Segre-driven radicality testing

Helmer, Martin; Tsigaridas, Elias

Segre-driven radicality testing

Document detail

ID

oai:HAL:hal-04222033v1

Topic

[MATH]Mathematics [math] [INFO]Computer Science [cs]

Author

Helmer, Martin Tsigaridas, Elias

Langue

Editor

HAL CCSD;Elsevier

Year

2024

listing date

12/7/2023

Keywords

exponential

Metrics

Abstract

International audience; We present a probabilistic algorithm to test if a homogeneous polynomial ideal I defining a scheme X in ℙn is radical using Segre classes and other geometric notions from intersection theory.

Its worst case complexity depends on the geometry of X.

If the scheme X has reduced isolated primary components and no embedded components supported the singular locus of Xred=V(I√), then the worst case complexity is doubly exponential in n; in all the other cases the complexity is singly exponential.

The realm of the ideals for which our radical testing procedure requires only single exponential time includes examples which are often considered pathological, such as the ones drawn from the famous Mayr-Meyer set of ideals which exhibit doubly exponential complexity for the ideal membership problem.

Helmer, Martin,Tsigaridas, Elias, 2024, Segre-driven radicality testing, HAL CCSD;Elsevier