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In this work, we present the package NeatIBP , which automatically generates small-size integration-by-parts (IBP) identities for Feynman integrals. Based on the syzygy and module intersection techniques, the generated IBP identities' propagator degree is controlled and thus the size of the system of IBP identities is shorter than that generated by the standard Laporta algorithm. This package is powered by the computer algebra systems Mathematica and Singular , and the library SpaSM. It is parallelized on the level of Feynman integral sectors. The generated small-size IBP identities can subsequently be used for either finite field reduction or analytic reduction. We demonstrate the capabilities of this package on several multi-loop IBP examples. Program Title: NeatIBP CPC Library link to program files: https://doi.org/10.17632/ms85fpfm7b.1 Developer's repository link: https://github.com/yzhphy/NeatIBP Licensing provisions: GPLv3 Programming language: Mathematica , Singular , C Nature of problem: The difficulty of the IBP reduction of Feynman integrals stems from the large size of the IBP system. Solution method: We apply the module intersection method to generate IBP relations by algebraic geometry methods, and compare the smaller IBP system we generate with that from Laporta's algorithm. NeatIBP generates the module intersection in Singular [1] and selects relevant and independent IBP relations via an algorithm relying on the library SpaSM [2]. The workflow is parallelized by a task manager written in Mathematica [3]. [1] W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann, Singular 4-3-1 – A computer algebra system for polynomial computations, http://www.singular.uni-kl.de , 2022. [2] The SpaSM group, SpaSM : a Sparse direct Solver Modulo p , http://github.com/cbouilla/spasm , 2017. [3] Wolfram Research, Mathematica 13.2, https://www.wolfram.com/mathematica/. [ABSTRACT FROM AUTHOR]

Multivariate partial fractioning is a powerful tool for simplifying rational function coefficients in scattering amplitude computations. Since current research problems lead to large sets of complicated rational functions, performance of the partial fractioning as well as size of the obtained expressions are a prime concern. We develop a large scale parallel framework for multivariate partial fractioning, which implements and combines an improved version of Leinartas' algorithm and the MultivariateApart algorithm. Our approach relies only on open source software. It combines parallelism over the different rational function coefficients with parallelism for individual expressions. The implementation is based on the Singular / GPI-Space framework for massively parallel computer algebra, which formulates parallel algorithms in terms of Petri nets. The modular nature of this approach allows for easy incorporation of future algorithmic developments into our package. We demonstrate the performance of our framework by simplifying expressions arising from current multiloop scattering amplitude problems. We also provide a Mathematica interface to our package, which is available on https://github.com/Wu-Zihao/PfdParallelM. Program Title: pfd-parallel CPC Library link to program files: https://doi.org/10.17632/r99gdp9v76.1 Developer's repository link: https://github.com/singular-gpispace/pfd-parallel Licensing provisions: GPLv3 Programming language: Singular language, GPI-Space Petri net Nature of problem: In scattering amplitude computation, we often encounter complicated rational functions, which may be simplified using the multivariate partial fraction decomposition. With the consideration of the increasing complexity of the problems, an efficient implementation of such a method is needed. Solution method: We present the package pfd-parallel , which is a large-scale parallelized framework for multivariate partial fractioning. Our package relies only on open source software. It combines different algorithms and provides parallelization based on the Singular/GPI-Space framework [1–3]. The package combines both the improved Leinartars' algorithm [4], as well as the MultivariateApart algorithm [5], and combines parallelism over the different rational function coefficients and parallelism for individual expressions. Using this approach cutting-edge computations can be handled in an efficient way. Additional comments including restrictions and unusual features: The software, including all dependencies like Singular, GPI-2, GPI-Space, and the Singular/GPI-Space framework, is distributed via the supercomputing package manager Spack, which allows for convenient installation of scientific software, in particular in HPC environments. The code has been tested on Centos 7 and 8, Ubuntu 18.04 LTS and 20.04 LTS. [1] J. Böhm, W. Decker, A. Frühbis-Krüger, F.-J. Pfreundt, M. Rahn, L. Ristau, Found. Comput. Math. 21 (2021), 767–806. https://dx.doi.org/10.1007/s10208-020-09464-x , arXiv:1808.09727 [math.AG]. [2] W. Decker, G.-M. Greuel, G. Pfister, H. Schönemann, Singular 4-3-1 – A computer algebra system for polynomial computations, http://www.singular.uni-kl.de , 2022. [3] F.-J. Pfreundt, M. Rahn, GPI-Space , Fraunhofer ITWM Kaiserslautern, 2022, http://www.gpi-space.de/. [4] J. Böhm, M. Wittmann, Z. Wu, Y. Xu, Y. Zhang, J. High Energy Phys. 12 (2020) 054, https://dx.doi.org/10.1007/JHEP12(2020)054 , arXiv:2008.13194 [hep-ph]. [5] M. Heller, A. von Manteuffel, Comput. Phys. Commun. 271 (2022) 108174, https://dx.doi.org/10.1016/j.cpc.2021.108174 , arXiv:2101.08283 [cs.SC]. [ABSTRACT FROM AUTHOR]