Solution 27 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
1 2 2 2 1 1 2
---*a11 *r6149 - ---*a11 *r6336 - ---*a11*b12*r6302 + ---*b12 *kap*r6336
3 3 6 3
r60=--------------------------------------------------------------------------
2 2
b12 *kap
r61=0
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336
2
r62=----------------------------------------------------------------
2 2
b12 *kap
r63=0
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336
2
r64=----------------------------------------------------------------
2 2
b12 *kap
r65=0
1 2 2 2 1 1 2
---*a11 *r6149 - ---*a11 *r6336 - ---*a11*b12*r6302 + ---*b12 *kap*r6336
3 3 6 3
r66=--------------------------------------------------------------------------
2 2
b12 *kap
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336
2
r613=----------------------------------------------------------------
2 2
b12 *kap
r614=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r615=----------------------------------------------------------------
2 2
b12 *kap
r616=0
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336
2
r617=----------------------------------------------------------------
2 2
b12 *kap
r618=0
r619=0
r620=0
r621=0
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336
2
r622=----------------------------------------------------------------
2 2
b12 *kap
r623=0
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336
2
r624=----------------------------------------------------------------
2 2
b12 *kap
r625=0
r626=0
1 2 2 2 1 1 2
---*a11 *r6149 - ---*a11 *r6336 - ---*a11*b12*r6302 + ---*b12 *kap*r6336
3 3 6 3
r627=--------------------------------------------------------------------------
2 2
b12 *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
2 2
r649=(2*a11 *r6259 - 2*a11 *r6295 - a11*b12*kap*r6356 + 2*a11*b12*r6389
2 2 2 2 2
+ b12 *kap *r6243 + 2*b12 *kap*r6165)/(4*b12 *kap )
r650=0
2 2
r651=(2*a11 *r6259 - 2*a11 *r6295 - a11*b12*kap*r6356 + 2*a11*b12*r6389
2 2 2
+ 2*b12 *kap*r6165)/(2*b12 *kap )
r652=0
2 2
r653=(2*a11 *r6259 - 2*a11 *r6295 - a11*b12*kap*r6356 + 2*a11*b12*r6389
2 2 2 2 2
- b12 *kap *r6243 + 2*b12 *kap*r6165)/(4*b12 *kap )
r654=0
r655=0
r656=0
r657=0
2 2
r658=(2*a11 *r6259 - 2*a11 *r6295 - a11*b12*kap*r6356 + 2*a11*b12*r6389
2 2 2
+ 2*b12 *kap*r6165)/(2*b12 *kap )
r659=0
2 2
r660=(2*a11 *r6259 - 2*a11 *r6295 - a11*b12*kap*r6356 + 2*a11*b12*r6389
2 2 2 2 2
- b12 *kap *r6243 + 2*b12 *kap*r6165)/(2*b12 *kap )
r661=0
r662=0
2 2
r663=(2*a11 *r6259 - 2*a11 *r6295 - a11*b12*kap*r6356 + 2*a11*b12*r6389
2 2 2 2 2
- b12 *kap *r6243 + 2*b12 *kap*r6165)/(4*b12 *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
a11*r6149 - 2*a11*r6336 - ---*b12*r6302
2
r690=-----------------------------------------
b12*kap
r691=0
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r692=---------------------------------------
b12*kap
r693=0
1
a11*r6149 - 2*a11*r6336 - ---*b12*r6302
2
r694=-----------------------------------------
b12*kap
r695=0
r696=2*r6230
r697=0
r698=2*r6230
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r699=---------------------------------------
b12*kap
r6100=0
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r6101=---------------------------------------
b12*kap
r6102=0
r6103=r6230
1
a11*r6149 - 2*a11*r6336 - ---*b12*r6302
2
r6104=-----------------------------------------
b12*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
