Solution 5 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2 2
0=a11 + 16*a13 + b12 *kap
Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r13=0
r14=0
r15=0
r20=0
r21=0
r22=0
r23=0
r24=0
r27=0
r28=0
1
---*n2*r341
2
r29=-------------
b12
r210=0
r211=0
r212=0
r213=0
1
---*n2*r341
2
r214=-------------
b12
r215=0
r217=0
r218=0
r219=0
1
---*n2*r341
2
r220=-------------
b12
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r310=0
r311=0
r312=0
r313=0
r314=0
r315=0
r316=0
r317=0
r318= - r341
r319=0
r320=0
r321=0
r322=0
r323=0
r324=0
r325=0
r326=0
r327=0
r328=0
a11*r341
r329=----------
b12
r330=0
r331=0
r332= - r341
r333=0
a11*r341
r334=----------
b12
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
r342=0
r343=0
r344=0
r345=0
r346=r341
r347=0
r348=0
r349=0
r350=0
r351=0
r352=0
r353=0
a11*r341
r354=----------
b12
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
r427=0
r428=0
r429=0
1
---*b12*r341
2
r430=--------------
n2
r431=0
2*a13*r341
r432=------------
n2
r433=0
2 2
- a11 *r341 - b12 *kap*r341
r434=------------------------------
2*b12*n2
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
r445=0
r446=0
r447=0
r448=0
r449=0
r450=0
- 2*a13*r341
r451=---------------
n2
r452=0
- a11*r341
r453=-------------
n2
r454=0
r455=0
r456=0
r457=0
r458=0
r459=0
1
---*b12*r341
2
r460=--------------
n2
r461=0
r462=0
r463=0
2 2
a11 *r341 + 16*a13 *r341
r464=--------------------------
2*b12*n2
r465=0
r466=0
- a11*r341
r467=-------------
n2
r468=0
2
a11 *r341
r469=-----------
2*b12*n2
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r479=0
r480=0
r482=0
- b12*r341
r483=-------------
n2
r484=0
r485=0
r486=0
r487=0
r488=0
2*a11*a13*r341
r489=----------------
b12*n2
r490=0
r491=0
r492=0
r493=0
- b12*r341
r494=-------------
n2
r495=0
a11*r341
r496=----------
n2
r497=0
- 2*a13*r341
r498=---------------
n2
r499=0
r4100=0
a11*r341
r4101=----------
n2
r4102=0
2*a11*a13*r341
r4103=----------------
b12*n2
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
1
- ---*b12*r341
2
r4110=-----------------
n2
r4111=0
2*a13*r341
r4112=------------
n2
r4113=0
2 2
- a11 *r341 - b12 *kap*r341
r4114=------------------------------
2*b12*n2
r4115=0
r4116=0
r4117=0
r4118=0
2 2 2
2*a11 *r341 + 16*a13 *r341 + b12 *kap*r341
r4119=--------------------------------------------
2*b12*n2
r4120=0
r4121=0
r4122=0
2*a11*a13*r341
r4123=----------------
b12*n2
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=0
r522=0
r523=0
r524=0
r525=0
r526=0
r527=0
r528=0
r529=0
r530=0
r531=0
r532=0
r533=0
r534=0
r535=0
r536=0
r537=0
r538=0
r539=0
r540=0
r541=0
r542=0
r543=0
r544=0
r545=0
r546=0
r547=0
r548=0
r549=0
- 2*a13*b12*r341
r550=-------------------
2
n2
r551=0
r552=0
r553=0
2 2 2
2*a11 *r341 + 8*a13 *r341 + 2*b12 *kap*r341
r554=---------------------------------------------
2
