Prednapeti sistemi
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Primjer 1.
Opis rešetke:
Zadavanje čvorova:
{ oznaka0: (x0, y0, z0), oznaka1: (x1, y1, z1), oznaka2: (x2, y2, z2), ... }
Zadavanje štapova:
{ oznaka0: (čvor00, čvor10), oznaka1: (čvor01, čvor11), oznaka2: (čvor02, čvor12), ... }
Zadavanje ležajeva:
[ oznaka0, oznaka1, ... ]
Zadavanje opterećenja u čvorovima:
{ oznaka0: (Fx0, Fy0, Fz0), oznaka1: (Fx1, Fy1, Fz1), oznaka2: (Fx2, Fy2, Fz2), ... }
Primjer CN1. — Mreža kabela
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Tvorba rječnika čvorova, rječnika štapova i liste ležajnih čvorova:
surface_net (f, lx, ly, m, n)
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3 * 20 - 49 == 11 != 0 3 * 20 - 49 == 11 != 0 |
[7, 8, 9, 10, 13, 14, 15, 16, 19, 20, 21, 22, 25, 26, 27, 28, 31, 32, 33, 34] [7, 8, 9, 10, 13, 14, 15, 16, 19, 20, 21, 22, 25, 26, 27, 28, 31, 32, 33, 34] |
60 x 49 dense matrix over Real Double Field (use the '.str()' method to see the entries) 60 x 49 dense matrix over Real Double Field (use the '.str()' method to see the entries) |
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Row space: Vector space of degree 49 and dimension 48 Row space: Vector space of degree 49 and dimension 48 |
Column space: Vector space of degree 60 and dimension 48 Column space: Vector space of degree 60 and dimension 48 |
Kernel: Vector space of degree 49 and dimension 1 Kernel: Vector space of degree 49 and dimension 1 |
0: 0.9186369279044543 1: 0.7973407128633153 2: 0.7525766947068775 3: 0.7973407128633153 4: 0.9186369279044544 5: 0.9186369279044532 6: 0.7973407128633143 7: 0.7525766947068765 8: 0.7973407128633143 9: 0.9186369279044532 10: 0.9186369279044533 11: 0.7973407128633144 12: 0.7525766947068766 13: 0.7973407128633144 14: 0.9186369279044533 15: 0.9186369279044534 16: 0.7973407128633145 17: 0.7525766947068767 18: 0.7973407128633145 19: 0.9186369279044534 20: 0.9186369279044537 21: 0.7973407128633148 22: 0.7525766947068769 23: 0.7973407128633148 24: 0.9186369279044537 25: 0.9999999999999988 26: 0.849986985845191 27: 0.7640136217105626 28: 0.7640136217105626 29: 0.8499869858451911 30: 0.9999999999999989 31: 0.9999999999999997 32: 0.8499869858451917 33: 0.7640136217105632 34: 0.7640136217105632 35: 0.8499869858451917 36: 0.9999999999999996 37: 0.9999999999999979 38: 0.8499869858451902 39: 0.7640136217105618 40: 0.7640136217105618 41: 0.8499869858451902 42: 0.9999999999999978 43: 0.9999999999999999 44: 0.849986985845192 45: 0.7640136217105635 46: 0.7640136217105635 47: 0.849986985845192 48: 1.0 0: 0.9186369279044543 1: 0.7973407128633153 2: 0.7525766947068775 3: 0.7973407128633153 4: 0.9186369279044544 5: 0.9186369279044532 6: 0.7973407128633143 7: 0.7525766947068765 8: 0.7973407128633143 9: 0.9186369279044532 10: 0.9186369279044533 11: 0.7973407128633144 12: 0.7525766947068766 13: 0.7973407128633144 14: 0.9186369279044533 15: 0.9186369279044534 16: 0.7973407128633145 17: 0.7525766947068767 18: 0.7973407128633145 19: 0.9186369279044534 20: 0.9186369279044537 21: 0.7973407128633148 22: 0.7525766947068769 23: 0.7973407128633148 24: 0.9186369279044537 25: 0.9999999999999988 26: 0.849986985845191 27: 0.7640136217105626 28: 0.7640136217105626 29: 0.8499869858451911 30: 0.9999999999999989 31: 0.9999999999999997 32: 0.8499869858451917 33: 0.7640136217105632 34: 0.7640136217105632 35: 0.8499869858451917 36: 0.9999999999999996 37: 0.9999999999999979 38: 0.8499869858451902 39: 0.7640136217105618 40: 0.7640136217105618 41: 0.8499869858451902 42: 0.9999999999999978 43: 0.9999999999999999 44: 0.849986985845192 45: 0.7640136217105635 46: 0.7640136217105635 47: 0.849986985845192 48: 1.0 |
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Left kernel: Vector space of degree 60 and dimension 12 Left kernel: Vector space of degree 60 and dimension 12 |
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Primjer CN2. — Mreža kabela
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3 * 20 - 49 == 11 != 0 3 * 20 - 49 == 11 != 0 |
20 20 |
60 x 49 dense matrix over Real Double Field (use the '.str()' method to see the entries) 60 x 49 dense matrix over Real Double Field (use the '.str()' method to see the entries) |
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Row space: Vector space of degree 49 and dimension 40 Row space: Vector space of degree 49 and dimension 40 |
Column space: Vector space of degree 60 and dimension 40 Column space: Vector space of degree 60 and dimension 40 |
Kernel: Vector space of degree 49 and dimension 9 Kernel: Vector space of degree 49 and dimension 9 |
0: 1.0 1: 1.0 2: 1.0 3: 1.0 4: 1.0 0: 1.0 1: 1.0 2: 1.0 3: 1.0 4: 1.0 |
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5: 1.0 6: 1.0 7: 1.0 8: 1.0 9: 1.0 5: 1.0 6: 1.0 7: 1.0 8: 1.0 9: 1.0 |
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43: 0.9999999999999994 44: 0.9999999999999996 45: 0.9999999999999997 46: 0.9999999999999998 47: 0.9999999999999999 48: 1.0 43: 0.9999999999999994 44: 0.9999999999999996 45: 0.9999999999999997 46: 0.9999999999999998 47: 0.9999999999999999 48: 1.0 |
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Left kernel: Vector space of degree 60 and dimension 20 Left kernel: Vector space of degree 60 and dimension 20 |
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Primjer T1. — Trostrana prizma
joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (-1/2*sqrt(3), -1/2, 2) 4: (1/2*sqrt(3), -1/2, 2) 5: (0, 1, 2) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) supports: [] joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (-1/2*sqrt(3), -1/2, 2) 4: (1/2*sqrt(3), -1/2, 2) 5: (0, 1, 2) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) supports: [] |
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3 * 6 - 12 == 6 != 0 3 * 6 - 12 == 6 != 0 |
[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
