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$