Solution 31 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
1 3 1 3 1 3
r60=( - ---*a11 *r6356 + ---*a11 *r6377 + ---*a11 *r6407
3 3 6
1 2 1 2 1 2
- ---*a11 *b12*kap*r6336 + ---*a11 *b12*r6443 - ---*a11*b12 *kap*r6407
3 3 6
1 3 2 3 3
+ ---*b12 *kap *r6336)/(b12 *kap )
3
r61=0
3 3 1 3 2
r62=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11 *b12*kap*r6336
2
2 1 2 3 2 3 3
+ a11 *b12*r6443 - ---*a11*b12 *kap*r6407 + b12 *kap *r6336)/(b12 *kap )
2
r63=0
3 3 1 3 2
r64=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11 *b12*kap*r6336
2
2 1 2 3 2 3 3
+ a11 *b12*r6443 - ---*a11*b12 *kap*r6407 + b12 *kap *r6336)/(b12 *kap )
2
r65=0
1 3 1 3 1 3
r66=( - ---*a11 *r6356 + ---*a11 *r6377 + ---*a11 *r6407
3 3 6
1 2 1 2 1 2
- ---*a11 *b12*kap*r6336 + ---*a11 *b12*r6443 - ---*a11*b12 *kap*r6407
3 3 6
1 3 2 3 3
+ ---*b12 *kap *r6336)/(b12 *kap )
3
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
3 3 1 3 2
r613=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11 *b12*kap*r6336
2
2 1 2 3 2 3 3
+ a11 *b12*r6443 - ---*a11*b12 *kap*r6407 + b12 *kap *r6336)/(b12 *kap )
2
r614=0
3 3 3 2
r615=( - 2*a11 *r6356 + 2*a11 *r6377 + a11 *r6407 - 2*a11 *b12*kap*r6336
2 2 3 2 3 3
+ 2*a11 *b12*r6443 - a11*b12 *kap*r6407 + 2*b12 *kap *r6336)/(b12 *kap )
r616=0
3 3 1 3 2
r617=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11 *b12*kap*r6336
2
2 1 2 3 2 3 3
+ a11 *b12*r6443 - ---*a11*b12 *kap*r6407 + b12 *kap *r6336)/(b12 *kap )
2
r618=0
r619=0
r620=0
r621=0
3 3 1 3 2
r622=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11 *b12*kap*r6336
2
2 1 2 3 2 3 3
+ a11 *b12*r6443 - ---*a11*b12 *kap*r6407 + b12 *kap *r6336)/(b12 *kap )
2
r623=0
3 3 1 3 2
r624=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11 *b12*kap*r6336
2
2 1 2 3 2 3 3
+ a11 *b12*r6443 - ---*a11*b12 *kap*r6407 + b12 *kap *r6336)/(b12 *kap )
2
r625=0
r626=0
1 3 1 3 1 3
r627=( - ---*a11 *r6356 + ---*a11 *r6377 + ---*a11 *r6407
3 3 6
1 2 1 2 1 2
- ---*a11 *b12*kap*r6336 + ---*a11 *b12*r6443 - ---*a11*b12 *kap*r6407
3 3 6
1 3 2 3 3
+ ---*b12 *kap *r6336)/(b12 *kap )
3
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
r649=---*r6243 + ---*r658
4 2
r650=0
r651=r658
r652=0
1 1
r653= - ---*r6243 + ---*r658
4 2
r654=0
r655=0
r656=0
r657=0
r659=0
1
r660= - ---*r6243 + r658
2
r661=0
r662=0
1 1
r663= - ---*r6243 + ---*r658
4 2
1 2 1
- ---*a11*r6349 - ---*b12*kap*r6230 + b12*r6255 + ---*b12*r6358
3 3 3
r664=------------------------------------------------------------------
b12
r665=0
r666=r6255
r667=0
r668=0
r669=0
r670=0
r671=r6255
r672=0
r673=0
1
r674=---*r6259 + r679
2
r675=0
r676=r679
r677=0
r678=0
r680=r6264
r681=0
r682=0
r684=0
r685=r6230
r686=0
r687=2*r6230
r688=0
r689=r6230
2 2 1 2
r690=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11*b12*kap*r6336
2
1 2 2 2
+ a11*b12*r6443 - ---*b12 *kap*r6407)/(b12 *kap )
2
r691=0
2 2 2
r692=( - 2*a11 *r6356 + 2*a11 *r6377 + a11 *r6407 - 2*a11*b12*kap*r6336
2 2 2
+ 2*a11*b12*r6443 - b12 *kap*r6407)/(b12 *kap )
r693=0
2 2 1 2
r694=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11*b12*kap*r6336
2
1 2 2 2
+ a11*b12*r6443 - ---*b12 *kap*r6407)/(b12 *kap )
2
r695=0
r696=2*r6230
r697=0
r698=2*r6230
2 2 2
r699=( - 2*a11 *r6356 + 2*a11 *r6377 + a11 *r6407 - 2*a11*b12*kap*r6336
2 2 2
+ 2*a11*b12*r6443 - b12 *kap*r6407)/(b12 *kap )
r6100=0
2 2 2
r6101=( - 2*a11 *r6356 + 2*a11 *r6377 + a11 *r6407 - 2*a11*b12*kap*r6336
2 2 2
+ 2*a11*b12*r6443 - b12 *kap*r6407)/(b12 *kap )
r6102=0
r6103=r6230
2 2 1 2
r6104=( - a11 *r6356 + a11 *r6377 + ---*a11 *r6407 - a11*b12*kap*r6336
2
1 2 2 2
+ a11*b12*r6443 - ---*b12 *kap*r6407)/(b12 *kap )
2
r6105=0
r6106=r6243
r6107=0
