### Related

rowx:[1,log(x),(log(x...

x:110.0;

mc:matrix(ev(rowx));

Calculate

##### matrix

N:3;

P:matrix([0.5,0.25,0....

P[1,2];

Calculate

##### append

:lisp (setf expr '(* ...

:lisp (nodes-deep expr);

Calculate

##### append-assume-declare-eliminate-ev-first-fpprintprec-lambda-map-plot2d-solve-sublist

fpprintprec: 2;

declare(Vgs,real);

assume(Vgs<0,Vgs&g...

Calculate

fpprec:4;

fpprintprec:fpprec;

Calculate

obj:4*x1+3*x2;

cnst:[x1+x1<=100,(...

Calculate

##### append-block-lambda-listify-makelist-map-primep-rest-return-setify

prime(z):=block([y:1,...

prime(10);

prime(20);

Calculate

##### false-simp

simp: false;

4*pi*pi;

Calculate

linsolve_params:true;

h[i,j]:=random(5)+1;

A:genmatrix(h,2,3);

Calculate

a:matrix([1,2],[2,3],...

Calculate

Run Example
```(%i1)load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) P: matrix([0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0]);
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
(%o2)                  [                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
(%i3) Pdag: ctranspose(P);
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
(%o3)                  [                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
(%i4) A: P+Pdag;
[ 0  1  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  1  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  1  0  0  0  0 ]
(%o4)                  [                              ]
[ 0  0  0  0  1  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  1  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  1  0 ]
(%i5) Test: matrix();
(%o5)                              matrix()
(%o6)                             [ 1  2  3 ]
[ 1  2  3 ]
(%o7)                             [         ]
[ 3  4  5 ]
(%i8) hermitianmatrix: false;
(%o8)                                false
(%i9) [L, V]: eigenvectors(A);
sqrt(sqrt(5) + 3)  sqrt(sqrt(5) + 3)    sqrt(3 - sqrt(5))
(%o9) [[[- -----------------, -----------------, - -----------------,
sqrt(2)            sqrt(2)              sqrt(2)
sqrt(3 - sqrt(5))
-----------------, - 2, 2], [2, 2, 2, 2, 1, 1]],
sqrt(2)
sqrt(sqrt(5) + 3)    2 sqrt(5) + 2
[[[1, 0, - 1, -----------------, - -------------,
sqrt(2)               4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))  sqrt(5) + 1
- ---------------------------------------------, -----------,
4                             2
sqrt(sqrt(5) + 3)            sqrt(sqrt(5) + 3)  sqrt(5) + 1
- -----------------], [0, 1, - -----------------, -----------,
sqrt(2)                      sqrt(2)            2
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
- ---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))    2 sqrt(5) + 2
---------------------------------------------, - -------------,
4                                4
sqrt(sqrt(5) + 3)                        sqrt(sqrt(5) + 3)  - 2 sqrt(5) - 2
-----------------, - 1]], [[1, 0, - 1, - -----------------, ---------------,
sqrt(2)                                  sqrt(2)              4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
- ---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) - sqrt(2) sqrt(5))    - sqrt(5) - 1
- ---------------------------------------------, - -------------,
4                                2
sqrt(sqrt(5) + 3)          sqrt(sqrt(5) + 3)  sqrt(5) + 1
-----------------], [0, 1, -----------------, -----------,
sqrt(2)                    sqrt(2)            2
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))    2 sqrt(5) + 2
- ---------------------------------------------, - -------------,
4                                4
sqrt(sqrt(5) + 3)                      sqrt(3 - sqrt(5))  2 sqrt(5) - 2
- -----------------, - 1]], [[1, 0, - 1, -----------------, -------------,
sqrt(2)                                sqrt(2)             4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
- -------------------------------------------------------------, 0,
4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))  1 - sqrt(5)
-------------------------------------------------------------, -----------,
4                                     2
sqrt(3 - sqrt(5))            sqrt(3 - sqrt(5))    sqrt(5) - 1
- -----------------], [0, 1, - -----------------, - -----------,
sqrt(2)                      sqrt(2)              2
