Solution 10 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
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Equations
The following unsolved equations remain:
2 2
0=a22 + b12 *kap
Expressions
The solution is given through the following expressions:
2 2 2 2
r60=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(6*b12 *kap )
r61=0
2 2 2 2
r62=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(2*b12 *kap )
r63=0
2 2 2 2
r64=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(2*b12 *kap )
r65=0
2 2 2 2
r66=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(6*b12 *kap )
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
2 2 2 2
r613=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(2*b12 *kap )
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
2 2 2 2
r617=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(2*b12 *kap )
r618=0
r619=0
r620=0
r621=0
2 2 2 2
r622=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(2*b12 *kap )
r623=0
2 2 2 2
r624=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(2*b12 *kap )
r625=0
r626=0
2 2 2 2
r627=( - a22 *r6115 + 2*a22 *r6149 + a22 *r6243 - 4*a22 *r6336 - a22*b12*r6407
2 2 2
+ 2*b12 *kap*r6336)/(6*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 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=r657
r656=0
1
r658=---*r6115 + r660
2
r659=0
r661=0
r662=r657
1 1 1
r663=---*r6115 - ---*r6243 + ---*r660
4 4 2
- a22*r6270 - 2*a22*r657 - 2*b12*kap*r6230 + b12*r6157 + 3*b12*r666
r664=----------------------------------------------------------------------
3*b12
r665=0
r667=0
r668=0
r670=0
r672=0
r673=0
r675=0
- a22*r669 - b12*r6131 + 2*b12*r674
r676=--------------------------------------
2*b12
r677=0
2*a22*r666 - 2*a22*r671 - b12*r6133 - b12*r6257
r678=-------------------------------------------------
2*b12
a22*r669 - b12*r6259 + 2*b12*r674
r679=-----------------------------------
2*b12
r681=0
r682=0
r684=0
r685=r6230
r686=0
r687=2*r6230
r688=0
r689=r6230
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r690=------------------------------------------------------------------
2*b12*kap
r691=0
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r692=------------------------------------------------------------------
b12*kap
r693=0
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r694=------------------------------------------------------------------
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
- a22*r6115 + 2*a22*r6149 + a22*r6243 - 4*a22*r6336 - b12*r6407
r6104=------------------------------------------------------------------
2*b12*kap
r6105=0
r6106=r6115
r6107=0
r6108=r6115
r6109=0
r6110= - r6270 - 2*r657
r6111=0
r6112= - r6270 - 2*r657
r6113=0
r6114=0
r6116=0
r6117= - r6270 - 2*r657
r6118=0
r6119=0
r6120=0
- a22*r6270 - 3*a22*r657 - 2*b12*kap*r6230 + b12*r6157 + b12*r666
r6121=--------------------------------------------------------------------
b12
