1matrix(QQ,
2 [[0, 1],
3  [-1, 0]])
4matrix(QQ,
5 [[0, 1],
6  [-1, 0]])
7matrix(QQ,
8 [[0, 1],
9  [-1, 0]])
10matrix(QQ,
11 [[0, 1, 0, 0, 1, 0],
12  [-1, 0, 0, 0, 0, 1],
13  [0, 0, 0, 1, 0, 0],
14  [0, 0, -1, 0, 0, 0],
15  [0, 0, 0, 0, 0, 1],
16  [0, 0, 0, 0, -1, 0]])
17z^6 +3*z^4 +3*z^2 +1
18z^6 +3*z^4 +3*z^2 +1
19z^4 +2*z^2 +1
20matrix(QQ,
21 [[0, 0, 0, 0, 0, 0],
22  [0, 0, 0, 0, 0, 0],
23  [0, 0, 0, 0, 0, 0],
24  [0, 0, 0, 0, 0, 0],
25  [0, 0, 0, 0, 0, 0],
26  [0, 0, 0, 0, 0, 0]])
27matrix(QQ,
28 [[0, 0, 0, 0, 0, 0],
29  [0, 0, 0, 0, 0, 0],
30  [0, 0, 0, 0, 0, 0],
31  [0, 0, 0, 0, 0, 0],
32  [0, 0, 0, 0, 0, 0],
33  [0, 0, 0, 0, 0, 0]])
34[1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  0,  0,  1]
35[0,  1,  0,  0,  1,  0,  -1,  0,  0,  0,  0,  1,  0,  0,  0,  1,  0,  0,  0,  0,  -1,  0,  0,  0,  0,  0,  0,  0,  0,  1,  0,  0,  0,  0,  -1,  0]
36matrix(QQ,
37 [[1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],
38  [0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0],
39  [-1, 0, 0, 0, 0, 2, 0, -1, 0, 0, -2, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1]])
40[]
41[]
42[[1,  0,  2,  0,  1]]
43matrix(QQ,
44 [[0, 0, 0, 0, 0, 0],
45  [0, 0, 0, 0, 0, 0],
46  [0, 0, 0, 0, 0, 0],
47  [0, 0, 0, 0, 0, 0],
48  [0, 0, 0, 0, 0, 0],
49  [0, 0, 0, 0, 0, 0]])
50matrix(QQ,
51 [[0, 0, 0, 0, 0, 0],
52  [0, 0, 0, 0, 0, 0],
53  [0, 0, 0, 0, 0, 0],
54  [0, 0, 0, 0, 0, 0],
55  [0, 0, 0, 0, 0, 0],
56  [0, 0, 0, 0, 0, 0]])
57true
58matrix(QQ,
59 [[0, 1, 1, 0, 0, 0],
60  [-1, 0, 0, 1, 0, 0],
61  [0, 0, 0, 1, 1, 0],
62  [0, 0, -1, 0, 0, 1],
63  [0, 0, 0, 0, 0, 1],
64  [0, 0, 0, 0, -1, 0]])
65z^6 +3*z^4 +3*z^2 +1
66z^6 +3*z^4 +3*z^2 +1
67true
68record[RemainingFactor := 1, factors := [z^2 +1], multiplicities := [3]]
69record[RemainingFactor := 1, factors := [z^2 +1], multiplicities := [2]]
70record[RemainingFactor := 1, factors := [z^2 +1], multiplicities := [3]]
71z^3 +4*z^2 +4*z
72record[RemainingFactor := 1, factors := [z,  z +2], multiplicities := [1,  2]]
73z^2 +2*z
74record[RemainingFactor := 1, factors := [z +2,  z], multiplicities := [1,  1]]
75z^3 +2*z^2 -7*z +4
76[z +4,  z -1]
77z^2 +3*z -4
78[z +4,  z -1]
79[]
80[]
81[[0,  0,  1]]
82matrix(QQ,
83 [[1, 0, 0],
84  [0, 0, 0],
85  [0, 0, 0]])
86[[0,  1,  0],  [0,  0,  1]]
87matrix(QQ,
88 [[1, 0, 0],
89  [0, 0, 0],
90  [0, 0, 0]])
91[[0,  1,  0],  [0,  0,  1]]
92z^3 -z^2 -2*z +2
93[z -1,  z^2 -2]
94[z -1,  z^2 -2]
95[z -1,  z^2 -2]
96matrix(QQ,
97 [[-1/5],
98  [1],
99  [1]])
100[[-1/5,  1,  1]]
101[[0,  1,  0],  [0,  0,  1]]
102[[-1/5,  1,  1]]
103[[0,  1,  0],  [0,  0,  1]]
104[z -1,  z]
105[1,  2]
106matrix(QQ,
107 [[0, 0, 0],
108  [0, -1, 0],
109  [0, 1, -1]])
110[[1,  0,  0]]
111matrix(QQ,
112 [[0],
113  [0],
114  [0]])
115matrix(QQ,
116 [[1, 0, 0],
117  [0, 0, 0],
118  [0, 1, 0]])
119[[0,  1,  0],  [0,  0,  1]]
120matrix(QQ,
121 [[0, 0],
122  [0, 0],
123  [1, 0]])
124matrix(QQ,
125 [[0, 0],
126  [0, 0],
127  [0, 0]])
128matrix(QQ,
129 [[0, 0],
130  [-1, 0],
131  [1, -1]])
132matrix(QQ,
133 [[1],
134  [0],
135  [0]])
136[1,  2]
137[[1,  0,  0]]
138[[1,  0,  0]]
139[[0,  0,  1]]
140[[0,  1,  0],  [0,  0,  1]]
141[z -1]
142[2]
143[[1,  0]]
144true
145