3*n2
r555=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=0
r573=0
r574=0
r575=0
r576=0
r577=0
r578=0
r579=0
r580=0
r581=0
r582=0
r583=0
2*a13*b12*r341
r584=----------------
2
n2
r585=0
r586=0
r587=0
2*a11*a13*r341
r588=----------------
2
n2
r589=0
3 2 2
- 5*a11 *r341 - 32*a11*a13 *r341 - 5*a11*b12 *kap*r341
r590=---------------------------------------------------------
2
6*b12*n2
r591=0
r592=0
r593=0
r594=0
r595=0
r596=0
r597=0
r598=0
r599=0
r5100=0
r5101=0
r5102=0
r5103=0
r5104=0
r5105=0
r5106=0
- 2*a11*a13*r341
r5107=-------------------
2
n2
r5108=0
2
- 8*a13 *r341
r5109=----------------
2
n2
r5110=0
r5111=0
r5112=0
r5113=0
r5114=0
r5115=0
r5116=0
r5117=0
r5118=0
r5119=0
2
8*a11*a13 *r341
r5120=-----------------
2
b12*n2
r5121=0
r5122=0
r5123=0
r5124=0
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
r5142=0
r5143=0
r5144=0
r5145=0
r5146=0
r5147=0
r5148=0
r5149=0
r5150=0
r5151=0
2*a13*b12*r341
r5152=----------------
2
n2
r5153=0
r5154=0
r5155=0
r5156=0
2 2 2
- 2*a11 *r341 - 8*a13 *r341 - 2*b12 *kap*r341
r5157=------------------------------------------------
2
3*n2
r5158=0
- 2*a11*a13*r341
r5159=-------------------
2
n2
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
2*a13*b12*r341
r5173=----------------
2
n2
r5174=0
r5175=0
2*a13*b12*r341
r5176=----------------
2
n2
r5177=0
2
8*a13 *r341
r5178=-------------
2
n2
r5179=0
2 3 2
4*a11 *a13*r341 + 32*a13 *r341 + 2*a13*b12 *kap*r341
r5180=------------------------------------------------------
2
b12*n2
r5181=0
r5182=0
r5183=0
r5184=0
r5185=0
r5186=0
r5187=0
r5188=0
- 4*a11*a13*r341
r5189=-------------------
2
n2
r5190=0
r5191=0
r5192=0
r5193=0
2
2*a11 *a13*r341
r5194=-----------------
2
b12*n2
r5195=0
r5196=0
r5197=0
r5198=0
r5199=0
r5200=0
r5201=0
r5202=0
r5203=0
r5204=0
r5205=0
r5206=0
r5207=0
r5208=0
r5209=0
r5210=0
r5211=0
2*a11*a13*r341
r5212=----------------
2
n2
r5213=0
r5214=0
r5215=0
r5216=0
r5217=0
r5218=0
r5219=0
r5220=0
r5221=0
r5222=0
4*a11*a13*r341
r5223=----------------
2
n2
r5224=0
3 2 2
- 2*a11 *r341 - 8*a11*a13 *r341 - 2*a11*b12 *kap*r341
r5225=--------------------------------------------------------
2
3*b12*n2
r5226=0
r5227=0
r5228=0
r5229=0
r5230=0
r5231=0
r5232=0
r5233=0
r5234=0
r5235=0
r5236=0
r5237=0
r5238=0
r5239=0
r5240=0
r5241=0
r5242=0
r5243=0
2 3 2
4*a11 *a13*r341 + 32*a13 *r341 + 2*a13*b12 *kap*r341
r5244=------------------------------------------------------
2
b12*n2
r5245=0
r5246=0
r5247=0
r5248=0
r5249=0
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
1 2 2 2 1 3
- ---*a11 *b12*r341 - ---*a13 *b12*r341 - ---*b12 *kap*r341
6 3 6
r674=--------------------------------------------------------------
3
n2
r675=0
2 2 3
- a11 *b12*r341 - 4*a13 *b12*r341 - b12 *kap*r341
r676=----------------------------------------------------
3
6*n2
r677=0
r678=0
2 2 3
