Solution 3 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=4*a23 + a33
Expressions
The solution is given through the following expressions:
r10=0
r11=0
1
- ---*m1*r213
2
r12=----------------
a23
r13=0
r14=0
1
---*n1*r213
2
r15=-------------
a23
1 2 2 1 2 2
---*a23 *m1 *r213 + ---*a33 *m1 *r213
2 2
r20=---------------------------------------
2
a23*a33*n1
2 2 2 2
a23 *m1 *r213 + a33 *m1 *r213
r21=-------------------------------
2 2
a33 *n1
r23=0
r24=0
2
- a23*m1 *r213
r25=-----------------
2
a33*n1
- a33*m1*r213
r26=----------------
a23*n1
- m1*r213
r27=------------
n1
r28=0
- m1*r213
r210=------------
n1
r212=0
1
- ---*a33*r213
2
r214=-----------------
a23
r215=0
r216=0
a23*m1*r213
r217=-------------
a33*n1
r218=0
r219=0
1
- ---*a33*r213
2
r220=-----------------
a23
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r312=0
r314=0
r315=0
r316=r327
r317=0
r318=0
r319=0
r320=0
r321=r310
r322=r311
r323=0
r324=r313
r325=0
r326=r331
r328=0
r329=0
r330=0
r332=0
r333=0
r334=0
r335=0
r336=0
r337=0
r338=r310
r339=r311
r340=r313
r342=0
r343=r327
r344=0
r345=0
r346=r341
r347=r331
r348=0
r349=0
r350=0
r351=0
r352=r341
r353=0
r354=0
r355=0
r40=0
r41=0
r42=0
r43=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r414=0
r417=0
r418=0
r421=0
r423=0
r424=0
r426=r447
r428=r485
r429=0
r430=0
r431=0
r432=0
r433=0
r435=0
r436=r415
r437=r416
r439=0
r440=r419
r441=r420
r442=0
r443=r422
r444=0
r446=r425
r449=r485
r450=0
r453=0
r454=0
r455=0
r456=r445
r458=0
r459=r448
r460=0
r462=r451
r463=0
r464=0
r465=0
r466=r461
r467=0
r468=0
r469=0
r470=0
r471=0
r472=0
r473=0
r474=r415
r475=r416
r476=0
r477=r419
r478=r420
r479=r422
r482=0
r483=r425 + r494
r484=r447
r486=r4113
r487=0
r488=0
r489=0
r490=0
r491=r480
r492=r481
r493=r445
r495=r448
r497=r4113
r498=r451
r499=0
r4100=0
r4101=r496
r4102=r461
r4103=0
r4104=0
r4105=0
r4106=0
r4107=0
r4108=r480
r4109=r481
r4110=r494
r4112=0
r4114=0
r4115=0
r4116=r4111
r4117=r496
r4118=0
r4119=0
r4120=0
r4121=0
r4122=r4111
r4123=0
r4124=0
r4125=0
m3=0
m2=0
n3=0
n2=0
c33=0
3 2
a23 *m1
c23=----------
2 2
a33 *n1
2 2
- a23 *m1
c22=-------------
2
a33*n1
c13=0
c12=0
b33=0
b23=0
b13=0
b12=0
2
2*a23 *m1
b11=-----------
a33*n1
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:
r415, r310, r425, r419, r313, r422, r311, r416, r420,
r341, r485, r445, r480, r481, r4111, r448, r4113, r331,
r451, r327, r447, r461, r494, r496, r213, m1, n1, a33,
a23
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.
{r213,
a23,
a33,
n1,
2
{r485,r425,r448,r451,r445,r461,r415,r416,r419,r420,r422,r480,r481,2*a23 *r425
2
+ 2*a23 *r494,r447,r4113,r496,r494,r4111}}
Relevance for the application:
Modulo the following equation:
2 2
0=4*a23 + a33
the system of equations related to the Hamiltonian HAM:
