Solution 19 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
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Equations
The following unsolved equations remain:
2 2
0=a11 + b12 *kap
Expressions
The solution is given through the following expressions:
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r60=----------------------------------------------------------------
2 2
6*b12 *kap
r61=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r62=----------------------------------------------------------------
2 2
2*b12 *kap
r63=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r64=----------------------------------------------------------------
2 2
2*b12 *kap
r65=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r66=----------------------------------------------------------------
2 2
6*b12 *kap
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r613=----------------------------------------------------------------
2 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 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r617=----------------------------------------------------------------
2 2
2*b12 *kap
r618=0
r619=0
r620=0
r621=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r622=----------------------------------------------------------------
2 2
2*b12 *kap
r623=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r624=----------------------------------------------------------------
2 2
2*b12 *kap
r625=0
r626=0
2 2 2
2*a11 *r6149 - 4*a11 *r6336 - a11*b12*r6302 + 2*b12 *kap*r6336
r627=----------------------------------------------------------------
2 2
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 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= - r6232 + r6349
r656=0
r657= - r6232 + r6349
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= - r6232 + r6349
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
1 2 1 1
r664=( - ---*a11*r6349 - ---*b12*kap*r6230 - ---*b12*r6162 + ---*b12*r6286
3 3 3 6
1
- ---*b12*r6353 + b12*r6412 + b12*r671)/b12
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
2 2
r678=(a11*kap*r6353 - a11*kap*r6412 + 2*b12*kap *r6232 - 2*b12*kap *r6349
+ b12*r6435)/(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
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r690=---------------------------------------
2*b12*kap
r691=0
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r692=---------------------------------------
b12*kap
r693=0
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r694=---------------------------------------
2*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
2*a11*r6149 - 4*a11*r6336 - b12*r6302
r6104=---------------------------------------
2*b12*kap
r6105=0
r6106=r6115
r6107=0
r6108=r6115
r6109=0
r6110=r6232 - 2*r6349
r6111=0
r6112=r6232 - 2*r6349
r6113=0
r6114=0
r6116=0
r6117=r6232 - 2*r6349
r6118=0
r6119=0
r6120=0
r6121=(2*a11*r6232 - 4*a11*r6349 - 4*b12*kap*r6230 + 2*b12*r6162 + b12*r6286
+ 2*b12*r6353 - 2*b12*r6412 + 2*b12*r671)/(2*b12)
r6122=0
a11*r6232 - a11*r6349 - b12*r6162 - b12*r6353 + 2*b12*r6412 + b12*r671
r6123=------------------------------------------------------------------------
