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We present an algorithm to compute the primary decomposition of any ideal in a polynomial ring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic(More)
This paper introduces singular value decomposition (SVD) algorithms for some standard polynomial computations, in the case where the coefficients are inexact or imperfectly known. We first give an algorithm for computing univariate GCD's which gives exact results for interesting nearby problems , and give efficient algorithms for computing precisely how(More)
Algorithms are developed that adopt a novel implicit representation for multi-variate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation. We show that within this representation the polynomial greatest common divisor and factorization problems, as well as the problem of extracting the numerator and(More)
Given a squarefree polynomial P ∈ k 0 [x, y], k 0 a number field, we construct a linear differential operator that allows one to calculate the genus of the complex curve defined by P = 0 (when P is absolutely irreducible), the absolute factorization of P over the algebraic closure of k 0 , and calculate information concerning the Galois group of P over k 0(More)
Atntract \Ve discuss the use of a single generic linear combination of multiplication matrices, and its reordered Schur factoriza-tion, to find the roots of a system of multivariate polynomial equations. The principal contribution of this paper is to show how to reduce thr multivariate problem to a univariate problem, even in the raw of multiple roots, in a(More)