r6122=0
- a22*r657 + b12*r666
r6123=------------------------
b12
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
r6137
2 2 2
- 2*a22 *r666 + 2*a22 *r671 + a22*b12*r6133 + a22*b12*r6257 + 2*b12 *r680
=----------------------------------------------------------------------------
2
2*b12
r6139=0
r6140=r6336
r6141=0
r6115 + 4*r6336
r6142=-----------------
2
r6143=0
r6115 + 2*r6336
r6144=-----------------
2
r6145=0
r6146= - r6270 - r657
r6147=0
r6148= - r6270 - r657
r6150=0
1
r6151=---*r6115 + r6149
2
r6152=0
r6153= - r6270 - r657
r6154=r6149 - r6336
a22*r6270 + 2*a22*r657 + 2*b12*kap*r6230
r6155=------------------------------------------
b12
r6156=0
r6158=0
r6159=0
r6161=0
2 7 2 1 2
r6162=(a22 *r6270 + ---*a22 *r657 + 2*a22*b12*kap*r6230 - ---*b12 *kap*r6270
4 2
5 2 1 2
- ---*b12 *kap*r657 - ---*b12 *r6188)/(a22*b12)
4 2
r6163=0
r6164=0
2 2
r6165=( - a22 *r6115 + a22 *r6243 - 2*a22*b12*r6129 + a22*b12*r6356
2 2 2
+ 3*a22*b12*r669 + b12 *kap*r6243 + 2*b12 *kap*r660)/(2*b12 )
r6166=0
2 2
r6167=( - a22 *r6115 + a22 *r6243 - 2*a22*b12*r6129 + a22*b12*r6160
2 2
+ a22*b12*r6356 + a22*b12*r669 - b12 *kap*r6115 + b12 *kap*r6243
2 2 2
+ 2*b12 *kap*r660 + b12 *r6131)/(2*b12 )
r6168=0
2
r6169=( - 4*a22 *r657 + 4*a22*b12*r6252 - 2*a22*b12*r666 - 2*a22*b12*r671
2 2 2 2
+ 2*b12 *kap*r657 + b12 *r6133 - b12 *r6257)/(2*b12 )
3 3 2 2
r6170=( - 6*a22 *r6115 + 6*a22 *r6243 - 12*a22 *b12*r6129 - 3*a22 *b12*r6160
2 2 2
- 3*a22 *b12*r6356 + 22*a22 *b12*r669 + 12*a22*b12 *kap*r660
2 2 3
+ 6*a22*b12 *r6131 - 6*a22*b12 *r6259 + 6*b12 *kap*r6129
3 3 2
+ 22*b12 *kap*r669 - 6*b12 *r6389)/(12*a22*b12 )
2 2 2
a22 *r666 - a22 *r671 - a22*b12*r6133 + b12 *kap*r666
r6171=-------------------------------------------------------
2
b12
r6172=0
r6173=0
3 2 2 2
r6174=( - 2*a22 *r669 - a22 *b12*r6131 + a22 *b12*r6259 - a22*b12 *kap*r669
2 3 3 3
- 2*a22*b12 *r6138 - b12 *kap*r6131 + 2*b12 *kap*r674)/(2*b12 )
r6175=0
a22*r6270 + a22*r657 + 2*b12*kap*r6230
r6176=----------------------------------------
b12
r6177=0
2*a22*r6270 + a22*r657 + 4*b12*kap*r6230 + b12*r6157
r6178=------------------------------------------------------
3*b12
- a22*r6115 + a22*r6243 - b12*r6407
r6179=--------------------------------------
b12
r6180=0
- 2*a22*r6115 + 2*a22*r6243 + b12*r6160 - 2*b12*r6407 + b12*r669
r6181=-------------------------------------------------------------------
2*b12
r6182=0
2 7 2
r6183=(a22 *r6270 + ---*a22 *r657 + 2*a22*b12*kap*r6230 - a22*b12*r6252
4
1 2 5 2 1 2
+ a22*b12*r666 - ---*b12 *kap*r6270 - ---*b12 *kap*r657 - ---*b12 *r6188
2 4 2
)/(a22*b12)
2 2
r6184=( - 6*a22 *r6115 + 6*a22 *r6243 + 3*a22*b12*r6160 + 2*a22*b12*r6356
2 2
- 6*a22*b12*r6407 + 7*a22*b12*r669 - b12 *kap*r6115 + 2*b12 *kap*r6149
2 2
- 4*b12 *kap*r6336 + b12 *r6430)/(6*a22*b12)
r6185=0
- a22*r6160 + b12*kap*r6115
r6186=------------------------------
b12
r6187=0
r6189=0
r6190=0
r6191=0
3 2 2 2
