Computational techniques for proving identities in symmetric compositions

TL;DR

This paper introduces a computational approach using Mathematica to verify identities in symmetric compositions, providing explicit calculations and strategies for simplifying and proving these identities.

Contribution

It offers a complete Mathematica notebook with explicit computations and a systematic method for checking identities in symmetric compositions, complementing previous theoretical work.

Findings

Provides a comprehensive computational tool for symmetric composition identities

Demonstrates effective use of patterns and rules for simplification

Includes explicit calculations to verify identities

Abstract

We present in this work a complete session in a Mathematica notebook. The aim of this notebook is to check identities in symmetric compositions. This notebook is a complement of our work [1] and it has all the explicit computations. We refer the reader to that paper which can be seen in http://www.uibk.ac.at/mathematik/loos/jordan/index.html. First of all we will present a few number of comands in order to simplify identities by extracting scalars, SOut. The rest of the strategy holds on the powerfull of using patterns and rules.