2*a11*r6259 - 2*a11*r6295 - b12*kap*r6356 + 2*b12*r6389
r6124=---------------------------------------------------------
2*b12*kap
r6125=0
a11*r6259 - a11*r6295 + b12*r6389
r6126=-----------------------------------
b12*kap
r6127=0
r6128=r671
a11*r6259 - a11*r6295 + b12*r6389
r6129=-----------------------------------
b12*kap
r6130=0
r6131=r6259
r6132=0
r6133= - r6257
r6134=0
r6135=0
r6136=0
r6137=r680
r6139=0
r6140=r6336
r6141=0
r6243 + 4*r6336
r6142=-----------------
2
r6143=0
r6243 + 2*r6336
r6144=-----------------
2
r6145=0
r6146=0
r6147=0
r6148=0
r6150=0
2*r6149 + r6243
r6151=-----------------
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
- a11*r6356 - b12*kap*r6243 + 2*b12*r6165 + b12*r6259
r6167=--------------------------------------------------------
2*b12
r6168=0
r6169= - r6257
- a11*r6356 - b12*kap*r6243 + 2*b12*r6165 + b12*r6259 - b12*r6295
r6170=--------------------------------------------------------------------
2*b12
a11*r6257 + b12*kap*r671
r6171=--------------------------
b12
r6172=0
r6173=0
- a11*r6138 + b12*kap*r676
r6174=-----------------------------
b12
r6175=0
r6176=2*kap*r6230
r6177=0
8*kap*r6230 + r6286 + 2*r6412
r6178=-------------------------------
6
r6179= - r6302
r6180=0
- 2*r6302 - r6356
r6181=--------------------
2
r6182=0
r6183=r6412
- 2*r6302 - r6309 - r6356
r6184=----------------------------
3
r6185=0
a11*r6356 + b12*kap*r6243
r6186=---------------------------
b12
r6187=0
4*a11*kap*r6230 - 2*a11*r6412
r6188=-------------------------------
b12
r6189=0
r6190=0
r6191=0
a11*r6257 + b12*kap*r671
r6192=--------------------------
b12
r6193=r6389
r6194=0
1
---*a11*r6302 + b12*kap*r6336
2
r6195=-------------------------------
b12
r6196=0
a11*r6302 + a11*r6356 + b12*kap*r6243 + 2*b12*kap*r6336
r6197=---------------------------------------------------------
2*b12
r6198=0
4*a11*kap*r6230 - 2*a11*r6412
r6199=-------------------------------
b12
r6200
- a11*r6302 + 2*a11*r6309 + 2*a11*r6356 + 2*b12*kap*r6149 - 2*b12*kap*r6336
=------------------------------------------------------------------------------
2*b12
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6201=----------------------------------------------------
2
b12
r6202=0
r6203=0
2
- a11*kap*r6356 - 2*a11*r6389 - b12*kap *r6243 + 2*b12*kap*r6165
r6204=-------------------------------------------------------------------
4*b12
r6205=0
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6206=----------------------------------------------------
2
b12
2 2 2
r6207=(2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11*b12*kap*r6149
2 2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302)/(2*b12 )
r6208=0
3 3 3 2
r6209=( - a11 *r6302 + a11 *r6309 + a11 *r6356 + a11 *b12*kap*r6149
2 2 3 2 3
- 2*a11 *b12*kap*r6336 + a11*b12 *kap*r6302 + b12 *kap *r6336)/(3*b12 )
r6210=0
1
- a11*r6149 + 2*a11*r6336 + ---*b12*r6302
2
r6211=--------------------------------------------
b12*kap
r6212=0
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6213=------------------------------------------
b12*kap
r6214=0
1
- a11*r6149 + 2*a11*r6336 + ---*b12*r6302
2
r6215=--------------------------------------------
b12*kap
r6216=r6230
r6217=0
r6218=2*r6230
r6219=0
r6220=r6230
r6221=0
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6222=------------------------------------------
b12*kap
r6223=0
