Solution 10 to problem over
Expressions |
Parameters |
Inequalities |
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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=r6345
r657=0
r660=2*r6345
r662=0
r663=r6345
r667=0
r670=0
r672=0
r673=0
r676=r679
r678=0
r681=0
r682=0
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= - r6254
r6128=0
r6129= - r6254
r6132=0
r6134=0
r6135=0
r6137=0
r6139=0
r6140=0
r6141=0
r6142=r6345
r6143=0
r6144=2*r6345
r6145=0
r6146=0
r6147=0
r6148=0
r6149= - 2*r6345
r6150=0
r6151=0
r6152=0
r6153=0
r6154= - 2*r6345
r6158=0
r6161=0
r6163=0
r6164=0
a11*r6254 + 2*b12*kap*r6345 + b12*r679
r6167=----------------------------------------
b12
r6169=0
1
a11*r6254 + 2*b12*kap*r6345 - ---*b12*r6295 + b12*r679
2
r6170=--------------------------------------------------------
b12
r6172=0
r6173=0
- a11*r6138 + b12*kap*r679
r6174=-----------------------------
b12
r6175=0
r6176=0
r6177=0
r6178=0
4*a11*r6345
r6179=-------------
b12
r6180=0
4*a11*r6345 - b12*r6254
r6181=-------------------------
b12
r6182=0
r6183=0
r6184=0
r6187=0
r6189=0
r6190=0
r6192=0
a11*r6295 - 2*a11*r679 - b12*kap*r6254
r6193=----------------------------------------
b12
r6194=0
2
- 2*a11 *r6345
r6195=-----------------
2
b12
r6196=0
2 2
- 2*a11 *r6345 + a11*b12*r6254 + 2*b12 *kap*r6345
r6197=----------------------------------------------------
2
b12
r6198=0
r6199=0
2 2
10*a11 *r6345 - 2*b12 *kap*r6345
r6200=----------------------------------
2
b12
r6202=0
r6203=0
1 2 2 2 2
- ---*a11 *r6295 + a11 *r679 + a11*b12*kap*r6254 + b12 *kap *r6345
2
r6204=---------------------------------------------------------------------
2
b12
r6205=0
r6206=0
3 2
- 12*a11 *r6345 + 4*a11*b12 *kap*r6345
r6207=-----------------------------------------
3
b12
r6208=0
4 2 2
4*a11 *r6345 - 2*a11 *b12 *kap*r6345
r6209=--------------------------------------
4
b12
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=r6254
r6252=0
r6255=0
r6258=0
r6260=0
r6261=0
r6263= - r6138
r6264=0
r6265=0
r6266=0
r6267=0
r6268=0
r6269=0
r6270=0
r6271=0
r6272=6*r6345
r6273=0
r6274=8*r6345
r6275=0
r6276=0
r6277=0
r6278=0
r6279=8*r6345
r6280=0
r6284=0
r6287=0
r6289=0
r6290=0
r6293=0
r6296=0
r6298=0
r6299=0
r6300=0
r6301=0
- 4*a11*r6345
r6302=----------------
b12
r6303=0
- 4*a11*r6345 + b12*r6254
r6304=----------------------------
b12
r6305=0
r6306=0
r6307=0
r6308=0
8*a11*r6345 - 2*b12*r6254
r6309=---------------------------
b12
r6310=0
r6313=0
r6315=0
r6316=0
- a11*r6295 + 2*a11*r679 + b12*kap*r6254
r6318=-------------------------------------------
b12
r6319=0
r6320=0
r6321=0
r6322=0
r6323=0
r6324=0
2 2
- 24*a11 *r6345 + 2*a11*b12*r6254 + 8*b12 *kap*r6345
r6325=-------------------------------------------------------
2
b12
r6326=0
r6328=0
r6329=0
r6330=0
r6331=0
3 2
12*a11 *r6345 - 4*a11*b12 *kap*r6345
r6332=--------------------------------------
3
b12
r6333=0
r6334=0
r6335=0
r6336=0
r6337=0
r6338= - 2*r6345
r6339=0
r6340= - 2*r6345
r6341=0
r6342=0
r6343=0
r6344=0
r6346=0
r6348=0
r6349=0
r6350=2*r6345
r6354=0
r6357=0
r6359=0
r6360=0
1
a11*r6254 + 2*b12*kap*r6345 - ---*b12*r6295 + b12*r679
2
r6363=--------------------------------------------------------
b12
r6365=0
a11*r6254 + 2*b12*kap*r6345 + b12*r679
r6366=----------------------------------------
b12
r6368=0
r6369=0
- a11*r6138 + b12*kap*r679
r6370=-----------------------------
b12
r6371=0
r6372=0
r6373=0
r6374=0
4*a11*r6345
r6375=-------------
b12
r6376=0
- 8*a11*r6345 + 2*b12*r6254
r6377=------------------------------
b12
r6378=0
r6379=0
4*a11*r6345 - b12*r6254
r6380=-------------------------
b12
r6383=0
r6385=0
r6386=0
r6388=0
a11*r6295 - 2*a11*r679 - b12*kap*r6254
r6389=----------------------------------------
b12
r6390=0
2
- 4*a11 *r6345
r6391=-----------------
2
b12
r6392=0
2
8*a11 *r6345 + a11*b12*r6254
r6393=------------------------------
2
b12
r6394=0
r6395=0
2
8*a11 *r6345 + a11*b12*r6254
r6396=------------------------------
2
b12
r6398=0
r6399=0
2 2 2 2
- a11 *r6295 + 2*a11 *r679 + 2*a11*b12*kap*r6254 + 2*b12 *kap *r6345
r6400=-----------------------------------------------------------------------
2
b12
r6401=0
r6402=0
3 2
- 24*a11 *r6345 + 8*a11*b12 *kap*r6345
r6403=-----------------------------------------
3
b12
r6404=0
4 2 2
12*a11 *r6345 - 6*a11 *b12 *kap*r6345
r6405=---------------------------------------
4
b12
r6406=0
- 4*a11*r6345
r6407=----------------
b12
r6408=0
r6410=0
r6411=0
r6412=0
r6413=0
- 4*a11*r6345 + b12*r6254
r6414=----------------------------
b12
r6415=0
r6418=0
r6420=0
r6421=0
- a11*r6295 + 2*a11*r679 + b12*kap*r6254
r6423=-------------------------------------------
b12
r6424=0
r6425=0
r6426=0
r6427=0
r6428=0
r6429=0
2 2
- 24*a11 *r6345 + 2*a11*b12*r6254 + 8*b12 *kap*r6345
r6430=-------------------------------------------------------
2
b12
r6431=0
r6433=0
r6434=0
r6435=0
r6436=0
3 2
24*a11 *r6345 - 8*a11*b12 *kap*r6345
r6437=--------------------------------------
3
b12
r6438=0
r6439=0
r6440=0
2
- 2*a11 *r6345
r6441=-----------------
2
b12
r6442=0
2 2
10*a11 *r6345 - 2*b12 *kap*r6345
r6443=----------------------------------
2
b12
r6444=0
r6445=0
2 2
- 2*a11 *r6345 + a11*b12*r6254 + 2*b12 *kap*r6345
r6446=----------------------------------------------------
2
b12
r6448=0
r6449=0
1 2 2 2 2
- ---*a11 *r6295 + a11 *r679 + a11*b12*kap*r6254 + b12 *kap *r6345
2
r6450=---------------------------------------------------------------------
2
b12
r6451=0
r6452=0
3 2
- 12*a11 *r6345 + 4*a11*b12 *kap*r6345
r6453=-----------------------------------------
3
b12
r6454=0
4 2 2
12*a11 *r6345 - 6*a11 *b12 *kap*r6345
r6455=---------------------------------------
4
b12
r6456=0
3 2
12*a11 *r6345 - 4*a11*b12 *kap*r6345
r6457=--------------------------------------
3
b12
r6458=0
r6459=0
r6460=0
4 2 2
4*a11 *r6345 - 2*a11 *b12 *kap*r6345
r6461=--------------------------------------
4
b12
a23=0
a22=a11
a13=0
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:
r683, r679, r6138, r6254, r6295, r6345, a11, a33, 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.
{b12,a11 - 2*a33}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs the following 6 first integrals:
6 4 2 2 5 3 3
FI=u1 *(4*a11 - 2*a11 *b12 *kap) + u1 *v2*(12*a11 *b12 - 4*a11*b12 *kap)
4 2 4 2 2
+ u1 *u2 *(12*a11 - 6*a11 *b12 *kap)
4 3 3 4 2 4 2
+ u1 *u2*v1*( - 12*a11 *b12 + 4*a11*b12 *kap) + u1 *u3 *b12 *kap
4 2 2 2 4
+ u1 *v1 *( - 2*a11 *b12 + 2*b12 *kap)
4 2 2 2 4 4 2 2 2
+ u1 *v2 *(10*a11 *b12 - 2*b12 *kap) - 2*u1 *v3 *a11 *b12
3 2 3 3
+ u1 *u2 *v2*(24*a11 *b12 - 8*a11*b12 *kap)
3 2 2 4 3 2 3
+ u1 *u2*v1*v2*( - 24*a11 *b12 + 8*b12 *kap) - 4*u1 *v1 *v2*a11*b12
3 2 3 2 4 4 2 2
- 4*u1 *v2*v3 *a11*b12 + u1 *u2 *(12*a11 - 6*a11 *b12 *kap)
2 3 3 3 2 2 2 4 2
+ u1 *u2 *v1*( - 24*a11 *b12 + 8*a11*b12 *kap) + 2*u1 *u2 *u3 *b12 *kap
2 2 2 2 2 2 2 2 2 2
+ 8*u1 *u2 *v1 *a11 *b12 + 8*u1 *u2 *v2 *a11 *b12
2 2 2 2 2 2 3 3 2 2 3
- 4*u1 *u2 *v3 *a11 *b12 + 4*u1 *u2*v1 *a11*b12 - 8*u1 *u2*v1*v2 *a11*b12
2 2 3 2 2 2 4 2 2 2 4
+ 4*u1 *u2*v1*v3 *a11*b12 + 2*u1 *u3 *v1 *b12 *kap + 2*u1 *u3 *v2 *b12 *kap
2 4 4 2 2 2 4 2 4 4 2 2 2 4
+ 2*u1 *v1 *b12 + u1 *v1 *v3 *b12 - 2*u1 *v2 *b12 - 2*u1 *v2 *v3 *b12
4 3 3
+ u1*u2 *v2*(12*a11 *b12 - 4*a11*b12 *kap)
3 2 2 4 2 2 3
+ u1*u2 *v1*v2*( - 24*a11 *b12 + 8*b12 *kap) + 8*u1*u2 *v1 *v2*a11*b12
2 3 3 2 2 3 3 4
- 4*u1*u2 *v2 *a11*b12 - 4*u1*u2 *v2*v3 *a11*b12 + 8*u1*u2*v1 *v2*b12
3 4 2 4
+ 8*u1*u2*v1*v2 *b12 + 6*u1*u2*v1*v2*v3 *b12
6 4 2 2 5 3 3
+ u2 *(4*a11 - 2*a11 *b12 *kap) + u2 *v1*( - 12*a11 *b12 + 4*a11*b12 *kap)
4 2 4 2 4 2 2 2 4
+ u2 *u3 *b12 *kap + u2 *v1 *(10*a11 *b12 - 2*b12 *kap)
4 2 2 2 4 4 2 2 2
+ u2 *v2 *( - 2*a11 *b12 + 2*b12 *kap) - 2*u2 *v3 *a11 *b12
3 2 3 3 2 3 2 2 2 4
+ 4*u2 *v1*v2 *a11*b12 + 4*u2 *v1*v3 *a11*b12 + 2*u2 *u3 *v1 *b12 *kap
2 2 2 4 2 4 4 2 2 2 4
+ 2*u2 *u3 *v2 *b12 *kap - 2*u2 *v1 *b12 - 2*u2 *v1 *v3 *b12
2 4 4 2 2 2 4 2 4 4 2 2 2 4
