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PolyKit

A toolkit for polylogarithms. Contains a set functions that compute polylogarithm symbols and formal symbols. These functions are highly specific. This is neither a computer algebra system nor a tool for numeric computations. Only polylogarithms of pure variables and cross-ratio are supported. The advantage of this software is that it's faster that general-purpose computer algerbra systems.

PolyKit was used to verify some results in “On the Goncharov depth conjecture and a formula for volumes of orthoschemes” (https://arxiv.org/abs/2012.05599) and most results in “Cluster Polylogarithms” (https://arxiv.org/abs/2208.01564). It was presented at ISSAC 2021.

Authors

  • Software development by Andrei Matveiakin
  • Maths by Daniil Rudenko

Folder structure

  • cpp — main implementation, most mature;
  • python — implementation of some basic features in pure Python;
  • pybind — bindings allowing to use a subset of C++ functionality from Python;
  • rust — an experimental implementation of the project in Rust, promising but nascent;
  • the rest is mostly technical folders of no general interest.

The workspace.cpp/workspace.py files and associated run.sh/run.bat scripts are used internally for development. See example.cpp/example.py and corresponding run_example.sh/run_example.bat for sample usage.