Solution 29 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
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Back to problem over
Equations
The following unsolved equations remain:
2 2
0=a11 + b12 *kap
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
1 3 1 3 1 2
r649=( - ---*a11 *r6160 - ---*a11 *r6356 + ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
- ---*a11 *b12*kap*r6243 + ---*a11 *b12*r6259 - ---*a11 *b12*r6295
4 2 2
1 2 1 2 1 3 2
- ---*a11*b12 *kap*r6356 + ---*a11*b12 *r6389 + ---*b12 *kap *r6115
4 2 4
1 3 3 2
+ ---*b12 *kap*r6165)/(b12 *kap )
2
r650=0
1 3 1 3 1 2
r651=( - ---*a11 *r6160 - ---*a11 *r6356 + ---*a11 *b12*kap*r6115
2 2 2
1 2 2 2
- ---*a11 *b12*kap*r6243 + a11 *b12*r6259 - a11 *b12*r6295
2
1 2 2 3 3 2
- ---*a11*b12 *kap*r6356 + a11*b12 *r6389 + b12 *kap*r6165)/(b12 *kap )
2
r652=0
1 3 1 3 1 2
r653=( - ---*a11 *r6160 - ---*a11 *r6356 + ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
- ---*a11 *b12*kap*r6243 + ---*a11 *b12*r6259 - ---*a11 *b12*r6295
4 2 2
1 2 1 2 1 3 2
- ---*a11*b12 *kap*r6356 + ---*a11*b12 *r6389 - ---*b12 *kap *r6115
4 2 4
1 3 3 2
+ ---*b12 *kap*r6165)/(b12 *kap )
2
r654=0
r655=0
r656=0
r657=0
1 3 1 3 1 2
r658=( - ---*a11 *r6160 - ---*a11 *r6356 + ---*a11 *b12*kap*r6115
2 2 2
1 2 2 2
- ---*a11 *b12*kap*r6243 + a11 *b12*r6259 - a11 *b12*r6295
2
1 2 2 1 3 2
- ---*a11*b12 *kap*r6356 + a11*b12 *r6389 + ---*b12 *kap *r6115
2 2
1 3 2 3 3 2
- ---*b12 *kap *r6243 + b12 *kap*r6165)/(b12 *kap )
2
r659=0
1 3 1 3 1 2
r660=( - ---*a11 *r6160 - ---*a11 *r6356 + ---*a11 *b12*kap*r6115
2 2 2
1 2 2 2
- ---*a11 *b12*kap*r6243 + a11 *b12*r6259 - a11 *b12*r6295
2
1 2 2 1 3 2
- ---*a11*b12 *kap*r6356 + a11*b12 *r6389 - ---*b12 *kap *r6243
2 2
3 3 2
+ b12 *kap*r6165)/(b12 *kap )
r661=0
r662=0
1 3 1 3 1 2
r663=( - ---*a11 *r6160 - ---*a11 *r6356 + ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
- ---*a11 *b12*kap*r6243 + ---*a11 *b12*r6259 - ---*a11 *b12*r6295
4 2 2
1 2 1 2 1 3 2
- ---*a11*b12 *kap*r6356 + ---*a11*b12 *r6389 + ---*b12 *kap *r6115
4 2 4
1 3 2 1 3 3 2
- ---*b12 *kap *r6243 + ---*b12 *kap*r6165)/(b12 *kap )
2 2
2 1 1 1
r664= - ---*kap*r6230 - ---*r6162 + ---*r6286 - ---*r6353 + r6412 + r671
3 3 6 3
r665=0
r666= - r6162 - r6353 + 2*r6412 + r671
r667=0
r668=0
r669=0
r670=0
r672=0
r673=0
1
r674=---*r6131 + r676
2
r675=0
r677=0
a11*kap*r6353 - a11*kap*r6412 + b12*r6435
r678=-------------------------------------------
b12*kap
1 1
r679=---*r6131 - ---*r6259 + r676
2 2
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=r6115
r6107=0
r6108=r6115
r6109=0
r6110=0
r6111=0
r6112=0
r6113=0
r6114=0
r6116=0
r6117=0
r6118=0
r6119=0
r6120=0
1
r6121= - 2*kap*r6230 + r6162 + ---*r6286 + r6353 - r6412 + r671
2
r6122=0
r6123= - r6162 - r6353 + 2*r6412 + r671
1 2 1 2
r6124=( - ---*a11 *r6160 - ---*a11 *r6356 + a11*b12*r6259 - a11*b12*r6295
2 2
1 2 2 2
- ---*b12 *kap*r6356 + b12 *r6389)/(b12 *kap)
2
r6125=0
1 2 1 2
r6126=( - ---*a11 *r6160 - ---*a11 *r6356 + a11*b12*r6259 - a11*b12*r6295
2 2
1 2 1 2 2 2
- ---*b12 *kap*r6160 - ---*b12 *kap*r6356 + b12 *r6389)/(b12 *kap)
2 2
r6127=0
r6128=r6353 - r6412 + r671
1 2 1 2
r6129=( - ---*a11 *r6160 - ---*a11 *r6356 + a11*b12*r6259 - a11*b12*r6295
2 2
2 2
+ b12 *r6389)/(b12 *kap)
r6130=0
r6132=0
r6133=( - 2*a11*kap*r6162 - 4*a11*kap*r6353 + 6*a11*kap*r6412 - b12*kap*r6257
- 2*b12*r6435)/(b12*kap)
r6134=0
r6135=0
r6136=0
2 2 2
- a11 *kap*r6353 + a11 *kap*r6412 - a11*b12*r6435 + b12 *kap*r680
r6137=--------------------------------------------------------------------
2
b12 *kap
r6139=0
r6140=r6336
r6141=0
1
r6142=---*r6115 + 2*r6336
2
r6143=0
1
r6144=---*r6115 + r6336
2
r6145=0
r6146=0
r6147=0
r6148=0
r6150=0
1
r6151=---*r6115 + r6149
2
r6152=0
r6153=0
r6154=r6149 - r6336
r6155=2*kap*r6230
r6156=0
1
r6157=2*r6162 + ---*r6286 + 2*r6353 - 3*r6412
2
r6158=0
r6159=0
r6161=0
r6163=0
r6164=0
r6166=0
1 1 1
---*a11*r6160 - ---*b12*kap*r6115 + ---*b12*r6131 + b12*r6165
2 2 2
r6167=---------------------------------------------------------------
b12
r6168=0
3 3 3 3 2
r6169=(---*a11 *kap*r6162 - ---*a11 *kap*r6353 - 3*a11 *b12*r6435
2 2
1 2 2 13 2 2
- ---*a11*b12 *kap *r6162 - ----*a11*b12 *kap *r6353
2 2
2 2 3 2 3 3 2
+ 7*a11*b12 *kap *r6412 - b12 *kap *r6257 - 4*b12 *kap*r6435)/(b12 *kap
)
1 1 1
r6170=( - ---*a11*r6160 - a11*r6356 - ---*b12*kap*r6243 + ---*b12*r6131
2 2 2
1
