aha! Apparently the thing I'm looking for is called the "Hadamard product" of power series, (Σ a_n x^n) ⋆ (Σ b_n x^n) = (Σ a_n b_n x^n) So, question: how ought I understand the categorification of the hadamard product?
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it's also worth noting that there are points other than x=1 for which /trace over the diagonal/ continues to be true due to wacky hypergeometric identities, but I have no idea how to image those into algorithm memoization..
Thanks. Twitter will use this to make your timeline better. UndoUndo
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