A simplified version of the "Axis of Evil Theorem" for distinct points

2012/08/08 by Michela Ceria, Ceria, Michela
Computer Science · #13P10 #Commutative Algebra (math.AC) #FOS: Mathematics #Scientific Research and Philosophical Inquiry

paper · pdf · doi:10.48550/arxiv.1208.1695

openalex publication_date 2012/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite set X of distinct points, Marinari-Mora's 'Axis of Evil Theorem' states that a combinatorial algorithm and interpolation enable to find a 'linear' factorization for a lexicographical minimal Groebner basis G(I(X)) of the zerodimensional radical ideal I(X). In this work we provide such algorithm, showing that it ends in a finite number of steps and that it actually provides the correct result. The 'Axis of Evil' algorithm takes as input the monomial basis of the initial ideal T(I(X)) but its starting point is the (finite) Groebner escalier N (obtained via Cerlienco-Mureddu correspondence) so we will also define the `potential expansion' 's algorithm, a combinatorical algorithm which computes the minimal basis from a finite Groebner escalier.

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