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- W3111235592 abstract "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 $E_dsubset Pi_d$ 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 $s$ ($1leq sleq [d/2]$) 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 $dleq 4$, we draw pictures of the sets $Pi_d$ and~$E_d$." @default.
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- W3111235592 date "2020-12-08" @default.
- W3111235592 modified "2023-09-27" @default.
- W3111235592 title "Sign patterns and rigid moduli orders" @default.
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