qFunctions

A Mathematica implementation for q-series and partition theory applications.

Jointly with Jakob Ablinger, I put together a Mathematica implementation that can help remedy some tedious and error prone calculations that arise in q-series and partition theory. This implementation is designed to work with Christoph Koutschan’s HolonomicFunctions package and Carsten Schneider’s package Sigma.

This package has tools to guess and formally manipulate q-recurrences/shift equations/differential equations, automates the Method of Weighted Words, includes a method on Cylindric partitions, and it has experimental fitting functions, where one can try to write q-polynomials as an expression involving known functions such as qBinomials, qTrinomials, etc.

We are open to adding more tools, and any and all updates to the package can be found here or on the related website on RISC servers.

The related manuscript about this package is here:

Here is me demonstrating this package at University of Florida colloquium on my laptop at real time: