Solution 25 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
1
---*r6336
3
r60=-----------
kap
r61=0
r6336
r62=-------
kap
r63=0
r6336
r64=-------
kap
r65=0
1
---*r6336
3
r66=-----------
kap
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
r6336
r613=-------
kap
r614=0
2*r6336
r615=---------
kap
r616=0
r6336
r617=-------
kap
r618=0
r619=0
r620=0
r621=0
r6336
r622=-------
kap
r623=0
r6336
r624=-------
kap
r625=0
r626=0
1
---*r6336
3
r627=-----------
kap
r628=r6230
r629=0
r630=2*r6230
r631=0
r632=r6230
r633=0
r634=0
r635=0
r636=0
r637=0
r638=0
r639=2*r6230
r640=0
r641=2*r6230
r642=0
r643=0
r644=0
r645=0
r646=r6230
r647=0
r648=0
1 1
---*kap*r6243 + ---*r6165
4 2
r649=---------------------------
kap
r650=0
r6165
r651=-------
kap
r652=0
1 1
- ---*kap*r6243 + ---*r6165
4 2
r653=------------------------------
kap
r654=0
r655=0
r656=0
r657=0
r6165
r658=-------
kap
r659=0
1
- ---*kap*r6243 + r6165
2
r660=--------------------------
kap
r661=0
r662=0
1 1
- ---*kap*r6243 + ---*r6165
4 2
r663=------------------------------
kap
- 4*kap*r6230 + r6286 + 2*r6412 + 6*r671
r664=-------------------------------------------
6
r665=0
r666=r671
r667=0
r668=0
r669=0
r670=0
r672=0
r673=0
r6259 + 2*r676
r674=----------------
2
r675=0
r677=0
r678=0
r679=r676
r681=0
r682=0
r684=0
r685=r6230
r686=0
r687=2*r6230
r688=0
r689=r6230
1
- ---*r6302
2
r690=--------------
kap
r691=0
- r6302
r692=----------
kap
r693=0
1
- ---*r6302
2
r694=--------------
kap
r695=0
r696=2*r6230
r697=0
r698=2*r6230
- r6302
r699=----------
kap
r6100=0
- r6302
r6101=----------
kap
r6102=0
r6103=r6230
1
- ---*r6302
2
r6104=--------------
kap
r6105=0
r6106=r6243
r6107=0
r6108=r6243
r6109=0
r6110=0
r6111=0
r6112=0
r6113=0
r6114=0
r6115=r6243
r6116=0
r6117=0
r6118=0
r6119=0
r6120=0
- 4*kap*r6230 + r6286 + 2*r6412 + 2*r671
r6121=-------------------------------------------
2
r6122=0
r6123=r671
1
- ---*kap*r6356 + r6389
2
r6124=--------------------------
kap
r6125=0
r6389
r6126=-------
kap
r6127=0
r6128=r671
r6389
r6129=-------
kap
r6130=0
r6131=r6259
r6132=0
r6133= - r6257
r6134=0
r6135=0
r6136=0
r6137=r680
r6139=0
r6140=r6336
r6141=0
1
r6142=---*r6243 + 2*r6336
2
r6143=0
1
r6144=---*r6243 + r6336
2
r6145=0
r6146=0
r6147=0
r6148=0
r6150=0
1
r6151=r6149 + ---*r6243
2
r6152=0
r6153=0
r6154=r6149 - r6336
r6155=2*kap*r6230
r6156=0
r6286 + 2*r6412
r6157=-----------------
2
r6158=0
r6159=0
r6160= - r6356
r6161=0
r6162=r6412
r6163=0
r6164=0
r6166=0
1 1
r6167= - ---*kap*r6243 + r6165 + ---*r6259
2 2
r6168=0
r6169= - r6257
1 1 1
r6170= - ---*kap*r6243 + r6165 + ---*r6259 - ---*r6295
2 2 2
r6171=kap*r671
r6172=0
r6173=0
r6174=kap*r676
r6175=0
r6176=2*kap*r6230
r6177=0
8*kap*r6230 + r6286 + 2*r6412
r6178=-------------------------------
6
r6179= - r6302
r6180=0
1
r6181= - r6302 - ---*r6356
2
r6182=0