2 2 3 2 2 2 3 2
HAM=(2*u1*v1*a23 *a33*m1*n1 + u1*a33 *n1 + 2*u2*u3*a23*a33 *n1 + u3 *a33 *n1
2 2 2 2 2 3 2 2 2
+ v1*a33 *m1*n1 - v2 *a23 *a33*m1 + 2*v2*v3*a23 *m1 )/(a33 *n1 )
has apart from the Hamiltonian and Casimirs the following 25 first integrals:
2 3 2 2 2 3 2 3 2
FI= - u1 *a33 *n1 + 2*u1*v1*a23 *a33*m1*n1 + u1*a33 *n1 - u2 *a33 *n1
2 2 2 2
+ 2*u2*u3*a23*a33 *n1 - 2*u2*v3*a23*a33 *m1*n1 - 2*u3*v2*a23*a33 *m1*n1
3 2 2 2 2 2
- 2*u3*v3*a33 *m1*n1 - 2*v1 *a23 *a33*m1 - v1*a33 *m1*n1
3 2 2 2 2 2 2 3 2
+ v2*v3*(2*a23 *m1 + 2*a23*a33 *m1 ) + v3 *(a23 *a33*m1 + a33 *m1 )
{HAM,FI} = 0
2 2
FI=u1 *u2*v1 + u1*u2 *v2 + u1*u2*u3*v3
3 3 2 3 2 2
{HAM,FI} = 8*u1 *u2*v1*a23 *n1 + 8*u1 *u3*v1*a23 *a33*n1
3 2 2 2 3 2
+ 2*u1 *v1*v3*a23 *a33*m1*n1 + 8*u1 *u2 *v2*a23 *n1
2 2 2 2 3 2
+ 8*u1 *u2*u3*v2*a23 *a33*n1 + 8*u1 *u2*u3*v3*a23 *n1
2 2 2 2 2 2
+ 2*u1 *u2*v2*v3*a23 *a33*m1*n1 + 8*u1 *u3 *v3*a23 *a33*n1
2 2 2 2 2 3
+ 2*u1 *u3*v1 *a23 *a33*m1*n1 - 4*u1 *u3*v1*a23 *n1
2 2 2 2 2 3 2
+ 2*u1 *u3*v3 *a23 *a33*m1*n1 - 2*u1 *v1 *v2*a23 *m1
2 2 2 3 3 2
- 4*u1 *v1*v3*a23 *m1*n1 - 8*u1*u2 *v1*a23 *n1
2 2 2 2 3 2
- 8*u1*u2 *u3*v1*a23 *a33*n1 + 8*u1*u2*u3 *v1*a23 *n1
2 2 3
+ 2*u1*u2*u3*v1*v2*a23 *a33*m1*n1 - 4*u1*u2*u3*v2*a23 *n1
2 2 2 3 2
+ 2*u1*u2*v1*v2*v3*a23 *a33*m1 - 2*u1*u2*v1*v3 *a23 *m1
2 2 2 2
- 4*u1*u2*v2*v3*a23 *m1*n1 + 2*u1*u3 *v1*v3*a23 *a33*m1*n1
2 2 3 3 2
- 4*u1*u3 *v3*a23 *n1 - 2*u1*u3*v1*v2*v3*a23 *m1
2 2 2 4 3 2
- 4*u1*u3*v3 *a23 *m1*n1 - 8*u2 *v2*a23 *n1
3 2 2 3 3 2
- 8*u2 *u3*v2*a23 *a33*n1 - 8*u2 *u3*v3*a23 *n1
2 2 3 2 2 2 2 2
+ 8*u2 *u3 *v2*a23 *n1 - 8*u2 *u3 *v3*a23 *a33*n1
2 3 3 2 2 2 2 2
+ 2*u2 *v2 *a23 *m1 + 2*u2 *v2 *v3*a23 *a33*m1
2 2 3 2 3 3 2
- 2*u2 *v2*v3 *a23 *m1 + 8*u2*u3 *v3*a23 *n1
2 3 2 2 2 2
+ 2*u2*u3*v2 *v3*a23 *m1 + 2*u2*u3*v2*v3 *a23 *a33*m1
3 3 2
- 2*u2*u3*v3 *a23 *m1
2 2
FI=u1 *v1 + u1*u2*v1*v2 + u1*u3*v1*v3
2 3 2 2 2 2
{HAM,FI} = - 8*u1 *u2*v1*v2*a23 *n1 - 8*u1 *u3*v1*v2*a23 *a33*n1
2 3 2 2 2 3 2
+ 8*u1 *u3*v1*v3*a23 *n1 - 8*u1*u2 *v1 *a23 *n1
2 2 3 2 2 2 2
- 8*u1*u2 *v2 *a23 *n1 - 8*u1*u2*u3*v1 *a23 *a33*n1
2 2 2 2 2 3 2
- 8*u1*u2*u3*v2 *a23 *a33*n1 + 8*u1*u3 *v1 *a23 *n1
2 2 2 2 2 3 2
- 8*u1*u3 *v2*v3*a23 *a33*n1 + 8*u1*u3 *v3 *a23 *n1
2 2 3 2 2 2 2
+ 2*u1*v1 *v2 *a23 *m1 + 2*u1*v1 *v2*v3*a23 *a33*m1
2 2 3 2 3 3 2
- 2*u1*v1 *v3 *a23 *m1 - 8*u2 *v1*v2*a23 *n1
2 2 2 2 3 2
- 8*u2 *u3*v1*v2*a23 *a33*n1 - 8*u2 *u3*v1*v3*a23 *n1
2 3 2 2 2 2
+ 8*u2*u3 *v1*v2*a23 *n1 - 8*u2*u3 *v1*v3*a23 *a33*n1
3 3 2 2 2 2
+ 2*u2*v1*v2 *a23 *m1 + 2*u2*v1*v2 *v3*a23 *a33*m1
2 3 2 3 3 2
- 2*u2*v1*v2*v3 *a23 *m1 + 8*u3 *v1*v3*a23 *n1
2 3 2 2 2 2
+ 2*u3*v1*v2 *v3*a23 *m1 + 2*u3*v1*v2*v3 *a23 *a33*m1
3 3 2
- 2*u3*v1*v3 *a23 *m1
2 3 2
FI=u1*u2 *v1 + u2 *v2 + u2 *u3*v3
