Solution 4 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
r14=0
r15=0
r20=0
r21=0
r23=0
r24=0
r25=0
m3*r333
r26=---------
a11
r27=0
r28=0
r210=0
r212=0
r213=0
r214=0
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
r312=r315
r313=r340
r314=0
r317=0
r318=0
r320=0
a11*r310 - a11*r315 - c33*r333
r321=--------------------------------
a11
r322=r311
r323=0
r324=r340
r325=0
a11*r316 - b33*r333 - m3*r464
r327=-------------------------------
a11
r328=0
r329=0
r330=0
r331=r326
r332=0
r334=0
r335=0
r336=0
r337=0
a11*r310 - a11*r315 - c33*r333
r338=--------------------------------
a11
r339=r311
r342=0
a11*r316 - b33*r333 - m3*r464
r343=-------------------------------
a11
r344=0
r345=0
r346=r341
r347=r326
r348=0
r349=0
r350=0
r351=0
r352=r341
r353=r333
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=r484
r428=r485
r429=0
r430=r427
r432=0
r433=0
r435=0
r436=r415
r437=r416
r439=0
r440=r419
r441=r420
r442=0
r443=r422
r444=0
a11*r425 - a11*r427 - c33*r464
r446=--------------------------------
a11
r447=r484
r448=r459
r449=r485
r450=0
a11*r431 - b33*r464
r452=---------------------
a11
r453=0
r454=0
r455=0
r456=r445
r458=0
r460=0
r461=r466
r462=r451
r463=0
r465=0
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
r481=r492
r482=0
r486=r497
r487=0
a11*r431 - b33*r464
r488=---------------------
a11
r489=0
r490=0
r491=r480
r493=r445
- a11*r425 + a11*r427 + a11*r483 + c33*r464
r494=----------------------------------------------
a11
r495=r459
r496=r4101
r498=r451
r499=0
r4100=0
r4102=r466
r4103=0
r4104=0
r4105=0
r4106=0
r4108=r480
r4109=r492
- a11*r425 + a11*r427 + a11*r483 + c33*r464
r4110=----------------------------------------------
a11
r4111=0
r4112=0
r4113=r497
r4114=r464
r4115=0
r4117=r4101
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
m2=0
m1=0
n2=0
n1=0
c23=0
c22=0
c13=0
c12=0
b32=0
b31=0
b11=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:
r434, r319, r29, r13, r427, r310, r315, r415, r316, r431,
r425, r340, r311, r416, r419, r422, r420, r326, r341,
r485, r480, r445, r484, r333, r483, r451, r459, r492,
