Solution 20 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
r6461
r60=-------
3
kap
r61=0
3*r6461
r62=---------
3
kap
r63=0
3*r6461
r64=---------
3
kap
r65=0
r6461
r66=-------
3
kap
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
3*r6461
r613=---------
3
kap
r614=0
6*r6461
r615=---------
3
kap
r616=0
3*r6461
r617=---------
3
kap
r618=0
r619=0
r620=0
r621=0
3*r6461
r622=---------
3
kap
r623=0
3*r6461
r624=---------
3
kap
r625=0
r626=0
r6461
r627=-------
3
kap
r6458
r628=-------
2
kap
r629=0
2*r6458
r630=---------
2
kap
r631=0
r6458
r632=-------
2
kap
r633=0
r634=0
r635=0
r636=0
r637=0
r638=0
2*r6458
r639=---------
2
kap
r640=0
2*r6458
r641=---------
2
kap
r642=0
r643=0
r644=0
r645=0
r6458
r646=-------
2
kap
r647=0
r648=0
1 1
---*kap*r658 + ---*r6419
2 4
r649=--------------------------
kap
r650=0
r651=r658
r652=0
1 1
---*kap*r658 - ---*r6419
2 4
r653=--------------------------
kap
r654=0
r655=0
r656=0
r657=0
r659=0
1
kap*r658 - ---*r6419
2
r660=----------------------
kap
r661=0
r662=0
1 1
---*kap*r658 - ---*r6419
2 4
r663=--------------------------
kap
1 2
---*kap*r6358 + kap*r671 - ---*r6458
3 3
r664=--------------------------------------
kap
r665=0
r666=r671
r667=0
r668=0
r669=0
r670=0
r672=0
r673=0
r675=0
1
r676= - ---*r6259 + r674
2
r677=0
r678=0
1
r679= - ---*r6259 + r674
2
r681=0
r682=0
r684=0
r6458
r685=-------
2
kap
r686=0
2*r6458
r687=---------
2
kap
r688=0
r6458
r689=-------
2
kap
1 1
- ---*r6160 + ---*r6181
4 2
r690=--------------------------
kap
r691=0
1
- ---*r6160 + r6181
2
r692=----------------------
kap
r693=0
1 1
- ---*r6160 + ---*r6181
4 2
r694=--------------------------
kap
r695=0
2*r6458
r696=---------
2
kap
r697=0
2*r6458
r698=---------
2
kap
1
- ---*r6160 + r6181
2
r699=----------------------
kap
r6100=0
1
- ---*r6160 + r6181
2
r6101=----------------------
kap
r6102=0
r6458
r6103=-------
2
kap
1 1
- ---*r6160 + ---*r6181
4 2
r6104=--------------------------
kap
r6105=0
r6419
r6106=-------
kap
r6107=0
r6419
r6108=-------
kap
r6109=0
r6111=0
r6112=r6110
r6113=0
r6114=0
r6419
r6115=-------
kap
r6116=0
r6117=r6110
r6118=0
r6119=0
r6120=0
kap*r6358 + kap*r671 - 2*r6458
r6121=--------------------------------
kap
r6122=0
r6123=r671
1
r6124=r6129 + ---*r6160
2
r6125=0
r6126=r6129
r6127=0
r6128=r671
r6130=0
r6131=r6259
r6132=0
r6133= - r6365
r6134=0
r6135=0
r6136=0
r6137=r680
r6139=0
3*r6461
r6140=---------
2
kap
r6141=0
1
---*kap*r6419 + 6*r6461
2
r6142=-------------------------
2