+ b12*r6165 - ---*b12*r6295)/b12
2
2 2 2
r6171=(a11 *kap*r6162 + 3*a11 *kap*r6353 - 4*a11 *kap*r6412 + a11*b12*kap*r6257
2 2 2 2
+ 2*a11*b12*r6435 - b12 *kap *r6162 - b12 *kap *r6353
2 2 2 2 2
+ 2*b12 *kap *r6412 + b12 *kap *r671)/(b12 *kap)
r6172=0
r6173=0
1 2 1 2 2
- ---*a11 *r6131 + ---*a11 *r6259 - a11*b12*r6138 + b12 *kap*r676
2 2
r6174=--------------------------------------------------------------------
2
b12
r6175=0
r6176=2*kap*r6230
r6177=0
4 2 1 2
r6178=---*kap*r6230 + ---*r6162 + ---*r6286 + ---*r6353 - r6412
3 3 6 3
r6179= - r6302
r6180=0
1
r6181=---*r6160 - r6302
2
r6182=0
r6183=r6162 + r6353 - r6412
1 2 1
r6184=---*r6160 - ---*r6302 - ---*r6309
3 3 3
r6185=0
- a11*r6160 + b12*kap*r6115
r6186=------------------------------
b12
r6187=0
4*a11*kap*r6230 - 2*a11*r6162
r6188=-------------------------------
b12
r6189=0
r6190=0
r6191=0
1 4 1 4 3
r6192=( - ---*a11 *kap*r6162 + ---*a11 *kap*r6353 + a11 *b12*r6435
2 2
1 2 2 2 7 2 2 2
+ ---*a11 *b12 *kap *r6162 + ---*a11 *b12 *kap *r6353
2 2
2 2 2 3 2 3
- 4*a11 *b12 *kap *r6412 + a11*b12 *kap *r6257 + 2*a11*b12 *kap*r6435
4 3 4 3 4 3 4 3
- b12 *kap *r6162 - b12 *kap *r6353 + 2*b12 *kap *r6412 + b12 *kap *r671
4 2
)/(b12 *kap )
r6193
1 1
- a11*r6131 + a11*r6259 - ---*b12*kap*r6160 - ---*b12*kap*r6356 + b12*r6389
2 2
=------------------------------------------------------------------------------
b12
r6194=0
1
---*a11*r6302 + b12*kap*r6336
2
r6195=-------------------------------
b12
r6196=0
1 1 1
- ---*a11*r6160 + ---*a11*r6302 + ---*b12*kap*r6115 + b12*kap*r6336
2 2 2
r6197=----------------------------------------------------------------------
b12
r6198=0
4*a11*kap*r6230 - 2*a11*r6162 - 2*a11*r6353 + 2*a11*r6412
r6199=-----------------------------------------------------------
b12
1
- a11*r6160 - ---*a11*r6302 + a11*r6309 + b12*kap*r6149 - b12*kap*r6336
2
r6200=--------------------------------------------------------------------------
b12
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6162 + b12 *kap *r6230
r6201=----------------------------------------------------
2
b12
r6202=0
r6203=0
1 3 1 3 1 2
r6204=(---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
+ ---*a11 *b12*kap*r6243 + ---*a11 *b12*r6131 - ---*a11 *b12*r6259
4 2 2
1 2 1 2 1 2
+ ---*a11*b12 *kap*r6160 + ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389
2 4 2
1 3 2 1 3 3
- ---*b12 *kap *r6115 + ---*b12 *kap*r6165)/b12
4 2
r6205=0
r6206
2 2 2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6162 + a11 *r6353 - a11 *r6412 + b12 *kap *r6230
=------------------------------------------------------------------------------
2
b12
2 2 2
r6207=(a11 *r6160 + a11 *r6302 - a11 *r6309 - a11*b12*kap*r6149
1 2 2
+ 2*a11*b12*kap*r6336 - ---*b12 *kap*r6302)/b12
2
r6208=0
1 3 1 3 1 3
r6209=( - ---*a11 *r6160 - ---*a11 *r6302 + ---*a11 *r6309
3 3 3
1 2 2 2
+ ---*a11 *b12*kap*r6149 - ---*a11 *b12*kap*r6336
3 3
1 2 1 3 2 3
+ ---*a11*b12 *kap*r6302 + ---*b12 *kap *r6336)/b12
3 3
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
1 2 1 2
r6247=(---*a11 *r6160 + ---*a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
2 2
1 2 2 2
- a11*b12*r6259 + a11*b12*r6295 + ---*b12 *kap*r6356 - b12 *r6389)/(b12
2
*kap)
r6248=0
1 2 1 2
r6249=(---*a11 *r6160 + ---*a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
2 2
1 2
- a11*b12*r6259 + a11*b12*r6295 + ---*b12 *kap*r6160
2
1 2 2 2
+ ---*b12 *kap*r6356 - b12 *r6389)/(b12 *kap)
2
1
r6250= - 2*kap*r6230 - r6162 + ---*r6286 - r6353 + 3*r6412 + r671
2
r6251=0
r6252= - r6162 - 2*r6353 + 3*r6412 + r671
r6253=0
1 2 1 2
r6254=(---*a11 *r6160 + ---*a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
2 2
2 2
- a11*b12*r6259 + a11*b12*r6295 - b12 *r6389)/(b12 *kap)
r6255=r671
r6256=0
r6258=0
r6260=0
r6261=0
r6262=0
- a11*r6131 + a11*r6259 - b12*r6138
r6263=--------------------------------------
b12
2 2 2
a11 *kap*r6353 - a11 *kap*r6412 + a11*b12*r6435 + b12 *kap*r680
r6264=-----------------------------------------------------------------
2
b12 *kap
r6265=0
r6266=0
r6267=0
r6268=0
r6269=0
r6270=0
r6271=0
r6272=r6115 - 2*r6149 + 4*r6336
r6273=0
r6274=r6115 - 2*r6149 + 4*r6336
r6275=0
r6276=0
r6277=0
r6278=0
r6279=r6115 - 2*r6149 + 4*r6336
r6280=0
a11*r6115 - a11*r6243
r6281=-----------------------
b12
r6282=0
a11*r6115 - a11*r6243 - b12*r6160
r6283=-----------------------------------
b12
r6284=0
r6285=0
r6287=0
