def test_dmp_subresultants():
assert dmp_resultant([[]], [[]], 1, ZZ) == []
assert dmp_prs_resultant([[]], [[]], 1, ZZ)[0] == []
assert dmp_zz_collins_resultant([[]], [[]], 1, ZZ) == []
assert dmp_qq_collins_resultant([[]], [[]], 1, ZZ) == []
assert dmp_resultant([[ZZ(1)]], [[]], 1, ZZ) == []
assert dmp_resultant([[ZZ(1)]], [[]], 1, ZZ) == []
assert dmp_resultant([[ZZ(1)]], [[]], 1, ZZ) == []
assert dmp_resultant([[]], [[ZZ(1)]], 1, ZZ) == []
assert dmp_prs_resultant([[]], [[ZZ(1)]], 1, ZZ)[0] == []
assert dmp_zz_collins_resultant([[]], [[ZZ(1)]], 1, ZZ) == []
assert dmp_qq_collins_resultant([[]], [[ZZ(1)]], 1, ZZ) == []
f = dmp_normal([[3, 0], [], [-1, 0, 0, -4]], 1, ZZ)
g = dmp_normal([[1], [1, 0, 0, 0], [-9]], 1, ZZ)
a = dmp_normal([[3, 0, 0, 0, 0], [1, 0, -27, 4]], 1, ZZ)
b = dmp_normal([[-3, 0, 0, -12, 1, 0, -54, 8, 729, -216, 16]], 1, ZZ)
r = dmp_LC(b, ZZ)
assert dmp_subresultants(f, g, 1, ZZ) == [f, g, a, b]
assert dmp_resultant(f, g, 1, ZZ) == r
assert dmp_prs_resultant(f, g, 1, ZZ)[0] == r
assert dmp_zz_collins_resultant(f, g, 1, ZZ) == r
assert dmp_qq_collins_resultant(f, g, 1, ZZ) == r
f = dmp_normal([[-1], [], [], [5]], 1, ZZ)
g = dmp_normal([[3, 1], [], []], 1, ZZ)
a = dmp_normal([[45, 30, 5]], 1, ZZ)
b = dmp_normal([[675, 675, 225, 25]], 1, ZZ)
r = dmp_LC(b, ZZ)
assert dmp_subresultants(f, g, 1, ZZ) == [f, g, a]
assert dmp_resultant(f, g, 1, ZZ) == r
assert dmp_prs_resultant(f, g, 1, ZZ)[0] == r
assert dmp_zz_collins_resultant(f, g, 1, ZZ) == r
assert dmp_qq_collins_resultant(f, g, 1, ZZ) == r
f = [[[[[6]]]], [[[[-3]]], [[[-2]], [[]]]], [[[[1]], [[]]], [[[]]]]]
g = [[[[[1]]]], [[[[-1], [-1, 0]]]], [[[[1, 0], []]]]]
r = [[[[1]], [[-3], [-3, 0]], [[9, 0], []]],
[[[-2], [-2, 0]], [[6], [12, 0], [6, 0, 0]],
[[-18, 0], [-18, 0, 0], []]],
[[[4, 0], []], [[-12, 0], [-12, 0, 0], []], [[36, 0, 0], [], []]]]
assert dmp_zz_collins_resultant(f, g, 4, ZZ) == r
f = [[[[[QQ(1, 1)]]]], [[[[QQ(-1, 2)]]], [[[QQ(-1, 3)]], [[]]]],
[[[[QQ(1, 6)]], [[]]], [[[]]]]]
g = [[[[[QQ(1, 1)]]]], [[[[QQ(-1, 1)], [QQ(-1, 1), QQ(0, 1)]]]],
[[[[QQ(1, 1), QQ(0, 1)], []]]]]
r = [[[[QQ(1, 36)]], [[QQ(-1, 12)], [QQ(-1, 12), QQ(0, 1)]],
[[QQ(1, 4), QQ(0, 1)], []]],
[[[QQ(-1, 18)], [QQ(-1, 18), QQ(0, 1)]],
[[QQ(1, 6)], [QQ(1, 3), QQ(0, 1)], [QQ(1, 6),
QQ(0, 1),
QQ(0, 1)]],
[[QQ(-1, 2), QQ(0, 1)], [QQ(-1, 2), QQ(0, 1),
QQ(0, 1)], []]],
[[[QQ(1, 9), QQ(0, 1)], []],
[[QQ(-1, 3), QQ(0, 1)], [QQ(-1, 3), QQ(0, 1),
QQ(0, 1)], []],
[[QQ(1, 1), QQ(0, 1), QQ(0, 1)], [], []]]]
assert dmp_qq_collins_resultant(f, g, 4, QQ) == r
def test_dmp_subresultants():
assert dmp_resultant([[]], [[]], 1, ZZ) == []
assert dmp_prs_resultant([[]], [[]], 1, ZZ)[0] == []
