Saturation and vanishing ideals
- Philippe Gimenez 1
- Diego Ruano 1
- Rodrigo San-José 1
- 1 IMUVA-Mathematics Research Institute, Universidad de Valladolid
- Galindo Pastor, Carlos (coord.)
- Gimenez, Philippe (coord.)
- Hernando Carrillo, Fernando (coord.)
- Monserrat Delpalillo, Francisco José (coord.)
- 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
Sustainable development goals
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.