Solution 18 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
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Equations
The following unsolved equations remain:
2 2
0=4*a33 + b12 *kap
Expressions
The solution is given through the following expressions:
2 2 4 2 2 2 8 2
r60=( - ---*a33 *r6115 + ---*a33 *r6149 + ---*a33 *r6243 - ---*a33 *r6336
3 3 3 3
1 1 2 2 2
- ---*a33*b12*r6407 + ---*b12 *kap*r6336)/(b12 *kap )
3 3
r61=0
2 2 2 2
r62=( - 2*a33 *r6115 + 4*a33 *r6149 + 2*a33 *r6243 - 8*a33 *r6336
2 2 2
- a33*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
r63=0
2 2 2 2
r64=( - 2*a33 *r6115 + 4*a33 *r6149 + 2*a33 *r6243 - 8*a33 *r6336
2 2 2
- a33*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
r65=0
2 2 4 2 2 2 8 2
r66=( - ---*a33 *r6115 + ---*a33 *r6149 + ---*a33 *r6243 - ---*a33 *r6336
3 3 3 3
1 1 2 2 2
- ---*a33*b12*r6407 + ---*b12 *kap*r6336)/(b12 *kap )
3 3
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
2 2 2 2
r613=( - 2*a33 *r6115 + 4*a33 *r6149 + 2*a33 *r6243 - 8*a33 *r6336
2 2 2
- a33*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
r614=0
2 2 2 2
r615=( - 4*a33 *r6115 + 8*a33 *r6149 + 4*a33 *r6243 - 16*a33 *r6336
2 2 2
- 2*a33*b12*r6407 + 2*b12 *kap*r6336)/(b12 *kap )
r616=0
2 2 2 2
r617=( - 2*a33 *r6115 + 4*a33 *r6149 + 2*a33 *r6243 - 8*a33 *r6336
2 2 2
- a33*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
r618=0
r619=0
r620=0
r621=0
2 2 2 2
r622=( - 2*a33 *r6115 + 4*a33 *r6149 + 2*a33 *r6243 - 8*a33 *r6336
2 2 2
- a33*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
r623=0
2 2 2 2
r624=( - 2*a33 *r6115 + 4*a33 *r6149 + 2*a33 *r6243 - 8*a33 *r6336
2 2 2
- a33*b12*r6407 + b12 *kap*r6336)/(b12 *kap )
r625=0
r626=0
2 2 4 2 2 2 8 2
r627=( - ---*a33 *r6115 + ---*a33 *r6149 + ---*a33 *r6243 - ---*a33 *r6336
3 3 3 3
1 1 2 2 2
- ---*a33*b12*r6407 + ---*b12 *kap*r6336)/(b12 *kap )
3 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
2 2 1
- ---*a33*r6270 - ---*b12*kap*r6230 + ---*b12*r6157 + b12*r666
3 3 3
r664=-----------------------------------------------------------------
b12
r665=0
r667=0
r668=0
r669=0
r670=0
r672=0
r673=0
r675=0
1
r676= - ---*r6131 + r674
2
r677=0
- 2*a33*kap*r6252 + 2*a33*kap*r666 + b12*r6435
r678=-------------------------------------------------
b12*kap
1
r679= - ---*r6259 + r674
2
r681=0
r682=0
r684=0
r685=r6230
r686=0
r687=2*r6230
r688=0
r689=r6230
1
- a33*r6115 + 2*a33*r6149 + a33*r6243 - 4*a33*r6336 - ---*b12*r6407
2
r690=----------------------------------------------------------------------
b12*kap
r691=0
- 2*a33*r6115 + 4*a33*r6149 + 2*a33*r6243 - 8*a33*r6336 - b12*r6407
r692=----------------------------------------------------------------------
b12*kap
r693=0
1
- a33*r6115 + 2*a33*r6149 + a33*r6243 - 4*a33*r6336 - ---*b12*r6407
2
r694=----------------------------------------------------------------------
b12*kap
r695=0
r696=2*r6230
r697=0
r698=2*r6230
- 2*a33*r6115 + 4*a33*r6149 + 2*a33*r6243 - 8*a33*r6336 - b12*r6407
r699=----------------------------------------------------------------------
b12*kap
r6100=0
- 2*a33*r6115 + 4*a33*r6149 + 2*a33*r6243 - 8*a33*r6336 - b12*r6407
r6101=----------------------------------------------------------------------
b12*kap
r6102=0
r6103=r6230
1
- a33*r6115 + 2*a33*r6149 + a33*r6243 - 4*a33*r6336 - ---*b12*r6407
2
r6104=----------------------------------------------------------------------
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
- 2*a33*r6270 - 2*b12*kap*r6230 + b12*r6157 + b12*r666
r6121=---------------------------------------------------------
b12
r6122=0
r6123=r666
1
r6124=r6129 - ---*r6356
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
4*a33 *kap*r6252 - 4*a33 *kap*r666 - 2*a33*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
2*a33*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
2 2
r6165=( - 2*a33 *r6115 + 2*a33 *r6243 - 2*a33*b12*r6129 + a33*b12*r6356
1 2 2 2
+ ---*b12 *kap*r6243 + b12 *kap*r660)/b12
2
r6166=0
2 2
r6167=( - 2*a33 *r6115 + 2*a33 *r6243 - 2*a33*b12*r6129 + a33*b12*r6160
1 2 1 2
+ a33*b12*r6356 - ---*b12 *kap*r6115 + ---*b12 *kap*r6243
2 2
2 1 2 2
+ b12 *kap*r660 + ---*b12 *r6131)/b12
2
r6168=0
2*a33*kap*r6252 - 2*a33*kap*r666 + b12*kap*r6133 + b12*r6435
r6169=--------------------------------------------------------------
b12*kap
3 3 2 1 2
r6170=( - 2*a33 *r6115 + 2*a33 *r6243 - 2*a33 *b12*r6129 - ---*a33 *b12*r6160
2
1 2 2 1 2
- ---*a33 *b12*r6356 + a33*b12 *kap*r660 + ---*a33*b12 *r6131
2 2
1 2 1 3 1 3 2
- ---*a33*b12 *r6259 + ---*b12 *kap*r6129 - ---*b12 *r6389)/(a33*b12 )
2 4 4
2 2 2
4*a33 *r666 - 4*a33 *r671 - 2*a33*b12*r6133 + b12 *kap*r666
r6171=-------------------------------------------------------------
2
b12
r6172=0
r6173=0
2 2 1 2
r6174=( - 2*a33 *r6131 + 2*a33 *r6259 - 2*a33*b12*r6138 - ---*b12 *kap*r6131
2
2 2
+ b12 *kap*r674)/b12
r6175=0
2*a33*r6270 + 2*b12*kap*r6230
r6176=-------------------------------
b12
r6177=0
4 4 1
---*a33*r6270 + ---*b12*kap*r6230 + ---*b12*r6157
3 3 3
r6178=---------------------------------------------------
b12
- 2*a33*r6115 + 2*a33*r6243 - b12*r6407
r6179=------------------------------------------
