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@BoltonBailey BoltonBailey commented Dec 29, 2025

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?

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@github-actions github-actions bot added t-analysis Analysis (normed *, calculus) large-import Automatically added label for PRs with a significant increase in transitive imports labels Dec 29, 2025
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github-actions bot commented Dec 29, 2025

PR summary 1a6e4fde6a

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Analysis.Convex.SimplicialComplex.AffineIndependentUnion (new file) 913

Declarations diff

+ AbstractSimplicialComplex
+ LinearIndependent.affineIndependent
+ instance : Min (AbstractSimplicialComplex ι)
+ instance : SemilatticeInf (AbstractSimplicialComplex ι)
+ ofAffineIndependent
+ onFinsupp
++ ofSimpleGraph

You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@BoltonBailey BoltonBailey added the WIP Work in progress label Dec 29, 2025
@github-actions github-actions bot removed the large-import Automatically added label for PRs with a significant increase in transitive imports label Dec 29, 2025
@BoltonBailey BoltonBailey added awaiting-CI This PR doesn't pass CI yet. This label is automatically removed once it does. and removed WIP Work in progress labels Dec 29, 2025
@BoltonBailey BoltonBailey added the WIP Work in progress label Dec 29, 2025
@github-actions github-actions bot removed the awaiting-CI This PR doesn't pass CI yet. This label is automatically removed once it does. label Dec 29, 2025
@BoltonBailey BoltonBailey removed the WIP Work in progress label Dec 29, 2025
@BoltonBailey BoltonBailey added the WIP Work in progress label Dec 29, 2025
@github-actions github-actions bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Dec 29, 2025
@github-actions github-actions bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. (this label is managed by a bot) label Dec 30, 2025
@BoltonBailey BoltonBailey changed the title feat(Analysis/Convex/SimplicialComplex): add constructions when union is affinely independent feat(Analysis/Convex/SimplicialComplex): add AbstractSimplicialComplex + constructions Dec 30, 2025
@BoltonBailey BoltonBailey removed the WIP Work in progress label Dec 30, 2025
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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.

@BoltonBailey BoltonBailey added the WIP Work in progress label Dec 30, 2025
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