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 test_zzX_factor():
assert zzX_factor([]) == (0, [])
assert zzX_factor([7]) == (7, [])
assert zzX_factor([[7]]) == (7, [])
assert zzX_factor([[1], []]) == \
(1, [([[1], []], 1)])
assert zzX_factor([[4], []]) == \
(4, [([[1], []], 1)])
assert zzX_factor([[4], [2]]) == \
(2, [([[2], [1]], 1)])
assert zzX_factor([[1,0,1]]) == \
(1, [([[1, 0, 1]], 1)])
assert zzX_factor([[1,0,-1]]) == \
(1, [([[1,-1]], 1),
([[1, 1]], 1)])
assert zzX_factor(f_1) == \
(1, [([[[1]], [[1, 0], [20]]], 1),
([[[1], []], [[1, 10]]], 1),
([[[1, 0]], [[1], [30]]], 1)])
assert zzX_factor(f_2) == \
(1, [([[[1], [], [1, 0, 0]], [[]], [[1], [90]]], 1),
([[[1], [1, 0]], [[]], [[]], [[1, -11]]], 1)])
assert zzX_factor(f_3) == \
(1, [([[[1], [], []], [[1, 0, 0, 0, 1]], [[1, 0]]], 1),
([[[1]], [[]], [[1, 0], []], [[1], [1, 0, 0, 0], []]], 1)])
assert zzX_factor(f_4) == \
(-1, [([[[1], [], [], []], [[1, 0, 0]]], 1),
([[[1, 0]], [[]], [[1, 0, 0], [], [], [], [5]]], 1),
([[[1], []], [[]], [[]], [[-1, 0, -3]]], 1),
([[[1], [], [], [], []], [[]], [[]], [[1, 0, 0]]], 1)])
assert zzX_factor(f_5) == \
(-1, [([[[1]], [[1], [-1, 0]]], 3)])
assert zzX_factor(f_6) == \
(1, [([[[[47]], [[]]], [[[1, 0, 0], [], [], [-1, 0, 0]]]], 1),
([[[[45]]], [[[]]], [[[]]], [[[-9]], [[-1]], [[]], [[3], [], [2, 0], []]]], 1)])
def test_zzX_factor():
assert zzX_factor([]) == (0, [])
assert zzX_factor([7]) == (7, [])
assert zzX_factor([[7]]) == (7, [])
assert zzX_factor([[1], []]) == \
(1, [([[1], []], 1)])
assert zzX_factor([[4], []]) == \
(4, [([[1], []], 1)])
assert zzX_factor([[4], [2]]) == \
(2, [([[2], [1]], 1)])
assert zzX_factor([[1,0,1]]) == \
(1, [([[1, 0, 1]], 1)])
assert zzX_factor([[1,0,-1]]) == \
(1, [([[1,-1]], 1),
([[1, 1]], 1)])
assert zzX_factor(f_1) == \
(1, [([[[1]], [[1, 0], [20]]], 1),
([[[1], []], [[1, 10]]], 1),
([[[1, 0]], [[1], [30]]], 1)])
assert zzX_factor(f_2) == \
(1, [([[[1], [], [1, 0, 0]], [[]], [[1], [90]]], 1),
([[[1], [1, 0]], [[]], [[]], [[1, -11]]], 1)])
assert zzX_factor(f_3) == \
(1, [([[[1], [], []], [[1, 0, 0, 0, 1]], [[1, 0]]], 1),
([[[1]], [[]], [[1, 0], []], [[1], [1, 0, 0, 0], []]], 1)])
assert zzX_factor(f_4) == \
(-1, [([[[1], [], [], []], [[1, 0, 0]]], 1),
([[[1, 0]], [[]], [[1, 0, 0], [], [], [], [5]]], 1),
([[[1], []], [[]], [[]], [[-1, 0, -3]]], 1),
([[[1], [], [], [], []], [[]], [[]], [[1, 0, 0]]], 1)])
assert zzX_factor(f_5) == \
(-1, [([[[1]], [[1], [-1, 0]]], 3)])
assert zzX_factor(f_6) == \
(1, [([[[[47]], [[]]], [[[1, 0, 0], [], [], [-1, 0, 0]]]], 1),
([[[[45]]], [[[]]], [[[]]], [[[-9]], [[-1]], [[]], [[3], [], [2, 0], []]]], 1)])
