Calculate the determinant by Gaussian method (Python - Lab)

gauss_det.py

import numpy as np


def mcd(x, y):
    while y != 0:
        x, y = y, x % y
    return x


def equiv(A, m, n):
    x, y = A[m, m], A[n, m]
    if x == 0 or y == 0:
        return 1
    z = mcd(x, y)
    x /= z
    y /= z
    if x != y:
        A[m] *= y
        A[n] *= x
    A[n] -= A[m]
    return 1 if x == y else x * y


def det(A):
    q, d, n = 1, 1, len(A)
    for i in range(n):
        for j in range(n - i - 1):
            q *= equiv(A, i, j + i + 1)
        d *= A[i, i]
    return d / q


a = np.array([
    [2, 0, 2, 4],
    [3, 3, 1, 2],
    [0, 1, 3, 1],
    [4, 1, 7, 1],
], dtype=float)

print(a)
print(np.linalg.det(a))
print("......")
r = det(a)
print(a)
print(r)
print("......")