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arXiv · 1208.1695

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

Michela Ceria
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Abstract

Given a finite set $\mathbf{X}$ 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 $\mathcal{G}(I(\mathbf{X}))$ of the zerodimensional radical ideal $I(\mathbf{X})$. 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 $T(I(\mathbf{X}))$ 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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Michela Ceria. 2012-08-08. A simplified version of the "Axis of Evil Theorem" for distinct points. https://arxiv.org/abs/1208.1695

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