r6183=r6412
2 1 1
r6184= - ---*r6302 - ---*r6309 - ---*r6356
3 3 3
r6185=0
r6186=kap*r6243
r6187=0
r6188=0
r6189=0
r6190=0
r6191=0
r6192=kap*r671
r6193=r6389
r6194=0
r6195=kap*r6336
r6196=0
1
r6197=---*kap*r6243 + kap*r6336
2
r6198=0
r6199=0
r6200=kap*r6149 - kap*r6336
2
r6201=kap *r6230
r6202=0
r6203=0
1 2 1
r6204= - ---*kap *r6243 + ---*kap*r6165
4 2
r6205=0
2
r6206=kap *r6230
1
r6207= - ---*kap*r6302
2
r6208=0
1 2
r6209=---*kap *r6336
3
r6210=0
1
---*r6302
2
r6211=-----------
kap
r6212=0
r6302
r6213=-------
kap
r6214=0
1
---*r6302
2
r6215=-----------
kap
r6216=r6230
r6217=0
r6218=2*r6230
r6219=0
r6220=r6230
r6221=0
r6302
r6222=-------
kap
r6223=0
r6302
r6224=-------
kap
r6225=2*r6230
r6226=0
r6227=2*r6230
r6228=0
1
---*r6302
2
r6229=-----------
kap
r6231=0
r6232=0
r6233=0
r6234=0
r6235=0
r6236=r6243
r6237=0
r6238=r6243
r6239=0
r6240=0
r6241=0
r6242=0
r6244=0
r6245=0
r6246=0
1
---*kap*r6356 - r6389
2
r6247=-----------------------
kap
r6248=0
- r6389
r6249=----------
kap
- 4*kap*r6230 + r6286 + 2*r6412 + 2*r671
r6250=-------------------------------------------
2
r6251=0
r6252=r671
r6253=0
- r6389
r6254=----------
kap
r6255=r671
r6256=0
r6258=0
r6260=0
r6261=0
r6262=0
r6263= - r6138
r6264=r680
r6265=0
r6266=0
r6267=0
r6268=0
r6269=0
r6270=0
r6271=0
r6272= - 2*r6149 + r6243 + 4*r6336
r6273=0
r6274= - 2*r6149 + r6243 + 4*r6336
r6275=0
r6276=0
r6277=0
r6278=0
r6279= - 2*r6149 + r6243 + 4*r6336
r6280=0
r6281=0
r6282=0
r6283=r6356
r6284=0
r6285=0
r6287=0
r6288= - r6356
r6289=0
r6290=0
r6291=0
r6292=0
r6293=r6257
r6294=0
r6296= - r6257
r6297=0
r6298=0
r6299=0
r6300=0
r6301=0
r6303=0
1
r6304=r6302 + ---*r6356
2
r6305=2*kap*r6230
r6306=0
8*kap*r6230 + r6286 - 2*r6412
r6307=-------------------------------
2
r6308=0
r6310=r6412
r6311=0
r6312=0
r6313=0
r6314=kap*r6243
r6315=0
r6316=0
r6317=0
r6318= - r6389
r6319=kap*r671
r6320=0
r6321=0
r6322=0
r6323=0
r6324=0
r6325= - 2*kap*r6149 + kap*r6243 + 4*kap*r6336
r6326=0
r6327=0
r6328=0
r6329=0
r6330=0
r6331=0
1
r6332=---*kap*r6302
2
2
r6333=kap *r6230
r6334=0
r6335=0
r6337=0
r6338=r6149
r6339=0
r6340=r6149 - r6336
r6341=0
r6342=0
r6343=0
r6344=0
1
r6345=---*r6243 + 2*r6336
2
r6346=0
1
r6347=r6149 + ---*r6243
2
r6348=0
r6349=0
1
r6350=---*r6243 + r6336
2
r6351=2*kap*r6230
r6352=0
r6353=r6412
r6354=0
r6355=0
r6357=0
r6286 + 2*r6412
r6358=-----------------
2
r6359=0
r6360=0
r6361=r6165
r6362=0
1 1 1
r6363= - ---*kap*r6243 + r6165 + ---*r6259 - ---*r6295
2 2 2
r6364=0
r6365=r6257
1 1
r6366= - ---*kap*r6243 + r6165 + ---*r6259
2 2
r6367=kap*r671
r6368=0
r6369=0
r6370=kap*r676
r6371=0
r6372=2*kap*r6230
r6373=0
r6374=r6412
r6375= - r6302
r6376=0
r6377= - r6309
r6378=0
8*kap*r6230 + r6286 - 2*r6412
r6379=-------------------------------
2
1
r6380= - r6302 - ---*r6356
2
r6381=0
r6382=kap*r6243
r6383=0
r6384=0