(1.0000.00000.50000.00000.00000.00000.00000.00000.00000.65470.00000.00000.00000.00000.86600.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.75590.00000.0000−1.000−0.50000.00000.00000.00000.00000.00000.00000.00000.0000−0.32730.00000.00000.86600.00000.00000.00000.00000.00000.00000.00000.00000.56690.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.75590.00000.00000.5000−0.50000.00000.00000.00000.00000.00000.00000.00000.0000−0.32730.0000−0.8660−0.86600.00000.00000.00000.00000.00000.00000.00000.0000−0.56690.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.75590.00000.00000.00001.0000.00000.50000.00000.00000.00000.00000.00000.32730.00000.00000.00000.00000.00000.86600.00000.00000.00000.00000.00000.56690.00000.00000.00000.00000.00000.0000−1.0000.00000.00000.00000.0000−0.75590.00000.00000.0000−1.000−0.50000.00000.00000.00000.0000−0.65470.00000.00000.00000.00000.00000.00000.86600.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−1.0000.0000−0.75590.00000.00000.00000.00000.00000.00000.5000−0.50000.00000.00000.00000.00000.32730.00000.00000.00000.00000.0000−0.8660−0.86600.00000.00000.00000.0000−0.56690.00000.00000.00000.00000.00000.00000.00000.00000.0000−1.0000.0000−0.75590.0000)
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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 18 and dimension 6 Basis: (0.0, -0.5773502691896258, 0.43301270189221935, 0.0, 0.5773502691896258, -0.43301270189221935, -1.0, 0.0, 0.0, 1.0, -0.5773502691896258, 0.43301270189221935, 1.0, 0.5773502691896258, -0.43301270189221935, 0.0, 0.0, 0.0) (1.0, 0.0, -0.43301270189221935, 1.0, 0.0, 0.43301270189221935, 1.0, 0.0, 0.0, 0.0, 0.0, -0.43301270189221935, 0.0, 0.0, 0.43301270189221935, 0.0, 0.0, 0.0) (0.0, 1.0, -0.75, 0.0, 1.0, -0.75, 0.0, 1.0, 0.0, 0.0, 0.0, -0.75, 0.0, 0.0, -0.75, 0.0, 0.0, 0.0) (0.0, 0.5773502691896258, 0.0, 0.0, -0.5773502691896258, 0.0, 1.0, 0.0, 0.0, 0.0, 0.5773502691896258, 0.0, 0.0, -0.5773502691896258, 0.0, 1.0, 0.0, 0.0) (0.0, 0.0, 0.75, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 1.0, 0.75, 0.0, 1.0, 0.75, 0.0, 1.0, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) Left kernel: Vector space of degree 18 and dimension 6 Basis: (0.0, -0.5773502691896258, 0.43301270189221935, 0.0, 0.5773502691896258, -0.43301270189221935, -1.0, 0.0, 0.0, 1.0, -0.5773502691896258, 0.43301270189221935, 1.0, 0.5773502691896258, -0.43301270189221935, 0.0, 0.0, 0.0) (1.0, 0.0, -0.43301270189221935, 1.0, 0.0, 0.43301270189221935, 1.0, 0.0, 0.0, 0.0, 0.0, -0.43301270189221935, 0.0, 0.0, 0.43301270189221935, 0.0, 0.0, 0.0) (0.0, 1.0, -0.75, 0.0, 1.0, -0.75, 0.0, 1.0, 0.0, 0.0, 0.0, -0.75, 0.0, 0.0, -0.75, 0.0, 0.0, 0.0) (0.0, 0.5773502691896258, 0.0, 0.0, -0.5773502691896258, 0.0, 1.0, 0.0, 0.0, 0.0, 0.5773502691896258, 0.0, 0.0, -0.5773502691896258, 0.0, 1.0, 0.0, 0.0) (0.0, 0.0, 0.75, 0.0, 0.0, 0.75, 0.0, 0.0, 0.0, 0.0, 1.0, 0.75, 0.0, 1.0, 0.75, 0.0, 1.0, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) |
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Primjer T2. — Trostrana „zakrenuta” prizma
joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (0, -1, 2) 4: (1/2*sqrt(3), 1/2, 2) 5: (-1/2*sqrt(3), 1/2, 2) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) supports: [] joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (0, -1, 2) 4: (1/2*sqrt(3), 1/2, 2) 5: (-1/2*sqrt(3), 1/2, 2) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) supports: [] |
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3 * 6 - 12 == 6 != 0 3 * 6 - 12 == 6 != 0 |
[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
(1.0000.00000.50000.00000.00000.00000.38730.00000.00000.61240.00000.00000.00000.00000.86600.00000.00000.0000−0.22360.00000.00000.35360.00000.00000.00000.00000.00000.00000.00000.00000.89440.00000.00000.70710.00000.0000−1.000−0.50000.00000.00000.00000.00000.00000.00000.00000.0000−0.61240.00000.00000.86600.00000.00000.00000.00000.00000.44720.00000.00000.35360.00000.00000.00000.00000.00000.00000.00000.00000.89440.00000.00000.70710.00000.00000.5000−0.50000.00000.00000.00000.00000.0000−0.38730.00000.00000.00000.0000−0.8660−0.86600.00000.00000.00000.00000.0000−0.22360.00000.0000−0.70710.00000.00000.00000.00000.00000.00000.00000.00000.89440.00000.00000.70710.00000.00000.00000.50000.0000−0.5000−0.38730.00000.00000.00000.00000.00000.00000.00000.00000.86600.00000.86600.22360.00000.00000.00000.00000.70710.00000.00000.00000.00000.00000.0000−0.89440.00000.00000.00000.0000−0.70710.00000.00000.0000−0.5000−1.0000.00000.00000.00000.0000−0.61240.00000.00000.00000.00000.0000−0.86600.00000.00000.0000−0.44720.0000−0.35360.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.89440.0000−0.70710.00000.00000.00000.00000.00000.00001.0000.50000.00000.00000.38730.00000.61240.00000.00000.00000.00000.00000.0000−0.86600.00000.00000.22360.0000−0.35360.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.89440.0000−0.70710.0000)
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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 18 and dimension 6 Basis: (0.0, 1.0, -0.5, 0.0, 1.0, -0.5, 0.0, 1.0, 0.25, 0.0, 0.0, -0.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, -0.49999999999999994, 0.24999999999999992, 0.0, 0.49999999999999994, -0.25000000000000006, -0.8660254037844385, 0.0, -0.37499999999999994, 0.8660254037844385, 0.5, 0.12499999999999994, 0.0, 1.0, -0.5, 0.0, 0.0, 0.0) (1.0, 0.0, 1.1102230246251565e-16, 1.0, 0.0, 0.8660254037844387, 1.0, 0.0, 0.4330127018922193, 0.0, 0.0, 0.4330127018922195, 0.0, 0.0, 0.8660254037844386, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, -0.8660254037844386, 0.0, 0.0, -0.43301270189221935, 1.0, 0.0, -0.43301270189221935, 1.0, 0.0, -0.8660254037844386, 1.0, 0.0, 0.0) (0.0, 0.49999999999999994, 0.2500000000000001, 0.0, -0.49999999999999994, 0.75, 0.8660254037844385, 0.0, 0.12499999999999994, -0.8660254037844385, 0.5, 0.625, 0.0, 0.0, 0.5, 0.0, 1.0, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) Left kernel: Vector space of degree 18 and dimension 6 Basis: (0.0, 1.0, -0.5, 0.0, 1.0, -0.5, 0.0, 1.0, 0.25, 0.0, 0.0, -0.75, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, -0.49999999999999994, 0.24999999999999992, 0.0, 0.49999999999999994, -0.25000000000000006, -0.8660254037844385, 0.0, -0.37499999999999994, 0.8660254037844385, 0.5, 0.12499999999999994, 0.0, 1.0, -0.5, 0.0, 0.0, 0.0) (1.0, 0.0, 1.1102230246251565e-16, 1.0, 0.0, 0.8660254037844387, 1.0, 0.0, 0.4330127018922193, 0.0, 0.0, 0.4330127018922195, 0.0, 0.0, 0.8660254037844386, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, -0.8660254037844386, 0.0, 0.0, -0.43301270189221935, 1.0, 0.0, -0.43301270189221935, 1.0, 0.0, -0.8660254037844386, 1.0, 0.0, 0.0) (0.0, 0.49999999999999994, 0.2500000000000001, 0.0, -0.49999999999999994, 0.75, 0.8660254037844385, 0.0, 0.12499999999999994, -0.8660254037844385, 0.5, 0.625, 0.0, 0.0, 0.5, 0.0, 1.0, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) |
