Solution 42 to problem over
Expressions |
Parameters |
Inequalities |
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Expressions
The solution is given through the following expressions:
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r60=--------------------------------------------------------------
2 2
3*b12 *kap
r61=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r62=--------------------------------------------------------------
2 2
b12 *kap
r63=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r64=--------------------------------------------------------------
2 2
b12 *kap
r65=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r66=--------------------------------------------------------------
2 2
3*b12 *kap
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r613=--------------------------------------------------------------
2 2
b12 *kap
r614=0
2 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407 + 2*b12 *kap*r6336
r615=-------------------------------------------------------------------
2 2
b12 *kap
r616=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r617=--------------------------------------------------------------
2 2
b12 *kap
r618=0
r619=0
r620=0
r621=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r622=--------------------------------------------------------------
2 2
b12 *kap
r623=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r624=--------------------------------------------------------------
2 2
b12 *kap
r625=0
r626=0
2 2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407 + b12 *kap*r6336
r627=--------------------------------------------------------------
2 2
3*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
r6243 + r660
r649=--------------
2
r650=0
1
r651=---*r6243 + r660
2
r652=0
r660
r653=------
2
r654=0
r655=0
r656=0
r657=0
r6243 + 2*r660
r658=----------------
2
r659=0
r661=0
r662=0
r660
r663=------
2
- 2*a33*r6270 - 2*b12*kap*r6230 + b12*r6157 + 3*b12*r6252
r664=------------------------------------------------------------
3*b12
r665=0
r666=r6252
r667=0
r668=0
r669=0
r670=0
r671=r6252
r672=0
r673=0
r675=0
- r6259 + 2*r674
r676=-------------------
2
r677=0
r678=0
1
r679= - ---*r6259 + r674
2
r681=0
r682=0
r684=0
r685=r6230
r686=0
r687=2*r6230
r688=0
r689=r6230
4*a33*r6149 - 8*a33*r6336 - b12*r6407
r690=---------------------------------------
2*b12*kap
r691=0
4*a33*r6149 - 8*a33*r6336 - b12*r6407
r692=---------------------------------------
b12*kap
r693=0
4*a33*r6149 - 8*a33*r6336 - b12*r6407
r694=---------------------------------------
2*b12*kap
r695=0
r696=2*r6230
r697=0
r698=2*r6230
4*a33*r6149 - 8*a33*r6336 - b12*r6407
r699=---------------------------------------
b12*kap
r6100=0
4*a33*r6149 - 8*a33*r6336 - b12*r6407
r6101=---------------------------------------
b12*kap
r6102=0
r6103=r6230
4*a33*r6149 - 8*a33*r6336 - b12*r6407
r6104=---------------------------------------
2*b12*kap
r6105=0
r6106=r6243
r6107=0
r6108=r6243
r6109=0
r6110= - r6270
r6111=0
r6112= - r6270
r6113=0
r6114=0
r6115=r6243
r6116=0
r6117= - r6270
r6118=0
r6119=0
r6120=0
- 2*a33*r6270 - 2*b12*kap*r6230 + b12*r6157 + b12*r6252
r6121=----------------------------------------------------------
b12
r6122=0
r6123=r6252
1
r6124=r6129 - ---*r6356
2
r6125=0
r6126=r6129
r6127=0
r6128=r6252
r6130=0
r6131=r6259
r6132=0
