Representing simple d-dimensional polytopes by d polynomials

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dc.creatorAverkov, Gennadiy
dc.creatorHenk, Martin
dc.date2007-09-13
dc.date.accessioned2026-07-07T08:29:21Z
dc.date.available2026-07-07T08:29:21Z
dc.descriptionA polynomial representation of a convex d-polytope P is a finite set \{p_1(x),...,p_n(x)\} of polynomials over E^d such that P=\setcond{x \in \E^d}{p_1(x) \ge 0 {for every} 1 \le i \le n}. By s(d,P) we denote the least possible number of polynomials in a polynomial representation of P. It is known that d \le s(d,P) \le 2d-1. Moreover, it is conjectured that s(d,P)=d for all convex d-polytopes P. We confirm this conjecture for simple d-polytopes by providing an explicit construction of d polynomials that represent a given simple d-polytope P.
dc.description19 pages, 7 figures
dc.identifierhttps://arxiv.org/abs/0709.2099
dc.identifierhttp://arxiv.org/abs/0709.2099
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137939
dc.subjectMetric Geometry
dc.subjectAlgebraic Geometry
dc.subject14P05; 52B11; 52A20
dc.titleRepresenting simple d-dimensional polytopes by d polynomials
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