Resultant-based Elimination in Ore Algebra

TL;DR

This paper introduces a novel resultant-based elimination method for Ore polynomial systems, utilizing Dieudonne determinants and noncommutative evaluation techniques to improve computational efficiency in algebraic elimination tasks.

Contribution

It defines a new concept of resultants for bivariate Ore polynomials and develops algorithms using Dieudonne determinants and noncommutative evaluation for efficient elimination.

Findings

Implementation in Maple demonstrates improved efficiency.

New algorithms successfully compute resultants for Ore polynomials.

Potential applications in algebraic systems solving and symbolic computation.

Abstract

We consider resultant-based methods for elimination of indeterminates of Ore polynomial systems in Ore algebra. We start with defining the concept of resultant for bivariate Ore polynomials then compute it by the Dieudonne determinant of the polynomial coefficients. Additionally, we apply noncommutative versions of evaluation and interpolation techniques to the computation process to improve the efficiency of the method. The implementation of the algorithms will be performed in Maple to evaluate the performance of the approaches.