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- W2955473669 abstract "A sequence of $d+1$ signs $+$ and $-$ beginning with a $+$ is called a {em sign pattern (SP)}. We say that the real polynomial $P:=x^d+sum _{j=0}^{d-1}a_jx^j$, $a_jneq 0$, defines the SP $sigma :=(+$,sgn$(a_{d-1})$, $ldots$, sgn$(a_0))$. By Descartes' rule of signs, for the quantity $pos$ of positive (resp. $neg$ of negative) roots of $P$, one has $posleq c$ (resp. $negleq p=d-c$), where $c$ and $p$ are the numbers of sign changes and sign preservations in $sigma$; the numbers $c-pos$ and $p-neg$ are even. We say that $P$ realizes the SP $sigma$ with the pair $(pos, neg)$. For SPs with $c=2$, we give some sufficient conditions for the (non)realizability of pairs $(pos, neg)$ of the form $(0,d-2k)$, $k=1$, $ldots$, $[(d-2)/2]$." @default.
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- W2955473669 date "2019-05-06" @default.
- W2955473669 modified "2023-09-27" @default.
- W2955473669 title "On Descartes' rule of signs" @default.
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