Solution 1 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2 2 2
0=a11 + 4*a13 + 4*a23 + b12 *kap
Expressions
The solution is given through the following expressions:
r10=0
1 2 1 2
- ---*a11 *m3*n3*r312 - ---*b12 *kap*m3*n3*r312
2 2
r11=--------------------------------------------------
2
a11*a23*b12
r12=0
2 2
- kap*m3 *r312 + n3 *r312
r13=----------------------------
2
b12
1 2 2 1 2 2
---*a11 *n3 *r312 + ---*b12 *kap*n3 *r312
2 2
r14=-------------------------------------------
2
a11*a23*b12
r15=0
r20=0
r21=0
r22=0
r23=0
r24=0
1 2 2 1 2
---*a11 *m3*r312 - 2*a23 *m3*r312 + ---*b12 *kap*m3*r312
2 2
r27=----------------------------------------------------------
2
a23*b12
1 2 1 3
- ---*a11 *b12*n3*r312 - 2*a11*a13*a23*m3*r312 - ---*b12 *kap*n3*r312
2 2
r28=------------------------------------------------------------------------
2
a11*a23*b12
1 4 2 1 2 2 2
r29=( - ---*a11 *n3 *r312 + ---*a11 *a23 *kap*m3 *r312
8 2
1 2 2 2 1 2 2 2
- ---*a11 *b12 *kap*n3 *r312 + ---*a23 *b12 *kap*n3 *r312
4 2
1 4 2 2 2 2
- ---*b12 *kap *n3 *r312)/(a11*a23 *b12 *n3)
8
r210=0
- 2*a11*m3*r312
r211=------------------
2
b12
r212=0
1 2 2 1 2
---*a11 *n3*r312 + 2*a23 *n3*r312 + ---*b12 *kap*n3*r312
2 2
r213=----------------------------------------------------------
2
a23*b12
1 2 1 2
---*a11 *n3*r312 + ---*b12 *kap*n3*r312
2 2
r214=-----------------------------------------
2
a11*b12
1 2 1 2
---*a11 *n3*r312 + ---*b12 *kap*n3*r312
2 2
r215=-----------------------------------------
a11*a23*b12
- 2*a11*m3*r312
r217=------------------
2
b12
2*a13*n3*r312
r218=---------------
2
b12
r219=0
1 4 1 2 2 1 2 2
r220=( - ---*a11 *n3*r312 + ---*a11 *a23 *n3*r312 - ---*a11 *b12 *kap*n3*r312
8 2 4
1 2 2 1 4 2 2 2
+ ---*a23 *b12 *kap*n3*r312 - ---*b12 *kap *n3*r312)/(a11*a23 *b12 )
2 8
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r310=r312
r311=0
r313=0
r314=0
r315=r312
2
- a11 *m3*r312
r316=-----------------
2
b12 *n3
2*a11*a23*m3*r312 + 2*a13*b12*n3*r312
r317=---------------------------------------
2
b12 *n3
1 2 2
r318=(---*a11 *b12*n3*r312 + 2*a11*a13*a23*m3*r312 - 2*a23 *b12*n3*r312
2
1 3 2
+ ---*b12 *kap*n3*r312)/(a23*b12 *n3)
2
2 2
- a11 *r312 - b12 *kap*r312
r319=------------------------------
2
b12
r320=0
r321=0
r322=0
r323=0
r324=0
r325=0
- 2*a13*r312
r326=---------------
b12
r327=0
- 2*a11*r312
r328=---------------
b12
1 3 2 1 2
