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Semantic preserving bijective mappings for expressions involving special functions between computer algebra systems
André Greiner-Petter1, Moritz Schubotz1, Howard S Cohl2
1School of Electrical, Information and Media Engineering, University of Wuppertal, Wuppertal, Germany.
Aslib Journal of Information Management
|October 4, 2021
Summary
This study introduces an automated tool for translating mathematical expressions between Document Preparation Systems (DPS) like LaTeX and Computer Algebra Systems (CAS) such as Maple. This system reduces errors and saves time in scientific writing and computation.
Area of Science:
- Mathematics
- Computer Science
- Scientific Computing
Background:
- Mathematicians and scientists commonly use separate systems for writing (Document Preparation Systems - DPS) and computation (Computer Algebra Systems - CAS).
- Manual translation of mathematical expressions between DPS (e.g., LaTeX) and CAS (e.g., Maple, Mathematica) is a frequent, yet time-consuming and error-prone task.
- Existing tools lack robust methods for direct translation of complex mathematical functions.
Purpose of the Study:
- To automate the translation of mathematical expressions between DPS and CAS.
- To develop a system that reduces manual effort and potential errors in scientific workflows.
- To facilitate the seamless transfer of mathematical content between different software environments.
Main Methods:
- Leveraging special LaTeX macros developed at NIST for linking mathematical symbols to definitions in the NIST Digital Library of Mathematical Functions (DLMF).
- Implementing a rule-based translation approach between DLMF formulae and CAS.
- Developing software to streamline the creation of new translation rules and identify inconsistencies.
Main Results:
- Successfully translated 58.8% of DLMF formulae (2,405 expressions) between Maple and DLMF using 396 created mappings.
- Identified discrepancies in special function definitions between Maple and DLMF, with some symbols mapping to composite expressions.
- The translation tool was effectively used for automatic verification of mathematical online compendia and CAS, uncovering errors in both DLMF and Maple.
Conclusions:
- This work presents the first tool for translating special functions between LaTeX and Computer Algebra Systems.
- The automated approach significantly improves upon traditional error-prone manual translation methods.
- The developed system offers valuable utility for verifying mathematical databases and computational systems.
Keywords:
Computer Algebra System (CAS)Document Preparation System (DPS)LaTeXPresentation to Computation (P2C)Special functionsTranslationMore Related Videos
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