Solution 3 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2 2
0=16*a23 + 4*a33 + b12 *kap
Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r13=0
r14=0
r15=0
1 2 2
- ---*m3 *n1 *r679
4
r20=---------------------
2 2
a23 *b12
r21=0
1 2 2
- ---*m3 *n1 *r679
4
r22=---------------------
2 2
a23 *b12
r23=0
r24=0
r27=0
1 3
- ---*m3*n1 *r679
2
r28=--------------------
2 2
a23 *b12
1 2 2 1 4
- ---*kap*m3 *n1 *r679 + ---*n1 *r679
4 4
r29=----------------------------------------
2 2
a23 *b12
r210=0
r211=0
r212=0
r213=0
1 4
---*n1 *r679
4
r214=--------------
2 2
a23 *b12
r215=0
r217=0
r218=0
r219=0
1 2 2
- ---*kap*m3 *n1 *r679
4
r220=-------------------------
2 2
a23 *b12
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r312=0
2 1 2
a23*m3 *n1*r679 - ---*b12*m3*n1 *r679
2
r314=---------------------------------------
2 2
a23 *b12
r315=0
2 1 3
- a23*m3*n1 *r679 + ---*b12*n1 *r679
2
r317=---------------------------------------
2 2
a23 *b12
r318=0
r319=0
r320=0
r321=0
r322=0
1 2
---*m3*n1 *r679
2
r323=-----------------
2
a23 *b12
r324=0
r325=0
1 2
---*a33*m3*n1 *r679
2
r327=---------------------
2 2
a23 *b12
r328=0
r329=0
2
- a33*m3*n1 *r679
r330=--------------------
2 2
a23 *b12
1 3
---*n1 *r679
2
r331=--------------
2
a23 *b12
r332=0
r333=0
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
r342=0
1 2
- ---*a33*m3*n1 *r679
2
r343=------------------------
2 2
a23 *b12
1 3
---*a33*n1 *r679
2
r344=------------------
2 2
a23 *b12
r345=0
r346=0
1 3
---*n1 *r679
2
r347=--------------
2
a23 *b12
2 3
- kap*m3 *n1*r679 - n1 *r679
r348=-------------------------------
2
a23*b12
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
r418=0
r421=0
r423=0
r424=0
1 2
- a23*m3*n1*r679 + ---*b12*n1 *r679
4
r427=--------------------------------------
2
a23 *b12
r429=0
2
- a23*m3 *r679 + b12*m3*n1*r679
r430=----------------------------------
2
a23*b12
r432=0
2
- 4*a23*m3*n1*r679 - b12*n1 *r679
r433=------------------------------------
2
a23*b12
2 2 5 2 2 1 2 2
- a23 *kap*m3 *r679 - ---*a33 *n1 *r679 - ---*b12 *kap*n1 *r679
4 4
r434=------------------------------------------------------------------
2 2
a23 *b12
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
r447=0
r449=0
r450=0
r452=0
1 2
- 2*a23*a33*m3*n1*r679 + ---*a33*b12*n1 *r679
2
r453=------------------------------------------------
2 2
a23 *b12
2
a33*n1 *r679
