1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
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')
|
