本文整理汇总了Python中sage.rings.all.Integer.mod方法的典型用法代码示例。如果您正苦于以下问题：Python Integer.mod方法的具体用法？Python Integer.mod怎么用？Python Integer.mod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.Integer的用法示例。
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示例1: victor_miller_basis
# 需要导入模块: from sage.rings.all import Integer [as 别名]
# 或者: from sage.rings.all.Integer import mod [as 别名]
def victor_miller_basis(k, prec=10, cusp_only=False, var='q'):
r"""
Compute and return the Victor Miller basis for modular forms of
weight `k` and level 1 to precision `O(q^{prec})`. If
``cusp_only`` is True, return only a basis for the cuspidal
subspace.
INPUT:
- ``k`` -- an integer
- ``prec`` -- (default: 10) a positive integer
- ``cusp_only`` -- bool (default: False)
- ``var`` -- string (default: 'q')
OUTPUT:
A sequence whose entries are power series in ``ZZ[[var]]``.
EXAMPLES::
sage: victor_miller_basis(1, 6)
[]
sage: victor_miller_basis(0, 6)
[
1 + O(q^6)
]
sage: victor_miller_basis(2, 6)
[]
sage: victor_miller_basis(4, 6)
[
1 + 240*q + 2160*q^2 + 6720*q^3 + 17520*q^4 + 30240*q^5 + O(q^6)
]
sage: victor_miller_basis(6, 6, var='w')
[
1 - 504*w - 16632*w^2 - 122976*w^3 - 532728*w^4 - 1575504*w^5 + O(w^6)
]
sage: victor_miller_basis(6, 6)
[
1 - 504*q - 16632*q^2 - 122976*q^3 - 532728*q^4 - 1575504*q^5 + O(q^6)
]
sage: victor_miller_basis(12, 6)
[
1 + 196560*q^2 + 16773120*q^3 + 398034000*q^4 + 4629381120*q^5 + O(q^6),
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 + O(q^6)
]
sage: victor_miller_basis(12, 6, cusp_only=True)
[
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 + O(q^6)
]
sage: victor_miller_basis(24, 6, cusp_only=True)
[
q + 195660*q^3 + 12080128*q^4 + 44656110*q^5 + O(q^6),
q^2 - 48*q^3 + 1080*q^4 - 15040*q^5 + O(q^6)
]
sage: victor_miller_basis(24, 6)
[
1 + 52416000*q^3 + 39007332000*q^4 + 6609020221440*q^5 + O(q^6),
q + 195660*q^3 + 12080128*q^4 + 44656110*q^5 + O(q^6),
q^2 - 48*q^3 + 1080*q^4 - 15040*q^5 + O(q^6)
]
sage: victor_miller_basis(32, 6)
[
1 + 2611200*q^3 + 19524758400*q^4 + 19715347537920*q^5 + O(q^6),
q + 50220*q^3 + 87866368*q^4 + 18647219790*q^5 + O(q^6),
q^2 + 432*q^3 + 39960*q^4 - 1418560*q^5 + O(q^6)
]
sage: victor_miller_basis(40,200)[1:] == victor_miller_basis(40,200,cusp_only=True)
True
sage: victor_miller_basis(200,40)[1:] == victor_miller_basis(200,40,cusp_only=True)
True
AUTHORS:
- William Stein, Craig Citro: original code
- Martin Raum (2009-08-02): use FLINT for polynomial arithmetic (instead of NTL)
"""
k = Integer(k)
if k%2 == 1 or k==2:
return Sequence([])
elif k < 0:
raise ValueError("k must be non-negative")
elif k == 0:
return Sequence([PowerSeriesRing(ZZ,var)(1).add_bigoh(prec)], cr=True)
e = k.mod(12)
if e == 2: e += 12
n = (k-e) // 12
if n == 0 and cusp_only:
return Sequence([])
# If prec is less than or equal to the dimension of the space of
# cusp forms, which is just n, then we know the answer, and we
#.........这里部分代码省略.........