r466, r497, r4101, r464, m3, c33, b33, n3, a11
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.
{n3,a11}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u2 *a11 + u3*v3*b33 + u3*n3 + v3 *c33 + v3*m3
has apart from the Hamiltonian and Casimirs the following 32 first integrals:
2 2 2 2 2
FI=u1 *u3 *a11 + u1 *v1 *c33 + u1*u2*v1*v2*c33 - u1*u3 *v1*b33 - u1*u3*v1*m3
2 2 2
+ u2 *u3 *a11 - u2*u3 *v2*b33 - u2*u3*v2*v3*c33 - u2*u3*v2*m3
2 2
{HAM,FI} = - 2*u1 *u2*v1*v3*a11*c33 + 2*u1 *u3*v1*v2*a11*c33
2 2 2
+ u1 *v1*v2*v3*b33*c33 + u1 *v1*v2*c33*n3 - 2*u1*u2 *v2*v3*a11*c33
2 2
- 4*u1*u2*u3*v1 *a11*c33 + 2*u1*u2*u3*v2 *a11*c33
2 2 2
- 2*u1*u2*u3*v3 *a11*c33 + u1*u2*v1 *v3*b33*c33 + u1*u2*v1 *c33*n3
2 2 2
+ u1*u2*v2 *v3*b33*c33 + u1*u2*v2 *c33*n3 + 2*u1*u3 *v2*v3*a11*c33
2 2
+ u1*u3*v1 *v2*b33*c33 + u1*u3*v2*v3 *b33*c33 + u1*u3*v2*v3*c33*n3
2 2 2 2
+ 2*u1*v1 *v2*v3*c33 + u1*v1 *v2*c33*m3 - 4*u2 *u3*v1*v2*a11*c33
2 2 2
+ u2 *v1*v2*v3*b33*c33 + u2 *v1*v2*c33*n3 - 4*u2*u3 *v1*v3*a11*c33
2 2
+ u2*u3*v1*v2 *b33*c33 + u2*u3*v1*v3 *b33*c33 + u2*u3*v1*v3*c33*n3
2 2 2 2
+ 2*u2*v1*v2 *v3*c33 + u2*v1*v2 *c33*m3 + u3 *v1*v2*v3*b33*c33
2 2
+ 2*u3*v1*v2*v3 *c33 + u3*v1*v2*v3*c33*m3
2 2
FI=u1 *u2*v1 + u1*u2 *v2 + u1*u2*u3*v3
3 3 3 2
{HAM,FI} = 2*u1 *u3*v1*a11 - u1 *v1*v3*b33 - u1 *v1*n3 + 2*u1 *u2*u3*v2*a11
2 2 2 2
- u1 *u2*v2*v3*b33 - u1 *u2*v2*n3 + 2*u1 *u3 *v3*a11
2 2 2 2 2 2 2
- u1 *u3*v1 *b33 - u1 *u3*v3 *b33 - u1 *u3*v3*n3 - 2*u1 *v1 *v3*c33
2 2 2 2 2
- u1 *v1 *m3 - 2*u1*u2 *u3*v1*a11 + u1*u2 *v1*v3*b33 + u1*u2 *v1*n3
2 2
- u1*u3 *v1*v3*b33 - 2*u1*u3*v1*v3 *c33 - u1*u3*v1*v3*m3
3 3 3 2 2
- 2*u2 *u3*v2*a11 + u2 *v2*v3*b33 + u2 *v2*n3 - 2*u2 *u3 *v3*a11
2 2 2 2 2 2 2
+ u2 *u3*v2 *b33 + u2 *u3*v3 *b33 + u2 *u3*v3*n3 + 2*u2 *v2 *v3*c33
2 2 2 2
+ u2 *v2 *m3 + u2*u3 *v2*v3*b33 + 2*u2*u3*v2*v3 *c33
+ u2*u3*v2*v3*m3
2 2
FI=u1 *u3*v1 + u1*u2*u3*v2 + u1*u3 *v3
2
{HAM,FI} = - 2*u1*u2*u3 *v1*a11 + u1*u2*u3*v1*v3*b33 + u1*u2*u3*v1*n3
2
+ u1*u3 *v1*v2*b33 + 2*u1*u3*v1*v2*v3*c33 + u1*u3*v1*v2*m3
2 2 2 2
- 2*u2 *u3 *v2*a11 + u2 *u3*v2*v3*b33 + u2 *u3*v2*n3
3 2 2 2 2 2
