Solution 3 to problem l112o23

Expressions | Parameters | Relevance | Back to problem l112o23

Expressions

The solution is given through the following expressions:


      1     2    4   3        1     4    2   3       1     3    2       3
b42=(----*a1 *a14 *a4 *b24 - ---*a12 *a15 *a4 *b1 + ---*a12 *a14 *a15*a4 *b1
      64                      4                      8

         1      2    4   3        5    3
      - ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14)
         64


      3     2    4   2        3     4    2   2       3     3    2       2
b41=(----*a1 *a14 *a4 *b24 - ---*a12 *a15 *a4 *b1 + ---*a12 *a14 *a15*a4 *b1
      32                      2                      4

         3      2    4   2        4    3
      - ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14)
         32


      3        2   2        3     2       2       3         2   2
     ---*a1*a14 *a4 *b24 + ---*a12 *a15*a4 *b1 - ---*a12*a14 *a4 *b1
      8                     2                     8
b40=-----------------------------------------------------------------
                                  3    2
                                a1 *a12


      3      2   2
     ----*a14 *a4 *b24
      16
b39=-------------------
           2    2
         a1 *a12


      3     2    4               4    2          3     3    2
b38=(----*a1 *a14 *a4*b24 - 3*a12 *a15 *a4*b1 + ---*a12 *a14 *a15*a4*b1
      16                                         2

         3      2    4           3    3
      - ----*a12 *a14 *a4*b1)/(a1 *a12 *a14)
         16


      3        2               2              3         2
     ---*a1*a14 *a4*b24 + 3*a12 *a15*a4*b1 - ---*a12*a14 *a4*b1
      4                                       4
b37=------------------------------------------------------------
                                2    2
                              a1 *a12


      3     2
     ---*a14 *a4*b24
      4
b36=-----------------
               2
         a1*a12


      3        2           3     2              3         2
     ---*a1*a14 *a4*b24 + ---*a12 *a15*a4*b1 - ---*a12*a14 *a4*b1
      8                    2                    8
b35=--------------------------------------------------------------
                                 2    2
                               a1 *a12


         1               1
      - ---*a14*a4*b1 + ---*a14*a4*b24
         2               2
b34=-----------------------------------
                  a1*a12


         1               1
      - ---*a14*a4*b1 + ---*a14*a4*b24
         2               2
b33=-----------------------------------
                  a1*a12


      3
     ---*a14*a4*b24
      2
b32=----------------
         a1*a12


      3
     ---*a14*a4*b24
      4
b31=----------------
         a1*a12


      1    2    4            4    2         3    2           1     2    4
     ---*a1 *a14 *b24 - 2*a12 *a15 *b1 + a12 *a14 *a15*b1 - ---*a12 *a14 *b1
      8                                                      8
b30=-------------------------------------------------------------------------
                                    2    3
                                  a1 *a12 *a14


      3     2
     ---*a14 *b24
      4
b29=--------------
            2
         a12


      3        2            2           3         2
     ---*a1*a14 *b24 + 3*a12 *a15*b1 - ---*a12*a14 *b1
      4                                 4
b28=---------------------------------------------------
                                2
                          a1*a12


      3
     ---*a14*b24
      2
b27=-------------
         a12


      3
     ---*a14*b24
      2
b26=-------------
         a12


         1            1
      - ---*a14*b1 + ---*a14*b24
         2            2
b25=-----------------------------
                 a12


         1     2    4   4        1     4    2   4       1     3    2       4
b23=( - ----*a1 *a14 *a4 *b24 + ---*a12 *a15 *a4 *b1 - ---*a12 *a14 *a15*a4 *b1
         64                      4                      8

         1      2    4   4        6    3
      + ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14)
         64


         3     2    4   3        3     4    2   3       3     3    2       3
b22=( - ----*a1 *a14 *a4 *b24 + ---*a12 *a15 *a4 *b1 - ---*a12 *a14 *a15*a4 *b1
         32                      2                      4

         3      2    4   3        5    3
      + ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14)
         32


         9     2    4   3        3        2    2       3
b21=( - ----*a1 *a14 *a4 *b24 - ---*a1*a12 *a14 *a15*a4 *b1
         16                      2

         3            4   3           4    2   3       3     3    2       3
      + ---*a1*a12*a14 *a4 *b1 + 3*a12 *a15 *a4 *b1 - ---*a12 *a14 *a15*a4 *b1
         8                                             2

         3      2    4   3        5    2    2
      + ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14 )
         16


         3     2    4   2            4    2   2       3     3    2       2
b20=( - ----*a1 *a14 *a4 *b24 + 3*a12 *a15 *a4 *b1 - ---*a12 *a14 *a15*a4 *b1
         16                                           2

         3      2    4   2        4    3
      + ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14)
         16


         3    2    4   2               2    2       2
b19=( - ---*a1 *a14 *a4 *b24 - 3*a1*a12 *a14 *a15*a4 *b1
         2

         3            4   2            4    2   2           3    2       2
      + ---*a1*a12*a14 *a4 *b1 + 12*a12 *a15 *a4 *b1 - 6*a12 *a14 *a15*a4 *b1
         4

         3     2    4   2        4    2    2
      + ---*a12 *a14 *a4 *b1)/(a1 *a12 *a14 )
         4


         3    2    4   2        3        2    2       2
b18=( - ---*a1 *a14 *a4 *b24 - ---*a1*a12 *a14 *a15*a4 *b1
         8                      2

         3            4   2           4    2   2       3     3    2       2
      + ---*a1*a12*a14 *a4 *b1 + 3*a12 *a15 *a4 *b1 - ---*a12 *a14 *a15*a4 *b1
         8                                             2

         3      2    4   2        4    2    2
      + ----*a12 *a14 *a4 *b1)/(a1 *a12 *a14 )
         16


         3        2   2            2       2       3         2   2
      - ---*a1*a14 *a4 *b24 - 6*a12 *a15*a4 *b1 + ---*a12*a14 *a4 *b1
         2                                         2
b17=------------------------------------------------------------------
                                 3
                               a1 *a12*a14


      1        2   2       5        2   2            2       2
b16=(---*a1*a14 *a4 *b1 - ---*a1*a14 *a4 *b24 - 3*a12 *a15*a4 *b1
      2                    4

         3         2   2        3
      + ---*a12*a14 *a4 *b1)/(a1 *a12*a14)
         4


      1        2   2       1        2   2            2       2
b15=(---*a1*a14 *a4 *b1 - ---*a1*a14 *a4 *b24 - 3*a12 *a15*a4 *b1
      2                    2

         3         2   2        3
      + ---*a12*a14 *a4 *b1)/(a1 *a12*a14)
         4


         1    2    4               4    2            3    2
b14=( - ---*a1 *a14 *a4*b24 + 2*a12 *a15 *a4*b1 - a12 *a14 *a15*a4*b1
         8

         1     2    4           3    3
      + ---*a12 *a14 *a4*b1)/(a1 *a12 *a14)
         8


         3    2    4                4    2              3    2
b13=( - ---*a1 *a14 *a4*b24 + 12*a12 *a15 *a4*b1 - 6*a12 *a14 *a15*a4*b1
         4

         3     2    4           3    2    2
      + ---*a12 *a14 *a4*b1)/(a1 *a12 *a14 )
         4


         3    2    4                  2    2              3            4
b12=( - ---*a1 *a14 *a4*b24 - 3*a1*a12 *a14 *a15*a4*b1 + ---*a1*a12*a14 *a4*b1
         4                                                4

              4    2              3    2              3     2    4           3
      + 12*a12 *a15 *a4*b1 - 6*a12 *a14 *a15*a4*b1 + ---*a12 *a14 *a4*b1)/(a1
                                                      4

       2    2
   *a12 *a14 )


         3        2               2              3         2
      - ---*a1*a14 *a4*b24 - 6*a12 *a15*a4*b1 + ---*a12*a14 *a4*b1
         2                                       2
b11=---------------------------------------------------------------
                                2
                              a1 *a12*a14


                           3     2
      - 6*a12*a15*a4*b1 + ---*a14 *a4*b1
                           2
b10=-------------------------------------
                     2
                   a1 *a14


        3        2                2                      2
     - ---*a1*a14 *a4*b24 - 12*a12 *a15*a4*b1 + 3*a12*a14 *a4*b1
        2
b9=--------------------------------------------------------------
                              2
                            a1 *a12*a14


b8=

  1        2          1        2               2              3         2
 ---*a1*a14 *a4*b1 - ---*a1*a14 *a4*b24 - 3*a12 *a15*a4*b1 + ---*a12*a14 *a4*b1
  2                   2                                       4
--------------------------------------------------------------------------------
                                    2
                                  a1 *a12*a14


    a4*b1 - a4*b24
b7=----------------
          a1


    3*a4*b1
b6=---------
      a1


b5=0


          2    2               2           3     4
    12*a12 *a15 *b1 - 6*a12*a14 *a15*b1 + ---*a14 *b1
                                           4
b4=---------------------------------------------------
                          2    2
                        a1 *a14


