Solution 38 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=a22 + b12 *kap
Expressions
The solution is given through the following expressions:
1 2 1 2 1 2 2 2
r60=( - ---*a22 *r6115 + ---*a22 *r6149 + ---*a22 *r6243 - ---*a22 *r6336
6 3 6 3
1 1 2 2 2
- ---*a22*b12*r6407 + ---*b12 *kap*r6336)/(b12 *kap )
6 3
r61=0
1 2 2 1 2 2
r62=( - ---*a22 *r6115 + a22 *r6149 + ---*a22 *r6243 - 2*a22 *r6336
2 2
1 2 2 2
- ---*a22*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
2
r63=0
1 2 2 1 2 2
r64=( - ---*a22 *r6115 + a22 *r6149 + ---*a22 *r6243 - 2*a22 *r6336
2 2
1 2 2 2
- ---*a22*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
2
r65=0
1 2 1 2 1 2 2 2
r66=( - ---*a22 *r6115 + ---*a22 *r6149 + ---*a22 *r6243 - ---*a22 *r6336
6 3 6 3
1 1 2 2 2
- ---*a22*b12*r6407 + ---*b12 *kap*r6336)/(b12 *kap )
6 3
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
1 2 2 1 2 2
r613=( - ---*a22 *r6115 + a22 *r6149 + ---*a22 *r6243 - 2*a22 *r6336
2 2
1 2 2 2
- ---*a22*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
2
r614=0
2 2 2 2
r615=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(b12 *kap )
r616=0
1 2 2 1 2 2
r617=( - ---*a22 *r6115 + a22 *r6149 + ---*a22 *r6243 - 2*a22 *r6336
2 2
1 2 2 2
- ---*a22*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
2
r618=0
r619=0
r620=0
r621=0
1 2 2 1 2 2
r622=( - ---*a22 *r6115 + a22 *r6149 + ---*a22 *r6243 - 2*a22 *r6336
2 2
1 2 2 2
- ---*a22*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
2
r623=0
1 2 2 1 2 2
r624=( - ---*a22 *r6115 + a22 *r6149 + ---*a22 *r6243 - 2*a22 *r6336
2 2
1 2 2 2
- ---*a22*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
2
r625=0
r626=0
1 2 1 2 1 2 2 2
r627=( - ---*a22 *r6115 + ---*a22 *r6149 + ---*a22 *r6243 - ---*a22 *r6336
6 3 6 3
1 1 2 2 2
- ---*a22*b12*r6407 + ---*b12 *kap*r6336)/(b12 *kap )
6 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 1
r649=---*r6115 + ---*r6243 + ---*r660
4 4 2
r650=0
1
r651=---*r6243 + r660
2
r652=0
1 1 1
r653= - ---*r6115 + ---*r6243 + ---*r660
4 4 2
r654=0
r655=0
r656=0
r657=0
1
r658=---*r6115 + r660
2
r659=0
r661=0
r662=0
1 1 1
r663=---*r6115 - ---*r6243 + ---*r660
4 4 2
1 2 1
- ---*a22*r6270 - ---*b12*kap*r6230 + ---*b12*r6157 + b12*r666
3 3 3
r664=-----------------------------------------------------------------
b12
r665=0
r667=0
r668=0
r670=0
r672=0
r673=0
r675=0
1 1
- ---*a22*r669 - ---*b12*r6131 + b12*r674
2 2
r676=--------------------------------------------
b12
r677=0
- a22*kap*r6252 + a22*kap*r666 + b12*r6435
r678=---------------------------------------------
b12*kap
1 1
---*a22*r669 - ---*b12*r6259 + b12*r674
2 2
r679=-----------------------------------------
b12
r681=0
r682=0
r684=0
r685=r6230
r686=0
r687=2*r6230
r688=0
r689=r6230
r690
1 1 1
- ---*a22*r6115 + a22*r6149 + ---*a22*r6243 - 2*a22*r6336 - ---*b12*r6407
2 2 2
=----------------------------------------------------------------------------
b12*kap
r691=0
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r692=------------------------------------------------------------------
