MPL - a program for computations with iterated integrals on moduli spaces of curves of genus zero
Christian Bogner
TL;DR
The paper presents MPL, a Maple-based tool for analytic computations of homotopy-invariant iterated integrals on the moduli spaces $\mathcal{M}_{0,n}$ and for a class of Feynman integrals obtained by mapping to these integrals. It details the mathematical framework (cubical coordinates, symbol and unshuffle maps, primitives, limits) and the algorithmic workflow that yields a basis of iterated integrals and their analytic evaluation. It also describes how Feynman parameter integrals can be reduced to such period integrals through polynomial reduction and variable changes, with criteria for linear reducibility and unramifiedness, and provides practical guidance and examples. The work offers a practical, end-to-end tool for automated analytic computation of period integrals and finite Feynman integrals, with explicit algorithms and implementation notes to support researchers in mathematical physics and perturbative QFT.
Abstract
We introduce the computer program MPL for computations with homotopy invariant iterated integrals on moduli spaces $\mathcal{M}_{0,n}$ of curves of genus 0 with $n$ ordered marked points. The program is an implementation of the algorithms presented in [13], based on Maple. It includes the symbol map and procedures for the analytic computation of period integrals on $\mathcal{M}_{0,n}.$ It supports the automated computation of a certain class of Feynman integrals.