- a11 *b12*r341 - 16*a13 *b12*r341 - b12 *kap*r341
r679=-----------------------------------------------------
3
6*n2
r680=0
2 3 2
- 4*a11 *a13*r341 - 16*a13 *r341 - 4*a13*b12 *kap*r341
r681=---------------------------------------------------------
3
3*n2
r682=0
4 2 2 2 2 4
r683=(3*a11 *r341 - 40*a11 *a13 *r341 + 5*a11 *b12 *kap*r341 - 256*a13 *r341
2 2 4 2 3
- 56*a13 *b12 *kap*r341 + 2*b12 *kap *r341)/(36*b12*n2 )
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=0
r6132=0
r6133=0
r6134=0
r6135=0
2 3 2
4*a11 *a13*r341 + 16*a13 *r341 + 4*a13*b12 *kap*r341
r6136=------------------------------------------------------
3
3*n2
r6137=0
3 2 2
a11 *r341 + 16*a11*a13 *r341 + a11*b12 *kap*r341
r6138=--------------------------------------------------
3
6*n2
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
r6167=0
r6168=0
r6169=0
r6170=0
r6171=0
r6172=0
r6173=0
4 2 2 2 2 4
r6174=( - a11 *r341 - 36*a11 *a13 *r341 - 2*a11 *b12 *kap*r341 - 128*a13 *r341
2 2 4 2 3
- 36*a13 *b12 *kap*r341 - b12 *kap *r341)/(6*b12*n2 )
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
r6193=0
r6194=0
r6195=0
r6196=0
r6197=0
r6198=0
r6199=0
r6200=0
r6201=0
r6202=0
r6203=0
r6204=0
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
2
4*a13 *b12*r341
r6259=-----------------
3
n2
r6260=0
r6261=0
r6262=0
3 2 2
- a11 *r341 + 8*a11*a13 *r341 - a11*b12 *kap*r341
r6263=----------------------------------------------------
3
6*n2
r6264=0
3 3 2
- 5*a11 *a13*r341 - 32*a11*a13 *r341 - 5*a11*a13*b12 *kap*r341
r6265=-----------------------------------------------------------------
3
3*b12*n2
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
r6295=0
r6296=0
2
- 4*a11*a13 *r341
r6297=--------------------
3
n2
r6298=0
3
- 16*a13 *r341
r6299=-----------------
3
n2
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
r6318=0
r6319=0
3 3 2
- 4*a11 *a13*r341 - 16*a11*a13 *r341 - 4*a11*a13*b12 *kap*r341
r6320=-----------------------------------------------------------------
3
3*b12*n2
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
2
2*a13 *b12*r341
r6363=-----------------
3
n2
r6364=0
r6365=0
2
2*a13 *b12*r341
r6366=-----------------
3
n2
r6367=0
3
16*a13 *r341
r6368=--------------
3
n2
r6369=0
4 2 2 2 2 4
r6370=( - a11 *r341 - 12*a11 *a13 *r341 - 2*a11 *b12 *kap*r341 + 64*a13 *r341
2 2 4 2 3
- 24*a13 *b12 *kap*r341 - b12 *kap *r341)/(6*b12*n2 )
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
2
- 4*a11*a13 *r341
r6389=--------------------
3
n2
r6390=0
r6391=0
r6392=0
r6393=0
r6394=0
r6395=0
r6396=0
r6397=0
r6398=0
r6399=0
4 2 2
- 32*a13 *r341 - 2*a13 *b12 *kap*r341
r6400=----------------------------------------
3
b12*n2
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
2
4*a11*a13 *r341
r6423=-----------------
3
n2
r6424=0
3
16*a11*a13 *r341
r6425=------------------