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6224=------------------------------------------
b12*kap
r6225=2*r6230
r6226=0
r6227=2*r6230
r6228=0
1
- a11*r6149 + 2*a11*r6336 + ---*b12*r6302
2
r6229=--------------------------------------------
b12*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
- 2*a11*r6259 + 2*a11*r6295 + b12*kap*r6356 - 2*b12*r6389
r6247=------------------------------------------------------------
2*b12*kap
r6248=0
- a11*r6259 + a11*r6295 - b12*r6389
r6249=--------------------------------------
b12*kap
- 4*kap*r6230 + r6286 + 2*r6412 + 2*r671
r6250=-------------------------------------------
2
r6251=0
r6252=r671
r6253=0
- a11*r6259 + a11*r6295 - b12*r6389
r6254=--------------------------------------
b12*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
2*r6302 + r6356
r6304=-----------------
2
r6305=2*kap*r6230
r6306=0
8*kap*r6230 + r6286 - 2*r6412
r6307=-------------------------------
2
r6308=0
r6310=r6412
r6311=0
- 4*a11*kap*r6230 + 2*a11*r6412
r6312=----------------------------------
b12
r6313=0
a11*r6356 + b12*kap*r6243
r6314=---------------------------
b12
r6315=0
r6316=0
r6317=0
r6318= - r6389
a11*r6257 + b12*kap*r671
r6319=--------------------------
b12
r6320=0
r6321=0
r6322=0
- 4*a11*kap*r6230 + 2*a11*r6412
r6323=----------------------------------
b12
r6324=0
r6325=(2*a11*r6302 - 2*a11*r6309 - a11*r6356 - 2*b12*kap*r6149 + b12*kap*r6243
+ 4*b12*kap*r6336)/b12
4*a11*kap*r6230 - 2*a11*r6412
r6326=-------------------------------
b12
r6327=0
r6328=0
r6329=0
r6330=0
r6331=0
2 2 2
r6332=( - 2*a11 *r6302 + 2*a11 *r6309 + 2*a11 *r6356 + 2*a11*b12*kap*r6149
2 2
- 4*a11*b12*kap*r6336 + b12 *kap*r6302)/(2*b12 )
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6333=----------------------------------------------------
2
b12
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
2*r6149 + r6243
r6347=-----------------
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
- a11*r6356 - b12*kap*r6243 + 2*b12*r6165 + b12*r6259 - b12*r6295
r6363=--------------------------------------------------------------------
2*b12
r6364=0
r6365=r6257
- a11*r6356 - b12*kap*r6243 + 2*b12*r6165 + b12*r6259
r6366=--------------------------------------------------------
2*b12
a11*r6257 + b12*kap*r671
r6367=--------------------------
b12
r6368=0
r6369=0
- a11*r6138 + b12*kap*r676
r6370=-----------------------------
b12
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
- 2*r6302 - r6356
r6380=--------------------
2
r6381=0
a11*r6356 + b12*kap*r6243
r6382=---------------------------
b12
r6383=0
4*a11*kap*r6230 - 2*a11*r6412
r6384=-------------------------------
b12
r6385=0
r6386=0
r6387=0
a11*r6257 + b12*kap*r671
r6388=--------------------------
b12
r6390=0
a11*r6302 + 2*b12*kap*r6336
r6391=-----------------------------
b12
r6392=0
2*a11*r6309 + 3*a11*r6356 + 2*b12*kap*r6149 + b12*kap*r6243
r6393=-------------------------------------------------------------
2*b12
r6394=0
r6395=0
2*a11*r6309 + 3*a11*r6356 + 2*b12*kap*r6149 + b12*kap*r6243
r6396=-------------------------------------------------------------
2*b12
2 2 2 2
- 4*a11 *kap*r6230 + 2*a11 *r6412 + 2*b12 *kap *r6230
r6397=--------------------------------------------------------
2
b12
r6398=0
r6399=0
2
- a11*kap*r6356 - 2*a11*r6389 - b12*kap *r6243 + 2*b12*kap*r6165
r6400=-------------------------------------------------------------------
2*b12
r6401=0
2 2 2 2