2 2 3 2 2 2 2
{HAM,FI} = 16*u1 *u2 *v1*a23 *n1 + 16*u1 *u2*u3*v1*a23 *a33*n1
2 2 3 3 2
+ 4*u1 *u2*v1*v3*a23 *a33*m1*n1 + 16*u1*u2 *v2*a23 *n1
2 2 2 2 3 2
+ 16*u1*u2 *u3*v2*a23 *a33*n1 + 16*u1*u2 *u3*v3*a23 *n1
2 2 2 2 2
+ 4*u1*u2 *v2*v3*a23 *a33*m1*n1 + 16*u1*u2*u3 *v3*a23 *a33*n1
2 2 2 3
+ 4*u1*u2*u3*v1 *a23 *a33*m1*n1 - 8*u1*u2*u3*v1*a23 *n1
2 2 2 3 2
+ 4*u1*u2*u3*v3 *a23 *a33*m1*n1 - 4*u1*u2*v1 *v2*a23 *m1
2 2 2 2
- 8*u1*u2*v1*v3*a23 *m1*n1 + 4*u2 *u3*v1*v2*a23 *a33*m1*n1
2 2 3 2 2 3 2
- 8*u2 *u3*v2*a23 *n1 - 4*u2 *v1*v2 *a23 *m1
2 2 2 2 2
- 8*u2 *v2*v3*a23 *m1*n1 + 4*u2*u3 *v1*v3*a23 *a33*m1*n1
2 2 3 3 2
- 8*u2*u3 *v3*a23 *n1 - 4*u2*u3*v1*v2*v3*a23 *m1
2 2 2
- 8*u2*u3*v3 *a23 *m1*n1
2 2
FI=u1*u3*v1*v2 + u2*u3*v2 + u3 *v2*v3
2 3 2 2 2 2
{HAM,FI} = - 8*u1 *u3*v1*v2*a23 *n1 - 2*u1 *v1*v2 *a23 *a33*m1*n1
2 3 2 2 3 2
+ 8*u1*u2*u3*v1 *a23 *n1 - 8*u1*u2*u3*v2 *a23 *n1
2 2 2 3
- 2*u1*u2*v1 *v2*a23 *a33*m1*n1 + 4*u1*u2*v1*v2*a23 *n1
3 2 2 2 2 2
- 2*u1*u2*v2 *a23 *a33*m1*n1 + 8*u1*u3 *v1 *a23 *a33*n1
2 3 2 2 2
- 8*u1*u3 *v2*v3*a23 *n1 + 2*u1*u3*v1 *v3*a23 *a33*m1*n1
2 3 2 2
- 4*u1*u3*v1*v3*a23 *n1 - 2*u1*u3*v2 *v3*a23 *a33*m1*n1
2 2 2 2 2 3 2
- 2*u1*v1 *v2 *a23 *a33*m1 + 2*u1*v1 *v2*v3*a23 *m1
2 2 2 2 3 2
+ 4*u1*v1*v2 *a23 *m1*n1 + 8*u2 *u3*v1*v2*a23 *n1
2 2 2 2 2 2 3
- 2*u2 *v1*v2 *a23 *a33*m1*n1 + 4*u2 *v2 *a23 *n1
2 2 2 2 3 2
+ 8*u2*u3 *v1*v2*a23 *a33*n1 + 8*u2*u3 *v1*v3*a23 *n1
3 2 2 2 3 2
- 2*u2*v1*v2 *a23 *a33*m1 + 2*u2*v1*v2 *v3*a23 *m1
3 2 2 3 2 2
+ 4*u2*v2 *a23 *m1*n1 + 8*u3 *v1*v3*a23 *a33*n1
2 2 2 2 2 2 3
+ 2*u3 *v1*v3 *a23 *a33*m1*n1 - 4*u3 *v3 *a23 *n1
2 2 2 2 3 2
- 2*u3*v1*v2 *v3*a23 *a33*m1 + 2*u3*v1*v2*v3 *a23 *m1
2 2 2
+ 4*u3*v2 *v3*a23 *m1*n1
2
FI=u1*u3*v1 + u2*u3*v2 + u3 *v3
2 3 2 2 2
{HAM,FI} = - 8*u1 *u3*v1*a23 *n1 - 2*u1 *v1*v2*a23 *a33*m1*n1
3 2 2 2
- 8*u1*u2*u3*v2*a23 *n1 - 2*u1*u2*v1 *a23 *a33*m1*n1
2 3 2 2
+ 4*u1*u2*v1*a23 *n1 - 2*u1*u2*v2 *a23 *a33*m1*n1
2 3 2 2
- 8*u1*u3 *v3*a23 *n1 - 2*u1*u3*v2*v3*a23 *a33*m1*n1
2 2 2 2 3 2
- 2*u1*v1 *v2*a23 *a33*m1 + 2*u1*v1 *v3*a23 *m1
2 2 2 2
+ 4*u1*v1*v2*a23 *m1*n1 - 2*u2 *v1*v2*a23 *a33*m1*n1
2 2 3 2
+ 4*u2 *v2*a23 *n1 - 2*u2*u3*v1*v3*a23 *a33*m1*n1
2 3 2 2 2
+ 4*u2*u3*v3*a23 *n1 - 2*u2*v1*v2 *a23 *a33*m1
3 2 2 2 2
+ 2*u2*v1*v2*v3*a23 *m1 + 4*u2*v2 *a23 *m1*n1
2 2 2 3 2
- 2*u3*v1*v2*v3*a23 *a33*m1 + 2*u3*v1*v3 *a23 *m1
2 2
+ 4*u3*v2*v3*a23 *m1*n1
2 2
FI=u1*u2*u3*v1 + u2 *u3*v2 + u2*u3 *v3
2 2 2 2 2 2
{HAM,FI} = - 2*u1 *u2*v1*v2*a23 *a33*m1*n1 + 8*u1 *u3 *v1*a23 *a33*n1
2 2 2 2 2
+ 2*u1 *u3*v1*v3*a23 *a33*m1*n1 - 2*u1*u2 *v1 *a23 *a33*m1*n1
2 2 3 2 2 2
+ 4*u1*u2 *v1*a23 *n1 - 2*u1*u2 *v2 *a23 *a33*m1*n1
2 2 2 2 2 2
+ 8*u1*u2*u3 *v2*a23 *a33*n1 - 2*u1*u2*v1 *v2*a23 *a33*m1
2 3 2 2 2
