Jednostavni(ji) sistemi
|
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), ... }
joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (4.00000000000000, -1.50000000000000, 0.000000000000000) 2: (2.00000000000000, 3.50000000000000, 0.000000000000000) 3: (1.50000000000000, 2.00000000000000, 3.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) supports: [0, 1, 2] loads: 3: (75.0000000000000, 100.000000000000, -25.0000000000000) joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (4.00000000000000, -1.50000000000000, 0.000000000000000) 2: (2.00000000000000, 3.50000000000000, 0.000000000000000) 3: (1.50000000000000, 2.00000000000000, 3.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) supports: [0, 1, 2] loads: 3: (75.0000000000000, 100.000000000000, -25.0000000000000) |
Grafički prikaz rešetke:
![]() ![]() |
Izračunavanje vrijednosti sila u štapovima:
truss3D (joints, bars, supports, loads)
rezultat: rječnik s komponentama oznakai: silai
{0: 121.55658196570405, 1: -22.492836817374567, 2: -119.27259222775442} {0: 121.55658196570405, 1: -22.492836817374567, 2: -119.27259222775442} |
0: 121.55658196570405 1: -22.492836817374567 2: -119.27259222775442 0: 121.55658196570405 1: -22.492836817374567 2: -119.27259222775442 |
Grafički prikaz rješenja:
![]() ![]() |
Rješavanje u koracima:
others (a1, a2) — rezultat: komponente liste ili ključevi komponenata rječnika a2 koje nisu u listi ili rječniku a1
[3] [3] |
3nj=nb
nj — broj slobodnih čvorova
nb — broj štapova
3 * 1 - 3 == 0 3 * 1 - 3 == 0 |
(−0.38411063979868790.47673129462279620.14744195615489714−0.5121475197315839−0.66742381247191460.4423258684646914−0.7682212795973759−0.5720775535473553−0.8846517369293828)
|
(75.0,100.0,−25.0)
|
(121.55658196570404,−22.492836817374574,−119.2725922277544)
|
dict_bar_force (bars, forces) — rezultat: rječnik s komponentama oznakai: silai
0: 121.55658196570404 1: -22.492836817374574 2: -119.2725922277544 0: 121.55658196570404 1: -22.492836817374574 2: -119.2725922277544 |
Rješavanje u koracima (drugi način):
(−0.38411063979868790.47673129462279620.14744195615489714−75.0−0.5121475197315839−0.66742381247191460.4423258684646914−100.0−0.7682212795973759−0.5720775535473553−0.884651736929382825.0)
|
rezultat funkcije ref_wpp(): matrica u gornjem stepeničastom obliku i lista indeksa baznih/uporišnih stupaca
(1.00.74467808786445061.1515584902738285−32.5427069829443950.00.99999999999999990.7731921410338582−114.713467768610330.0−5.551115123125783×10−171.0−119.27259222775442)
|
(1.00000000.744678091.1515585−32.5427070.000000001.00000000.77319214−114.713470.000000000.000000001.0000000−119.27259)
|
[0, 1, 2] [0, 1, 2] |
(121.55658196570405, -22.492836817374567, -119.27259222775442) (121.55658196570405, -22.492836817374567, -119.27259222775442) |
0: 121.55658196570405 1: -22.492836817374567 2: -119.27259222775442 0: 121.55658196570405 1: -22.492836817374567 2: -119.27259222775442 |
Potprostori ravnotežne matrice:
|
