Saturation and vanishing ideals
We consider an homogeneous ideal I in the polynomial ring S=K[x_1,β¦, x_m] over a finite field K=π½_q and the finite set of projective rational points π that it defines in the projective space β^m-1. We concern ourselves with the problem of computing the vanishing ideal I(π). This is usually done by adding the equations of the projective space I(β^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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