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In this paper we briefly discuss \Rings --- an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gr\"obner bases are implemented with the use of modern asymptotically fast…

Symbolic Computation · Computer Science 2018-09-25 Stanislav Poslavsky

A software for simplification of Dirac matrix polynomials that arise in particle physics problems is implemented.

High Energy Physics - Theory · Physics 2023-09-26 Sergii Kutnii

Braidlab is a Matlab package for analyzing data using braids. It was designed to be fast, so it can be used on relatively large problems. It uses the object-oriented features of Matlab to provide a class for braids on punctured disks and a…

Geometric Topology · Mathematics 2019-11-18 Jean-Luc Thiffeault , Marko Budisic

Developing intuition about quantum information theory problems is difficult, as is verifying or ruling-out of hypothesis. We present a Matlab package intended to provide the QIT community with a new and powerful tool-set for quantum…

Quantum Physics · Physics 2007-08-06 Shai Machnes

We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations. Gridap is an open-source software project exclusively written in the Julia…

Mathematical Software · Computer Science 2020-04-23 Francesc Verdugo , Santiago Badia

The boundary of the multi-scale differential compactification of strata of abelian differentials admits an explicit combinatorial description. However, even for low-dimensional strata, the complexity of the boundary requires use of a…

Algebraic Geometry · Mathematics 2020-06-24 Matteo Costantini , Martin Möller , Jonathan Zachhuber

We report on the higher-order differential calculus library developed inside the Lean mathematical library mathlib. To support a broad range of applications, we depart in several ways from standard textbook definitions: we allow arbitrary…

Logic in Computer Science · Computer Science 2025-09-08 Sébastien Gouëzel

We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman…

High Energy Physics - Theory · Physics 2026-04-24 Mathieu Giroux , Sebastian Mizera , Giulio Salvatori

This paper describes mathlib, a community-driven effort to build a unified library of mathematics formalized in the Lean proof assistant. Among proof assistant libraries, it is distinguished by its dependently typed foundations, focus on…

Logic in Computer Science · Computer Science 2020-01-28 The mathlib Community

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to…

High Energy Physics - Phenomenology · Physics 2008-11-26 Christian Bogner , Stefan Weinzierl

We present a package to perform partial fraction decompositions of multivariate rational functions. The algorithm allows to systematically avoid spurious denominator factors and is capable of producing unique results also when being applied…

Symbolic Computation · Computer Science 2022-01-05 Matthias Heller , Andreas von Manteuffel

I will present a new method for thinking about and for computing loop integrals based on differential equations. All required information is obtained by algebraic means and is encoded in a small set of simple quantities that I will…

High Energy Physics - Phenomenology · Physics 2014-05-16 Johannes M. Henn

This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR Tools, serves two related purposes: we provide implementations…

Numerical Analysis · Mathematics 2018-07-03 Silvia Gazzola , Per Christian Hansen , James G. Nagy

This paper presents TIRA, a Matlab library gathering several methods for the computation of interval over-approximations of the reachable sets for both continuous- and discrete-time nonlinear systems. Unlike other existing tools, the main…

Systems and Control · Computer Science 2019-02-15 Pierre-Jean Meyer , Alex Devonport , Murat Arcak

This paper is devoted to present the Mathematics Grammar Library, a system for multilingual mathematical text processing. We explain the context in which it originated, its current design and functionality and the current development goals.…

Mathematical Software · Computer Science 2012-02-23 Jordi Saludes , Sebastian Xambó

As developers of libraries implementing interval arithmetic, we faced the same difficulties when it comes to testing our libraries. What must be tested? How can we devise relevant test cases for unit testing? How can we ensure a high (and…

Mathematical Software · Computer Science 2023-07-17 Luis Benet , Luca Ferranti , Nathalie Revol

We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

High Energy Physics - Theory · Physics 2007-05-23 Ulf Gran

Fractional calculus has become widely studied and applied to physical problems in recent years. As a result, many methods for the numerical computation of fractional derivatives and integrals have been defined. However, these algorithms are…

Mathematical Software · Computer Science 2019-12-12 Matthew Adams

The automation of the traditional Painleve test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of ordinary and partial differential equations which may be parameterized by arbitrary…

Exactly Solvable and Integrable Systems · Physics 2013-01-08 Douglas Baldwin , Willy Hereman

We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an…

Optimization and Control · Mathematics 2026-05-26 Oscar Dowson , Xavier Gandibleux , Gökhan Kof