Gaussian method programmed objectively

#Basic Gaussian method; Objective programming; Side effects
def gaussian_up(matrix):
    N=len(matrix)
    M=len(matrix[0])
    for k in range(N-1): #stulpeliu indeksai
        if matrix[k][k]==0:
            for l in range(k+1,N+1):
                if l==N:
                    print 'gavom issigimusia matrica'
                    return None
                if matrix[l][k]<>0:
                    matrix[l][k],matrix[k][k]=matrix[k][k],matrix[l][k]
                    break
        else:
            for i in range(k+1,N): #eiluciu indeksaie
                if matrix[i][k]<>0:
                    const=matrix[i][k]/matrix[k][k]
                    matrix[i][k]=0
                    for j in range(k+1,M): matrix[i][j]=matrix[i][j]-const*matrix[k][j]#ka keisim i-tojoje eiluteje
    return matrix
def gaussian_down(matrix):
    #Input and output - matrix of floats
    #Efficiency= (M-N)N*N
    N=len(matrix)
    M=len(matrix[0])
    for k in xrange(N-1,0,-1): #stulpeliai, pagal kuriuos keisim eilutes
        if matrix[k][k]<>0:
            for i in xrange(k-1,-1,-1): #einam per eilutes
                const=matrix[i][k]/matrix[k][k]
                matrix[i][k]=0
                for j in xrange(N,M): matrix[i][j]=matrix[i][j]-matrix[k][j]*const
                #eiluteje keisim visus reikiamo stulpelio skaicius, tada visus, kurie yra ne kvadrate
    return matrix
print
def diag(matrix):
    N,M=len(matrix),len(matrix[0])
    for i in range(N):
        for j in range(N,M): matrix[i][j]=matrix[i][j]/matrix[i][i]
        matrix[i][i]=1.
    return matrix
def gaussian(matrix): return diag(gaussian_down(gaussian_up(matrix)))