George Collins' discovery of Cylindrical Algebraic Decomposition (CAD) as a method for
Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major …

We present a new method for solving symbolically zero-dimensional polynomial equation
systems in the affine and toric case. The main feature of our method is the use of problem …

We introduce a subexponential algorithm for geometric solving of multivariate polynomial
equation systems whose bit complexity depends mainly on intrinsic geometric invariants of …

We present a new method for solving symbolically zero-dimensional polynomial equation
systems in the affine and toric case. The main feature of our method is the use of an …

We show that any algebraic computation tree or any fixed-degree algebraic tree for solving
the membership question of a compact set S~ R “must have height greater than Cl (log (@ i …

In this paper we apply for the first time a new method for multivariate equation solving which
was developed in\cite {gh1},\cite {gh2},\cite {gh3} for complex root determination to the {\em …

The procedures to solve algebraic geometry elimination problems have usually been
designed from the point of view of commutative algebra. For instance, let us consider the …

Computer algebra is a research field that combines two main subjects that were separated
for years: algebra and computer science. A short characterization would be: computer …

A survey on real structural complexity theory Page 1 A survey on real structural complexity
theory Klaus Meer ∗ Christian Michaux † Abstract In this tutorial paper we overview research …

These pages are a first attempt to compare the efficiency of symbolic and numerical analysis
procedures that solve systems of multivariate polynomial equations. In particular, we …