r454=--------------
2
a23*b12
r455=0
r456=0
1 2
- a23*m3*n1*r679 + ---*b12*n1 *r679
4
r457=--------------------------------------
2
a23 *b12
r458=0
r459=0
1 2
- ---*n1 *r679
4
r460=-----------------
2
a23
r462=0
r463=0
r464=
2 2 2 2 2 2 1 2 2
- a23 *kap*m3 *r679 - a23 *n1 *r679 - 2*a33 *n1 *r679 - ---*b12 *kap*n1 *r679
4
--------------------------------------------------------------------------------
2 2
a23 *b12
r465=0
r466=0
2
a33*n1 *r679
r467=--------------
2
a23 *b12
r468=0
2 2
- a33 *n1 *r679
r469=------------------
2 2
a23 *b12
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r479=0
r482=0
r484=0
r485=0
1 2
- 2*a23*a33*m3*n1*r679 + ---*a33*b12*n1 *r679
2
r487=------------------------------------------------
2 2
a23 *b12
r488=0
r489=0
r490=0
r491=0
r492=0
r493=0
1 2
---*n1 *r679
2
r494=--------------
2
a23
r495=0
2
- 4*a23*m3*n1*r679 - b12*n1 *r679
r497=------------------------------------
2
a23*b12
r498=0
r499=0
r4100=0
- 4*a33*m3*n1*r679
r4101=---------------------
2
a23*b12
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
m3*n1*r679
r4110=------------
a23*b12
r4112=0
2
- 4*a23*m3*n1*r679 - b12*n1 *r679
r4113=------------------------------------
2
a23*b12
2 2 1 2 2
- a33 *n1 *r679 - ---*b12 *kap*n1 *r679
4
r4114=------------------------------------------
2 2
a23 *b12
r4115=0
r4116=0
2
- 4*a23*a33*m3*n1*r679 + a33*b12*n1 *r679
r4117=--------------------------------------------
2 2
a23 *b12
r4118=0
2 2
- a33 *n1 *r679
r4119=------------------
2 2
a23 *b12
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
r525=0
r529=0
r532=0
r534=0
r535=0
r539=0
r542=0
r544=0
r545=0
r548=0
2*a23*m3*r679 - b12*n1*r679
r550=-----------------------------
a23*b12
r551=0
- 8*a23*m3*r679 + 4*b12*n1*r679
r553=----------------------------------
2
b12
r554=0
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
r574=0
r577=0
r579=0
r580=0
r583=0
r585=0
r586=0
- 4*a23*a33*m3*r679 + 2*a33*b12*n1*r679
r588=------------------------------------------
2
a23*b12
r589=0
r590=0
r591=0
r592=0
r593=0
r594=0
r595=0
r596=0
r597=0
r598=0
r599=0
r5100=0
r5103=0
2*a23*m3*r679 - b12*n1*r679
r5105=-----------------------------
a23*b12
r5106=0
- 8*a23*m3*r679 + 4*b12*n1*r679
r5108=----------------------------------
2
b12
r5109=0
r5110=0
r5111=0
r5112=0
r5113=0
r5114=0
r5115=0
r5116=0
- 4*a23*a33*m3*r679 + 2*a33*b12*n1*r679
