@misc{AverkovBroecker, author = {Averkov, Gennadiy and Br{\"o}cker, Ludwig}, title = {Minimal polynomial descriptions of polyhedra and special semialgebraic sets}, series = {Advances in geometry}, volume = {12}, journal = {Advances in geometry}, number = {3}, issn = {1615-715X}, doi = {10.1515/advgeom-2011-059}, pages = {447 -- 459}, abstract = {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)}, language = {en} }