Explicit representation of membership in polynomial ideals

2008/06/16 by Mats Andersson, Andersson, Mats, Elin Götmark +1
Computer Science · Mathematics · #32A26 #32A27 #32B15 #32C30 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0806.2592

openalex publication_date 2008/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new division formula on projective space which provides explicit solutions to various polynomial division problems with sharp degree estimates. We consider simple examples as the classical Macaulay theorem as well as a quite recent result by Hickel, related to the effective Nullstellensatz. We also obtain a related result that generalizes Max Noether's classical AF+BG theorem.

Related

• On the effective membership problem for polynomial ideals
• Division formulas on projective varieties
• Some variants of Macaulay's and Max Noether's theorems
• Sparse effective membership problems via residue currents
• Effective membership problem and systems of polynomial equations with multiple roots