3
b12*n2
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
2 2
2*a11 *a13 *r341
r6450=------------------
3
b12*n2
r6451=0
r6452=0
r6453=0
r6454=0
r6455=0
r6456=0
r6457=0
r6458=0
r6459=0
r6460=0
r6461=0
m3=0
m2=0
m1=0
n3=0
n1=0
1
a33=---*a11
2
a23=0
a22=a11
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:
r341, a13, a11, n2, 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,
n2,
a13,
2 5
{1531586804182367708160*a11 *b12 *kap*r341
7 2
+ 1531586804182367708160*b12 *kap *r341,
2
2953352425009835056568909606257717664971955421101938971901824768000*a11 *a13
4
*b12 *kap*r341 +
6
2953352425009835056568909606257717664971955421101938971901824768000*a13*b12
2
*kap *r341,
1639946221896459520336475536700652416798873586303922015743567896225388167136\
4 4
49586585124807090708897557537606499868691005440000000*a11 *b12 *kap*r341 + 3\
2798924437929190406729510734013048335977471726078440314871357924507763342729\
2 6 2
9173170249614181417795115075212999737382010880000000*a11 *b12 *kap *r341 + 1\
6399462218964595203364755367006524167988735863039220157435678962253881671364\
8 3
9586585124807090708897557537606499868691005440000000*b12 *kap *r341,
4891888215276909644643793429588008993438999851732442956569423265784396986677\
4 4
59646043660925407231127098988354536079360000000*a11 *b12 *kap*r341 + 9783776\
4305538192892875868591760179868779997034648859131388465315687939733551929208\
2 6 2
7321850814462254197976709072158720000000*a11 *b12 *kap *r341 + 4891888215276\
9096446437934295880089934389998517324429565694232657843969866775964604366092\
8 3
5407231127098988354536079360000000*b12 *kap *r341,
2 5 7 2
13342560*a11 *b12 *kap*r341 + 13342560*b12 *kap *r341,
3 5
2953405840191522249422985254934695640067119593176170294480000000*a11 *b12 *kap
*r341 + 2953405840191522249422985254934695640067119593176170294480000000*a11
7 2
*b12 *kap *r341,
1384165116583263976250475147578077996132342725897448429276541484720211623114\
3 7 2
5298850473380001959808866939272745161436160000*a11 *a13*b12 *kap *r341 + 138\
4165116583263976250475147578077996132342725897448429276541484720211623114529\
9 3
8850473380001959808866939272745161436160000*a11*a13*b12 *kap *r341,
3 5
7614850695089301013934500654537800000*a11 *b12 *kap*r341
7 2
+ 7614850695089301013934500654537800000*a11*b12 *kap *r341,
2 4
41273842196968419909024000*a11 *a13*b12 *kap*r341
6 2
+ 41273842196968419909024000*a13*b12 *kap *r341,
3 5
13498424758616111660037634690136905359764464282605643392000*a11 *a13*b12 *kap
*r341 + 13498424758616111660037634690136905359764464282605643392000*a11*a13
7 2
*b12 *kap *r341,
2
1529940775734028835300942822951152232838288541003426271666997916800000*a11
6 2
*b12 *kap *r341 +
8
1529940775734028835300942822951152232838288541003426271666997916800000*b12
3
*kap *r341,
2 5 7 2
