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.

翻译：由于消除了地名录单项命令所持有的财产,相应的格罗布纳基底显示出强大的结构特性,可以很容易地从中提取有意义的信息。我们研究这些特性是为了实现(co)dimension 零的激进理想。所提供的证据依赖于对一组有限点的组合分解,通过这些分解,迭代的拉格朗内插公式可以重新构建一个最小的格罗布纳基。这是形成地名录格罗布纳基底的多名数的首个完全明确的内插公式,可以很容易地从中读取结构属性。证据的诱导性也从格罗布纳基底的三角分解算法中产生副产品。