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arXiv · 2202.04683

Saturation and vanishing ideals

Philippe Gimenez·Diego Ruano·Rodrigo San-José
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Abstract

We consider an homogeneous ideal $I$ in the polynomial ring $S=K[x_1,\dots,$ $x_m]$ over a finite field $K=\mathbb{F}_q$ and the finite set of projective rational points $\mathbb{X}$ that it defines in the projective space $\mathbb{P}^{m-1}$. We concern ourselves with the problem of computing the vanishing ideal $I(\mathbb{X})$. This is usually done by adding the equations of the projective space $I(\mathbb{P}^{m-1})$ to $I$ and computing the radical. We give an alternative and more efficient way using the saturation with respect to the homogeneous maximal ideal.

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Philippe Gimenez, Diego Ruano, Rodrigo San-José. 2022-02-09. Saturation and vanishing ideals. https://doi.org/10.1007/s40863-022-00330-y

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