feat(Mathlib/Analysis/Polynomial/MahlerMeasure): Mahler Measure estimate in terms of supNorm

[khwilson]

The Mahler measure of a polynomial is bounded above by √(p.natDegree + 1) * p.supNorm. This is a tighter estimate than (p.natDegree + 1) * p.supNorm, which is implied by mahlerMeasure_le_sum_norm_coeff.

AI Usage: Claude Code (Opus 4.6) provided first drafts for several sorries in the main calc block. Gemini Pro was used for one-off looks ups of lemma names like ae_restrict_iff'. The final code was edited by me.

[github-actions]

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[github-actions]

PR summary f618ef9056

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.Polynomial.MahlerMeasure	2683	2731	+48 (+1.79%)

Import changes for all files

Files	Import difference
Mathlib.NumberTheory.MahlerMeasure	44
Mathlib.Analysis.Polynomial.MahlerMeasure	48

---

Declarations diff

+ mahlerMeasure_le_sqrt_natDegree_add_one_mul_supNorm

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 scripts/declarations_diff.sh contains some details about this script.

---

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

Current number	Change	Type
11958	1	backward.isDefEq

Current commit 095fe9333b
Reference commit f618ef9056

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).

[mathlib-merge-conflicts]

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

[j-loreaux]

overall this looks pretty nice!

[khwilson]

Thanks! Responded to comments and pushed.

[khwilson]

-awaiting-author