A countable structure is indivisible if for every coloring with finite range there is a monochromatic isomorphic subcopy of the structure. Each indivisible structure $\mathcal{S}$ naturally corresponds to an indivisibility problem $\mathsf{Ind}\ \mathcal{S}$, which outputs such a subcopy given a presentation and coloring. We investigate the Weihrauch complexity of the indivisibility problems for two structures: the rational numbers $\mathbb{Q}$ as a linear order, and the equivalence relation $\mathscr{E}$ with countably many equivalence classes each having countably many members. We separate the Weihrauch degrees of both $\mathsf{Ind}\ \mathbb{Q}$ and $\mathsf{Ind}\ \mathscr{E}$ from several benchmark problems, showing in particular that $\mathsf{C}_\mathbb{N} \vert_\mathrm{W} \mathsf{Ind}\ \mathbb{Q}$ and hence $\mathsf{Ind}\ \mathbb{Q}$ is strictly weaker than the problem of finding an interval in which some color is dense for a given coloring of $\mathbb{Q}$; and that the Weihrauch degree of $\mathsf{Ind}\ \mathscr{E}_k$ is strictly between those of $\mathsf{SRT}^2_k$ and $\mathsf{RT}^2_k$, where $\mathsf{Ind}\ \mathcal{S}_k$ is the restriction of $\mathsf{Ind}\ \mathcal{S}$ to $k$-colorings.

翻译：一个可数结构称为不可分的，若对每个有限值域的着色，该结构都存在一个同构的单色子拷贝。每个不可分结构 $\mathcal{S}$ 自然对应一个不可分性问题 $\mathsf{Ind}\ \mathcal{S}$，该问题在给定呈现与着色时输出这样一个子拷贝。我们研究两个结构的不可分性问题的Weihrauch复杂度：作为线性序的有理数集 $\mathbb{Q}$，以及具有可数多个等价类且每类包含可数多个元素的等价关系 $\mathscr{E}$。我们将 $\mathsf{Ind}\ \mathbb{Q}$ 和 $\mathsf{Ind}\ \mathscr{E}$ 的Weihrauch度与若干基准问题分离，特别证明 $\mathsf{C}_\mathbb{N} \vert_\mathrm{W} \mathsf{Ind}\ \mathbb{Q}$，从而 $\mathsf{Ind}\ \mathbb{Q}$ 严格弱于在给定的 $\mathbb{Q}$ 的着色中寻找某颜色稠密区间的问题；并且 $\mathsf{Ind}\ \mathscr{E}_k$ 的Weihrauch度严格介于 $\mathsf{SRT}^2_k$ 和 $\mathsf{RT}^2_k$ 之间，其中 $\mathsf{Ind}\ \mathcal{S}_k$ 是 $\mathsf{Ind}\ \mathcal{S}$ 在 $k$-着色上的限制。