rem stringlengths 1 322k | add stringlengths 0 2.05M | context stringlengths 4 228k | meta stringlengths 156 215 |
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if pdflatex: | if not engine or engine == "latex": command = "latex" suffix = "ps" return_suffix = "dvi" elif engine == "pdflatex": | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
command = "latex" suffix = "ps" return_suffix = "dvi" | raise ValueError, "Unsupported LaTeX engine." | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
if pdflatex: | if engine == "pdflatex" or engine == "xelatex": | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
else: | else: | def _run_latex_(filename, debug=False, density=150, pdflatex=None, png=False, do_in_background=False): """ This runs LaTeX on the TeX file "filename.tex". It produces files "filename.dvi" (or "filename.pdf"` if ``pdflatex`` is ``True``) and if ``png`` is True, "filename.png". If ``png`` is True and dvipng can't conve... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
def __init__(self, debug=False, slide=False, density=150, pdflatex=None): | def __init__(self, debug=False, slide=False, density=150, pdflatex=None, engine=None): | def __init__(self, debug=False, slide=False, density=150, pdflatex=None): self.__debug = debug self.__slide = slide self.__pdflatex = pdflatex self.__density = density | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
density=None, pdflatex=None, locals={}): | density=None, pdflatex=None, engine=None, locals={}): | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
- ``pdflatex`` - whether to use pdflatex. | - ``pdflatex`` - whether to use pdflatex. This is deprecated. Use ``engine`` option instead. - ``engine`` - latex engine to use. Currently latex, pdflatex, and xelatex are supported. | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
or this command won't work. When using pdflatex, you must | or this command won't work. When using pdflatex or xelatex, you must | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
if pdflatex is None: if self.__pdflatex is None: pdflatex = _Latex_prefs._option["pdflatex"] | if engine is None: if self.__engine is None: engine = _Latex_prefs._option["engine"] | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
pdflatex = bool(self.__pdflatex) | engine = self.__engine | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
density=density, pdflatex=pdflatex, png=True) | density=density, engine=engine, png=True) | def eval(self, x, globals, strip=False, filename=None, debug=None, density=None, pdflatex=None, locals={}): """ INPUT: | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
def pdflatex(self, t = None): """ | def pdflatex(self, t = None): """ This is deprecated. Use engine("pdflatex") instead. | def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
return _Latex_prefs._option["pdflatex"] _Latex_prefs._option["pdflatex"] = bool(t) | from sage.misc.misc import deprecation deprecation('Use engine() instead.') return _Latex_prefs._option["engine"] == "pdflatex" elif t: from sage.misc.misc import deprecation deprecation('Use engine("pdflatex") instead.') self.engine("pdflatex") else: from sage.misc.misc import deprecation deprecation('Use engine("late... | def pdflatex(self, t = None): """ Controls whether Sage uses PDFLaTeX or LaTeX when typesetting with :func:`view`, in ``%latex`` cells, etc. | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, engine=None, viewer = None, tightpage = None, mode='inline', **kwds): | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
- ``pdflatex`` - bool (default: False): use pdflatex. | - ``pdflatex`` - bool (default: False): use pdflatex. This is deprecated. Use 'engine' option instead. - ``engine`` - 'latex', 'pdflatex', or 'xelatex' | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
If ``pdflatex`` is ``True``, then this produces a pdf file. Otherwise, it produces a dvi file, and if the program dvipng is | If ``pdflatex`` is ``True``, then the latex engine is set to pdflatex. If the engine is either pdflatex or xelatex, it produces a pdf file. Otherwise, it produces a dvi file, and if the program dvipng is | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
viewer, even in notebook mode. This also sets ``pdflatex`` to ``True``. | viewer, even in notebook mode. This also sets the latex engine to be ``pdflatex`` if the current engine is latex. | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
debug=debug, do_in_background=False, pdflatex=pdflatex) | debug=debug, do_in_background=False, engine=engine) | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
if viewer == "pdf": pdflatex = True if pdflatex is None: pdflatex = _Latex_prefs._option["pdflatex"] | if pdflatex: engine = "pdflatex" else: engine = _Latex_prefs._option["engine"] if viewer == "pdf" and engine == "latex": engine = "pdflatex" | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
suffix = _run_latex_(tex_file, debug=debug, pdflatex=pdflatex, png=False) | suffix = _run_latex_(tex_file, debug=debug, engine=engine, png=False) | def view(objects, title='SAGE', debug=False, sep='', tiny=False, pdflatex=None, viewer = None, tightpage = None, mode='inline', **kwds): r"""nodetex Compute a latex representation of each object in objects, compile, and display typeset. If used from the command line, this requires that latex be installed. INPUT: - `... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
do_in_background=False, tiny=False, pdflatex=True): | do_in_background=False, tiny=False, pdflatex=True, engine='pdflatex'): | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
- ``pdflatex`` - bool (default: False): use pdflatex. | - ``pdflatex`` - bool (default: True): use pdflatex. This option is deprecated. Use ``engine`` option instead. See below. - ``engine`` - 'latex', 'pdflatex', or 'xelatex' (default: 'pdflatex') | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
