2012/07/17 by Xavier Dahan, Dahan, Xavier
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Commutative Algebra and Its Applications #FOS: Computer and information sciences #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.1207.3887
openalex publication_date 2012/07/17 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Due to the elimination property held by the lexicographic monomial order, the\ncorresponding Groebner bases display strong structural properties from which\nmeaningful informations can easily be extracted. We study these properties for\nradical ideals of (co)dimension zero. The proof presented relies on a\ncombinatorial decomposition of the finite set of points whereby iterated\nLagrange interpolation formulas permit to reconstruct a minimal Groebner basis.\nThis is the first fully explicit interpolation formula for polynomials forming\na lexicographic Groebner basis, from which the structure property can easily be\nread off. The inductive nature of the proof also yield as a byproduct a\ntriangular decomposition algorithm from the Groebner basis.\n