本文整理汇总了Python中sympy.core.C类的典型用法代码示例。如果您正苦于以下问题：Python C类的具体用法？Python C怎么用？Python C使用的例子？那么恭喜您, 这里精选的类代码示例或许可以为您提供帮助。
在下文中一共展示了C类的15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: monomial_count
def monomial_count(V, N):
r"""
Computes the number of monomials.
The number of monomials is given by the following formula:
.. math::
\frac{(\#V + N)!}{\#V! N!}
where `N` is a total degree and `V` is a set of variables.
**Examples**
>>> from sympy import monomials, monomial_count
>>> from sympy.abc import x, y
>>> monomial_count(2, 2)
6
>>> M = monomials([x, y], 2)
>>> sorted(M)
[1, x, y, x**2, y**2, x*y]
>>> len(M)
6
"""
return C.factorial(V + N) / C.factorial(V) / C.factorial(N)示例2: arbitrary_point
def arbitrary_point(self, parameter='t'):
"""A parameterized point on the ellipse.
Parameters
----------
parameter : str, optional
Default value is 't'.
Returns
-------
arbitrary_point : Point
Raises
------
ValueError
When `parameter` already appears in the functions.
See Also
--------
Point
Examples
--------
>>> from sympy import Point, Ellipse
>>> e1 = Ellipse(Point(0, 0), 3, 2)
>>> e1.arbitrary_point()
Point(3*cos(t), 2*sin(t))
"""
t = _symbol(parameter)
if t.name in (f.name for f in self.free_symbols):
raise ValueError('Symbol %s already appears in object and cannot be used as a parameter.' % t.name)
return Point(self.center[0] + self.hradius*C.cos(t),
self.center[1] + self.vradius*C.sin(t))示例3: monomial_count
def monomial_count(V, N):
r"""
Computes the number of monomials.
The number of monomials is given by the following formula:
.. math::
\frac{(\#V + N)!}{\#V! N!}
where `N` is a total degree and `V` is a set of variables.
Examples
========
>>> from sympy.polys.monomials import itermonomials, monomial_count
>>> from sympy.polys.orderings import monomial_key
>>> from sympy.abc import x, y
>>> monomial_count(2, 2)
6
>>> M = itermonomials([x, y], 2)
>>> sorted(M, key=monomial_key('grlex', [y, x]))
[1, x, y, x**2, x*y, y**2]
>>> len(M)
6
"""
return C.factorial(V + N) / C.factorial(V) / C.factorial(N)示例4: vertices
def vertices(self):
"""The vertices of the regular polygon.
Returns
-------
vertices : list
Each vertex is a Point.
See Also
--------
Point
Examples
--------
>>> from sympy.geometry import RegularPolygon, Point
>>> rp = RegularPolygon(Point(0, 0), 5, 4)
>>> rp.vertices
[Point(5, 0), Point(0, 5), Point(-5, 0), Point(0, -5)]
"""
points = []
c, r, n = self
v = 2*S.Pi/n
for k in xrange(0, n):
points.append(Point(c[0] + r*C.cos(k*v), c[1] + r*C.sin(k*v)))
return points示例5: eval
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6: eval
def eval(cls, arg):
arg = sympify(arg)
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Infinity:
return S.Infinity
elif arg is S.NegativeInfinity:
return S.NegativeInfinity
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return C.log(2**S.Half + 1)
elif arg is S.NegativeOne:
return C.log(2**S.Half - 1)
elif arg.is_negative:
return -cls(-arg)
else:
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return S.ImaginaryUnit * C.asin(i_coeff)
else:
if arg.as_coeff_mul()[0].is_negative:
return -cls(-arg)示例7: vertices
def vertices(self):
points = []
c, r, n = self
v = 2*S.Pi/n
for k in xrange(0, n):
points.append( Point(c[0] + r*C.cos(k*v), c[1] + r*C.sin(k*v)) )
return points示例8: arbitrary_point
def arbitrary_point(self, parameter_name='t'):
"""A parametric point on the ellipse.
Parameters
----------
parameter_name : str, optional
Default value is 't'.
Returns
-------
arbitrary_point : Point
See Also
--------
Point
Examples
--------
>>> from sympy import Point, Ellipse
>>> e1 = Ellipse(Point(0, 0), 3, 2)
>>> e1.arbitrary_point()
Point(3*cos(t), 2*sin(t))
"""
t = C.Symbol(parameter_name, real=True)
return Point(self.center[0] + self.hradius*C.cos(t),
self.center[1] + self.vradius*C.sin(t))示例9: as_real_imag
def as_real_imag(self, deep=True, **hints):
re, im = self.args[0].as_real_imag()
if deep:
re = re.expand(deep, **hints)
im = im.expand(deep, **hints)
cos, sin = C.cos(im), C.sin(im)
return (exp(re) * cos, exp(re) * sin)示例10: _eval_expand_complex
def _eval_expand_complex(self, deep=True, **hints):
re, im = self.args[0].as_real_imag()
if deep:
re = re.expand(deep, **hints)
im = im.expand(deep, **hints)
cos, sin = C.cos(im), C.sin(im)
return exp(re) * cos + S.ImaginaryUnit * exp(re) * sin示例11: as_real_imag
def as_real_imag(self, deep=True, **hints):
"""
Returns this function as a 2-tuple representing a complex number.