b12
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
r6134=0
r6135=0
r6136=0
2 2 2
r6137=( - a11 *kap*r6353 + a11 *kap*r6412 - 2*a11*b12*kap *r6232
2 2 2
+ 2*a11*b12*kap *r6349 - a11*b12*r6435 + b12 *kap*r680)/(b12 *kap)
r6139=0
r6140=r6336
r6141=0
1
r6142=---*r6115 + 2*r6336
2
r6143=0
1
r6144=---*r6115 + r6336
2
r6145=0
r6146= - r6349
r6147=0
r6148= - r6349
r6150=0
1
r6151=---*r6115 + r6149
2
r6152=0
r6153= - r6349
r6154=r6149 - r6336
- a11*r6232 + 2*a11*r6349 + 2*b12*kap*r6230
r6155=----------------------------------------------
b12
r6156=0
1
r6157=( - a11*r6232 + a11*r6349 + 2*b12*r6162 + ---*b12*r6286 + 2*b12*r6353
2
- 3*b12*r6412)/b12
r6158=0
r6159=0
r6161=0
r6163=0
r6164=0
r6166=0
a11*r6160 - b12*kap*r6115 + b12*r6131 + 2*b12*r6165
r6167=-----------------------------------------------------
2*b12
r6168=0
2 2
r6169=( - a11 *kap*r6232 + a11 *kap*r6349 - a11*b12*kap*r6353
2 2 2 2
+ a11*b12*kap*r6412 - 2*b12 *kap *r6232 + 2*b12 *kap *r6349
2 2 2
+ b12 *kap*r6133 + b12 *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 *r6162 - a11 *r6353 + 2*a11 *r6412 - a11*b12*r6133
2 2 2 2
- b12 *kap*r6162 - b12 *kap*r6353 + 2*b12 *kap*r6412 + b12 *kap*r671)/
2
b12
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
a11*r6349 + 2*b12*kap*r6230
r6176=-----------------------------
b12
r6177=0
2 4 2 1
r6178=(---*a11*r6349 + ---*b12*kap*r6230 + ---*b12*r6162 + ---*b12*r6286
3 3 3 6
2
+ ---*b12*r6353 - b12*r6412)/b12
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
2 2
r6188=( - 3*a11 *r6232 + 7*a11 *r6349 + 8*a11*b12*kap*r6230 - 4*a11*b12*r6162
2 2 2
+ 3*b12 *kap*r6232 - 5*b12 *kap*r6349)/(2*b12 )
r6189=0
r6190=0
r6191=0
2 2 2
r6192=( - a11 *kap*r6162 - a11 *kap*r6353 + 2*a11 *kap*r6412 - a11*b12*kap*r6133
2 2 2 2 2 2
- a11*b12*r6435 - b12 *kap *r6162 - b12 *kap *r6353 + 2*b12 *kap *r6412
2 2 2
+ b12 *kap *r671)/(b12 *kap)
r6193
1 1
- a11*r6131 + a11*r6259 - ---*b12*kap*r6160 - ---*b12*kap*r6356 + b12*r6389
2 2
=------------------------------------------------------------------------------
b12
r6194=0
a11*r6302 + 2*b12*kap*r6336
r6195=-----------------------------
2*b12
r6196=0
- a11*r6160 + a11*r6302 + b12*kap*r6115 + 2*b12*kap*r6336
r6197=------------------------------------------------------------
2*b12
r6198=0
2
r6199=(2*a11 *r6349 + 4*a11*b12*kap*r6230 - 2*a11*b12*r6162 - 2*a11*b12*r6353
2 2
+ 2*a11*b12*r6412 - b12 *kap*r6349)/b12
r6200
- 2*a11*r6160 - a11*r6302 + 2*a11*r6309 + 2*b12*kap*r6149 - 2*b12*kap*r6336
=------------------------------------------------------------------------------
2*b12
3 2 2
r6201=( - a11 *r6349 - 2*a11 *b12*kap*r6230 + a11 *b12*r6162
2 2 3 2 3
- 2*a11*b12 *kap*r6232 + 3*a11*b12 *kap*r6349 + b12 *kap *r6230)/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
3 2 2 2
r6206=( - a11 *r6349 - 2*a11 *b12*kap*r6230 + a11 *b12*r6162 + a11 *b12*r6353
2 2 3 2 3
- a11 *b12*r6412 + a11*b12 *kap*r6349 + b12 *kap *r6230)/b12
2 2 2
r6207=(2*a11 *r6160 + 2*a11 *r6302 - 2*a11 *r6309 - 2*a11*b12*kap*r6149
2 2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302)/(2*b12 )
r6208=0
3 3 3 2
