feat(Analysis/Complex): Cartan inverse factor bound

[jonwashburn]

PR 12 of the Hadamard Factorization pipeline
Co-authored with Matteo Cipollina (matteo.cipollina@yahoo.it)

• depends on: feat(Analysis/Complex): WeierstrassFactor #34320
• depends on: feat(Analysis/Complex): probabilistic radius / averaging lemmas used in proof Hadamard factorization #34325

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[github-actions]

PR summary 18ef4ef4f3

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Analysis.Complex.CartanBound (new file)	2454
Mathlib.Analysis.Complex.WeierstrassFactor (new file)	2455
Mathlib.Analysis.Complex.CartanInverseFactorBound (new file)	2461

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Declarations diff

+ Cφ
+ Cφ_pos
+ K
+ K_nonneg
+ ae_restrict_norm_phi_le_of_forall_mem
+ differentiable_partialLogSum
+ differentiable_weierstrassFactor
+ exists_radius_Ioc_sum_mul_phi_div_le_Cφ_mul_sum
+ exists_radius_Ioc_sum_mul_phi_div_le_Cφ_mul_sum_avoid
+ integral_phi_div_le_Cφ_mul
+ integral_phi_le_Cφ_mul
+ intervalIntegrable_phi_div
+ intervalIntegrable_phi_dyadic
+ intervalIntegrable_sqrt_two_div_abs_one_sub_Icc
+ logTail
+ log_norm_one_sub_div_ge_neg_phi
+ log_norm_weierstrassFactor_ge_log_norm_one_sub_sub
+ log_norm_weierstrassFactor_ge_neg_two_pow
+ max_one_norm_div_pow_le_one_add_rpow
+ measurable_phi
+ neg_log_le_sqrt_two_div
+ neg_log_one_sub_eq_tsum
+ neg_posLog_inv_le_log
+ norm_inv_weierstrassFactor_le_exp_far
+ norm_inv_weierstrassFactor_le_exp_near
+ norm_logTail_le
+ norm_pow_div_one_sub_le_two
+ partialLogSum
+ partialLogSum_zero
+ phi_eq_zero_of_one_le_abs_one_sub
+ phi_le_log_two_of_le_half
+ posLog_one_div_abs_one_sub_le_sqrt_two_div
+ posLog_one_div_norm_one_sub_le_posLog_one_div_abs_one_sub
+ posLog_one_div_norm_one_sub_le_posLog_one_div_abs_one_sub_norm
+ summable_logTail
+ weierstrassFactor
+ weierstrassFactor_at_one
+ weierstrassFactor_at_zero
+ weierstrassFactor_eq_exp_neg_tail
+ weierstrassFactor_eq_zero_iff
+ weierstrassFactor_sub_one_pow_bound
+ weierstrassFactor_zero
+ φ
+ φ_le_sqrt
+ φ_nonneg

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.

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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-dependent-issues-bot]

This PR/issue depends on:

• feat(Analysis/Complex): WeierstrassFactor #34320
• feat(Analysis/Complex): probabilistic radius / averaging lemmas used in proof Hadamard factorization #34325
  By Dependent Issues (🤖). Happy coding!