Semantic preserving bijective mappings for expressions involving special functions between computer algebra systems and document preparation systems

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2019
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Aslib Journal of Information Management. 2019, 71(3), pp. 415-439. ISSN 2050-3806. Available under: doi: 10.1108/AJIM-08-2018-0185
Zusammenfassung

Purpose
Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the expressions manually between DPS and CAS. This process is time-consuming and error-prone. The purpose of this paper is to automate this translation. This paper uses Maple and Mathematica as the CAS, and LaTeX as the DPS.

Design/methodology/approach
Bruce Miller at the National Institute of Standards and Technology (NIST) developed a collection of special LaTeX macros that create links from mathematical symbols to their definitions in the NIST Digital Library of Mathematical Functions (DLMF). The authors are using these macros to perform rule-based translations between the formulae in the DLMF and CAS. Moreover, the authors develop software to ease the creation of new rules and to discover inconsistencies.

Findings
The authors created 396 mappings and translated 58.8 percent of DLMF formulae (2,405 expressions) successfully between Maple and DLMF. For a significant percentage, the special function definitions in Maple and the DLMF were different. An atomic symbol in one system maps to a composite expression in the other system. The translator was also successfully used for automatic verification of mathematical online compendia and CAS. The evaluation techniques discovered two errors in the DLMF and one defect in Maple.

Originality/value
This paper introduces the first translation tool for special functions between LaTeX and CAS. The approach improves error-prone manual translations and can be used to verify mathematical online compendia and CAS.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
004 Informatik
Schlagwörter
Translation, Computer Algebra System (CAS), Document Preparation System (DPS), LaTeX, Presentation to Computation (P2C), Special functions
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undefined / . - undefined, undefined
Zitieren
ISO 690GREINER-PETTER, André, Moritz SCHUBOTZ, Howard S. COHL, Bela GIPP, 2019. Semantic preserving bijective mappings for expressions involving special functions between computer algebra systems and document preparation systems. In: Aslib Journal of Information Management. 2019, 71(3), pp. 415-439. ISSN 2050-3806. Available under: doi: 10.1108/AJIM-08-2018-0185
BibTex
@article{GreinerPetter2019-05-20Seman-46001,
  year={2019},
  doi={10.1108/AJIM-08-2018-0185},
  title={Semantic preserving bijective mappings for expressions involving special functions between computer algebra systems and document preparation systems},
  number={3},
  volume={71},
  issn={2050-3806},
  journal={Aslib Journal of Information Management},
  pages={415--439},
  author={Greiner-Petter, André and Schubotz, Moritz and Cohl, Howard S. and Gipp, Bela}
}
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    <dcterms:abstract xml:lang="eng">Purpose&lt;br /&gt;Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the expressions manually between DPS and CAS. This process is time-consuming and error-prone. The purpose of this paper is to automate this translation. This paper uses Maple and Mathematica as the CAS, and LaTeX as the DPS.&lt;br /&gt;&lt;br /&gt;Design/methodology/approach&lt;br /&gt;Bruce Miller at the National Institute of Standards and Technology (NIST) developed a collection of special LaTeX macros that create links from mathematical symbols to their definitions in the NIST Digital Library of Mathematical Functions (DLMF). The authors are using these macros to perform rule-based translations between the formulae in the DLMF and CAS. Moreover, the authors develop software to ease the creation of new rules and to discover inconsistencies.&lt;br /&gt;&lt;br /&gt;Findings&lt;br /&gt;The authors created 396 mappings and translated 58.8 percent of DLMF formulae (2,405 expressions) successfully between Maple and DLMF. For a significant percentage, the special function definitions in Maple and the DLMF were different. An atomic symbol in one system maps to a composite expression in the other system. The translator was also successfully used for automatic verification of mathematical online compendia and CAS. The evaluation techniques discovered two errors in the DLMF and one defect in Maple.&lt;br /&gt;&lt;br /&gt;Originality/value&lt;br /&gt;This paper introduces the first translation tool for special functions between LaTeX and CAS. The approach improves error-prone manual translations and can be used to verify mathematical online compendia and CAS.</dcterms:abstract>
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