ + \frac{d}{dt}\bigl[tA(E,\overline E)\bigr] + =t\bigl(A_t+A h_t^{-1}A+t^{-1}A\bigr)(E,\overline E)\ge0. +\] +Initial strict bisectional positivity and local smooth convergence +give $A>0$ at sufficiently small positive times on any prescribed +compact set. The preceding inequality propagates this positivity +and gives $tA\ge a_Kh_t$ there for $t\ge1$, after changing the compact +constant. Integrating $\partial_t h_t=-A$ proves the asserted +power contraction. Applied to the trace, the same inequality gives +monotonicity of $tR(o,t)$. The linear bound for $\rho(o,t)$ in +Theorem~\ref{thm:localized-flow} implies, for $t\ge1$, +\[ + tR(o,t)\log2 + \le\int_t^{2t}R(o,v)\,dv + =\rho(o,2t)-\rho(o,t)\le C(1+2t). +\] +Smoothness on compact time intervals supplies the remaining +basepoint bound. + +For clarity, the next integration precedes the completeness proof. +Choose a piecewise smooth path from $x$ to $y$ whose $h_t$ length is +within $\eps$ of their distance, and run it at constant $h_t$ speed +on $[t,t']$. Such paths exist by the definition of the distance. +Along this path, \eqref{chart:scalar-harnack}, divided by $R>0$, +and $A\le Rh_v$ give +\[ + \frac{d}{dv}\log R(\gamma(v),v) + \ge-\frac1v-C|\dot\gamma(v)|_{h_v}^2. +\] +Since $h_v\le h_t$, its energy is at most +$(\dist_{h_t}(x,y)+\eps)^2/(t'-t)$. Integrating and then letting +$\eps\downarrow0$ proves \eqref{chart:integrated-harnack} without +using a minimizing geodesic or completeness of $h_t$. + +Fix $T<\infty$. Put $d=\dist_{h_t}(x,o)$ and apply +\eqref{chart:integrated-harnack} with $y=o$ and +$t'=t+1+d^2$. The basepoint bound gives +\begin{equation}\label{chart:quadratic-curvature} + R(x,t)\le\frac{C_T(1+d^2)}t, + \qquad 00$ +such that, for sufficiently large $t$ and every $p\in K$, there is +a holomorphic local biholomorphism +\[ + \Phi:B_{\C^n}(r_K)\longrightarrow M,\qquad + \Phi(0)=p,\qquad d\Phi(0)\text{ unitary for }h_t, +\] +with $c_Kg_{\rm eucl}\le\Phi^*h_t\le C_Kg_{\rm eucl}$. +The pullback metrics have bounds of every fixed derivative order +on smaller balls. The corresponding local smooth compactness +statement holds for rescaled flows whenever curvature is uniformly +bounded on fixed-radius moving balls during a fixed two-sided time +interval. +\end{lemma} + +\begin{proof} +For $t\ge1$, \eqref{chart:integrated-harnack}, with a fixed future +time increment, bounds $R$ on every fixed-radius $h_t$ ball about +$o$. Nonnegative bisectional curvature gives $|\Rm|\le C_nR$. +Centers in $K$ are handled by a compact family of paths from $o$: +their $h_t$ lengths are bounded, so balls about these centers lie +in a bounded-radius ball about $o$. + +To apply local curvature derivative estimates, take a ball for the +earliest time of a short time interval. It remains inside the +corresponding larger later-time balls because metrics decrease. +The curvature bound gives metric equivalence on this fixed region +throughout the interval. A path measured in the later metric +cannot first exit the earlier ball at arbitrarily small length; +thus a smaller later-time ball is contained in this region. +Local Ricci-flow derivative estimates +\cite{Shi}\cite[Theorem~1.4]{Kotschwar} now give all curvature +derivatives on smaller balls and inner time intervals. +Here the estimate is applied on shifted sufficiently short cylinders, +with a time buffer before each observation slice. Metric equivalence +keeps the initial balls required by the local estimate compactly +inside the fixed region. This construction applies verbatim after +a fixed rescaling. + +Here is why no injectivity-radius hypothesis enters the chart +statement; compare \cite[Lemma~2.2]{ChauTamSimply}. +Pull back by the exponential map on a small tangent ball. The +curvature bound excludes conjugate points at this scale, although +the exponential map may identify distinct points. Jacobi-field +estimates and their differentiated equations give uniformly +controlled pullback metrics and parallel complex structures, with +a fixed Euclidean lower metric bound. In particular any sequence +has a smoothly convergent subsequence on a smaller tangent ball. +The identities $J^2=-\Id$ and $N_J=0$ pass to the smooth limit. +The Newlander--Nirenberg theorem supplies local holomorphic coordinates +for the limit complex structure \cite{NewlanderNirenberg} +\cite[Theorem~1.1]{HillTaylor}. In the smooth case their components +satisfy the smooth elliptic equation $\bar\partial_J^*\bar\partial_J f=0$, +so interior elliptic regularity makes these coordinates smooth. +Restrict them to a still smaller ball. Their squared radius is uniformly strictly +plurisubharmonic for all sufficiently close complex structures. +Solve the small $\dbar$ errors of these coordinate functions on +a smaller strictly pseudoconvex coordinate ball. One can use the +weighted $L^2$ estimate \cite{Hormander,Demailly}, viewing scalar +functions as top forms with