Examples
========
>>> from sympy import I
>>> from sympy.abc import x
>>> from sympy.functions import exp
>>> exp(x).as_real_imag()
(exp(re(x))*cos(im(x)), exp(re(x))*sin(im(x)))
>>> exp(1).as_real_imag()
(E, 0)
>>> exp(I).as_real_imag()
(cos(1), sin(1))
>>> exp(1+I).as_real_imag()
(E*cos(1), E*sin(1))
See Also
========
sympy.functions.elementary.complexes.re
sympy.functions.elementary.complexes.im
"""
re, im = self.args[0].as_real_imag()
if deep:
re = re.expand(deep, **hints)
im = im.expand(deep, **hints)
cos, sin = C.cos(im), C.sin(im)
return (exp(re)*cos, exp(re)*sin)示例12: eval
def eval(cls, arg):
arg = sympify(arg)
if arg.is_Number:
if arg is S.NaN:
return S.NaN
elif arg is S.Zero:
return S.Zero
elif arg is S.One:
return S.Infinity
elif arg is S.NegativeOne:
return S.NegativeInfinity
elif arg is S.Infinity:
return -S.ImaginaryUnit * C.atan(arg)
elif arg is S.NegativeInfinity:
return S.ImaginaryUnit * C.atan(-arg)
elif arg.is_negative:
return -cls(-arg)
else:
if arg is S.ComplexInfinity:
return S.NaN
i_coeff = arg.as_coefficient(S.ImaginaryUnit)
if i_coeff is not None:
return S.ImaginaryUnit * C.atan(i_coeff)
else:
if _coeff_isneg(arg):
return -cls(-arg)示例13: real_root
def real_root(arg, n=None):
"""Return the real nth-root of arg if possible. If n is omitted then
all instances of (-n)**(1/odd) will be changed to -n**(1/odd); this
will only create a real root of a principle root -- the presence of
other factors may cause the result to not be real.
Examples
========
>>> from sympy import root, real_root, Rational
>>> from sympy.abc import x, n
>>> real_root(-8, 3)
-2
>>> root(-8, 3)
2*(-1)**(1/3)
>>> real_root(_)
-2
If one creates a non-principle root and applies real_root, the
result will not be real (so use with caution):
>>> root(-8, 3, 2)
-2*(-1)**(2/3)
>>> real_root(_)
-2*(-1)**(2/3)
See Also
========
sympy.polys.rootoftools.RootOf
sympy.core.power.integer_nthroot
root, sqrt
"""
if n is not None:
try:
n = as_int(n)
arg = sympify(arg)
if arg.is_positive or arg.is_negative:
rv = root(arg, n)
else:
raise ValueError
except ValueError:
return root(arg, n)*C.Piecewise(
(S.One, ~C.Equality(C.im(arg), 0)),
(C.Pow(S.NegativeOne, S.One/n)**(2*C.floor(n/2)), C.And(
C.Equality(n % 2, 1),
arg < 0)),
(S.One, True))
else:
rv = sympify(arg)
n1pow = Transform(lambda x: -(-x.base)**x.exp,
lambda x:
x.is_Pow and
x.base.is_negative and
x.exp.is_Rational and
x.exp.p == 1 and x.exp.q % 2)
return rv.xreplace(n1pow)示例14: eval
def eval(cls, arg):
from sympy.simplify.simplify import signsimp
if hasattr(arg, '_eval_Abs'):
obj = arg._eval_Abs()
if obj is not None:
return obj
# handle what we can
arg = signsimp(arg, evaluate=False)
if arg.is_Mul:
known = []
unk = []
for t in arg.args:
tnew = cls(t)
if tnew.func is cls:
unk.append(tnew.args[0])
else:
known.append(tnew)
known = Mul(*known)
unk = cls(Mul(*unk), evaluate=False) if unk else S.One
return known*unk
if arg is S.NaN:
return S.NaN
if arg.is_Pow:
base, exponent = arg.as_base_exp()
if base.is_real:
if exponent.is_integer:
if exponent.is_even:
return arg
if base is S.NegativeOne:
return S.One
if base.func is cls and exponent is S.NegativeOne:
return arg
return Abs(base)**exponent
if base.is_positive == True:
return base**re(exponent)
return (-base)**re(exponent)*C.exp(-S.Pi*im(exponent))
if isinstance(arg, C.exp):
return C.exp(re(arg.args[0]))
if arg.is_zero: # it may be an Expr that is zero
return S.Zero
if arg.is_nonnegative:
return arg
if arg.is_nonpositive:
return -arg
if arg.is_imaginary:
arg2 = -S.ImaginaryUnit * arg
if arg2.is_nonnegative:
return arg2
if arg.is_Add:
if arg.has(S.Infinity, S.NegativeInfinity):
if any(a.is_infinite for a in arg.as_real_imag()):
return S.Infinity
if arg.is_real is None and arg.is_imaginary is None:
if all(a.is_real or a.is_imaginary or (S.ImaginaryUnit*a).is_real for a in arg.args):
from sympy import expand_mul
return sqrt(expand_mul(arg*arg.conjugate()))
if arg.is_real is False and arg.is_imaginary is False:
from sympy import expand_mul
return sqrt(expand_mul(arg*arg.conjugate()))示例15: eval
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