+ 2*u2 *v2 *b12 + u2 *v2 *v3 *b12 + u3 *v1 *b12 + 2*u3 *v1 *v2 *b12
2 4 4
+ u3 *v2 *b12
5 5 2 4 5 2
{HAM,FI} = - 4*u1 *u3*v1*b12 *kap - 4*u1 *u2*u3*v2*b12 *kap
4 2 5 2 4 4
- 4*u1 *u3 *v3*b12 *kap + 8*u1 *u3*v1*v2*a11*b12 *kap
4 2 5 3 2 5 2
- 2*u1 *v1 *v3*b12 *kap - 8*u1 *u2 *u3*v1*b12 *kap
3 2 4 3 2 4
- 8*u1 *u2*u3*v1 *a11*b12 *kap + 8*u1 *u2*u3*v2 *a11*b12 *kap
3 5 3 2 4
- 4*u1 *u2*v1*v2*v3*b12 *kap + 8*u1 *u3 *v2*v3*a11*b12 *kap
3 2 5 3 2 4
- 2*u1 *u3*v1*v3 *b12 *kap + 4*u1 *v1 *v2*v3*a11*b12
2 3 5 2 2 2 2 5 2
- 8*u1 *u2 *u3*v2*b12 *kap - 8*u1 *u2 *u3 *v3*b12 *kap
2 2 2 5 2 2 2 5
- 2*u1 *u2 *v1 *v3*b12 *kap - 2*u1 *u2 *v2 *v3*b12 *kap
2 2 4 2 2 5
- 8*u1 *u2*u3 *v1*v3*a11*b12 *kap - 2*u1 *u2*u3*v2*v3 *b12 *kap
2 3 4 2 2 4
- 4*u1 *u2*v1 *v3*a11*b12 + 8*u1 *u2*v1*v2 *v3*a11*b12
2 3 4 2 3 4
+ 8*u1 *u3*v1 *v2*a11*b12 + 8*u1 *u3*v1*v2 *a11*b12
2 2 4 2 4 5
+ 4*u1 *u3*v1*v2*v3 *a11*b12 + 2*u1 *v1 *v3*b12
2 2 2 5 4 5 2
+ 2*u1 *v1 *v2 *v3*b12 - 4*u1*u2 *u3*v1*b12 *kap
3 2 4 3 2 4
- 8*u1*u2 *u3*v1 *a11*b12 *kap + 8*u1*u2 *u3*v2 *a11*b12 *kap
3 5 2 2 4
- 4*u1*u2 *v1*v2*v3*b12 *kap + 8*u1*u2 *u3 *v2*v3*a11*b12 *kap
2 2 5 2 2 4
- 2*u1*u2 *u3*v1*v3 *b12 *kap - 8*u1*u2 *v1 *v2*v3*a11*b12
2 3 4 4 4
+ 4*u1*u2 *v2 *v3*a11*b12 - 8*u1*u2*u3*v1 *a11*b12
2 2 4 4 4
- 4*u1*u2*u3*v1 *v3 *a11*b12 + 8*u1*u2*u3*v2 *a11*b12
2 2 4 3 5
+ 4*u1*u2*u3*v2 *v3 *a11*b12 + 4*u1*u2*v1 *v2*v3*b12
3 5 2 2 4
+ 4*u1*u2*v1*v2 *v3*b12 + 8*u1*u3 *v1 *v2*v3*a11*b12
2 3 4 5 5 3 2 5
+ 8*u1*u3 *v2 *v3*a11*b12 + 4*u1*u3*v1 *b12 + 8*u1*u3*v1 *v2 *b12
3 2 5 4 5
+ 2*u1*u3*v1 *v3 *b12 + 4*u1*u3*v1*v2 *b12
2 2 5 5 5 2
+ 2*u1*u3*v1*v2 *v3 *b12 - 4*u2 *u3*v2*b12 *kap
4 2 5 2 4 4
- 4*u2 *u3 *v3*b12 *kap - 8*u2 *u3*v1*v2*a11*b12 *kap
4 2 5 3 2 4
- 2*u2 *v2 *v3*b12 *kap - 8*u2 *u3 *v1*v3*a11*b12 *kap
3 2 5 3 2 4
