def test_dmp_gcd():
assert dmp_zz_heu_gcd([[]], [[]], 1, ZZ) == ([[]], [[]], [[]])
assert dmp_rr_prs_gcd([[]], [[]], 1, ZZ) == ([[]], [[]], [[]])
assert dmp_zz_heu_gcd([[2]], [[]], 1, ZZ) == ([[2]], [[1]], [[]])
assert dmp_rr_prs_gcd([[2]], [[]], 1, ZZ) == ([[2]], [[1]], [[]])
assert dmp_zz_heu_gcd([[-2]], [[]], 1, ZZ) == ([[2]], [[-1]], [[]])
assert dmp_rr_prs_gcd([[-2]], [[]], 1, ZZ) == ([[2]], [[-1]], [[]])
assert dmp_zz_heu_gcd([[]], [[-2]], 1, ZZ) == ([[2]], [[]], [[-1]])
assert dmp_rr_prs_gcd([[]], [[-2]], 1, ZZ) == ([[2]], [[]], [[-1]])
assert dmp_zz_heu_gcd([[]], [[2], [4]], 1, ZZ) == ([[2], [4]], [[]], [[1]])
assert dmp_rr_prs_gcd([[]], [[2], [4]], 1, ZZ) == ([[2], [4]], [[]], [[1]])
assert dmp_zz_heu_gcd([[2], [4]], [[]], 1, ZZ) == ([[2], [4]], [[1]], [[]])
assert dmp_rr_prs_gcd([[2], [4]], [[]], 1, ZZ) == ([[2], [4]], [[1]], [[]])
assert dmp_zz_heu_gcd([[2]], [[2]], 1, ZZ) == ([[2]], [[1]], [[1]])
assert dmp_rr_prs_gcd([[2]], [[2]], 1, ZZ) == ([[2]], [[1]], [[1]])
assert dmp_zz_heu_gcd([[-2]], [[2]], 1, ZZ) == ([[2]], [[-1]], [[1]])
assert dmp_rr_prs_gcd([[-2]], [[2]], 1, ZZ) == ([[2]], [[-1]], [[1]])
assert dmp_zz_heu_gcd([[2]], [[-2]], 1, ZZ) == ([[2]], [[1]], [[-1]])
assert dmp_rr_prs_gcd([[2]], [[-2]], 1, ZZ) == ([[2]], [[1]], [[-1]])
assert dmp_zz_heu_gcd([[-2]], [[-2]], 1, ZZ) == ([[2]], [[-1]], [[-1]])
assert dmp_rr_prs_gcd([[-2]], [[-2]], 1, ZZ) == ([[2]], [[-1]], [[-1]])
assert dmp_zz_heu_gcd([[1], [2], [1]], [[1]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[1]])
assert dmp_rr_prs_gcd([[1], [2], [1]], [[1]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[1]])
assert dmp_zz_heu_gcd([[1], [2], [1]], [[2]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[2]])
assert dmp_rr_prs_gcd([[1], [2], [1]], [[2]], 1,
ZZ) == ([[1]], [[1], [2], [1]], [[2]])
assert dmp_zz_heu_gcd([[2], [4], [2]], [[2]], 1,
ZZ) == ([[2]], [[1], [2], [1]], [[1]])
assert dmp_rr_prs_gcd([[2], [4], [2]], [[2]], 1,
ZZ) == ([[2]], [[1], [2], [1]], [[1]])
assert dmp_zz_heu_gcd([[2]], [[2], [4], [2]], 1,
ZZ) == ([[2]], [[1]], [[1], [2], [1]])
assert dmp_rr_prs_gcd([[2]], [[2], [4], [2]], 1,
ZZ) == ([[2]], [[1]], [[1], [2], [1]])
assert dmp_zz_heu_gcd([[2], [4], [2]], [[1], [1]], 1,
ZZ) == ([[1], [1]], [[2], [2]], [[1]])
assert dmp_rr_prs_gcd([[2], [4], [2]], [[1], [1]], 1,
ZZ) == ([[1], [1]], [[2], [2]], [[1]])
assert dmp_zz_heu_gcd([[1], [1]], [[2], [4], [2]], 1,
ZZ) == ([[1], [1]], [[1]], [[2], [2]])
assert dmp_rr_prs_gcd([[1], [1]], [[2], [4], [2]], 1,
ZZ) == ([[1], [1]], [[1]], [[2], [2]])
assert dmp_zz_heu_gcd([[[[1, 2, 1]]]], [[[[2, 2]]]], 3,
ZZ) == ([[[[1, 1]]]], [[[[1, 1]]]], [[[[2]]]])
assert dmp_rr_prs_gcd([[[[1, 2, 1]]]], [[[[2, 2]]]], 3,
ZZ) == ([[[[1, 1]]]], [[[[1, 1]]]], [[[[2]]]])
f, g = [[[[1, 2, 1], [1, 1], []]]], [[[[1, 2, 1]]]]
h, cff, cfg = [[[[1, 1]]]], [[[[1, 1], [1], []]]], [[[[1, 1]]]]