40027680*a11 *b12 *kap*r341 + 40027680*b12 *kap *r341,
2 4
2187513636439326255178272000*a11 *a13*b12 *kap*r341
6 2
+ 2187513636439326255178272000*a13*b12 *kap *r341,
1151032521241625798739716101079531527867999965113515989781040768419858114512\
2 6 2
37563774979041272289676964467848126136320000000*a11 *b12 *kap *r341 + 115103\
2521241625798739716101079531527867999965113515989781040768419858114512375637\
8 3
74979041272289676964467848126136320000000*b12 *kap *r341,
3 5
4070932653465927527768126619149554200000*a11 *b12 *kap*r341
7 2
+ 4070932653465927527768126619149554200000*a11*b12 *kap *r341,
159489115383841415082980842265477683024830117652177100903209929989328000000
4 4
*a11 *b12 *kap*r341 +
159489115383841415082980842265477683024830117652177100903209929989328000000
2 6 2
*a11 *b12 *kap *r341,
3 5
407051843905998585699868732488318099000000*a11 *b12 *kap*r341
7 2
+ 407051843905998585699868732488318099000000*a11*b12 *kap *r341,
3
1060104109807419945140442595406362312270343844860837085435274924416000*a11
5
*a13*b12 *kap*r341 +
1060104109807419945140442595406362312270343844860837085435274924416000*a11*a13
7 2
*b12 *kap *r341,
4 4
1554707596879083361994064710226161118750169391070758400000*a11 *b12 *kap*r341
2 6 2
+ 1554707596879083361994064710226161118750169391070758400000*a11 *b12 *kap
*r341}}
Relevance for the application:
Modulo the following equation:
2 2 2
0=a11 + 16*a13 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2
HAM=(2*u1 *a11 + 4*u1*u3*a13 + 2*u1*v2*b12 + 2*u2 *a11 - 2*u2*v1*b12 + 2*u2*n2
2
+ u3 *a11)/2
has apart from the Hamiltonian and Casimirs only the following first integral:
4 2 2 2
FI=72*u1 *u3 *a11 *a13
3 2 3 2
+ u1 *u2*u3*(144*a11 *a13*n2 + 1152*a13 *n2 + 72*a13*b12 *kap*n2)
3 3 3 3 2 2 3 2
+ 576*u1 *u3 *a11*a13 + 144*u1 *u3 *v2*a11*a13 *b12 + 72*u1 *u3*a11*a13*n2
2 2 2 4 2 2
+ u1 *u2 *u3 *( - 1152*a13 - 72*a13 *b12 *kap)
2 2 2 2 2 2 2 2
+ u1 *u2 *(36*a11 *n2 + 288*a13 *n2 + 18*b12 *kap*n2 )
2 2 2
- 144*u1 *u2*u3 *v1*a11*a13 *b12
2 2 3 2 2
+ u1 *u2*u3 *( - 24*a11 *n2 - 96*a11*a13 *n2 - 24*a11*b12 *kap*n2)
2 2 3 2 4 4
+ 144*u1 *u2*u3*v2*a11*a13*b12*n2 + 36*u1 *u2*a11*n2 + u1 *u3 *( - 6*a11
2 2 2 2 4 2 2
- 72*a11 *a13 - 12*a11 *b12 *kap + 384*a13 - 144*a13 *b12 *kap
4 2 2 3 3 2 2 2 2 2
- 6*b12 *kap ) + 576*u1 *u3 *v2*a13 *b12 + 72*u1 *u3 *v1 *a13 *b12
2 2 2 2 2 2 2
+ 72*u1 *u3 *v2 *a13 *b12 + 72*u1 *u3 *v3*a11*a13*b12*n2
2 2 2 2 2 2 2 2
+ u1 *u3 *( - 18*a11 *n2 - 18*b12 *kap*n2 ) + 72*u1 *u3*v2*a13*b12*n2
2 2 2 2 2 4 3 2
- 18*u1 *v1 *b12 *n2 + 18*u1 *n2 + 72*u1*u2 *u3*a11 *a13*n2
2 3 3 3 2
+ u1*u2 *u3 *( - 48*a11 *a13 - 192*a11*a13 - 48*a11*a13*b12 *kap)
2 2 2
- 144*u1*u2 *u3*v1*a11*a13*b12*n2 + 72*u1*u2 *u3*a11*a13*n2
2 2 3 3
+ 36*u1*u2 *v2*a11*b12*n2 - 576*u1*u2*u3 *v1*a13 *b12
3 2
- 144*u1*u2*u3 *v3*a11*a13 *b12
3 2 3 2
