We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees of its rational solutions, and thus derive a complete algorithm for computing corresponding rational solutions.

中文翻译：

---

一阶代数常微分方程的有理解

我们提出了一种代数几何方法来研究一阶代数常差分方程的有理解。对于一个自治的一阶代数常微分方程，我们给出了其有理解的度数的上限，从而推导出了计算相应有理解的完整算法。