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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