def dup_gf_sqf_list(f, K, all=False):
"""Compute square-free decomposition of ``f`` in ``GF(p)[x]``. """
f = dup_convert(f, K, K.dom)
coeff, factors = gf_sqf_list(f, K.mod, K.dom, all=all)
for i, (f, k) in enumerate(factors):
factors[i] = (dup_convert(f, K.dom, K), k)
return K.convert(coeff, K.dom), factors
def dup_gf_sqf_list(f, K, all=False):
"""Compute square-free decomposition of ``f`` in ``GF(p)[x]``. """
f = dup_convert(f, K, K.dom)
coeff, factors = gf_sqf_list(f, K.mod, K.dom, all=all)
for i, (f, k) in enumerate(factors):
factors[i] = (dup_convert(f, K.dom, K), k)
return K.convert(coeff, K.dom), factors
def test_gf_squarefree():
assert gf_sqf_list([], 11, ZZ) == (0, [])
assert gf_sqf_list([1], 11, ZZ) == (1, [])
assert gf_sqf_list([1,1], 11, ZZ) == (1, [([1, 1], 1)])
assert gf_sqf_p([], 11, ZZ) == True
assert gf_sqf_p([1], 11, ZZ) == True
assert gf_sqf_p([1,1], 11, ZZ) == True
f = gf_from_dict({11: 1, 0: 1}, 11, ZZ)
assert gf_sqf_p(f, 11, ZZ) == False
assert gf_sqf_list(f, 11, ZZ) == \
(1, [([1, 1], 11)])
f = [1, 5, 8, 4]
assert gf_sqf_p(f, 11, ZZ) == False
assert gf_sqf_list(f, 11, ZZ) == \
(1, [([1, 1], 1),
([1, 2], 2)])
assert gf_sqf_part(f, 11, ZZ) == [1, 3, 2]
f = [1,0,0,2,0,0,2,0,0,1,0]
assert gf_sqf_list(f, 3, ZZ) == \
(1, [([1, 0], 1),
([1, 1], 3),
([1, 2], 6)])
