No. 34 (00122)

Family name : Aranson
Given name : Alexander
Affiliation : Keldysh Institute of Applied Mathematics, RAS
Abbreviation : KIAM RAS
E-mail address : aranson@spp.keldysh.ru

Title : Fast Computation of Collections of Correlated Faces for Several
        Polyhedra

Authors : Alexander B. Aranson

Abstract : 
The computer algebra method of the Newton-Bruno Polyhedron (NBP) is very
effective to analyze solutions to systems of algebraic and differential
equations.
To single equation, there corresponds one NBP and it is necessary to
calculate all its faces and their normal cones. Algorithm solving this
problem is based on the correspondence between polyhedrons and cones
then the Motzkin-Burger theorem is applied. This algorithm was
implemented by author as the computer program.

To a system of algebraic and differential equations, there corresponds a
set of NBPs, one for each equation, and it is necessary to calculate all
such collections of their faces, containing one face from each NBP, that
intersections of normal cones of the faces is nonempty. And the
intersections of the normal cones must be calculated as well. Author
finds out the correspondence between collections of faces of the set of
polyhedrons and faces of the single cone. Original fast algorithm to
calculate collections and their normal cones is based on the found
correspondence and it was also implemented as the computer program. The
program was successfully applied to analyze solutions to the ODE system,
describing motions of a rigid body with a fixed point.