- 2*u2*u3 *v3*a11 + u2*u3 *v2 *b33 + u2*u3 *v3 *b33 + u2*u3 *v3*n3
2 2 3
+ 2*u2*u3*v2 *v3*c33 + u2*u3*v2 *m3 + u3 *v2*v3*b33
2 2 2
+ 2*u3 *v2*v3 *c33 + u3 *v2*v3*m3
2 3 2
FI=u1*u2 *v1 + u2 *v2 + u2 *u3*v3
2 2 2
{HAM,FI} = 4*u1 *u2*u3*v1*a11 - 2*u1 *u2*v1*v3*b33 - 2*u1 *u2*v1*n3
2 2 2
+ 4*u1*u2 *u3*v2*a11 - 2*u1*u2 *v2*v3*b33 - 2*u1*u2 *v2*n3
2 2 2
+ 4*u1*u2*u3 *v3*a11 - 2*u1*u2*u3*v1 *b33 - 2*u1*u2*u3*v3 *b33
2 2
- 2*u1*u2*u3*v3*n3 - 4*u1*u2*v1 *v3*c33 - 2*u1*u2*v1 *m3
2 2 2
- 2*u2 *u3*v1*v2*b33 - 4*u2 *v1*v2*v3*c33 - 2*u2 *v1*v2*m3
2 2
- 2*u2*u3 *v1*v3*b33 - 4*u2*u3*v1*v3 *c33 - 2*u2*u3*v1*v3*m3
2 2
FI=u1 *v1*v2 + u1*u2*v2 + u1*u3*v2*v3
3 2 2 2
{HAM,FI} = 2*u1 *v1*v3*a11 + 2*u1 *u2*v2*v3*a11 + 2*u1 *u3*v3 *a11
2 2 2 2
- u1 *v1 *v3*b33 - u1 *v1 *n3 - 2*u1*u2*u3*v1*v2*a11
2 2
+ u1*u3*v1*v2 *b33 - u1*u3*v1*v3 *b33 - u1*u3*v1*v3*n3
2 2 2 2
+ 2*u1*v1*v2 *v3*c33 + u1*v1*v2 *m3 - 2*u2 *u3*v2 *a11
2 2 2 2 2 3
+ u2 *v2 *v3*b33 + u2 *v2 *n3 - 2*u2*u3 *v2*v3*a11 + u2*u3*v2 *b33
2 3 3
+ u2*u3*v2*v3 *b33 + u2*u3*v2*v3*n3 + 2*u2*v2 *v3*c33 + u2*v2 *m3
2 2 2 2 2
+ u3 *v2 *v3*b33 + 2*u3*v2 *v3 *c33 + u3*v2 *v3*m3
2 2
FI=u1*u2*v1 + u2 *v1*v2 + u2*u3*v1*v3
2 2 2 2 2 2 2
{HAM,FI} = 2*u1 *u3*v1 *a11 - u1 *v1 *v3*b33 - u1 *v1 *n3 - 2*u1*u2 *v1*v3*a11
2 3
+ 2*u1*u2*u3*v1*v2*a11 + 2*u1*u3 *v1*v3*a11 - u1*u3*v1 *b33
2 3 3
- u1*u3*v1*v3 *b33 - u1*u3*v1*v3*n3 - 2*u1*v1 *v3*c33 - u1*v1 *m3
3 2 2 2 2 2 2
- 2*u2 *v2*v3*a11 - 2*u2 *u3*v3 *a11 + u2 *v2 *v3*b33 + u2 *v2 *n3
2 2
- u2*u3*v1 *v2*b33 + u2*u3*v2*v3 *b33 + u2*u3*v2*v3*n3
2 2 2 2
- 2*u2*v1 *v2*v3*c33 - u2*v1 *v2*m3 - u3 *v1 *v3*b33
2 2 2
- 2*u3*v1 *v3 *c33 - u3*v1 *v3*m3
2 2
FI=u1*u2*u3*v1 + u2 *u3*v2 + u2*u3 *v3
2 2 2 2
{HAM,FI} = 2*u1 *u3 *v1*a11 - u1 *u3*v1*v3*b33 - u1 *u3*v1*n3
2
+ 2*u1*u2*u3 *v2*a11 - u1*u2*u3*v2*v3*b33 - u1*u2*u3*v2*n3
3 2 2 2 2 2
+ 2*u1*u3 *v3*a11 - u1*u3 *v1 *b33 - u1*u3 *v3 *b33 - u1*u3 *v3*n3
2 2 2
- 2*u1*u3*v1 *v3*c33 - u1*u3*v1 *m3 - u2*u3 *v1*v2*b33
3
- 2*u2*u3*v1*v2*v3*c33 - u2*u3*v1*v2*m3 - u3 *v1*v3*b33
2 2 2
- 2*u3 *v1*v3 *c33 - u3 *v1*v3*m3
2 2
FI=u1 *v1 + u1*u2*v1*v2 + u1*u3*v1*v3
2 2 2
