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
r13=0
r14=0
r15=0
2 2 2 2 2
a11 *b33 *r29 - 2*a11*a22*b33 *r29 + a22 *b33 *r29
r20=----------------------------------------------------
2 2
4*a11 *a22
r21=0
2 2
a11*b33 *r29 - a22*b33 *r29
r22=-----------------------------
2
4*a11*a22
r23=0
r24=0
r26=0
r27=0
r28=0
r210=0
r212=0
r213=0
a11*r29 - a22*r29
r214=-------------------
a11
r215=0
r216=0
- a11*b33*r29 + a22*b33*r29
r217=------------------------------
a11*a22
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
4 2 3 2 2 3 3
r40=( - 4*a11 *a22*b33 *r446 + 8*a11 *a22 *b33 *r446 - 8*a11 *a22*b33 *r452
3 4 2 2 3 2 4
- 3*a11 *b33 *r4114 + 8*a11 *a22 *b33 *r452 + 3*a11 *a22*b33 *r4114
2 4 3 4 4 3
- a11*a22 *b33 *r4114 + a22 *b33 *r4114)/(32*a11 *a22 )
r41=0
4 2 3 2 2 3 3
r42=( - 4*a11 *a22*b33 *r446 + 4*a11 *a22 *b33 *r446 - 4*a11 *a22*b33 *r452
3 4 2 3 2 2 4
- 2*a11 *b33 *r4114 + 2*a11 *a22 *b33 *r446 + a11 *a22*b33 *r4114
3 3 2 4 3 4 4
+ 4*a11*a22 *b33 *r452 - a11*a22 *b33 *r4114 + 2*a22 *b33 *r4114)/(16*a11
3
*a22 )
r43=0
4 2 3 4 2 3 2
r44=( - 4*a11 *a22*b33 *r446 - a11 *b33 *r4114 + 4*a11 *a22 *b33 *r446
2 2 3 2 4 3 3
- 8*a11 *a22 *b33 *r452 + a11 *a22*b33 *r4114 + 8*a11*a22 *b33 *r452
2 4 3 4 4 3
- 4*a11*a22 *b33 *r4114 + 4*a22 *b33 *r4114)/(32*a11 *a22 )
r45=0
r46=0
r47=0
r48=0
4 2 3 2 2 3 3
r49=( - 2*a11 *a22*b33 *r446 + 4*a11 *a22 *b33 *r446 - 4*a11 *a22*b33 *r452
3 4 2 2 3 2 4
- a11 *b33 *r4114 + 4*a11 *a22 *b33 *r452 + a11 *a22*b33 *r4114
2 4 3 4 4 3
- a11*a22 *b33 *r4114 + a22 *b33 *r4114)/(16*a11 *a22 )
r410=0
4 2 3 4 2 3 2
r411=( - 2*a11 *a22*b33 *r446 - a11 *b33 *r4114 + 2*a11 *a22 *b33 *r446
2 2 3 2 4 3 3
- 4*a11 *a22 *b33 *r452 + 2*a11 *a22*b33 *r4114 + 4*a11*a22 *b33 *r452
2 4 3 4 4 3
- 3*a11*a22 *b33 *r4114 + 2*a22 *b33 *r4114)/(16*a11 *a22 )
r412=0
r413=0
3 2 2 2 2 2
r415=(a11 *b33 *r452 - 2*a11 *a22 *b33*r446 + 2*a11 *a22*b33 *r452
2 3 2 2 2 3 3 2
+ a11 *b33 *r4114 - 3*a11*a22 *b33 *r452 - a22 *b33 *r4114)/(4*a11 *a22 )
r416=0
3 2 2 2 2 2
r417=(a11 *b33 *r452 - 2*a11 *a22 *b33*r446 + 3*a11 *a22*b33 *r452
2 3 2 2 3
+ a11 *b33 *r4114 - 4*a11*a22 *b33 *r452 + a11*a22*b33 *r4114
2 3 3 2
- 2*a22 *b33 *r4114)/(4*a11 *a22 )
r418=0
r419=0
r420=0
r421=0
2 2 2 2
r422=( - a11 *a22*b33*r446 + 2*a11 *b33 *r452 - 2*a11*a22*b33 *r452
3 3 3
+ a11*b33 *r4114 - a22*b33 *r4114)/(2*a11 *a22)
r423=0
r424=0
2 2
- 4*a11*a22*b33*r452 - 2*a11*b33 *r4114 - a22*b33 *r4114
r425=-----------------------------------------------------------
2
4*a11 *a22
r426=0
r427
2 2 2
- 2*a11 *a22*r446 - 4*a11*a22*b33*r452 - a11*b33 *r4114 - 2*a22*b33 *r4114
=-----------------------------------------------------------------------------
2
4*a11 *a22
r428=0
r429=0
2 2 2
- 2*a11 *a22*r446 - 4*a11*a22*b33*r452 - a11*b33 *r4114 - a22*b33 *r4114
r430=---------------------------------------------------------------------------
2
4*a11 *a22
a11*r452 + b33*r4114
r431=----------------------
a11
r432=0
r433=0
- a22*r4114
r434=---------------
2*a11 - 2*a22
r435=0
2 2 2 2 2
