Solution 14 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=a11 + b12 *kap
Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r14=0
r15=0
r20=0
r21=0
r22=0
r23=0
r24=0
r27=0
r28=0
r210=0
m3*r328
r211=---------
b12
r212=0
r213=0
r214=0
r215=0
m3*r328
r217=---------
b12
r218=0
r219=0
r220=0
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
2 1 2 1 2
a11*b12*r328 + b12 *r333 - ---*kap*m3 *r5154 + ---*kap*m3 *r5175
2 2
r310=------------------------------------------------------------------
2
b12 *kap
r311=0
a11*r328 + b12*r333
r312=---------------------
b12*kap
r313=0
r314=0
a11*r328 + b12*r333
r315=---------------------
b12*kap
b12*r327 - m3*r453
r316=--------------------
b12
r317=0
r318=0
r320=0
2 2
- m3 *r5154 + m3 *r5175
r321=--------------------------
2
b12
r322=0
r323=0
r324=0
r325=0
r326=0
r329=0
r330=0
r331=0
r332=0
r334=0
r335=0
r336=0
r337=0
2 2
- m3 *r5154 + m3 *r5175
r338=--------------------------
2
b12
r339=0
r340=0
r341=0
r342= - r328
r343=r327
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r350=0
r351=0
r352=0
r353=r333
r354=0
r355=0
r40=0
r41=0
r42=0
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r415=0
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r423=0
r424=0
r426=0
a11*r453 + b12*r464
r427=---------------------
b12*kap
r428=0
r429=0
a11*r453 + b12*r464
r430=---------------------
b12*kap
b12*r452 + m3*r5158
r431=---------------------
b12
r432=0
r433=0
r435=0
- m3*r5142
r436=-------------
b12
r437=0
- m3*r5142
r438=-------------
b12
r439=0
r440=0
r441=0
r442=0
- m3*r5142
r443=-------------
b12
r444=0
r445=0
2 2
r446=( - 2*a11*b12*r453 - 2*b12 *r464 - b12*kap*m3*r5173 - kap*m3 *r6259
2 2
+ kap*m3 *r6295)/(b12 *kap)
r447=0
r448=0
r449=0
r450=0
r451=0
r454=0
r455=0
r456=0
2 1 2
r457=( - a11*b12*r453 - b12 *r464 - b12*kap*m3*r5173 - ---*kap*m3 *r6259
2
1 2 2
+ ---*kap*m3 *r6295)/(b12 *kap)
2
r458=0
m3*r5154 - m3*r5175
r459=---------------------
b12
r460=0
r461=0
r462=0
r463=0
r465=0
- a11*m3*r5154 + a11*m3*r5175 - b12*kap*m3*r5142
r466=---------------------------------------------------
2
b12
r467=0
r468=0
r469=0
r470=0
r471=0
r472=0
r473=0
- m3*r5142
r474=-------------
b12
r475=0
- m3*r5142
r476=-------------
b12
r477=0
- m3*r5142
r479=-------------
b12
r480=0
r482=0
2 2
r483=( - 2*a11*b12*r453 - 2*b12 *r464 - b12*kap*m3*r5173 - kap*m3 *r6259
2 2
+ kap*m3 *r6295)/(b12 *kap)
r484=0
r485=0
r486=0
r487= - r453
r488=r452
r489=0
r490=0
r491=0
- m3*r5154 + m3*r5175
r492=------------------------
b12
r493=0
2 2
r494=( - 2*a11*b12*r453 - 2*b12 *r464 - 2*b12*kap*m3*r5173 - kap*m3 *r6259
2 2
+ kap*m3 *r6295)/(b12 *kap)
m3*r5154 - m3*r5175
r495=---------------------
b12
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
- a11*m3*r5154 + a11*m3*r5175 - b12*kap*m3*r5142
r4102=---------------------------------------------------
2
b12
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
- m3*r5154 + m3*r5175
r4109=------------------------
b12
2 1 2
r4110=( - a11*b12*r453 - b12 *r464 - b12*kap*m3*r5173 - ---*kap*m3 *r6259
2
1 2 2
+ ---*kap*m3 *r6295)/(b12 *kap)
2
r4111=0
r4112=0
r4113=0
r4114=r464
r4115=0
- a11*m3*r5154 + a11*m3*r5175 - b12*kap*m3*r5142
r4116=---------------------------------------------------
2
b12
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
- a11*m3*r5154 + a11*m3*r5175 - b12*kap*m3*r5142
r4122=---------------------------------------------------
2
b12
r4123=0
r4124=0
r4125=0
r50=0
r51=0
r52=0
r53=0
r54=0
r55=0
r56=0
r57=0
r58=0
r59=0
r510=0
r511=0
r512=0
r513=0
r514=0
r515=0
r516=0
r517=0
r518=0
r519=0
r520=0
r521=r525
r522=0
r523=2*r525
r524=0
r526=0
r527=0
r528=0
r529=0
r530=2*r525
r531=0
r532=2*r525
r533=0
r534=0
r535=r525
r536=r538
r537=0
r539=0
r540=0
r541=0
r542=0
r543=r538
r544=0
r545=0
r547=0
1
r548= - ---*r5154 + r546
2
r549=0
r550=0
- r5154 + 2*r546
r551=-------------------
2
b12*r588 - m3*r6138
r552=---------------------
b12
r553=0
r554=0
r556=0
r557=0
r558=0
r559=0
r560=0
r561=0
r562=0
r563=0
r564=0
r565=0
r566=0
r567=0
r568=0
r569=0
r570=0
r571=0
r572=r538
r573=0
r574=r538
r575= - r5142
r576=0
r577= - r5142
