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arXiv · 1805.09165

Combinatorics of ideals of points: a Cerlienco-Mureddu-like approach for an iterative lex game

M. Ceria
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Abstract

In 1990 Cerlienco and Mureddu gave a combinatorial iterative algorithm which, given an ordered set of points, returns the lexicographical Groebner escalier of the ideal of these points. There are many alternatives to this algorithm and in particular, the most efficient is the Lex Game, which is not iterative on the points, but its performances are definitely better. In this paper, we develop an iterative alternative to Lex Game algorithm, whose performances are very near to those of the original Lex Game, by means of the Bar Code, a diagram which allows to keep track of information on the points and the corresponding monomials, that are lost and usually recomputed many times in Cerlienco-Mureddu algorithm. Using the same Bar Code, we will also give an efficient algorithm to compute squarefree separator polynomials of the points and the Auzinger-Stetter matrices with respect to the lexicographical Groebner escalier of the ideal of the points.

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M. Ceria. 2018-05-22. Combinatorics of ideals of points: a Cerlienco-Mureddu-like approach for an iterative lex game. https://arxiv.org/abs/1805.09165

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