a11 *b33 *r452 - 2*a11*a22*b33 *r452 + a22 *b33 *r452
r436=-------------------------------------------------------
2 2
4*a11 *a22
r437=0
2 2
a11*b33 *r452 - a22*b33 *r452
r438=-------------------------------
2
4*a11*a22
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
r447=0
r448=0
r449=0
r450=0
r451=0
r453=0
r454=0
2 2 2
- 2*a11 *a22*r446 - a11*b33 *r4114 + a22*b33 *r4114
r455=------------------------------------------------------
2
4*a11 *a22
r456=0
r458=0
r459=0
r460
3 2 2 2 2 2
- 2*a11 *a22*r446 - a11 *b33 *r4114 + 2*a11*a22*b33 *r4114 - a22 *b33 *r4114
=-------------------------------------------------------------------------------
3
4*a11 *a22
2
a11 *r452 - a11*a22*r452 + a11*b33*r4114 - a22*b33*r4114
r461=----------------------------------------------------------
2
a11
r462=0
r463=0
r464=0
r465=0
a11*r452 - a22*r452
r466=---------------------
a11
r467=0
r468=0
2
a11*a22*r4114 - a22 *r4114
r469=----------------------------
2
2*a11
r470=0
r471=0
r472=0
r473=0
3 3 2 2 2
r474=(2*a11 *a22*b33*r446 + a11 *b33 *r452 - 2*a11 *a22 *b33*r446
2 2 2 3 2 2
+ 2*a11 *a22*b33 *r452 + 2*a11 *b33 *r4114 - 3*a11*a22 *b33 *r452
3 2 3 3 2
- a11*a22*b33 *r4114 - a22 *b33 *r4114)/(4*a11 *a22 )
r475=0
3 3 2 2 2
r476=(2*a11 *a22*b33*r446 + a11 *b33 *r452 - 2*a11 *a22 *b33*r446
2 2 2 3 2 2
+ 3*a11 *a22*b33 *r452 + a11 *b33 *r4114 - 4*a11*a22 *b33 *r452
3 2 3 3 2
+ a11*a22*b33 *r4114 - 2*a22 *b33 *r4114)/(4*a11 *a22 )
r477=0
r478=0
3 2 2 2 2
r479=(2*a11 *a22*b33*r446 - 2*a11 *a22 *b33*r446 + 4*a11 *a22*b33 *r452
2 3 2 2 2 3 3 2
+ a11 *b33 *r4114 - 4*a11*a22 *b33 *r452 - a22 *b33 *r4114)/(4*a11 *a22 )
r480=0
r481=0
r482=0
2 2 2
r483=(a11 *a22*r446 - a11 *b33*r452 + a11*a22*b33*r452 - a11*b33 *r4114
2 2
+ a22*b33 *r4114)/(a11 *a22)
r484=0
r485=0
r486=0
r487=0
a11*r452 + b33*r4114
r488=----------------------
a11
r489=0
r490=0
r491=0
r492=0
r493=0
a11*a22*r446 - a11*b33*r452 + a22*b33*r452
r494=--------------------------------------------
a11*a22
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
a11*r452 - a22*r452
r4102=---------------------
a11
r4103=0
r4104=0
2 2 2 2 2
r4105=( - 2*a11 *a22 *r446 + 4*a11 *a22*b33*r452 + a11 *b33 *r4114
2 2 2 2 2
- 4*a11*a22 *b33*r452 - a22 *b33 *r4114)/(4*a11 *a22 )
r4106=0
2 2 2 2 2
r4107=( - 2*a11 *a22 *r446 + 4*a11 *a22*b33*r452 + a11 *b33 *r4114
2 2 2 2 2
- 4*a11*a22 *b33*r452 + a11*a22*b33 *r4114 - 2*a22 *b33 *r4114)/(4*a11
2
*a22 )
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
r4115=0
r4117=0
r4118=0
a11*r4114 - a22*r4114
r4119=-----------------------
a11
r4120=0
r4121=0
- a11*b33*r4114 + a22*b33*r4114
r4122=----------------------------------
a11*a22
r4123=0
r4124=0
m3=0
m2=0
m1=0
n3=0
n2=0
n1=0
2
- b33
c33=---------
4*a11
c23=0
2 2
a11*b33 - a22*b33
c22=---------------------
4*a11*a22
c13=0
c12=0
c11=0
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
b11=0
a33=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, r446, r4114, r452, b33, 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.