r5118=------------------------------------------
2
a23*b12
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
r5144=0
r5147=0
r5149=0
r5150=0
r5153=0
r5155=0
r5156=0
r5158=0
- 2*a33*n1*r679
r5159=------------------
a23*b12
8*a33*n1*r679
r5160=---------------
2
b12
r5161=0
r5162=0
r5163=0
r5164=0
r5165=0
r5166=0
r5167=0
r5168=0
r5169=0
r5170=0
r5173=0
r5175=0
2*m3*r679
r5176=-----------
b12
r5178=0
- 8*a23*m3*r679
r5179=------------------
2
b12
2 2
- 16*a23 *n1*r679 - b12 *kap*n1*r679
r5180=---------------------------------------
2
a23*b12
r5181=0
r5182=0
r5183=0
r5184=0
r5185=0
r5186=0
r5188=0
- 4*a23*a33*m3*r679 - 2*a33*b12*n1*r679
r5189=------------------------------------------
2
a23*b12
8*a33*n1*r679
r5190=---------------
2
b12
r5191=0
r5192=0
r5193=0
2
4*a33 *n1*r679
r5194=----------------
2
a23*b12
r5195=0
r5196=0
r5197=0
r5198=0
r5199=0
r5200=0
r5201=0
r5202=0
r5203=0
r5204=0
r5205=0
r5208=0
- n1*r679
r5210=------------
a23
r5211=0
4*n1*r679
r5213=-----------
b12
r5214=0
r5215=0
r5216=0
r5217=0
r5218=0
r5219=0
r5220=0
r5221=0
2*a33*n1*r679
r5223=---------------
a23*b12
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
r5238=0
- 2*a33*n1*r679
r5239=------------------
a23*b12
8*a33*n1*r679
r5240=---------------
2
b12
r5241=0
r5242=0
r5243=0
2
4*a33 *n1*r679
r5244=----------------
2
a23*b12
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
r633=0
r638=0
r642=0
r645=0
r647=0
r648=0
r653=0
r657=0
r660=0
r662=0
r663=0
r667=0
r670=0
r672=0
r673=0
r676=0
r678=0
r681=0
- 8*a23*r679
r682=---------------
b12
32 2 4 2 1 2
----*a23 *r679 - ---*a33 *r679 - ---*b12 *kap*r679
3 3 3
r683=----------------------------------------------------
2
b12
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
r6109=0
r6113=0
r6116=0
r6118=0
r6119=0
r6123=0
r6126=0
r6128=0
r6129=0
r6132=0
r6134=0
r6135=0
r6137=0
- 4*a33*r679
r6138=---------------
b12
16*a23*a33*r679
r6139=-----------------
2
b12
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
r6158=0
r6161=0
r6163=0
r6164=0
r6167=0
r6169=0
r6170=r679
r6172=0
- 8*a23*r679
r6173=---------------
b12
2 2
16*a23 *r679 + 4*a33 *r679
r6174=----------------------------
2
b12
r6175=0
r6176=0
r6177=0
r6178=0
r6179=0
r6180=0
r6181=0
r6182=0
r6183=0
r6184=0
r6187=0
r6189=0
r6190=0
r6192=0
2 3
64*a23 *a33*r679 + 16*a33 *r679
r6193=---------------------------------
3
b12 *kap