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= - r6270
r6147=0
r6148= - r6270
r6150=0
2*r6149 + r6243
r6151=-----------------
2
r6152=0
r6153= - r6270
r6154=r6149 - r6336
2*a33*r6270 + 2*b12*kap*r6230
r6155=-------------------------------
b12
r6156=0
r6158=0
r6159=0
r6160= - r6356
r6161=0
r6162=r6353
r6163=0
r6164=0
- 4*a33*r6129 + 2*a33*r6356 + b12*kap*r6243 + 2*b12*kap*r660
r6165=---------------------------------------------------------------
2*b12
r6166=0
- 4*a33*r6129 + 2*b12*kap*r660 + b12*r6259
r6167=---------------------------------------------
2*b12
r6168=0
r6169=r6133
2 2 2
- 8*a33 *r6129 + 4*a33*b12*kap*r660 + b12 *kap*r6129 - b12 *r6389
r6170=--------------------------------------------------------------------
4*a33*b12
- 2*a33*r6133 + b12*kap*r6252
r6171=--------------------------------
b12
r6172=0
r6173=0
- 4*a33*r6138 - b12*kap*r6259 + 2*b12*kap*r674
r6174=-------------------------------------------------
2*b12
r6175=0
2*a33*r6270 + 2*b12*kap*r6230
r6176=-------------------------------
b12
r6177=0
4 4 1
---*a33*r6270 + ---*b12*kap*r6230 + ---*b12*r6157
3 3 3
r6178=---------------------------------------------------
b12
r6179= - r6407
r6180=0
- r6356 - 2*r6407
r6181=--------------------
2
r6182=0
r6183=r6353
r6184=( - 2*a33*r6356 - 12*a33*r6407 + 2*b12*kap*r6149 - b12*kap*r6243
- 4*b12*kap*r6336 + b12*r6430)/(12*a33)
r6185=0
2*a33*r6356 + b12*kap*r6243
r6186=-----------------------------
b12
r6187=0
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270
r6188=-----------------------------------------------------------------------
2
b12
r6189=0
r6190=0
r6191=0
- 2*a33*r6133 + b12*kap*r6252
r6192=--------------------------------
b12
r6193=r6389
r6194=0
a33*r6407 + b12*kap*r6336
r6195=---------------------------
b12
r6196=0
2*a33*r6356 + 2*a33*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
r6197=-------------------------------------------------------------
2*b12
r6198=0
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270
r6199=-----------------------------------------------------------------------
2
b12
2*a33*r6356 + 2*a33*r6407 + b12*kap*r6243 + 2*b12*kap*r6336 - b12*r6430
r6200=-------------------------------------------------------------------------
2*b12
3 2 2
r6201=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6202=0
r6203=0
2
- 2*a33*kap*r6129 - 2*a33*r6389 + b12*kap *r660
r6204=--------------------------------------------------
2*b12
r6205=0
3 2 2
r6206=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
2 2
- 4*a33 *r6356 - 2*a33*b12*kap*r6243 + 2*a33*b12*r6430 - b12 *kap*r6407
r6207=--------------------------------------------------------------------------
2
2*b12
r6208=0
3 2 2
r6209=(4*a33 *r6356 + 2*a33 *b12*kap*r6243 - 2*a33 *b12*r6430
2 3 2 3
+ 2*a33*b12 *kap*r6407 + b12 *kap *r6336)/(3*b12 )
r6210=0
- 4*a33*r6149 + 8*a33*r6336 + b12*r6407
r6211=------------------------------------------
2*b12*kap
r6212=0
- 4*a33*r6149 + 8*a33*r6336 + b12*r6407
r6213=------------------------------------------
b12*kap
r6214=0
- 4*a33*r6149 + 8*a33*r6336 + b12*r6407
r6215=------------------------------------------
2*b12*kap
r6216=r6230
r6217=0
r6218=2*r6230
r6219=0
r6220=r6230
r6221=0
- 4*a33*r6149 + 8*a33*r6336 + b12*r6407
r6222=------------------------------------------
b12*kap
r6223=0
- 4*a33*r6149 + 8*a33*r6336 + b12*r6407
r6224=------------------------------------------