{b33,r452,a11,a22,a11 - a22,r4114}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a12,
a13,
a23,
a33,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
c11,
c12,
c13,
4*a11*a22*c22 - a11*b33**2 + a22*b33**2,
c23,
4*a11*c33 + b33**2,
n1,
n2,
n3,
m1,
m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2 2 2 2
2 2 2 a11*b33 - a22*b33 - v3 *b33
HAM=u1 *a11 + u2 *a22 + u3*v3*b33 + v2 *--------------------- + -------------
4*a11*a22 4*a11
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
2 2 3 2 2
FI=u1 *v2 *(4*a11 *a22*b33 - 4*a11 *a22 *b33)
2 2 3 2 2
+ u1 *v3 *(4*a11 *a22*b33 - 4*a11 *a22 *b33)
2 3 2 2 3
+ u1*u2 *v1*(4*a11 *a22 - 4*a11 *a22 )
3 2 2 2 3 2
+ u1*u2*v1*v2*( - 4*a11 *a22*b33 + 4*a11 *a22 *b33) + 4*u1*u3 *v1*a11 *a22
3 2 2
+ u1*u3*v1*v3*( - 4*a11 *a22*b33 + 4*a11 *a22 *b33)
3 2 2 2 2
+ u1*v1 *(4*a11 *a22*b33 - 4*a11*a22 *b33 )
2 3 2 2 2 2 2
+ u1*v1*v2 *(a11 *b33 + 3*a11 *a22*b33 - 4*a11*a22 *b33 )
2 3 2 2 2 2 2
+ u1*v1*v3 *(a11 *b33 + 2*a11 *a22*b33 - 3*a11*a22 *b33 )
3 3 2 2 3 2 3 2 2 3
+ u2 *v2*(4*a11 *a22 - 4*a11 *a22 ) + u2 *u3*v3*(4*a11 *a22 - 4*a11 *a22 )
2 3 2 3 3 2 2 2
+ 4*u2*u3 *v2*a11 *a22 + u2*v2 *(a11 *b33 - a11 *a22*b33 )
2 3 2 2 2 2 2
+ u2*v2*v3 *(a11 *b33 - 2*a11 *a22*b33 + a11*a22 *b33 )
3 3 2 2 2 2 2 2 2 2 2
+ 4*u3 *v3*a11 *a22 - 4*u3 *v1 *a11 *a22 *b33 - 4*u3 *v2 *a11 *a22 *b33
2 2 2 2 2 2 2 2 2
- 4*u3 *v3 *a11 *a22 *b33 + u3*v1 *v3*(4*a11 *a22*b33 - 4*a11*a22 *b33 )
2 3 2 2 2 2 2
+ u3*v2 *v3*(a11 *b33 + 3*a11 *a22*b33 - 4*a11*a22 *b33 )
3 3 2 2 2 2 2
+ u3*v3 *(a11 *b33 + 2*a11 *a22*b33 - 3*a11*a22 *b33 )
2 2 3 2 3
+ v1 *v2 *( - a11*a22*b33 + a22 *b33 )
2 2 2 3 3 4 3 2 3
+ v1 *v3 *( - a11 *b33 + a11*a22*b33 ) + v2 *( - a11*a22*b33 + a22 *b33 )
2 2 2 3 2 3 4 2 3 3
+ v2 *v3 *( - a11 *b33 + a22 *b33 ) + v3 *( - a11 *b33 + a11*a22*b33 )
= a product of the elements of: {4,
2 2 3 2 2
u1 *v2 *(a11 *a22*b33 - a11 *a22 *b33)
2 2 3 2 2 2 3 2 2 3
+ u1 *v3 *(a11 *a22*b33 - a11 *a22 *b33) + u1*u2 *v1*(a11 *a22 - a11 *a22 )
3 2 2 2 3 2
