Making Presentation Math Computable: A Context-Sensitive Approach for Translating LaTeX to Computer Algebra Systems

This thesis addresses the issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS) and proposes an approach to semantically enhance LaTeX expressions with sufficient information for translations. It also demonstrates the first context-aware LaTeX to CAS translation framework, LaCASt, and provides a novel approach to evaluate the performance of LaTeX to CAS translations on large-scaled datasets with automatic verification of equations in digital mathematical libraries.

Format: Paperback / softback
Length: 197 pages
Publication date: 01 January 2023
Publisher: Springer Fachmedien Wiesbaden

The issue of translating mathematical expressions from LaTeX to the syntax of Computer Algebra Systems (CAS) is addressed in this book. Over the past decades, LaTeX has become the de facto standard for typesetting mathematical formulae in publications, particularly in the fields of Sciences, Technology, Engineering, and Mathematics (STEM). Scientists are generally required to publish their work, making LaTeX 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 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.

This book aims to facilitate the seamless integration of LaTeX and CAS, enabling researchers to leverage the power of both tools in their mathematical workflows. By providing a comprehensive translation framework and evaluating its performance on large-scale datasets, this thesis contributes to the advancement of scientific publishing and computational mathematics.

Weight: 288g
Dimension: 210 x 148 (mm)
ISBN-13: 9783658404727
Edition number: 1st ed. 2023