b12*kap
r6225=2*r6230
r6226=0
r6227=2*r6230
r6228=0
- 4*a33*r6149 + 8*a33*r6336 + b12*r6407
r6229=------------------------------------------
2*b12*kap
r6231=0
r6232=r6270
r6233=0
r6234=r6270
r6235=0
r6236=r6243
r6237=0
r6238=r6243
r6239=0
r6240=0
r6241=r6270
r6242=0
r6244=0
r6245=0
r6246=0
- 2*r6129 + r6356
r6247=--------------------
2
r6248=0
r6249= - r6129
- 2*a33*r6270 - 2*b12*kap*r6230 + b12*r6157 + b12*r6252
r6250=----------------------------------------------------------
b12
r6251=0
r6253=0
r6254= - r6129
r6255=r6252
r6256=0
r6257= - r6133
r6258=0
r6260=0
r6261=0
r6262=0
r6263= - r6138
r6264=r680
r6265=0
r6266=0
r6267=0
r6268=r6270
r6269=0
r6271=0
r6272= - 2*r6149 + r6243 + 4*r6336
r6273=0
r6274= - 2*r6149 + r6243 + 4*r6336
r6275= - r6270
r6276=0
r6277=0
r6278=0
r6279= - 2*r6149 + r6243 + 4*r6336
r6280= - r6270
r6281=0
r6282=0
r6283=r6356
r6284=0
r6285=0
r6286=2*r6157 - 2*r6353
r6287=0
r6288= - r6356
r6289=0
r6290=0
r6291=0
r6292=0
r6293= - r6133
r6294=0
2*a33*r6259 - b12*kap*r6129 + b12*r6389
r6295=-----------------------------------------
2*a33
r6296=r6133
r6297=0
r6298=0
r6299=0
r6300=0
r6301=0
r6302=r6407
r6303=0
r6356 + 2*r6407
r6304=-----------------
2
2*a33*r6270 + 2*b12*kap*r6230
r6305=-------------------------------
b12
r6306=0
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - 2*b12*r6353
r6307=---------------------------------------------------------
b12
r6308=0
r6309=( - 2*a33*r6356 + 4*a33*r6407 - 2*b12*kap*r6149 + b12*kap*r6243
+ 4*b12*kap*r6336 - b12*r6430)/(4*a33)
r6310=r6353
r6311=0
2 2
- 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6353 + b12 *kap*r6270
r6312=--------------------------------------------------------------------------
2
b12
r6313=0
2*a33*r6356 + b12*kap*r6243
r6314=-----------------------------
b12
r6315=0
r6316=0
r6317=0
r6318= - r6389
- 2*a33*r6133 + b12*kap*r6252
r6319=--------------------------------
b12
r6320=0
r6321=0
r6322=0
2 2
- 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6353 + b12 *kap*r6270
r6323=--------------------------------------------------------------------------
2
b12
r6324=0
r6325=r6430
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270
r6326=-----------------------------------------------------------------------
2
b12
r6327=0
r6328=0
r6329=0
r6330=0
r6331=0
2 2
4*a33 *r6356 + 2*a33*b12*kap*r6243 - 2*a33*b12*r6430 + b12 *kap*r6407
r6332=-----------------------------------------------------------------------
2
2*b12
3 2 2
r6333=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6334=0
r6335=0
r6337=0
r6338=r6149
r6339=0
r6340=r6149 - r6336
r6341=0
r6342=r6270
r6343=0
r6344=r6270
1
r6345=---*r6243 + 2*r6336
2
r6346=0
2*r6149 + r6243
r6347=-----------------
2
r6348=0
r6349=r6270
1
r6350=---*r6243 + r6336
2
2*a33*r6270 + 2*b12*kap*r6230
r6351=-------------------------------
b12
r6352=0
r6354=0
r6355=0
r6357=0
r6358=r6157
r6359=0
r6360=0
- 4*a33*r6129 + 2*a33*r6356 + b12*kap*r6243 + 2*b12*kap*r660
r6361=---------------------------------------------------------------
2*b12
r6362=0
2 2 2
- 8*a33 *r6129 + 4*a33*b12*kap*r660 + b12 *kap*r6129 - b12 *r6389
r6363=--------------------------------------------------------------------
4*a33*b12
r6364=0
r6365= - r6133
- 4*a33*r6129 + 2*b12*kap*r660 + b12*r6259
r6366=---------------------------------------------
2*b12
