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 …

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 …

Let S_0 be a smooth and compact real variety given by a reduced regular sequence of
polynomials f_1,...,f_p. This paper is devoted to the algorithmic problem of finding efficiently …

We present a new probabilistic method for solving systems of polynomial equations and
inequations. Our algorithm computes the equidimensional decomposition of the Zariski …

We propose an efficient algorithm for computing triangular decompositions of algebraic
varieties. It is based on an incremental process and produces components in order of …

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 …

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 …

Smale's 17th Problem asks “Can a zero of n complex polynomial equations in n unknowns
be found approximately, on the average [for a suitable probability measure on the space of …