Column space: Vector space of degree 3 and dimension 3 Basis: (-0.3841106397986879, -0.5121475197315839, -0.7682212795973759) (0.4767312946227962, -0.6674238124719146, -0.5720775535473553) (0.14744195615489714, 0.4423258684646914, -0.8846517369293828) Column space: Vector space of degree 3 and dimension 3 Basis: (-0.3841106397986879, -0.5121475197315839, -0.7682212795973759) (0.4767312946227962, -0.6674238124719146, -0.5720775535473553) (0.14744195615489714, 0.4423258684646914, -0.8846517369293828) |
(−0.38411063979868790.47673129462279620.14744195615489714−0.5121475197315839−0.66742381247191460.4423258684646914−0.7682212795973759−0.5720775535473553−0.8846517369293828)
|
Row space: Vector space of degree 3 and dimension 3 Basis: (1.0, 0.7446780878644506, 1.1515584902738285) (0.0, 0.9999999999999999, 0.7731921410338582) (0.0, -5.551115123125783e-17, 1.0) Row space: Vector space of degree 3 and dimension 3 Basis: (1.0, 0.7446780878644506, 1.1515584902738285) (0.0, 0.9999999999999999, 0.7731921410338582) (0.0, -5.551115123125783e-17, 1.0) |
(1.00.74467808786445061.15155849027382850.00.99999999999999990.77319214103385820.0−5.551115123125783×10−171.0)
|
Kernel: Vector space of degree 3 and dimension 0 Kernel: Vector space of degree 3 and dimension 0 |
Left kernel: Vector space of degree 3 and dimension 0 Left kernel: Vector space of degree 3 and dimension 0 |
Rješavanje u koracima (treći način):
rezultat funkcije rref_wpp(): reducirana matrica i lista indeksa baznih/uporišnih stupaca
(1.01.1102230246251565×10−160.0121.556581965704050.00.99999999999999990.0−22.4928368173745670.0−5.551115123125783×10−171.0−119.27259222775442)
|
(1.00000000.000000000.00000000121.556580.000000001.00000000.00000000−22.4928370.000000000.000000001.0000000−119.27259)
|
0: 121.55658196570405 1: -22.492836817374567 2: -119.27259222775442 0: 121.55658196570405 1: -22.492836817374567 2: -119.27259222775442 |
Primjer 2.
joints: 0: (-2.00000000000000, -1.00000000000000, 0.000000000000000) 1: (0.000000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 1.00000000000000, 0.000000000000000) 3: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) supports: [0, 1, 2] loads: 3: (100.000000000000, 50.0000000000000, 0.000000000000000) joints: 0: (-2.00000000000000, -1.00000000000000, 0.000000000000000) 1: (0.000000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 1.00000000000000, 0.000000000000000) 3: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) supports: [0, 1, 2] loads: 3: (100.000000000000, 50.0000000000000, 0.000000000000000) |
|
Rješavanje sustava:
[3] [3] |
3 * 1 - 3 == 0 3 * 1 - 3 == 0 |
(−0.66666666666666660.00.6666666666666666−100.0−0.33333333333333330.00.3333333333333333−50.0−0.6666666666666666−1.0−0.6666666666666666−0.0)
|
(1.0−0.0−1.0150.00.01.01.3333333333333333−100.00.00.00.00.0)
|
[0, 1] [0, 1] |
[0, 1] [0, 1] |
[2] [2] |
0: 150.0 1: -100.0 2: 0.0 0: 150.0 1: -100.0 2: 0.0 |
|
Potprostori ravnotežne matrice:
|