b12
r6180=0
1
- 2*a33*r6115 + 2*a33*r6243 + ---*b12*r6160 - b12*r6407
2
r6181=----------------------------------------------------------
b12
r6182=0
r6183=r6252 + r6353 - 2*r666 + r671
2 2 1 1
r6184=( - 2*a33 *r6115 + 2*a33 *r6243 + ---*a33*b12*r6160 + ---*a33*b12*r6356
2 3
1 2 1 2
- a33*b12*r6407 - ----*b12 *kap*r6115 + ---*b12 *kap*r6149
12 6
1 2 1 2
- ---*b12 *kap*r6336 + ----*b12 *r6430)/(a33*b12)
3 12
r6185=0
- 2*a33*r6160 + b12*kap*r6115
r6186=--------------------------------
b12
r6187=0
2
r6188=(8*a33 *r6270 + 8*a33*b12*kap*r6230 - 8*a33*b12*r6252 - 4*a33*b12*r6353
2 2
+ 12*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270)/b12
r6189=0
r6190=0
r6191=0
2 2
r6192=(4*a33 *kap*r666 - 4*a33 *kap*r671 - 2*a33*b12*kap*r6133 - 2*a33*b12*r6435
2 2 2
+ b12 *kap *r666)/(b12 *kap)
1 1
r6193=( - 2*a33*r6131 + 2*a33*r6259 - ---*b12*kap*r6160 - ---*b12*kap*r6356
2 2
+ b12*r6389)/b12
r6194=0
2 2 2
2*a33 *r6115 - 2*a33 *r6243 + a33*b12*r6407 + b12 *kap*r6336
r6195=--------------------------------------------------------------
2
b12
r6196=0
2 2
r6197=(2*a33 *r6115 - 2*a33 *r6243 - a33*b12*r6160 + a33*b12*r6407
1 2 2 2
+ ---*b12 *kap*r6115 + b12 *kap*r6336)/b12
2
r6198=0
2
r6199=(8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6252 - 4*a33*b12*r6353
2 2
+ 8*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270)/b12
2 2
r6200=(2*a33 *r6115 - 2*a33 *r6243 - 3*a33*b12*r6160 - 2*a33*b12*r6356
1 2 2 1 2
+ a33*b12*r6407 + ---*b12 *kap*r6115 + b12 *kap*r6336 - ---*b12 *r6430)/
2 2
2
b12
3 2 2
r6201=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 8*a33 *b12*r6252
2 2 2
+ 4*a33 *b12*r6353 - 12*a33 *b12*r666 + 4*a33 *b12*r671
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6202=0
r6203=0
3 3 2 2
r6204=(2*a33 *r6160 + 2*a33 *r6356 - 2*a33 *b12*kap*r6115 + 2*a33 *b12*kap*r6243
2 2 2
+ 2*a33 *b12*r6131 - 2*a33 *b12*r6259 - a33*b12 *kap*r6129
2 2 2
+ a33*b12 *kap*r6160 + a33*b12 *kap*r6356 - a33*b12 *r6389
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
r6206=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6252
2 2 2
+ 4*a33 *b12*r6353 - 8*a33 *b12*r666 + 4*a33 *b12*r671
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
2 2
r6207=(6*a33 *r6160 + 4*a33 *r6356 - 2*a33*b12*kap*r6115 + a33*b12*kap*r6243
1 2 2
+ a33*b12*r6430 - ---*b12 *kap*r6407)/b12
2
r6208=0
3 8 3 2
r6209=( - 4*a33 *r6160 - ---*a33 *r6356 + 2*a33 *b12*kap*r6115
3
4 2 2 2 2 2
- ---*a33 *b12*kap*r6243 - ---*a33 *b12*r6430 + ---*a33*b12 *kap*r6407
3 3 3
1 3 2 3
+ ---*b12 *kap *r6336)/b12
3
r6210=0
1
a33*r6115 - 2*a33*r6149 - a33*r6243 + 4*a33*r6336 + ---*b12*r6407
2
r6211=-------------------------------------------------------------------
b12*kap
r6212=0
2*a33*r6115 - 4*a33*r6149 - 2*a33*r6243 + 8*a33*r6336 + b12*r6407
r6213=-------------------------------------------------------------------
b12*kap
r6214=0
1
a33*r6115 - 2*a33*r6149 - a33*r6243 + 4*a33*r6336 + ---*b12*r6407
2
r6215=-------------------------------------------------------------------
b12*kap
r6216=r6230
r6217=0
r6218=2*r6230
r6219=0
r6220=r6230
r6221=0
2*a33*r6115 - 4*a33*r6149 - 2*a33*r6243 + 8*a33*r6336 + b12*r6407
r6222=-------------------------------------------------------------------
b12*kap
r6223=0
2*a33*r6115 - 4*a33*r6149 - 2*a33*r6243 + 8*a33*r6336 + b12*r6407
r6224=-------------------------------------------------------------------
b12*kap
r6225=2*r6230
r6226=0
r6227=2*r6230
r6228=0
1
a33*r6115 - 2*a33*r6149 - a33*r6243 + 4*a33*r6336 + ---*b12*r6407
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
- 2*a33*r6115 + 2*a33*r6243 - b12*r6129 + ---*b12*r6356
2
r6247=----------------------------------------------------------
b12
r6248=0
1 1
- 2*a33*r6115 + 2*a33*r6243 - b12*r6129 + ---*b12*r6160 + ---*b12*r6356
2 2
r6249=--------------------------------------------------------------------------
b12
- 2*a33*r6270 - 2*b12*kap*r6230 + b12*r6157 + 3*b12*r666 - 2*b12*r671
r6250=------------------------------------------------------------------------
b12
r6251=0
r6253=0
- 2*a33*r6115 + 2*a33*r6243 - b12*r6129
r6254=------------------------------------------
b12
r6255=r671
r6256=0
4*a33*kap*r6252 - 4*a33*kap*r671 - b12*kap*r6133 - 2*b12*r6435
r6257=----------------------------------------------------------------
b12*kap
r6258=0
r6260=0
r6261=0
r6262=0
- 2*a33*r6131 + 2*a33*r6259 - b12*r6138
r6263=------------------------------------------
b12
2 2 2
- 4*a33 *kap*r6252 + 4*a33 *kap*r666 + 2*a33*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
2*a33*r6115 - 2*a33*r6243
r6281=---------------------------
b12
r6282=0
2*a33*r6115 - 2*a33*r6243 - b12*r6160
r6283=---------------------------------------
b12
r6284=0
r6285=0
r6286=2*r6157 - 2*r6252 - 2*r6353 + 6*r666 - 4*r671
r6287=0
2*a33*r6115 - 2*a33*r6243 - b12*r6356
r6288=---------------------------------------
b12
r6289=0
r6290=0
- 4*a33*r666 + 4*a33*r671
r6291=----------------------------
b12
r6292=0
r6293=(2*a33*kap*r6252 + 2*a33*kap*r666 - 4*a33*kap*r671 - b12*kap*r6133
- 2*b12*r6435)/(b12*kap)
r6294=0
2 2 1 2
r6295=( - a33 *r6160 - a33 *r6356 + a33*b12*r6259 - ---*b12 *kap*r6129
