Složeniji sistemi
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Primjer 1.
joints: 0: (-1.73205080756888, -1.00000000000000) 1: (0.000000000000000, -2.00000000000000) 2: (1.73205080756888, -1.00000000000000) 3: (1.73205080756888, 1.00000000000000) 4: (0.000000000000000, 2.00000000000000) 5: (-1.73205080756888, 1.00000000000000) 6: (-1.93205080756888, -1.00000000000000) 7: (-1.73205080756888, -1.20000000000000) 8: (1.73205080756888, -1.20000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 4) 4: (4, 5) 5: (5, 0) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 6) 10: (0, 7) 11: (2, 8) supports: [6, 7, 8] joints: 0: (-1.73205080756888, -1.00000000000000) 1: (0.000000000000000, -2.00000000000000) 2: (1.73205080756888, -1.00000000000000) 3: (1.73205080756888, 1.00000000000000) 4: (0.000000000000000, 2.00000000000000) 5: (-1.73205080756888, 1.00000000000000) 6: (-1.93205080756888, -1.00000000000000) 7: (-1.73205080756888, -1.20000000000000) 8: (1.73205080756888, -1.20000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 4) 4: (4, 5) 5: (5, 0) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 6) 10: (0, 7) 11: (2, 8) supports: [6, 7, 8] |
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[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
2 * 6 - 12 == 0 2 * 6 - 12 == 0 |
(0.8660250.0000000.0000000.0000000.0000000.0000000.8660250.0000000.000000−1.000000.0000000.000000−0.5000000.0000000.0000000.0000000.0000001.000000.5000000.0000000.0000000.000000−1.000000.000000−0.8660250.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.5000000.5000000.0000000.0000000.0000000.0000000.0000001.000000.0000000.0000000.0000000.0000000.000000−0.8660250.0000000.0000000.0000000.0000000.0000000.000000−0.8660250.0000000.0000000.0000000.000000−0.5000001.000000.0000000.0000000.0000000.0000000.0000000.5000000.0000000.000000−1.000000.0000000.0000000.000000−0.8660250.0000000.000000−0.8660250.0000000.0000000.0000000.0000000.0000000.0000000.000000−1.000000.5000000.0000000.000000−0.5000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.866025−0.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000−0.500000−0.5000000.0000000.000000−1.000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.8660250.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.500000−1.000000.0000000.000000−0.5000000.0000000.0000000.000000)
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Column space: Vector space of degree 12 and dimension 11 Column space: Vector space of degree 12 and dimension 11 |
Row space: Vector space of degree 12 and dimension 11 Row space: Vector space of degree 12 and dimension 11 |
Kernel: Vector space of degree 12 and dimension 1 Basis: (-1.0, -1.0, -1.0000000000000002, -1.0, -1.0, -1.0000000000000002, 1.0, 1.0000000000000002, 1.0, -0.0, -0.0, -0.0) Kernel: Vector space of degree 12 and dimension 1 Basis: (-1.0, -1.0, -1.0000000000000002, -1.0, -1.0, -1.0000000000000002, 1.0, 1.0000000000000002, 1.0, -0.0, -0.0, -0.0) |
0: -1.0 1: -1.0 2: -1.0000000000000002 3: -1.0 4: -1.0 5: -1.0000000000000002 6: 1.0 7: 1.0000000000000002 8: 1.0 9: -0.0 10: -0.0 11: -0.0 0: -1.0 1: -1.0 2: -1.0000000000000002 3: -1.0 4: -1.0 5: -1.0000000000000002 6: 1.0 7: 1.0000000000000002 8: 1.0 9: -0.0 10: -0.0 11: -0.0 |
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Left kernel: Vector space of degree 12 and dimension 1 Basis: (0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0, 0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0) Left kernel: Vector space of degree 12 and dimension 1 Basis: (0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0, 0.0, 0.0, 0.5, 0.8660254037844385, 1.0, 0.0) |
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Primjer 2.