pdflatex=pdflatex) | engine=engine) | def png(x, filename, density=150, debug=False, do_in_background=False, tiny=False, pdflatex=True): """ Create a png image representation of ``x`` and save to the given filename. INPUT: - ``x`` - object to be displayed - ``filename`` - file in which to save the image - ``density`` - integer (default: 150) - ``d... | 12cbced4c423573c5a4da0ddb9e58a2d0102170d /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/12cbced4c423573c5a4da0ddb9e58a2d0102170d/latex.py |
this function is not called) is n=15, but it might have to be | this function is not called) is ``n=15``, but it might have to be | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- `n` (long) -- real precision used for floating point | - ``n`` (long) -- real precision used for floating point | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
.. note:: This change is global and affects all of Sage. | .. warning:: This change is global and affects *all* of Sage. | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
curve using the Curvedata class from eclib, called here an 'mwrank | curve using the ``Curvedata`` class from ``eclib``, called here an 'mwrank | def set_precision(n): r""" Set the global NTL real number precision. This has a massive effect on the speed of mwrank calculations. The default (used if this function is not called) is n=15, but it might have to be increased if a computation fails. In this case, one must recreate the mwrank curve from scratch after ... | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. If strictly less than 5 invariants are given, then the first ones are set to 0, so, e.g., ``[3,4] means `a_1=a_2=a_3=0` and `a_4=3`, `a_6=4`. INPUT: - `ainvs` (list or tuple) -- a list of <= 5 integers, the coefficients o... | ``ainvs``, which is a list of 5 or less *integers* `a_1`, `a_2`, `a_3`, `a_4`, and `a_5`. See the docstring of this class for full documentation. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
This example illustrates that omitted $a$-invariants default to $0$:: sage: e = mwrank_EllipticCurve([3, -4]) sage: e y^2 = x^3 + 3*x - 4 sage: e.ainvs() [0, 0, 0, 3, -4] The entries of the input list are coerced to :class:`int`. If this is impossible then an error is raised:: sage: e = mwrank_EllipticCurve([3, -4.... | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py | |
if not isinstance(ainvs, list) and len(ainvs) <= 5: raise TypeError, "ainvs must be a list of length at most 5." | if not isinstance(ainvs, (list,tuple)) or not len(ainvs) <= 5: raise TypeError, "ainvs must be a list or tuple of length at most 5." | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py | ||
raise TypeError, "ainvs must be a list of integers." | raise TypeError, "ainvs must be a list or tuple of integers." | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Set the verbosity of printing of output by the 2-descent and | Set the verbosity of printing of output by the :meth:`two_descent()` and | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- `verbose` (int) -- if positive, print lots of output when | - ``verbose`` (int) -- if positive, print lots of output when | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
sage: E.saturate() | sage: E.saturate() | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Returns the underlying _Curvedata class for this mwrank elliptic curve. | Returns the underlying :class:`_Curvedata` class for this mwrank elliptic curve. | def _curve_data(self): r""" Returns the underlying _Curvedata class for this mwrank elliptic curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- ``verbose`` (bool, default True) -- print what mwrank is doing - ``selmer_only`` (bool, default False) -- selmer_only switch | - ``verbose`` (bool, default ``True``) -- print what mwrank is doing. - ``selmer_only`` (bool, default ``False``) -- ``selmer_only`` switch. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
quartic point search - ``second_limit`` (int, default 8) -- bound on `\log `max(|x|,|z|)`, i.e. logarithmic | quartic point search. - ``second_limit`` (int, default 8) -- bound on `\log \max(|x|,|z|)`, i.e. logarithmic. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
quartic search. n_aux=-1 causes default (8) to be used. | quartic search. ``n_aux=-1`` causes default (8) to be used. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- ``second_descent`` (bool, default True) -- (only relevant | - ``second_descent`` (bool, default ``True``) -- (only relevant | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
descent. Default strongloy recommended. | descent. *Default strongly recommended.* | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Nothing -- nothing is returned | Nothing -- nothing is returned. | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
second_descent = int(second_descent) | second_descent = int(second_descent) | def two_descent(self, verbose = True, selmer_only = False, first_limit = 20, second_limit = 8, n_aux = -1, second_descent = True): """ Compute 2-descent data for this curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Returns the rank of this curve, computed using 2-descent. | Returns the rank of this curve, computed using :meth:`two_descent()`. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
upper bound may be obtained using the function rank_bound(). | upper bound may be obtained using the function :meth:`rank_bound()`. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
the method :meth:`certain`. | the method :meth:`certain()`. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
using 2-descent. | using :meth:`two_descent()`. | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
of order 4, we only obtain an upper bound of 2: | of order 4, we only obtain an upper bound of 2:: | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
