feat: group markings

[YaelDillies]

From LeanCamCombi

---

• depends on: refactor(Normed/Group/Quotient): generalise to non-abelian groups  #21342

[github-actions]

PR summary 0231ea944e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Geometry.Group.Marking (new file)	1530

---

Declarations diff

+ AddGroupMarking
+ GroupMarking
+ GroupMarking.refl
+ MarkedGroup
+ MarkedGroup.instGroup
+ MarkedGroup.instInhabited
+ MarkedGroup.instMulAction
+ MarkedGroup.instSmul
+ Subgroup.continuousConstSMul
+ Submonoid.continuousConstSMul
+ coe_surjective
+ instFunLike
+ instMonoidHomClass
+ instance : Inhabited (GroupMarking G G) := ⟨.refl⟩
+ instance : NormedGroup (MarkedGroup m)
+ norm_le_iff
+ ofMarkedGroup
+ ofMarkedGroup_inj
+ ofMarkedGroup_smul
+ ofMarkedGroup_symm_eq
+ ofMarkedGroup_toMarkedGroup
+ quotientEquivMarkedGroup
+ toMarkedGroup
+ toMarkedGroup_inj
+ toMarkedGroup_ofMarkedGroup
+ toMarkedGroup_smul
+ toMarkedGroup_symm_eq

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).

[b-mehta]

Is there a reference you can give here? I'm not familiar with this definition

[YaelDillies]

I can't find a reference, but eg this MathOverflow question says "A $k$-marked groups is a pair $(G,S)$ where $G$ is a group and $S$ is an ordered set of $k$ generators of $G$." which you can see is the same definition as I have here, only that the set of generators can be extended to give a hom from the free group.

[b-mehta]

If there isn't a reference for a definition you wish to add, does it really belong in mathlib?

[YaelDillies]

Okay, here's a reference: https://math.huji.ac.il/~perin/Documents/GGT/GGTCourse.pdf, Remark 5.3

[b-mehta]

Please add this to the module docstring. It would also be nice to also add the explanation of why you choose a definition different from the one which seems more standard.

[b-mehta]

It would be nice to give here a clearer description of what the metric and norm actually are. Currently the documentation only says that a norm is induced, with no clue as to how they are defined, or what they mean.

[b-mehta]

It's generally not a great idea to have a lemma of this form, where the definition depends on a private lemma. You should instead give properties of the norm which can be useful without referencing private lemmas. For instance, the lemma that there exists a word in the free group with length n which corresponds to x is tricky to prove from the public API. This, and related lemmas (the norm is the smallest n with that property) should be included as part of the norm API.

[YaelDillies]

I've realised that I'm basically redoing the content of Analysis.Normed.Group.Quotient for the multiplicative non-abelian group FreeGroup S, so I've opened #21341 and #21342.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• refactor(Normed/Group/Quotient): generalise to non-abelian groups  #21342
  By Dependent Issues (🤖). Happy coding!

[leanprover-community-bot-assistant]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.