Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 50, No. 1, pp. 271282 (2009) 

Notes on the algebra and geometry of polynomial representationsGennadiy AverkovInstitute of Algebra and Geometry, Faculty of Mathematics, OttovonGuericke University of Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany, email: gennadiy.averkov@googlemail.comhttp://fma2.math.unimagdeburg.de/$\sim$averkov} Abstract: The paper deals with a semialgebraic 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 semialgebraic 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, semialgebraic set Classification (MSC2000): 14P10, 52B11 Full text of the article:
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