r6385=0
r6386=0
r6387=0
r6388=kap*r671
r6390=0
r6391=2*kap*r6336
r6392=0
1
r6393=kap*r6149 + ---*kap*r6243
2
r6394=0
r6395=0
1
r6396=kap*r6149 + ---*kap*r6243
2
2
r6397=2*kap *r6230
r6398=0
r6399=0
1 2
r6400= - ---*kap *r6243 + kap*r6165
2
r6401=0
2
r6402=2*kap *r6230
r6403= - kap*r6302
r6404=0
2
r6405=kap *r6336
r6406=0
r6407=r6302
r6408=0
2 1 1
r6409=---*r6302 + ---*r6309 + ---*r6356
3 3 3
r6410=2*kap*r6230
r6411=0
r6413=0
1
r6414=r6302 + ---*r6356
2
8*kap*r6230 + r6286 + 2*r6412
r6415=-------------------------------
6
r6416=0
r6417=0
r6418=0
r6419=kap*r6243
r6420=0
r6421=0
r6422=0
r6423= - r6389
r6424=kap*r671
r6425=0
r6426=0
r6427=0
r6428=0
r6429=0
r6430= - 2*kap*r6149 + kap*r6243 + 4*kap*r6336
r6431=0
r6432=0
r6433=0
r6434=0
r6435=0
r6436=0
r6437=kap*r6302
2
r6438=2*kap *r6230
r6439=0
r6440=0
r6441=kap*r6336
r6442=0
r6443=kap*r6149 - kap*r6336
r6444=0
r6445=0
1
r6446=---*kap*r6243 + kap*r6336
2
2
r6447=kap *r6230
r6448=0
r6449=0
1 2 1
r6450= - ---*kap *r6243 + ---*kap*r6165
4 2
r6451=0
2
r6452=kap *r6230
1
r6453= - ---*kap*r6302
2
r6454=0
2
r6455=kap *r6336
r6456=0
1
r6457=---*kap*r6302
2
2
r6458=kap *r6230
r6459=0
r6460=0
1 2
r6461=---*kap *r6336
3
a23=0
a22=0
a13=0
a11=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:
r671, r676, r680, r683, r6138, r6149, r6165, r6230, r6243,
r6257, r6259, r6286, r6295, r6302, r6309, r6336, r6356,
r6389, r6412, 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.
{a33,
b12,
1 4 2
{---*b12 *kap *r6336,
3
3 2
b12 *kap *r6230,
1 3
---*b12 *kap*r6302,
2
4 2
b12 *kap *r6336,
1 3
---*b12 *kap*r6302,
2
3 2
b12 *kap *r6230,
1 3 2 1 3
---*b12 *kap *r6243 - ---*b12 *kap*r6165,
4 2
3 2
b12 *kap *r6230,
1 2 2
---*b12 *kap*r6243 + b12 *kap*r6336,
2
2 2
b12 *kap*r6149 - b12 *kap*r6336,
2
b12 *kap*r6336,
3 2
2*b12 *kap *r6230,
3
b12 *kap*r6302,
2 2 2
2*b12 *kap*r6149 - b12 *kap*r6243 - 4*b12 *kap*r6336,
3 2
b12 *kap *r671,
2
b12 *r6389,
b12*kap*r6243,
8*b12*kap*r6230 + b12*r6286 + 2*b12*r6412,
1
b12*r6302 + ---*b12*r6356,
2
r6412,
2*b12*kap*r6230,
2 1 1
---*b12*r6302 + ---*b12*r6309 + ---*b12*r6356,
3 3 3
b12*r6302,
3 2
b12 *kap *r6336,
2
b12 *kap*r6302,
3 2
2*b12 *kap *r6230,
3 2 3
8*b12 *kap *r6243 - 16*b12 *kap*r6165,
3 2
2*b12 *kap *r6230,
2 1 2
b12 *kap*r6149 + ---*b12 *kap*r6243,
2
2 1 2
b12 *kap*r6149 + ---*b12 *kap*r6243,
2
2
2*b12 *kap*r6336,
r6389,
2 3 2
28*a33 *b12 *kap *r671,
b12*kap*r6243,
1
b12*r6302 + ---*b12*r6356,
2
8*b12*kap*r6230 + b12*r6286 - 2*b12*r6412,
b12*r6309,
b12*r6302,
b12*r6412,
2*b12*kap*r6230,
3
b12 *kap*r676,
3
b12 *kap*r671,
1 2 2 1 2
---*b12 *kap*r6243 - b12 *r6165 - ---*b12 *r6259,
2 2
3 2
56*a33 *b12 *kap*r6257,
1 2 2 1 2 1 2
---*b12 *kap*r6243 - b12 *r6165 - ---*b12 *r6259 + ---*b12 *r6295,
2 2 2
2
b12 *r6165,
b12*r6286 + 2*b12*r6412,
r6356,
r6412,
2*b12*kap*r6230,