r6192=(a22 *r657 - 2*a22 *b12*r6252 + 2*a22 *b12*r666 - 3*a22*b12 *kap*r657
2 2 3 3
- a22*b12 *r6133 + a22*b12 *r6257 + 2*b12 *kap*r666)/(2*b12 )
2 2
r6193=( - 92*a22 *r669 - 18*a22*b12*r6131 + 18*a22*b12*r6259 - 9*b12 *kap*r6160
2 2 2 2
- 9*b12 *kap*r6356 - 92*b12 *kap*r669 + 18*b12 *r6389)/(18*b12 )
r6194=0
2 2 2
a22 *r6115 - a22 *r6243 + a22*b12*r6407 + 2*b12 *kap*r6336
r6195=------------------------------------------------------------
2
2*b12
r6196=0
2 2
r6197=(a22 *r6115 - a22 *r6243 - a22*b12*r6160 + a22*b12*r6407 - a22*b12*r669
2 2 2
+ b12 *kap*r6115 + 2*b12 *kap*r6336)/(2*b12 )
r6198=0
3 2 3 2
r6199=( - ---*a22 *r657 + 2*a22*b12*r6252 - 2*a22*b12*r666 + ---*b12 *kap*r657
2 2
2 2
+ b12 *r6188)/b12
2 2
r6200=(a22 *r6115 - a22 *r6243 - 3*a22*b12*r6160 - 2*a22*b12*r6356
2 2
+ a22*b12*r6407 - 7*a22*b12*r669 + b12 *kap*r6115 + 2*b12 *kap*r6336
2 2
- b12 *r6430)/(2*b12 )
3 2 2 2
r6201=(a22 *r657 + 2*a22*b12 *kap*r6270 + 5*a22*b12 *kap*r657 - 2*a22*b12 *r6188
3 2 3
+ 4*b12 *kap *r6230)/(4*b12 )
r6202=0
r6203=0
3 3 3 2
r6204=(9*a22 *r6160 + 9*a22 *r6356 + 118*a22 *r669 - 18*a22 *b12*kap*r6115
2 2 2
+ 18*a22 *b12*kap*r6243 + 18*a22 *b12*r6131 - 18*a22 *b12*r6259
2 2 2
- 18*a22*b12 *kap*r6129 + 18*a22*b12 *kap*r6160 + 18*a22*b12 *kap*r6356
2 2 3 2
+ 118*a22*b12 *kap*r669 - 18*a22*b12 *r6389 - 9*b12 *kap *r6115
3 2 3 2 3
+ 9*b12 *kap *r6243 + 18*b12 *kap *r660)/(36*b12 )
r6205=0
3 3 2 2 1 2
r6206=(---*a22 *r657 - a22 *b12*r6252 + a22 *b12*r666 + ---*a22*b12 *kap*r6270
4 2
1 2 1 2 3 2 3
- ---*a22*b12 *kap*r657 - ---*a22*b12 *r6188 + b12 *kap *r6230)/b12
4 2
2 2 2
r6207=(3*a22 *r6160 + 2*a22 *r6356 + 7*a22 *r669 - 2*a22*b12*kap*r6115
2 2
+ a22*b12*kap*r6243 + a22*b12*r6430 - b12 *kap*r6407)/(2*b12 )
r6208=0
3 3 3 2
r6209=( - 3*a22 *r6160 - 2*a22 *r6356 - 7*a22 *r669 + 3*a22 *b12*kap*r6115
2 2 2
- 2*a22 *b12*kap*r6243 - a22 *b12*r6430 + 2*a22*b12 *kap*r6407
3 2 3
+ 2*b12 *kap *r6336)/(6*b12 )
r6210=0
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6211=---------------------------------------------------------------
2*b12*kap
r6212=0
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6213=---------------------------------------------------------------
b12*kap
r6214=0
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6215=---------------------------------------------------------------
2*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
a22*r6115 - 2*a22*r6149 - a22*r6243 + 4*a22*r6336 + b12*r6407
r6229=---------------------------------------------------------------
2*b12*kap
r6231=0
r6232=r6270
r6233=0
r6234=r6270
r6235=0
r6236=r6243
r6237=0
r6238=r6243
r6239=0
r6240=0
r6241=r6270
r6242=0
r6244=0
r6245=0
r6246=0
- 2*a22*r6115 + 2*a22*r6243 - 2*b12*r6129 + b12*r6356 - b12*r669
r6247=-------------------------------------------------------------------
2*b12
r6248=0
r6249=( - 2*a22*r6115 + 2*a22*r6243 - 2*b12*r6129 + b12*r6160 + b12*r6356
