The group of units modulo constants of an affine variety over an algebraically closed field is free abelian of finite rank. Computing this group is difficult but of fundamental importance in tropical geometry, where it is necessary in order to realize intrinsic tropicalizations. We present practical algorithms for computing unit groups of smooth curves of low genus. Our approach is rooted in divisor theory, based on interpolation in the case of rational curves and on methods from algebraic number theory in the case of elliptic curves.

中文翻译：

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计算曲线的单位组

代数封闭域上仿射变体的单位模常数的组是有限秩的自由阿贝尔。计算该组是困难的，但在热带几何中至关重要，而热带几何对于实现固有的热带化是必不可少的。我们提出了实用的算法来计算低类平滑曲线的单位组。我们的方法基于除数理论，在有理曲线的情况下基于插值，在椭圆曲线的情况下基于代数数论的方法。