Hiding canonicalisation in tensor computer algebra

TL;DR

This paper introduces a novel approach to tensor expression simplification in computer algebra systems by hiding canonical forms from users, improving naturalness and usability, demonstrated through implementation in Cadabra.

Contribution

It proposes a new method for tensor expression handling that avoids explicit canonicalisation, enhancing naturalness and usability in computer algebra systems.

Findings

Implemented in Cadabra, the method effectively simplifies tensor expressions.

Hiding canonical forms improves user experience and expression naturalness.

The approach handles tensor multi-term symmetries more intuitively.

Abstract

Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a pen-and-paper computation, or may be unwieldy, or both. This is, for example, the case for expressions involving tensor multi-term symmetries. We propose an alternative strategy to handle such tensor expressions, which hides canonical forms from the user entirely, and present an implementation of this idea in the Cadabra computer algebra system.