+ 2*b12*r669)/(2*b12)
r6250=( - a22*r6270 - a22*r657 - 2*b12*kap*r6230 + b12*r6157 + 3*b12*r666
- 2*b12*r671)/b12
r6251=0
r6253=0
- a22*r6115 + a22*r6243 - b12*r6129 + b12*r669
r6254=-------------------------------------------------
b12
a22*r657 + b12*r671
r6255=---------------------
b12
r6256=0
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
2*a22 *r666 - 2*a22 *r671 - a22*b12*r6133 - a22*b12*r6257 + 2*b12 *r680
r6264=-------------------------------------------------------------------------
2
2*b12
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 - 2*r657
r6276=0
r6277= - 2*r657
r6278=0
r6279=r6115 - 2*r6149 + 4*r6336
r6280= - r6270 - 2*r657
a22*r6115 - a22*r6243
r6281=-----------------------
b12
r6282=0
a22*r6115 - a22*r6243 - b12*r6160 - 3*b12*r669
r6283=------------------------------------------------
b12
r6284=0
r6285=0
2 11 2
r6286=( - 2*a22 *r6270 - ----*a22 *r657 - 4*a22*b12*kap*r6230 + 2*a22*b12*r6157
2
2 5 2
+ 2*a22*b12*r6252 - 2*a22*b12*r671 + b12 *kap*r6270 + ---*b12 *kap*r657
2
2
+ b12 *r6188)/(a22*b12)
r6287=0
a22*r6115 - a22*r6243 - b12*r6356 - 3*b12*r669
r6288=------------------------------------------------
b12
r6289=0
r6290=0
- 2*a22*r666 + 2*a22*r671 + b12*kap*r657
r6291=-------------------------------------------
b12
r6292=0
2 2 2
a22 *r657 - a22*b12*r6252 + a22*b12*r666 + b12 *kap*r657 + b12 *r6257
r6293=-----------------------------------------------------------------------
2
b12
r6294=0
2 2 2
r6295=( - 3*a22 *r6160 - 3*a22 *r6356 - 28*a22 *r669 + 6*a22*b12*r6259
2 2 2
- 6*b12 *kap*r6129 - 22*b12 *kap*r669 + 6*b12 *r6389)/(6*a22*b12)
2 2 2
a22 *r657 - a22*b12*r6252 + a22*b12*r666 + b12 *kap*r657 + b12 *r6133
r6296=-----------------------------------------------------------------------
2
b12
2 2
2*a22 *r669 + a22*b12*r6131 - a22*b12*r6259 + b12 *kap*r669
r6297=-------------------------------------------------------------
2
b12
r6298=0
r6299=0
2*a22*kap*r666 - 2*a22*kap*r671 - b12*kap*r6133 - b12*kap*r6257
r6300=-----------------------------------------------------------------
2*b12
r6301=0
a22*r6115 - a22*r6243 + b12*r6407
r6302=-----------------------------------
b12
r6303=0
2*a22*r6115 - 2*a22*r6243 - b12*r6160 + 2*b12*r6407 - 3*b12*r669
r6304=------------------------------------------------------------------
2*b12
a22*r6270 + 3*a22*r657 + 2*b12*kap*r6230
r6305=------------------------------------------
b12
r6306=0
3 2
r6307=( - ---*a22 *r657 + a22*b12*r6157 + 3*a22*b12*r6252 - 3*a22*b12*r666
2
2 5 2 2
+ b12 *kap*r6270 + ---*b12 *kap*r657 + b12 *r6188)/(a22*b12)
2
r6308=0
2 2
r6309=(2*a22 *r6115 - 2*a22 *r6243 - a22*b12*r6160 - 2*a22*b12*r6356
2 2
+ 2*a22*b12*r6407 - 7*a22*b12*r669 + b12 *kap*r6115 - 2*b12 *kap*r6149
2 2
+ 4*b12 *kap*r6336 - b12 *r6430)/(2*a22*b12)
2 11 2 1 2
r6310=(a22 *r6270 + ----*a22 *r657 + 2*a22*b12*kap*r6230 - ---*b12 *kap*r6270
4 2
5 2 1 2
- ---*b12 *kap*r657 - ---*b12 *r6188)/(a22*b12)
