The vanishing ideal of a finite set of closed points in affine space
The vanishing ideal of a finite set of closed points in affine space
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DOI：
10.1016/j.jpaa.2007.08.002
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发表时间：
2006-04
影响因子：
0.8
通讯作者：
M. Lederer
中科院分区：
文献类型：
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作者：
M. Lederer
给定域上仿射空间的闭有理点的有限集合，我们给出了在所有给定点处为零的多项式理想的字典序的Gröbner基。我们的方法是一种替代的Buchberger-Möller算法，但与此相反，我们确定了一套领导项的理想，而不解决任何线性方程，但通过归纳的维仿射空间。Gröbner基的元素也可以通过一维插值某些多项式的系数来计算。
Given a finite set of closed rational points of affine space over a field, we give a Gröbner basis for the lexicographic ordering of the ideal of polynomials which vanish at all given points. Our method is an alternative to the Buchberger–Möller algorithm, but in contrast to that, we determine the set of leading terms of the ideal without solving any linear equation but by induction over the dimension of affine space. The elements of the Gröbner basis are also computed by induction over the dimension, using one-dimensional interpolation of coefficients of certain polynomials.