def main():
operation = sys.argv[1]
if operation == '-a':
p, n, a = read('test.txt')
les = LinearEquationSystem(a, p)
test_accuracy(les)
elif operation == '-g':
gen_test(5, 9, 29, '-s' in sys.argv)
elif operation == '-gauss':
p, n, a = read('test.txt')
les = LinearEquationSystem(a, p)
sol, count = gaussian(les)
if count == 0:
x = sol([])
print('Решение:', x)
print('Ответ верный' if M.mul(les.a, M.t([x]), les.p) == les.b else 'Ответ неверный')
return
while True:
t = input('Введите {} чисел в Z_{} через пробел или -1 для выхода\n'.format(count, les.p))
if t == '-1':
return
x = sol(list(map(lambda el: int(el), t.split())))
print('Решение:', x)
print('Ответ верный' if M.mul(les.a, M.t([x]), les.p) == les.b else 'Ответ неверный')
else:
print('Некорректная операция')
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
def wiedemann1(les: LinearEquationSystem):
a, b, p, n = les.a, M.t(les.b)[0], les.p, les.n
for trial in range(MAX_TRIALS):
bs = [b]
ys = [[0] * n]
ds = [0]
k = 0
while bs[k] != V.zero(n):
u = [random.randint(0, p - 1) for _idx in range(n)]
seq = []
for i in range(2 * (n - ds[k])):
ai = M.power(a, i, p)
aib = M.mul_vec(ai, b, p)
uaib = V.mul_sum(u, aib, p)
seq.append(uaib)
if not len(seq):
break
f = berlekamp(seq, p)
if f is None:
break
ys.append(V.add(ys[k], M.mul_vec(f_tilda(f, a, p), b, p), p))
bs.append(V.add(b, M.mul_vec(a, ys[k + 1], p), p))
ds.append(ds[k] + len(f))
k += 1
if bs[k] != V.zero(n):
print(trial, end='\r')
continue
return V.mul_scalar(ys[k], -1, p)
def test_accuracy(les):
for func, func_name in FUNCS:
x = func(les)
if x is None:
print(func_name, ': ответ не найден')
else:
correct = M.mul(les.a, M.t([x]), les.p) == les.b
print(func_name, ':', x, 'Ответ верный' if correct else 'Ответ неверный')