We present an algorithm to compute the primary decomposition of any ideal in a polynomialring over a factorially closed algorithmic principal ideal domain R. We show how basic ideal theoretic operations can be performed using Grobner bases and we exploit these constructions to inductively reduce the problem to zero dimensional ideals.Expand

This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coecients are inexact or imperfectly known.Expand

Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation.Expand

Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation.Expand

The technique of solving systems of multivariate polynomial equations via rigenproblems has become a topic of active research (with applications in computer-aided design and untrul theory, for example) at least since the papers [2, 6, 9].Expand

This paper shows how Grobner basis computations can be used to compute multivariate gcds, perform Hensel lifting, and reduce multivariate factorization to univariate.Expand

We solve this problem by reducing it to the problem of finding a decomposition of finite communtative Q-algebras as a direct product of local Q- algebnas over finite field.Expand

We show that for the common case of affine domains, i.e. domains which are finitely generated over fields, we can use an effective localization in order to perform most of the computation in one dimensional rings where it can be done with linear algebra.Expand