Pattern matching based on free index?

Question

Is there a way to define patterns for use in substitute or zoom containing a fixed free index? Indices in patterns seem to always treated as wildcards, meaning x^{a} matches x^{b} as well. Whereas this is often what I want, there are many cases where I want to select terms based on a fixed free index, so x^{a} should match x^{a} only, not x^{b} for a dummy or another free index b. Is there a way to achieve this?

Answer 1

There isn't a pattern for that, but you can simulate it by first contracting your expression with a dummy vector and then substituting in there. So e.g.

{a,b,c}::Indices.
ex:= x^a + x^b x_b y^a;
ex := @(ex) f_a:
distribute(_);
substitute(_, $x^a f_a -> z^a f_a$);
factor_out(_, $f_a$);

Comments

Why is the substitute step necessary here? This seems to work without the substitute step. Is there some subtlety that necessitates this substitute step in more complicated cases?