Saturation and vanishing ideals

02/09/2022

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by   Philippe Gimenez, et al.

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We consider an homogeneous ideal I in the polynomial ring S=K[x_1,…, x_m] over a finite field K=𝔽_q and the finite set of projective rational points 𝕏 that it defines in the projective space ℙ^m-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(ℙ^m-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.