feat(RingTheory/DedekindDomain): add divisor group core

[vaca22]

Add the formal divisor group of a Dedekind domain and bundle the existing factorization API as an additive equivalence between nonzero fractional ideals and divisors.

Divisors are finitely supported integer-valued functions on height-one primes. divisor records FractionalIdeal.count, ofDivisor reconstructs a fractional ideal from prime powers, and divisorEquiv proves these operations are inverse and send ideal multiplication to divisor addition.

This is the core of the earlier larger proposal. Principal divisors and weighted degrees are deliberately left for later pull requests.

[github-actions]

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[github-actions]

PR summary 57d16c3ffc

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.RingTheory.DedekindDomain.Divisor (new file)	2436

---

Declarations diff (regex)

+ Divisor
+ count_ofDivisor
+ divisor
+ divisorEquiv
+ divisor_apply
+ eq_of_count_eq
+ ofDivisor

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 57d16c3).

• +6 new declarations
• −0 removed declarations

+FractionalIdeal.count_ofDivisor
+FractionalIdeal.divisor
+FractionalIdeal.divisorEquiv
+FractionalIdeal.divisor_apply
+FractionalIdeal.ofDivisor
+IsDedekindDomain.Divisor

---

No changes to strong technical debt.

Increase in weak tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (weak)
5011	1	exposed public sections

Current commit 57d16c3ffc
Reference commit 7fff4171d6

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.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).