Solution 1 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r13=0
r14=0
r15=0
c22*r29
r20=---------
a33
r21=0
c22*r29
r22=---------
a33
r23=0
r24=0
r26=0
r27=0
r28=0
r210=0
r212=0
r213=0
a11*r29 - a22*r29
r214=-------------------
a11 - a33
r215=0
r216=0
r217=0
r218=0
r219=0
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=0
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=0
r333=0
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
r341=0
r342=0
r343=0
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r350=0
r351=0
r352=0
r353=0
r354=0
r355=0
1 2 1 2 2 1
r40=( - ---*a11 *a33*c22*r446 - ---*a11 *c22 *r464 + ---*a11*a22*a33*c22*r446
2 2 2
1 2 1 2 1 2
+ ---*a11*a22*c22 *r4114 + ---*a11*a22*c22 *r464 + ---*a11*a33 *c22*r446
2 2 2
1 2 1 2 1 2 2
- ---*a11*a33*c22 *r4114 + ---*a11*a33*c22 *r464 - ---*a22 *c22 *r4114
2 2 2
1 2 1 2 1 2
- ---*a22*a33 *c22*r446 + ---*a22*a33*c22 *r4114 - ---*a22*a33*c22 *r464)/
2 2 2
2 2 2 2 2
(a11 *a33 - 2*a11*a22*a33 + a22 *a33 )
r41=0
2 1
r42=( - a11*a33*c22*r446 - a11*c22 *r464 + ---*a22*a33*c22*r446
2
1 2 2 2 2
+ ---*a33 *c22*r446 + a33*c22 *r464)/(a11*a33 - a22*a33 )
2
r43=0
1 1 2 1
r44=( - ---*a11*a33*c22*r446 - ---*a11*c22 *r464 + ---*a22*a33*c22*r446
2 2 2
1 2 1 2 1 2 2
- ---*a22*c22 *r4114 + ---*a33*c22 *r4114 + ---*a33*c22 *r464)/(a11*a33
2 2 2
2
- a22*a33 )
r45=0
r46=0
r47=0
r48=0
1 2 2 2 1
r49=( - ---*a11 *a33*c22*r446 - a11 *c22 *r464 + ---*a11*a22*a33*c22*r446
2 2
2 1 2 2
+ a11*a22*c22 *r464 + ---*a11*a33 *c22*r446 + a11*a33*c22 *r464
2
1 2 2 2 2 2
- ---*a22*a33 *c22*r446 - a22*a33*c22 *r464)/(a11 *a33 - 2*a11*a22*a33
2
2 2
+ a22 *a33 )
r410=0
r411=
1 2 1 2
- ---*a11*a33*c22*r446 - a11*c22 *r464 + ---*a22*a33*c22*r446 + a33*c22 *r464
2 2
--------------------------------------------------------------------------------
2 2
a11*a33 - a22*a33
r412=0
r413=0
r415
2
a11 *c22*r4102 - a11*a22*c22*r4102 - a11*a33*c22*r4102 + a22*a33*c22*r4102
=----------------------------------------------------------------------------
2 2
a11 *a33 - 2*a11*a22*a33 + a22 *a33
r416=0
a11*c22*r4102 - a33*c22*r4102
r417=-------------------------------
a11*a33 - a22*a33
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
r425=0
r426=0
1 1
- ---*a11*a33*r446 + ---*a22*a33*r446 - a22*c22*r4114 + a33*c22*r4114