values in the anticanonical bundle. +Give this bundle the metric induced by the original uniformly +controlled pullback metric. A fixed large multiple of the squared +radius pays its uniformly +bounded curvature, and the strictly plurisubharmonic exhaustion +of the ball supplies an auxiliary complete K\"ahler metric. +The source errors tend to zero smoothly, so the correcting +functions tend to zero in local $L^2$. We first justify smoothness of +each correction, then obtain uniform estimates on a fixed smaller +real ball. Write the corrections as $u_j$ +and their equations as $\dbar_{J_j}u_j=\eta_j$. +For each index separately, the existing complex structure $J_j$ +has smooth holomorphic coordinates, with no uniform radius asserted. +In those coordinates, +\[ + \Delta_{\mathrm{eucl}}u_j + =4\sum_a\partial_{z_a}\eta_{j,a} +\] +is an identity of distributions with smooth right side. A compactly +supported smooth extension of the right side, convolved with the +Euclidean fundamental solution, gives a smooth particular solution +on a smaller ball. +The remaining harmonic distribution is smooth: its mollifications +satisfy the mean-value identity against a fixed smooth radial +unit-mass kernel, and passage to the distributional limit identifies +the distribution with its smooth convolution by that kernel. +Thus each $u_j$ is qualitatively smooth. + +For uniform estimates return to the fixed real ball and use +$P_j=\dbar_{J_j}^*\dbar_{J_j}$ with the original controlled +pullback K\"ahler metric, rather than the auxiliary weighted metric. +The scalar K\"ahler identity identifies $P_j$, up to a fixed sign +and normalization, with the real Laplace--Beltrami operator. +Its coefficients have uniform bounds of every fixed order and a +uniform ellipticity lower bound. Moreover +$P_ju_j=\dbar_{J_j}^*\eta_j=:F_j$ tends smoothly to zero. +Testing this equation with $\chi^2\overline{u_j}$ and absorbing +the cross term gives the Caccioppoli estimate +\[ + \int\chi^2|\nabla u_j|^2 + \le C\int_{\supp\chi}(|u_j|^2+|F_j|^2) +\] +for a fixed interior cutoff. The qualitative smoothness just +proved legitimizes this test. Uniform metric equivalence gives a +$W^{1,2}$ bound in the fixed real coordinates. Interior elliptic +estimates \cite[Theorems~8.8 and~8.10]{GilbargTrudinger}, on +successively smaller fixed balls, now yield +\[ + \|u_j\|_{H^{m+2}(B')} + \le C_m\bigl(\|u_j\|_{L^2(B)}+\|F_j\|_{H^m(B)}\bigr). +\] +Choose $m+2>k+n$ and use Sobolev embedding in real dimension $2n$ +\cite[Section~5.6.3, Theorem~6]{EvansPDE}. This proves convergence +to zero in every fixed $C^k$ norm on smaller balls. The corrected +coordinate maps are therefore $C^1$ close to the limiting coordinate +map. On a sufficiently small fixed ball their derivatives are +uniformly close to its invertible center derivative. They are +injective on that ball, and their images contain a common ball about +their center values, by the quantitative inverse function theorem. +Subtract the coordinate center values and invert on this common ball. +Composing with the exponential parametrization and making a bounded +linear normalization, with one further fixed reduction of radius, +gives the required maps into $M$ with unitary center derivative. +If no common radius and bounds existed for the original family, a +sequence witnessing their failure would have a smoothly convergent +subsequence of pullbacks. The construction just given supplies common +charts on that subsequence, a contradiction. This proves the uniform +chart assertion. + +For a flow, use the exponential parametrization at its central +time as a fixed parametrization. The curvature bound controls +the time derivative of the metric; the first Ricci derivative +controls that of its connection. Induction using the higher +covariant derivative estimates gives ordinary space-time +derivative bounds for the metrics and their parallel complex +structures. Arzel\`a--Ascoli on smaller balls gives the claimed +local smooth limits. +\end{proof} + +\subsection{Total distortion in the initial metric} + +In an $h_t$-unitary chart at $x$, the product of the initial-metric +singular lengths is $e^{\rho(x,t)/2}$. This determinant identity alone +allows the growth to occur in only some directions. The next lemma +bounds the greatest singular length by a fixed power of the least, +so volume loss will force contraction in every direction. + +\begin{lemma}[Static distortion]\label{lem:static-distortion} +Fix $r,c>0$ and a compact set $K\subset M$. Suppose +$\Phi:B_{\C^n}(r)\to M$ is a holomorphic local biholomorphism, +$\Phi(0)\in K$, and $\widetilde g=\Phi^*g\ge c g_{\rm eucl}$. +Let $A$ and $B$ be the least and greatest singular lengths of +$d\Phi(0)$, using the Euclidean metric in the domain and $g$ in +the target. There are constants depending only on $K,r,c$ and +the initial geometry on a compact neighborhood of $K$ such that +\begin{equation}\label{chart:static-distortion} + B\le C(1+A)^C. +\end{equation} +In particular these constants are independent of the particular +chart and its total distortion. +\end{lemma} + +\begin{proof} +We construct a plurisubharmonic weight whose upper bound is of order +$\log(1+A)$ and whose Levi form is strict near the center. +Its moving-ball definition will also give a nonnegative lower bound +on the support of the weighted $\dbar$ construction. These bounds +make the extension estimate independent of the total distortion. +We then extend a local function whose differential detects $B$; +its $L^2$ bound gives the required polynomial bound. + +Choose a constant holomorphic covector $\alpha=df$ with +$|\alpha|_{\rm eucl}=A$ and $|\alpha|_{\widetilde g}(0)=1$. +The logarithmic dual norm +\[ + \psi=\log|\alpha|_{\widetilde g}^2 + \quad\text{satisfies}\quad + \psi(0)=0,\qquad \psi\le C+2\log A. +\] +For a tangent $X$, the curvature formula for this logarithmic norm is +\[ + \dd\psi(X,\overline X) + =\frac{\Rm(X,\overline X,v,\overline v)}{|v|^2} + +\frac{|D'_X\alpha|^2|\alpha|^2 + -|\langle D'_X\alpha,\alpha\rangle|^2}{|\alpha|^4}, +\] +where $v$ is the metric dual of $\alpha$ and all norms in this +formula use $\widetilde g$. The second summand is nonnegative. +Initial bisectional positivity therefore makes $\psi$ +plurisubharmonic. On any region whose target image +lies in a prescribed compact neighborhood $K^+$ of $K$, it gives +\begin{equation}\label{chart:strict-covector} + \dd\psi\ge\kappa\widetilde g +\end{equation} +with $\kappa>0$ uniform. The normalization of $\alpha$ cancels +from this estimate. + +Shrink the Euclidean domain by a fixed factor. Choose $r_0>0$ +so small that any path of $\widetilde g$ length at most $3r_0$ +starting in this smaller domain stays in $B(r)$; the lower +metric bound makes this choice uniform. The small closed metric +balls used below are compact there and their distances are +attained by minimizing segments. Put +\begin{equation}\label{chart:metric-ball-envelope} + \Psi(z)=\max_{\dist_{\widetilde g}(z,y)\le r_0}\psi(y). +\end{equation} +This function is continuous. Compactness gives upper +semicontinuity. For lower semicontinuity, move a maximizing +endpoint a little towards the center along a minimizing segment; +the resulting endpoint is admissible for all nearby centers and +its value tends to the maximum. + +We verify the Levi inequality for this moving-ball maximum. +Let $\varphi$ be a smooth upper test at $z$, let $y$ realize the +maximum, and prescribe a nonzero complex tangent $V$ at $z$. +Choose a holomorphic center germ with this derivative. If +$\dist_{\widetilde g}(z,y)0$ for large $s$, and +\begin{equation}\label{chart:q-growth} + s\longrightarrow\infty,\qquad + q\le Ce^\tau,\qquad + \liminf_{s\to\infty}\frac{q(s)}s\le2. +\end{equation} +Uniformly on every fixed compact set, $\rho(x,t)/s\to1$, and +there is $c_K>0$ such that, eventually on that compact set, +\begin{equation}\label{chart:metric-decay} + e^{-2s}g\le h_t\le e^{-c_Ks}g. +\end{equation} +There are fixed $a_0\in(0,1)$ and $b_0>0$ such that the least +eigenvalue at $o$ of $t\Ric(h_t)$ relative to $h_t$ satisfies +\begin{equation}\label{chart:ricci-lower} + \lambda_{\min}(s)\ge b_0q(a_0s) + \quad\text{for all sufficiently large }s. +\end{equation} +Moreover there are $S_i\to\infty$ and $K_0<\infty$ with +\begin{equation}\label{chart:good-windows} + q(2S_i)\le K_0q(a_0S_i). +\end{equation} +One can choose $s_i\in[5S_i/4,7S_i/4]$ so that +$(\log q)'(s_i)\to0$. If $t_i$ corresponds to $s_i$ and +$R_i=R(o,t_i)$, the rescaled flows +\begin{equation}\label{chart:rescaled-flows} + g_i(z)=R_i h_{t_i+z/R_i} +\end{equation} +have uniform curvature and derivative bounds on each fixed-radius +moving ball about $o$ in a fixed small two-sided time interval. +At $(o,0)$ their scalar curvature is one and their Ricci +eigenvalues have a fixed positive lower bound. +\end{proposition} + +\begin{proof} +Proposition~\ref{prop:harnack-completeness} gives monotonicity and +the positive lower bound for $q$, together with $q\le Ce^\tau$. +Hence $s\to\infty$. If $q(s)>2s$ for every sufficiently large +$s$, integration of $ds/d\tau>2s$ would give +$s\ge ce^{2\tau}$, contradicting the linear-in-$t$ bound for +$\rho(o,t)$. This proves \eqref{chart:q-growth}. + +For a compact family of initial paths from $o$, the power +contraction in Proposition~\ref{prop:harnack-completeness} makes +their $h_t$ lengths tend uniformly to zero. The factor on the +right of \eqref{chart:integrated-harnack}, with time increment +one, therefore tends uniformly to one on the compact set. Apply +the inequality in both spatial directions and integrate in time. +More explicitly, for every $\eps>0$ and all sufficiently large +$v$, uniformly on the compact set, +\[ + R(x,v)\le(1+\eps)R(o,v+1),\qquad + R(o,v)\le(1+\eps)R(x,v+1). +\] +The first inequality also bounds $R(x,v)$ there. Shifting either +integral endpoint by one costs a bounded amount. After division +by $s\to\infty$, and then letting $\eps\downarrow0$, the two +inequalities give $\rho(x,t)/s\to1$. No integrability of the +error factor is required. + +Let $\lambda_1,\ldots,\lambda_n$ be the eigenvalues of $h_t$ +relative to $g$ at $x$. They lie in $(0,1]$, and their product +is $e^{-\rho(x,t)}$. Thus every $\lambda_j\ge e^{-\rho(x,t)}$, +which proves the lower bound of \eqref{chart:metric-decay}. +Choose the instantaneous unitary chart of +Lemma~\ref{chart:local-charts} at $x$. Its initial-metric +singular lengths are $\lambda_j^{-1/2}$, whose product is +$e^{\rho(x,t)/2}$. Lemma~\ref{lem:static-distortion} bounds +their largest value by a fixed power of their smallest, uniformly +for $x$ in the compact set. Since all these lengths are at least +one, their product forces the smallest to be at least +$C^{-1}e^{c\rho(x,t)}$. This proves the upper bound of +\eqref{chart:metric-decay}, after reducing $c_K$ and increasing +the starting time. + +For each fixed nonzero covector $\xi\in T_o^{*(1,0)}M$, the +function +\[ + L_\xi(\tau)=\log|\xi|_{h_{e^\tau}^{-1}}^2 +\] +is convex. Indeed the logarithmic norm of a holomorphic dual +section is plurisubharmonic for a Griffiths-nonnegative tangent +metric, and its restriction to complexified $\tau$ is independent +of the imaginary part. Its derivative is the Rayleigh quotient +of $t\Ric$ on the dual unit vector. Normalize $|\xi|_{g^{-1}}=1$. +At $o$, \eqref{chart:metric-decay} gives +\[ + L_\xi(\tau(s))-L_\xi(\tau(a_0s)) + \ge(c_o-2a_0)s. +\] +Choose $a_01$ and choose $K_0>L^2$. If +\eqref{chart:good-windows} failed for all large $S$, then +$q(Lr)>K_0q(r)$ for all large $r$. Iteration and monotonicity +would give $q(r)\ge cr^{\log K_0/\log L}$ for every large $r$, +contradicting \eqref{chart:q-growth}. Thus such windows occur +arbitrarily far out. On their middle halves, +\[ + \int_{5S_i/4}^{7S_i/4}(\log q)'(s)\,ds\le\log K_0. +\] +Choose $s_i$ there with +$(\log q)'(s_i)\le2\log K_0/S_i$. + +Write $q_i=q(s_i)=t_iR_i$. On the rescaled clock of +\eqref{chart:rescaled-flows}, +\begin{equation}\label{chart:clock-rescaling} + \frac{ds}{dz}=\frac{q(s)}{q_i+z},\qquad + \widehat R_i(o,z)=\frac{R(o,t_i+z/R_i)}{R_i} + =\frac{q(s)}{q_i+z}. +\end{equation} +Since $q_i\ge c>0$, choose $\delta0$. +Formula~\eqref{chart:clock-rescaling} gives the exact identity +\[ + \left[\partial_z\widehat R_i+k_i\widehat R_i\right]_{(o,0)} + =(\log q)'(s_i)\longrightarrow0. +\] +The limit therefore has $S:=R_z+kR=0$ at the central point. + +The matrix Harnack inequality has the rescaled form +$A_z+A g^{-1}A+kA\ge0$. Its trace is $S$, because +$R_z=\tr_g A_z+|A|_g^2$. Thus this nonnegative matrix vanishes +at the point in question. Also $A_z=\dd R$ under K\"ahler--Ricci +flow. If $H_{j\bar l}=\nabla_j\nabla_{\bar l}R$, then +\begin{equation}\label{chart:equality-mixed-hessian} + H=-A^2-kA +\end{equation} +there, writing endomorphism products in a unitary frame. +On a small spacetime neighborhood, $A$ is positive definite. +Minimizing the scalar Harnack inequality over $X$ gives +\begin{equation}\label{chart:equality-Z} + Z=S-Q\ge0,\qquad Q=|\partial R|_{A^{-1}}^2. +\end{equation} +At the equality point $S=0$, so $\partial R=0$ and $Z=0$. + +We give the scalar Hessian calculation, since a vanishing +Harnack quantity by itself does not supply real strict concavity. +Use $R_z=\Delta R+|A|^2$, $A_z=\dd R$, and $k_z=-k^2$. +The derivative of the Laplacian on a scalar is +$(\partial_z\Delta)R=\langle A,\dd R\rangle$, while +\[ + \partial_z|A|^2=2\langle A,\dd R\rangle+2\tr(A^3). +\] +Consequently +\begin{equation}\label{chart:equality-evolution} + (\partial_z-\Delta)S + =3\langle A,\dd R\rangle+2\tr(A^3) + +k|A|^2-k^2R. +\end{equation} +At the equality point, substitution of +\eqref{chart:equality-mixed-hessian} reduces this to +$-\tr\bigl(A(A+k\Id)^2\bigr)$. +Diagonalize $A$ there, with eigenvalues $\lambda_j>0$. +Since $\partial R=0$, derivatives of the coefficients of +$A^{-1}$ make no contribution to $\Delta Q$ or $Q_z$, and +\[ + Q_z=0,\qquad + \Delta Q=\sum_{j,l}\lambda_j^{-1} + \left(|R_{j\bar l}|^2+|R_{jl}|^2\right). +\] +The first square sum is exactly +$\tr\bigl(A(A+k\Id)^2\bigr)$ by +\eqref{chart:equality-mixed-hessian}. Hence at this point +\[ + (\partial_z-\Delta)Z + =\sum_{j,l}\lambda_j^{-1}|R_{jl}|^2\ge0. +\] +On the other hand $Z\ge0$ has an interior spacetime zero, so +$Z_z=0$ and $\Delta Z\ge0$ there. The displayed sum must +vanish. Thus the pure complex Hessian $R_{jl}$ is zero, while +the mixed Hessian is negative definite by +\eqref{chart:equality-mixed-hessian}. The real Hessian of $R$ +is therefore negative definite at the center, with a definite +bound furnished by the positive lower bound for $A$. + +This conclusion holds uniformly on actual small metric balls +in the original rescaled manifolds, not