论文标题
饱和和消失的理想
Saturation and vanishing ideals
论文作者
论文摘要
我们在多项式环$ s = k [x_1，\ dots，$ x_m] $上考虑一个同质的理想$ i $上的有限字段$ k = \ mathbb {f} _q $和一组有限的投影性有理点$ \ \ \ \ m athbb {x} $的有限套件，该集合定义了投影范围的$ \ \ bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb {x} $ {p}。我们关注的是计算消失的理想$ i（\ mathbb {x}）$的问题。这通常是通过将投射空间$ i（\ mathbb {p}^{m-1}）$添加到$ i $并计算激进的方程来完成的。我们使用饱和度相对于同质最大理想提供了一种替代性，更有效的方式。
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.
