Given a system of polynomial equations and inequations with coefficients in the field of
rational numbers, we show how to compute a geometric resolution of the set of common …

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 …

The subject of this book is the solution of polynomial equations, that is, systems of
(generally) non-linear algebraic equations. This study is at the heart of several areas of …

We present sharp estimates for the degree and the height of the polynomials in the
Nullstellensatz over the integer ring ℤ. The result improves previous work of P. Philippon, C …

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 …

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 …

In this paper, we survey some of our new results on the complexity of a number of problems
related to polynomial ideals. We consider multivariate polynomials over some ring, like the …

Systems of polynomial equations can be used to model an astonishing variety of
phenomena. This book explores the geometry and algebra of such systems and includes …

Geometric constructions applied to a rational action of an algebraic group lead to a new
algorithm for computing rational invariants. A finite generating set of invariants appears as …