2 2
r427=------------------------------------------------------------------------
a11*a33 - a22*a33
r428=0
r429=0
1 1
- ---*a11*a33*r446 - a11*c22*r464 + ---*a22*a33*r446 + a33*c22*r464
2 2
r430=----------------------------------------------------------------------
a11*a33 - a22*a33
a11*r4102 - a33*r4102
r431=-----------------------
a11 - a22
r432=0
r433=0
1 1 1 1
---*a11*r464 - ---*a22*r4114 + ---*a33*r4114 - ---*a33*r464
2 2 2 2
r434=-------------------------------------------------------------
a11 - a22
r435=0
a11*c22*r4102 - a33*c22*r4102
r436=-------------------------------
a11*a33 - a22*a33
r437=0
2 2
a11 *c22*r4102 - 2*a11*a33*c22*r4102 + a33 *c22*r4102
r438=-------------------------------------------------------
2 2 2
a11 *a33 - a11*a22*a33 - a11*a33 + a22*a33
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
r447=0
r448=0
r449=0
r450=0
r451=0
a11*r4102 - a33*r4102
r452=-----------------------
a11 - a22
r453=0
r454=0
1 1 2
- ---*a11*a33*r446 + a22*c22*r4114 + ---*a33 *r446 - a33*c22*r4114
2 2
r455=---------------------------------------------------------------------
2
a11*a33 - a33
r456=0
r458=0
r459=0
1
- ---*a33*r446 - c22*r464
2
r460=----------------------------
a33
r461=r4102
r462=0
r463=0
r465=0
r466=r4102
r467=0
r468=0
1 2 1 1 1
r469=(---*a11 *r464 + ---*a11*a22*r4114 - ---*a11*a22*r464 - ---*a11*a33*r4114
2 2 2 2
1 1 2 1
- ---*a11*a33*r464 - ---*a22 *r4114 + ---*a22*a33*r4114
2 2 2
1 2 2
+ ---*a22*a33*r464)/(a11 - 2*a11*a33 + a33 )
2
r470=0
r471=0
r472=0
r473=0
a11*c22*r4102 - a33*c22*r4102
r474=-------------------------------
a11*a33 - a22*a33
r475=0
a11*c22*r4102 - a33*c22*r4102
r476=-------------------------------
a11*a33 - a22*a33
r477=0
r478=0
r479=0
r480=0
r481=0
r482=0
r483=r446
r484=0
r485=0
r486=0
r487=0
a11*r4102 - a33*r4102
r488=-----------------------
a11 - a22
r489=0
r490=0
r491=0
r492=0
r493=0
r494=r446
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4103=0
r4104=0
1
- ---*a33*r446 + c22*r4114
2
r4105=-----------------------------
a33
r4106=0
1
- ---*a33*r446 + c22*r4114
2
r4107=-----------------------------
a33
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
r4115=0
r4117=0
r4118=0
a11*r4114 - a22*r4114
r4119=-----------------------
