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：可数结构称为不可分的，若对每个有限值域染色，该结构均存在一个单色同构子结构。每个不可分结构$\mathcal{S}$自然对应一个不可分性问题$\mathsf{Ind}\ \mathcal{S}$，给定一个展示和染色后输出这样的子结构。我们研究了两种结构不可分性问题的魏劳赫复杂度：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个等价类包含可数多个元素的等价关系$\mathscr{E}$。我们将$\mathsf{Ind}\ \mathbb{Q}$和$\mathsf{Ind}\ \mathscr{E}$的魏劳赫度与若干个基准问题进行了分离，特别证明了$\mathsf{C}_\mathbb{N} \vert_\mathrm{W} \mathsf{Ind}\ \mathbb{Q}$，从而$\mathsf{Ind}\ \mathbb{Q}$严格弱于寻找$\mathbb{Q}$的给定染色中某种颜色稠密的区间的问题；同时证明了$\mathsf{Ind}\ \mathscr{E}_k$的魏劳赫度严格介于$\mathsf{SRT}^2_k$和$\mathsf{RT}^2_k$之间，其中$\mathsf{Ind}\ \mathcal{S}_k$是$\mathsf{Ind}\ \mathcal{S}$在$k$-染色上的限制。