feat: extended canonical decomposition

[kebekus]

Establish the Extended Canonical Decomposition of meromorphic functions, where a complex-meromorphic function f on a closed disk is written, up to modification over a discrete set, as a product of a non-vanishing analytic function, canonical factors and meromorphic functions of the form (x - const) ^ n where const is on the circumference of the disk.

This extended decomposition is key in the proof of the classic Poisson-Jensen formula.

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[github-actions]

PR summary 65d4b00cfe

Import changes exceeding 2%

%	File
+4.00%	Mathlib.Analysis.Complex.CanonicalDecomposition

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Complex.CanonicalDecomposition	2001	2081	+80 (+4.00%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.Complex.CanonicalDecomposition	80

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Declarations diff

+ CanonicalDecomp.divisor_eq_divisor
+ ECanonicalDecomp
+ _root_.MeromorphicOn.exists_ecanonicalDecomp
+ finprod_apply_ne_zero
+ mem_codiscreteWithin_subsingleton

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.

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 65d4b00cfe
Reference commit 8c5c6391a3

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).