- 2*u2 *u3*v2*v3 *b12 *kap - 4*u2 *v1*v2 *v3*a11*b12
2 3 4 2 3 4
- 8*u2 *u3*v1 *v2*a11*b12 - 8*u2 *u3*v1*v2 *a11*b12
2 2 4 2 2 2 5
- 4*u2 *u3*v1*v2*v3 *a11*b12 + 2*u2 *v1 *v2 *v3*b12
2 4 5 2 3 4
+ 2*u2 *v2 *v3*b12 - 8*u2*u3 *v1 *v3*a11*b12
2 2 4 4 5
- 8*u2*u3 *v1*v2 *v3*a11*b12 + 4*u2*u3*v1 *v2*b12
2 3 5 2 2 5 5 5
+ 8*u2*u3*v1 *v2 *b12 + 2*u2*u3*v1 *v2*v3 *b12 + 4*u2*u3*v2 *b12
3 2 5 2 4 5 2 2 2 5
+ 2*u2*u3*v2 *v3 *b12 + 4*u3 *v1 *v3*b12 + 8*u3 *v1 *v2 *v3*b12
2 4 5
+ 4*u3 *v2 *v3*b12
1 4 2 2 3 2 2 2 2 2
FI= - ---*u1 *u3 *a11 - u1 *u3 *v2*a11*b12 - u1 *u2 *u3 *a11
2
2 2 1 2 2 2 2 2 2
+ u1 *u2*u3 *v1*a11*b12 - ---*u1 *u3 *v2 *b12 - u1*u2 *u3 *v2*a11*b12
2
2 2 1 4 2 2 3 2
+ u1*u2*u3 *v1*v2*b12 - ---*u2 *u3 *a11 + u2 *u3 *v1*a11*b12
2
1 2 2 2 2
- ---*u2 *u3 *v1 *b12
2
{HAM,FI} = 0
4 2 4 2 3 3 2
FI=u1 *u3 *a11*kap + u1 *v1 *a11 + 2*u1 *u2*v1*v2*a11 + u1 *u3 *v2*b12*kap
3 2 2 2 2 2 2 2 2 2 2
+ u1 *v1 *v2*b12 + 2*u1 *u2 *u3 *a11*kap + u1 *u2 *v1 *a11 + u1 *u2 *v2 *a11
2 2 2 3 2 2
- u1 *u2*u3 *v1*b12*kap - u1 *u2*v1 *b12 + 2*u1 *u2*v1*v2 *b12
2 2 2 2 2 2 3
+ u1 *u3 *v1 *a11 + u1 *u3 *v2 *a11 + 2*u1*u2 *v1*v2*a11
2 2 2 2 2 3
+ u1*u2 *u3 *v2*b12*kap - 2*u1*u2 *v1 *v2*b12 + u1*u2 *v2 *b12
2 2 2 3 4 2 4 2
+ u1*u3 *v1 *v2*b12 + u1*u3 *v2 *b12 + u2 *u3 *a11*kap + u2 *v2 *a11
3 2 3 2 2 2 2 2 2 2
- u2 *u3 *v1*b12*kap - u2 *v1*v2 *b12 + u2 *u3 *v1 *a11 + u2 *u3 *v2 *a11
2 3 2 2
- u2*u3 *v1 *b12 - u2*u3 *v1*v2 *b12
5 4
{HAM,FI} = - 2*u1 *u3*v1*a11*b12*kap - 2*u1 *u2*u3*v2*a11*b12*kap
4 2 4 2 2
- 2*u1 *u3 *v3*a11*b12*kap + u1 *u3*v1*v2*(4*a11 - 2*b12 *kap)
3 2
- 4*u1 *u2 *u3*v1*a11*b12*kap
3 2 2 2
+ u1 *u2*u3*v1 *( - 4*a11 + 2*b12 *kap)
3 2 2 2
+ u1 *u2*u3*v2 *(4*a11 - 2*b12 *kap)
3 2 2 2 3 3
+ u1 *u3 *v2*v3*(4*a11 - 2*b12 *kap) + 2*u1 *u3*v1 *a11*b12
3 2 2 3
+ 6*u1 *u3*v1*v2 *a11*b12 - 4*u1 *u2 *u3*v2*a11*b12*kap
