本文整理汇总了Python中sympy.polys.Poly.sturm方法的典型用法代码示例。如果您正苦于以下问题：Python Poly.sturm方法的具体用法？Python Poly.sturm怎么用？Python Poly.sturm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.sturm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: number_of_real_roots
# 需要导入模块: from sympy.polys import Poly [as 别名]
# 或者: from sympy.polys.Poly import sturm [as 别名]
def number_of_real_roots(f, *gens, **args):
"""Returns the number of distinct real roots of `f` in `(inf, sup]`.
Examples
========
>>> from sympy import Poly
>>> from sympy.abc import x, y
>>> from sympy.polys.polyroots import number_of_real_roots
>>> f = Poly(x**2 - 1, x)
Count real roots in the (-oo, oo) interval:
>>> number_of_real_roots(f)
2
Count real roots in the (0, 2) interval:
>>> number_of_real_roots(f, inf=0, sup=2)
1
Count real roots in the (2, oo) interval:
>>> number_of_real_roots(f, inf=2)
0
References
==========
.. [Davenport88] J.H. Davenport, Y. Siret, E. Tournier, Computer
Algebra Systems and Algorithms for Algebraic Computation,
Academic Press, London, 1988, pp. 124-128
"""
def sign_changes(seq):
count = 0
for i in xrange(1, len(seq)):
if (seq[i-1] < 0 and seq[i] >= 0) or \
(seq[i-1] > 0 and seq[i] <= 0):
count += 1
return count
F = Poly(f, *gens, **args)
if not F.is_Poly:
return 0
if F.is_multivariate:
raise ValueError('multivariate polynomials not supported')
if F.degree() < 1:
return 0
inf = args.get('inf', None)
if inf is not None:
inf = sympify(inf)
if not inf.is_number:
raise ValueError("Not a number: %s" % inf)
elif abs(inf) is S.Infinity:
inf = None
sup = args.get('sup', None)
if sup is not None:
sup = sympify(sup)
if not sup.is_number:
raise ValueError("Not a number: %s" % sup)
elif abs(sup) is S.Infinity:
sup = None
sturm = F.sturm()
if inf is None:
signs_inf = sign_changes([ s.LC()*(-1)**s.degree() for s in sturm ])
else:
signs_inf = sign_changes([ s.eval(inf) for s in sturm ])
if sup is None:
signs_sup = sign_changes([ s.LC() for s in sturm ])
else:
signs_sup = sign_changes([ s.eval(sup) for s in sturm ])
return abs(signs_inf - signs_sup)