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Erschienen in:
1999 | OriginalPaper | Buchkapitel
A New Criterion for Normal Form Algorithms
verfasst von : B. Mourrain
Erschienen in: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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In this paper, we present a new approach for computing normal forms in the quotient algebra A of a polynomial ring R by an ideal I. It is based on a criterion, which gives a necessary and sufficient condition for a projection onto a set of polynomials, to be a normal form modulo the ideal I. This criterion does not require any monomial ordering and generalizes the Buchberger criterion of S-polynomials. It leads to a newa lgorithm for constructing the multiplicative structure of a zero- dimensional algebra. Described in terms of intrinsic operations on vector spaces in the ring of polynomials, this algorithm extends naturally to Laurent polynomials.