joints: 0: (-1.73205080756888, -1.00000000000000) 1: (0.000000000000000, -0.666666666666667) 2: (1.73205080756888, -1.00000000000000) 3: (1.73205080756888, 1.00000000000000) 4: (0.000000000000000, 1.33333333333333) 5: (-1.73205080756888, 1.00000000000000) 6: (-1.93205080756888, -1.00000000000000) 7: (-1.73205080756888, -1.20000000000000) 8: (1.73205080756888, -1.20000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 4) 4: (4, 5) 5: (5, 0) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 6) 10: (0, 7) 11: (2, 8) supports: [6, 7, 8] joints: 0: (-1.73205080756888, -1.00000000000000) 1: (0.000000000000000, -0.666666666666667) 2: (1.73205080756888, -1.00000000000000) 3: (1.73205080756888, 1.00000000000000) 4: (0.000000000000000, 1.33333333333333) 5: (-1.73205080756888, 1.00000000000000) 6: (-1.93205080756888, -1.00000000000000) 7: (-1.73205080756888, -1.20000000000000) 8: (1.73205080756888, -1.20000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 4) 4: (4, 5) 5: (5, 0) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 6) 10: (0, 7) 11: (2, 8) supports: [6, 7, 8] |
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[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
2 * 6 - 12 == 0 2 * 6 - 12 == 0 |
(0.9819810.0000000.0000000.0000000.0000000.0000000.8660250.0000000.000000−1.000000.0000000.0000000.1889820.0000000.0000000.0000000.0000001.000000.5000000.0000000.0000000.000000−1.000000.000000−0.9819810.9819810.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000−0.188982−0.1889820.0000000.0000000.0000000.0000000.0000001.000000.0000000.0000000.0000000.0000000.000000−0.9819810.0000000.0000000.0000000.0000000.0000000.000000−0.8660250.0000000.0000000.0000000.0000000.1889821.000000.0000000.0000000.0000000.0000000.0000000.5000000.0000000.000000−1.000000.0000000.0000000.000000−0.9819810.0000000.000000−0.8660250.0000000.0000000.0000000.0000000.0000000.0000000.000000−1.000000.1889820.0000000.000000−0.5000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.981981−0.9819810.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.000000−0.188982−0.1889820.0000000.000000−1.000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.0000000.9819810.0000000.0000000.0000000.8660250.0000000.0000000.0000000.0000000.0000000.0000000.0000000.188982−1.000000.0000000.000000−0.5000000.0000000.0000000.000000)
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Column space: Vector space of degree 12 and dimension 12 Column space: Vector space of degree 12 and dimension 12 |
Row space: Vector space of degree 12 and dimension 12 Row space: Vector space of degree 12 and dimension 12 |
Kernel: Vector space of degree 12 and dimension 0 Kernel: Vector space of degree 12 and dimension 0 |
Left kernel: Vector space of degree 12 and dimension 0 Left kernel: Vector space of degree 12 and dimension 0 |
Primjer 3. — „Ely”
joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000, 0.000000000000000) 4: (1.00000000000000, 0.000000000000000, 1.00000000000000) 5: (2.00000000000000, 1.00000000000000, 1.00000000000000) 6: (1.00000000000000, 2.00000000000000, 1.00000000000000) 7: (0.000000000000000, 1.00000000000000, 1.00000000000000) bars: 0: (0, 4) 1: (1, 4) 2: (1, 5) 3: (2, 5) 4: (2, 6) 5: (3, 6) 6: (3, 7) 7: (0, 7) 8: (7, 4) 9: (4, 5) 10: (5, 6) 11: (6, 7) supports: [0, 1, 2, 3] joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000, 0.000000000000000) 4: (1.00000000000000, 0.000000000000000, 1.00000000000000) 5: (2.00000000000000, 1.00000000000000, 1.00000000000000) 6: (1.00000000000000, 2.00000000000000, 1.00000000000000) 7: (0.000000000000000, 1.00000000000000, 1.00000000000000) bars: 0: (0, 4) 1: (1, 4) 2: (1, 5) 3: (2, 5) 4: (2, 6) 5: (3, 6) 6: (3, 7) 7: (0, 7) 8: (7, 4) 9: (4, 5) 10: (5, 6) 11: (6, 7) supports: [0, 1, 2, 3] |
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3 * 4 - 12 == 0 3 * 4 - 12 == 0 |
[4, 5, 6, 7] [4, 5, 6, 7] |
(−0.70710.70710.00000.00000.00000.00000.00000.0000−0.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.0000−0.70710.70710.00000.00000.00000.00000.0000−0.70710.70710.00000.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.7071−0.70710.00000.00000.00000.00000.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.7071−0.7071−0.70710.00000.00000.70710.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.0000)
