Corrigendum: 'On bounds for the effective differential Nullstellensatz, arXiv:1508.07508'

TL;DR

This paper corrects a previous mathematical result on bounds for the differential Nullstellensatz by addressing a gap and providing a detailed proof under an additional assumption, ensuring the validity of the original conclusions.

Contribution

It identifies and fixes a gap in prior work by establishing the conditions under which the key inequality holds, strengthening the original results.

Findings

The correction confirms the validity of the original bounds under the new assumption.

A detailed proof of the corrected inequality is provided.

The assumption is satisfied in all cases where the inequality was previously applied.

Abstract

We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional assumption, it does hold. In this note, we provide a detailed proof of this. We then point out that this assumption is satisfied in all instances in which the inequality was used.