本文整理汇总了Python中congroup_gammaH.GammaH_class.dimension_eis方法的典型用法代码示例。如果您正苦于以下问题：Python GammaH_class.dimension_eis方法的具体用法？Python GammaH_class.dimension_eis怎么用？Python GammaH_class.dimension_eis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congroup_gammaH.GammaH_class的用法示例。
在下文中一共展示了GammaH_class.dimension_eis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: dimension_eis
# 需要导入模块: from congroup_gammaH import GammaH_class [as 别名]
# 或者: from congroup_gammaH.GammaH_class import dimension_eis [as 别名]
def dimension_eis(self, k=2, eps=None, algorithm="CohenOesterle"):
r"""
Return the dimension of the space of Eisenstein series forms for self,
or the dimension of the subspace corresponding to the given character
if one is supplied.
INPUT:
- ``k`` - an integer (default: 2), the weight.
- ``eps`` - either None or a Dirichlet character modulo N, where N is
the level of this group. If this is None, then the dimension of the
whole space is returned; otherwise, the dimension of the subspace of
Eisenstein series of character eps.
- ``algorithm`` -- either "CohenOesterle" (the default) or "Quer". This
specifies the method to use in the case of nontrivial character:
either the Cohen--Oesterle formula as described in Stein's book, or
by Moebius inversion using the subgroups GammaH (a method due to
Jordi Quer).
AUTHORS:
- William Stein - Cohen--Oesterle algorithm
- Jordi Quer - algorithm based on GammaH subgroups
- David Loeffler (2009) - code refactoring
EXAMPLES:
The following two computations use different algorithms: ::
sage: [Gamma1(36).dimension_eis(1,eps) for eps in DirichletGroup(36)]
[0, 4, 3, 0, 0, 2, 6, 0, 0, 2, 3, 0]
sage: [Gamma1(36).dimension_eis(1,eps,algorithm="Quer") for eps in DirichletGroup(36)]
[0, 4, 3, 0, 0, 2, 6, 0, 0, 2, 3, 0]
So do these: ::
sage: [Gamma1(48).dimension_eis(3,eps) for eps in DirichletGroup(48)]
[0, 12, 0, 4, 0, 8, 0, 4, 12, 0, 4, 0, 8, 0, 4, 0]
sage: [Gamma1(48).dimension_eis(3,eps,algorithm="Quer") for eps in DirichletGroup(48)]
[0, 12, 0, 4, 0, 8, 0, 4, 12, 0, 4, 0, 8, 0, 4, 0]
"""
from all import Gamma0
# first deal with special cases
if eps is None:
return GammaH_class.dimension_eis(self, k)
N = self.level()
eps = DirichletGroup(N)(eps)
if eps.is_trivial():
return Gamma0(N).dimension_eis(k)
# Note case of k = 0 and trivial character already dealt with separately, so k <= 0 here is valid:
if (k <= 0) or ((k % 2) == 1 and eps.is_even()) or ((k%2) == 0 and eps.is_odd()):
return ZZ(0)
if algorithm == "Quer":
n = eps.order()
dim = ZZ(0)
for d in n.divisors():
G = GammaH_constructor(N,(eps**d).kernel())
dim = dim + moebius(d)*G.dimension_eis(k)
return dim//phi(n)
elif algorithm == "CohenOesterle":
from sage.modular.dims import CohenOesterle
K = eps.base_ring()
j = 2-k
# We use the Cohen-Oesterle formula in a subtle way to
# compute dim M_k(N,eps) (see Ch. 6 of William Stein's book on
# computing with modular forms).
alpha = -ZZ( K(Gamma0(N).index()*(j-1)/ZZ(12)) + CohenOesterle(eps,j) )
if k == 1:
return alpha
else:
return alpha - self.dimension_cusp_forms(k, eps)
else: #algorithm not in ["CohenOesterle", "Quer"]:
raise ValueError, "Unrecognised algorithm in dimension_eis"