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Optimal Descartes’ rule of signs for systems supported on circuits
Mathematische Annalen ( IF 1.4 ) Pub Date : 2021-06-02 , DOI: 10.1007/s00208-021-02216-4 Frédéric Bihan , Alicia Dickenstein , Jens Forsgård
中文翻译:
电路上支持的系统的最优笛卡尔符号规则
更新日期:2021-06-02
Mathematische Annalen ( IF 1.4 ) Pub Date : 2021-06-02 , DOI: 10.1007/s00208-021-02216-4 Frédéric Bihan , Alicia Dickenstein , Jens Forsgård
We present an optimal version of Descartes’ rule of signs to bound the number of positive real roots of a sparse system of polynomial equations in n variables with \(n+2\) monomials. This sharp upper bound is given in terms of the sign variation of a sequence associated to the exponents and the coefficients of the system.
中文翻译:
电路上支持的系统的最优笛卡尔符号规则
我们提出了笛卡尔符号规则的最佳版本,以使用\(n+2\)单项式限制n 个变量中多项式方程的稀疏系统的正实根的数量。这个尖锐的上限是根据与系统的指数和系数相关联的序列的符号变化给出的。