a11*r6115 - a11*r6243 - b12*r6356
r6288=-----------------------------------
b12
r6289=0
r6290=0
2*a11*r6162 + 2*a11*r6353 - 4*a11*r6412
r6291=-----------------------------------------
b12
r6292=0
a11*r6353 - a11*r6412 + b12*r6257
r6293=-----------------------------------
b12
r6294=0
r6296=( - 2*a11*kap*r6162 - 3*a11*kap*r6353 + 5*a11*kap*r6412 - b12*kap*r6257
- 2*b12*r6435)/(b12*kap)
a11*r6131 - a11*r6259
r6297=-----------------------
b12
r6298=0
r6299=0
a11*kap*r6353 - a11*kap*r6412 + b12*r6435
r6300=-------------------------------------------
b12
r6301=0
r6303=0
1
r6304= - ---*r6160 + r6302
2
r6305=2*kap*r6230
r6306=0
1
r6307=4*kap*r6230 + ---*r6286 - r6353
2
r6308=0
r6310=r6162
r6311=0
- 4*a11*kap*r6230 + 4*a11*r6162 + 4*a11*r6353 - 6*a11*r6412
r6312=--------------------------------------------------------------
b12
r6313=0
a11*r6160 + 2*a11*r6356 + b12*kap*r6243
r6314=-----------------------------------------
b12
r6315=0
r6316=0
r6317=0
2 2
r6318=(a11 *r6160 + a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
1 2
+ a11*b12*r6131 - a11*b12*r6259 + ---*b12 *kap*r6160
2
1 2 2 2
+ ---*b12 *kap*r6356 - b12 *r6389)/b12
2
3 4 3 4 3
r6319=(---*a11 *kap*r6162 - ---*a11 *kap*r6353 - 3*a11 *b12*r6435
2 2
5 2 2 2 3 2 2 2
+ ---*a11 *b12 *kap *r6162 + ---*a11 *b12 *kap *r6353
2 2
2 2 2 3 2 4 3
- 4*a11 *b12 *kap *r6412 + a11*b12 *kap *r6257 - b12 *kap *r6162
4 3 4 3 4 2
+ b12 *kap *r6412 + b12 *kap *r671)/(b12 *kap )
r6320=0
r6321=0
r6322=0
- 4*a11*kap*r6230 + 2*a11*r6162 + 3*a11*r6353 - 3*a11*r6412
r6323=--------------------------------------------------------------
b12
r6324=0
r6325=(a11*r6160 + 2*a11*r6302 - 2*a11*r6309 + b12*kap*r6115 - 2*b12*kap*r6149
+ 4*b12*kap*r6336)/b12
4*a11*kap*r6230 - 2*a11*r6162 + a11*r6353 - a11*r6412
r6326=-------------------------------------------------------
b12
2 2
- a11 *r6160 - a11 *r6356 + a11*b12*kap*r6115 - a11*b12*kap*r6243
r6327=--------------------------------------------------------------------
2
b12
r6328=0
r6329=0
1 3 1 3 2
r6330=(---*a11 *kap*r6162 - ---*a11 *kap*r6353 - a11 *b12*r6435
2 2
1 2 2 1 2 2 3
+ ---*a11*b12 *kap *r6162 - ---*a11*b12 *kap *r6353)/(b12 *kap)
2 2
r6331=0
2 2 2
r6332=( - a11 *r6160 - a11 *r6302 + a11 *r6309 + a11*b12*kap*r6149
1 2 2
- 2*a11*b12*kap*r6336 + ---*b12 *kap*r6302)/b12
2
2 2 2 2
r6333=( - 2*a11 *kap*r6230 + a11 *r6162 - a11 *r6353 + a11 *r6412
2 2 2 2 2
+ b12 *kap *r6230 + b12 *kap*r6353 - b12 *kap*r6412)/b12
r6334=0
- a11*kap*r6353 + a11*kap*r6412
r6335=----------------------------------
b12
r6337=0
1 1
r6338= - ---*r6115 + r6149 + ---*r6243
2 2
r6339=0
1 1
r6340= - ---*r6115 + r6149 + ---*r6243 - r6336
2 2
r6341=0
r6342=0
r6343=0
r6344=0
1
r6345=---*r6243 + 2*r6336
2
r6346=0
1
r6347= - ---*r6115 + r6149 + r6243
2
r6348=0
r6349=0
1
r6350=---*r6243 + r6336
2
r6351=2*kap*r6230
r6352=0
r6354=0
r6355=0
r6357=0
1
r6358= - r6162 + ---*r6286 - r6353 + 3*r6412
2
r6359=0
r6360=0
1 2 1 2 5 2 5 2
r6361=(---*a11 *r6115 - ---*a11 *r6243 + ---*b12 *kap*r6115 - ---*b12 *kap*r6243
8 8 8 8
2 2
+ b12 *r6165)/b12
r6362=0
1 2 1 2 1
r6363=(---*a11 *r6115 - ---*a11 *r6243 + a11*b12*r6160 + ---*a11*b12*r6356
8 8 2
1 2 5 2 2 1 2
+ ---*b12 *kap*r6115 - ---*b12 *kap*r6243 + b12 *r6165 + ---*b12 *r6259
8 8 2
1 2 2
- ---*b12 *r6295)/b12
2
r6364=0
- a11*kap*r6353 + a11*kap*r6412 + b12*kap*r6257 + b12*r6435
r6365=--------------------------------------------------------------
b12*kap
1 2 1 2 1 5 2
r6366=(---*a11 *r6115 - ---*a11 *r6243 - ---*a11*b12*r6356 + ---*b12 *kap*r6115
8 8 2 8
9 2 2 1 2 2
- ---*b12 *kap*r6243 + b12 *r6165 + ---*b12 *r6259)/b12
8 2
2 2 2 2
a11 *r6162 + a11 *r6353 - 2*a11 *r6412 + a11*b12*r6257 + b12 *kap*r671
r6367=------------------------------------------------------------------------
2
b12
r6368=0
r6369=0
1 2 1 2 1 2
r6370=( - ---*a11 *r6131 + ---*a11 *r6259 - a11*b12*r6138 + ---*b12 *kap*r6131
2 2 2
1 2 2 2
- ---*b12 *kap*r6259 + b12 *kap*r676)/b12
2
r6371=0
r6372=2*kap*r6230
r6373=0
r6374=r6353
a11*r6115 - a11*r6243 - b12*r6302
r6375=-----------------------------------
b12
r6376=0
1 1
a11*r6115 - a11*r6243 - ---*b12*r6160 - b12*r6309 - ---*b12*r6356
2 2
r6377=-------------------------------------------------------------------
b12
r6378=0
1
r6379=4*kap*r6230 - r6162 + ---*r6286
2
1
a11*r6115 - a11*r6243 - b12*r6302 - ---*b12*r6356
2
r6380=---------------------------------------------------
