本文整理汇总了Python中sage.all.ZZ.is_squarefree方法的典型用法代码示例。如果您正苦于以下问题：Python ZZ.is_squarefree方法的具体用法？Python ZZ.is_squarefree怎么用？Python ZZ.is_squarefree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.all.ZZ的用法示例。
在下文中一共展示了ZZ.is_squarefree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: TripleProductLseries
# 需要导入模块: from sage.all import ZZ [as 别名]
# 或者: from sage.all.ZZ import is_squarefree [as 别名]
class TripleProductLseries(object):
"""
A triple product `L`-series attached to three newforms of level `N`.
"""
def __init__(self, N, f, g, h):
"""
INPUT:
- N -- squarefree integer
- f -- an object such that for n>=0, we have
f[n] = a_n(f) = n-th Fourier coefficient of
a newform on Gamma_0(N).
- g -- like f
- h -- like f
"""
self._N = ZZ(N)
if not (self._N.is_squarefree() and self._N > 0):
raise ValueError, "N (=%s) must be a squarefree positive integer"%self._N
self._newforms = (f,g,h)
self._gen = RDF['X'].gen()
self._genC = CDF['X'].gen()
self._series = RDF[['X']]
def __repr__(self):
"""
Return text representation of this triple product `L`-function.
"""
return "Triple product L-function L(s,f,g,h) of three newforms on Gamma_0(%s)"%self._N
def level(self):
"""
Return the common level `N` of the newforms in the triple product.
OUTPUT:
- Integer
EXAMPLES::
"""
return self._N
def newforms(self):
"""
Return 3-tuple (f,g,h) of the data that defines the newforms
in the triple product.
OUTPUT:
- 3-tuple
EXAMPLES::
"""
return self._newforms
def _local_series(self, p, prec):
"""
Return power series in `X` (which you should think of as `p^{-s}`)
that is the expansion to precision prec of the local factor at `p`
of this `L`-series.
INPUT:
- p -- prime
- prec -- positive integer
OUTPUT:
- power series that ends in a term ``O(X^prec)``.
"""
f = self._series(self.charpoly(p), prec)
return f**(-1)
def dirichlet_series(self, prec, eps=1e-10):
"""
Return the Dirichlet series representation of self, up to the given
precision.
INPUT:
- prec -- positive integer
- eps -- None or a positive real; any coefficient with absolute
value less than eps is set to 0.
"""
coeffs = self.dirichlet_series_coeffs(prec, eps)
return DirichletSeries(coeffs, 's')
def dirichlet_series_coeffs(self, prec, eps=1e-10):
"""
Return the coefficients of the Dirichlet series representation
of self, up to the given precision.
INPUT:
- prec -- positive integer
- eps -- None or a positive real; any coefficient with absolute
value less than eps is set to 0.
"""
# Use multiplicativity to compute the Dirichlet series
# coefficients, then make a DirichletSeries object.
zero = RDF(0)
coeffs = [RDF(0),RDF(1)] + [None]*(prec-2)
from sage.all import log, floor # TODO: slow
# prime-power indexed coefficients
for p in prime_range(2, prec):
B = floor(log(prec, p)) + 1
#.........这里部分代码省略.........