    ## Descartes' rule of signs and moduli of roots. (arXiv:1904.10694v1 [math.CA])

A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly \$c\$ positive and exactly \$p\$ negative roots counted with multiplicity, where \$c\$ and \$p\$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. For \$c=1\$ and \$2\$, we discuss the question: When the moduli of all the roots of a HP are arranged in the increasing order on the real half-line, at which positions can be the moduli of its positive roots depending on the positions of the sign changes in the sequence of coefficients?查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly \$c\$ positive and exactly \$p\$ negative roots counted with multiplicity, where \$c\$ and \$p\$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. For \$c=1\$ and \$2\$, we discuss the question: When the moduli of all the roots of a HP are arranged in the increasing order on the real half-line, at which positions can be the moduli of its positive roots depending on the positions of the sign changes in the sequence of coefficients?