Column space: Vector space of degree 3 and dimension 2 Basis: (-0.6666666666666666, -0.3333333333333333, -0.6666666666666666) (0.0, 0.0, -1.0) Column space: Vector space of degree 3 and dimension 2 Basis: (-0.6666666666666666, -0.3333333333333333, -0.6666666666666666) (0.0, 0.0, -1.0) |
(−0.66666666666666660.00.6666666666666666−0.33333333333333330.00.3333333333333333−0.6666666666666666−1.0−0.6666666666666666)
|
[0, 1] [0, 1] |
Row space: Vector space of degree 3 and dimension 2 Basis: (1.0, -0.0, -1.0) (0.0, 1.0, 1.3333333333333333) Row space: Vector space of degree 3 and dimension 2 Basis: (1.0, -0.0, -1.0) (0.0, 1.0, 1.3333333333333333) |
(1.0−0.0−1.00.01.01.33333333333333330.00.00.0)
|
Kernel: Vector space of degree 3 and dimension 1 Basis: (1.0, -1.3333333333333333, 1.0) Kernel: Vector space of degree 3 and dimension 1 Basis: (1.0, -1.3333333333333333, 1.0) |
0: 1.0 1: -1.3333333333333333 2: 1.0 0: 1.0 1: -1.3333333333333333 2: 1.0 |
|
Left kernel: Vector space of degree 3 and dimension 1 Basis: (-0.5, 1.0, 0.0) Left kernel: Vector space of degree 3 and dimension 1 Basis: (-0.5, 1.0, 0.0) |
|
(100.0, 50.0, 0.0) (100.0, 50.0, 0.0) |
True True |
(-50, 100, 0) (-50, 100, 0) |
False False |
True True |
(100, 0, 0) (100, 0, 0) |
False False |
False False |
True True |
„Zabranjena” opterećenja:
|
|
(−0.66666666666666660.00.666666666666666650.0−0.33333333333333330.00.3333333333333333−100.0−0.6666666666666666−1.0−0.6666666666666666−0.0)
|
(1.00.0−1.00.00.01.01.33333333333333330.00.00.00.01.0)
|
[0, 1, 3] [0, 1, 3] |
|
|
(−0.66666666666666660.00.6666666666666666−100.0−0.33333333333333330.00.3333333333333333−0.0−0.6666666666666666−1.0−0.6666666666666666−0.0)
|
(1.00.0−1.00.00.01.01.33333333333333330.00.00.00.01.0)
|
[0, 1, 3] [0, 1, 3] |
Varijacija — promjena redoslijeda štapova:
bars: 0: (0, 3) 1: (2, 3) 2: (1, 3) bars: 0: (0, 3) 1: (2, 3) 2: (1, 3) |
(−0.66666666666666660.66666666666666660.0−100.0−0.33333333333333330.33333333333333330.0−50.0−0.6666666666666666−0.6666666666666666−1.0−0.0)
|
(−0.66666666666666660.00.6666666666666666−100.0−0.33333333333333330.00.3333333333333333−50.0−0.6666666666666666−1.0−0.6666666666666666−0.0)
|
(1.0−1.0−0.0150.00.01.00.75−75.00.00.00.00.0)
|
0: 75.0 1: -75.0 2: 0.0 0: 75.0 1: -75.0 2: 0.0 |
|
|
Column space: Vector space of degree 3 and dimension 2 Basis: (-0.6666666666666666, -0.3333333333333333, -0.6666666666666666) (0.6666666666666666, 0.3333333333333333, -0.6666666666666666) Column space: Vector space of degree 3 and dimension 2 Basis: (-0.6666666666666666, -0.3333333333333333, -0.6666666666666666) (0.6666666666666666, 0.3333333333333333, -0.6666666666666666) |
(−0.66666666666666660.66666666666666660.0−0.33333333333333330.33333333333333330.0−0.6666666666666666−0.6666666666666666−1.0)
|
Row space: Vector space of degree 3 and dimension 2 Basis: (1.0, -1.0, -0.0) (0.0, 1.0, 0.75) Row space: Vector space of degree 3 and dimension 2 Basis: (1.0, -1.0, -0.0) (0.0, 1.0, 0.75) |
(1.0−1.0−0.00.01.00.750.00.00.0)
|
0: -0.75 1: -0.75 2: 1.0 0: -0.75 1: -0.75 2: 1.0 |
|
Primjer 3.
joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 2) 1: (1, 2) supports: [0, 1] loads: 2: (100.000000000000, 0.000000000000000, 0.000000000000000) joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 2) 1: (1, 2) supports: [0, 1] loads: 2: (100.000000000000, 0.000000000000000, 0.000000000000000) |
|
Rješavanje sustava:
[2] [2] |
3 * 1 - 2 == 1 != 0 3 * 1 - 2 == 1 != 0 |
(0.00.7071067811865475−100.00.00.0−0.0−1.0−0.7071067811865475−0.0)
|
(1.00.70710678118654750.00.01.0−141.42135623730950.00.00.0)
|
0: 100.0 1: -141.4213562373095 0: 100.0 1: -141.4213562373095 |
[0, 1] [0, 1] |
|
Potprostori ravnotežne matrice:
|
Column space: Vector space of degree 3 and dimension 2 Basis: (0.0, 0.0, -1.0) (0.7071067811865475, 0.0, -0.7071067811865475) Column space: Vector space of degree 3 and dimension 2 Basis: (0.0, 0.0, -1.0) (0.7071067811865475, 0.0, -0.7071067811865475) |
(0.00.70710678118654750.00.0−1.0−0.7071067811865475)
|
(100.0,0.0,0.0)
|
True True |
Row space: Vector space of degree 2 and dimension 2 Basis: (1.0, 0.7071067811865475) (0.0, 1.0) Row space: Vector space of degree 2 and dimension 2 Basis: (1.0, 0.7071067811865475) (0.0, 1.0) |
(1.00.70710678118654750.01.00.00.0)
|
Kernel: Vector space of degree 2 and dimension 0 Kernel: Vector space of degree 2 and dimension 0 |
Left kernel: Vector space of degree 3 and dimension 1 Basis: (0.0, 1.0, 0.0) Left kernel: Vector space of degree 3 and dimension 1 Basis: (0.0, 1.0, 0.0) |
|
Primjer 4.
joints: 0: (-1.00000000000000, 0.000000000000000) 1: (0.000000000000000, 0.000000000000000) 2: (4.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) supports: [0, 1, 2] loads: 3: (100.000000000000, 0.000000000000000) joints: 0: (-1.00000000000000, 0.000000000000000) 1: (0.000000000000000, 0.000000000000000) 2: (4.00000000000000, 0.000000000000000) 3: (0.000000000000000, 2.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) supports: [0, 1, 2] loads: 3: (100.000000000000, 0.000000000000000) |
![]() |
[3] [3] |
2 * 1 - 3 == -1 != 0 2 * 1 - 3 == -1 != 0 |
(−0.44721359549995790.00.8944271909999159−100.0−0.8944271909999159−1.0−0.4472135954999579−0.0)
|
(1.01.1180339887498950.50.00.01.02.23606797749979−200.0)
|
[0, 1] [0, 1] |
[2] [2] |
(223.60679774997897, -200.0, 0.0) (223.60679774997897, -200.0, 0.0) |
0: 223.60679774997897 1: -200.0 2: 0.0 0: 223.60679774997897 1: -200.0 2: 0.0 |
![]() |
|
Column space: Vector space of degree 2 and dimension 2 Basis: (-0.4472135954999579, -0.8944271909999159) (0.0, -1.0) Column space: Vector space of degree 2 and dimension 2 Basis: (-0.4472135954999579, -0.8944271909999159) (0.0, -1.0) |
(−0.44721359549995790.00.8944271909999159−0.8944271909999159−1.0−0.4472135954999579)
|
Row space: Vector space of degree 3 and dimension 2 Basis: (1.0, 1.118033988749895, 0.5) (0.0, 1.0, 2.23606797749979) Row space: Vector space of degree 3 and dimension 2 Basis: (1.0, 1.118033988749895, 0.5) (0.0, 1.0, 2.23606797749979) |
(1.01.1180339887498950.50.01.02.23606797749979)
|
Kernel: Vector space of degree 3 and dimension 1 Basis: (2.0000000000000004, -2.23606797749979, 1.0) Kernel: Vector space of degree 3 and dimension 1 Basis: (2.0000000000000004, -2.23606797749979, 1.0) |
0: 2.0000000000000004 1: -2.23606797749979 2: 1.0 0: 2.0000000000000004 1: -2.23606797749979 2: 1.0 |
![]() |
Left kernel: Vector space of degree 2 and dimension 0 Basis: [] Left kernel: Vector space of degree 2 and dimension 0 Basis: [] |
Primjer 5.
