Size reduction and partial decoupling of systems of equations

TL;DR

This paper introduces a method to reduce the size of systems of equations, making them more manageable and partially decoupled, with applications to algebraic, differential, and non-linear systems, enhancing computational efficiency.

Contribution

The paper presents a novel size reduction technique that also partially decouples systems, applicable to linear and non-linear equations, improving solvability and computational performance.

Findings

Reduced number of terms in systems of equations.

Increased likelihood of factorization or integrability.

Applicable to differential Groebner basis computations.

Abstract

A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely to be factorizable or integrable. A variation of this method is applicable to non-linear systems. Modifications to improve efficiency are given and examples are shown. This procedure can be used in connection with the computation of the radical of a differential ideal (differential Groebner basis).