Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}
Abstract
We present an algorithm for the numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and to arbitrary precision. The cornerstone of our approach is a procedure to obtain a convergent -series representation of elliptic multiple polylogarithms. Its coefficients are expressed in terms of ordinary multiple polylogarithms, which can be evaluated efficiently using existing libraries. In a series of preparation steps the elliptic polylogarithms are mapped into a region where the -series converges rapidly. We also present an implementation of our algorithm into the \texttt{GiNaC} framework. This release constitutes the first public package capable of evaluating elliptic multiple polylogarithms to high precision and for arbitrary values of the arguments.
Keywords
Cite
@article{arxiv.2602.09956,
title = {Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}},
author = {Claude Duhr and Florian Lorkowski and Robin Marzucca and Sofia Mauc and Stefan Weinzierl},
journal= {arXiv preprint arXiv:2602.09956},
year = {2026}
}
Comments
29 pages, 3 figures, discussed code to be released in GiNaC