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Primjer T3. — Trostrani prizmatični tensegrity
joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (-1/2, -1/2*sqrt(3), 2) 4: (1, 0, 2) 5: (-1/2, 1/2*sqrt(3), 2) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) supports: [] joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (-1/2, -1/2*sqrt(3), 2) 4: (1, 0, 2) 5: (-1/2, 1/2*sqrt(3), 2) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) supports: [] |
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3 * 6 - 12 == 6 != 0 3 * 6 - 12 == 6 != 0 |
[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
(1.0000.00000.50000.00000.00000.00000.17720.00000.00000.67110.00000.00000.00000.00000.86600.00000.00000.0000−0.17720.00000.00000.17980.00000.00000.00000.00000.00000.00000.00000.00000.96810.00000.00000.71930.00000.0000−1.000−0.50000.00000.00000.00000.00000.00000.064850.00000.0000−0.49130.00000.00000.86600.00000.00000.00000.00000.00000.24200.00000.00000.49130.00000.00000.00000.00000.00000.00000.00000.00000.96810.00000.00000.71930.00000.00000.5000−0.50000.00000.00000.00000.00000.0000−0.24200.00000.0000−0.17980.0000−0.8660−0.86600.00000.00000.00000.00000.0000−0.064850.00000.0000−0.67110.00000.00000.00000.00000.00000.00000.00000.00000.96810.00000.00000.71930.00000.00000.00000.86600.00000.0000−0.17720.00000.00000.00000.00000.17980.00000.00000.00000.50000.00001.0000.17720.00000.00000.00000.00000.67110.00000.00000.00000.00000.00000.0000−0.96810.00000.00000.00000.0000−0.71930.00000.00000.0000−0.8660−0.86600.00000.0000−0.064850.0000−0.67110.00000.00000.00000.00000.0000−0.50000.50000.00000.0000−0.24200.0000−0.17980.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.96810.0000−0.71930.00000.00000.00000.00000.00000.00000.86600.00000.00000.00000.24200.00000.49130.00000.00000.00000.00000.0000−0.5000−1.0000.00000.00000.064850.0000−0.49130.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.96810.0000−0.71930.0000)
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Row space: Vector space of degree 12 and dimension 11 Basis: (1.0, 0.0, 0.5000000000000001, 0.0, 0.0, 0.0, 0.17717466000345752, 0.0, 0.0, 0.6710736745934498, 0.0, 0.0) (0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2794664976500341, 0.0, 0.0, 0.5672582158417004, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 0.0, -0.20458367529315324, 0.0, 0.0, 0.20763091750349863, 0.0, 0.0) (0.0, 0.0, 0.0, 1.0, 0.0, 0.0, -0.20458367529315324, 0.0, 0.0, 0.0, 0.0, 0.20763091750349863) (0.0, 0.0, 0.0, 0.0, 1.0, -0.0, 0.20458367529315324, 0.07488282235688086, -0.0, 0.774889133345199, -0.0, -0.20763091750349863) (0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.2794664976500342, 0.0, 0.0, 0.0, 0.0, 0.5672582158417004) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, 0.7429545911564234) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.7429545911564233, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.7429545911564233) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, -0.9999999999999999) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999999) Row space: Vector space of degree 12 and dimension 11 Basis: (1.0, 0.0, 0.5000000000000001, 0.0, 0.0, 0.0, 0.17717466000345752, 0.0, 0.0, 0.6710736745934498, 0.0, 0.0) (0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2794664976500341, 0.0, 0.0, 0.5672582158417004, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 0.0, -0.20458367529315324, 0.0, 0.0, 0.20763091750349863, 0.0, 0.0) (0.0, 0.0, 0.0, 1.0, 0.0, 0.0, -0.20458367529315324, 0.0, 0.0, 0.0, 0.0, 0.20763091750349863) (0.0, 0.0, 0.0, 0.0, 1.0, -0.0, 0.20458367529315324, 0.07488282235688086, -0.0, 0.774889133345199, -0.0, -0.20763091750349863) (0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.2794664976500342, 0.0, 0.0, 0.0, 0.0, 0.5672582158417004) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, 0.7429545911564234) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.7429545911564233, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.7429545911564233) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, -0.9999999999999999) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999999) |
Column space: Vector space of degree 18 and dimension 11 Basis: (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, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, -0.5000000000000001, 0.8660254037844387, 0.0, 0.5000000000000001, -0.8660254037844387, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.5000000000000001, 0.8660254037844387, 0.0, 0.0, 0.0, 0.0, -0.5000000000000001, -0.8660254037844387, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.8660254037844387, 0.5000000000000001, 0.0, -0.8660254037844387, -0.5000000000000001, 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, 0.0, 0.0, 0.0, -0.8660254037844387, 0.5000000000000001, 0.0, 0.8660254037844387, -0.5000000000000001, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0) (0.17717466000345752, -0.17717466000345752, 0.9681003458863746, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.17717466000345752, 0.17717466000345752, -0.9681003458863746, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.06485042646813614, 0.2420250864715937, 0.9681003458863748, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.06485042646813614, -0.2420250864715937, -0.9681003458863748, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.2420250864715937, -0.06485042646813614, 0.9681003458863748, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2420250864715937, 0.06485042646813614, -0.9681003458863748) (0.6710736745934498, 0.1798136491691009, 0.7192545966764036, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.6710736745934498, -0.1798136491691009, -0.7192545966764036, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, -0.49126002542434893, 0.49126002542434893, 