Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 271-282 (2009)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Notes on the algebra and geometry of polynomial representations

Gennadiy Averkov

Institute of Algebra and Geometry, Faculty of Mathematics, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany, e-mail:$\sim$averkov}

Abstract: The paper deals with a semi-algebraic set $A$ in $\real^d$ constructed by the inequalities $p_i(x)>0$, $p_i(x) \ge 0$, and $p_i(x) = 0$ for a given list of polynomials $p_1,\ldots,p_m$, and presents several statements that fit into the following template. Assume that in a neighborhood of a boundary point the semi-algebraic set $A$ can be described by an irreducible polynomial $f$. Then $f$ is a factor of a certain multiplicity of some of the polynomials 3$p_1,\ldots,p_m$. Special attention is paid to the case when $A$ is a polytope.

Keywords: irreducible polynomial, polygon, polytope, polynomial representation, real algebraic geometry, semi-algebraic set

Classification (MSC2000): 14P10, 52B11

Full text of the article:

Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.

© 2008 Heldermann Verlag
© 2008–2013 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition