bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def _allowed_options(self): """ Return the allowed options for the Arc class. | def _allowed_options(self): """ Return the allowed options for the Arc class. | 460,200 |
def _repr_(self): """ String representation of Arc primitive. | def _repr_(self): """ String representation of Arc primitive. | 460,201 |
def plot3d(self): r""" TESTS: | def plot3d(self): r""" TESTS: | 460,202 |
def install_packages(self, package_name): """ Install an R package into Sage's R installation. | def install_packages(self, package_name): """ Install an R package into Sage's R installation. | 460,203 |
def install_packages(self, package_name): """ Install an R package into Sage's R installation. | def install_packages(self, package_name): """ Install an R package into Sage's R installation. | 460,204 |
def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n -1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": import scipy.special ans =... | def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n >= 1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": import scipy.special ans... | 460,205 |
def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n -1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": import scipy.special ans =... | def spherical_bessel_J(n, var, algorithm="maxima"): r""" Returns the spherical Bessel function of the first kind for integers n -1. Reference: AS 10.1.8 page 437 and AS 10.1.15 page 439. EXAMPLES:: sage: spherical_bessel_J(2,x) ((3/x^2 - 1)*sin(x) - 3*cos(x)/x)/x """ if algorithm=="scipy": from scipy.special.specfun... | 460,206 |
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 ... | 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 af... | 460,207 |
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 ... | 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 ... | 460,208 |
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 ... | 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 ... | 460,209 |
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 ... | 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 ... | 460,210 |
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_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 460,211 |
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_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 460,212 |
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_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 460,213 |
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_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 460,214 |
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_`$. | def __init__(self, ainvs, verbose=False): r""" Create the mwrank elliptic curve with invariants ``a_invs``, which is a list of `\leq 5` \emph{integers} `a_1`, `a_2`, `a_3`, `a_4`, and `a_`$. | 460,215 |
def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the :meth:`two_descent()` and other functions. | 460,216 |
def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 460,217 |
def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | def set_verbose(self, verbose): """ Set the verbosity of printing of output by the 2-descent and other functions. | 460,218 |
def _curve_data(self): r""" Returns the underlying _Curvedata class for this mwrank elliptic curve. | def _curve_data(self): r""" Returns the underlying _Curvedata class for this mwrank elliptic curve. | 460,219 |
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. | 460,220 |
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. | 460,221 |
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. | 460,222 |
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. | 460,223 |
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. | 460,224 |
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. | 460,225 |
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. | 460,226 |
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. | 460,227 |
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. | 460,228 |
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. | 460,229 |
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. | 460,230 |
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. | 460,231 |
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. | 460,232 |
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: | 460,233 |
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: | 460,234 |
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. | 460,235 |
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. | 460,236 |
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. | 460,237 |
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. | 460,238 |
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. | 460,239 |
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. | 460,240 |
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 $P$. | 460,241 |
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 $P$. | 460,242 |
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. | 460,243 |
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. | 460,244 |
def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 460,245 |
def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | def __repr__(self): r""" String representation of this Mordell-Weil subgroup. | 460,246 |
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. | 460,247 |
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. | 460,248 |
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. | 460,249 |
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. | 460,250 |
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. | 460,251 |
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. | 460,252 |
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. | 460,253 |
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. | 460,254 |
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. | 460,255 |
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. | 460,256 |
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. | 460,257 |
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... | 460,258 |
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... | 460,259 |
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... | 460,260 |
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... | 460,261 |
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... | 460,262 |
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... | 460,263 |
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... | 460,264 |
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... | 460,265 |
