1 files changed, 28 insertions, 0 deletions
diff --git a/4/two.py b/4/two.py
new file mode 100644
index 0000000..1302f6e
--- /dev/null
+++ b/4/two.py
@@ -0,0 +1,28 @@
+from libsolve2 import *
+from fractions import Fraction
+
+def f_eye(dim):
+    return Matrix([
+        [0 if i != j else 1 for i in range(dim)]
+        for j in range(dim)
+    ])
+
+m = Matrix([
+    [ 4,  -3,  -2,   0,   0,  0],
+    [ 0,   2,  -1,   0,   0,  0],
+    [ 0,   2,   5,   0,   0,  0],
+    [ 1,   1,   1,   2,  -1,  0],
+    [-2,  -3,  -3,   4,   6,  0],
+    [ 1,   8,   7,  -5,  -3,  3]
+])
+
+print('char polynomial is  ', (m - f_eye(6) * x).det())
+print('(x - 3)^2(x - 4)^4 =', (x - 3)*(x - 3)*(x - 4)*(x - 4)*(x - 4)*(x - 4))
+
+root1 = m - f_eye(6) * 3
+print(f'rank of m - 3E = {root1.rank()} => one cell of size 2')
+
+root2 = m - f_eye(6) * 4
+print(f'rank of m - 4E = {root2.rank()} => two cells')
+print(f'rank of (m - 4E)^2 = {(root2@root2).rank()} => two cells of size 2')
+