+ u1*u2*v1*v2*( - a11 *a22*b33 + a11 *a22 *b33) + u1*u3 *v1*a11 *a22
3 2 2
+ u1*u3*v1*v3*( - a11 *a22*b33 + a11 *a22 *b33)
3 2 2 2 2
+ u1*v1 *(a11 *a22*b33 - a11*a22 *b33 )
3 2 2 2 2 2
2 a11 *b33 + 3*a11 *a22*b33 - 4*a11*a22 *b33
+ u1*v1*v2 *-----------------------------------------------
4
3 2 2 2 2 2
2 a11 *b33 + 2*a11 *a22*b33 - 3*a11*a22 *b33
+ u1*v1*v3 *-----------------------------------------------
4
3 3 2 2 3 2 3 2 2 3
+ u2 *v2*(a11 *a22 - a11 *a22 ) + u2 *u3*v3*(a11 *a22 - a11 *a22 )
3 2 2 2
2 3 2 3 a11 *b33 - a11 *a22*b33
+ u2*u3 *v2*a11 *a22 + u2*v2 *---------------------------
4
3 2 2 2 2 2
2 a11 *b33 - 2*a11 *a22*b33 + a11*a22 *b33 3 3 2
+ u2*v2*v3 *--------------------------------------------- + u3 *v3*a11 *a22
4
2 2 2 2 2 2 2 2 2 2 2 2
- u3 *v1 *a11 *a22 *b33 - u3 *v2 *a11 *a22 *b33 - u3 *v3 *a11 *a22 *b33
2 2 2 2 2
+ u3*v1 *v3*(a11 *a22*b33 - a11*a22 *b33 )
3 2 2 2 2 2
2 a11 *b33 + 3*a11 *a22*b33 - 4*a11*a22 *b33
+ u3*v2 *v3*-----------------------------------------------
4
3 2 2 2 2 2
3 a11 *b33 + 2*a11 *a22*b33 - 3*a11*a22 *b33
+ u3*v3 *-----------------------------------------------
4
3 2 3
2 2 - a11*a22*b33 + a22 *b33
+ v1 *v2 *-----------------------------
4
2 3 3 3 2 3
2 2 - a11 *b33 + a11*a22*b33 4 - a11*a22*b33 + a22 *b33
+ v1 *v3 *----------------------------- + v2 *-----------------------------
4 4
2 3 2 3 2 3 3
2 2 - a11 *b33 + a22 *b33 4 - a11 *b33 + a11*a22*b33
+ v2 *v3 *-------------------------- + v3 *-----------------------------}
4 4
{HAM,FI} = 0
3 5 2 4 3 3 4
FI=u1 *v1*( - 32*a11 *a22 *b33 + 64*a11 *a22 *b33 - 32*a11 *a22 *b33)
2 2 5 3 4 4 3 5
+ u1 *u2 *(32*a11 *a22 - 64*a11 *a22 + 32*a11 *a22 )
2 2 5 3 4 4
+ u1 *u3 *(32*a11 *a22 - 32*a11 *a22 )
2 2 5 2 3 3 2 2 4 2 2
+ u1 *v2 *(8*a11 *a22*b33 - 24*a11 *a22 *b33 + 16*a11 *a22 *b33 ) + u1
2
*v3
5 2 4 2 2 3 3 2 2 4 2
*(8*a11 *a22*b33 - 8*a11 *a22 *b33 - 8*a11 *a22 *b33 + 8*a11 *a22 *b33 )
2 4 3 3 4
+ u1*u3 *v1*(32*a11 *a22 *b33 - 32*a11 *a22 *b33)
4 2 2 3 3 2 2 4 2
