Abstract
Document preparation systems like 
offer the ability to render mathematical expressions as one would write these on paper. Using 
, 
, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical 
markup (semantic 
) 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 
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 
, semantic 
, and now CAS representations as well.
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Notes
- 1.
The mention of specific products, trademarks, or brand names is for purposes of identification only. Such mention is not to be interpreted in any way as an endorsement or certification of such products or brands by the National Institute of Standards and Technology, nor does it imply that the products so identified are necessarily the best available for the purpose. All trademarks mentioned herein belong to their respective owners.
- 2.
The usage of multiple @ symbols in Miller’s
macro set provides capability for alternative presentations, such as \(\sin (z)\) and \(\sin \;z\) for one and two @ symbols respectively. - 3.
\idot is our semantic
macro which represents multiplication without any corresponding presentation appearance. - 4.
See for instance: http://dlmf.nist.gov/software.
- 5.
We are planning to make the dataset available from http://drmf.wmflabs.org.
macro set provides capability for alternative presentations, such as 
macro which represents multiplication without any corresponding presentation appearance.References
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to XML converter. 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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Cohl, H.S. et al. (2017). Semantic Preserving Bijective Mappings of Mathematical Formulae Between Document Preparation Systems and Computer Algebra Systems. In: Geuvers, H., England, M., Hasan, O., Rabe, F., Teschke, O. (eds) Intelligent Computer Mathematics. CICM 2017. Lecture Notes in Computer Science(), vol 10383. Springer, Cham. https://doi.org/10.1007/978-3-319-62075-6_9
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