Solution 2 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=a12 + a13
Expressions
The solution is given through the following expressions:
1 7 5 6 2 2
r40=(----*a12 *a13*a33*c23*r482 + ----*a12 *a13 *c23 *r4103
12 24
7 6 2 2 1 5 3
- ----*a12 *a33 *c23 *r4103 + ---*a12 *a13 *a33*c23*r482
24 6
5 5 3 7 4 4 2
- ---*a12 *a13*a33 *c23*r482 + ----*a12 *a13 *c23 *r4103
8 24
1 4 2 3 29 4 2 2 2
- ---*a12 *a13 *a33 *c23*r481 - ----*a12 *a13 *a33 *c23 *r4103
8 60
1 3 5 3 3 3
+ ----*a12 *a13 *a33*c23*r482 + a12 *a13 *a33 *c23*r482
12
1 2 6 2 1 2 4 3
- ---*a12 *a13 *c23 *r4103 + ---*a12 *a13 *a33 *c23*r481
6 4
53 2 4 2 2 3 2 2 4 2
+ -----*a12 *a13 *a33 *c23 *r4103 + ----*a12 *a13 *a33 *c23 *r4103
240 16
1 5 3 1 8 2
+ ---*a12*a13 *a33 *c23*r482 - ---*a13 *c23 *r4103
8 4
1 6 3 33 6 2 2
- ---*a13 *a33 *c23*r481 + ----*a13 *a33 *c23 *r4103
8 80
3 4 4 2 4 3 3
+ ----*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
16
3 2 2
r41=(2*a12 *a13*a33*c23*r482 + a12 *a13 *a33*c23*r481
5 2 2 2 1 2 2 2
+ ----*a12 *a13 *c23 *r4103 - ---*a12 *a33 *c23 *r4103
12 4
5 4 2 1 2 2 2 3 2
+ ----*a13 *c23 *r4103 - ---*a13 *a33 *c23 *r4103)/(a12 *a13 *a33)
12 4
1 7 3 1 6 4 2
r42=(---*a12 *a13*a33 *c23*r482 - ---*a12 *a13 *c23 *r4103
4 8
1 6 2 3 5 6 2 2 2
- ----*a12 *a13 *a33 *c23*r481 + ----*a12 *a13 *a33 *c23 *r4103
12 12
1 6 4 2 1 5 3 3
- ---*a12 *a33 *c23 *r4103 - ---*a12 *a13 *a33 *c23*r482
6 2
5 4 6 2 5 4 4 3
+ ---*a12 *a13 *c23 *r4103 + ---*a12 *a13 *a33 *c23*r481
4 6
17 4 4 2 2 1 4 2 5
- ----*a12 *a13 *a33 *c23 *r4103 + ---*a12 *a13 *a33 *c23*r481
4 2
7 4 2 4 2 3 3 5 3
+ ---*a12 *a13 *a33 *c23 *r4103 - ---*a12 *a13 *a33 *c23*r482
8 4
1 3 3 5 11 2 8 2
+ ---*a12 *a13 *a33 *c23*r482 + ----*a12 *a13 *c23 *r4103
2 8
11 2 6 3 115 2 6 2 2
+ ----*a12 *a13 *a33 *c23*r481 - -----*a12 *a13 *a33 *c23 *r4103
12 24
67 2 4 4 2 1 8 2 2
+ ----*a12 *a13 *a33 *c23 *r4103 - ---*a13 *a33 *c23 *r4103
60 8
3 6 4 2 4 3 5
+ ----*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
40
1 5 3 1 4 4 2
r43=( - ---*a12 *a13*a33 *c23*r482 + ---*a12 *a13 *c23 *r4103
2 4
1 4 2 3 5 4 2 2 2
+ ---*a12 *a13 *a33 *c23*r481 - ---*a12 *a13 *a33 *c23 *r4103
6 6
1 4 4 2 1 3 3 3
+ ---*a12 *a33 *c23 *r4103 + ---*a12 *a13 *a33 *c23*r482
3 3
1 2 6 2 1 2 4 3
+ ---*a12 *a13 *c23 *r4103 + ---*a12 *a13 *a33 *c23*r481
2 3
13 2 4 2 2 7 2 2 4 2
- ----*a12 *a13 *a33 *c23 *r4103 + ----*a12 *a13 *a33 *c23 *r4103
6 12
1 5 3 1 8 2
- ---*a12*a13 *a33 *c23*r482 + ---*a13 *c23 *r4103
6 4
1 6 3 4 6 2 2
+ ---*a13 *a33 *c23*r481 - ---*a13 *a33 *c23 *r4103
6 3
1 4 4 2 3 4 3
+ ---*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
4
5 2 2 2 3 2 2 2 5 4 2
r45=(----*a12 *a13 *c23 *r4103 + ---*a12 *a33 *c23 *r4103 + ----*a13 *c23 *r4103
12 4 12
5 2 2 2 2 2 2
- ---*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
4
1 5 5 4 2 2
r46=( - ---*a12 *a13*a33*c23*r482 - ---*a12 *a13 *c23 *r4103
3 6
7 4 2 2 1 3 3
+ ---*a12 *a33 *c23 *r4103 - ---*a12 *a13 *a33*c23*r482
6 3
11 2 4 2 67 2 2 2 2
- ----*a12 *a13 *c23 *r4103 - ----*a12 *a13 *a33 *c23 *r4103
6 30
6 2 3 4 2 2 3 3 2
- a13 *c23 *r4103 + ---*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
5
1 5 7 4 2 2
r47=(---*a12 *a13*a33*c23*r482 + ----*a12 *a13 *c23 *r4103
3 12
5 4 2 2 1 3 3
- ---*a12 *a33 *c23 *r4103 + ---*a12 *a13 *a33*c23*r482
3 3
1 2 4 2 29 2 2 2 2
+ ---*a12 *a13 *c23 *r4103 + ----*a12 *a13 *a33 *c23 *r4103
3 60
1 6 2 3 4 2 2 4 2 2
- ---*a13 *c23 *r4103 + ----*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
4 20
1 5 3 1 4 4 2
