08-07
Notes on the algebra and geometry of polynomial representations
by Averkov, G.
Preprint series: 08-07, Preprints
- MSC:
- 14P10 Semialgebraic sets and related spaces
- 52B05 Combinatorial properties (number of faces, shortest paths, etc.), See also {05Cxx}
Abstract: Consider a semi-algebraic set A in Rd constructed from the sets which are determinedby inequalities pi(x)> 0, pi(x) 0, or pi(x)=0for a given list of polynomials p1,...,pm. We prove several statements that t 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 p1,...,pm. Special cases when A is elementary closed, elementary open,a polygon, or a polytope are considered separately.
Keywords: Irreduciblepolynomial,polygon,polytope,polynomial representation, real algebraic geometry, semi-algebraic set
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