def all_solutions(a: list, d, p):
if not any(a):
raise ValueError('Найдена линейно-независимая строка')
n = len(a)
a_mat = [a[:]] + M.unit(n, n)
while len(list(filter(lambda el: el != 0, a_mat[0]))) > 1:
ai = min(filter(lambda el: el != 0, a_mat[0]))
i = a_mat[0].index(ai)
j = next(filter(lambda jj: i != jj and a_mat[0][jj] != 0, range(n)))
q, r, = divmod(a_mat[0][j], a_mat[0][i])
for row in range(n + 1):
a_mat[row][j] = (a_mat[row][j] - a_mat[row][i] * q) % p
lam = max(a_mat[0])
s = a_mat[0].index(lam)
dlam = ratio(d, lam, p)
c = a_mat[1:]
def solution(t):
t.insert(s, dlam)
# t[s:s] = dlam
x = V.zero(n)
for sol_i in range(n):
x = V.add(x, V.mul_scalar(M.column(c, sol_i), t[sol_i], p), p)
return x
return solution
def wiedemann2(les: LinearEquationSystem):
a, b, p, n = les.a, M.t(les.b)[0], les.p, les.n
a_powers = [M.unit(n, n)]
for i in range(1, 2 * n):
a_powers.append(M.mul(a_powers[-1], a, p))
aib = [M.mul_vec(ai, b, p) for ai in a_powers]
k = 0
gs = [[1]]
uk1 = [0, 1] + ([0] * (n - 2))
while Poly.deg(gs[k]) < n and k < n:
seq = []
for i in range(2 * n - Poly.deg(gs[k])):
gab = M.mul_vec(fa(gs[k], a, p), aib[i], p)
ugab = V.mul_sum(uk1, gab, p)
seq.append(ugab)
assert len(seq)
f = berlekamp(seq, p)
gs.append(Poly.mul(f, gs[k], p))
k += 1
uk1 = ([0] * k) + [1] + ([0] * (n - k - 1))
print('k =', k)
g = gs[-1]
x = V.zero(n)
for i in range(Poly.deg(g)):
x = V.add(x, V.mul_scalar(aib[i], -g[i], p), p)
return x