r578=0
r579=r538
r580= - r5142
r581=0
r582=r5154
r583=0
- b12*r5173 - m3*r6259 + m3*r6295
r584=------------------------------------
b12
r585=0
r586=0
r587=0
r589= - r5158
r590=0
r591=0
r592=0
r593=0
r594=0
r595=0
r596=0
r597=0
r598=0
r599=0
r5100=0
a11*r5142 + 2*b12*kap*r525
r5101=----------------------------
b12
r5102=0
1
a11*r5142 + 2*b12*kap*r525 + ---*b12*r5154
2
r5103=--------------------------------------------
b12
r5104=0
r5105= - r5173
1 1
a11*r5142 + 2*b12*kap*r525 + ---*b12*r5154 - ---*b12*r5175
2 2
r5106=------------------------------------------------------------
b12
2
a11*b12*r5173 + a11*m3*r6259 - a11*m3*r6295 + b12 *kap*r538
r5107=-------------------------------------------------------------
2
b12
r5108=0
r5109=0
1
a11*r5158 - ---*b12*kap*r5154 + b12*kap*r546
2
r5110=----------------------------------------------
b12
r5111=0
r5112=0
r5113=0
r5114=0
r5115=0
r5116=0
r5117=0
a11*r5173 + b12*kap*r538
r5118=--------------------------
b12
- a11*r5154 + a11*r5175 - b12*kap*r5142
r5119=------------------------------------------
b12
r5120=0
r5121=0
r5122=0
r5123=0
1 2 1 2 2 2
---*a11 *r5154 - ---*a11 *r5175 + a11*b12*kap*r5142 + b12 *kap *r525
2 2
r5124=----------------------------------------------------------------------
2
b12
r5125=0
r5126=0
r5127=0
r5128=0
r5129=0
r5130=0
r5131=0
r5132=0
r5133=0
r5134=0
r5135=0
r5136=0
r5137=0
r5138=0
r5139=0
r5140=0
r5141=0
r5143=0
r5144=r5142
r5145=r538
r5146=0
r5147=r538
r5148=0
r5149=r5142
r5150=r538
r5151=0
b12*r5173 + m3*r6259 - m3*r6295
r5152=---------------------------------
b12
r5153=0
r5155=0
r5156=0
r5157=0
r5159=r588
r5160=0
r5161=0
r5162=0
r5163=0
r5164=0
r5165=0
r5166=0
r5167=0
r5168=0
r5169=0
r5170=0
r5171=0
r5172=0
r5174=0
r5176= - r5173
r5177=0
r5178=0
r5179=0
r5180=0
r5181=0
r5182=0
r5183=0
r5184=0
r5185=0
r5186=0
r5187=0
a11*r5154 - a11*r5175 + b12*kap*r5142
r5188=---------------------------------------
b12
a11*r5173 + b12*kap*r538
r5189=--------------------------
b12
r5190=0
r5191=0
r5192=0
r5193=0
r5194=0
r5195=0
r5196=0
r5197=0
r5198=0
r5199=0
r5200=0
r5201=0
r5202=0
r5203=0
r5204=0
r5205=0
a11*r5142 + 2*b12*kap*r525
r5206=----------------------------
b12
r5207=0
1 1
a11*r5142 + 2*b12*kap*r525 + ---*b12*r5154 - ---*b12*r5175
2 2
r5208=------------------------------------------------------------
b12
r5209=0
r5210=r5173
1
a11*r5142 + 2*b12*kap*r525 + ---*b12*r5154
2
r5211=--------------------------------------------
b12
2
a11*b12*r5173 + a11*m3*r6259 - a11*m3*r6295 + b12 *kap*r538
r5212=-------------------------------------------------------------
2
b12
r5213=0
r5214=0
1
a11*r5158 - ---*b12*kap*r5154 + b12*kap*r546
2
r5215=----------------------------------------------
b12
r5216=0
r5217=0
r5218=0
r5219=0
r5220=0
r5221=0
r5222=0
a11*r5173 + b12*kap*r538
r5223=--------------------------
b12
- a11*r5154 + a11*r5175 - b12*kap*r5142
r5224=------------------------------------------
b12
r5225=0
r5226=0
r5227=0
r5228=0
2 2 2 2
a11 *r5154 - a11 *r5175 + 2*a11*b12*kap*r5142 + 2*b12 *kap *r525
r5229=------------------------------------------------------------------
2
b12
r5230=0
r5231=0
r5232=0
r5233=0
r5234=0
r5235=0
r5236=0
r5237=0
a11*r5154 - a11*r5175 + b12*kap*r5142
r5238=---------------------------------------
b12
a11*r5173 + b12*kap*r538
r5239=--------------------------
b12
r5240=0
r5241=0
r5242=0
r5243=0
r5244=0
r5245=0
r5246=0
r5247=0
r5248=0
1 2 1 2 2 2
---*a11 *r5154 - ---*a11 *r5175 + a11*b12*kap*r5142 + b12 *kap *r525
2 2
r5249=----------------------------------------------------------------------
2
b12
r5250=0
r5251=0
r60=0
r61=0
r62=0
r63=0
r64=0
r65=0
r66=0
r67=0
r68=0
r69=0
r610=0
r611=0
r612=0
r613=0
r614=0
r615=0
r616=0
r617=0
r618=0
r619=0
r620=0
r621=0
r622=0
r623=0
r624=0
r625=0
r626=0
r628=0
r629=0
r630=0
r631=0
r632=0
r633=0
r634=0
r635=0
r636=0
r637=0
r638=0
r639=0
r640=0
r641=0
r642=0
r643=0
r644=0
r645=0
r647=0
r648=0
r649=0
r650=0
r651=0
r652=0
r653=0
r654=0
r655=0
r656=0
r657=0
r659=0
r660=0
r661=0
r662=0
r663=0
r665=0
r666=0
r667=0
r668=0
r669=0
r670=0
r671=0
r672=0
r673=0
r675=0
1