{HAM,FI} = - 2*u1 *u2*v1*v3*a11 + u1 *v1*v2*v3*b33 + u1 *v1*v2*n3
2 2 2
- 2*u1*u2 *v2*v3*a11 - 2*u1*u2*u3*v1 *a11 - 2*u1*u2*u3*v3 *a11
2 2 2 2
+ u1*u2*v1 *v3*b33 + u1*u2*v1 *n3 + u1*u2*v2 *v3*b33 + u1*u2*v2 *n3
2 2
+ u1*u3*v1 *v2*b33 + u1*u3*v2*v3 *b33 + u1*u3*v2*v3*n3
2 2 2
+ 2*u1*v1 *v2*v3*c33 + u1*v1 *v2*m3 - 2*u2 *u3*v1*v2*a11
2 2 2
+ u2 *v1*v2*v3*b33 + u2 *v1*v2*n3 - 2*u2*u3 *v1*v3*a11
2 2
+ u2*u3*v1*v2 *b33 + u2*u3*v1*v3 *b33 + u2*u3*v1*v3*n3
2 2 2
+ 2*u2*v1*v2 *v3*c33 + u2*v1*v2 *m3 + u3 *v1*v2*v3*b33
2
+ 2*u3*v1*v2*v3 *c33 + u3*v1*v2*v3*m3
2 2
FI=u1 *u3*a11 - u1*u3*v1*b33 - u1*v1*v3*c33 + u2 *u3*a11 - u2*u3*v2*b33
- u2*v2*v3*c33 + u3*v3*m3
2 2 2
{HAM,FI} = 2*u1 *v1*v2*a11*c33 - 2*u1*u2*v1 *a11*c33 + 2*u1*u2*v2 *a11*c33
2
+ 2*u1*u3*v2*v3*a11*c33 - 2*u2 *v1*v2*a11*c33
- 2*u2*u3*v1*v3*a11*c33
2 2
FI=u1*u3*v1*v2 + u2*u3*v2 + u3 *v2*v3
2 2 2
{HAM,FI} = 2*u1 *u3*v1*v3*a11 + 2*u1*u2*u3*v2*v3*a11 + 2*u1*u3 *v3 *a11
2 2
- u1*u3*v1 *v3*b33 - u1*u3*v1 *n3 - u2*u3*v1*v2*v3*b33
2 2 2
- u2*u3*v1*v2*n3 - u3 *v1*v3 *b33 - u3 *v1*v3*n3
2 2
FI=u1*u2*v1*v3 + u2 *v2*v3 + u2*u3*v3
2 2 2 2
{HAM,FI} = - 2*u1 *u2*v1*v2*a11 + 2*u1 *u3*v1*v3*a11 - u1 *v1*v3 *b33
2 2 2 2 2
- u1 *v1*v3*n3 + 2*u1*u2 *v1 *a11 - 2*u1*u2 *v2 *a11
2 2 2
- u1*u2*v2*v3 *b33 - u1*u2*v2*v3*n3 + 2*u1*u3 *v3 *a11
2 3 2 2 2
- u1*u3*v1 *v3*b33 - u1*u3*v3 *b33 - u1*u3*v3 *n3 - 2*u1*v1 *v3 *c33
2 3 2
- u1*v1 *v3*m3 + 2*u2 *v1*v2*a11 + 2*u2 *u3*v1*v3*a11
2
- u2*u3*v1*v2*v3*b33 - 2*u2*v1*v2*v3 *c33 - u2*v1*v2*v3*m3
2 2 3 2
- u3 *v1*v3 *b33 - 2*u3*v1*v3 *c33 - u3*v1*v3 *m3
2 2
FI=u1 *v1*v3 + u1*u2*v2*v3 + u1*u3*v3
3 2 2 2 2
{HAM,FI} = - 2*u1 *v1*v2*a11 + 2*u1 *u2*v1 *a11 - 2*u1 *u2*v2 *a11
2 2 2
- 2*u1 *u3*v2*v3*a11 + 2*u1*u2 *v1*v2*a11 + u1*u2*v1*v3 *b33
2
+ u1*u2*v1*v3*n3 + u1*u3*v1*v2*v3*b33 + 2*u1*v1*v2*v3 *c33
2 2 2
+ u1*v1*v2*v3*m3 - 2*u2 *u3*v2*v3*a11 + u2 *v2*v3 *b33
2 2 2 2 3
+ u2 *v2*v3*n3 - 2*u2*u3 *v3 *a11 + u2*u3*v2 *v3*b33 + u2*u3*v3 *b33
2 2 2 2 2 2
+ u2*u3*v3 *n3 + 2*u2*v2 *v3 *c33 + u2*v2 *v3*m3 + u3 *v2*v3 *b33
3 2
+ 2*u3*v2*v3 *c33 + u3*v2*v3 *m3
2 2
FI=u1*u3*v1 + u2*u3*v1*v2 + u3 *v1*v3
