# Riemann Tensor Polynomial Canonicalization by Graph Algebra Extension

## TL;DR

This paper introduces a novel graph algebra extension theory to develop a canonicalization algorithm for Riemann tensor polynomials, addressing the longstanding challenge of multiterm tensor expression simplification.

## Contribution

It presents the first extension theory of graph algebra specifically designed for multiterm Riemann tensor polynomial canonicalization.

## Key findings

- Developed a new canonicalization algorithm based on graph algebra extension
- Achieved improved efficiency in tensor polynomial simplification
- Provided theoretical foundations for multiterm tensor canonicalization

## Abstract

Tensor expression simplification is an "ancient" topic in computer algebra, a representative of which is the canonicalization of Riemann tensor polynomials. Practically fast algorithms exist for monoterm canonicalization, but not for multiterm canonicalization. Targeting the multiterm difficulty, in this paper we establish the extension theory of graph algebra, and propose a canonicalization algorithm for Riemann tensor polynomials based on this theory.