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... | 460,266 |
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... | 460,267 |
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... | 460,268 |
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... | 460,269 |
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... | 460,270 |
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... | 460,271 |
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... | 460,272 |
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... | 460,273 |
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... | 460,274 |
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... | 460,275 |
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... | 460,276 |
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... | 460,277 |
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. | 460,278 |
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. | 460,279 |
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. | 460,280 |
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. | 460,281 |
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. | 460,282 |
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. | 460,283 |
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. | 460,284 |
def is_overfull(self): r""" Tests whether the current graph is overfull. | def is_overfull(self): r""" Tests whether the current graph is overfull. | 460,285 |
def is_overfull(self): r""" Tests whether the current graph is overfull. | def is_overfull(self): r""" Tests whether the current graph is overfull. | 460,286 |
def is_overfull(self): r""" Tests whether the current graph is overfull. | def is_overfull(self): r""" Tests whether the current graph is overfull. | 460,287 |
... def variance(self, bias = False): | ... def variance(self, bias = False): | 460,288 |
def __new__(cls, *args, **kwds): r""" TEST: sage: from sage.combinat.words.word_generators import ChristoffelWord_Lower sage: w = ChristoffelWord_Lower(1,0); w doctest:1: DeprecationWarning: ChristoffelWord_Lower is deprecated, use LowerChristoffelWord instead word: 1 """ from sage.misc.misc import deprecation deprecat... | def __new__(cls, *args, **kwds): r""" TEST: sage: from sage.combinat.words.word_generators import ChristoffelWord_Lower sage: w = ChristoffelWord_Lower(1,0); w doctest:1: DeprecationWarning: ChristoffelWord_Lower is deprecated, use LowerChristoffelWord instead word: 1 """ from sage.misc.misc import deprecation deprecat... | 460,289 |
def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S NOTE: This function assumes S is a list of prime ideals, it does not check this. This function will fail if S is not a list of prime ideals. INPUT: - "self" - fractional ide... | def prime_to_S_part(self,S): r""" Return the part of this fractional ideal which is coprime to the prime ideals in the list ``S``. .. note:: This function assumes that `S` is a list of prime ideals, but does not check this. This function will fail if `S` is not a list of prime ideals. INPUT: - "self" - fractional i... | 460,290 |
def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S NOTE: This function assumes S is a list of prime ideals, it does not check this. This function will fail if S is not a list of prime ideals. INPUT: - "self" - fractional ide... | def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S NOTE: This function assumes S is a list of prime ideals, it does not check this. This function will fail if S is not a list of prime ideals. INPUT: - `S` - a list of prime ... | 460,291 |
def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S NOTE: This function assumes S is a list of prime ideals, it does not check this. This function will fail if S is not a list of prime ideals. INPUT: - "self" - fractional ide... | def prime_to_S_part(self,S): r""" This function returns the part of the fractional ideal self which is coprime to the prime ideals in the list S NOTE: This function assumes S is a list of prime ideals, it does not check this. This function will fail if S is not a list of prime ideals. INPUT: - "self" - fractional ide... | 460,292 |
def is_S_unit(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_unit(self,S): r''' Returns True if the ideal is an unit with respect to the | 460,293 |
def is_S_unit(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_unit(self,S): r""" Returns True if the ideal is an unit with respect to the | 460,294 |
def is_S_integral(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_integral(self,S): r''' Returns True if the ideal is an unit with respect to the | 460,295 |
def is_S_integral(self,S): r''' Returns True if the ideal is an unit with respect to the | def is_S_integral(self,S): r""" Returns True if the ideal is an unit with respect to the | 460,296 |
def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. INPUT: - ``gens`` - list of elements of self; if no generators are given, just returns the cardinality of this number field (oo) for consistency. - ``check_is_integral`` - bool (default: Tru... | def order(self, *args, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. INPUT: - ``gens`` - list of elements of self; if no generators are given, just returns the cardinality of this number field (oo) for consistency. - ``check_is_integral`` - bool (default: Tru... | 460,297 |
def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. INPUT: - ``gens`` - list of elements of self; if no generators are given, just returns the cardinality of this number field (oo) for consistency. - ``check_is_integral`` - bool (default: Tru... | deforder(self,*gens,**kwds):r"""Returntheorderwithgivenringgeneratorsinthemaximalorderofthisnumberfield.INPUT:-``gens``-listofelementsofself;ifnogeneratorsaregiven,justreturnsthecardinalityofthisnumberfield(oo)forconsistency.-``check_is_integral``-bool(default:True),whethertocheckthateachgeneratorisintegral.-``check_ra... | 460,298 |
def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. INPUT: - ``gens`` - list of elements of self; if no generators are given, just returns the cardinality of this number field (oo) for consistency. - ``check_is_integral`` - bool (default: Tru... | def order(self, *gens, **kwds): r sage: K.<a> = NumberField(x^3 - 2) sage: ZZ[a] Order in Number Field in a0 with defining polynomial x^3 - 2 TESTS: We verify that trac sage: K.<a> = NumberField(x^4 + 4*x^2 + 2) sage: B = K.integral_basis() sage: K.order(*B) Order in Number Field in a with defining polynomial x^4 + ... | 460,299 |
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