bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
|---|---|---|
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. | 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. | 461,600 |
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. | 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. | 461,601 |
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. | 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. | 461,602 |
def rank(self): """ Returns the rank of this curve, computed using 2-descent. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 461,603 |
def rank(self): """ Returns the rank of this curve, computed using 2-descent. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 461,604 |
def rank(self): """ Returns the rank of this curve, computed using 2-descent. | def rank(self): """ Returns the rank of this curve, computed using 2-descent. | 461,605 |
def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 461,606 |
def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 461,607 |
def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | def rank_bound(self): """ Returns an upper bound for the rank of this curve, computed using 2-descent. | 461,608 |
def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. EXAMPLES: | def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. EXAMPLES: | 461,609 |
def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. EXAMPLES: | def selmer_rank(self): r""" Returns the rank of the 2-Selmer group of the curve. EXAMPLES: | 461,610 |
def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | 461,611 |
def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | def saturate(self, bound=-1): """ Compute the saturation of the Mordell-Weil group at all primes up to bound. | 461,612 |
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. | def certain(self): r""" 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()` using the default parameters. | 461,613 |
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. | 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. | 461,614 |
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. | 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. | 461,615 |
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. | 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. | 461,616 |
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 $P$. | 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 $P$. | 461,617 |
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 $P$. | 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 $P$. | 461,618 |
def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | 461,619 |
def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | def __init__(self, curve, verbose=True, pp=1, maxr=999): r""" Constructor for the :class:`mwrank_MordellWeil` class. | 461,620 |
def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 461,621 |
def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 461,622 |
def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 461,623 |
def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 461,624 |
def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 461,625 |
def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 461,626 |
def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 461,627 |
def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | def process(self, v, sat=0): """ This function allows one to add points to a mwrank_MordellWeil object. | 461,628 |
def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | 461,629 |
def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | def regulator(self): """ Return the regulator of the points in this subgroup of the Mordell-Weil group. | 461,630 |
def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 461,631 |
def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 461,632 |
def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | def rank(self): """ Return the rank of this subgroup of the Mordell-Weil group. | 461,633 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to ``max_prime``. If `-1` (the default), an upper bound is computed for the primes at which the subgroup may not be satu... | 461,634 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,635 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,636 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,637 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,638 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,639 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,640 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,641 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,642 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,643 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,644 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,645 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,646 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,647 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,648 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,649 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,650 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,651 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,652 |
def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | def saturate(self, max_prime=-1, odd_primes_only=False): r""" Saturate this subgroup of the Mordell-Weil group. INPUT: - ``max_prime`` (int, default -1) -- saturation is performed for all primes up to `max_prime`. If `-1` (default) then an upper bound is computed for the primes at which the subgroup may not be satura... | 461,653 |
def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the 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. | 461,654 |
def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the 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. | 461,655 |
def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the 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. | 461,656 |
def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the 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. | 461,657 |
def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the 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. | 461,658 |
def search(self, height_limit=18, verbose=False): r""" Search for new points, and add them to this subgroup of the 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. | 461,659 |
