本文整理汇总了Python中sage.rings.all.ZZ.one_element方法的典型用法代码示例。如果您正苦于以下问题：Python ZZ.one_element方法的具体用法？Python ZZ.one_element怎么用？Python ZZ.one_element使用的例子？那么恭喜您, 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sage.rings.all.ZZ的用法示例。
在下文中一共展示了ZZ.one_element方法的1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: is_gamma0_equiv
# 需要导入模块: from sage.rings.all import ZZ [as 别名]
# 或者: from sage.rings.all.ZZ import one_element [as 别名]
def is_gamma0_equiv(self, other, N, transformation = None):
r"""
Return whether self and other are equivalent modulo the action of
`\Gamma_0(N)` via linear fractional transformations.
INPUT:
- ``other`` - Cusp
- ``N`` - an integer (specifies the group
Gamma_0(N))
- ``transformation`` - None (default) or either the string 'matrix' or 'corner'. If 'matrix',
it also returns a matrix in Gamma_0(N) that sends self to other. The matrix is chosen such that the lower left entry is as small as possible in absolute value. If 'corner' (or True for backwards compatibility), it returns only the upper left entry of such a matrix.
OUTPUT:
- a boolean - True if self and other are equivalent
- a matrix or an integer- returned only if transformation is 'matrix' or 'corner', respectively.
EXAMPLES::
sage: x = Cusp(2,3)
sage: y = Cusp(4,5)
sage: x.is_gamma0_equiv(y, 2)
True
sage: _, ga = x.is_gamma0_equiv(y, 2, 'matrix'); ga
[-1 2]
[-2 3]
sage: x.is_gamma0_equiv(y, 3)
False
sage: x.is_gamma0_equiv(y, 3, 'matrix')
(False, None)
sage: Cusp(1/2).is_gamma0_equiv(1/3,11,'corner')
(True, 19)
sage: Cusp(1,0)
Infinity
sage: z = Cusp(1,0)
sage: x.is_gamma0_equiv(z, 3, 'matrix')
(
[-1 1]
True, [-3 2]
)
ALGORITHM: See Proposition 2.2.3 of Cremona's book 'Algorithms for
Modular Elliptic Curves', or Prop 2.27 of Stein's Ph.D. thesis.
"""
if transformation not in [False,True,"matrix",None,"corner"]:
raise ValueError, "Value %s of the optional argument transformation is not valid."
if not isinstance(other, Cusp):
other = Cusp(other)
N = ZZ(N)
u1 = self.__a
v1 = self.__b
u2 = other.__a
v2 = other.__b
zero = ZZ.zero_element()
one = ZZ.one_element()
if transformation == "matrix":
from sage.matrix.constructor import matrix
#if transformation :
# transformation = "corner"
if v1 == v2 and u1 == u2:
if not transformation:
return True
elif transformation == "matrix":
return True, matrix(ZZ,[[1,0],[0,1]])
else:
return True, one
# a necessary, but not sufficient condition unless N is square-free
if v1.gcd(N) != v2.gcd(N):
if not transformation:
return False
else:
return False, None
if (u1,v1) != (zero,one):
if v1 in [zero, one]:
s1 = one
else:
s1 = u1.inverse_mod(v1)
else:
s1 = 0
if (u2,v2) != (zero, one):
if v2 in [zero,one]:
s2 = one
else:
#.........这里部分代码省略.........