joints: 0: (-2.00000000000000, 0.000000000000000, 0.000000000000000) 1: (0.000000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 0.000000000000000, 0.000000000000000) 3: (0.000000000000000, -2.00000000000000, 0.000000000000000) 4: (0.000000000000000, 2.00000000000000, 0.000000000000000) 5: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 5) 1: (1, 5) 2: (2, 5) 3: (3, 5) 4: (4, 5) supports: [0, 1, 2, 3, 4] loads: 5: (100.000000000000, 100.000000000000, 0.000000000000000) joints: 0: (-2.00000000000000, 0.000000000000000, 0.000000000000000) 1: (0.000000000000000, 0.000000000000000, 0.000000000000000) 2: (2.00000000000000, 0.000000000000000, 0.000000000000000) 3: (0.000000000000000, -2.00000000000000, 0.000000000000000) 4: (0.000000000000000, 2.00000000000000, 0.000000000000000) 5: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 5) 1: (1, 5) 2: (2, 5) 3: (3, 5) 4: (4, 5) supports: [0, 1, 2, 3, 4] loads: 5: (100.000000000000, 100.000000000000, 0.000000000000000) |
|
[5] [5] |
3 * 1 - 5 == -2 != 0 3 * 1 - 5 == -2 != 0 |
(−0.70710678118654750.00.70710678118654750.00.0−100.00.00.00.0−0.70710678118654750.7071067811865475−100.0−0.7071067811865475−1.0−0.7071067811865475−0.7071067811865475−0.7071067811865475−0.0)
|
(1.0−0.0−1.0−0.0−0.0141.42135623730950.01.01.4142135623730950.70710678118654750.7071067811865475−100.00.00.00.01.0−1.0141.4213562373095)
|
[0, 1, 3] [0, 1, 3] |
[2, 4] [2, 4] |
0: 141.4213562373095 1: -200.0 2: 0.0 3: 141.4213562373095 4: 0.0 0: 141.4213562373095 1: -200.0 2: 0.0 3: 141.4213562373095 4: 0.0 |
|
(−0.70710678118654750.00.70710678118654750.00.00.00.00.0−0.70710678118654750.7071067811865475−0.7071067811865475−1.0−0.7071067811865475−0.7071067811865475−0.7071067811865475)
|
|
Row space: Vector space of degree 5 and dimension 3 Basis: (1.0, -0.0, -1.0, -0.0, -0.0) (0.0, 1.0, 1.414213562373095, 0.7071067811865475, 0.7071067811865475) (0.0, 0.0, 0.0, 1.0, -1.0) Row space: Vector space of degree 5 and dimension 3 Basis: (1.0, -0.0, -1.0, -0.0, -0.0) (0.0, 1.0, 1.414213562373095, 0.7071067811865475, 0.7071067811865475) (0.0, 0.0, 0.0, 1.0, -1.0) |
Column space: Vector space of degree 3 and dimension 3 Basis: (-0.7071067811865475, 0.0, -0.7071067811865475) (0.0, 0.0, -1.0) (0.0, -0.7071067811865475, -0.7071067811865475) Column space: Vector space of degree 3 and dimension 3 Basis: (-0.7071067811865475, 0.0, -0.7071067811865475) (0.0, 0.0, -1.0) (0.0, -0.7071067811865475, -0.7071067811865475) |
Kernel: Vector space of degree 5 and dimension 2 Basis: (1.0, -1.414213562373095, 1.0, -0.0, 0.0) (0.0, -1.414213562373095, 0.0, 1.0, 1.0) Kernel: Vector space of degree 5 and dimension 2 Basis: (1.0, -1.414213562373095, 1.0, -0.0, 0.0) (0.0, -1.414213562373095, 0.0, 1.0, 1.0) |
0: 1.0 1: -1.414213562373095 2: 1.0 3: -0.0 4: 0.0 0: 1.0 1: -1.414213562373095 2: 1.0 3: -0.0 4: 0.0 |
|
0: 0.0 1: -1.414213562373095 2: 0.0 3: 1.0 4: 1.0 0: 0.0 1: -1.414213562373095 2: 0.0 3: 1.0 4: 1.0 |
|
Left kernel: Vector space of degree 3 and dimension 0 Basis: [] Left kernel: Vector space of degree 3 and dimension 0 Basis: [] |
Primjer 6. — Slobodni tetraedar
joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (0.000000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) 3: (0, 1) 4: (1, 2) 5: (2, 0) joints: 0: (0.000000000000000, 0.000000000000000, 0.000000000000000) 1: (2.00000000000000, 0.000000000000000, 0.000000000000000) 2: (0.000000000000000, 2.00000000000000, 0.000000000000000) 3: (0.000000000000000, 0.000000000000000, 2.00000000000000) bars: 0: (0, 3) 1: (1, 3) 2: (2, 3) 3: (0, 1) 4: (1, 2) 5: (2, 0) |
3 * 4 - 6 == 6 != 0 3 * 4 - 6 == 6 != 0 |
[0, 1, 2, 3] [0, 1, 2, 3] |
|
(0.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00001.0001.0000.00000.00000.00000.00000.00000.0000−0.70710.0000−1.000−0.70710.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.0000−0.70710.0000−0.7071−1.0000.00000.00000.70710.00000.00000.00000.00000.70710.00000.00000.00000.00000.00000.00000.70710.00000.00000.0000−1.000−0.7071−0.70710.00000.00000.0000)
|
|
Row space: Vector space of degree 6 and dimension 6 Basis: (1.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 1.0, -0.0, 1.4142135623730951, 1.0, -0.0) (0.0, 0.0, 1.0, -0.0, 1.0, 1.4142135623730951) (0.0, 0.0, 0.0, 1.0, 0.7071067811865475, -0.0) (0.0, 0.0, 0.0, 0.0, 1.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 1.0) Row space: Vector space of degree 6 and dimension 6 Basis: (1.0, 0.0, 0.0, 0.0, 0.0, 0.0) (0.0, 1.0, -0.0, 1.4142135623730951, 1.0, -0.0) (0.0, 0.0, 1.0, -0.0, 1.0, 1.4142135623730951) (0.0, 0.0, 0.0, 1.0, 0.7071067811865475, -0.0) (0.0, 0.0, 0.0, 0.0, 1.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, 1.0) |
Column space: Vector space of degree 12 and dimension 6 Basis: (0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0) (0.0, 0.0, 0.0, -0.7071067811865475, 0.0, 0.7071067811865475, 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, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475) (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, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475, 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, 0.0, 0.0, 0.0) Column space: Vector space of degree 12 and dimension 6 Basis: (0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0) (0.0, 0.0, 0.0, -0.7071067811865475, 0.0, 0.7071067811865475, 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, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475) (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, -0.7071067811865475, 0.7071067811865475, 0.0, 0.7071067811865475, -0.7071067811865475, 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, 0.0, 0.0, 0.0) |
Kernel: Vector space of degree 6 and dimension 0 Basis: [] Kernel: Vector space of degree 6 and dimension 0 Basis: [] |
Left kernel: Vector space of degree 12 and dimension 6 Basis: (0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0) (1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 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, 1.0, 1.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 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, 1.0, 0.0, -1.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0) Left kernel: Vector space of degree 12 and dimension 6 Basis: (0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0) (1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 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, 1.0, 1.0, 0.0, 0.0, 0.0) (0.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 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, 1.0, 0.0, -1.0, 1.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0) |
|
|
|
|
|
|
|