r676= - ---*r6259 + r674
2
r677=0
r678=0
1
r679= - ---*r6259 + r674
2
r680=r6264
r681=0
r682=0
r684=0
r685=0
r686=0
r687=0
r688=0
r689=0
r690=0
r691=0
r692=0
r693=0
r694=0
r695=0
r696=0
r697=0
r698=0
r699=0
r6100=0
r6101=0
r6102=0
r6103=0
r6104=0
r6105=0
r6106=0
r6107=0
r6108=0
r6109=0
r6110=0
r6111=0
r6112=0
r6113=0
r6114=0
r6115=0
r6116=0
r6117=0
r6118=0
r6119=0
r6120=0
r6121=0
r6122=0
r6123=0
r6124=0
r6125=0
r6126=0
r6127=0
r6128=0
r6129=0
r6130=0
r6131=r6259
r6132=0
r6133=0
r6134=0
r6135=0
r6136=0
r6137=r6264
r6139=0
r6140=0
r6141=0
r6142=0
r6143=0
r6144=0
r6145=0
r6146=0
r6147=0
r6148=0
r6149=0
r6150=0
r6151=0
r6152=0
r6153=0
r6154=0
r6155=0
r6156=0
r6157=0
r6158=0
r6159=0
r6160=0
r6161=0
r6162=0
r6163=0
r6164=0
r6165=0
r6166=0
1
r6167=---*r6259
2
r6168=0
r6169=0
1 1
r6170=---*r6259 - ---*r6295
2 2
r6171=0
r6172=0
r6173=0
1
- a11*r6138 - ---*b12*kap*r6259 + b12*kap*r674
2
r6174=-------------------------------------------------
b12
r6175=0
r6176=0
r6177=0
r6178=0
r6179=0
r6180=0
r6181=0
r6182=0
r6183=0
r6184=0
r6185=0
r6186=0
r6187=0
r6188=0
r6189=0
r6190=0
r6191=0
r6192=0
- a11*r6259 + a11*r6295
r6193=--------------------------
b12
r6194=0
r6195=0
r6196=0
r6197=0
r6198=0
r6199=0
r6200=0
r6201=0
r6202=0
r6203=0
1 2 1 2
---*a11 *r6259 - ---*a11 *r6295
2 2
r6204=---------------------------------
2
b12
r6205=0
r6206=0
r6207=0
r6208=0
r6209=0
r6210=0
r6211=0
r6212=0
r6213=0
r6214=0
r6215=0
r6216=0
r6217=0
r6218=0
r6219=0
r6220=0
r6221=0
r6222=0
r6223=0
r6224=0
r6225=0
r6226=0
r6227=0
r6228=0
r6230=0
r6231=0
r6232=0
r6233=0
r6234=0
r6235=0
r6236=0
r6237=0
r6238=0
r6239=0
r6240=0
r6242=0
r6243=0
r6244=0
r6245=0
r6246=0
r6248=0
r6249=0
r6250=0
r6251=0
r6252=0
r6253=0
r6254=0
r6255=0
r6256=0
r6257=0
r6258=0
r6260=0
r6261=0
r6262=0
r6263= - r6138
r6265=0
r6266=0
r6267=0
r6268=0
r6269=0
r6270=0
r6271=0
r6272=0
r6273=0
r6274=0
r6275=0
r6276=0
r6277=0
r6278=0
r6279=0
r6280=0
r6281=0
r6282=0
r6283=0
r6284=0
r6285=0
r6286=0
r6287=0
r6288=0
r6289=0
r6290=0
r6291=0
r6292=0
r6293=0
r6294=0
r6296=0
r6297=0
r6298=0
r6299=0
r6300=0
r6301=0
r6302=0
r6303=0
r6304=0
r6305=0
r6306=0
r6307=0
r6308=0
r6309=0
r6310=0
r6311=0
r6312=0
r6313=0
r6314=0
r6315=0
r6316=0
r6317=0
a11*r6259 - a11*r6295
r6318=-----------------------
b12
r6319=0
r6320=0
r6321=0
r6322=0
r6323=0
r6324=0
r6325=0
r6326=0
r6327=0
r6328=0
r6329=0
r6330=0
r6331=0
r6332=0
r6333=0
r6334=0
r6335=0
r6336=0
r6337=0
r6338=0
r6339=0
r6340=0
r6341=0
r6342=0
r6343=0
r6344=0
r6345=0
r6346=0
r6348=0
r6349=0
r6350=0
r6351=0
r6352=0
r6354=0
r6355=0
r6356=0
r6357=0
r6358=0
r6359=0
r6360=0
r6361=0
r6362=0
1 1
r6363=---*r6259 - ---*r6295
2 2
r6364=0
r6365=0
1
r6366=---*r6259
2
r6367=0
r6368=0
r6369=0
1
- a11*r6138 - ---*b12*kap*r6259 + b12*kap*r674
2
r6370=-------------------------------------------------
b12
r6371=0
r6372=0
r6373=0
r6374=0
r6375=0
r6376=0
r6377=0
r6378=0
r6379=0
r6380=0
r6381=0
r6382=0
r6383=0
r6384=0
r6385=0
r6386=0
r6387=0
r6388=0
- a11*r6259 + a11*r6295
r6389=--------------------------
b12
r6390=0
r6391=0
r6392=0
r6393=0
r6394=0
r6395=0
r6396=0
r6397=0
r6398=0
r6399=0
2 2
a11 *r6259 - a11 *r6295
r6400=-------------------------
2
b12
r6401=0
r6402=0
r6403=0
r6404=0
r6405=0
r6406=0
r6407=0
r6408=0
r6410=0
r6411=0
r6412=0
r6413=0
r6414=0
r6415=0
r6416=0
r6417=0
r6418=0
r6419=0
r6420=0
r6421=0
r6422=0
a11*r6259 - a11*r6295
r6423=-----------------------
b12
r6424=0
r6425=0
r6426=0
r6427=0
r6428=0
r6429=0
r6430=0
r6431=0
r6432=0
r6433=0
r6434=0
r6435=0
r6436=0
r6437=0
r6438=0
r6439=0
r6440=0
r6441=0
r6442=0
r6443=0
r6444=0
r6445=0
r6446=0
r6447=0
r6448=0
r6449=0
1 2 1 2
---*a11 *r6259 - ---*a11 *r6295
2 2
r6450=---------------------------------
2
b12
r6451=0
r6452=0
r6453=0
r6454=0
r6455=0
r6456=0
r6457=0
r6458=0
r6459=0
r6460=0
r6461=0
m2=0
m1=0
n2=0
n1=0
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:
r683, r555, r434, r319, r29, r13, r327, r6264, r674, r546,
r5173, r328, r452, r588, r5175, r5154, r464, r6295, r453,
r333, r5158, r6138, r6259, r538, r5142, r525, m3, a11, n3,
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.