In this case the value returned by :meth:`rank` is only a lower bound in general (though in this is correct):: | In this case the value returned by :meth:`rank()` is only a lower bound in general (though this is correct):: | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
the computation again but turn off the second descent:: | the computation again but turn off ``second_descent``:: | def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
but with no 2-torsion, the selmer rank is strictly greater | but with no 2-torsion, the Selmer rank is strictly greater | def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
primes up to bound. | primes up to ``bound``. | def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- `bound` (int, default -1) -- Use `-1` (the default) to | - ``bound`` (int, default -1) -- Use `-1` (the default) to | def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` | Returns ``True`` if the last :meth:`two_descent()` call provably correctly computed the rank. If :meth:`two_descent()` hasn't been called, then it is first called by :meth:`certain()` | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
The result is true if and only if the results of the methods :meth:`rank` and :meth:`rank_bound` are equal. | The result is ``True`` if and only if the results of the methods :meth:`rank()` and :meth:`rank_bound()` are equal. | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
for the curve `y^2 + y = x^3 - x^2 - 120x - 2183`.:: | for the curve `y^2 + y = x^3 - x^2 - 120x - 2183`:: | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
computing the L-function), but Sha has order 4 and the $2$-torsion is trivial, so mwrank cannot conclusively | computing the `L`-function), but Sha has order 4 and the 2-torsion is trivial, so mwrank cannot conclusively | def certain(self): r""" True if the last :meth:`two_descent` call provably correctly computed the rank. If :meth:`two_descent` hasn't been called, then it is first called by :meth:`certain` using the default parameters. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
floating point number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | floating point number `B` such that if `P` is a point on the curve, then the naive logarithmic height `h(P)` is less than `B+\hat{h}(P)`, where `\hat{h}(P)` is the canonical height of `P`. | def CPS_height_bound(self): r""" Return the Cremona-Prickett-Siksek height bound. This is a floating point number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | number `B` such that if `P` is a point on the curve, then the naive logarithmic height `h(P)` is less than `B+\hat{h}(P)`, where `\hat{h}(P)` is the canonical height of `P`. | def silverman_bound(self): r""" Return the Silverman height bound. This is a floating point number $B$ such that if $P$ is a point on the curve, then the naive logarithmic height $h(P)$ is less than $B+\hat{h}(P)$, where $\hat{h}(P)$ is the canonical height of $P$. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
INPUT: - `curve` (:class:`mwrank_EllipticCurve`) -- the underlying elliptic curve. - `verbose` (bool, default False) -- verbosity flag (controls amount of output produced in point searches) - `pp` (int, default 1) -- process points flag (if nonzero, the points found are processed, so that at all times only a `\ZZ`-b... | See the docstring of this class for full documentation. | def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [] sage: EQ.search(2) The previous command produces the following output:: P1 = [0:1:0] is torsion point, order 1 P1 = [1:-1:1] is torsion point, order 2 P1 = [2:2:1] is torsion point, order 3 P1 = [9:23:1] is torsion point, order 6 sage: E = mwrank_EllipticCurve([0,0,1,-7,6]) sag... | Subgroup of Mordell-Weil group: [] | def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
'Subgroup of Mordell Weil group: []' | 'Subgroup of Mordell-Weil group: []' | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
'Subgroup of Mordell Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]]' """ return "Subgroup of Mordell Weil group: %s"%self.__mw | 'Subgroup of Mordell-Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]]' """ return "Subgroup of Mordell-Weil group: %s"%self.__mw | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
This function allows one to add points to a mwrank_MordellWeil object. Process points in the list v, with saturation at primes up to sat. If sat = 0 (the default), do no saturation. | This function allows one to add points to a :class:`mwrank_MordellWeil` object. Process points in the list ``v``, with saturation at primes up to ``sat``. If ``sat`` is zero (the default), do no saturation. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- `v` (list of 3-tuples or lists of ints or Integers) -- a | - ``v`` (list of 3-tuples or lists of ints or Integers) -- a | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- `sat` (int, default 0) --saturate at primes up to sat, or at all primes if sat=0. | - ``sat`` (int, default 0) -- saturate at primes up to ``sat``, or at *all* primes if ``sat`` is zero. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
None. But note that if the verbose flag is set, then there | None. But note that if the ``verbose`` flag is set, then there | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Example to illustrate the saturation parameter:: | Example to illustrate the saturation parameter ``sat``:: | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
raise TypeError, "v (=%s) must be a list of 3-tuples of ints"%v | raise TypeError, "v (=%s) must be a list of 3-tuples (or 3-element lists) of ints"%v | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
but the interface currently returns the output as a float. | but the interface currently returns the output as a ``float``. | def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
(float) the regulator of the points in this subgroup. | (float) The regulator of the points in this subgroup. | def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
