 class="math">\(2\times 2\)</span> LMIs that depends on both <span class="math">\(p_n\)</span> and <span class="math">\(p_d\)</span>;
we denote this number by <span class="math">\(k(p_n,p_d)\)</span>. (In some cases additional
linear constraints are also generated, but we ignore them for this
analysis.) For instance, for <span class="math">\(p=3/1\)</span>, we have</p>
<div class="math">
\[\begin{split}x^3\leq y, x\geq 0 \quad\Longleftrightarrow\quad \exists z ~
    \begin{bmatrix} z &amp; x \\ x &amp; 1 \e