a11 - a33
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
m3=0
m2=0
m1=0
n3=0
n2=0
n1=0
a11*a22*c22 - a22*a33*c22
c33=---------------------------
a11*a33 - a22*a33
c23=0
c13=0
c12=0
c11=0
b33=0
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
b11=0
a23=0
a13=0
a12=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:
r29, r4114, r4102, r446, r464, c22, a33, a11, a22
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*a22 + a11*a33 - a22*a33,
a11,
a22,
a33,
a11 - a22,
a22 - a33,
a11 - a33,
a11*a22 - a11*a33 - a22*a33}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a12,
a13,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
b33,
c11,
c12,
c13,
c23,
- a11*a22*c22 + a11*a33*c33 + a22*a33*c22 - a22*a33*c33,
n1,
n2,
n3,
m1,
m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2 2 2 2 2 a11*a22*c22 - a22*a33*c22
HAM=u1 *a11 + u2 *a22 + u3 *a33 + v2 *c22 + v3 *---------------------------
a11*a33 - a22*a33
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
4 3 2 2 2 2 3 2 2 3
FI=u2 *(a11 *a33 - 2*a11 *a22*a33 - a11 *a33 + a11*a22 *a33 + 2*a11*a22*a33
2 3 2 2 3 2 2 2 2 3
- a22 *a33 ) + u2 *u3 *(2*a11 *a33 - 2*a11 *a22*a33 - 4*a11 *a33
3 4 4 2 2 3
+ 4*a11*a22*a33 + 2*a11*a33 - 2*a22*a33 ) + u2 *v1 *( - 2*a11 *a33*c22
2 2 2 2
+ 2*a11 *a22*a33*c22 + 4*a11 *a33 *c22 - 4*a11*a22*a33 *c22
3 3
- 2*a11*a33 *c22 + 2*a22*a33 *c22)
4 3 2 2 3 4 5 2 2
+ u3 *(a11 *a33 - 3*a11 *a33 + 3*a11*a33 - a33 ) + u3 *v1
3 2 2 3 4
*( - 2*a11 *a33*c22 + 6*a11 *a33 *c22 - 6*a11*a33 *c22 + 2*a33 *c22)
2 2 3 2 2 2 2 2 3 2
+ v1 *v2 *( - 2*a11 *c22 + 6*a11 *a33*c22 - 6*a11*a33 *c22 + 2*a33 *c22 )
2 2 3 2 2 2 2 2 3 2
+ v1 *v3 *( - 2*a11 *c22 + 6*a11 *a33*c22 - 6*a11*a33 *c22 + 2*a33 *c22 )
4 3 2 2 2 2 2 3 2
+ v2 *( - a11 *c22 + 3*a11 *a33*c22 - 3*a11*a33 *c22 + a33 *c22 )
2 2 3 2 2 2 2 2 3 2
+ v2 *v3 *( - 2*a11 *c22 + 6*a11 *a33*c22 - 6*a11*a33 *c22 + 2*a33 *c22 )
4 3 2 2 2 2 2 3 2
+ v3 *( - a11 *c22 + 3*a11 *a33*c22 - 3*a11*a33 *c22 + a33 *c22 )
= a product of the elements of: {a11 - a33,
2 2 2 2
u2 *(a11*a33 - a22*a33) + u3 *(a11*a33 - a33 ) + v2 *(a11*c22 - a33*c22)
2
+ v3 *(a11*c22 - a33*c22),
2 2 2
u2 *(a11*a33 - a22*a33) + u3 *(a11*a33 - a33 )
2 2
+ v1 *( - 2*a11*c22 + 2*a33*c22) + v2 *( - a11*c22 + a33*c22)
2
