def poly_factors(f, *symbols, **flags):
"""Factor polynomials over rationals.
>>> from sympy.polys.factortools import poly_factors
>>> from sympy.abc import x, y
>>> poly_factors(x**2 - y**2, x, y)
(1, [(Poly(x - y, x, y), 1), (Poly(x + y, x, y), 1)])
"""
if not isinstance(f, Poly):
f = Poly(f, *symbols)
elif symbols:
raise SymbolsError("Redundant symbols were given")
symbols = list(f.symbols)
try:
denom, F = f.as_integer()
except CoefficientError:
other = set([])
for coeff in f.iter_coeffs():
other |= coeff.atoms(Symbol)
symbols += sorted(other)
F = Poly(f, *symbols)
denom, F = F.as_integer()
cont, factors = zzX_factor(zzX_from_poly(F))
for i, (h, k) in enumerate(factors):
h = zzX_to_poly(h, *symbols)
if f.symbols != symbols:
h = h.as_poly(*f.symbols)
factors[i] = (h, k)
return Rational(cont, denom), factors
def poly_factors(f, *symbols, **flags):
"""Factor polynomials over rationals.
>>> from sympy import *
>>> x, y = symbols("x y")
>>> poly_factors(x**2 - y**2, x, y)
(1, [(Poly(x - y, x, y), 1), (Poly(x + y, x, y), 1)])
"""
if not isinstance(f, Poly):
f = Poly(f, *symbols)
elif symbols:
raise SymbolsError("Redundant symbols were given")
symbols = list(f.symbols)
try:
denom, F = f.as_integer()
except CoefficientError:
other = set([])
for coeff in f.iter_coeffs():
other |= coeff.atoms(Symbol)
symbols += sorted(other)
F = Poly(f, *symbols)
denom, F = F.as_integer()
cont, factors = zzX_factor(zzX_from_poly(F))
for i, (h, k) in enumerate(factors):
h = zzX_to_poly(h, *symbols)
if f.symbols != symbols:
h = h.as_poly(*f.symbols)
factors[i] = (h, k)
return Rational(cont, denom), factors
def poly_factors(f, *symbols, **flags):
"""Factor polynomials over rationals.
>>> from sympy import *
>>> x, y = symbols("x y")
>>> poly_factors(x**2 - y**2, x, y)
(1, [(Poly(x - y, x, y), 1), (Poly(x + y, x, y), 1)])
"""
if not isinstance(f, Poly):
f = Poly(f, *symbols)
elif symbols:
raise SymbolsError("Redundant symbols were given")
denom, f = f.as_integer()
if f.is_univariate:
coeffs = map(int, f.iter_all_coeffs())
content, factors = zzx_factor(coeffs)
for i in xrange(len(factors)):
factor, k = factors[i]
n = zzx_degree(factor)
terms = {}
for j, coeff in enumerate(factor):
if coeff != 0:
terms[(n - j, )] = Integer(coeff)
factors[i] = Poly(terms, *f.symbols), k
else:
content, factors = kronecker_mv(f, **flags)
return Rational(content, denom), factors
def poly_factors(f, *symbols, **flags):
"""Factor polynomials over rationals.
>>> from sympy import *
>>> x, y = symbols("x y")
>>> poly_factors(x**2 - y**2, x, y)
(1, [(Poly(x - y, x, y), 1), (Poly(x + y, x, y), 1)])
"""
if not isinstance(f, Poly):
f = Poly(f, *symbols)
elif symbols:
raise SymbolsError("Redundant symbols were given")
denom, f = f.as_integer()
if f.is_univariate:
coeffs = map(int, f.iter_all_coeffs())
content, factors = zzx_factor(coeffs)
for i in xrange(len(factors)):
factor, k = factors[i]
n = zzx_degree(factor)
terms = {}
for j, coeff in enumerate(factor):
if coeff != 0:
terms[(n-j,)] = Integer(coeff)
factors[i] = Poly(terms, *f.symbols), k
else:
content, factors = kronecker_mv(f, **flags)
return Rational(content, denom), factors