b12
r6381=0
- 2*a11*r6160 - a11*r6356 + b12*kap*r6115
r6382=--------------------------------------------
b12
r6383=0
4*a11*kap*r6230 + 2*a11*r6162 + 2*a11*r6353 - 6*a11*r6412
r6384=-----------------------------------------------------------
b12
r6385=0
r6386=0
r6387=0
2 2 2
r6388=(a11 *kap*r6162 + a11 *kap*r6353 - 2*a11 *kap*r6412 + a11*b12*kap*r6257
2 2 2 2 2 2
- a11*b12*r6435 - b12 *kap *r6353 + b12 *kap *r6412 + b12 *kap *r671)/(
2
b12 *kap)
r6390=0
1 2 1 2 2
- ---*a11 *r6115 + ---*a11 *r6243 + a11*b12*r6302 + 2*b12 *kap*r6336
2 2
r6391=-----------------------------------------------------------------------
2
b12
r6392=0
1 2 1 2
r6393=( - ---*a11 *r6115 + ---*a11 *r6243 - a11*b12*r6160 + a11*b12*r6309
2 2
1 2 1 2 2
+ ---*a11*b12*r6356 + b12 *kap*r6149 + ---*b12 *kap*r6243)/b12
2 2
r6394=0
2*a11*r6162 - 2*a11*r6353
r6395=---------------------------
b12
1 2 1 2 3
r6396=( - ---*a11 *r6115 + ---*a11 *r6243 + a11*b12*r6309 + ---*a11*b12*r6356
2 2 2
2 1 2 2
+ b12 *kap*r6149 + ---*b12 *kap*r6243)/b12
2
2 2 2 2 2
- 4*a11 *kap*r6230 + a11 *r6162 + a11 *r6353 + 2*b12 *kap *r6230
r6397=-------------------------------------------------------------------
2
b12
r6398=0
r6399=0
1 3 1 3 7 2
r6400=(---*a11 *r6160 + ---*a11 *r6356 - ----*a11 *b12*kap*r6115
2 2 16
7 2 1 2 1 2
+ ----*a11 *b12*kap*r6243 + ---*a11 *b12*r6131 - ---*a11 *b12*r6259
16 2 2
1 2 2 1 3 2
+ ---*a11*b12 *kap*r6160 - a11*b12 *r6389 + ----*b12 *kap *r6115
2 16
9 3 2 3 3
- ----*b12 *kap *r6243 + b12 *kap*r6165)/b12
16
r6401=0
2 2 2 2
r6402=( - 4*a11 *kap*r6230 + a11 *r6162 + 4*a11 *r6353 - 3*a11 *r6412
2 2 2
+ 2*b12 *kap *r6230)/b12
1 2 2 2 3 2
r6403=(---*a11 *r6160 + 2*a11 *r6302 - 2*a11 *r6309 - ---*a11 *r6356
2 2
+ a11*b12*kap*r6115 - 2*a11*b12*kap*r6149 - a11*b12*kap*r6243
2 2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302)/b12
r6404=0
1 3 3 3 1 3
r6405=( - ---*a11 *r6160 - a11 *r6302 + a11 *r6309 + ---*a11 *r6356
2 2
1 2 2 1 2
- ---*a11 *b12*kap*r6115 + a11 *b12*kap*r6149 + ---*a11 *b12*kap*r6243
2 2
2 2 3 2 3
- 2*a11 *b12*kap*r6336 + a11*b12 *kap*r6302 + b12 *kap *r6336)/b12
r6406=0
- a11*r6115 + a11*r6243 + b12*r6302
r6407=--------------------------------------
b12
r6408=0
1 2 1
r6409=( - a11*r6115 + a11*r6243 + ---*b12*r6160 + ---*b12*r6302 + ---*b12*r6309
6 3 3
1
+ ---*b12*r6356)/b12
2
r6410=2*kap*r6230
r6411=0
r6413=0
1
- a11*r6115 + a11*r6243 + b12*r6302 + ---*b12*r6356
2
r6414=------------------------------------------------------
b12
4 1 1 1
r6415=---*kap*r6230 - ---*r6162 + ---*r6286 - ---*r6353 + r6412
3 3 6 3
r6416=0
- 4*a11*kap*r6230 + 2*a11*r6353
r6417=----------------------------------
b12
r6418=0
a11*r6356 + b12*kap*r6243
r6419=---------------------------
b12
r6420=0
r6421=0
r6422=0
r6423
2 2 2
a11 *r6160 + a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243 - b12 *r6389
=------------------------------------------------------------------------------
2
b12
2 2 2
r6424=(a11 *kap*r6162 + a11 *kap*r6353 - 2*a11 *kap*r6412 + a11*b12*kap*r6257
2 2 2
+ a11*b12*r6435 + b12 *kap *r671)/(b12 *kap)
r6425=0
r6426=0
r6427=0
- 4*a11*kap*r6230 + 3*a11*r6353 - a11*r6412
r6428=----------------------------------------------
b12
r6429=0
r6430=( - a11*r6160 + 2*a11*r6302 - 2*a11*r6309 - 2*a11*r6356 + b12*kap*r6115
- 2*b12*kap*r6149 + 4*b12*kap*r6336)/b12
4*a11*kap*r6230 + a11*r6353 - 3*a11*r6412
r6431=-------------------------------------------
b12
2 2
- a11 *r6160 - a11 *r6356 + a11*b12*kap*r6115 - a11*b12*kap*r6243
r6432=--------------------------------------------------------------------
2
b12
r6433=0
r6434=0
r6436=0
1 2 2 2 3 2
r6437=( - ---*a11 *r6160 - 2*a11 *r6302 + 2*a11 *r6309 + ---*a11 *r6356
2 2
- a11*b12*kap*r6115 + 2*a11*b12*kap*r6149 + a11*b12*kap*r6243
2 2
- 4*a11*b12*kap*r6336 + b12 *kap*r6302)/b12
2 2 2 2
r6438=( - 4*a11 *kap*r6230 + a11 *r6162 - 2*a11 *r6353 + 3*a11 *r6412
2 2 2
+ 2*b12 *kap *r6230)/b12
r6439=0
3 3
2*a11 *r6353 - 2*a11 *r6412
r6440=-----------------------------
3
b12
1 2 1 2 1 2
- ---*a11 *r6115 + ---*a11 *r6243 + ---*a11*b12*r6302 + b12 *kap*r6336
2 2 2
r6441=-------------------------------------------------------------------------
2
b12
r6442=0
1 2 1 2 1
r6443=( - ---*a11 *r6115 + ---*a11 *r6243 + ---*a11*b12*r6160
2 2 2
1 3
- ---*a11*b12*r6302 + a11*b12*r6309 + ---*a11*b12*r6356
2 2
1 2 2 1 2
- ---*b12 *kap*r6115 + b12 *kap*r6149 + ---*b12 *kap*r6243
