Solution 13 to problem over


Remaining equations | Expressions | Parameters | Inequalities | Relevance | Back to problem over

Equations

The following unsolved equations remain:
        2         2        2      2
0=16*a13  + 16*a23  + 4*a33  + b12 *kap


Expressions

The solution is given through the following expressions:

r60=0


r61=0


r62=0


r63=0


r64=0


r65=0


r66=0


r67=0


r68=0


r69=0


r610=0


r611=0


r612=0


r613=0


r614=0


r615=0


r616=0


r617=0


r618=0


r619=0


r620=0


r621=0


r622=0


r623=0


r624=0


r625=0


r626=0


r633=0


r638=0


r642=0


r645=0


r647=0


r648=0


r653=0


r657=0


r660=0


r662=0


r663=0


r667=0


r670=0


r672=0


r673=0


         2
      a13 *r679
r676=-----------
           2
        a23


           3                 2
      8*a13 *r679 + 8*a13*a23 *r679
r681=-------------------------------
                   2
                a23 *b12


              2             2
       - 8*a13 *r679 - 8*a23 *r679
r682=------------------------------
                a23*b12


            4              2    2              4
      16*a13 *r679 + 32*a13 *a23 *r679 + 16*a23 *r679
r683=-------------------------------------------------
                            2    2
                         a23 *b12


r684=0


r685=0


r686=0


r687=0


r688=0


r689=0


r690=0


r691=0


r692=0


r693=0


r694=0


r695=0


r696=0


r697=0


r698=0


r699=0


r6100=0


r6101=0


r6102=0


r6103=0


r6104=0


r6109=0


r6113=0


r6116=0


r6118=0


r6119=0


r6123=0


r6126=0


r6128=0


r6129=0


r6132=0


r6134=0


r6135=0


       4*a13*a33*r679
r6137=----------------
          a23*b12


        - 4*a33*r679
r6138=---------------
            b12


             2                  2
       16*a13 *a33*r679 + 16*a23 *a33*r679
r6139=-------------------------------------
                           2
                    a23*b12


r6140=0


r6141=0


r6142=0


r6143=0


r6144=0


r6145=0


r6146=0


r6147=0


r6148=0


r6149=0


r6150=0


r6151=0


r6152=0


r6153=0


r6154=0


r6158=0


r6161=0


r6163=0


r6164=0


          2
       a13 *r679
r6167=-----------
            2
         a23


        - 2*a13*r679
r6169=---------------
            a23


r6170=r679


                 5               3    2              3    2
r6172=( - 256*a13 *r679 - 448*a13 *a23 *r679 - 64*a13 *a33 *r679

               3    2                       4                  2    2
        - 8*a13 *b12 *kap*r679 - 192*a13*a23 *r679 - 48*a13*a23 *a33 *r679

                   2    2               2    3
        - 4*a13*a23 *b12 *kap*r679)/(a23 *b12 *kap)


               2             2
        - 8*a13 *r679 - 8*a23 *r679
r6173=------------------------------
                 a23*b12


             4              2    2             2    2           2    2
r6174=(32*a13 *r679 + 48*a13 *a23 *r679 + 4*a13 *a33 *r679 + a13 *b12 *kap*r679

                4             2    2           2    2
        + 16*a23 *r679 + 4*a23 *a33 *r679)/(a23 *b12 )


r6175=0


r6176=0


r6177=0


r6178=0


r6179=0


r6180=0


r6181=0


r6182=0


r6183=0


r6184=0


r6187=0


r6189=0


r6190=0


                3                      2                      3
        - 64*a13 *a33*r679 - 64*a13*a23 *a33*r679 - 16*a13*a33 *r679
r6192=---------------------------------------------------------------
                                      3
                               a23*b12 *kap


                4                  2    3             2        2
r6193=( - 64*a13 *a33*r679 - 16*a13 *a33 *r679 - 4*a13 *a33*b12 *kap*r679

                4                  2    3           2    3
        + 64*a23 *a33*r679 + 16*a23 *a33 *r679)/(a23 *b12 *kap)


