Digital Collections of Examples in Mathematical Sciences

TL;DR

The paper advocates for developing community-maintained digital databases of mathematical examples, especially in polynomial areas, to improve reproducibility and utility across computational algebra and related fields.

Contribution

It highlights the need for comprehensive, community-driven databases of mathematical examples to support research and reproducibility in computational algebra.

Findings

Existing databases are limited in polynomial areas.

Community-maintained databases can enhance reproducibility.

Such databases have proven useful in SAT and SMT solving.

Abstract

Some aspects of Computer Algebra (notably Computation Group Theory and Computational Number Theory) have some good databases of examples, typically of the form "all the X up to size n". But most of the others, especially on the polynomial side, are lacking such, despite the utility they have demonstrated in the related fields of SAT and SMT solving. We claim that the field would be enhanced by such community-maintained databases, rather than each author hand-selecting a few, which are often too large or error-prone to print, and therefore difficult for subsequent authors to reproduce.