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
-------------------------------------------------------------, 0,
4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
- -------------------------------------------------------------,
4
2 sqrt(5) - 2  sqrt(3 - sqrt(5))
-------------, -----------------, - 1]],
4             sqrt(2)
sqrt(3 - sqrt(5))    2 - 2 sqrt(5)
[[1, 0, - 1, - -----------------, - -------------,
sqrt(2)               4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
-------------------------------------------------------------, 0,
4
- sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) - sqrt(2) sqrt(3 - sqrt(5))
---------------------------------------------------------------,
4
sqrt(5) - 1  sqrt(3 - sqrt(5))          sqrt(3 - sqrt(5))    sqrt(5) - 1
- -----------, -----------------], [0, 1, -----------------, - -----------,
2            sqrt(2)                    sqrt(2)              2
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
- -------------------------------------------------------------, 0,
4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))  2 sqrt(5) - 2
-------------------------------------------------------------, -------------,
4                                      4
sqrt(3 - sqrt(5))
- -----------------, - 1]], [[1, - 1, 1, - 1, 1, - 1, 1, - 1, 1, - 1]],
sqrt(2)
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]]]
(%i10) Ltmp: [];
(%o10)                                []
(%i11) for i:1 thru length(L[1]) do  for j:1 thru L[2][i] do    Ltmp: append(Ltmp, [L[1][i]]);
(%o11)                               done
(%i12) Ltmp;
sqrt(sqrt(5) + 3)    sqrt(sqrt(5) + 3)  sqrt(sqrt(5) + 3)
(%o12) [- -----------------, - -----------------, -----------------,
sqrt(2)              sqrt(2)            sqrt(2)
sqrt(sqrt(5) + 3)    sqrt(3 - sqrt(5))    sqrt(3 - sqrt(5))
-----------------, - -----------------, - -----------------,
sqrt(2)              sqrt(2)              sqrt(2)
sqrt(3 - sqrt(5))  sqrt(3 - sqrt(5))
-----------------, -----------------, - 2, 2]
sqrt(2)            sqrt(2)
(%i13) D: apply(diag_matrix, Ltmp);
[   sqrt(sqrt(5) + 3) ]         [          0          ]
[ - ----------------- ]         [                     ]
[        sqrt(2)      ]         [   sqrt(sqrt(5) + 3) ]
[                     ]         [ - ----------------- ]
[          0          ]         [        sqrt(2)      ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
(%o13)  Col 1 = [          0          ] Col 2 = [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[ sqrt(sqrt(5) + 3) ]         [         0         ]
[ ----------------- ]         [                   ]
[      sqrt(2)      ]         [ sqrt(sqrt(5) + 3) ]
[                   ]         [ ----------------- ]
[         0         ]         [      sqrt(2)      ]
[                   ]         [                   ]
Col 3 = [         0         ] Col 4 = [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[   sqrt(3 - sqrt(5)) ]         [          0          ]
[ - ----------------- ]         [                     ]
Col 5 = [        sqrt(2)      ] Col 6 = [   sqrt(3 - sqrt(5)) ]
[                     ]         [ - ----------------- ]
[          0          ]         [        sqrt(2)      ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[         0         ]         [         0         ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
Col 7 = [         0         ] Col 8 = [         0         ] Col 9 = [     ]
[                   ]         [                   ]         [  0  ]
[ sqrt(3 - sqrt(5)) ]         [         0         ]         [     ]
[ ----------------- ]         [                   ]         [  0  ]
[      sqrt(2)      ]         [ sqrt(3 - sqrt(5)) ]         [     ]
[                   ]         [ ----------------- ]         [  0  ]
[         0         ]         [      sqrt(2)      ]         [     ]
[                   ]         [                   ]         [ - 2 ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
Col 10 = [   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 2 ]
(%i14) ```
Run Example
```load(eigen);
(%o1)           /usr/share/maxima/5.21.1/share/matrix/eigen.mac
(%i2) P: matrix([0,1,0,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0],[0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,0]);