2 2 2
- 4*u1 *u2 *u3 *v3*a11*b12*kap
2 2 2 2
+ u1 *u2*u3 *v1*v3*( - 4*a11 + 2*b12 *kap)
2 2 2 3
- 6*u1 *u2*u3*v1 *v2*a11*b12 + 6*u1 *u2*u3*v2 *a11*b12
2 2 2 2 2 2
+ 2*u1 *u3 *v1 *v3*a11*b12 + 6*u1 *u3 *v2 *v3*a11*b12
2 3 2 2 3 2
+ 2*u1 *u3*v1 *v2*b12 + 2*u1 *u3*v1*v2 *b12
4
- 2*u1*u2 *u3*v1*a11*b12*kap
3 2 2 2
+ u1*u2 *u3*v1 *( - 4*a11 + 2*b12 *kap)
3 2 2 2
+ u1*u2 *u3*v2 *(4*a11 - 2*b12 *kap)
2 2 2 2 2 3
+ u1*u2 *u3 *v2*v3*(4*a11 - 2*b12 *kap) + 6*u1*u2 *u3*v1 *a11*b12
2 2 2
- 6*u1*u2 *u3*v1*v2 *a11*b12 - 8*u1*u2*u3 *v1*v2*v3*a11*b12
4 2 4 2
- 2*u1*u2*u3*v1 *b12 + 2*u1*u2*u3*v2 *b12
2 2 2 2 3 2
+ 2*u1*u3 *v1 *v2*v3*b12 + 2*u1*u3 *v2 *v3*b12
5 4 2
- 2*u2 *u3*v2*a11*b12*kap - 2*u2 *u3 *v3*a11*b12*kap
4 2 2
+ u2 *u3*v1*v2*( - 4*a11 + 2*b12 *kap)
3 2 2 2 3 2
+ u2 *u3 *v1*v3*( - 4*a11 + 2*b12 *kap) + 6*u2 *u3*v1 *v2*a11*b12
3 3 2 2 2
+ 2*u2 *u3*v2 *a11*b12 + 6*u2 *u3 *v1 *v3*a11*b12
2 2 2 2 3 2
+ 2*u2 *u3 *v2 *v3*a11*b12 - 2*u2 *u3*v1 *v2*b12
2 3 2 2 3 2
- 2*u2 *u3*v1*v2 *b12 - 2*u2*u3 *v1 *v3*b12
2 2 2
- 2*u2*u3 *v1*v2 *v3*b12
2 4 4 2 4 4
FI= - u1 *u3 *a11 - u1*u3 *v2*b12 - u2 *u3 *a11 + u2*u3 *v1*b12
{HAM,FI} = 0
4 2 2 3 2 2 2 2 2
FI=u1 *u3 *a11 + 2*u1 *u3 *v2*a11*b12 + 2*u1 *u2 *u3 *a11
2 2 2 4 2 2 2 2 2
- 2*u1 *u2*u3 *v1*a11*b12 + u1 *u3 *b12 *kap + u1 *u3 *v1 *b12
2 2 2 2 2 2 4 2 2
+ u1 *u3 *v2 *b12 + 2*u1*u2 *u3 *v2*a11*b12 + u2 *u3 *a11
3 2 2 4 2 2 2 2 2
- 2*u2 *u3 *v1*a11*b12 + u2 *u3 *b12 *kap + u2 *u3 *v1 *b12
2 2 2 2 4 2 2 4 2 2
+ u2 *u3 *v2 *b12 + u3 *v1 *b12 + u3 *v2 *b12
3 3 3 2 3 3
{HAM,FI} = - 2*u1 *u3 *v1*b12 *kap - 2*u1 *u2*u3 *v2*b12 *kap
2 4 3 2 3 2
- 2*u1 *u3 *v3*b12 *kap + 4*u1 *u3 *v1*v2*a11*b12
2 3 3 3 2 2
- 2*u1*u2 *u3 *v1*b12 *kap - 4*u1*u2*u3 *v1 *a11*b12
3 2 2 4 2
+ 4*u1*u2*u3 *v2 *a11*b12 + 4*u1*u3 *v2*v3*a11*b12
3 3 3 3 2 3 3 3 3
