A Triangular Decomposition Algorithm for Differential Polynomial Systems with Elementary Computation Complexity

TL;DR

This paper introduces a novel triangular decomposition algorithm for differential polynomial systems that achieves elementary computational complexity, using multivariate resultants to efficiently eliminate variables.

Contribution

It presents the first differential triangular decomposition algorithm with elementary computational complexity, advancing the efficiency of solving differential polynomial systems.

Findings

Achieves triple exponential complexity in differential polynomial system decomposition

Uses multivariate resultants for variable elimination in one step

First to demonstrate elementary complexity in this context

Abstract

In this paper, a new triangular decomposition algorithm is proposed for ordinary differential polynomial systems, which has triple exponential computational complexity. The key idea is to eliminate one algebraic variable from a set of polynomials in one step using the theory of multivariate resultant. This seems to be the first differential triangular decomposition algorithm with elementary computation complexity.