Computing differential subresultants with Maple

TL;DR

This paper discusses implementing the computation of differential subresultants in Maple to efficiently find GCRDs of differential operators, including those with parameters, with applications demonstrated on commuting operators.

Contribution

It introduces a Maple implementation for differential subresultants that handles operators with parameters, enhancing computational tools for differential algebra.

Findings

Effective Maple implementation for differential subresultants

Handles operators with non-rational coefficients and parameters

Applications to commuting differential operators demonstrate utility

Abstract

We review the definition and main properties of differential subresultants in order to achieve their implementation in Maple, using the DEtools package. The focus is on computing GCRDs of ordinary differential operators with non necessarily rational coefficients. Determinant expressions provide explicit control, enabling the treatment of coefficients with parameters. Applications to commuting ordinary differential operators illustrate the effectiveness of the method.