Canonical representatives for residue classes of a polynomial ideal and orthogonality

Details Canonical representatives for residue classes of a polynomial ideal and orthogonality Canonical representatives for residue classes of a polynomial ideal and orthogonality

2007-06-13

arxiv.org/abs/0706.1952v1

Mathematics

Commutative Algebra

19 pages; Submitted to journal, currently under review

Scientific paper

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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