2
1 2
+ ---*b12 *r6389)/(a33*b12)
2
- 2*a33*r6252 + 2*a33*r666 + b12*r6133
r6296=-----------------------------------------
b12
2*a33*r6131 - 2*a33*r6259
r6297=---------------------------
b12
r6298=0
r6299=0
- 2*a33*kap*r6252 + 2*a33*kap*r666 + b12*r6435
r6300=-------------------------------------------------
b12
r6301=0
2*a33*r6115 - 2*a33*r6243 + b12*r6407
r6302=---------------------------------------
b12
r6303=0
1
2*a33*r6115 - 2*a33*r6243 - ---*b12*r6160 + b12*r6407
2
r6304=-------------------------------------------------------
b12
2*a33*r6270 + 2*b12*kap*r6230
r6305=-------------------------------
b12
r6306=0
r6307=(4*a33*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=(2*a33 *r6115 - 2*a33 *r6243 - ---*a33*b12*r6160 - a33*b12*r6356
2
1 2 1 2
+ a33*b12*r6407 + ---*b12 *kap*r6115 - ---*b12 *kap*r6149
4 2
2 1 2
+ b12 *kap*r6336 - ---*b12 *r6430)/(a33*b12)
4
r6310=2*r6252 + r6353 - 3*r666 + r671
r6311=0
2
r6312=( - 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6252 + 4*a33*b12*r6353
2 2
- 12*a33*b12*r666 + 8*a33*b12*r671 + b12 *kap*r6270)/b12
r6313=0
2*a33*r6160 + 4*a33*r6356 + b12*kap*r6243
r6314=-------------------------------------------
b12
r6315=0
r6316=0
r6317=0
2 2
r6318=(4*a33 *r6160 + 4*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*kap*r6243
1 2
+ 2*a33*b12*r6131 - 2*a33*b12*r6259 + ---*b12 *kap*r6160
2
1 2 2 2
+ ---*b12 *kap*r6356 - b12 *r6389)/b12
2
2 2
r6319=(4*a33 *kap*r666 - 4*a33 *kap*r671 - 2*a33*b12*kap*r6133 + 2*a33*b12*r6435
2 2 2 2 2
- b12 *kap *r6252 + 2*b12 *kap *r666)/(b12 *kap)
r6320=0
r6321=0
r6322=0
2
r6323=( - 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 2*a33*b12*r6252 + 4*a33*b12*r6353
2 2
- 6*a33*b12*r666 + 4*a33*b12*r671 + b12 *kap*r6270)/b12
r6324=0
4*a33*r6160 + 4*a33*r6356 + b12*r6430
r6325=---------------------------------------
b12
2
r6326=(8*a33 *r6270 + 8*a33*b12*kap*r6230 - 10*a33*b12*r6252 - 4*a33*b12*r6353
2 2
+ 14*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270)/b12
r6327
2 2
- 4*a33 *r6160 - 4*a33 *r6356 + 2*a33*b12*kap*r6115 - 2*a33*b12*kap*r6243
=----------------------------------------------------------------------------
2
b12
r6328=0
r6329=0
r6330=r6435
r6331=0
2 2
r6332=( - 6*a33 *r6160 - 4*a33 *r6356 + 2*a33*b12*kap*r6115 - a33*b12*kap*r6243
1 2 2
- a33*b12*r6430 + ---*b12 *kap*r6407)/b12
2
3 2 2
r6333=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 16*a33 *b12*r6252
2 2 2
+ 4*a33 *b12*r6353 - 20*a33 *b12*r666 + 4*a33 *b12*r671
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6334=0
3 3
- 8*a33 *r6252 + 8*a33 *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
2*a33*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
2 2
r6361=( - 2*a33 *r6115 + 2*a33 *r6243 - 2*a33*b12*r6129 + a33*b12*r6356
1 2 2 2
+ ---*b12 *kap*r6115 + b12 *kap*r660)/b12
2
r6362=0
3 3 2 5 2
r6363=( - 2*a33 *r6115 + 2*a33 *r6243 - 2*a33 *b12*r6129 + ---*a33 *b12*r6160
2
5 2 2 1 3
+ ---*a33 *b12*r6356 + a33*b12 *kap*r660 + ---*b12 *kap*r6129
2 4
1 3 2
- ---*b12 *r6389)/(a33*b12 )
4
r6364=0
r6365
6*a33*kap*r6252 - 2*a33*kap*r666 - 4*a33*kap*r671 - b12*kap*r6133 - b12*r6435
=-------------------------------------------------------------------------------
b12*kap
2 2 1 2
r6366=( - 2*a33 *r6115 + 2*a33 *r6243 - 2*a33*b12*r6129 + ---*b12 *kap*r6115
2
1 2 2 1 2 2
- ---*b12 *kap*r6243 + b12 *kap*r660 + ---*b12 *r6259)/b12
2 2
2 2 2
r6367=(8*a33 *kap*r6252 - 4*a33 *kap*r666 - 4*a33 *kap*r671
2 2 2
- 2*a33*b12*kap*r6133 - 4*a33*b12*r6435 + b12 *kap *r671)/(b12 *kap)
r6368=0
r6369=0
2 2 1 2
r6370=( - 2*a33 *r6131 + 2*a33 *r6259 - 2*a33*b12*r6138 - ---*b12 *kap*r6259
2
2 2
+ b12 *kap*r674)/b12
r6371=0
2*a33*r6270 + 2*b12*kap*r6230
r6372=-------------------------------
b12
r6373=0
r6374=r6353
r6375= - r6407
r6376=0
1 1 1
r6377=(---*a33*r6356 - a33*r6407 - ---*b12*kap*r6115 + ---*b12*kap*r6149
2 4 2
1
- b12*kap*r6336 + ---*b12*r6430)/a33
4
r6378=0
r6379=(4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - 3*b12*r6252 - 2*b12*r6353
+ 6*b12*r666 - 3*b12*r671)/b12
1
r6380= - ---*r6356 - r6407
2
r6381=0
- 4*a33*r6160 - 2*a33*r6356 + b12*kap*r6115
r6382=----------------------------------------------
b12
r6383=0
2
r6384=(8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6252 - 4*a33*b12*r6353
2 2
+ 4*a33*b12*r671 - b12 *kap*r6270)/b12
r6385=0
r6386=0
r6387=0
2 2 2
r6388=(8*a33 *kap*r6252 - 4*a33 *kap*r666 - 4*a33 *kap*r671
2 2
- 2*a33*b12*kap*r6133 - 6*a33*b12*r6435 + b12 *kap *r6252
2 2 2 2 2
- b12 *kap *r666 + b12 *kap *r671)/(b12 *kap)
r6390=0
2 2 2
2*a33 *r6115 - 2*a33 *r6243 + 2*a33*b12*r6407 + 2*b12 *kap*r6336
r6391=------------------------------------------------------------------
2
b12
r6392=0
2 2
r6393=(2*a33 *r6115 - 2*a33 *r6243 - 3*a33*b12*r6160 - a33*b12*r6356
1 2 1 2
+ 2*a33*b12*r6407 + ---*b12 *kap*r6115 + ---*b12 *kap*r6243
2 2
2 1 2 2
+ 2*b12 *kap*r6336 - ---*b12 *r6430)/b12
2
r6394=0
8*a33*r6252 - 12*a33*r666 + 4*a33*r671
r6395=----------------------------------------
b12
2 2
r6396=(2*a33 *r6115 - 2*a33 *r6243 - a33*b12*r6160 + a33*b12*r6356
1 2 1 2
+ 2*a33*b12*r6407 + ---*b12 *kap*r6115 + ---*b12 *kap*r6243
