本文整理汇总了Python中sympy.ntheory.perfect_power函数的典型用法代码示例。如果您正苦于以下问题：Python perfect_power函数的具体用法？Python perfect_power怎么用？Python perfect_power使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了perfect_power函数的6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: is_square
def is_square(n, prep=True):
"""Return True if n == a * a for some integer a, else False.
If n is suspected of *not* being a square then this is a
quick method of confirming that it is not.
References
==========
[1] http://mersenneforum.org/showpost.php?p=110896
See Also
========
sympy.core.power.integer_nthroot
"""
if prep:
n = as_int(n)
if n < 0:
return False
if n in [0, 1]:
return True
m = n & 127
if not ((m*0x8bc40d7d) & (m*0xa1e2f5d1) & 0x14020a):
m = n % 63
if not ((m*0x3d491df7) & (m*0xc824a9f9) & 0x10f14008):
from sympy.ntheory import perfect_power
if perfect_power(n, [2]):
return True
return False示例2: eval
def eval(cls, arg, base=None):
from sympy import unpolarify
if base is not None:
base = sympify(base)
if arg.is_positive and arg.is_Integer and \
base.is_positive and base.is_Integer:
base = int(base)
arg = int(arg)
n = multiplicity(base, arg)
return S(n) + log(arg // base ** n) / log(base)
if base is not S.Exp1:
return cls(arg)/cls(base)
else:
return cls(arg)
arg = sympify(arg)
if arg.is_Number:
if arg is S.Zero:
return S.ComplexInfinity
elif arg is S.One:
return S.Zero
elif arg is S.Infinity:
return S.Infinity
elif arg is S.NegativeInfinity:
return S.Infinity
elif arg is S.NaN:
return S.NaN
elif arg.is_negative:
return S.Pi * S.ImaginaryUnit + cls(-arg)
elif arg.is_Rational:
if arg.q != 1:
return cls(arg.p) - cls(arg.q)
# remove perfect powers automatically
p = perfect_power(int(arg))
if p is not False:
return p[1]*cls(p[0])
elif arg is S.ComplexInfinity:
return S.ComplexInfinity
elif arg is S.Exp1:
return S.One
elif arg.func is exp and arg.args[0].is_real:
return arg.args[0]
elif arg.func is exp_polar:
return unpolarify(arg.exp)
#don't autoexpand Pow or Mul (see the issue 252):
elif not arg.is_Add:
coeff = arg.as_coefficient(S.ImaginaryUnit)
if coeff is not None:
if coeff is S.Infinity:
return S.Infinity
elif coeff is S.NegativeInfinity:
return S.Infinity
elif coeff.is_Rational:
if coeff.is_nonnegative:
return S.Pi * S.ImaginaryUnit * S.Half + cls(coeff)
else:
return -S.Pi * S.ImaginaryUnit * S.Half + cls(-coeff)示例3: _eval_expand_log
def _eval_expand_log(self, deep=True, **hints):
from sympy import unpolarify, expand_log
from sympy.concrete import Sum, Product
force = hints.get('force', False)
if (len(self.args) == 2):
return expand_log(self.func(*self.args), deep=deep, force=force)
arg = self.args[0]
if arg.is_Integer:
# remove perfect powers
p = perfect_power(int(arg))
if p is not False:
return p[1]*self.func(p[0])
elif arg.is_Rational:
return log(arg.p) - log(arg.q)
elif arg.is_Mul:
expr = []
nonpos = []
for x in arg.args:
if force or x.is_positive or x.is_polar:
a = self.func(x)
if isinstance(a, log):
expr.append(self.func(x)._eval_expand_log(**hints))
else:
expr.append(a)
elif x.is_negative:
a = self.func(-x)
expr.append(a)
nonpos.append(S.NegativeOne)
else:
nonpos.append(x)
return Add(*expr) + log(Mul(*nonpos))
elif arg.is_Pow or isinstance(arg, exp):
if force or (arg.exp.is_real and (arg.base.is_positive or ((arg.exp+1)
.is_positive and (arg.exp-1).is_nonpositive))) or arg.base.is_polar:
b = arg.base
e = arg.exp
a = self.func(b)
if isinstance(a, log):
return unpolarify(e) * a._eval_expand_log(**hints)
else:
return unpolarify(e) * a
elif isinstance(arg, Product):
if arg.function.is_positive:
return Sum(log(arg.function), *arg.limits)
return self.func(arg)示例4: _eval_expand_log