16*a23*a33*r679
r6194=-----------------
2
b12
r6195=0
r6196=0
r6197=0
r6198=0
r6199=0
r6200=0
r6202=0
r6203=0
2
4*a33 *r679
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
r6235=0
r6239=0
r6242=0
r6244=0
r6245=0
r6249=0
r6252=0
r6254=0
r6255=0
r6258=0
r6260=0
r6261=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
r6284=0
r6287=0
r6289=0
r6290=0
r6293=0
r6295=0
r6296=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
r6313=0
r6315=0
r6316=0
r6318=0
r6319=0
r6320=0
r6321=0
r6322=0
r6323=0
r6324=0
r6325=0
r6326=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
r6354=0
r6357=0
r6359=0
r6360=0
r6363=0
r6365=0
r6366=r679
r6368=0
- 8*a23*r679
r6369=---------------
b12
2 2 2
32*a23 *r679 + 4*a33 *r679 + b12 *kap*r679
r6370=--------------------------------------------
2
b12
r6371=0
r6372=0
r6373=0
r6374=0
r6375=0
r6376=0
r6377=0
r6378=0
r6379=0
r6380=0
r6383=0
r6385=0
r6386=0
r6388=0
- 4*a33*r679
r6389=---------------
b12
16*a23*a33*r679
r6390=-----------------
2
b12
r6391=0
r6392=0
r6393=0
r6394=0
r6395=0
r6396=0
r6398=0
r6399=0
2
4*a33 *r679
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
r6418=0
r6420=0
r6421=0
2 3 2
64*a23 *a33*r679 + 16*a33 *r679 + 4*a33*b12 *kap*r679
r6423=-------------------------------------------------------
3
b12 *kap
r6424=0
r6425=0
r6426=0
r6427=0
r6428=0
r6429=0
r6430=0
r6431=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
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
m2=0
m1=0
n3=0
n2=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:
r679, n1, a33, m3, a23, 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,a23,m3,r679,a33}
Relevance for the application:
Modulo the following equation:
2 2 2
0=16*a23 + 4*a33 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2
HAM=2*u1 *a33 + u1*v2*b12 + u1*n1 + 2*u2 *a33 + 2*u2*u3*a23 - u2*v1*b12
2
+ u3 *a33 + v3*m3
has apart from the Hamiltonian and Casimirs only the following first integral:
3 2
FI=4*u1 *u2*u3*a23*a33 *b12*kap*n1
3 2 4 2 3 2 2
+ u1 *u3 *v2*(64*a23 *a33 + 16*a23 *a33 + 4*a23 *a33*b12 *kap)
3 2 2 3 2
+ 8*u1 *u3 *a23 *a33*b12*kap*n1 - 2*u1 *u3*v1*a23*a33*b12 *kap*n1
2 2 2 2 2 2 2 2 2
+ 4*u1 *u2 *u3 *a23 *a33 *b12*kap - u1 *u2 *a33 *b12*kap*n1
2 3 3 2 2 2 2
+ 16*u1 *u2*u3 *a23 *a33*b12*kap - 4*u1 *u2*u3 *v1*a23 *a33*b12 *kap
2 2
+ 2*u1 *u2*u3*v2*a23*a33*b12 *kap*n1
2 2 2
