Saturation and vanishing ideals

  1. Philippe Gimenez 1
  2. Diego Ruano 1
  3. Rodrigo San-José 1
  1. 1 IMUVA-Mathematics Research Institute, Universidad de Valladolid
Book:
EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones
  1. Galindo Pastor, Carlos (coord.)
  2. Gimenez, Philippe (coord.)
  3. Hernando Carrillo, Fernando (coord.)
  4. Monserrat Delpalillo, Francisco José (coord.)
  5. Moyano-Fernández, Julio José (coord.)

Publisher: Servei de Comunicació i Publicacions ; Universitat Jaume I

ISBN: 978-84-19647-46-7

Year of publication: 2023

Pages: 95-98

Congress: Encuentro de Álgebra Computacional y Aplicaciones (17. 2022. Castelló de la Plana)

Type: Conference paper

DIALNET GOOGLE SCHOLAR lock_openRepositori UJI editor

Abstract

We consider an homogeneous ideal I in the polynomial ring S = Fq [x1, . . . ,xm] over a finite field Fq and the finite set of projective rational points X that it defines in the projective space Pm−1. We concern ourselves with the problem of computing the vanishing ideal I(X). This is usually done by adding the equations of the projective space I(Pm−1) to I and computing the radical. We give an alternative and more efficient way using the saturation with respect to the homogeneous maximal ideal.

Data source: Dialnet