r48=( - ---*a12 *a13*a33 *c23*r482 + ---*a12 *a13 *c23 *r4103
2 4
1 4 2 3 5 4 2 2 2
+ ---*a12 *a13 *a33 *c23*r481 - ---*a12 *a13 *a33 *c23 *r4103
6 6
1 4 4 2 2 3 3 3
+ ---*a12 *a33 *c23 *r4103 - ---*a12 *a13 *a33 *c23*r482
3 3
1 2 6 2 1 2 4 3
+ ---*a12 *a13 *c23 *r4103 + ---*a12 *a13 *a33 *c23*r481
2 3
13 2 4 2 2 7 2 2 4 2
- ----*a12 *a13 *a33 *c23 *r4103 + ----*a12 *a13 *a33 *c23 *r4103
6 12
1 5 3 1 8 2
- ---*a12*a13 *a33 *c23*r482 + ---*a13 *c23 *r4103
6 4
1 6 3 4 6 2 2
+ ---*a13 *a33 *c23*r481 - ---*a13 *a33 *c23 *r4103
6 3
1 4 4 2 3 3 4
+ ---*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
4
1 5 2 1 5 3
r49=(---*a12 *a13 *a33*c23*r482 - ---*a12 *a33 *c23*r482
6 4
7 4 3 2 1 4 3
+ ----*a12 *a13 *c23 *r4103 + ---*a12 *a13*a33 *c23*r481
24 4
23 4 2 2 1 3 4
- ----*a12 *a13*a33 *c23 *r4103 + ---*a12 *a13 *a33*c23*r482
24 6
3 2 3 5 2 5 2
+ 2*a12 *a13 *a33 *c23*r482 - ----*a12 *a13 *c23 *r4103
24
1 2 3 3 2 2 3 2 2
+ ---*a12 *a13 *a33 *c23*r481 - ----*a12 *a13 *a33 *c23 *r4103
2 15
3 2 4 2 1 4 3
+ ---*a12 *a13*a33 *c23 *r4103 + ---*a12*a13 *a33 *c23*r482
8 4
1 7 2 1 5 3 33 5 2 2
- ---*a13 *c23 *r4103 - ---*a13 *a33 *c23*r481 + ----*a13 *a33 *c23 *r4103
2 4 40
3 3 4 2 4 2 3
+ ---*a13 *a33 *c23 *r4103)/(a12 *a13 *a33 )
8
3 3 3 2 3 2
r410=(2*a12 *a33 *c23*r482 - ---*a12 *a13 *c23 *r4103
4
11 2 2 2 1 2 3
+ ----*a12 *a13*a33 *c23 *r4103 + ---*a12*a13 *a33 *c23*r482
4 2
3 5 2 1 3 3
- ---*a13 *c23 *r4103 - ---*a13 *a33 *c23*r481
4 2
11 3 2 2 3 3
+ ----*a13 *a33 *c23 *r4103)/(a12 *a13*a33 )
4
1 5 1 4 2 2
r411=(---*a12 *a13*a33*c23*r482 - ---*a12 *a13 *c23 *r4103
6 3
13 4 2 2 1 3 3
+ ----*a12 *a33 *c23 *r4103 + ---*a12 *a13 *a33*c23*r482
24 6
1 3 3 11 2 4 2
+ ---*a12 *a13*a33 *c23*r482 - ----*a12 *a13 *c23 *r4103
2 24
37 2 2 2 2 1 6 2
+ ----*a12 *a13 *a33 *c23 *r4103 - ---*a13 *c23 *r4103
60 8
3 4 2 2 4 3
+ ----*a13 *a33 *c23 *r4103)/(a12 *a13*a33 )
40
2
- c23 *r4103
r412=---------------
2
a12
2
- c23 *r4103
r413=---------------
a12*a13
1 5 1 4 2 2
r414=(----*a12 *a13*a33*c23*r482 - ---*a12 *a13 *c23 *r4103
12 6
13 4 2 2 1 3 3
+ ----*a12 *a33 *c23 *r4103 + ----*a12 *a13 *a33*c23*r482
48 12
3 3 3 5 2 4 2
+ ---*a12 *a13*a33 *c23*r482 - ----*a12 *a13 *c23 *r4103
8 12
1 2 2 3 41 2 2 2 2
- ---*a12 *a13 *a33 *c23*r481 + ----*a12 *a13 *a33 *c23 *r4103
8 60
3 2 4 2 1 3 3
+ ----*a12 *a33 *c23 *r4103 - ---*a12*a13 *a33 *c23*r482
16 4
1 6 2 1 4 3
- ---*a13 *c23 *r4103 - ---*a13 *a33 *c23*r481
4 4
33 4 2 2 3 2 4 2 4 3
+ ----*a13 *a33 *c23 *r4103 + ----*a13 *a33 *c23 *r4103)/(a12 *a13*a33 )
80 16
r415=0
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
1 2 1 2
- ---*a12 *c23*r4103 + ---*a13 *c23*r4103
2 2
r425=--------------------------------------------
2
a12*a13
c23*r4103
r426=-----------
a13
r428=0
r429=0
1
---*c23*r4103
2
r430=---------------
a12
r431=0
r432=0
r433=0
r435=0
r439=0
r442=0
r444=0
- c23*r4103
r445=--------------
a13
r448=0
r450=0
r451=0
r453=0
r454=0
1 2 1 2
- ---*a12 *c23*r4103 + ---*a13 *c23*r4103
2 2
r455=--------------------------------------------
2
a12*a13
r458=0
1
---*c23*r4103
2
r460=---------------
a12
r461=0
r463=0
r464=0
r465=0
r467=0
r468=0
r469=0
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r478=0
r479=0
3*a12*r482 + 2*a13*r481
r480=-------------------------
a12
- 4*c23*r4103
r483=----------------
a12
5 2 2 11 2 2 5 4
r484=(---*a12 *a13 *c23*r4103 - ----*a12 *a33 *c23*r4103 + ---*a13 *c23*r4103
4 4 4
3 2 2 2 2
- ---*a13 *a33 *c23*r4103)/(a12 *a13*a33 )
4
1 3 3 3 2 4 1 2 2 3
r485=(---*a12 *a13*a33 *r482 - ---*a12 *a13 *c23*r4103 - ---*a12 *a13 *a33 *r481