+ u1*u3*v1*v3*( - 32*a11 *a22 *b33 + 64*a11 *a22 *b33 - 32*a11 *a22 *b33 )
3
+ u1*v1
4 3 3 2 3 2 3 3 4 3
*(8*a11 *a22*b33 - 8*a11 *a22 *b33 - 8*a11 *a22 *b33 + 8*a11*a22 *b33 )
2 4 3 2 3 3 4 3
+ u1*v1*v2 *(8*a11 *a22*b33 - 24*a11 *a22 *b33 + 16*a11*a22 *b33 )
2 4 3 3 2 3 4 3
+ u1*v1*v3 *(16*a11 *a22*b33 - 24*a11 *a22 *b33 + 8*a11*a22 *b33 )
4 4 4 3 5 2 6
+ u2 *(16*a11 *a22 - 32*a11 *a22 + 16*a11 *a22 )
2 4 3 3 4 2 5 2
+ u2 *u3*v3*(32*a11 *a22 *b33 - 64*a11 *a22 *b33 + 32*a11 *a22 *b33) + u2
2 4 2 2 3 3 2 2 4 2
*v1 *( - 8*a11 *a22 *b33 + 24*a11 *a22 *b33 - 24*a11 *a22 *b33
5 2
+ 8*a11*a22 *b33 )
2 2 4 2 2 3 3 2 2 4 2
+ u2 *v3 *( - 8*a11 *a22 *b33 + 16*a11 *a22 *b33 - 8*a11 *a22 *b33 )
4 4 4 3 4 3 3 4
- 16*u3 *a11 *a22 + u3 *v3*(32*a11 *a22 *b33 - 32*a11 *a22 *b33)
2 2 4 2 2 2 4 2
+ u3 *v1 *( - 8*a11 *a22 *b33 + 8*a11 *a22 *b33 )
2 2 4 2 2 3 3 2 2 4 2
+ u3 *v2 *( - 8*a11 *a22 *b33 - 8*a11 *a22 *b33 + 16*a11 *a22 *b33 )
2 2 4 2 2 3 3 2 2 4 2
+ u3 *v3 *( - 16*a11 *a22 *b33 + 8*a11 *a22 *b33 + 8*a11 *a22 *b33 )
2 3 2 3 2 3 3 4 3
+ u3*v1 *v3*(16*a11 *a22 *b33 - 32*a11 *a22 *b33 + 16*a11*a22 *b33 )
2 4 3 2 3 3 4 3
+ u3*v2 *v3*(8*a11 *a22*b33 - 24*a11 *a22 *b33 + 16*a11*a22 *b33 ) + u3
3
*v3
4 3 3 2 3 2 3 3 4 3
*(8*a11 *a22*b33 - 8*a11 *a22 *b33 - 8*a11 *a22 *b33 + 8*a11*a22 *b33 ) +
2 2 4 4 3 4 2 2 4
v1 *v2 *( - 2*a11 *b33 + 6*a11 *a22*b33 - 10*a11 *a22 *b33
3 4 4 4 2 2 4 4
+ 10*a11*a22 *b33 - 4*a22 *b33 ) + v1 *v3 *( - 2*a11 *b33
3 4 2 2 4 3 4 4 4
+ 4*a11 *a22*b33 - 4*a11 *a22 *b33 + 4*a11*a22 *b33 - 2*a22 *b33 ) +
4 4 4 3 4 2 2 4 3 4
v2 *( - a11 *b33 + 2*a11 *a22*b33 - 5*a11 *a22 *b33 + 8*a11*a22 *b33
4 4 2 2 4 4 3 4
- 4*a22 *b33 ) + v2 *v3 *( - 4*a11 *b33 + 6*a11 *a22*b33
2 2 4 3 4 4 4 4 4 4
- 4*a11 *a22 *b33 + 6*a11*a22 *b33 - 4*a22 *b33 ) + v3 *( - 3*a11 *b33
3 4 2 2 4 3 4 4 4
+ 6*a11 *a22*b33 - 4*a11 *a22 *b33 + 2*a11*a22 *b33 - a22 *b33 )
Stop of a subroutine.
Number of garbage collections exceeds max_gc_fac.
The factorization crashed!
which the program can not factorize further.
