Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 271-282 (2009)
Notes on the algebra and geometry of polynomial representations
Gennadiy AverkovInstitute of Algebra and Geometry, Faculty of Mathematics, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany, e-mail: email@example.com
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
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Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.