On the effective membership problem for polynomial ideals

2012/11/21 by Andersson, Mats, Wulcan, Elizabeth
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1211.5096

Abstract

We discuss the possibility of representing elements in polynomial ideals in \C^N with optimal degree bounds. Classical theorems due to Macaulay and Max Noether say that such a representation is possible under certain conditions on the variety of the associated homogeneous ideal. We present some variants of these results, as well as generalizations to subvarieties of \C^N.

Related

• Explicit representation of membership in polynomial ideals
• Some variants of Macaulay's and Max Noether's theorems
• Short proofs of ideal membership
• Ideal Membership in Polynomial Rings over the Integers
• Sparse effective membership problems via residue currents