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 …

Written by the founders of the new and expanding field of numerical algebraic geometry, this
is the first book that uses an algebraic-geometric approach to the numerical solution of …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

Smale's α-theory uses estimates related to the convergence of Newton's method to certify
that Newton iterations will converge quadratically to solutions to a square polynomial …

We present a new probabilistic method for solving systems of polynomial equations and
inequations. Our algorithm computes the equidimensional decomposition of the Zariski …

Many polynomial systems have solution sets comprised of multiple irreducible components,
possibly of different dimensions. A fundamental problem of numerical algebraic geometry is …

Given a polynomial system f, a fundamental question is to determine if f has real roots. Many
algorithms involving the use of infinitesimal deformations have been proposed to answer …

To decompose solution sets of polynomial systems into irreducible components, homotopy
continuation methods generate the action of a natural monodromy group which partially …

For many mechanical systems, including nearly all robotic manipulators, the set of possible
configurations that the links may assume can be described by a system of polynomial …

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 …