NRPyLaTeX: A LaTeX interface to computer algebra systems for general relativity

TL;DR

NRPyLaTeX provides a seamless LaTeX interface for inputting complex tensor expressions into SymPy, facilitating easier manipulation and code generation for general relativity research.

Contribution

It introduces a LaTeX-based input method for tensor expressions into SymPy, with configuration, error handling, and compatibility with other CASs, streamlining tensor computations in relativity.

Findings

Enables direct LaTeX input of tensor expressions into SymPy.

Supports output compatible with Mathematica and Maple.

Includes error handling and configuration features.

Abstract

While each computer algebra system (CAS) contains its own unique syntax for inputting mathematical expressions, LaTeX is perhaps the most widespread language for typesetting mathematics. NRPyLaTeX (NL) enables direct LaTeX input of complex tensorial expressions (written in Einstein notation) relevant to general relativity and differential geometry into the SymPy CAS. As SymPy also supports output compatible with the Mathematica and Maple CASs, NL lowers the learning curve for inputting and manipulating tensorial expressions in three widely used CASs. LaTeX however is a typesetting language, and as such is not designed to resolve ambiguities in mathematical expressions. To address this, NL implements a convenient configuration interface that, e.g., defines variables with certain attributes. Configuration commands appear as LaTeX comments, so that entire NL workflows can fit seamlessly into the LaTeX source code of scientific papers without interfering with the rendered mathematical expressions. Further, NL adopts NRPy+'s rigid syntax for indexed symbols (e.g., tensors), which enables NL output to be directly converted into highly optimized C/C++-code kernels using NRPy+. Finally NL has robust and user-friendly error-handling, which catches common tensor indexing errors and reports unresolved ambiguities, further expediting the input and validation of LaTeX expressions into a CAS.