2 2
2 2
- b12 *kap*r6336)/b12
r6444=0
- 4*a11*kap*r6230 + 2*a11*r6412
r6445=----------------------------------
b12
1 2 1 2 1
r6446=( - ---*a11 *r6115 + ---*a11 *r6243 + ---*a11*b12*r6302
2 2 2
1 1 2 2 2
+ ---*a11*b12*r6356 + ---*b12 *kap*r6243 + b12 *kap*r6336)/b12
2 2
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6353 + b12 *kap *r6230
r6447=----------------------------------------------------
2
b12
r6448=0
r6449=0
1 3 1 3 3 2
r6450=(---*a11 *r6160 + ---*a11 *r6356 - ----*a11 *b12*kap*r6115
4 4 16
3 2 1 2 1 2
+ ----*a11 *b12*kap*r6243 - ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389
16 4 2
5 3 2 9 3 2 1 3 3
+ ----*b12 *kap *r6115 - ----*b12 *kap *r6243 + ---*b12 *kap*r6165)/b12
16 16 2
r6451=0
2 2 2 2 2
- 2*a11 *kap*r6230 + 3*a11 *r6353 - 2*a11 *r6412 + b12 *kap *r6230
r6452=---------------------------------------------------------------------
2
b12
1 2 2 2 3 2
r6453=( - ---*a11 *r6160 + a11 *r6302 - a11 *r6309 - ---*a11 *r6356
2 2
+ a11*b12*kap*r6115 - a11*b12*kap*r6149 - a11*b12*kap*r6243
1 2 2
+ 2*a11*b12*kap*r6336 - ---*b12 *kap*r6302)/b12
2
r6454=0
3 3 3 2
r6455=( - a11 *r6302 + a11 *r6309 + a11 *r6356 - a11 *b12*kap*r6115
2 2 2
+ a11 *b12*kap*r6149 + a11 *b12*kap*r6243 - 2*a11 *b12*kap*r6336
2 3 2 3
+ a11*b12 *kap*r6302 + b12 *kap *r6336)/b12
r6456=0
1 2 2 2 3 2
r6457=(---*a11 *r6160 - a11 *r6302 + a11 *r6309 + ---*a11 *r6356
2 2
- a11*b12*kap*r6115 + a11*b12*kap*r6149 + a11*b12*kap*r6243
1 2 2
- 2*a11*b12*kap*r6336 + ---*b12 *kap*r6302)/b12
2
2 2 2 2
- 2*a11 *kap*r6230 + a11 *r6412 + b12 *kap *r6230
r6458=----------------------------------------------------
2
b12
r6459=0
3 3
a11 *r6353 - a11 *r6412
r6460=-------------------------
3
b12
1 3 1 3 1 3 1 3
r6461=(---*a11 *r6160 - ---*a11 *r6302 + ---*a11 *r6309 + ---*a11 *r6356
6 3 3 2
1 2 1 2
- ---*a11 *b12*kap*r6115 + ---*a11 *b12*kap*r6149
2 3
1 2 2 2
+ ---*a11 *b12*kap*r6243 - ---*a11 *b12*kap*r6336
2 3
1 2 1 3 2 3
+ ---*a11*b12 *kap*r6302 + ---*b12 *kap *r6336)/b12
3 3
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, r6115, r6131, r6138, r6149, r6160,
r6162, r6165, r6230, r6243, r6257, r6259, r6286, r6295,
r6302, r6309, r6336, r6353, r6356, r6389, r6412, r6435, 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,
1 3 1 3 1 3
{---*a11 *b12*r6160 - ---*a11 *b12*r6302 + ---*a11 *b12*r6309
6 3 3
1 3 1 2 2 1 2 2
+ ---*a11 *b12*r6356 - ---*a11 *b12 *kap*r6115 + ---*a11 *b12 *kap*r6149
2 2 3
1 2 2 2 2 2 1 3
+ ---*a11 *b12 *kap*r6243 - ---*a11 *b12 *kap*r6336 + ---*a11*b12 *kap*r6302
2 3 3
1 4 2
+ ---*b12 *kap *r6336,
3
3 3
a11 *b12*r6353 - a11 *b12*r6412,
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6412 - b12 *kap *r6230,
1 2 2 2 3 2
---*a11 *b12*r6160 - a11 *b12*r6302 + a11 *b12*r6309 + ---*a11 *b12*r6356
2 2
2 2 2
- a11*b12 *kap*r6115 + a11*b12 *kap*r6149 + a11*b12 *kap*r6243
2 1 3
- 2*a11*b12 *kap*r6336 + ---*b12 *kap*r6302,
2
3 3 3 2 2
a11 *b12*r6302 - a11 *b12*r6309 - a11 *b12*r6356 + a11 *b12 *kap*r6115
2 2 2 2 2 2
- a11 *b12 *kap*r6149 - a11 *b12 *kap*r6243 + 2*a11 *b12 *kap*r6336
3 4 2
- a11*b12 *kap*r6302 - b12 *kap *r6336,
1 2 2 2 3 2
---*a11 *b12*r6160 - a11 *b12*r6302 + a11 *b12*r6309 + ---*a11 *b12*r6356
2 2
2 2 2
- a11*b12 *kap*r6115 + a11*b12 *kap*r6149 + a11*b12 *kap*r6243
2 1 3
- 2*a11*b12 *kap*r6336 + ---*b12 *kap*r6302,
2
2 2 2 3 2
2*a11 *b12*kap*r6230 - 3*a11 *b12*r6353 + 2*a11 *b12*r6412 - b12 *kap *r6230,
1 3 1 3 3 2
---*a11 *r6160 + ---*a11 *r6356 - ----*a11 *b12*kap*r6115
4 4 16
3 2 1 2 1 2
+ ----*a11 *b12*kap*r6243 - ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389
16 4 2
5 3 2 9 3 2 1 3
+ ----*b12 *kap *r6115 - ----*b12 *kap *r6243 + ---*b12 *kap*r6165,
16 16 2
2 2 3 2
2*a11 *b12*kap*r6230 - a11 *b12*r6353 - b12 *kap *r6230,
1 2 1 2 1 1
---*a11 *r6115 - ---*a11 *r6243 - ---*a11*b12*r6302 - ---*a11*b12*r6356
2 2 2 2
1 2 2
- ---*b12 *kap*r6243 - b12 *kap*r6336,
2
4*a11*b12*kap*r6230 - 2*a11*b12*r6412,
1 2 1 2 1 1
---*a11 *r6115 - ---*a11 *r6243 - ---*a11*b12*r6160 + ---*a11*b12*r6302
2 2 2 2
3 1 2 2
- a11*b12*r6309 - ---*a11*b12*r6356 + ---*b12 *kap*r6115 - b12 *kap*r6149
2 2
1 2 2
- ---*b12 *kap*r6243 + b12 *kap*r6336,
2
1 2 1 2 1 2
---*a11 *r6115 - ---*a11 *r6243 - ---*a11*b12*r6302 - b12 *kap*r6336,
2 2 2
3 3
2*a11 *b12*r6353 - 2*a11 *b12*r6412,
2 2 2 2
4*a11 *b12*kap*r6230 - a11 *b12*r6162 + 2*a11 *b12*r6353 - 3*a11 *b12*r6412
