feat(Analysis/Polynomial/MahlerMeasure): the Mahler measure of a linear polynomial and applications #30548
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PR summary 71a105d772Import changes exceeding 2%
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| 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 |
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
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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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