b12*kap
r693=0
r694
1 1 1
- ---*a22*r6115 + a22*r6149 + ---*a22*r6243 - 2*a22*r6336 - ---*b12*r6407
2 2 2
=----------------------------------------------------------------------------
b12*kap
r695=0
r696=2*r6230
r697=0
r698=2*r6230
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r699=------------------------------------------------------------------
b12*kap
r6100=0
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r6101=------------------------------------------------------------------
b12*kap
r6102=0
r6103=r6230
r6104
1 1 1
- ---*a22*r6115 + a22*r6149 + ---*a22*r6243 - 2*a22*r6336 - ---*b12*r6407
2 2 2
=----------------------------------------------------------------------------
b12*kap
r6105=0
r6106=r6115
r6107=0
r6108=r6115
r6109=0
r6110= - r6270
r6111=0
r6112= - r6270
r6113=0
r6114=0
r6116=0
r6117= - r6270
r6118=0
r6119=0
r6120=0
- a22*r6270 - 2*b12*kap*r6230 + b12*r6157 + b12*r666
r6121=-------------------------------------------------------
b12
r6122=0
r6123=r666
1 3
r6124=r6129 - ---*r6356 - ---*r669
2 2
r6125=0
1 1
r6126=r6129 - ---*r6160 - ---*r6356
2 2
r6127=0
r6128= - r6252 + r666 + r671
r6130=0
r6132=0
r6134=0
r6135=0
r6136=0
2 2 2
a22 *kap*r6252 - a22 *kap*r666 - a22*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= - r6270
r6147=0
r6148= - r6270
r6150=0
1
r6151=---*r6115 + r6149
2
r6152=0
r6153= - r6270
r6154=r6149 - r6336
a22*r6270 + 2*b12*kap*r6230
r6155=-----------------------------
b12
r6156=0
r6158=0
r6159=0
r6161=0
r6162=2*r6252 + r6353 - 3*r666 + r671
r6163=0
r6164=0
1 2 1 2 1
r6165=( - ---*a22 *r6115 + ---*a22 *r6243 - a22*b12*r6129 + ---*a22*b12*r6356
2 2 2
3 1 2 2 2
+ ---*a22*b12*r669 + ---*b12 *kap*r6243 + b12 *kap*r660)/b12
2 2
r6166=0
1 2 1 2 1
r6167=( - ---*a22 *r6115 + ---*a22 *r6243 - a22*b12*r6129 + ---*a22*b12*r6160
2 2 2
1 1 1 2
+ ---*a22*b12*r6356 + ---*a22*b12*r669 - ---*b12 *kap*r6115
2 2 2
1 2 2 1 2 2
+ ---*b12 *kap*r6243 + b12 *kap*r660 + ---*b12 *r6131)/b12
2 2
r6168=0
a22*kap*r6252 - a22*kap*r666 + b12*kap*r6133 + b12*r6435
r6169=----------------------------------------------------------
b12*kap
1 3 1 3 2 1 2
r6170=( - ---*a22 *r6115 + ---*a22 *r6243 - a22 *b12*r6129 - ---*a22 *b12*r6160
2 2 4
1 2 11 2 2
- ---*a22 *b12*r6356 + ----*a22 *b12*r669 + a22*b12 *kap*r660
4 6
1 2 1 2 1 3
+ ---*a22*b12 *r6131 - ---*a22*b12 *r6259 + ---*b12 *kap*r6129
2 2 2
11 3 1 3 2
+ ----*b12 *kap*r669 - ---*b12 *r6389)/(a22*b12 )
6 2
2 2 2
a22 *r666 - a22 *r671 - a22*b12*r6133 + b12 *kap*r666
r6171=-------------------------------------------------------
2
b12
r6172=0
r6173=0
3 1 2 1 2
r6174=( - a22 *r669 - ---*a22 *b12*r6131 + ---*a22 *b12*r6259
2 2
1 2 2 1 3
- ---*a22*b12 *kap*r669 - a22*b12 *r6138 - ---*b12 *kap*r6131
2 2
3 3
+ b12 *kap*r674)/b12
r6175=0
a22*r6270 + 2*b12*kap*r6230
r6176=-----------------------------
b12
r6177=0
2 4 1
---*a22*r6270 + ---*b12*kap*r6230 + ---*b12*r6157
3 3 3
r6178=---------------------------------------------------