+ v3 *( - a11*c22 + a33*c22)}
{HAM,FI} = 0
2 2 3 2 2 2 2 3
FI=u1 *v2 *( - a11 *a33 + a11 *a22*a33 + 2*a11 *a33 - 2*a11*a22*a33 - a11*a33
3 2 2 3 2 2 2
+ a22*a33 ) + u1 *v3 *( - a11 *a33 + a11 *a22*a33 + 2*a11 *a33
2 3 3 3
- 2*a11*a22*a33 - a11*a33 + a22*a33 ) + u1*u2*v1*v2*(2*a11 *a33
2 2 2 2 3 3
- 2*a11 *a22*a33 - 4*a11 *a33 + 4*a11*a22*a33 + 2*a11*a33 - 2*a22*a33
3 2 2 2
) + u1*u3*v1*v3*(2*a11 *a33 - 2*a11 *a22*a33 - 4*a11 *a33
2 3 3 2 2 3
+ 4*a11*a22*a33 + 2*a11*a33 - 2*a22*a33 ) + u2 *v1 *( - a11 *a33
2 2 2 2 3 3
+ a11 *a22*a33 + 2*a11 *a33 - 2*a11*a22*a33 - a11*a33 + a22*a33 ) +
2 2 3 2 2 2 2 3
u2 *v3 *( - a11 *a33 + a11 *a22*a33 + 2*a11 *a33 - 2*a11*a22*a33 - a11*a33
3 3 2
+ a22*a33 ) + u2*u3*v2*v3*(2*a11 *a33 - 2*a11 *a22*a33
2 2 2 3 3 2 2
- 4*a11 *a33 + 4*a11*a22*a33 + 2*a11*a33 - 2*a22*a33 ) + u3 *v1 *(
3 2 2 2 2 3
- a11 *a33 + a11 *a22*a33 + 2*a11 *a33 - 2*a11*a22*a33 - a11*a33
3 2 2 3 2 2 2
+ a22*a33 ) + u3 *v2 *( - a11 *a33 + a11 *a22*a33 + 2*a11 *a33
2 3 3 2 2 3
- 2*a11*a22*a33 - a11*a33 + a22*a33 ) + v1 *v2 *( - a11 *c22
2 2 2
+ a11 *a22*c22 + 2*a11 *a33*c22 - 2*a11*a22*a33*c22 - a11*a33 *c22
2
+ a22*a33 *c22)
2 2 3 2 2 3 4
+ v1 *v3 *( - a11 *c22 + 3*a11 *a33*c22 - 3*a11*a33 *c22 + a33 *c22) + v2 *(
3 2 2
- a11 *c22 + a11 *a22*c22 + 2*a11 *a33*c22 - 2*a11*a22*a33*c22
2 2 2 2 3 2
- a11*a33 *c22 + a22*a33 *c22) + v2 *v3 *( - 2*a11 *c22 + a11 *a22*c22
2 2 2
+ 5*a11 *a33*c22 - 2*a11*a22*a33*c22 - 4*a11*a33 *c22 + a22*a33 *c22
3
+ a33 *c22)
4 3 2 2 3
+ v3 *( - a11 *c22 + 3*a11 *a33*c22 - 3*a11*a33 *c22 + a33 *c22)
= a product of the elements of: { - a11 + a33,
a11 - a33,
2 2 2 2
u1 *v2 *(a11*a33 - a22*a33) + u1 *v3 *(a11*a33 - a22*a33)
+ u1*u2*v1*v2*( - 2*a11*a33 + 2*a22*a33)
2 2
+ u1*u3*v1*v3*( - 2*a11*a33 + 2*a22*a33) + u2 *v1 *(a11*a33 - a22*a33)
2 2
+ u2 *v3 *(a11*a33 - a22*a33) + u2*u3*v2*v3*( - 2*a11*a33 + 2*a22*a33)
2 2 2 2
+ u3 *v1 *(a11*a33 - a22*a33) + u3 *v2 *(a11*a33 - a22*a33)
2 2 2 2
+ v1 *v2 *(a11*c22 - a22*c22) + v1 *v3 *(a11*c22 - a33*c22)
4 2 2
+ v2 *(a11*c22 - a22*c22) + v2 *v3 *(2*a11*c22 - a22*c22 - a33*c22)
4
+ v3 *(a11*c22 - a33*c22)}
{HAM,FI} = 0
2 3 2 2 2 2 3
FI=u1*u2 *v1*(a11 *a33 - a11 *a22*a33 - 2*a11 *a33 + 2*a11*a22*a33 + a11*a33
3
- a22*a33 )
2 3 2 2 3 4