1
---*r6243 + r6336,
2
1
r6149 + ---*r6243,
2
1
---*r6243 + 2*r6336,
2
r6149 - r6336,
r6149,
r6336,
3 2
b12 *kap *r6230,
1 2
---*b12 *kap*r6302,
2
2*b12*kap*r6149 - b12*kap*r6243 - 4*b12*kap*r6336,
2 4 3
28*a33 *b12 *kap *r671,
2
2*b12 *r6389,
b12*kap*r6243,
b12*r6412,
r6309,
8*b12*kap*r6230 + b12*r6286 - 2*b12*r6412,
2*b12*kap*r6230,
1
r6302 + ---*r6356,
2
r6302,
2 2
14*a33 *b12 *kap*r6257,
r6295,
2
b12 *r6257,
b12*r6356,
r6286,
b12*r6356,
2*r6149 - r6243 - 4*r6336,
2*r6149 - r6243 - 4*r6336,
2*r6149 - r6243 - 4*r6336,
3
14*a33*b12 *kap*r680,
2
b12 *r6138,
r6259,
r6257,
b12*r671,
2
b12 *r6389,
b12*r671,
4*b12*kap*r6230 - b12*r6286 - 2*b12*r6412 - 2*b12*r671,
2
b12 *r6389,
1 2 2
---*b12 *kap*r6356 - b12 *r6389,
2
r6243,
r6243,
r6243,
r6230,
1
---*b12*r6302,
2
2*r6230,
2*r6230,
b12*r6302,
b12*r6302,
r6230,
2*r6230,
2*r6230,
b12*r6302,
b12*r6302,
b12*r6302,
1 3 2
---*b12 *kap *r6336,
3
1 2
---*b12 *kap*r6302,
2
3 2
b12 *kap *r6230,
3 2 3
b12 *kap *r6243 - 2*b12 *kap*r6165,
3 3
b12 *kap *r6230,
b12*kap*r6149 - b12*kap*r6336,
1
---*b12*kap*r6243 + b12*kap*r6336,
2
b12*kap*r6336,
2
2*b12 *r6389,
2 4 3
14*a33 *b12 *kap *r671,
b12*kap*r6243,
2 1 1
---*r6302 + ---*r6309 + ---*r6356,
3 3 3
b12*r6412,
1
r6302 + ---*r6356,
2
r6302,
8*b12*kap*r6230 + b12*r6286 + 2*b12*r6412,
2*b12*kap*r6230,
3
b12 *kap*r676,
2 3 2
14*a33 *b12 *kap *r671,
b12*kap*r6243 - 2*b12*r6165 - b12*r6259 + b12*r6295,
3 3 2
28*a33 *b12 *kap *r6257,
b12*kap*r6243 - 2*b12*r6165 - b12*r6259,
r6165,
r6412,
r6356,
b12*r6286 + 2*b12*r6412,
2*b12*kap*r6230,
r6149 - r6336,
1
r6149 + ---*r6243,
2
r6149,
1
---*r6243 + r6336,
2
1
---*r6243 + 2*r6336,
2
r6336,
r6138,
3
14*a33*b12 *kap*r680,
2 2
14*a33 *b12 *kap*r6257,
r6259,
2
b12 *r6389,
b12*r671,
2
b12 *r6389,
1 2 2
---*b12 *kap*r6356 - b12 *r6389,
2
b12*r671,
4*b12*kap*r6230 - b12*r6286 - 2*b12*r6412 - 2*b12*r671,
r6243,
r6243,
r6243,
1
---*b12*r6302,
2
r6230,
b12*r6302,
b12*r6302,
2*r6230,
2*r6230,
1
---*b12*r6302,
2
b12*r6302,
b12*r6302,
r6230,
2*r6230,
2*r6230,
r683,
r680,
b12*r676,
r676,
b12*r6259 + 2*b12*r676,
r671,
b12*r671,
4*b12*kap*r6230 - b12*r6286 - 2*b12*r6412 - 6*b12*r671,
1 3 2 1 3
---*b12 *kap *r6243 - ---*b12 *kap*r6165,
4 2
1 3 2 3
---*b12 *kap *r6243 - b12 *kap*r6165,
2
3
b12 *kap*r6165,
1 3 2 1 3
---*b12 *kap *r6243 - ---*b12 *kap*r6165,
4 2
3
b12 *kap*r6165,
1 3 2 1 3
---*b12 *kap *r6243 + ---*b12 *kap*r6165,
4 2
r6230,
2*r6230,
2*r6230,
r6230,
2*r6230,
r6230,
1 2
---*b12 *kap*r6336,
3
2
b12 *kap*r6336,
2
b12 *kap*r6336,
2
b12 *kap*r6336,
2
2*b12 *kap*r6336,
2
b12 *kap*r6336,
1 2
---*b12 *kap*r6336,
3
2
b12 *kap*r6336,
2
b12 *kap*r6336,
2
b12 *kap*r6336}}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2
HAM=u1*v2*b12 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=u1*v2*b12 - u2*v1*b12 + u3**2*a33$