Semantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems

TL;DR

This paper presents algorithms and tools for translating mathematical expressions between semantic LaTeX and computer algebra system representations, enabling semantically enriched MathML for digital mathematical libraries.

Contribution

It introduces novel algorithms and tools for bidirectional translation between semantic LaTeX and CAS representations, enhancing digital mathematics repositories.

Findings

Developed translation algorithms between semantic LaTeX and CAS formats.

Created tools for converting datasets into semantically enriched MathML.

Enabled integration of mathematical formulae into digital libraries with semantic clarity.

Abstract

Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) is achieved by using a semantic macro set. Computer algebra systems (CAS) such as Maple and Mathematica use alternative markup to represent mathematical expressions. By taking advantage of Youssef's Part-of-Math tagger and CAS internal representations, we develop algorithms to translate mathematical expressions represented in semantic LaTeX to corresponding CAS representations and vice versa. We have also developed tools for translating the entire Wolfram Encoding Continued Fraction Knowledge and University of Antwerp Continued Fractions for Special Functions datasets, for use in the NIST Digital Repository of Mathematical Formulae. The overall goal of these efforts is to provide semantically enriched standard conforming MathML representations to the public for formulae in digital mathematics libraries. These representations include presentation MathML, content MathML, generic LaTeX, semantic LaTeX, and now CAS representations as well.