+ u1*u3 *v1*(a11 *a33 - 3*a11 *a33 + 3*a11*a33 - a33 )
2 3 2 2 3
+ u1*v1*v2 *(a11 *c22 - 3*a11 *a33*c22 + 3*a11*a33 *c22 - a33 *c22)
2 3 2 2 3 3
+ u1*v1*v3 *(a11 *c22 - 3*a11 *a33*c22 + 3*a11*a33 *c22 - a33 *c22) + u2 *v2
3 2 2 2 2 3
*(a11 *a33 - a11 *a22*a33 - 2*a11 *a33 + 2*a11*a22*a33 + a11*a33
3 2 3 2 2 2
- a22*a33 ) + u2 *u3*v3*(a11 *a33 - a11 *a22*a33 - 2*a11 *a33
2 3 3
+ 2*a11*a22*a33 + a11*a33 - a22*a33 )
2 3 2 2 3 4
+ u2*u3 *v2*(a11 *a33 - 3*a11 *a33 + 3*a11*a33 - a33 )
3 3 2 2 3
+ u2*v2 *(a11 *c22 - 3*a11 *a33*c22 + 3*a11*a33 *c22 - a33 *c22)
2 3 2 2 3
+ u2*v2*v3 *(a11 *c22 - 3*a11 *a33*c22 + 3*a11*a33 *c22 - a33 *c22)
3 3 2 2 3 4
+ u3 *v3*(a11 *a33 - 3*a11 *a33 + 3*a11*a33 - a33 )
2 3 2 2 3
+ u3*v2 *v3*(a11 *c22 - 3*a11 *a33*c22 + 3*a11*a33 *c22 - a33 *c22)
3 3 2 2 3
+ u3*v3 *(a11 *c22 - 3*a11 *a33*c22 + 3*a11*a33 *c22 - a33 *c22)
= a product of the elements of: {a11 - a33,
a11 - a33,
u1*v1 + u2*v2 + u3*v3,
2 2 2 2
u2 *(a11*a33 - a22*a33) + u3 *(a11*a33 - a33 ) + v2 *(a11*c22 - a33*c22)
2
+ v3 *(a11*c22 - a33*c22)}
{HAM,FI} = 0
2 2 3 2 2 2 2 3 2 2
FI=u1 *u2 *(2*a11 *a33 - 4*a11 *a22*a33 - 2*a11 *a33 + 2*a11*a22 *a33
3 2 3 2 2 3 2
+ 4*a11*a22*a33 - 2*a22 *a33 ) + u1 *u3 *(2*a11 *a33
2 2 2 3 3 4
- 2*a11 *a22*a33 - 4*a11 *a33 + 4*a11*a22*a33 + 2*a11*a33
4 2 2 3 2
- 2*a22*a33 ) + u1 *v2 *(2*a11 *a33*c22 - 2*a11 *a22*a33*c22
2 2 2 3 3
- 4*a11 *a33 *c22 + 4*a11*a22*a33 *c22 + 2*a11*a33 *c22 - 2*a22*a33 *c22)
2 2 3 2 2 2
+ u1 *v3 *(2*a11 *a33*c22 - 2*a11 *a22*a33*c22 - 4*a11 *a33 *c22
2 3 3 4
+ 4*a11*a22*a33 *c22 + 2*a11*a33 *c22 - 2*a22*a33 *c22) + u2 *(
2 2 2 3 2 2 3 3 2
a11 *a22*a33 - a11 *a33 - 2*a11*a22 *a33 + 2*a11*a22*a33 + a22 *a33
2 3 2 2 2 2 2
- a22 *a33 ) + u2 *v3 *(2*a11 *a22*a33*c22 - 2*a11 *a33 *c22
2 3 2 2 3
- 2*a11*a22 *a33*c22 + 2*a11*a33 *c22 + 2*a22 *a33 *c22 - 2*a22*a33 *c22)
4 2 2 2 3 3 4 4
+ u3 *( - a11 *a22*a33 + a11 *a33 + 2*a11*a22*a33 - 2*a11*a33 - a22*a33
5 2 2 2 2 2
+ a33 ) + u3 *v2 *( - 2*a11 *a22*a33*c22 + 2*a11 *a33 *c22
2 3 3 4
+ 4*a11*a22*a33 *c22 - 4*a11*a33 *c22 - 2*a22*a33 *c22 + 2*a33 *c22) +
4 2 2 2 2 2 2 2
v2 *( - a11 *a22*c22 + a11 *a33*c22 + 2*a11*a22*a33*c22 - 2*a11*a33 *c22
2 2 3 2 4 2 2 2 2
- a22*a33 *c22 + a33 *c22 ) + v3 *(a11 *a22*c22 - a11 *a33*c22
2 2 2 2 2 3 2
