Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Numerical homotopies to compute generic points on positive dimensional algebraic sets
Journal of Complexity
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
SIAM Journal on Numerical Analysis
Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
SIAM Journal on Numerical Analysis
On approximate irreducibility of polynomials in several variables
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Algorithm 835: MultRoot---a Matlab package for computing polynomial roots and multiplicities
ACM Transactions on Mathematical Software (TOMS)
The approximate GCD of inexact polynomials
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Numerical factorization of multivariate complex polynomials
Theoretical Computer Science - Algebraic and numerical algorithm
Homotopies for Intersecting Solution Components of Polynomial Systems
SIAM Journal on Numerical Analysis
Solving Polynomial Equations: Foundations, Algorithms, and Applications (Algorithms and Computation in Mathematics)
Computing the multiplicity structure in solving polynomial systems
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Newton's method with deflation for isolated singularities of polynomial systems
Theoretical Computer Science
Exceptional Sets and Fiber Products
Foundations of Computational Mathematics
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Numerical algebraic geometry uses numerical methods, principally numerical tracking of paths defined by polynomial homotopies, to find and manipulate algebraic sets defined by systems of polynomial equations. Kinematics is the study of the geometrical aspects of mechanical motion. The kinematical problems arising in the analysis and design of most robots and mechanisms are essentially algebraic, because these devices are well-modeled as rigid bodies in contact along algebraic surfaces. In particular, the constraints imposed by the most common types of joints, such as simple hinges or ball-and-socket joints, are equivalent to containments of linear features (points, lines, and planes) that are maintained during rigid body motion of the parts. Kinematical studies have driven the development of numerical algebraic geometry and remain one of its most important application areas. Numerical algebraic geometry has proven to be particularly apt for the natural parameterizations presented by problems from kinematics. This extended abstract gives brief overviews of basic numerical algebraic geometry and kinematics.