def dup_factor_list(f, K0):
"""Factor polynomials into irreducibles in `K[x]`. """
j, f = dup_terms_gcd(f, K0)
cont, f = dup_primitive(f, K0)
if K0.is_FiniteField:
coeff, factors = dup_gf_factor(f, K0)
elif K0.is_Algebraic:
coeff, factors = dup_ext_factor(f, K0)
else:
if not K0.is_Exact:
K0_inexact, K0 = K0, K0.get_exact()
f = dup_convert(f, K0_inexact, K0)
else:
K0_inexact = None
if K0.has_Field:
K = K0.get_ring()
denom, f = dup_clear_denoms(f, K0, K)
f = dup_convert(f, K0, K)
else:
K = K0
if K.is_ZZ:
coeff, factors = dup_zz_factor(f, K)
elif K.is_Poly:
f, u = dmp_inject(f, 0, K)
coeff, factors = dmp_factor_list(f, u, K.domain)
for i, (f, k) in enumerate(factors):
factors[i] = (dmp_eject(f, u, K), k)
coeff = K.convert(coeff, K.domain)
else: # pragma: no cover
raise DomainError('factorization not supported over %s' % K0)
if K0.has_Field:
for i, (f, k) in enumerate(factors):
factors[i] = (dup_convert(f, K, K0), k)
coeff = K0.convert(coeff, K)
if K0_inexact is None:
coeff = coeff / denom
else:
for i, (f, k) in enumerate(factors):
f = dup_quo_ground(f, denom, K0)
f = dup_convert(f, K0, K0_inexact)
factors[i] = (f, k)
coeff = K0_inexact.convert(coeff * denom**i, K0)
K0 = K0_inexact
if j:
factors.insert(0, ([K0.one, K0.zero], j))
return coeff * cont, _sort_factors(factors)
def test_dmp_eject():
R, x, y = ring("x,y", ZZ)
assert dmp_eject([[[]]], 2, R) == []
assert dmp_eject([[[[]]]], 3, R) == [[]]
assert dmp_eject([[[1]]], 2, R) == [R(1)]
assert dmp_eject([[[[1]]]], 3, R) == [[R(1)]]
f = [[[1]], [[2], [3, 4]]]
assert dmp_eject(f, 2, R) == [R(1), 2 * x + 3 * y + 4]
assert dmp_eject(f, 2, R, front=True) == [R(3), x + 2 * y + 4]
f = [3 * x**2 + 7 * x * y + 5 * y**2, 2 * x, R(0), x * y**2 + 11]
g = [[[3], [7, 0], [5, 0, 0]], [[2], []], [[]], [[1, 0, 0], [11]]]
assert dmp_eject(g, 2, R) == f
def test_dmp_eject():
R, x, y = ring("x,y", ZZ)
K = R.to_domain()
assert dmp_eject([[[]]], 2, K) == []
assert dmp_eject([[[[]]]], 3, K) == [[]]
assert dmp_eject([[[1]]], 2, K) == [R(1)]
assert dmp_eject([[[[1]]]], 3, K) == [[R(1)]]
assert dmp_eject([[[1]], [[2], [3, 4]]], 2, K) == [R(1), 2*x + 3*y + 4]
f = [3*x**2 + 7*x*y + 5*y**2, 2*x, R(0), x*y**2 + 11]
g = [[[3], [7, 0], [5, 0, 0]], [[2], []], [[]], [[1, 0, 0], [11]]]
assert dmp_eject(g, 2, K) == f
def dmp_factor_list(f, u, K0):
"""Factor polynomials into irreducibles in `K[X]`. """
if not u:
return dup_factor_list(f, K0)
J, f = dmp_terms_gcd(f, u, K0)
cont, f = dmp_ground_primitive(f, u, K0)
if K0.is_FiniteField: # pragma: no cover
coeff, factors = dmp_gf_factor(f, u, K0)
elif K0.is_Algebraic:
coeff, factors = dmp_ext_factor(f, u, K0)
else:
if not K0.is_Exact:
K0_inexact, K0 = K0, K0.get_exact()
f = dmp_convert(f, u, K0_inexact, K0)
else:
K0_inexact = None
if K0.has_Field:
K = K0.get_ring()
denom, f = dmp_clear_denoms(f, u, K0, K)
f = dmp_convert(f, u, K0, K)
else:
K = K0
if K.is_ZZ:
levels, f, v = dmp_exclude(f, u, K)
coeff, factors = dmp_zz_factor(f, v, K)
for i, (f, k) in enumerate(factors):
factors[i] = (dmp_include(f, levels, v, K), k)
elif K.is_Poly:
f, v = dmp_inject(f, u, K)
coeff, factors = dmp_factor_list(f, v, K.domain)
for i, (f, k) in enumerate(factors):
factors[i] = (dmp_eject(f, v, K), k)
coeff = K.convert(coeff, K.domain)
else: # pragma: no cover
raise DomainError('factorization not supported over %s' % K0)
if K0.has_Field:
for i, (f, k) in enumerate(factors):
factors[i] = (dmp_convert(f, u, K, K0), k)
coeff = K0.convert(coeff, K)
if K0_inexact is None:
coeff = coeff / denom
else:
for i, (f, k) in enumerate(factors):
f = dmp_quo_ground(f, denom, u, K0)
f = dmp_convert(f, u, K0, K0_inexact)
factors[i] = (f, k)
coeff = K0_inexact.convert(coeff * denom**i, K0)
K0 = K0_inexact
for i, j in enumerate(reversed(J)):
if not j:
continue
term = {(0, ) * (u - i) + (1, ) + (0, ) * i: K0.one}
factors.insert(0, (dmp_from_dict(term, u, K0), j))
return coeff * cont, _sort_factors(factors)