  We show that a $d$-dimensional polyhedron $S$ in $\real^d$ can be represented
by $d$-polynomial inequalities, that is, $S = \{x \in \real^d : p_0(x) \ge 0,
>..., p_{d-1}(x) \ge 0 \}$, 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 $x \in S$ 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 $x
\in S$ in which $s$ $q_i$'s vanish is finite).
