On lexicographic Groebner bases of radical ideals in dimension zero: interpolation and structure
On lexicographic Groebner bases of radical ideals in dimension zero: interpolation and structure
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发表时间：
2012-07
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通讯作者：
X. Dahan
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作者：
X. Dahan
由于词典单项式顺序所具有的消除特性，相应的 Groebner 基显示出强大的结构特性，可以轻松地从中提取有意义的信息。我们研究零（共）维的激进理想的这些性质。所提出的证明依赖于有限点集的组合分解，由此迭代拉格朗日插值公式允许重建最小格罗布纳基。这是第一个完全明确的多项式插值公式，形成词典编排的 Groebner 基，可以轻松地从中读出结构属性。该证明的归纳性质还产生了来自 Groebner 基础的三角分解算法作为副产品。
Due to the elimination property held by the lexicographic monomial order, the corresponding Groebner bases display strong structural properties from which meaningful informations can easily be extracted. We study these properties for radical ideals of (co)dimension zero. The proof presented relies on a combinatorial decomposition of the finite set of points whereby iterated Lagrange interpolation formulas permit to reconstruct a minimal Groebner basis. This is the first fully explicit interpolation formula for polynomials forming a lexicographic Groebner basis, from which the structure property can easily be read off. The inductive nature of the proof also yield as a byproduct a triangular decomposition algorithm from the Groebner basis.