本文整理汇总了Python中sage.rings.all.PowerSeriesRing.base_ring方法的典型用法代码示例。如果您正苦于以下问题：Python PowerSeriesRing.base_ring方法的具体用法？Python PowerSeriesRing.base_ring怎么用？Python PowerSeriesRing.base_ring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sage.rings.all.PowerSeriesRing的用法示例。
在下文中一共展示了PowerSeriesRing.base_ring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: JFSeriesConstructor
# 需要导入模块: from sage.rings.all import PowerSeriesRing [as 别名]
# 或者: from sage.rings.all.PowerSeriesRing import base_ring [as 别名]
#.........这里部分代码省略.........
#returns coefficient c(d,r) p^r q^d of i q^(-1/8) theta1; s = shift = i q^{-1/8}
k = r - QQ(1/2)
if k in ZZ and 2*d == (k**2+k):
return (-1)**k
else:
return 0
@cached_method
def _cseta(self, m):
#returns coefficient q^m of q^{1/24} eta^{-1}
if m < 0: return 0
return Partitions(m).cardinality()
@cached_method
def _cseta3(self, m):
#returns coeffcient q^m of q^{1/8} eta^{-3}
if m < 0: return 0
return PartitionTuples(3,m).cardinality()
@cached_method
def _cK(self, d, r):
#K = i theta_1 / \eta^3 = stheta*seta3
#return coefficient c(d,r) p^r q^d
## Since Jacobi form coffs satisfy r^2 < 4mn. theta1 coffs satisfy r^2 < 2 n. Here n = d + 1/8 so zero except for r^2 <= 2d + 1/4.
if d < 0: return 0
return sum( self._cseta3(d - a)*self._cstheta(a,r) for a in range(0,d+1) )
@cached_method
def _cK2(self, d, r):
## theta1^2 satisfy 4^2 < 4 n. n = d + 1/4, we get c(d,r) non-zero for r^2 <= 4d + 1.
if d < 0: return 0
coff = 0
for a in range(0,d+1):
L = sqrt(2*a + QQ(1/4)).round()
#print "a,L", a, L
coff += sum( self._cK(d - a,r-QQ(b/2))*self._cK(a,QQ(b/2)) for b in range(-2*L,2*L+1) if is_odd(b) )
return coff
@cached_method
def _cWP(self, d, r):
#\wp(z) & = \frac{1}{12} + \frac{p}{(1-p)^2} + \sum_{k,r \geq 1} k (p^k - 2 + p^{-k}) q^{kr}
if d < 0: return 0
if d == 0:
if r < 0: return 0
elif r == 0: return QQ(1/12)
else: return r
if d > 0:
if r == 0: return -2*sigma(d,1)
elif d % r == 0:
return abs(r)
else:
return 0
@cached_method
def _cZ(self, d, r):
#elliptic genus 24*K**2*wp
if d < 0: return 0
coff = 0
for a in range(0,d + 1):
L = sqrt(4*a + 1).round()
coff += sum( 24*self._cWP(d - a,r-b)*self._cK2(a,b) for b in range(-L,L+1) )
return coff
@cached_method
def K(self):
q = self._series_ring.gen()
p = self._series_ring.base_ring().gen()
def min_rcoeff(d):
#TODO
return -10
def max_rcoeff(d):
#TODO
return 10
return sum([sum([self._cK(d,r)*p**r for r in range(min_rcoeff(d), max_rcoeff(d) + 1)])*q**d for d in range(self.prec())])
@cached_method
def wp(self):
q = self._series_ring.gen()
p = self._series_ring.base_ring().gen()
def min_rcoeff(d):
#TODO
return -10
def max_rcoeff(d):
#TODO
return 10
return sum([sum([self._cWP(d,r)*p**r for r in range(min_rcoeff(d), max_rcoeff(d) + 1)])*q**d for d in range(self.prec())])
#TODO
@cached_method
def J1(self):
q = self._series_ring.gen()
p = self._series_ring.base_ring().gen()
def min_rcoeff(d):
#TODO
return -10
def max_rcoeff(d):
#TODO
return 10
return sum([sum([self._cK(d,r)*p**r for r in range(min_rcoeff(d), max_rcoeff(d) + 1)])*q**d for d in range(self.prec())])