+ u1 *u2*v1*( - 4*a23*a33*b12*kap*m3*n1 + a33*b12 *kap*n1 )
2 4 4 2 2 2 3 2
+ u1 *u3 *(32*a23 *b12*kap + 4*a23 *a33 *b12*kap + a23 *b12 *kap )
2 3 3 2 2 2 2 2 3
- 8*u1 *u3 *v1*a23 *b12 *kap + u1 *u3 *v1 *a23 *b12 *kap
2 2 2 2
+ 4*u1 *u3 *v2*a23 *b12 *kap*n1
2 2 2 2 1 3 2 2
+ u1 *u3 *( - a33 *b12*kap*n1 - ---*b12 *kap *n1 )
4
2 3
- u1 *u3*v1*v2*a23*b12 *kap*n1
2 2 2 2
+ u1 *u3*v1*( - 4*a23 *b12*kap*m3*n1 - a23*b12 *kap*n1 )
2 2 2 1 2 2 2 2
+ u1 *v1 *a23*b12 *kap*m3*n1 - ---*u1 *b12*kap *m3 *n1
4
3 2 2 2 2
+ 4*u1*u2 *u3*a23*a33 *b12*kap*n1 + 8*u1*u2 *u3 *a23 *a33*b12*kap*n1
2 2 2
+ u1*u2 *u3*v1*( - 4*a23 *a33*b12*kap*m3 - 2*a23*a33*b12 *kap*n1)
2
- 4*u1*u2 *v2*a23*a33*b12*kap*m3*n1
3 3 3 2
+ u1*u2*u3 *( - 16*a23 *b12*kap*n1 - a23*b12 *kap *n1)
2 3 2 2 2
- 8*u1*u2*u3 *v1*a23 *b12*kap*m3 + 2*u1*u2*u3*v1 *a23 *b12 *kap*m3
2 2 2
+ u1*u2*u3*v2*( - 4*a23 *b12*kap*m3*n1 - a23*b12 *kap*n1 )
2 2 3
+ u1*u2*u3*( - a23*b12*kap *m3 *n1 - a23*b12*kap*n1 )
1 3 2 1 2 3
+ ---*u1*u2*v1*v2*b12 *kap*n1 + ---*u1*u2*v1*b12 *kap*n1
2 2
4 2 3 2
+ 8*u1*u3 *a23 *a33*b12*kap*n1 - 2*u1*u3 *v1*a23*a33*b12 *kap*n1
2 1 2 2
+ u1*u3 *v2*( - 2*a23*a33*b12*kap*m3*n1 + ---*a33*b12 *kap*n1 )
2
1 2 3 1 2
+ ---*u1*u3 *a33*b12*kap*n1 - ---*u1*u3*v1*a33*b12*kap*m3*n1
2 2
4 2 2 2 4 2 2
+ 4*u2 *u3 *a23 *a33 *b12*kap - u2 *a33 *b12*kap*n1
3 3 3 3 2 4 2 3
+ 16*u2 *u3 *a23 *a33*b12*kap + u2 *u3 *v1*(64*a23 *a33 + 16*a23 *a33 )
3 2 2
+ u2 *u3*v2*( - 4*a23 *a33*b12*kap*m3 + 2*a23*a33*b12 *kap*n1)
3 2 2 2 4 4 2 2
+ u2 *v1*a33*b12 *kap*n1 + u2 *u3 *(16*a23 *b12*kap + 4*a23 *a33 *b12*kap)
2 3 3 2 2 2 2 2 3
- 8*u2 *u3 *v1*a23 *b12 *kap + u2 *u3 *v1 *a23 *b12 *kap
2 2 3 2 2 2 2
+ u2 *u3 *v2*( - 8*a23 *b12*kap*m3 + 4*a23 *b12 *kap*n1) + u2 *u3 *(
2 2 2 2 2 2 2
- a23 *b12*kap *m3 - a23 *b12*kap*n1 - 2*a33 *b12*kap*n1
1 3 2 2
- ---*b12 *kap *n1 )
4
2 2 2 3
+ u2 *u3*v1*v2*(2*a23 *b12 *kap*m3 - a23*b12 *kap*n1)
1 2 2 3 2
- ---*u2 *v1 *b12 *kap*n1
4
2 2 2 1 3 2
+ u2 *v2 *( - a23*b12 *kap*m3*n1 + ---*b12 *kap*n1 )
4
1 2 2 3 2 2 1 2 4
+ ---*u2 *v2*b12 *kap*n1 - u2 *v3*a33*b12*kap*m3*n1 + ---*u2 *b12*kap*n1
2 4
5 3 4 2 2
+ 16*u2*u3 *a23 *a33*b12*kap - 4*u2*u3 *v1*a23 *a33*b12 *kap
3 2 2
+ u2*u3 *v2*( - 4*a23 *a33*b12*kap*m3 + 2*a23*a33*b12 *kap*n1)
3 2
+ u2*u3 *a23*a33*b12*kap*n1
2 1 2 2
+ u2*u3 *v1*( - 2*a23*a33*b12*kap*m3*n1 + ---*a33*b12 *kap*n1 )
2
1 2 1 2 2