4 2
r6311=0
r6312
2 2 2
3*a22 *r657 - 2*a22*b12*r6252 + 2*a22*b12*r671 - b12 *kap*r657 - b12 *r6188
=-----------------------------------------------------------------------------
2
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=(2*a22 *r6160 + 2*a22 *r6356 + 16*a22 *r669 - 2*a22*b12*kap*r6115
+ 2*a22*b12*kap*r6243 + 2*a22*b12*r6131 - 2*a22*b12*r6259
2 2 2 2
+ b12 *kap*r6160 + b12 *kap*r6356 + 14*b12 *kap*r669 - 2*b12 *r6389)/(2
2
*b12 )
3 2 2 2
r6319=( - a22 *r657 + 2*a22 *b12*r6252 + 2*a22 *b12*r666 - 4*a22 *b12*r671
2 2 2
+ 5*a22*b12 *kap*r657 - 3*a22*b12 *r6133 - a22*b12 *r6257
3 3 3
- 2*b12 *kap*r6252 + 4*b12 *kap*r666)/(2*b12 )
r6320=0
2
- a22 *r657
r6321=--------------
2
b12
r6322=0
3 2 5 2
r6323=(---*a22 *r657 - 3*a22*b12*r6252 + 3*a22*b12*r666 - ---*b12 *kap*r657
2 2
2 2
- b12 *r6188)/b12
r6324=0
2*a22*r6160 + 2*a22*r6356 + 8*a22*r669 + b12*r6430
r6325=----------------------------------------------------
b12
r6326
1 2 1 2 2
---*a22 *r657 - a22*b12*r6252 + a22*b12*r666 + ---*b12 *kap*r657 + b12 *r6188
2 2
=-------------------------------------------------------------------------------
2
b12
2 2 2
r6327=( - 9*a22 *r6160 - 9*a22 *r6356 - 26*a22 *r669 + 9*a22*b12*kap*r6115
2 2
- 9*a22*b12*kap*r6243 + b12 *kap*r669)/(9*b12 )
r6328=0
r6329=0
2
r6330=( - a22 *kap*r657 + 2*a22*b12*kap*r6252 - 2*a22*b12*kap*r671
2 2 2 2 2
+ 3*b12 *kap *r657 - b12 *kap*r6133 - b12 *kap*r6257)/(2*b12 )
r6331=0
2 2 2
r6332=( - 3*a22 *r6160 - 2*a22 *r6356 - 9*a22 *r669 + 2*a22*b12*kap*r6115
2 2
- a22*b12*kap*r6243 - a22*b12*r6430 + b12 *kap*r6407)/(2*b12 )
3 2 2
r6333=( - 9*a22 *r657 + 8*a22 *b12*r6252 - 8*a22 *b12*r666
2 2 2
+ 2*a22*b12 *kap*r6270 + 7*a22*b12 *kap*r657 - 2*a22*b12 *r6188
3 2 3
+ 4*b12 *kap *r6230)/(4*b12 )
r6334=0
4 3 3 2 2
a22 *r657 - a22 *b12*r6252 + a22 *b12*r666 - a22 *b12 *kap*r657
r6335=-----------------------------------------------------------------
4
b12
r6337=0
- r6115 + 2*r6149 + r6243
r6338=----------------------------
2
r6339=0
- r6115 + 2*r6149 + r6243 - 2*r6336
r6340=--------------------------------------
2
r6341=0
r6342=r6270 + r657
r6343=0
r6344=r6270 + r657
1
r6345=---*r6243 + 2*r6336
2
r6346=0
- r6115 + 2*r6149 + 2*r6243
r6347=------------------------------
2
r6348=0
r6349=r6270 + r657
1
r6350=---*r6243 + r6336
2
a22*r6270 + 2*b12*kap*r6230
r6351=-----------------------------
b12
r6352=0
2 7 2
r6353=(a22 *r6270 + ---*a22 *r657 + 2*a22*b12*kap*r6230 - 2*a22*b12*r6252
4
1 2 5 2
+ 3*a22*b12*r666 - a22*b12*r671 - ---*b12 *kap*r6270 - ---*b12 *kap*r657
2 4
1 2
- ---*b12 *r6188)/(a22*b12)
2
r6354=0
r6355=0
r6357=0
- 2*a22*r657 + b12*r6157 + 3*b12*r666 - 3*b12*r671
r6358=-----------------------------------------------------
b12
r6359=0
r6360=0
2 2
r6361=( - a22 *r6115 + a22 *r6243 - 2*a22*b12*r6129 + a22*b12*r6356
2 2 2
- a22*b12*r669 + b12 *kap*r6115 + 2*b12 *kap*r660)/(2*b12 )
r6362=0
3 3 2 2
