Processing math: 100%

NS_Truss_2_(v0.6)

907 days ago by fresl

 

Schwedlerove i „Schwedlerove” „kupole”

 

       

 

Primjer 1. — Schwedlerova „kupola” tipa 1.

 

Tvorba rječnika čvorova, rječnika štapova i liste ležajnih čvorova:

schwedler_1 (r0, [h1, h2, ...], n)

    • r0radijus ležajnog prstena
    • h1, h2, ... — visine na kojima su prsteni (0 < h1 < h2 < ...);  uzima se da je za ležajni prsten h0 = 0;  posljednji h je visina sferina odsječka na kojemu su čvorovi;  posljednji h mora biti r0
    • nbroj polja; n mora biti paran broj
    • rezultat: redom rječnik čvorova, rječnik štapova, lista oznaka ležajnih čvorova
       
joints:
   0:   (10.0000000000000, 0.000000000000000, 0.000000000000000)
   1:   (6.12323399573676e-16, 10.0000000000000, 0.000000000000000)
   2:   (-10.0000000000000, 1.22464679914735e-15, 0.000000000000000)
   3:   (-1.83697019872103e-15, -10.0000000000000, 0.000000000000000)
   4:   (6.61437827766148, 0.000000000000000, 7.50000000000000)
   5:   (4.05013859304395e-16, 6.61437827766148, 7.50000000000000)
   6:   (-6.61437827766148, 8.10027718608790e-16, 7.50000000000000)
   7:   (-1.21504157791318e-15, -6.61437827766148, 7.50000000000000)

bars:
   0:   (0, 4)
   1:   (1, 5)
   2:   (2, 6)
   3:   (3, 7)
   4:   (4, 5)
   5:   (5, 6)
   6:   (6, 7)
   7:   (7, 4)
   8:   (0, 5)
   9:   (2, 7)
   10:  (0, 7)
   11:  (2, 5)

supports: [0, 1, 2, 3]
joints:
   0:   (10.0000000000000, 0.000000000000000, 0.000000000000000)
   1:   (6.12323399573676e-16, 10.0000000000000, 0.000000000000000)
   2:   (-10.0000000000000, 1.22464679914735e-15, 0.000000000000000)
   3:   (-1.83697019872103e-15, -10.0000000000000, 0.000000000000000)
   4:   (6.61437827766148, 0.000000000000000, 7.50000000000000)
   5:   (4.05013859304395e-16, 6.61437827766148, 7.50000000000000)
   6:   (-6.61437827766148, 8.10027718608790e-16, 7.50000000000000)
   7:   (-1.21504157791318e-15, -6.61437827766148, 7.50000000000000)

bars:
   0:   (0, 4)
   1:   (1, 5)
   2:   (2, 6)
   3:   (3, 7)
   4:   (4, 5)
   5:   (5, 6)
   6:   (6, 7)
   7:   (7, 4)
   8:   (0, 5)
   9:   (2, 7)
   10:  (0, 7)
   11:  (2, 5)

supports: [0, 1, 2, 3]
       
       
3 * 4 - 12  ==  0
3 * 4 - 12  ==  0

Tvorba rječnika opterećenja:

make_loads (generator)

  • generatorlista uređenih trojki (nl, j0, (Fx, Fy, Fz)) ili uređenih četvorki (nl, j0, step, (Fx, Fy, Fz))
  • nl — broj čvorova opterećenih silom (Fx, Fy, Fz)
  • joznaka prvoga čvora u nizu opterećenih čvorova
  • step — opterećuju se čvorovi s oznakama j0, j0 + step, j0 + 2 step, ... , j0 + (nl 1) step; podrazumijeva se vrijednost 1
       
4:   (0.000000000000000, 0.000000000000000, -100.000000000000)
5:   (0.000000000000000, 0.000000000000000, -100.000000000000)
6:   (0.000000000000000, 0.000000000000000, -100.000000000000)
7:   (0.000000000000000, 0.000000000000000, -100.000000000000)
4:   (0.000000000000000, 0.000000000000000, -100.000000000000)
5:   (0.000000000000000, 0.000000000000000, -100.000000000000)
6:   (0.000000000000000, 0.000000000000000, -100.000000000000)
7:   (0.000000000000000, 0.000000000000000, -100.000000000000)
       
  • plot_truss (joints, bars, supports, loads, load_scale)
  • load_scalevrijednost kojom se množe vrijednosti sila za određivanje duljina strelica; podrazumijeva se vrijednost 0,01


Izračunavanje vrijednosti sila u štapovima:

       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.919947711973975
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   -2.5121479338940403e-15
9:   5.02429586778808e-15
10:  -1.6734266864842076e-30
11:  -2.5121479338940403e-15
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.919947711973975
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   -2.5121479338940403e-15
9:   5.02429586778808e-15
10:  -1.6734266864842076e-30
11:  -2.5121479338940403e-15
       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.919947711973975
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   0.0
9:   0.0
10:  0.0
11:  0.0
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.919947711973975
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   0.0
9:   0.0
10:  0.0
11:  0.0

 

Rješavanje u koracima:

       
[4, 5, 6, 7]
[4, 5, 6, 7]
       
(0.41140.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000100.00.00002.519×10170.00000.00000.70710.70710.00000.00000.70710.00000.00000.70710.00000.00000.41140.00000.00000.70710.70710.00000.00000.46770.00000.00000.46770.00000.00000.91140.00000.00000.00000.00000.00000.00000.53030.00000.00000.5303100.00.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.0000100.00.00000.00000.00007.558×10170.00000.00000.70710.70710.00000.70710.70710.00000.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.46770.46770.00000.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.53030.53030.0000100.0)

                                
  •  indeksi jednadžbi ravnoteže: 

dict_equation_index (free_joints)

rezultat: rječnik parova  oznakai: indeksj

  •  oznakaioznaka čvora i za koji su jednadžbe napisane
  •  indeksjindeks retka matrice u kojem su koefijenti jednadžbe  Fx=0  za čvor oznakai; koeficijenti jednadžbi  Fy=0  i  Fz=0  u sljedeća su dva retka
       
4:   0
5:   3
6:   6
7:   9
4:   0
5:   3
6:   6
7:   9
  •  indeksi nepoznanica:

dict_unknown_index (bars)

rezultat: rječnik parova  oznakai: indeksj

  •  oznakai oznaka štapa i s nepoznatom silom
  •  indeksjindeks komponente vektora nepoznanica
       
0:   0
1:   1
2:   2
3:   3
4:   4
5:   5
6:   6
7:   7
8:   8
9:   9
10:  10
11:  11
0:   0
1:   1
2:   2
3:   3
4:   4
5:   5
6:   6
7:   7
8:   8
9:   9
10:  10
11:  11
       
       
(1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000109.70.00001.0000.00000.00000.00000.00000.00000.00000.58190.00000.00000.5819109.70.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.0000109.70.00000.00000.00001.0000.00000.00000.00000.00000.00000.58190.58190.0000109.70.00000.00000.00000.00001.0001.0000.00000.00001.0000.00000.00001.00063.840.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00001.00031.920.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00001.00031.920.00000.00000.00000.00000.00000.00000.00001.0001.0000.00000.00000.000031.920.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00002.512×10150.00000.00000.00000.00000.00000.00000.00000.00000.00001.0001.0001.0007.536×10150.00000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00001.673×10300.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0002.512×1015)

                                
       
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197398
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   -2.5121479338940403e-15
9:   5.02429586778808e-15
10:  -1.6734266864842076e-30
11:  -2.5121479338940403e-15
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197398
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   -2.5121479338940403e-15
9:   5.02429586778808e-15
10:  -1.6734266864842076e-30
11:  -2.5121479338940403e-15
       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197398
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   0.0
9:   0.0
10:  0.0
11:  0.0
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197398
5:   -31.919947711973975
6:   -31.919947711973983
7:   -31.91994771197398
8:   0.0
9:   0.0
10:  0.0
11:  0.0
       

 

Potprostori ravnotežne matrice:

       
(0.41140.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00002.519×10170.00000.00000.70710.70710.00000.00000.70710.00000.00000.70710.00000.41140.00000.00000.70710.70710.00000.00000.46770.00000.00000.46770.00000.91140.00000.00000.00000.00000.00000.00000.53030.00000.00000.53030.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.00000.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00007.558×10170.00000.00000.70710.70710.00000.70710.70710.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.46770.46770.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.53030.53030.0000)

                                
       
       
Row space:
   Vector space of degree 12 and dimension 12
   Basis:
     (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, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0,
-0.0, 0.5818609561002115)
     (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, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002116,
0.5818609561002115, -0.0)
     (0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -0.0, -0.0, 1.0, -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, -0.0, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0,
0.9999999999999998)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999998, -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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.9999999999999997,
-0.9999999999999997)
     (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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0)
Row space:
   Vector space of degree 12 and dimension 12
   Basis:
     (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, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0, -0.0, 0.5818609561002115)
     (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, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002116, 0.5818609561002115, -0.0)
     (0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -0.0, -0.0, 1.0, -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, -0.0, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, 0.9999999999999998)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999998, -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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.9999999999999997, -0.9999999999999997)
     (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, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0)
       
