4.14.2 Substituting indices

Sometimes you will want to substitute one symbolic index with another symbolic or numeric index, for example when calculating one specific element of a tensor expression. This is done with the .subs() method, as it is done for symbols (see Substituting expressions).

You have two possibilities here. You can either substitute the whole index by another index or expression:

    ...
    ex e = indexed(A, mu_co);
    cout << e << " becomes " << e.subs(mu_co == nu) << endl;
     // -> A.mu becomes A~nu
    cout << e << " becomes " << e.subs(mu_co == varidx(0, 4)) << endl;
     // -> A.mu becomes A~0
    cout << e << " becomes " << e.subs(mu_co == 0) << endl;
     // -> A.mu becomes A.0
    ...

The third example shows that trying to replace an index with something that is not an index will substitute the index value instead.

Alternatively, you can substitute the symbol of a symbolic index by another expression:

    ...
    ex e = indexed(A, mu_co);
    cout << e << " becomes " << e.subs(mu_sym == nu_sym) << endl;
     // -> A.mu becomes A.nu
    cout << e << " becomes " << e.subs(mu_sym == 0) << endl;
     // -> A.mu becomes A.0
    ...

As you see, with the second method only the value of the index will get substituted. Its other properties, including its dimension, remain unchanged. If you want to change the dimension of an index you have to substitute the whole index by another one with the new dimension.

Finally, substituting the base expression of an indexed object works as expected:

    ...
    ex e = indexed(A, mu_co);
    cout << e << " becomes " << e.subs(A == A+B) << endl;
     // -> A.mu becomes (B+A).mu
    ...