Let K be a field and (f 1,…, fs, ϕ) be multivariate polynomials in K [x 1,…, xn](with s< n) each
invariant under the action of S n, the group of permutations of {1,…, n}. We consider the …

Let R be a real closed field. We prove that for each fixed ℓ, d≥ 0, there exists an algorithm
that takes as input a quantifier-free first-order formula Φ with atoms P= 0, P> 0, P< 0 with P∈ …

The question of how to certify the non-negativity of a polynomial function lies at the heart of
Real Algebra and has important applications to optimization. Building on work by Choi, Lam …

Let R be a real closed field. We consider basic semi-algebraic sets defined by n-variate
equations/inequalities of s symmetric polynomials and an equivariant family of polynomials …

In this paper, we consider the problem of deciding the existence of real solutions to a system
of polynomial equations having real coefficients, and which are invariant under the action of …

This is an experimental case study in real algebraic geometry, aimed at computing the
image of a semialgebraic subset of 3-space under a polynomial map into the plane. For …

We consider symmetric (under the action of products of finite symmetric groups) real
algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine …

Let R be a real closed field and D⊂ R an ordered domain. We consider the algorithmic
problem of computing the generalized Euler-Poincaré characteristic of real algebraic as well …

The Image-Computing Spectral Sequence computes the homology of the image of a finite
map from the alternating homology of the multiple point spaces of the map. A related …

The question how to certify non-negativity of a polynomial function lies at the heart of Real
Algebra and also has important applications to Optimization. In this article we investigate the …