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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?

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One of the standard ways for such things is using TagSetDelayed

Operator /: Operator[a_, b_] + Operator[c_, d_] := Operator[a + c, b + d]
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  • $\begingroup$ Thanks, that works really well! I'm a bit mystified about semantics behind /: but I'll read up. $\endgroup$
    – Dom Miketa
    Commented Dec 21, 2018 at 15:44

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