r6363=( - 6*a22 *r6115 + 6*a22 *r6243 - 12*a22 *b12*r6129 + 15*a22 *b12*r6160
2 2 2
+ 15*a22 *b12*r6356 + 46*a22 *b12*r669 + 12*a22*b12 *kap*r660
3 3 3 2
+ 6*b12 *kap*r6129 + 22*b12 *kap*r669 - 6*b12 *r6389)/(12*a22*b12 )
r6364=0
2
r6365=( - 4*a22 *r657 + 4*a22*b12*r6252 - 2*a22*b12*r666 - 2*a22*b12*r671
2 2 2 2
+ 2*b12 *kap*r657 - b12 *r6133 + b12 *r6257)/(2*b12 )
2 2
r6366=( - a22 *r6115 + a22 *r6243 - 2*a22*b12*r6129 + a22*b12*r669
2 2 2 2
+ b12 *kap*r6115 - b12 *kap*r6243 + 2*b12 *kap*r660 + b12 *r6259)/(2
2
*b12 )
2 2 2
- a22 *r666 + a22 *r671 + a22*b12*r6257 + b12 *kap*r671
r6367=----------------------------------------------------------
2
b12
r6368=0
r6369=0
3 2 2 2
r6370=( - 2*a22 *r669 - a22 *b12*r6131 + a22 *b12*r6259 + a22*b12 *kap*r669
2 3 3 3
- 2*a22*b12 *r6138 - b12 *kap*r6259 + 2*b12 *kap*r674)/(2*b12 )
r6371=0
a22*r6270 - a22*r657 + 2*b12*kap*r6230
r6372=----------------------------------------
b12
r6373=0
2 3 2
r6374=(a22 *r6270 + ---*a22 *r657 + 2*a22*b12*kap*r6230 - 2*a22*b12*r6252
4
1 2 5 2
+ 3*a22*b12*r666 - a22*b12*r671 - ---*b12 *kap*r6270 - ---*b12 *kap*r657
2 4
1 2
- ---*b12 *r6188)/(a22*b12)
2
r6375= - r6407
r6376=0
r6377=(a22*r6356 - 2*a22*r6407 + a22*r669 - b12*kap*r6115 + 2*b12*kap*r6149
- 4*b12*kap*r6336 + b12*r6430)/(2*a22)
r6378=0
7 2
r6379=( - ---*a22 *r657 + a22*b12*r6157 + a22*b12*r6252 - a22*b12*r671
2
2 5 2 2
+ b12 *kap*r6270 + ---*b12 *kap*r657 + b12 *r6188)/(a22*b12)
2
- r6356 - 2*r6407 - 3*r669
r6380=-----------------------------
2
r6381=0
- 2*a22*r6160 - a22*r6356 - 6*a22*r669 + b12*kap*r6115
r6382=---------------------------------------------------------
b12
r6383=0
2*a22*r6252 - 6*a22*r666 + 4*a22*r671 + 2*b12*kap*r657 + b12*r6188
r6384=--------------------------------------------------------------------
b12
r6385=0
r6386=0
r6387=0
7 3 2 2 2
r6388=(---*a22 *r657 - a22 *b12*r6252 - a22 *b12*r666 + 2*a22 *b12*r671
2
1 2 1 2 3 2
+ ---*a22*b12 *kap*r657 + ---*a22*b12 *r6133 + ---*a22*b12 *r6257
2 2 2
3 3 3 3
+ b12 *kap*r6252 - b12 *kap*r666 + b12 *kap*r671)/b12
r6390=0
2 2 2
a22 *r6115 - a22 *r6243 + 2*a22*b12*r6407 + 4*b12 *kap*r6336
r6391=--------------------------------------------------------------
2
2*b12
r6392=0
2 2
r6393=(a22 *r6115 - a22 *r6243 - 3*a22*b12*r6160 - a22*b12*r6356
2 2
+ 2*a22*b12*r6407 - 10*a22*b12*r669 + b12 *kap*r6115 + b12 *kap*r6243
2 2 2
+ 4*b12 *kap*r6336 - b12 *r6430)/(2*b12 )
r6394=0
2
- 4*a22 *r657 + 4*a22*b12*r6252 - 6*a22*b12*r666 + 2*a22*b12*r671
r6395=--------------------------------------------------------------------
2
b12
2 2
r6396=(a22 *r6115 - a22 *r6243 - a22*b12*r6160 + a22*b12*r6356 + 2*a22*b12*r6407
2 2 2
+ 2*a22*b12*r669 + b12 *kap*r6115 + b12 *kap*r6243 + 4*b12 *kap*r6336
2 2
- b12 *r6430)/(2*b12 )
3 3 2 2 2
r6397=(---*a22 *r657 - 2*a22 *b12*r6252 + 3*a22 *b12*r666 - a22 *b12*r671
2
2 1 2 2
+ a22*b12 *kap*r6270 - ---*a22*b12 *kap*r657 - a22*b12 *r6188
2
3 2 3
+ 2*b12 *kap *r6230)/b12