Vector space of degree 12 and dimension 11 over Real Double Field
Basis matrix:
[     0.9999999999999999                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     1.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0      0.9999999999999999        
-0.0                    -0.0                     0.0                     0.0    
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
1.0                    -0.0                    -0.0                     0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     1.0                     0.0                    -0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[-1.1102230246251565e-16                     0.0                     0.0        
0.0                     0.0                     1.0                    -0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0   6.162975822039155e-33        
0.0                     0.0                     0.0                     1.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0 -1.1102230246251565e-16        
0.0                     0.0                     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                     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                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     1.0     
-0.0]
Vector space of degree 12 and dimension 11 over Real Double Field
Basis matrix:
[     0.9999999999999999                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     1.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0      0.9999999999999999                    -0.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     1.0                    -0.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     1.0                     0.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[-1.1102230246251565e-16                     0.0                     0.0                     0.0                     0.0                     1.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0   6.162975822039155e-33                     0.0                     0.0                     0.0                     1.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0 -1.1102230246251565e-16                     0.0                     0.0                     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                     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                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0                    -0.0]
       
Column space:
   Vector space of degree 12 and dimension 12
   Basis:
     (0.4114378277661477, 0.0, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 2.5193300941097603e-17, 0.4114378277661477,
-0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.4114378277661477, 5.0386601882195206e-17,
-0.9114378277661477, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -7.557990282329279e-17,
-0.4114378277661477, -0.9114378277661477)
     (-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, -0.7071067811865476, -0.7071067811865475, 0.0,
0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865474, -0.7071067811865476,
0.0, -0.7071067811865474, 0.7071067811865476, 0.0)
     (-0.7071067811865476, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.7071067811865476, 0.7071067811865475, 0.0)
     (0.0, 0.0, 0.0, 0.7071067811865475, -0.46770717334674267,
-0.5303300858899106, 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, -0.7071067811865475,
0.4677071733467428, -0.5303300858899107)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865476,
0.4677071733467426, -0.5303300858899106)
     (0.0, 0.0, 0.0, -0.7071067811865475, -0.4677071733467426,
-0.5303300858899106, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
Column space:
   Vector space of degree 12 and dimension 12
   Basis:
     (0.4114378277661477, 0.0, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 2.5193300941097603e-17, 0.4114378277661477, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.4114378277661477, 5.0386601882195206e-17, -0.9114378277661477, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -7.557990282329279e-17, -0.4114378277661477, -0.9114378277661477)
     (-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, -0.7071067811865476, -0.7071067811865475, 0.0, 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865474, -0.7071067811865476, 0.0, -0.7071067811865474, 0.7071067811865476, 0.0)
     (-0.7071067811865476, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865476, 0.7071067811865475, 0.0)
     (0.0, 0.0, 0.0, 0.7071067811865475, -0.46770717334674267, -0.5303300858899106, 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, -0.7071067811865475, 0.4677071733467428, -0.5303300858899107)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865476, 0.4677071733467426, -0.5303300858899106)
     (0.0, 0.0, 0.0, -0.7071067811865475, -0.4677071733467426, -0.5303300858899106, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
       
Vector space of degree 12 and dimension 11 over Real Double Field
Basis matrix:
[     0.9999999999999999                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0      2.2152504370215294                     0.0                     0.0     
0.0]
[-1.1102230246251565e-16                     1.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0       -2.21525043702153                     0.0                     0.0     
0.0]
[-1.1102230246251565e-16                     0.0                     1.0        
0.0                     0.0                     0.0                     0.0     
0.0     0.21679069697780667                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
1.0                     0.0                     0.0                     0.0     
0.0        4.43050087404306                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     1.0                     0.0                     0.0     
0.0     -1.7350047507992417                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     1.0                     0.0     
0.0     -0.7832093030221933                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     1.0     
0.0      2.2152504370215302                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
1.0        2.21525043702153                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     1.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     1.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     0.0     
1.0]
Vector space of degree 12 and dimension 11 over Real Double Field
Basis matrix:
[     0.9999999999999999                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0      2.2152504370215294                     0.0                     0.0                     0.0]
[-1.1102230246251565e-16                     1.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0       -2.21525043702153                     0.0                     0.0                     0.0]
[-1.1102230246251565e-16                     0.0                     1.0                     0.0                     0.0                     0.0                     0.0                     0.0     0.21679069697780667                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     1.0                     0.0                     0.0                     0.0                     0.0        4.43050087404306                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     1.0                     0.0                     0.0                     0.0     -1.7350047507992417                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     1.0                     0.0                     0.0     -0.7832093030221933                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0                     0.0      2.2152504370215302                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0        2.21525043702153                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0]
       
Kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
Kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
       
Vector space of degree 12 and dimension 1 over Real Double Field
Basis matrix:
[                 1.0  -1.0000000000000002  0.09786283905186281  
2.0000000000000004  -0.7832093030221936 -0.35355339059327384  
1.0000000000000004   1.0000000000000002 -0.45141622964513667                 
0.0                  0.0                  0.0]
Vector space of degree 12 and dimension 1 over Real Double Field
Basis matrix:
[                 1.0  -1.0000000000000002  0.09786283905186281   2.0000000000000004  -0.7832093030221936 -0.35355339059327384   1.0000000000000004   1.0000000000000002 -0.45141622964513667                  0.0                  0.0                  0.0]
       
Left kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
Left kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
       
Vector space of degree 12 and dimension 1 over Real Double Field
Basis matrix:
[                 1.0  -1.0000000000000002  0.09786283905186281  
2.0000000000000004  -0.7832093030221936 -0.35355339059327384  
1.0000000000000004   1.0000000000000002 -0.45141622964513667                 
0.0                  0.0                  0.0]
Vector space of degree 12 and dimension 1 over Real Double Field
Basis matrix:
[                 1.0  -1.0000000000000002  0.09786283905186281   2.0000000000000004  -0.7832093030221936 -0.35355339059327384   1.0000000000000004   1.0000000000000002 -0.45141622964513667                  0.0                  0.0                  0.0]
       
[     0.9999999999999999                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     0.0     
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      0.9999999999999999        
-0.0                    -0.0                     0.0                     0.0    
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
1.0                    -0.0                    -0.0                     0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     1.0                     0.0                    -0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[-1.1102230246251565e-16                     0.0                     0.0        
0.0                     0.0                     1.0                    -0.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0   6.162975822039155e-33        
0.0                     0.0                     0.0                     1.0     
0.0                     0.0                     0.0                     0.0     
0.0]
[                    0.0                     0.0 -1.1102230246251565e-16        
0.0                     0.0                     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                     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                     0.0     
0.0]
[                    0.0                     0.0                     0.0        
0.0                     0.0                     0.0                     0.0     
0.0                     0.0                     0.0                     1.0     
-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]
[     0.9999999999999999                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     1.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0      0.9999999999999999                    -0.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     1.0                    -0.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     1.0                     0.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[-1.1102230246251565e-16                     0.0                     0.0                     0.0                     0.0                     1.0                    -0.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0   6.162975822039155e-33                     0.0                     0.0                     0.0                     1.0                     0.0                     0.0                     0.0                     0.0                     0.0]
[                    0.0                     0.0 -1.1102230246251565e-16                     0.0                     0.0                     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                     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                     0.0                     0.0]
[                    0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     0.0                     1.0                    -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]
       
(0.41143782776614770.00.00.00.70710678118654750.00.00.70710678118654760.00.00.00.00.00.00.00.00.70710678118654750.00.00.70710678118654750.00.00.00.00.91143782776614770.00.00.00.00.00.00.00.00.00.00.00.02.5193300941097603×10170.00.00.70710678118654750.70710678118654760.00.00.70710678118654750.00.00.70710678118654750.00.41143782776614770.00.00.70710678118654750.70710678118654750.00.00.467707173346742670.00.00.46770717334674260.00.91143782776614770.00.00.00.00.00.00.53033008588991060.00.00.53033008588991060.00.00.41143782776614770.00.00.70710678118654760.70710678118654740.00.00.00.00.00.00.05.0386601882195206×10170.00.00.70710678118654750.70710678118654760.00.00.00.00.00.00.00.91143782776614770.00.00.00.00.00.00.00.00.00.00.00.07.557990282329279×10170.00.00.70710678118654740.70710678118654760.00.70710678118654750.70710678118654760.00.00.00.00.41143782776614770.00.00.70710678118654760.70710678118654750.00.46770717334674280.46770717334674260.00.00.00.00.91143782776614770.00.00.00.00.00.53033008588991070.53033008588991060.0)

                                
       