{n3,
b12,
a11,
4 4
{36*b12 *kap*n3*r6259 - 36*b12 *kap*n3*r6295,
2 2
6*a11*b12 *r6259 - 6*a11*b12 *r6295,
4 4
6*b12 *kap*n3*r6259 - 6*b12 *kap*n3*r6295,
2*a11*b12*r6259 - 2*a11*b12*r6295,
3 2 4 2
397440*a11*b12 *n3 *r6138 + 198720*b12 *kap*n3 *r6259
4 2
- 397440*b12 *kap*n3 *r674,
2
3*b12 *r6259,
4 4
3*b12 *kap*n3*r6259 - 3*b12 *kap*n3*r6295,
2 2
2*a11*b12 *n3*r6259 - 2*a11*b12 *n3*r6295,
r6295,
r6264,
3
b12 *n3*r6138,
r6259,
4 4
35424*b12 *kap*n3*r6259 - 35424*b12 *kap*n3*r6295,
2 2
4*a11*b12 *n3*r6259 - 4*a11*b12 *n3*r6295,
3 2 4 2 4 2
99360*a11*b12 *n3 *r6138 + 49680*b12 *kap*n3 *r6259 - 99360*b12 *kap*n3 *r674,
2 2
b12 *n3*r6259 - b12 *n3*r6295,
r6138,
3
636336*b12 *n3*r6264,
2
b12 *n3*r6259,
r683,
5 2
258127662983853600*b12 *kap *n3*r6264,
4 4
24*b12 *kap*r6259 - 48*b12 *kap*r674,
4 4
b12 *kap*n3*r6259 - 2*b12 *kap*n3*r674,
r674}}
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
HAM=(2*u1 *a11 + 2*u1*v2*b12 + 2*u2 *a11 - 2*u2*v1*b12 + u3 *a11 + 2*u3*n3
+ 2*v3*m3)/2
has apart from the Hamiltonian and Casimirs the following 26 first integrals:
4 2 2 2 2 2 2 2 2
FI=u1 *u3*kap + 2*u1 *u2 *u3*kap + 2*u1 *u3*v1 *kap + 2*u1 *u3*v2 *kap
2 2 4 2 2 2 2 2
+ 2*u1 *u3*v3 *kap + u2 *u3*kap + 2*u2 *u3*v1 *kap + 2*u2 *u3*v2 *kap
2 2 4 2 2 2 2 4
+ 2*u2 *u3*v3 *kap + u3*v1 + 2*u3*v1 *v2 + 2*u3*v1 *v3 + u3*v2
2 2 4
+ 2*u3*v2 *v3 + u3*v3
2 2 2 2 2
= a product of the elements of: {u1 *kap + u2 *kap + v1 + v2 + v3 ,
2 2 2 2 2
u1 *kap + u2 *kap + v1 + v2 + v3 ,
u3}
{HAM,FI} = 0
4 3 3 2 2
FI=u1 *u3*a11*kap + u1 *u3*v2*b12*kap - u1 *v1*kap*m3 + 2*u1 *u2 *u3*a11*kap
2 2 2 2 2 2
- u1 *u2*u3*v1*b12*kap - u1 *u2*v2*kap*m3 + u1 *u3*v1 *a11 + u1 *u3*v2 *a11
2 2 2 2
+ u1 *u3*v3 *a11 + u1*u2 *u3*v2*b12*kap - u1*u2 *v1*kap*m3
2 3 2 3
+ u1*u3*v1 *v2*b12 + u1*u3*v2 *b12 + u1*u3*v2*v3 *b12 - u1*v1 *m3
2 2 4 3
- u1*v1*v2 *m3 - u1*v1*v3 *m3 + u2 *u3*a11*kap - u2 *u3*v1*b12*kap
3 2 2 2 2 2 2
- u2 *v2*kap*m3 + u2 *u3*v1 *a11 + u2 *u3*v2 *a11 + u2 *u3*v3 *a11
3 2 2 2
- u2*u3*v1 *b12 - u2*u3*v1*v2 *b12 - u2*u3*v1*v3 *b12 - u2*v1 *v2*m3
3 2
- u2*v2 *m3 - u2*v2*v3 *m3
2 2 2 2 2
= a product of the elements of: {u1 *kap + u2 *kap + v1 + v2 + v3 ,
2 2
u1 *u3*a11 + u1*u3*v2*b12 - u1*v1*m3 + u2 *u3*a11 - u2*u3*v1*b12 - u2*v2*m3}
{HAM,FI} = 0
3 2 2 2 2
FI=u1 *u3*v1*kap + u1 *u2*u3*v2*kap + u1 *u3 *v3*kap + u1*u2 *u3*v1*kap
3 2 2 3 2 2
+ u1*u3*v1 + u1*u3*v1*v2 + u1*u3*v1*v3 + u2 *u3*v2*kap + u2 *u3 *v3*kap
2 3 2 2 2 2 2
+ u2*u3*v1 *v2 + u2*u3*v2 + u2*u3*v2*v3 + u3 *v1 *v3 + u3 *v2 *v3
2 3
+ u3 *v3