r6108=r6243
r6109=0
r6110= - r6349
r6111=0
r6112= - r6349
r6113=0
r6114=0
r6115=r6243
r6116=0
r6117= - r6349
r6118=0
r6119=0
r6120=0
- a11*r6349 - 2*b12*kap*r6230 + b12*r6255 + b12*r6358
r6121=--------------------------------------------------------
b12
r6122=0
r6123=r6255
1
r6124= - r6249 - ---*r6356
2
r6125=0
r6126= - r6249
r6127=0
r6128=r6255
r6129= - r6249
r6130=0
r6131=r6259
r6132=0
r6133= - r6257
r6134=0
r6135=0
r6136=0
r6137=r6264
r6138= - r6263
r6139=0
r6140=r6336
r6141=0
1
r6142=---*r6243 + 2*r6336
2
r6143=0
1
r6144=---*r6243 + r6336
2
r6145=0
r6146= - r6349
r6147=0
r6148= - r6349
1
- a11*r6356 + a11*r6377 + ---*a11*r6407 + b12*kap*r6336 + b12*r6443
2
r6149=----------------------------------------------------------------------
b12*kap
r6150=0
1 1
r6151=( - a11*r6356 + a11*r6377 + ---*a11*r6407 + ---*b12*kap*r6243
2 2
+ b12*kap*r6336 + b12*r6443)/(b12*kap)
r6152=0
r6153= - r6349
1
- a11*r6356 + a11*r6377 + ---*a11*r6407 + b12*r6443
2
r6154=------------------------------------------------------
b12*kap
a11*r6349 + 2*b12*kap*r6230
r6155=-----------------------------
b12
r6156=0
r6157=r6358
r6158=0
r6159=0
r6160= - r6356
r6161=0
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358
2 2
r6162=-------------------------------------------------------------
b12
r6163=0
r6164=0
1
a11*r6249 + ---*a11*r6356 + b12*kap*r658
2
r6165=------------------------------------------
b12
r6166=0
1 1
a11*r6249 - ---*b12*kap*r6243 + b12*kap*r658 + ---*b12*r6259
2 2
r6167=--------------------------------------------------------------
b12
r6168=0
r6169= - r6257
r6170
1 1 1
a11*r6249 - ---*b12*kap*r6243 + b12*kap*r658 + ---*b12*r6259 - ---*b12*r6295
2 2 2
=------------------------------------------------------------------------------
b12
a11*r6257 + b12*kap*r6255
r6171=---------------------------
b12
r6172=0
r6173=0
a11*r6263 + b12*kap*r679
r6174=--------------------------
b12
r6175=0
a11*r6349 + 2*b12*kap*r6230
r6176=-----------------------------
b12
r6177=0
2 4 1
---*a11*r6349 + ---*b12*kap*r6230 + ---*b12*r6358
3 3 3
r6178=---------------------------------------------------
b12
r6179= - r6407
r6180=0
1
r6181= - ---*r6356 - r6407
2
r6182=0
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358
2 2
r6183=-------------------------------------------------------------
b12
1 1 2
r6184= - ---*r6356 + ---*r6377 - ---*r6407
3 3 3
r6185=0
a11*r6356 + b12*kap*r6243
r6186=---------------------------
b12
r6187=0
a11*r6307 - a11*r6358 - b12*kap*r6349
r6188=---------------------------------------
b12
r6189=0
r6190=0
r6191=0
a11*r6257 + b12*kap*r6255
r6192=---------------------------
b12
- a11*r6259 + a11*r6295 - b12*kap*r6249
r6193=------------------------------------------
b12
r6194=0
1
---*a11*r6407 + b12*kap*r6336
2
r6195=-------------------------------
b12
r6196=0
1 1 1
---*a11*r6356 + ---*a11*r6407 + ---*b12*kap*r6243 + b12*kap*r6336
2 2 2
r6197=-------------------------------------------------------------------
b12
r6198=0
a11*r6307 - a11*r6358 - b12*kap*r6349
r6199=---------------------------------------
b12
r6200=r6443
1 2 1 2 2 2
- ---*a11 *r6307 + ---*a11 *r6358 + a11*b12*kap*r6349 + b12 *kap *r6230
2 2
r6201=--------------------------------------------------------------------------
2
b12
r6202=0
r6203=0
1 2 1 2 1 2 2
r6204=(---*a11 *r6259 - ---*a11 *r6295 + a11*b12*kap*r6249 - ---*b12 *kap *r6243
2 2 4
1 2 2 2
+ ---*b12 *kap *r658)/b12
2
r6205=0
1 2 1 2 2 2
- ---*a11 *r6307 + ---*a11 *r6358 + a11*b12*kap*r6349 + b12 *kap *r6230
2 2
r6206=--------------------------------------------------------------------------
2
b12
1 2 1 2
---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443 - ---*b12 *kap*r6407
