# Load MatrixUtils before!
# All indices (of vectors, matrices) are assumed to start at 0
# B is assumed to be a list (otherwise replace B by B.list() )

def step_3(A,c,B,i):              

    z = A.matrix_from_rows(B).solve_left(c)
    y = A.matrix_from_rows(B).solve_left(-A.row(i))

    r = ratios(z,y)

    l = infinity
    j = -1
    for k in range (A.ncols()):

       if (r[k] >= 0):
           if (r[k] < l):
               l = r[k]
               j = k
    
    if (j < 0):
        print "PL n'est pas admissible"
        return []

    B[j] = i

    return B