In this paper we propose a unified methodology for computing the set VK (I) of complex (K=
ℂ) or real (K= ℝ) roots of an ideal R [x], assuming Vk (I) is finite. We show how moment …

We present a symbolic-numeric technique to find the closest multivariate polynomial system
to a given one which has roots with prescribed multiplicity structure. Our method generalizes …

Adapting a 1915 method of Macaulay, one can give a calculation of the local ring of an
isolated zero of a polynomial system {f 1, f 2,..., ft}⊆ C [x 1, x 2,..., xs] using oating point …

Triangular decompositions for systems of polynomial equations with n variables, with exact
coefficients, are well developed theoretically and in terms of implemented algorithms in …

We introduce a matrix of traces, attached to a zero dimensional ideal ̃ I. We show that the
matrix of traces can be a useful tool in handling systems of polynomial equations with …

Let f1,..., fs be a system of polynomials in K [x1,..., xm] generating a zero-dimensional ideal I,
where K is an arbitrary algebraically closed field. Assume that the factor algebra A= K [x1 …

Let f1,…, fs∈ K [x1,…, xm] be a system of polynomials generating a zero-dimensional ideal
I, where K is an arbitrary algebraically closed field. We study the computation of “matrices of …

We introduce in this paper a new algebraic approach to some problems arising in signal
processing and communications that can be described as or reduced to systems of …

General (eg under and over-determined) systems of polynomially nonlinear partial
differential equations (pde) arise frequently in diverse applications. Analyzing such systems …

In these last years, some tools from algebraic geometry found their way into many
applications in signal processing and systems theory. By using these new algorithms, many …