                       3     2
     - 6*a12*a15*b1 + ---*a14 *b1
                       2
b3=-------------------------------
               a1*a14


                       3     2
     - 6*a12*a15*b1 + ---*a14 *b1
                       2
b2=-------------------------------
               a1*a14


      1        2
     ---*a15*a4
      4
a19=-------------
           2
         a1


     a15*a4
a18=--------
       a1


         1               1
      - ---*a1*a14*a4 + ---*a12*a14*a4
         2               2
a17=-----------------------------------
                  a1*a12


      1
     ---*a14*a4
      2
a16=------------
         a1


         1            1
      - ---*a1*a14 + ---*a12*a14
         2            2
a13=-----------------------------
                 a12


         1        3
      - ---*a15*a4
         4
a11=----------------
            3
          a1


              2
      - a15*a4
a10=------------
          2
        a1


     1        2   2        2       2    1         2   2
    ---*a1*a14 *a4  - 2*a12 *a15*a4  - ---*a12*a14 *a4
     2                                  2
a9=-----------------------------------------------------
                          2
                        a1 *a12*a14


     - a15*a4
a8=-----------
       a1


     - 4*a12*a15*a4
a7=-----------------
        a1*a14


     1        2           2
    ---*a1*a14 *a4 - 2*a12 *a15*a4
     2
a6=--------------------------------
              a1*a12*a14


    a1*a4 - a12*a4
a5=----------------
          a1


a3=0


                      2
     - 4*a12*a15 + a14
a2=---------------------
            a14

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:

 b24,b1,a4,a15,a14,a12,a1

Relevance for the application:

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

               4            1              3    2
df(u,t)=(u  *a1 *a12*a14 + ---*u *f(v,v)*a1 *a14 *a4
          2x                2   x

                          2    2                 3    2
          - 2*u *f(v,v)*a1 *a12 *a15*a4 - 4*u *a1 *a12 *a15*u
               x                             x

                 3        2                3
          + u *a1 *a12*a14 *u + f(v ,v )*a1 *a12*a14*a4
             x                     x  x

                       3                         2    2
          + f(v,v  )*a1 *a12*a14*a4 - f(v,v  )*a1 *a12 *a14*a4
                 2x                        2x

             1                   2    2   2                          2       2
          + ---*f(v,v )*f(v,v)*a1 *a14 *a4  - 2*f(v,v )*f(v,v)*a1*a12 *a15*a4
             2       x                               x

             1                           2   2               2    2
          - ---*f(v,v )*f(v,v)*a1*a12*a14 *a4  - 4*f(v,v )*a1 *a12 *a15*a4*u
             2       x                                  x

             1        3               3         2                  2
          - ---*f(v,v) *a12*a14*a15*a4  - f(v,v) *a1*a12*a14*a15*a4 *u
             4

                     2                 2     3
          - f(v,v)*a1 *a12*a14*a15*a4*u )/(a1 *a12*a14)

             1       3          1       2                   2    2
df(v,t)=( - ---*u *a1 *a14*v + ---*u *a1 *a12*a14*v + v  *a1 *a12
             2   x              2   x                  2x

             1                                 2
          + ---*v *f(v,v)*a1*a12*a14*a4 + v *a1 *a12*a14*u
             2   x                         x

             1            2             1
          - ---*f(v,v )*a1 *a14*a4*v + ---*f(v,v )*a1*a12*a14*a4*v
             2       x                  2       x

             1        2           2
          + ---*f(v,v) *a12*a15*a4 *v + f(v,v)*a1*a12*a15*a4*u*v
             4

              2          2       2
          + a1 *a12*a15*u *v)/(a1 *a12)

               6    3    2       1               5    2    3
df(u,s)=(u  *a1 *a12 *a14 *b1 + ---*u  *f(v,v)*a1 *a12 *a14 *a4*b1
          3x                     2   2x

             1               5    2    3
          - ---*u  *f(v,v)*a1 *a12 *a14 *a4*b24
             2   2x

                           4    4
          - 3*u  *f(v,v)*a1 *a12 *a14*a15*a4*b1
               2x

             3               4    3    3                 5    4
          + ---*u  *f(v,v)*a1 *a12 *a14 *a4*b1 - 6*u  *a1 *a12 *a14*a15*b1*u
             4   2x                                 2x