0.7192545966764036, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.49126002542434893, -0.49126002542434893, -0.7192545966764036) Column space: Vector space of degree 18 and dimension 11 Basis: (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, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, -0.5000000000000001, 0.8660254037844387, 0.0, 0.5000000000000001, -0.8660254037844387, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.5000000000000001, 0.8660254037844387, 0.0, 0.0, 0.0, 0.0, -0.5000000000000001, -0.8660254037844387, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.8660254037844387, 0.5000000000000001, 0.0, -0.8660254037844387, -0.5000000000000001, 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, 0.0, 0.0, 0.0, -0.8660254037844387, 0.5000000000000001, 0.0, 0.8660254037844387, -0.5000000000000001, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0) (0.17717466000345752, -0.17717466000345752, 0.9681003458863746, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.17717466000345752, 0.17717466000345752, -0.9681003458863746, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.06485042646813614, 0.2420250864715937, 0.9681003458863748, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.06485042646813614, -0.2420250864715937, -0.9681003458863748, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.2420250864715937, -0.06485042646813614, 0.9681003458863748, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2420250864715937, 0.06485042646813614, -0.9681003458863748) (0.6710736745934498, 0.1798136491691009, 0.7192545966764036, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.6710736745934498, -0.1798136491691009, -0.7192545966764036, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, -0.49126002542434893, 0.49126002542434893, 0.7192545966764036, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.49126002542434893, -0.49126002542434893, -0.7192545966764036) |
Kernel: Vector space of degree 12 and dimension 1 Basis: (-0.3596272983382016, -0.35962729833820173, -0.35962729833820173, -0.3596272983382018, -0.35962729833820173, -0.35962729833820173, -0.7429545911564234, -0.7429545911564231, -0.7429545911564233, 0.9999999999999999, 0.9999999999999999, 1.0) Kernel: Vector space of degree 12 and dimension 1 Basis: (-0.3596272983382016, -0.35962729833820173, -0.35962729833820173, -0.3596272983382018, -0.35962729833820173, -0.35962729833820173, -0.7429545911564234, -0.7429545911564231, -0.7429545911564233, 0.9999999999999999, 0.9999999999999999, 1.0) |
0: -0.3596272983382016 1: -0.35962729833820173 2: -0.35962729833820173 3: -0.3596272983382018 4: -0.35962729833820173 5: -0.35962729833820173 6: -0.7429545911564234 7: -0.7429545911564231 8: -0.7429545911564233 9: 0.9999999999999999 10: 0.9999999999999999 11: 1.0 0: -0.3596272983382016 1: -0.35962729833820173 2: -0.35962729833820173 3: -0.3596272983382018 4: -0.35962729833820173 5: -0.35962729833820173 6: -0.7429545911564234 7: -0.7429545911564231 8: -0.7429545911564233 9: 0.9999999999999999 10: 0.9999999999999999 11: 1.0 |
0: 0.3596272983382016 1: 0.35962729833820173 2: 0.35962729833820173 3: 0.3596272983382018 4: 0.35962729833820173 5: 0.35962729833820173 6: 0.7429545911564234 7: 0.7429545911564231 8: 0.7429545911564233 9: -0.9999999999999999 10: -0.9999999999999999 11: -1.0 0: 0.3596272983382016 1: 0.35962729833820173 2: 0.35962729833820173 3: 0.3596272983382018 4: 0.35962729833820173 5: 0.35962729833820173 6: 0.7429545911564234 7: 0.7429545911564231 8: 0.7429545911564233 9: -0.9999999999999999 10: -0.9999999999999999 11: -1.0 |
|
Left kernel: Vector space of degree 18 and dimension 7 Basis: (1.0, -0.5773502691896258, -0.28867513459481287, 1.0, 0.5773502691896258, 0.28867513459481287, 0.0, 0.0, 0.0, 0.0, 0.0, 5.551115123125783e-17, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0) (0.0, 0.5773502691896258, 0.10566243270259365, 0.0, -0.5773502691896258, 0.39433756729740654, 1.0, 0.0, 0.25, 0.0, 0.0, 5.551115123125783e-17, 0.0, 0.0, 0.2500000000000001, 0.0, 0.0, 0.0) (0.0, 0.0, 0.5000000000000002, 0.0, 0.0, -5.551115123125783e-17, 0.0, 0.0, 0.0, 1.1547005383792517, 0.0, 0.28867513459481303, 0.5773502691896258, 1.0, -0.2886751345948129, 0.0, 0.0, 0.0) (0.0, 1.0, -0.6830127018922194, 0.0, 1.0, -0.6830127018922194, 0.0, 1.0, 0.06698729810778065, 0.0, 0.0, -0.8660254037844388, 0.0, 0.0, -0.43301270189221946, 0.0, 0.0, 0.0) (0.0, 0.0, 0.1830127018922193, 0.0, 0.0, -0.6830127018922194, 0.0, 0.0, -0.25, 1.0, 0.0, -1.1102230246251565e-16, 1.0, 0.0, -0.7500000000000001, 1.0, 0.0, 0.0) (0.0, 0.0, 0.1830127018922193, 0.0, 0.0, 0.6830127018922194, 0.0, 0.0, -0.06698729810778065, -1.1547005383792517, 1.0, 0.577350269189626, -0.5773502691896258, 0.0, 0.7216878364870323, 0.0, 1.0, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) Left kernel: Vector space of degree 18 and dimension 7 Basis: (1.0, -0.5773502691896258, -0.28867513459481287, 1.0, 0.5773502691896258, 0.28867513459481287, 0.0, 0.0, 0.0, 0.0, 0.0, 5.551115123125783e-17, 0.0, 0.0, 0.5, 0.0, 0.0, 0.0) (0.0, 0.5773502691896258, 0.10566243270259365, 0.0, -0.5773502691896258, 0.39433756729740654, 1.0, 0.0, 0.25, 0.0, 0.0, 5.551115123125783e-17, 0.0, 0.0, 0.2500000000000001, 0.0, 0.0, 0.0) (0.0, 0.0, 0.5000000000000002, 0.0, 0.0, -5.551115123125783e-17, 0.0, 0.0, 0.0, 1.1547005383792517, 0.0, 0.28867513459481303, 0.5773502691896258, 1.0, -0.2886751345948129, 0.0, 0.0, 0.0) (0.0, 1.0, -0.6830127018922194, 0.0, 1.0, -0.6830127018922194, 0.0, 1.0, 0.06698729810778065, 0.0, 0.0, -0.8660254037844388, 0.0, 0.0, -0.43301270189221946, 0.0, 0.0, 0.0) (0.0, 0.0, 0.1830127018922193, 0.0, 0.0, -0.6830127018922194, 0.0, 0.0, -0.25, 1.0, 0.0, -1.1102230246251565e-16, 1.0, 0.0, -0.7500000000000001, 1.0, 0.0, 0.0) (0.0, 0.0, 0.1830127018922193, 0.0, 0.0, 0.6830127018922194, 0.0, 0.0, -0.06698729810778065, -1.1547005383792517, 1.0, 0.577350269189626, -0.5773502691896258, 0.0, 0.7216878364870323, 0.0, 1.0, 0.0) (0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0) |