- 2*a33*r6133 + b12*kap*r6252
r6367=--------------------------------
b12
r6368=0
r6369=0
- 4*a33*r6138 - b12*kap*r6259 + 2*b12*kap*r674
r6370=-------------------------------------------------
2*b12
r6371=0
2*a33*r6270 + 2*b12*kap*r6230
r6372=-------------------------------
b12
r6373=0
r6374=r6353
r6375= - r6407
r6376=0
r6377=(2*a33*r6356 - 4*a33*r6407 + 2*b12*kap*r6149 - b12*kap*r6243
- 4*b12*kap*r6336 + b12*r6430)/(4*a33)
r6378=0
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - 2*b12*r6353
r6379=---------------------------------------------------------
b12
1
r6380= - ---*r6356 - r6407
2
r6381=0
2*a33*r6356 + b12*kap*r6243
r6382=-----------------------------
b12
r6383=0
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270
r6384=-----------------------------------------------------------------------
2
b12
r6385=0
r6386=0
r6387=0
- 2*a33*r6133 + b12*kap*r6252
r6388=--------------------------------
b12
r6390=0
2*a33*r6407 + 2*b12*kap*r6336
r6391=-------------------------------
b12
r6392=0
r6393
4*a33*r6356 + 4*a33*r6407 + 2*b12*kap*r6243 + 4*b12*kap*r6336 - b12*r6430
=---------------------------------------------------------------------------
2*b12
r6394=0
r6395=0
r6396
4*a33*r6356 + 4*a33*r6407 + 2*b12*kap*r6243 + 4*b12*kap*r6336 - b12*r6430
=---------------------------------------------------------------------------
2*b12
3 2 2
r6397=( - 16*a33 *r6270 - 16*a33 *b12*kap*r6230 + 8*a33 *b12*r6353
2 3 2 3
+ 4*a33*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
r6398=0
r6399=0
2
- 2*a33*kap*r6129 - 2*a33*r6389 + b12*kap *r660
r6400=--------------------------------------------------
b12
r6401=0
3 2 2
r6402=( - 16*a33 *r6270 - 16*a33 *b12*kap*r6230 + 8*a33 *b12*r6353
2 3 2 3
+ 4*a33*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
2 2
- 4*a33 *r6356 - 2*a33*b12*kap*r6243 + 2*a33*b12*r6430 - b12 *kap*r6407
r6403=--------------------------------------------------------------------------
2
b12
r6404=0
3 2 2
r6405=(4*a33 *r6356 + 2*a33 *b12*kap*r6243 - 2*a33 *b12*r6430
2 3 2 3
+ 2*a33*b12 *kap*r6407 + b12 *kap *r6336)/b12
r6406=0
r6408=0
r6409=(2*a33*r6356 + 12*a33*r6407 - 2*b12*kap*r6149 + b12*kap*r6243
+ 4*b12*kap*r6336 - b12*r6430)/(12*a33)
2*a33*r6270 + 2*b12*kap*r6230
r6410=-------------------------------
b12
r6411=0
r6412=r6353
r6413=0
1
r6414=---*r6356 + r6407
2
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157
r6415=-------------------------------------------
3*b12
r6416=0
2 2
- 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6353 + b12 *kap*r6270
r6417=--------------------------------------------------------------------------
2
b12
r6418=0
2*a33*r6356 + b12*kap*r6243
r6419=-----------------------------
b12
r6420=0
r6421=0
r6422=0
r6423= - r6389
- 2*a33*r6133 + b12*kap*r6252
r6424=--------------------------------
b12
r6425=0
r6426=0
r6427=0
2 2
- 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6353 + b12 *kap*r6270
r6428=--------------------------------------------------------------------------
2
b12
r6429=0
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270
r6431=-----------------------------------------------------------------------
2
b12
r6432=0
r6433=0
r6434=0
r6435=0
r6436=0
2 2
4*a33 *r6356 + 2*a33*b12*kap*r6243 - 2*a33*b12*r6430 + b12 *kap*r6407
r6437=-----------------------------------------------------------------------
2
b12