2 2
2 1 2 2
+ 2*b12 *kap*r6336 - ---*b12 *r6430)/b12
2
3 2 2
r6397=( - 16*a33 *r6270 - 16*a33 *b12*kap*r6230 + 8*a33 *b12*r6252
2 2 2
+ 8*a33 *b12*r6353 - 12*a33 *b12*r666 + 4*a33 *b12*r671
2 3 2 3
+ 4*a33*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
r6398=0
r6399=0
3 3 2 2
r6400=(4*a33 *r6160 + 4*a33 *r6356 - 4*a33 *b12*kap*r6115 + 4*a33 *b12*kap*r6243
2 2 2
+ 2*a33 *b12*r6131 - 2*a33 *b12*r6259 - 2*a33*b12 *kap*r6129
2 2 2
+ a33*b12 *kap*r6160 + a33*b12 *kap*r6356 - 2*a33*b12 *r6389
3 2 3
+ b12 *kap *r660)/b12
r6401=0
3 2 2
r6402=( - 16*a33 *r6270 - 16*a33 *b12*kap*r6230 + 16*a33 *b12*r6252
2 2 2
+ 8*a33 *b12*r6353 - 24*a33 *b12*r666 + 8*a33 *b12*r671
2 3 2 3
+ 4*a33*b12 *kap*r6270 + 2*b12 *kap *r6230 + 5*b12 *kap*r6252
3 3 3
- 6*b12 *kap*r666 + b12 *kap*r671)/b12
2 2
r6403=(6*a33 *r6160 + 2*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*r6430
2 2
- b12 *kap*r6407)/b12
r6404=0
3 3 2
r6405=( - 8*a33 *r6160 - 4*a33 *r6356 + 4*a33 *b12*kap*r6115
2 2 2
- 2*a33 *b12*kap*r6243 - 2*a33 *b12*r6430 + 2*a33*b12 *kap*r6407
3 2 3
+ b12 *kap *r6336)/b12
r6406=0
r6408=0
1 1 1
r6409=(---*a33*r6356 + a33*r6407 + ----*b12*kap*r6115 - ---*b12*kap*r6149
6 12 6
1 1
+ ---*b12*kap*r6336 - ----*b12*r6430)/a33
3 12
2*a33*r6270 + 2*b12*kap*r6230
r6410=-------------------------------
b12
r6411=0
r6412=r6252 + r6353 - r666
r6413=0
1
r6414=---*r6356 + r6407
2
4 4 1
---*a33*r6270 + ---*b12*kap*r6230 + ---*b12*r6157 + b12*r666 - b12*r671
3 3 3
r6415=-------------------------------------------------------------------------
b12
r6416=0
2 2
- 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6353 + b12 *kap*r6270
r6417=--------------------------------------------------------------------------
2
b12
r6418=0
2*a33*r6356 + b12*kap*r6243
r6419=-----------------------------
b12
r6420=0
r6421=0
r6422=0
2 2
r6423=(4*a33 *r6160 + 4*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*kap*r6243
2 2
- b12 *r6389)/b12
2 2 2
r6424=(8*a33 *kap*r6252 - 4*a33 *kap*r666 - 4*a33 *kap*r671
2 2 2
- 2*a33*b12*kap*r6133 - 2*a33*b12*r6435 + b12 *kap *r671)/(b12 *kap)
r6425=0
r6426=0
r6427=0
2
r6428=( - 8*a33 *r6270 - 8*a33*b12*kap*r6230 - 2*a33*b12*r6252 + 4*a33*b12*r6353
2 2
+ 2*a33*b12*r666 + b12 *kap*r6270)/b12
r6429=0
2
r6431=(8*a33 *r6270 + 8*a33*b12*kap*r6230 - 6*a33*b12*r6252 - 4*a33*b12*r6353
2 2
+ 6*a33*b12*r666 - b12 *kap*r6270)/b12
r6432
2 2
- 4*a33 *r6160 - 4*a33 *r6356 + 2*a33*b12*kap*r6115 - 2*a33*b12*kap*r6243
=----------------------------------------------------------------------------
2
b12
r6433=0
r6434=0
r6436=0
2 2
r6437=( - 6*a33 *r6160 - 2*a33 *r6356 + 2*a33*b12*kap*r6115 - 2*a33*b12*r6430
2 2
+ b12 *kap*r6407)/b12
3 2 2
r6438=( - 16*a33 *r6270 - 16*a33 *b12*kap*r6230 + 20*a33 *b12*r6252
2 2 2
+ 8*a33 *b12*r6353 - 24*a33 *b12*r666 + 4*a33 *b12*r671
2 3 2 3
+ 4*a33*b12 *kap*r6270 + 2*b12 *kap *r6230)/b12
r6439=0
8 3 8 3 10 2
r6440=( - ---*a33 *r6252 + ---*a33 *r671 + ----*a33*b12 *kap*r6252
3 3 3
2 2 2 3
- 4*a33*b12 *kap*r666 + ---*a33*b12 *kap*r671)/b12
3
a33*r6407 + b12*kap*r6336
r6441=---------------------------
b12
r6442=0
r6443
1 1
a33*r6356 + a33*r6407 + ---*b12*kap*r6243 + b12*kap*r6336 - ---*b12*r6430
2 2
=---------------------------------------------------------------------------
b12
r6444=0
2
r6445=( - 8*a33 *r6270 - 8*a33*b12*kap*r6230 + 4*a33*b12*r6252 + 4*a33*b12*r6353
2 2
- 4*a33*b12*r666 + b12 *kap*r6270)/b12
1
a33*r6356 + a33*r6407 + ---*b12*kap*r6243 + b12*kap*r6336
2
r6446=-----------------------------------------------------------
b12
3 2 2
r6447=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6353
2 3 2 3
+ 2*a33*b12 *kap*r6270 + b12 *kap *r6230)/b12
r6448=0
r6449=0
3 3 2 2
r6450=(2*a33 *r6160 + 2*a33 *r6356 - 2*a33 *b12*kap*r6115 + 2*a33 *b12*kap*r6243
2 2 1 3 2
- a33*b12 *kap*r6129 - a33*b12 *r6389 + ---*b12 *kap *r6115
4
1 3 2 1 3 2 3
- ---*b12 *kap *r6243 + ---*b12 *kap *r660)/b12
4 2
r6451=0
3 2 2
r6452=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 - 8*a33 *b12*r6252
2 2 2
+ 4*a33 *b12*r6353 + 8*a33 *b12*r666 + 2*a33*b12 *kap*r6270
3 2 3
+ b12 *kap *r6230)/b12
2 1 2
- 2*a33 *r6356 - a33*b12*kap*r6243 + a33*b12*r6430 - ---*b12 *kap*r6407
2
r6453=--------------------------------------------------------------------------
2
b12
r6454=0
3 2 2
r6455=( - 4*a33 *r6160 + 2*a33 *b12*kap*r6115 - 2*a33 *b12*r6430
2 3 2 3
+ 2*a33*b12 *kap*r6407 + b12 *kap *r6336)/b12
r6456=0
2 1 2
2*a33 *r6356 + a33*b12*kap*r6243 - a33*b12*r6430 + ---*b12 *kap*r6407
2
r6457=-----------------------------------------------------------------------
2
b12
3 2 2
r6458=( - 8*a33 *r6270 - 8*a33 *b12*kap*r6230 + 4*a33 *b12*r6252
2 2 2
+ 4*a33 *b12*r6353 - 4*a33 *b12*r666 + 2*a33*b12 *kap*r6270
3 2 3
+ b12 *kap *r6230)/b12
r6459=0
3 3
- 8*a33 *r6252 + 8*a33 *r666
r6460=-------------------------------
3
b12
4 3 2 2 2 2
r6461=(---*a33 *r6356 + ---*a33 *b12*kap*r6243 - ---*a33 *b12*r6430
3 3 3
2 2 1 3 2 3
+ ---*a33*b12 *kap*r6407 + ---*b12 *kap *r6336)/b12
3 3
a23=0
a22=2*a33
a13=0
a11=2*a33
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, a33, 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.
