Semantic Preserving Bijective Mappings for Expressions involving Special Functions in Computer Algebra Systems and Document Preparation Systems

06/27/2019
by   Andre Greiner-Petter, et al.
0

Purpose: Modern mathematicians and scientists of math-related disciplines often use Document Preparation Systems (DPS) to write and Computer Algebra Systems (CAS) to calculate mathematical expressions. Usually, they translate the expressions manually between DPS and CAS. This process is time-consuming and error-prone. Our goal is to automate this translation. This paper uses Maple and Mathematica as the CAS, and LaTeX as our DPS. Design/methodology/approach: Bruce Miller at the National Institute of Standards and Technology (NIST) developed a collection of special LaTeX macros that create links from mathematical symbols to their definitions in the NIST Digital Library of Mathematical Functions (DLMF). We are using these macros to perform rule-based translations between the formulae in the DLMF and CAS. Moreover, we develop software to ease the creation of new rules and to discover inconsistencies. Findings: We created 396 mappings and translated 58.8 (2,405 expressions) successfully between Maple and DLMF. For a significant percentage, the special function definitions in Maple and the DLMF were different. Therefore, an atomic symbol in one system maps to a composite expression in the other system. The translator was also successfully used for automatic verification of mathematical online compendia and CAS. Our evaluation techniques discovered two errors in the DLMF and one defect in Maple. Originality: This paper introduces the first translation tool for special functions between LaTeX and CAS. The approach improves error-prone manual translations and can be used to verify mathematical online compendia and CAS.

READ FULL TEXT
research
09/17/2021

Semantic Preserving Bijective Mappings of Mathematical Formulae between Document Preparation Systems and Computer Algebra Systems

Document preparation systems like LaTeX offer the ability to render math...
research
11/30/2020

Automatic Mathematical Information Retrieval to Perform Translations up to Computer Algebra Systems

In mathematics, LaTeX is the de facto standard to prepare documents, e.g...
research
01/24/2022

Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems

Digital mathematical libraries assemble the knowledge of years of mathem...
research
07/12/2017

VMEXT: A Visualization Tool for Mathematical Expression Trees

Mathematical expressions can be represented as a tree consisting of term...
research
03/26/2019

Interoperability and machine-to-machine translation model with mappings to machine learning tasks

Modern large-scale automation systems integrate thousands to hundreds of...
research
09/18/2021

Automated Symbolic and Numerical Testing of DLMF Formulae using Computer Algebra Systems

We have developed an automated procedure for symbolic and numerical test...
research
11/10/2018

Towards Formula Translation using Recursive Neural Networks

While it has become common to perform automated translations on natural ...

Please sign up or login with your details

Forgot password? Click here to reset