3 2 2
r6438=( - 16*a33 *r6270 - 16*a33 *b12*kap*r6230 + 8*a33 *b12*r6353
2 3 2 3
+ 4*a33*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
r6439=0
r6440=0
a33*r6407 + b12*kap*r6336
r6441=---------------------------
b12
r6442=0
r6443
1 1
a33*r6356 + a33*r6407 + ---*b12*kap*r6243 + b12*kap*r6336 - ---*b12*r6430
2 2
=---------------------------------------------------------------------------
b12
r6444=0
2 2
- 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6353 + b12 *kap*r6270
r6445=--------------------------------------------------------------------------
2
b12
1
a33*r6356 + a33*r6407 + ---*b12*kap*r6243 + b12*kap*r6336
2
r6446=-----------------------------------------------------------
b12
3 2 2
r6447=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6448=0
r6449=0
2
- 2*a33*kap*r6129 - 2*a33*r6389 + b12*kap *r660
r6450=--------------------------------------------------
2*b12
r6451=0
3 2 2
r6452=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
2 1 2
- 2*a33 *r6356 - a33*b12*kap*r6243 + a33*b12*r6430 - ---*b12 *kap*r6407
2
r6453=--------------------------------------------------------------------------
2
b12
r6454=0
3 2 2
r6455=(4*a33 *r6356 + 2*a33 *b12*kap*r6243 - 2*a33 *b12*r6430
2 3 2 3
+ 2*a33*b12 *kap*r6407 + b12 *kap *r6336)/b12
r6456=0
2 1 2
2*a33 *r6356 + a33*b12*kap*r6243 - a33*b12*r6430 + ---*b12 *kap*r6407
2
r6457=-----------------------------------------------------------------------
2
b12
3 2 2
r6458=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6459=0
r6460=0
4 3 2 2 2 2
r6461=(---*a33 *r6356 + ---*a33 *b12*kap*r6243 - ---*a33 *b12*r6430
3 3 3
2 2 1 3 2 3
+ ---*a33*b12 *kap*r6407 + ---*b12 *kap *r6336)/b12
3 3
a23=0
a22=2*a33
a13=0
a11=2*a33
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:
r660, r674, r680, r683, r6129, r6133, r6138, r6149, r6157,
r6230, r6243, r6252, r6259, r6270, r6336, r6353, r6356,
r6389, r6407, r6430, 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,
a11,
b12,
2 2
4*a33 + b12 *kap,
{r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
16*a33 *r6149 - 32*a33 *r6336 - 4*a33 *b12*r6407 + 4*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
r6230,
2*r6230,
r6230,
2*r6230,
2*r6230,
r6230,
r6243 + r660,
1
---*r6243 + r660,
2
r660,
r6243 + 2*r660,
r660,
r660,
2*a33*r6270 + 2*b12*kap*r6230 - b12*r6157 - 3*b12*r6252,
r6252,
r6252,
r674,
b12*r6259 - 2*b12*r674,
1
---*b12*r6259 - b12*r674,
2
r680,
r683,
r6230,
2*r6230,
r6230,
2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407,
2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407,
2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407,
2*r6230,
2*r6230,
2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407,
2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407,
r6230,
2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407,
r6243,
r6243,
r6270,
r6270,
r6243,
r6270,
2*a33*r6270 + 2*b12*kap*r6230 - b12*r6157 - b12*r6252,
b12*r6252,
1
r6129 - ---*r6356,
2
r6129,
r6252,
r6129,
r6259,
r6133,
2
2*a33*b12 *kap*r680,
r6138,
a33*r6243 + 4*a33*r6336,
a33*r6243 + 2*a33*r6336,
r6270,
r6270,
r6149,
2*r6149 + r6243,
r6270,
2*a33*r6149 - 2*a33*r6336,
2*a33*r6270 + 2*b12*kap*r6230,
r6157,
r6356,
b12*r6353,
2 2
4*a33*b12*r6129 - 2*a33*b12*r6356 - b12 *kap*r6243 - 2*b12 *kap*r660,
2 2
4*a33*b12*r6129 - 2*b12 *kap*r660 - b12 *r6259,
2
2*a33*b12 *kap*r6133,