{a33,
a11,
b12,
{r6336,
4 3 8 3 4 3 16 3
---*a33 *r6115 - ---*a33 *r6149 - ---*a33 *r6243 + ----*a33 *r6336
3 3 3 3
2 2 2 2
+ ---*a33 *b12*r6407 - ---*a33*b12 *kap*r6336,
3 3
3 3 3 3 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33 *b12*r6407
2
- 2*a33*b12 *kap*r6336,
3 3 3 3 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33 *b12*r6407
2
- 2*a33*b12 *kap*r6336,
4 3 8 3 4 3 16 3
---*a33 *r6115 - ---*a33 *r6149 - ---*a33 *r6243 + ----*a33 *r6336
3 3 3 3
2 2 2 2
+ ---*a33 *b12*r6407 - ---*a33*b12 *kap*r6336,
3 3
3 3 3 3 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33 *b12*r6407
2
- 2*a33*b12 *kap*r6336,
3 3 3 3 2
8*a33 *r6115 - 16*a33 *r6149 - 8*a33 *r6243 + 32*a33 *r6336 + 4*a33 *b12*r6407
2
- 4*a33*b12 *kap*r6336,
3 3 3 3 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33 *b12*r6407
2
- 2*a33*b12 *kap*r6336,
3 3 3 3 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33 *b12*r6407
2
- 2*a33*b12 *kap*r6336,
3 3 3 3 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33 *b12*r6407
2
- 2*a33*b12 *kap*r6336,
4 3 8 3 4 3 16 3
---*a33 *r6115 - ---*a33 *r6149 - ---*a33 *r6243 + ----*a33 *r6336
3 3 3 3
2 2 2 2
+ ---*a33 *b12*r6407 - ---*a33*b12 *kap*r6336,
3 3
r6230,
2*r6230,
r6230,
2*r6230,
2*r6230,
r6230,
1 1 1
---*r6115 + ---*r6243 + ---*r660,
4 4 2
1
---*r6243 + r660,
2
1 1 1
---*r6115 - ---*r6243 - ---*r660,
4 4 2
1
---*r6115 + r660,
2
r660,
1 1 1
---*r6115 - ---*r6243 + ---*r660,
4 4 2
2 2 1
---*a33*r6270 + ---*b12*kap*r6230 - ---*b12*r6157 - b12*r666,
3 3 3
r666,
r671,
r674,
1
---*b12*r6131 - b12*r674,
2
2 2
4*a33 *kap*r6252 - 4*a33 *kap*r666 - 2*a33*b12*r6435,
1
---*b12*r6259 - b12*r674,
2
r680,
r683,
r6230,
2*r6230,
r6230,
2 2 2 2
2*a33 *r6115 - 4*a33 *r6149 - 2*a33 *r6243 + 8*a33 *r6336 + a33*b12*r6407,
2 2 2 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33*b12*r6407,
2 2 2 2
2*a33 *r6115 - 4*a33 *r6149 - 2*a33 *r6243 + 8*a33 *r6336 + a33*b12*r6407,
2*r6230,
2*r6230,
2 2 2 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33*b12*r6407,
2 2 2 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33*b12*r6407,
r6230,
2 2 2 2
2*a33 *r6115 - 4*a33 *r6149 - 2*a33 *r6243 + 8*a33 *r6336 + a33*b12*r6407,
r6115,
r6115,
r6270,
r6270,
r6115,
r6270,
2*a33*r6270 + 2*b12*kap*r6230 - b12*r6157 - b12*r666,
b12*r666,
1
r6129 - ---*r6356,
2
1 1
r6129 - ---*r6160 - ---*r6356,
2 2
r6252 - r666 - r671,
r6129,
r6131,
r6133,
3 3 2 2
8*a33 *kap*r6252 - 8*a33 *kap*r666 - 4*a33 *b12*r6435 + 2*a33*b12 *kap*r680,
r6138,
a33*r6115 + 4*a33*r6336,
a33*r6115 + 2*a33*r6336,
r6270,
r6270,
r6149,
1
---*r6115 + r6149,
2
r6270,
2*a33*r6149 - 2*a33*r6336,
2*a33*r6270 + 2*b12*kap*r6230,
r6157,
r6160,
2*b12*r6252 + b12*r6353 - 3*b12*r666 + b12*r671,
2 2
2*a33 *r6115 - 2*a33 *r6243 + 2*a33*b12*r6129 - a33*b12*r6356
1 2 2
- ---*b12 *kap*r6243 - b12 *kap*r660,
2
2 2
2*a33 *r6115 - 2*a33 *r6243 + 2*a33*b12*r6129 - a33*b12*r6160 - a33*b12*r6356
1 2 1 2 2 1 2
+ ---*b12 *kap*r6115 - ---*b12 *kap*r6243 - b12 *kap*r660 - ---*b12 *r6131,
2 2 2
2 2 2
4*a33 *b12*kap*r6252 - 4*a33 *b12*kap*r666 + 2*a33*b12 *kap*r6133
2
+ 2*a33*b12 *r6435,
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 + 4*a33 *b12*r6129 + a33 *b12*r6160
2 2 2 2
+ a33 *b12*r6356 - 2*a33*b12 *kap*r660 - a33*b12 *r6131 + a33*b12 *r6259
1 3 1 3
- ---*b12 *kap*r6129 + ---*b12 *r6389,
2 2
3 3 2
8*a33 *kap*r666 - 8*a33 *kap*r671 - 4*a33 *b12*kap*r6133
2 2
+ 2*a33*b12 *kap *r666,
2 2 2 1 3
2*a33 *b12*r6131 - 2*a33 *b12*r6259 + 2*a33*b12 *r6138 + ---*b12 *kap*r6131
2
3
- b12 *kap*r674,
2*a33*r6270 + 2*b12*kap*r6230,
4 4 1
---*a33*r6270 + ---*b12*kap*r6230 + ---*b12*r6157,
3 3 3
2*a33*r6115 - 2*a33*r6243 + b12*r6407,
1
2*a33*r6115 - 2*a33*r6243 - ---*b12*r6160 + b12*r6407,
2
b12*r6252 + b12*r6353 - 2*b12*r666 + b12*r671,
3 3 2 4 2
8*a33 *r6115 - 8*a33 *r6243 - 2*a33 *b12*r6160 - ---*a33 *b12*r6356
3
2 1 2 2 2
+ 4*a33 *b12*r6407 + ---*a33*b12 *kap*r6115 - ---*a33*b12 *kap*r6149
3 3
4 2 1 2
+ ---*a33*b12 *kap*r6336 - ---*a33*b12 *r6430,
3 3