             2                  2
       16*a13 *a33*r679 + 16*a23 *a33*r679
r6194=-------------------------------------
                           2
                    a23*b12


r6195=0


r6196=0


r6197=0


r6198=0


r6199=0


r6200=0


r6202=0


r6203=0


            2
       4*a33 *r679
r6204=-------------
             2
          b12


r6205=0


r6206=0


r6207=0


r6208=0


r6209=0


r6210=0


r6211=0


r6212=0


r6213=0


r6214=0


r6215=0


r6216=0


r6217=0


r6218=0


r6219=0


r6220=0


r6221=0


r6222=0


r6223=0


r6224=0


r6225=0


r6226=0


r6227=0


r6228=0


r6230=0


r6235=0


r6239=0


r6242=0


r6244=0


r6245=0


r6249=0


r6252=0


r6254=0


r6255=0


r6258=0


r6260=0


r6261=0


            2
       4*a13 *a33*r679
r6263=-----------------
             2
          a23 *b12


        - 4*a13*a33*r679
r6264=-------------------
            a23*b12


             3                      2
       16*a13 *a33*r679 + 16*a13*a23 *a33*r679
r6265=-----------------------------------------
                         2    2
                      a23 *b12


r6266=0


r6267=0


r6268=0


r6269=0


r6270=0


r6271=0


r6272=0


r6273=0


r6274=0


r6275=0


r6276=0


r6277=0


r6278=0


r6279=0


r6280=0


r6284=0


r6287=0


r6289=0


r6290=0


r6293=0


r6295=0


r6296=0


r6298=0


r6299=0


                3                  2                 2
        - 32*a13 *r679 - 32*a13*a23 *r679 - 2*a13*b12 *kap*r679
r6300=----------------------------------------------------------
                                      2
                               a23*b12


r6301=0


r6302=0


r6303=0


r6304=0


r6305=0


r6306=0


r6307=0


r6308=0


r6309=0


r6310=0


r6313=0


r6315=0


r6316=0


            2
       4*a13 *a33*r679
r6318=-----------------
             2
          a23 *b12


        - 4*a13*a33*r679
r6319=-------------------
            a23*b12


             3                      2
       16*a13 *a33*r679 + 16*a13*a23 *a33*r679
r6320=-----------------------------------------
                         2    2
                      a23 *b12


r6321=0


r6322=0


r6323=0


r6324=0


r6325=0


r6326=0


r6328=0


r6329=0


                2
       8*a13*a33 *r679
r6330=-----------------
                 2
          a23*b12


r6331=0


r6332=0


r6333=0


r6334=0


r6335=0


r6336=0


r6337=0


r6338=0


r6339=0


r6340=0


r6341=0


r6342=0


r6343=0


r6344=0


r6345=0


r6346=0


r6348=0


r6349=0


r6350=0


r6354=0


r6357=0


r6359=0


r6360=0


          2
       a13 *r679
r6363=-----------
            2
         a23


        - 2*a13*r679
r6365=---------------
            a23


r6366=r679


            3                 2
       8*a13 *r679 + 8*a13*a23 *r679
r6368=-------------------------------
                    2
                 a23 *b12


              4               2    2              2    2
r6369=(192*a13 *r679 + 448*a13 *a23 *r679 + 48*a13 *a33 *r679

               2    2                   4              2    2
        + 4*a13 *b12 *kap*r679 + 256*a23 *r679 + 64*a23 *a33 *r679

               2    2                   3
        + 8*a23 *b12 *kap*r679)/(a23*b12 *kap)


             4              2    2             2    2              4
r6370=(16*a13 *r679 + 48*a13 *a23 *r679 + 4*a13 *a33 *r679 + 32*a23 *r679