(0.41143782776614770.00.00.00.70710678118654750.00.00.70710678118654760.00.00.00.00.00.00.00.00.70710678118654750.00.00.70710678118654750.00.00.00.00.91143782776614770.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.70710678118654750.70710678118654760.00.00.70710678118654750.00.00.70710678118654750.00.41143782776614770.00.00.70710678118654750.70710678118654750.00.00.467707173346742670.00.00.46770717334674260.00.91143782776614770.00.00.00.00.00.00.53033008588991060.00.00.53033008588991060.00.00.41143782776614770.00.00.70710678118654760.70710678118654740.00.00.00.00.00.00.00.00.00.00.70710678118654750.70710678118654760.00.00.00.00.00.00.00.91143782776614770.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.70710678118654740.70710678118654760.00.70710678118654750.70710678118654760.00.00.00.00.41143782776614770.00.00.70710678118654760.70710678118654750.00.46770717334674280.46770717334674260.00.00.00.00.91143782776614770.00.00.00.00.00.53033008588991070.53033008588991060.0)

                                
       
Vector space of degree 12 and dimension 0 over Real Double Field
Basis matrix:
[]
Vector space of degree 12 and dimension 0 over Real Double Field
Basis matrix:
[]
       
(0.0,0.0,100.0,0.0,0.0,100.0,0.0,0.0,100.0,0.0,0.0,100.0)

                                
       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197399
5:   -31.919947711973983
6:   -31.919947711973986
7:   -31.919947711973986
8:   -2.5121479338940403e-15
9:   5.0242958677880805e-15
10:  -1.1156177909894717e-30
11:  -2.5121479338940403e-15
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197399
5:   -31.919947711973983
6:   -31.919947711973986
7:   -31.919947711973986
8:   -2.5121479338940403e-15
9:   5.0242958677880805e-15
10:  -1.1156177909894717e-30
11:  -2.5121479338940403e-15
       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.919947711973983
5:   -31.91994771197399
6:   -31.919947711973986
7:   -31.919947711973986
8:   -2.5121479338940403e-15
9:   -5.024295867788079e-15
10:  5.0242958677880805e-15
11:  2.5121479338940403e-15
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.919947711973983
5:   -31.91994771197399
6:   -31.919947711973986
7:   -31.919947711973986
8:   -2.5121479338940403e-15
9:   -5.024295867788079e-15
10:  5.0242958677880805e-15
11:  2.5121479338940403e-15
       
(0.0, 0.0, 0.0, 0.0, -7.105427357601002e-15, 7.105427357601002e-15, 0.0, 0.0,
0.0, 1.004859173557616e-14, -5.024295867788081e-15, -5.0242958677880805e-15)
(0.0, 0.0, 0.0, 0.0, -7.105427357601002e-15, 7.105427357601002e-15, 0.0, 0.0, 0.0, 1.004859173557616e-14, -5.024295867788081e-15, -5.0242958677880805e-15)

 

Primjer 2. — Schwedlerova „kupola” tipa 1.

 

       
       
       
3 * 24 - 72  ==  0
3 * 24 - 72  ==  0
       
24
24
       
72 x 72 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
72 x 72 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
Row space:
   Vector space of degree 72 and dimension 72
Row space:
   Vector space of degree 72 and dimension 72
       
Column space:
   Vector space of degree 72 and dimension 72
Column space:
   Vector space of degree 72 and dimension 72
       
Kernel:
   Vector space of degree 72 and dimension 0
Kernel:
   Vector space of degree 72 and dimension 0
       
Left kernel:
   Vector space of degree 72 and dimension 0
Left kernel:
   Vector space of degree 72 and dimension 0
       
       
       
72 x 73 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
72 x 73 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
0:   -204.91580904761287
1:   -204.91580904761227
2:   -204.91580904761298
3:   -204.91580904761219
4:   -204.9158090476129
5:   -204.91580904761247
6:   -204.91580904761287
7:   -204.91580904761256
8:   74.3059609475446
9:   74.30596094754472
10:  74.30596094754472
11:  74.30596094754463
12:  74.3059609475446
13:  74.30596094754459
14:  74.30596094754459
15:  74.30596094754458
16:  -2.606318687120518e-13
17:  -4.2236974711845096e-13
18:  -2.1947195061226836e-13
19:  -1.693773836673669e-13
20:  -1.8474111129762605e-13
21:  -3.926064496917477e-13
22:  -3.543558413594664e-13
23:  -2.2581518513761258e-13
24:  -164.9225629678831
25:  -164.92256296788287
26:  -164.92256296788315
27:  -164.92256296788284
28:  -164.92256296788312
29:  -164.92256296788298
30:  -164.9225629678831
31:  -164.922562967883
32:  -22.84939741307862
33:  -22.849397413078577
34:  -22.849397413078577
35:  -22.849397413078616
36:  -22.849397413078623
37:  -22.849397413078627
38:  -22.84939741307864
39:  -22.84939741307867
40:  -8.865316478186533e-14
41:  -1.4920223943569423e-13
42:  -6.311238576426562e-14
43:  -4.60592233830089e-14
44:  -2.7514912727717167e-14
45:  -1.309216201802303e-13
46:  -1.0667157776330011e-13
47:  -7.495874938948224e-14
48:  -97.7531136904162
49:  -97.7531136904161
50:  -97.7531136904162
51:  -97.75311369041609
52:  -97.7531136904162
53:  -97.75311369041617
54:  -97.7531136904162
55:  -97.75311369041617
56:  -109.74873217076869
57:  -109.74873217076868
58:  -109.74873217076868
59:  -109.7487321707687
60:  -109.74873217076868
61:  -109.74873217076868
62:  -109.74873217076869
63:  -109.74873217076869
64:  -7.675729386064e-14
65:  -9.210875263276802e-14
66:  -4.605437631638406e-14
67:  -2.596296755947127e-14
68:  1.5351458772128003e-14
69:  -9.210875263276803e-14
70:  -6.140583508851202e-14
71:  -5.0794326301168806e-14
0:   -204.91580904761287
1:   -204.91580904761227
2:   -204.91580904761298
3:   -204.91580904761219
4:   -204.9158090476129
5:   -204.91580904761247
6:   -204.91580904761287
7:   -204.91580904761256
8:   74.3059609475446
9:   74.30596094754472
10:  74.30596094754472
11:  74.30596094754463
12:  74.3059609475446
13:  74.30596094754459
14:  74.30596094754459
15:  74.30596094754458
16:  -2.606318687120518e-13
17:  -4.2236974711845096e-13
18:  -2.1947195061226836e-13
19:  -1.693773836673669e-13
20:  -1.8474111129762605e-13
21:  -3.926064496917477e-13
22:  -3.543558413594664e-13
23:  -2.2581518513761258e-13
24:  -164.9225629678831
25:  -164.92256296788287
26:  -164.92256296788315
27:  -164.92256296788284
28:  -164.92256296788312
29:  -164.92256296788298
30:  -164.9225629678831
31:  -164.922562967883
32:  -22.84939741307862
33:  -22.849397413078577
34:  -22.849397413078577
35:  -22.849397413078616
36:  -22.849397413078623
37:  -22.849397413078627
38:  -22.84939741307864
39:  -22.84939741307867
40:  -8.865316478186533e-14
41:  -1.4920223943569423e-13
42:  -6.311238576426562e-14
43:  -4.60592233830089e-14
44:  -2.7514912727717167e-14
45:  -1.309216201802303e-13
46:  -1.0667157776330011e-13
47:  -7.495874938948224e-14
48:  -97.7531136904162
49:  -97.7531136904161
50:  -97.7531136904162
51:  -97.75311369041609
52:  -97.7531136904162
53:  -97.75311369041617
54:  -97.7531136904162
55:  -97.75311369041617
56:  -109.74873217076869
57:  -109.74873217076868
58:  -109.74873217076868
59:  -109.7487321707687
60:  -109.74873217076868
61:  -109.74873217076868
62:  -109.74873217076869
63:  -109.74873217076869
64:  -7.675729386064e-14
65:  -9.210875263276802e-14
66:  -4.605437631638406e-14
67:  -2.596296755947127e-14
68:  1.5351458772128003e-14
69:  -9.210875263276803e-14
70:  -6.140583508851202e-14
71:  -5.0794326301168806e-14
       
