gauss elimination determinant calculator, Python 3

gauss elimination determinant calculator

matrix = [[3, 1, 1, 1, 3, 3, 1, 2, 1, 2, 1, 1, 0, 3, 0, 3, 2, 0, 3, 3, 3, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 0, 3], [1, 1, 0, 1, 2, 1, 2, 2, 3, 3, 0, 2, 3, 2, 3, 0, 1, 0, 2, 3, 3, 1, 2, 1, 3, 3, 1, 0, 0, 0, 3, 2, 3, 3, 3, 0, 1, 3, 0, 0], [3, 1, 2, 0, 1, 1, 1, 1, 1, 0, 3, 1, 0, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 0, 0, 3, 1, 2, 0, 1, 0, 3, 3, 0, 3, 2, 3, 3], [0, 1, 0, 3, 2, 3, 3, 3, 0, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 3, 1, 0, 1, 3, 3, 2, 0, 2, 3, 2, 3, 3, 3, 3, 1, 2, 2, 2], [0, 1, 0, 0, 2, 3, 0, 2, 0, 1, 3, 1, 1, 0, 2, 1, 2, 1, 2, 3, 0, 2, 1, 0, 0, 3, 0, 2, 0, 0, 2, 2, 3, 3, 0, 2, 3, 3, 1, 3], [0, 0, 0, 0, 1, 2, 2, 0, 3, 1, 1, 3, 3, 0, 0, 1, 3, 1, 2, 0, 1, 3, 2, 1, 2, 1, 2, 3, 2, 3, 1, 1, 3, 3, 0, 2, 2, 1, 0, 0], [1, 2, 3, 1, 3, 2, 2, 3, 3, 0, 2, 2, 3, 1, 1, 2, 0, 0, 2, 0, 1, 3, 3, 1, 2, 1, 2, 3, 3, 2, 3, 3, 0, 1, 3, 2, 3, 0, 3, 2], [3, 0, 1, 0, 1, 1, 0, 3, 3, 3, 0, 2, 1, 1, 2, 2, 3, 3, 3, 0, 3, 2, 1, 0, 3, 1, 2, 3, 2, 1, 3, 3, 3, 1, 0, 0, 3, 2, 3, 1], [2, 0, 1, 3, 2, 2, 0, 2, 1, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 3, 3, 3, 2, 3, 3, 1, 1, 1, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 3, 1], [1, 0, 0, 0, 3, 2, 1, 1, 2, 1, 0, 3, 0, 3, 2, 0, 2, 3, 3, 1, 0, 2, 0, 0, 3, 3, 1, 3, 2, 2, 2, 2, 1, 2, 0, 3, 2, 0, 2, 1], [0, 0, 2, 3, 3, 2, 3, 3, 2, 3, 2, 2, 2, 0, 1, 3, 2, 1, 3, 3, 2, 1, 3, 0, 0, 0, 1, 1, 2, 0, 1, 3, 3, 2, 0, 3, 1, 1, 1, 2], [2, 1, 0, 2, 3, 3, 1, 1, 3, 3, 3, 1, 2, 1, 2, 0, 0, 3, 3, 2, 1, 3, 2, 3, 3, 1, 0, 3, 3, 3, 1, 1, 2, 3, 0, 0, 1, 2, 2, 0], [1, 3, 1, 2, 3, 2, 3, 3, 2, 3, 1, 2, 3, 0, 0, 0, 3, 0, 1, 0, 2, 3, 2, 3, 3, 3, 2, 2, 2, 0, 0, 3, 1, 1, 0, 3, 1, 1, 3, 2], [0, 1, 1, 2, 3, 1, 0, 0, 0, 1, 3, 0, 3, 2, 1, 2, 2, 1, 2, 1, 3, 1, 1, 1, 2, 2, 1, 2, 2, 0, 3, 3, 0, 2, 0, 2, 0, 1, 0, 0], [3, 0, 0, 1, 1, 3, 1, 3, 2, 3, 0, 1, 1, 3, 0, 3, 3, 2, 2, 2, 1, 2, 0, 3, 2, 2, 2, 0, 3, 3, 1, 1, 2, 0, 1, 3, 1, 0, 3, 0], [1, 1, 2, 3, 3, 0, 3, 3, 0, 0, 0, 2, 1, 1, 1, 3, 3, 1, 0, 0, 2, 0, 0, 1, 1, 3, 1, 1, 1, 0, 2, 2, 0, 1, 0, 3, 3, 3, 3, 3], [1, 3, 3, 0, 2, 2, 3, 3, 0, 0, 1, 0, 3, 1, 1, 3, 3, 0, 0, 3, 2, 1, 1, 1, 3, 2, 1, 3, 1, 0, 2, 3, 