diff --git a/3/TP3_voisin.py b/3/TP3_voisin.py
index 879c694..9ba9763 100755
--- a/3/TP3_voisin.py
+++ b/3/TP3_voisin.py
@@ -253,4 +253,15 @@ def main(argv):
 
 
 if __name__ == "__main__":
-    main(sys.argv[1:])
+    # main(sys.argv[1:])
+    m = np.array(
+        [
+            [2, 3],
+            [3, 2]
+        ]
+    )
+    u1, u2, l1, l2 = diagonaliser_matrice22(m)
+    u1 /= np.linalg.norm(u1)
+    u2 /= np.linalg.norm(u2)
+    print(u1, u2)
+    print(l1, l2)
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diff --git a/4/tp4.pdf b/4/tp4.pdf
new file mode 100644
index 0000000..fc385fe
Binary files /dev/null and b/4/tp4.pdf differ
diff --git a/4/tp4_Voisin.py b/4/tp4_Voisin.py
new file mode 100644
index 0000000..e0014de
--- /dev/null
+++ b/4/tp4_Voisin.py
@@ -0,0 +1,114 @@
+#!/usr/bin/env python3
+
+"""
+    auteur: Dylan Voisin - M1 Informatique Luminy
+    MNI: TP 4
+"""
+
+import numpy as np
+from numpy.polynomial import polynomial as P
+from copy import deepcopy as dp
+from math import isclose
+
+def vect_propre(A, µ=1, nb_iter=15):
+    I = np.identity(A.shape[0])
+    v = np.ones(A.shape[0])
+    inv = np.linalg.inv(A - µ*I)
+    for i in range(nb_iter):
+        v = inv @ v / np.linalg.norm(inv@v)
+    return v
+
+def vect_propre2(A, eps = 0.1):
+    v = np.random.random(A.shape[0])
+    v /= np.linalg.norm(v)
+    lambda_ = v.transpose() @ A @ v
+    eps = 1e-13
+    écart = float('inf')
+    while écart > eps:
+        w = lambda_ * A @ v
+        v = w / np.linalg.norm(w)
+        old = lambda_
+        lambda_ = (v.transpose() @ A @ v) / (v.transpose() @ v)
+        écart = abs(old - lambda_)
+    return v
+
+def vect_propre_généralisé(A, eps = 1-9):
+    A_ = A @ A.transpose()
+    v = vect_propre2(A_, eps)
+    v = (v.transpose() @ A @ v) / (v.transpose() * v)
+    return v
+
+def eval_poly(p, x):
+    """un polynome sera représenté par une liste pleine de ses coefficients
+    f = a_0 + a_1 * x ** 1 + … + a_n * x ** b_n
+    [a_0, a_1, a_2, …, a_n]
+    """
+    return sum(p[i] * x ** i for i in range(len(p)))
+
+def dichotomie(size, step):
+    l = [0, size]
+    lc = dp(l)
+    for i in range(step):
+        for j in range(len(l)-1):
+            m = (l[j+1] + l[j]) / 2
+            lc.insert(2*(j+1)-1, m)
+            yield m
+        l = dp(lc)
+
+def newton(p, epsilon_f = 1e-13, epsilon_c = 1e-9):
+    """peut faire une boucle infinie à cause de l'imprécision
+    à régler avec les paramètres epsilon, mais l'imprécision va
+    se répercuter sur les valeurs des racines"""
+    x = np.random.random() * 100
+    pp = np.polyder(p[::-1])[::-1]
+    roots = []
+    while True:
+        # toujours de l'imprécision à gérer
+        if abs(eval_poly(p, x)) < epsilon_f:
+            roots.append(x)
+            p = P.polydiv(p, (-x, 1))[0]
+            # on purge l'imprécision
+            p = list(map(lambda x: x if abs(x) > epsilon_c else 0, p))
+            pp = np.polyder(p[::-1])[::-1]
+            if len(p) == 1:
+                return roots # f = c
+        fpx = eval_poly(pp, x)
+        if fpx == 0:
+            print(x)
+            # extremum (local ou non)
+            old = x
+            step = 5
+            maxrange = 1000
+            eps = 1*10**(-8)
+            sg = np.sign(eval_poly(pp, x-eps))
+            sd = np.sign(eval_poly(pp, x+eps))
+            for diff in dichotomie(maxrange, step):
+                if np.sign(eval_poly(pp, x-diff)) != sg:
+                    x = x - diff
+                    break
+                elif np.sign(eval_poly(pp, x+diff)) != sd:
+                    x = x + diff
+                    break
+            if x == old:
+                return roots # on considère qu'on a toutes les racines
+        x -= eval_poly(p, x) / eval_poly(pp, x)
+    return roots
+
+if __name__ == '__main__':
+    m = np.array(
+        [
+            [2, 3],
+            [3, 2]
+        ]
+    )
+    v = vect_propre(m)
+    v /= np.linalg.norm(v)
+    print(v)
+    v = vect_propre2(m)
+    print(v)
+    v = vect_propre_généralisé(m)
+    v /= np.linalg.norm(v)
+    print(v)
+    # p = (0, 1, -2) # -2x²+x
+    p = (30, -19, -15, 3, 1) # (x+5)(x-3)(x-1)(x+2)
+    print(newton(p))
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