0:   -204.91580904761287
1:   -204.91580904761227
2:   -204.91580904761298
3:   -204.91580904761219
4:   -204.9158090476129
5:   -204.91580904761247
6:   -204.91580904761287
7:   -204.91580904761256
8:   74.3059609475446
9:   74.30596094754472
10:  74.30596094754472
11:  74.30596094754463
12:  74.3059609475446
13:  74.30596094754459
14:  74.30596094754459
15:  74.30596094754458
16:  0.0
17:  0.0
18:  0.0
19:  0.0
20:  0.0
21:  0.0
22:  0.0
23:  0.0
24:  -164.9225629678831
25:  -164.92256296788287
26:  -164.92256296788315
27:  -164.92256296788284
28:  -164.92256296788312
29:  -164.92256296788298
30:  -164.9225629678831
31:  -164.922562967883
32:  -22.84939741307862
33:  -22.849397413078577
34:  -22.849397413078577
35:  -22.849397413078616
36:  -22.849397413078623
37:  -22.849397413078627
38:  -22.84939741307864
39:  -22.84939741307867
40:  0.0
41:  0.0
42:  0.0
43:  0.0
44:  0.0
45:  0.0
46:  0.0
47:  0.0
48:  -97.7531136904162
49:  -97.7531136904161
50:  -97.7531136904162
51:  -97.75311369041609
52:  -97.7531136904162
53:  -97.75311369041617
54:  -97.7531136904162
55:  -97.75311369041617
56:  -109.74873217076869
57:  -109.74873217076868
58:  -109.74873217076868
59:  -109.7487321707687
60:  -109.74873217076868
61:  -109.74873217076868
62:  -109.74873217076869
63:  -109.74873217076869
64:  0.0
65:  0.0
66:  0.0
67:  0.0
68:  0.0
69:  0.0
70:  0.0
71:  0.0
0:   -204.91580904761287
1:   -204.91580904761227
2:   -204.91580904761298
3:   -204.91580904761219
4:   -204.9158090476129
5:   -204.91580904761247
6:   -204.91580904761287
7:   -204.91580904761256
8:   74.3059609475446
9:   74.30596094754472
10:  74.30596094754472
11:  74.30596094754463
12:  74.3059609475446
13:  74.30596094754459
14:  74.30596094754459
15:  74.30596094754458
16:  0.0
17:  0.0
18:  0.0
19:  0.0
20:  0.0
21:  0.0
22:  0.0
23:  0.0
24:  -164.9225629678831
25:  -164.92256296788287
26:  -164.92256296788315
27:  -164.92256296788284
28:  -164.92256296788312
29:  -164.92256296788298
30:  -164.9225629678831
31:  -164.922562967883
32:  -22.84939741307862
33:  -22.849397413078577
34:  -22.849397413078577
35:  -22.849397413078616
36:  -22.849397413078623
37:  -22.849397413078627
38:  -22.84939741307864
39:  -22.84939741307867
40:  0.0
41:  0.0
42:  0.0
43:  0.0
44:  0.0
45:  0.0
46:  0.0
47:  0.0
48:  -97.7531136904162
49:  -97.7531136904161
50:  -97.7531136904162
51:  -97.75311369041609
52:  -97.7531136904162
53:  -97.75311369041617
54:  -97.7531136904162
55:  -97.75311369041617
56:  -109.74873217076869
57:  -109.74873217076868
58:  -109.74873217076868
59:  -109.7487321707687
60:  -109.74873217076868
61:  -109.74873217076868
62:  -109.74873217076869
63:  -109.74873217076869
64:  0.0
65:  0.0
66:  0.0
67:  0.0
68:  0.0
69:  0.0
70:  0.0
71:  0.0
       
       
       
       
72 x 73 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
72 x 73 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
0:   -239.76073595130134
1:   206.38152515989935
2:   0.0
3:   203.4562777650432
4:   -242.95691841585648
5:   1018.4544193946058
6:   -367.20323158218105
7:   937.4651852340141
8:   227.7468448883277
9:   0.0
10:  0.0
11:  227.81120809920117
12:  352.6443504111476
13:  444.9532349580253
14:  432.5055156591877
15:  340.1322679014364
16:  -285.9345533121276
17:  -32.17523884092094
18:  -636.9556256561544
19:  -696.3853840875885
20:  -593.9850036654537
21:  -33.46574743376433
22:  -284.71539456827855
23:  -739.2846562292947
24:  -88.56185966037236
25:  52.5699511497478
26:  0.0
27:  50.542744860141596
28:  -85.14673077027103
29:  386.48091665746597
30:  -128.5408044108116
31:  340.76838576704404
32:  82.02454252345987
33:  0.0
34:  0.0
35:  78.86150613348937
36:  208.98498047770465
37:  214.66256055058608
38:  219.8816503793227
39:  217.36710669641175
40:  -86.37577499920883
41:  0.0
42:  -271.3356849643785
43:  -258.53906427400557
44:  -255.8911292450637
45:  0.0
46:  -83.04494606521916
47:  -277.31444892730985
48:  0.0
49:  0.0
50:  0.0
51:  0.0
52:  0.0
53:  81.00190372159868
54:  0.0
55:  42.6512887402572
56:  0.0
57:  0.0
58:  0.0
59:  0.0
60:  0.0
61:  0.0
62:  0.0
63:  0.0
64:  0.0
65:  0.0
66:  -213.02473265248045
67:  -165.06727362896063
68:  -221.56888827896535
69:  0.0
70:  0.0
71:  -156.52311800247568
0:   -239.76073595130134
1:   206.38152515989935
2:   0.0
3:   203.4562777650432
4:   -242.95691841585648
5:   1018.4544193946058
6:   -367.20323158218105
7:   937.4651852340141
8:   227.7468448883277
9:   0.0
10:  0.0
11:  227.81120809920117
12:  352.6443504111476
13:  444.9532349580253
14:  432.5055156591877
15:  340.1322679014364
16:  -285.9345533121276
17:  -32.17523884092094
18:  -636.9556256561544
19:  -696.3853840875885
20:  -593.9850036654537
21:  -33.46574743376433
22:  -284.71539456827855
23:  -739.2846562292947
24:  -88.56185966037236
25:  52.5699511497478
26:  0.0
27:  50.542744860141596
28:  -85.14673077027103
29:  386.48091665746597
30:  -128.5408044108116
31:  340.76838576704404
32:  82.02454252345987
33:  0.0
34:  0.0
35:  78.86150613348937
36:  208.98498047770465
37:  214.66256055058608
38:  219.8816503793227
39:  217.36710669641175
40:  -86.37577499920883
41:  0.0
42:  -271.3356849643785
43:  -258.53906427400557
44:  -255.8911292450637
45:  0.0
46:  -83.04494606521916
47:  -277.31444892730985
48:  0.0
49:  0.0
50:  0.0
51:  0.0
52:  0.0
53:  81.00190372159868
54:  0.0
55:  42.6512887402572
56:  0.0
57:  0.0
58:  0.0
59:  0.0
60:  0.0
61:  0.0
62:  0.0
63:  0.0
64:  0.0
65:  0.0
66:  -213.02473265248045
67:  -165.06727362896063
68:  -221.56888827896535
69:  0.0
70:  0.0
71:  -156.52311800247568
       

 

Primjer 3. — Schwedlerova „kupola” tipa 2.

 

       
       
       
3 * 27 - 81  ==  0
3 * 27 - 81  ==  0
       
27
27
       
81 x 81 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
81 x 81 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
Row space:
   Vector space of degree 81 and dimension 81
Row space:
   Vector space of degree 81 and dimension 81
       
Column space:
   Vector space of degree 81 and dimension 81
Column space:
   Vector space of degree 81 and dimension 81
       
Kernel:
   Vector space of degree 81 and dimension 0
Kernel:
   Vector space of degree 81 and dimension 0
       
Left kernel:
   Vector space of degree 81 and dimension 0
Left kernel:
   Vector space of degree 81 and dimension 0
       
       
       
81 x 82 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
81 x 82 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
0:   -242.7966913395939
1:   -242.7966913395941
2:   -242.7966913395934
3:   -242.79669133959428
4:   -242.7966913395939
5:   -242.79669133959408
6:   -242.79669133959348
7:   -242.7966913395943
8:   -242.79669133959374
9:   37.64244088604003
10:  37.64244088603975
11:  37.642440886040156
12:  37.642440886039765
13:  37.642440886039836
14:  37.6424408860397
15:  37.64244088604021
16:  37.64244088603968
17:  37.64244088604005
18:  0.0
19:  0.0
20:  0.0
21:  0.0
22:  0.0
23:  0.0
24:  0.0
25:  0.0
26:  0.0
27:  -208.81195719729712
28:  -208.8119571972972
29:  -208.81195719729678
30:  -208.81195719729715
31:  -208.81195719729703
32:  -208.81195719729712
33:  -208.81195719729686
34:  -208.81195719729718
35:  -208.8119571972971
36:  -72.1393138577007
37:  -72.1393138577008
38:  -72.13931385770046
39:  -72.13931385770066
40:  -72.13931385770067
41:  -72.1393138577008
42:  -72.13931385770046
43:  -72.13931385770073
44:  -72.1393138577007
45:  0.0
46:  0.0
47:  0.0
48:  0.0
49:  0.0
50:  0.0
51:  0.0
52:  0.0
53:  0.0
54:  -124.5402573858325
55:  -124.54025738583255
56:  -124.54025738583238
57:  -124.5402573858325
58:  -124.54025738583249
59:  -124.54025738583249
60:  -124.54025738583243
61:  -124.54025738583248
62:  -124.54025738583246
63:  -166.74835942081708
64:  -166.74835942081717
65:  -166.74835942081702
66:  -166.74835942081708
67:  -166.7483594208171
68:  -166.74835942081708
69:  -166.74835942081702
70:  -166.74835942081705
71:  -166.74835942081702
72:  0.0
73:  0.0
74:  0.0
75:  0.0
76:  0.0
77:  0.0
78:  0.0
79:  0.0
80:  0.0
0:   -242.7966913395939
1:   -242.7966913395941
2:   -242.7966913395934
3:   -242.79669133959428
4:   -242.7966913395939
5:   -242.79669133959408
6:   -242.79669133959348
7:   -242.7966913395943
8:   -242.79669133959374
9:   37.64244088604003
10:  37.64244088603975
11:  37.642440886040156
12:  37.642440886039765
13:  37.642440886039836
14:  37.6424408860397
15:  37.64244088604021
16:  37.64244088603968
17:  37.64244088604005
18:  0.0
19:  0.0
20:  0.0
21:  0.0
22:  0.0
23:  0.0
24:  0.0
25:  0.0
26:  0.0
27:  -208.81195719729712
28:  -208.8119571972972
29:  -208.81195719729678
30:  -208.81195719729715
31:  -208.81195719729703
32:  -208.81195719729712
33:  -208.81195719729686
34:  -208.81195719729718
35:  -208.8119571972971
36:  -72.1393138577007
37:  -72.1393138577008
38:  -72.13931385770046
39:  -72.13931385770066
40:  -72.13931385770067
41:  -72.1393138577008
42:  -72.13931385770046
43:  -72.13931385770073
44:  -72.1393138577007
45:  0.0
46:  0.0
47:  0.0
48:  0.0
49:  0.0
50:  0.0
51:  0.0
52:  0.0
53:  0.0
54:  -124.5402573858325
55:  -124.54025738583255
56:  -124.54025738583238
57:  -124.5402573858325
58:  -124.54025738583249
59:  -124.54025738583249
60:  -124.54025738583243
61:  -124.54025738583248
62:  -124.54025738583246
63:  -166.74835942081708
64:  -166.74835942081717
65:  -166.74835942081702
66:  -166.74835942081708
67:  -166.7483594208171
68:  -166.74835942081708
69:  -166.74835942081702
70:  -166.74835942081705
71:  -166.74835942081702
72:  0.0
73:  0.0
74:  0.0
75:  0.0
76:  0.0
77:  0.0
78:  0.0
79:  0.0
80:  0.0
       