b12
- a22*r6115 + a22*r6243 - b12*r6407
r6179=--------------------------------------
b12
r6180=0
1 1
- a22*r6115 + a22*r6243 + ---*b12*r6160 - b12*r6407 + ---*b12*r669
2 2
r6181=---------------------------------------------------------------------
b12
r6182=0
r6183=r6252 + r6353 - 2*r666 + r671
2 2 1 1
r6184=( - a22 *r6115 + a22 *r6243 + ---*a22*b12*r6160 + ---*a22*b12*r6356
2 3
7 1 2
- a22*b12*r6407 + ---*a22*b12*r669 - ---*b12 *kap*r6115
6 6
1 2 2 2 1 2
+ ---*b12 *kap*r6149 - ---*b12 *kap*r6336 + ---*b12 *r6430)/(a22*b12)
3 3 6
r6185=0
- a22*r6160 + b12*kap*r6115
r6186=------------------------------
b12
r6187=0
2
r6188=(2*a22 *r6270 + 4*a22*b12*kap*r6230 - 4*a22*b12*r6252 - 2*a22*b12*r6353
2 2
+ 6*a22*b12*r666 - 2*a22*b12*r671 - b12 *kap*r6270)/b12
r6189=0
r6190=0
r6191=0
2 2
r6192=(a22 *kap*r666 - a22 *kap*r671 - a22*b12*kap*r6133 - a22*b12*r6435
2 2 2
+ b12 *kap *r666)/(b12 *kap)
46 2 1 2
r6193=( - ----*a22 *r669 - a22*b12*r6131 + a22*b12*r6259 - ---*b12 *kap*r6160
9 2
1 2 46 2 2 2
- ---*b12 *kap*r6356 - ----*b12 *kap*r669 + b12 *r6389)/b12
2 9
r6194=0
1 2 1 2 1 2
---*a22 *r6115 - ---*a22 *r6243 + ---*a22*b12*r6407 + b12 *kap*r6336
2 2 2
r6195=----------------------------------------------------------------------
2
b12
r6196=0
1 2 1 2 1 1
r6197=(---*a22 *r6115 - ---*a22 *r6243 - ---*a22*b12*r6160 + ---*a22*b12*r6407
2 2 2 2
1 1 2 2 2
- ---*a22*b12*r669 + ---*b12 *kap*r6115 + b12 *kap*r6336)/b12
2 2
r6198=0
2
r6199=(2*a22 *r6270 + 4*a22*b12*kap*r6230 - 2*a22*b12*r6252 - 2*a22*b12*r6353
2 2
+ 4*a22*b12*r666 - 2*a22*b12*r671 - b12 *kap*r6270)/b12
1 2 1 2 3
r6200=(---*a22 *r6115 - ---*a22 *r6243 - ---*a22*b12*r6160 - a22*b12*r6356
2 2 2
1 7 1 2
+ ---*a22*b12*r6407 - ---*a22*b12*r669 + ---*b12 *kap*r6115
2 2 2
2 1 2 2
+ b12 *kap*r6336 - ---*b12 *r6430)/b12
2
3 2 2 2
r6201=( - a22 *r6270 - 2*a22 *b12*kap*r6230 + 2*a22 *b12*r6252 + a22 *b12*r6353
2 2 2 3 2
- 3*a22 *b12*r666 + a22 *b12*r671 + a22*b12 *kap*r6270 + b12 *kap *r6230
3
)/b12
r6202=0
r6203=0
1 3 1 3 59 3 1 2
r6204=(---*a22 *r6160 + ---*a22 *r6356 + ----*a22 *r669 - ---*a22 *b12*kap*r6115
4 4 18 2
1 2 1 2 1 2
+ ---*a22 *b12*kap*r6243 + ---*a22 *b12*r6131 - ---*a22 *b12*r6259
2 2 2
1 2 1 2
- ---*a22*b12 *kap*r6129 + ---*a22*b12 *kap*r6160
2 2
1 2 59 2 1 2
+ ---*a22*b12 *kap*r6356 + ----*a22*b12 *kap*r669 - ---*a22*b12 *r6389
2 18 2
1 3 2 1 3 2 1 3 2 3
- ---*b12 *kap *r6115 + ---*b12 *kap *r6243 + ---*b12 *kap *r660)/b12
4 4 2
r6205=0
3 2 2 2
r6206=( - a22 *r6270 - 2*a22 *b12*kap*r6230 + a22 *b12*r6252 + a22 *b12*r6353
2 2 2 3 2
- 2*a22 *b12*r666 + a22 *b12*r671 + a22*b12 *kap*r6270 + b12 *kap *r6230
3
)/b12
3 2 2 7 2
r6207=(---*a22 *r6160 + a22 *r6356 + ---*a22 *r669 - a22*b12*kap*r6115
2 2
1 1 1 2 2
+ ---*a22*b12*kap*r6243 + ---*a22*b12*r6430 - ---*b12 *kap*r6407)/b12
2 2 2
r6208=0
1 3 1 3 7 3
r6209=( - ---*a22 *r6160 - ---*a22 *r6356 - ---*a22 *r669
2 3 6
1 2 1 2 1 2
+ ---*a22 *b12*kap*r6115 - ---*a22 *b12*kap*r6243 - ---*a22 *b12*r6430
2 3 6
1 2 1 3 2 3
