12 citations · 18 across the 3 of their papers we have counts for
3 papers
A bound on the minimum of a real positive polynomial over the standard simplex
Saugata Basu, Richard Leroy, Marie-Francoise Roy
We consider the problem of bounding away from 0 the minimum value m taken by a polynomial P of Z[X_1,...,X_k] over the standard simplex, assuming that m>0. Recent algorithmic devel…
Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets
Saugata Basu, Richard Pollack, Marie-Francoise Roy
In this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zero-th…
An asymptotically tight bound on the number of semi-algebraically connected components of realizable sign conditions
Saugata Basu, Richard Pollack, Marie-Francoise Roy
We prove an asymptotically tight bound (asymptotic with respect to the number of polynomials for fixed degrees and number of variables) on the number of semi-algebraically connecte…