2*a33*r6160 - b12*kap*r6115,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 8*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 12*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270,
3 3 3 3 2 4
8*a33 *b12 *kap*r666 - 8*a33 *b12 *kap*r671 - 4*a33 *b12 *kap*r6133
2 4 5 2
- 4*a33 *b12 *r6435 + 2*a33*b12 *kap *r666,
2 2 2 2
4*a33 *b12*r6131 - 4*a33 *b12*r6259 + a33*b12 *kap*r6160 + a33*b12 *kap*r6356
2
- 2*a33*b12 *r6389,
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 + 2*a33 *b12*r6407 + 2*a33*b12 *kap*r6336,
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 - 2*a33 *b12*r6160 + 2*a33 *b12*r6407
2 2
+ a33*b12 *kap*r6115 + 2*a33*b12 *kap*r6336,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 8*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270,
4 4 3 3
8*a33 *r6115 - 8*a33 *r6243 - 12*a33 *b12*r6160 - 8*a33 *b12*r6356
3 2 2 2 2
+ 4*a33 *b12*r6407 + 2*a33 *b12 *kap*r6115 + 4*a33 *b12 *kap*r6336
2 2
- 2*a33 *b12 *r6430,
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 8*a33 *b12*r6252 - 4*a33 *b12*r6353
2 2 2 3 2
+ 12*a33 *b12*r666 - 4*a33 *b12*r671 - 2*a33*b12 *kap*r6270 - b12 *kap *r6230
,
4 4 3 3
4*a33 *r6160 + 4*a33 *r6356 - 4*a33 *b12*kap*r6115 + 4*a33 *b12*kap*r6243
3 3 2 2
+ 4*a33 *b12*r6131 - 4*a33 *b12*r6259 - 2*a33 *b12 *kap*r6129
2 2 2 2 2 2
+ 2*a33 *b12 *kap*r6160 + 2*a33 *b12 *kap*r6356 - 2*a33 *b12 *r6389
1 3 2 1 3 2 3 2
- ---*a33*b12 *kap *r6115 + ---*a33*b12 *kap *r6243 + a33*b12 *kap *r660,
2 2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6252 - 4*a33 *b12*r6353
2 2 2 3 2
+ 8*a33 *b12*r666 - 4*a33 *b12*r671 - 2*a33*b12 *kap*r6270 - b12 *kap *r6230,
3 3 2 2
12*a33 *b12*r6160 + 8*a33 *b12*r6356 - 4*a33 *b12 *kap*r6115
2 2 2 2 3
+ 2*a33 *b12 *kap*r6243 + 2*a33 *b12 *r6430 - a33*b12 *kap*r6407,
4 16 4 3 2
8*a33 *b12*r6160 + ----*a33 *b12*r6356 - 4*a33 *b12 *kap*r6115
3
8 3 2 4 3 2 4 2 3
+ ---*a33 *b12 *kap*r6243 + ---*a33 *b12 *r6430 - ---*a33 *b12 *kap*r6407
3 3 3
2 4 2
- ---*a33*b12 *kap *r6336,
3
2 2 2 2
2*a33 *r6115 - 4*a33 *r6149 - 2*a33 *r6243 + 8*a33 *r6336 + a33*b12*r6407,
2 2 2 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33*b12*r6407,
2 2 2 2
2*a33 *r6115 - 4*a33 *r6149 - 2*a33 *r6243 + 8*a33 *r6336 + a33*b12*r6407,
r6230,
2*r6230,
r6230,
2 2 2 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33*b12*r6407,
2 2 2 2
4*a33 *r6115 - 8*a33 *r6149 - 4*a33 *r6243 + 16*a33 *r6336 + 2*a33*b12*r6407,
2*r6230,
2*r6230,
2 2 2 2
2*a33 *r6115 - 4*a33 *r6149 - 2*a33 *r6243 + 8*a33 *r6336 + a33*b12*r6407,
r6230,
r6270,
r6270,
r6243,
r6243,
r6270,
r6243,
1
2*a33*r6115 - 2*a33*r6243 + b12*r6129 - ---*b12*r6356,
2
1 1
2*a33*r6115 - 2*a33*r6243 + b12*r6129 - ---*b12*r6160 - ---*b12*r6356,
2 2
2*a33*r6270 + 2*b12*kap*r6230 - b12*r6157 - 3*b12*r666 + 2*b12*r671,
r6252,
2*a33*r6115 - 2*a33*r6243 + b12*r6129,
b12*r671,
2 2
8*a33 *kap*r6252 - 8*a33 *kap*r671 - 2*a33*b12*kap*r6133 - 4*a33*b12*r6435,
r6259,
2
2*a33*b12*r6131 - 2*a33*b12*r6259 + b12 *r6138,
3 3 2 2
8*a33 *kap*r6252 - 8*a33 *kap*r666 - 4*a33 *b12*r6435 - 2*a33*b12 *kap*r680,
r6270,
r6270,
2*a33*r6115 - 4*a33*r6149 + 8*a33*r6336,
2*a33*r6115 - 4*a33*r6149 + 8*a33*r6336,
r6270,
2*a33*r6115 - 4*a33*r6149 + 8*a33*r6336,
r6270,
2*a33*r6115 - 2*a33*r6243,
2*a33*r6115 - 2*a33*r6243 - b12*r6160,
2*b12*r6157 - 2*b12*r6252 - 2*b12*r6353 + 6*b12*r666 - 4*b12*r671,
2*a33*r6115 - 2*a33*r6243 - b12*r6356,
4*a33*b12*r666 - 4*a33*b12*r671,
2 2 2
4*a33 *b12*kap*r6252 + 4*a33 *b12*kap*r666 - 8*a33 *b12*kap*r671
2 2
- 2*a33*b12 *kap*r6133 - 4*a33*b12 *r6435,
2 2 2 2
2*a33 *r6160 + 2*a33 *r6356 - 2*a33*b12*r6259 + b12 *kap*r6129 - b12 *r6389,
2
2*a33*b12*r6252 - 2*a33*b12*r666 - b12 *r6133,
2*a33*b12*r6131 - 2*a33*b12*r6259,
2 2 2 2 2 2 3
4*a33 *b12 *kap *r6252 - 4*a33 *b12 *kap *r666 - 2*a33*b12 *kap*r6435,
2*a33*r6115 - 2*a33*r6243 + b12*r6407,
1
2*a33*r6115 - 2*a33*r6243 - ---*b12*r6160 + b12*r6407,
2
2*a33*r6270 + 2*b12*kap*r6230,
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - b12*r6252 - 2*b12*r6353
+ 3*b12*r666 - 2*b12*r671,
3 3 2 2
8*a33 *r6115 - 8*a33 *r6243 - 2*a33 *b12*r6160 - 4*a33 *b12*r6356