             3        5    3    3            2   5    4
          + ---*u  *a1 *a12 *a14 *b1*u - 6*u  *a1 *a12 *a14*a15*b1
             2   2x                         x

             3    2   5    3    3       3               5    2    3
          + ---*u  *a1 *a12 *a14 *b1 - ---*u *f(v,v )*a1 *a12 *a14 *a4*b24
             2   x                      2   x      x

                            4    4
          - 12*u *f(v,v )*a1 *a12 *a14*a15*a4*b1
                x      x

                           4    3    3
          + 3*u *f(v,v )*a1 *a12 *a14 *a4*b1
               x      x

             3           2   4        4   2
          - ---*u *f(v,v) *a1 *a12*a14 *a4 *b24
             8   x

             3           2   3    3    2       2
          - ---*u *f(v,v) *a1 *a12 *a14 *a15*a4 *b1
             2   x

             3           2   3    2    4   2
          + ---*u *f(v,v) *a1 *a12 *a14 *a4 *b1
             8   x

                       2   2    5    2   2
          + 3*u *f(v,v) *a1 *a12 *a15 *a4 *b1
               x

             3           2   2    4    2       2
          - ---*u *f(v,v) *a1 *a12 *a14 *a15*a4 *b1
             2   x

             3            2   2    3    4   2
          + ----*u *f(v,v) *a1 *a12 *a14 *a4 *b1
             16   x

             3              5        4
          - ---*u *f(v,v)*a1 *a12*a14 *a4*b24*u
             4   x

                          4    3    2
          - 3*u *f(v,v)*a1 *a12 *a14 *a15*a4*b1*u
               x

             3              4    2    4
          + ---*u *f(v,v)*a1 *a12 *a14 *a4*b1*u
             4   x

                           3    5    2
          + 12*u *f(v,v)*a1 *a12 *a15 *a4*b1*u
                x

                          3    4    2
          - 6*u *f(v,v)*a1 *a12 *a14 *a15*a4*b1*u
               x

             3              3    3    4                   4    5    2     2
          + ---*u *f(v,v)*a1 *a12 *a14 *a4*b1*u + 12*u *a1 *a12 *a15 *b1*u
             4   x                                    x

                   4    4    2         2    3       4    3    4     2
          - 6*u *a1 *a12 *a14 *a15*b1*u  + ---*u *a1 *a12 *a14 *b1*u
               x                            4   x

                          5    3    2
          + 3*f(v ,v  )*a1 *a12 *a14 *a4*b1
                 x  2x

             1                    4    2    3   2
          + ---*f(v ,v )*f(v,v)*a1 *a12 *a14 *a4 *b1
             2     x  x

             1                    4    2    3   2
          - ---*f(v ,v )*f(v,v)*a1 *a12 *a14 *a4 *b24
             2     x  x

                                3    4           2
          - 3*f(v ,v )*f(v,v)*a1 *a12 *a14*a15*a4 *b1
                 x  x

             3                    3    3    3   2
          + ---*f(v ,v )*f(v,v)*a1 *a12 *a14 *a4 *b1
             4     x  x

                         4    4
          - 6*f(v ,v )*a1 *a12 *a14*a15*a4*b1*u
                 x  x

             3             4    3    3                      5    3    2
          + ---*f(v ,v )*a1 *a12 *a14 *a4*b1*u + f(v,v  )*a1 *a12 *a14 *a4*b1
             2     x  x                               3x

                       5    3    2
          - f(v,v  )*a1 *a12 *a14 *a4*b24
                 3x

             1                    4    2    3   2
          + ---*f(v,v  )*f(v,v)*a1 *a12 *a14 *a4 *b1
             2       2x

             5                    4    2    3   2
          - ---*f(v,v  )*f(v,v)*a1 *a12 *a14 *a4 *b24
             4       2x

                                3    4           2
          - 3*f(v,v  )*f(v,v)*a1 *a12 *a14*a15*a4 *b1
                   2x

             3                    3    3    3   2
          + ---*f(v,v  )*f(v,v)*a1 *a12 *a14 *a4 *b1
             4       2x

             3             5    2    3
          - ---*f(v,v  )*a1 *a12 *a14 *a4*b24*u
             2       2x

                         4    4
          - 6*f(v,v  )*a1 *a12 *a14*a15*a4*b1*u
                   2x

             3             4    3    3
          + ---*f(v,v  )*a1 *a12 *a14 *a4*b1*u
             2       2x

             3         2   4    2    3   2
          - ---*f(v,v ) *a1 *a12 *a14 *a4 *b24
             2       x