- ---*a11 *r312 + 2*a11*a23 *r312 - ---*a11*b12 *kap*r312
2 2
r329=------------------------------------------------------------
2
a23*b12
r330=0
r331=0
r332=0
3 2 2 2 1 2
---*a11 *r312 + 2*a13 *r312 + 2*a23 *r312 + ---*b12 *kap*r312
2 2
r333=---------------------------------------------------------------
2
b12
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
1 2 2 1 2
- ---*a11 *r312 + 2*a23 *r312 - ---*b12 *kap*r312
2 2
r341=----------------------------------------------------
a23*b12
2*a11*r312
r342=------------
b12
r343=0
2*a11*a13*r312
r344=----------------
2
b12
r345=0
r346=0
r347=0
2 2
a11 *a13*r312 + a13*b12 *kap*r312
r348=-----------------------------------
2
a23*b12
r349=0
r350=0
r351=0
r352=0
1 2 2 2 1 2
---*a11 *r312 + 2*a13 *r312 + 2*a23 *r312 - ---*b12 *kap*r312
2 2
r353=---------------------------------------------------------------
2
b12
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
1
- ---*a11*r312
2
r427=-----------------
n3
r428=0
r429=0
1
- ---*a11*r312
2
r430=-----------------
n3
r431=0
- 2*a11*a13*r312
r432=-------------------
b12*n3
2*a11*a23*r312
r433=----------------
b12*n3
2 2
- 2*a11*a13 *r312 - 2*a11*a23 *r312
r434=--------------------------------------
2
b12 *n3
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r443=0
r444=0
r445=0
a11*r312
r446=----------
n3
r447=0
r448=0
r449=0
r450=0
2*a11*a13*r312
r451=----------------
b12*n3
r452=0
2
a11 *r312
r453=-----------
b12*n3
2
- 2*a11 *a23*r312
r454=--------------------
2
b12 *n3
r455=0
r456=0
1
---*a11*r312
2
r457=--------------
n3
r458=0
r459=0
r460=0
r461=0
r462=0
r463=0
3 2 2 1 2
- a11 *r312 - 4*a11*a13 *r312 - 2*a11*a23 *r312 - ---*a11*b12 *kap*r312
2
r464=--------------------------------------------------------------------------
2
b12 *n3
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
a11*r312
r483=----------
n3
r484=0
r485=0
- 2*a11*a23*r312
r486=-------------------
b12*n3
2
- a11 *r312
r487=--------------
b12*n3
r488=0
2
- 2*a11 *a13*r312
r489=--------------------
2
b12 *n3
r490=0
r491=0
r492=0
r493=0
a11*r312
r494=----------
n3
r495=0
r496=0
r497=0
r498=0
4*a11*a13*a23*r312
r499=--------------------
2
b12 *n3
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
r4108=0
r4109=0
1
---*a11*r312
2
r4110=--------------
n3
r4111=0
r4112=0
r4113=0
3 2 2 1 2
- a11 *r312 - 2*a11*a13 *r312 - 4*a11*a23 *r312 - ---*a11*b12 *kap*r312
