This paper proposes the matrix representation of formal polynomials over max-plus algebra and obtains the maximum and minimum canonical forms of a polynomial function by standardizing this representation into a canonical form. A necessary and sufficient condition for two formal polynomials corresponding to the same polynomial function is derived. Such a matrix method is constructive and intuitive, and leads to a polynomial algorithm for factorization of polynomial functions. Some illustrative examples are presented to demonstrate the results.

中文翻译：

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最大加代数上形式多项式的矩阵表示

本文提出了max-plus代数上形式多项式的矩阵表示，并通过将该表示标准化为规范形式，得到多项式函数的最大和最小规范形式。推导了同一个多项式函数对应的两个形式多项式的充要条件。这种矩阵方法是建设性的和直观的，并导致多项式函数分解的多项式算法。提供了一些说明性示例来演示结果。