def _eval_expand_log(self, deep=True, **hints):
from sympy import unpolarify
from sympy.concrete import Sum, Product
force = hints.get('force', False)
arg = self.args[0]
if arg.is_Integer:
# remove perfect powers
p = perfect_power(int(arg))
if p is not False:
return p[1]*self.func(p[0])
elif arg.is_Mul:
expr = []
nonpos = []
for x in arg.args:
if force or x.is_positive or x.is_polar:
a = self.func(x)
if isinstance(a, log):
expr.append(self.func(x)._eval_expand_log(**hints))
else:
expr.append(a)
else:
nonpos.append(x)
return Add(*expr) + log(Mul(*nonpos))
elif arg.is_Pow:
if force or (arg.exp.is_real and arg.base.is_positive) or \
arg.base.is_polar:
b = arg.base
e = arg.exp
a = self.func(b)
if isinstance(a, log):
return unpolarify(e) * a._eval_expand_log(**hints)
else:
return unpolarify(e) * a
elif isinstance(arg, Product):
if arg.function.is_positive:
return Sum(log(arg.function), *arg.limits)
return self.func(arg)示例5: test_perfect_power
def test_perfect_power():
assert perfect_power(0) is False
assert perfect_power(1) is False
assert perfect_power(2) is False
assert perfect_power(3) is False
assert perfect_power(4) == (2, 2)
assert perfect_power(14) is False
assert perfect_power(25) == (5, 2)
assert perfect_power(22) is False
assert perfect_power(22, [2]) is False
assert perfect_power(137**(3*5*13)) == (137, 3*5*13)
assert perfect_power(137**(3*5*13) + 1) is False
assert perfect_power(137**(3*5*13) - 1) is False
assert perfect_power(103005006004**7) == (103005006004, 7)
assert perfect_power(103005006004**7 + 1) is False
assert perfect_power(103005006004**7 - 1) is False
assert perfect_power(103005006004**12) == (103005006004, 12)
assert perfect_power(103005006004**12 + 1) is False
assert perfect_power(103005006004**12 - 1) is False
assert perfect_power(2**10007) == (2, 10007)
assert perfect_power(2**10007 + 1) is False
assert perfect_power(2**10007 - 1) is False
assert perfect_power((9**99 + 1)**60) == (9**99 + 1, 60)
assert perfect_power((9**99 + 1)**60 + 1) is False
assert perfect_power((9**99 + 1)**60 - 1) is False
assert perfect_power((10**40000)**2, big=False) == (10**40000, 2)
assert perfect_power(10**100000) == (10, 100000)
assert perfect_power(10**100001) == (10, 100001)
assert perfect_power(13**4, [3, 5]) is False
assert perfect_power(3**4, [3, 10], factor=0) is False
assert perfect_power(3**3*5**3) == (15, 3)
assert perfect_power(2**3*5**5) is False
assert perfect_power(2*13**4) is False
assert perfect_power(2**5*3**3) is False示例6: test_perfect_power
def test_perfect_power():
assert perfect_power(0) == None
assert perfect_power(1) == None
assert perfect_power(2) == None
assert perfect_power(3) == None
assert perfect_power(4) == (2, 2)
assert perfect_power(14) == None
assert perfect_power(25) == (5, 2)
assert perfect_power(137**(3*5*13)) == (137, 3*5*13)
assert perfect_power(137**(3*5*13) + 1) == None
assert perfect_power(137**(3*5*13) - 1) == None
assert perfect_power(103005006004**7) == (103005006004, 7)
assert perfect_power(103005006004**7+1) == None
assert perfect_power(103005006004**7-1) == None
assert perfect_power(103005006004**12) == (103005006004, 12)
assert perfect_power(103005006004**12+1) == None
assert perfect_power(103005006004**12-1) == None
assert perfect_power(2**10007) == (2, 10007)
assert perfect_power(2**10007+1) == None
assert perfect_power(2**10007-1) == None
assert perfect_power((9**99 + 1)**60) == (9**99 + 1, 60)
assert perfect_power((9**99 + 1)**60+1) == None
assert perfect_power((9**99 + 1)**60-1) == None
assert perfect_power((10**40000)**2, recursive=False) == (10**40000, 2)
assert perfect_power(10**100000) == (10, 100000)