{HAM,FI} = - 2*u1*u2*u3*v1*v3*a11 + u1*u3*v1*v2*v3*b33 + u1*u3*v1*v2*n3
2 2 2 2
- 2*u2 *u3*v2*v3*a11 - 2*u2*u3 *v3 *a11 + u2*u3*v2 *v3*b33
2 2 2 2
+ u2*u3*v2 *n3 + u3 *v2*v3 *b33 + u3 *v2*v3*n3
2
FI=u1 *v1 + u1*u2*v2 + u1*u3*v3
{HAM,FI} = - 2*u1*u2*u3*v1*a11 + u1*u2*v1*v3*b33 + u1*u2*v1*n3
+ u1*u3*v1*v2*b33 + 2*u1*v1*v2*v3*c33 + u1*v1*v2*m3
2 2 2 2
- 2*u2 *u3*v2*a11 + u2 *v2*v3*b33 + u2 *v2*n3 - 2*u2*u3 *v3*a11
2 2 2
+ u2*u3*v2 *b33 + u2*u3*v3 *b33 + u2*u3*v3*n3 + 2*u2*v2 *v3*c33
2 2 2
+ u2*v2 *m3 + u3 *v2*v3*b33 + 2*u3*v2*v3 *c33 + u3*v2*v3*m3
2
FI=u1*u2*v1 + u2 *v2 + u2*u3*v3
2 2 2
{HAM,FI} = 2*u1 *u3*v1*a11 - u1 *v1*v3*b33 - u1 *v1*n3 + 2*u1*u2*u3*v2*a11
2 2
- u1*u2*v2*v3*b33 - u1*u2*v2*n3 + 2*u1*u3 *v3*a11 - u1*u3*v1 *b33
2 2 2
- u1*u3*v3 *b33 - u1*u3*v3*n3 - 2*u1*v1 *v3*c33 - u1*v1 *m3
2
- u2*u3*v1*v2*b33 - 2*u2*v1*v2*v3*c33 - u2*v1*v2*m3 - u3 *v1*v3*b33
2
- 2*u3*v1*v3 *c33 - u3*v1*v3*m3
2 2
FI=u1*v1 *v2 + u2*v1*v2 + u3*v1*v2*v3
2 2 2 3 3
{HAM,FI} = 2*u1 *v1 *v3*a11 + 2*u1*u3*v1*v3 *a11 - u1*v1 *v3*b33 - u1*v1 *n3
2 2 2 2
+ u1*v1*v2 *v3*b33 + u1*v1*v2 *n3 - 2*u2 *v2 *v3*a11
2 2 2
- 2*u2*u3*v2*v3 *a11 - u2*v1 *v2*v3*b33 - u2*v1 *v2*n3
3 3 2 2 2
+ u2*v2 *v3*b33 + u2*v2 *n3 - u3*v1 *v3 *b33 - u3*v1 *v3*n3
2 2 2
+ u3*v2 *v3 *b33 + u3*v2 *v3*n3
3 2 2
FI=u1*v1 + u2*v1 *v2 + u3*v1 *v3
2 2 2
{HAM,FI} = - 4*u1*u2*v1 *v3*a11 + 2*u1*v1 *v2*v3*b33 + 2*u1*v1 *v2*n3
2 2 2
- 4*u2 *v1*v2*v3*a11 - 4*u2*u3*v1*v3 *a11 + 2*u2*v1*v2 *v3*b33
2 2
+ 2*u2*v1*v2 *n3 + 2*u3*v1*v2*v3 *b33 + 2*u3*v1*v2*v3*n3
2 2
FI=u1*v1 *v3 + u2*v1*v2*v3 + u3*v1*v3
2 2 3 2
{HAM,FI} = - 2*u1 *v1 *v2*a11 + 2*u1*u2*v1 *a11 - 2*u1*u2*v1*v2 *a11
2 2
- 2*u1*u2*v1*v3 *a11 - 2*u1*u3*v1*v2*v3*a11 + u1*v1*v2*v3 *b33
2 2 2 2
+ u1*v1*v2*v3*n3 + 2*u2 *v1 *v2*a11 - 2*u2 *v2*v3 *a11
2 3 2 2
+ 2*u2*u3*v1 *v3*a11 - 2*u2*u3*v3 *a11 + u2*v2 *v3 *b33
2 3 2
+ u2*v2 *v3*n3 + u3*v2*v3 *b33 + u3*v2*v3 *n3
2 2
FI=u1*v1*v2*v3 + u2*v2 *v3 + u3*v2*v3
2 2 2 2 2
{HAM,FI} = - 2*u1 *v1*v2 *a11 + 2*u1 *v1*v3 *a11 + 2*u1*u2*v1 *v2*a11
3 2 2
- 2*u1*u2*v2 *a11 + 2*u1*u2*v2*v3 *a11 - 2*u1*u3*v2 *v3*a11
3 2 2 2 2 2