assert dmp_zz_heu_gcd(f, g, 3, ZZ) == (h, cff, cfg)
assert dmp_rr_prs_gcd(f, g, 3, ZZ) == (h, cff, cfg)
assert dmp_zz_heu_gcd(g, f, 3, ZZ) == (h, cfg, cff)
assert dmp_rr_prs_gcd(g, f, 3, ZZ) == (h, cfg, cff)
f, g, h = dmp_fateman_poly_F_1(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(4, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 4, ZZ)
assert H == h and dmp_mul(H, cff, 4, ZZ) == f \
and dmp_mul(H, cfg, 4, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(6, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 6, ZZ)
assert H == h and dmp_mul(H, cff, 6, ZZ) == f \
and dmp_mul(H, cfg, 6, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(8, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 8, ZZ)
assert H == h and dmp_mul(H, cff, 8, ZZ) == f \
and dmp_mul(H, cfg, 8, ZZ) == g
f, g, h = dmp_fateman_poly_F_2(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_3(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_3(4, ZZ)
H, cff, cfg = dmp_inner_gcd(f, g, 4, ZZ)
assert H == h and dmp_mul(H, cff, 4, ZZ) == f \
and dmp_mul(H, cfg, 4, ZZ) == g
f = [[QQ(1, 2)], [QQ(1)], [QQ(1, 2)]]
g = [[QQ(1, 2)], [QQ(1, 2)]]
h = [[QQ(1)], [QQ(1)]]
assert dmp_qq_heu_gcd(f, g, 1, QQ) == (h, g, [[QQ(1, 2)]])
assert dmp_ff_prs_gcd(f, g, 1, QQ) == (h, g, [[QQ(1, 2)]])
f = [[RR(2.1), RR(-2.2), RR(2.1)], []]
g = [[RR(1.0)], [], [], []]
assert dmp_ff_prs_gcd(f, g, 1, RR) == \
([[RR(1.0)], []], [[RR(2.1), RR(-2.2), RR(2.1)]], [[RR(1.0)], [], []])
def test_dmp_gcd():
assert dmp_zz_heu_gcd([[]], [[]], 1, ZZ) == ([[]], [[]], [[]])
assert dmp_rr_prs_gcd([[]], [[]], 1, ZZ) == ([[]], [[]], [[]])
assert dmp_zz_heu_gcd([[2]], [[]], 1, ZZ) == ([[2]], [[1]], [[]])
assert dmp_rr_prs_gcd([[2]], [[]], 1, ZZ) == ([[2]], [[1]], [[]])
assert dmp_zz_heu_gcd([[-2]], [[]], 1, ZZ) == ([[2]], [[-1]], [[]])
assert dmp_rr_prs_gcd([[-2]], [[]], 1, ZZ) == ([[2]], [[-1]], [[]])
assert dmp_zz_heu_gcd([[]], [[-2]], 1, ZZ) == ([[2]], [[]], [[-1]])
assert dmp_rr_prs_gcd([[]], [[-2]], 1, ZZ) == ([[2]], [[]], [[-1]])
assert dmp_zz_heu_gcd([[]], [[2],[4]], 1, ZZ) == ([[2],[4]], [[]], [[1]])
assert dmp_rr_prs_gcd([[]], [[2],[4]], 1, ZZ) == ([[2],[4]], [[]], [[1]])
assert dmp_zz_heu_gcd([[2],[4]], [[]], 1, ZZ) == ([[2],[4]], [[1]], [[]])
assert dmp_rr_prs_gcd([[2],[4]], [[]], 1, ZZ) == ([[2],[4]], [[1]], [[]])
assert dmp_zz_heu_gcd([[2]], [[2]], 1, ZZ) == ([[2]], [[1]], [[1]])
assert dmp_rr_prs_gcd([[2]], [[2]], 1, ZZ) == ([[2]], [[1]], [[1]])
assert dmp_zz_heu_gcd([[-2]], [[2]], 1, ZZ) == ([[2]], [[-1]], [[1]])
assert dmp_rr_prs_gcd([[-2]], [[2]], 1, ZZ) == ([[2]], [[-1]], [[1]])
assert dmp_zz_heu_gcd([[2]], [[-2]], 1, ZZ) == ([[2]], [[1]], [[-1]])
assert dmp_rr_prs_gcd([[2]], [[-2]], 1, ZZ) == ([[2]], [[1]], [[-1]])
assert dmp_zz_heu_gcd([[-2]], [[-2]], 1, ZZ) == ([[2]], [[-1]], [[-1]])