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joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (-1/2, -1/2*sqrt(3), 2) 4: (1, 0, 2) 5: (-1/2, 1/2*sqrt(3), 2) 6: (-1/2*sqrt(3) - 0.300000000000000, -1/2, 0) 7: (-1/2*sqrt(3), -0.800000000000000, 0) 8: (-1/2*sqrt(3), -1/2, -0.300000000000000) 9: (1/2*sqrt(3), -0.800000000000000, 0) 10: (1/2*sqrt(3), -1/2, -0.300000000000000) 11: (0, 1, -0.300000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) 12: (0, 6) 13: (0, 7) 14: (0, 8) 15: (1, 9) 16: (1, 10) 17: (2, 11) supports: [6, 7, 8, 9, 10, 11] joints: 0: (-1/2*sqrt(3), -1/2, 0) 1: (1/2*sqrt(3), -1/2, 0) 2: (0, 1, 0) 3: (-1/2, -1/2*sqrt(3), 2) 4: (1, 0, 2) 5: (-1/2, 1/2*sqrt(3), 2) 6: (-1/2*sqrt(3) - 0.300000000000000, -1/2, 0) 7: (-1/2*sqrt(3), -0.800000000000000, 0) 8: (-1/2*sqrt(3), -1/2, -0.300000000000000) 9: (1/2*sqrt(3), -0.800000000000000, 0) 10: (1/2*sqrt(3), -1/2, -0.300000000000000) 11: (0, 1, -0.300000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 3) 7: (1, 4) 8: (2, 5) 9: (0, 4) 10: (1, 5) 11: (2, 3) 12: (0, 6) 13: (0, 7) 14: (0, 8) 15: (1, 9) 16: (1, 10) 17: (2, 11) supports: [6, 7, 8, 9, 10, 11] |
|
3 * 6 - 18 == 0 3 * 6 - 18 == 0 |
[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
(1.0000.00000.50000.00000.00000.00000.17720.00000.00000.67110.00000.0000−1.0000.00000.00000.00000.00000.00000.00000.00000.86600.00000.00000.0000−0.17720.00000.00000.17980.00000.00000.0000−1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.96810.00000.00000.71930.00000.00000.00000.0000−1.0000.00000.00000.0000−1.000−0.50000.00000.00000.00000.00000.00000.064850.00000.0000−0.49130.00000.00000.00000.00000.00000.00000.00000.00000.86600.00000.00000.00000.00000.00000.24200.00000.00000.49130.00000.00000.00000.0000−1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00000.96810.00000.00000.71930.00000.00000.00000.00000.0000−1.0000.00000.00000.5000−0.50000.00000.00000.00000.00000.0000−0.24200.00000.0000−0.17980.00000.00000.00000.00000.00000.00000.0000−0.8660−0.86600.00000.00000.00000.00000.0000−0.064850.00000.0000−0.67110.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.96810.00000.00000.71930.00000.00000.00000.00000.0000−1.0000.00000.00000.00000.86600.00000.0000−0.17720.00000.00000.00000.00000.17980.00000.00000.00000.00000.00000.00000.00000.00000.00000.50000.00001.0000.17720.00000.00000.00000.00000.67110.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.96810.00000.00000.00000.0000−0.71930.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.8660−0.86600.00000.0000−0.064850.0000−0.67110.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.50000.50000.00000.0000−0.24200.0000−0.17980.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.96810.0000−0.71930.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.86600.00000.00000.00000.24200.00000.49130.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.5000−1.0000.00000.00000.064850.0000−0.49130.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.96810.0000−0.71930.00000.00000.00000.00000.00000.00000.0000)
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Row space: Vector space of degree 18 and dimension 17 Row space: Vector space of degree 18 and dimension 17 |
Column space: Vector space of degree 18 and dimension 17 Column space: Vector space of degree 18 and dimension 17 |
Kernel: Vector space of degree 18 and dimension 1 Basis: (-0.3596272983382016, -0.35962729833820173, -0.35962729833820173, -0.3596272983382018, -0.3596272983382016, -0.35962729833820173, -0.7429545911564234, -0.7429545911564231, -0.7429545911564233, 0.9999999999999998, 0.9999999999999998, 1.0, 9.92914159000831e-17, 3.519265968729763e-17, -1.1102230246251565e-16, -0.0, -0.0, -0.0) Kernel: Vector space of degree 18 and dimension 1 Basis: (-0.3596272983382016, -0.35962729833820173, -0.35962729833820173, -0.3596272983382018, -0.3596272983382016, -0.35962729833820173, -0.7429545911564234, -0.7429545911564231, -0.7429545911564233, 0.9999999999999998, 0.9999999999999998, 1.0, 9.92914159000831e-17, 3.519265968729763e-17, -1.1102230246251565e-16, -0.0, -0.0, -0.0) |
0: 0.3596272983382016 1: 0.35962729833820173 2: 0.35962729833820173 3: 0.3596272983382018 4: 0.3596272983382016 5: 0.35962729833820173 6: 0.7429545911564234 7: 0.7429545911564231 8: 0.7429545911564233 9: -0.9999999999999998 10: -0.9999999999999998 11: -1.0 12: 0.0 13: 0.0 14: 0.0 15: 0.0 16: 0.0 17: 0.0 0: 0.3596272983382016 1: 0.35962729833820173 2: 0.35962729833820173 3: 0.3596272983382018 4: 0.3596272983382016 5: 0.35962729833820173 6: 0.7429545911564234 7: 0.7429545911564231 8: 0.7429545911564233 9: -0.9999999999999998 10: -0.9999999999999998 11: -1.0 12: 0.0 13: 0.0 14: 0.0 15: 0.0 16: 0.0 17: 0.0 |
|
Left kernel: Vector space of degree 18 and dimension 1 Basis: (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.8660254037844388, -0.5000000000000004, -0.25000000000000017, -1.1102230246251565e-16, 1.0, -0.25, -0.866025403784439, -0.5000000000000004, -0.2500000000000001) Left kernel: Vector space of degree 18 and dimension 1 Basis: (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.8660254037844388, -0.5000000000000004, -0.25000000000000017, -1.1102230246251565e-16, 1.0, -0.25, -0.866025403784439, -0.5000000000000004, -0.2500000000000001) |
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Primjer T4. — (Još jedan) trostrani prizmatični tensegrity
joints: 0: (1/2, 1/2*sqrt(3), 0) 1: (0, 0, 0) 2: (1, 0, 0) 3: (0, 0, 1.25000000000000) 4: (1/2*sqrt(3), 1/2, 1.25000000000000) 5: (0, 1, 1.25000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 5) 7: (1, 3) 8: (2, 4) 9: (0, 3) 10: (1, 4) 11: (2, 5) supports: [] joints: 0: (1/2, 1/2*sqrt(3), 0) 1: (0, 0, 0) 2: (1, 0, 0) 3: (0, 0, 1.25000000000000) 4: (1/2*sqrt(3), 1/2, 1.25000000000000) 5: (0, 1, 1.25000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 5) 7: (1, 3) 8: (2, 4) 9: (0, 3) 10: (1, 4) 11: (2, 5) supports: [] |
|
3 * 6 - 12 == 6 != 0 3 * 6 - 12 == 6 != 0 |
[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
