feat(NumberField): Image of torsion modulo an ideal

[xroblot]

Let I be an integral ideal of a number field K. We define the morphism from the torsion of K to (𝓞 K ⧸ I)ˣ and prove that it is injective if the norm of I is coprime with the order of the torsion of K.

As a consequence, we prove that for a prime ideal P coprime with the order of the torsion of K, the norm of P is congruent to 1 modulo torsionOrder K.

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[github-actions]

PR summary 0114eff24c

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.Cyclotomic.Rat	1
Mathlib.NumberTheory.NumberField.Ideal.Basic (new file)	2775

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Declarations diff

+ Ideal.torsionMapQuot
+ Ideal.torsionMapQuot_apply
+ Ideal.torsionMapQuot_injective
+ IsPrimitiveRoot.not_coprime_norm_of_mk_eq_one
+ NumberField.torsionOrder_dvd_absNorm_sub_one
+ _root_.IsPrimitiveRoot.intermediateField_adjoin_isCyclotomicExtension
+ _root_.isPrimitiveRoot_of_mem_rootsOfUnity
+ norm_toInteger_sub_one_eq_one
+ norm_toInteger_sub_one_of_eq_two
+ norm_toInteger_sub_one_of_eq_two_pow
+ prime_dvd_of_dvd_norm_sub_one

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).

[xroblot]

This PR has been migrated to a fork-based workflow: #26072