1, 3, 2, 1, 2, 3, 0, 1], [2, 2, 0, 1, 3, 2, 3, 0, 0, 0, 2, 2, 0, 2, 2, 3, 3, 3, 0, 3, 0, 1, 3, 2, 2, 0, 1, 3, 1, 0, 0, 0, 2, 2, 0, 2, 1, 0, 3, 3], [2, 0, 0, 3, 3, 2, 3, 2, 0, 0, 3, 1, 0, 2, 1, 1, 2, 2, 2, 0, 0, 0, 0, 3, 1, 1, 3, 3, 2, 2, 1, 0, 0, 2, 2, 1, 3, 1, 0, 0], [3, 2, 3, 0, 2, 1, 0, 2, 3, 0, 2, 3, 1, 1, 1, 3, 1, 1, 2, 1, 0, 2, 1, 3, 0, 3, 1, 3, 1, 3, 0, 2, 1, 1, 2, 1, 0, 3, 2, 1], [3, 2, 3, 1, 0, 3, 1, 1, 1, 2, 3, 3, 0, 3, 2, 3, 2, 0, 1, 3, 1, 3, 1, 3, 3, 1, 1, 1, 3, 1, 0, 3, 0, 3, 1, 3, 2, 0, 1, 3], [2, 0, 0, 1, 0, 0, 3, 0, 2, 1, 0, 2, 2, 1, 3, 0, 3, 1, 2, 3, 3, 1, 0, 1, 0, 3, 2, 3, 3, 1, 1, 3, 3, 1, 0, 0, 3, 0, 3, 3], [0, 3, 1, 0, 2, 2, 1, 1, 0, 3, 0, 1, 3, 2, 3, 0, 3, 0, 2, 2, 0, 2, 2, 1, 2, 3, 3, 2, 3, 2, 0, 2, 2, 3, 3, 1, 1, 0, 2, 3], [0, 1, 3, 2, 2, 3, 2, 0, 1, 3, 3, 3, 0, 1, 1, 3, 1, 0, 2, 1, 0, 1, 3, 1, 3, 0, 2, 3, 3, 2, 2, 2, 1, 3, 1, 0, 3, 1, 3, 1], [1, 1, 0, 0, 2, 2, 3, 3, 0, 1, 0, 2, 1, 2, 3, 3, 1, 1, 3, 1, 2, 0, 2, 1, 3, 2, 3, 2, 3, 0, 0, 3, 0, 1, 3, 0, 3, 3, 0, 1], [3, 0, 0, 1, 2, 0, 2, 1, 2, 2, 3, 0, 2, 0, 2, 1, 2, 0, 1, 1, 0, 2, 0, 1, 1, 2, 0, 3, 0, 3, 3, 1, 0, 0, 1, 1, 1, 2, 2, 3], [0, 1, 2, 0, 1, 0, 2, 0, 2, 3, 2, 1, 0, 3, 3, 3, 1, 0, 1, 2, 0, 3, 3, 2, 2, 0, 0, 2, 2, 3, 1, 3, 0, 3, 2, 3, 2, 2, 0, 1], [0, 0, 3, 2, 0, 1, 2, 0, 3, 0, 3, 0, 3, 2, 3, 1, 3, 2, 2, 3, 0, 2, 1, 2, 0, 2, 1, 0, 3, 0, 2, 2, 2, 3, 3, 0, 3, 2, 3, 0], [1, 1, 2, 1, 1, 1, 3, 1, 1, 2, 3, 3, 3, 3, 2, 2, 1, 0, 3, 0, 2, 0, 0, 3, 3, 2, 1, 3, 0, 3, 1, 3, 2, 3, 2, 2, 2, 3, 2, 0], [1, 2, 2, 1, 1, 0, 3, 0, 3, 2, 3, 1, 3, 2, 2, 0, 1, 1, 1, 3, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0], [0, 2, 2, 2, 0, 0, 0, 2, 3, 1, 3, 1, 1, 0, 0, 1, 3, 1, 0, 0, 1, 2, 2, 3, 2, 0, 0, 2, 0, 2, 1, 1, 3, 3, 0, 0, 1, 2, 3, 0], [0, 3, 0, 3, 1, 1, 3, 0, 3, 3, 1, 0, 3, 2, 2, 1, 2, 0, 1, 3, 2, 2, 0, 3, 2, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 3, 0, 0, 2], [1, 1, 1, 1, 2, 0, 1, 2, 2, 3, 0, 0, 0, 2, 1, 1, 0, 3, 1, 1, 2, 2, 0, 3, 3, 1, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 3, 1], [2, 0, 0, 1, 3, 0, 0, 0, 3, 3, 0, 2, 1, 0, 3, 1, 2, 1, 3, 0, 2, 0, 0, 1, 1, 3, 2, 1, 0, 0, 3, 1, 3, 3, 2, 1, 0, 3, 3, 2], [0, 0, 0, 3, 1, 1, 2, 2, 3, 1, 2, 0, 0, 2, 0, 2, 0, 3, 0, 1, 3, 0, 2, 1, 2, 0, 3, 3, 2, 2, 2, 0, 3, 1, 3, 