论文标题
双曲线多项式和规范符号模式
Hyperbolic polynomials and canonical sign patterns
论文作者
论文摘要
如果其所有根都是真实的，则真正的单变量多项式是双曲线。根据笛卡尔的符号规则，具有所有系数的双曲线多项式（HP）具有$ c $正面的$ c $正面，而$ p $ p $ pug $ p $ pungots c $ c $ and $ c $和$ p $是其系数顺序的符号更改和符号保存的数量。我们讨论了一个问题：是否所有$ C+P $根的模量是不同的，并在正半轴上订购，那么在哪个位置上可以根据$ p $ oduli的负面根部模量，这取决于多项式系数的积极和负迹象的位置？我们对这些符号的选择特别感兴趣，这些标志正是根部模量的一个顺序。
A real univariate polynomial is hyperbolic if all its roots are real. By Descartes' rule of signs a hyperbolic polynomial (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. We discuss the question: If the moduli of all $c+p$ roots are distinct and ordered on the positive half-axis, then at which positions can the $p$ moduli of negative roots be depending on the positions of the positive and negative signs of the coefficients of the polynomial? We are especially interested in the choices of these signs for which exactly one order of the moduli of the roots is possible.