+ 2*u1*u2*v1 *v3*a23 *m1 + 4*u1*u2*v1*v2*a23 *m1*n1
3 2 2 2 2 2
+ 8*u1*u3 *v3*a23 *a33*n1 + 2*u1*u3 *v1 *a23 *a33*m1*n1
2 2 3 2 2 2
- 4*u1*u3 *v1*a23 *n1 + 2*u1*u3 *v3 *a23 *a33*m1*n1
2 3 2 2 2
- 2*u1*u3*v1 *v2*a23 *m1 - 4*u1*u3*v1*v3*a23 *m1*n1
3 2 3 2 3
- 2*u2 *v1*v2*a23 *a33*m1*n1 + 4*u2 *v2*a23 *n1
2 2 2 2 3
- 2*u2 *u3*v1*v3*a23 *a33*m1*n1 + 4*u2 *u3*v3*a23 *n1
2 2 2 2 2 3 2
- 2*u2 *v1*v2 *a23 *a33*m1 + 2*u2 *v1*v2*v3*a23 *m1
2 2 2 2 2 2
+ 4*u2 *v2 *a23 *m1*n1 + 2*u2*u3 *v1*v2*a23 *a33*m1*n1
2 2 3 2 3 2
- 4*u2*u3 *v2*a23 *n1 - 2*u2*u3*v1*v2 *a23 *m1
2 2 2 3 2
- 2*u2*u3*v1*v2*v3*a23 *a33*m1 + 2*u2*u3*v1*v3 *a23 *m1
3 2 3 2 3
+ 2*u3 *v1*v3*a23 *a33*m1*n1 - 4*u3 *v3*a23 *n1
2 3 2 2 2 2 2
- 2*u3 *v1*v2*v3*a23 *m1 - 4*u3 *v3 *a23 *m1*n1
2
FI=u1*u2*v1 + u2 *v2 + u2*u3*v3
2 3 2 2 2 2
{HAM,FI} = 8*u1 *u2*v1*a23 *n1 + 8*u1 *u3*v1*a23 *a33*n1
2 2 2 3 2
+ 2*u1 *v1*v3*a23 *a33*m1*n1 + 8*u1*u2 *v2*a23 *n1
2 2 3 2
+ 8*u1*u2*u3*v2*a23 *a33*n1 + 8*u1*u2*u3*v3*a23 *n1
2 2 2 2
+ 2*u1*u2*v2*v3*a23 *a33*m1*n1 + 8*u1*u3 *v3*a23 *a33*n1
2 2 2 3
+ 2*u1*u3*v1 *a23 *a33*m1*n1 - 4*u1*u3*v1*a23 *n1
2 2 2 3 2
+ 2*u1*u3*v3 *a23 *a33*m1*n1 - 2*u1*v1 *v2*a23 *m1
2 2 2
- 4*u1*v1*v3*a23 *m1*n1 + 2*u2*u3*v1*v2*a23 *a33*m1*n1
2 3 2 3 2
- 4*u2*u3*v2*a23 *n1 - 2*u2*v1*v2 *a23 *m1
2 2 2 2
- 4*u2*v2*v3*a23 *m1*n1 + 2*u3 *v1*v3*a23 *a33*m1*n1
2 2 3 3 2 2 2 2
- 4*u3 *v3*a23 *n1 - 2*u3*v1*v2*v3*a23 *m1 - 4*u3*v3 *a23 *m1*n1
2 2
FI=u1 *u3*v1 + u1*u2*u3*v2 + u1*u3 *v3
3 3 2 3 2
{HAM,FI} = - 8*u1 *u3*v1*a23 *n1 - 2*u1 *v1*v2*a23 *a33*m1*n1
2 3 2 2 2 2
- 8*u1 *u2*u3*v2*a23 *n1 - 2*u1 *u2*v1 *a23 *a33*m1*n1
2 2 3 2 2 2
+ 4*u1 *u2*v1*a23 *n1 - 2*u1 *u2*v2 *a23 *a33*m1*n1
2 2 3 2 2 2
- 8*u1 *u3 *v3*a23 *n1 - 2*u1 *u3*v2*v3*a23 *a33*m1*n1
2 2 2 2 2 2 3 2
- 2*u1 *v1 *v2*a23 *a33*m1 + 2*u1 *v1 *v3*a23 *m1
2 2 2 2 3 2
+ 4*u1 *v1*v2*a23 *m1*n1 - 8*u1*u2 *u3*v1*a23 *n1
2 2 2 2 3
- 2*u1*u2 *v1*v2*a23 *a33*m1*n1 + 4*u1*u2 *v2*a23 *n1
2 2 2 2
- 8*u1*u2*u3 *v1*a23 *a33*n1 - 2*u1*u2*u3*v1*v3*a23 *a33*m1*n1
2 3 2 2 2
+ 4*u1*u2*u3*v3*a23 *n1 - 2*u1*u2*v1*v2 *a23 *a33*m1
3 2 2 2 2
+ 2*u1*u2*v1*v2*v3*a23 *m1 + 4*u1*u2*v2 *a23 *m1*n1
3 3 2 2 3 2
+ 8*u1*u3 *v1*a23 *n1 + 2*u1*u3*v1*v2 *a23 *m1
2 2 3 3 2
+ 4*u1*u3*v2*v3*a23 *m1*n1 - 8*u2 *u3*v2*a23 *n1
2 2 2 2 2 2 3 2
- 8*u2 *u3 *v2*a23 *a33*n1 - 8*u2 *u3 *v3*a23 *n1
3 3 2 3 2 2
+ 8*u2*u3 *v2*a23 *n1 - 8*u2*u3 *v3*a23 *a33*n1
3 3 2 2 2 2
+ 2*u2*u3*v2 *a23 *m1 + 2*u2*u3*v2 *v3*a23 *a33*m1
2 3 2 4 3 2
- 2*u2*u3*v2*v3 *a23 *m1 + 8*u3 *v3*a23 *n1
2 2 3 2 2 2 2 2
+ 2*u3 *v2 *v3*a23 *m1 + 2*u3 *v2*v3 *a23 *a33*m1
2 3 3 2
- 2*u3 *v3 *a23 *m1
2 2
FI=u1*u2*v1 + u2 *v1*v2 + u2*u3*v1*v3
2 2 3 2 2 2 2 2
{HAM,FI} = 8*u1 *u2*v1 *a23 *n1 + 8*u1 *u3*v1 *a23 *a33*n1
2 2 2 3 2
+ 2*u1 *v1 *v3*a23 *a33*m1*n1 + 16*u1*u2*u3*v1*v3*a23 *n1
