Computer Physics Communications· 2026Q1
Elliptic Multiple Polylogarithms with Arbitrary Arguments in GiNaC
- 2citations
- Q1SCImago
- 2026year
Short summary
A new algorithm numerically evaluates elliptic multiple polylogarithms for arbitrary arguments to arbitrary precision by converting them into a rapidly converging q-series representation.
AI-generated from the title and abstract; the full text is not read.
Key points
- Developed an algorithm for numerical evaluation of elliptic multiple polylogarithms for arbitrary arguments and precision.
- The algorithm relies on a convergent q-series representation of these polylogarithms.
- Coefficients of the q-series are expressed in terms of ordinary multiple polylogarithms.
- Implemented the algorithm in the GiNaC framework, creating the first public package for this evaluation.
AI-generated from the title and abstract; the full text is not read.
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 $q$-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.
The authors' abstract, as published at the source. Computer Physics Communications, 2026 · DOI ↗
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Field: Algebra and Number Theory
Algebra and Number TheoryMathematics