In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism
spaces) are introduced. This provides a common schema for many kinds of problems that …

Abstract HOM4PS-2.0 is a software package in FORTRAN 90 which implements the
polyhedral homotopy continuation method for solving polynomial systems. It updates its …

We present a new technique, based on polynomial continuation, for solving systems of $ n $
polynomials in $ N $ complex variables. The method allows equations to be introduced one …

As an attempt to bridge between numerical analysis and algebraic geometry, this paper
formulates the multiplicity for the general nonlinear system at an isolated zero, presents an …

This article introduces the concept of isosingular sets, which are irreducible algebraic
subsets of the set of solutions to a system of polynomial equations constructed by taking the …

Elimination is a basic algebraic operation which geometrically corresponds to projections.
This article describes using the numerical algebraic geometric concept of witness sets to …

We describe, for the first time, a completely rigorous homotopy (path-following) algorithm (in
the Turing machine model) to find approximate zeros of systems of polynomial equations. If …

Given a homotopy connecting two polynomial systems, we provide a rigorous algorithm for
tracking a regular homotopy path connecting an approximate zero of the start system to an …

The solution set V of a polynomial system, ie, the set of common zeroes of a set of
multivariate polynomials with complex coefficients, may contain several components, eg …

We develop a new symbolic-numeric algorithm for the certification of singular isolated
points, using their associated local ring structure and certified numerical computations. An …