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
(%o2)                  [                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
(%i3) Pdag: ctranspose(P);
[ 0  0  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  1  0  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  0  0  0  0  0 ]
(%o3)                  [                              ]
[ 0  0  0  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  0  0  1  0 ]
(%i4) A: P+Pdag;
[ 0  1  0  0  0  0  0  0  0  1 ]
[                              ]
[ 1  0  1  0  0  0  0  0  0  0 ]
[                              ]
[ 0  1  0  1  0  0  0  0  0  0 ]
[                              ]
[ 0  0  1  0  1  0  0  0  0  0 ]
[                              ]
[ 0  0  0  1  0  1  0  0  0  0 ]
(%o4)                  [                              ]
[ 0  0  0  0  1  0  1  0  0  0 ]
[                              ]
[ 0  0  0  0  0  1  0  1  0  0 ]
[                              ]
[ 0  0  0  0  0  0  1  0  1  0 ]
[                              ]
[ 0  0  0  0  0  0  0  1  0  1 ]
[                              ]
[ 1  0  0  0  0  0  0  0  1  0 ]
(%i5) Test: matrix();
(%o5)                              matrix()
(%o6)                             [ 1  2  3 ]
[ 1  2  3 ]
(%o7)                             [         ]
[ 3  4  5 ]
[ 1  2  3  9 ]
(%o8)                           [            ]
[ 3  4  5  8 ]
(%i9) hermitianmatrix: false;
(%o9)                                false
(%i10) [L, V]: eigenvectors(A);
sqrt(sqrt(5) + 3)  sqrt(sqrt(5) + 3)    sqrt(3 - sqrt(5))
(%o10) [[[- -----------------, -----------------, - -----------------,
sqrt(2)            sqrt(2)              sqrt(2)
sqrt(3 - sqrt(5))
-----------------, - 2, 2], [2, 2, 2, 2, 1, 1]],
sqrt(2)
sqrt(sqrt(5) + 3)    2 sqrt(5) + 2
[[[1, 0, - 1, -----------------, - -------------,
sqrt(2)               4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))  sqrt(5) + 1
- ---------------------------------------------, -----------,
4                             2
sqrt(sqrt(5) + 3)            sqrt(sqrt(5) + 3)  sqrt(5) + 1
- -----------------], [0, 1, - -----------------, -----------,
sqrt(2)                      sqrt(2)            2
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
- ---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))    2 sqrt(5) + 2
---------------------------------------------, - -------------,
4                                4
sqrt(sqrt(5) + 3)                        sqrt(sqrt(5) + 3)  - 2 sqrt(5) - 2
-----------------, - 1]], [[1, 0, - 1, - -----------------, ---------------,
sqrt(2)                                  sqrt(2)              4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
- ---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) - sqrt(2) sqrt(5))    - sqrt(5) - 1
- ---------------------------------------------, - -------------,
4                                2
sqrt(sqrt(5) + 3)          sqrt(sqrt(5) + 3)  sqrt(5) + 1
-----------------], [0, 1, -----------------, -----------,
sqrt(2)                    sqrt(2)            2
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))
---------------------------------------------, 0,
4
sqrt(sqrt(5) + 3) (sqrt(2) sqrt(5) - sqrt(2))    2 sqrt(5) + 2
- ---------------------------------------------, - -------------,
4                                4
sqrt(sqrt(5) + 3)                      sqrt(3 - sqrt(5))  2 sqrt(5) - 2
- -----------------, - 1]], [[1, 0, - 1, -----------------, -------------,
sqrt(2)                                sqrt(2)             4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
- -------------------------------------------------------------, 0,
4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))  1 - sqrt(5)
-------------------------------------------------------------, -----------,
4                                     2
sqrt(3 - sqrt(5))            sqrt(3 - sqrt(5))    sqrt(5) - 1
- -----------------], [0, 1, - -----------------, - -----------,
sqrt(2)                      sqrt(2)              2
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
-------------------------------------------------------------, 0,
4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
- -------------------------------------------------------------,
4
