  We consider the set of monic degree $d$ real univariate polynomials
$Q_d=x^d+\sum_{j=0}^{d-1}a_jx^j$ and its {\em hyperbolicity domain} $\Pi_d$,
i.e. the subset of values of the coefficients $a_j$ for which the polynomial
$Q_d$ has all roots real. The subset $E_d\subset \Pi_d$ is the one on which a
modulus of a negative root of $Q_d$ is equal to a positive root of $Q_d$. At a
point, where $Q_d$ has $d$ distinct roots with exactly $s$ ($1\leq s\leq
[d/2]$) equalities between positive roots and moduli of negative roots, the set
$E_d$ is locally the transversal intersection of $s$ smooth hypersurfaces. At a
point, where $Q_d$ has two double opposite roots and no other equalities
between moduli of roots, the set $E_d$ is locally the direct product of
$\mathbb{R}^{d-3}$ and a hypersurface in $\mathbb{R}^3$ having a Whitney
umbrella singularity. For $d\leq 4$, we draw pictures of the sets $\Pi_d$
and~$E_d$.
