Название: Making Presentation Math Computable: A Context-Sensitive Approach for Translating LaTeX to Computer Algebra Systems
Автор: Andre Greiner-Petter
Издательство: Springer
Год: 2023
Страниц: 209
Язык: английский
Формат: pdf (true)
Размер: 10.2 MB

This book addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS). Over the past decades, especially in the domain of Sciences, Technology, Engineering, and Mathematics (STEM), LaTeX has become the de-facto standard to typeset mathematical formulae in publications. Since scientists are generally required to publish their work, LaTeX has become an integral part of today's publishing workflow. On the other hand, modern research increasingly relies on CAS to simplify, manipulate, compute, and visualize mathematics. However, existing LaTeX import functions in CAS are limited to simple arithmetic expressions and are, therefore, insufficient for most use 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.

To address the lack of a reliable and comprehensive translation tool between LaTeX and CAS, this thesis makes the following three contributions. First, it provides an approach to semantically enhance LaTeX expressions with sufficient semantic information for translations into CAS syntaxes. Second, it demonstrates the first context-aware LaTeX to CAS translation framework LaCASt. Third, the thesis provides a novel approach to evaluate the performance for LaTeX to CAS translations on large-scaled datasets with an automatic verification of equations in digital mathematical libraries.

If a translation between LATEX and CAS is so essential, why are there no translation tools available? As is often the case in research, the reasons for this are diversified. First, there are translation approaches available. Some CAS, such as Mathematica and SymPy, allow to import LATEX expressions. Most CAS support at least the Mathematical Markup Language (MathML), since it is the current web standard to encode mathematical formulae. With numerous tools available to transfer LATEX to MathML, a translation from LATEX to CAS syntaxes should not be a difficult task. However, none of these available translation techniques are reliable and comprehensive. Table illustrates how Mathematica, one of the major proprietary CAS, fails to import even simple formulae. Another option is SnuggleTeX, a LATEX to MathML converter which also supports translations to Maxima. SnuggleTeX fail to translate all expressions in Table. Alternative translations via MathML as an intermediate format perform similarly.