2
r4114=--------------------------------------------------------------------------
2
b12 *n3
r4115=0
r4116=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
m2=0
m1=0
1 2 1 2
---*a11 *n3 + ---*b12 *kap*n3
2 2
n2=-------------------------------
a11*a23
n1=0
a33=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:
r312, a23, a11, n3, a13, m3, 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.
{r312,a13,b12,n3,a11,a23}
Relevance for the application:
Modulo the following equation:
2 2 2 2
0=a11 + 4*a13 + 4*a23 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2 2 2
HAM=(u1 *a11 *a23 + 2*u1*u3*a11*a13*a23 + u1*v2*a11*a23*b12 + u2 *a11 *a23
2
+ 2*u2*u3*a11*a23 - u2*v1*a11*a23*b12
1 2 1 2
+ u2*(---*a11 *n3 + ---*b12 *kap*n3) + u3*a11*a23*n3 + v3*a11*a23*m3)/(a11
2 2
*a23)
has apart from the Hamiltonian and Casimirs only the following first integral:
2 2
FI=u1 *u3
4 2 2 2 2 2 4 1 2 2 2
*( - a11 *a23 - 2*a11 *a13 *a23 - 4*a11 *a23 - ---*a11 *a23 *b12 *kap) +
2
2 1 3 2 2 2 4
u1 *u3*(---*a11 *a23 *n3 + 2*a11*a13 *a23 *n3 + 2*a11*a23 *n3
2
1 2 2 1 2 2 2 2 2 2
- ---*a11*a23 *b12 *kap*n3) + ---*u1 *v1 *a11 *a23 *b12 + u1 *(
2 2
1 4 2 1 2 2 2 1 2 2 2
- ---*a11 *n3 + ---*a11 *a23 *n3 - ---*a11 *b12 *kap*n3
8 2 4
1 2 2 2 1 4 2 2 2 2 3
+ ---*a23 *b12 *kap*n3 - ---*b12 *kap *n3 ) + 4*u1*u2*u3 *a11 *a13*a23
2 8
3 2
+ u1*u2*u3*(a11 *a13*a23*n3 + a11*a13*a23*b12 *kap*n3)
2 2 2 3 3 2
+ u1*u2*v1*v2*a11 *a23 *b12 - 2*u1*u3 *a11 *a13*a23
2 3 2 2 2 3
- u1*u3 *v2*a11 *a23 *b12 - 2*u1*u3 *v3*a11 *a23 *b12
2 2 2 2 2 2
+ 2*u1*u3 *a11 *a13*a23 *n3 + u1*u3*v1*v3*a11 *a23 *b12
2 2
+ 2*u1*u3*v2*a11 *a23 *b12*n3 + u1*u3*v3
1 3 3 1 3
*( - ---*a11 *a23*b12*n3 + 2*a11*a23 *b12*n3 - ---*a11*a23*b12 *kap*n3)
2 2
2 2 2 2
+ 2*u1*u3*a11*a13*a23 *n3 - 2*u1*v1*a11 *a23 *m3*n3
1 2 2 1 3 2 2 2
+ u1*v3*(---*a11 *a23*b12*n3 + ---*a23*b12 *kap*n3 ) + u2 *u3
2 2
4 2 2 2 2 2 4 1 2 2 2
*( - a11 *a23 - 4*a11 *a13 *a23 - 2*a11 *a23 - ---*a11 *a23 *b12 *kap) +
2
2 3 3 2 2 2 4
u2 *u3*(---*a11 *a23 *n3 + 2*a11*a13 *a23 *n3 + 2*a11*a23 *n3
2
1 2 2 1 2 2 2 2 2
+ ---*a11*a23 *b12 *kap*n3) + ---*u2 *v2 *a11 *a23 *b12
2 2
2 1 2 2 2 1 2 2 2 3 3 3
+ u2 *(---*a11 *a23 *n3 + ---*a23 *b12 *kap*n3 ) - 2*u2*u3 *a11 *a23
2 2
2 3 2 2 2 2
+ u2*u3 *v1*a11 *a23 *b12 + 2*u2*u3 *v3*a11 *a13*a23 *b12
2 1 4 2 3 1 2 2