- 4*a11 *kap*r6230 + 2*a11 *r6412 + 2*b12 *kap *r6230
r6402=--------------------------------------------------------
2
b12
2 2 2
r6403=(2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11*b12*kap*r6149
2 2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302)/b12
r6404=0
3 3 3 2
r6405=( - a11 *r6302 + a11 *r6309 + a11 *r6356 + a11 *b12*kap*r6149
2 2 3 2 3
- 2*a11 *b12*kap*r6336 + a11*b12 *kap*r6302 + b12 *kap *r6336)/b12
r6406=0
r6407=r6302
r6408=0
2*r6302 + r6309 + r6356
r6409=-------------------------
3
r6410=2*kap*r6230
r6411=0
r6413=0
2*r6302 + r6356
r6414=-----------------
2
8*kap*r6230 + r6286 + 2*r6412
r6415=-------------------------------
6
r6416=0
- 4*a11*kap*r6230 + 2*a11*r6412
r6417=----------------------------------
b12
r6418=0
a11*r6356 + b12*kap*r6243
r6419=---------------------------
b12
r6420=0
r6421=0
r6422=0
r6423= - r6389
a11*r6257 + b12*kap*r671
r6424=--------------------------
b12
r6425=0
r6426=0
r6427=0
- 4*a11*kap*r6230 + 2*a11*r6412
r6428=----------------------------------
b12
r6429=0
r6430=(2*a11*r6302 - 2*a11*r6309 - a11*r6356 - 2*b12*kap*r6149 + b12*kap*r6243
+ 4*b12*kap*r6336)/b12
4*a11*kap*r6230 - 2*a11*r6412
r6431=-------------------------------
b12
r6432=0
r6433=0
r6434=0
r6435=0
r6436=0
2 2 2
r6437=( - 2*a11 *r6302 + 2*a11 *r6309 + 2*a11 *r6356 + 2*a11*b12*kap*r6149
2 2
- 4*a11*b12*kap*r6336 + b12 *kap*r6302)/b12
2 2 2 2
- 4*a11 *kap*r6230 + 2*a11 *r6412 + 2*b12 *kap *r6230
r6438=--------------------------------------------------------
2
b12
r6439=0
r6440=0
a11*r6302 + 2*b12*kap*r6336
r6441=-----------------------------
2*b12
r6442=0
r6443
- a11*r6302 + 2*a11*r6309 + 2*a11*r6356 + 2*b12*kap*r6149 - 2*b12*kap*r6336
=------------------------------------------------------------------------------
2*b12
r6444=0
- 4*a11*kap*r6230 + 2*a11*r6412
r6445=----------------------------------
b12
a11*r6302 + a11*r6356 + b12*kap*r6243 + 2*b12*kap*r6336
r6446=---------------------------------------------------------
2*b12
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6447=----------------------------------------------------
2
b12
r6448=0
r6449=0
2
- a11*kap*r6356 - 2*a11*r6389 - b12*kap *r6243 + 2*b12*kap*r6165
r6450=-------------------------------------------------------------------
4*b12
r6451=0
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6452=----------------------------------------------------
2
b12
2 2 2
r6453=(2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11*b12*kap*r6149
2 2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302)/(2*b12 )
r6454=0
3 3 3 2
r6455=( - a11 *r6302 + a11 *r6309 + a11 *r6356 + a11 *b12*kap*r6149
2 2 3 2 3
- 2*a11 *b12*kap*r6336 + a11*b12 *kap*r6302 + b12 *kap *r6336)/b12
r6456=0
2 2 2
r6457=( - 2*a11 *r6302 + 2*a11 *r6309 + 2*a11 *r6356 + 2*a11*b12*kap*r6149
2 2
- 4*a11*b12*kap*r6336 + b12 *kap*r6302)/(2*b12 )
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6458=----------------------------------------------------
2
b12
r6459=0
r6460=0
3 3 3 2
r6461=( - a11 *r6302 + a11 *r6309 + a11 *r6356 + a11 *b12*kap*r6149
2 2 3 2 3
- 2*a11 *b12*kap*r6336 + a11*b12 *kap*r6302 + b12 *kap *r6336)/(3*b12 )
1
a33=---*a11
2
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:
r671, r676, r680, r683, r6138, r6149, r6165, r6230, r6243,
r6257, r6259, r6286, r6295, r6302, r6309, r6336, r6356,
r6389, r6412, a11, 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.
