Deciding efficiently the emptiness of a real algebraic set defined by a single equation is a fundamental problem of computational real algebraic geometry. We propose an algorithm for this test. We find, when the algebraic set is non empty, at least one point on each semialgebraically connected component. The problem is reduced to deciding the existence of real critical points of the distance fu...

In this paper we present an implicit time-stepping scheme for multibody systems with intermittent contact by incorporating the contact constraints as a set of complementarity and algebraic equations within the dynamics model. Two primary sources of stability and accuracy problems in prior time stepping schemes for differential complementarity models of multibody systems are the use of polyhedra...

We introduce and study the minimum distance function of a graded ideal in a polynomial ring with coefficients in a field, and show that it generalizes the minimum distance of projective Reed-Muller-type codes over finite fields. This gives an algebraic formulation of the minimum distance of a projective Reed-Muller-type code in terms of the algebraic invariants and structure of the underlying v...

The problem of computing the distance in the Frobenius norm of a given real irreducible tridiagonal matrix T to the algebraic variety of real normal irreducible tridiagonal matrices is solved. Simple formulas for computing the distance and a normal tridiagonal matrix at this distance are presented. The special case of tridiagonal Toeplitz matrices also is considered.

We deduce some approximate formulas for the distance evaluation problem between a point and an ellipse in IR2 and a point and an ellipsoid in IR3. The proposed approach is based on the analytical representation of the distance function as a zero of an appropriate univariate algebraic equation. Key–Words: Distance, point-to-ellipse, point-to-ellipsoid

Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.