kap
r6143=0
1
---*kap*r6419 + 3*r6461
2
r6144=-------------------------
2
kap
r6145=0
r6146=r6110
r6147=0
r6148=r6110
1 1
- ---*kap*r6325 + ---*kap*r6419 + 6*r6461
2 2
r6149=--------------------------------------------
2
kap
r6150=0
1
- ---*kap*r6325 + kap*r6419 + 6*r6461
2
r6151=----------------------------------------
2
kap
r6152=0
r6153=r6110
1 1
- ---*kap*r6325 + ---*kap*r6419 + 3*r6461
2 2
r6154=--------------------------------------------
2
kap
2*r6458
r6155=---------
kap
r6156=0
r6157=r6358
r6158=0
r6159=0
r6161=0
r6162=r6353
r6163=0
r6164=0
r6165=kap*r658
r6166=0
1 1
r6167=kap*r658 + ---*r6259 - ---*r6419
2 2
r6168=0
r6169= - r6365
1 1 1
r6170=kap*r658 + ---*r6259 - ---*r6295 - ---*r6419
2 2 2
r6171=kap*r671
r6172=0
r6173=0
1
r6174= - ---*kap*r6259 + kap*r674
2
r6175=0
2*r6458
r6176=---------
kap
r6177=0
1 4
---*kap*r6358 + ---*r6458
3 3
r6178=---------------------------
kap
1
r6179= - ---*r6160 + r6181
2
r6180=0
r6182=0
r6183=r6353
2 1
r6184=---*r6181 - ---*r6309
3 3
r6185=0
r6186=r6419
r6187=0
r6188=kap*r6110
r6189=0
r6190=0
r6191=0
r6192=kap*r671
r6193=kap*r6129
r6194=0
3*r6461
r6195=---------
kap
r6196=0
1
---*kap*r6419 + 3*r6461
2
r6197=-------------------------
kap
r6198=0
r6199=kap*r6110
1 1
- ---*kap*r6325 + ---*kap*r6419 + 3*r6461
2 2
r6200=--------------------------------------------
kap
r6201=r6458
r6202=0
r6203=0
1 2 1
r6204=---*kap *r658 - ---*kap*r6419
2 4
r6205=0
r6206=r6458
1 1
r6207= - ---*kap*r6160 + ---*kap*r6181
4 2
r6208=0
r6209=r6461
r6210=0
1 1
---*r6160 - ---*r6181
4 2
r6211=-----------------------
kap
r6212=0
1
---*r6160 - r6181
2
r6213=-------------------
kap
r6214=0
1 1
---*r6160 - ---*r6181
4 2
r6215=-----------------------
kap
r6458
r6216=-------
2
kap
r6217=0
2*r6458
r6218=---------
2
kap
r6219=0
r6458
r6220=-------
2
kap
r6221=0
1
---*r6160 - r6181
2
r6222=-------------------
kap
r6223=0
1
---*r6160 - r6181
2
r6224=-------------------
kap
2*r6458
r6225=---------
2
kap
r6226=0
2*r6458
r6227=---------
2
kap
r6228=0
1 1
---*r6160 - ---*r6181
4 2
r6229=-----------------------
kap
r6458
r6230=-------
2
kap
r6231=0
r6232= - r6110
r6233=0
r6234= - r6110
r6235=0
r6419
r6236=-------
kap
r6237=0
r6419
r6238=-------
kap
r6239=0
r6240=0
r6241= - r6110
r6242=0
r6419
r6243=-------
kap
r6244=0
r6245=0
r6246=0
1
r6247= - r6129 - ---*r6160
2
r6248=0
r6249= - r6129
kap*r6358 + kap*r671 - 2*r6458
r6250=--------------------------------
kap
r6251=0
r6252=r671
r6253=0
r6254= - r6129
r6255=r671