{a11,
b12,
2 2
a11 + b12 *kap,
3 3 3 2 2
{2*a11 *b12*r6302 - 2*a11 *b12*r6309 - 2*a11 *b12*r6356 - 2*a11 *b12 *kap*r6149
2 2 3 4 2
+ 4*a11 *b12 *kap*r6336 - 2*a11*b12 *kap*r6302 - 2*b12 *kap *r6336,
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6412 - b12 *kap *r6230,
2 2 2 2
2*a11 *b12*r6302 - 2*a11 *b12*r6309 - 2*a11 *b12*r6356 - 2*a11*b12 *kap*r6149
2 3
+ 4*a11*b12 *kap*r6336 - b12 *kap*r6302,
3 3 3 2 2
a11 *b12*r6302 - a11 *b12*r6309 - a11 *b12*r6356 - a11 *b12 *kap*r6149
2 2 3 4 2
+ 2*a11 *b12 *kap*r6336 - a11*b12 *kap*r6302 - b12 *kap *r6336,
2 2 2 2
2*a11 *b12*r6302 - 2*a11 *b12*r6309 - 2*a11 *b12*r6356 - 2*a11*b12 *kap*r6149
2 3
+ 4*a11*b12 *kap*r6336 - b12 *kap*r6302,
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6412 - b12 *kap *r6230,
2 2 3 2 3
4*a11*b12 *kap*r6356 + 8*a11*b12 *r6389 + 4*b12 *kap *r6243 - 8*b12 *kap*r6165
,
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6412 - b12 *kap *r6230,
2 2
a11*b12*r6302 + a11*b12*r6356 + b12 *kap*r6243 + 2*b12 *kap*r6336,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
2
a11*b12*r6302 - 2*a11*b12*r6309 - 2*a11*b12*r6356 - 2*b12 *kap*r6149
2
+ 2*b12 *kap*r6336,
2
a11*b12*r6302 + 2*b12 *kap*r6336,
2 2 3 2
4*a11 *b12*kap*r6230 - 2*a11 *b12*r6412 - 2*b12 *kap *r6230,
2 2 2 2
2*a11 *b12*r6302 - 2*a11 *b12*r6309 - 2*a11 *b12*r6356 - 2*a11*b12 *kap*r6149
2 3
+ 4*a11*b12 *kap*r6336 - b12 *kap*r6302,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
2
2*a11*b12*r6302 - 2*a11*b12*r6309 - a11*b12*r6356 - 2*b12 *kap*r6149
2 2
+ b12 *kap*r6243 + 4*b12 *kap*r6336,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
2 3 2
a11*b12 *kap*r6257 + b12 *kap *r671,
2
b12 *r6389,
a11*r6356 + b12*kap*r6243,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
8*b12*kap*r6230 + b12*r6286 + 2*b12*r6412,
2*b12*r6302 + b12*r6356,
r6412,
2*b12*kap*r6230,
2*b12*r6302 + b12*r6309 + b12*r6356,
b12*r6302,
3 3 3 2
2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11 *b12*kap*r6149
2 2 3 2
+ 4*a11 *b12*kap*r6336 - 2*a11*b12 *kap*r6302 - 2*b12 *kap *r6336,
2 2 2
2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11*b12*kap*r6149
2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302,
2 2 3 2
4*a11 *b12*kap*r6230 - 2*a11 *b12*r6412 - 2*b12 *kap *r6230,
2 2 3 2
8*a11*b12 *kap*r6356 + 16*a11*b12 *r6389 + 8*b12 *kap *r6243
3
- 16*b12 *kap*r6165,
2 2 3 2
4*a11 *b12*kap*r6230 - 2*a11 *b12*r6412 - 2*b12 *kap *r6230,
2 2
2*a11*b12*r6309 + 3*a11*b12*r6356 + 2*b12 *kap*r6149 + b12 *kap*r6243,
2 2
2*a11*b12*r6309 + 3*a11*b12*r6356 + 2*b12 *kap*r6149 + b12 *kap*r6243,
2
a11*b12*r6302 + 2*b12 *kap*r6336,
r6389,
3 2 2 3 2
a11 *b12 *kap*r6257 + a11 *b12 *kap *r671,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
a11*r6356 + b12*kap*r6243,
