Master Thesis Topic: Integrating Computer Algebra Systems- and Word Processors Formulae Moritz Schubotz Howard S

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Master Thesis Topic: Integrating Computer Algebra Systems- and Word Processors Formulae Moritz Schubotz Howard S. Cohl June 2, 2015 Computer Algebra Systems (CAS) and Word Processors (WP) serve different purposes. While the purpose of CAS is to rewrite, solve, or visualize formulae, WP are focused on the presentation of the formulae to human subjects. In science, both tasks are highly coupled. As a result, researchers manually translate formulae from one representa- tion to the other and back again. One approach to solve this are computable documents, serve for CAS and WP purposes at the same [5, 4, 3]. An exam- ple for a computable document is the Wolfram CDF format [7]. However, most solutions available force authors to use certain tools and do not provide a mechanism to export to standardized formats. Fur- Figure 1: LATEX typesetting of π as continued frac- thermore, formulae usually are context dependent tion. and thus cannot be transfered from one system to another as standalone entities. We propose a Master Thesis that tackles this work. The NIST DRMF Project’s goal is to build problem by (1) describing related works in the field a community-based online compendium of orthog- of computable / active documents and available onal polynomial and special function formulae in- data formats to store mathematical documents; (2) cluding related mathematical data in a full context- analyzing the requirements for suitable formulae free semantic computer-based encapsulation. data formats; (3) analyzing existing formats and The NIST Digital Repository of Mathematical their applicability to the given problem; (4) imple- Formulae is designed for a mathematically liter- menting a prototype for the Wolfram eCF, NIST ate audience and should (1) facilitate interaction DRMF use-case (see below); (5) evaluating the among a community of mathematicians and sci- strengths and weaknesses of the proposed solution; entists interested in compendia formulae data for and (6) summarizing the results and describing fu- orthogonal polynomials and special functions; (2) ture steps beyond the thesis scope. be expandable, allowing the input of new formu- In the following, we describe our use case ex- lae from the literature; (3) represent the context- ample for the proposed research, starting with a free full semantic information concerning individual brief description of the NIST DRMF Project, the formulas; (4) have a user friendly, consistent, and Wolfram eCF Project and the envisioned data- hyperlinkable viewpoint and authoring perspective; integration task. The Applied and Computational (5) contain easily searchable mathematics; and (6) Mathematics Division at the National Institute of take advantage of modern MathML tools for easy Standards and Technology (NIST), Gaithersburg, to read, scalably rendered content driven mathe- MD, U.S.A., in collaboration with Technische Uni- matics. versitätBerlin is developing an online compendium The Wolfram Computational Knowledge of Con- of mathematical formulae called the Digital Repos- tinued Fractions Project[6] (eCF Project) was as itory of Mathematical Formulae (DRMF) [2, 1]. a one-year research project granted by the U.S.- We have been developing this project since April based Alfred P. Sloan Foundation to Wolfram Re- 2013. We are using a semantic MediaWiki frame- search, the company that develops the computer

1 algebra system Mathematica as well as the compu- [2] HowardS. Cohl, Marjorie A. McClain, tational knowledge engine Wolfram|Alpha. The goal Bonita V. Saunders, Moritz Schubotz, and of the project was to collect information about con- Janelle C. Williams, Digital repository of tinued fractions from the literature and integrate it mathematical formulae, Intelligent Computer to Wolfram Alpha. Mathematics (StephenM. Watt, JamesH. In this master thesis the prototypical use case Davenport, AlanP. Sexton, Petr Sojka, and for the research result is to integrate Mathematica Josef Urban, eds.), Lecture Notes in Computer data generated by the eCF Project supplied to us Science, vol. 8543, Springer International by Eric Weisstein, Wolfram Research, to incorpo- Publishing, 2014, pp. 419–422 (English). rate into our digital library. The key here is to extract the semantic information encapsulated in [3] Catalin David, Christoph Lange, and Flo- the Mathematica function calls and then embed it rian Rabe, Interactive documents as inter- in our Wiki. In addition, already existing semantic faces to computer algebra systems: Jobad and macros used in the DRMF Wiki will be exported wolfram— alpha, CALCULEMUS (Emerging to Mathematica Notebooks. Trends) (2010), 13–30. [4] A.M. Elizarov, A.V. Kirillovich, E.K. Li- Prerequisites The optimal student has knowl- pachev, O.A. Nevzorova, V.D. Solovyev, and edge in the following ﬁelds N.G. Zhiltsov, Mathematical knowledge repre- sentation: semantic models and formalisms, • Data Integration Lobachevskii Journal of Mathematics 35 (2014), no. 4, 348–354 (English). • Mathematica [5] Michael Kohlhase, Joseph Corneli, Catalin • MathML David, Deyan Ginev, Constantin Jucovschi, Andrea Kohlhase, Christoph Lange, Bog- • LATEX dan Matican, Stefan Mirea, and Vyacheslav Zholudev, The planetary system: Web 3.0 Advisors The thesis is advised by & active documents for {STEM}, Proce- • Moritz Schubotz, TU Berlin dia Computer Science 4 (2011), no. 0, 598 – 607, Proceedings of the International Conference on • Dr. Howard Cohl (PhD), National Institute of Computational Science, {ICCS} 2011. Standards and Technology USA [6] Michael Trott and Eric W. Weisstein, Computa- • Eric Weisstein (PhD), Wolfram Research tional Knowledge of Continued Fractions, 2013.

• Reviewer: Prof. Dr. Volker Markl, TU Berlin [7] Stephen Wolfram, Cellular automata and com- plexity: Collected papers, vol. 152, Addison- There is a potential opportunity for the student to Wesley Reading, 1994. visit NIST, which includes funding to cover travel and living expenses. For further information con- tact Moritz Schubotz ([email protected], +49 30 314 22784).

References

[1] H. S. Cohl, M. Schubotz, M. A. McClain, B. V. Saunders, C. Y. Zou, A. S. Mohammed, and A. A. Danoﬀ, Growing the Digital Repository of Mathematical Formulae with Generic LaTeX Sources, ArXiv e-prints (2015).