r6256=0
r6257=r6365
r6258=0
r6260=0
r6261=0
r6262=0
r6263= - r6138
r6264=r680
r6265=0
r6266=0
r6267=0
r6268= - r6110
r6269=0
r6270= - r6110
r6271=0
r6325
r6272=-------
kap
r6273=0
r6325
r6274=-------
kap
r6275=r6110
r6276=0
r6277=0
r6278=0
r6325
r6279=-------
kap
r6280=r6110
r6281=0
r6282=0
r6283= - r6160
r6284=0
r6285=0
r6286= - 2*r6353 + 2*r6358
r6287=0
r6288=r6160
r6289=0
r6290=0
r6291=0
r6292=0
r6293=r6365
r6294=0
r6296= - r6365
r6297=0
r6298=0
r6299=0
r6300=0
r6301=0
1
r6302=---*r6160 - r6181
2
r6303=0
r6304= - r6181
2*r6458
r6305=---------
kap
r6306=0
- 2*kap*r6353 + kap*r6358 + 4*r6458
r6307=--------------------------------------
kap
r6308=0
r6310=r6353
r6311=0
r6312= - kap*r6110
r6313=0
r6314=r6419
r6315=0
r6316=0
r6317=0
r6318= - kap*r6129
r6319=kap*r671
r6320=0
r6321=0
r6322=0
r6323= - kap*r6110
r6324=0
r6326=kap*r6110
r6327=0
r6328=0
r6329=0
r6330=0
r6331=0
1 1
r6332=---*kap*r6160 - ---*kap*r6181
4 2
r6333=r6458
r6334=0
r6335=0
3*r6461
r6336=---------
2
kap
r6337=0
1 1
- ---*kap*r6325 + ---*kap*r6419 + 6*r6461
2 2
r6338=--------------------------------------------
2
kap
r6339=0
1 1
- ---*kap*r6325 + ---*kap*r6419 + 3*r6461
2 2
r6340=--------------------------------------------
2
kap
r6341=0
r6342= - r6110
r6343=0
r6344= - r6110
1
---*kap*r6419 + 6*r6461
2
r6345=-------------------------
2
kap
r6346=0
1
- ---*kap*r6325 + kap*r6419 + 6*r6461
2
r6347=----------------------------------------
2
kap
r6348=0
r6349= - r6110
1
---*kap*r6419 + 3*r6461
2
r6350=-------------------------
2
kap
2*r6458
r6351=---------
kap
r6352=0
r6354=0
r6355=0
r6356= - r6160
r6357=0
r6359=0
r6360=0
r6361=kap*r658
r6362=0
1 1 1
r6363=kap*r658 + ---*r6259 - ---*r6295 - ---*r6419
2 2 2
r6364=0
1 1
r6366=kap*r658 + ---*r6259 - ---*r6419
2 2
r6367=kap*r671
r6368=0
r6369=0
1
r6370= - ---*kap*r6259 + kap*r674
2
r6371=0
2*r6458
r6372=---------
kap
r6373=0
r6374=r6353
1
r6375= - ---*r6160 + r6181
2
r6376=0
r6377= - r6309
r6378=0
- 2*kap*r6353 + kap*r6358 + 4*r6458
r6379=--------------------------------------
kap
r6380=r6181
r6381=0
r6382=r6419
r6383=0
r6384=kap*r6110
r6385=0
r6386=0
r6387=0
r6388=kap*r671
r6389=kap*r6129
r6390=0
6*r6461
r6391=---------
kap
r6392=0
1
- ---*kap*r6325 + kap*r6419 + 6*r6461
2
r6393=----------------------------------------
kap
r6394=0
r6395=0
1
- ---*kap*r6325 + kap*r6419 + 6*r6461
2
r6396=----------------------------------------
kap
r6397=2*r6458
r6398=0
r6399=0
2 1
r6400=kap *r658 - ---*kap*r6419