2 2 3 3
8*a33 *b12*r6129 - 4*a33*b12 *kap*r660 - b12 *kap*r6129 + b12 *r6389,
2 2 2
4*a33 *b12*kap*r6133 - 2*a33*b12 *kap *r6252,
2 3 3
4*a33*b12 *r6138 + b12 *kap*r6259 - 2*b12 *kap*r674,
2*a33*r6270 + 2*b12*kap*r6230,
4 4 1
---*a33*r6270 + ---*b12*kap*r6230 + ---*b12*r6157,
3 3 3
b12*r6407,
b12*r6356 + 2*b12*r6407,
b12*r6353,
2 2 2
2*a33 *b12*r6356 + 12*a33 *b12*r6407 - 2*a33*b12 *kap*r6149
2 2 2
+ a33*b12 *kap*r6243 + 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
2*a33*r6356 + b12*kap*r6243,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2 4 5 2
4*a33 *b12 *kap*r6133 - 2*a33*b12 *kap *r6252,
2
2*a33*b12 *r6389,
2 2
2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
2 2 2
2*a33 *b12*r6356 + 2*a33 *b12*r6407 + a33*b12 *kap*r6243
2
+ 2*a33*b12 *kap*r6336,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
3 3 2 2
4*a33 *b12*r6356 + 4*a33 *b12*r6407 + 2*a33 *b12 *kap*r6243
2 2 2 2
+ 4*a33 *b12 *kap*r6336 - 2*a33 *b12 *r6430,
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
2 2 2 2 3 2
4*a33 *b12 *kap*r6129 + 4*a33 *b12 *r6389 - 2*a33*b12 *kap *r660,
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
3 2 2 2 2
4*a33 *b12*r6356 + 2*a33 *b12 *kap*r6243 - 2*a33 *b12 *r6430
3
+ a33*b12 *kap*r6407,
4 3 2 3 2
8*a33 *b12*r6356 + 4*a33 *b12 *kap*r6243 - 4*a33 *b12 *r6430
2 3 4 2
+ 4*a33 *b12 *kap*r6407 + 2*a33*b12 *kap *r6336,
2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407,
2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407,
2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407,
r6230,
2*r6230,
r6230,
2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407,
2 2
8*a33 *r6149 - 16*a33 *r6336 - 2*a33*b12*r6407,
2*r6230,
2*r6230,
2 2
4*a33 *r6149 - 8*a33 *r6336 - a33*b12*r6407,
r6230,
r6270,
r6270,
r6243,
r6243,
r6270,
r6243,
2*b12*r6129 - b12*r6356,
b12*r6129,
2*a33*r6270 + 2*b12*kap*r6230 - b12*r6157 - b12*r6252,
r6252,
b12*r6129,
b12*r6252,
2*a33*b12*kap*r6133,
r6259,
2
b12 *r6138,
2
2*a33*b12 *kap*r680,
r6270,
r6270,
4*a33*r6149 - 2*a33*r6243 - 8*a33*r6336,
4*a33*r6149 - 2*a33*r6243 - 8*a33*r6336,
r6270,
4*a33*r6149 - 2*a33*r6243 - 8*a33*r6336,
r6270,
b12*r6356,
2*b12*r6157 - 2*b12*r6353,
b12*r6356,
2
2*a33*b12 *kap*r6133,
2 2
2*a33*b12*r6259 - b12 *kap*r6129 + b12 *r6389,
2
b12 *r6133,
b12*r6407,
b12*r6356 + 2*b12*r6407,
2*a33*r6270 + 2*b12*kap*r6230,
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - 2*b12*r6353,
2 2 2
2*a33 *b12*r6356 - 4*a33 *b12*r6407 + 2*a33*b12 *kap*r6149
2 2 2
- a33*b12 *kap*r6243 - 4*a33*b12 *kap*r6336 + a33*b12 *r6430,
b12*r6353,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2*a33*r6356 + b12*kap*r6243,
2
2*a33*b12 *r6389,
2 2 3 2
4*a33 *b12 *kap*r6133 - 2*a33*b12 *kap *r6252,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2
b12 *r6430,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2 2 2 3
4*a33 *b12*r6356 + 2*a33*b12 *kap*r6243 - 2*a33*b12 *r6430 + b12 *kap*r6407,
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
r6336,
2*a33*r6149,
2*a33*r6149 - 2*a33*r6336,
r6270,
r6270,
1
---*r6243 + 2*r6336,
2
2*a33*r6149 + a33*r6243,
r6270,
1
---*r6243 + r6336,
2
2*a33*r6270 + 2*b12*kap*r6230,
r6353,
r6356,
b12*r6157,
2 2
4*a33*b12*r6129 - 2*a33*b12*r6356 - b12 *kap*r6243 - 2*b12 *kap*r660,
2 2 3 3
8*a33 *b12*r6129 - 4*a33*b12 *kap*r660 - b12 *kap*r6129 + b12 *r6389,
2
2*a33*b12 *kap*r6133,
