[Merged by Bors] - feat(GroupTheory/Cyclic): formula for the card & index of kernel & range of powMonoidHom on a cyclic group

[xroblot]

We prove formula for the cardinal and index of the kernel and range of powMonoidHom : x ↦ x ^ d on a finite cyclic group.

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[github-actions]

PR summary 71bb8b767a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ IsCyclic.card_powMonoidHom_ker
+ IsCyclic.card_powMonoidHom_range
+ IsCyclic.index_powMonoidHom_ker
+ IsCyclic.index_powMonoidHom_range
+ index_range
+ orderOf_eq_card_of_zpowers_eq_top

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.

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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).

[tb65536]

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by tb65536.

[xroblot]

@tb65536 Sorry, I didn't have time to post a comment before but thank you for the review and the great golf.

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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