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

  • Howard S. CohlEmail author
  • Moritz Schubotz
  • Abdou Youssef
  • André Greiner-Petter
  • Jürgen Gerhard
  • Bonita V. Saunders
  • Marjorie A. McClain
  • Joon Bang
  • Kevin Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10383)

Abstract

Document preparation systems like Open image in new window   offer the ability to render mathematical expressions as one would write these on paper. Using Open image in new window , Open image in new window , and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical Open image in new window markup (semantic Open image in new window ) 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 Open image in new window 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 Open image in new window , semantic Open image in new window , and now CAS representations as well.

Notes

Acknowledgements

We are indebted to Wikimedia Labs, the XSEDE project, Springer-Verlag, the California Institute of Technology, and Maplesoft for their contributions and continued support. We would also like to thank Eric Weisstein for supplying the Wolfram eCF dataset, Annie Cuyt, Franky Backeljauw, and Stefan Becuwe for supplying the University of Antwerp CFSF Maple dataset, and Adri Olde Daalhuis for discussions related to complex multivalued functions.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Howard S. Cohl
    • 1
    Email author
  • Moritz Schubotz
    • 2
  • Abdou Youssef
    • 3
  • André Greiner-Petter
    • 4
  • Jürgen Gerhard
    • 5
  • Bonita V. Saunders
    • 1
  • Marjorie A. McClain
    • 1
  • Joon Bang
    • 6
  • Kevin Chen
    • 6
  1. 1.Applied and Computational Mathematics DivisionNISTGaithersburgUSA
  2. 2.Department of Computer and Information ScienceUniversity of KonstanzKonstanzGermany
  3. 3.Department of Computer ScienceGWUWashington DCUSA
  4. 4.DSIMGTechnische UniversitätBerlinGermany
  5. 5.MaplesoftWaterlooCanada
  6. 6.Poolesville High SchoolPoolesvilleUSA

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