def test_dmp_sqf():
assert dmp_sqf_part([[]], 1, ZZ) == [[]]
assert dmp_sqf_p([[]], 1, ZZ) == True
assert dmp_sqf_part([[7]], 1, ZZ) == [[1]]
assert dmp_sqf_p([[7]], 1, ZZ) == True
assert dmp_sqf_p(f_0, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_0, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_1, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_1, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_2, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_2, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_3, 2, ZZ) == True
assert dmp_sqf_p(dmp_sqr(f_3, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_5, 2, ZZ) == False
assert dmp_sqf_p(dmp_sqr(f_5, 2, ZZ), 2, ZZ) == False
assert dmp_sqf_p(f_4, 2, ZZ) == True
assert dmp_sqf_part(f_4, 2, ZZ) == dmp_neg(f_4, 2, ZZ)
assert dmp_sqf_p(f_6, 3, ZZ) == True
assert dmp_sqf_part(f_6, 3, ZZ) == f_6
assert dmp_sqf_part(f_5, 2, ZZ) == [[[1]], [[1], [-1, 0]]]
assert dup_sqf_list([], ZZ) == (ZZ(0), [])
assert dup_sqf_list_include([], ZZ) == [([], 1)]
assert dmp_sqf_list([[ZZ(3)]], 1, ZZ) == (ZZ(3), [])
assert dmp_sqf_list_include([[ZZ(3)]], 1, ZZ) == [([[ZZ(3)]], 1)]
f = [-1,1,0,0,1,-1]
assert dmp_sqf_list(f, 0, ZZ) == \
(-1, [([1,1,1,1], 1), ([1,-1], 2)])
assert dmp_sqf_list_include(f, 0, ZZ) == \
[([-1,-1,-1,-1], 1), ([1,-1], 2)]
f = [[-1],[1],[],[],[1],[-1]]
assert dmp_sqf_list(f, 1, ZZ) == \
(-1, [([[1],[1],[1],[1]], 1), ([[1],[-1]], 2)])
assert dmp_sqf_list_include(f, 1, ZZ) == \
[([[-1],[-1],[-1],[-1]], 1), ([[1],[-1]], 2)]
K = FF(2)
f = [[-1], [2], [-1]]
assert dmp_sqf_list_include(f, 1, ZZ) == \
[([[-1]], 1), ([[1], [-1]], 2)]
raises(DomainError, "dmp_sqf_list([[K(1), K(0), K(1)]], 1, K)")
def test_dup_sqf():
assert dup_sqf_part([], ZZ) == []
assert dup_sqf_p([], ZZ) == True
assert dup_sqf_part([7], ZZ) == [1]
assert dup_sqf_p([7], ZZ) == True
assert dup_sqf_part([2,2], ZZ) == [1,1]
assert dup_sqf_p([2,2], ZZ) == True
assert dup_sqf_part([1,0,1,1], ZZ) == [1,0,1,1]
assert dup_sqf_p([1,0,1,1], ZZ) == True
assert dup_sqf_part([-1,0,1,1], ZZ) == [1,0,-1,-1]
assert dup_sqf_p([-1,0,1,1], ZZ) == True
assert dup_sqf_part([2,3,0,0], ZZ) == [2,3,0]
assert dup_sqf_p([2,3,0,0], ZZ) == False
assert dup_sqf_part([-2,3,0,0], ZZ) == [2,-3,0]
assert dup_sqf_p([-2,3,0,0], ZZ) == False
assert dup_sqf_list([], ZZ) == (0, [])
assert dup_sqf_list([1], ZZ) == (1, [])
assert dup_sqf_list([1,0], ZZ) == (1, [([1,0], 1)])
assert dup_sqf_list([2,0,0], ZZ) == (2, [([1,0], 2)])
assert dup_sqf_list([3,0,0,0], ZZ) == (3, [([1,0], 3)])
assert dup_sqf_list([ZZ(2),ZZ(4),ZZ(2)], ZZ) == \
(ZZ(2), [([ZZ(1),ZZ(1)], 2)])
assert dup_sqf_list([QQ(2),QQ(4),QQ(2)], QQ) == \
(QQ(2), [([QQ(1),QQ(1)], 2)])
assert dup_sqf_list([-1,1,0,0,1,-1], ZZ) == \
(-1, [([1,1,1,1], 1), ([1,-1], 2)])
assert dup_sqf_list([1,0,6,0,12,0,8,0,0], ZZ) == \
(1, [([1,0], 2), ([1,0,2], 3)])
K = FF(2)
f = map(K, [1,0,1])
assert dup_sqf_list(f, K) == \
(K(1), [([K(1),K(1)], 2)])
K = FF(3)
f = map(K, [1,0,0,2,0,0,2,0,0,1,0])
assert dup_sqf_list(f, K) == \
(K(1), [([K(1), K(0)], 1),
([K(1), K(1)], 3),
([K(1), K(2)], 6)])
f = [1,0,0,1]
g = map(K, f)
assert dup_sqf_part(f, ZZ) == f
assert dup_sqf_part(g, K) == [K(1), K(1)]
assert dup_sqf_p(f, ZZ) == True
assert dup_sqf_p(g, K) == False
A = [[1],[],[-3],[],[6]]
D = [[1],[],[-5],[],[5],[],[4]]
f, g = D, dmp_sub(A, dmp_mul(dmp_diff(D, 1, 1, ZZ), [[1,0]], 1, ZZ), 1, ZZ)
res = dmp_resultant(f, g, 1, ZZ)
assert dup_sqf_list(res, ZZ) == (45796, [([4,0,1], 3)])
assert dup_sqf_list_include([DMP([1, 0, 0, 0], ZZ), DMP([], ZZ), DMP([], ZZ)], ZZ[x]) == \
[([DMP([1, 0, 0, 0], ZZ)], 1), ([DMP([1], ZZ), DMP([], ZZ)], 2)]