{HAM,FI} = 0
2 2 2 2 2 2 2 2 2 2
FI= - 4*u1 *v2 *a11 *a22 - 4*u1 *v3 *a11 *a22 + 8*u1*u2*v1*v2*a11 *a22
2 2 3 2 2
+ 8*u1*u3*v1*v3*a11 *a22 + u1*v1 *(4*a11 *a22*b33 - 4*a11*a22 *b33)
2 2 2
+ u1*v1*v2 *(4*a11 *a22*b33 - 4*a11*a22 *b33)
2 2 2 2 2 2 2
+ u1*v1*v3 *(4*a11 *a22*b33 - 4*a11*a22 *b33) - 4*u2 *v1 *a11 *a22
2 2 2 2 2 2 2 2 2 2
- 4*u2 *v3 *a11 *a22 + 8*u2*u3*v2*v3*a11 *a22 - 4*u3 *v1 *a11 *a22
2 2 2 2 2 2 2 2
- 4*u3 *v2 *a11 *a22 - 4*u3*v1 *v3*a11*a22 *b33 - 4*u3*v2 *v3*a11*a22 *b33
3 2 2 2 2 2 2 2
- 4*u3*v3 *a11*a22 *b33 + v1 *v2 *( - a11 *b33 + a22 *b33 )
2 2 2 2 2 4 2 2 2 2
+ v1 *v3 *( - a11 *b33 + 2*a11*a22*b33 ) + v2 *( - a11 *b33 + a22 *b33 )
2 2 2 2 2 2 2
+ v2 *v3 *( - 2*a11 *b33 + 2*a11*a22*b33 + a22 *b33 )
4 2 2 2
+ v3 *( - a11 *b33 + 2*a11*a22*b33 )
= a product of the elements of: {4,
2 2 2 2 2 2 2 2 2 2
- u1 *v2 *a11 *a22 - u1 *v3 *a11 *a22 + 2*u1*u2*v1*v2*a11 *a22
2 2 3 2 2
+ 2*u1*u3*v1*v3*a11 *a22 + u1*v1 *(a11 *a22*b33 - a11*a22 *b33)
2 2 2
+ u1*v1*v2 *(a11 *a22*b33 - a11*a22 *b33)
2 2 2 2 2 2 2
+ u1*v1*v3 *(a11 *a22*b33 - a11*a22 *b33) - u2 *v1 *a11 *a22
2 2 2 2 2 2 2 2 2 2
- u2 *v3 *a11 *a22 + 2*u2*u3*v2*v3*a11 *a22 - u3 *v1 *a11 *a22
2 2 2 2 2 2 2 2
- u3 *v2 *a11 *a22 - u3*v1 *v3*a11*a22 *b33 - u3*v2 *v3*a11*a22 *b33
2 2 2 2
3 2 2 2 - a11 *b33 + a22 *b33
- u3*v3 *a11*a22 *b33 + v1 *v2 *--------------------------
4
2 2 2 2 2 2 2
2 2 - a11 *b33 + 2*a11*a22*b33 4 - a11 *b33 + a22 *b33
+ v1 *v3 *------------------------------- + v2 *--------------------------
4 4
2 2 2 2 2
2 2 - 2*a11 *b33 + 2*a11*a22*b33 + a22 *b33
+ v2 *v3 *---------------------------------------------
4
2 2 2
4 - a11 *b33 + 2*a11*a22*b33
+ v3 *-------------------------------}
4
{HAM,FI} = 0
2 2 2 2 2 3
FI=u1*v1*( - 4*a11 *a22*b33 + 4*a11*a22 *b33) + u2 *(4*a11 *a22 - 4*a11*a22 )
2 2 2 2 2 2 2
+ 4*u3 *a11 *a22 + v2 *(a11 *b33 - a11*a22*b33 )
2 2 2 2 2 2
+ v3 *(a11 *b33 - 2*a11*a22*b33 + a22 *b33 )
= a product of the elements of: {4,
2 2 2 2 2 3
u1*v1*( - a11 *a22*b33 + a11*a22 *b33) + u2 *(a11 *a22 - a11*a22 )
2 2 2
2 2 2 2 a11 *b33 - a11*a22*b33
+ u3 *a11 *a22 + v2 *--------------------------
4
2 2 2 2 2
2 a11 *b33 - 2*a11*a22*b33 + a22 *b33
+ v3 *----------------------------------------}
4
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u2**2*a22 + u3*v3*b33 + v2**2*(a11*b33**2 - a22*b33**2)/(4*a11*
a22) + ( - v3**2*b33**2)/(4*a11)$