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Row space: Vector space of degree 12 and dimension 11 Basis: (1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0, -0.0) (0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0, -0.0) (0.0, 0.0, 1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0) (0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0) (0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0) (0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, -1.0, 0.0, 0.0, 1.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, -0.0, -0.0, -0.5) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0) Row space: Vector space of degree 12 and dimension 11 Basis: (1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0, -0.0) (0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0, -0.0) (0.0, 0.0, 1.0, -1.0, -0.0, -0.0, -0.0, -0.0, -0.0, 1.0, -1.0, -0.0) (0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5, -0.0) (0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0) (0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.5, 0.5) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, -1.0, 0.0, 0.0, 1.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.5, -0.0, -0.0, -0.5) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0) |
Column space: Vector space of degree 12 and dimension 11 Basis: (-0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475) (-0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0) (0.7071067811865475, 0.7071067811865475, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0) Column space: Vector space of degree 12 and dimension 11 Basis: (-0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, 0.0, -0.7071067811865475, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.7071067811865475, -0.7071067811865475) (-0.7071067811865475, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0) (0.7071067811865475, 0.7071067811865475, 0.0, -0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0) |
Kernel: Vector space of degree 12 and dimension 1 Basis: (1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0) Kernel: Vector space of degree 12 and dimension 1 Basis: (1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0) |
0: 1.0 1: -1.0 2: -1.0 3: 1.0 4: 1.0 5: -1.0 6: -1.0 7: 1.0 8: -1.0 9: 1.0 10: -1.0 11: 1.0 0: 1.0 1: -1.0 2: -1.0 3: 1.0 4: 1.0 5: -1.0 6: -1.0 7: 1.0 8: -1.0 9: 1.0 10: -1.0 11: 1.0 |
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Left kernel: Vector space of degree 12 and dimension 1 Basis: (0.0, -1.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0) Left kernel: Vector space of degree 12 and dimension 1 Basis: (0.0, -1.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0) |
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Primjer 4. — Nesimetrični „Ely”
joints: 0: (0.000000000000000, -0.250000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000, 0.000000000000000) 4: (1.00000000000000, 0.000000000000000, 1.00000000000000) 5: (2.00000000000000, 1.00000000000000, 1.00000000000000) 6: (1.00000000000000, 2.00000000000000, 1.00000000000000) 7: (0.000000000000000, 1.00000000000000, 1.00000000000000) bars: 0: (0, 4) 1: (1, 4) 2: (1, 5) 3: (2, 5) 4: (2, 6) 5: (3, 6) 6: (3, 7) 7: (0, 7) 8: (7, 4) 9: (4, 5) 10: (5, 6) 11: (6, 7) supports: [0, 1, 2, 3] joints: 0: (0.000000000000000, -0.250000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000, 0.000000000000000) 4: (1.00000000000000, 0.000000000000000, 1.00000000000000) 5: (2.00000000000000, 1.00000000000000, 1.00000000000000) 6: (1.00000000000000, 2.00000000000000, 1.00000000000000) 7: (0.000000000000000, 1.00000000000000, 1.00000000000000) bars: 0: (0, 4) 1: (1, 4) 2: (1, 5) 3: (2, 5) 4: (2, 6) 5: (3, 6) 6: (3, 7) 7: (0, 7) 8: (7, 4) 9: (4, 5) 10: (5, 6) 11: (6, 7) supports: [0, 1, 2, 3] |
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[4, 5, 6, 7] [4, 5, 6, 7] |
