How to specify a pair of elements with a particular property as underscript?

Question

Say I have $n$ pairs $(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)$, how do I specify for instance all the pairs where $y$ value is zero succinctly? I'm using it for the underscript of a sum to subset it.

Answer 1

I would just define an indexing set and iterate over that instead. Let: $$ A = \{k \in \{1, \ldots, n\} \mid y_k = 0\} $$ Then we want: $$ \sum_{k \in A} f(x_k, y_k) $$