Solution 1 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=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
r329=0
r330=0
r331=0
r332= - r341
r333=0
r334=0
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
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
r427=0
r428=0
r429=0
1
---*b12*r341
2
r430=--------------
n2
r431=0
2*a13*r341
r432=------------
n2
r433=0
1
- ---*b12*kap*r341
2
r434=---------------------
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
r453=0
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
8*a13 *r341
r464=-------------
b12*n2
r465=0
r466=0
r467=0
r468=0
r469=0
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
r489=0
r490=0
r491=0
r492=0
r493=0
- b12*r341
r494=-------------
n2
r495=0
r496=0
r497=0
- 2*a13*r341
r498=---------------
n2
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
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
1
- ---*b12*kap*r341
2
r4114=---------------------
n2
r4115=0
r4116=0
r4117=0
r4118=0
2 1 2
8*a13 *r341 + ---*b12 *kap*r341
2
r4119=---------------------------------
b12*n2
r4120=0
r4121=0
r4122=0
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=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
8 2 2 2
---*a13 *r341 + ---*b12 *kap*r341
3 3
r554=-----------------------------------
2
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
r588=0
r589=0
r590=0
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
r5107=0
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
r5120=0
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
8 2 2 2
- ---*a13 *r341 - ---*b12 *kap*r341
3 3
r5157=--------------------------------------
2
n2
r5158=0
r5159=0
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
3 2
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
r5189=0
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
r5206=0
r5207=0
r5208=0
r5209=0
r5210=0
r5211=0
r5212=0
r5213=0
r5214=0
r5215=0
r5216=0
r5217=0
r5218=0
r5219=0
r5220=0
r5221=0
r5222=0
r5223=0
r5224=0
r5225=0
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
3 2
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
2 2 1 3
- ---*a13 *b12*r341 - ---*b12 *kap*r341
3 6
r674=------------------------------------------
3
n2
r675=0
2 2 1 3
- ---*a13 *b12*r341 - ---*b12 *kap*r341
3 6
r676=------------------------------------------
3
n2
r677=0
r678=0
8 2 1 3
- ---*a13 *b12*r341 - ---*b12 *kap*r341
3 6
r679=------------------------------------------
3
n2
r680=0
16 3 4 2
- ----*a13 *r341 - ---*a13*b12 *kap*r341
3 3
r681=-------------------------------------------
3
n2
r682=0
64 4 14 2 2 1 4 2
- ----*a13 *r341 - ----*a13 *b12 *kap*r341 + ----*b12 *kap *r341
9 9 18
r683=-------------------------------------------------------------------
3
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
16 3 4 2
----*a13 *r341 + ---*a13*b12 *kap*r341
3 3
r6136=----------------------------------------
3
n2
r6137=0
r6138=0
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
64 4 2 2 1 4 2
- ----*a13 *r341 - 6*a13 *b12 *kap*r341 - ---*b12 *kap *r341
3 6
r6174=---------------------------------------------------------------
3
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
r6263=0
r6264=0
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
r6295=0
r6296=0
r6297=0
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
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
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
32 4 2 2 1 4 2
----*a13 *r341 - 4*a13 *b12 *kap*r341 - ---*b12 *kap *r341
3 6
r6370=------------------------------------------------------------
3
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
r6389=0
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
r6423=0
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
r6450=0
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
a33=0
a23=0
a22=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:
r341, a13, 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.