2 2
r6207=-------------------------------------------------------------------------
2
b12
r6208=0
1 3 1 2 1 2
r6209=( - ---*a11 *r6407 - ---*a11 *b12*kap*r6336 + ---*a11 *b12*r6443
6 3 3
1 2 1 3 2 3
+ ---*a11*b12 *kap*r6407 + ---*b12 *kap *r6336)/b12
3 3
r6210=0
2 2 1 2
r6211=(a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336
2
1 2 2 2
- a11*b12*r6443 + ---*b12 *kap*r6407)/(b12 *kap )
2
r6212=0
2 2 2
r6213=(2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2 2 2
- 2*a11*b12*r6443 + b12 *kap*r6407)/(b12 *kap )
r6214=0
2 2 1 2
r6215=(a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336
2
1 2 2 2
- a11*b12*r6443 + ---*b12 *kap*r6407)/(b12 *kap )
2
r6216=r6230
r6217=0
r6218=2*r6230
r6219=0
r6220=r6230
r6221=0
2 2 2
r6222=(2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2 2 2
- 2*a11*b12*r6443 + b12 *kap*r6407)/(b12 *kap )
r6223=0
2 2 2
r6224=(2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2 2 2
- 2*a11*b12*r6443 + b12 *kap*r6407)/(b12 *kap )
r6225=2*r6230
r6226=0
r6227=2*r6230
r6228=0
2 2 1 2
r6229=(a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336
2
1 2 2 2
- a11*b12*r6443 + ---*b12 *kap*r6407)/(b12 *kap )
2
r6231=0
r6232=r6349
r6233=0
r6234=r6349
r6235=0
r6236=r6243
r6237=0
r6238=r6243
r6239=0
r6240=0
r6241=r6349
r6242=0
r6244=0
r6245=0
r6246=0
1
r6247=r6249 + ---*r6356
2
r6248=0
- a11*r6349 - 2*b12*kap*r6230 + b12*r6255 + b12*r6358
r6250=--------------------------------------------------------
b12
r6251=0
r6252=r6255
r6253=0
r6254=r6249
r6256=0
r6258=0
r6260=0
r6261=0
r6262=0
r6265=0
r6266=0
r6267=0
r6268=r6349
r6269=0
r6270=r6349
r6271=0
r6272=(2*a11*r6356 - 2*a11*r6377 - a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
- 2*b12*r6443)/(b12*kap)
r6273=0
r6274=(2*a11*r6356 - 2*a11*r6377 - a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
- 2*b12*r6443)/(b12*kap)
r6275= - r6349
r6276=0
r6277=0
r6278=0
r6279=(2*a11*r6356 - 2*a11*r6377 - a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
- 2*b12*r6443)/(b12*kap)
r6280= - r6349
r6281=0
r6282=0
r6283=r6356
r6284=0
r6285=0
- 2*a11*r6349 - 4*b12*kap*r6230 + b12*r6307 + b12*r6358
r6286=----------------------------------------------------------
b12
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
r6302=r6407
r6303=0
1
r6304=---*r6356 + r6407
2
a11*r6349 + 2*b12*kap*r6230
r6305=-----------------------------
b12
r6306=0
r6308=0
r6309= - r6377
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358
2 2
r6310=-------------------------------------------------------------
b12
r6311=0
- a11*r6307 + a11*r6358 + b12*kap*r6349
r6312=------------------------------------------
b12
r6313=0
a11*r6356 + b12*kap*r6243
r6314=---------------------------
b12
r6315=0
r6316=0
r6317=0
a11*r6259 - a11*r6295 + b12*kap*r6249
r6318=---------------------------------------
b12
a11*r6257 + b12*kap*r6255
r6319=---------------------------
b12
r6320=0
r6321=0
r6322=0
- a11*r6307 + a11*r6358 + b12*kap*r6349
r6323=------------------------------------------
b12
r6324=0
a11*r6356 + a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336 - 2*b12*r6443
r6325=-----------------------------------------------------------------------
b12
a11*r6307 - a11*r6358 - b12*kap*r6349
r6326=---------------------------------------
b12
r6327=0
r6328=0
r6329=0
r6330=0
r6331=0
r6332
1 2 1 2
- ---*a11 *r6407 - a11*b12*kap*r6336 + a11*b12*r6443 + ---*b12 *kap*r6407
2 2
=----------------------------------------------------------------------------
2
b12
1 2 1 2 2 2
- ---*a11 *r6307 + ---*a11 *r6358 + a11*b12*kap*r6349 + b12 *kap *r6230
2 2
r6333=--------------------------------------------------------------------------