r6209=( - a11 *r6160 - a11 *r6302 + a11 *r6309 + a11 *b12*kap*r6149
2 2 3 2 3
- 2*a11 *b12*kap*r6336 + a11*b12 *kap*r6302 + b12 *kap *r6336)/(3*b12 )
r6210=0
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6211=------------------------------------------
2*b12*kap
r6212=0
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6213=------------------------------------------
b12*kap
r6214=0
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6215=------------------------------------------
2*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
- 2*a11*r6149 + 4*a11*r6336 + b12*r6302
r6229=------------------------------------------
2*b12*kap
r6231=0
r6233=0
r6234=r6232
r6235=0
r6236=r6243
r6237=0
r6238=r6243
r6239=0
r6240=0
r6241=r6232
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=( - a11*r6232 - 2*b12*kap*r6230 - b12*r6162 + ---*b12*r6286 - b12*r6353
2
+ 3*b12*r6412 + b12*r671)/b12
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)
- a11*r6232 + a11*r6349 + b12*r671
r6255=-------------------------------------
b12
r6256=0
2
r6257=( - 2*a11*kap*r6162 - 4*a11*kap*r6353 + 6*a11*kap*r6412 - 4*b12*kap *r6232
2
+ 4*b12*kap *r6349 - b12*kap*r6133 - 2*b12*r6435)/(b12*kap)
r6258=0
r6260=0
r6261=0
r6262=0
- a11*r6131 + a11*r6259 - b12*r6138
r6263=--------------------------------------
b12
2 2 2
r6264=(a11 *kap*r6353 - a11 *kap*r6412 + 2*a11*b12*kap *r6232
2 2 2
- 2*a11*b12*kap *r6349 + a11*b12*r6435 + b12 *kap*r680)/(b12 *kap)
r6265=0
r6266=0
r6267=0
r6268=r6232
r6269=0
r6270=r6232
r6271=0
r6272=r6115 - 2*r6149 + 4*r6336
r6273=0
r6274=r6115 - 2*r6149 + 4*r6336
r6275=r6232 - 2*r6349
r6276=0
r6277=2*r6232 - 2*r6349
r6278=0
r6279=r6115 - 2*r6149 + 4*r6336
r6280=r6232 - 2*r6349
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 - b12*kap*r6232 + b12*kap*r6349
r6291=-------------------------------------------------------------------------
b12
r6292=0
2 2
r6293=( - a11 *kap*r6232 + a11 *kap*r6349 - 2*a11*b12*kap*r6162
2 2
- 3*a11*b12*kap*r6353 + 5*a11*b12*kap*r6412 - 5*b12 *kap *r6232
2 2 2 2 2
+ 5*b12 *kap *r6349 - b12 *kap*r6133 - 2*b12 *r6435)/(b12 *kap)
r6294=0
2 2
r6296=( - a11 *r6232 + a11 *r6349 + a11*b12*r6353 - a11*b12*r6412
2 2 2 2
- b12 *kap*r6232 + b12 *kap*r6349 + b12 *r6133)/b12
a11*r6131 - a11*r6259
r6297=-----------------------
b12
r6298=0
r6299=0
2 2
r6300=(a11*kap*r6353 - a11*kap*r6412 + 2*b12*kap *r6232 - 2*b12*kap *r6349
+ b12*r6435)/b12
r6301=0
r6303=0
1
r6304= - ---*r6160 + r6302
2
- 2*a11*r6232 + 3*a11*r6349 + 2*b12*kap*r6230
r6305=------------------------------------------------
b12
r6306=0
- 2*a11*r6232 + 6*a11*r6349 + 8*b12*kap*r6230 + b12*r6286 - 2*b12*r6353
r6307=--------------------------------------------------------------------------
2*b12
r6308=0
- a11*r6232 + a11*r6349 + b12*r6162
r6310=--------------------------------------
b12
r6311=0
3 2 1 2
r6312=( - ---*a11 *r6232 - ---*a11 *r6349 - 4*a11*b12*kap*r6230
2 2
+ 4*a11*b12*r6162 + 4*a11*b12*r6353 - 6*a11*b12*r6412
1 2 3 2 2
- ---*b12 *kap*r6232 + ---*b12 *kap*r6349)/b12
2 2
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 3 2 2
r6319=(a11 *kap*r6232 - a11 *kap*r6349 - a11 *b12*kap*r6162 - a11 *b12*kap*r6353
