科研之友
微信
新浪微博
Facebook
分享链接
摘要
We show that a d-dimensional polyhedron S in R-d can be represented by d-polynomial inequalities, that is, S = {x is an element of R-d : p(0)(x) %26gt;= 0, ... , p(d-1)(x) %26gt;= 0}, where p(0), ... , p(d-1) are appropriate polynomials. Furthermore, if an elementary closed semialgebraic set S is given by polynomials q(1), ... , q(k) and for each x is an element of S at most s of these polynomials vanish in x, then S can be represented by s + 1 polynomials (and by s polynomials under the extra assumption that the number of points x is an element of S in which s of the q(i) vanish is finite).
- 出版日期2012
