Exemplo n.º 1
0
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)
Exemplo n.º 2
0
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
Exemplo n.º 3
0
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