2 2 2 2
+ 2*u1*u2*v1*v2*v3*a23 *a33*m1*n1 + 8*u1*u3 *v1*v3*a23 *a33*n1
3 2 2 2 3
+ 2*u1*u3*v1 *a23 *a33*m1*n1 - 4*u1*u3*v1 *a23 *n1
2 2 3 3 2
+ 2*u1*u3*v1*v3 *a23 *a33*m1*n1 - 2*u1*v1 *v2*a23 *m1
2 2 2 3 2 3 2
- 4*u1*v1 *v3*a23 *m1*n1 - 8*u2 *v2 *a23 *n1
2 2 2 2 2 2 2
- 8*u2 *u3*v2 *a23 *a33*n1 - 8*u2*u3 *v2*v3*a23 *a33*n1
2 2 3 2 2 2
+ 8*u2*u3 *v3 *a23 *n1 + 2*u2*u3*v1 *v2*a23 *a33*m1*n1
2 3 2 2 3 2
- 4*u2*u3*v1*v2*a23 *n1 - 2*u2*v1 *v2 *a23 *m1
2 2 2 2 2
- 4*u2*v1*v2*v3*a23 *m1*n1 + 2*u3 *v1 *v3*a23 *a33*m1*n1
2 2 3 2 3 2
- 4*u3 *v1*v3*a23 *n1 - 2*u3*v1 *v2*v3*a23 *m1
2 2 2
- 4*u3*v1*v3 *a23 *m1*n1
3 2 2
FI=u1 *v1 + u1 *u2*v2 + u1 *u3*v3
2 2 3 2 2 2 2
{HAM,FI} = - 16*u1 *u2 *v1*a23 *n1 - 16*u1 *u2*u3*v1*a23 *a33*n1
2 2 3 2 2 2 3 2
+ 16*u1 *u3 *v1*a23 *n1 + 4*u1 *v1*v2 *a23 *m1
2 2 2 2 2 3 2
+ 4*u1 *v1*v2*v3*a23 *a33*m1 - 4*u1 *v1*v3 *a23 *m1
3 3 2 2 2 2
- 16*u1*u2 *v2*a23 *n1 - 16*u1*u2 *u3*v2*a23 *a33*n1
2 3 2 2 3 2
- 16*u1*u2 *u3*v3*a23 *n1 + 16*u1*u2*u3 *v2*a23 *n1
2 2 2 3 3 2
- 16*u1*u2*u3 *v3*a23 *a33*n1 + 4*u1*u2*v2 *a23 *m1
2 2 2 2 3 2
+ 4*u1*u2*v2 *v3*a23 *a33*m1 - 4*u1*u2*v2*v3 *a23 *m1
3 3 2 2 3 2
+ 16*u1*u3 *v3*a23 *n1 + 4*u1*u3*v2 *v3*a23 *m1
2 2 2 3 3 2
+ 4*u1*u3*v2*v3 *a23 *a33*m1 - 4*u1*u3*v3 *a23 *m1
2 2
FI=u1 *v1*v2 + u1*u2*v2 + u1*u3*v2*v3
2 2 3 2 2 2 2 2
{HAM,FI} = 8*u1 *u2*v1 *a23 *n1 + 8*u1 *u3*v1 *a23 *a33*n1
2 2 2 2 2 3
+ 2*u1 *v1 *v3*a23 *a33*m1*n1 - 4*u1 *v1*v3*a23 *n1
3 2 2
+ 8*u1*u2*u3*v1*v3*a23 *n1 + 2*u1*u2*v1*v2*v3*a23 *a33*m1*n1
2 3 2 3 2
- 4*u1*u2*v2*v3*a23 *n1 + 8*u1*u3 *v1*v2*a23 *n1
2 2 2 2 2
+ 8*u1*u3 *v1*v3*a23 *a33*n1 + 2*u1*u3*v1*v3 *a23 *a33*m1*n1
2 2 3 3 3 2
- 4*u1*u3*v3 *a23 *n1 + 2*u1*v1*v2 *a23 *m1
2 2 2 2 3 2
+ 2*u1*v1*v2 *v3*a23 *a33*m1 - 2*u1*v1*v2*v3 *a23 *m1
3 2 3 2 2 2 2 2
- 8*u2 *v2 *a23 *n1 - 8*u2 *u3*v2 *a23 *a33*n1
2 3 2 2 2 3 2
- 8*u2 *u3*v2*v3*a23 *n1 + 8*u2*u3 *v2 *a23 *n1
2 2 2 4 3 2
- 8*u2*u3 *v2*v3*a23 *a33*n1 + 2*u2*v2 *a23 *m1
3 2 2 2 2 3 2
+ 2*u2*v2 *v3*a23 *a33*m1 - 2*u2*v2 *v3 *a23 *m1
3 3 2 3 3 2
+ 8*u3 *v2*v3*a23 *n1 + 2*u3*v2 *v3*a23 *m1
2 2 2 2 3 3 2
+ 2*u3*v2 *v3 *a23 *a33*m1 - 2*u3*v2*v3 *a23 *m1
2 2
FI=u1 *v1*v3 + u1*u2*v2*v3 + u1*u3*v3
2 2 3 2 2 2 2
{HAM,FI} = - 8*u1 *u3*v1 *a23 *n1 - 2*u1 *v1 *v2*a23 *a33*m1*n1
2 2 3 2 3 2
+ 4*u1 *v1*v2*a23 *n1 - 8*u1*u2 *v1*v3*a23 *n1
3 2 2 2
- 8*u1*u2*u3*v1*v2*a23 *n1 - 8*u1*u2*u3*v1*v3*a23 *a33*n1
2 2 2 2 3
- 2*u1*u2*v1*v2 *a23 *a33*m1*n1 + 4*u1*u2*v2 *a23 *n1
2 2 3
- 2*u1*u3*v1*v2*v3*a23 *a33*m1*n1 + 4*u1*u3*v2*v3*a23 *n1
2 3 2 2 2 2
+ 2*u1*v1*v2 *v3*a23 *m1 + 2*u1*v1*v2*v3 *a23 *a33*m1
3 3 2 3 3 2
- 2*u1*v1*v3 *a23 *m1 - 8*u2 *v2*v3*a23 *n1
2 2 2 2 2 3 2
- 8*u2 *u3*v2*v3*a23 *a33*n1 - 8*u2 *u3*v3 *a23 *n1
2 3 2 2 2 2 2