only on their immersed +parametrizations. Smooth convergence gives the center Hessian +bound and $|\nabla\widehat R_i|(o,0)\to0$. The intrinsic +third-derivative estimates from +Proposition~\ref{prop:ricci-windows} allow one to parallel +transport the Hessian along any minimizing radial geodesic. +Shrinking a fixed radius $r_*>0$, independently of $i$, gives +constants $a>0$ with +\begin{equation}\label{chart:intrinsic-concavity} + \operatorname{Hess}_{g_i(0)}\widehat R_i + \le-a g_i(0) + \quad\text{on }B_{g_i(0)}(o,2r_*),\qquad + |\nabla\widehat R_i|(o,0)\longrightarrow0. +\end{equation} +Indeed the change in the transported Hessian is bounded by +$Cr_*$, so one chooses $r_*$ after the uniform center bound. +This argument uses intrinsic derivative estimates along actual +geodesics and is unaffected by multiple sheets of a local chart. + +Hold the complete metric $g_i(0)$ fixed and flow by the real +vector field $Y_i=\nabla\widehat R_i(\cdot,0)$. Along a +minimizing radial geodesic of length $r\le2r_*$, +\[ + \langle Y_i,\partial_r\rangle + \le |Y_i(o)|-ar. +\] +For large $i$ this is negative on $r=r_*$. At cut points, +first variation along any minimizing radial segment gives the +same upper bound for the upper directional derivative of +distance. Thus the closed ball of radius $r_*$ traps trajectories +starting inside it. Completeness makes this closed ball compact, +so these trajectories exist for all positive flow time. +For a carried tangent vector $V$, \eqref{chart:intrinsic-concavity} +gives +\[ + \frac{d}{dv}|V|_{g_i(0)}^2 + =2\operatorname{Hess}\widehat R_i(V,V) + \le-2a|V|_{g_i(0)}^2. +\] +Every loop contained well inside the trapping ball consequently +has carried length tending exponentially to zero. + +Let a fixed piecewise smooth loop in $M$ be given. Its image +and a finite collection of paths from $o$ lie in a fixed compact +set. Their $h_{t_i}$ lengths tend to zero by +\eqref{chart:metric-decay}, and $R_i\le C$ by +Proposition~\ref{prop:harnack-completeness}. Thus this loop +lies inside $B_{g_i(0)}(o,r_*/4)$ for sufficiently large $i$. +Fix one such $i$. The compact trapping ball has a positive +minimum injectivity radius for this one smooth metric. A +sufficiently short carried loop lies in a normal ball and is +contractible. The gradient flow up to that finite time is a +homotopy from the original loop to it. Approximation of +continuous loops by piecewise smooth loops finishes the proof. +\end{proof} + +\subsection{Inverse charts and one contraction exponent} + +Simple connectivity permits continuation of the inverse germs, but +their first contraction estimates will depend on the compact set. +The following Liouville principle, applied to limits of logarithmic +norms, will make the exponent common to all compact sets. We state it +in the required regularity class; it is also a special case of +\cite[Theorem~9]{LiuThreeCircle}. + +\begin{lemma}\label{chart:psh-liouville} +Every bounded-above plurisubharmonic function on $M$ is constant, +including a function which is not assumed continuous. +\end{lemma} + +\begin{proof} +Allow the constant $-\infty$, and otherwise let $v$ be such a +function. The compact-ball maximum +$m(r)=\max_{\overline B_g(o,r)}v$ is finite and nondecreasing. +It is convex as a function of $\log r$. To see this, fix +$00$, common to all compact sets, satisfies +\begin{equation}\label{chart:common-exponent} + \sup_K|f_s|\le e^{-\sigma s} + \quad\text{for every fixed compact }K + \text{ and all sufficiently large }s. +\end{equation} +For every fixed jet order $d$ there is $C_d$ such that +\begin{equation}\label{chart:transition-jets} + |J_dF_{s,u}|\le C_d\min\{1,e^{C_ds-\sigma u}\} + \qquad(u\ge s\text{ sufficiently large}). +\end{equation} +There are $c,\gamma_0>0$ such that, for each fixed +$0<\gamma\le\gamma_0$, one has +\begin{equation}\label{chart:transition-small-balls} + \sup_{|z|\le e^{-\gamma s}}|F_{s,u}(z)| + \le e^{-c\gamma u} + \qquad\text{for every }u\ge s\ge s_\gamma. +\end{equation} +The constants in the last two estimates are independent of the +later endpoint $u$; the starting threshold in +\eqref{chart:common-exponent} may depend on $K$. +\end{proposition} + +\begin{proof} +Take the charts of Lemma~\ref{chart:local-charts} at $o$. +We use the elementary short-path lifting property of these +possibly noninjective charts; compare +\cite[Lemmas~2.2--2.3 and Corollary~2.2]{ChauTamStein}. +A path beginning at the center and having sufficiently small +current-metric length lifts from $0$ by local inversion. +The lower bound in \eqref{chart:uniform-chart-metric} bounds +the Euclidean length of its lift. If the given length is +smaller than the fixed distance to the chart boundary, the +lift cannot escape, and hence extends over the whole path. +The same reasoning applies to a homotopy all of whose paths +obey this length bound. Local uniqueness of lifts supplies +uniqueness