2
b12
r6334=0
r6335=0
r6337=0
1
- a11*r6356 + a11*r6377 + ---*a11*r6407 + b12*kap*r6336 + b12*r6443
2
r6338=----------------------------------------------------------------------
b12*kap
r6339=0
1
- a11*r6356 + a11*r6377 + ---*a11*r6407 + b12*r6443
2
r6340=------------------------------------------------------
b12*kap
r6341=0
r6342=r6349
r6343=0
r6344=r6349
1
r6345=---*r6243 + 2*r6336
2
r6346=0
1 1
r6347=( - a11*r6356 + a11*r6377 + ---*a11*r6407 + ---*b12*kap*r6243
2 2
+ b12*kap*r6336 + b12*r6443)/(b12*kap)
r6348=0
1
r6350=---*r6243 + r6336
2
a11*r6349 + 2*b12*kap*r6230
r6351=-----------------------------
b12
r6352=0
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358
2 2
r6353=-------------------------------------------------------------
b12
r6354=0
r6355=0
r6357=0
r6359=0
r6360=0
1
a11*r6249 + ---*a11*r6356 + b12*kap*r658
2
r6361=------------------------------------------
b12
r6362=0
r6363
1 1 1
a11*r6249 - ---*b12*kap*r6243 + b12*kap*r658 + ---*b12*r6259 - ---*b12*r6295
2 2 2
=------------------------------------------------------------------------------
b12
r6364=0
r6365=r6257
1 1
a11*r6249 - ---*b12*kap*r6243 + b12*kap*r658 + ---*b12*r6259
2 2
r6366=--------------------------------------------------------------
b12
a11*r6257 + b12*kap*r6255
r6367=---------------------------
b12
r6368=0
r6369=0
a11*r6263 + b12*kap*r679
r6370=--------------------------
b12
r6371=0
a11*r6349 + 2*b12*kap*r6230
r6372=-----------------------------
b12
r6373=0
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358
2 2
r6374=-------------------------------------------------------------
b12
r6375= - r6407
r6376=0
r6378=0
r6379=r6307
1
r6380= - ---*r6356 - r6407
2
r6381=0
a11*r6356 + b12*kap*r6243
r6382=---------------------------
b12
r6383=0
a11*r6307 - a11*r6358 - b12*kap*r6349
r6384=---------------------------------------
b12
r6385=0
r6386=0
r6387=0
a11*r6257 + b12*kap*r6255
r6388=---------------------------
b12
- a11*r6259 + a11*r6295 - b12*kap*r6249
r6389=------------------------------------------
b12
r6390=0
a11*r6407 + 2*b12*kap*r6336
r6391=-----------------------------
b12
r6392=0
r6393
1 1 1
---*a11*r6356 + ---*a11*r6407 + ---*b12*kap*r6243 + b12*kap*r6336 + b12*r6443
2 2 2
=-------------------------------------------------------------------------------
b12
r6394=0
r6395=0
r6396
1 1 1
---*a11*r6356 + ---*a11*r6407 + ---*b12*kap*r6243 + b12*kap*r6336 + b12*r6443
2 2 2
=-------------------------------------------------------------------------------
b12
2 2 2 2
- a11 *r6307 + a11 *r6358 + 2*a11*b12*kap*r6349 + 2*b12 *kap *r6230
r6397=----------------------------------------------------------------------
2
b12
r6398=0
r6399=0
2 2 1 2 2
r6400=(a11 *r6259 - a11 *r6295 + 2*a11*b12*kap*r6249 - ---*b12 *kap *r6243
2
2 2 2
+ b12 *kap *r658)/b12
r6401=0
2 2 2 2
- a11 *r6307 + a11 *r6358 + 2*a11*b12*kap*r6349 + 2*b12 *kap *r6230
r6402=----------------------------------------------------------------------
2
b12
2 2
a11 *r6407 + 2*a11*b12*kap*r6336 - 2*a11*b12*r6443 - b12 *kap*r6407
r6403=---------------------------------------------------------------------
2
b12
r6404=0
1 3 2 2
r6405=( - ---*a11 *r6407 - a11 *b12*kap*r6336 + a11 *b12*r6443
2
2 3 2 3
+ a11*b12 *kap*r6407 + b12 *kap *r6336)/b12
r6406=0
r6408=0
1 1 2
r6409=---*r6356 - ---*r6377 + ---*r6407
3 3 3
a11*r6349 + 2*b12*kap*r6230
r6410=-----------------------------
b12
r6411=0
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358
2 2
r6412=-------------------------------------------------------------
b12
r6413=0
1
r6414=---*r6356 + r6407
2
2 4 1
---*a11*r6349 + ---*b12*kap*r6230 + ---*b12*r6358