FI=u1**2*v2**2*(4*a11**3*a22*b33 - 4*a11**2*a22**2*b33) + u1**2*v3**2*(4*a11**3*
a22*b33 - 4*a11**2*a22**2*b33) + u1*u2**2*v1*(4*a11**3*a22**2 - 4*a11**2*a22**3)
+ u1*u2*v1*v2*( - 4*a11**3*a22*b33 + 4*a11**2*a22**2*b33) + 4*u1*u3**2*v1*a11**
3*a22**2 + u1*u3*v1*v3*( - 4*a11**3*a22*b33 + 4*a11**2*a22**2*b33) + u1*v1**3*(4
*a11**2*a22*b33**2 - 4*a11*a22**2*b33**2) + u1*v1*v2**2*(a11**3*b33**2 + 3*a11**
2*a22*b33**2 - 4*a11*a22**2*b33**2) + u1*v1*v3**2*(a11**3*b33**2 + 2*a11**2*a22*
b33**2 - 3*a11*a22**2*b33**2) + u2**3*v2*(4*a11**3*a22**2 - 4*a11**2*a22**3) +
u2**2*u3*v3*(4*a11**3*a22**2 - 4*a11**2*a22**3) + 4*u2*u3**2*v2*a11**3*a22**2 +
u2*v2**3*(a11**3*b33**2 - a11**2*a22*b33**2) + u2*v2*v3**2*(a11**3*b33**2 - 2*
a11**2*a22*b33**2 + a11*a22**2*b33**2) + 4*u3**3*v3*a11**3*a22**2 - 4*u3**2*v1**
2*a11**2*a22**2*b33 - 4*u3**2*v2**2*a11**2*a22**2*b33 - 4*u3**2*v3**2*a11**2*a22
**2*b33 + u3*v1**2*v3*(4*a11**2*a22*b33**2 - 4*a11*a22**2*b33**2) + u3*v2**2*v3*
(a11**3*b33**2 + 3*a11**2*a22*b33**2 - 4*a11*a22**2*b33**2) + u3*v3**3*(a11**3*
b33**2 + 2*a11**2*a22*b33**2 - 3*a11*a22**2*b33**2) + v1**2*v2**2*( - a11*a22*
b33**3 + a22**2*b33**3) + v1**2*v3**2*( - a11**2*b33**3 + a11*a22*b33**3) + v2**
4*( - a11*a22*b33**3 + a22**2*b33**3) + v2**2*v3**2*( - a11**2*b33**3 + a22**2*
b33**3) + v3**4*( - a11**2*b33**3 + a11*a22*b33**3)$
FI=u1**3*v1*( - 32*a11**5*a22**2*b33 + 64*a11**4*a22**3*b33 - 32*a11**3*a22**4*
b33) + u1**2*u2**2*(32*a11**5*a22**3 - 64*a11**4*a22**4 + 32*a11**3*a22**5) + u1
**2*u3**2*(32*a11**5*a22**3 - 32*a11**4*a22**4) + u1**2*v2**2*(8*a11**5*a22*b33
**2 - 24*a11**3*a22**3*b33**2 + 16*a11**2*a22**4*b33**2) + u1**2*v3**2*(8*a11**5
*a22*b33**2 - 8*a11**4*a22**2*b33**2 - 8*a11**3*a22**3*b33**2 + 8*a11**2*a22**4*
b33**2) + u1*u3**2*v1*(32*a11**4*a22**3*b33 - 32*a11**3*a22**4*b33) + u1*u3*v1*
v3*( - 32*a11**4*a22**2*b33**2 + 64*a11**3*a22**3*b33**2 - 32*a11**2*a22**4*b33
**2) + u1*v1**3*(8*a11**4*a22*b33**3 - 8*a11**3*a22**2*b33**3 - 8*a11**2*a22**3*
b33**3 + 8*a11*a22**4*b33**3) + u1*v1*v2**2*(8*a11**4*a22*b33**3 - 24*a11**2*a22
**3*b33**3 + 16*a11*a22**4*b33**3) + u1*v1*v3**2*(16*a11**4*a22*b33**3 - 24*a11
**3*a22**2*b33**3 + 8*a11*a22**4*b33**3) + u2**4*(16*a11**4*a22**4 - 32*a11**3*
a22**5 + 16*a11**2*a22**6) + u2**2*u3*v3*(32*a11**4*a22**3*b33 - 64*a11**3*a22**
4*b33 + 32*a11**2*a22**5*b33) + u2**2*v1**2*( - 8*a11**4*a22**2*b33**2 + 24*a11
