Elliptic Multiple Polylogarithms with Arbitrary Arguments in \textsc{GiNaC}

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 $q$-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 $q$-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.

Source: arXiv:2602.09956v1 - http://arxiv.org/abs/2602.09956v1 PDF: https://arxiv.org/pdf/2602.09956v1 Original Link: http://arxiv.org/abs/2602.09956v1