+ 2*u1*u3 *v1 *b12 + 2*u1*u3 *v1*v2 *b12 - 2*u2 *u3 *v2*b12 *kap
2 4 3 2 3 2
- 2*u2 *u3 *v3*b12 *kap - 4*u2 *u3 *v1*v2*a11*b12
4 2 3 2 3 3 3 3
- 4*u2*u3 *v1*v3*a11*b12 + 2*u2*u3 *v1 *v2*b12 + 2*u2*u3 *v2 *b12
4 2 3 4 2 3
+ 2*u3 *v1 *v3*b12 + 2*u3 *v2 *v3*b12
6
FI=u3
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u1*v2*b12 + u2**2*a11 - u2*v1*b12 + u3**2*a33$
FI=u1**6*(4*a11**4 - 2*a11**2*b12**2*kap) + u1**5*v2*(12*a11**3*b12 - 4*a11*b12
**3*kap) + u1**4*u2**2*(12*a11**4 - 6*a11**2*b12**2*kap) + u1**4*u2*v1*( - 12*
a11**3*b12 + 4*a11*b12**3*kap) + u1**4*u3**2*b12**4*kap**2 + u1**4*v1**2*( - 2*
a11**2*b12**2 + 2*b12**4*kap) + u1**4*v2**2*(10*a11**2*b12**2 - 2*b12**4*kap) -
2*u1**4*v3**2*a11**2*b12**2 + u1**3*u2**2*v2*(24*a11**3*b12 - 8*a11*b12**3*kap)
+ u1**3*u2*v1*v2*( - 24*a11**2*b12**2 + 8*b12**4*kap) - 4*u1**3*v1**2*v2*a11*b12
**3 - 4*u1**3*v2*v3**2*a11*b12**3 + u1**2*u2**4*(12*a11**4 - 6*a11**2*b12**2*kap
) + u1**2*u2**3*v1*( - 24*a11**3*b12 + 8*a11*b12**3*kap) + 2*u1**2*u2**2*u3**2*
b12**4*kap**2 + 8*u1**2*u2**2*v1**2*a11**2*b12**2 + 8*u1**2*u2**2*v2**2*a11**2*
b12**2 - 4*u1**2*u2**2*v3**2*a11**2*b12**2 + 4*u1**2*u2*v1**3*a11*b12**3 - 8*u1
**2*u2*v1*v2**2*a11*b12**3 + 4*u1**2*u2*v1*v3**2*a11*b12**3 + 2*u1**2*u3**2*v1**
2*b12**4*kap + 2*u1**2*u3**2*v2**2*b12**4*kap + 2*u1**2*v1**4*b12**4 + u1**2*v1
**2*v3**2*b12**4 - 2*u1**2*v2**4*b12**4 - 2*u1**2*v2**2*v3**2*b12**4 + u1*u2**4*
v2*(12*a11**3*b12 - 4*a11*b12**3*kap) + u1*u2**3*v1*v2*( - 24*a11**2*b12**2 + 8*
b12**4*kap) + 8*u1*u2**2*v1**2*v2*a11*b12**3 - 4*u1*u2**2*v2**3*a11*b12**3 - 4*
u1*u2**2*v2*v3**2*a11*b12**3 + 8*u1*u2*v1**3*v2*b12**4 + 8*u1*u2*v1*v2**3*b12**4
+ 6*u1*u2*v1*v2*v3**2*b12**4 + u2**6*(4*a11**4 - 2*a11**2*b12**2*kap) + u2**5*
v1*( - 12*a11**3*b12 + 4*a11*b12**3*kap) + u2**4*u3**2*b12**4*kap**2 + u2**4*v1
