In recent years, the discovery of new algorithms for dealing with polynomial equations,
coupled with their implementation on fast inexpensive computers, has sparked a minor …

Polynomial systems occur in a wide variety of application domains. Homotopy continuation
methods are reliable and powerful methods to compute numerically approximations to all …

An ordered tree is a tree in which each node's incident edges are cyclically ordered; think of
the tree as being embedded in the plane. Let A and B be two ordered trees. The edit …

The last decade has witnessed the rebirth of resultant methods as a powerful computational
tool for variable elimination and polynomial system solving. In particular, the advent of …

Many applications modeled by polynomial systems have positive dimensional solution
components (eg, the path synthesis problems for four-bar mechanisms) that are challenging …

We present bounds for the sparseness in the Nullstellensatz. These bounds can give a
much sharper characterization than degree bounds of the monomial structure of the …

Consider a system F of n polynomial equations in n unknowns, over an algebraically closed
field of arbitrary characteristic. We present a fast method to find a point in every irreducible …

We present a bounded probability algorithm for the computation of the Chowforms of the
equidimensional components of an algebraic variety. In particular, this gives an alternative …

Bernshtein's theorem provides a generically exact upper bound on the number of isolated
solutions a sparse polynomial system can have in (ℂ*) n, with ℂ*= ℂ\{0}. When a sparse …

Given any polynomial system with fixed monomial term structure, we give explicit formulae
for the generic number of roots with specified coordinate vanishing restrictions. For the case …