ACMD Seminar: Semantic Preserving Translations between NIST's Digital Library of Mathematical Functions and Computer Algebra Systems

André Greiner-Petter
University of Wuppertal, Germany and National Institute of Informatics, Tokyo, Japan

Tuesday, July 20, 2021, 10:00 AM EDT (8:00 AM MDT)

A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.

Note! Because the speaker is in Japan, this talk is scheduled for 10 AM EDT, instead of the usual 3 PM.

Abstract: Over the past decades, especially in Science, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset math formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. Likewise, digital mathematical libraries, such as the Digital Library of Mathematical Functions (DLMF), play a crucial role in modern mathematics and many related disciplines (e.g., physics and engineering).  On the other hand, today's research increasingly takes advantage of Computer Algebra Systems (CAS) to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and, therefore, insufficient for most cases. Consequently, the workflow of experimenting and publishing in the Sciences often includes time-consuming and error-prone manual conversions between presentational LaTeX and computational CAS formats.

The DLMF source is written in LaTeX but uses specific semantic macros which allow an unambiguous representation of mathematical functions. We can use these semantic macros to define a bijective mapping between functions in the DLMF and their counterparts in CAS. While there is an inevitable overlap between supported functions in general-purpose CAS and the functions in the DLMF, many expressions cannot and should not be translated directly, e.g., because of a disparity in the domain or branch cut positioning.

This talk will explain how we created the modular semantic preserving translation system LaCASt to translate math expressions from the DLMF to the two general-purpose CAS Maple and Mathematica. Further, we demonstrate the reliability and benefits of LaCASt via an automatic evaluation engine that can detect errors in the DLMF and CAS. Finally, we provide an outlook on using LaCASt for translations beyond the manually annotated LaTeX expressions in the DLMF.

Bio: I am a Ph.D. candidate at the University of Wuppertal in Germany.  Currently, I spend my time at the National Institute of Informatics (NII) in Tokyo as a guest researcher. I made my B.S. and M.S. in Mathematics at the TU Berlin, Germany. My research interests are mainly Mathematical Information Retrieval (MathIR) and related fields, such as Natural Language Processing (NLP), data mining, and others. My dissertation focuses on translating mathematical expressions between different formats, such as LaTeX and Computer Algebra Systems. During my research, I had the chance to work as a guest researcher at the National Institute of Standards and Technology (NIST) in 2017. Further, I had research internships at Maplesoft in Canada in 2018 and the NII in Japan in 2019 and 2020. I received two research scholarships from the German Academic Exchange Service (DAAD) and an EXIST scholarship for funding a start-up from the Federal Ministry for Economic Affairs and Energy in Germany.

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Host: Howard Cohl