3 2
- 2*b12 *kap *r6230,
1 2 2 2 3 2
---*a11 *b12*r6160 + 2*a11 *b12*r6302 - 2*a11 *b12*r6309 - ---*a11 *b12*r6356
2 2
2 2 2
+ a11*b12 *kap*r6115 - 2*a11*b12 *kap*r6149 - a11*b12 *kap*r6243
2 3
+ 4*a11*b12 *kap*r6336 - b12 *kap*r6302,
r6435,
2 2
a11 *r6160 + a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243,
4*a11*b12*kap*r6230 + a11*b12*r6353 - 3*a11*b12*r6412,
a11*b12*r6160 - 2*a11*b12*r6302 + 2*a11*b12*r6309 + 2*a11*b12*r6356
2 2 2
- b12 *kap*r6115 + 2*b12 *kap*r6149 - 4*b12 *kap*r6336,
4*a11*b12*kap*r6230 - 3*a11*b12*r6353 + a11*b12*r6412,
2 2 2
a11 *b12*kap*r6162 + a11 *b12*kap*r6353 - 2*a11 *b12*kap*r6412
2 2 3 2
+ a11*b12 *kap*r6257 + a11*b12 *r6435 + b12 *kap *r671,
2 2 2
a11 *r6160 + a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243 - b12 *r6389,
a11*r6356 + b12*kap*r6243,
4*a11*b12*kap*r6230 - 2*a11*b12*r6353,
4 1 1 1
---*b12*kap*r6230 - ---*b12*r6162 + ---*b12*r6286 - ---*b12*r6353 + b12*r6412,
3 3 6 3
1
a11*r6115 - a11*r6243 - b12*r6302 - ---*b12*r6356,
2
r6412,
2*b12*kap*r6230,
1 2 1
a11*r6115 - a11*r6243 - ---*b12*r6160 - ---*b12*r6302 - ---*b12*r6309
6 3 3
1
- ---*b12*r6356,
2
a11*r6115 - a11*r6243 - b12*r6302,
1 3 3 3 1 3
---*a11 *r6160 + a11 *r6302 - a11 *r6309 - ---*a11 *r6356
2 2
1 2 2 1 2
+ ---*a11 *b12*kap*r6115 - a11 *b12*kap*r6149 - ---*a11 *b12*kap*r6243
2 2
2 2 3 2
+ 2*a11 *b12*kap*r6336 - a11*b12 *kap*r6302 - b12 *kap *r6336,
1 2 2 2 3 2
---*a11 *r6160 + 2*a11 *r6302 - 2*a11 *r6309 - ---*a11 *r6356
2 2
+ a11*b12*kap*r6115 - 2*a11*b12*kap*r6149 - a11*b12*kap*r6243
2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302,
2 2 2 2
4*a11 *b12*kap*r6230 - a11 *b12*r6162 - 4*a11 *b12*r6353 + 3*a11 *b12*r6412
3 2
- 2*b12 *kap *r6230,
1 3 1 3 7 2
---*a11 *r6160 + ---*a11 *r6356 - ----*a11 *b12*kap*r6115
2 2 16
7 2 1 2 1 2
+ ----*a11 *b12*kap*r6243 + ---*a11 *b12*r6131 - ---*a11 *b12*r6259
16 2 2
1 2 2 1 3 2
+ ---*a11*b12 *kap*r6160 - a11*b12 *r6389 + ----*b12 *kap *r6115
2 16
9 3 2 3
- ----*b12 *kap *r6243 + b12 *kap*r6165,
16
2 2 2 3 2
4*a11 *b12*kap*r6230 - a11 *b12*r6162 - a11 *b12*r6353 - 2*b12 *kap *r6230,
1 2 1 2 3
---*a11 *r6115 - ---*a11 *r6243 - a11*b12*r6309 - ---*a11*b12*r6356
2 2 2
2 1 2
- b12 *kap*r6149 - ---*b12 *kap*r6243,
2
2*a11*b12*r6162 - 2*a11*b12*r6353,
1 2 1 2
---*a11 *r6115 - ---*a11 *r6243 + a11*b12*r6160 - a11*b12*r6309
2 2
1 2 1 2
- ---*a11*b12*r6356 - b12 *kap*r6149 - ---*b12 *kap*r6243,
2 2
1 2 1 2 2
---*a11 *r6115 - ---*a11 *r6243 - a11*b12*r6302 - 2*b12 *kap*r6336,
2 2
r6389,
1 4 1 4 1 4
---*a11 *b12*kap*r6162 + ---*a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412
4 4 2
1 3 2 1 3 2 1 2 3 2
+ ---*a11 *b12 *kap*r6257 - ---*a11 *b12 *r6435 - ---*a11 *b12 *kap *r6353
4 4 4
1 2 3 2 1 2 3 2
+ ---*a11 *b12 *kap *r6412 + ---*a11 *b12 *kap *r671,
4 4
4*a11*b12*kap*r6230 + 2*a11*b12*r6162 + 2*a11*b12*r6353 - 6*a11*b12*r6412,
2*a11*r6160 + a11*r6356 - b12*kap*r6115,
1
a11*r6115 - a11*r6243 - b12*r6302 - ---*b12*r6356,
2
1
4*b12*kap*r6230 - b12*r6162 + ---*b12*r6286,
2
1 1
a11*r6115 - a11*r6243 - ---*b12*r6160 - b12*r6309 - ---*b12*r6356,
2 2
a11*r6115 - a11*r6243 - b12*r6302,
b12*r6353,
2*b12*kap*r6230,
1 2 1 2 2 1 3
---*a11 *b12*r6131 - ---*a11 *b12*r6259 + a11*b12 *r6138 - ---*b12 *kap*r6131
2 2 2
1 3 3
+ ---*b12 *kap*r6259 - b12 *kap*r676,
2
2 2 2 2
a11 *b12*r6162 + a11 *b12*r6353 - 2*a11 *b12*r6412 + a11*b12 *r6257
3
+ b12 *kap*r671,
1 2 1 2 1 5 2
---*a11 *r6115 - ---*a11 *r6243 - ---*a11*b12*r6356 + ---*b12 *kap*r6115
8 8 2 8
9 2 2 1 2
- ---*b12 *kap*r6243 + b12 *r6165 + ---*b12 *r6259,
8 2
1 4 1 4 1 3 2
---*a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412 - ---*a11 *b12 *kap*r6257
8 8 8
1 3 2
- ---*a11 *b12 *r6435,
8
1 2 1 2 1
---*a11 *r6115 - ---*a11 *r6243 + a11*b12*r6160 + ---*a11*b12*r6356
8 8 2
1 2 5 2 2 1 2
+ ---*b12 *kap*r6115 - ---*b12 *kap*r6243 + b12 *r6165 + ---*b12 *r6259
8 8 2
1 2
- ---*b12 *r6295,
2
1 2 1 2 5 2 5 2
---*a11 *r6115 - ---*a11 *r6243 + ---*b12 *kap*r6115 - ---*b12 *kap*r6243
8 8 8 8
2
+ b12 *r6165,
1
b12*r6162 - ---*b12*r6286 + b12*r6353 - 3*b12*r6412,
2
r6356,
r6353,
2*b12*kap*r6230,
1
---*r6243 + r6336,
2
1
---*r6115 - r6149 - r6243,
2
1
---*r6243 + 2*r6336,
2
1 1
---*r6115 - r6149 - ---*r6243 + r6336,
2 2
1 1
---*r6115 - r6149 - ---*r6243,
2 2
r6336,
a11*b12*kap*r6353 - a11*b12*kap*r6412,
2 2 2 2
2*a11 *b12*kap*r6230 - a11 *b12*r6162 + a11 *b12*r6353 - a11 *b12*r6412