               2    2           2    2               2    2
        + 4*a23 *a33 *r679 + a23 *b12 *kap*r679)/(a23 *b12 )


r6371=0


r6372=0


r6373=0


r6374=0


r6375=0


r6376=0


r6377=0


r6378=0


r6379=0


r6380=0


r6383=0


r6385=0


r6386=0


       4*a13*a33*r679
r6388=----------------
          a23*b12


        - 4*a33*r679
r6389=---------------
            b12


             2                  2
       16*a13 *a33*r679 + 16*a23 *a33*r679
r6390=-------------------------------------
                           2
                    a23*b12


r6391=0


r6392=0


r6393=0


r6394=0


r6395=0


r6396=0


r6398=0


r6399=0


            2    2             2    2
       4*a13 *a33 *r679 + 4*a23 *a33 *r679
r6400=-------------------------------------
                       2    2
                    a23 *b12


r6401=0


r6402=0


r6403=0


r6404=0


r6405=0


r6406=0


r6407=0


r6408=0


r6410=0


r6411=0


r6412=0


r6413=0


r6414=0


r6415=0


r6418=0


r6420=0


r6421=0


                4                  2    3              4
r6423=( - 64*a13 *a33*r679 - 16*a13 *a33 *r679 + 64*a23 *a33*r679

                2    3             2        2               2    3
        + 16*a23 *a33 *r679 + 4*a23 *a33*b12 *kap*r679)/(a23 *b12 *kap)


             3                      2                      3
       64*a13 *a33*r679 + 64*a13*a23 *a33*r679 + 16*a13*a33 *r679
r6424=------------------------------------------------------------
                                     3
                              a23*b12 *kap


             3                      2
       16*a13 *a33*r679 + 16*a13*a23 *a33*r679
r6425=-----------------------------------------
                         2    2
                      a23 *b12


r6426=0


r6427=0


r6428=0


r6429=0


r6430=0


r6431=0


r6433=0


r6434=0


                2
       8*a13*a33 *r679
r6435=-----------------
                 2
          a23*b12


r6436=0


r6437=0


r6438=0


r6439=0


r6440=0


r6441=0


r6442=0


r6443=0


r6444=0


r6445=0


r6446=0


r6448=0


r6449=0


            2    2
       4*a13 *a33 *r679
r6450=------------------
             2    2
          a23 *b12


r6451=0


r6452=0


r6453=0


r6454=0


r6455=0


r6456=0


r6457=0


r6458=0


r6459=0


r6460=0


r6461=0


a22=2*a33


a11=2*a33


       - 2*a13*r679
r678=---------------
           a23


Parameters

Apart from the condition that they must not vanish to give a non-trivial solution and a non-singular solution with non-vanishing denominators, the following parameters are free:
 r679, a33, a23, a13, b12

Inequalities

In the following not identically vanishing expressions are shown. Any auxiliary variables g00?? are used to express that at least one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3 means that either p4 or p3 or both are non-vanishing.
 
{a23,b12}


Relevance for the application:

Modulo the following equation:

        2         2        2      2
0=16*a13  + 16*a23  + 4*a33  + b12 *kap


the system of equations related to the Hamiltonian HAM:

        2                                     2
HAM=2*u1 *a33 + 2*u1*u3*a13 + u1*v2*b12 + 2*u2 *a33 + 2*u2*u3*a23 - u2*v1*b12

         2
     + u3 *a33

has apart from the Hamiltonian and Casimirs only the following first integral: 

       4   2    2    2               3      2            2
FI=4*u1 *u3 *a13 *a33 *b12*kap + 8*u1 *u2*u3 *a13*a23*a33 *b12*kap

        3   3        3                         2
    + u1 *u3 *(16*a13 *a33*b12*kap + 16*a13*a23 *a33*b12*kap)

        3   2           3                     3                     3      3   2
    + u1 *u3 *v1*(64*a13 *a23*a33 + 64*a13*a23 *a33 + 16*a13*a23*a33 ) + u1 *u3

                 4             2    3         4             2    3
   *v2*( - 64*a13 *a33 - 16*a13 *a33  + 64*a23 *a33 + 16*a23 *a33

                2        2
         + 4*a23 *a33*b12 *kap)

        2   2   2       2    2                2    2
    + u1 *u2 *u3 *(4*a13 *a33 *b12*kap + 4*a23 *a33 *b12*kap)

        2      3        2                         3
    + u1 *u2*u3 *(16*a13 *a23*a33*b12*kap + 16*a23 *a33*b12*kap)

          2      2       2        2           2      2                   2
    - 4*u1 *u2*u3 *v1*a23 *a33*b12 *kap + 4*u1 *u2*u3 *v2*a13*a23*a33*b12 *kap +

