本文整理汇总了Python中sympy.polys.Poly.as_poly方法的典型用法代码示例。如果您正苦于以下问题：Python Poly.as_poly方法的具体用法？Python Poly.as_poly怎么用？Python Poly.as_poly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sympy.polys.Poly的用法示例。
在下文中一共展示了Poly.as_poly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: parametric_log_deriv_heu
# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import as_poly [as 别名]
def parametric_log_deriv_heu(fa, fd, wa, wd, DE, c1=None):
"""
Parametric logarithmic derivative heuristic.
Given a derivation D on k[t], f in k(t), and a hyperexponential monomial
theta over k(t), raises either NotImplementedError, in which case the
heuristic failed, or returns None, in which case it has proven that no
solution exists, or returns a solution (n, m, v) of the equation
n*f == Dv/v + m*Dtheta/theta, with v in k(t)* and n, m in ZZ with n != 0.
If this heuristic fails, the structure theorem approach will need to be
used.
The argument w == Dtheta/theta
"""
# TODO: finish writing this and write tests
c1 = c1 or Dummy('c1')
p, a = fa.div(fd)
q, b = wa.div(wd)
B = max(0, derivation(DE.t, DE).degree(DE.t) - 1)
C = max(p.degree(DE.t), q.degree(DE.t))
if q.degree(DE.t) > B:
eqs = [p.nth(i) - c1*q.nth(i) for i in range(B + 1, C + 1)]
s = solve(eqs, c1)
if not s or not s[c1].is_Rational:
# deg(q) > B, no solution for c.
return None
N, M = s[c1].as_numer_denom() # N and M are integers
N, M = Poly(N, DE.t), Poly(M, DE.t)
nfmwa = N*fa*wd - M*wa*fd
nfmwd = fd*wd
Qv = is_log_deriv_k_t_radical_in_field(N*fa*wd - M*wa*fd, fd*wd, DE,
'auto')
if Qv is None:
# (N*f - M*w) is not the logarithmic derivative of a k(t)-radical.
return None
Q, e, v = Qv
if e != 1:
return None
if Q.is_zero or v.is_zero:
# Q == 0 or v == 0.
return None
return (Q*N, Q*M, v)
if p.degree(DE.t) > B:
return None
c = lcm(fd.as_poly(DE.t).LC(), wd.as_poly(DE.t).LC())
l = fd.monic().lcm(wd.monic())*Poly(c, DE.t)
ln, ls = splitfactor(l, DE)
z = ls*ln.gcd(ln.diff(DE.t))
if not z.has(DE.t):
raise NotImplementedError("parametric_log_deriv_heu() "
"heuristic failed: z in k.")
u1, r1 = (fa*l.quo(fd)).div(z) # (l*f).div(z)
u2, r2 = (wa*l.quo(wd)).div(z) # (l*w).div(z)
eqs = [r1.nth(i) - c1*r2.nth(i) for i in range(z.degree(DE.t))]
s = solve(eqs, c1)
if not s or not s[c1].is_Rational:
# deg(q) <= B, no solution for c.
return None
M, N = s[c1].as_numer_denom()
nfmwa = N.as_poly(DE.t)*fa*wd - M.as_poly(DE.t)*wa*fd
nfmwd = fd*wd
Qv = is_log_deriv_k_t_radical_in_field(nfmwa, nfmwd, DE)
if Qv is None:
# (N*f - M*w) is not the logarithmic derivative of a k(t)-radical.
return None
Q, v = Qv
if Q.is_zero or v.is_zero:
# Q == 0 or v == 0.
return None
return (Q*N, Q*M, v)