2 2 2
+ 4*a33 *b12*r6407 + a33*b12 *kap*r6115 - 2*a33*b12 *kap*r6149
2 2
+ 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
2*b12*r6252 + b12*r6353 - 3*b12*r666 + b12*r671,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 12*a33*b12*r666 - 8*a33*b12*r671 - b12 *kap*r6270,
2*a33*r6160 + 4*a33*r6356 + b12*kap*r6243,
3 3 2 2
8*a33 *r6160 + 8*a33 *r6356 - 4*a33 *b12*kap*r6115 + 4*a33 *b12*kap*r6243
2 2 2
+ 4*a33 *b12*r6131 - 4*a33 *b12*r6259 + a33*b12 *kap*r6160
2 2
+ a33*b12 *kap*r6356 - 2*a33*b12 *r6389,
3 3 2 2
8*a33 *b12*kap*r666 - 8*a33 *b12*kap*r671 - 4*a33 *b12 *kap*r6133
2 2 3 2 3 2
+ 4*a33 *b12 *r6435 - 2*a33*b12 *kap *r6252 + 4*a33*b12 *kap *r666,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 2*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 6*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270,
2
4*a33*b12*r6160 + 4*a33*b12*r6356 + b12 *r6430,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 10*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 14*a33*b12*r666 - 4*a33*b12*r671 - b12 *kap*r6270,
2 2
4*a33 *r6160 + 4*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*kap*r6243,
4
2*a33*b12 *r6435,
2 2 2
6*a33 *b12*r6160 + 4*a33 *b12*r6356 - 2*a33*b12 *kap*r6115
2 2 1 3
+ a33*b12 *kap*r6243 + a33*b12 *r6430 - ---*b12 *kap*r6407,
2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 16*a33 *b12*r6252 - 4*a33 *b12*r6353
2 2 2 3 2
+ 20*a33 *b12*r666 - 4*a33 *b12*r671 - 2*a33*b12 *kap*r6270 - b12 *kap *r6230
,
3 3
8*a33 *b12*r6252 - 8*a33 *b12*r666,
r6336,
a33*r6115 - 2*a33*r6149 - a33*r6243,
a33*r6115 - 2*a33*r6149 - a33*r6243 + 2*a33*r6336,
r6270,
r6270,
1
---*r6243 + 2*r6336,
2
a33*r6115 - 2*a33*r6149 - 2*a33*r6243,
r6270,
1
---*r6243 + r6336,
2
2*a33*r6270 + 2*b12*kap*r6230,
r6353,
r6356,
b12*r6157 + 3*b12*r666 - 3*b12*r671,
2 2
2*a33 *r6115 - 2*a33 *r6243 + 2*a33*b12*r6129 - a33*b12*r6356
1 2 2
- ---*b12 *kap*r6115 - b12 *kap*r660,
2
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 + 4*a33 *b12*r6129 - 5*a33 *b12*r6160
2 2 1 3
- 5*a33 *b12*r6356 - 2*a33*b12 *kap*r660 - ---*b12 *kap*r6129
2
1 3
+ ---*b12 *r6389,
2
2 2 2
12*a33 *b12*kap*r6252 - 4*a33 *b12*kap*r666 - 8*a33 *b12*kap*r671
2 2
- 2*a33*b12 *kap*r6133 - 2*a33*b12 *r6435,
2 2 1 2
2*a33 *r6115 - 2*a33 *r6243 + 2*a33*b12*r6129 - ---*b12 *kap*r6115
2
1 2 2 1 2
+ ---*b12 *kap*r6243 - b12 *kap*r660 - ---*b12 *r6259,
2 2
3 3 3 2
16*a33 *kap*r6252 - 8*a33 *kap*r666 - 8*a33 *kap*r671 - 4*a33 *b12*kap*r6133
2 2 2
- 8*a33 *b12*r6435 + 2*a33*b12 *kap *r671,
2 2 2 1 3
2*a33 *b12*r6131 - 2*a33 *b12*r6259 + 2*a33*b12 *r6138 + ---*b12 *kap*r6259
2
3
- b12 *kap*r674,
2*a33*r6270 + 2*b12*kap*r6230,
b12*r6353,
r6407,
2 2 2
2*a33 *b12*r6356 - 4*a33 *b12*r6407 - a33*b12 *kap*r6115
2 2 2
+ 2*a33*b12 *kap*r6149 - 4*a33*b12 *kap*r6336 + a33*b12 *r6430,
4*a33*r6270 + 4*b12*kap*r6230 + b12*r6157 - 3*b12*r6252 - 2*b12*r6353
+ 6*b12*r666 - 3*b12*r671,
a33*b12*r6356 + 2*a33*b12*r6407,
4*a33*r6160 + 2*a33*r6356 - b12*kap*r6115,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 4*a33*b12*r671 - b12 *kap*r6270,
3 3 3 3 3 3
16*a33 *b12 *kap*r6252 - 8*a33 *b12 *kap*r666 - 8*a33 *b12 *kap*r671
2 4 2 4 5 2
- 4*a33 *b12 *kap*r6133 - 12*a33 *b12 *r6435 + 2*a33*b12 *kap *r6252
5 2 5 2
- 2*a33*b12 *kap *r666 + 2*a33*b12 *kap *r671,
r6389,
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 + 4*a33 *b12*r6407 + 4*a33*b12 *kap*r6336,
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 - 6*a33 *b12*r6160 - 2*a33 *b12*r6356
2 2 2
+ 4*a33 *b12*r6407 + a33*b12 *kap*r6115 + a33*b12 *kap*r6243
2 2
+ 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
8*a33*b12*r6252 - 12*a33*b12*r666 + 4*a33*b12*r671,
3 3 2 2
4*a33 *r6115 - 4*a33 *r6243 - 2*a33 *b12*r6160 + 2*a33 *b12*r6356
2 2 2
+ 4*a33 *b12*r6407 + a33*b12 *kap*r6115 + a33*b12 *kap*r6243
2 2
+ 4*a33*b12 *kap*r6336 - a33*b12 *r6430,
3 2 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 8*a33 *b12*r6252 - 8*a33 *b12*r6353
2 2 2
+ 12*a33 *b12*r666 - 4*a33 *b12*r671 - 4*a33*b12 *kap*r6270
3 2
- 2*b12 *kap *r6230,