2 4 2
3 2 2 2 3 2 4
+ ---*a12 *a13 *a33 *c23*r4103 + ---*a12 *a33 *c23*r4103
2 4
3 3 3 6 4 3
- a12*a13 *a33 *r482 - ---*a13 *c23*r4103 - a13 *a33 *r481
4
3 4 2 3 2 4 3 3
+ ---*a13 *a33 *c23*r4103 + ---*a13 *a33 *c23*r4103)/(a12 *a13*a33 )
2 4
r486=0
r487=0
r488=0
r489=r4103
2*a12*r482 + a13*r481
r490=-----------------------
a13
5 2 2 9 2 2 5 4
r493=( - ---*a12 *a13 *c23*r4103 - ---*a12 *a33 *c23*r4103 - ---*a13 *c23*r4103
4 4 4
3 2 2 2 2
+ ---*a13 *a33 *c23*r4103)/(a12 *a13*a33 )
4
1 3 3 3 2 3 1 2 3
r495=(---*a12 *a33 *r482 - ---*a12 *a13 *c23*r4103 - ---*a12 *a13*a33 *r481
2 4 2
11 2 2 2 3 3 5
+ ----*a12 *a13*a33 *c23*r4103 - a12*a13 *a33 *r482 - ---*a13 *c23*r4103
4 4
3 3 11 3 2 2 3
- a13 *a33 *r481 + ----*a13 *a33 *c23*r4103)/(a12 *a13*a33 )
4
r496=0
r498=0
a12*r4103
r499=-----------
a13
r4100=0
r4102=0
a12*r4103
r4104=-----------
a13
1 4 3 1 4 2 1 3 3
r4105=( - ---*a12 *a33 *r481 - ----*a12 *a33 *c23*r4103 + ---*a12 *a13*a33 *r482
2 16 4
3 2 4 1 2 2 3
+ ---*a12 *a13 *c23*r4103 - ---*a12 *a13 *a33 *r481
8 4
23 2 2 2 2 4
- ----*a12 *a13 *a33 *c23*r4103 + a12 *a33 *c23*r4103
16
1 3 3 3 6 1 4 3
+ ---*a12*a13 *a33 *r482 + ---*a13 *c23*r4103 + ---*a13 *a33 *r481
4 8 4
11 4 2 3 4
- ----*a13 *a33 *c23*r4103)/(a12 *a33 )
8
1 3 3 3 2 4
r4106=( - ---*a12 *a13*a33 *r482 + ---*a12 *a13 *c23*r4103
2 4
1 2 2 3 11 2 2 2
+ ---*a12 *a13 *a33 *r481 - ----*a12 *a13 *a33 *c23*r4103
2 4
2 4 1 3 3 3 6
+ a12 *a33 *c23*r4103 - ---*a12*a13 *a33 *r482 + ---*a13 *c23*r4103
2 4
1 4 3 11 4 2 2 4
+ ---*a13 *a33 *r481 - ----*a13 *a33 *c23*r4103)/(a12 *a13*a33 )
2 4
1 3 3 3 2 4
r4107=( - ---*a12 *a13*a33 *r482 + ---*a12 *a13 *c23*r4103
4 8
1 2 2 3 23 2 2 2
+ ---*a12 *a13 *a33 *r481 - ----*a12 *a13 *a33 *c23*r4103
4 16
1 2 4 1 3 3 3 6
+ ---*a12 *a33 *c23*r4103 - ---*a12*a13 *a33 *r482 + ---*a13 *c23*r4103
2 4 8
1 4 3 23 4 2
+ ---*a13 *a33 *r481 - ----*a13 *a33 *c23*r4103
4 16
1 2 4 2 4
+ ---*a13 *a33 *c23*r4103)/(a12*a13 *a33 )
2
1 3 3 3 2 4
r4108=(---*a12 *a13*a33 *r482 - ---*a12 *a13 *c23*r4103
2 4
3 2 2 3 11 2 2 2
- ---*a12 *a13 *a33 *r481 + ----*a12 *a13 *a33 *c23*r4103
2 4
2 4 3 3 3 3 6
- a12 *a33 *c23*r4103 + ---*a12*a13 *a33 *r482 - ---*a13 *c23*r4103
2 4
1 4 3 11 4 2 2 4
- ---*a13 *a33 *r481 + ----*a13 *a33 *c23*r4103 - a13 *a33 *c23*r4103)/(
2 4
3 3
a12*a13 *a33 )
1 3 3 3 2 3 1 2 3
r4109=( - ---*a12 *a33 *r482 + ---*a12 *a13 *c23*r4103 + ---*a12 *a13*a33 *r481
2 4 2
11 2 2 1 2 3
- ----*a12 *a13*a33 *c23*r4103 + ---*a12*a13 *a33 *r482
4 2
3 5 1 3 3 11 3 2
+ ---*a13 *c23*r4103 + ---*a13 *a33 *r481 - ----*a13 *a33 *c23*r4103)/(
4 2 4
2 3
a12 *a13*a33 )
1 4 1 4 3 3
r4110=( - ---*a12 *a33*r481 - ----*a12 *c23*r4103 + ---*a12 *a13*a33*r482
2 16 2
41 2 2 3 3 1 4
- ----*a12 *a13 *c23*r4103 + ---*a12*a13 *a33*r482 + ---*a13 *a33*r481
16 2 2
5 4 3 2 2 3 2
- ---*a13 *c23*r4103 + ---*a13 *a33 *c23*r4103)/(a12 *a33 )
2 2
r4111=0
r4112=0
r4113=0
r4115=0
r4117=0
2
a12 *r482 + a12*a13*r481
r4118=--------------------------
a13*c23
1 3 1 2
---*a12 *r482 + ---*a12 *a13*r481
2 2
r4119=-----------------------------------
2
a13 *c23
r4120=0
r4121=0
r4122=0
r4123=r4103
a12*r4103
r4124=-----------
a13
r4125=0
a13*c23
c33=---------
a12
- a13*c23
c22=------------
a12
- a33*c23
c13=------------
a12
- a33*c23
c12=------------
a13
b33=0
b23=0
b13=0
b12=0
b11=0
1 1
---*a12*r482 + ---*a13*r481
2 2
r4114=-----------------------------
c23
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:
r482, r481, r4103, c23, a12, a13, a33
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.