      2   4        4                 2    2                2    2
    u1 *u3 *(16*a13 *b12*kap + 48*a13 *a23 *b12*kap + 4*a13 *a33 *b12*kap

                      4                2    2              2    3    2      2
              + 32*a23 *b12*kap + 4*a23 *a33 *b12*kap + a23 *b12 *kap ) + u1

      3            4              2    3         2        2
   *u3 *v1*(192*a13 *a23 + 448*a13 *a23  + 48*a13 *a23*a33

                    2        2              5         3    2        3    2
             + 4*a13 *a23*b12 *kap + 256*a23  + 64*a23 *a33  + 8*a23 *b12 *kap)

        2   3          3    2                2    2
    + u1 *u3 *v2*(8*a13 *b12 *kap + 8*a13*a23 *b12 *kap)

        2   2   2    2    3           2   2                  3
    + u1 *u3 *v1 *a23 *b12 *kap - 2*u1 *u3 *v1*v2*a13*a23*b12 *kap

        2   2   2    2    3              3   2            2
    + u1 *u3 *v2 *a13 *b12 *kap + 8*u1*u2 *u3 *a13*a23*a33 *b12*kap

           2   3        3                         2
    + u1*u2 *u3 *(16*a13 *a33*b12*kap + 16*a13*a23 *a33*b12*kap)

             2   2                   2              2   2       2        2
    - 4*u1*u2 *u3 *v1*a13*a23*a33*b12 *kap + 4*u1*u2 *u3 *v2*a13 *a33*b12 *kap +

            4
    u1*u2*u3

              3                         3                        3    2
   *( - 32*a13 *a23*b12*kap - 32*a13*a23 *b12*kap - 2*a13*a23*b12 *kap )

           5        3                         2
    + u1*u3 *(16*a13 *a33*b12*kap + 16*a13*a23 *a33*b12*kap)

             4                   2              4       2        2
    - 4*u1*u3 *v1*a13*a23*a33*b12 *kap + 4*u1*u3 *v2*a13 *a33*b12 *kap

          4   2    2    2
    + 4*u2 *u3 *a23 *a33 *b12*kap

        3   3        2                         3                  3   2
    + u2 *u3 *(16*a13 *a23*a33*b12*kap + 16*a23 *a33*b12*kap) + u2 *u3 *v1*(

               4             2    3        2        2             4
       - 64*a13 *a33 - 16*a13 *a33  - 4*a13 *a33*b12 *kap + 64*a23 *a33

               2    3
       + 16*a23 *a33 )

        3   2              3                     3                     3      2
    + u2 *u3 *v2*( - 64*a13 *a23*a33 - 64*a13*a23 *a33 - 16*a13*a23*a33 ) + u2

      4        4                 2    2                2    2
   *u3 *(32*a13 *b12*kap + 48*a13 *a23 *b12*kap + 4*a13 *a33 *b12*kap

               2    3    2         4                2    2
          + a13 *b12 *kap  + 16*a23 *b12*kap + 4*a23 *a33 *b12*kap)

        2   3             2        2            3    2          2   3
    + u2 *u3 *v1*( - 8*a13 *a23*b12 *kap - 8*a23 *b12 *kap) + u2 *u3 *v2*(

                5          3    2         3    2        3    2
       - 256*a13  - 448*a13 *a23  - 64*a13 *a33  - 8*a13 *b12 *kap

                    4             2    2            2    2
       - 192*a13*a23  - 48*a13*a23 *a33  - 4*a13*a23 *b12 *kap)

        2   2   2    2    3           2   2                  3
    + u2 *u3 *v1 *a23 *b12 *kap - 2*u2 *u3 *v1*v2*a13*a23*b12 *kap

        2   2   2    2    3
    + u2 *u3 *v2 *a13 *b12 *kap

           5        2                         3
    + u2*u3 *(16*a13 *a23*a33*b12*kap + 16*a23 *a33*b12*kap)

             4       2        2              4                   2
    - 4*u2*u3 *v1*a23 *a33*b12 *kap + 4*u2*u3 *v2*a13*a23*a33*b12 *kap

        6        4                 2    2                 4
    + u3 *(16*a13 *b12*kap + 32*a13 *a23 *b12*kap + 16*a23 *b12*kap)

