def _get_roots(cls, method, poly, radicals):
"""Return postprocessed roots of specified kind. """
if not poly.is_univariate:
raise PolynomialError("only univariate polynomials are allowed")
coeff, poly = cls._preprocess_roots(poly)
roots = []
for root in getattr(cls, method)(poly):
roots.append(coeff*cls._postprocess_root(root, radicals))
return roots
def _get_roots(cls, method, poly, radicals):
"""Return postprocessed roots of specified kind. """
if not poly.is_univariate:
raise PolynomialError("only univariate polynomials are allowed")
coeff, poly = cls._preprocess_roots(poly)
roots = []
for root in getattr(cls, method)(poly):
roots.append(coeff * cls._postprocess_root(root, radicals))
return roots
def _real_roots(cls, poly):
"""Get real roots of a composite polynomial. """
factors = _pure_factors(poly)
reals = cls._get_reals(factors)
reals_count = cls._count_roots(reals)
roots = []
for index in range(0, reals_count):
roots.append(cls._reals_index(reals, index))
return roots
def _real_roots(cls, poly):
"""Get real roots of a composite polynomial. """
factors = _pure_factors(poly)
reals = cls._get_reals(factors)
reals_count = cls._count_roots(reals)
roots = []
for index in range(0, reals_count):
roots.append(cls._reals_index(reals, index))
return roots
def _real_roots(cls, poly):
"""Get real roots of a composite polynomial. """
(_, factors) = poly.factor_list()
reals = cls._get_reals(factors)
reals = cls._reals_sorted(reals)
reals_count = cls._count_roots(reals)
roots = []
for index in xrange(0, reals_count):
roots.append(cls._reals_index(reals, index))
return roots
def _real_roots(cls, poly):
"""Get real roots of a composite polynomial. """
(_, factors) = poly.factor_list()
reals = cls._get_reals(factors)
reals = cls._reals_sorted(reals)
reals_count = cls._count_roots(reals)
roots = []
for index in range(0, reals_count):
roots.append(cls._reals_index(reals, index))
return roots
def _all_roots(cls, poly, use_cache=True):
"""Get real and complex roots of a composite polynomial. """
factors = _pure_factors(poly)
reals = cls._get_reals(factors, use_cache=use_cache)
reals_count = cls._count_roots(reals)
roots = []
for index in range(0, reals_count):
roots.append(cls._reals_index(reals, index))
complexes = cls._get_complexes(factors, use_cache=use_cache)
complexes_count = cls._count_roots(complexes)
for index in range(0, complexes_count):
roots.append(cls._complexes_index(complexes, index))
return roots
def _all_roots(cls, poly, use_cache=True):
"""Get real and complex roots of a composite polynomial. """
factors = _pure_factors(poly)
reals = cls._get_reals(factors, use_cache=use_cache)
reals_count = cls._count_roots(reals)
roots = []
for index in range(0, reals_count):
roots.append(cls._reals_index(reals, index))
complexes = cls._get_complexes(factors, use_cache=use_cache)
complexes_count = cls._count_roots(complexes)
for index in range(0, complexes_count):
roots.append(cls._complexes_index(complexes, index))
return roots
def _get_roots(cls, method, poly, radicals):
"""Return postprocessed roots of specified kind. """
if not poly.is_univariate:
raise PolynomialError("only univariate polynomials are allowed")
# get rid of gen and it's free symbol
d = Dummy()
poly = poly.subs(poly.gen, d)
x = symbols('x')
# see what others are left and select x or a numbered x
# that doesn't clash
free_names = {str(i) for i in poly.free_symbols}
for x in chain((symbols('x'),), numbered_symbols('x')):
if x.name not in free_names:
poly = poly.xreplace({d: x})
break
coeff, poly = cls._preprocess_roots(poly)
roots = []
for root in getattr(cls, method)(poly):
roots.append(coeff*cls._postprocess_root(root, radicals))
return roots