= a product of the elements of: {u3,
u1*v1 + u2*v2 + u3*v3,
2 2 2 2 2
u1 *kap + u2 *kap + v1 + v2 + v3 }
{HAM,FI} = 0
4 2 2 3 2 2 2 2 2
FI=u1 *u3 *a11 + 2*u1 *u3 *v2*a11*b12 + 2*u1 *u2 *u3 *a11
2 2 2 4 2 2 2 2 2
- 2*u1 *u2*u3 *v1*a11*b12 - u1 *u3 *b12 *kap + u1 *u3 *v1 *b12
2 2 2 2 2 2 2 2 2
+ u1 *u3 *v2 *b12 + 2*u1 *u3 *v3*a11*m3 - u1 *v1 *m3
2 2 2 3 2
+ 2*u1*u2 *u3 *v2*a11*b12 - 2*u1*u2*v1*v2*m3 + 2*u1*u3 *v1*v3*b12
2 2 4 2 2
+ 2*u1*u3 *v2*v3*b12*m3 - 2*u1*u3*v1*v3*m3 + u2 *u3 *a11
3 2 2 4 2 2 2 2 2
- 2*u2 *u3 *v1*a11*b12 - u2 *u3 *b12 *kap + u2 *u3 *v1 *b12
2 2 2 2 2 2 2 2 2 3 2
+ u2 *u3 *v2 *b12 + 2*u2 *u3 *v3*a11*m3 - u2 *v2 *m3 + 2*u2*u3 *v2*v3*b12
2 2 4 2 2 4 2 2
- 2*u2*u3 *v1*v3*b12*m3 - 2*u2*u3*v2*v3*m3 - u3 *v1 *b12 - u3 *v2 *b12
which the program can not factorize further.
{HAM,FI} = 0
2 4 4 2 4 4 4
FI= - u1 *u3 *a11 - u1*u3 *v2*b12 - u2 *u3 *a11 + u2*u3 *v1*b12 - u3 *v3*m3
= a product of the elements of: { - u3,
u3,
u3,
u3,
2 2
u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12 + v3*m3}
{HAM,FI} = 0
2 3 3 2 3 3 3
FI=u1 *u3 *a11 + u1*u3 *v2*b12 + u2 *u3 *a11 - u2*u3 *v1*b12 + u3 *v3*m3
= a product of the elements of: {u3,
u3,
u3,
2 2
u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12 + v3*m3}
{HAM,FI} = 0
2 2 2 2 2
FI=u1 *u3*kap + u2 *u3*kap + u3*v1 + u3*v2 + u3*v3
2 2 2 2 2
= a product of the elements of: {u3,u1 *kap + u2 *kap + v1 + v2 + v3 }
{HAM,FI} = 0
2 2 2
FI= - u1 *v1 *a11 - 2*u1*u2*v1*v2*a11 - u1*u3 *v2*b12*kap - 2*u1*u3*v1*v3*a11
2 2 2 2 2
- u2 *v2 *a11 + u2*u3 *v1*b12*kap - 2*u2*u3*v2*v3*a11 + u3 *v1 *a11
2 2 2
+ u3 *v2 *a11 - u3 *v3*kap*m3
which the program can not factorize further.
{HAM,FI} = 0
4 2 2 3 2 2 2 2 2
FI= - u1 *u3 *a11 - 2*u1 *u3 *v2*a11*b12 - 2*u1 *u2 *u3 *a11
2 2 2 2 2 2 2 2
+ 2*u1 *u2*u3 *v1*a11*b12 - u1 *u3 *v2 *b12 - 2*u1 *u3 *v3*a11*m3
2 2 2 2 2 2 2
+ u1 *v1 *m3 - 2*u1*u2 *u3 *v2*a11*b12 + 2*u1*u2*u3 *v1*v2*b12
2 2 2
+ 2*u1*u2*v1*v2*m3 - 2*u1*u3 *v2*v3*b12*m3 + 2*u1*u3*v1*v3*m3
4 2 2 3 2 2 2 2 2
- u2 *u3 *a11 + 2*u2 *u3 *v1*a11*b12 - u2 *u3 *v1 *b12
2 2 2 2 2 2
- 2*u2 *u3 *v3*a11*m3 + u2 *v2 *m3 + 2*u2*u3 *v1*v3*b12*m3
2
+ 2*u2*u3*v2*v3*m3
2
= a product of the elements of: { - u1 *u3*a11 - u1*u3*v2*b12 + u1*v1*m3
2
- u2 *u3*a11 + u2*u3*v1*b12 + u2*v2*m3,
2 2
u1 *u3*a11 + u1*u3*v2*b12 + u1*v1*m3 + u2 *u3*a11 - u2*u3*v1*b12 + u2*v2*m3
+ 2*u3*v3*m3}
{HAM,FI} = 0
2 2 2 2 2 2 2 2
FI=u1 *u3 *kap - u1 *v1 - 2*u1*u2*v1*v2 - 2*u1*u3*v1*v3 + u2 *u3 *kap - u2 *v2
2 2 2 2
- 2*u2*u3*v2*v3 + u3 *v1 + u3 *v2
which the program can not factorize further.
