论文标题
热带和符号多项式的因素化
Factorizations of tropical and sign polynomials
论文作者
论文摘要
在本文中，我们研究了热带超场和标志高场上多项式的因素，我们分别称为“热带多项式”和“符号多项式”。在任何一种情况下，我们都对所有不可约多项式进行了分类。我们表明，热带多项式因素是独特的因素，但由于符号多物质而失败了。我们通过线性项描述了热带和符号多项式的分裂算法，与多项式的根相对应。
In this text, we study factorizations of polynomials over the tropical hyperfield and the sign hyperfield, which we call `tropical polynomials' and `sign polynomials', respectively. We classify all irreducible polynomials in either case. We show that tropical polynomials factor uniquely into irreducible factors, but that unique factorization fails for sign polyomials. We describe division algorithms for tropical and sign polynomials by linear terms that correspond to roots of the polynomials.