 

Primjer 4. — Pseudo-Schwedlerova „kupola” bez dijagonalnih štapova

 

       
joints:
   0:   (10.0000000000000, 0.000000000000000, 0.000000000000000)
   1:   (6.12323399573676e-16, 10.0000000000000, 0.000000000000000)
   2:   (-10.0000000000000, 1.22464679914735e-15, 0.000000000000000)
   3:   (-1.83697019872103e-15, -10.0000000000000, 0.000000000000000)
   4:   (6.61437827766148, 0.000000000000000, 7.50000000000000)
   5:   (4.05013859304395e-16, 6.61437827766148, 7.50000000000000)
   6:   (-6.61437827766148, 8.10027718608790e-16, 7.50000000000000)
   7:   (-1.21504157791318e-15, -6.61437827766148, 7.50000000000000)

bars:
   0:   (0, 4)
   1:   (1, 5)
   2:   (2, 6)
   3:   (3, 7)
   4:   (4, 5)
   5:   (5, 6)
   6:   (6, 7)
   7:   (7, 4)

supports: [0, 1, 2, 3]
joints:
   0:   (10.0000000000000, 0.000000000000000, 0.000000000000000)
   1:   (6.12323399573676e-16, 10.0000000000000, 0.000000000000000)
   2:   (-10.0000000000000, 1.22464679914735e-15, 0.000000000000000)
   3:   (-1.83697019872103e-15, -10.0000000000000, 0.000000000000000)
   4:   (6.61437827766148, 0.000000000000000, 7.50000000000000)
   5:   (4.05013859304395e-16, 6.61437827766148, 7.50000000000000)
   6:   (-6.61437827766148, 8.10027718608790e-16, 7.50000000000000)
   7:   (-1.21504157791318e-15, -6.61437827766148, 7.50000000000000)

bars:
   0:   (0, 4)
   1:   (1, 5)
   2:   (2, 6)
   3:   (3, 7)
   4:   (4, 5)
   5:   (5, 6)
   6:   (6, 7)
   7:   (7, 4)

supports: [0, 1, 2, 3]
       
       
3 * 4 - 8  ==  4  !=  0
3 * 4 - 8  ==  4  !=  0
       
[4, 5, 6, 7]
[4, 5, 6, 7]
       
(0.41140.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.70710.00000.00000.70710.91140.00000.00000.00000.00000.00000.00000.00000.00002.519×10170.00000.00000.70710.70710.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00007.558×10170.00000.00000.70710.70710.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.91140.00000.00000.00000.0000)

                                
       
4:   0
5:   3
6:   6
7:   9
4:   0
5:   3
6:   6
7:   9
       
0:   0
1:   1
2:   2
3:   3
4:   4
5:   5
6:   6
7:   7
0:   0
1:   1
2:   2
3:   3
4:   4
5:   5
6:   6
7:   7
       
       
Row space:
   Vector space of degree 8 and dimension 8
   Basis:
     (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, -0.0, -0.0, -0.0)
     (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, -0.0)
     (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, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0)
Row space:
   Vector space of degree 8 and dimension 8
   Basis:
     (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, -0.0, -0.0, -0.0)
     (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, -0.0)
     (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, 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, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0)
       
Column space:
   Vector space of degree 12 and dimension 8
   Basis:
     (0.4114378277661477, 0.0, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 2.5193300941097603e-17, 0.4114378277661477,
-0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.4114378277661477, 5.0386601882195206e-17,
-0.9114378277661477, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -7.557990282329279e-17,
-0.4114378277661477, -0.9114378277661477)
     (-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, -0.7071067811865476, -0.7071067811865475, 0.0,
0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865474, -0.7071067811865476,
0.0, -0.7071067811865474, 0.7071067811865476, 0.0)
     (-0.7071067811865476, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.7071067811865476, 0.7071067811865475, 0.0)
Column space:
   Vector space of degree 12 and dimension 8
   Basis:
     (0.4114378277661477, 0.0, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 2.5193300941097603e-17, 0.4114378277661477, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.4114378277661477, 5.0386601882195206e-17, -0.9114378277661477, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -7.557990282329279e-17, -0.4114378277661477, -0.9114378277661477)
     (-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, -0.7071067811865476, -0.7071067811865475, 0.0, 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865474, -0.7071067811865476, 0.0, -0.7071067811865474, 0.7071067811865476, 0.0)
     (-0.7071067811865476, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865476, 0.7071067811865475, 0.0)
       
Kernel:
   Vector space of degree 8 and dimension 0
   Basis:
     []
Kernel:
   Vector space of degree 8 and dimension 0
   Basis:
     []
       
Left kernel:
   Vector space of degree 12 and dimension 4
   Basis:
     (0.0, 0.0, 0.0, 1.0, 1.0, 0.45141622964513645, 1.0, 0.9999999999999997,
-0.45141622964513645, 0.0, 0.0, 0.0)
     (1.0, 0.0, 0.4514162296451365, 1.6653345369377348e-16, -0.9999999999999998,
-0.4514162296451364, 0.0, -0.9999999999999997, -5.5282544071808195e-17, 1.0,
0.0, -8.292381610771231e-17)
     (0.9999999999999998, 0.0, 0.4514162296451364, 0.9999999999999999,
1.1102230246251565e-16, 5.551115123125783e-17, 0.0, 1.0, 5.5282544071808213e-17,
0.0, 1.0, -0.4514162296451365)
     (-0.9999999999999998, 1.0, -0.4514162296451364, -0.9999999999999999,
0.9999999999999999, 0.45141622964513645, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
Left kernel:
   Vector space of degree 12 and dimension 4
   Basis:
     (0.0, 0.0, 0.0, 1.0, 1.0, 0.45141622964513645, 1.0, 0.9999999999999997, -0.45141622964513645, 0.0, 0.0, 0.0)
     (1.0, 0.0, 0.4514162296451365, 1.6653345369377348e-16, -0.9999999999999998, -0.4514162296451364, 0.0, -0.9999999999999997, -5.5282544071808195e-17, 1.0, 0.0, -8.292381610771231e-17)
     (0.9999999999999998, 0.0, 0.4514162296451364, 0.9999999999999999, 1.1102230246251565e-16, 5.551115123125783e-17, 0.0, 1.0, 5.5282544071808213e-17, 0.0, 1.0, -0.4514162296451365)
     (-0.9999999999999998, 1.0, -0.4514162296451364, -0.9999999999999999, 0.9999999999999999, 0.45141622964513645, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
       
