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arXiv · 0706.1952

Canonical representatives for residue classes of a polynomial ideal and orthogonality

Edgar Delgado-Eckert
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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.

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Edgar Delgado-Eckert. 2007-06-13. Canonical representatives for residue classes of a polynomial ideal and orthogonality. https://arxiv.org/abs/0706.1952

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