        5             2        2            3    2
    + u3 *v1*( - 8*a13 *a23*b12 *kap - 8*a23 *b12 *kap)

        5          3    2                2    2          4   2    2    3
    + u3 *v2*(8*a13 *b12 *kap + 8*a13*a23 *b12 *kap) + u3 *v1 *a23 *b12 *kap

          4                  3         4   2    2    3
    - 2*u3 *v1*v2*a13*a23*b12 *kap + u3 *v2 *a13 *b12 *kap

             4   2             3        2                2        2
{HAM,FI} = u1 *u3 *v1*( - 8*a13 *a33*b12 *kap - 8*a13*a23 *a33*b12 *kap)

                3      2             2            2            3        2
            + u1 *u2*u3 *v1*( - 8*a13 *a23*a33*b12 *kap - 8*a23 *a33*b12 *kap)

                3      2             3        2                2        2
            + u1 *u2*u3 *v2*( - 8*a13 *a33*b12 *kap - 8*a13*a23 *a33*b12 *kap) +

              3   3              4    2             2    2    2
            u1 *u3 *v1*( - 48*a13 *b12 *kap - 64*a13 *a23 *b12 *kap

                      2    4    2         4    2
               - 2*a13 *b12 *kap  - 16*a23 *b12 *kap)

                3   3             3        2                2        2
            + u1 *u3 *v3*( - 8*a13 *a33*b12 *kap - 8*a13*a23 *a33*b12 *kap)

                3   2   2       2        3            3    3
            + u1 *u3 *v1 *(4*a13 *a23*b12 *kap + 4*a23 *b12 *kap)

                3   2                3    3                2    3
            + u1 *u3 *v1*v2*( - 4*a13 *b12 *kap - 4*a13*a23 *b12 *kap)

                2   2   2             3        2                2        2
            + u1 *u2 *u3 *v1*( - 8*a13 *a33*b12 *kap - 8*a13*a23 *a33*b12 *kap)

                2   2   2             2            2            3        2
            + u1 *u2 *u3 *v2*( - 8*a13 *a23*a33*b12 *kap - 8*a23 *a33*b12 *kap) 

               2      3              3        2                 3    2
           + u1 *u2*u3 *v1*( - 64*a13 *a23*b12 *kap - 64*a13*a23 *b12 *kap

                              4    2      2      3              4    2
               - 4*a13*a23*b12 *kap ) + u1 *u2*u3 *v2*( - 48*a13 *b12 *kap

                       2    2    2            2    4    2         4    2
               - 64*a13 *a23 *b12 *kap - 2*a13 *b12 *kap  - 16*a23 *b12 *kap)

                2      3             2            2            3        2
            + u1 *u2*u3 *v3*( - 8*a13 *a23*a33*b12 *kap - 8*a23 *a33*b12 *kap)

                2      2             2        3            3    3
            + u1 *u2*u3 *v1*v2*(4*a13 *a23*b12 *kap + 4*a23 *b12 *kap)

                2      2   2          3    3                2    3
            + u1 *u2*u3 *v2 *( - 4*a13 *b12 *kap - 4*a13*a23 *b12 *kap)

                2   4           3        2                 2        2          2
            + u1 *u3 *v1*(24*a13 *a33*b12 *kap + 24*a13*a23 *a33*b12 *kap) + u1

              4              4    2             2    2    2
           *u3 *v3*( - 48*a13 *b12 *kap - 64*a13 *a23 *b12 *kap

                      2    4    2         4    2
               - 2*a13 *b12 *kap  - 16*a23 *b12 *kap)

                  2   3   2                3
            - 8*u1 *u3 *v1 *a13*a23*a33*b12 *kap

                  2   3          2        3
            + 8*u1 *u3 *v1*v2*a13 *a33*b12 *kap

                2   3             2        3            3    3
            + u1 *u3 *v1*v3*(4*a13 *a23*b12 *kap + 4*a23 *b12 *kap)

                2   3                3    3                2    3
            + u1 *u3 *v2*v3*( - 4*a13 *b12 *kap - 4*a13*a23 *b12 *kap)

