本文整理汇总了Python中sympy.core.C.harmonic方法的典型用法代码示例。如果您正苦于以下问题：Python C.harmonic方法的具体用法？Python C.harmonic怎么用？Python C.harmonic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.core.C的用法示例。
在下文中一共展示了C.harmonic方法的7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: eval
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
def eval(cls, z, a=S.One):
z, a = map(sympify, (z, a))
if a.is_Number:
if a is S.NaN:
return S.NaN
elif a is S.Zero:
return cls(z)
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
return S.One
elif z is S.Zero:
if a.is_negative:
return S.Half - a - 1
else:
return S.Half - a
elif z is S.One:
return S.ComplexInfinity
elif z.is_Integer:
if a.is_Integer:
if z.is_negative:
zeta = (-1)**z * C.bernoulli(-z+1)/(-z+1)
elif z.is_even:
B, F = C.bernoulli(z), C.factorial(z)
zeta = 2**(z-1) * abs(B) * pi**z / F
else:
return
if a.is_negative:
return zeta + C.harmonic(abs(a), z)
else:
return zeta - C.harmonic(a-1, z)示例2: eval
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
def eval(cls, n, z):
n, z = list(map(sympify, (n, z)))
from sympy import unpolarify
if n.is_integer:
if n.is_nonnegative:
nz = unpolarify(z)
if z != nz:
return polygamma(n, nz)
if n == -1:
return loggamma(z)
else:
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
if n.is_Number:
if n is S.Zero:
return S.Infinity
else:
return S.Zero
elif z.is_Integer:
if z.is_nonpositive:
return S.ComplexInfinity
else:
if n is S.Zero:
return -S.EulerGamma + C.harmonic(z - 1, 1)
elif n.is_odd:
return (-1) ** (n + 1) * C.factorial(n) * zeta(n + 1, z)
if n == 0:
if z is S.NaN:
return S.NaN
elif z.is_Rational:
# TODO actually *any* n/m can be done, but that is messy
lookup = {
S(1) / 2: -2 * log(2) - S.EulerGamma,
S(1) / 3: -S.Pi / 2 / sqrt(3) - 3 * log(3) / 2 - S.EulerGamma,
S(1) / 4: -S.Pi / 2 - 3 * log(2) - S.EulerGamma,
S(3) / 4: -3 * log(2) - S.EulerGamma + S.Pi / 2,
S(2) / 3: -3 * log(3) / 2 + S.Pi / 2 / sqrt(3) - S.EulerGamma,
}
if z > 0:
n = floor(z)
z0 = z - n
if z0 in lookup:
return lookup[z0] + Add(*[1 / (z0 + k) for k in range(n)])
elif z < 0:
n = floor(1 - z)
z0 = z + n
if z0 in lookup:
return lookup[z0] - Add(*[1 / (z0 - 1 - k) for k in range(n)])
elif z in (S.Infinity, S.NegativeInfinity):
return S.Infinity
else:
t = z.extract_multiplicatively(S.ImaginaryUnit)
if t in (S.Infinity, S.NegativeInfinity):
return S.Infinity示例3: eval
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
def eval(cls, z, a_=None):
if a_ is None:
z, a = list(map(sympify, (z, 1)))
else:
z, a = list(map(sympify, (z, a_)))
if a.is_Number:
if a is S.NaN:
return S.NaN
elif a is S.One and a_ is not None:
return cls(z)
# TODO Should a == 0 return S.NaN as well?
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
return S.One
elif z is S.Zero:
if a.is_negative:
return S.Half - a - 1
else:
return S.Half - a
elif z is S.One:
return S.ComplexInfinity
elif z.is_Integer:
if a.is_Integer:
if z.is_negative:
zeta = (-1)**z * C.bernoulli(-z + 1)/(-z + 1)
elif z.is_even:
B, F = C.bernoulli(z), C.factorial(z)
zeta = 2**(z - 1) * abs(B) * pi**z / F
else:
return
if a.is_negative:
return zeta + C.harmonic(abs(a), z)
else:
return zeta - C.harmonic(a - 1, z)示例4: eval
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
def eval(cls, n, z):
n, z = map(sympify, (n, z))
if n.is_integer:
if n.is_negative:
return loggamma(z)
else:
if z.is_Number:
if z is S.NaN:
return S.NaN
elif z is S.Infinity:
if n.is_Number:
if n is S.Zero:
return S.Infinity
else:
return S.Zero
elif z.is_Integer:
if z.is_nonpositive:
return S.ComplexInfinity
else:
if n is S.Zero:
return -S.EulerGamma + C.harmonic(z-1, 1)
elif n.is_odd:
return (-1)**(n+1)*C.Factorial(n)*zeta(n+1, z)示例5: eval_sum_symbolic
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