+ 8*u2*u3 *v2*v3*a23 *n1 - 8*u2*u3 *v3 *a23 *a33*n1
3 3 2 2 2 2 2
+ 2*u2*v2 *v3*a23 *m1 + 2*u2*v2 *v3 *a23 *a33*m1
3 3 2 3 2 3 2 2 2 3 2
- 2*u2*v2*v3 *a23 *m1 + 8*u3 *v3 *a23 *n1 + 2*u3*v2 *v3 *a23 *m1
3 2 2 4 3 2
+ 2*u3*v2*v3 *a23 *a33*m1 - 2*u3*v3 *a23 *m1
2 2
FI=u1*u2*v1*v3 + u2 *v2*v3 + u2*u3*v3
2 3 2 2 2 2
{HAM,FI} = 8*u1 *u2*v1*v3*a23 *n1 + 8*u1 *u3*v1*v3*a23 *a33*n1
2 2 2 2 3 2
+ 2*u1 *v1*v3 *a23 *a33*m1*n1 + 8*u1*u2 *v2*v3*a23 *n1
2 3 2 2 2
- 8*u1*u2*u3*v1 *a23 *n1 + 8*u1*u2*u3*v2*v3*a23 *a33*n1
2 3 2 2 2
+ 8*u1*u2*u3*v3 *a23 *n1 - 2*u1*u2*v1 *v2*a23 *a33*m1*n1
2 3 2 2
+ 4*u1*u2*v1*v2*a23 *n1 + 2*u1*u2*v2*v3 *a23 *a33*m1*n1
2 2 2 2 2 2
+ 8*u1*u3 *v3 *a23 *a33*n1 + 2*u1*u3*v1 *v3*a23 *a33*m1*n1
2 3 3 2
- 4*u1*u3*v1*v3*a23 *n1 + 2*u1*u3*v3 *a23 *a33*m1*n1
2 3 2 2 2 2
- 2*u1*v1 *v2*v3*a23 *m1 - 4*u1*v1*v3 *a23 *m1*n1
2 3 2 2 2 2
- 8*u2 *u3*v1*v2*a23 *n1 - 2*u2 *v1*v2 *a23 *a33*m1*n1
2 2 2 3 2 3 2
+ 4*u2 *v2 *a23 *n1 - 8*u2*u3 *v1*v3*a23 *n1
2 3 2 2 2 2
- 2*u2*v1*v2 *v3*a23 *m1 - 4*u2*v2*v3 *a23 *m1*n1
2 2 2 2 2 2 3
+ 2*u3 *v1*v3 *a23 *a33*m1*n1 - 4*u3 *v3 *a23 *n1
2 3 2 3 2 2
- 2*u3*v1*v2*v3 *a23 *m1 - 4*u3*v3 *a23 *m1*n1
2 2
FI=u1*u3*v1 + u2*u3*v1*v2 + u3 *v1*v3
2 2 3 2 2 2 2
{HAM,FI} = - 8*u1 *u3*v1 *a23 *n1 - 2*u1 *v1 *v2*a23 *a33*m1*n1
3 2 3 2
- 16*u1*u2*u3*v1*v2*a23 *n1 - 2*u1*u2*v1 *a23 *a33*m1*n1
2 2 3 2 2
+ 4*u1*u2*v1 *a23 *n1 - 2*u1*u2*v1*v2 *a23 *a33*m1*n1
2 2 2 2
- 8*u1*u3 *v1*v2*a23 *a33*n1 - 2*u1*u3*v1*v2*v3*a23 *a33*m1*n1
3 2 2 3 3 2
- 2*u1*v1 *v2*a23 *a33*m1 + 2*u1*v1 *v3*a23 *m1
2 2 2 2 2 3 2
+ 4*u1*v1 *v2*a23 *m1*n1 - 8*u2 *u3*v2 *a23 *n1
2 2 2 2 2 3
- 2*u2 *v1 *v2*a23 *a33*m1*n1 + 4*u2 *v1*v2*a23 *n1
2 2 2 2 2 2
- 8*u2*u3 *v2 *a23 *a33*n1 - 2*u2*u3*v1 *v3*a23 *a33*m1*n1
2 3 2 2 2 2
+ 4*u2*u3*v1*v3*a23 *n1 - 2*u2*v1 *v2 *a23 *a33*m1
2 3 2 2 2 2
+ 2*u2*v1 *v2*v3*a23 *m1 + 4*u2*v1*v2 *a23 *m1*n1
3 2 2 3 2 3 2
- 8*u3 *v2*v3*a23 *a33*n1 + 8*u3 *v3 *a23 *n1
2 2 2 2 2 3 2
- 2*u3*v1 *v2*v3*a23 *a33*m1 + 2*u3*v1 *v3 *a23 *m1
2 2
+ 4*u3*v1*v2*v3*a23 *m1*n1
2
FI=u1 *v1 + u1*u2*v2 + u1*u3*v3
2 3 2 2 2
{HAM,FI} = - 8*u1*u2 *v1*a23 *n1 - 8*u1*u2*u3*v1*a23 *a33*n1
2 3 2 2 3 2
+ 8*u1*u3 *v1*a23 *n1 + 2*u1*v1*v2 *a23 *m1
2 2 2 3 2
+ 2*u1*v1*v2*v3*a23 *a33*m1 - 2*u1*v1*v3 *a23 *m1
3 3 2 2 2 2
- 8*u2 *v2*a23 *n1 - 8*u2 *u3*v2*a23 *a33*n1
2 3 2 2 3 2
- 8*u2 *u3*v3*a23 *n1 + 8*u2*u3 *v2*a23 *n1
2 2 2 3 3 2
- 8*u2*u3 *v3*a23 *a33*n1 + 2*u2*v2 *a23 *m1
2 2 2 2 3 2
+ 2*u2*v2 *v3*a23 *a33*m1 - 2*u2*v2*v3 *a23 *m1
3 3 2 2 3 2
+ 8*u3 *v3*a23 *n1 + 2*u3*v2 *v3*a23 *m1
2 2 2 3 3 2
+ 2*u3*v2*v3 *a23 *a33*m1 - 2*u3*v3 *a23 *m1
2 2
FI=u1*v1 *v2 + u2*v1*v2 + u3*v1*v2*v3
3 2
{HAM,FI} = - 2*u1*u2*v1 *a23*a33*n1 + 2*u1*u2*v1*v2 *a23*a33*n1
3 2 2 2
+ 8*u1*u3*v1 *a23 *n1 - 8*u1*u3*v1*v2 *a23 *n1
3 2