2 2 2
+ 2*a11 *b12*kap*r6412 - a11*b12 *kap*r6133 + a11*b12 *r6435
3 2 3 2 3 2 3
- b12 *kap *r6162 + b12 *kap *r6412 + b12 *kap *r671)/(b12 *kap)
r6320=0
2 2
a11 *r6232 - a11 *r6349
r6321=-------------------------
2
b12
r6322=0
2
r6323=( - 2*a11 *r6349 - 4*a11*b12*kap*r6230 + 2*a11*b12*r6162 + 3*a11*b12*r6353
2 2
- 3*a11*b12*r6412 + b12 *kap*r6232)/b12
r6324=0
r6325=(a11*r6160 + 2*a11*r6302 - 2*a11*r6309 + b12*kap*r6115 - 2*b12*kap*r6149
+ 4*b12*kap*r6336)/b12
2 2
r6326=( - 2*a11 *r6232 + 4*a11 *r6349 + 4*a11*b12*kap*r6230 - 2*a11*b12*r6162
2 2
+ a11*b12*r6353 - a11*b12*r6412 + b12 *kap*r6232 - 2*b12 *kap*r6349)/
2
b12
2 2
- a11 *r6160 - a11 *r6356 + a11*b12*kap*r6115 - a11*b12*kap*r6243
r6327=--------------------------------------------------------------------
2
b12
r6328=0
r6329=0
r6330=r6435
r6331=0
2 2 2
r6332=( - 2*a11 *r6160 - 2*a11 *r6302 + 2*a11 *r6309 + 2*a11*b12*kap*r6149
2 2
- 4*a11*b12*kap*r6336 + b12 *kap*r6302)/(2*b12 )
3 2 2 2
r6333=( - a11 *r6349 - 2*a11 *b12*kap*r6230 + a11 *b12*r6162 - a11 *b12*r6353
2 2 2
+ a11 *b12*r6412 - 5*a11*b12 *kap*r6232 + 6*a11*b12 *kap*r6349
3 2 3 3 3
+ b12 *kap *r6230 + b12 *kap*r6353 - b12 *kap*r6412)/b12
r6334=0
2 2
- a11*kap*r6353 + a11*kap*r6412 - 2*b12*kap *r6232 + 2*b12*kap *r6349
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=r6349
r6343=0
r6344=r6349
1
r6345=---*r6243 + 2*r6336
2
r6346=0
1
r6347= - ---*r6115 + r6149 + r6243
2
r6348=0
1
r6350=---*r6243 + r6336
2
a11*r6232 + 2*b12*kap*r6230
r6351=-----------------------------
b12
r6352=0
r6354=0
r6355=0
r6357=0
r6358
1
a11*r6232 - a11*r6349 - b12*r6162 + ---*b12*r6286 - b12*r6353 + 3*b12*r6412
2
=-----------------------------------------------------------------------------
b12
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
2 2
r6365=(2*a11 *kap*r6232 - 2*a11 *kap*r6349 - 2*a11*b12*kap*r6162
2 2
- 5*a11*b12*kap*r6353 + 7*a11*b12*kap*r6412 - 3*b12 *kap *r6232
2 2 2 2 2
+ 3*b12 *kap *r6349 - b12 *kap*r6133 - b12 *r6435)/(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
r6367=( - a11 *kap*r6162 - 3*a11 *kap*r6353 + 4*a11 *kap*r6412
2 2
- 4*a11*b12*kap *r6232 + 4*a11*b12*kap *r6349 - a11*b12*kap*r6133
2 2 2
- 2*a11*b12*r6435 + b12 *kap *r671)/(b12 *kap)
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
2*a11*r6232 - a11*r6349 + 2*b12*kap*r6230
r6372=-------------------------------------------
b12
r6373=0
a11*r6232 - a11*r6349 + b12*r6353
r6374=-----------------------------------
b12
a11*r6115 - a11*r6243 - b12*r6302
r6375=-----------------------------------
b12
r6376=0
2*a11*r6115 - 2*a11*r6243 - b12*r6160 - 2*b12*r6309 - b12*r6356
r6377=-----------------------------------------------------------------
2*b12
r6378=0
1
a11*r6232 + a11*r6349 + 4*b12*kap*r6230 - b12*r6162 + ---*b12*r6286
2
r6379=---------------------------------------------------------------------
b12
2*a11*r6115 - 2*a11*r6243 - 2*b12*r6302 - b12*r6356
r6380=-----------------------------------------------------
2*b12
r6381=0
- 2*a11*r6160 - a11*r6356 + b12*kap*r6115
r6382=--------------------------------------------
b12
r6383=0
2 2