r6398=0
r6399=0
3 3 3 2
r6400=(3*a22 *r6160 + 3*a22 *r6356 + 28*a22 *r669 - 6*a22 *b12*kap*r6115
2 2 2
+ 6*a22 *b12*kap*r6243 + 3*a22 *b12*r6131 - 3*a22 *b12*r6259
2 2 2
- 6*a22*b12 *kap*r6129 + 3*a22*b12 *kap*r6160 + 3*a22*b12 *kap*r6356
2 2 3 2 3
+ 28*a22*b12 *kap*r669 - 6*a22*b12 *r6389 + 6*b12 *kap *r660)/(6*b12 )
r6401=0
3 2 2
r6402=( - 21*a22 *r657 + 2*a22*b12 *kap*r6270 - 35*a22*b12 *kap*r657
2 3 2 3
- 2*a22*b12 *r6188 + 4*b12 *kap *r6230 + 10*b12 *kap*r6252
3 3 3
- 12*b12 *kap*r666 + 2*b12 *kap*r671)/(2*b12 )
2 2 2
r6403=(3*a22 *r6160 + a22 *r6356 + 6*a22 *r669 - 2*a22*b12*kap*r6115
2 2
+ 2*a22*b12*r6430 - 2*b12 *kap*r6407)/(2*b12 )
r6404=0
3 3 3 2
r6405=( - 2*a22 *r6160 - a22 *r6356 - 5*a22 *r669 + 2*a22 *b12*kap*r6115
2 2 2
- a22 *b12*kap*r6243 - a22 *b12*r6430 + 2*a22*b12 *kap*r6407
3 2 3
+ 2*b12 *kap *r6336)/(2*b12 )
r6406=0
r6408=0
r6409=(a22*r6356 + 6*a22*r6407 - a22*r669 + b12*kap*r6115 - 2*b12*kap*r6149
+ 4*b12*kap*r6336 - b12*r6430)/(6*a22)
a22*r6270 + a22*r657 + 2*b12*kap*r6230
r6410=----------------------------------------
b12
r6411=0
2 7 2
r6412=(a22 *r6270 + ---*a22 *r657 + 2*a22*b12*kap*r6230 - a22*b12*r6252
4
1 2 5 2
+ 2*a22*b12*r666 - a22*b12*r671 - ---*b12 *kap*r6270 - ---*b12 *kap*r657
2 4
1 2
- ---*b12 *r6188)/(a22*b12)
2
r6413=0
r6356 + 2*r6407 + r669
r6414=------------------------
2
r6415=
2*a22*r6270 + a22*r657 + 4*b12*kap*r6230 + b12*r6157 + 3*b12*r666 - 3*b12*r671
--------------------------------------------------------------------------------
3*b12
r6416=0
2
r6417=(3*a22 *r657 - 4*a22*b12*r6252 + 6*a22*b12*r666 - 2*a22*b12*r671
2 2 2
- 3*b12 *kap*r657 - b12 *r6188)/b12
r6418=0
a22*r6356 + b12*kap*r6243
r6419=---------------------------
b12
r6420=0
r6421=0
r6422=0
2 2 2
r6423=(9*a22 *r6160 + 9*a22 *r6356 + 34*a22 *r669 - 9*a22*b12*kap*r6115
2 2 2
+ 9*a22*b12*kap*r6243 + 25*b12 *kap*r669 - 9*b12 *r6389)/(9*b12 )
3 3 2 2 1 2
r6424=( - ---*a22 *r657 + a22 *b12*r6252 - a22 *b12*r666 + ---*a22*b12 *kap*r657
2 2
1 2 1 2 3 3
- ---*a22*b12 *r6133 + ---*a22*b12 *r6257 + b12 *kap*r671)/b12
2 2
r6425=0
2
- a22 *r657
r6426=--------------
2
b12
r6427=0
2
r6428=(4*a22 *r657 - 5*a22*b12*r6252 + 7*a22*b12*r666 - 2*a22*b12*r671
2 2 2
- 2*b12 *kap*r657 - b12 *r6188)/b12
r6429=0
3 2
r6431=( - ---*a22 *r657 + a22*b12*r6252 - 3*a22*b12*r666 + 2*a22*b12*r671
2
1 2 2 2
+ ---*b12 *kap*r657 + b12 *r6188)/b12
2
2 2 2
r6432=( - 9*a22 *r6160 - 9*a22 *r6356 - 34*a22 *r669 + 9*a22*b12*kap*r6115
2 2
- 9*a22*b12*kap*r6243 - 7*b12 *kap*r669)/(9*b12 )
r6433=0
r6434=0
3 2
r6435=( - ---*a22 *kap*r657 + a22*b12*kap*r6252 - a22*b12*kap*r671
2
1 2 2 1 2 1 2 2
+ ---*b12 *kap *r657 - ---*b12 *kap*r6133 - ---*b12 *kap*r6257)/b12
2 2 2
r6436=0
2 2 2
r6437=( - 3*a22 *r6160 - a22 *r6356 - 10*a22 *r669 + 2*a22*b12*kap*r6115
2 2
- 2*a22*b12*r6430 + 2*b12 *kap*r6407)/(2*b12 )
3 3 2 2 2
r6438=( - ---*a22 *r657 + a22 *b12*r6252 - a22 *b12*r671 + a22*b12 *kap*r6270