{a13,
n2,
b12,
6 2
{2953352425009835056568909606257717664971955421101938971901824768000*b12 *kap
*r341,
6 2
41273842196968419909024000*b12 *kap *r341,
6 2
2187513636439326255178272000*b12 *kap *r341,
1151032521241625798739716101079531527867999965113515989781040768419858114512\
8 3
37563774979041272289676964467848126136320000000*b12 *kap *r341,
7 2
40027680*b12 *kap *r341,
8
1529940775734028835300942822951152232838288541003426271666997916800000*b12
3
*kap *r341,
7 2
13342560*b12 *kap *r341,
4891888215276909644643793429588008993438999851732442956569423265784396986677\
8 3
59646043660925407231127098988354536079360000000*b12 *kap *r341,
1639946221896459520336475536700652416798873586303922015743567896225388167136\
8 3
49586585124807090708897557537606499868691005440000000*b12 *kap *r341,
7 2
1531586804182367708160*b12 *kap *r341}}
Relevance for the application:
Modulo the following equation:
2 2
0=16*a13 + b12 *kap
the system of equations related to the Hamiltonian HAM:
HAM=2*u1*u3*a13 + u1*v2*b12 - u2*v1*b12 + u2*n2
has apart from the Hamiltonian and Casimirs only the following first integral:
3 3 2
FI=u1 *u2*u3*(32*a13 *n2 + 2*a13*b12 *kap*n2)
2 2 2 4 2 2
+ u1 *u2 *u3 *( - 32*a13 - 2*a13 *b12 *kap)
2 2 2 2 1 2 2
+ u1 *u2 *(8*a13 *n2 + ---*b12 *kap*n2 )
2
2 4 32 4 2 2 1 4 2
+ u1 *u3 *(----*a13 - 4*a13 *b12 *kap - ---*b12 *kap )
3 6
2 3 3 2 2 2 2 2 2 2 2 2 2
+ 16*u1 *u3 *v2*a13 *b12 + 2*u1 *u3 *v1 *a13 *b12 + 2*u1 *u3 *v2 *a13 *b12
1 2 2 2 2 2 2 1 2 2 2 2
- ---*u1 *u3 *b12 *kap*n2 + 2*u1 *u3*v2*a13*b12*n2 - ---*u1 *v1 *b12 *n2
2 2
1 2 4 3 3
+ ---*u1 *n2 - 16*u1*u2*u3 *v1*a13 *b12
2
3 3 2 2 2
+ u1*u2*u3 *(32*a13 *n2 + 2*a13*b12 *kap*n2) + 8*u1*u2*u3 *v2*a13 *b12*n2
2 2 2
+ 2*u1*u2*u3*v1 *a13*b12 *n2 - 2*u1*u2*u3*v1*a13*b12*n2
2 2 2 2 3
+ 2*u1*u2*u3*v2 *a13*b12 *n2 - u1*u2*v1*v2*b12 *n2 + u1*u2*v2*b12*n2
3 2 2
+ 4*u1*u3 *v1*v3*a13 *b12
3 8 2 2 3
+ u1*u3 *v3*( - ---*a13 *b12*n2 - ---*b12 *kap*n2)
3 3
2 2 2 2 3
+ 2*u1*u3 *v2*v3*a13*b12 *n2 - u1*u3*v1*v3*b12 *n2 + u1*u3*v3*b12*n2
2 4 64 4 2 2 1 4 2
+ u2 *u3 *( - ----*a13 - 6*a13 *b12 *kap - ---*b12 *kap )
3 6
2 2 2 2 2 2 2 1 2 2 2 2