2 2
4*a33*b12*r6129 - 2*b12 *kap*r660 - b12 *r6259,
2 2 2
4*a33 *b12*kap*r6133 - 2*a33*b12 *kap *r6252,
2 3 3
4*a33*b12 *r6138 + b12 *kap*r6259 - 2*b12 *kap*r674,
2*a33*r6270 + 2*b12*kap*r6230,
b12*r6353,
r6407,
2 2 2
2*a33 *b12*r6356 - 4*a33 *b12*r6407 + 2*a33*b12 *kap*r6149
2 2 2
- a33*b12 *kap*r6243 - 4*a33*b12 *kap*r6336 + a33*b12 *r6430,
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - 2*b12*r6353,
a33*b12*r6356 + 2*a33*b12*r6407,
2*a33*r6356 + b12*kap*r6243,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2 4 5 2
4*a33 *b12 *kap*r6133 - 2*a33*b12 *kap *r6252,
r6389,
2 2
4*a33 *b12*r6407 + 4*a33*b12 *kap*r6336,
2 2 2
4*a33 *b12*r6356 + 4*a33 *b12*r6407 + 2*a33*b12 *kap*r6243
2 2
+ 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
2 2 2
4*a33 *b12*r6356 + 4*a33 *b12*r6407 + 2*a33*b12 *kap*r6243
2 2
+ 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
3 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 8*a33 *b12*r6353
2 3 2
- 4*a33*b12 *kap*r6270 - 2*b12 *kap *r6230,
2 2 3 2
2*a33*b12 *kap*r6129 + 2*a33*b12 *r6389 - b12 *kap *r660,
3 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 8*a33 *b12*r6353
2 3 2
- 4*a33*b12 *kap*r6270 - 2*b12 *kap *r6230,
3 2 2 2 2
8*a33 *b12*r6356 + 4*a33 *b12 *kap*r6243 - 4*a33 *b12 *r6430
3
+ 2*a33*b12 *kap*r6407,
4 3 2 3 2
8*a33 *b12*r6356 + 4*a33 *b12 *kap*r6243 - 4*a33 *b12 *r6430
2 3 4 2
+ 4*a33 *b12 *kap*r6407 + 2*a33*b12 *kap *r6336,
r6407,
2 2 2
2*a33 *b12*r6356 + 12*a33 *b12*r6407 - 2*a33*b12 *kap*r6149
2 2 2
+ a33*b12 *kap*r6243 + 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
2*a33*r6270 + 2*b12*kap*r6230,
2*a33*b12*r6353,
a33*b12*r6356 + 2*a33*b12*r6407,
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2*a33*r6356 + b12*kap*r6243,
2
b12 *r6389,
2 2 2
4*a33 *b12*kap*r6133 - 2*a33*b12 *kap *r6252,
3 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 8*a33 *b12*r6353
2
- 2*a33*b12 *kap*r6270,
r6430,
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2 2
4*a33 *r6356 + 2*a33*b12*kap*r6243 - 2*a33*b12*r6430 + b12 *kap*r6407,
3 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 8*a33 *b12*r6353
2 3 2
- 4*a33*b12 *kap*r6270 - 2*b12 *kap *r6230,
a33*r6407 + b12*kap*r6336,
1 2 2
a33*b12*r6356 + a33*b12*r6407 + ---*b12 *kap*r6243 + b12 *kap*r6336
2
1 2
- ---*b12 *r6430,
2
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
1 2 2
a33*b12*r6356 + a33*b12*r6407 + ---*b12 *kap*r6243 + b12 *kap*r6336,
2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
2 2 3 2
4*a33*b12 *kap*r6129 + 4*a33*b12 *r6389 - 2*b12 *kap *r660,
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
3 2 2 2 2
4*a33 *b12*r6356 + 2*a33 *b12 *kap*r6243 - 2*a33 *b12 *r6430
3
+ a33*b12 *kap*r6407,
4 3 2 3 2
8*a33 *b12*r6356 + 4*a33 *b12 *kap*r6243 - 4*a33 *b12 *r6430
2 3 4 2
+ 4*a33 *b12 *kap*r6407 + 2*a33*b12 *kap *r6336,
2 2 2 1 3
2*a33 *b12*r6356 + a33*b12 *kap*r6243 - a33*b12 *r6430 + ---*b12 *kap*r6407,
2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
4 3 2 2 2 2 2 2
---*a33 *b12*r6356 + ---*a33 *b12 *kap*r6243 - ---*a33 *b12 *r6430
3 3 3
2 3 1 4 2
+ ---*a33*b12 *kap*r6407 + ---*b12 *kap *r6336}}
3 3
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=2*u1 *a33 + u1*v2*b12 + 2*u2 *a33 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=2*u1**2*a33 + u1*v2*b12 + 2*u2**2*a33 - u2*v1*b12 + u3**2*a33$