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Related

addrow-ev-log-matrix

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

addcol-echelon-fpprec-fpprintprec-load-matrix

load(linearalgebra);

fpprec:4;

fpprintprec:fpprec;

Calculate

load-true

load("simplex");

obj:4*x1+3*x2;

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

Calculate

false-simp

simp: false;

4*pi*pi;

Calculate

addrow-genmatrix-linsolve_params-random-true

linsolve_params:true;

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

A:genmatrix(h,2,3);

Calculate

addcol-matrix

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

b:addcol(a,[10,20,30]);

Calculate

[addcol,addrow,append,apply,ctranspose,eigenvectors,false,load,matrix]

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()
(%i6) Test: addcol(Test, [1,2,3]);
(%o6)                             [ 1  2  3 ]
(%i7) Test: addrow(Test, [3,4,5]);
                                  [ 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()
(%i6) Test: addcol(Test, [1,2,3]);
(%o6)                             [ 1  2  3 ]
(%i7) Test: addrow(Test, [3,4,5]);
                                  [ 1  2  3 ]
(%o7)                             [         ]
                                  [ 3  4  5 ]
(%i8) Test: addcol(Test, covect([9,8]));
                                [ 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) 
[abs,addcol,addrow,floor,fullmap,matrix,mod,transpose] [addcol,addrow,diff,do,ev,genmatrix,invert,kill,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,addrow,diff,ev,genmatrix,invert,kill,length,lmax,lmin,load,matrix,plot2d,romberg,sqrt,submatrix] [addcol,bfloat,echelon,fpprec,fpprintprec,load,matrix,rowop] [addcol,echelon,ident,matrix] [addcol,matrix,transpose] [addrow,block,concat,display,false,if,log,matrix,numer,print,return,round,true,while] [addrow,block,concat,false,if,log,matrix,numer,print,return,round,true,while] [addrow,block,load,matrix,plot2d] [addrow,ev,log,matrix] [addrow,matrix] [append,apply,cartesian_product,cos,draw,listify,load,makelist,product,setify] [append,apply,ctranspose,do,eigenvectors,false,load,matrix] [append,apply,ctranspose,do,load,matrix,true] [append,apply,ctranspose,eigenvectors,false,load,matrix] [append,atom,block,delete,flatten,if,lambda,load,map,return] [bfloat,eigenvectors,load,matrix] [charpoly,determinant,eigenvalues,eigenvectors,ident,invert,load,matrix] [christof,depends,diag_matrix,gcd,load,matrix,ratfac,riemann,scurvature,sin] [christof,depends,gcd,load,matrix,ratfac,riemann,scurvature] [christof,einstein,exp,load,matrix,riemann,scurvature,sin,true] [christof,einstein,load,matrix,riemann,scurvature,sin,true] [christof,load,matrix,sin] [cos,display2d,false,matrix,sin] [cos,gramschmidt,integrate,load,map,matrix,sin] [cos,load,matrix,sin] [ctranspose,load,matrix,true] [define,load,matrix] [determinant,eigenvalues,eigenvectors,ident,invert,matrix,rank,submatrix,transpose] [determinant,eigenvalues,eigenvectors,ident,load,matrix,ratsimp,solve,sqrt,transpose] [display2d,expand,false,load,plot2d] [eigenvalues,eigenvectors,invert,matrix] [eigenvalues,eigenvectors,load,matrix,ratsimp,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt,transpose] [eigenvalues,eigenvectors,load,matrix,sqrt] [eigenvalues,eigenvectors,load,matrix] [eigenvalues,eigenvectors,matrix] [eigenvectors,invert,matrix] [eigenvectors,load,matrix] [eigenvectors,matrix,transpose] [eigenvectors,matrix] [einstein,false,invert,kill,load,ratfac,ratriemann,rinvariant,scurvature,sin,true] [false,integrate,kill,load,quad_qags,ratprint,sin] [false,invert,load,rateinstein,ratfac,ratriemann,sin,true] [false,load] [gramschmidt,load,matrix] [invert,load,matrix] [load,matrix,transpose] [load,matrix,true] [load,matrix]

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