The Handbook of Geometric Constraint Systems Principles is an entry point to the currently
used principal mathematical and computational tools and techniques of the geometric …

Given a set of multivariate polynomials $\{f\sb1,\..., f\sb {k}\}\subset {\rm l\! k}\lbrack x\sb1,\...,
x\sb {n}\rbrack, $ consider the algebraic set $ V=\{x\in {\bf K}\sp {n}\vert f\sb1 (x)=\...= f\sb …

The complexity of computing the Galois group of a linear differential equation is of general
interest. In a recent work, Feng gave the first degree bound on Hrushovski's algorithm for …

We give a uniform method for the two problems of counting the connected and irreducible
components of complex algebraic varieties. Our algorithms are purely algebraic, ie, they use …

In this paper, we first introduce a new vertex order of graphs called the substrong elimination
ordering based on maximal cliques of the graphs and prove that such an ordering can fully …

When using resultants for elimination, one standard issue is that the resultant vanishes if the
variety contains components of dimension larger than the expected dimension. J. Canny …

Invariant sets are a key ingredient for verifying safety and other properties of cyber-physical
systems that mix discrete and continuous dynamics. We adapt the elimination-theoretic …

When using resultants for elimination, one standard issue is that the resultant vanishes if the
variety contains components of dimension larger than the expected dimension. J. Canny …

Triangular decomposition is one of the standard ways to represent the radical of a
polynomial ideal. A general algorithm for computing such a decomposition was proposed by …

We describe a parallel polynomial time algorithm for computing the topological Betti
numbers of a smooth complex projective variety X. It is the first single exponential time …