{c23,a12,a13,a33}
Relevance for the application:
Modulo the following equation:
2 2
0=a12 + a13
the system of equations related to the Hamiltonian HAM:
2 2 2 2
HAM=(u1 *a12*a13*a33 + 2*u1*u2*a12 *a13 + 2*u1*u3*a12*a13 + u2 *a12*a13*a33
2
+ u3 *a12*a13*a33 - 2*v1*v2*a12*a33*c23 - 2*v1*v3*a13*a33*c23
2 2 2 2
- v2 *a13 *c23 + 2*v2*v3*a12*a13*c23 + v3 *a13 *c23)/(a12*a13)
has apart from the Hamiltonian and Casimirs the following 3 first integrals:
3 5 3 5 3 4 4 5 2 2
FI=u1 *u2*a12 *a13 *a33 + u1 *u3*a12 *a13 *a33 + u1 *v1 *(
1 5 4 3 41 3 6 3
- ----*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23
16 16
5 8 3 3 6 5 2
- ---*a12*a13 *a33 *c23 + ---*a12*a13 *a33 *c23) + u1 *v1*v2*(
2 2
3 4 6 2 11 4 4 4 3 2 8 2
---*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23
4 4 4
11 2 6 4 2 3 5 5 2
- ----*a12 *a13 *a33 *c23) + u1 *v1*v3*( - ---*a12 *a13 *a33 *c23
4 4
11 5 3 4 5 6 3 3 7 2
+ ----*a12 *a13 *a33 *c23 - a12 *a13*a33 *c23 - ---*a12 *a13 *a33 *c23
4 4
11 3 5 4 3 3 6 2 2
+ ----*a12 *a13 *a33 *c23 - a12 *a13 *a33 *c23) + u1 *v2 *(
4
3 5 6 23 5 4 3 1 5 2 5
---*a12 *a13 *a33*c23 - ----*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23
8 16 2
3 3 8 23 3 6 3
+ ---*a12 *a13 *a33*c23 - ----*a12 *a13 *a33 *c23
8 16
1 3 4 5 2 3 4 7
+ ---*a12 *a13 *a33 *c23) + u1 *v2*v3*(---*a12 *a13 *a33*c23
2 4
11 4 5 3 4 3 5 3 2 9
- ----*a12 *a13 *a33 *c23 + a12 *a13 *a33 *c23 + ---*a12 *a13 *a33*c23
4 4
11 2 7 3 2 2 1 5 4 3
- ----*a12 *a13 *a33 *c23) + u1 *v3 *( - ----*a12 *a13 *a33 *c23
4 16
3 3 8 23 3 6 3 3 4 5
+ ---*a12 *a13 *a33*c23 - ----*a12 *a13 *a33 *c23 + a12 *a13 *a33 *c23
8 16
3 10 11 8 3 3 5 3 5
+ ---*a12*a13 *a33*c23 - ----*a12*a13 *a33 *c23) + u1*u2 *a12 *a13 *a33
8 8
2 4 4 5 2 5 3 5 2
+ u1*u2 *u3*a12 *a13 *a33 + u1*u2*u3 *a12 *a13 *a33 + u1*u2*v1 *(
3 4 6 2 11 4 4 4
- ---*a12 *a13 *a33 *c23 + ----*a12 *a13 *a33 *c23
4 4
3 2 8 2 11 2 6 4
- ---*a12 *a13 *a33 *c23 + ----*a12 *a13 *a33 *c23) + u1*u2*v1*v3*(
4 4
5 4 5 3 9 4 3 5
- ---*a12 *a13 *a33 *c23 - ---*a12 *a13 *a33 *c23
4 4
5 2 7 3 3 2 5 5
- ---*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23)
4 4
3 4 4 5 2 3 3 7 2
+ u1*u3 *a12 *a13 *a33 + u1*u3*v1 *( - ---*a12 *a13 *a33 *c23
4
3 3 5 4 3 3 3 6 3 9 2
+ ---*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23 - ---*a12*a13 *a33 *c23
2 4 4
3 7 4 3 5 6
+ ---*a12*a13 *a33 *c23 + ---*a12*a13 *a33 *c23) + u1*u3*v1*v2*(
2 4
5 4 5 3 11 4 3 5 5 2 7 3
---*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23
4 4 4
3 2 5 5 3 4 5
- ---*a12 *a13 *a33 *c23) - 4*u1*u3*v1*v3*a12 *a13 *a33 *c23
4
1 2 2 3 4 5
+ ---*u2 *v1 *a12 *a13 *a33 *c23
2
2 2 1 5 2 5 1 3 4 5
+ u2 *v3 *( - ---*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23)
2 2
2 4 3 5 1 2 2 3 4 5
- u2*u3*v3 *a12 *a13 *a33 *c23 + ---*u3 *v1 *a12 *a13 *a33 *c23
2
2 4 3 5
+ u3 *v2*v3*a12 *a13 *a33 *c23
2 2 1 5 2 5 1 3 4 5 4
+ u3 *v3 *( - ---*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23) + v1 *(
2 2
1 4 5 2 2 13 4 3 4 2
- ---*a12 *a13 *a33 *c23 + ----*a12 *a13 *a33 *c23
6 48
5 2 7 2 2 41 2 5 4 2
- ----*a12 *a13 *a33 *c23 + ----*a12 *a13 *a33 *c23
12 60
3 2 3 6 2 1 9 2 2 33 7 4 2
+ ----*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 + ----*a13 *a33 *c23
16 4 80
3 5 6 2 3 3 3 5 2
+ ----*a13 *a33 *c23 ) - v1 *v2*a12 *a13 *a33 *c23
16
3 2 4 5 2 2 2 1 4 5 2 2
- v1 *v3*a12 *a13 *a33 *c23 + v1 *v2 *( - ---*a12 *a13 *a33 *c23
3
13 4 3 4 2 11 2 7 2 2
+ ----*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23
24 24
37 2 5 4 2 1 9 2 2 3 7 4 2
+ ----*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 + ----*a13 *a33 *c23 ) +
60 8 40
2 3 3 6 2 2 11 3 4 4 2
v1 *v2*v3*( - ---*a12 *a13 *a33 *c23 + ----*a12 *a13 *a33 *c23
4 4
3 8 2 2 11 6 4 2 2 2
- ---*a12*a13 *a33 *c23 + ----*a12*a13 *a33 *c23 ) + v1 *v3 *(
4 4
7 4 5 2 2 23 4 3 4 2
----*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23
24 24
5 2 7 2 2 2 2 5 4 2