- 8*u2 *u3 *v1*a13 *b12*n2 + 8*u2 *u3 *a13 *n2 + ---*u2 *v1 *b12 *n2
2
2 3 1 2 4
- u2 *v1*b12*n2 + ---*u2 *n2
2
4 16 3 4 3 2 2
+ u2*u3 *v3*(----*a13 *b12 + ---*a13*b12 *kap) + 2*u2*u3 *v1*v3*a13*b12 *n2
3 3
2 2
- 2*u2*u3 *v3*a13*b12*n2
6 64 4 14 2 2 1 4 2
+ u3 *( - ----*a13 - ----*a13 *b12 *kap + ----*b12 *kap )
9 9 18
5 16 3 4 3
+ u3 *v2*( - ----*a13 *b12 - ---*a13*b12 *kap)
3 3
4 2 8 2 2 1 4
+ u3 *v1 *( - ---*a13 *b12 - ---*b12 *kap)
3 6
4 8 2 2 3
+ u3 *v1*(---*a13 *b12*n2 + ---*b12 *kap*n2)
3 3
4 2 2 2 2 1 4
+ u3 *v2 *( - ---*a13 *b12 - ---*b12 *kap)
3 6
4 2 2 2 2 1 4 1 4 2 2
+ u3 *v3 *( - ---*a13 *b12 - ---*b12 *kap) - ---*u3 *b12 *kap*n2
3 6 2
3 2 3 2 1 2 2 2 2
- 2*u3 *v1*v2*a13*b12 *n2 + 2*u3 *v2*a13*b12*n2 + ---*u3 *v1 *b12 *n2
2
2 3 1 2 4
- u3 *v1*b12*n2 + ---*u3 *n2
2
1
= a product of the elements of: { - ----,
18
3 3 2
u1 *u2*u3*( - 576*a13 *n2 - 36*a13*b12 *kap*n2)
2 2 2 4 2 2
+ u1 *u2 *u3 *(576*a13 + 36*a13 *b12 *kap)
2 2 2 2 2 2
+ u1 *u2 *( - 144*a13 *n2 - 9*b12 *kap*n2 )
2 4 4 2 2 4 2
+ u1 *u3 *( - 192*a13 + 72*a13 *b12 *kap + 3*b12 *kap )
2 3 3 2 2 2 2 2
- 288*u1 *u3 *v2*a13 *b12 - 36*u1 *u3 *v1 *a13 *b12
2 2 2 2 2 2 2 2 2
- 36*u1 *u3 *v2 *a13 *b12 + 9*u1 *u3 *b12 *kap*n2
2 2 2 2 2 2 2 4
- 36*u1 *u3*v2*a13*b12*n2 + 9*u1 *v1 *b12 *n2 - 9*u1 *n2
3 3
+ 288*u1*u2*u3 *v1*a13 *b12
3 3 2
+ u1*u2*u3 *( - 576*a13 *n2 - 36*a13*b12 *kap*n2)
2 2 2 2
- 144*u1*u2*u3 *v2*a13 *b12*n2 - 36*u1*u2*u3*v1 *a13*b12 *n2
2 2 2
+ 36*u1*u2*u3*v1*a13*b12*n2 - 36*u1*u2*u3*v2 *a13*b12 *n2
2 2 3 3 2 2
+ 18*u1*u2*v1*v2*b12 *n2 - 18*u1*u2*v2*b12*n2 - 72*u1*u3 *v1*v3*a13 *b12
3 2 3 2 2
+ u1*u3 *v3*(48*a13 *b12*n2 + 12*b12 *kap*n2) - 36*u1*u3 *v2*v3*a13*b12 *n2
2 2 3
+ 18*u1*u3*v1*v3*b12 *n2 - 18*u1*u3*v3*b12*n2
2 4 4 2 2 4 2
+ u2 *u3 *(384*a13 + 108*a13 *b12 *kap + 3*b12 *kap )
2 2 2 2 2 2 2 2 2 2 2
+ 144*u2 *u3 *v1*a13 *b12*n2 - 144*u2 *u3 *a13 *n2 - 9*u2 *v1 *b12 *n2
2 3 2 4
+ 18*u2 *v1*b12*n2 - 9*u2 *n2
4 3 3 2 2
+ u2*u3 *v3*( - 96*a13 *b12 - 24*a13*b12 *kap) - 36*u2*u3 *v1*v3*a13*b12 *n2
2 2 6 4 2 2 4 2
+ 36*u2*u3 *v3*a13*b12*n2 + u3 *(128*a13 + 28*a13 *b12 *kap - b12 *kap )
5 3 3
+ u3 *v2*(96*a13 *b12 + 24*a13*b12 *kap)
4 2 2 2 4