(−0.69630.70710.00000.00000.00000.00000.00000.0000−0.70710.70710.00000.0000−0.17410.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.0000−0.6963−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.0000−0.70710.70710.00000.00000.00000.00000.0000−0.70710.70710.00000.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.7071−0.70710.00000.00000.00000.00000.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.7071−0.7809−0.70710.00000.00000.70710.00000.00000.00000.00000.00000.0000−0.7071−0.62470.00000.00000.00000.0000)
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Kernel: Vector space of degree 12 and dimension 0 Basis: [] Kernel: Vector space of degree 12 and dimension 0 Basis: [] |
Left kernel: Vector space of degree 12 and dimension 0 Basis: [] Left kernel: Vector space of degree 12 and dimension 0 Basis: [] |
Primjer 5. — „Ely” s jednom osi simetrije
joints: 0: (-0.250000000000000, -0.250000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000, 0.000000000000000) 4: (1.00000000000000, 0.000000000000000, 1.00000000000000) 5: (2.00000000000000, 1.00000000000000, 1.00000000000000) 6: (1.00000000000000, 2.00000000000000, 1.00000000000000) 7: (0.000000000000000, 1.00000000000000, 1.00000000000000) bars: 0: (0, 4) 1: (1, 4) 2: (1, 5) 3: (2, 5) 4: (2, 6) 5: (3, 6) 6: (3, 7) 7: (0, 7) 8: (7, 4) 9: (4, 5) 10: (5, 6) 11: (6, 7) supports: [0, 1, 2, 3] joints: 0: (-0.250000000000000, -0.250000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000, 0.000000000000000) 4: (1.00000000000000, 0.000000000000000, 1.00000000000000) 5: (2.00000000000000, 1.00000000000000, 1.00000000000000) 6: (1.00000000000000, 2.00000000000000, 1.00000000000000) 7: (0.000000000000000, 1.00000000000000, 1.00000000000000) bars: 0: (0, 4) 1: (1, 4) 2: (1, 5) 3: (2, 5) 4: (2, 6) 5: (3, 6) 6: (3, 7) 7: (0, 7) 8: (7, 4) 9: (4, 5) 10: (5, 6) 11: (6, 7) supports: [0, 1, 2, 3] |
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[4, 5, 6, 7] [4, 5, 6, 7] |
(−0.77150.70710.00000.00000.00000.00000.00000.0000−0.70710.70710.00000.0000−0.15430.00000.00000.00000.00000.00000.00000.00000.70710.70710.00000.0000−0.6172−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.0000−0.70710.70710.00000.00000.00000.00000.0000−0.70710.70710.00000.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.7071−0.70710.00000.00000.00000.00000.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.0000−0.7071−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.15430.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.7071−0.7715−0.70710.00000.00000.70710.00000.00000.00000.00000.00000.0000−0.7071−0.61720.00000.00000.00000.0000)
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Kernel: Vector space of degree 12 and dimension 1 Basis: (0.9165151389911679, -0.8, -1.0, 1.0, 1.0, -1.0, -0.8, 0.9165151389911681, -0.8, 1.0, -1.0, 1.0) Kernel: Vector space of degree 12 and dimension 1 Basis: (0.9165151389911679, -0.8, -1.0, 1.0, 1.0, -1.0, -0.8, 0.9165151389911681, -0.8, 1.0, -1.0, 1.0) |
0: 0.9165151389911679 1: -0.8 2: -1.0 3: 1.0 4: 1.0 5: -1.0 6: -0.8 7: 0.9165151389911681 8: -0.8 9: 1.0 10: -1.0 11: 1.0 0: 0.9165151389911679 1: -0.8 2: -1.0 3: 1.0 4: 1.0 5: -1.0 6: -0.8 7: 0.9165151389911681 8: -0.8 9: 1.0 10: -1.0 11: 1.0 |
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Left kernel: Vector space of degree 12 and dimension 1 Basis: (-0.11111111111111112, 1.0, -0.11111111111111112, 0.8888888888888888, 0.0, 0.0, 0.0, -0.8888888888888888, 0.0, -1.0, 0.11111111111111115, 0.11111111111111115) Left kernel: Vector space of degree 12 and dimension 1 Basis: (-0.11111111111111112, 1.0, -0.11111111111111112, 0.8888888888888888, 0.0, 0.0, 0.0, -0.8888888888888888, 0.0, -1.0, 0.11111111111111115, 0.11111111111111115) |
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Primjer 18. — Ely
joints: 0: (0.000000000000000, -2.00000000000000, 0.000000000000000) 1: (1.41421356237310, -1.41421356237310, 0.000000000000000) 2: (2.00000000000000, 0.000000000000000, 0.000000000000000) 3: (1.41421356237310, 1.41421356237310, 0.000000000000000) 4: (0.000000000000000, 2.00000000000000, 0.000000000000000) 5: (-1.41421356237310, 1.41421356237310, 0.000000000000000) 6: (-2.00000000000000, 0.000000000000000, 0.000000000000000) 7: (-1.41421356237310, -1.41421356237310, 0.000000000000000) 8: (sin(0.125000000000000*pi), -cos(0.125000000000000*pi), 1.41421356237310) 9: (sin(0.375000000000000*pi), -cos(0.375000000000000*pi), 1.41421356237310) 