We introduce a characterization for affine equivalence of two surfaces of translation defined by either rational or meromorphic generators. In turn, this induces a similar characterization for minimal surfaces. In the rational case, our results provide algorithms for detecting affine equivalence of these surfaces, and therefore, in particular, the symmetries of a surface of translation or a minimal surface of the considered types. Additionally, we apply our results to designing surfaces of translation and minimal surfaces with symmetries, and to computing the symmetries of the higher-order Enneper surfaces.

翻译：我们引入了合理或中色生成器定义的两种翻译表面的等同特征特征,这反过来又引发了对最低表面的类似特征特征。在合理的情况下,我们的结果为检测这些表面的等同性提供了算法,因此,特别是,翻译表面的对称性或所考虑类型中最低表面的对称性。此外,我们运用我们的结果来设计翻译表面和有对称性的最小表面,并计算Eneper表面的对称性。