2 sqrt(5) - 2  sqrt(3 - sqrt(5))
-------------, -----------------, - 1]],
4             sqrt(2)
sqrt(3 - sqrt(5))    2 - 2 sqrt(5)
[[1, 0, - 1, - -----------------, - -------------,
sqrt(2)               4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
-------------------------------------------------------------, 0,
4
- sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) - sqrt(2) sqrt(3 - sqrt(5))
---------------------------------------------------------------,
4
sqrt(5) - 1  sqrt(3 - sqrt(5))          sqrt(3 - sqrt(5))    sqrt(5) - 1
- -----------, -----------------], [0, 1, -----------------, - -----------,
2            sqrt(2)                    sqrt(2)              2
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))
- -------------------------------------------------------------, 0,
4
sqrt(2) sqrt(3 - sqrt(5)) sqrt(5) + sqrt(2) sqrt(3 - sqrt(5))  2 sqrt(5) - 2
-------------------------------------------------------------, -------------,
4                                      4
sqrt(3 - sqrt(5))
- -----------------, - 1]], [[1, - 1, 1, - 1, 1, - 1, 1, - 1, 1, - 1]],
sqrt(2)
[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]]]]
(%i11) Ltmp: [];
(%o11)                                []
(%i12) for i:1 thru length(L[1]) do  for j:1 thru L[2][i] do    Ltmp: append(Ltmp, [L[1][i]]);
(%o12)                               done
(%i13) Ltmp;
sqrt(sqrt(5) + 3)    sqrt(sqrt(5) + 3)  sqrt(sqrt(5) + 3)
(%o13) [- -----------------, - -----------------, -----------------,
sqrt(2)              sqrt(2)            sqrt(2)
sqrt(sqrt(5) + 3)    sqrt(3 - sqrt(5))    sqrt(3 - sqrt(5))
-----------------, - -----------------, - -----------------,
sqrt(2)              sqrt(2)              sqrt(2)
sqrt(3 - sqrt(5))  sqrt(3 - sqrt(5))
-----------------, -----------------, - 2, 2]
sqrt(2)            sqrt(2)
(%i14) D: apply(diag_matrix, Ltmp);
[   sqrt(sqrt(5) + 3) ]         [          0          ]
[ - ----------------- ]         [                     ]
[        sqrt(2)      ]         [   sqrt(sqrt(5) + 3) ]
[                     ]         [ - ----------------- ]
[          0          ]         [        sqrt(2)      ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
(%o14)  Col 1 = [          0          ] Col 2 = [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[ sqrt(sqrt(5) + 3) ]         [         0         ]
[ ----------------- ]         [                   ]
[      sqrt(2)      ]         [ sqrt(sqrt(5) + 3) ]
[                   ]         [ ----------------- ]
[         0         ]         [      sqrt(2)      ]
[                   ]         [                   ]
Col 3 = [         0         ] Col 4 = [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[                   ]         [                   ]
[         0         ]         [         0         ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[   sqrt(3 - sqrt(5)) ]         [          0          ]
[ - ----------------- ]         [                     ]
Col 5 = [        sqrt(2)      ] Col 6 = [   sqrt(3 - sqrt(5)) ]
[                     ]         [ - ----------------- ]
[          0          ]         [        sqrt(2)      ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[                     ]         [                     ]
[          0          ]         [          0          ]
[         0         ]         [         0         ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
Col 7 = [         0         ] Col 8 = [         0         ] Col 9 = [     ]
[                   ]         [                   ]         [  0  ]
[ sqrt(3 - sqrt(5)) ]         [         0         ]         [     ]
[ ----------------- ]         [                   ]         [  0  ]
[      sqrt(2)      ]         [ sqrt(3 - sqrt(5)) ]         [     ]
[                   ]         [ ----------------- ]         [  0  ]
[         0         ]         [      sqrt(2)      ]         [     ]
[                   ]         [                   ]         [ - 2 ]
[         0         ]         [         0         ]         [     ]
[                   ]         [                   ]         [  0  ]
[         0         ]         [         0         ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
Col 10 = [   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 0 ]
[   ]
[ 2 ]
(%i15) ```