Work

A Maple Implementation for Deterministically Certifying Isolated Simple Zeros of Over-Determined Polynomial Systems with Interval Arithmetic and Its Applications

Year: 2026

Type: article

Abstract: This paper presents a Maple implementation of an interval verification method for identifying isolated simple zeros in square polynomial systems. Compared to the known MATLAB (R2019b) implementation, the Maple-based approach achieves significantly higher numerical accuracy. The implementation enables polynomial evaluation at specific points to yield results with very small absolute values—sufficiently precise to reach error bounds computed through theoretical formulations for moderate-sized systems. This advancement allows the deterministic certification of isolated simple zeros in over-determined polynomial systems containing approximately 10,000 complex zeros. As a practical demonstration, the method is further applied to rigorously verify isolated multiple zeros in smaller-scale polynomial systems.

Source: AppliedMath

DOI: 10.3390/appliedmath6010015

Authors: Xiaojie Dou, Jin-San Cheng, Junyi Wen

Institutions: Civil Aviation University of China, Chinese Academy of Sciences, Academy of Mathematics and Systems Science

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,207

Funder: Fundamental Research Funds for the Central Universities