throughout the homotopy. + +For $u\ge s$, the image under $\Phi_s$ of a short radial path +has $h_{t(u)}$ length at most its $h_{t(s)}$ length. Lift it +through $\Phi_u$ from $0$. Short radial homotopies give a +well-defined map on a fixed ball $B(r_1)$; locally this map +is $\Phi_u^{-1}\Phi_s$, so it is holomorphic with nonsingular +derivative. Its lift has a fixed Euclidean length bound, and +therefore the maps are uniformly bounded on $B(r_1)$. +They compose wherever both sides are defined near $0$ by +uniqueness of local inverses. This is the local transition +construction of \cite[Lemmas~3.1--3.2]{ChauTamStein} with the +metric bounds already established here. + +Unitary center normalization and $h_{t(u)}\le h_{t(s)}$ +give the first estimate in \eqref{chart:center-transitions}. +Taking determinants of these normalizations and using +$\det h_{t(s)}(o)=e^{-s}\det g(o)$ gives the determinant +identity. All singular values are at most one and their +product is $e^{-(u-s)/2}$, so the least is at least this +product. This proves the inverse estimate. + +We now use simple connectivity to continue the inverse germs. +Fix a connected relatively compact neighborhood of a compact +set and $o$. Cover its closure by finitely many small convex +initial target neighborhoods with connected pairwise +intersections, enlarging the connected neighborhood if +necessary to include fixed paths from $o$ to their centers. +Choose one such path to each center. On each target +neighborhood it extends the inverse germ at $o$ by path +lifting. For each nonempty overlap, use one point in the +overlap to form the two-path loop. By +Proposition~\ref{prop:simple-connectivity} this loop bounds +a fixed piecewise smooth homotopy. There are only finitely +many paths and homotopies; their images lie in a fixed +compact set and their initial lengths have a uniform bound. +Equation~\eqref{chart:metric-decay} makes every path in these +homotopies sufficiently short in the current metric when +$s$ is large. All lifts stay inside the chart. Thus the +two inverse germs agree at the chosen overlap point, and +then throughout the connected overlap by analytic +continuation. They patch to an inverse $f_s$ on a +neighborhood of the compact set. + +Choose nested connected relatively compact open exhaustion +sets $D_m$, and choose nondecreasing thresholds $T_m\ge m$ +so that all shortness conditions for $D_m$ hold whenever +$s\ge T_m$. At clock $s$, use the construction on +$D_{\max\{m:T_m\le s\}}$. On a smaller set, the branches +obtained from two larger constructions agree by continuation +from $o$. This gives the stated coherent branches with +domains exhausting $M$. The length estimate for a lift, +together with \eqref{chart:metric-decay} on the finite path +compact, gives for each fixed $K$ +\begin{equation}\label{chart:local-exponent} + \sup_K|f_s|\le C_Ke^{-a_Ks} +\end{equation} +with $a_K>0$. It also gives +$f_u=F_{s,u}\circ f_s$ on any fixed compact set whenever +$s$ is sufficiently large and $u\ge s$: both sides are +the same continued inverse, and +\eqref{chart:local-exponent} keeps $f_s$ in the transition +domain. + +It remains to make the exponent independent of the compact. +The functions $v_s=s^{-1}\log|f_s|$ are plurisubharmonic on +their exhausting domains and locally bounded above. +For any sequence $s\to\infty$, +Lemma~\ref{lem:psh-compactness-bridge} and diagonal extraction +give either convergence to +$-\infty$ locally uniformly from above, or local $L^1$ +convergence to a plurisubharmonic function on $M$. +In the second case the upper-regularized limit is at most +zero everywhere by \eqref{chart:local-exponent}. +Lemma~\ref{chart:psh-liouville} makes it constant. On one +fixed neighborhood of $o$, \eqref{chart:local-exponent} +bounds this constant by a fixed negative number, say +$-a_*$. The constant-limit conclusion of +Lemma~\ref{lem:psh-compactness-bridge} then gives +$\limsup\sup_Kv_s\le-a_*$ on every fixed compact along +this subsequence. The collapsing case gives the same +conclusion with $-\infty$. A sequence violating +\eqref{chart:common-exponent}, with $\sigma=a_*/2$, would +contradict these alternatives. This proves a common +exponent on the full family of clocks. + +For the two remaining transition estimates, transfer the common +exponent from a fixed initial neighborhood back to a small ball in +the chart domain. Choose a fixed compact initial neighborhood $K_0$ +of $o$ with positive initial distance from $o$ to its +boundary. Until a path $\Phi_s(rz)$ first exits $K_0$, +\eqref{chart:metric-decay} and +\eqref{chart:uniform-chart-metric} bound its initial length +by $Ce^s|z|$. It follows that, for a fixed $C_0>1$ and +all large $s$, +\[ + \Phi_s\bigl(B(e^{-C_0s})\bigr)\subset K_0. +\] +For every $u\ge s$, the map $f_u\Phi_s$ on this ball is +the same local inverse composition as $F_{s,u}$ near zero, +and hence everywhere