+ ---*a22*b12 *kap*r6407 + ---*b12 *kap *r6336)/b12
3 3
r6210=0
1 1 1
---*a22*r6115 - a22*r6149 - ---*a22*r6243 + 2*a22*r6336 + ---*b12*r6407
2 2 2
r6211=-------------------------------------------------------------------------
b12*kap
r6212=0
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6213=---------------------------------------------------------------
b12*kap
r6214=0
1 1 1
---*a22*r6115 - a22*r6149 - ---*a22*r6243 + 2*a22*r6336 + ---*b12*r6407
2 2 2
r6215=-------------------------------------------------------------------------
b12*kap
r6216=r6230
r6217=0
r6218=2*r6230
r6219=0
r6220=r6230
r6221=0
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6222=---------------------------------------------------------------
b12*kap
r6223=0
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6224=---------------------------------------------------------------
b12*kap
r6225=2*r6230
r6226=0
r6227=2*r6230
r6228=0
1 1 1
---*a22*r6115 - a22*r6149 - ---*a22*r6243 + 2*a22*r6336 + ---*b12*r6407
2 2 2
r6229=-------------------------------------------------------------------------
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
1 1
- a22*r6115 + a22*r6243 - b12*r6129 + ---*b12*r6356 - ---*b12*r669
2 2
r6247=---------------------------------------------------------------------
b12
r6248=0
1 1
r6249=( - a22*r6115 + a22*r6243 - b12*r6129 + ---*b12*r6160 + ---*b12*r6356
2 2
+ b12*r669)/b12
- a22*r6270 - 2*b12*kap*r6230 + b12*r6157 + 3*b12*r666 - 2*b12*r671
r6250=----------------------------------------------------------------------
b12
r6251=0
r6253=0
- a22*r6115 + a22*r6243 - b12*r6129 + b12*r669
r6254=-------------------------------------------------
b12
r6255=r671
r6256=0
2*a22*kap*r6252 - 2*a22*kap*r671 - b12*kap*r6133 - 2*b12*r6435
r6257=----------------------------------------------------------------
b12*kap
r6258=0
r6260=0
r6261=0
r6262=0
2 2
- 2*a22 *r669 - a22*b12*r6131 + a22*b12*r6259 - b12 *r6138
r6263=-------------------------------------------------------------
2
b12
2 2 2
- a22 *kap*r6252 + a22 *kap*r666 + a22*b12*r6435 + b12 *kap*r680
r6264=-------------------------------------------------------------------
2
b12 *kap
r6265=0
r6266=0
r6267=0
r6268=r6270
r6269=0
r6271=0
r6272=r6115 - 2*r6149 + 4*r6336
r6273=0
r6274=r6115 - 2*r6149 + 4*r6336
r6275= - r6270
r6276=0
r6277=0
r6278=0
r6279=r6115 - 2*r6149 + 4*r6336
r6280= - r6270
a22*r6115 - a22*r6243
r6281=-----------------------
b12
r6282=0
a22*r6115 - a22*r6243 - b12*r6160 - 3*b12*r669
r6283=------------------------------------------------
b12
r6284=0
r6285=0
r6286=2*r6157 - 2*r6252 - 2*r6353 + 6*r666 - 4*r671
r6287=0
a22*r6115 - a22*r6243 - b12*r6356 - 3*b12*r669
r6288=------------------------------------------------
b12
r6289=0
r6290=0
- 2*a22*r666 + 2*a22*r671
r6291=----------------------------
b12
r6292=0
r6293
a22*kap*r6252 + a22*kap*r666 - 2*a22*kap*r671 - b12*kap*r6133 - 2*b12*r6435
=-----------------------------------------------------------------------------