+ u3 *v1 *(48*a13 *b12 + 3*b12 *kap)
4 2 3
+ u3 *v1*( - 48*a13 *b12*n2 - 12*b12 *kap*n2)
4 2 2 2 4 4 2 2 2 4
+ u3 *v2 *(12*a13 *b12 + 3*b12 *kap) + u3 *v3 *(12*a13 *b12 + 3*b12 *kap)
4 2 2 3 2 3 2
+ 9*u3 *b12 *kap*n2 + 36*u3 *v1*v2*a13*b12 *n2 - 36*u3 *v2*a13*b12*n2
2 2 2 2 2 3 2 4
- 9*u3 *v1 *b12 *n2 + 18*u3 *v1*b12*n2 - 9*u3 *n2 }
{HAM,FI} = 0
And again in machine readable form:
HAM=2*u1*u3*a13 + u1*v2*b12 - u2*v1*b12 + u2*n2$
FI=u1**3*u2*u3*(32*a13**3*n2 + 2*a13*b12**2*kap*n2) + u1**2*u2**2*u3**2*( - 32*
a13**4 - 2*a13**2*b12**2*kap) + u1**2*u2**2*(8*a13**2*n2**2 + 1/2*b12**2*kap*n2
**2) + u1**2*u3**4*(32/3*a13**4 - 4*a13**2*b12**2*kap - 1/6*b12**4*kap**2) + 16*
u1**2*u3**3*v2*a13**3*b12 + 2*u1**2*u3**2*v1**2*a13**2*b12**2 + 2*u1**2*u3**2*v2
**2*a13**2*b12**2 - 1/2*u1**2*u3**2*b12**2*kap*n2**2 + 2*u1**2*u3*v2*a13*b12*n2
**2 - 1/2*u1**2*v1**2*b12**2*n2**2 + 1/2*u1**2*n2**4 - 16*u1*u2*u3**3*v1*a13**3*
b12 + u1*u2*u3**3*(32*a13**3*n2 + 2*a13*b12**2*kap*n2) + 8*u1*u2*u3**2*v2*a13**2
*b12*n2 + 2*u1*u2*u3*v1**2*a13*b12**2*n2 - 2*u1*u2*u3*v1*a13*b12*n2**2 + 2*u1*u2
*u3*v2**2*a13*b12**2*n2 - u1*u2*v1*v2*b12**2*n2**2 + u1*u2*v2*b12*n2**3 + 4*u1*
u3**3*v1*v3*a13**2*b12**2 + u1*u3**3*v3*( - 8/3*a13**2*b12*n2 - 2/3*b12**3*kap*
n2) + 2*u1*u3**2*v2*v3*a13*b12**2*n2 - u1*u3*v1*v3*b12**2*n2**2 + u1*u3*v3*b12*
n2**3 + u2**2*u3**4*( - 64/3*a13**4 - 6*a13**2*b12**2*kap - 1/6*b12**4*kap**2) -
8*u2**2*u3**2*v1*a13**2*b12*n2 + 8*u2**2*u3**2*a13**2*n2**2 + 1/2*u2**2*v1**2*
b12**2*n2**2 - u2**2*v1*b12*n2**3 + 1/2*u2**2*n2**4 + u2*u3**4*v3*(16/3*a13**3*
b12 + 4/3*a13*b12**3*kap) + 2*u2*u3**2*v1*v3*a13*b12**2*n2 - 2*u2*u3**2*v3*a13*
b12*n2**2 + u3**6*( - 64/9*a13**4 - 14/9*a13**2*b12**2*kap + 1/18*b12**4*kap**2)
+ u3**5*v2*( - 16/3*a13**3*b12 - 4/3*a13*b12**3*kap) + u3**4*v1**2*( - 8/3*a13
**2*b12**2 - 1/6*b12**4*kap) + u3**4*v1*(8/3*a13**2*b12*n2 + 2/3*b12**3*kap*n2)
+ u3**4*v2**2*( - 2/3*a13**2*b12**2 - 1/6*b12**4*kap) + u3**4*v3**2*( - 2/3*a13
**2*b12**2 - 1/6*b12**4*kap) - 1/2*u3**4*b12**2*kap*n2**2 - 2*u3**3*v1*v2*a13*
b12**2*n2 + 2*u3**3*v2*a13*b12*n2**2 + 1/2*u3**2*v1**2*b12**2*n2**2 - u3**2*v1*
b12*n2**3 + 1/2*u3**2*n2**4$