                     2   3    4           2
          - 6*f(v,v ) *a1 *a12 *a14*a15*a4 *b1
                   x

             3         2   3    3    3   2
          + ---*f(v,v ) *a1 *a12 *a14 *a4 *b1
             2       x

             9                 2   3        4   3
          - ----*f(v,v )*f(v,v) *a1 *a12*a14 *a4 *b24
             16       x

             3                2   2    3    2       3
          - ---*f(v,v )*f(v,v) *a1 *a12 *a14 *a15*a4 *b1
             2       x

             3                2   2    2    4   3
          + ---*f(v,v )*f(v,v) *a1 *a12 *a14 *a4 *b1
             8       x

                            2       5    2   3
          + 3*f(v,v )*f(v,v) *a1*a12 *a15 *a4 *b1
                   x

             3                2       4    2       3
          - ---*f(v,v )*f(v,v) *a1*a12 *a14 *a15*a4 *b1
             2       x

             3                 2       3    4   3
          + ----*f(v,v )*f(v,v) *a1*a12 *a14 *a4 *b1
             16       x

             3                   4        4   2
          - ---*f(v,v )*f(v,v)*a1 *a12*a14 *a4 *b24*u
             2       x

                               3    3    2       2
          - 3*f(v,v )*f(v,v)*a1 *a12 *a14 *a15*a4 *b1*u
                   x

             3                   3    2    4   2
          + ---*f(v,v )*f(v,v)*a1 *a12 *a14 *a4 *b1*u
             4       x

                                2    5    2   2
          + 12*f(v,v )*f(v,v)*a1 *a12 *a15 *a4 *b1*u
                    x

                               2    4    2       2
          - 6*f(v,v )*f(v,v)*a1 *a12 *a14 *a15*a4 *b1*u
                   x

             3                   2    3    4   2
          + ---*f(v,v )*f(v,v)*a1 *a12 *a14 *a4 *b1*u
             4       x

             3            5        4         2
          - ---*f(v,v )*a1 *a12*a14 *a4*b24*u
             4       x

                         3    5    2        2
          + 12*f(v,v )*a1 *a12 *a15 *a4*b1*u
                    x

                        3    4    2            2
          - 6*f(v,v )*a1 *a12 *a14 *a15*a4*b1*u
                   x

             3            3    3    4        2    1         4   2    5   4
          + ---*f(v,v )*a1 *a12 *a14 *a4*b1*u  - ----*f(v,v) *a1 *a14 *a4 *b24
             4       x                            64

             1        4    4        2   4       1        4    3    3       4
          + ---*f(v,v) *a12 *a14*a15 *a4 *b1 - ---*f(v,v) *a12 *a14 *a15*a4 *b1
             4                                  8

             1         4    2    5   4       3         3   3    5   3
          + ----*f(v,v) *a12 *a14 *a4 *b1 - ----*f(v,v) *a1 *a14 *a4 *b24*u
             64                              32

             3        3       4        2   3
          + ---*f(v,v) *a1*a12 *a14*a15 *a4 *b1*u
             2

             3        3       3    3       3
          - ---*f(v,v) *a1*a12 *a14 *a15*a4 *b1*u
             4

             3         3       2    5   3
          + ----*f(v,v) *a1*a12 *a14 *a4 *b1*u
             32

             3         2   4    5   2      2
          - ----*f(v,v) *a1 *a14 *a4 *b24*u
             16

                    2   2    4        2   2     2
          + 3*f(v,v) *a1 *a12 *a14*a15 *a4 *b1*u

             3        2   2    3    3       2     2
          - ---*f(v,v) *a1 *a12 *a14 *a15*a4 *b1*u
             2

             3         2   2    2    5   2     2    1           5    5         3
          + ----*f(v,v) *a1 *a12 *a14 *a4 *b1*u  - ---*f(v,v)*a1 *a14 *a4*b24*u
             16                                     8

                       3    4        2        3
          + 2*f(v,v)*a1 *a12 *a14*a15 *a4*b1*u

                     3    3    3            3
          - f(v,v)*a1 *a12 *a14 *a15*a4*b1*u

             1           3    2    5        3     6    3    2
          + ---*f(v,v)*a1 *a12 *a14 *a4*b1*u )/(a1 *a12 *a14 )
             8

             1        5    2    2         1        5    2    2
df(v,s)=( - ---*u  *a1 *a12 *a14 *b1*v + ---*u  *a1 *a12 *a14 *b24*v
             2   2x                       2   2x

