feat: companion lemmas to MeromorphicOn.exists_ecanonicalDecomp, API for the extended canonical decomposition

[kebekus]

To prepare for the proof of the classic Poisson-Jensen formula in the next PR, establish several companion lemmas to MeromorphicOn.exists_ecanonicalDecomp that provide an API for using the extended canonical decomposition introduced in #40191.

This material is used in Project VD, formalizing Value Distribution Theory for meromorphic functions on the complex plane.

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[github-actions]

PR summary f849b49544

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 (regex)

+ ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAt
+ ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAt_of_meromorphicOrderAt
+ ECanonicalDecomp.log_norm_eq

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 f849b49).

• +3 new declarations
• −0 removed declarations

+Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAt
+Complex.ECanonicalDecomp.eq_smul_meromorphicTrailingCoeffAt_of_meromorphicOrderAt
+Complex.ECanonicalDecomp.log_norm_eq

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit f849b49544
Reference commit 1c3e8f34a8

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).