{HAM,FI} = 0
4 2 3 3 2 2 2
FI=u1 *u3*a11 + 2*u1 *u3*v2*a11*b12 - 2*u1 *v1*a11*m3 + 2*u1 *u2 *u3*a11
2 2 2 3 2
- 2*u1 *u2*u3*v1*a11*b12 - 2*u1 *u2*v2*a11*m3 - u1 *u3 *b12 *kap
2 2 2 2 2 2 2
+ u1 *u3*v1 *b12 + u1 *u3*v2 *b12 - 2*u1 *v1*v2*b12*m3
2 2 2
+ 2*u1*u2 *u3*v2*a11*b12 - 2*u1*u2 *v1*a11*m3 + 2*u1*u2*v1 *b12*m3
2 2 2 2 4 2
- 2*u1*u2*v2 *b12*m3 + 2*u1*u3 *v1*v3*b12 - 2*u1*v1*v3*m3 + u2 *u3*a11
3 3 2 3 2 2 2 2
- 2*u2 *u3*v1*a11*b12 - 2*u2 *v2*a11*m3 - u2 *u3 *b12 *kap + u2 *u3*v1 *b12
2 2 2 2 2 2
+ u2 *u3*v2 *b12 + 2*u2 *v1*v2*b12*m3 + 2*u2*u3 *v2*v3*b12
2 3 2 2 3 2 2 2 2
- 2*u2*v2*v3*m3 - u3 *v1 *b12 - u3 *v2 *b12 - u3*v3 *m3
which the program can not factorize further.
{HAM,FI} = 0
4 2 3 3 2 2 2
FI= - u1 *u3*a11 - 2*u1 *u3*v2*a11*b12 + 2*u1 *v1*a11*m3 - 2*u1 *u2 *u3*a11
2 2 2 2 2
+ 2*u1 *u2*u3*v1*a11*b12 + 2*u1 *u2*v2*a11*m3 - u1 *u3*v2 *b12
2 2 2
+ 2*u1 *v1*v2*b12*m3 - 2*u1*u2 *u3*v2*a11*b12 + 2*u1*u2 *v1*a11*m3
2 2 2
+ 2*u1*u2*u3*v1*v2*b12 - 2*u1*u2*v1 *b12*m3 + 2*u1*u2*v2 *b12*m3
2 4 2 3 3
+ 2*u1*v1*v3*m3 - u2 *u3*a11 + 2*u2 *u3*v1*a11*b12 + 2*u2 *v2*a11*m3
2 2 2 2 2 2 2
- u2 *u3*v1 *b12 - 2*u2 *v1*v2*b12*m3 + 2*u2*v2*v3*m3 + u3*v3 *m3
2 2
= a product of the elements of: { - u1 *a11 - u1*v2*b12 - u2 *a11 + u2*v1*b12
- v3*m3,
2 2
u1 *u3*a11 + u1*u3*v2*b12 - 2*u1*v1*m3 + u2 *u3*a11 - u2*u3*v1*b12
- 2*u2*v2*m3 - u3*v3*m3}
{HAM,FI} = 0
3 3 4
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
= a product of the elements of: {u3,
u3,
u3,
u1*v1 + u2*v2 + u3*v3}
{HAM,FI} = 0
2 2 3
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
= a product of the elements of: {u3,
u3,
u1*v1 + u2*v2 + u3*v3}
{HAM,FI} = 0
FI= - u1*u3*v2*b12*kap + u1*v1*kap*m3 + u2*u3*v1*b12*kap + u2*v2*kap*m3
2 2 2
+ u3*v1 *a11 + u3*v2 *a11 + u3*v3 *a11
which the program can not factorize further.
{HAM,FI} = 0
3 2 2 2 2
FI=u1 *u3*v1*a11 + u1 *u2*u3*v2*a11 + u1 *u3 *v3*a11 + u1 *u3*v1*v2*b12
2 2 2 2 2
- u1 *v1 *m3 + u1*u2 *u3*v1*a11 - u1*u2*u3*v1 *b12 + u1*u2*u3*v2 *b12
2 3
- 2*u1*u2*v1*v2*m3 + u1*u3 *v2*v3*b12 - u1*u3*v1*v3*m3 + u2 *u3*v2*a11
2 2 2 2 2 2
+ u2 *u3 *v3*a11 - u2 *u3*v1*v2*b12 - u2 *v2 *m3 - u2*u3 *v1*v3*b12
- u2*u3*v2*v3*m3
= a product of the elements of: {u1*v1 + u2*v2 + u3*v3,
2 2
u1 *u3*a11 + u1*u3*v2*b12 - u1*v1*m3 + u2 *u3*a11 - u2*u3*v1*b12 - u2*v2*m3}
{HAM,FI} = 0
2 3 2 3 3 2 3 2 3 2
FI=u1 *u3 *kap + u2 *u3 *kap + u3 *v1 + u3 *v2 + u3 *v3
= a product of the elements of: {u3,
u3,
u3,
2 2 2 2 2
u1 *kap + u2 *kap + v1 + v2 + v3 }
{HAM,FI} = 0
2 4 2 4 4 2 4 2 4 2
FI=u1 *u3 *kap + u2 *u3 *kap + u3 *v1 + u3 *v2 + u3 *v3
= a product of the elements of: {u3,
u3,
u3,
u3,
2 2 2 2 2
u1 *kap + u2 *kap + v1 + v2 + v3 }
{HAM,FI} = 0
4 4 5
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
= a product of the elements of: {u3,
u3,
u3,
u3,
u1*v1 + u2*v2 + u3*v3}
{HAM,FI} = 0
2
FI=u1*u3*v1 + u2*u3*v2 + u3 *v3
= a product of the elements of: {u3,u1*v1 + u2*v2 + u3*v3}
{HAM,FI} = 0
FI=u3
which the program can not factorize further.
