Consider a polynomial ring in a finite number of variables over a field of characteristic $0$. We implement in CoCoA some algorithms in order to easy compute graded ideals of this ring with given extremal Betti numbers (positions as well as values). More precisely, we develop a package for determining the conditions under which, given two positive integers $n, r$, $1le r le n-1$, there exists a graded ideal of a polynomial ring in $n$ variables with $r$ extremal Betti numbers in the given position. An algorithm to check whether an $r$-tuple of positive integers represents the admissible values of the $r$ extremal Betti numbers is also described. An example in order to show how the package works is also presented.

Computation of graded ideals with given extremal Betti numbers in a polynomial ring

AMATA, Luca;Crupi, Marilena
2019

Abstract

Consider a polynomial ring in a finite number of variables over a field of characteristic $0$. We implement in CoCoA some algorithms in order to easy compute graded ideals of this ring with given extremal Betti numbers (positions as well as values). More precisely, we develop a package for determining the conditions under which, given two positive integers $n, r$, $1le r le n-1$, there exists a graded ideal of a polynomial ring in $n$ variables with $r$ extremal Betti numbers in the given position. An algorithm to check whether an $r$-tuple of positive integers represents the admissible values of the $r$ extremal Betti numbers is also described. An example in order to show how the package works is also presented.
File in questo prodotto:
File Dimensione Formato  
Computation of graded ideals with given extremal Betti numbers in a polynomial ring.pdf

solo gestori archivio

Descrizione: Articolo principale
Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 2.48 MB
Formato Adobe PDF
2.48 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
3134277.pdf

solo utenti autorizzati

Descrizione: Articolo principale
Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 355.74 kB
Formato Adobe PDF
355.74 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Caricamento pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3134277
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? 5
social impact