(0.0, 0.0, 0.0, 1.0, 1.0, 0.45141622964513645, 1.0, 0.9999999999999997,
-0.45141622964513645, 0.0, 0.0, 0.0)
(1.0, 0.0, 0.4514162296451365, 0.0, -0.9999999999999998, -0.4514162296451364,
0.0, -0.9999999999999997, 0.0, 1.0, 0.0, 0.0)
(0.9999999999999998, 0.0, 0.4514162296451364, 0.9999999999999999, 0.0, 0.0, 0.0,
1.0, 0.0, 0.0, 1.0, -0.4514162296451365)
(-0.9999999999999998, 1.0, -0.4514162296451364, -0.9999999999999999,
0.9999999999999999, 0.45141622964513645, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
(0.0, 0.0, 0.0, 1.0, 1.0, 0.45141622964513645, 1.0, 0.9999999999999997, -0.45141622964513645, 0.0, 0.0, 0.0)
(1.0, 0.0, 0.4514162296451365, 0.0, -0.9999999999999998, -0.4514162296451364, 0.0, -0.9999999999999997, 0.0, 1.0, 0.0, 0.0)
(0.9999999999999998, 0.0, 0.4514162296451364, 0.9999999999999999, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, -0.4514162296451365)
(-0.9999999999999998, 1.0, -0.4514162296451364, -0.9999999999999999, 0.9999999999999999, 0.45141622964513645, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
       
       
       
       
       
       
       
       
       
4:   (0.000000000000000, 0.000000000000000, -100.000000000000)
5:   (0.000000000000000, 0.000000000000000, -100.000000000000)
6:   (0.000000000000000, 0.000000000000000, -100.000000000000)
7:   (0.000000000000000, 0.000000000000000, -100.000000000000)
4:   (0.000000000000000, 0.000000000000000, -100.000000000000)
5:   (0.000000000000000, 0.000000000000000, -100.000000000000)
6:   (0.000000000000000, 0.000000000000000, -100.000000000000)
7:   (0.000000000000000, 0.000000000000000, -100.000000000000)
       
       
(0.0, 0.0, -100.0, 0.0, 0.0, -100.0, 0.0, 0.0, -100.0, 0.0, 0.0, -100.0)
(0.0, 0.0, -100.0, 0.0, 0.0, -100.0, 0.0, 0.0, -100.0, 0.0, 0.0, -100.0)
       
True
True
       
False
False
       
(0.41140.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.91140.00000.00000.00000.00000.00000.00000.0000100.00.00002.519×10170.00000.00000.70710.70710.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.0000100.00.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.0000100.00.00000.00000.00007.558×10170.00000.00000.70710.70710.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.0000100.0)

                                
       
(1.0000.00000.00000.00000.00000.00000.00000.0000109.70.00001.0000.00000.00000.00000.00000.00000.0000109.70.00000.00001.0000.00000.00000.00000.00000.0000109.70.00000.00000.00001.0000.00000.00000.00000.0000109.70.00000.00000.00000.00001.0001.0000.00000.000063.840.00000.00000.00000.00000.00001.0000.00000.000031.920.00000.00000.00000.00000.00000.00001.0000.000031.920.00000.00000.00000.00000.00000.00000.00001.00031.920.00000.00000.00000.00000.00000.00000.00000.00007.105×10150.00000.00000.00000.00000.00000.00000.00000.00003.553×10150.00000.00000.00000.00000.00000.00000.00000.00003.553×10150.00000.00000.00000.00000.00000.00000.00000.00003.553×1015)

                                
       
(1.0000.00000.00000.00000.00000.00000.00000.0000109.70.00001.0000.00000.00000.00000.00000.00000.0000109.70.00000.00001.0000.00000.00000.00000.00000.0000109.70.00000.00000.00001.0000.00000.00000.00000.0000109.70.00000.00000.00000.00001.0001.0000.00000.000063.840.00000.00000.00000.00000.00001.0000.00000.000031.920.00000.00000.00000.00000.00000.00001.0000.000031.920.00000.00000.00000.00000.00000.00000.00001.00031.920.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000)

                                
       
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197398
5:   -31.91994771197398
6:   -31.919947711973986
7:   -31.919947711973975
0:   -109.7167540709727
1:   -109.7167540709727
2:   -109.7167540709727
3:   -109.7167540709727
4:   -31.91994771197398
5:   -31.91994771197398
6:   -31.919947711973986
7:   -31.919947711973975
       
       
4:   (100.000000000000, 0.000000000000000, 0.000000000000000)
5:   (0.000000000000000, 100.000000000000, 0.000000000000000)
6:   (-100.000000000000, 0.000000000000000, 0.000000000000000)
7:   (0.000000000000000, -100.000000000000, 0.000000000000000)
4:   (100.000000000000, 0.000000000000000, 0.000000000000000)
5:   (0.000000000000000, 100.000000000000, 0.000000000000000)
6:   (-100.000000000000, 0.000000000000000, 0.000000000000000)
7:   (0.000000000000000, -100.000000000000, 0.000000000000000)
       
       
(100.0, 0.0, 0.0, 0.0, 100.0, 0.0, -100.0, 0.0, 0.0, 0.0, -100.0, 0.0)
(100.0, 0.0, 0.0, 0.0, 100.0, 0.0, -100.0, 0.0, 0.0, 0.0, -100.0, 0.0)
       
True
True
       
(0.41140.00000.00000.00000.70710.00000.00000.7071100.00.00000.00000.00000.00000.70710.00000.00000.70710.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00002.519×10170.00000.00000.70710.70710.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.0000100.00.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00000.41140.00000.00000.70710.70710.0000100.00.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00007.558×10170.00000.00000.70710.70710.00000.00000.00000.00000.41140.00000.00000.70710.7071100.00.00000.00000.00000.91140.00000.00000.00000.00000.0000)

                                
       
(1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0001.0000.00000.0000141.40.00000.00000.00000.00000.00001.0000.00000.000070.710.00000.00000.00000.00000.00000.00001.0000.000070.710.00000.00000.00000.00000.00000.00000.00001.00070.710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000)

                                
       
0:   0.0
1:   0.0
2:   0.0
3:   0.0
4:   70.71067811865476
5:   70.71067811865476
6:   70.71067811865474
7:   70.71067811865474
0:   0.0
1:   0.0
2:   0.0
3:   0.0
4:   70.71067811865476
5:   70.71067811865476
6:   70.71067811865474
7:   70.71067811865474
       
       
4:   (100.000000000000, 0.000000000000000, 0.000000000000000)
5:   (-100.000000000000, 0.000000000000000, 0.000000000000000)
6:   (100.000000000000, 0.000000000000000, 0.000000000000000)
7:   (-100.000000000000, 0.000000000000000, 0.000000000000000)
4:   (100.000000000000, 0.000000000000000, 0.000000000000000)
5:   (-100.000000000000, 0.000000000000000, 0.000000000000000)
6:   (100.000000000000, 0.000000000000000, 0.000000000000000)
7:   (-100.000000000000, 0.000000000000000, 0.000000000000000)
       
       
(100.0, 0.0, 0.0, -100.0, 0.0, 0.0, 100.0, 0.0, 0.0, -100.0, 0.0, 0.0)
(100.0, 0.0, 0.0, -100.0, 0.0, 0.0, 100.0, 0.0, 0.0, -100.0, 0.0, 0.0)
       
True
True
       
(0.41140.00000.00000.00000.70710.00000.00000.7071100.00.00000.00000.00000.00000.70710.00000.00000.70710.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00002.519×10170.00000.00000.70710.70710.00000.0000100.00.00000.41140.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00000.41140.00000.00000.70710.70710.0000100.00.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00007.558×10170.00000.00000.70710.7071100.00.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.00000.00000.91140.00000.00000.00000.00000.0000)

                                
       
(1.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.00000.00000.00000.00000.00000.00000.00000.00001.0001.0000.00000.00000.00000.00000.00000.00000.00000.00001.0000.00000.000070.710.00000.00000.00000.00000.00000.00001.0000.000070.710.00000.00000.00000.00000.00000.00000.00001.00070.710.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.0000)

                                
       
0:   0.0
1:   0.0
2:   0.0
3:   0.0
4:   70.71067811865476
5:   -70.71067811865476
6:   -70.71067811865474
7:   70.71067811865474
0:   0.0
1:   0.0
2:   0.0
3:   0.0
4:   70.71067811865476
5:   -70.71067811865476
6:   -70.71067811865474
7:   70.71067811865474
       

 

Primjer 5. — Pseudo-Schwedlerova „kupola” bez dijagonalnih štapova

 

       
       
       
3 * 27 - 54  ==  27  !=  0
3 * 27 - 54  ==  27  !=  0
       
27
27
       
81 x 54 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
81 x 54 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
Row space:
   Vector space of degree 54 and dimension 54
Row space:
   Vector space of degree 54 and dimension 54
       
Column space:
   Vector space of degree 81 and dimension 54
Column space:
   Vector space of degree 81 and dimension 54
       
Kernel:
   Vector space of degree 54 and dimension 0
Kernel:
   Vector space of degree 54 and dimension 0
       
Left kernel:
   Vector space of degree 81 and dimension 27
Left kernel:
   Vector space of degree 81 and dimension 27
       
       
       
(0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0,
-70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0,
0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0,
0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0,
-50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0,
0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0)
(0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -70.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -80.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0, 0.0, 0.0, -50.0)
       
