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feat(Analysis/Convex/SimplicialComplex): add AbstractSimplicialComplex + constructions #33364
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feat(Analysis/Convex/SimplicialComplex): add AbstractSimplicialComplex + constructions #33364
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… is affinely independent
PR summary 1a6e4fde6aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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I would be open to comments about whether I should refactor more of this to other files, and if so, where those files should live. |
This adds the concept of abstract simplicial complex (and refactors SimplicialComplex in terms of it.
It also adds constructions that makes it easy to define a simplicial complex for any index family of points which is downward closed and which is affinely independent. I also include a construction of (abstract and geometric) simplicial complexes associated with a SimpleGraph, where vertices become 0-faces and edges become 1-faces, which could be useful later in defining the topological notion of a graph embedding.
Co-authored-by: Claude Opus 4.5
Notes: Perhaps it would be better to use stdSimplex as the underlying space for the graph?