2
r6401=0
r6402=2*r6458
1
r6403= - ---*kap*r6160 + kap*r6181
2
r6404=0
r6405=3*r6461
r6406=0
1
r6407=---*r6160 - r6181
2
r6408=0
2 1
r6409= - ---*r6181 + ---*r6309
3 3
2*r6458
r6410=---------
kap
r6411=0
r6412=r6353
r6413=0
r6414= - r6181
1 4
---*kap*r6358 + ---*r6458
3 3
r6415=---------------------------
kap
r6416=0
r6417= - kap*r6110
r6418=0
r6420=0
r6421=0
r6422=0
r6423= - kap*r6129
r6424=kap*r671
r6425=0
r6426=0
r6427=0
r6428= - kap*r6110
r6429=0
r6430=r6325
r6431=kap*r6110
r6432=0
r6433=0
r6434=0
r6435=0
r6436=0
1
r6437=---*kap*r6160 - kap*r6181
2
r6438=2*r6458
r6439=0
r6440=0
3*r6461
r6441=---------
kap
r6442=0
1 1
- ---*kap*r6325 + ---*kap*r6419 + 3*r6461
2 2
r6443=--------------------------------------------
kap
r6444=0
r6445= - kap*r6110
1
---*kap*r6419 + 3*r6461
2
r6446=-------------------------
kap
r6447=r6458
r6448=0
r6449=0
1 2 1
r6450=---*kap *r658 - ---*kap*r6419
2 4
r6451=0
r6452=r6458
1 1
r6453= - ---*kap*r6160 + ---*kap*r6181
4 2
r6454=0
r6455=3*r6461
r6456=0
1 1
r6457=---*kap*r6160 - ---*kap*r6181
4 2
r6459=0
r6460=0
a23=0
a22=0
a13=0
a11=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:
r658, r671, r674, r680, r683, r6110, r6129, r6138, r6160,
r6181, r6259, r6295, r6309, r6325, r6353, r6358, r6365,
r6419, r6458, r6461, 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.
{b12,
{r6461,
3*r6461,
3*r6461,
r6461,
3*r6461,
6*r6461,
3*r6461,
3*r6461,
3*r6461,
r6461,
r6458,
2*r6458,
r6458,
2*r6458,
2*r6458,
r6458,
1 1
---*kap*r658 + ---*r6419,
2 4
4 3
b12 *kap *r658,
1 4 3 1 4 2
---*b12 *kap *r658 - ---*b12 *kap *r6419,
2 4
r658,
4 3 1 4 2
b12 *kap *r658 - ---*b12 *kap *r6419,
2
1 1
---*kap*r658 - ---*r6419,
2 4
1 3 2 3 2 2 3
---*b12 *kap *r6358 + b12 *kap *r671 - ---*b12 *kap*r6458,
3 3
3
b12 *kap*r671,
r671,
r674,
1 2 2 2 2
---*b12 *kap *r6259 - b12 *kap *r674,
2
1 2 2 2 2
---*b12 *kap *r6259 - b12 *kap *r674,
2
r680,
r683,
r6458,
2*r6458,
r6458,
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
2*r6458,
2*r6458,
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
r6458,
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
4 2
b12 *kap *r6419,
4 2
b12 *kap *r6419,
r6110,
2
b12*kap *r6110,
4 2
b12 *kap *r6419,
2
b12*kap *r6110,
3 2 3 2 3
b12 *kap *r6358 + b12 *kap *r671 - 2*b12 *kap*r6458,
3 2
b12 *kap *r671,
2 2 1 2 2
b12 *kap *r6129 + ---*b12 *kap *r6160,
2
2
b12 *kap*r6129,
2
b12 *kap*r671,
r6129,
r6259,
5 2
b12 *kap *r6365,
6 2
b12 *kap *r680,
r6138,
3*r6461,
1 4 2 4
