Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems

TL;DR

This paper introduces a novel method for verifying digital mathematical libraries and computer algebra systems by translating and comparing mathematical expressions, enhancing accuracy and providing open access to verified formulae.

Contribution

It presents the most comprehensive verification of digital libraries and CASs, improves translation performance, and offers open access to translated formulae.

Findings

Enhanced translation coverage and accuracy

Most comprehensive verification to date

Open access to translated formulae

Abstract

Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra systems is a crucial attribute for modern research. In this paper, we present a novel approach to verify a digital mathematical library and two computer algebra systems with one another by converting mathematical expressions from one system to the other. We use our previously eveloped conversion tool (referred to as LaCASt) to translate formulae from the NIST Digital Library of Mathematical Functions to the computer algebra systems Maple and Mathematica. The contributions of our presented work are as follows: (1) we present the most comprehensive verification of computer algebra systems and digital mathematical libraries with one another; (2) we significantly enhance the performance of the underlying translator in terms of coverage and accuracy; and (3) we provide open access to translations for Maple and Mathematica of the formulae in the NIST Digital Library of Mathematical Functions.