(−0.50000.00000.50000.00000.00000.0000−0.36960.00000.0000−0.31230.00000.0000−0.86600.0000−0.86600.00000.00000.00000.099020.00000.0000−0.54100.00000.00000.00000.00000.00000.00000.00000.00000.92390.00000.00000.78090.00000.00000.50001.0000.00000.00000.00000.00000.00000.00000.00000.00000.54100.00000.86600.00000.00000.00000.00000.00000.00000.00000.00000.00000.31230.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.78090.00000.0000−1.000−0.50000.00000.00000.00000.00000.0000−0.099020.00000.0000−0.52980.00000.00000.86600.00000.00000.00000.00000.00000.36960.00000.00000.52980.00000.00000.00000.00000.00000.00000.00000.00000.92390.00000.00000.66230.00000.00000.00000.86600.00000.00000.00000.00000.00000.31230.00000.00000.00000.00000.00000.50000.00001.0000.00000.00000.00000.54100.00000.00000.00000.00000.00000.00000.00000.00000.0000−1.0000.0000−0.78090.00000.00000.00000.00000.0000−0.8660−0.86600.00000.00000.00000.099020.0000−0.54100.00000.00000.00000.0000−0.50000.50000.00000.00000.0000−0.36960.0000−0.31230.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.92390.0000−0.78090.00000.00000.00000.00000.00000.86600.00000.36960.00000.00000.00000.00000.52980.00000.00000.00000.0000−0.5000−1.000−0.099020.00000.00000.00000.0000−0.52980.00000.00000.00000.00000.00000.0000−0.92390.00000.00000.00000.0000−0.6623)
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Row space: Vector space of degree 12 and dimension 11 Row space: Vector space of degree 12 and dimension 11 |
Column space: Vector space of degree 18 and dimension 11 Column space: Vector space of degree 18 and dimension 11 |
Kernel: Vector space of degree 12 and dimension 1 Basis: (-0.3058876451607489, -0.30588764516074907, -0.305887645160749, -0.30588764516074896, -0.30588764516074896, -0.305887645160749, -0.716805621929536, -0.6622661785325219, -0.716805621929536, 0.8481145238787241, 0.8481145238787241, 1.0) Kernel: Vector space of degree 12 and dimension 1 Basis: (-0.3058876451607489, -0.30588764516074907, -0.305887645160749, -0.30588764516074896, -0.30588764516074896, -0.305887645160749, -0.716805621929536, -0.6622661785325219, -0.716805621929536, 0.8481145238787241, 0.8481145238787241, 1.0) |
0: 0.3058876451607489 1: 0.30588764516074907 2: 0.305887645160749 3: 0.30588764516074896 4: 0.30588764516074896 5: 0.305887645160749 6: 0.716805621929536 7: 0.6622661785325219 8: 0.716805621929536 9: -0.8481145238787241 10: -0.8481145238787241 11: -1.0 0: 0.3058876451607489 1: 0.30588764516074907 2: 0.305887645160749 3: 0.30588764516074896 4: 0.30588764516074896 5: 0.305887645160749 6: 0.716805621929536 7: 0.6622661785325219 8: 0.716805621929536 9: -0.8481145238787241 10: -0.8481145238787241 11: -1.0 |
|
Left kernel: Vector space of degree 18 and dimension 7 Left kernel: Vector space of degree 18 and dimension 7 |
joints: 0: (1/2, 1/2*sqrt(3), 0) 1: (0, 0, 0) 2: (1, 0, 0) 3: (0, 0, 1.25000000000000) 4: (1/2*sqrt(3), 1/2, 1.25000000000000) 5: (0, 1, 1.25000000000000) 6: (1/2, 1/2*sqrt(3), -0.300000000000000) 7: (-0.300000000000000, 0, 0) 8: (0, -0.300000000000000, 0) 9: (0, 0, -0.300000000000000) 10: (1, -0.300000000000000, 0) 11: (1, 0, -0.300000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 5) 7: (1, 3) 8: (2, 4) 9: (0, 3) 10: (1, 4) 11: (2, 5) 12: (0, 6) 13: (1, 7) 14: (1, 8) 15: (1, 9) 16: (2, 10) 17: (2, 11) supports: [6, 7, 8, 9, 10, 11] joints: 0: (1/2, 1/2*sqrt(3), 0) 1: (0, 0, 0) 2: (1, 0, 0) 3: (0, 0, 1.25000000000000) 4: (1/2*sqrt(3), 1/2, 1.25000000000000) 5: (0, 1, 1.25000000000000) 6: (1/2, 1/2*sqrt(3), -0.300000000000000) 7: (-0.300000000000000, 0, 0) 8: (0, -0.300000000000000, 0) 9: (0, 0, -0.300000000000000) 10: (1, -0.300000000000000, 0) 11: (1, 0, -0.300000000000000) bars: 0: (0, 1) 1: (1, 2) 2: (2, 0) 3: (3, 4) 4: (4, 5) 5: (5, 3) 6: (0, 5) 7: (1, 3) 8: (2, 4) 9: (0, 3) 10: (1, 4) 11: (2, 5) 12: (0, 6) 13: (1, 7) 14: (1, 8) 15: (1, 9) 16: (2, 10) 17: (2, 11) supports: [6, 7, 8, 9, 10, 11] |
|
3 * 6 - 18 == 0 3 * 6 - 18 == 0 |
[0, 1, 2, 3, 4, 5] [0, 1, 2, 3, 4, 5] |
(−0.50000.00000.50000.00000.00000.0000−0.36960.00000.0000−0.31230.00000.00000.00000.00000.00000.00000.00000.0000−0.86600.0000−0.86600.00000.00000.00000.099020.00000.0000−0.54100.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.92390.00000.00000.78090.00000.0000−1.0000.00000.00000.00000.00000.00000.50001.0000.00000.00000.00000.00000.00000.00000.00000.00000.54100.00000.0000−1.0000.00000.00000.00000.00000.86600.00000.00000.00000.00000.00000.00000.00000.00000.00000.31230.00000.00000.0000−1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.78090.00000.00000.00000.0000−1.0000.00000.00000.0000−1.000−0.50000.00000.00000.00000.00000.0000−0.099020.00000.0000−0.52980.00000.00000.00000.00000.00000.00000.00000.00000.86600.00000.00000.00000.00000.00000.36960.00000.00000.52980.00000.00000.00000.0000−1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00000.92390.00000.00000.66230.00000.00000.00000.00000.0000−1.0000.00000.00000.00000.86600.00000.00000.00000.00000.00000.31230.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.50000.00001.0000.00000.00000.00000.54100.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−1.0000.0000−0.78090.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.8660−0.86600.00000.00000.00000.099020.0000−0.54100.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.50000.50000.00000.00000.0000−0.36960.0000−0.31230.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.92390.0000−0.78090.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.86600.00000.36960.00000.00000.00000.00000.52980.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.5000−1.000−0.099020.00000.00000.00000.0000−0.52980.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000−0.92390.00000.00000.00000.0000−0.66230.00000.00000.00000.00000.00000.0000)
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Row space: Vector space of degree 18 and dimension 17 Row space: Vector space of degree 18 and dimension 17 |
Column space: Vector space of degree 18 and dimension 17 Column space: Vector space of degree 18 and dimension 17 |
Kernel: Vector space of degree 18 and dimension 1 Basis: (-0.3058876451607489, -0.30588764516074907, -0.305887645160749, -0.30588764516074896, -0.30588764516074896, -0.305887645160749, -0.716805621929536, -0.6622661785325219, -0.7168056219295359, 0.8481145238787241, 0.848114523878724, 1.0, 1.232595164407831e-32, 1.1102230246251563e-17, -2.2204460492503132e-17, -5.551115123125784e-17, 2.2204460492503132e-17, 5.551115123125783e-17) Kernel: Vector space of degree 18 and dimension 1 Basis: (-0.3058876451607489, -0.30588764516074907, -0.305887645160749, -0.30588764516074896, -0.30588764516074896, -0.305887645160749, -0.716805621929536, -0.6622661785325219, -0.7168056219295359, 0.8481145238787241, 0.848114523878724, 1.0, 1.232595164407831e-32, 1.1102230246251563e-17, -2.2204460492503132e-17, -5.551115123125784e-17, 2.2204460492503132e-17, 5.551115123125783e-17) |
