1 files changed, 47 insertions, 0 deletions
diff --git a/4/two_basis.py b/4/two_basis.py
new file mode 100644
index 0000000..d1d71a2
--- /dev/null
+++ b/4/two_basis.py
@@ -0,0 +1,47 @@
+from libsolve2 import *
+from fractions import Fraction as F
+
+def f_eye(dim):
+    return Matrix([
+        [0 if i != j else 1 for i in range(dim)]
+        for j in range(dim)
+    ])
+
+eye = f_eye(6)
+
+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]
+])
+
+for_root1 = m - eye * 3
+
+print('(m - 3E)^2 =')
+print((for_root1@for_root1).triangled(swap=True))
+print()
+print()
+
+for_root2 = m - eye * 4
+
+print('(m - 4E)^2 =')
+print((for_root2@for_root2).triangled(swap=True))
+
+def make_vec(iter):
+    return Matrix([[i] for i in iter])
+
+print()
+print('Проверим, лежит ли кто-нибудь из ФСР в ядре:')
+print(((for_root2) @ make_vec([0, -F(1, 3), F(2, 3), 0, 0, 1])).T)
+print(((for_root2) @ make_vec([0, -F(2, 3), F(4, 3), 0, 1, 0])).T)
+print(((for_root2) @ make_vec([0, -1, 2, 1, 0, 0])).T)
+print(((for_root2) @ make_vec([1, 0, 0, 0, 0, 0])).T)
+
+print('кажется, ни один вектор не лежит в ядре.')
+print()
+print('а вот эти уже лежат в ядре')
+print((for_root2 @ make_vec([0, -1, 2, 1, 0, 0])).T)
+print((for_root2 @ make_vec([1, 0, 0, 0, 0, 0])).T)