b12*kap
r6294=0
1 2 1 2 14 2
r6295=( - ---*a22 *r6160 - ---*a22 *r6356 - ----*a22 *r669 + a22*b12*r6259
2 2 3
2 11 2 2
- b12 *kap*r6129 - ----*b12 *kap*r669 + b12 *r6389)/(a22*b12)
3
- a22*r6252 + a22*r666 + b12*r6133
r6296=-------------------------------------
b12
2 2
2*a22 *r669 + a22*b12*r6131 - a22*b12*r6259 + b12 *kap*r669
r6297=-------------------------------------------------------------
2
b12
r6298=0
r6299=0
- a22*kap*r6252 + a22*kap*r666 + b12*r6435
r6300=---------------------------------------------
b12
r6301=0
a22*r6115 - a22*r6243 + b12*r6407
r6302=-----------------------------------
b12
r6303=0
1 3
a22*r6115 - a22*r6243 - ---*b12*r6160 + b12*r6407 - ---*b12*r669
2 2
r6304=------------------------------------------------------------------
b12
a22*r6270 + 2*b12*kap*r6230
r6305=-----------------------------
b12
r6306=0
r6307=(2*a22*r6270 + 4*b12*kap*r6230 + b12*r6157 - b12*r6252 - 2*b12*r6353
+ 3*b12*r666 - 2*b12*r671)/b12
r6308=0
2 2 1
r6309=(a22 *r6115 - a22 *r6243 - ---*a22*b12*r6160 - a22*b12*r6356
2
7 1 2 2
+ a22*b12*r6407 - ---*a22*b12*r669 + ---*b12 *kap*r6115 - b12 *kap*r6149
2 2
2 1 2
+ 2*b12 *kap*r6336 - ---*b12 *r6430)/(a22*b12)
2
r6310=2*r6252 + r6353 - 3*r666 + r671
r6311=0
2
r6312=( - 2*a22 *r6270 - 4*a22*b12*kap*r6230 + 2*a22*b12*r6252 + 2*a22*b12*r6353
2 2
- 6*a22*b12*r666 + 4*a22*b12*r671 + b12 *kap*r6270)/b12
r6313=0
a22*r6160 + 2*a22*r6356 + 6*a22*r669 + b12*kap*r6243
r6314=------------------------------------------------------
b12
r6315=0
r6316=0
r6317=0
2 2 2
r6318=(a22 *r6160 + a22 *r6356 + 8*a22 *r669 - a22*b12*kap*r6115
1 2
+ a22*b12*kap*r6243 + a22*b12*r6131 - a22*b12*r6259 + ---*b12 *kap*r6160
2
1 2 2 2 2
+ ---*b12 *kap*r6356 + 7*b12 *kap*r669 - b12 *r6389)/b12
2
2 2
r6319=(a22 *kap*r666 - a22 *kap*r671 - a22*b12*kap*r6133 + a22*b12*r6435
2 2 2 2 2
- b12 *kap *r6252 + 2*b12 *kap *r666)/(b12 *kap)
r6320=0
r6321=0
r6322=0
2
r6323=( - 2*a22 *r6270 - 4*a22*b12*kap*r6230 + a22*b12*r6252 + 2*a22*b12*r6353
2 2
- 3*a22*b12*r666 + 2*a22*b12*r671 + b12 *kap*r6270)/b12
r6324=0
2*a22*r6160 + 2*a22*r6356 + 8*a22*r669 + b12*r6430
r6325=----------------------------------------------------
b12
2
r6326=(2*a22 *r6270 + 4*a22*b12*kap*r6230 - 5*a22*b12*r6252 - 2*a22*b12*r6353
2 2
+ 7*a22*b12*r666 - 2*a22*b12*r671 - b12 *kap*r6270)/b12
2 2 26 2
r6327=( - a22 *r6160 - a22 *r6356 - ----*a22 *r669 + a22*b12*kap*r6115
9
1 2 2
- a22*b12*kap*r6243 + ---*b12 *kap*r669)/b12
9
r6328=0
r6329=0
r6330=r6435
r6331=0
3 2 2 9 2
r6332=( - ---*a22 *r6160 - a22 *r6356 - ---*a22 *r669 + a22*b12*kap*r6115
2 2
1 1 1 2 2
- ---*a22*b12*kap*r6243 - ---*a22*b12*r6430 + ---*b12 *kap*r6407)/b12
2 2 2
3 2 2 2
r6333=( - a22 *r6270 - 2*a22 *b12*kap*r6230 + 4*a22 *b12*r6252 + a22 *b12*r6353
2 2 2 3 2
- 5*a22 *b12*r666 + a22 *b12*r671 + a22*b12 *kap*r6270 + b12 *kap *r6230
3
)/b12
r6334=0
3 3
- a22 *r6252 + a22 *r666
r6335=---------------------------
3
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=r6270
r6343=0
