A field-theory motivated approach to symbolic computer algebra

TL;DR

This paper introduces a novel computer algebra system inspired by field theory, featuring TeX-like input and advanced data structures to simplify manipulation of field-theory expressions and improve usability.

Contribution

It presents a new system with specialized data structures and input methods tailored for field theory, addressing limitations of traditional list-based algebra systems.

Findings

Enhanced handling of field-theory expressions

Simplified input with TeX-like syntax

Demonstrated effectiveness on explicit problems

Abstract

Field theory is an area in physics with a deceptively compact notation. Although general purpose computer algebra systems, built around generic list-based data structures, can be used to represent and manipulate field-theory expressions, this often leads to cumbersome input formats, unexpected side-effects, or the need for a lot of special-purpose code. This makes a direct translation of problems from paper to computer and back needlessly time-consuming and error-prone. A prototype computer algebra system is presented which features TeX-like input, graph data structures, lists with Young-tableaux symmetries and a multiple-inheritance property system. The usefulness of this approach is illustrated with a number of explicit field-theory problems.