+ u1*u2*u3 *(144*a11 *a13*n2 + 1152*a13 *n2 + 72*a13*b12 *kap*n2)
2 2 2 2
+ 288*u1*u2*u3 *v2*a13 *b12*n2 + 72*u1*u2*u3*v1 *a13*b12 *n2
2 2 2
- 72*u1*u2*u3*v1*a13*b12*n2 + 72*u1*u2*u3*v2 *a13*b12 *n2
2 2 2 3
+ 36*u1*u2*u3*v3*a11*b12*n2 - 36*u1*u2*v1*v2*b12 *n2 + 36*u1*u2*v2*b12*n2
5 3 3 2
+ u1*u3 *( - 60*a11 *a13 - 384*a11*a13 - 60*a11*a13*b12 *kap)
4 3 2 3
+ u1*u3 *v2*( - 6*a11 *b12 + 48*a11*a13 *b12 - 6*a11*b12 *kap)
3 2 2 3
+ 144*u1*u3 *v1*v3*a13 *b12 - 72*u1*u3 *v1*a11*a13*b12*n2
3 2 2 3
+ u1*u3 *v3*( - 24*a11 *b12*n2 - 96*a13 *b12*n2 - 24*b12 *kap*n2)
3 2 2 2
+ 72*u1*u3 *a11*a13*n2 + 72*u1*u3 *v2*v3*a13*b12 *n2
2 2 3 4 2 2
- 36*u1*u3*v1*v3*b12 *n2 + 36*u1*u3*v3*b12*n2 + 18*u2 *a11 *n2
3 2 2 3 2 3 3 2 4
+ 288*u2 *u3 *a11*a13 *n2 - 36*u2 *v1*a11*b12*n2 + 36*u2 *a11*n2 + u2 *u3
4 2 2 2 2 4 2 2
*( - 6*a11 - 216*a11 *a13 - 12*a11 *b12 *kap - 768*a13 - 216*a13 *b12 *kap
4 2 2 2 2 2 2
- 6*b12 *kap ) - 288*u2 *u3 *v1*a13 *b12*n2 - 72*u2 *u3 *v3*a11*a13*b12*n2
2 2 2 2 2 2 2 2 2 2
+ u2 *u3 *(18*a11 *n2 + 288*a13 *n2 ) + 18*u2 *v1 *b12 *n2
2 3 2 4
- 36*u2 *v1*b12*n2 + 18*u2 *n2
4 3 2 3
+ u2*u3 *v1*(6*a11 *b12 + 96*a11*a13 *b12 + 6*a11*b12 *kap)
4 2 3 3
+ u2*u3 *v3*(48*a11 *a13*b12 + 192*a13 *b12 + 48*a13*b12 *kap)
4 3 2 2
+ u2*u3 *( - 30*a11 *n2 - 192*a11*a13 *n2 - 30*a11*b12 *kap*n2)
3 2 2
+ 72*u2*u3 *v2*a11*a13*b12*n2 + 72*u2*u3 *v1*v3*a13*b12 *n2
2 2 2 2 2 3
- 36*u2*u3 *v1*a11*b12*n2 - 72*u2*u3 *v3*a13*b12*n2 + 36*u2*u3 *a11*n2 +
6 4 2 2 2 2 4 2 2
u3 *(3*a11 - 40*a11 *a13 + 5*a11 *b12 *kap - 256*a13 - 56*a13 *b12 *kap
4 2
+ 2*b12 *kap )
5 2 3 3
+ u3 *v2*( - 48*a11 *a13*b12 - 192*a13 *b12 - 48*a13*b12 *kap)
4 2 2 2 2 2 4
+ u3 *v1 *( - 6*a11 *b12 - 96*a13 *b12 - 6*b12 *kap)
4 2 2 3
+ u3 *v1*(24*a11 *b12*n2 + 96*a13 *b12*n2 + 24*b12 *kap*n2)
4 2 2 2 2 2 4
+ u3 *v2 *( - 6*a11 *b12 - 24*a13 *b12 - 6*b12 *kap)
4 2 2 2 2 2 4
+ u3 *v3 *( - 6*a11 *b12 - 24*a13 *b12 - 6*b12 *kap)
4 2 2 2 2 3 2
+ u3 *( - 18*a11 *n2 - 18*b12 *kap*n2 ) - 72*u3 *v1*v2*a13*b12 *n2
3 2 2 2 2 2 2 3
+ 72*u3 *v2*a13*b12*n2 + 18*u3 *v1 *b12 *n2 - 36*u3 *v1*b12*n2
2 4
+ 18*u3 *n2
which the program can not factorize further.
{HAM,FI} = 0
And again in machine readable form:
HAM=(2*u1**2*a11 + 4*u1*u3*a13 + 2*u1*v2*b12 + 2*u2**2*a11 - 2*u2*v1*b12 + 2*u2*
n2 + u3**2*a11)/2$
FI=72*u1**4*u3**2*a11**2*a13**2 + u1**3*u2*u3*(144*a11**2*a13*n2 + 1152*a13**3*
n2 + 72*a13*b12**2*kap*n2) + 576*u1**3*u3**3*a11*a13**3 + 144*u1**3*u3**2*v2*a11
*a13**2*b12 + 72*u1**3*u3*a11*a13*n2**2 + u1**2*u2**2*u3**2*( - 1152*a13**4 - 72
*a13**2*b12**2*kap) + u1**2*u2**2*(36*a11**2*n2**2 + 288*a13**2*n2**2 + 18*b12**
2*kap*n2**2) - 144*u1**2*u2*u3**2*v1*a11*a13**2*b12 + u1**2*u2*u3**2*( - 24*a11
**3*n2 - 96*a11*a13**2*n2 - 24*a11*b12**2*kap*n2) + 144*u1**2*u2*u3*v2*a11*a13*
b12*n2 + 36*u1**2*u2*a11*n2**3 + u1**2*u3**4*( - 6*a11**4 - 72*a11**2*a13**2 -
12*a11**2*b12**2*kap + 384*a13**4 - 144*a13**2*b12**2*kap - 6*b12**4*kap**2) +
576*u1**2*u3**3*v2*a13**3*b12 + 72*u1**2*u3**2*v1**2*a13**2*b12**2 + 72*u1**2*u3
**2*v2**2*a13**2*b12**2 + 72*u1**2*u3**2*v3*a11*a13*b12*n2 + u1**2*u3**2*( - 18*
a11**2*n2**2 - 18*b12**2*kap*n2**2) + 72*u1**2*u3*v2*a13*b12*n2**2 - 18*u1**2*v1
**2*b12**2*n2**2 + 18*u1**2*n2**4 + 72*u1*u2**3*u3*a11**2*a13*n2 + u1*u2**2*u3**
3*( - 48*a11**3*a13 - 192*a11*a13**3 - 48*a11*a13*b12**2*kap) - 144*u1*u2**2*u3*
v1*a11*a13*b12*n2 + 72*u1*u2**2*u3*a11*a13*n2**2 + 36*u1*u2**2*v2*a11*b12*n2**2
- 576*u1*u2*u3**3*v1*a13**3*b12 - 144*u1*u2*u3**3*v3*a11*a13**2*b12 + u1*u2*u3**
3*(144*a11**2*a13*n2 + 1152*a13**3*n2 + 72*a13*b12**2*kap*n2) + 288*u1*u2*u3**2*
v2*a13**2*b12*n2 + 72*u1*u2*u3*v1**2*a13*b12**2*n2 - 72*u1*u2*u3*v1*a13*b12*n2**
2 + 72*u1*u2*u3*v2**2*a13*b12**2*n2 + 36*u1*u2*u3*v3*a11*b12*n2**2 - 36*u1*u2*v1
*v2*b12**2*n2**2 + 36*u1*u2*v2*b12*n2**3 + u1*u3**5*( - 60*a11**3*a13 - 384*a11*
a13**3 - 60*a11*a13*b12**2*kap) + u1*u3**4*v2*( - 6*a11**3*b12 + 48*a11*a13**2*
b12 - 6*a11*b12**3*kap) + 144*u1*u3**3*v1*v3*a13**2*b12**2 - 72*u1*u3**3*v1*a11*
a13*b12*n2 + u1*u3**3*v3*( - 24*a11**2*b12*n2 - 96*a13**2*b12*n2 - 24*b12**3*kap
*n2) + 72*u1*u3**3*a11*a13*n2**2 + 72*u1*u3**2*v2*v3*a13*b12**2*n2 - 36*u1*u3*v1
*v3*b12**2*n2**2 + 36*u1*u3*v3*b12*n2**3 + 18*u2**4*a11**2*n2**2 + 288*u2**3*u3
**2*a11*a13**2*n2 - 36*u2**3*v1*a11*b12*n2**2 + 36*u2**3*a11*n2**3 + u2**2*u3**4
*( - 6*a11**4 - 216*a11**2*a13**2 - 12*a11**2*b12**2*kap - 768*a13**4 - 216*a13
**2*b12**2*kap - 6*b12**4*kap**2) - 288*u2**2*u3**2*v1*a13**2*b12*n2 - 72*u2**2*
u3**2*v3*a11*a13*b12*n2 + u2**2*u3**2*(18*a11**2*n2**2 + 288*a13**2*n2**2) + 18*
u2**2*v1**2*b12**2*n2**2 - 36*u2**2*v1*b12*n2**3 + 18*u2**2*n2**4 + u2*u3**4*v1*
(6*a11**3*b12 + 96*a11*a13**2*b12 + 6*a11*b12**3*kap) + u2*u3**4*v3*(48*a11**2*
a13*b12 + 192*a13**3*b12 + 48*a13*b12**3*kap) + u2*u3**4*( - 30*a11**3*n2 - 192*
a11*a13**2*n2 - 30*a11*b12**2*kap*n2) + 72*u2*u3**3*v2*a11*a13*b12*n2 + 72*u2*u3
**2*v1*v3*a13*b12**2*n2 - 36*u2*u3**2*v1*a11*b12*n2**2 - 72*u2*u3**2*v3*a13*b12*
n2**2 + 36*u2*u3**2*a11*n2**3 + u3**6*(3*a11**4 - 40*a11**2*a13**2 + 5*a11**2*
b12**2*kap - 256*a13**4 - 56*a13**2*b12**2*kap + 2*b12**4*kap**2) + u3**5*v2*( -
48*a11**2*a13*b12 - 192*a13**3*b12 - 48*a13*b12**3*kap) + u3**4*v1**2*( - 6*a11
**2*b12**2 - 96*a13**2*b12**2 - 6*b12**4*kap) + u3**4*v1*(24*a11**2*b12*n2 + 96*
a13**2*b12*n2 + 24*b12**3*kap*n2) + u3**4*v2**2*( - 6*a11**2*b12**2 - 24*a13**2*
b12**2 - 6*b12**4*kap) + u3**4*v3**2*( - 6*a11**2*b12**2 - 24*a13**2*b12**2 - 6*
b12**4*kap) + u3**4*( - 18*a11**2*n2**2 - 18*b12**2*kap*n2**2) - 72*u3**3*v1*v2*
a13*b12**2*n2 + 72*u3**3*v2*a13*b12*n2**2 + 18*u3**2*v1**2*b12**2*n2**2 - 36*u3
**2*v1*b12*n2**3 + 18*u3**2*n2**4$