r6384=( - 2*a11 *r6232 + 4*a11 *r6349 + 4*a11*b12*kap*r6230 + 2*a11*b12*r6162
2 2
+ 2*a11*b12*r6353 - 6*a11*b12*r6412 - b12 *kap*r6232)/b12
r6385=0
r6386=0
r6387=0
3 3 2
r6388=( - a11 *kap*r6232 + a11 *kap*r6349 - a11 *b12*kap*r6162
2 2 2 2
- 3*a11 *b12*kap*r6353 + 4*a11 *b12*kap*r6412 - 4*a11*b12 *kap *r6232
2 2 2 2
+ 4*a11*b12 *kap *r6349 - a11*b12 *kap*r6133 - 3*a11*b12 *r6435
3 2 3 2 3 2 3
- b12 *kap *r6353 + b12 *kap *r6412 + b12 *kap *r671)/(b12 *kap)
r6390=0
2 2 2
- a11 *r6115 + a11 *r6243 + 2*a11*b12*r6302 + 4*b12 *kap*r6336
r6391=-----------------------------------------------------------------
2
2*b12
r6392=0
2 2
r6393=( - a11 *r6115 + a11 *r6243 - 2*a11*b12*r6160 + 2*a11*b12*r6309
2 2 2
+ a11*b12*r6356 + 2*b12 *kap*r6149 + b12 *kap*r6243)/(2*b12 )
r6394=0
2 2
4*a11 *r6232 - 4*a11 *r6349 + 2*a11*b12*r6162 - 2*a11*b12*r6353
r6395=-----------------------------------------------------------------
2
b12
2 2
r6396=( - a11 *r6115 + a11 *r6243 + 2*a11*b12*r6309 + 3*a11*b12*r6356
2 2 2
+ 2*b12 *kap*r6149 + b12 *kap*r6243)/(2*b12 )
1 3 9 3 2 2
r6397=(---*a11 *r6232 - ---*a11 *r6349 - 4*a11 *b12*kap*r6230 + a11 *b12*r6162
4 4
2 1 2 7 2
+ a11 *b12*r6353 + ---*a11*b12 *kap*r6232 + ---*a11*b12 *kap*r6349
4 4
3 2 3
+ 2*b12 *kap *r6230)/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
3 3 2 2
r6402=( - 3*a11 *r6232 + a11 *r6349 - 4*a11 *b12*kap*r6230 + a11 *b12*r6162
2 2 2
+ 4*a11 *b12*r6353 - 3*a11 *b12*r6412 + 2*a11*b12 *kap*r6232
3 2 3
+ 2*b12 *kap *r6230)/b12
2 2 2 2
r6403=(a11 *r6160 + 4*a11 *r6302 - 4*a11 *r6309 - 3*a11 *r6356
+ 2*a11*b12*kap*r6115 - 4*a11*b12*kap*r6149 - 2*a11*b12*kap*r6243
2 2
+ 8*a11*b12*kap*r6336 - 2*b12 *kap*r6302)/(2*b12 )
r6404=0
3 3 3 3
r6405=( - a11 *r6160 - 2*a11 *r6302 + 2*a11 *r6309 + a11 *r6356
2 2 2
- a11 *b12*kap*r6115 + 2*a11 *b12*kap*r6149 + a11 *b12*kap*r6243
2 2 3 2
- 4*a11 *b12*kap*r6336 + 2*a11*b12 *kap*r6302 + 2*b12 *kap *r6336)/(2
3
*b12 )
r6406=0
- a11*r6115 + a11*r6243 + b12*r6302
r6407=--------------------------------------
b12
r6408=0
r6409=( - 6*a11*r6115 + 6*a11*r6243 + b12*r6160 + 4*b12*r6302 + 2*b12*r6309
+ 3*b12*r6356)/(6*b12)
a11*r6349 + 2*b12*kap*r6230
r6410=-----------------------------
b12
r6411=0
r6413=0
- 2*a11*r6115 + 2*a11*r6243 + 2*b12*r6302 + b12*r6356
r6414=--------------------------------------------------------
2*b12
2 4 1 1
r6415=(---*a11*r6349 + ---*b12*kap*r6230 - ---*b12*r6162 + ---*b12*r6286
3 3 3 6
1
- ---*b12*r6353 + b12*r6412)/b12
3
r6416=0
2 2
r6417=( - a11 *r6232 - a11 *r6349 - 4*a11*b12*kap*r6230 + 2*a11*b12*r6353
2 2 2
+ 2*b12 *kap*r6232 - b12 *kap*r6349)/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 - 3*a11 *kap*r6353 + 4*a11 *kap*r6412
2 2
- 4*a11*b12*kap *r6232 + 4*a11*b12*kap *r6349 - a11*b12*kap*r6133
2 2 2
- a11*b12*r6435 + b12 *kap *r671)/(b12 *kap)
r6425=0
2 2
a11 *r6232 - a11 *r6349
r6426=-------------------------
2
b12
r6427=0
2
r6428=( - 2*a11 *r6232 - 4*a11*b12*kap*r6230 + 3*a11*b12*r6353 - a11*b12*r6412
2 2
+ b12 *kap*r6232)/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
2
r6431=(2*a11 *r6349 + 4*a11*b12*kap*r6230 + a11*b12*r6353 - 3*a11*b12*r6412
2 2 2
+ b12 *kap*r6232 - 2*b12 *kap*r6349)/b12
