feat(Analysis/Polynomial/MahlerMeasure): the Mahler measure of a linear polynomial and applications

[fbarroero]

We prove
theorem logMahlerMeasure_X_sub_C (z : ℂ) : (X - C z).logMahlerMeasure = log⁺ ‖z‖
and
theorem logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots (p : ℂ[X]) : p.logMahlerMeasure = log ‖p.leadingCoeff‖ + ((p.roots).map (fun a ↦ log⁺ ‖a‖)).sum

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• depends on: [Merged by Bors] - feat(Analysis/SpecialFunctions/Log): log_prod for Lists and Multisets #30681

[github-actions]

PR summary 71a105d772

Import changes exceeding 2%

%	File
+6.94%	Mathlib.Analysis.Polynomial.MahlerMeasure

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Polynomial.MahlerMeasure	2480	2652	+172 (+6.94%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.Polynomial.MahlerMeasure	172

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Declarations diff

+ logMahlerMeasure_C_mul
+ logMahlerMeasure_C_mul_X_add_C
+ logMahlerMeasure_X_add_C
+ logMahlerMeasure_X_sub_C
+ logMahlerMeasure_degree_eq_one
+ logMahlerMeasure_eq_log_leadingCoeff_add_sum_log_roots
+ mahlerMeasure_C_mul_X_add_C
+ mahlerMeasure_X_add_C
+ mahlerMeasure_X_sub_C
+ mahlerMeasure_degree_eq_one
+ mahlerMeasure_eq_leadingCoeff_mul_prod_roots

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.

---

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).

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(Analysis/SpecialFunctions/Log): log_prod for Lists and Multisets #30681
  By Dependent Issues (🤖). Happy coding!