- 2*a11*a22*a33*c22 + 2*a11*a33 *c22 + a22*a33 *c22 - a33 *c22 )
= a product of the elements of: {2,
2 2 2 2
u2 *(a11*a33 - a22*a33) + u3 *(a11*a33 - a33 ) + v2 *(a11*c22 - a33*c22)
2
+ v3 *(a11*c22 - a33*c22),
2 2 2 2
u1 *(a11 *a33 - a11*a22*a33 - a11*a33 + a22*a33 )
2 2 2
2 a11*a22*a33 - a11*a33 - a22 *a33 + a22*a33
+ u2 *----------------------------------------------
2
2 2 3
2 - a11*a22*a33 + a11*a33 + a22*a33 - a33
+ u3 *---------------------------------------------
2
2
2 - a11*a22*c22 + a11*a33*c22 + a22*a33*c22 - a33 *c22
+ v2 *-------------------------------------------------------
2
2
2 a11*a22*c22 - a11*a33*c22 - a22*a33*c22 + a33 *c22
+ v3 *----------------------------------------------------}
2
{HAM,FI} = 0
2 3 2 2 2 2 2
FI=u2 *(a11 *a33 - 2*a11 *a22*a33 - a11 *a33 + a11*a22 *a33 + 2*a11*a22*a33
2 2 2 3 2 2 2
- a22 *a33 ) + u3 *(a11 *a33 - a11 *a22*a33 - 2*a11 *a33
2 3 3 2 3 2
+ 2*a11*a22*a33 + a11*a33 - a22*a33 ) + v2 *(a11 *c22 - a11 *a22*c22
2 2 2 2
- 2*a11 *a33*c22 + 2*a11*a22*a33*c22 + a11*a33 *c22 - a22*a33 *c22) + v3
3 2 2 2
*(a11 *c22 - a11 *a22*c22 - 2*a11 *a33*c22 + 2*a11*a22*a33*c22 + a11*a33 *c22
2
- a22*a33 *c22)
= a product of the elements of: {a11 - a33,
a11 - a22,
2 2 2 2
u2 *(a11*a33 - a22*a33) + u3 *(a11*a33 - a33 ) + v2 *(a11*c22 - a33*c22)
2
+ v3 *(a11*c22 - a33*c22)}
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u2**2*a22 + u3**2*a33 + v2**2*c22 + v3**2*(a11*a22*c22 - a22*a33
*c22)/(a11*a33 - a22*a33)$
FI=u2**4*(a11**3*a33**2 - 2*a11**2*a22*a33**2 - a11**2*a33**3 + a11*a22**2*a33**
2 + 2*a11*a22*a33**3 - a22**2*a33**3) + u2**2*u3**2*(2*a11**3*a33**2 - 2*a11**2*
a22*a33**2 - 4*a11**2*a33**3 + 4*a11*a22*a33**3 + 2*a11*a33**4 - 2*a22*a33**4) +
u2**2*v1**2*( - 2*a11**3*a33*c22 + 2*a11**2*a22*a33*c22 + 4*a11**2*a33**2*c22 -
4*a11*a22*a33**2*c22 - 2*a11*a33**3*c22 + 2*a22*a33**3*c22) + u3**4*(a11**3*a33
**2 - 3*a11**2*a33**3 + 3*a11*a33**4 - a33**5) + u3**2*v1**2*( - 2*a11**3*a33*
c22 + 6*a11**2*a33**2*c22 - 6*a11*a33**3*c22 + 2*a33**4*c22) + v1**2*v2**2*( - 2
*a11**3*c22**2 + 6*a11**2*a33*c22**2 - 6*a11*a33**2*c22**2 + 2*a33**3*c22**2) +
v1**2*v3**2*( - 2*a11**3*c22**2 + 6*a11**2*a33*c22**2 - 6*a11*a33**2*c22**2 + 2*
a33**3*c22**2) + v2**4*( - a11**3*c22**2 + 3*a11**2*a33*c22**2 - 3*a11*a33**2*
