def test_gf_division():
raises(ZeroDivisionError, lambda: gf_div([1,2,3], [], 11, ZZ))
raises(ZeroDivisionError, lambda: gf_rem([1,2,3], [], 11, ZZ))
raises(ZeroDivisionError, lambda: gf_quo([1,2,3], [], 11, ZZ))
raises(ZeroDivisionError, lambda: gf_quo([1,2,3], [], 11, ZZ))
assert gf_div([1], [1,2,3], 7, ZZ) == ([], [1])
assert gf_rem([1], [1,2,3], 7, ZZ) == [1]
assert gf_quo([1], [1,2,3], 7, ZZ) == []
f, g, q, r = [5,4,3,2,1,0], [1,2,3], [5,1,0,6], [3,3]
assert gf_div(f, g, 7, ZZ) == (q, r)
assert gf_rem(f, g, 7, ZZ) == r
assert gf_quo(f, g, 7, ZZ) == q
raises(ExactQuotientFailed, lambda: gf_exquo(f, g, 7, ZZ))
f, g, q, r = [5,4,3,2,1,0], [1,2,3,0], [5,1,0], [6,1,0]
assert gf_div(f, g, 7, ZZ) == (q, r)
assert gf_rem(f, g, 7, ZZ) == r
assert gf_quo(f, g, 7, ZZ) == q
raises(ExactQuotientFailed, lambda: gf_exquo(f, g, 7, ZZ))
assert gf_quo([1,2,1], [1,1], 11, ZZ) == [1,1]
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
def mul(self, x, y):
return gf_rem(gf_mul(x, y, self.p, ZZ), self.reducing, self.p, ZZ)
def mul(self, x: list, y: list) -> list:
return gf_rem(gf_mul(x, y, self.p, ZZ), self.reducing, self.p, ZZ)