- ----*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23
24 15
3 2 3 6 2 1 9 2 2 33 7 4 2
+ ---*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 + ----*a13 *a33 *c23
8 2 40
3 5 6 2 3 1 5 5 2
+ ---*a13 *a33 *c23 ) + v1*v2 *(---*a12 *a13 *a33*c23
8 4
5 5 3 3 2 1 5 5 2
- ---*a12 *a13 *a33 *c23 + ---*a12 *a13*a33 *c23
6 3
1 3 7 2 13 3 5 3 2
+ ---*a12 *a13 *a33*c23 - ----*a12 *a13 *a33 *c23
2 6
7 3 3 5 2 1 9 2
+ ----*a12 *a13 *a33 *c23 + ---*a12*a13 *a33*c23
12 4
4 7 3 2 1 5 5 2 2
- ---*a12*a13 *a33 *c23 + ---*a12*a13 *a33 *c23 ) + v1*v2 *v3*(
3 4
7 4 4 3 2 5 4 2 5 2
----*a12 *a13 *a33 *c23 - ---*a12 *a13 *a33 *c23
12 3
1 2 6 3 2 29 2 4 5 2 1 8 3 2
+ ---*a12 *a13 *a33 *c23 + ----*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23
3 60 4
3 6 5 2 2 5 5 3 3 2
+ ----*a13 *a33 *c23 ) + v1*v2*v3 *( - ---*a12 *a13 *a33 *c23
20 6
7 5 5 2 11 3 5 3 2
+ ---*a12 *a13*a33 *c23 - ----*a12 *a13 *a33 *c23
6 6
67 3 3 5 2 7 3 2 3 5 5 2
- ----*a12 *a13 *a33 *c23 - a12*a13 *a33 *c23 + ---*a12*a13 *a33 *c23 )
30 5
3 5 4 4 3 2 3 4 2 5 2
+ v1*v3 *(----*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23
12 4
5 2 6 3 2 5 2 4 5 2 3
+ ----*a12 *a13 *a33 *c23 - ---*a12 *a13 *a33 *c23 ) + v2 *v3*(
12 4
1 5 4 2 2 5 5 2 4 2 1 5 6 2
---*a12 *a13 *a33 *c23 - ---*a12 *a13 *a33 *c23 + ---*a12 *a33 *c23
4 6 3
1 3 6 2 2 13 3 4 4 2
+ ---*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23
2 6
7 3 2 6 2 1 8 2 2
+ ----*a12 *a13 *a33 *c23 + ---*a12*a13 *a33 *c23
12 4
4 6 4 2 1 4 6 2 2 2
- ---*a12*a13 *a33 *c23 + ---*a12*a13 *a33 *c23 ) + v2 *v3 *(
3 4
1 6 5 2 5 6 3 2 2 1 6 4 2
- ---*a12 *a13 *c23 + ----*a12 *a13 *a33 *c23 - ---*a12 *a13*a33 *c23
8 12 6
5 4 7 2 17 4 5 2 2 7 4 3 4 2
+ ---*a12 *a13 *c23 - ----*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23
4 4 8
11 2 9 2 115 2 7 2 2
+ ----*a12 *a13 *c23 - -----*a12 *a13 *a33 *c23
8 24
67 2 5 4 2 1 9 2 2 3 7 4 2
+ ----*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 + ----*a13 *a33 *c23 ) +
60 8 40
3 5 3 4 4 2 1 3 2 6 2
v2*v3 *(----*a12 *a13 *a33 *c23 - ---*a12 *a13 *a33 *c23
12 4
5 6 4 2 1 4 6 2 4
+ ----*a12*a13 *a33 *c23 - ---*a12*a13 *a33 *c23 ) + v3 *(
12 4
5 6 3 2 2 7 6 4 2
----*a12 *a13 *a33 *c23 - ----*a12 *a13*a33 *c23
24 24
7 4 5 2 2 29 4 3 4 2
+ ----*a12 *a13 *a33 *c23 - ----*a12 *a13 *a33 *c23
24 60
1 2 7 2 2 53 2 5 4 2
- ---*a12 *a13 *a33 *c23 + -----*a12 *a13 *a33 *c23
6 240
3 2 3 6 2 1 9 2 2 33 7 4 2
+ ----*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 + ----*a13 *a33 *c23
16 4 80
3 5 6 2
+ ----*a13 *a33 *c23 )
16
{HAM,FI} = too large to simplify
1 2 2 6 2 2 5 2 2
FI=---*u1 *u2 *a12 *a13*a33 + u1 *u2*u3*a12 *a13 *a33
2
1 2 2 4 3 2
+ ---*u1 *u3 *a12 *a13 *a33
2
2 2 1 5 2 1 6
+ u1 *v1 *( - ---*a12 *a13 *a33*c23 + ---*a12*a13 *a33*c23)
2 2
2 1 4 2 2 1 2 4 2
+ u1 *v1*v2*(---*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23)
2 2
2 3 5 2 1 3 3 2
+ u1 *v1*v3*( - ---*a12 *a13*a33 *c23 - ---*a12 *a13 *a33 *c23)
2 2
2 2 1 5 2 1 3 4
+ u1 *v2 *(---*a12 *a13 *a33*c23 + ---*a12 *a13 *a33*c23)
4 4
2 1 4 3 1 2 5 2 2
+ u1 *v2*v3*(---*a12 *a13 *a33*c23 + ---*a12 *a13 *a33*c23) + u1 *v3
2 2
1 5 2 1 3 4 1 6
*( - ---*a12 *a13 *a33*c23 - ---*a12 *a13 *a33*c23 + ---*a12*a13 *a33*c23)
2 4 4
2 1 4 2 2 2 4 2
+ u1*u2*v1 *( - ---*a12 *a13 *a33 *c23 - a12 *a13 *a33 *c23)
2
2 4 2 2
+ u1*u2*v3 *a12 *a13 *a33 *c23
2 1 3 3 2 5 2
+ u1*u3*v1 *( - ---*a12 *a13 *a33 *c23 - a12*a13 *a33 *c23)
2
4 2 2 2 3 3 2
+ u1*u3*v2*v3*a12 *a13 *a33 *c23 + 2*u1*u3*v3 *a12 *a13 *a33 *c23
4 1 2 3 2 2 1 5 2 2
+ v1 *( - ---*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 )
8 4
1 2 4 2 2 2 2
- ---*v1 *v2*v3*a12*a13 *a33 *c23 + v1 *v3
2
1 4 2 2 1 2 3 2 2 1 5 2 2
*(---*a12 *a13*a33 *c23 + ---*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 ) + v1
4 2 4
3 1 5 2 1 3 3 2 1 5 2
*v2 *(---*a12 *a13*a33*c23 + ---*a12 *a13 *a33*c23 + ---*a12*a13 *a33*c23 )
6 3 6
3
+ v2 *v3
1 5 2 2 1 3 2 2 2 1 4 2 2
