Semantic Preserving Bijective Mappings of Mathematical Formulae between Word Processors and Computer Algebra Systems

Published

June 28, 2017

Author(s)

Howard S. Cohl, Bonita V. Saunders, Marjorie A. McClain, Moritz Schubotz, Joon Bang, Juergen Gerhardt, Andre Greiner Petter

Abstract

There are many different approaches to represent mathematical expressions on computers. Word processors 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 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. For the conversion from semantic LaTeX to CAS representations, we have adapted the approach of Part of Speech Tagging from Natural Language Processing which we coin Part-of-Math (POM) Tagging. By taking advantage of POM tags and CAS internal representations, we develop algorithms to map individual formulae represented in semantic LaTeX to their corresponding representations in CAS and vice versa. 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. In connection with these efforts, we have developed software which translates between CAS representations through semantic LaTeX to generate MathML for the NIST Digital Repository of Mathematical Formulae associated with the Wolfram Encoding Continued Fraction Knowledge dataset and the University of Antwerp Continued Fractions for Special Functions dataset.

Proceedings Title

Conference on Intelligent Computer Mathematics 2017

Volume

10383

Conference Dates

July 17-21, 2017

Conference Location

Edinburgh

Pub Type

Conferences

Download Paper

https://doi.org/10.1007/978-3-319-62075-6_9

Local Download

Keywords

LaTeX, Computer Algebra Systems, Representation Translation

Citation

Cohl, H. , Saunders, B. , McClain, M. , Schubotz, M. , Bang, J. , Gerhardt, J. and Greiner, A. (2017), Semantic Preserving Bijective Mappings of Mathematical Formulae between Word Processors and Computer Algebra Systems, Conference on Intelligent Computer Mathematics 2017, Edinburgh, -1, [online], https://doi.org/10.1007/978-3-319-62075-6_9 (Accessed January 2, 2025)