                   3   2             2            2            3        2
            + u1*u2 *u3 *v1*( - 8*a13 *a23*a33*b12 *kap - 8*a23 *a33*b12 *kap)

                   3   2             3        2                2        2
            + u1*u2 *u3 *v2*( - 8*a13 *a33*b12 *kap - 8*a13*a23 *a33*b12 *kap) +

                 2   3              4    2             2    2    2
            u1*u2 *u3 *v1*( - 16*a13 *b12 *kap - 64*a13 *a23 *b12 *kap

                       4    2            2    4    2         2   3
               - 48*a23 *b12 *kap - 2*a23 *b12 *kap ) + u1*u2 *u3 *v2*(

                       3        2                 3    2
               - 64*a13 *a23*b12 *kap - 64*a13*a23 *b12 *kap

                              4    2
               - 4*a13*a23*b12 *kap )

                   2   3             3        2                2        2
            + u1*u2 *u3 *v3*( - 8*a13 *a33*b12 *kap - 8*a13*a23 *a33*b12 *kap)

                   2   2   2       2        3            3    3
            + u1*u2 *u3 *v1 *(4*a13 *a23*b12 *kap + 4*a23 *b12 *kap)

                   2   2                3    3                2    3
            + u1*u2 *u3 *v1*v2*( - 4*a13 *b12 *kap - 4*a13*a23 *b12 *kap)

                      4           2            2             3        2
            + u1*u2*u3 *v1*(24*a13 *a23*a33*b12 *kap + 24*a23 *a33*b12 *kap)

                      4           3        2                 2        2
            + u1*u2*u3 *v2*(24*a13 *a33*b12 *kap + 24*a13*a23 *a33*b12 *kap) + 

                   4              3        2                 3    2
           u1*u2*u3 *v3*( - 64*a13 *a23*b12 *kap - 64*a13*a23 *b12 *kap

                              4    2              3   2    2        3
               - 4*a13*a23*b12 *kap ) - 8*u1*u2*u3 *v1 *a23 *a33*b12 *kap

                        3   2    2        3            5
            + 8*u1*u2*u3 *v2 *a13 *a33*b12 *kap + u1*u3 *v1

                   4    2             2    2    2             4    2
           *(16*a13 *b12 *kap + 32*a13 *a23 *b12 *kap + 16*a23 *b12 *kap)

                   5           3        2                 2        2
            + u1*u3 *v3*(24*a13 *a33*b12 *kap + 24*a13*a23 *a33*b12 *kap)

                   4   2           2        3             3    3
            + u1*u3 *v1 *( - 12*a13 *a23*b12 *kap - 12*a23 *b12 *kap)

                   4              3    3                 2    3
            + u1*u3 *v1*v2*(12*a13 *b12 *kap + 12*a13*a23 *b12 *kap)

                     4                      3
            - 8*u1*u3 *v1*v3*a13*a23*a33*b12 *kap

                     4          2        3              3   3    2    4
            + 8*u1*u3 *v2*v3*a13 *a33*b12 *kap + 2*u1*u3 *v1 *a23 *b12 *kap

                     3   2               4              3      2    2    4
            - 4*u1*u3 *v1 *v2*a13*a23*b12 *kap + 2*u1*u3 *v1*v2 *a13 *b12 *kap

                4   2             2            2            3        2
            + u2 *u3 *v2*( - 8*a13 *a23*a33*b12 *kap - 8*a23 *a33*b12 *kap) + 

             3   3              4    2             2    2    2
           u2 *u3 *v2*( - 16*a13 *b12 *kap - 64*a13 *a23 *b12 *kap

                       4    2            2    4    2
               - 48*a23 *b12 *kap - 2*a23 *b12 *kap )

                3   3             2            2            3        2
            + u2 *u3 *v3*( - 8*a13 *a23*a33*b12 *kap - 8*a23 *a33*b12 *kap)

                3   2             2        3            3    3
            + u2 *u3 *v1*v2*(4*a13 *a23*b12 *kap + 4*a23 *b12 *kap)

                3   2   2          3    3                2    3
            + u2 *u3 *v2 *( - 4*a13 *b12 *kap - 4*a13*a23 *b12 *kap)

