2017/10/17 by Xavier Dahan, Dahan, Xavier
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Commutative Algebra and Its Applications #FOS: Computer and information sciences #G.1.1 #I.1.2 #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC
paper · pdf · doi:10.48550/arxiv.1710.06396
Extended abstract
arxiv created 2017/10/17 · openalex publication_date 2017/10/17 · arxiv updated 2017/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present upper bounds on the bit-size of coefficients of non-radical lexicographical Groebner bases in purely triangular form (triangular sets) of dimension zero. This extends a previous work [Dahan-Schost, Issac'2004], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are less universal and depend on some input data. We also introduce a related family of non- monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.