3 3 3
r6415=---------------------------------------------------
b12
r6416=0
- a11*r6307 + a11*r6358 + b12*kap*r6349
r6417=------------------------------------------
b12
r6418=0
a11*r6356 + b12*kap*r6243
r6419=---------------------------
b12
r6420=0
r6421=0
r6422=0
a11*r6259 - a11*r6295 + b12*kap*r6249
r6423=---------------------------------------
b12
a11*r6257 + b12*kap*r6255
r6424=---------------------------
b12
r6425=0
r6426=0
r6427=0
- a11*r6307 + a11*r6358 + b12*kap*r6349
r6428=------------------------------------------
b12
r6429=0
a11*r6356 + a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336 - 2*b12*r6443
r6430=-----------------------------------------------------------------------
b12
a11*r6307 - a11*r6358 - b12*kap*r6349
r6431=---------------------------------------
b12
r6432=0
r6433=0
r6434=0
r6435=0
r6436=0
2 2
- a11 *r6407 - 2*a11*b12*kap*r6336 + 2*a11*b12*r6443 + b12 *kap*r6407
r6437=------------------------------------------------------------------------
2
b12
2 2 2 2
- a11 *r6307 + a11 *r6358 + 2*a11*b12*kap*r6349 + 2*b12 *kap *r6230
r6438=----------------------------------------------------------------------
2
b12
r6439=0
r6440=0
1
---*a11*r6407 + b12*kap*r6336
2
r6441=-------------------------------
b12
r6442=0
r6444=0
- a11*r6307 + a11*r6358 + b12*kap*r6349
r6445=------------------------------------------
b12
1 1 1
---*a11*r6356 + ---*a11*r6407 + ---*b12*kap*r6243 + b12*kap*r6336
2 2 2
r6446=-------------------------------------------------------------------
b12
1 2 1 2 2 2
- ---*a11 *r6307 + ---*a11 *r6358 + a11*b12*kap*r6349 + b12 *kap *r6230
2 2
r6447=--------------------------------------------------------------------------
2
b12
r6448=0
r6449=0
1 2 1 2 1 2 2
r6450=(---*a11 *r6259 - ---*a11 *r6295 + a11*b12*kap*r6249 - ---*b12 *kap *r6243
2 2 4
1 2 2 2
+ ---*b12 *kap *r658)/b12
2
r6451=0
1 2 1 2 2 2
- ---*a11 *r6307 + ---*a11 *r6358 + a11*b12*kap*r6349 + b12 *kap *r6230
2 2
r6452=--------------------------------------------------------------------------
2
b12
1 2 1 2
---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443 - ---*b12 *kap*r6407
2 2
r6453=-------------------------------------------------------------------------
2
b12
r6454=0
1 3 2 2
r6455=( - ---*a11 *r6407 - a11 *b12*kap*r6336 + a11 *b12*r6443
2
2 3 2 3
+ a11*b12 *kap*r6407 + b12 *kap *r6336)/b12
r6456=0
r6457
1 2 1 2
- ---*a11 *r6407 - a11*b12*kap*r6336 + a11*b12*r6443 + ---*b12 *kap*r6407
2 2
=----------------------------------------------------------------------------
2
b12
1 2 1 2 2 2
- ---*a11 *r6307 + ---*a11 *r6358 + a11*b12*kap*r6349 + b12 *kap *r6230
2 2
r6458=--------------------------------------------------------------------------
2
b12
r6459=0
r6460=0
1 3 1 2 1 2
r6461=( - ---*a11 *r6407 - ---*a11 *b12*kap*r6336 + ---*a11 *b12*r6443
6 3 3
1 2 1 3 2 3
+ ---*a11*b12 *kap*r6407 + ---*b12 *kap *r6336)/b12
3 3
a33=0
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:
r658, r679, r683, r6230, r6243, r6249, r6255, r6257, r6259,
r6263, r6264, r6295, r6307, r6336, r6349, r6356, r6358,
r6377, r6407, r6443, 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.
{b12,
1 3 1 3 1 3 1 2
{---*a11 *r6356 - ---*a11 *r6377 - ---*a11 *r6407 + ---*a11 *b12*kap*r6336
3 3 6 3
1 2 1 2 1 3 2
- ---*a11 *b12*r6443 + ---*a11*b12 *kap*r6407 - ---*b12 *kap *r6336,
3 6 3
3 3 1 3 2 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11 *b12*kap*r6336 - a11 *b12*r6443
2
1 2 3 2
+ ---*a11*b12 *kap*r6407 - b12 *kap *r6336,
2
3 3 1 3 2 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11 *b12*kap*r6336 - a11 *b12*r6443
2
1 2 3 2
+ ---*a11*b12 *kap*r6407 - b12 *kap *r6336,
2