2*b12*r6302 + b12*r6356,
8*b12*kap*r6230 + b12*r6286 - 2*b12*r6412,
b12*r6309,
b12*r6302,
b12*r6412,
2*b12*kap*r6230,
2 3
a11*b12 *r6138 - b12 *kap*r676,
2 3
a11*b12 *r6257 + b12 *kap*r671,
2 2 2
a11*b12*r6356 + b12 *kap*r6243 - 2*b12 *r6165 - b12 *r6259,
3 2
a11 *b12 *kap*r6257,
2 2 2
4*a11*b12*r6356 + 4*b12 *kap*r6243 - 8*b12 *r6165 - 4*b12 *r6259
2
+ 4*b12 *r6295,
2
b12 *r6165,
b12*r6286 + 2*b12*r6412,
r6356,
r6412,
2*b12*kap*r6230,
1
---*r6243 + r6336,
2
2*r6149 + r6243,
1
---*r6243 + 2*r6336,
2
r6149 - r6336,
r6149,
r6336,
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6412 - b12 *kap *r6230,
2 2 2
2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11*b12*kap*r6149
2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
2*a11*r6302 - 2*a11*r6309 - a11*r6356 - 2*b12*kap*r6149 + b12*kap*r6243
+ 4*b12*kap*r6336,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
3 3 2 2 4 3
2*a11 *b12 *kap *r6257 + 2*a11 *b12 *kap *r671,
2
b12 *r6389,
a11*r6356 + b12*kap*r6243,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
b12*r6412,
r6309,
8*b12*kap*r6230 + b12*r6286 - 2*b12*r6412,
2*b12*kap*r6230,
2*r6302 + r6356,
r6302,
2 2
a11 *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
a11*b12 *kap*r680,
2
b12 *r6138,
r6259,
r6257,
b12*r671,
2
a11*b12*r6259 - a11*b12*r6295 + b12 *r6389,
b12*r671,
4*b12*kap*r6230 - b12*r6286 - 2*b12*r6412 - 2*b12*r671,
2
a11*b12*r6259 - a11*b12*r6295 + b12 *r6389,
2 2
2*a11*b12*r6259 - 2*a11*b12*r6295 - b12 *kap*r6356 + 2*b12 *r6389,
r6243,
r6243,
r6243,
r6230,
1
a11*r6149 - 2*a11*r6336 - ---*b12*r6302,
2
2*r6230,
2*r6230,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
r6230,
2*r6230,
2*r6230,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
3 3 3 2
a11 *r6302 - a11 *r6309 - a11 *r6356 - a11 *b12*kap*r6149
2 2 3 2
+ 2*a11 *b12*kap*r6336 - a11*b12 *kap*r6302 - b12 *kap *r6336,
2 2 2
2*a11 *r6302 - 2*a11 *r6309 - 2*a11 *r6356 - 2*a11*b12*kap*r6149
2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302,
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6412 - b12 *kap *r6230,
2 2 3 2 3
a11*b12 *kap*r6356 + 2*a11*b12 *r6389 + b12 *kap *r6243 - 2*b12 *kap*r6165,
2 2 2 3 3
2*a11 *b12*kap *r6230 - a11 *b12*kap*r6412 - b12 *kap *r6230,
a11*r6302 - 2*a11*r6309 - 2*a11*r6356 - 2*b12*kap*r6149 + 2*b12*kap*r6336,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
a11*r6302 + a11*r6356 + b12*kap*r6243 + 2*b12*kap*r6336,
1
---*a11*r6302 + b12*kap*r6336,
2
2
b12 *r6389,
3 3 2 2 4 3
2*a11 *b12 *kap *r6257 + 2*a11 *b12 *kap *r671,
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
a11*r6356 + b12*kap*r6243,
2*r6302 + r6309 + r6356,
b12*r6412,
2*r6302 + r6356,
r6302,
8*b12*kap*r6230 + b12*r6286 + 2*b12*r6412,
2*b12*kap*r6230,
2 3
a11*b12 *r6138 - b12 *kap*r676,
