符号模式的实多项式可实现性
On realizability of sign patterns by real polynomials
摘要：
经典的笛卡尔符号法则通过系数序列中符号变化的次数来限制一元实一元多项式的正根的个数。人们可以问这样一个问题，根据这一规则和其他一些自然条件选择的非负整数对$(p,n)$，可以是具有规定系数符号的实多项式的正负根的数目对。本文解决了这个问题的次数$8$多项式。
英文摘要：
The classical Descartes' rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers $(p,n)$, chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree $8$ polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