assert dmp_rr_prs_gcd([[-2]], [[-2]], 1, ZZ) == ([[2]], [[-1]], [[-1]])
assert dmp_zz_heu_gcd([[1],[2],[1]], [[1]], 1, ZZ) == ([[1]], [[1], [2], [1]], [[1]])
assert dmp_rr_prs_gcd([[1],[2],[1]], [[1]], 1, ZZ) == ([[1]], [[1], [2], [1]], [[1]])
assert dmp_zz_heu_gcd([[1],[2],[1]], [[2]], 1, ZZ) == ([[1]], [[1], [2], [1]], [[2]])
assert dmp_rr_prs_gcd([[1],[2],[1]], [[2]], 1, ZZ) == ([[1]], [[1], [2], [1]], [[2]])
assert dmp_zz_heu_gcd([[2],[4],[2]], [[2]], 1, ZZ) == ([[2]], [[1], [2], [1]], [[1]])
assert dmp_rr_prs_gcd([[2],[4],[2]], [[2]], 1, ZZ) == ([[2]], [[1], [2], [1]], [[1]])
assert dmp_zz_heu_gcd([[2]], [[2],[4],[2]], 1, ZZ) == ([[2]], [[1]], [[1], [2], [1]])
assert dmp_rr_prs_gcd([[2]], [[2],[4],[2]], 1, ZZ) == ([[2]], [[1]], [[1], [2], [1]])
assert dmp_zz_heu_gcd([[2],[4],[2]], [[1],[1]], 1, ZZ) == ([[1], [1]], [[2], [2]], [[1]])
assert dmp_rr_prs_gcd([[2],[4],[2]], [[1],[1]], 1, ZZ) == ([[1], [1]], [[2], [2]], [[1]])
assert dmp_zz_heu_gcd([[1],[1]], [[2],[4],[2]], 1, ZZ) == ([[1], [1]], [[1]], [[2], [2]])
assert dmp_rr_prs_gcd([[1],[1]], [[2],[4],[2]], 1, ZZ) == ([[1], [1]], [[1]], [[2], [2]])
assert dmp_zz_heu_gcd([[[[1,2,1]]]], [[[[2,2]]]], 3, ZZ) == ([[[[1,1]]]], [[[[1,1]]]], [[[[2]]]])
assert dmp_rr_prs_gcd([[[[1,2,1]]]], [[[[2,2]]]], 3, ZZ) == ([[[[1,1]]]], [[[[1,1]]]], [[[[2]]]])
f, g = [[[[1,2,1],[1,1],[]]]], [[[[1,2,1]]]]
h, cff, cfg = [[[[1,1]]]], [[[[1,1],[1],[]]]], [[[[1,1]]]]
assert dmp_zz_heu_gcd(f, g, 3, ZZ) == (h, cff, cfg)
assert dmp_rr_prs_gcd(f, g, 3, ZZ) == (h, cff, cfg)
assert dmp_zz_heu_gcd(g, f, 3, ZZ) == (h, cfg, cff)
assert dmp_rr_prs_gcd(g, f, 3, ZZ) == (h, cfg, cff)
f, g, h = dmp_fateman_poly_F_1(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(4, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 4, ZZ)
assert H == h and dmp_mul(H, cff, 4, ZZ) == f \
and dmp_mul(H, cfg, 4, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(6, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 6, ZZ)
assert H == h and dmp_mul(H, cff, 6, ZZ) == f \
and dmp_mul(H, cfg, 6, ZZ) == g
f, g, h = dmp_fateman_poly_F_1(8, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 8, ZZ)
assert H == h and dmp_mul(H, cff, 8, ZZ) == f \
and dmp_mul(H, cfg, 8, ZZ) == g
f, g, h = dmp_fateman_poly_F_2(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_3(2, ZZ)
H, cff, cfg = dmp_zz_heu_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
H, cff, cfg = dmp_rr_prs_gcd(f, g, 2, ZZ)
assert H == h and dmp_mul(H, cff, 2, ZZ) == f \
and dmp_mul(H, cfg, 2, ZZ) == g
f, g, h = dmp_fateman_poly_F_3(4, ZZ)
H, cff, cfg = dmp_inner_gcd(f, g, 4, ZZ)
assert H == h and dmp_mul(H, cff, 4, ZZ) == f \
and dmp_mul(H, cfg, 4, ZZ) == g
f = [[QQ(1,2)],[QQ(1)],[QQ(1,2)]]
g = [[QQ(1,2)],[QQ(1,2)]]
h = [[QQ(1)],[QQ(1)]]
assert dmp_qq_heu_gcd(f, g, 1, QQ) == (h, g, [[QQ(1,2)]])
assert dmp_ff_prs_gcd(f, g, 1, QQ) == (h, g, [[QQ(1,2)]])