10: (sin(0.625000000000000*pi), -cos(0.625000000000000*pi), 1.41421356237310) 11: (sin(0.875000000000000*pi), -cos(0.875000000000000*pi), 1.41421356237310) 12: (sin(1.12500000000000*pi), -cos(1.12500000000000*pi), 1.41421356237310) 13: (sin(1.37500000000000*pi), -cos(1.37500000000000*pi), 1.41421356237310) 14: (sin(1.62500000000000*pi), -cos(1.62500000000000*pi), 1.41421356237310) 15: (sin(1.87500000000000*pi), -cos(1.87500000000000*pi), 1.41421356237310) bars: 0: (0, 8) 1: (1, 8) 2: (1, 9) 3: (2, 9) 4: (2, 10) 5: (3, 10) 6: (3, 11) 7: (4, 11) 8: (4, 12) 9: (5, 12) 10: (5, 13) 11: (6, 13) 12: (6, 14) 13: (7, 14) 15: (7, 15) 16: (0, 15) 17: (15, 8) 18: (8, 9) 19: (9, 10) 20: (10, 11) 21: (11, 12) 22: (12, 13) 23: (13, 14) 24: (14, 15) supports: [0, 1, 2, 3, 4, 5, 6, 7] joints: 0: (0.000000000000000, -2.00000000000000, 0.000000000000000) 1: (1.41421356237310, -1.41421356237310, 0.000000000000000) 2: (2.00000000000000, 0.000000000000000, 0.000000000000000) 3: (1.41421356237310, 1.41421356237310, 0.000000000000000) 4: (0.000000000000000, 2.00000000000000, 0.000000000000000) 5: (-1.41421356237310, 1.41421356237310, 0.000000000000000) 6: (-2.00000000000000, 0.000000000000000, 0.000000000000000) 7: (-1.41421356237310, -1.41421356237310, 0.000000000000000) 8: (sin(0.125000000000000*pi), -cos(0.125000000000000*pi), 1.41421356237310) 9: (sin(0.375000000000000*pi), -cos(0.375000000000000*pi), 1.41421356237310) 10: (sin(0.625000000000000*pi), -cos(0.625000000000000*pi), 1.41421356237310) 11: (sin(0.875000000000000*pi), -cos(0.875000000000000*pi), 1.41421356237310) 12: (sin(1.12500000000000*pi), -cos(1.12500000000000*pi), 1.41421356237310) 13: (sin(1.37500000000000*pi), -cos(1.37500000000000*pi), 1.41421356237310) 14: (sin(1.62500000000000*pi), -cos(1.62500000000000*pi), 1.41421356237310) 15: (sin(1.87500000000000*pi), -cos(1.87500000000000*pi), 1.41421356237310) bars: 0: (0, 8) 1: (1, 8) 2: (1, 9) 3: (2, 9) 4: (2, 10) 5: (3, 10) 6: (3, 11) 7: (4, 11) 8: (4, 12) 9: (5, 12) 10: (5, 13) 11: (6, 13) 12: (6, 14) 13: (7, 14) 15: (7, 15) 16: (0, 15) 17: (15, 8) 18: (8, 9) 19: (9, 10) 20: (10, 11) 21: (11, 12) 22: (12, 13) 23: (13, 14) 24: (14, 15) supports: [0, 1, 2, 3, 4, 5, 6, 7] |
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3 * 8 - 24 == 0 3 * 8 - 24 == 0 |
[8, 9, 10, 11, 12, 13, 14, 15] [8, 9, 10, 11, 12, 13, 14, 15] |
24 x 24 dense matrix over Real Double Field (use the '.str()' method to see the entries) 24 x 24 dense matrix over Real Double Field (use the '.str()' method to see the entries) |
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Row space: Vector space of degree 24 and dimension 23 Row space: Vector space of degree 24 and dimension 23 |
Column space: Vector space of degree 24 and dimension 23 Column space: Vector space of degree 24 and dimension 23 |
Kernel: Vector space of degree 24 and dimension 1 Kernel: Vector space of degree 24 and dimension 1 |
0: 2.1943069386526513 1: -2.1943069386526513 2: -2.1943069386526517 3: 2.1943069386526517 4: 2.1943069386526526 5: -2.1943069386526526 6: -2.194306938652653 7: 2.194306938652653 8: 2.1943069386526557 9: -2.1943069386526557 10: -2.194306938652659 11: 2.1943069386526592 12: 2.1943069386526624 13: -2.194306938652662 15: -2.1943069386526552 16: 2.1943069386526557 17: -0.9999999999999946 18: 0.999999999999995 19: -0.9999999999999953 20: 0.9999999999999953 21: -0.9999999999999962 22: 0.9999999999999972 23: -0.9999999999999994 24: 1.0 0: 2.1943069386526513 1: -2.1943069386526513 2: -2.1943069386526517 3: 2.1943069386526517 4: 2.1943069386526526 5: -2.1943069386526526 6: -2.194306938652653 7: 2.194306938652653 8: 2.1943069386526557 9: -2.1943069386526557 10: -2.194306938652659 11: 2.1943069386526592 12: 2.1943069386526624 13: -2.194306938652662 15: -2.1943069386526552 16: 2.1943069386526557 17: -0.9999999999999946 18: 0.999999999999995 19: -0.9999999999999953 20: 0.9999999999999953 21: -0.9999999999999962 22: 0.9999999999999972 23: -0.9999999999999994 24: 1.0 |
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Left kernel: Vector space of degree 24 and dimension 1 Left kernel: Vector space of degree 24 and dimension 1 |
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