3 3 2 2
4*a33 *r6160 + 4*a33 *r6356 - 4*a33 *b12*kap*r6115 + 4*a33 *b12*kap*r6243
2 2 2
+ 2*a33 *b12*r6131 - 2*a33 *b12*r6259 - 2*a33*b12 *kap*r6129
2 2 2 3 2
+ a33*b12 *kap*r6160 + a33*b12 *kap*r6356 - 2*a33*b12 *r6389 + b12 *kap *r660
,
3 2 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 16*a33 *b12*r6252 - 8*a33 *b12*r6353
2 2 2
+ 24*a33 *b12*r666 - 8*a33 *b12*r671 - 4*a33*b12 *kap*r6270
3 2 3 3 3
- 2*b12 *kap *r6230 - 5*b12 *kap*r6252 + 6*b12 *kap*r666 - b12 *kap*r671,
3 3 2 2
12*a33 *b12*r6160 + 4*a33 *b12*r6356 - 4*a33 *b12 *kap*r6115
2 2 3
+ 4*a33 *b12 *r6430 - 2*a33*b12 *kap*r6407,
4 4 3 2
16*a33 *b12*r6160 + 8*a33 *b12*r6356 - 8*a33 *b12 *kap*r6115
3 2 3 2 2 3
+ 4*a33 *b12 *kap*r6243 + 4*a33 *b12 *r6430 - 4*a33 *b12 *kap*r6407
4 2
- 2*a33*b12 *kap *r6336,
r6407,
2 2 2 1 2
---*a33 *b12*r6356 + 4*a33 *b12*r6407 + ---*a33*b12 *kap*r6115
3 3
2 2 4 2 1 2
- ---*a33*b12 *kap*r6149 + ---*a33*b12 *kap*r6336 - ---*a33*b12 *r6430,
3 3 3
2*a33*r6270 + 2*b12*kap*r6230,
2*a33*b12*r6252 + 2*a33*b12*r6353 - 2*a33*b12*r666,
a33*b12*r6356 + 2*a33*b12*r6407,
4 4 1
---*a33*r6270 + ---*b12*kap*r6230 + ---*b12*r6157 + b12*r666 - b12*r671,
3 3 3
2 2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6353 - b12 *kap*r6270,
2*a33*r6356 + b12*kap*r6243,
2 2
4*a33 *r6160 + 4*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*kap*r6243
2
- b12 *r6389,
3 3 3 2
16*a33 *kap*r6252 - 8*a33 *kap*r666 - 8*a33 *kap*r671 - 4*a33 *b12*kap*r6133
2 2 2
- 4*a33 *b12*r6435 + 2*a33*b12 *kap *r671,
3 2 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 + 4*a33 *b12*r6252 - 8*a33 *b12*r6353
2 2
- 4*a33 *b12*r666 - 2*a33*b12 *kap*r6270,
r6430,
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 6*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 6*a33*b12*r666 - b12 *kap*r6270,
2 2
4*a33 *r6160 + 4*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*kap*r6243,
r6435,
2 2
6*a33 *r6160 + 2*a33 *r6356 - 2*a33*b12*kap*r6115 + 2*a33*b12*r6430
2
- b12 *kap*r6407,
3 2 2 2
16*a33 *r6270 + 16*a33 *b12*kap*r6230 - 20*a33 *b12*r6252 - 8*a33 *b12*r6353
2 2 2
+ 24*a33 *b12*r666 - 4*a33 *b12*r671 - 4*a33*b12 *kap*r6270
3 2
- 2*b12 *kap *r6230,
8 3 8 3 10 3
---*a33 *b12*r6252 - ---*a33 *b12*r671 - ----*a33*b12 *kap*r6252
3 3 3
3 2 3
+ 4*a33*b12 *kap*r666 - ---*a33*b12 *kap*r671,
3
a33*r6407 + b12*kap*r6336,
1 2 2
a33*b12*r6356 + a33*b12*r6407 + ---*b12 *kap*r6243 + b12 *kap*r6336
2
1 2
- ---*b12 *r6430,
2
2
8*a33 *r6270 + 8*a33*b12*kap*r6230 - 4*a33*b12*r6252 - 4*a33*b12*r6353
2
+ 4*a33*b12*r666 - b12 *kap*r6270,
1 2 2
a33*b12*r6356 + a33*b12*r6407 + ---*b12 *kap*r6243 + b12 *kap*r6336,
2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6353 - 2*a33*b12 *kap*r6270
3 2
- b12 *kap *r6230,
3 3 2 2
2*a33 *r6160 + 2*a33 *r6356 - 2*a33 *b12*kap*r6115 + 2*a33 *b12*kap*r6243
2 2 1 3 2
- a33*b12 *kap*r6129 - a33*b12 *r6389 + ---*b12 *kap *r6115
4
1 3 2 1 3 2
- ---*b12 *kap *r6243 + ---*b12 *kap *r660,
4 2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 + 8*a33 *b12*r6252 - 4*a33 *b12*r6353
2 2 3 2
- 8*a33 *b12*r666 - 2*a33*b12 *kap*r6270 - b12 *kap *r6230,
3 2 2 2 2
4*a33 *b12*r6356 + 2*a33 *b12 *kap*r6243 - 2*a33 *b12 *r6430
3
+ a33*b12 *kap*r6407,
4 3 2 3 2
8*a33 *b12*r6160 - 4*a33 *b12 *kap*r6115 + 4*a33 *b12 *r6430
2 3 4 2
- 4*a33 *b12 *kap*r6407 - 2*a33*b12 *kap *r6336,
2 2 2 1 3
2*a33 *b12*r6356 + a33*b12 *kap*r6243 - a33*b12 *r6430 + ---*b12 *kap*r6407,
2
3 2 2 2
8*a33 *r6270 + 8*a33 *b12*kap*r6230 - 4*a33 *b12*r6252 - 4*a33 *b12*r6353
2 2 3 2
+ 4*a33 *b12*r666 - 2*a33*b12 *kap*r6270 - b12 *kap *r6230,
3 3
8*a33 *b12*r6252 - 8*a33 *b12*r666,
4 3 2 2 2 2 2 2
---*a33 *b12*r6356 + ---*a33 *b12 *kap*r6243 - ---*a33 *b12 *r6430
3 3 3
2 3 1 4 2
+ ---*a33*b12 *kap*r6407 + ---*b12 *kap *r6336}}
3 3
Relevance for the application:
Modulo the following equation:
2 2
0=4*a33 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2 2
HAM=2*u1 *a33 + u1*v2*b12 + 2*u2 *a33 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=2*u1**2*a33 + u1*v2*b12 + 2*u2**2*a33 - u2*v1*b12 + u3**2*a33$