# return the transition matrix for a graph G
def tm(G):
    A = G.am()
    n = G.order()
    T = []
    for i in xrange(n):
        d = sum(A[i])
        if d > 0:
            rowi = []
            for j in xrange(n):
                rowi.append(1.0*A[i][j]/d)
        else:
            rowi = [0 for j in xrange(n)]
            rowi[i] = 1
        T.append(rowi)
    return matrix(T).transpose()


# print a Sage real matrix with less precision
def matprint(A, precis = 5):
    n = len(A.rows())
    for i in xrange(n):
        print "[",
        for x in A[i]:
            print (str(x)+'      ')[:precis],
        print "]"