Article ID Journal Published Year Pages File Type
4597561 Journal of Pure and Applied Algebra 2008 18 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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