+ u2*u3 *( - ---*a11 *a23*n3 + 2*a11 *a23 *n3 - ---*a11 *a23*b12 *kap*n3)
2 2
2 2 2 2 2
- 2*u2*u3*v1*a11 *a23 *b12*n3 + u2*u3*v2*v3*a11 *a23 *b12
2
- 2*u2*u3*v3*a11*a13*a23 *b12*n3
1 3 2 3 2 1 2 2
+ u2*u3*(---*a11 *a23*n3 + 2*a11*a23 *n3 + ---*a11*a23*b12 *kap*n3 )
2 2
2 2 1 2 3 1 2 3
- 2*u2*v2*a11 *a23 *m3*n3 + u2*(---*a11 *a23*n3 + ---*a23*b12 *kap*n3 )
2 2
4 2 2 2 2 4 3 2 3
+ u3 *( - 2*a11 *a13 *a23 - 2*a11 *a23 ) + 2*u3 *v1*a11 *a23 *b12
3 2 2 3 3 2 2 2
- 2*u3 *v2*a11 *a13*a23 *b12 + u3 *( - a11 *a23 *n3 - a11*a23 *b12 *kap*n3)
1 2 2 2 2 2 2 1 3
- ---*u3 *v1 *a11 *a23 *b12 + u3 *v1*(---*a11 *a23*b12*n3
2 2
2 2 3 1 3
+ 2*a11 *a13*a23 *m3 - 2*a11*a23 *b12*n3 + ---*a11*a23*b12 *kap*n3)
2
1 2 2 2 2 2
- ---*u3 *v2 *a11 *a23 *b12
2
2 2 3 2 2 3 2
+ u3 *v2*(2*a11 *a23 *m3 + 2*a11*a13*a23 *b12*n3) - u3 *v3*a11 *a23 *m3 +
2 1 4 2 1 2 2 2 1 2 2 2
u3 *( - ---*a11 *n3 + ---*a11 *a23 *kap*m3 - ---*a11 *b12 *kap*n3
8 2 4
1 2 2 2 1 4 2 2 2 2 2
+ ---*a23 *b12 *kap*n3 - ---*b12 *kap *n3 ) + u3*v1 *a11*a23 *b12 *n3
2 8
+ u3*v1
1 2 2 2 1 3 2
*( - ---*a11 *a23*b12*n3 - 2*a11*a13*a23 *m3*n3 - ---*a23*b12 *kap*n3 )
2 2
2 2 2
+ u3*v2 *a11*a23 *b12 *n3
1 3 3 1 2
+ u3*v2*(---*a11 *a23*m3*n3 - 2*a11*a23 *m3*n3 + ---*a11*a23*b12 *kap*m3*n3)
2 2
2 2 2 2 2 2 3
+ u3*v3 *a11*a23 *b12 *n3 + u3*( - a11*a23 *kap*m3 *n3 + a11*a23 *n3 )
1 2 2 1 2 2
+ v2*( - ---*a11 *a23*m3*n3 - ---*a23*b12 *kap*m3*n3 )
2 2
1
= a product of the elements of: { - ---,
8
2 2
u1 *u3
4 2 2 2 2 2 4 2 2 2
*(8*a11 *a23 + 16*a11 *a13 *a23 + 32*a11 *a23 + 4*a11 *a23 *b12 *kap) +
2 3 2 2 2 4
u1 *u3*( - 4*a11 *a23 *n3 - 16*a11*a13 *a23 *n3 - 16*a11*a23 *n3
2 2 2 2 2 2 2 2 4 2
+ 4*a11*a23 *b12 *kap*n3) - 4*u1 *v1 *a11 *a23 *b12 + u1 *(a11 *n3
2 2 2 2 2 2 2 2 2
- 4*a11 *a23 *n3 + 2*a11 *b12 *kap*n3 - 4*a23 *b12 *kap*n3
4 2 2 2 2 3
+ b12 *kap *n3 ) - 32*u1*u2*u3 *a11 *a13*a23
3 2
+ u1*u2*u3*( - 8*a11 *a13*a23*n3 - 8*a11*a13*a23*b12 *kap*n3)
2 2 2 3 3 2
- 8*u1*u2*v1*v2*a11 *a23 *b12 + 16*u1*u3 *a11 *a13*a23
2 3 2 2 2 3
+ 8*u1*u3 *v2*a11 *a23 *b12 + 16*u1*u3 *v3*a11 *a23 *b12
2 2 2 2 2 2
- 16*u1*u3 *a11 *a13*a23 *n3 - 8*u1*u3*v1*v3*a11 *a23 *b12
2 2
- 16*u1*u3*v2*a11 *a23 *b12*n3
3 3 3
+ u1*u3*v3*(4*a11 *a23*b12*n3 - 16*a11*a23 *b12*n3 + 4*a11*a23*b12 *kap*n3)
2 2 2 2
- 16*u1*u3*a11*a13*a23 *n3 + 16*u1*v1*a11 *a23 *m3*n3
2 2 3 2 2 2
+ u1*v3*( - 4*a11 *a23*b12*n3 - 4*a23*b12 *kap*n3 ) + u2 *u3