+ ---*u2*u3*v2*a33*b12*kap*m3*n1 + ---*u2*v1*v3*b12 *kap*m3*n1
2 2
6 32 4 4 2 2 1 2 3 2
+ u3 *(----*a23 *b12*kap - ---*a23 *a33 *b12*kap - ---*a23 *b12 *kap )
3 3 3
5 3 2 4 2 2 3
- 8*u3 *v1*a23 *b12 *kap + u3 *v1 *a23 *b12 *kap
4 3 2 2
+ u3 *v2*( - 8*a23 *b12*kap*m3 + 4*a23 *b12 *kap*n1)
4 2 2 2 5 2 2 1 3 2 2
+ u3 *( - a23 *b12*kap *m3 - ---*a33 *b12*kap*n1 - ---*b12 *kap *n1 )
4 4
3 2 2 3
+ u3 *v1*v2*(2*a23 *b12 *kap*m3 - a23*b12 *kap*n1)
3 2 2 2
+ u3 *v1*( - 4*a23 *b12*kap*m3*n1 - a23*b12 *kap*n1 )
2 2 2 2 2
+ u3 *v1 *( - a23 *b12*kap*m3 + a23*b12 *kap*m3*n1)
2 2 2 1 3 2
+ u3 *v2 *( - a23*b12 *kap*m3*n1 + ---*b12 *kap*n1 )
4
2 2 1 2 3
+ u3 *v2*( - a23*b12*kap*m3*n1 + ---*b12 *kap*n1 )
2
2 1 2 2 2 1 4
+ u3 *( - ---*b12*kap *m3 *n1 + ---*b12*kap*n1 )
4 4
2 1 2 2
+ u3*v1*v2*(a23*b12*kap*m3 *n1 - ---*b12 *kap*m3*n1 )
2
1 3 1 2 2 2
- ---*u3*v1*b12*kap*m3*n1 - ---*v2 *b12*kap*m3 *n1
2 4
1 2 2 2
- ---*v3 *b12*kap*m3 *n1
4
{HAM,FI} = too large to simplify
And again in machine readable form:
HAM=2*u1**2*a33 + u1*v2*b12 + u1*n1 + 2*u2**2*a33 + 2*u2*u3*a23 - u2*v1*b12 + u3
**2*a33 + v3*m3$
FI=4*u1**3*u2*u3*a23*a33**2*b12*kap*n1 + u1**3*u3**2*v2*(64*a23**4*a33 + 16*a23
**2*a33**3 + 4*a23**2*a33*b12**2*kap) + 8*u1**3*u3**2*a23**2*a33*b12*kap*n1 - 2*
u1**3*u3*v1*a23*a33*b12**2*kap*n1 + 4*u1**2*u2**2*u3**2*a23**2*a33**2*b12*kap -
u1**2*u2**2*a33**2*b12*kap*n1**2 + 16*u1**2*u2*u3**3*a23**3*a33*b12*kap - 4*u1**
2*u2*u3**2*v1*a23**2*a33*b12**2*kap + 2*u1**2*u2*u3*v2*a23*a33*b12**2*kap*n1 +
u1**2*u2*v1*( - 4*a23*a33*b12*kap*m3*n1 + a33*b12**2*kap*n1**2) + u1**2*u3**4*(
32*a23**4*b12*kap + 4*a23**2*a33**2*b12*kap + a23**2*b12**3*kap**2) - 8*u1**2*u3
**3*v1*a23**3*b12**2*kap + u1**2*u3**2*v1**2*a23**2*b12**3*kap + 4*u1**2*u3**2*
v2*a23**2*b12**2*kap*n1 + u1**2*u3**2*( - a33**2*b12*kap*n1**2 - 1/4*b12**3*kap
**2*n1**2) - u1**2*u3*v1*v2*a23*b12**3*kap*n1 + u1**2*u3*v1*( - 4*a23**2*b12*kap
*m3*n1 - a23*b12**2*kap*n1**2) + u1**2*v1**2*a23*b12**2*kap*m3*n1 - 1/4*u1**2*
b12*kap**2*m3**2*n1**2 + 4*u1*u2**3*u3*a23*a33**2*b12*kap*n1 + 8*u1*u2**2*u3**2*
a23**2*a33*b12*kap*n1 + u1*u2**2*u3*v1*( - 4*a23**2*a33*b12*kap*m3 - 2*a23*a33*
b12**2*kap*n1) - 4*u1*u2**2*v2*a23*a33*b12*kap*m3*n1 + u1*u2*u3**3*( - 16*a23**3
*b12*kap*n1 - a23*b12**3*kap**2*n1) - 8*u1*u2*u3**2*v1*a23**3*b12*kap*m3 + 2*u1*
u2*u3*v1**2*a23**2*b12**2*kap*m3 + u1*u2*u3*v2*( - 4*a23**2*b12*kap*m3*n1 - a23*