r6344=r6270
1
r6345=---*r6243 + 2*r6336
2
r6346=0
1
r6347= - ---*r6115 + r6149 + r6243
2
r6348=0
r6349=r6270
1
r6350=---*r6243 + r6336
2
a22*r6270 + 2*b12*kap*r6230
r6351=-----------------------------
b12
r6352=0
r6354=0
r6355=0
r6357=0
r6358=r6157 + 3*r666 - 3*r671
r6359=0
r6360=0
1 2 1 2 1
r6361=( - ---*a22 *r6115 + ---*a22 *r6243 - a22*b12*r6129 + ---*a22*b12*r6356
2 2 2
1 1 2 2 2
- ---*a22*b12*r669 + ---*b12 *kap*r6115 + b12 *kap*r660)/b12
2 2
r6362=0
1 3 1 3 2 5 2
r6363=( - ---*a22 *r6115 + ---*a22 *r6243 - a22 *b12*r6129 + ---*a22 *b12*r6160
2 2 4
5 2 23 2 2
+ ---*a22 *b12*r6356 + ----*a22 *b12*r669 + a22*b12 *kap*r660
4 6
1 3 11 3 1 3 2
+ ---*b12 *kap*r6129 + ----*b12 *kap*r669 - ---*b12 *r6389)/(a22*b12 )
2 6 2
r6364=0
r6365
3*a22*kap*r6252 - a22*kap*r666 - 2*a22*kap*r671 - b12*kap*r6133 - b12*r6435
=-----------------------------------------------------------------------------
b12*kap
1 2 1 2 1
r6366=( - ---*a22 *r6115 + ---*a22 *r6243 - a22*b12*r6129 + ---*a22*b12*r669
2 2 2
1 2 1 2 2
+ ---*b12 *kap*r6115 - ---*b12 *kap*r6243 + b12 *kap*r660
2 2
1 2 2
+ ---*b12 *r6259)/b12
2
2 2 2
r6367=(2*a22 *kap*r6252 - a22 *kap*r666 - a22 *kap*r671 - a22*b12*kap*r6133
2 2 2
- 2*a22*b12*r6435 + b12 *kap *r671)/(b12 *kap)
r6368=0
r6369=0
3 1 2 1 2
r6370=( - a22 *r669 - ---*a22 *b12*r6131 + ---*a22 *b12*r6259
2 2
1 2 2 1 3
+ ---*a22*b12 *kap*r669 - a22*b12 *r6138 - ---*b12 *kap*r6259
2 2
3 3
+ b12 *kap*r674)/b12
r6371=0
a22*r6270 + 2*b12*kap*r6230
r6372=-----------------------------
b12
r6373=0
r6374=r6353
r6375= - r6407
r6376=0
1 1 1
r6377=(---*a22*r6356 - a22*r6407 + ---*a22*r669 - ---*b12*kap*r6115
2 2 2
1
+ b12*kap*r6149 - 2*b12*kap*r6336 + ---*b12*r6430)/a22
2
r6378=0
r6379=(2*a22*r6270 + 4*b12*kap*r6230 + b12*r6157 - 3*b12*r6252 - 2*b12*r6353
+ 6*b12*r666 - 3*b12*r671)/b12
1 3
r6380= - ---*r6356 - r6407 - ---*r669
2 2
r6381=0
- 2*a22*r6160 - a22*r6356 - 6*a22*r669 + b12*kap*r6115
r6382=---------------------------------------------------------
b12
r6383=0
2
r6384=(2*a22 *r6270 + 4*a22*b12*kap*r6230 - 2*a22*b12*r6252 - 2*a22*b12*r6353
2 2
+ 2*a22*b12*r671 - b12 *kap*r6270)/b12
r6385=0
r6386=0
r6387=0
2 2 2
r6388=(2*a22 *kap*r6252 - a22 *kap*r666 - a22 *kap*r671 - a22*b12*kap*r6133
2 2 2 2 2 2
- 3*a22*b12*r6435 + b12 *kap *r6252 - b12 *kap *r666 + b12 *kap *r671)/(
2
b12 *kap)
r6390=0
1 2 1 2 2
---*a22 *r6115 - ---*a22 *r6243 + a22*b12*r6407 + 2*b12 *kap*r6336
2 2
r6391=--------------------------------------------------------------------
2
b12
r6392=0
1 2 1 2 3 1
r6393=(---*a22 *r6115 - ---*a22 *r6243 - ---*a22*b12*r6160 - ---*a22*b12*r6356
2 2 2 2
1 2
+ a22*b12*r6407 - 5*a22*b12*r669 + ---*b12 *kap*r6115
2
1 2 2 1 2 2
+ ---*b12 *kap*r6243 + 2*b12 *kap*r6336 - ---*b12 *r6430)/b12
2 2
r6394=0
4*a22*r6252 - 6*a22*r666 + 2*a22*r671
r6395=---------------------------------------
b12
1 2 1 2 1 1
r6396=(---*a22 *r6115 - ---*a22 *r6243 - ---*a22*b12*r6160 + ---*a22*b12*r6356
2 2 2 2
1 2 1 2
+ a22*b12*r6407 + a22*b12*r669 + ---*b12 *kap*r6115 + ---*b12 *kap*r6243