                2   4           2            2             3        2          2
            + u2 *u3 *v2*(24*a13 *a23*a33*b12 *kap + 24*a23 *a33*b12 *kap) + u2

              4              4    2             2    2    2
           *u3 *v3*( - 16*a13 *b12 *kap - 64*a13 *a23 *b12 *kap

                       4    2            2    4    2
               - 48*a23 *b12 *kap - 2*a23 *b12 *kap )

                  2   3          2        3
            - 8*u2 *u3 *v1*v2*a23 *a33*b12 *kap

                2   3             2        3            3    3
            + u2 *u3 *v1*v3*(4*a13 *a23*b12 *kap + 4*a23 *b12 *kap)

                  2   3   2                3
            + 8*u2 *u3 *v2 *a13*a23*a33*b12 *kap

                2   3                3    3                2    3             5
            + u2 *u3 *v2*v3*( - 4*a13 *b12 *kap - 4*a13*a23 *b12 *kap) + u2*u3

                      4    2             2    2    2             4    2
           *v2*(16*a13 *b12 *kap + 32*a13 *a23 *b12 *kap + 16*a23 *b12 *kap)

                   5           2            2             3        2
            + u2*u3 *v3*(24*a13 *a23*a33*b12 *kap + 24*a23 *a33*b12 *kap)

                   4                 2        3             3    3
            + u2*u3 *v1*v2*( - 12*a13 *a23*b12 *kap - 12*a23 *b12 *kap)

                     4          2        3
            - 8*u2*u3 *v1*v3*a23 *a33*b12 *kap

                   4   2        3    3                 2    3
            + u2*u3 *v2 *(12*a13 *b12 *kap + 12*a13*a23 *b12 *kap)

                     4                      3
            + 8*u2*u3 *v2*v3*a13*a23*a33*b12 *kap

                     3   2       2    4              3      2            4
            + 2*u2*u3 *v1 *v2*a23 *b12 *kap - 4*u2*u3 *v1*v2 *a13*a23*b12 *kap

                     3   3    2    4         6
            + 2*u2*u3 *v2 *a13 *b12 *kap + u3 *v3

                   4    2             2    2    2             4    2
           *(16*a13 *b12 *kap + 32*a13 *a23 *b12 *kap + 16*a23 *b12 *kap)

                5                 2        3             3    3
            + u3 *v1*v3*( - 12*a13 *a23*b12 *kap - 12*a23 *b12 *kap)

                5              3    3                 2    3
            + u3 *v2*v3*(12*a13 *b12 *kap + 12*a13*a23 *b12 *kap)

                  4   2       2    4           4                     4
            + 2*u3 *v1 *v3*a23 *b12 *kap - 4*u3 *v1*v2*v3*a13*a23*b12 *kap

                  4   2       2    4
            + 2*u3 *v2 *v3*a13 *b12 *kap





And again in machine readable form:



HAM=2*u1**2*a33 + 2*u1*u3*a13 + u1*v2*b12 + 2*u2**2*a33 + 2*u2*u3*a23 - u2*v1*
b12 + u3**2*a33$