def points(self): """ Return a list of the generating points in this Mordell-Weil group. | def points(self): """ Return a list of the generating points in this Mordell-Weil group. | 461,660 |
def edge_coloring(g, value_only=False, vizing=False, hex_colors=False, log=0): r""" Properly colors the edges of a graph. See the URL http://en.wikipedia.org/wiki/Edge_coloring for further details on edge coloring. INPUT: - ``g`` -- a graph. - ``value_only`` -- (default: ``False``): - When set to ``True``, only the... | def edge_coloring(g, value_only=False, vizing=False, hex_colors=False, log=0): r""" Properly colors the edges of a graph. See the URL http://en.wikipedia.org/wiki/Edge_coloring for further details on edge coloring. INPUT: - ``g`` -- a graph. - ``value_only`` -- (default: ``False``): - When set to ``True``, only the... | 461,661 |
def metaclass(name, bases): """ Creates a new class in this metaclass INPUT:: - name: a string - bases: a tuple of classes EXAMPLES:: sage: from sage.misc.test_class_pickling import metaclass, bar sage: c = metaclass("foo2", (object, bar,)) constructing class sage: c <class 'sage.misc.test_class_pickling.foo2'> sage... | def metaclass(name, bases): """ Creates a new class in this metaclass INPUT:: - name: a string - bases: a tuple of classes EXAMPLES:: sage: from sage.misc.test_class_pickling import metaclass, bar sage: c = metaclass("foo2", (object, bar,)) constructing class sage: c <class 'sage.misc.test_class_pickling.foo2'> sage... | 461,662 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,663 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,664 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,665 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,666 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,667 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,668 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,669 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,670 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,671 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,672 |
def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | def _find_scaling_L_ratio(self): r""" This function is use to set ``_scaling``, the factor used to adjust the scalar multiple of the modular symbol. If `[0]`, the modular symbol evaluated at 0, is non-zero, we can just scale it with respect to the approximation of the L-value. It is known that the quotient is a rationa... | 461,673 |
def plot(self, *args, **kwds): """ Plot the real points of an affine patch of this projective plane curve. | def plot(self, *args, **kwds): """ Plot the real points of an affine patch of this projective plane curve. | 461,674 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points_iterator(self): r""" Return the rational points on this curve computed via enumeration. | 461,675 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,676 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,677 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,678 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,679 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,680 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,681 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,682 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | 461,683 |
def rational_points(self, algorithm="enum", sort=True): r""" Return the rational points on this curve computed via enumeration. | defrational_points(self,algorithm="enum",sort=True):r"""Returntherationalpointsonthiscurvecomputedviaenumeration. | 461,684 |
def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | def tamagawa_product_bsd(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product ... | 461,685 |
def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | 461,686 |
def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | 461,687 |
def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | def tamagawa_product(self): r""" Given an elliptic curve `E` over a number field `K`, this function returns the integer `C(E/K)` that appears in the Birch and Swinnerton-Dyer conjecture accounting for the local information at finite places. If the model is a global minimal model then `C(E/K)` is simply the product of t... | 461,688 |
def global_minimal_model(self, proof = None): r""" Returns a model of self that is integral, minimal at all primes. .. note:: | def global_minimal_model(self, proof = None): r""" Returns a model of self that is integral, minimal at all primes. .. note:: | 461,689 |
def _sage_doc_(self): """ EXAMPLES:: sage: 'groebner' in singular.groebner._sage_doc_() True """ if not nodes: generate_docstring_dictionary() | def _sage_doc_(self): """ EXAMPLES:: sage: 'groebner' in singular.groebner._sage_doc_() True """ if not nodes: generate_docstring_dictionary() | 461,690 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | def eigenvalues(self,extend=True): r""" Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.e... | 461,691 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. INPUT: - ``extend`` -- boolean (default: True) decides if base field extensions should be considered or not. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.endo... | 461,692 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of `\QQ^3`:: sage: V=QQ^3 sage: H=V... | 461,693 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 461,694 |
def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | def eigenvalues(self,extend=True): """ Returns a list with the eigenvalues of the endomorphism of vector spaces. If the option extend is set to True (default), then eigenvalues in extensions of the base field are considered. EXAMPLES: We compute the eigenvalues of an endomorphism of QQ^3:: sage: V=QQ^3 sage: H=V.en... | 461,695 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - ``extend`` -- boolean (default: True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding ... | 461,696 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a sequence with a basis of the corresponding subspace of eigenvec... | 461,697 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 461,698 |
def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | def eigenvectors(self,extend=True): """ Computes the subspace of eigenvectors of a given eigenvalue. INPUT: - extend (True) decides if base field extensions should be considered or not. OUTPUT: A sequence of tuples. Each tuple contains an eigenvalue, a list with a basis of the corresponding subspace of eigenvectors... | 461,699 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.