How to take the index of a variable in sagemath?

edit

It's better to set things up more conveniently from the beginning. Symbolically:

indices = [(i,j) for i in range(3) for j in range(5)]
variables = [var('y_{}_{}'.format(i,j)) for (i,j) in indices]
y = dict(zip(indices, variables))
M = matrix(SR, 3, 5, variables)

Or with polynomials:

indices = [(i,j) for i in range(3) for j in range(5)]
R = PolynomialRing(QQ, ['y_{}_{}'.format(i,j) for (i,j) in indices])
y = dict(zip(indices, R.gens()))
M = matrix(R, 3, 5, R.gens())

In both cases:

sage: y[2,0]
y_2_0
sage: M[1,3] is y[1,3]
True

One possible solution is to construct/return not only a matrix but also a mapping (dict) of variables to their indices - like:

def symbolic_matrix(root,m,n):
    var2ind = {}
    mlist=[]
    for i in range(m):
        for j in range(n):
            v = SR(root+'_'+str(i)+'_'+str(j))
            var2ind[v] = [i,j]
            mlist.append(v)
    return Matrix(SR,m,n,mlist), var2ind

k,n=4,8
r1, v2i = symbolic_matrix('y',k,n)

v2i[r1[2,3]]

I think the easiest thing to do, maybe the only thing to do, is to parse the name of the variable as a string. Try str(r1[0,0]).split('_'), for example. If you let a = r1[0,0], then str(a).split('_')[1:] will give you the two indices as strings, so you could do [int(s) for s in str(a).split('_')[1:]].