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Fix(notebook,#11044): Sendov 3 commentaires c.8267+1 pointent §5-8 -- ferme EPIC #19235

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myia-ai-01 merged 3 commits into from
Oct 7, 2026
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Fix(notebook,#11044): Sendov 3 commentaires c.8267+1 pointent §5-8 -- ferme EPIC #19235

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Fix(notebook,#11044): Sendov 3 commentaires c.8267+1 pointent §5-8 --…
jsboige Oct 5, 2026
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Merge branch 'main' into fix/11044-sendov-comments-point-58
jsboige Oct 5, 2026
af76443
Fix(notebook,#19235,#11044): Phelps-Rodriguez AFFIRME (conjecture), p…
jsboige Oct 5, 2026
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19 changes: 19 additions & 0 deletions MyIA.AI.Notebooks/SymbolicAI/Lean/ANALYSE/ANALYSE-01-Sendov-Lean-Python.ipynb
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{
"cells": [
{
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"# Theoreme Sendov pour a = 0 : il existe zeta point critique avec |zeta| <= 1.\n",
"#\n",
"# Source Lean : Sendov/Interior.lean (sendov_center) + Sendov/Analytic/*\n",
"#\n",
"# Contexte dans ce carnet : voir §5 (enonce), §6 (cas 0 < |a| < 1, Code 6.1),\n",
"# §7 (cas |a| = 1, Rubinstein, Code 7.1), §8 (recollement, Code 8.1).\n",
"# Sendov se decompose en 3 cas par position de a : centre (ce §5),\n",
"# interieur (Code 6.1, §6), frontiere (Code 7.1, §7) ; le recollement\n",
"# (§8) elimine la normalisation a in [0, 1) et conclut le theoreme.\n",
"\n",
"import numpy as np\n",
"\n",
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"# Source : Sendov/Analytic/LowDegree.lean (Sendov.lowJ_lt_one)\n",
"# Formule : J_m(a) = integral_0^1 (a + (1-a^2)*t)^m dt\n",
"# Pour 0 < a < 1 et 1 <= m <= 4 : J_m(a) < 1.\n",
"#\n",
"# Contexte dans ce carnet : voir §5 (cas du centre, Code 5.1),\n",
"# ce §6 (cas interieur 0 < |a| < 1), §7 (cas boundary |a| = 1,\n",
"# Rubinstein, Code 7.1), §8 (recollement, Code 8.1). Le branch point\n",
"# J_m(a) < 1 est la cle du cas interieur ; il s'insere dans la\n",
"# decomposition par cas (§5/§6/§7) que §8 recolle pour conclure.\n",
"\n",
"from scipy.integrate import quad\n",
"\n",
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"# Pour p(z) = z^n - 1, zeros = racines n-iemes de l'unite, tous sur |z| = 1.\n",
"# Points critiques = {0} (tous en 0, p'(z) = n z^{n-1}).\n",
"# Distance d'un zero omega (|omega| = 1) a 0 : |omega - 0| = 1 exactement.\n",
"#\n",
"# Contexte dans ce carnet : voir §5 (cas du centre, Code 5.1), §6 (cas\n",
"# interieur 0 < |a| < 1, Code 6.1), ce §7 (cas boundary |a| = 1,\n",
"# Rubinstein), §8 (recollement, Code 8.1). Rubinstein identifie le cas\n",
"# extreme ou l'inegalite stricte < 1 echoue (egalite). Phelps-Rodriguez\n",
"# AFFIRME que c'est le seul cas d'echec, ce qui complete la preuve\n",
"# apres le recollement de §8.\n",
"\n",
"import cmath\n",
"import numpy as np\n",
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