Saturation and vanishing ideals

• Philippe Gimenez ^[1] ; Diego Ruano ^[1] ; Rodrigo San-José ^[1]
  1. [1] Universidad de Valladolid

     Universidad de Valladolid

     Valladolid, España

     
• Localización: EACA 2022: XVII Encuentro de Álgebra Computacional y Aplicaciones / coord. por Carlos Galindo Pastor, Philippe Giménez, Fernando Javier Hernando Carrillo, F. Monserrat Delpalillo, Julio José Moyano Fernández, 2023, ISBN 978-84-19647-46-7, págs. 95-98
• Idioma: inglés
• Enlaces
  • Texto Completo Libro
• Resumen

  • 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.