Element–wise summation for custom function

Question

I use a custom function/head Operator[low, high] which encodes a generic polynomial expression split into "low" and "high" summands following considerations which are irrelevant to this question.

Two Operator objects should sum in the following way:

Operator[a,b] + Operator[c,d] -> Operator[a+c,b+d]

which is just standard element–wise summation that List does automatically. How can I tell Mathematica that this kind of automatic simplification or rearrangement is not only allowed, but desirable?

Answer 1

One of the standard ways for such things is using TagSetDelayed

Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]