Smale's 17th problem asks:“Can a zero of $ n $ complex polynomial equations in $ n $
unknowns be found approximately, on the average, in polynomial time with a uniform …

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 …

We show lower bounds for depth of arithmetic networks over algebraically closed fields, real
closed fields and the field of the rationals. The parameters used are either the degree or the …

We show lower bounds for the parallel complexity of membership problems in semialgebraic
sets. Our lower bounds are obtained from the Euler characteristic and the sum of Betti …

We obtain nonlinear complexity lower bounds for randomized computation trees with
branching signs {=,\not=\} over zero charac-teristic fields. As consequences we get the …

We discuss Riemannian distances in the Lie groups 50 (3) and SE {3), in relation with
proximity problems in robotics. We study the problem of the computability of this kind of …

In their 1989 paper [2], L. Blum, M. Shub and S. Smale introduced a model of computation
and a theory of recursiveness that accepted an ordered field or ring as alphabet for the …

Relations between discrete and continuous complexity models are considered. The present
paper is devoted to combine both models. In particular we analyze the 3‐Satisfiability …

We discuss Riemannian distances in the Lie groups 80 (3) and 8E (3), in relation with
proximity problems in robotics. We study the problem of the computability of this kind of …