**2*(10*a11**2*b12**2 - 2*b12**4*kap) + u2**4*v2**2*( - 2*a11**2*b12**2 + 2*b12
**4*kap) - 2*u2**4*v3**2*a11**2*b12**2 + 4*u2**3*v1*v2**2*a11*b12**3 + 4*u2**3*
v1*v3**2*a11*b12**3 + 2*u2**2*u3**2*v1**2*b12**4*kap + 2*u2**2*u3**2*v2**2*b12**
4*kap - 2*u2**2*v1**4*b12**4 - 2*u2**2*v1**2*v3**2*b12**4 + 2*u2**2*v2**4*b12**4
+ u2**2*v2**2*v3**2*b12**4 + u3**2*v1**4*b12**4 + 2*u3**2*v1**2*v2**2*b12**4 +
u3**2*v2**4*b12**4$
FI= - 1/2*u1**4*u3**2*a11**2 - u1**3*u3**2*v2*a11*b12 - u1**2*u2**2*u3**2*a11**2
+ u1**2*u2*u3**2*v1*a11*b12 - 1/2*u1**2*u3**2*v2**2*b12**2 - u1*u2**2*u3**2*v2*
a11*b12 + u1*u2*u3**2*v1*v2*b12**2 - 1/2*u2**4*u3**2*a11**2 + u2**3*u3**2*v1*a11
*b12 - 1/2*u2**2*u3**2*v1**2*b12**2$
FI=u1**4*u3**2*a11*kap + u1**4*v1**2*a11 + 2*u1**3*u2*v1*v2*a11 + u1**3*u3**2*v2
*b12*kap + u1**3*v1**2*v2*b12 + 2*u1**2*u2**2*u3**2*a11*kap + u1**2*u2**2*v1**2*
a11 + u1**2*u2**2*v2**2*a11 - u1**2*u2*u3**2*v1*b12*kap - u1**2*u2*v1**3*b12 + 2
*u1**2*u2*v1*v2**2*b12 + u1**2*u3**2*v1**2*a11 + u1**2*u3**2*v2**2*a11 + 2*u1*u2
**3*v1*v2*a11 + u1*u2**2*u3**2*v2*b12*kap - 2*u1*u2**2*v1**2*v2*b12 + u1*u2**2*
v2**3*b12 + u1*u3**2*v1**2*v2*b12 + u1*u3**2*v2**3*b12 + u2**4*u3**2*a11*kap +
u2**4*v2**2*a11 - u2**3*u3**2*v1*b12*kap - u2**3*v1*v2**2*b12 + u2**2*u3**2*v1**
2*a11 + u2**2*u3**2*v2**2*a11 - u2*u3**2*v1**3*b12 - u2*u3**2*v1*v2**2*b12$
FI= - u1**2*u3**4*a11 - u1*u3**4*v2*b12 - u2**2*u3**4*a11 + u2*u3**4*v1*b12$
FI=u1**4*u3**2*a11**2 + 2*u1**3*u3**2*v2*a11*b12 + 2*u1**2*u2**2*u3**2*a11**2 -
2*u1**2*u2*u3**2*v1*a11*b12 + u1**2*u3**4*b12**2*kap + u1**2*u3**2*v1**2*b12**2
+ u1**2*u3**2*v2**2*b12**2 + 2*u1*u2**2*u3**2*v2*a11*b12 + u2**4*u3**2*a11**2 -
2*u2**3*u3**2*v1*a11*b12 + u2**2*u3**4*b12**2*kap + u2**2*u3**2*v1**2*b12**2 +
u2**2*u3**2*v2**2*b12**2 + u3**4*v1**2*b12**2 + u3**4*v2**2*b12**2$
FI=u3**6$