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[Merged by Bors] - feat(LinearAlgebra/RootSystem/Finite): Coxeter weights are bounded above by 4#19343

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[Merged by Bors] - feat(LinearAlgebra/RootSystem/Finite): Coxeter weights are bounded above by 4#19343
ScottCarnahan wants to merge 10 commits intomasterfrom
ScottCarnahan/CoxeterWeight

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This PR adds a version of the Cauchy-Schwarz inequality for positive semidefinite bilinear forms on modules over linearly ordered commutative rings, and applies it to restrict Coxeter weights for root systems.


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@ScottCarnahan ScottCarnahan added the t-algebra Algebra (groups, rings, fields, etc) label Nov 21, 2024
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github-actions bot commented Nov 21, 2024

PR summary fa0c7e1036

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear 1380 1381 +1 (+0.07%)
Import changes for all files
Files Import difference
Mathlib.Algebra.Lie.Weights.RootSystem Mathlib.LinearAlgebra.RootSystem.Finite.CanonicalBilinear 1

Declarations diff

+ apply_mul_apply_le_of_forall_zero_le
+ apply_mul_apply_lt_iff_linearIndependent
+ apply_smul_sub_smul_sub_eq
+ apply_sq_le_of_symm
+ apply_sq_lt_iff_linearIndependent_of_symm
+ coxeterWeight_le_four
+ coxeterWeight_mem_set_of_isCrystallographic
+ coxeterWeight_ne_four_of_linearIndependent
+ exists_int_eq_coxeterWeight
+ four_smul_rootForm_sq_eq_coxeterWeight_smul
+ infinite_of_linearIndependent_coxeterWeight_four
+ instIsRootPositiveRootForm
+ not_linearIndependent_of_apply_mul_apply_eq
+ toPerfectPairing_apply_CoPolarization
+ toPerfectPairing_apply_apply_Polarization
- infinite_of_linearly_independent_coxeterWeight_four
- rootForm_rootPositive

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).

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ocfnash commented Nov 22, 2024

This looks great!

I’m still travelling (with phone-only internet access) so I can’t review until Tuesday, but I’ll prioritise this then if it’s still pending.

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Just two quick comments for now; will return this evening.

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I had a few moments over lunch.

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Thanks for the suggestions! I hadn't noticed that positive-definiteness on the root span was not used.

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Another round of mostly nitpicks!

@ocfnash ocfnash added the awaiting-author A reviewer has asked the author a question or requested changes. label Nov 30, 2024
@leanprover-community-bot-assistant leanprover-community-bot-assistant 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 2, 2024
@ScottCarnahan ScottCarnahan removed the awaiting-author A reviewer has asked the author a question or requested changes. label Dec 3, 2024
@leanprover-community-bot-assistant leanprover-community-bot-assistant 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 3, 2024
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One last round of small suggestions. Thanks for going the extra mile with Cauchy-Schwarz!

bors d+

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mathlib-bors bot commented Dec 3, 2024

✌️ ScottCarnahan can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@ghost ghost added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Dec 3, 2024
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ocfnash commented Dec 3, 2024

bors merge

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Dec 3, 2024
mathlib-bors bot pushed a commit that referenced this pull request Dec 3, 2024
…ove by 4 (#19343)

This PR adds a version of the Cauchy-Schwarz inequality for positive semidefinite bilinear forms on modules over linearly ordered commutative rings, and applies it to restrict Coxeter weights for root systems.



Co-authored-by: Oliver Nash <github@olivernash.org>
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mathlib-bors bot commented Dec 3, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(LinearAlgebra/RootSystem/Finite): Coxeter weights are bounded above by 4 [Merged by Bors] - feat(LinearAlgebra/RootSystem/Finite): Coxeter weights are bounded above by 4 Dec 3, 2024
@mathlib-bors mathlib-bors bot closed this Dec 3, 2024
@mathlib-bors mathlib-bors bot deleted the ScottCarnahan/CoxeterWeight branch December 3, 2024 14:22
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3 participants