---*b12 *kap *r6419 + 6*b12 *kap*r6461,
2
1 4 2 4
---*b12 *kap *r6419 + 3*b12 *kap*r6461,
2
2 2
b12 *kap *r6110,
2 2
b12 *kap *r6110,
1 4 2 1 4 2 4
---*b12 *kap *r6325 - ---*b12 *kap *r6419 - 6*b12 *kap*r6461,
2 2
1 4 2 4 2 4
---*b12 *kap *r6325 - b12 *kap *r6419 - 6*b12 *kap*r6461,
2
2 2
b12 *kap *r6110,
1 4 2 1 4 2 4
---*b12 *kap *r6325 - ---*b12 *kap *r6419 - 3*b12 *kap*r6461,
2 2
2*b12*r6458,
3 2
b12 *kap *r6358,
r6160,
3 2
b12 *kap *r6353,
4 3
b12 *kap *r658,
4 3 1 4 2 1 4 2
b12 *kap *r658 + ---*b12 *kap *r6259 - ---*b12 *kap *r6419,
2 2
4
b12 *kap*r6365,
6 4 1 6 3 1 6 3
b12 *kap *r658 + ---*b12 *kap *r6259 - ---*b12 *kap *r6295
2 2
1 6 3
- ---*b12 *kap *r6419,
2
6 3
b12 *kap *r671,
1 4 3 4 3
---*b12 *kap *r6259 - b12 *kap *r674,
2
3
2*b12 *kap*r6458,
1 3 2 4 3
---*b12 *kap *r6358 + ---*b12 *kap*r6458,
3 3
1
---*b12*kap*r6160 - b12*kap*r6181,
2
r6181,
3 2
b12 *kap *r6353,
2 5 3 1 5 3
---*b12 *kap *r6181 - ---*b12 *kap *r6309,
3 3
6 3
b12 *kap *r6419,
2 2
b12 *kap *r6110,
7 3
b12 *kap *r671,
7 4
b12 *kap *r6129,
2
3*b12 *r6461,
1 4 2 4
---*b12 *kap *r6419 + 3*b12 *kap*r6461,
2
2 2
b12 *kap *r6110,
1 6 3 1 6 3 6 2
---*b12 *kap *r6325 - ---*b12 *kap *r6419 - 3*b12 *kap *r6461,
2 2
3
b12 *kap*r6458,
1 8 5 1 8 4
---*b12 *kap *r658 - ---*b12 *kap *r6419,
2 4
3
b12 *kap*r6458,
1 3 2 1 3 2
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
4
b12 *kap*r6461,
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
r6458,
2*r6458,
r6458,
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
2*r6458,
2*r6458,
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
r6458,
2 2
b12 *kap *r6110,
2 2
b12 *kap *r6110,
r6419,
r6419,
2 2
b12 *kap *r6110,
r6419,
2 2 1 2 2
b12 *kap *r6129 + ---*b12 *kap *r6160,
2
2 2
b12 *kap *r6129,
3 2 3 2 3
b12 *kap *r6358 + b12 *kap *r671 - 2*b12 *kap*r6458,
3
b12 *kap*r671,
2
b12*kap *r6129,
3 2
b12 *kap *r671,
5 2
b12 *kap *r6365,
r6259,
3 2
b12 *kap *r6138,
6 2
b12 *kap *r680,
2 2
b12 *kap *r6110,
2 2
b12 *kap *r6110,
2
b12 *kap*r6325,
2
b12 *kap*r6325,
2
b12*kap *r6110,
2
b12 *kap*r6325,
2
b12*kap *r6110,
2
b12*kap *r6160,
3 2 3 2
2*b12 *kap *r6353 - 2*b12 *kap *r6358,
2 2
b12 *kap *r6160,
5 2
b12 *kap *r6365,
r6295,
5 2
b12 *kap *r6365,
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
5 3
b12 *kap *r6181,
2*b12*r6458,
3 2 3 2 3
2*b12 *kap *r6353 - b12 *kap *r6358 - 4*b12 *kap*r6458,
r6309,
3 2
b12 *kap *r6353,
4 2
b12 *kap *r6110,
6 3
b12 *kap *r6419,
7 4
b12 *kap *r6129,
6 3