2 2
2 1 2 2
+ 2*b12 *kap*r6336 - ---*b12 *r6430)/b12
2
3 2 2
r6397=( - 2*a22 *r6270 - 4*a22 *b12*kap*r6230 + 2*a22 *b12*r6252
2 2 2
+ 2*a22 *b12*r6353 - 3*a22 *b12*r666 + a22 *b12*r671
2 3 2 3
+ 2*a22*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
r6398=0
r6399=0
1 3 1 3 14 3 2
r6400=(---*a22 *r6160 + ---*a22 *r6356 + ----*a22 *r669 - a22 *b12*kap*r6115
2 2 3
2 1 2 1 2
+ a22 *b12*kap*r6243 + ---*a22 *b12*r6131 - ---*a22 *b12*r6259
2 2
2 1 2 1 2
- a22*b12 *kap*r6129 + ---*a22*b12 *kap*r6160 + ---*a22*b12 *kap*r6356
2 2
14 2 2 3 2 3
+ ----*a22*b12 *kap*r669 - a22*b12 *r6389 + b12 *kap *r660)/b12
3
r6401=0
3 2 2
r6402=( - 2*a22 *r6270 - 4*a22 *b12*kap*r6230 + 4*a22 *b12*r6252
2 2 2
+ 2*a22 *b12*r6353 - 6*a22 *b12*r666 + 2*a22 *b12*r671
2 3 2 3
+ 2*a22*b12 *kap*r6270 + 2*b12 *kap *r6230 + 5*b12 *kap*r6252
3 3 3
- 6*b12 *kap*r666 + b12 *kap*r671)/b12
3 2 1 2 2
r6403=(---*a22 *r6160 + ---*a22 *r6356 + 3*a22 *r669 - a22*b12*kap*r6115
2 2
2 2
+ a22*b12*r6430 - b12 *kap*r6407)/b12
r6404=0
3 1 3 5 3 2
r6405=( - a22 *r6160 - ---*a22 *r6356 - ---*a22 *r669 + a22 *b12*kap*r6115
2 2
1 2 1 2 2
- ---*a22 *b12*kap*r6243 - ---*a22 *b12*r6430 + a22*b12 *kap*r6407
2 2
3 2 3
+ b12 *kap *r6336)/b12
r6406=0
r6408=0
1 1 1
r6409=(---*a22*r6356 + a22*r6407 - ---*a22*r669 + ---*b12*kap*r6115
6 6 6
1 2 1
- ---*b12*kap*r6149 + ---*b12*kap*r6336 - ---*b12*r6430)/a22
3 3 6
a22*r6270 + 2*b12*kap*r6230
r6410=-----------------------------
b12
r6411=0
r6412=r6252 + r6353 - r666
r6413=0
1 1
r6414=---*r6356 + r6407 + ---*r669
2 2
2 4 1
---*a22*r6270 + ---*b12*kap*r6230 + ---*b12*r6157 + b12*r666 - b12*r671
3 3 3
r6415=-------------------------------------------------------------------------
b12
r6416=0
2 2
- 2*a22 *r6270 - 4*a22*b12*kap*r6230 + 2*a22*b12*r6353 + b12 *kap*r6270
r6417=--------------------------------------------------------------------------
2
b12
r6418=0
a22*r6356 + b12*kap*r6243
r6419=---------------------------
b12
r6420=0
r6421=0
r6422=0
2 2 34 2
r6423=(a22 *r6160 + a22 *r6356 + ----*a22 *r669 - a22*b12*kap*r6115
9
25 2 2 2
+ a22*b12*kap*r6243 + ----*b12 *kap*r669 - b12 *r6389)/b12
9
2 2 2
r6424=(2*a22 *kap*r6252 - a22 *kap*r666 - a22 *kap*r671 - a22*b12*kap*r6133
2 2 2
- a22*b12*r6435 + b12 *kap *r671)/(b12 *kap)
r6425=0
r6426=0
r6427=0
2
r6428=( - 2*a22 *r6270 - 4*a22*b12*kap*r6230 - a22*b12*r6252 + 2*a22*b12*r6353
2 2
+ a22*b12*r666 + b12 *kap*r6270)/b12
r6429=0
2
r6431=(2*a22 *r6270 + 4*a22*b12*kap*r6230 - 3*a22*b12*r6252 - 2*a22*b12*r6353
2 2
+ 3*a22*b12*r666 - b12 *kap*r6270)/b12
2 2 34 2
r6432=( - a22 *r6160 - a22 *r6356 - ----*a22 *r669 + a22*b12*kap*r6115
9
7 2 2
- a22*b12*kap*r6243 - ---*b12 *kap*r669)/b12
9
r6433=0
r6434=0
r6436=0
3 2 1 2 2
r6437=( - ---*a22 *r6160 - ---*a22 *r6356 - 5*a22 *r669 + a22*b12*kap*r6115
2 2
2 2
- a22*b12*r6430 + b12 *kap*r6407)/b12
3 2 2
r6438=( - 2*a22 *r6270 - 4*a22 *b12*kap*r6230 + 5*a22 *b12*r6252
2 2 2
+ 2*a22 *b12*r6353 - 6*a22 *b12*r666 + a22 *b12*r671