FI=4*u1**4*u3**2*a13**2*a33**2*b12*kap + 8*u1**3*u2*u3**2*a13*a23*a33**2*b12*kap
 + u1**3*u3**3*(16*a13**3*a33*b12*kap + 16*a13*a23**2*a33*b12*kap) + u1**3*u3**2
*v1*(64*a13**3*a23*a33 + 64*a13*a23**3*a33 + 16*a13*a23*a33**3) + u1**3*u3**2*v2
*( - 64*a13**4*a33 - 16*a13**2*a33**3 + 64*a23**4*a33 + 16*a23**2*a33**3 + 4*a23
**2*a33*b12**2*kap) + u1**2*u2**2*u3**2*(4*a13**2*a33**2*b12*kap + 4*a23**2*a33
**2*b12*kap) + u1**2*u2*u3**3*(16*a13**2*a23*a33*b12*kap + 16*a23**3*a33*b12*kap
) - 4*u1**2*u2*u3**2*v1*a23**2*a33*b12**2*kap + 4*u1**2*u2*u3**2*v2*a13*a23*a33*
b12**2*kap + u1**2*u3**4*(16*a13**4*b12*kap + 48*a13**2*a23**2*b12*kap + 4*a13**
2*a33**2*b12*kap + 32*a23**4*b12*kap + 4*a23**2*a33**2*b12*kap + a23**2*b12**3*
kap**2) + u1**2*u3**3*v1*(192*a13**4*a23 + 448*a13**2*a23**3 + 48*a13**2*a23*a33
**2 + 4*a13**2*a23*b12**2*kap + 256*a23**5 + 64*a23**3*a33**2 + 8*a23**3*b12**2*
kap) + u1**2*u3**3*v2*(8*a13**3*b12**2*kap + 8*a13*a23**2*b12**2*kap) + u1**2*u3
**2*v1**2*a23**2*b12**3*kap - 2*u1**2*u3**2*v1*v2*a13*a23*b12**3*kap + u1**2*u3
**2*v2**2*a13**2*b12**3*kap + 8*u1*u2**3*u3**2*a13*a23*a33**2*b12*kap + u1*u2**2
*u3**3*(16*a13**3*a33*b12*kap + 16*a13*a23**2*a33*b12*kap) - 4*u1*u2**2*u3**2*v1
*a13*a23*a33*b12**2*kap + 4*u1*u2**2*u3**2*v2*a13**2*a33*b12**2*kap + u1*u2*u3**
4*( - 32*a13**3*a23*b12*kap - 32*a13*a23**3*b12*kap - 2*a13*a23*b12**3*kap**2) +
 u1*u3**5*(16*a13**3*a33*b12*kap + 16*a13*a23**2*a33*b12*kap) - 4*u1*u3**4*v1*
a13*a23*a33*b12**2*kap + 4*u1*u3**4*v2*a13**2*a33*b12**2*kap + 4*u2**4*u3**2*a23
**2*a33**2*b12*kap + u2**3*u3**3*(16*a13**2*a23*a33*b12*kap + 16*a23**3*a33*b12*
kap) + u2**3*u3**2*v1*( - 64*a13**4*a33 - 16*a13**2*a33**3 - 4*a13**2*a33*b12**2
*kap + 64*a23**4*a33 + 16*a23**2*a33**3) + u2**3*u3**2*v2*( - 64*a13**3*a23*a33 
- 64*a13*a23**3*a33 - 16*a13*a23*a33**3) + u2**2*u3**4*(32*a13**4*b12*kap + 48*
a13**2*a23**2*b12*kap + 4*a13**2*a33**2*b12*kap + a13**2*b12**3*kap**2 + 16*a23
**4*b12*kap + 4*a23**2*a33**2*b12*kap) + u2**2*u3**3*v1*( - 8*a13**2*a23*b12**2*
kap - 8*a23**3*b12**2*kap) + u2**2*u3**3*v2*( - 256*a13**5 - 448*a13**3*a23**2 -
 64*a13**3*a33**2 - 8*a13**3*b12**2*kap - 192*a13*a23**4 - 48*a13*a23**2*a33**2 
- 4*a13*a23**2*b12**2*kap) + u2**2*u3**2*v1**2*a23**2*b12**3*kap - 2*u2**2*u3**2
*v1*v2*a13*a23*b12**3*kap + u2**2*u3**2*v2**2*a13**2*b12**3*kap + u2*u3**5*(16*
a13**2*a23*a33*b12*kap + 16*a23**3*a33*b12*kap) - 4*u2*u3**4*v1*a23**2*a33*b12**
2*kap + 4*u2*u3**4*v2*a13*a23*a33*b12**2*kap + u3**6*(16*a13**4*b12*kap + 32*a13
**2*a23**2*b12*kap + 16*a23**4*b12*kap) + u3**5*v1*( - 8*a13**2*a23*b12**2*kap -
 8*a23**3*b12**2*kap) + u3**5*v2*(8*a13**3*b12**2*kap + 8*a13*a23**2*b12**2*kap)
 + u3**4*v1**2*a23**2*b12**3*kap - 2*u3**4*v1*v2*a13*a23*b12**3*kap + u3**4*v2**
2*a13**2*b12**3*kap$