3 2 3 3
- b12 *kap *r6230 - b12 *kap*r6353 + b12 *kap*r6412,
2 2 2
a11 *r6160 + a11 *r6302 - a11 *r6309 - a11*b12*kap*r6149 + 2*a11*b12*kap*r6336
1 2
- ---*b12 *kap*r6302,
2
1 5 1 5 1 4
---*a11 *kap*r6162 - ---*a11 *kap*r6353 - ---*a11 *b12*r6435
8 8 4
1 3 2 2 1 3 2 2
+ ---*a11 *b12 *kap *r6162 - ---*a11 *b12 *kap *r6353,
8 8
2 2
a11 *r6160 + a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243,
4*a11*b12*kap*r6230 - 2*a11*b12*r6162 + a11*b12*r6353 - a11*b12*r6412,
a11*r6160 + 2*a11*r6302 - 2*a11*r6309 + b12*kap*r6115 - 2*b12*kap*r6149
+ 4*b12*kap*r6336,
4*a11*b12*kap*r6230 - 2*a11*b12*r6162 - 3*a11*b12*r6353 + 3*a11*b12*r6412,
3 6 3 6 3 5
---*a11 *kap*r6162 - ---*a11 *kap*r6353 - ---*a11 *b12*r6435
8 8 4
5 4 2 2 3 4 2 2 4 2 2
+ ---*a11 *b12 *kap *r6162 + ---*a11 *b12 *kap *r6353 - a11 *b12 *kap *r6412
8 8
1 3 3 2 1 2 4 3
+ ---*a11 *b12 *kap *r6257 - ---*a11 *b12 *kap *r6162
4 4
1 2 4 3 1 2 4 3
+ ---*a11 *b12 *kap *r6412 + ---*a11 *b12 *kap *r671,
4 4
2 2
a11 *r6160 + a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
1 2 1 2
+ a11*b12*r6131 - a11*b12*r6259 + ---*b12 *kap*r6160 + ---*b12 *kap*r6356
2 2
2
- b12 *r6389,
a11*r6160 + 2*a11*r6356 + b12*kap*r6243,
4*a11*b12*kap*r6230 - 4*a11*b12*r6162 - 4*a11*b12*r6353 + 6*a11*b12*r6412,
b12*r6162,
r6309,
1
4*b12*kap*r6230 + ---*b12*r6286 - b12*r6353,
2
2*b12*kap*r6230,
1
---*r6160 - r6302,
2
r6302,
1 3 3 2 1 3 3 2 1 2 4
---*a11 *b12 *kap *r6353 - ---*a11 *b12 *kap *r6412 + ---*a11 *b12 *kap*r6435,
4 4 4
a11*b12*r6131 - a11*b12*r6259,
1 3 3 3 5 3
---*a11 *b12*kap*r6162 + ---*a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412
2 4 4
1 2 2 1 2 2
+ ---*a11 *b12 *kap*r6257 + ---*a11 *b12 *r6435,
4 2
r6295,
2
a11*b12*r6353 - a11*b12*r6412 + b12 *r6257,
2*a11*b12*r6162 + 2*a11*b12*r6353 - 4*a11*b12*r6412,
a11*r6115 - a11*r6243 - b12*r6356,
r6286,
a11*r6115 - a11*r6243 - b12*r6160,
a11*r6115 - a11*r6243,
r6115 - 2*r6149 + 4*r6336,
r6115 - 2*r6149 + 4*r6336,
r6115 - 2*r6149 + 4*r6336,
1 3 1 3 1 2 2
---*a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412 + ---*a11 *b12 *r6435
2 2 2
1 3
+ ---*a11*b12 *kap*r680,
2
2
a11*b12*r6131 - a11*b12*r6259 + b12 *r6138,
r6259,
r6257,
b12*r671,
1 2 1 2
---*a11 *r6160 + ---*a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
2 2
2
- a11*b12*r6259 + a11*b12*r6295 - b12 *r6389,
b12*r6162 + 2*b12*r6353 - 3*b12*r6412 - b12*r671,
1
2*b12*kap*r6230 + b12*r6162 - ---*b12*r6286 + b12*r6353 - 3*b12*r6412
2
- b12*r671,
1 2 1 2
---*a11 *r6160 + ---*a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
2 2
1 2 1 2
- a11*b12*r6259 + a11*b12*r6295 + ---*b12 *kap*r6160 + ---*b12 *kap*r6356
2 2
2
- b12 *r6389,
1 2 1 2
---*a11 *r6160 + ---*a11 *r6356 - a11*b12*kap*r6115 + a11*b12*kap*r6243
2 2
1 2 2
- a11*b12*r6259 + a11*b12*r6295 + ---*b12 *kap*r6356 - b12 *r6389,
2
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,
1 3 1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6302 - ---*a11 *r6309 - ---*a11 *b12*kap*r6149
3 3 3 3
2 2 1 2 1 3 2
+ ---*a11 *b12*kap*r6336 - ---*a11*b12 *kap*r6302 - ---*b12 *kap *r6336,
3 3 3
2 2 2
a11 *r6160 + a11 *r6302 - a11 *r6309 - a11*b12*kap*r6149 + 2*a11*b12*kap*r6336
1 2
- ---*b12 *kap*r6302,
2
2 2 2 2
2*a11 *b12*kap*r6230 - a11 *b12*r6162 - a11 *b12*r6353 + a11 *b12*r6412
3 2
- b12 *kap *r6230,
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
+ ---*a11 *b12*kap*r6243 + ---*a11 *b12*r6131 - ---*a11 *b12*r6259
4 2 2
1 2 1 2 1 2
+ ---*a11*b12 *kap*r6160 + ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389
2 4 2
1 3 2 1 3
- ---*b12 *kap *r6115 + ---*b12 *kap*r6165,
4 2
2 2 2 3 3
2*a11 *b12*kap *r6230 - a11 *b12*kap*r6162 - b12 *kap *r6230,
1
a11*r6160 + ---*a11*r6302 - a11*r6309 - b12*kap*r6149 + b12*kap*r6336,
2
4*a11*b12*kap*r6230 - 2*a11*b12*r6162 - 2*a11*b12*r6353 + 2*a11*b12*r6412,
1 1 1
---*a11*r6160 - ---*a11*r6302 - ---*b12*kap*r6115 - b12*kap*r6336,
2 2 2
1
---*a11*r6302 + b12*kap*r6336,
2
1 2 1 2
a11*b12*r6131 - a11*b12*r6259 + ---*b12 *kap*r6160 + ---*b12 *kap*r6356
2 2
2
- b12 *r6389,
1 6 1 6 1 5
---*a11 *kap*r6162 - ---*a11 *kap*r6353 - ---*a11 *b12*r6435
8 8 4
1 4 2 2 7 4 2 2 4 2 2
- ---*a11 *b12 *kap *r6162 - ---*a11 *b12 *kap *r6353 + a11 *b12 *kap *r6412
8 8
1 3 3 2 1 3 3
- ---*a11 *b12 *kap *r6257 - ---*a11 *b12 *kap*r6435
4 2
1 2 4 3 1 2 4 3
+ ---*a11 *b12 *kap *r6162 + ---*a11 *b12 *kap *r6353