1 3 1 3 1 3 1 2
---*a11 *r6356 - ---*a11 *r6377 - ---*a11 *r6407 + ---*a11 *b12*kap*r6336
3 3 6 3
1 2 1 2 1 3 2
- ---*a11 *b12*r6443 + ---*a11*b12 *kap*r6407 - ---*b12 *kap *r6336,
3 6 3
3 3 1 3 2 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11 *b12*kap*r6336 - a11 *b12*r6443
2
1 2 3 2
+ ---*a11*b12 *kap*r6407 - b12 *kap *r6336,
2
3 3 3 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11 *b12*kap*r6336
2 2 3 2
- 2*a11 *b12*r6443 + a11*b12 *kap*r6407 - 2*b12 *kap *r6336,
3 3 1 3 2 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11 *b12*kap*r6336 - a11 *b12*r6443
2
1 2 3 2
+ ---*a11*b12 *kap*r6407 - b12 *kap *r6336,
2
3 3 1 3 2 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11 *b12*kap*r6336 - a11 *b12*r6443
2
1 2 3 2
+ ---*a11*b12 *kap*r6407 - b12 *kap *r6336,
2
3 3 1 3 2 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11 *b12*kap*r6336 - a11 *b12*r6443
2
1 2 3 2
+ ---*a11*b12 *kap*r6407 - b12 *kap *r6336,
2
1 3 1 3 1 3 1 2
---*a11 *r6356 - ---*a11 *r6377 - ---*a11 *r6407 + ---*a11 *b12*kap*r6336
3 3 6 3
1 2 1 2 1 3 2
- ---*a11 *b12*r6443 + ---*a11*b12 *kap*r6407 - ---*b12 *kap *r6336,
3 6 3
r6230,
2*r6230,
r6230,
2*r6230,
2*r6230,
r6230,
1 1
---*r6243 + ---*r658,
4 2
r658,
1 1
---*r6243 - ---*r658,
4 2
r658,
1
---*r6243 - r658,
2
1 1
---*r6243 - ---*r658,
4 2
1 2 2 2 2
---*a11*b12*kap*r6349 + ---*b12 *kap *r6230 - b12 *kap*r6255
3 3
1 2
- ---*b12 *kap*r6358,
3
4 2
b12 *kap *r6255,
r6255,
1
---*r6259 + r679,
2
r679,
r679,
r6264,
r683,
r6230,
2*r6230,
r6230,
2 2 1 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443
2
1 2
+ ---*b12 *kap*r6407,
2
2 2 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2
- 2*a11*b12*r6443 + b12 *kap*r6407,
2 2 1 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443
2
1 2
+ ---*b12 *kap*r6407,
2
2*r6230,
2*r6230,
2 2 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2
- 2*a11*b12*r6443 + b12 *kap*r6407,
2 2 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2
- 2*a11*b12*r6443 + b12 *kap*r6407,
r6230,
2 2 1 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443
2
1 2
+ ---*b12 *kap*r6407,
2
r6243,
r6243,
b12*kap*r6349,
r6349,
r6243,
r6349,
3 2 4 3 4 2 4 2
a11*b12 *kap *r6349 + 2*b12 *kap *r6230 - b12 *kap *r6255 - b12 *kap *r6358,
4 2
b12 *kap *r6255,
1
b12*kap*r6249 + ---*b12*kap*r6356,
2
b12*kap*r6249,
4 2
b12 *kap *r6255,
b12*kap*r6249,
r6259,
3
b12 *kap*r6257,
r6264,
r6263,
r6336,
1
---*r6243 + 2*r6336,
2
1
---*r6243 + r6336,
2
r6349,
r6349,
1
a11*r6356 - a11*r6377 - ---*a11*r6407 - b12*kap*r6336 - b12*r6443,
2
1 1
a11*r6356 - a11*r6377 - ---*a11*r6407 - ---*b12*kap*r6243 - b12*kap*r6336
2 2
- b12*r6443,
r6349,
1
a11*r6356 - a11*r6377 - ---*a11*r6407 - b12*r6443,
2
2 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230,
r6358,
r6356,
2 2 1 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230 - ---*b12 *kap*r6307
2
1 2
+ ---*b12 *kap*r6358,
2
1 2 2
a11*b12*kap*r6249 + ---*a11*b12*kap*r6356 + b12 *kap *r658,
2
1 1
a11*r6249 - ---*b12*kap*r6243 + b12*kap*r658 + ---*b12*r6259,
2 2
5 2
b12 *kap *r6257,
1 2 2 2 2 1 2
a11*b12*kap*r6249 - ---*b12 *kap *r6243 + b12 *kap *r658 + ---*b12 *kap*r6259
2 2
1 2
- ---*b12 *kap*r6295,
2
3 4 2
a11*b12 *kap*r6257 + b12 *kap *r6255,
a11*r6263 + b12*kap*r679,
a11*r6349 + 2*b12*kap*r6230,
2 4 1
---*a11*r6349 + ---*b12*kap*r6230 + ---*b12*r6358,
3 3 3
b12*r6407,
1
---*b12*kap*r6356 + b12*kap*r6407,
2
3 2 4 3 1 4 2
a11*b12 *kap *r6349 + 2*b12 *kap *r6230 - ---*b12 *kap *r6307
2
1 4 2
+ ---*b12 *kap *r6358,
2
1 1 2
---*b12*kap*r6356 - ---*b12*kap*r6377 + ---*b12*kap*r6407,
3 3 3
a11*r6356 + b12*kap*r6243,
a11*r6307 - a11*r6358 - b12*kap*r6349,
5 2 6 3