there. Equation~\eqref{chart:common-exponent} +therefore gives the bound +\begin{equation}\label{chart:transition-inner-bound} + \sup_{B(e^{-C_0s})}|F_{s,u}|\le e^{-\sigma u} + \qquad\text{for all }u\ge s\text{ and large }s. +\end{equation} +Cauchy's estimates on this inner ball give the factor +$e^{dC_0s-\sigma u}$ for derivatives of order at most $d$. +Cauchy's estimates on a fixed transition ball give a uniform +bound. Combining the two proves +\eqref{chart:transition-jets}. + +For completeness, fix an outer radius $R0$, +\[ + \log\sup_{B(e^{-\gamma s})}|F_{s,u}| + \le-\theta_s\sigma u+(1-\theta_s)\log B_*, + \qquad + \theta_s=\frac{\log(R/e^{-\gamma s})} + {\log(R/e^{-C_0s})} + \ge\frac{\gamma}{2C_0} +\] +for all sufficiently large $s$. In this formula choose +$\gamma_00$ and $\sigma>0$ such that +\begin{equation}\label{disc:extra-integrability} + \int_{0<|z|0. +\] +These images extend across zero by the same $L^2$ argument. The set +$S$ is an $R$-submodule: for a sum take the smaller of the two positive +exponents, and multiplication by a holomorphic germ is bounded after +shrinking the neighborhood. The ring $R$ is Noetherian, so $S$ is a +submodule of a finite free module and $Q=R^q/S$ is a finite module. +For each $k$, the image of $S$ in $R^q/\mathfrak m^kR^q$ is a +finite-dimensional vector subspace and is closed. Jet convergence of +$Aa_m\in S$ consequently gives +\[ + Aa\in S+\mathfrak m^kR^q\qquad\hbox{for every }k. +\] +Krull's intersection Theorem for the finite local module $Q$ gives +$\bigcap_k\mathfrak m^kQ=0$ \cite[Lemma 10.51.4]{StacksKrull}. +Thus $Aa\in S$. By definition it is the image of one section $b$ +with some positive extra exponent. Pointwise injectivity of $A$ +implies $a=b$ on a sufficiently small punctured neighborhood, proving +\eqref{disc:extra-integrability}. No common exponent for $a_m$ was +used. +\end{proof} + +Let $F=(F_1,\ldots,F_N):M\to\C^N$ be the global injective +holomorphic immersion of Proposition~\ref{prop:initial-data}. Set +\[ + \psi=\log\sum_{|I|=n}|dF_I|_g^2, + \qquad dF_I=dF_{i_1}\wedge\cdots\wedge dF_{i_n}. +\] +Immersivity makes $\psi$ smooth. Along any holomorphic disc, +$\psi$ is subharmonic: each $dF_I$ is a holomorphic canonical form, +whose logarithmic squared norm is plurisubharmonic under the curvature +hypothesis, and the log-sum has the same property. Similarly +$|dF|_g^2=\sum_i|dF_i|_g^2$ is plurisubharmonic. + +\begin{lemma}[Compactness with a lower anchor]\label{lem:psh-compactness-bridge} +Let $\Omega_j$ be increasing open subsets exhausting a connected +complex manifold $X$, and let $u_j$ be plurisubharmonic on $\Omega_j$. +Assume that for each compact $K\subset X$, the functions $u_j$ are +uniformly bounded above on $K$ once $K\subset\Omega_j$. +Every sequence has a subsequence for which either $u_j$ tends to +$-\infty$ locally uniformly from above, or $u_j$ converges in +$L^1_{\mathrm{loc}}$ to a plurisubharmonic function. +A lower bound $u_j(z_j)\ge-A$ at points $z_j$ in a fixed compact set +excludes the first alternative along that sequence. In particular, +lower bounds on moving subsets of a fixed compact set of uniformly +positive measure suffice. If the $L^1_{\mathrm{loc}}$ limit is the +constant $c$, then +\[ + \limsup_j\sup_K u_j\le c +\] +for every compact $K\subset X$. +\end{lemma} + +\begin{proof} +We explain the lower-anchor step rather than building it into the +compactness theorem. Pass to a subsequence with $z_j\to z_*$ and +work in a coordinate ball about $z_*$. On a slightly larger ball +choose a common upper bound $C$ and set $w_j=C-u_j$. +These functions are nonnegative and superharmonic. The supermean +inequality at $z_j$ bounds their integrals on a ball of fixed radius +about $z_j$ by its volume times $C+A$. A fixed smaller ball about +$z_*$ is eventually contained in those balls, so the $L^1$ norms +there are bounded. + +Such a bound propagates along finite chains of overlapping coordinate +balls. In a fixed overlap of positive measure, the integral bound +supplies a point at which $w_j$ is bounded by its average over the +overlap. Applying the supermean inequality on a larger ball centered +at that point, still contained in the coordinate neighborhood, bounds +the integral on the next smaller ball. On each fixed compact overlap, the Euclidean volume measures in +the two coordinate charts are uniformly comparable. Increasing the +local upper bound $C$ when moving between charts only adds a fixed constant. +Connectedness and a finite covering therefore give $L^1$ bounds on +every fixed compact subset of $X$. + +Families of subharmonic functions bounded in $L^1_{\mathrm{loc}}$ +are relatively compact in that topology \cite[Chapter~I, Proposition~4.21]{DemaillyBook}. +Apply this result in coordinate balls and take a diagonal subsequence. +Positivity of the complex Hessians passes to the distributional +limit, so its upper semicontinuous