c22**2 + a33**3*c22**2) + v2**2*v3**2*( - 2*a11**3*c22**2 + 6*a11**2*a33*c22**2
- 6*a11*a33**2*c22**2 + 2*a33**3*c22**2) + v3**4*( - a11**3*c22**2 + 3*a11**2*
a33*c22**2 - 3*a11*a33**2*c22**2 + a33**3*c22**2)$
FI=u1**2*v2**2*( - a11**3*a33 + a11**2*a22*a33 + 2*a11**2*a33**2 - 2*a11*a22*a33
**2 - a11*a33**3 + a22*a33**3) + u1**2*v3**2*( - a11**3*a33 + a11**2*a22*a33 + 2
*a11**2*a33**2 - 2*a11*a22*a33**2 - a11*a33**3 + a22*a33**3) + u1*u2*v1*v2*(2*
a11**3*a33 - 2*a11**2*a22*a33 - 4*a11**2*a33**2 + 4*a11*a22*a33**2 + 2*a11*a33**
3 - 2*a22*a33**3) + u1*u3*v1*v3*(2*a11**3*a33 - 2*a11**2*a22*a33 - 4*a11**2*a33
**2 + 4*a11*a22*a33**2 + 2*a11*a33**3 - 2*a22*a33**3) + u2**2*v1**2*( - a11**3*
a33 + a11**2*a22*a33 + 2*a11**2*a33**2 - 2*a11*a22*a33**2 - a11*a33**3 + a22*a33
**3) + u2**2*v3**2*( - a11**3*a33 + a11**2*a22*a33 + 2*a11**2*a33**2 - 2*a11*a22
*a33**2 - a11*a33**3 + a22*a33**3) + u2*u3*v2*v3*(2*a11**3*a33 - 2*a11**2*a22*
a33 - 4*a11**2*a33**2 + 4*a11*a22*a33**2 + 2*a11*a33**3 - 2*a22*a33**3) + u3**2*
v1**2*( - a11**3*a33 + a11**2*a22*a33 + 2*a11**2*a33**2 - 2*a11*a22*a33**2 - a11
*a33**3 + a22*a33**3) + u3**2*v2**2*( - a11**3*a33 + a11**2*a22*a33 + 2*a11**2*
a33**2 - 2*a11*a22*a33**2 - a11*a33**3 + a22*a33**3) + v1**2*v2**2*( - a11**3*
c22 + a11**2*a22*c22 + 2*a11**2*a33*c22 - 2*a11*a22*a33*c22 - a11*a33**2*c22 +
a22*a33**2*c22) + v1**2*v3**2*( - a11**3*c22 + 3*a11**2*a33*c22 - 3*a11*a33**2*
c22 + a33**3*c22) + v2**4*( - a11**3*c22 + a11**2*a22*c22 + 2*a11**2*a33*c22 - 2
*a11*a22*a33*c22 - a11*a33**2*c22 + a22*a33**2*c22) + v2**2*v3**2*( - 2*a11**3*
c22 + a11**2*a22*c22 + 5*a11**2*a33*c22 - 2*a11*a22*a33*c22 - 4*a11*a33**2*c22 +
a22*a33**2*c22 + a33**3*c22) + v3**4*( - a11**3*c22 + 3*a11**2*a33*c22 - 3*a11*
a33**2*c22 + a33**3*c22)$
FI=u1*u2**2*v1*(a11**3*a33 - a11**2*a22*a33 - 2*a11**2*a33**2 + 2*a11*a22*a33**2
+ a11*a33**3 - a22*a33**3) + u1*u3**2*v1*(a11**3*a33 - 3*a11**2*a33**2 + 3*a11*
a33**3 - a33**4) + u1*v1*v2**2*(a11**3*c22 - 3*a11**2*a33*c22 + 3*a11*a33**2*c22
- a33**3*c22) + u1*v1*v3**2*(a11**3*c22 - 3*a11**2*a33*c22 + 3*a11*a33**2*c22 -
a33**3*c22) + u2**3*v2*(a11**3*a33 - a11**2*a22*a33 - 2*a11**2*a33**2 + 2*a11*
a22*a33**2 + a11*a33**3 - a22*a33**3) + u2**2*u3*v3*(a11**3*a33 - a11**2*a22*a33