2
3 2 2 3 2 3
+ ---*a22*b12 *kap*r657 - a22*b12 *r6188 + 2*b12 *kap *r6230)/b12
2
r6439=0
4 1 3 1 3
r6440=( - 3*a22 *r657 - ---*a22 *b12*r6252 + ---*a22 *b12*r671
3 3
2 2 5 3 3
- 7*a22 *b12 *kap*r657 + ---*a22*b12 *kap*r6252 - 2*a22*b12 *kap*r666
3
1 3 4
+ ---*a22*b12 *kap*r671)/b12
3
a22*r6407 + 2*b12*kap*r6336
r6441=-----------------------------
2*b12
r6442=0
r6443=
a22*r6356 + a22*r6407 - a22*r669 + b12*kap*r6243 + 2*b12*kap*r6336 - b12*r6430
--------------------------------------------------------------------------------
2*b12
r6444=0
3 2
r6445=(---*a22 *r657 - 2*a22*b12*r6252 + 4*a22*b12*r666 - 2*a22*b12*r671
2
3 2 2 2
- ---*b12 *kap*r657 - b12 *r6188)/b12
2
a22*r6356 + a22*r6407 + a22*r669 + b12*kap*r6243 + 2*b12*kap*r6336
r6446=--------------------------------------------------------------------
2*b12
3 3 2 2 2
r6447=(---*a22 *r657 - 2*a22 *b12*r6252 + 3*a22 *b12*r666 - a22 *b12*r671
4
1 2 9 2 1 2
+ ---*a22*b12 *kap*r6270 - ---*a22*b12 *kap*r657 - ---*a22*b12 *r6188
2 4 2
3 2 3
+ b12 *kap *r6230)/b12
r6448=0
r6449=0
3 3 3 2
r6450=(9*a22 *r6160 + 9*a22 *r6356 + 34*a22 *r669 - 18*a22 *b12*kap*r6115
2 2 2
+ 18*a22 *b12*kap*r6243 - 18*a22*b12 *kap*r6129 + 34*a22*b12 *kap*r669
2 3 2 3 2
- 18*a22*b12 *r6389 + 9*b12 *kap *r6115 - 9*b12 *kap *r6243
3 2 3
+ 18*b12 *kap *r660)/(36*b12 )
r6451=0
15 3 2 2 2
r6452=(----*a22 *r657 - 4*a22 *b12*r6252 + 5*a22 *b12*r666 - a22 *b12*r671
4
1 2 9 2 1 2
+ ---*a22*b12 *kap*r6270 - ---*a22*b12 *kap*r657 - ---*a22*b12 *r6188
2 4 2
3 2 3
+ b12 *kap *r6230)/b12
2 2
r6453=( - a22 *r6356 + a22 *r669 - a22*b12*kap*r6243 + a22*b12*r6430
2 2 2
- b12 *kap*r6407 + 2*b12 *kap*r669)/(2*b12 )
r6454=0
3 3 2 2
r6455=( - 3*a22 *r6160 - 11*a22 *r669 + 3*a22 *b12*kap*r6115 - 3*a22 *b12*r6430
2 2 3 2
+ 6*a22*b12 *kap*r6407 - 2*a22*b12 *kap*r669 + 6*b12 *kap *r6336)/(6
3
*b12 )
r6456=0
r6457
2 2 2
a22 *r6356 - a22 *r669 + a22*b12*kap*r6243 - a22*b12*r6430 + b12 *kap*r6407
=-----------------------------------------------------------------------------
2
2*b12
3 3 2 2 2
r6458=(---*a22 *r657 - a22 *b12*r6252 + 2*a22 *b12*r666 - a22 *b12*r671
4
1 2 1 2 1 2
+ ---*a22*b12 *kap*r6270 - ---*a22*b12 *kap*r657 - ---*a22*b12 *r6188
2 4 2
3 2 3
+ b12 *kap *r6230)/b12
r6459=0
4 3 3 2 2
a22 *r657 - a22 *b12*r6252 + a22 *b12*r666 - a22 *b12 *kap*r657
r6460=-----------------------------------------------------------------
4
b12
3 3 2 2
r6461=(a22 *r6356 - a22 *r669 + a22 *b12*kap*r6243 - a22 *b12*r6430
2 3 2 3
+ 2*a22*b12 *kap*r6407 + 2*b12 *kap *r6336)/(6*b12 )
a22
a33=-----
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, r669, r671, r674, r680, r683, r6115, r6129,
r6131, r6133, r6138, r6149, r6157, r6160, r6188, r6230,
r6243, r6252, r6257, r6259, r6270, r6336, r6356, r6389,
r6407, r6430, r657, 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,r657}
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$