本文整理汇总了Python中sage.rings.all.Integer.is_power_of方法的典型用法代码示例。如果您正苦于以下问题：Python Integer.is_power_of方法的具体用法？Python Integer.is_power_of怎么用？Python Integer.is_power_of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。
在下文中一共展示了Integer.is_power_of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: hecke_operator_on_qexp
# 需要导入模块: from sage.rings.all import Integer [as 别名]
# 或者: from sage.rings.all.Integer import is_power_of [as 别名]
def hecke_operator_on_qexp(f, n, k, eps = None,
prec=None, check=True, _return_list=False):
r"""
Given the `q`-expansion `f` of a modular form with character
`\varepsilon`, this function computes the image of `f` under the
Hecke operator `T_{n,k}` of weight `k`.
EXAMPLES::
sage: M = ModularForms(1,12)
sage: hecke_operator_on_qexp(M.basis()[0], 3, 12)
252*q - 6048*q^2 + 63504*q^3 - 370944*q^4 + O(q^5)
sage: hecke_operator_on_qexp(M.basis()[0], 1, 12, prec=7)
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 + O(q^7)
sage: hecke_operator_on_qexp(M.basis()[0], 1, 12)
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 577738*q^13 + O(q^14)
sage: M.prec(20)
20
sage: hecke_operator_on_qexp(M.basis()[0], 3, 12)
252*q - 6048*q^2 + 63504*q^3 - 370944*q^4 + 1217160*q^5 - 1524096*q^6 + O(q^7)
sage: hecke_operator_on_qexp(M.basis()[0], 1, 12)
q - 24*q^2 + 252*q^3 - 1472*q^4 + 4830*q^5 - 6048*q^6 - 16744*q^7 + 84480*q^8 - 113643*q^9 - 115920*q^10 + 534612*q^11 - 370944*q^12 - 577738*q^13 + 401856*q^14 + 1217160*q^15 + 987136*q^16 - 6905934*q^17 + 2727432*q^18 + 10661420*q^19 - 7109760*q^20 + O(q^21)
sage: (hecke_operator_on_qexp(M.basis()[0], 1, 12)*252).add_bigoh(7)
252*q - 6048*q^2 + 63504*q^3 - 370944*q^4 + 1217160*q^5 - 1524096*q^6 + O(q^7)
sage: hecke_operator_on_qexp(M.basis()[0], 6, 12)
-6048*q + 145152*q^2 - 1524096*q^3 + O(q^4)
An example on a formal power series::
sage: R.<q> = QQ[[]]
sage: f = q + q^2 + q^3 + q^7 + O(q^8)
sage: hecke_operator_on_qexp(f, 3, 12)
q + O(q^3)
sage: hecke_operator_on_qexp(delta_qexp(24), 3, 12).prec()
8
sage: hecke_operator_on_qexp(delta_qexp(25), 3, 12).prec()
9
An example of computing `T_{p,k}` in characteristic `p`::
sage: p = 199
sage: fp = delta_qexp(prec=p^2+1, K=GF(p))
sage: tfp = hecke_operator_on_qexp(fp, p, 12)
sage: tfp == fp[p] * fp
True
sage: tf = hecke_operator_on_qexp(delta_qexp(prec=p^2+1), p, 12).change_ring(GF(p))
sage: tfp == tf
True
"""
if eps is None:
# Need to have base_ring=ZZ to work over finite fields, since
# ZZ can coerce to GF(p), but QQ can't.
eps = DirichletGroup(1, base_ring=ZZ)[0]
if check:
if not (is_PowerSeries(f) or is_ModularFormElement(f)):
raise TypeError("f (=%s) must be a power series or modular form"%f)
if not is_DirichletCharacter(eps):
raise TypeError("eps (=%s) must be a Dirichlet character"%eps)
k = Integer(k)
n = Integer(n)
v = []
if prec is None:
if is_ModularFormElement(f):
# always want at least three coefficients, but not too many, unless
# requested
pr = max(f.prec(), f.parent().prec(), (n+1)*3)
pr = min(pr, 100*(n+1))
prec = pr // n + 1
else:
prec = (f.prec() / ZZ(n)).ceil()
if prec == Infinity: prec = f.parent().default_prec() // n + 1
if f.prec() < prec:
f._compute_q_expansion(prec)
p = Integer(f.base_ring().characteristic())
if k != 1 and p.is_prime() and n.is_power_of(p):
# if computing T_{p^a} in characteristic p, use the simpler (and faster)
# formula
v = [f[m*n] for m in range(prec)]
else:
l = k-1
for m in range(prec):
am = sum([eps(d) * d**l * f[m*n//(d*d)] for \
d in divisors(gcd(n, m)) if (m*n) % (d*d) == 0])
v.append(am)
if _return_list:
return v
if is_ModularFormElement(f):
R = f.parent()._q_expansion_ring()
else:
R = f.parent()
return R(v, prec)