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 …

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 if the Generalized Riemann Hypothesis is true, the problem of deciding
whether a system of polynomial equations in several complex variables has a solution is in …

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 …

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 …

Valiant developed a nonuniform algebraic analogue of the theory of NP-completeness for
computations with polynomials over a field k in (Valiant, Proceedings of the 11th ACM …

We present a new approach to the ideal membership problem for polynomial rings over the
integers: given polynomials $ f_0, f_1,\dots, f_n\in\mathbb Z [X] $, where $ X=(X_1,\dots …