True
True
       
False
False
       
81 x 55 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
81 x 55 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
0:   -242.79669133959382
1:   -242.79669133959385
2:   -242.79669133959368
3:   -242.79669133959402
4:   -242.79669133959396
5:   -242.79669133959396
6:   -242.7966913395938
7:   -242.79669133959396
8:   -242.79669133959396
9:   37.64244088603994
10:  37.64244088603988
11:  37.6424408860399
12:  37.64244088603995
13:  37.642440886039964
14:  37.64244088603994
15:  37.64244088603993
16:  37.642440886039935
17:  37.64244088603995
18:  -208.811957197297
19:  -208.811957197297
20:  -208.8119571972969
21:  -208.8119571972971
22:  -208.81195719729703
23:  -208.81195719729703
24:  -208.81195719729695
25:  -208.8119571972971
26:  -208.8119571972971
27:  -72.13931385770061
28:  -72.13931385770066
29:  -72.13931385770066
30:  -72.1393138577007
31:  -72.1393138577007
32:  -72.13931385770066
33:  -72.13931385770063
34:  -72.1393138577006
35:  -72.13931385770063
36:  -124.54025738583246
37:  -124.5402573858324
38:  -124.54025738583235
39:  -124.54025738583246
40:  -124.54025738583243
41:  -124.54025738583243
42:  -124.54025738583243
43:  -124.54025738583248
44:  -124.54025738583248
45:  -166.74835942081702
46:  -166.74835942081702
47:  -166.748359420817
48:  -166.74835942081702
49:  -166.74835942081702
50:  -166.748359420817
51:  -166.74835942081702
52:  -166.74835942081705
53:  -166.74835942081705
0:   -242.79669133959382
1:   -242.79669133959385
2:   -242.79669133959368
3:   -242.79669133959402
4:   -242.79669133959396
5:   -242.79669133959396
6:   -242.7966913395938
7:   -242.79669133959396
8:   -242.79669133959396
9:   37.64244088603994
10:  37.64244088603988
11:  37.6424408860399
12:  37.64244088603995
13:  37.642440886039964
14:  37.64244088603994
15:  37.64244088603993
16:  37.642440886039935
17:  37.64244088603995
18:  -208.811957197297
19:  -208.811957197297
20:  -208.8119571972969
21:  -208.8119571972971
22:  -208.81195719729703
23:  -208.81195719729703
24:  -208.81195719729695
25:  -208.8119571972971
26:  -208.8119571972971
27:  -72.13931385770061
28:  -72.13931385770066
29:  -72.13931385770066
30:  -72.1393138577007
31:  -72.1393138577007
32:  -72.13931385770066
33:  -72.13931385770063
34:  -72.1393138577006
35:  -72.13931385770063
36:  -124.54025738583246
37:  -124.5402573858324
38:  -124.54025738583235
39:  -124.54025738583246
40:  -124.54025738583243
41:  -124.54025738583243
42:  -124.54025738583243
43:  -124.54025738583248
44:  -124.54025738583248
45:  -166.74835942081702
46:  -166.74835942081702
47:  -166.748359420817
48:  -166.74835942081702
49:  -166.74835942081702
50:  -166.748359420817
51:  -166.74835942081702
52:  -166.74835942081705
53:  -166.74835942081705

 

Primjer 6. — Pseudo-Schwedlerova „kupola” s ukriženim dijagonalama

 

       
joints:
   0:   (10.0000000000000, 0.000000000000000, 0.000000000000000)
   1:   (6.12323399573676e-16, 10.0000000000000, 0.000000000000000)
   2:   (-10.0000000000000, 1.22464679914735e-15, 0.000000000000000)
   3:   (-1.83697019872103e-15, -10.0000000000000, 0.000000000000000)
   4:   (6.61437827766148, 0.000000000000000, 7.50000000000000)
   5:   (4.05013859304395e-16, 6.61437827766148, 7.50000000000000)
   6:   (-6.61437827766148, 8.10027718608790e-16, 7.50000000000000)
   7:   (-1.21504157791318e-15, -6.61437827766148, 7.50000000000000)

bars:
   0:   (0, 4)
   1:   (1, 5)
   2:   (2, 6)
   3:   (3, 7)
   4:   (4, 5)
   5:   (5, 6)
   6:   (6, 7)
   7:   (7, 4)
   8:   (0, 5)
   9:   (1, 6)
   10:  (2, 7)
   11:  (3, 4)
   12:  (0, 7)
   13:  (1, 4)
   14:  (2, 5)
   15:  (3, 6)

supports: [0, 1, 2, 3]
joints:
   0:   (10.0000000000000, 0.000000000000000, 0.000000000000000)
   1:   (6.12323399573676e-16, 10.0000000000000, 0.000000000000000)
   2:   (-10.0000000000000, 1.22464679914735e-15, 0.000000000000000)
   3:   (-1.83697019872103e-15, -10.0000000000000, 0.000000000000000)
   4:   (6.61437827766148, 0.000000000000000, 7.50000000000000)
   5:   (4.05013859304395e-16, 6.61437827766148, 7.50000000000000)
   6:   (-6.61437827766148, 8.10027718608790e-16, 7.50000000000000)
   7:   (-1.21504157791318e-15, -6.61437827766148, 7.50000000000000)

bars:
   0:   (0, 4)
   1:   (1, 5)
   2:   (2, 6)
   3:   (3, 7)
   4:   (4, 5)
   5:   (5, 6)
   6:   (6, 7)
   7:   (7, 4)
   8:   (0, 5)
   9:   (1, 6)
   10:  (2, 7)
   11:  (3, 4)
   12:  (0, 7)
   13:  (1, 4)
   14:  (2, 5)
   15:  (3, 6)

supports: [0, 1, 2, 3]
       
       
3 * 4 - 16  ==  -4  !=  0
3 * 4 - 16  ==  -4  !=  0
       
[4, 5, 6, 7]
[4, 5, 6, 7]
       
(0.41140.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.46770.00000.46770.00000.00000.00000.00000.00000.00000.70710.00000.00000.70710.00000.00000.00000.70710.00000.70710.00000.00000.91140.00000.00000.00000.00000.00000.00000.00000.00000.00000.00000.53030.00000.53030.00000.00000.00002.519×10170.00000.00000.70710.70710.00000.00000.70710.00000.00000.00000.00000.00000.70710.00000.00000.41140.00000.00000.70710.70710.00000.00000.46770.00000.00000.00000.00000.00000.46770.00000.00000.91140.00000.00000.00000.00000.00000.00000.53030.00000.00000.00000.00000.00000.53030.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.46770.00000.00000.00000.00000.00000.46770.00000.00005.039×10170.00000.00000.70710.70710.00000.00000.70710.00000.00000.00000.00000.00000.70710.00000.00000.91140.00000.00000.00000.00000.00000.00000.53030.00000.00000.00000.00000.00000.53030.00000.00000.00007.558×10170.00000.00000.70710.70710.00000.00000.70710.00000.70710.00000.00000.00000.00000.00000.00000.41140.00000.00000.70710.70710.00000.00000.46770.00000.46770.00000.00000.00000.00000.00000.00000.91140.00000.00000.00000.00000.00000.00000.53030.00000.53030.00000.00000.0000)

                                
       
4:   0
5:   3
6:   6
7:   9
4:   0
5:   3
6:   6
7:   9
       
(1.00.00.00.00.00.00.00.00.00.00.00.58186095610021150.00.58186095610021150.00.00.01.00.00.00.00.00.00.00.58186095610021150.00.00.00.00.00.58186095610021150.00.00.01.00.00.00.00.00.00.00.58186095610021150.00.00.00.00.00.58186095610021160.00.00.01.00.00.00.00.00.00.00.58186095610021160.00.58186095610021150.00.00.00.00.00.00.01.01.00.00.01.00.00.00.00.00.01.00.00.00.00.00.00.01.00.00.00.00.00.00.00.00.01.00.00.00.00.00.00.00.01.00.00.00.99999999999999980.00.00.00.00.99999999999999981.00.00.00.00.00.00.00.01.00.99999999999999980.00.01.00.00.99999999999999980.00.00.00.00.00.00.00.00.00.01.00.00.00.00.01.00.00.00.00.00.00.00.00.00.00.00.01.00.00.00.00.01.07.850462293418876×10170.00.00.00.00.00.00.00.00.00.01.00.99999999999999970.99999999999999970.00.01.00.00.00.00.00.00.00.00.00.00.00.01.01.00.00.07.850462293418876×1017)

                                
       
       
[12, 13, 14, 15]
[12, 13, 14, 15]
       
