本文整理汇总了Python中constructor.EllipticCurve.has_good_reduction_outside_S方法的典型用法代码示例。如果您正苦于以下问题：Python EllipticCurve.has_good_reduction_outside_S方法的具体用法？Python EllipticCurve.has_good_reduction_outside_S怎么用？Python EllipticCurve.has_good_reduction_outside_S使用的例子？那么, 这里精选的方法代码示例或许可以为您提供帮助。您也可以进一步了解该方法所在类constructor.EllipticCurve的用法示例。
在下文中一共展示了EllipticCurve.has_good_reduction_outside_S方法的2个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: egros_from_j_0
# 需要导入模块: from constructor import EllipticCurve [as 别名]
# 或者: from constructor.EllipticCurve import has_good_reduction_outside_S [as 别名]
def egros_from_j_0(S=[]):
r"""
Given a list of primes S, returns a list of elliptic curves over `\QQ`
with j-invariant 0 and good reduction outside S, by checking all
relevant sextic twists.
INPUT:
- S -- list of primes (default: empty list).
.. note::
Primality of elements of S is not checked, and the output
is undefined if S is not a list or contains non-primes.
OUTPUT:
A sorted list of all elliptic curves defined over `\QQ` with
`j`-invariant equal to `0` and with good reduction at
all primes outside the list ``S``.
EXAMPLES::
sage: from sage.schemes.elliptic_curves.ell_egros import egros_from_j_0
sage: egros_from_j_0([])
[]
sage: egros_from_j_0([2])
[]
sage: [e.label() for e in egros_from_j_0([3])]
['27a1', '27a3', '243a1', '243a2', '243b1', '243b2']
sage: len(egros_from_j_0([2,3,5])) # long time (8s on sage.math, 2013)
432
"""
Elist=[]
if not 3 in S:
return Elist
no2 = not 2 in S
for ei in xmrange([2] + [6]*len(S)):
u = prod([p**e for p,e in zip([-1]+S,ei)],QQ(1))
if no2:
u*=16 ## make sure 12|val(D,2)
Eu = EllipticCurve([0,0,0,0,u]).minimal_model()
if Eu.has_good_reduction_outside_S(S):
Elist += [Eu]
Elist.sort(cmp=curve_cmp)
return Elist示例2: egros_from_j_1728
# 需要导入模块: from constructor import EllipticCurve [as 别名]
# 或者: from constructor.EllipticCurve import has_good_reduction_outside_S [as 别名]
def egros_from_j_1728(S=[]):
r"""
Given a list of primes S, returns a list of elliptic curves over `\QQ`
with j-invariant 1728 and good reduction outside S, by checking
all relevant quartic twists.
INPUT:
- S -- list of primes (default: empty list).
.. note::
Primality of elements of S is not checked, and the output
is undefined if S is not a list or contains non-primes.
OUTPUT:
A sorted list of all elliptic curves defined over `\QQ` with
`j`-invariant equal to `1728` and with good reduction at
all primes outside the list ``S``.
EXAMPLES::
sage: from sage.schemes.elliptic_curves.ell_egros import egros_from_j_1728
sage: egros_from_j_1728([])
[]
sage: egros_from_j_1728([3])
[]
sage: [e.cremona_label() for e in egros_from_j_1728([2])]
['32a1', '32a2', '64a1', '64a4', '256b1', '256b2', '256c1', '256c2']
"""
Elist=[]
no2 = not 2 in S
for ei in xmrange([2] + [4]*len(S)):
u = prod([p**e for p,e in zip([-1]+S,ei)],QQ(1))
if no2:
u*=4 ## make sure 12|val(D,2)
Eu = EllipticCurve([0,0,0,u,0]).minimal_model()
if Eu.has_good_reduction_outside_S(S):
Elist += [Eu]
Elist.sort(cmp=curve_cmp)
return Elist