Canonical representatives for residue classes of a polynomial ideal and orthogonality
Commutative Algebra
2007-06-14 v1 Algebraic Geometry
Abstract
The aim of this paper is to unveil an unexpected relationship between the normal form of a polynomial with respect to a polynomial ideal and the more geometric concept of orthogonality. We present a new way to calculate the normal form of a polynomial with respect to a polynomial ideal I in the ring of multivariate polynomials over a field K, provided the field K is finite and the ideal I is a vanishing ideal. In order to use the concept of orthogonality, we introduce a symmetric bilinear form on a vector space over a finite field.
Keywords
Cite
@article{arxiv.0706.1952,
title = {Canonical representatives for residue classes of a polynomial ideal and orthogonality},
author = {Edgar Delgado-Eckert},
journal= {arXiv preprint arXiv:0706.1952},
year = {2007}
}
Comments
19 pages; Submitted to journal, currently under review