1 files changed, 38 insertions, 0 deletions
diff --git a/4/one.py b/4/one.py
new file mode 100644
index 0000000..341c383
--- /dev/null
+++ b/4/one.py
@@ -0,0 +1,38 @@
+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)
+    ])
+
+matrices = {
+    'A': Matrix([
+        [ 2,  -3,   1,   3],
+        [ 9,  -9,   1,   4],
+        [-5,   2,  -6,  -2],
+        [-5,   2,  -1,  -7]
+    ]),
+    'B': Matrix([
+        [ 2,  -3,   1,   3],
+        [ 5,  -7,   1,   2],
+        [-5,   2,  -6,  -2],
+        [-9,   4,  -1,  -9]
+    ]),
+    'C': Matrix([
+        [-6,  -8,  -4,   3],
+        [ 1,   1,   3,  -2],
+        [-1,  -4,  -7,   1],
+        [ 1,   8,   4,  -8]
+    ])
+}
+
+for name, m in matrices.items():
+    print()
+    print(f'{name} polynomial is {(m - f_eye(4) * x).det()}')
+    m5 = m + f_eye(4) * 5
+    print(f'{name} + 5E =\n{m5}')
+    print(f'rank({name} + 5E) = {m5.rank()}')
+    print(f'rank({name} + 5E)**2 = {(m5@m5).rank()}')
+    print(f'rank({name} + 5E)**3 = {(m5@m5@m5).rank()}')