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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)
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