*(---*a12 *a33 *c23 + ---*a12 *a13 *a33 *c23 + ---*a12*a13 *a33 *c23 ) +
6 3 6
2 2 1 6 2 5 4 3 2 1 4 2 2
v2 *v3 *( - ----*a12 *a13*c23 + ---*a12 *a13 *c23 + ---*a12 *a13*a33 *c23
12 6 2
11 2 5 2 3 3 2 2 2 4
+ ----*a12 *a13 *c23 ) + v2*v3 *a12 *a13 *a33 *c23 + v3
12
1 4 2 2 1 2 3 2 2 1 5 2 2
*( - ---*a12 *a13*a33 *c23 + ---*a12 *a13 *a33 *c23 - ---*a13 *a33 *c23 )
8 4 8
{HAM,FI} = too large to simplify
1 2 2 6 2 2 5 2 2
FI=---*u1 *u2 *a12 *a13*a33 + u1 *u2*u3*a12 *a13 *a33
2
1 2 2 4 3 2
+ ---*u1 *u3 *a12 *a13 *a33
2
2 2 3 3 4 3 6
+ u1 *v1 *(---*a12 *a13 *a33*c23 + ---*a12*a13 *a33*c23)
2 2
2 1 4 2 2 1 2 4 2
+ u1 *v1*v2*( - ---*a12 *a13 *a33 *c23 + ---*a12 *a13 *a33 *c23)
2 2
2 1 5 2 3 3 3 2
+ u1 *v1*v3*(---*a12 *a13*a33 *c23 + ---*a12 *a13 *a33 *c23)
2 2
2 2 1 5 2 1 3 4
+ u1 *v2 *( - ---*a12 *a13 *a33*c23 - ---*a12 *a13 *a33*c23)
4 4
2 1 4 3 1 2 5
+ u1 *v2*v3*( - ---*a12 *a13 *a33*c23 - ---*a12 *a13 *a33*c23)
2 2
2 2 1 3 4 1 6
+ u1 *v3 *(---*a12 *a13 *a33*c23 + ---*a12*a13 *a33*c23)
4 4
2 1 4 2 2 2 4 2
+ u1*u2*v1 *(---*a12 *a13 *a33 *c23 - a12 *a13 *a33 *c23)
2
2 4 2 2
+ 2*u1*u2*v3 *a12 *a13 *a33 *c23
2 1 3 3 2 5 2
+ u1*u3*v1 *(---*a12 *a13 *a33 *c23 - a12*a13 *a33 *c23)
2
2 3 3 2 2 3 3 2 4
+ u1*u3*v2 *a12 *a13 *a33 *c23 + 3*u1*u3*v3 *a12 *a13 *a33 *c23 + v1 *(
1 4 3 2 1 2 5 2 3 2 3 2 2
----*a12 *a13 *c23 + ----*a12 *a13 *c23 + ---*a12 *a13 *a33 *c23
12 12 8
1 5 2 2 2 2
- ---*a13 *a33 *c23 ) + v1 *v2
4
1 4 3 2 1 2 5 2 1 2 3 2 2
*(---*a12 *a13 *c23 + ---*a12 *a13 *c23 + ---*a12 *a13 *a33 *c23 )
6 6 2
2 3 2 2 2 1 4 2 2 2 2
+ v1 *v2*v3*(2*a12 *a13 *a33 *c23 + ---*a12*a13 *a33 *c23 ) + v1 *v3 *(
2
1 4 3 2 1 4 2 2 1 2 5 2
---*a12 *a13 *c23 - ---*a12 *a13*a33 *c23 + ---*a12 *a13 *c23
6 4 6
2 3 2 2 1 5 2 2 3
+ 2*a12 *a13 *a33 *c23 + ---*a13 *a33 *c23 ) + v1*v2
4
1 5 2 2 3 3 2 1 5 2
*( - ---*a12 *a13*a33*c23 - ---*a12 *a13 *a33*c23 - ---*a12*a13 *a33*c23 )
2 3 6
2 1 4 2 2 1 2 4 2
+ v1*v2 *v3*(---*a12 *a13 *a33*c23 + ---*a12 *a13 *a33*c23 )
3 3
2 1 5 2 1 3 3 2 3
+ v1*v2*v3 *( - ---*a12 *a13*a33*c23 - ---*a12 *a13 *a33*c23 ) + v2 *v3
3 3
1 5 2 2 1 3 2 2 2 1 4 2 2
*( - ---*a12 *a33 *c23 + ---*a12 *a13 *a33 *c23 - ---*a12*a13 *a33 *c23 ) +
2 3 6
2 2 1 6 2 1 4 3 2 3 2 5 2
v2 *v3 *(---*a12 *a13*c23 - ---*a12 *a13 *c23 - ---*a12 *a13 *c23
4 2 4
1 2 3 2 2 3 3 2 2 2 4
+ ---*a12 *a13 *a33 *c23 ) + 2*v2*v3 *a12 *a13 *a33 *c23 + v3 *(
2
1 6 2 1 4 3 2 5 4 2 2
----*a12 *a13*c23 + ---*a12 *a13 *c23 - ---*a12 *a13*a33 *c23
12 6 8
1 2 5 2 2 3 2 2 1 5 2 2
+ ----*a12 *a13 *c23 + a12 *a13 *a33 *c23 + ---*a13 *a33 *c23 )
12 8
{HAM,FI} = too large to simplify
And again in machine readable form:
HAM=(u1**2*a12*a13*a33 + 2*u1*u2*a12**2*a13 + 2*u1*u3*a12*a13**2 + u2**2*a12*a13
*a33 + u3**2*a12*a13*a33 - 2*v1*v2*a12*a33*c23 - 2*v1*v3*a13*a33*c23 - v2**2*a13
**2*c23 + 2*v2*v3*a12*a13*c23 + v3**2*a13**2*c23)/(a12*a13)$
FI=u1**3*u2*a12**5*a13**3*a33**5 + u1**3*u3*a12**4*a13**4*a33**5 + u1**2*v1**2*(
- 1/16*a12**5*a13**4*a33**3*c23 - 41/16*a12**3*a13**6*a33**3*c23 - 5/2*a12*a13
**8*a33**3*c23 + 3/2*a12*a13**6*a33**5*c23) + u1**2*v1*v2*(3/4*a12**4*a13**6*a33
**2*c23 - 11/4*a12**4*a13**4*a33**4*c23 + 3/4*a12**2*a13**8*a33**2*c23 - 11/4*
a12**2*a13**6*a33**4*c23) + u1**2*v1*v3*( - 3/4*a12**5*a13**5*a33**2*c23 + 11/4*
a12**5*a13**3*a33**4*c23 - a12**5*a13*a33**6*c23 - 3/4*a12**3*a13**7*a33**2*c23
+ 11/4*a12**3*a13**5*a33**4*c23 - a12**3*a13**3*a33**6*c23) + u1**2*v2**2*(3/8*
a12**5*a13**6*a33*c23 - 23/16*a12**5*a13**4*a33**3*c23 + 1/2*a12**5*a13**2*a33**
5*c23 + 3/8*a12**3*a13**8*a33*c23 - 23/16*a12**3*a13**6*a33**3*c23 + 1/2*a12**3*
a13**4*a33**5*c23) + u1**2*v2*v3*(3/4*a12**4*a13**7*a33*c23 - 11/4*a12**4*a13**5
*a33**3*c23 + a12**4*a13**3*a33**5*c23 + 3/4*a12**2*a13**9*a33*c23 - 11/4*a12**2
*a13**7*a33**3*c23) + u1**2*v3**2*( - 1/16*a12**5*a13**4*a33**3*c23 + 3/8*a12**3
*a13**8*a33*c23 - 23/16*a12**3*a13**6*a33**3*c23 + a12**3*a13**4*a33**5*c23 + 3/
