This paper proposes a symbolic representation of non-linear maps $F$ in $\ff^n$ in terms of linear combination of basis functions of a subspace of $(\ff^n)^0$, the dual space of $\ff^n$. Using this representation, it is shown that the inverse of $F$ whenever it exists can also be represented in a similar symbolic form using the same basis functions (using different coefficients). This form of representation should be of importance to solving many problems of iterations or compositions of non-linear maps using linear algebraic methods which would otherwise require solving hard computational problems due to non-linear nature of $F$.

中文翻译：

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使用简化的 Koopman 对偶线性映射计算有限域上多项式映射的逆

本文提出了$\ff^n$中非线性映射$F$的符号表示，用$(\ff^n)^0$子空间的基函数线性组合表示，$\的对偶空间ff^n$。使用这种表示，表明只要存在 $F$ 的倒数，也可以使用相同的基函数（使用不同的系数）以类似的符号形式表示。这种表示形式对于使用线性代数方法解决非线性映射的迭代或组合问题很重要，否则由于 $F$ 的非线性性质，这些问题将需要解决困难的计算问题。