- 2*a11**2*a33**2 + 2*a11*a22*a33**2 + a11*a33**3 - a22*a33**3) + u2*u3**2*v2*(
a11**3*a33 - 3*a11**2*a33**2 + 3*a11*a33**3 - a33**4) + u2*v2**3*(a11**3*c22 - 3
*a11**2*a33*c22 + 3*a11*a33**2*c22 - a33**3*c22) + u2*v2*v3**2*(a11**3*c22 - 3*
a11**2*a33*c22 + 3*a11*a33**2*c22 - a33**3*c22) + u3**3*v3*(a11**3*a33 - 3*a11**
2*a33**2 + 3*a11*a33**3 - a33**4) + u3*v2**2*v3*(a11**3*c22 - 3*a11**2*a33*c22 +
3*a11*a33**2*c22 - a33**3*c22) + u3*v3**3*(a11**3*c22 - 3*a11**2*a33*c22 + 3*
a11*a33**2*c22 - a33**3*c22)$
FI=u1**2*u2**2*(2*a11**3*a33**2 - 4*a11**2*a22*a33**2 - 2*a11**2*a33**3 + 2*a11*
a22**2*a33**2 + 4*a11*a22*a33**3 - 2*a22**2*a33**3) + u1**2*u3**2*(2*a11**3*a33
**2 - 2*a11**2*a22*a33**2 - 4*a11**2*a33**3 + 4*a11*a22*a33**3 + 2*a11*a33**4 -
2*a22*a33**4) + u1**2*v2**2*(2*a11**3*a33*c22 - 2*a11**2*a22*a33*c22 - 4*a11**2*
a33**2*c22 + 4*a11*a22*a33**2*c22 + 2*a11*a33**3*c22 - 2*a22*a33**3*c22) + u1**2
*v3**2*(2*a11**3*a33*c22 - 2*a11**2*a22*a33*c22 - 4*a11**2*a33**2*c22 + 4*a11*
a22*a33**2*c22 + 2*a11*a33**3*c22 - 2*a22*a33**3*c22) + u2**4*(a11**2*a22*a33**2
- a11**2*a33**3 - 2*a11*a22**2*a33**2 + 2*a11*a22*a33**3 + a22**3*a33**2 - a22
**2*a33**3) + u2**2*v3**2*(2*a11**2*a22*a33*c22 - 2*a11**2*a33**2*c22 - 2*a11*
a22**2*a33*c22 + 2*a11*a33**3*c22 + 2*a22**2*a33**2*c22 - 2*a22*a33**3*c22) + u3
**4*( - a11**2*a22*a33**2 + a11**2*a33**3 + 2*a11*a22*a33**3 - 2*a11*a33**4 -
a22*a33**4 + a33**5) + u3**2*v2**2*( - 2*a11**2*a22*a33*c22 + 2*a11**2*a33**2*
c22 + 4*a11*a22*a33**2*c22 - 4*a11*a33**3*c22 - 2*a22*a33**3*c22 + 2*a33**4*c22)
+ v2**4*( - a11**2*a22*c22**2 + a11**2*a33*c22**2 + 2*a11*a22*a33*c22**2 - 2*
a11*a33**2*c22**2 - a22*a33**2*c22**2 + a33**3*c22**2) + v3**4*(a11**2*a22*c22**
2 - a11**2*a33*c22**2 - 2*a11*a22*a33*c22**2 + 2*a11*a33**2*c22**2 + a22*a33**2*
c22**2 - a33**3*c22**2)$
FI=u2**2*(a11**3*a33 - 2*a11**2*a22*a33 - a11**2*a33**2 + a11*a22**2*a33 + 2*a11
*a22*a33**2 - a22**2*a33**2) + u3**2*(a11**3*a33 - a11**2*a22*a33 - 2*a11**2*a33
**2 + 2*a11*a22*a33**2 + a11*a33**3 - a22*a33**3) + v2**2*(a11**3*c22 - a11**2*
a22*c22 - 2*a11**2*a33*c22 + 2*a11*a22*a33*c22 + a11*a33**2*c22 - a22*a33**2*c22
) + v3**2*(a11**3*c22 - a11**2*a22*c22 - 2*a11**2*a33*c22 + 2*a11*a22*a33*c22 +
a11*a33**2*c22 - a22*a33**2*c22)$