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feat: product of Coxeter matrices#37160

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vihdzp:mul
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feat: product of Coxeter matrices#37160
vihdzp wants to merge 2 commits intoleanprover-community:masterfrom
vihdzp:mul

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@vihdzp vihdzp commented Mar 25, 2026

The Coxeter matrix A * B is the block matrix !![A, 2; 2, B].

I've used multiplication to denote this under the logic that the product of Coxeter groups has a Coxeter matrix given by this construction. Perhaps this isn't desirable, considering it doesn't match matrix multiplication. I'm open to suggestions.

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@vihdzp vihdzp added the t-group-theory Group theory label Mar 25, 2026
@vihdzp vihdzp changed the title feat: product of Coxeter matrix feat: product of Coxeter matrices Mar 25, 2026
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github-actions bot commented Mar 25, 2026

PR summary fb131a4c00

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ instance : CoeFun (CoxeterMatrix B) fun _ ↦ Matrix B B ℕ := ⟨M⟩
+ instance : HMul (CoxeterMatrix B) (CoxeterMatrix B') (CoxeterMatrix (B ⊕ B'))
- instance : CoeFun (CoxeterMatrix B) fun _ ↦ (Matrix B B ℕ) := ⟨M⟩

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

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

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

No changes to technical debt.

You can run this locally as

./scripts/reporting/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).

tb65536
tb65536 reviewed Mar 28, 2026
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Mathlib/GroupTheory/Coxeter/Matrix.lean
theorem reindex_apply (i i' : B') : M.reindex e i i' = M (e.symm i) (e.symm i') := rfl

/-- The Coxeter matrix `A * B` is the block matrix `!![A, 2; 2, B]`. -/
instance : HMul (CoxeterMatrix B) (CoxeterMatrix B') (CoxeterMatrix (B ⊕ B')) where
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@tb65536 tb65536 Mar 28, 2026 •
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Yeah, maybe this should just be a def with API instead?

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@vihdzp vihdzp Mar 29, 2026

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a) What should I call this?
b) What API should I put on this? This is mostly intended as a way to prove products of Coxeter groups are Coxeter, should I hold off on adding it before I prove that theorem?

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