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Suppose I have two ordered pairs $(a_1, b_1)$ and $(a_2, b_2)$, each of type $A \times B$

I want to combine them into a single pair of type $A^2 \times B^2$:

$(a_1,b_1)$ OP $(a_2,b_2)$ = $( (a_1,a_2), (b_1,b_2) )$

Is there a name for this operation, or a standard operator? Someone suggested $\triangle$, but I've only ever seen that used for the Laplacian. It's called "zip" in functional programming.

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    I don't think there's any standard terminology, though it looks similar to a tensor product, so you could use $\otimes$. In any case, you can use whatever symbol you want as long as you define it.2011-05-23
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    Thanks. That's kind of what I thought, but I didn't want to write it down in a paper and then have someone say "Why didn't you use the standard 'foo' notation?!" I'll use $\otimes$2011-05-23
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    Does it actually matter to your application that you don't use $((a_1, b_1), (a_2, b_2))$? (If so I'll delete my answer.)2011-05-23
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    My application uses functions on pairs of $A \times B$ pairs. I'm trying to avoid writing them all out as $(a_i,b_i)$ just to make things cleaner.2011-05-23

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