+ 2*u1*u3*v3 *a11 - u1*v1 *v3 *b33 - u1*v1 *v3*n3 + 2*u2 *v1*v2 *a11
2
+ 2*u2*u3*v1*v2*v3*a11 - u2*v1*v2*v3 *b33 - u2*v1*v2*v3*n3
3 2
- u3*v1*v3 *b33 - u3*v1*v3 *n3
2
FI=u1*v1*v2 + u2*v2 + u3*v2*v3
2 2 2
{HAM,FI} = 2*u1 *v1*v3*a11 + 2*u1*u2*v2*v3*a11 + 2*u1*u3*v3 *a11 - u1*v1 *v3*b33
2 2
- u1*v1 *n3 - u2*v1*v2*v3*b33 - u2*v1*v2*n3 - u3*v1*v3 *b33
- u3*v1*v3*n3
2
FI=u1*v1 + u2*v1*v2 + u3*v1*v3
{HAM,FI} = - 2*u1*u2*v1*v3*a11 + u1*v1*v2*v3*b33 + u1*v1*v2*n3
2 2 2 2
- 2*u2 *v2*v3*a11 - 2*u2*u3*v3 *a11 + u2*v2 *v3*b33 + u2*v2 *n3
2
+ u3*v2*v3 *b33 + u3*v2*v3*n3
2 2 2 2
FI= - u1 *v1 - u1*u2*v1*v2 + u2*u3*v2*v3 + u3 *v3
2 2 2
{HAM,FI} = 2*u1 *u2*v1*v3*a11 - 2*u1 *u3*v1*v2*a11 - u1 *v1*v2*v3*b33
2 2 2
- u1 *v1*v2*n3 + 2*u1*u2 *v2*v3*a11 + 4*u1*u2*u3*v1 *a11
2 2 2
- 2*u1*u2*u3*v2 *a11 + 2*u1*u2*u3*v3 *a11 - u1*u2*v1 *v3*b33
2 2 2
- u1*u2*v1 *n3 - u1*u2*v2 *v3*b33 - u1*u2*v2 *n3
2 2 2
- 2*u1*u3 *v2*v3*a11 - u1*u3*v1 *v2*b33 - u1*u3*v2*v3 *b33
2 2
- u1*u3*v2*v3*n3 - 2*u1*v1 *v2*v3*c33 - u1*v1 *v2*m3
2 2 2
+ 4*u2 *u3*v1*v2*a11 - u2 *v1*v2*v3*b33 - u2 *v1*v2*n3
2 2 2
+ 4*u2*u3 *v1*v3*a11 - u2*u3*v1*v2 *b33 - u2*u3*v1*v3 *b33
2 2
- u2*u3*v1*v3*n3 - 2*u2*v1*v2 *v3*c33 - u2*v1*v2 *m3
2 2
- u3 *v1*v2*v3*b33 - 2*u3*v1*v2*v3 *c33 - u3*v1*v2*v3*m3
2 2 3
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
{HAM,FI} = 0
2
FI=u1*u3*v1 + u2*u3*v2 + u3 *v3
{HAM,FI} = 0
2 2 3
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
2 2 2
{HAM,FI} = - 4*u1 *v1*v2*v3*a11 + 4*u1*u2*v1 *v3*a11 - 4*u1*u2*v2 *v3*a11
2 2 2
- 4*u1*u3*v2*v3 *a11 + 4*u2 *v1*v2*v3*a11 + 4*u2*u3*v1*v3 *a11
2 2
FI= - u1*v1*v3 - u2*v2*v3 + u3*v1 + u3*v2
2 2 2
{HAM,FI} = 2*u1 *v1*v2*a11 - 2*u1*u2*v1 *a11 + 2*u1*u2*v2 *a11
2
+ 2*u1*u3*v2*v3*a11 - 2*u2 *v1*v2*a11 - 2*u2*u3*v1*v3*a11
2
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
2 2 2
{HAM,FI} = - 2*u1 *v1*v2*a11 + 2*u1*u2*v1 *a11 - 2*u1*u2*v2 *a11
2
- 2*u1*u3*v2*v3*a11 + 2*u2 *v1*v2*a11 + 2*u2*u3*v1*v3*a11
2 2 2 2 2 2
FI=u1 *v1 + u1*u2*v1*v2 - u2*u3*v2*v3 + u3 *v1 + u3 *v2
2 2 2
{HAM,FI} = - 2*u1 *u2*v1*v3*a11 + 2*u1 *u3*v1*v2*a11 + u1 *v1*v2*v3*b33
2 2 2