4 2 2 2 2 2 4 2 2 2
*(8*a11 *a23 + 32*a11 *a13 *a23 + 16*a11 *a23 + 4*a11 *a23 *b12 *kap) +
2 3 2 2 2 4
u2 *u3*( - 12*a11 *a23 *n3 - 16*a11*a13 *a23 *n3 - 16*a11*a23 *n3
2 2 2 2 2 2 2
- 4*a11*a23 *b12 *kap*n3) - 4*u2 *v2 *a11 *a23 *b12
2 2 2 2 2 2 2 3 3 3
+ u2 *( - 4*a11 *a23 *n3 - 4*a23 *b12 *kap*n3 ) + 16*u2*u3 *a11 *a23
2 3 2 2 2 2
- 8*u2*u3 *v1*a11 *a23 *b12 - 16*u2*u3 *v3*a11 *a13*a23 *b12
2 4 2 3 2 2
+ u2*u3 *(4*a11 *a23*n3 - 16*a11 *a23 *n3 + 4*a11 *a23*b12 *kap*n3)
2 2 2 2 2
+ 16*u2*u3*v1*a11 *a23 *b12*n3 - 8*u2*u3*v2*v3*a11 *a23 *b12
2
+ 16*u2*u3*v3*a11*a13*a23 *b12*n3
3 2 3 2 2 2
+ u2*u3*( - 4*a11 *a23*n3 - 16*a11*a23 *n3 - 4*a11*a23*b12 *kap*n3 )
2 2 2 3 2 3
+ 16*u2*v2*a11 *a23 *m3*n3 + u2*( - 4*a11 *a23*n3 - 4*a23*b12 *kap*n3 )
4 2 2 2 2 4 3 2 3
+ u3 *(16*a11 *a13 *a23 + 16*a11 *a23 ) - 16*u3 *v1*a11 *a23 *b12
3 2 2
+ 16*u3 *v2*a11 *a13*a23 *b12
3 3 2 2 2 2 2 2 2 2
+ u3 *(8*a11 *a23 *n3 + 8*a11*a23 *b12 *kap*n3) + 4*u3 *v1 *a11 *a23 *b12 +
2 3 2 2 3
u3 *v1*( - 4*a11 *a23*b12*n3 - 16*a11 *a13*a23 *m3 + 16*a11*a23 *b12*n3
3 2 2 2 2 2
- 4*a11*a23*b12 *kap*n3) + 4*u3 *v2 *a11 *a23 *b12
2 2 3 2
+ u3 *v2*( - 16*a11 *a23 *m3 - 16*a11*a13*a23 *b12*n3)
2 3 2 2 4 2 2 2 2
+ 8*u3 *v3*a11 *a23 *m3 + u3 *(a11 *n3 - 4*a11 *a23 *kap*m3
2 2 2 2 2 2 4 2 2
+ 2*a11 *b12 *kap*n3 - 4*a23 *b12 *kap*n3 + b12 *kap *n3 )
2 2 2
- 8*u3*v1 *a11*a23 *b12 *n3
2 2 2 3 2
+ u3*v1*(4*a11 *a23*b12*n3 + 16*a11*a13*a23 *m3*n3 + 4*a23*b12 *kap*n3 )
2 2 2
- 8*u3*v2 *a11*a23 *b12 *n3
3 3 2
+ u3*v2*( - 4*a11 *a23*m3*n3 + 16*a11*a23 *m3*n3 - 4*a11*a23*b12 *kap*m3*n3)
2 2 2 2 2 2 3
- 8*u3*v3 *a11*a23 *b12 *n3 + u3*(8*a11*a23 *kap*m3 *n3 - 8*a11*a23 *n3 )
2 2 2 2
+ v2*(4*a11 *a23*m3*n3 + 4*a23*b12 *kap*m3*n3 )}
{HAM,FI} = 0
And again in machine readable form:
HAM=(u1**2*a11**2*a23 + 2*u1*u3*a11*a13*a23 + u1*v2*a11*a23*b12 + u2**2*a11**2*
a23 + 2*u2*u3*a11*a23**2 - u2*v1*a11*a23*b12 + u2*(1/2*a11**2*n3 + 1/2*b12**2*
kap*n3) + u3*a11*a23*n3 + v3*a11*a23*m3)/(a11*a23)$
FI=u1**2*u3**2*( - a11**4*a23**2 - 2*a11**2*a13**2*a23**2 - 4*a11**2*a23**4 - 1/
2*a11**2*a23**2*b12**2*kap) + u1**2*u3*(1/2*a11**3*a23**2*n3 + 2*a11*a13**2*a23
**2*n3 + 2*a11*a23**4*n3 - 1/2*a11*a23**2*b12**2*kap*n3) + 1/2*u1**2*v1**2*a11**
2*a23**2*b12**2 + u1**2*( - 1/8*a11**4*n3**2 + 1/2*a11**2*a23**2*n3**2 - 1/4*a11
