Ideal Bases and Primary Decomposition: Case of Two Variables

Authors:
D. Lazard
Affiliations:
Institut de Programmation, Université Paris VI, F-75230 Paris Cedex 05
Venue:
Journal of Symbolic Computation
Year:
1985

Citing 3
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Abstract

A complete structure theorem is given for standard (= Grobner) bases for bivariate polynomials over a field and lexicographical orderings or for univariate polynomials over a Euclidian ring. An easy computation of primary decomposition in such rings is deduced. Another consequence is a natural factorisation of the resultant of two univariate polynomials over the integers which is a generalisation of the ''reduced discriminant'' of a polynomial of degree 2.