3 2 2 3 2
a11 *b12 *kap*r6257 + a11 *b12 *kap *r671,
a11*r6356 + b12*kap*r6243 - 2*b12*r6165 - b12*r6259 + b12*r6295,
3 3 2
2*a11 *b12 *kap *r6257,
a11*r6356 + b12*kap*r6243 - 2*b12*r6165 - b12*r6259,
r6165,
r6412,
r6356,
b12*r6286 + 2*b12*r6412,
2*b12*kap*r6230,
r6149 - r6336,
2*r6149 + r6243,
r6149,
r6243 + 2*r6336,
r6243 + 4*r6336,
r6336,
r6138,
3
a11*b12 *kap*r680,
2 2
a11 *b12 *kap*r6257,
r6259,
2
a11*b12*r6259 - a11*b12*r6295 + b12 *r6389,
b12*r671,
2
a11*b12*r6259 - a11*b12*r6295 + b12 *r6389,
2 2
2*a11*b12*r6259 - 2*a11*b12*r6295 - b12 *kap*r6356 + 2*b12 *r6389,
b12*r671,
4*b12*kap*r6230 - b12*r6286 - 2*b12*r6412 - 2*b12*r671,
r6243,
r6243,
r6243,
1
a11*r6149 - 2*a11*r6336 - ---*b12*r6302,
2
r6230,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
2*r6230,
2*r6230,
1
a11*r6149 - 2*a11*r6336 - ---*b12*r6302,
2
2*a11*r6149 - 4*a11*r6336 - b12*r6302,
2*a11*r6149 - 4*a11*r6336 - 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,
2 2 2 2
2*a11 *b12*r6259 - 2*a11 *b12*r6295 - a11*b12 *kap*r6356 + 2*a11*b12 *r6389
3 2 3
- b12 *kap *r6243 + 2*b12 *kap*r6165,
2 2 2 2
2*a11 *b12*r6259 - 2*a11 *b12*r6295 - a11*b12 *kap*r6356 + 2*a11*b12 *r6389
3 2 3
- b12 *kap *r6243 + 2*b12 *kap*r6165,
2 2 2 2
2*a11 *b12*r6259 - 2*a11 *b12*r6295 - a11*b12 *kap*r6356 + 2*a11*b12 *r6389
3
+ 2*b12 *kap*r6165,
2 2 2 2
2*a11 *b12*r6259 - 2*a11 *b12*r6295 - a11*b12 *kap*r6356 + 2*a11*b12 *r6389
3 2 3
- b12 *kap *r6243 + 2*b12 *kap*r6165,
2 2 2 2
2*a11 *b12*r6259 - 2*a11 *b12*r6295 - a11*b12 *kap*r6356 + 2*a11*b12 *r6389
3
+ 2*b12 *kap*r6165,
2 2 2 2
2*a11 *b12*r6259 - 2*a11 *b12*r6295 - a11*b12 *kap*r6356 + 2*a11*b12 *r6389
3 2 3
+ b12 *kap *r6243 + 2*b12 *kap*r6165,
r6230,
2*r6230,
2*r6230,
r6230,
2*r6230,
r6230,
1 2 2 2 1 1 2
---*a11 *r6149 - ---*a11 *r6336 - ---*a11*b12*r6302 + ---*b12 *kap*r6336,
3 3 6 3
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336,
2
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336,
2
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336,
2
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336,
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336,
2
1 2 2 2 1 1 2
---*a11 *r6149 - ---*a11 *r6336 - ---*a11*b12*r6302 + ---*b12 *kap*r6336,
3 3 6 3
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336,
2
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336,
2
2 2 1 2
a11 *r6149 - 2*a11 *r6336 - ---*a11*b12*r6302 + b12 *kap*r6336}}
2
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2
2*u1 *a11 + 2*u1*v2*b12 + 2*u2 *a11 - 2*u2*v1*b12 + u3 *a11
HAM=-------------------------------------------------------------
2
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=(2*u1**2*a11 + 2*u1*v2*b12 + 2*u2**2*a11 - 2*u2*v1*b12 + u3**2*a11)/2$