**2*b12**2*kap*n3**2 + 1/2*a23**2*b12**2*kap*n3**2 - 1/8*b12**4*kap**2*n3**2) +
4*u1*u2*u3**2*a11**2*a13*a23**3 + u1*u2*u3*(a11**3*a13*a23*n3 + a11*a13*a23*b12
**2*kap*n3) + u1*u2*v1*v2*a11**2*a23**2*b12**2 - 2*u1*u3**3*a11**3*a13*a23**2 -
u1*u3**2*v2*a11**3*a23**2*b12 - 2*u1*u3**2*v3*a11**2*a23**3*b12 + 2*u1*u3**2*a11
**2*a13*a23**2*n3 + u1*u3*v1*v3*a11**2*a23**2*b12**2 + 2*u1*u3*v2*a11**2*a23**2*
b12*n3 + u1*u3*v3*( - 1/2*a11**3*a23*b12*n3 + 2*a11*a23**3*b12*n3 - 1/2*a11*a23*
b12**3*kap*n3) + 2*u1*u3*a11*a13*a23**2*n3**2 - 2*u1*v1*a11**2*a23**2*m3*n3 + u1
*v3*(1/2*a11**2*a23*b12*n3**2 + 1/2*a23*b12**3*kap*n3**2) + u2**2*u3**2*( - a11
**4*a23**2 - 4*a11**2*a13**2*a23**2 - 2*a11**2*a23**4 - 1/2*a11**2*a23**2*b12**2
*kap) + u2**2*u3*(3/2*a11**3*a23**2*n3 + 2*a11*a13**2*a23**2*n3 + 2*a11*a23**4*
n3 + 1/2*a11*a23**2*b12**2*kap*n3) + 1/2*u2**2*v2**2*a11**2*a23**2*b12**2 + u2**
2*(1/2*a11**2*a23**2*n3**2 + 1/2*a23**2*b12**2*kap*n3**2) - 2*u2*u3**3*a11**3*
a23**3 + u2*u3**2*v1*a11**3*a23**2*b12 + 2*u2*u3**2*v3*a11**2*a13*a23**2*b12 +
u2*u3**2*( - 1/2*a11**4*a23*n3 + 2*a11**2*a23**3*n3 - 1/2*a11**2*a23*b12**2*kap*
n3) - 2*u2*u3*v1*a11**2*a23**2*b12*n3 + u2*u3*v2*v3*a11**2*a23**2*b12**2 - 2*u2*
u3*v3*a11*a13*a23**2*b12*n3 + u2*u3*(1/2*a11**3*a23*n3**2 + 2*a11*a23**3*n3**2 +
1/2*a11*a23*b12**2*kap*n3**2) - 2*u2*v2*a11**2*a23**2*m3*n3 + u2*(1/2*a11**2*
a23*n3**3 + 1/2*a23*b12**2*kap*n3**3) + u3**4*( - 2*a11**2*a13**2*a23**2 - 2*a11
**2*a23**4) + 2*u3**3*v1*a11**2*a23**3*b12 - 2*u3**3*v2*a11**2*a13*a23**2*b12 +
u3**3*( - a11**3*a23**2*n3 - a11*a23**2*b12**2*kap*n3) - 1/2*u3**2*v1**2*a11**2*
a23**2*b12**2 + u3**2*v1*(1/2*a11**3*a23*b12*n3 + 2*a11**2*a13*a23**2*m3 - 2*a11
*a23**3*b12*n3 + 1/2*a11*a23*b12**3*kap*n3) - 1/2*u3**2*v2**2*a11**2*a23**2*b12
**2 + u3**2*v2*(2*a11**2*a23**3*m3 + 2*a11*a13*a23**2*b12*n3) - u3**2*v3*a11**3*
a23**2*m3 + u3**2*( - 1/8*a11**4*n3**2 + 1/2*a11**2*a23**2*kap*m3**2 - 1/4*a11**
2*b12**2*kap*n3**2 + 1/2*a23**2*b12**2*kap*n3**2 - 1/8*b12**4*kap**2*n3**2) + u3
*v1**2*a11*a23**2*b12**2*n3 + u3*v1*( - 1/2*a11**2*a23*b12*n3**2 - 2*a11*a13*a23
**2*m3*n3 - 1/2*a23*b12**3*kap*n3**2) + u3*v2**2*a11*a23**2*b12**2*n3 + u3*v2*(1
/2*a11**3*a23*m3*n3 - 2*a11*a23**3*m3*n3 + 1/2*a11*a23*b12**2*kap*m3*n3) + u3*v3
**2*a11*a23**2*b12**2*n3 + u3*( - a11*a23**2*kap*m3**2*n3 + a11*a23**2*n3**3) +
v2*( - 1/2*a11**2*a23*m3*n3**2 - 1/2*a23*b12**2*kap*m3*n3**2)$