4 4
1 2 4 3 1 2 4 3
- ---*a11 *b12 *kap *r6412 - ---*a11 *b12 *kap *r671,
2 4
4*a11*b12*kap*r6230 - 2*a11*b12*r6162,
a11*r6160 - b12*kap*r6115,
1 2 1
---*r6160 - ---*r6302 - ---*r6309,
3 3 3
b12*r6162 + b12*r6353 - b12*r6412,
1
---*r6160 - r6302,
2
r6302,
4 2 1 2
---*b12*kap*r6230 + ---*b12*r6162 + ---*b12*r6286 + ---*b12*r6353 - b12*r6412,
3 3 6 3
2*b12*kap*r6230,
1 2 1 2 2 3
---*a11 *b12*r6131 - ---*a11 *b12*r6259 + a11*b12 *r6138 - b12 *kap*r676,
2 2
1 4 3 4 4
---*a11 *b12*kap*r6162 + ---*a11 *b12*kap*r6353 - a11 *b12*kap*r6412
4 4
1 3 2 1 3 2 1 2 3 2
+ ---*a11 *b12 *kap*r6257 + ---*a11 *b12 *r6435 - ---*a11 *b12 *kap *r6162
4 2 4
1 2 3 2 1 2 3 2
- ---*a11 *b12 *kap *r6353 + ---*a11 *b12 *kap *r6412
4 2
1 2 3 2
+ ---*a11 *b12 *kap *r671,
4
1 1 1
---*a11*r6160 + a11*r6356 + ---*b12*kap*r6243 - ---*b12*r6131 - b12*r6165
2 2 2
1
+ ---*b12*r6295,
2
3 6 3 6 3 5
----*a11 *kap*r6162 - ----*a11 *kap*r6353 - ---*a11 *b12*r6435
16 16 8
1 4 2 2 13 4 2 2
- ----*a11 *b12 *kap *r6162 - ----*a11 *b12 *kap *r6353
16 16
7 4 2 2 1 3 3 2
+ ---*a11 *b12 *kap *r6412 - ---*a11 *b12 *kap *r6257
8 8
1 3 3
- ---*a11 *b12 *kap*r6435,
2
1 1 1
---*a11*r6160 - ---*b12*kap*r6115 + ---*b12*r6131 + b12*r6165,
2 2 2
r6165,
r6162,
r6160,
1
2*b12*r6162 + ---*b12*r6286 + 2*b12*r6353 - 3*b12*r6412,
2
2*b12*kap*r6230,
r6149 - r6336,
1
---*r6115 + r6149,
2
r6149,
1
---*r6115 + r6336,
2
1
---*r6115 + 2*r6336,
2
r6336,
r6138,
1 3 1 3 1 2 2
---*a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412 + ---*a11 *b12 *r6435
2 2 2
1 3
- ---*a11*b12 *kap*r680,
2
1 3 3 3 3
---*a11 *b12*kap*r6162 + a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412
2 2
1 2 2 1 2 2
+ ---*a11 *b12 *kap*r6257 + ---*a11 *b12 *r6435,
4 2
r6131,
1 2 1 2 2
---*a11 *r6160 + ---*a11 *r6356 - a11*b12*r6259 + a11*b12*r6295 - b12 *r6389,
2 2
b12*r6353 - b12*r6412 + b12*r671,
1 2 1 2
---*a11 *r6160 + ---*a11 *r6356 - a11*b12*r6259 + a11*b12*r6295
2 2
1 2 1 2 2
+ ---*b12 *kap*r6160 + ---*b12 *kap*r6356 - b12 *r6389,
2 2
1 2 1 2
---*a11 *r6160 + ---*a11 *r6356 - a11*b12*r6259 + a11*b12*r6295
2 2
1 2 2
+ ---*b12 *kap*r6356 - b12 *r6389,
2
b12*r6162 + b12*r6353 - 2*b12*r6412 - b12*r671,
1
2*b12*kap*r6230 - b12*r6162 - ---*b12*r6286 - b12*r6353 + b12*r6412 - b12*r671
2
,
r6115,
r6115,
r6115,
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,
1 1
---*b12*r6131 - ---*b12*r6259 + b12*r676,
2 2
1 3 1 3 1 2 2
---*a11 *b12*kap*r6353 - ---*a11 *b12*kap*r6412 + ---*a11 *b12 *r6435,
4 4 4
r676,
1
---*b12*r6131 + b12*r676,
2
r671,
b12*r6162 + b12*r6353 - 2*b12*r6412 - b12*r671,
2 1 1 1
---*b12*kap*r6230 + ---*b12*r6162 - ---*b12*r6286 + ---*b12*r6353 - b12*r6412
3 3 6 3
- b12*r671,
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
+ ---*a11 *b12*kap*r6243 - ---*a11 *b12*r6259 + ---*a11 *b12*r6295
4 2 2
1 2 1 2 1 3 2
+ ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389 - ---*b12 *kap *r6115
4 2 4
1 3 2 1 3
+ ---*b12 *kap *r6243 - ---*b12 *kap*r6165,
2 2
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
2 2 2
1 2 2 2
+ ---*a11 *b12*kap*r6243 - a11 *b12*r6259 + a11 *b12*r6295
2
1 2 2 1 3 2
+ ---*a11*b12 *kap*r6356 - a11*b12 *r6389 + ---*b12 *kap *r6243
2 2
3
- b12 *kap*r6165,
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
2 2 2
1 2 2 2
+ ---*a11 *b12*kap*r6243 - a11 *b12*r6259 + a11 *b12*r6295
2
1 2 2 1 3 2
+ ---*a11*b12 *kap*r6356 - a11*b12 *r6389 - ---*b12 *kap *r6115
2 2
1 3 2 3
+ ---*b12 *kap *r6243 - b12 *kap*r6165,
2
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
+ ---*a11 *b12*kap*r6243 - ---*a11 *b12*r6259 + ---*a11 *b12*r6295
4 2 2
1 2 1 2 1 3 2
+ ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389 + ---*b12 *kap *r6115
4 2 4
1 3
- ---*b12 *kap*r6165,
2
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
2 2 2
1 2 2 2
+ ---*a11 *b12*kap*r6243 - a11 *b12*r6259 + a11 *b12*r6295
2
1 2 2 3
+ ---*a11*b12 *kap*r6356 - a11*b12 *r6389 - b12 *kap*r6165,
2
1 3 1 3 1 2
---*a11 *r6160 + ---*a11 *r6356 - ---*a11 *b12*kap*r6115
4 4 4
1 2 1 2 1 2
+ ---*a11 *b12*kap*r6243 - ---*a11 *b12*r6259 + ---*a11 *b12*r6295
4 2 2
1 2 1 2 1 3 2
+ ---*a11*b12 *kap*r6356 - ---*a11*b12 *r6389 - ---*b12 *kap *r6115
4 2 4
1 3
- ---*b12 *kap*r6165,
2
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:
Modulo the following equation:
2 2
0=a11 + b12 *kap
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$