- 2*u1*u3*v1*v2*v3*a23*a33*n1 + 2*u1*v1 *v3*a23 *m1
2 2 2 2 2 3
+ u1*v1 *v3*a33*n1 - 2*u2 *v1 *v2*a23*a33*n1 + 2*u2 *v2 *a23*a33*n1
2 2 2
+ 8*u2*u3*v1 *v2*a23 *n1 - 2*u2*u3*v1 *v3*a23*a33*n1
3 2 2 2 2
- 8*u2*u3*v2 *a23 *n1 + 2*u2*v1 *v2*v3*a23 *m1 + u2*v1*v2*v3*a33*n1
2 2 2 2 2 2
+ 8*u3 *v1 *v3*a23 *n1 - 8*u3 *v2 *v3*a23 *n1
2 2 2 2 2 2 2
- 2*u3 *v2*v3 *a23*a33*n1 + 2*u3*v1 *v3 *a23 *m1 + u3*v1*v3 *a33*n1
2 2
FI=u1*v1*v2*v3 + u2*v2 *v3 + u3*v2*v3
2 2
{HAM,FI} = - 2*u1*u2*v1 *v3*a23*a33*n1 + 2*u1*u3*v1 *v2*a23*a33*n1
2 2 2 2 2
+ 8*u1*u3*v1 *v3*a23 *n1 - 2*u1*v1 *v2 *a23 *m1
2 2 2 2 2 2 2
+ 2*u1*v1 *v3 *a23 *m1 - u1*v1*v2 *a33*n1 + u1*v1*v3 *a33*n1
2 2
- 2*u2 *v1*v2*v3*a23*a33*n1 + 2*u2*u3*v1*v2 *a23*a33*n1
2 2
+ 8*u2*u3*v1*v2*v3*a23 *n1 - 2*u2*u3*v1*v3 *a23*a33*n1
3 2 2 2 3 2
- 2*u2*v1*v2 *a23 *m1 + 2*u2*v1*v2*v3 *a23 *m1 - u2*v2 *a33*n1
2 2 2
+ u2*v2*v3 *a33*n1 + 2*u3 *v1*v2*v3*a23*a33*n1
2 2 2 2 2
+ 8*u3 *v1*v3 *a23 *n1 - 2*u3*v1*v2 *v3*a23 *m1
3 2 2 2 3 2
+ 2*u3*v1*v3 *a23 *m1 - u3*v2 *v3*a33*n1 + u3*v3 *a33*n1
2
FI=u1*v1*v2 + u2*v2 + u3*v2*v3
2 2 2 2 2
{HAM,FI} = - 2*u1*u2*v1 *a23*a33*n1 + 8*u1*u3*v1 *a23 *n1 + 2*u1*v1 *v3*a23 *m1
2 2 2
+ u1*v1*v3*a33*n1 - 2*u2 *v1*v2*a23*a33*n1 + 8*u2*u3*v1*v2*a23 *n1
2
- 2*u2*u3*v1*v3*a23*a33*n1 + 2*u2*v1*v2*v3*a23 *m1
2 2 2 2 2
+ u2*v2*v3*a33*n1 + 8*u3 *v1*v3*a23 *n1 + 2*u3*v1*v3 *a23 *m1
2 2
+ u3*v3 *a33*n1
3 2 2
FI=u1*v1 + u2*v1 *v2 + u3*v1 *v3
2 2 2
{HAM,FI} = 4*u1*u2*v1 *v2*a23 + 4*u1*u3*v1 *v2*a33 - 4*u1*u3*v1 *v3*a23
2 2 2 2
+ 4*u2 *v1*v2 *a23 + 4*u2*u3*v1*v2 *a33 + 4*u3 *v1*v2*v3*a33
2 2
- 4*u3 *v1*v3 *a23
2
FI=u1*v1 + u2*v1*v2 + u3*v1*v3
{HAM,FI} = 2*u1*u2*v1*v2*a23 + 2*u1*u3*v1*v2*a33 - 2*u1*u3*v1*v3*a23
2 2 2 2 2 2
+ 2*u2 *v2 *a23 + 2*u2*u3*v2 *a33 + 2*u3 *v2*v3*a33 - 2*u3 *v3 *a23
2 2
FI=u1*v1 *v3 + u2*v1*v2*v3 + u3*v1*v3
3
{HAM,FI} = 2*u1*u2*v1*v2*v3*a23*a33*n1 + 2*u1*u3*v1 *a23*a33*n1
2 2
- 8*u1*u3*v1*v2*v3*a23 *n1 - 2*u1*u3*v1*v3 *a23*a33*n1
3 2 2 2 2 2
- 2*u1*v1 *v2*a23 *m1 - u1*v1 *v2*a33*n1 + 2*u2 *v2 *v3*a23*a33*n1
2 2 2
+ 2*u2*u3*v1 *v2*a23*a33*n1 - 8*u2*u3*v2 *v3*a23 *n1
2 2 2 2 2 2 2
- 2*u2*v1 *v2 *a23 *m1 - u2*v1*v2 *a33*n1 + 2*u3 *v1 *v3*a23*a33*n1
2 2 2 2 3
- 8*u3 *v2*v3 *a23 *n1 - 2*u3 *v3 *a23*a33*n1
2 2 2
- 2*u3*v1 *v2*v3*a23 *m1 - u3*v1*v2*v3*a33*n1
2 2
FI=u1*u3*v1*v3 + u2*u3*v2*v3 + u3 *v3
2 3 2 2 2
{HAM,FI} = - 8*u1 *u3*v1*v3*a23 *n1 - 2*u1 *v1*v2*v3*a23 *a33*m1*n1
3 2 2 2
- 8*u1*u2*u3*v2*v3*a23 *n1 - 2*u1*u2*v1 *v3*a23 *a33*m1*n1
2 3 2 2
+ 4*u1*u2*v1*v3*a23 *n1 - 2*u1*u2*v2 *v3*a23 *a33*m1*n1
2 2 3 2 2 2 3 2
- 8*u1*u3 *v1 *a23 *n1 - 8*u1*u3 *v3 *a23 *n1
2 2 2 3
- 2*u1*u3*v1 *v2*a23 *a33*m1*n1 + 4*u1*u3*v1*v2*a23 *n1
2 2 2 2 2
- 2*u1*u3*v2*v3 *a23 *a33*m1*n1 - 2*u1*v1 *v2*v3*a23 *a33*m1
2 2 3 2 2 2