0: 0.3058876451607489 1: 0.30588764516074907 2: 0.305887645160749 3: 0.30588764516074896 4: 0.30588764516074896 5: 0.305887645160749 6: 0.716805621929536 7: 0.6622661785325219 8: 0.7168056219295359 9: -0.8481145238787241 10: -0.848114523878724 11: -1.0 0: 0.3058876451607489 1: 0.30588764516074907 2: 0.305887645160749 3: 0.30588764516074896 4: 0.30588764516074896 5: 0.305887645160749 6: 0.716805621929536 7: 0.6622661785325219 8: 0.7168056219295359 9: -0.8481145238787241 10: -0.848114523878724 11: -1.0 |
|
Left kernel: Vector space of degree 18 and dimension 1 Basis: (0.0, 0.0, 0.0, 0.0, 0.0, 7.153584028445419e-17, 0.0, 0.0, 0.0, -0.9999999999999997, 0.5773502691896257, 7.153584028445419e-17, 1.1102230246251565e-16, -1.1547005383792515, 0.4618802153517006, 1.0, 0.5773502691896257, 0.33811978464829945) Left kernel: Vector space of degree 18 and dimension 1 Basis: (0.0, 0.0, 0.0, 0.0, 0.0, 7.153584028445419e-17, 0.0, 0.0, 0.0, -0.9999999999999997, 0.5773502691896257, 7.153584028445419e-17, 1.1102230246251565e-16, -1.1547005383792515, 0.4618802153517006, 1.0, 0.5773502691896257, 0.33811978464829945) |
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Primjer T4. — Četverostrani prizmatični tensegrity
joints: 0: (-1, -1, 0) 1: (1, -1, 0) 2: (1, 1, 0) 3: (-1, 1, 0) 4: (0, -sqrt(2), 3) 5: (sqrt(2), 0, 3) 6: (0, sqrt(2), 3) 7: (-sqrt(2), 0, 3) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 0) 4: (4, 5) 5: (5, 6) 6: (6, 7) 7: (7, 4) 8: (0, 4) 9: (1, 5) 10: (2, 6) 11: (3, 7) 12: (0, 5) 13: (1, 6) 14: (2, 7) 15: (3, 4) supports: [] joints: 0: (-1, -1, 0) 1: (1, -1, 0) 2: (1, 1, 0) 3: (-1, 1, 0) 4: (0, -sqrt(2), 3) 5: (sqrt(2), 0, 3) 6: (0, sqrt(2), 3) 7: (-sqrt(2), 0, 3) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 0) 4: (4, 5) 5: (5, 6) 6: (6, 7) 7: (7, 4) 8: (0, 4) 9: (1, 5) 10: (2, 6) 11: (3, 7) 12: (0, 5) 13: (1, 6) 14: (2, 7) 15: (3, 4) supports: [] |
|
3 * 8 - 16 == 8 != 0 3 * 8 - 16 == 8 != 0 |
[0, 1, 2, 3, 4, 5, 6, 7] [0, 1, 2, 3, 4, 5, 6, 7] |
24 x 16 dense matrix over Real Double Field (use the '.str()' method to see the entries) 24 x 16 dense matrix over Real Double Field (use the '.str()' method to see the entries) |
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Row space: Vector space of degree 16 and dimension 15 Row space: Vector space of degree 16 and dimension 15 |
Column space: Vector space of degree 24 and dimension 15 Column space: Vector space of degree 24 and dimension 15 |
Kernel: Vector space of degree 16 and dimension 1 Basis: (-0.3554644040543818, -0.35546440405438173, -0.3554644040543817, -0.3554644040543817, -0.3554644040543818, -0.3554644040543817, -0.3554644040543817, -0.35546440405438184, -0.8016322430806896, -0.8016322430806894, -0.8016322430806895, -0.8016322430806896, 1.0, 0.9999999999999998, 0.9999999999999999, 1.0) Kernel: Vector space of degree 16 and dimension 1 Basis: (-0.3554644040543818, -0.35546440405438173, -0.3554644040543817, -0.3554644040543817, -0.3554644040543818, -0.3554644040543817, -0.3554644040543817, -0.35546440405438184, -0.8016322430806896, -0.8016322430806894, -0.8016322430806895, -0.8016322430806896, 1.0, 0.9999999999999998, 0.9999999999999999, 1.0) |
0: 0.3554644040543818 1: 0.35546440405438173 2: 0.3554644040543817 3: 0.3554644040543817 4: 0.3554644040543818 5: 0.3554644040543817 6: 0.3554644040543817 7: 0.35546440405438184 8: 0.8016322430806896 9: 0.8016322430806894 10: 0.8016322430806895 11: 0.8016322430806896 12: -1.0 13: -0.9999999999999998 14: -0.9999999999999999 15: -1.0 0: 0.3554644040543818 1: 0.35546440405438173 2: 0.3554644040543817 3: 0.3554644040543817 4: 0.3554644040543818 5: 0.3554644040543817 6: 0.3554644040543817 7: 0.35546440405438184 8: 0.8016322430806896 9: 0.8016322430806894 10: 0.8016322430806895 11: 0.8016322430806896 12: -1.0 13: -0.9999999999999998 14: -0.9999999999999999 15: -1.0 |
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Left kernel: Vector space of degree 24 and dimension 9 Left kernel: Vector space of degree 24 and dimension 9 |
joints: 0: (-1, -1, 0) 1: (1, -1, 0) 2: (1, 1, 0) 3: (-1, 1, 0) 4: (0, -sqrt(2), 3) 5: (sqrt(2), 0, 3) 6: (0, sqrt(2), 3) 7: (-sqrt(2), 0, 3) 8: (-1.30000000000000, -1, 0) 9: (-1, -1.30000000000000, 0) 10: (-1, -1, -0.300000000000000) 11: (1, -1.30000000000000, 0) 12: (1, -1, -0.300000000000000) 13: (sqrt(2), -0.300000000000000, 3) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 0) 4: (4, 5) 5: (5, 6) 6: (6, 7) 7: (7, 4) 8: (0, 4) 9: (1, 5) 10: (2, 6) 11: (3, 7) 12: (0, 5) 13: (1, 6) 14: (2, 7) 15: (3, 4) 16: (0, 8) 17: (0, 9) 18: (0, 10) 19: (1, 11) 20: (1, 12) 21: (5, 13) supports: [8, 9, 10, 11, 12, 13] joints: 0: (-1, -1, 0) 1: (1, -1, 0) 2: (1, 1, 0) 3: (-1, 1, 0) 4: (0, -sqrt(2), 3) 5: (sqrt(2), 0, 3) 6: (0, sqrt(2), 3) 7: (-sqrt(2), 0, 3) 8: (-1.30000000000000, -1, 0) 9: (-1, -1.30000000000000, 0) 10: (-1, -1, -0.300000000000000) 11: (1, -1.30000000000000, 0) 12: (1, -1, -0.300000000000000) 13: (sqrt(2), -0.300000000000000, 3) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 0) 4: (4, 5) 5: (5, 6) 6: (6, 7) 7: (7, 4) 8: (0, 4) 9: (1, 5) 10: (2, 6) 11: (3, 7) 12: (0, 5) 13: (1, 6) 14: (2, 7) 15: (3, 4) 16: (0, 8) 17: (0, 9) 18: (0, 10) 19: (1, 11) 20: (1, 12) 21: (5, 13) supports: [8, 9, 10, 11, 12, 13] |
|
3 * 8 - 22 == 2 != 0 3 * 8 - 22 == 2 != 0 |
[0, 1, 2, 3, 4, 5, 6, 7] [0, 1, 2, 3, 4, 5, 6, 7] |
24 x 22 dense matrix over Real Double Field (use the '.str()' method to see the entries) 24 x 22 dense matrix over Real Double Field (use the '.str()' method to see the entries) |
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Column space: Vector space of degree 24 and dimension 21 Column space: Vector space of degree 24 and dimension 21 |
Row space: Vector space of degree 22 and dimension 21 Row space: Vector space of degree 22 and dimension 21 |