2 3 2 3
+ 2*a22*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
r6439=0
1 3 1 3 5 2
r6440=( - ---*a22 *r6252 + ---*a22 *r671 + ---*a22*b12 *kap*r6252
3 3 3
2 1 2 3
- 2*a22*b12 *kap*r666 + ---*a22*b12 *kap*r671)/b12
3
1
---*a22*r6407 + b12*kap*r6336
2
r6441=-------------------------------
b12
r6442=0
1 1 1 1
r6443=(---*a22*r6356 + ---*a22*r6407 - ---*a22*r669 + ---*b12*kap*r6243
2 2 2 2
1
+ b12*kap*r6336 - ---*b12*r6430)/b12
2
r6444=0
2
r6445=( - 2*a22 *r6270 - 4*a22*b12*kap*r6230 + 2*a22*b12*r6252 + 2*a22*b12*r6353
2 2
- 2*a22*b12*r666 + b12 *kap*r6270)/b12
1 1 1 1
r6446=(---*a22*r6356 + ---*a22*r6407 + ---*a22*r669 + ---*b12*kap*r6243
2 2 2 2
+ b12*kap*r6336)/b12
3 2 2
r6447=( - a22 *r6270 - 2*a22 *b12*kap*r6230 + a22 *b12*r6353
2 3 2 3
+ a22*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6448=0
r6449=0
1 3 1 3 17 3 1 2
r6450=(---*a22 *r6160 + ---*a22 *r6356 + ----*a22 *r669 - ---*a22 *b12*kap*r6115
4 4 18 2
1 2 1 2
+ ---*a22 *b12*kap*r6243 - ---*a22*b12 *kap*r6129
2 2
17 2 1 2 1 3 2
+ ----*a22*b12 *kap*r669 - ---*a22*b12 *r6389 + ---*b12 *kap *r6115
18 2 4
1 3 2 1 3 2 3
- ---*b12 *kap *r6243 + ---*b12 *kap *r660)/b12
4 2
r6451=0
3 2 2 2
r6452=( - a22 *r6270 - 2*a22 *b12*kap*r6230 - 2*a22 *b12*r6252 + a22 *b12*r6353
2 2 3 2 3
+ 2*a22 *b12*r666 + a22*b12 *kap*r6270 + b12 *kap *r6230)/b12
1 2 1 2 1
r6453=( - ---*a22 *r6356 + ---*a22 *r669 - ---*a22*b12*kap*r6243
2 2 2
1 1 2 2 2
+ ---*a22*b12*r6430 - ---*b12 *kap*r6407 + b12 *kap*r669)/b12
2 2
r6454=0
1 3 11 3 1 2
r6455=( - ---*a22 *r6160 - ----*a22 *r669 + ---*a22 *b12*kap*r6115
2 6 2
1 2 2 1 2
- ---*a22 *b12*r6430 + a22*b12 *kap*r6407 - ---*a22*b12 *kap*r669
2 3
3 2 3
+ b12 *kap *r6336)/b12
r6456=0
1 2 1 2 1
r6457=(---*a22 *r6356 - ---*a22 *r669 + ---*a22*b12*kap*r6243
2 2 2
1 1 2 2
- ---*a22*b12*r6430 + ---*b12 *kap*r6407)/b12
2 2
3 2 2 2
r6458=( - a22 *r6270 - 2*a22 *b12*kap*r6230 + a22 *b12*r6252 + a22 *b12*r6353
2 2 3 2 3
- a22 *b12*r666 + a22*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6459=0
3 3
- a22 *r6252 + a22 *r666
r6460=---------------------------
3
b12
1 3 1 3 1 2
r6461=(---*a22 *r6356 - ---*a22 *r669 + ---*a22 *b12*kap*r6243
6 6 6
1 2 1 2 1 3 2
- ---*a22 *b12*r6430 + ---*a22*b12 *kap*r6407 + ---*b12 *kap *r6336)/
6 3 3
3
b12
1
a33=---*a22
2
a23=0
a13=0
a11=a22
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, r666, r671, r674, r680, r683, r6115, r6129, r6131,
r6133, r6138, r6149, r6157, r6160, r6230, r6243, r6252,
r6259, r6270, r6336, r6353, r6356, r6389, r6407, r6430,
r6435, r669, a22, 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,a22,r669}
Relevance for the application:
Modulo the following equation:
2 2
0=a22 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2 2
2*u1 *a22 + 2*u1*v2*b12 + 2*u2 *a22 - 2*u2*v1*b12 + u3 *a22
HAM=-------------------------------------------------------------
2
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=(2*u1**2*a22 + 2*u1*v2*b12 + 2*u2**2*a22 - 2*u2*v1*b12 + u3**2*a22)/2$