This dataset contains prompt-completion pairs focused on computational tasks within directed simplicial complexes, including facet validation, incidence sign calculation, and Betti number derivation. Samples demonstrate step-by-step reasoning for determining boundary maps, verifying simplex orientations, and applying rank-nullity theorems. The content is… See the full description on the dataset page: https://huggingface.co/datasets/Gro97/adaption-simplicial-homology-tasks.