def eval_sum_symbolic(f, limits):
(i, a, b) = limits
if not f.has(i):
return f*(b-a+1)
# Linearity
if f.is_Mul:
L, R = f.as_two_terms()
if not L.has(i):
sR = eval_sum_symbolic(R, (i, a, b))
if sR: return L*sR
if not R.has(i):
sL = eval_sum_symbolic(L, (i, a, b))
if sL: return R*sL
try:
f = apart(f, i) # see if it becomes an Add
except PolynomialError:
pass
if f.is_Add:
L, R = f.as_two_terms()
lrsum = telescopic(L, R, (i, a, b))
if lrsum:
return lrsum
lsum = eval_sum_symbolic(L, (i, a, b))
rsum = eval_sum_symbolic(R, (i, a, b))
if None not in (lsum, rsum):
return lsum + rsum
# Polynomial terms with Faulhaber's formula
n = Wild('n')
result = f.match(i**n)
if result is not None:
n = result[n]
if n.is_Integer:
if n >= 0:
return ((C.bernoulli(n+1, b+1) - C.bernoulli(n+1, a))/(n+1)).expand()
elif a.is_Integer and a >= 1:
if n == -1:
return C.harmonic(b) - C.harmonic(a - 1)
else:
return C.harmonic(b, abs(n)) - C.harmonic(a - 1, abs(n))
# Geometric terms
c1 = C.Wild('c1', exclude=[i])
c2 = C.Wild('c2', exclude=[i])
c3 = C.Wild('c3', exclude=[i])
e = f.match(c1**(c2*i+c3))
if e is not None:
c1 = c1.subs(e)
c2 = c2.subs(e)
c3 = c3.subs(e)
# TODO: more general limit handling
return c1**c3 * (c1**(a*c2) - c1**(c2+b*c2)) / (1 - c1**c2)
if not (a.has(S.Infinity, S.NegativeInfinity) or \
b.has(S.Infinity, S.NegativeInfinity)):
r = gosper_sum(f, (i, a, b))
if not r in (None, S.NaN):
return r
return eval_sum_hyper(f, (i, a, b))示例6: eval_sum_symbolic
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
def eval_sum_symbolic(f, limits):
(i, a, b) = limits
if not f.has(i):
return f * (b - a + 1)
# Linearity
if f.is_Mul:
L, R = f.as_two_terms()
if not L.has(i):
sR = eval_sum_symbolic(R, (i, a, b))
if sR:
return L * sR
if not R.has(i):
sL = eval_sum_symbolic(L, (i, a, b))
if sL:
return R * sL
try:
f = apart(f, i) # see if it becomes an Add
except PolynomialError:
pass
if f.is_Add:
L, R = f.as_two_terms()
lrsum = telescopic(L, R, (i, a, b))
if lrsum:
return lrsum
lsum = eval_sum_symbolic(L, (i, a, b))
rsum = eval_sum_symbolic(R, (i, a, b))
if None not in (lsum, rsum):
return lsum + rsum
# Polynomial terms with Faulhaber's formula
n = Wild("n")
result = f.match(i ** n)
if result is not None:
n = result[n]
if n.is_Integer:
if n >= 0:
return ((C.bernoulli(n + 1, b + 1) - C.bernoulli(n + 1, a)) / (n + 1)).expand()
elif a.is_Integer and a >= 1:
if n == -1:
return C.harmonic(b) - C.harmonic(a - 1)
else:
return C.harmonic(b, abs(n)) - C.harmonic(a - 1, abs(n))
if not (a.has(S.Infinity, S.NegativeInfinity) or b.has(S.Infinity, S.NegativeInfinity)):
# Geometric terms
c1 = C.Wild("c1", exclude=[i])
c2 = C.Wild("c2", exclude=[i])
c3 = C.Wild("c3", exclude=[i])
e = f.match(c1 ** (c2 * i + c3))
if e is not None:
p = (c1 ** c3).subs(e)
q = (c1 ** c2).subs(e)
r = p * (q ** a - q ** (b + 1)) / (1 - q)
l = p * (b - a + 1)
return Piecewise((l, Eq(q, S.One)), (r, True))
r = gosper_sum(f, (i, a, b))
if not r in (None, S.NaN):
return r
return eval_sum_hyper(f, (i, a, b))示例7: in
# 需要导入模块: from sympy.core import C [as 别名]
# 或者: from sympy.core.C import harmonic [as 别名]
if None not in (lsum, rsum):
return lsum + rsum
# Polynomial terms with Faulhaber's formula
n = Wild('n')
result = f.match(i**n)
if result is not None:
n = result[n]
if n.is_Integer:
if n >= 0:
return ((C.bernoulli(n+1, b+1) - C.bernoulli(n+1, a))/(n+1)).expand()
elif a.is_Integer and a >= 1:
if n == -1:
return C.harmonic(b) - C.harmonic(a - 1)
else:
return C.harmonic(b, abs(n)) - C.harmonic(a - 1, abs(n))
# Geometric terms
c1 = C.Wild('c1', exclude=[i])
c2 = C.Wild('c2', exclude=[i])
c3 = C.Wild('c3', exclude=[i])
e = f.match(c1**(c2*i+c3))
if e is not None:
c1 = c1.subs(e)
c2 = c2.subs(e)
c3 = c3.subs(e)