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 test_gf_arith():
assert gf_neg([], 11, ZZ) == []
assert gf_neg([1], 11, ZZ) == [10]
assert gf_neg([1,2,3], 11, ZZ) == [10,9,8]
assert gf_add_ground([], 0, 11, ZZ) == []
assert gf_sub_ground([], 0, 11, ZZ) == []
assert gf_add_ground([], 3, 11, ZZ) == [3]
assert gf_sub_ground([], 3, 11, ZZ) == [8]
assert gf_add_ground([1], 3, 11, ZZ) == [4]
assert gf_sub_ground([1], 3, 11, ZZ) == [9]
assert gf_add_ground([8], 3, 11, ZZ) == []
assert gf_sub_ground([3], 3, 11, ZZ) == []
assert gf_add_ground([1,2,3], 3, 11, ZZ) == [1,2,6]
assert gf_sub_ground([1,2,3], 3, 11, ZZ) == [1,2,0]
assert gf_mul_ground([], 0, 11, ZZ) == []
assert gf_mul_ground([], 1, 11, ZZ) == []
assert gf_mul_ground([1], 0, 11, ZZ) == []
assert gf_mul_ground([1], 1, 11, ZZ) == [1]
assert gf_mul_ground([1,2,3], 0, 11, ZZ) == []
assert gf_mul_ground([1,2,3], 1, 11, ZZ) == [1,2,3]
assert gf_mul_ground([1,2,3], 7, 11, ZZ) == [7,3,10]
assert gf_add([], [], 11, ZZ) == []
assert gf_add([1], [], 11, ZZ) == [1]
assert gf_add([], [1], 11, ZZ) == [1]
assert gf_add([1], [1], 11, ZZ) == [2]
assert gf_add([1], [2], 11, ZZ) == [3]
assert gf_add([1,2], [1], 11, ZZ) == [1,3]
assert gf_add([1], [1,2], 11, ZZ) == [1,3]
assert gf_add([1,2,3], [8,9,10], 11, ZZ) == [9,0,2]
assert gf_sub([], [], 11, ZZ) == []
assert gf_sub([1], [], 11, ZZ) == [1]
assert gf_sub([], [1], 11, ZZ) == [10]
assert gf_sub([1], [1], 11, ZZ) == []
assert gf_sub([1], [2], 11, ZZ) == [10]
assert gf_sub([1,2], [1], 11, ZZ) == [1,1]
assert gf_sub([1], [1,2], 11, ZZ) == [10,10]
assert gf_sub([3,2,1], [8,9,10], 11, ZZ) == [6,4,2]
assert gf_add_mul([1,5,6], [7,3], [8,0,6,1], 11, ZZ) == [1,2,10,8,9]
assert gf_sub_mul([1,5,6], [7,3], [8,0,6,1], 11, ZZ) == [10,9,3,2,3]
assert gf_mul([], [], 11, ZZ) == []
assert gf_mul([], [1], 11, ZZ) == []
assert gf_mul([1], [], 11, ZZ) == []
assert gf_mul([1], [1], 11, ZZ) == [1]
assert gf_mul([5], [7], 11, ZZ) == [2]
assert gf_mul([3,0,0,6,1,2], [4,0,1,0], 11, ZZ) == [1,0,3,2,4,3,1,2,0]
assert gf_mul([4,0,1,0], [3,0,0,6,1,2], 11, ZZ) == [1,0,3,2,4,3,1,2,0]
assert gf_mul([2,0,0,1,7], [2,0,0,1,7], 11, ZZ) == [4,0,0,4,6,0,1,3,5]
assert gf_sqr([], 11, ZZ) == []
assert gf_sqr([2], 11, ZZ) == [4]
assert gf_sqr([1,2], 11, ZZ) == [1,4,4]
assert gf_sqr([2,0,0,1,7], 11, ZZ) == [4,0,0,4,6,0,1,3,5]