3, 3, 3, 0, 0], [0, 1, 1, 2, 0, 0, 3, 1, 3, 2, 2, 0, 2, 2, 0, 3, 1, 1, 3, 1, 0, 1, 3, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 3, 1, 0, 0, 1, 1, 2], [2, 3, 1, 1, 2, 1, 3, 1, 2, 2, 0, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 3, 1, 2, 1, 1, 0, 0, 3, 3, 3, 3, 3, 3, 1, 2, 2, 1, 2, 3], [1, 3, 2, 3, 1, 1, 1, 3, 0, 2, 0, 0, 1, 1, 1, 0, 1, 3, 3, 1, 0, 1, 1, 0, 3, 2, 1, 2, 2, 2, 2, 0, 3, 1, 0, 1, 0, 2, 3, 2], [3, 1, 2, 0, 1, 3, 2, 1, 1, 2, 1, 2, 3, 2, 1, 2, 1, 3, 2, 2, 1, 2, 0, 0, 3, 1, 3, 1, 3, 3, 1, 1, 3, 0, 0, 3, 0, 2, 1, 0], [3, 3, 3, 3, 1, 1, 3, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 0, 1, 0, 3, 3, 2, 1, 0, 1, 0, 2, 3, 3, 0, 1, 2, 0, 3, 3, 3, 0, 1, 1]]
#matrix = [[3,1,0,2,6],
#          [4,0,2,1,3],
#          [2,1,0,1,2],
#          [4,3,2,5,1],
#          [0,2,1,0,3]]
def find_upper_triangular_matrix(matrix):
    i, j, k, n = 0, -1, 0, 40        # i timi tou "n" prepei na allazei me ti diastasi tou pinaka 
    while i < n - 1:
        k = i
        while k < n - 1:
              j = -1
              var = matrix[k + 1][i]
              for e in matrix[i]:
#                  var = matrix[k + 1][i]
#                  print ("var =", var)
                  j = j + 1
                  if e == 0:
                      matrix[k + 1][j] = matrix[k + 1][j] - e  # (6)
#                      continue   (2)
                  else:
#                      e = var * e / matrix[i][i]
                      e = e / matrix[i][i] * var
                      matrix[k + 1][j] = matrix[k + 1][j] - e 
#                      print ("k =", k, "", "j =", j, "", "matrix[k + 1][j] = ", matrix[k + 1][j])
#                      j = j + 1  (1)
              if i == 0:
                 j = -1  #(5)
              else:
                  j = i
              k = k + 1
        j = j + 1  #  (4)
        i = i + 1
#        print ('matrix =', matrix)
    i, product = 1, matrix[0][0]
    while i < n:
#        print ("matrix[0:7] =", matrix[0:7])
        product = product * matrix[i][i]
#        print ("matrix[i][i] =", matrix[i][i], "", "product =", product)
        i = i + 1
    return matrix, product

print (find_upper_triangular_matrix(matrix))


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