Systems of polynomial equations are a common occurrence in problem formulations in
engineering, science, and mathematics. Solution sets of such systems, ie, algebraic sets, are …

Researchers working with mathematical models are often confronted by the related
problems of parameter estimation, model validation and model selection. These are all …

We present a certified and complete algorithm to compute arrangements of real planar
algebraic curves. It computes the decomposition of the plane induced by a finite number of …

In this paper we extend complex homotopy methods to finding witness points on the
irreducible components of real varieties. In particular we construct such witness points as the …

Let K be a field and (f 1,…, fs, ϕ) be multivariate polynomials in K [x 1,…, xn](with s< n) each
invariant under the action of S n, the group of permutations of {1,…, n}. We consider the …

The foundation of algebraic geometry is the solving of systems of polynomial equations.
When the equations to be considered are defined over a subfield of the complex numbers …

The solution set of a system of polynomial equations, called an algebraic set, can be
decomposed into finitely many irreducible components. In numerical algebraic geometry …

Let K be a field of characteristic zero with K¯ its algebraic closure. Given a sequence of
polynomials g=(g 1,…, gs)∈ K [x 1,…, xn] s and a polynomial matrix F=[fi, j]∈ K [x 1,…, xn] …

Bertini_real is a compiled command line program for numerically decomposing the real
portion of a positive-dimensional complex component of an algebraic set. The software uses …

This paper considers single degree-of-freedom (DOF), closed-loop linkages with a
designated input angle and one design parameter. For a fixed value of the design …