{HAM,FI} = 0
2
FI=u3
= a product of the elements of: {u3,u3}
{HAM,FI} = 0
3
FI=u3
= a product of the elements of: {u3,u3,u3}
{HAM,FI} = 0
4
FI=u3
= a product of the elements of: {u3,u3,u3,u3}
{HAM,FI} = 0
5
FI=u3
= a product of the elements of: {u3,
u3,
u3,
u3,
u3}
{HAM,FI} = 0
6
FI=u3
= a product of the elements of: {u3,
u3,
u3,
u3,
u3,
u3}
{HAM,FI} = 0
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*u3*n3
+ 2*v3*m3)/2$
FI=u1**4*u3*kap**2 + 2*u1**2*u2**2*u3*kap**2 + 2*u1**2*u3*v1**2*kap + 2*u1**2*u3
*v2**2*kap + 2*u1**2*u3*v3**2*kap + u2**4*u3*kap**2 + 2*u2**2*u3*v1**2*kap + 2*
u2**2*u3*v2**2*kap + 2*u2**2*u3*v3**2*kap + u3*v1**4 + 2*u3*v1**2*v2**2 + 2*u3*
v1**2*v3**2 + u3*v2**4 + 2*u3*v2**2*v3**2 + u3*v3**4$
FI=u1**4*u3*a11*kap + u1**3*u3*v2*b12*kap - u1**3*v1*kap*m3 + 2*u1**2*u2**2*u3*
a11*kap - u1**2*u2*u3*v1*b12*kap - u1**2*u2*v2*kap*m3 + u1**2*u3*v1**2*a11 + u1
**2*u3*v2**2*a11 + u1**2*u3*v3**2*a11 + u1*u2**2*u3*v2*b12*kap - u1*u2**2*v1*kap
*m3 + u1*u3*v1**2*v2*b12 + u1*u3*v2**3*b12 + u1*u3*v2*v3**2*b12 - u1*v1**3*m3 -
u1*v1*v2**2*m3 - u1*v1*v3**2*m3 + u2**4*u3*a11*kap - u2**3*u3*v1*b12*kap - u2**3
*v2*kap*m3 + u2**2*u3*v1**2*a11 + u2**2*u3*v2**2*a11 + u2**2*u3*v3**2*a11 - u2*
u3*v1**3*b12 - u2*u3*v1*v2**2*b12 - u2*u3*v1*v3**2*b12 - u2*v1**2*v2*m3 - u2*v2
**3*m3 - u2*v2*v3**2*m3$
FI=u1**3*u3*v1*kap + u1**2*u2*u3*v2*kap + u1**2*u3**2*v3*kap + u1*u2**2*u3*v1*
kap + u1*u3*v1**3 + u1*u3*v1*v2**2 + u1*u3*v1*v3**2 + u2**3*u3*v2*kap + u2**2*u3
**2*v3*kap + u2*u3*v1**2*v2 + u2*u3*v2**3 + u2*u3*v2*v3**2 + u3**2*v1**2*v3 + u3
**2*v2**2*v3 + u3**2*v3**3$
FI=u1**4*u3**2*a11**2 + 2*u1**3*u3**2*v2*a11*b12 + 2*u1**2*u2**2*u3**2*a11**2 -
2*u1**2*u2*u3**2*v1*a11*b12 - u1**2*u3**4*b12**2*kap + u1**2*u3**2*v1**2*b12**2
+ u1**2*u3**2*v2**2*b12**2 + 2*u1**2*u3**2*v3*a11*m3 - u1**2*v1**2*m3**2 + 2*u1*
u2**2*u3**2*v2*a11*b12 - 2*u1*u2*v1*v2*m3**2 + 2*u1*u3**3*v1*v3*b12**2 + 2*u1*u3
**2*v2*v3*b12*m3 - 2*u1*u3*v1*v3*m3**2 + u2**4*u3**2*a11**2 - 2*u2**3*u3**2*v1*
a11*b12 - u2**2*u3**4*b12**2*kap + u2**2*u3**2*v1**2*b12**2 + u2**2*u3**2*v2**2*
b12**2 + 2*u2**2*u3**2*v3*a11*m3 - u2**2*v2**2*m3**2 + 2*u2*u3**3*v2*v3*b12**2 -
2*u2*u3**2*v1*v3*b12*m3 - 2*u2*u3*v2*v3*m3**2 - u3**4*v1**2*b12**2 - u3**4*v2**
2*b12**2$
FI= - u1**2*u3**4*a11 - u1*u3**4*v2*b12 - u2**2*u3**4*a11 + u2*u3**4*v1*b12 - u3
**4*v3*m3$
FI=u1**2*u3**3*a11 + u1*u3**3*v2*b12 + u2**2*u3**3*a11 - u2*u3**3*v1*b12 + u3**3
*v3*m3$
FI=u1**2*u3*kap + u2**2*u3*kap + u3*v1**2 + u3*v2**2 + u3*v3**2$
FI= - u1**2*v1**2*a11 - 2*u1*u2*v1*v2*a11 - u1*u3**2*v2*b12*kap - 2*u1*u3*v1*v3*
a11 - u2**2*v2**2*a11 + u2*u3**2*v1*b12*kap - 2*u2*u3*v2*v3*a11 + u3**2*v1**2*