a11*b12 *kap *r6257 + b12 *kap *r6255,
2 2 3 2
a11*b12 *kap*r6259 - a11*b12 *kap*r6295 + b12 *kap *r6249,
1 2
---*a11*b12*r6407 + b12 *kap*r6336,
2
1 1 1 2 2
---*a11*b12*kap*r6356 + ---*a11*b12*kap*r6407 + ---*b12 *kap *r6243
2 2 2
2 2
+ b12 *kap *r6336,
4 2 4 2 5 3
a11*b12 *kap *r6307 - a11*b12 *kap *r6358 - b12 *kap *r6349,
2
b12 *kap*r6443,
1 2 1 2 2 2
---*a11 *r6307 - ---*a11 *r6358 - a11*b12*kap*r6349 - b12 *kap *r6230,
2 2
1 2 2 1 2 2 3 2
---*a11 *b12 *kap*r6259 - ---*a11 *b12 *kap*r6295 + a11*b12 *kap *r6249
2 2
1 4 3 1 4 3
- ---*b12 *kap *r6243 + ---*b12 *kap *r658,
4 2
1 2 2 1 2 2 3 2
---*a11 *b12 *kap*r6307 - ---*a11 *b12 *kap*r6358 - a11*b12 *kap *r6349
2 2
4 3
- b12 *kap *r6230,
1 2 2 2 2
---*a11 *b12*kap*r6407 + a11*b12 *kap *r6336 - a11*b12 *kap*r6443
2
1 3 2
- ---*b12 *kap *r6407,
2
1 3 1 2 2 2 1 2 2
---*a11 *b12*kap*r6407 + ---*a11 *b12 *kap *r6336 - ---*a11 *b12 *kap*r6443
6 3 3
1 3 2 1 4 3
- ---*a11*b12 *kap *r6407 - ---*b12 *kap *r6336,
3 3
2 2 1 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443
2
1 2
+ ---*b12 *kap*r6407,
2
2 2 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2
- 2*a11*b12*r6443 + b12 *kap*r6407,
2 2 1 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443
2
1 2
+ ---*b12 *kap*r6407,
2
r6230,
2*r6230,
r6230,
2 2 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2
- 2*a11*b12*r6443 + b12 *kap*r6407,
2 2 2
2*a11 *r6356 - 2*a11 *r6377 - a11 *r6407 + 2*a11*b12*kap*r6336
2
- 2*a11*b12*r6443 + b12 *kap*r6407,
2*r6230,
2*r6230,
2 2 1 2
a11 *r6356 - a11 *r6377 - ---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443
2
1 2
+ ---*b12 *kap*r6407,
2
r6230,
b12*kap*r6349,
r6349,
r6243,
r6243,
r6349,
r6243,
1
b12*kap*r6249 + ---*b12*kap*r6356,
2
r6249,
2 2 2 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230 - b12 *kap*r6255 - b12 *kap*r6358,
r6255,
kap*r6249,
r6255,
r6257,
r6259,
r6263,
r6264,
b12*kap*r6349,
r6349,
2*a11*r6356 - 2*a11*r6377 - a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
- 2*b12*r6443,
2*a11*r6356 - 2*a11*r6377 - a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
- 2*b12*r6443,
b12*kap*r6349,
2*a11*r6356 - 2*a11*r6377 - a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336
- 2*b12*r6443,
r6349,
b12*kap*r6356,
2*a11*r6349 + 4*b12*kap*r6230 - b12*r6307 - b12*r6358,
b12*kap*r6356,
b12*r6257,
r6295,
3
b12 *kap*r6257,
b12*r6407,
1
---*b12*kap*r6356 + b12*kap*r6407,
2
2 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230,
r6307,
b12*kap*r6377,
2 2 1 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230 - ---*b12 *kap*r6307
2
1 2
+ ---*b12 *kap*r6358,
2
a11*r6307 - a11*r6358 - b12*kap*r6349,
2 2
a11*b12*kap*r6356 + b12 *kap *r6243,
2 2 3 2
a11*b12 *kap*r6259 - a11*b12 *kap*r6295 + b12 *kap *r6249,
3 4 2
a11*b12 *kap*r6257 + b12 *kap *r6255,
2 2 3 2
a11*b12 *kap*r6307 - a11*b12 *kap*r6358 - b12 *kap *r6349,
2 2 2 2
a11*b12*kap*r6356 + a11*b12*kap*r6407 + b12 *kap *r6243 + 2*b12 *kap *r6336
2
- 2*b12 *kap*r6443,
a11*r6307 - a11*r6358 - b12*kap*r6349,
1 2 2 2 2
---*a11 *b12*kap*r6407 + a11*b12 *kap *r6336 - a11*b12 *kap*r6443
2
1 3 2
- ---*b12 *kap *r6407,
2
1 2 2 1 2 2 3 2
---*a11 *b12 *kap*r6307 - ---*a11 *b12 *kap*r6358 - a11*b12 *kap *r6349
2 2
4 3
- b12 *kap *r6230,
r6336,
1
a11*r6356 - a11*r6377 - ---*a11*r6407 - b12*kap*r6336 - b12*r6443,
2
1
a11*r6356 - a11*r6377 - ---*a11*r6407 - b12*r6443,
2
r6349,
r6349,
1
---*r6243 + 2*r6336,
2
1 1
a11*r6356 - a11*r6377 - ---*a11*r6407 - ---*b12*kap*r6243 - b12*kap*r6336
2 2
- b12*r6443,
r6349,
1
---*r6243 + r6336,
2
2 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230,
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358,
2 2