representative is +plurisubharmonic. If no subsequence has a lower anchor in any fixed +compact set, then the suprema on each member of a compact exhaustion +tend to $-\infty$; this is the other alternative. This also proves +the assertion for exhausting domains, since each finite chain of +balls is contained in every sufficiently late $\Omega_j$. + +Finally suppose the limit is the constant $c$. In a coordinate ball +whose concentric enlargement is relatively compact, apply the +submean inequality on a fixed-radius ball centered at each point of +the smaller ball. It bounds $u_j-c$ from above by a fixed constant +times the $L^1$ norm of $u_j-c$ on the enlargement. This norm tends +to zero. A finite covering proves the asserted upper bound on $K$. +\end{proof} + +\begin{proof}[Proof of Proposition~\ref{prop:disc-compactness}] +We first control centers of discs $f_l$ in $M$. The maximum principle +gives uniform bounds +\begin{equation}\label{disc:boundary-upper} + |F\circ f_l|\le C_K,\qquad + |dF|_g\circ f_l\le C_K,\qquad + \psi_l:=\psi\circ f_l\le C_K. +\end{equation} +The area bound controls the energy, with a fixed normalization +constant. In particular, the functions +\[ + E_l(\theta)=\int_{1/2}^1 + |\partial_rf_l(re^{i\theta})|_g^2r\,dr +\] +have uniformly bounded angular integrals. On a set of angles of +measure bounded below, $E_l(\theta)\le C(A_0+1)$. For each such +angle and every $r\in[1/2,3/4]$, Cauchy--Schwarz gives +\[ + \dist_g(f_l(re^{i\theta}),K) + \le E_l(\theta)^{1/2} + \left(\int_{1/2}^1\frac{dr}{r}\right)^{1/2}. +\] +Completeness and Hopf--Rinow put these images in a fixed compact. +Thus on a subset of the fixed annulus of area bounded below, +$\psi_l$ has a fixed lower bound. Lemma~\ref{lem:psh-compactness-bridge}, together with +\eqref{disc:boundary-upper}, now gives a subsequence converging in +$L^1_{\mathrm{loc}}(\Delta)$ to a subharmonic function +$\psi_\infty$; the lower bounds on the anchor subsets exclude +collapse to $-\infty$. We retain their positive-area property for +the later step that avoids neighborhoods of the possible atoms. Let +$\mu_l=(2\pi)^{-1}\Delta_{\mathrm{eucl}}\psi_l$ and +$\mu=(2\pi)^{-1}\Delta_{\mathrm{eucl}}\psi_\infty$. +Then $\mu_l\to\mu$ weakly on compact subsets. + +We spell out the required inverse-Jacobian estimate. Let +$Z=\{z:\mu(\{z\})\ge1\}$, a locally finite subset of $\Delta$. +Near any point outside $Z$, choose a small disc $D$ whose boundary +has zero $\mu$-measure and for which $\mu(D)0. +\] +For small enough $r$, $F\circ f$ on $0<|z|0$ be the infimum on $K_0$ of the least singular value +of $dG$ in the coordinate Euclidean metric. By +\eqref{disc:frame-unitary}, $\|S(0)\|_{\mathrm{op}}\le\gamma^{-1}$. +The preceding identity gives +\[ + \|S(0)^{-1}\|_{\mathrm{op}} + \le \sup_\Delta\|J_{E_f}\|_{\mathrm{op}}\, + \gamma^{-1}\sup_{K_0}\|J^{-1}\|_{\mathrm{op}}. +\] +Every quantity on the right has the stated dependence. +\end{proof} diff --git a/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/sections/dynamics.tex b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/sections/dynamics.tex new file mode 100644 index 0000000000000000000000000000000000000000..28f649b85c8fe697e0b8d3ca8d2efd8869dc3ff9 --- /dev/null +++ b/preprints/Uniformization-of-complete-Kahler-manifolds-with-positive-bisectional-curvature-September-23-2026/build/sections/dynamics.tex @@ -0,0 +1,664 @@ +\section{Polynomial models with nonuniform contraction} +\label{sec:dynamics} + +We retain the volume clock $s=\rho(o,t)$, its logarithmic-time speed +$q(s)=ds/d\tau=tR(o,t)$, and the charts of +Proposition~\ref{prop:shrinking-charts}. +Polynomial normalization and inverse iteration are classical tools +for attracting basins, notably in Rosay--Rudin's work +\cite[Appendix]{RosayRudin1988}; Chau--Tam brought this strategy into +K\"ahler uniformization \cite{ChauTamComplex2006,ChauTamStein,ChauTamSimply}. +The estimates proved here address the nonuniform contraction permitted +by Proposition~\ref{prop:ricci-windows}. For sequences of holomorphic +automorphisms of $\C^n$, $n\ge2$, fixing zero and satisfying +$A|z|\le|f_j(z)|\le B|z|$ on one fixed ball about zero, with +$00,\qquad + \liminf_{s\to\infty}\frac{q(s)}s\le2,\qquad + \lambda_{\min}(t\Ric)(o)\ge b_0q(a_0s), + \label{eq:dyn:rate-input} +\end{equation} +where $00$ are fixed. + +We continue to use $J_d$ and the fixed coefficient norms introduced in +Section~\ref{sec:charts}. +All maps and jets in this Section fix zero. A coefficient bound +$\exp(o(s_k))$ means an upper bound $\exp(\eta_k s_k)$ with +$\eta_k\to0$; its rate of convergence may depend on parameters already +fixed. No assertion of uniformity as those parameters vary is intended. +For polynomial automorphisms put +$G_{k,l}=G_{l-1}\circ\cdots\circ G_k$ and $G_{k,k}=\Id$. + +\begin{proposition}[Polynomial models]\label{prop:polynomial-models} +Fix an integer $d\ge2$ and a macro width $0