def root_factors(f, *gens, **args):
"""
Returns all factors of a univariate polynomial.
**Examples**
>>> from sympy.abc import x, y
>>> from sympy.polys.polyroots import root_factors
>>> root_factors(x**2-y, x)
[x - y**(1/2), x + y**(1/2)]
"""
args = dict(args)
filter = args.pop('filter', None)
F = Poly(f, *gens, **args)
if not F.is_Poly:
return [f]
if F.is_multivariate:
raise ValueError('multivariate polynomials not supported')
x = F.gens[0]
zeros = roots(F, filter=filter)
if not zeros:
factors = [F]
else:
factors, N = [], 0
for r, n in zeros.iteritems():
factors, N = factors + [Poly(x-r, x)]*n, N + n
if N < F.degree():
G = reduce(lambda p,q: p*q, factors)
factors.append(F.exquo(G))
if not isinstance(f, Poly):
return [ f.as_expr() for f in factors ]
else:
return factors
def root_factors(f, *gens, **args):
"""
Returns all factors of a univariate polynomial.
**Examples**
>>> from sympy.abc import x, y
>>> from sympy.polys.polyroots import root_factors
>>> root_factors(x**2-y, x)
[x - y**(1/2), x + y**(1/2)]
"""
args = dict(args)
filter = args.pop('filter', None)
F = Poly(f, *gens, **args)
if not F.is_Poly:
return [f]
if F.is_multivariate:
raise ValueError('multivariate polynomials not supported')
x = F.gens[0]
zeros = roots(F, filter=filter)
if not zeros:
factors = [F]
else:
factors, N = [], 0
for r, n in zeros.iteritems():
factors, N = factors + [Poly(x - r, x)] * n, N + n
if N < F.degree():
G = reduce(lambda p, q: p * q, factors)
factors.append(F.exquo(G))
if not isinstance(f, Poly):
return [f.as_expr() for f in factors]
else:
return factors