assert dmp_zz_collins_resultant([[]], [[]], 1, ZZ) == []
assert dmp_qq_collins_resultant([[]], [[]], 1, ZZ) == []
assert dmp_resultant([[ZZ(1)]], [[]], 1, ZZ) == []
assert dmp_resultant([[ZZ(1)]], [[]], 1, ZZ) == []
assert dmp_resultant([[ZZ(1)]], [[]], 1, ZZ) == []
assert dmp_resultant([[]], [[ZZ(1)]], 1, ZZ) == []
assert dmp_prs_resultant([[]], [[ZZ(1)]], 1, ZZ)[0] == []
assert dmp_zz_collins_resultant([[]], [[ZZ(1)]], 1, ZZ) == []
assert dmp_qq_collins_resultant([[]], [[ZZ(1)]], 1, ZZ) == []
f = dmp_normal([[3,0],[],[-1,0,0,-4]], 1, ZZ)
g = dmp_normal([[1],[1,0,0,0],[-9]], 1, ZZ)
a = dmp_normal([[3,0,0,0,0],[1,0,-27,4]], 1, ZZ)
b = dmp_normal([[-3,0,0,-12,1,0,-54,8,729,-216,16]], 1, ZZ)
r = dmp_LC(b, ZZ)
assert dmp_subresultants(f, g, 1, ZZ) == [f, g, a, b]
assert dmp_resultant(f, g, 1, ZZ) == r
assert dmp_prs_resultant(f, g, 1, ZZ)[0] == r
assert dmp_zz_collins_resultant(f, g, 1, ZZ) == r
assert dmp_qq_collins_resultant(f, g, 1, ZZ) == r
f = dmp_normal([[-1],[],[],[5]], 1, ZZ)
g = dmp_normal([[3,1],[],[]], 1, ZZ)
a = dmp_normal([[45,30,5]], 1, ZZ)
b = dmp_normal([[675,675,225,25]], 1, ZZ)
r = dmp_LC(b, ZZ)
assert dmp_subresultants(f, g, 1, ZZ) == [f, g, a]
assert dmp_resultant(f, g, 1, ZZ) == r
assert dmp_prs_resultant(f, g, 1, ZZ)[0] == r
assert dmp_zz_collins_resultant(f, g, 1, ZZ) == r
assert dmp_qq_collins_resultant(f, g, 1, ZZ) == r
f = [[[[[6]]]], [[[[-3]]], [[[-2]], [[]]]], [[[[1]], [[]]], [[[]]]]]
g = [[[[[1]]]], [[[[-1], [-1, 0]]]], [[[[1, 0], []]]]]
r = [[[[1]], [[-3], [-3, 0]], [[9, 0], []]], [[[-2], [-2, 0]], [[6],
[12, 0], [6, 0, 0]], [[-18, 0], [-18, 0, 0], []]], [[[4, 0],
[]], [[-12, 0], [-12, 0, 0], []], [[36, 0, 0], [], []]]]
assert dmp_zz_collins_resultant(f, g, 4, ZZ) == r
f = [[[[[QQ(1,1)]]]], [[[[QQ(-1,2)]]], [[[QQ(-1,3)]], [[]]]], [[[[QQ(1,6)]], [[]]], [[[]]]]]
g = [[[[[QQ(1,1)]]]], [[[[QQ(-1,1)], [QQ(-1,1), QQ(0, 1)]]]], [[[[QQ(1,1), QQ(0,1)], []]]]]
r = [[[[QQ(1,36)]], [[QQ(-1,12)], [QQ(-1,12), QQ(0,1)]], [[QQ(1,4), QQ(0,1)], []]],
[[[QQ(-1,18)], [QQ(-1,18), QQ(0,1)]], [[QQ(1,6)], [QQ(1,3), QQ(0,1)], [QQ(1,6),
QQ(0,1), QQ(0,1)]], [[QQ(-1,2), QQ(0,1)], [QQ(-1,2), QQ(0,1), QQ(0,1)], []]],
[[[QQ(1,9), QQ(0,1)], []], [[QQ(-1,3), QQ(0,1)], [QQ(-1,3), QQ(0,1), QQ(0,1)], []],
[[QQ(1,1), QQ(0,1), QQ(0,1)], [], []]]]
assert dmp_qq_collins_resultant(f, g, 4, QQ) == r
def subresultants(f, g):
"""Computes subresultant PRS sequence of `f` and `g`. """
lev, dom, per, F, G = f.unify(g)
R = dmp_subresultants(F, G, lev, dom)
return map(per, R)
def subresultants(f, g):
"""Computes subresultant PRS sequence of `f` and `g`. """
lev, dom, per, F, G = f.unify(g)
R = dmp_subresultants(F, G, lev, dom)
return map(per, R)