Guidelines for writing and reviewing software in computer algebra

TL;DR

This paper argues that as computational tools become essential in modern mathematics, the accompanying software must undergo formal, structured review to ensure reproducibility and reliability. It outlines a two-track review model separating mathematical and software evaluation, and articulates four key coding guidelines: metadata, reproducibility, reliability, and readability. Empirical data from MaRDI-based assessments at ANTS and LuCaNT show meaningful improvements in code quality and reproducibility when software review is integrated, especially for accepted papers. The work provides concrete, practical guidelines for authors and reviewers and advocates broad community adoption to elevate the standards of research software in mathematics.

Abstract

The advent of computers has allowed mathematicians to do increasingly more difficult computations that used to be practically impossible. Peer reviewers will seldom look at any code attached to a math paper, however. In this article, we advocate for a software peer-reviewing process and will discuss some best practices for reviewers on how to peer review mathematical papers with code and providing guidelines for authors to improve the code that accompanies their mathematical paper.