Thomas Decomposition of Algebraic and Differential Systems

TL;DR

This paper introduces a new algorithm based on Thomas decomposition for disjointly decomposing algebraic and differential systems into simple, structured subsystems, enhancing analysis and solution methods.

Contribution

It develops a novel algorithm that extends Thomas decomposition to both algebraic and differential systems, ensuring simplicity and involutivity, with implementation in Maple.

Findings

Algorithm successfully decomposes systems into simple subsystems

Implementation in Maple demonstrates practical applicability

Enhances understanding of algebraic and differential system structure

Abstract

In this paper we consider disjoint decomposition of algebraic and non-linear partial differential systems of equations and inequations into so-called simple subsystems. We exploit Thomas decomposition ideas and develop them into a new algorithm. For algebraic systems simplicity means triangularity, squarefreeness and non-vanishing initials. For differential systems the algorithm provides not only algebraic simplicity but also involutivity. The algorithm has been implemented in Maple.