# PolyLogTools - Polylogs for the masses

## TL;DR

This paper reviews recent advances in multiple polylogarithms, focusing on their algebraic structures, computational tools, and applications in Feynman integral calculations, facilitated by the PolyLogTools software package.

## Contribution

It introduces algorithms and a Mathematica package for analyzing the algebraic and computational aspects of multiple polylogarithms, including their coproduct structure and single-valued variants.

## Key findings

- Implementation of algorithms in PolyLogTools for coproduct analysis
- Demonstration of computing iterated integrals in Feynman diagrams
- Insights into the algebraic structure of polylogarithms

## Abstract

We review recent developments in the study of multiple polylogarithms, including the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an algorithm for finding fibration bases. We document how these algorithms are implemented in the Mathematica package PolyLogTools and show how it can be used to study the coproduct structure of polylogarithmic expressions and how to compute iterated parametric integrals over polylogarithmic expressions that show up in Feynman integal computations at low loop orders.