b12**2*kap*n1**2) + u1*u2*u3*( - a23*b12*kap**2*m3**2*n1 - a23*b12*kap*n1**3) +
1/2*u1*u2*v1*v2*b12**3*kap*n1**2 + 1/2*u1*u2*v1*b12**2*kap*n1**3 + 8*u1*u3**4*
a23**2*a33*b12*kap*n1 - 2*u1*u3**3*v1*a23*a33*b12**2*kap*n1 + u1*u3**2*v2*( - 2*
a23*a33*b12*kap*m3*n1 + 1/2*a33*b12**2*kap*n1**2) + 1/2*u1*u3**2*a33*b12*kap*n1
**3 - 1/2*u1*u3*v1*a33*b12*kap*m3*n1**2 + 4*u2**4*u3**2*a23**2*a33**2*b12*kap -
u2**4*a33**2*b12*kap*n1**2 + 16*u2**3*u3**3*a23**3*a33*b12*kap + u2**3*u3**2*v1*
(64*a23**4*a33 + 16*a23**2*a33**3) + u2**3*u3*v2*( - 4*a23**2*a33*b12*kap*m3 + 2
*a23*a33*b12**2*kap*n1) + u2**3*v1*a33*b12**2*kap*n1**2 + u2**2*u3**4*(16*a23**4
*b12*kap + 4*a23**2*a33**2*b12*kap) - 8*u2**2*u3**3*v1*a23**3*b12**2*kap + u2**2
*u3**2*v1**2*a23**2*b12**3*kap + u2**2*u3**2*v2*( - 8*a23**3*b12*kap*m3 + 4*a23
**2*b12**2*kap*n1) + u2**2*u3**2*( - a23**2*b12*kap**2*m3**2 - a23**2*b12*kap*n1
**2 - 2*a33**2*b12*kap*n1**2 - 1/4*b12**3*kap**2*n1**2) + u2**2*u3*v1*v2*(2*a23
**2*b12**2*kap*m3 - a23*b12**3*kap*n1) - 1/4*u2**2*v1**2*b12**3*kap*n1**2 + u2**
2*v2**2*( - a23*b12**2*kap*m3*n1 + 1/4*b12**3*kap*n1**2) + 1/2*u2**2*v2*b12**2*
kap*n1**3 - u2**2*v3*a33*b12*kap*m3*n1**2 + 1/4*u2**2*b12*kap*n1**4 + 16*u2*u3**
5*a23**3*a33*b12*kap - 4*u2*u3**4*v1*a23**2*a33*b12**2*kap + u2*u3**3*v2*( - 4*
a23**2*a33*b12*kap*m3 + 2*a23*a33*b12**2*kap*n1) + u2*u3**3*a23*a33*b12*kap*n1**
2 + u2*u3**2*v1*( - 2*a23*a33*b12*kap*m3*n1 + 1/2*a33*b12**2*kap*n1**2) + 1/2*u2
*u3*v2*a33*b12*kap*m3*n1**2 + 1/2*u2*v1*v3*b12**2*kap*m3*n1**2 + u3**6*(32/3*a23
**4*b12*kap - 4/3*a23**2*a33**2*b12*kap - 1/3*a23**2*b12**3*kap**2) - 8*u3**5*v1
*a23**3*b12**2*kap + u3**4*v1**2*a23**2*b12**3*kap + u3**4*v2*( - 8*a23**3*b12*
kap*m3 + 4*a23**2*b12**2*kap*n1) + u3**4*( - a23**2*b12*kap**2*m3**2 - 5/4*a33**
2*b12*kap*n1**2 - 1/4*b12**3*kap**2*n1**2) + u3**3*v1*v2*(2*a23**2*b12**2*kap*m3
- a23*b12**3*kap*n1) + u3**3*v1*( - 4*a23**2*b12*kap*m3*n1 - a23*b12**2*kap*n1
**2) + u3**2*v1**2*( - a23**2*b12*kap*m3**2 + a23*b12**2*kap*m3*n1) + u3**2*v2**
2*( - a23*b12**2*kap*m3*n1 + 1/4*b12**3*kap*n1**2) + u3**2*v2*( - a23*b12*kap*m3
*n1**2 + 1/2*b12**2*kap*n1**3) + u3**2*( - 1/4*b12*kap**2*m3**2*n1**2 + 1/4*b12*
kap*n1**4) + u3*v1*v2*(a23*b12*kap*m3**2*n1 - 1/2*b12**2*kap*m3*n1**2) - 1/2*u3*
v1*b12*kap*m3*n1**3 - 1/4*v2**2*b12*kap*m3**2*n1**2 - 1/4*v3**2*b12*kap*m3**2*n1
**2$