feat(Analysis/LocallyConvex): characterize dense submodules by annihilators

[yuanyi-350]

used in LeanMachineLearning/LML#246

[github-actions]

PR summary 1c7a40bf34

Import changes exceeding 2%

%	File
+37.09%	Mathlib.Analysis.LocallyConvex.Polar

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.LocallyConvex.Polar	1642	2251	+609 (+37.09%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.LocallyConvex.Polar	609

---

Declarations diff (regex)

+ dense_iff_forall_dual_eq_zero
+ dense_iff_polarSubmodule_eq_bot
+ exists_dual_annihilator_of_not_dense

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

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

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 1c7a40b).

• +4 new declarations
• −0 removed declarations

+StrongDual.polarSubmodule.congr_simp
+Submodule.dense_iff_forall_dual_eq_zero
+Submodule.dense_iff_polarSubmodule_eq_bot
+Submodule.exists_dual_annihilator_of_not_dense

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit 1c7a40bf34
Reference commit a79b0d211a

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py 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).