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，若对每个具有有限值域的染色，该结构均包含一个同构的单色子结构。每个不可分结构$\mathcal{S}$自然对应一个不可分问题$\mathsf{Ind}\ \mathcal{S}$，给定结构表示与染色后输出这类子结构。我们研究两类结构的不可分问题的威赫拉复杂性：作为线性序的有理数集$\mathbb{Q}$，以及具有可数个等价类且每类包含可数成员的等价关系$\mathscr{E}$。我们分别将$\mathsf{Ind}\ \mathbb{Q}$和$\mathsf{Ind}\ \mathscr{E}$的威赫拉度与若干基准问题分离，特别证明了$\mathsf{C}_\mathbb{N} \vert_\mathrm{W} \mathsf{Ind}\ \mathbb{Q}$，因此$\mathsf{Ind}\ \mathbb{Q}$严格弱于在$\mathbb{Q}$的给定染色中寻找某种颜色稠密区间的问题；同时，$\mathsf{Ind}\ \mathscr{E}_k$的威赫拉度严格介于$\mathsf{SRT}^2_k$与$\mathsf{RT}^2_k$之间，其中$\mathsf{Ind}\ \mathcal{S}_k$是$\mathsf{Ind}\ \mathcal{S}$在$k$-染色上的限制。