def test_gf_shift():
f = [1,2,3,4,5]
assert gf_lshift([], 5, ZZ) == []
assert gf_rshift([], 5, ZZ) == ([], [])
assert gf_lshift(f, 1, ZZ) == [1,2,3,4,5,0]
assert gf_lshift(f, 2, ZZ) == [1,2,3,4,5,0,0]
assert gf_rshift(f, 0, ZZ) == (f, [])
assert gf_rshift(f, 1, ZZ) == ([1,2,3,4], [5])
assert gf_rshift(f, 3, ZZ) == ([1,2], [3,4,5])
assert gf_rshift(f, 5, ZZ) == ([], f)
def dup_zz_diophantine(F, m, p, K):
"""Wang/EEZ: Solve univariate Diophantine equations. """
if len(F) == 2:
a, b = F
f = gf_from_int_poly(a, p)
g = gf_from_int_poly(b, p)
s, t, G = gf_gcdex(g, f, p, K)
s = gf_lshift(s, m, K)
t = gf_lshift(t, m, K)
q, s = gf_div(s, f, p, K)
t = gf_add_mul(t, q, g, p, K)
s = gf_to_int_poly(s, p)
t = gf_to_int_poly(t, p)
result = [s, t]
else:
G = [F[-1]]
for f in reversed(F[1:-1]):
G.insert(0, dup_mul(f, G[0], K))
S, T = [], [[1]]
for f, g in zip(F, G):
t, s = dmp_zz_diophantine([g, f], T[-1], [], 0, p, 1, K)
T.append(t)
S.append(s)
result, S = [], S + [T[-1]]
for s, f in zip(S, F):
s = gf_from_int_poly(s, p)
f = gf_from_int_poly(f, p)
r = gf_rem(gf_lshift(s, m, K), f, p, K)
s = gf_to_int_poly(r, p)
result.append(s)
return result
def dup_zz_diophantine(F, m, p, K):
"""Wang/EEZ: Solve univariate Diophantine equations. """
if len(F) == 2:
a, b = F
f = gf_from_int_poly(a, p)
g = gf_from_int_poly(b, p)
s, t, G = gf_gcdex(g, f, p, K)
s = gf_lshift(s, m, K)
t = gf_lshift(t, m, K)
q, s = gf_div(s, f, p, K)
t = gf_add_mul(t, q, g, p, K)
s = gf_to_int_poly(s, p)
t = gf_to_int_poly(t, p)
result = [s, t]
else:
G = [F[-1]]
for f in reversed(F[1:-1]):
G.insert(0, dup_mul(f, G[0], K))
S, T = [], [[1]]
for f, g in zip(F, G):
t, s = dmp_zz_diophantine([g, f], T[-1], [], 0, p, 1, K)
T.append(t)
S.append(s)
result, S = [], S + [T[-1]]
for s, f in zip(S, F):
s = gf_from_int_poly(s, p)
f = gf_from_int_poly(f, p)
r = gf_rem(gf_lshift(s, m, K), f, p, K)
s = gf_to_int_poly(r, p)
result.append(s)
return result