### Dan Piponi

Shared publicly -I took my old formal power series library for combinatorics [2] (see also [3]) and tweaked it to work when the base ring isn't commutative. I can now use Haskell code to manipulate infinite series of powers of (one pair of) creation and annihilation operators.

I put the code at [1]. There are countless applications. Think of the things you can can enumerate with commutative generating functions, and now allow the possibility of connecting those objects with wires.

I included toy examples for:

0. basic stuff like counting non-capturing rook placements

1. using the Euler-Maclaurin formula to convert an integral to a sum

2. some polynomial manipulations related to umbral calculus

3. some quantum optics calculations

4. some "experimental" mathematics. See [4] for explanations.

Caveat: it's experimental incomplete code. I just wanted to see if the idea worked out.

[1] https://github.com/dpiponi/formal-weyl

[2] http://blog.sigfpe.com/2007/11/small-combinatorial-library.html

[3] https://hackage.haskell.org/package/species

[4] http://arxiv.org/abs/1010.0354

I put the code at [1]. There are countless applications. Think of the things you can can enumerate with commutative generating functions, and now allow the possibility of connecting those objects with wires.

I included toy examples for:

0. basic stuff like counting non-capturing rook placements

1. using the Euler-Maclaurin formula to convert an integral to a sum

2. some polynomial manipulations related to umbral calculus

3. some quantum optics calculations

4. some "experimental" mathematics. See [4] for explanations.

Caveat: it's experimental incomplete code. I just wanted to see if the idea worked out.

[1] https://github.com/dpiponi/formal-weyl

[2] http://blog.sigfpe.com/2007/11/small-combinatorial-library.html

[3] https://hackage.haskell.org/package/species

[4] http://arxiv.org/abs/1010.0354

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I like the "modular synth theorem". :)

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