b12 *kap *r671,
4 3
b12 *kap *r6110,
r6325,
4 3
b12 *kap *r6110,
1 7 4 1 7 4
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
3
b12 *kap*r6458,
3*r6461,
1 2 1 2 2
---*b12 *kap*r6325 - ---*b12 *kap*r6419 - 6*b12 *r6461,
2 2
1 2 1 2 2
---*b12 *kap*r6325 - ---*b12 *kap*r6419 - 3*b12 *r6461,
2 2
2 2
b12 *kap *r6110,
2 2
b12 *kap *r6110,
1
---*kap*r6419 + 6*r6461,
2
1 2 2 2
---*b12 *kap*r6325 - b12 *kap*r6419 - 6*b12 *r6461,
2
2 2
b12 *kap *r6110,
1
---*kap*r6419 + 3*r6461,
2
2*r6458,
r6353,
2
b12 *kap*r6160,
r6358,
2 3
b12 *kap *r658,
4 3 1 4 2 1 4 2
b12 *kap *r658 + ---*b12 *kap *r6259 - ---*b12 *kap *r6295
2 2
1 4 2
- ---*b12 *kap *r6419,
2
r6365,
2 3 1 2 2 1 2 2
b12 *kap *r658 + ---*b12 *kap *r6259 - ---*b12 *kap *r6419,
2 2
5 2
b12 *kap *r671,
1 2 2 2 2
---*b12 *kap *r6259 - b12 *kap *r674,
2
3
2*b12 *kap*r6458,
3 2
b12 *kap *r6353,
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
5 3
b12 *kap *r6309,
3 2 3 2 3
2*b12 *kap *r6353 - b12 *kap *r6358 - 4*b12 *kap*r6458,
5 3
b12 *kap *r6181,
4 2
b12 *kap *r6419,
2 2
b12 *kap *r6110,
6 3
b12 *kap *r671,
5 3
b12 *kap *r6129,
2
6*b12 *kap*r6461,
1 4 2 4 2 4
---*b12 *kap *r6325 - b12 *kap *r6419 - 6*b12 *kap*r6461,
2
1 4 2 4 2 4
---*b12 *kap *r6325 - b12 *kap *r6419 - 6*b12 *kap*r6461,
2
7 2
2*b12 *kap *r6458,
8 5 1 8 4
b12 *kap *r658 - ---*b12 *kap *r6419,
2
5 2
2*b12 *kap *r6458,
1 7 4 7 4
---*b12 *kap *r6160 - b12 *kap *r6181,
2
8 3
3*b12 *kap *r6461,
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
2 5 3 1 5 3
---*b12 *kap *r6181 - ---*b12 *kap *r6309,
3 3
2*r6458,
3 2
b12 *kap *r6353,
5 3
b12 *kap *r6181,
1 3 2 4 3
---*b12 *kap *r6358 + ---*b12 *kap*r6458,
3 3
2 2
b12 *kap *r6110,
r6419,
5 3
b12 *kap *r6129,
6 3
b12 *kap *r671,
4 3
b12 *kap *r6110,
2
b12 *kap*r6325,
2
b12*kap *r6110,
1 5 3 5 3
---*b12 *kap *r6160 - b12 *kap *r6181,
2
3
2*b12 *kap*r6458,
3*r6461,
1 2 1 2 2
---*b12 *kap*r6325 - ---*b12 *kap*r6419 - 3*b12 *r6461,
2 2
2 2
b12 *kap *r6110,
1
---*kap*r6419 + 3*r6461,
2
5 2
b12 *kap *r6458,
1 4 4 1 4 3
---*b12 *kap *r658 - ---*b12 *kap *r6419,
2 4
3
b12 *kap*r6458,
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
6 2
3*b12 *kap *r6461,
1 5 3 1 5 3
---*b12 *kap *r6160 - ---*b12 *kap *r6181,
4 2
r6458,
r6461}}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2
HAM=u1*v2*b12 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs the following 0 first integrals:
And again in machine readable form:
HAM=u1*v2*b12 - u2*v1*b12 + u3**2*a33$