Kernel: Vector space of degree 22 and dimension 1 Basis: (-0.355464404054382, -0.3554644040543818, -0.3554644040543817, -0.3554644040543816, -0.3554644040543818, -0.3554644040543817, -0.3554644040543817, -0.35546440405438184, -0.8016322430806896, -0.8016322430806891, -0.8016322430806895, -0.8016322430806896, 1.0, 0.9999999999999998, 0.9999999999999999, 1.0, -1.942890293094024e-16, 4.2812207464063204e-17, -3.8096831301583876e-17, 1.8503717077085932e-17, 2.220446049250313e-16, 1.3877787807814457e-16) Kernel: Vector space of degree 22 and dimension 1 Basis: (-0.355464404054382, -0.3554644040543818, -0.3554644040543817, -0.3554644040543816, -0.3554644040543818, -0.3554644040543817, -0.3554644040543817, -0.35546440405438184, -0.8016322430806896, -0.8016322430806891, -0.8016322430806895, -0.8016322430806896, 1.0, 0.9999999999999998, 0.9999999999999999, 1.0, -1.942890293094024e-16, 4.2812207464063204e-17, -3.8096831301583876e-17, 1.8503717077085932e-17, 2.220446049250313e-16, 1.3877787807814457e-16) |
0: 0.355464404054382 1: 0.3554644040543818 2: 0.3554644040543817 3: 0.3554644040543816 4: 0.3554644040543818 5: 0.3554644040543817 6: 0.3554644040543817 7: 0.35546440405438184 8: 0.8016322430806896 9: 0.8016322430806891 10: 0.8016322430806895 11: 0.8016322430806896 12: -1.0 13: -0.9999999999999998 14: -0.9999999999999999 15: -1.0 0: 0.355464404054382 1: 0.3554644040543818 2: 0.3554644040543817 3: 0.3554644040543816 4: 0.3554644040543818 5: 0.3554644040543817 6: 0.3554644040543817 7: 0.35546440405438184 8: 0.8016322430806896 9: 0.8016322430806891 10: 0.8016322430806895 11: 0.8016322430806896 12: -1.0 13: -0.9999999999999998 14: -0.9999999999999999 15: -1.0 |
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Left kernel: Vector space of degree 24 and dimension 3 Left kernel: Vector space of degree 24 and dimension 3 |
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Primjer CB1. — Prednapeta vlačno–tlačna „kupola”
joints: 0: (1, 1, 3) 1: (-1, 1, 3) 2: (-1, -1, 3) 3: (1, -1, 3) 4: (1, 1, 1) 5: (-1, 1, 1) 6: (-1, -1, 1) 7: (1, -1, 1) 8: (2, 2, 2) 9: (-2, 2, 2) 10: (-2, -2, 2) 11: (2, -2, 2) 12: (2, 2, 0) 13: (-2, 2, 0) 14: (-2, -2, 0) 15: (2, -2, 0) 16: (3, 3, 1) 17: (-3, 3, 1) 18: (-3, -3, 1) 19: (3, -3, 1) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 0) 4: (4, 5) 5: (5, 6) 6: (6, 7) 7: (7, 4) 8: (0, 4) 9: (1, 5) 10: (2, 6) 11: (3, 7) 12: (0, 8) 13: (4, 8) 14: (1, 9) 15: (5, 9) 16: (2, 10) 17: (6, 10) 18: (3, 11) 19: (7, 11) 20: (12, 13) 21: (13, 14) 22: (14, 15) 23: (15, 12) 24: (8, 12) 25: (9, 13) 26: (10, 14) 27: (11, 15) 28: (8, 16) 29: (12, 16) 30: (9, 17) 31: (13, 17) 32: (10, 18) 33: (14, 18) 34: (11, 19) 35: (15, 19) supports: [16, 17, 18, 19] joints: 0: (1, 1, 3) 1: (-1, 1, 3) 2: (-1, -1, 3) 3: (1, -1, 3) 4: (1, 1, 1) 5: (-1, 1, 1) 6: (-1, -1, 1) 7: (1, -1, 1) 8: (2, 2, 2) 9: (-2, 2, 2) 10: (-2, -2, 2) 11: (2, -2, 2) 12: (2, 2, 0) 13: (-2, 2, 0) 14: (-2, -2, 0) 15: (2, -2, 0) 16: (3, 3, 1) 17: (-3, 3, 1) 18: (-3, -3, 1) 19: (3, -3, 1) bars: 0: (0, 1) 1: (1, 2) 2: (2, 3) 3: (3, 0) 4: (4, 5) 5: (5, 6) 6: (6, 7) 7: (7, 4) 8: (0, 4) 9: (1, 5) 10: (2, 6) 11: (3, 7) 12: (0, 8) 13: (4, 8) 14: (1, 9) 15: (5, 9) 16: (2, 10) 17: (6, 10) 18: (3, 11) 19: (7, 11) 20: (12, 13) 21: (13, 14) 22: (14, 15) 23: (15, 12) 24: (8, 12) 25: (9, 13) 26: (10, 14) 27: (11, 15) 28: (8, 16) 29: (12, 16) 30: (9, 17) 31: (13, 17) 32: (10, 18) 33: (14, 18) 34: (11, 19) 35: (15, 19) supports: [16, 17, 18, 19] |
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3 * 16 - 36 == 12 != 0 3 * 16 - 36 == 12 != 0 |
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] |
48 x 36 dense matrix over Real Double Field (use the '.str()' method to see the entries) 48 x 36 dense matrix over Real Double Field (use the '.str()' method to see the entries) |
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Row space: Vector space of degree 36 and dimension 35 Row space: Vector space of degree 36 and dimension 35 |
Column space: Vector space of degree 48 and dimension 35 Column space: Vector space of degree 48 and dimension 35 |
Kernel: Vector space of degree 36 and dimension 1 Basis: (0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, -0.2886751345948129, -0.2886751345948129, -0.2886751345948129, -0.2886751345948129, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5773502691896258, 0.5773502691896258, 0.5773502691896258, 0.5773502691896258, -0.5773502691896258, -0.5773502691896258, -0.5773502691896258, -0.5773502691896258, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0) Kernel: Vector space of degree 36 and dimension 1 Basis: (0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, 0.2886751345948129, -0.2886751345948129, -0.2886751345948129, -0.2886751345948129, -0.2886751345948129, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5773502691896258, 0.5773502691896258, 0.5773502691896258, 0.5773502691896258, -0.5773502691896258, -0.5773502691896258, -0.5773502691896258, -0.5773502691896258, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0) |
0: 0.2886751345948129 1: 0.2886751345948129 2: 0.2886751345948129 3: 0.2886751345948129 4: 0.2886751345948129 5: 0.2886751345948129 6: 0.2886751345948129 7: 0.2886751345948129 8: -0.2886751345948129 9: -0.2886751345948129 10: -0.2886751345948129 11: -0.2886751345948129 12: 0.5 13: 0.5 14: 0.5 15: 0.5 16: 0.5 17: 0.5 18: 0.5 19: 0.5 20: 0.5773502691896258 21: 0.5773502691896258 22: 0.5773502691896258 23: 0.5773502691896258 24: -0.5773502691896258 25: -0.5773502691896258 26: -0.5773502691896258 27: -0.5773502691896258 28: 1.0 29: 1.0 30: 1.0 31: 1.0 32: 1.0 33: 1.0 34: 1.0 35: 1.0 0: 0.2886751345948129 1: 0.2886751345948129 2: 0.2886751345948129 3: 0.2886751345948129 4: 0.2886751345948129 5: 0.2886751345948129 6: 0.2886751345948129 7: 0.2886751345948129 8: -0.2886751345948129 9: -0.2886751345948129 10: -0.2886751345948129 11: -0.2886751345948129 12: 0.5 13: 0.5 14: 0.5 15: 0.5 16: 0.5 17: 0.5 18: 0.5 19: 0.5 20: 0.5773502691896258 21: 0.5773502691896258 22: 0.5773502691896258 23: 0.5773502691896258 24: -0.5773502691896258 25: -0.5773502691896258 26: -0.5773502691896258 27: -0.5773502691896258 28: 1.0 29: 1.0 30: 1.0 31: 1.0 32: 1.0 33: 1.0 34: 1.0 35: 1.0 |
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Left kernel: Vector space of degree 48 and dimension 13 Left kernel: Vector space of degree 48 and dimension 13 |
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