a11 + u3**2*v2**2*a11 - u3**2*v3*kap*m3$
FI= - u1**4*u3**2*a11**2 - 2*u1**3*u3**2*v2*a11*b12 - 2*u1**2*u2**2*u3**2*a11**2
+ 2*u1**2*u2*u3**2*v1*a11*b12 - u1**2*u3**2*v2**2*b12**2 - 2*u1**2*u3**2*v3*a11
*m3 + u1**2*v1**2*m3**2 - 2*u1*u2**2*u3**2*v2*a11*b12 + 2*u1*u2*u3**2*v1*v2*b12
**2 + 2*u1*u2*v1*v2*m3**2 - 2*u1*u3**2*v2*v3*b12*m3 + 2*u1*u3*v1*v3*m3**2 - u2**
4*u3**2*a11**2 + 2*u2**3*u3**2*v1*a11*b12 - u2**2*u3**2*v1**2*b12**2 - 2*u2**2*
u3**2*v3*a11*m3 + u2**2*v2**2*m3**2 + 2*u2*u3**2*v1*v3*b12*m3 + 2*u2*u3*v2*v3*m3
**2$
FI=u1**2*u3**2*kap - u1**2*v1**2 - 2*u1*u2*v1*v2 - 2*u1*u3*v1*v3 + u2**2*u3**2*
kap - u2**2*v2**2 - 2*u2*u3*v2*v3 + u3**2*v1**2 + u3**2*v2**2$
FI=u1**4*u3*a11**2 + 2*u1**3*u3*v2*a11*b12 - 2*u1**3*v1*a11*m3 + 2*u1**2*u2**2*
u3*a11**2 - 2*u1**2*u2*u3*v1*a11*b12 - 2*u1**2*u2*v2*a11*m3 - u1**2*u3**3*b12**2
*kap + u1**2*u3*v1**2*b12**2 + u1**2*u3*v2**2*b12**2 - 2*u1**2*v1*v2*b12*m3 + 2*
u1*u2**2*u3*v2*a11*b12 - 2*u1*u2**2*v1*a11*m3 + 2*u1*u2*v1**2*b12*m3 - 2*u1*u2*
v2**2*b12*m3 + 2*u1*u3**2*v1*v3*b12**2 - 2*u1*v1*v3*m3**2 + u2**4*u3*a11**2 - 2*
u2**3*u3*v1*a11*b12 - 2*u2**3*v2*a11*m3 - u2**2*u3**3*b12**2*kap + u2**2*u3*v1**
2*b12**2 + u2**2*u3*v2**2*b12**2 + 2*u2**2*v1*v2*b12*m3 + 2*u2*u3**2*v2*v3*b12**
2 - 2*u2*v2*v3*m3**2 - u3**3*v1**2*b12**2 - u3**3*v2**2*b12**2 - u3*v3**2*m3**2$
FI= - u1**4*u3*a11**2 - 2*u1**3*u3*v2*a11*b12 + 2*u1**3*v1*a11*m3 - 2*u1**2*u2**
2*u3*a11**2 + 2*u1**2*u2*u3*v1*a11*b12 + 2*u1**2*u2*v2*a11*m3 - u1**2*u3*v2**2*
b12**2 + 2*u1**2*v1*v2*b12*m3 - 2*u1*u2**2*u3*v2*a11*b12 + 2*u1*u2**2*v1*a11*m3
+ 2*u1*u2*u3*v1*v2*b12**2 - 2*u1*u2*v1**2*b12*m3 + 2*u1*u2*v2**2*b12*m3 + 2*u1*
v1*v3*m3**2 - u2**4*u3*a11**2 + 2*u2**3*u3*v1*a11*b12 + 2*u2**3*v2*a11*m3 - u2**
2*u3*v1**2*b12**2 - 2*u2**2*v1*v2*b12*m3 + 2*u2*v2*v3*m3**2 + u3*v3**2*m3**2$
FI=u1*u3**3*v1 + u2*u3**3*v2 + u3**4*v3$
FI=u1*u3**2*v1 + u2*u3**2*v2 + u3**3*v3$
FI= - u1*u3*v2*b12*kap + u1*v1*kap*m3 + u2*u3*v1*b12*kap + u2*v2*kap*m3 + u3*v1
**2*a11 + u3*v2**2*a11 + u3*v3**2*a11$
FI=u1**3*u3*v1*a11 + u1**2*u2*u3*v2*a11 + u1**2*u3**2*v3*a11 + u1**2*u3*v1*v2*
b12 - u1**2*v1**2*m3 + u1*u2**2*u3*v1*a11 - u1*u2*u3*v1**2*b12 + u1*u2*u3*v2**2*
b12 - 2*u1*u2*v1*v2*m3 + u1*u3**2*v2*v3*b12 - u1*u3*v1*v3*m3 + u2**3*u3*v2*a11 +
u2**2*u3**2*v3*a11 - u2**2*u3*v1*v2*b12 - u2**2*v2**2*m3 - u2*u3**2*v1*v3*b12 -
u2*u3*v2*v3*m3$
FI=u1**2*u3**3*kap + u2**2*u3**3*kap + u3**3*v1**2 + u3**3*v2**2 + u3**3*v3**2$
FI=u1**2*u3**4*kap + u2**2*u3**4*kap + u3**4*v1**2 + u3**4*v2**2 + u3**4*v3**2$
FI=u1*u3**4*v1 + u2*u3**4*v2 + u3**5*v3$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI=u3$
FI=u3**2$
FI=u3**3$
FI=u3**4$
FI=u3**5$
FI=u3**6$