Is there a standard solution for Gauss elimination in Python?

I finally found, that it can be done using LU decomposition. Here the U matrix represents the reduced form of the linear system.

from numpy import array
from scipy.linalg import lu

a = array([[2.,4.,4.,4.],[1.,2.,3.,3.],[1.,2.,2.,2.],[1.,4.,3.,4.]])

pl, u = lu(a, permute_l=True)

Then u reads

array([[ 2.,  4.,  4.,  4.],
       [ 0.,  2.,  1.,  2.],
       [ 0.,  0.,  1.,  1.],
       [ 0.,  0.,  0.,  0.]])

Depending on the solvability of the system this matrix has an upper triangular or trapezoidal structure. In the above case a line of zeros arises, as the matrix has only rank 3.