+ u1 *v1*v2*n3 - 2*u1*u2 *v2*v3*a11 - 4*u1*u2*u3*v1 *a11
2 2 2
+ 2*u1*u2*u3*v2 *a11 - 2*u1*u2*u3*v3 *a11 + u1*u2*v1 *v3*b33
2 2 2
+ u1*u2*v1 *n3 + u1*u2*v2 *v3*b33 + u1*u2*v2 *n3
2 2 2
+ 2*u1*u3 *v2*v3*a11 + u1*u3*v1 *v2*b33 + u1*u3*v2*v3 *b33
2 2
+ u1*u3*v2*v3*n3 + 2*u1*v1 *v2*v3*c33 + u1*v1 *v2*m3
2 2 2
- 4*u2 *u3*v1*v2*a11 + u2 *v1*v2*v3*b33 + u2 *v1*v2*n3
2 2 2
- 4*u2*u3 *v1*v3*a11 + u2*u3*v1*v2 *b33 + u2*u3*v1*v3 *b33
2 2
+ u2*u3*v1*v3*n3 + 2*u2*v1*v2 *v3*c33 + u2*v1*v2 *m3
2 2
+ u3 *v1*v2*v3*b33 + 2*u3*v1*v2*v3 *c33 + u3*v1*v2*v3*m3
FI=u3
{HAM,FI} = 0
2
FI=u3
{HAM,FI} = 0
3
FI=u3
{HAM,FI} = 0
4
FI=u3
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u2**2*a11 + u3*v3*b33 + u3*n3 + v3**2*c33 + v3*m3$
FI=u1**2*u3**2*a11 + u1**2*v1**2*c33 + u1*u2*v1*v2*c33 - u1*u3**2*v1*b33 - u1*u3
*v1*m3 + u2**2*u3**2*a11 - u2*u3**2*v2*b33 - u2*u3*v2*v3*c33 - u2*u3*v2*m3$
FI=u1**2*u2*v1 + u1*u2**2*v2 + u1*u2*u3*v3$
FI=u1**2*u3*v1 + u1*u2*u3*v2 + u1*u3**2*v3$
FI=u1*u2**2*v1 + u2**3*v2 + u2**2*u3*v3$
FI=u1**2*v1*v2 + u1*u2*v2**2 + u1*u3*v2*v3$
FI=u1*u2*v1**2 + u2**2*v1*v2 + u2*u3*v1*v3$
FI=u1*u2*u3*v1 + u2**2*u3*v2 + u2*u3**2*v3$
FI=u1**2*v1**2 + u1*u2*v1*v2 + u1*u3*v1*v3$
FI=u1**2*u3*a11 - u1*u3*v1*b33 - u1*v1*v3*c33 + u2**2*u3*a11 - u2*u3*v2*b33 - u2
*v2*v3*c33 + u3*v3*m3$
FI=u1*u3*v1*v2 + u2*u3*v2**2 + u3**2*v2*v3$
FI=u1*u2*v1*v3 + u2**2*v2*v3 + u2*u3*v3**2$
FI=u1**2*v1*v3 + u1*u2*v2*v3 + u1*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*u2*v1 + u2**2*v2 + u2*u3*v3$
FI=u1*v1**2*v2 + u2*v1*v2**2 + u3*v1*v2*v3$
FI=u1*v1**3 + u2*v1**2*v2 + u3*v1**2*v3$
FI=u1*v1**2*v3 + u2*v1*v2*v3 + u3*v1*v3**2$
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**2 + u2*v1*v2 + u3*v1*v3$
FI= - u1**2*v1**2 - u1*u2*v1*v2 + u2*u3*v2*v3 + u3**2*v3**2$
FI=u1*u3**2*v1 + u2*u3**2*v2 + u3**3*v3$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI=u1*v1*v3**2 + u2*v2*v3**2 + u3*v3**3$
FI= - u1*v1*v3 - u2*v2*v3 + u3*v1**2 + u3*v2**2$
FI=u1*v1*v3 + u2*v2*v3 + u3*v3**2$
FI=u1**2*v1**2 + u1*u2*v1*v2 - u2*u3*v2*v3 + u3**2*v1**2 + u3**2*v2**2$
FI=u3$
FI=u3**2$
FI=u3**3$
FI=u3**4$