2 2
- a11 *r6160 - a11 *r6356 + a11*b12*kap*r6115 - a11*b12*kap*r6243
r6432=--------------------------------------------------------------------
2
b12
r6433=0
r6434=0
r6436=0
2 2 2 2
r6437=( - a11 *r6160 - 4*a11 *r6302 + 4*a11 *r6309 + 3*a11 *r6356
- 2*a11*b12*kap*r6115 + 4*a11*b12*kap*r6149 + 2*a11*b12*kap*r6243
2 2
- 8*a11*b12*kap*r6336 + 2*b12 *kap*r6302)/(2*b12 )
3 3 2 2
r6438=(3*a11 *r6232 - 5*a11 *r6349 - 4*a11 *b12*kap*r6230 + a11 *b12*r6162
2 2 2
- 2*a11 *b12*r6353 + 3*a11 *b12*r6412 - 2*a11*b12 *kap*r6232
2 3 2 3
+ 4*a11*b12 *kap*r6349 + 2*b12 *kap *r6230)/b12
r6439=0
4 4 3 3
r6440=( - 2*a11 *r6232 + 2*a11 *r6349 + 2*a11 *b12*r6353 - 2*a11 *b12*r6412
2 2 2 2 4
+ 2*a11 *b12 *kap*r6232 - 2*a11 *b12 *kap*r6349)/b12
2 2 2
- a11 *r6115 + a11 *r6243 + a11*b12*r6302 + 2*b12 *kap*r6336
r6441=---------------------------------------------------------------
2
2*b12
r6442=0
2 2
r6443=( - a11 *r6115 + a11 *r6243 + a11*b12*r6160 - a11*b12*r6302
2 2
+ 2*a11*b12*r6309 + 3*a11*b12*r6356 - b12 *kap*r6115 + 2*b12 *kap*r6149
2 2 2
+ b12 *kap*r6243 - 2*b12 *kap*r6336)/(2*b12 )
r6444=0
2 2
- 2*a11 *r6349 - 4*a11*b12*kap*r6230 + 2*a11*b12*r6412 + b12 *kap*r6349
r6445=--------------------------------------------------------------------------
2
b12
2 2
r6446=( - a11 *r6115 + a11 *r6243 + a11*b12*r6302 + a11*b12*r6356
2 2 2
+ b12 *kap*r6243 + 2*b12 *kap*r6336)/(2*b12 )
1 3 3 3 2
r6447=( - ---*a11 *r6232 - ---*a11 *r6349 - 2*a11 *b12*kap*r6230
4 4
2 7 2 3 2
+ a11 *b12*r6353 + ---*a11*b12 *kap*r6232 - ---*a11*b12 *kap*r6349
4 4
3 2 3
+ b12 *kap *r6230)/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
3 3 2 2
r6452=( - 3*a11 *r6232 + 2*a11 *r6349 - 2*a11 *b12*kap*r6230 + 3*a11 *b12*r6353
2 2 2
- 2*a11 *b12*r6412 + 2*a11*b12 *kap*r6232 - a11*b12 *kap*r6349
3 2 3
+ b12 *kap *r6230)/b12
2 2 2 2
r6453=( - a11 *r6160 + 2*a11 *r6302 - 2*a11 *r6309 - 3*a11 *r6356
+ 2*a11*b12*kap*r6115 - 2*a11*b12*kap*r6149 - 2*a11*b12*kap*r6243
2 2
+ 4*a11*b12*kap*r6336 - b12 *kap*r6302)/(2*b12 )
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
2 2 2 2
r6457=(a11 *r6160 - 2*a11 *r6302 + 2*a11 *r6309 + 3*a11 *r6356
- 2*a11*b12*kap*r6115 + 2*a11*b12*kap*r6149 + 2*a11*b12*kap*r6243
2 2
- 4*a11*b12*kap*r6336 + b12 *kap*r6302)/(2*b12 )
3 2 2
r6458=( - a11 *r6349 - 2*a11 *b12*kap*r6230 + a11 *b12*r6412
2 3 2 3
+ a11*b12 *kap*r6349 + b12 *kap *r6230)/b12
r6459=0
4 4 3 3
r6460=( - 3*a11 *r6232 + 3*a11 *r6349 + a11 *b12*r6353 - a11 *b12*r6412
2 2 2 2 4 2
- 3*a11 *b12 *kap*r6232 + 3*a11 *b12 *kap*r6349 - 2*b12 *kap *r6232
4 2 4
+ 2*b12 *kap *r6349)/b12
3 3 3 3
r6461=(a11 *r6160 - 2*a11 *r6302 + 2*a11 *r6309 + 3*a11 *r6356
2 2 2
- 3*a11 *b12*kap*r6115 + 2*a11 *b12*kap*r6149 + 3*a11 *b12*kap*r6243
2 2 3 2
- 4*a11 *b12*kap*r6336 + 2*a11*b12 *kap*r6302 + 2*b12 *kap *r6336)/(6
3
*b12 )
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, r6133, r6138, r6149,
r6160, r6162, r6165, r6230, r6232, r6243, r6259, r6286,
r6295, r6302, r6309, r6336, r6353, r6356, r6389, r6412,
r6435, r6349, 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,r6349}
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$