def test_dup_gcdex():
f = dup_normal([1, -2, -6, 12, 15], QQ)
g = dup_normal([1, 1, -4, -4], QQ)
s = [QQ(-1, 5), QQ(3, 5)]
t = [QQ(1, 5), QQ(-6, 5), QQ(2)]
h = [QQ(1), QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
f = dup_normal([1, 4, 0, -1, 1], QQ)
g = dup_normal([1, 0, -1, 1], QQ)
s, t, h = dup_gcdex(f, g, QQ)
S, T, H = dup_gcdex(g, f, QQ)
assert dup_add(dup_mul(s, f, QQ), dup_mul(t, g, QQ), QQ) == h
assert dup_add(dup_mul(S, g, QQ), dup_mul(T, f, QQ), QQ) == H
f = dup_normal([2, 0], QQ)
g = dup_normal([1, 0, -16], QQ)
s = [QQ(1, 32), QQ(0)]
t = [QQ(-1, 16)]
h = [QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
def test_dup_gcdex():
f = dup_normal([1,-2,-6,12,15], QQ)
g = dup_normal([1,1,-4,-4], QQ)
s = [QQ(-1,5),QQ(3,5)]
t = [QQ(1,5),QQ(-6,5),QQ(2)]
h = [QQ(1),QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
f = dup_normal([1,4,0,-1,1], QQ)
g = dup_normal([1,0,-1,1], QQ)
s, t, h = dup_gcdex(f, g, QQ)
S, T, H = dup_gcdex(g, f, QQ)
assert dup_add(dup_mul(s, f, QQ),
dup_mul(t, g, QQ), QQ) == h
assert dup_add(dup_mul(S, g, QQ),
dup_mul(T, f, QQ), QQ) == H
f = dup_normal([2,0], QQ)
g = dup_normal([1,0,-16], QQ)
s = [QQ(1,32),QQ(0)]
t = [QQ(-1,16)]
h = [QQ(1)]
assert dup_half_gcdex(f, g, QQ) == (s, h)
assert dup_gcdex(f, g, QQ) == (s, t, h)
def half_gcdex(f, g):
"""Half extended Euclidean algorithm, if univariate. """
lev, dom, per, F, G = f.unify(g)
if not lev:
s, h = dup_half_gcdex(F, G, dom)
return per(s), per(h)
else:
raise ValueError('univariate polynomial expected')
def half_gcdex(f, g):
"""Half extended Euclidean algorithm, if univariate. """
lev, dom, per, F, G = f.unify(g)
if not lev:
s, h = dup_half_gcdex(F, G, dom)
return per(s), per(h)
else:
raise ValueError('univariate polynomial expected')