right = (p1.get_inverse_permutation() * (p2**13))**187
for permutation in all_permutations:
p = Permutation(permutation)
if (p * p3 * p).permutation == right.permutation:
print("Результат:")
print("(0 1 2 3 4 5 6 7)")
print("(", " ".join(str(i) for i in p.permutation), ")", sep="")
print("Задание 2.")
a = SquareMatrix([[2, -2, 2, -3], [1, -3, 2, -1], [1, 1, -3, 3],
[-2, -3, 3, 2]])
b = SquareMatrix([[-9, 3, 9, -4], [-6, -2, 4, 9], [-9, 6, 10, -3],
[6, -10, 9, 6]])
c = SquareMatrix([[2, 2, 3, 1], [2, 1, 1, -2], [2, 1, -1, -1], [-1, 2, -1, 2]])
d = SquareMatrix([[-1, -1, -1, -1], [-1, -2, -2, -2], [-1, -2, -3, -1],
[1, 2, 3, 2]])
left = (SquareMatrix.get_e(4).multiply_on_number(
a.compute_det() * c.compute_det()) -
(b * c.get_adjugate_matrix() * d * c.get_adjugate_matrix()))
left = left * c * d.get_adjugate_matrix() * a
print("Определителитель матрицы, на которую домножаем = ",
(c * d.get_adjugate_matrix() * a).compute_det())
print(left.multiply_on_number(1 / 851))
print("Задание 3.")
print("Характеристичексий многочлен:")
a = SquareMatrix(
[[-5.55111512e-17, -3.17915329e-02, 3.66312778e-02, 6.16848637e-02],
[6.73794700e-03, 1.53740961e-02, 1.15776919e-02, 9.67948978e-03],
[-6.73794700e-03, 2.94154278e-03, -1.15776919e-02, -2.79951287e-02],
[6.73794700e-03, -2.94154278e-03, 2.98933308e-02, 4.63107676e-02]])
for i, a_i in enumerate(a.get_characteristic_polynomial()[:4]):
print("(" + str(a_i) + ")x^" + str(4 - i) + " + ", end="")
print("(" + str(a.get_characteristic_polynomial()[4]) + ")")
p3 = Permutation([5, 4, 0, 2, 3, 7, 6, 1])
all_permutations = Permutation.get_permutations(8, list(range(8)))
right = (p1.get_inverse_permutation() * (p2**13))**187
for permutation in all_permutations:
p = Permutation(permutation)
if (p * p3 * p).permutation == right.permutation:
print("Результат:")
print("(0 1 2 3 4 5 6 7)")
print("(", " ".join(str(i) for i in p.permutation), ")", sep="")
print("Задание 2.")
print("Характеристичексий многочлен:")
a = SquareMatrix([
[-3, -4, -1, 4],
[1, -4, -3, 3],
[-5, -2, 2, 2],
[0, 0, 2, -2],
])
for i, a_i in enumerate(a.get_characteristic_polynomial()[:4]):
print("(" + str(a_i) + ")x^" + str(4 - i) + " + ", end="")
print("(" + str(a.get_characteristic_polynomial()[4]) + ")")
x = SquareMatrix((a**2 + a.multiply_on_number(3) +
SquareMatrix.get_e(4).multiply_on_number(2)).matrix)**2
print("Определитель посчитаю на листочке из значений характеристического")
print("Задание 5")
A = Matrix([[3, -3], [1, -1], [-1, 1], [4, -4], [-3, 3]])
B = Matrix([[-2, -1, 3, 2, 1], [3, 1, -2, -1, 2]])
res = SquareMatrix((A * B).matrix)
for i, a_i in enumerate(res.get_characteristic_polynomial()[:5]):
print("(" + str(a_i) + ")x^" + str(5 - i) + " + ", end="")
print("(" + str(res.get_characteristic_polynomial()[5]) + ")")