+ 2*u1*v1 *v3 *a23 *m1 + 4*u1*v1*v2*v3*a23 *m1*n1
2 2 2 2 3
- 2*u2 *v1*v2*v3*a23 *a33*m1*n1 + 4*u2 *v2*v3*a23 *n1
2 3 2 2 2
- 8*u2*u3 *v1*v2*a23 *n1 - 2*u2*u3*v1*v2 *a23 *a33*m1*n1
2 2 2 2 3
- 2*u2*u3*v1*v3 *a23 *a33*m1*n1 + 4*u2*u3*v2 *a23 *n1
2 2 3 2 2 2
+ 4*u2*u3*v3 *a23 *n1 - 2*u2*v1*v2 *v3*a23 *a33*m1
2 3 2 2 2 2
+ 2*u2*v1*v2*v3 *a23 *m1 + 4*u2*v2 *v3*a23 *m1*n1
3 3 2 2 2
- 8*u3 *v1*v3*a23 *n1 - 2*u3 *v1*v2*v3*a23 *a33*m1*n1
2 2 3 2 2 2
+ 4*u3 *v2*v3*a23 *n1 - 2*u3*v1*v2*v3 *a23 *a33*m1
3 3 2 2 2 2
+ 2*u3*v1*v3 *a23 *m1 + 4*u3*v2*v3 *a23 *m1*n1
2
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
2 2 2 2
{HAM,FI} = 2*u1*u3*v1 *a23*a33*n1 - 2*u1*v1 *v2*a23 *m1 - u1*v1*v2*a33*n1
2 2 2 2
+ 2*u2*u3*v1*v2*a23*a33*n1 - 2*u2*v1*v2 *a23 *m1 - u2*v2 *a33*n1
2 2 2
+ 2*u3 *v1*v3*a23*a33*n1 - 2*u3*v1*v2*v3*a23 *m1 - u3*v2*v3*a33*n1
2 2 3
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
2 2 2
{HAM,FI} = 4*u1*u3*v1 *v3*a23*a33*n1 - 4*u1*v1 *v2*v3*a23 *m1
2
- 2*u1*v1*v2*v3*a33*n1 + 4*u2*u3*v1*v2*v3*a23*a33*n1
2 2 2 2
- 4*u2*v1*v2 *v3*a23 *m1 - 2*u2*v2 *v3*a33*n1
2 2 2 2
+ 4*u3 *v1*v3 *a23*a33*n1 - 4*u3*v1*v2*v3 *a23 *m1
2 2
- 2*u3*v2*v3 *a33*n1
And again in machine readable form:
HAM=(2*u1*v1*a23**2*a33*m1*n1 + u1*a33**2*n1**3 + 2*u2*u3*a23*a33**2*n1**2 + u3
**2*a33**3*n1**2 + v1*a33**2*m1*n1**2 - v2**2*a23**2*a33*m1**2 + 2*v2*v3*a23**3*
m1**2)/(a33**2*n1**2)$
FI= - u1**2*a33**3*n1**2 + 2*u1*v1*a23**2*a33*m1*n1 + u1*a33**2*n1**3 - u2**2*
a33**3*n1**2 + 2*u2*u3*a23*a33**2*n1**2 - 2*u2*v3*a23*a33**2*m1*n1 - 2*u3*v2*a23
*a33**2*m1*n1 - 2*u3*v3*a33**3*m1*n1 - 2*v1**2*a23**2*a33*m1**2 - v1*a33**2*m1*
n1**2 + v2*v3*(2*a23**3*m1**2 + 2*a23*a33**2*m1**2) + v3**2*(a23**2*a33*m1**2 +
a33**3*m1**2)$
FI=u1**2*u2*v1 + u1*u2**2*v2 + u1*u2*u3*v3$
FI=u1**2*v1**2 + u1*u2*v1*v2 + u1*u3*v1*v3$
FI=u1*u2**2*v1 + u2**3*v2 + u2**2*u3*v3$
FI=u1*u3*v1*v2 + u2*u3*v2**2 + u3**2*v2*v3$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI=u1*u2*u3*v1 + u2**2*u3*v2 + u2*u3**2*v3$
FI=u1*u2*v1 + u2**2*v2 + u2*u3*v3$
FI=u1**2*u3*v1 + u1*u2*u3*v2 + u1*u3**2*v3$
FI=u1*u2*v1**2 + u2**2*v1*v2 + u2*u3*v1*v3$
FI=u1**3*v1 + u1**2*u2*v2 + u1**2*u3*v3$
FI=u1**2*v1*v2 + u1*u2*v2**2 + u1*u3*v2*v3$
FI=u1**2*v1*v3 + u1*u2*v2*v3 + u1*u3*v3**2$
FI=u1*u2*v1*v3 + u2**2*v2*v3 + u2*u3*v3**2$
FI=u1*u3*v1**2 + u2*u3*v1*v2 + u3**2*v1*v3$
FI=u1**2*v1 + u1*u2*v2 + u1*u3*v3$
FI=u1*v1**2*v2 + u2*v1*v2**2 + u3*v1*v2*v3$
FI=u1*v1*v2*v3 + u2*v2**2*v3 + u3*v2*v3**2$
FI=u1*v1*v2 + u2*v2**2 + u3*v2*v3$
FI=u1*v1**3 + u2*v1**2*v2 + u3*v1**2*v3$
FI=u1*v1**2 + u2*v1*v2 + u3*v1*v3$
FI=u1*v1**2*v3 + u2*v1*v2*v3 + u3*v1*v3**2$
FI=u1*u3*v1*v3 + u2*u3*v2*v3 + u3**2*v3**2$
FI=u1*v1*v3 + u2*v2*v3 + u3*v3**2$
FI=u1*v1*v3**2 + u2*v2*v3**2 + u3*v3**3$