Dokumentdetails
ID
oai:HAL:hal-04222033v1
Thema
[MATH]Mathematics [math] [INFO]Computer Science [cs]Autor
Helmer, Martin Tsigaridas, EliasLangue
enEditor
HAL CCSD;Elsevier
Kategorie
Technologien: Informatik
Jahr
2024
Auflistungsdatum
07.12.2023
Schlüsselwörter
exponentialZusammenfassung
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
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