8*a12*a13**10*a33*c23 - 11/8*a12*a13**8*a33**3*c23) + u1*u2**3*a12**5*a13**3*a33
**5 + u1*u2**2*u3*a12**4*a13**4*a33**5 + u1*u2*u3**2*a12**5*a13**3*a33**5 + u1*
u2*v1**2*( - 3/4*a12**4*a13**6*a33**2*c23 + 11/4*a12**4*a13**4*a33**4*c23 - 3/4*
a12**2*a13**8*a33**2*c23 + 11/4*a12**2*a13**6*a33**4*c23) + u1*u2*v1*v3*( - 5/4*
a12**4*a13**5*a33**3*c23 - 9/4*a12**4*a13**3*a33**5*c23 - 5/4*a12**2*a13**7*a33
**3*c23 + 3/4*a12**2*a13**5*a33**5*c23) + u1*u3**3*a12**4*a13**4*a33**5 + u1*u3*
v1**2*( - 3/4*a12**3*a13**7*a33**2*c23 + 3/2*a12**3*a13**5*a33**4*c23 + 3/4*a12
**3*a13**3*a33**6*c23 - 3/4*a12*a13**9*a33**2*c23 + 3/2*a12*a13**7*a33**4*c23 +
3/4*a12*a13**5*a33**6*c23) + u1*u3*v1*v2*(5/4*a12**4*a13**5*a33**3*c23 - 11/4*
a12**4*a13**3*a33**5*c23 + 5/4*a12**2*a13**7*a33**3*c23 - 3/4*a12**2*a13**5*a33
**5*c23) - 4*u1*u3*v1*v3*a12**3*a13**4*a33**5*c23 + 1/2*u2**2*v1**2*a12**3*a13**
4*a33**5*c23 + u2**2*v3**2*( - 1/2*a12**5*a13**2*a33**5*c23 + 1/2*a12**3*a13**4*
a33**5*c23) - u2*u3*v3**2*a12**4*a13**3*a33**5*c23 + 1/2*u3**2*v1**2*a12**3*a13
**4*a33**5*c23 + u3**2*v2*v3*a12**4*a13**3*a33**5*c23 + u3**2*v3**2*( - 1/2*a12
**5*a13**2*a33**5*c23 + 1/2*a12**3*a13**4*a33**5*c23) + v1**4*( - 1/6*a12**4*a13
**5*a33**2*c23**2 + 13/48*a12**4*a13**3*a33**4*c23**2 - 5/12*a12**2*a13**7*a33**
2*c23**2 + 41/60*a12**2*a13**5*a33**4*c23**2 + 3/16*a12**2*a13**3*a33**6*c23**2
- 1/4*a13**9*a33**2*c23**2 + 33/80*a13**7*a33**4*c23**2 + 3/16*a13**5*a33**6*c23
**2) - v1**3*v2*a12**3*a13**3*a33**5*c23**2 - v1**3*v3*a12**2*a13**4*a33**5*c23
**2 + v1**2*v2**2*( - 1/3*a12**4*a13**5*a33**2*c23**2 + 13/24*a12**4*a13**3*a33
**4*c23**2 - 11/24*a12**2*a13**7*a33**2*c23**2 + 37/60*a12**2*a13**5*a33**4*c23
**2 - 1/8*a13**9*a33**2*c23**2 + 3/40*a13**7*a33**4*c23**2) + v1**2*v2*v3*( - 3/
4*a12**3*a13**6*a33**2*c23**2 + 11/4*a12**3*a13**4*a33**4*c23**2 - 3/4*a12*a13**
8*a33**2*c23**2 + 11/4*a12*a13**6*a33**4*c23**2) + v1**2*v3**2*(7/24*a12**4*a13
**5*a33**2*c23**2 - 23/24*a12**4*a13**3*a33**4*c23**2 - 5/24*a12**2*a13**7*a33**
2*c23**2 - 2/15*a12**2*a13**5*a33**4*c23**2 + 3/8*a12**2*a13**3*a33**6*c23**2 -
1/2*a13**9*a33**2*c23**2 + 33/40*a13**7*a33**4*c23**2 + 3/8*a13**5*a33**6*c23**2
) + v1*v2**3*(1/4*a12**5*a13**5*a33*c23**2 - 5/6*a12**5*a13**3*a33**3*c23**2 + 1
/3*a12**5*a13*a33**5*c23**2 + 1/2*a12**3*a13**7*a33*c23**2 - 13/6*a12**3*a13**5*
a33**3*c23**2 + 7/12*a12**3*a13**3*a33**5*c23**2 + 1/4*a12*a13**9*a33*c23**2 - 4
/3*a12*a13**7*a33**3*c23**2 + 1/4*a12*a13**5*a33**5*c23**2) + v1*v2**2*v3*(7/12*
a12**4*a13**4*a33**3*c23**2 - 5/3*a12**4*a13**2*a33**5*c23**2 + 1/3*a12**2*a13**
6*a33**3*c23**2 + 29/60*a12**2*a13**4*a33**5*c23**2 - 1/4*a13**8*a33**3*c23**2 +
3/20*a13**6*a33**5*c23**2) + v1*v2*v3**2*( - 5/6*a12**5*a13**3*a33**3*c23**2 +
7/6*a12**5*a13*a33**5*c23**2 - 11/6*a12**3*a13**5*a33**3*c23**2 - 67/30*a12**3*
a13**3*a33**5*c23**2 - a12*a13**7*a33**3*c23**2 + 3/5*a12*a13**5*a33**5*c23**2)
+ v1*v3**3*(5/12*a12**4*a13**4*a33**3*c23**2 + 3/4*a12**4*a13**2*a33**5*c23**2 +
5/12*a12**2*a13**6*a33**3*c23**2 - 5/4*a12**2*a13**4*a33**5*c23**2) + v2**3*v3*
(1/4*a12**5*a13**4*a33**2*c23**2 - 5/6*a12**5*a13**2*a33**4*c23**2 + 1/3*a12**5*
a33**6*c23**2 + 1/2*a12**3*a13**6*a33**2*c23**2 - 13/6*a12**3*a13**4*a33**4*c23
**2 + 7/12*a12**3*a13**2*a33**6*c23**2 + 1/4*a12*a13**8*a33**2*c23**2 - 4/3*a12*
a13**6*a33**4*c23**2 + 1/4*a12*a13**4*a33**6*c23**2) + v2**2*v3**2*( - 1/8*a12**
6*a13**5*c23**2 + 5/12*a12**6*a13**3*a33**2*c23**2 - 1/6*a12**6*a13*a33**4*c23**
2 + 5/4*a12**4*a13**7*c23**2 - 17/4*a12**4*a13**5*a33**2*c23**2 + 7/8*a12**4*a13
**3*a33**4*c23**2 + 11/8*a12**2*a13**9*c23**2 - 115/24*a12**2*a13**7*a33**2*c23
**2 + 67/60*a12**2*a13**5*a33**4*c23**2 - 1/8*a13**9*a33**2*c23**2 + 3/40*a13**7
*a33**4*c23**2) + v2*v3**3*(5/12*a12**3*a13**4*a33**4*c23**2 - 1/4*a12**3*a13**2
*a33**6*c23**2 + 5/12*a12*a13**6*a33**4*c23**2 - 1/4*a12*a13**4*a33**6*c23**2) +