             3          5    2    2        3              4        3
          + ---*u *v *a1 *a12 *a14 *b24 + ---*u *f(v,v)*a1 *a12*a14 *a4*b24*v
             2   x  x                      8   x

             3              3    3
          + ---*u *f(v,v)*a1 *a12 *a14*a15*a4*b1*v
             2   x

             3              3    2    3            3       5        3
          - ---*u *f(v,v)*a1 *a12 *a14 *a4*b1*v + ---*u *a1 *a12*a14 *b24*u*v
             8   x                                 4   x

                   4    3                   3       4    2    3
          + 3*u *a1 *a12 *a14*a15*b1*u*v - ---*u *a1 *a12 *a14 *b1*u*v
               x                            4   x

                  5    3            3               4    2    2
          + v  *a1 *a12 *a14*b24 + ---*v  *f(v,v)*a1 *a12 *a14 *a4*b24
             3x                     4   2x

             3        5    2    2          3               4    2    2
          + ---*v  *a1 *a12 *a14 *b24*u + ---*v *f(v,v )*a1 *a12 *a14 *a4*b24
             2   2x                        2   x      x

             3            2   3        3   2
          + ----*v *f(v,v) *a1 *a12*a14 *a4 *b24
             16   x

             3              4        3             3       5        3      2
          + ---*v *f(v,v)*a1 *a12*a14 *a4*b24*u + ---*v *a1 *a12*a14 *b24*u
             4   x                                 4   x

             1             4    2    2
          - ---*f(v ,v )*a1 *a12 *a14 *a4*b1*v
             2     x  x

             1             4    2    2
          + ---*f(v ,v )*a1 *a12 *a14 *a4*b24*v
             2     x  x

             1             4    2    2
          - ---*f(v,v  )*a1 *a12 *a14 *a4*b1*v
             2       2x

             1             4    2    2
          + ---*f(v,v  )*a1 *a12 *a14 *a4*b24*v
             2       2x

             3                   3        3   2
          + ---*f(v,v )*f(v,v)*a1 *a12*a14 *a4 *b24*v
             8       x

             3                   2    3           2
          + ---*f(v,v )*f(v,v)*a1 *a12 *a14*a15*a4 *b1*v
             2       x

             3                   2    2    3   2
          - ---*f(v,v )*f(v,v)*a1 *a12 *a14 *a4 *b1*v
             8       x

             3            4        3
          + ---*f(v,v )*a1 *a12*a14 *a4*b24*u*v
             4       x

                        3    3
          + 3*f(v,v )*a1 *a12 *a14*a15*a4*b1*u*v
                   x

             3            3    2    3
          - ---*f(v,v )*a1 *a12 *a14 *a4*b1*u*v
             4       x

             1         3   2    4   3          1        3    4    2   3
          + ----*f(v,v) *a1 *a14 *a4 *b24*v - ---*f(v,v) *a12 *a15 *a4 *b1*v
             64                                4

             1        3    3    2       3         1         3    2    4   3
          + ---*f(v,v) *a12 *a14 *a15*a4 *b1*v - ----*f(v,v) *a12 *a14 *a4 *b1*v
             8                                    64

             3         2   3    4   2
          + ----*f(v,v) *a1 *a14 *a4 *b24*u*v
             32

             3        2       4    2   2
          - ---*f(v,v) *a1*a12 *a15 *a4 *b1*u*v
             2

             3        2       3    2       2
          + ---*f(v,v) *a1*a12 *a14 *a15*a4 *b1*u*v
             4

             3         2       2    4   2
          - ----*f(v,v) *a1*a12 *a14 *a4 *b1*u*v
             32

             3            4    4         2                2    4    2        2
          + ----*f(v,v)*a1 *a14 *a4*b24*u *v - 3*f(v,v)*a1 *a12 *a15 *a4*b1*u *v
             16

             3           2    3    2            2
          + ---*f(v,v)*a1 *a12 *a14 *a15*a4*b1*u *v
             2

             3            2    2    4        2      1    5    4      3
          - ----*f(v,v)*a1 *a12 *a14 *a4*b1*u *v + ---*a1 *a14 *b24*u *v
             16                                     8

                3    4    2     3       3    3    2         3
          - 2*a1 *a12 *a15 *b1*u *v + a1 *a12 *a14 *a15*b1*u *v

             1    3    2    4     3       5    3
          - ---*a1 *a12 *a14 *b1*u *v)/(a1 *a12 *a14)
             8