Row space:
   Vector space of degree 16 and dimension 12
   Basis:
     (1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0,
0.5818609561002115, -0.0, 0.5818609561002115, -0.0, -0.0)
     (0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0,
-0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0)
     (0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115,
-0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002116)
     (0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0,
0.5818609561002116, -0.0, 0.5818609561002115, -0.0, -0.0, -0.0)
     (0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -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, 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, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.9999999999999998, -0.0,
-0.0, -0.0, -0.0, 0.9999999999999998, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999998, -0.0, -0.0,
1.0, -0.0, 0.9999999999999998, -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, -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, 0.0, 0.0, 0.0, 0.0,
-1.0, 7.850462293418876e-17)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0,
-0.9999999999999997, 0.9999999999999997, 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, 1.0, -1.0, -0.0,
-0.0, 7.850462293418876e-17)
Row space:
   Vector space of degree 16 and dimension 12
   Basis:
     (1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0, 0.5818609561002115, -0.0, -0.0)
     (0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0)
     (0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002115, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002116)
     (0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.0, -0.0, -0.0, -0.0, 0.5818609561002116, -0.0, 0.5818609561002115, -0.0, -0.0, -0.0)
     (0.0, 0.0, 0.0, 0.0, 1.0, 1.0, -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, 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, 0.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, -0.9999999999999998, -0.0, -0.0, -0.0, -0.0, 0.9999999999999998, 1.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999998, -0.0, -0.0, 1.0, -0.0, 0.9999999999999998, -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, -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, 0.0, 0.0, 0.0, 0.0, -1.0, 7.850462293418876e-17)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -0.9999999999999997, 0.9999999999999997, 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, 1.0, -1.0, -0.0, -0.0, 7.850462293418876e-17)
       
Column space:
   Vector space of degree 12 and dimension 12
   Basis:
     (0.4114378277661477, 0.0, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 2.5193300941097603e-17, 0.4114378277661477,
-0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.4114378277661477, 5.0386601882195206e-17,
-0.9114378277661477, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -7.557990282329279e-17,
-0.4114378277661477, -0.9114378277661477)
     (-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, -0.7071067811865476, -0.7071067811865475, 0.0,
0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865474, -0.7071067811865476,
0.0, -0.7071067811865474, 0.7071067811865476, 0.0)
     (-0.7071067811865476, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.7071067811865476, 0.7071067811865475, 0.0)
     (0.0, 0.0, 0.0, 0.7071067811865475, -0.46770717334674267,
-0.5303300858899106, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.4677071733467427, 0.7071067811865475,
-0.5303300858899106, 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,
0.4677071733467428, -0.5303300858899107)
     (-0.4677071733467428, -0.7071067811865475, -0.5303300858899106, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
Column space:
   Vector space of degree 12 and dimension 12
   Basis:
     (0.4114378277661477, 0.0, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 2.5193300941097603e-17, 0.4114378277661477, -0.9114378277661477, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.4114378277661477, 5.0386601882195206e-17, -0.9114378277661477, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -7.557990282329279e-17, -0.4114378277661477, -0.9114378277661477)
     (-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, -0.7071067811865476, -0.7071067811865475, 0.0, 0.7071067811865476, 0.7071067811865475, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865474, -0.7071067811865476, 0.0, -0.7071067811865474, 0.7071067811865476, 0.0)
     (-0.7071067811865476, -0.7071067811865475, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.7071067811865476, 0.7071067811865475, 0.0)
     (0.0, 0.0, 0.0, 0.7071067811865475, -0.46770717334674267, -0.5303300858899106, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
     (0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.4677071733467427, 0.7071067811865475, -0.5303300858899106, 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, 0.4677071733467428, -0.5303300858899107)
     (-0.4677071733467428, -0.7071067811865475, -0.5303300858899106, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0)
       
Kernel:
   Vector space of degree 16 and dimension 4
   Basis:
     (-0.5818609561002115, 0.0, 0.0, -0.5818609561002115, 0.0, 0.0, 0.0, -1.0,
0.0, -0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0)
     (-0.5818609561002115, -0.5818609561002115, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0,
1.0, -0.0, -0.0, 0.0, 0.0, 1.0, 0.0, 0.0)
     (0.0, -0.5818609561002115, -0.5818609561002115, 0.0, 0.0, -1.0, 0.0, 0.0,
0.0, 1.0, -0.0, 0.0, 0.0, 0.0, 1.0, 0.0)
     (4.567877495877366e-17, 0.0, -0.5818609561002116, -0.5818609561002115, 0.0,
0.0, -1.0, 7.850462293418876e-17, 0.0, -7.850462293418876e-17,
0.9999999999999999, -7.850462293418876e-17, 0.0, 0.0, 0.0, 1.0)
Kernel:
   Vector space of degree 16 and dimension 4
   Basis:
     (-0.5818609561002115, 0.0, 0.0, -0.5818609561002115, 0.0, 0.0, 0.0, -1.0, 0.0, -0.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0)
     (-0.5818609561002115, -0.5818609561002115, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, -0.0, -0.0, 0.0, 0.0, 1.0, 0.0, 0.0)
     (0.0, -0.5818609561002115, -0.5818609561002115, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0, -0.0, 0.0, 0.0, 0.0, 1.0, 0.0)
     (4.567877495877366e-17, 0.0, -0.5818609561002116, -0.5818609561002115, 0.0, 0.0, -1.0, 7.850462293418876e-17, 0.0, -7.850462293418876e-17, 0.9999999999999999, -7.850462293418876e-17, 0.0, 0.0, 0.0, 1.0)
       
Left kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
Left kernel:
   Vector space of degree 12 and dimension 0
   Basis:
     []
       
0:   -0.5818609561002115
3:   -0.5818609561002115
7:   -1.0
11:  1.0
12:  1.0
0:   -0.5818609561002115
3:   -0.5818609561002115
7:   -1.0
11:  1.0
12:  1.0
       
       
0:   -0.5818609561002115
1:   -0.5818609561002115
4:   -1.0
8:   1.0
13:  1.0
0:   -0.5818609561002115
1:   -0.5818609561002115
4:   -1.0
8:   1.0
13:  1.0
       
       
1:   -0.5818609561002115
2:   -0.5818609561002115
5:   -1.0
9:   1.0
14:  1.0
1:   -0.5818609561002115
2:   -0.5818609561002115
5:   -1.0
9:   1.0
14:  1.0
       
       
2:   -0.5818609561002116
3:   -0.5818609561002115
6:   -1.0
10:  0.9999999999999999
15:  1.0
2:   -0.5818609561002116
3:   -0.5818609561002115
6:   -1.0
10:  0.9999999999999999
15:  1.0
       

 

Primjer 7. — Pseudo-Schwedlerova „kupola” s ukriženim dijagonalama

 

       
       
       
3 * 27 - 108  ==  -27  !=  0
3 * 27 - 108  ==  -27  !=  0
       
27
27
       
81 x 108 dense matrix over Real Double Field (use the '.str()' method to see the
entries)
81 x 108 dense matrix over Real Double Field (use the '.str()' method to see the entries)
       
       
[27,
 28,
 29,
 30,
 31,
 32,
 33,
 34,
 35,
 63,
 64,
 65,
 66,
 67,
 68,
 69,
 70,
 71,
 99,
 100,
 101,
 102,
 103,
 104,
 105,
 106,
 107]
[27,
 28,
 29,
 30,
 31,
 32,
 33,
 34,
 35,
 63,
 64,
 65,
 66,
 67,
 68,
 69,
 70,
 71,
 99,
 100,
 101,
 102,
 103,
 104,
 105,
 106,
 107]
       
Row space:
   Vector space of degree 108 and dimension 81
Row space:
   Vector space of degree 108 and dimension 81
       
Column space:
   Vector space of degree 81 and dimension 81
Column space:
   Vector space of degree 81 and dimension 81
       
Kernel:
   Vector space of degree 108 and dimension 27
Kernel:
   Vector space of degree 108 and dimension 27
       
0:   -0.472786879768055
8:   -0.47278687976805506
17:  -0.9776149204186074
26:  1.0
27:  1.0
0:   -0.472786879768055
8:   -0.47278687976805506
17:  -0.9776149204186074
26:  1.0
27:  1.0
       
       
0:   -0.47278687976805517
1:   -0.47278687976805517
9:   -0.9776149204186072
18:  1.0
28:  1.0
0:   -0.47278687976805517
1:   -0.47278687976805517
9:   -0.9776149204186072
18:  1.0
28:  1.0
       
       
17:  -0.6768676394036834
36:  -0.5769051689800252
44:  -0.5769051689800252
53:  -0.9856881717552798
62:  1.0
63:  1.0
17:  -0.6768676394036834
36:  -0.5769051689800252
44:  -0.5769051689800252
53:  -0.9856881717552798
62:  1.0
63:  1.0
       
       
16:  -0.6768676394036828
43:  -0.5769051689800252
44:  -0.5769051689800249
52:  -0.9856881717552793
61:  0.9999999999999993
71:  1.0
16:  -0.6768676394036828
43:  -0.5769051689800252
44:  -0.5769051689800249
52:  -0.9856881717552793
61:  0.9999999999999993
71:  1.0
       
       
53:  -0.5861098319452697
72:  -0.6471760666616739
80:  -0.6471760666616739
89:  -0.991560125875167
98:  1.0
99:  1.0
53:  -0.5861098319452697
72:  -0.6471760666616739
80:  -0.6471760666616739
89:  -0.991560125875167
98:  1.0
99:  1.0
       
       
Left kernel:
   Vector space of degree 81 and dimension 0
Left kernel:
   Vector space of degree 81 and dimension 0