本文整理汇总了Python中sympy.polys.Poly.atoms方法的典型用法代码示例。如果您正苦于以下问题：Python Poly.atoms方法的具体用法？Python Poly.atoms怎么用？Python Poly.atoms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.atoms方法的2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: ratint
# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import atoms [as 别名]
def ratint(f, x, **flags):
"""Performs indefinite integration of rational functions.
Given a field :math:`K` and a rational function :math:`f = p/q`,
where :math:`p` and :math:`q` are polynomials in :math:`K[x]`,
returns a function :math:`g` such that :math:`f = g'`.
>>> from sympy.integrals.rationaltools import ratint
>>> from sympy.abc import x
>>> ratint(36/(x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2), x)
(12*x + 6)/(x**2 - 1) + 4*log(x - 2) - 4*log(x + 1)
References
==========
.. [Bro05] M. Bronstein, Symbolic Integration I: Transcendental
Functions, Second Edition, Springer-Verlag, 2005, pp. 35-70
See Also
========
sympy.integrals.integrals.Integral.doit
ratint_logpart, ratint_ratpart
"""
if type(f) is not tuple:
p, q = f.as_numer_denom()
else:
p, q = f
p, q = Poly(p, x, composite=False, field=True), Poly(q, x, composite=False, field=True)
coeff, p, q = p.cancel(q)
poly, p = p.div(q)
result = poly.integrate(x).as_expr()
if p.is_zero:
return coeff*result
g, h = ratint_ratpart(p, q, x)
P, Q = h.as_numer_denom()
P = Poly(P, x)
Q = Poly(Q, x)
q, r = P.div(Q)
result += g + q.integrate(x).as_expr()
if not r.is_zero:
symbol = flags.get('symbol', 't')
if not isinstance(symbol, Symbol):
t = Dummy(symbol)
else:
t = symbol.as_dummy()
L = ratint_logpart(r, Q, x, t)
real = flags.get('real')
if real is None:
if type(f) is not tuple:
atoms = f.atoms()
else:
p, q = f
atoms = p.atoms() | q.atoms()
for elt in atoms - set([x]):
if not elt.is_real:
real = False
break
else:
real = True
eps = S(0)
if not real:
for h, q in L:
eps += RootSum(
q, Lambda(t, t*log(h.as_expr())), quadratic=True)
else:
for h, q in L:
R = log_to_real(h, q, x, t)
if R is not None:
eps += R
else:
eps += RootSum(
q, Lambda(t, t*log(h.as_expr())), quadratic=True)
result += eps
return coeff*result示例2: ratint
# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import atoms [as 别名]
def ratint(f, x, **flags):
"""Performs indefinite integration of rational functions.
Given a field K and a rational function f = p/q, where p and q
are polynomials in K[x], returns a function g such that f = g'.
>>> from sympy.integrals.rationaltools import ratint
>>> from sympy.abc import x
>>> ratint(36/(x**5 - 2*x**4 - 2*x**3 + 4*x**2 + x - 2), x)
-4*log(1 + x) + 4*log(-2 + x) - (6 + 12*x)/(1 - x**2)
References
==========
.. [Bro05] M. Bronstein, Symbolic Integration I: Transcendental
Functions, Second Edition, Springer-Verlag, 2005, pp. 35-70
"""
if type(f) is not tuple:
p, q = f.as_numer_denom()
else:
p, q = f
p, q = Poly(p, x), Poly(q, x)
c, p, q = p.cancel(q)
poly, p = p.div(q)
poly = poly.to_field()
result = c*poly.integrate(x).as_basic()
if p.is_zero:
return result
g, h = ratint_ratpart(p, q, x)
P, Q = h.as_numer_denom()
P = Poly(P, x)
Q = Poly(Q, x)
q, r = P.div(Q)
result += g + q.integrate(x).as_basic()
if not r.is_zero:
symbol = flags.get('symbol', 't')
if not isinstance(symbol, Symbol):
t = Dummy(symbol)
else:
t = symbol
L = ratint_logpart(r, Q, x, t)
real = flags.get('real')
if real is None:
if type(f) is not tuple:
atoms = f.atoms()
else:
p, q = f
atoms = p.atoms() \
| q.atoms()
for elt in atoms - set([x]):
if not elt.is_real:
real = False
break
else:
real = True
eps = S(0)
if not real:
for h, q in L:
eps += RootSum(Lambda(t, t*log(h.as_basic())), q)
else:
for h, q in L:
R = log_to_real(h, q, x, t)
if R is not None:
eps += R
else:
eps += RootSum(Lambda(t, t*log(h.as_basic())), q)
result += eps
return result