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TitleThe vanishing ideal of a finite set of closed points in affine space
Author(s) Mathias Lederer
TypeArticle in Journal
AbstractGiven 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.
ISSN0022-4049
URL http://www.sciencedirect.com/science/article/pii/S0022404907002150
LanguageEnglish
JournalJournal of Pure and Applied Algebra
Volume212
Number5
Pages1116 - 1133
Year2008
Edition0
Translation No
Refereed No
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