Definition 4.30 (Real stable). A polynomial $p(z_1,\dots ,z_n)\in ℝ[z_1,\dots ,z_n]$ is real stable if $p(z_1,\dots ,z_n)\ne 0$ for all $(z_1,\dots ,z_n)\in H^n$, $H=\{z\in ℂ|\mathrm{Im}z>0\}$.