TY - GEN A1 - Averkov, Gennadiy A1 - Bröcker, Ludwig T1 - Minimal polynomial descriptions of polyhedra and special semialgebraic sets T2 - Advances in geometry N2 - We show that a d-dimensional polyhedron S in Rd can be represented by d-polynomial inequalities, that is, S = fx 2 Rd : p0(x) 0; : : : ; pd(x) 0g, where p0; : : : ; pd1 are appropriate polynomials. Furthermore, if an elementary closed semialgebraic set S is given by polynomials q1; : : : ; qk and for each x 2 S at most s of these polynomials vanish in x, then S can be represented by s + 1 polynomials (and by s polynomials) KW - Hörmander–Łojasiewicz’s Inequality KW - polyhedron KW - polynomial KW - polytope KW - semialge-braic set KW - stability index KW - Theorem of Bröcker and Scheiderer Y1 - 2012 UR - https://www.degruyter.com/view/j/advg.2012.12.issue-3/advgeom-2011-059/advgeom-2011-059.xml U6 - https://doi.org/10.1515/advgeom-2011-059 SN - 1615-715X SN - 1615-7168 VL - 12 IS - 3 SP - 447 EP - 459 ER -