We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The implementation includes iterated integrals of modular forms as well as iterated integrals involving the Kronecker coefficient functions $g^{(k)}(z,\tau )$. For the Kronecker coefficient functions iterated integrals in dτ and dz are implemented. This includes elliptic multiple polylogarithms.

Program summary

Note: The program uploaded to the CPC Library is the full GiNaC program, original authors C. Bauer, A. Frink and R. Kreckel. The algorithms described in this article are integrated into GiNaC.

Program title: GiNaC_elipticFeynman

CPC Library link to program files: https://doi.org/10.17632/8vyydbc7zw.1

Developer's repository link: https://www.ginac.de/

Licensing provisions: GNU General Public License version 2

Programming language: C++

Other programs called: CLN library, available from https://www.ginac.de/CLN.

Nature of problem: Numerical evaluation of iterated integrals related to elliptic Feynman integrals.

Solution method: Removal of trailing zeros followed by series expansion.

中文翻译：

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与椭圆费曼积分有关的迭代积分的数值评估

我们报告了GiNaC内的一种实现，用于以整数的形式在被积数的级数收敛的收敛区域内，评估与椭圆费曼积分有关的迭代积分。该实现包括模块化形式的迭代积分以及涉及Kronecker系数函数的迭代积分$G^{（ķ）}（ž，\tau ）$。对于Kronecker系数函数，实现了dτ和dz中的迭代积分。这包括椭圆形的多个对数。

计划摘要

注意：上传到CPC图书馆的程序是完整的GiNaC程序，原始作者C. Bauer，A。Frink和R. Kreckel。本文介绍的算法已集成到GiNaC中。

程序标题： GiNaC_elipticFeynman

CPC库链接到程序文件： https : //doi.org/10.17632/8vyydbc7zw.1

开发人员的资料库链接： https : //www.ginac.de/

许可条款：GNU通用公共许可证版本2

编程语言： C ++

其他程序称为： CLN库，可从https://www.ginac.de/CLN获得。

问题性质：与椭圆费曼积分有关的迭代积分的数值评估。

解决方法：删除尾随零，然后进行级数展开。