v3**4*(5/24*a12**6*a13**3*a33**2*c23**2 - 7/24*a12**6*a13*a33**4*c23**2 + 7/24*
a12**4*a13**5*a33**2*c23**2 - 29/60*a12**4*a13**3*a33**4*c23**2 - 1/6*a12**2*a13
**7*a33**2*c23**2 + 53/240*a12**2*a13**5*a33**4*c23**2 + 3/16*a12**2*a13**3*a33
**6*c23**2 - 1/4*a13**9*a33**2*c23**2 + 33/80*a13**7*a33**4*c23**2 + 3/16*a13**5
*a33**6*c23**2)$
FI=1/2*u1**2*u2**2*a12**6*a13*a33**2 + u1**2*u2*u3*a12**5*a13**2*a33**2 + 1/2*u1
**2*u3**2*a12**4*a13**3*a33**2 + u1**2*v1**2*( - 1/2*a12**5*a13**2*a33*c23 + 1/2
*a12*a13**6*a33*c23) + u1**2*v1*v2*(1/2*a12**4*a13**2*a33**2*c23 + 1/2*a12**2*
a13**4*a33**2*c23) + u1**2*v1*v3*( - 3/2*a12**5*a13*a33**2*c23 - 1/2*a12**3*a13
**3*a33**2*c23) + u1**2*v2**2*(1/4*a12**5*a13**2*a33*c23 + 1/4*a12**3*a13**4*a33
*c23) + u1**2*v2*v3*(1/2*a12**4*a13**3*a33*c23 + 1/2*a12**2*a13**5*a33*c23) + u1
**2*v3**2*( - 1/2*a12**5*a13**2*a33*c23 - 1/4*a12**3*a13**4*a33*c23 + 1/4*a12*
a13**6*a33*c23) + u1*u2*v1**2*( - 1/2*a12**4*a13**2*a33**2*c23 - a12**2*a13**4*
a33**2*c23) + u1*u2*v3**2*a12**4*a13**2*a33**2*c23 + u1*u3*v1**2*( - 1/2*a12**3*
a13**3*a33**2*c23 - a12*a13**5*a33**2*c23) + u1*u3*v2*v3*a12**4*a13**2*a33**2*
c23 + 2*u1*u3*v3**2*a12**3*a13**3*a33**2*c23 + v1**4*( - 1/8*a12**2*a13**3*a33**
2*c23**2 - 1/4*a13**5*a33**2*c23**2) - 1/2*v1**2*v2*v3*a12*a13**4*a33**2*c23**2
+ v1**2*v3**2*(1/4*a12**4*a13*a33**2*c23**2 + 1/2*a12**2*a13**3*a33**2*c23**2 -
1/4*a13**5*a33**2*c23**2) + v1*v2**3*(1/6*a12**5*a13*a33*c23**2 + 1/3*a12**3*a13
**3*a33*c23**2 + 1/6*a12*a13**5*a33*c23**2) + v2**3*v3*(1/6*a12**5*a33**2*c23**2
+ 1/3*a12**3*a13**2*a33**2*c23**2 + 1/6*a12*a13**4*a33**2*c23**2) + v2**2*v3**2
*( - 1/12*a12**6*a13*c23**2 + 5/6*a12**4*a13**3*c23**2 + 1/2*a12**4*a13*a33**2*
c23**2 + 11/12*a12**2*a13**5*c23**2) + v2*v3**3*a12**3*a13**2*a33**2*c23**2 + v3
**4*( - 1/8*a12**4*a13*a33**2*c23**2 + 1/4*a12**2*a13**3*a33**2*c23**2 - 1/8*a13
**5*a33**2*c23**2)$
FI=1/2*u1**2*u2**2*a12**6*a13*a33**2 + u1**2*u2*u3*a12**5*a13**2*a33**2 + 1/2*u1
**2*u3**2*a12**4*a13**3*a33**2 + u1**2*v1**2*(3/2*a12**3*a13**4*a33*c23 + 3/2*
a12*a13**6*a33*c23) + u1**2*v1*v2*( - 1/2*a12**4*a13**2*a33**2*c23 + 1/2*a12**2*
a13**4*a33**2*c23) + u1**2*v1*v3*(1/2*a12**5*a13*a33**2*c23 + 3/2*a12**3*a13**3*
a33**2*c23) + u1**2*v2**2*( - 1/4*a12**5*a13**2*a33*c23 - 1/4*a12**3*a13**4*a33*
c23) + u1**2*v2*v3*( - 1/2*a12**4*a13**3*a33*c23 - 1/2*a12**2*a13**5*a33*c23) +
u1**2*v3**2*(1/4*a12**3*a13**4*a33*c23 + 1/4*a12*a13**6*a33*c23) + u1*u2*v1**2*(
1/2*a12**4*a13**2*a33**2*c23 - a12**2*a13**4*a33**2*c23) + 2*u1*u2*v3**2*a12**4*
a13**2*a33**2*c23 + u1*u3*v1**2*(1/2*a12**3*a13**3*a33**2*c23 - a12*a13**5*a33**
2*c23) + u1*u3*v2**2*a12**3*a13**3*a33**2*c23 + 3*u1*u3*v3**2*a12**3*a13**3*a33
**2*c23 + v1**4*(1/12*a12**4*a13**3*c23**2 + 1/12*a12**2*a13**5*c23**2 + 3/8*a12
**2*a13**3*a33**2*c23**2 - 1/4*a13**5*a33**2*c23**2) + v1**2*v2**2*(1/6*a12**4*
a13**3*c23**2 + 1/6*a12**2*a13**5*c23**2 + 1/2*a12**2*a13**3*a33**2*c23**2) + v1
**2*v2*v3*(2*a12**3*a13**2*a33**2*c23**2 + 1/2*a12*a13**4*a33**2*c23**2) + v1**2
*v3**2*(1/6*a12**4*a13**3*c23**2 - 1/4*a12**4*a13*a33**2*c23**2 + 1/6*a12**2*a13
**5*c23**2 + 2*a12**2*a13**3*a33**2*c23**2 + 1/4*a13**5*a33**2*c23**2) + v1*v2**
3*( - 1/2*a12**5*a13*a33*c23**2 - 2/3*a12**3*a13**3*a33*c23**2 - 1/6*a12*a13**5*
a33*c23**2) + v1*v2**2*v3*(1/3*a12**4*a13**2*a33*c23**2 + 1/3*a12**2*a13**4*a33*
c23**2) + v1*v2*v3**2*( - 1/3*a12**5*a13*a33*c23**2 - 1/3*a12**3*a13**3*a33*c23
**2) + v2**3*v3*( - 1/2*a12**5*a33**2*c23**2 + 1/3*a12**3*a13**2*a33**2*c23**2 -
1/6*a12*a13**4*a33**2*c23**2) + v2**2*v3**2*(1/4*a12**6*a13*c23**2 - 1/2*a12**4
*a13**3*c23**2 - 3/4*a12**2*a13**5*c23**2 + 1/2*a12**2*a13**3*a33**2*c23**2) + 2
*v2*v3**3*a12**3*a13**2*a33**2*c23**2 + v3**4*(1/12*a12**6*a13*c23**2 + 1/6*a12
**4*a13**3*c23**2 - 5/8*a12**4*a13*a33**2*c23**2 + 1/12*a12**2*a13**5*c23**2 +
a12**2*a13**3*a33**2*c23**2 + 1/8*a13**5*a33**2*c23**2)$