r6356,
r6358,
1 2 2
a11*b12*kap*r6249 + ---*a11*b12*kap*r6356 + b12 *kap *r658,
2
1 1 1
a11*r6249 - ---*b12*kap*r6243 + b12*kap*r658 + ---*b12*r6259 - ---*b12*r6295,
2 2 2
5 2
b12 *kap *r6257,
1 2 2 2 2 1 2
a11*b12*kap*r6249 - ---*b12 *kap *r6243 + b12 *kap *r658 + ---*b12 *kap*r6259,
2 2
3 4 2
a11*b12 *kap*r6257 + b12 *kap *r6255,
a11*r6263 + b12*kap*r679,
2 2
a11*b12*kap*r6349 + 2*b12 *kap *r6230,
1 1
a11*r6349 + 2*b12*kap*r6230 - ---*b12*r6307 + ---*b12*r6358,
2 2
r6407,
r6377,
r6307,
1
---*b12*kap*r6356 + b12*kap*r6407,
2
2 2
a11*b12*kap*r6356 + b12 *kap *r6243,
a11*r6307 - a11*r6358 - b12*kap*r6349,
3 4 2
a11*b12 *kap*r6257 + b12 *kap *r6255,
a11*r6259 - a11*r6295 + b12*kap*r6249,
2
a11*b12*r6407 + 2*b12 *kap*r6336,
1 1 1 2 2
---*a11*b12*kap*r6356 + ---*a11*b12*kap*r6407 + ---*b12 *kap *r6243
2 2 2
2 2 2
+ b12 *kap *r6336 + b12 *kap*r6443,
1 1 1 2 2
---*a11*b12*kap*r6356 + ---*a11*b12*kap*r6407 + ---*b12 *kap *r6243
2 2 2
2 2 2
+ b12 *kap *r6336 + b12 *kap*r6443,
2 2 2 2
a11 *r6307 - a11 *r6358 - 2*a11*b12*kap*r6349 - 2*b12 *kap *r6230,
2 2 2 2 3 2
a11 *b12 *kap*r6259 - a11 *b12 *kap*r6295 + 2*a11*b12 *kap *r6249
1 4 3 4 3
- ---*b12 *kap *r6243 + b12 *kap *r658,
2
2 2 2 2
a11 *r6307 - a11 *r6358 - 2*a11*b12*kap*r6349 - 2*b12 *kap *r6230,
2 2 2 2
a11 *b12*kap*r6407 + 2*a11*b12 *kap *r6336 - 2*a11*b12 *kap*r6443
3 2
- b12 *kap *r6407,
1 3 2 2 2 2 2
---*a11 *b12*kap*r6407 + a11 *b12 *kap *r6336 - a11 *b12 *kap*r6443
2
3 2 4 3
- a11*b12 *kap *r6407 - b12 *kap *r6336,
r6407,
1 2 1 2 2 2
---*b12 *kap*r6356 - ---*b12 *kap*r6377 + ---*b12 *kap*r6407,
3 3 3
a11*r6349 + 2*b12*kap*r6230,
3 2 4 3 1 4 2
a11*b12 *kap *r6349 + 2*b12 *kap *r6230 - ---*b12 *kap *r6307
2
1 4 2
+ ---*b12 *kap *r6358,
2
1
---*b12*kap*r6356 + b12*kap*r6407,
2
2 4 1
---*a11*r6349 + ---*b12*kap*r6230 + ---*b12*r6358,
3 3 3
a11*r6307 - a11*r6358 - b12*kap*r6349,
a11*r6356 + b12*kap*r6243,
a11*r6259 - a11*r6295 + b12*kap*r6249,
5 2 6 3
a11*b12 *kap *r6257 + b12 *kap *r6255,
a11*r6307 - a11*r6358 - b12*kap*r6349,
a11*r6356 + a11*r6407 + b12*kap*r6243 + 2*b12*kap*r6336 - 2*b12*r6443,
2 2 3 2
a11*b12 *kap*r6307 - a11*b12 *kap*r6358 - b12 *kap *r6349,
2 2 2 2
a11 *b12*kap*r6407 + 2*a11*b12 *kap *r6336 - 2*a11*b12 *kap*r6443
3 2
- b12 *kap *r6407,
2 2 2 2 3 2
a11 *b12 *kap*r6307 - a11 *b12 *kap*r6358 - 2*a11*b12 *kap *r6349
4 3
- 2*b12 *kap *r6230,
1
---*a11*r6407 + b12*kap*r6336,
2
r6443,
4 2 4 2 5 3
a11*b12 *kap *r6307 - a11*b12 *kap *r6358 - b12 *kap *r6349,
1 1 1 2 2
---*a11*b12*kap*r6356 + ---*a11*b12*kap*r6407 + ---*b12 *kap *r6243
2 2 2
2 2
+ b12 *kap *r6336,
1 2 1 2 2 2
---*a11 *r6307 - ---*a11 *r6358 - a11*b12*kap*r6349 - b12 *kap *r6230,
2 2
1 2 1 2 1 2 2
---*a11 *r6259 - ---*a11 *r6295 + a11*b12*kap*r6249 - ---*b12 *kap *r6243
2 2 4
1 2 2
+ ---*b12 *kap *r658,
2
1 2 2 1 2 2 3 2
---*a11 *b12 *kap*r6307 - ---*a11 *b12 *kap*r6358 - a11*b12 *kap *r6349
2 2
4 3
- b12 *kap *r6230,
1 2 1 2
---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443 - ---*b12 *kap*r6407,
2 2
1 3 2 2 2 2 2
---*a11 *b12*kap*r6407 + a11 *b12 *kap *r6336 - a11 *b12 *kap*r6443
2
3 2 4 3
- a11*b12 *kap *r6407 - b12 *kap *r6336,
1 2 1 2
---*a11 *r6407 + a11*b12*kap*r6336 - a11*b12*r6443 - ---*b12 *kap*r6407,
2 2
1 2 2 1 2 2 3 2
---*a11 *b12 *kap*r6307 - ---*a11 *b12 *kap*r6358 - a11*b12 *kap *r6349
2 2
4 3
- b12 *kap *r6230,
1 3 1 2 1 2
---*a11 *r6407 + ---*a11 *b12*kap*r6336 - ---*a11 *b12*r6443
6 3 3
1 2 1 3 2
- ---*a11*b12 *kap*r6407 - ---*b12 *kap *r6336}}
3 3
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2
HAM=u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=u1**2*a11 + u1*v2*b12 + u2**2*a11 - u2*v1*b12$