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



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


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
Conference Dates
July 17-21, 2017
Conference Location


LaTeX, Computer Algebra Systems, Representation Translation


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], (Accessed December 2, 2021)
Created June 27, 2017, Updated May 4, 2021