OUTPUT: (int) The rank of this subgroup of the Mordell-Weil group. | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py | |
Subgroup of Mordell Weil group: [] | Subgroup of Mordell-Weil group: [] | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] | Subgroup of Mordell-Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
all primes up to `max_prime`. If `-1` (default) then an | all primes up to ``max_prime``. If `-1` (the default), an | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
computed bound is greater than a value set by the eclib | computed bound is greater than a value set by the ``eclib`` | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- ``odd_primes_only`` (bool, default False) -- only do | - ``odd_primes_only`` (bool, default ``False``) -- only do | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
via 2-descent they should alreday be 2-saturated.) | via :meth:``two_descent()`` they should already be 2-saturated.) | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- ``ok`` (bool) is True if and only if the saturation was | - ``ok`` (bool) -- ``True`` if and only if the saturation was | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
the computed saturation bound being too high, then True indicates that the subgroup is saturated at `\emph{all}` | the computed saturation bound being too high, then ``True`` indicates that the subgroup is saturated at *all* | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
- ``index`` (int) is the index of the group generated by the | - ``index`` (int) -- the index of the group generated by the | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
uses floating points methods based on elliptic logarithms to | uses floating point methods based on elliptic logarithms to | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
We emphasize that if this function returns True as the first return argument, and if the default was used for the parameter ``sat_bnd``, then the points in the basis after calling this function are saturated at `\emph{all}` primes, | We emphasize that if this function returns ``True`` as the first return argument (``ok``), and if the default was used for the parameter ``max_prime``, then the points in the basis after calling this function are saturated at *all* primes, | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
saturate up to, and that prime is `\leq` ``max_prime``. | saturate up to, and that prime might be smaller than ``max_prime``. | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
calling search. So calling search up to height 20 then calling saturate results in another search up to height 18. | calling :meth:`search()`. So calling :meth:`search()` up to height 20 then calling :meth:`saturate()` results in another search up to height 18. | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[1547:-2967:343], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | Subgroup of Mordell-Weil group: [[1547:-2967:343], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[-2:3:1], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | Subgroup of Mordell-Weil group: [[-2:3:1], [2707496766203306:864581029138191:2969715140223272], [-13422227300:-49322830557:12167000000]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[-2:3:1], [-14:25:8], [-13422227300:-49322830557:12167000000]] | Subgroup of Mordell-Weil group: [[-2:3:1], [-14:25:8], [-13422227300:-49322830557:12167000000]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[-2:3:1], [-14:25:8], [1:-1:1]] | Subgroup of Mordell-Weil group: [[-2:3:1], [-14:25:8], [1:-1:1]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Of course, the ``process`` function would have done all this | Of course, the :meth:`process()` function would have done all this | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[-2:3:1], [-14:25:8], [1:-1:1]] | Subgroup of Mordell-Weil group: [[-2:3:1], [-14:25:8], [1:-1:1]] | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
But we would still need to use the ``saturate`` function to | But we would still need to use the :meth:`saturate()` function to | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
side-effect. It proves that the inde of the points in their | side-effect. It proves that the index of the points in their | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
by reducing the poits modulo all primes of good reduction up | by reducing the points modulo all primes of good reduction up | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
On 32-bit machines, this MUST be < 21.48 else $\exp(h_lim)>2^31$ and overflows. On 64-bit machines it must be at most 43.668. However, this bound is a logarithic | On 32-bit machines, this *must* be < 21.48 else `\exp(h_{\text{lim}}) > 2^{31}` and overflows. On 64-bit machines, it must be *at most* 43.668. However, this bound is a logarithmic | def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] In the next example, a serach bound of 12 is needed to find a non-torsin point:: | Subgroup of Mordell-Weil group: [[1:-1:1], [-2:3:1], [-14:25:8]] In the next example, a search bound of 12 is needed to find a non-torsion point:: | def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [] | Subgroup of Mordell-Weil group: [] | def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
Subgroup of Mordell Weil group: [[4413270:10381877:27000]] | Subgroup of Mordell-Weil group: [[4413270:10381877:27000]] | def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
if height_limit >= 21.4: | if height_limit >= 21.4: | def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
verbose == bool(verbose) | verbose = bool(verbose) | def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the Mordell-Weil group. | 9932a677a12413086a59217c4c0d425b0543b6eb /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/9932a677a12413086a59217c4c0d425b0543b6eb/interface.py |
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