**3*a22**3*b33**2 - 24*a11**2*a22**4*b33**2 + 8*a11*a22**5*b33**2) + u2**2*v3**2
*( - 8*a11**4*a22**2*b33**2 + 16*a11**3*a22**3*b33**2 - 8*a11**2*a22**4*b33**2)
- 16*u3**4*a11**4*a22**4 + u3**3*v3*(32*a11**4*a22**3*b33 - 32*a11**3*a22**4*b33
) + u3**2*v1**2*( - 8*a11**4*a22**2*b33**2 + 8*a11**2*a22**4*b33**2) + u3**2*v2
**2*( - 8*a11**4*a22**2*b33**2 - 8*a11**3*a22**3*b33**2 + 16*a11**2*a22**4*b33**
2) + u3**2*v3**2*( - 16*a11**4*a22**2*b33**2 + 8*a11**3*a22**3*b33**2 + 8*a11**2
*a22**4*b33**2) + u3*v1**2*v3*(16*a11**3*a22**2*b33**3 - 32*a11**2*a22**3*b33**3
+ 16*a11*a22**4*b33**3) + u3*v2**2*v3*(8*a11**4*a22*b33**3 - 24*a11**2*a22**3*
b33**3 + 16*a11*a22**4*b33**3) + u3*v3**3*(8*a11**4*a22*b33**3 - 8*a11**3*a22**2
*b33**3 - 8*a11**2*a22**3*b33**3 + 8*a11*a22**4*b33**3) + v1**2*v2**2*( - 2*a11
**4*b33**4 + 6*a11**3*a22*b33**4 - 10*a11**2*a22**2*b33**4 + 10*a11*a22**3*b33**
4 - 4*a22**4*b33**4) + v1**2*v3**2*( - 2*a11**4*b33**4 + 4*a11**3*a22*b33**4 - 4
*a11**2*a22**2*b33**4 + 4*a11*a22**3*b33**4 - 2*a22**4*b33**4) + v2**4*( - a11**
4*b33**4 + 2*a11**3*a22*b33**4 - 5*a11**2*a22**2*b33**4 + 8*a11*a22**3*b33**4 -
4*a22**4*b33**4) + v2**2*v3**2*( - 4*a11**4*b33**4 + 6*a11**3*a22*b33**4 - 4*a11
**2*a22**2*b33**4 + 6*a11*a22**3*b33**4 - 4*a22**4*b33**4) + v3**4*( - 3*a11**4*
b33**4 + 6*a11**3*a22*b33**4 - 4*a11**2*a22**2*b33**4 + 2*a11*a22**3*b33**4 -
a22**4*b33**4)$
FI= - 4*u1**2*v2**2*a11**2*a22**2 - 4*u1**2*v3**2*a11**2*a22**2 + 8*u1*u2*v1*v2*
a11**2*a22**2 + 8*u1*u3*v1*v3*a11**2*a22**2 + u1*v1**3*(4*a11**2*a22*b33 - 4*a11
*a22**2*b33) + u1*v1*v2**2*(4*a11**2*a22*b33 - 4*a11*a22**2*b33) + u1*v1*v3**2*(
4*a11**2*a22*b33 - 4*a11*a22**2*b33) - 4*u2**2*v1**2*a11**2*a22**2 - 4*u2**2*v3
**2*a11**2*a22**2 + 8*u2*u3*v2*v3*a11**2*a22**2 - 4*u3**2*v1**2*a11**2*a22**2 -
4*u3**2*v2**2*a11**2*a22**2 - 4*u3*v1**2*v3*a11*a22**2*b33 - 4*u3*v2**2*v3*a11*
a22**2*b33 - 4*u3*v3**3*a11*a22**2*b33 + v1**2*v2**2*( - a11**2*b33**2 + a22**2*
b33**2) + v1**2*v3**2*( - a11**2*b33**2 + 2*a11*a22*b33**2) + v2**4*( - a11**2*
b33**2 + a22**2*b33**2) + v2**2*v3**2*( - 2*a11**2*b33**2 + 2*a11*a22*b33**2 +
a22**2*b33**2) + v3**4*( - a11**2*b33**2 + 2*a11*a22*b33**2)$
FI=u1*v1*( - 4*a11**2*a22*b33 + 4*a11*a22**2*b33) + u2**2*(4*a11**2*a22**2 - 4*
a11*a22**3) + 4*u3**2*a11**2*a22**2 + v2**2*(a11**2*b33**2 - a11*a22*b33**2) +
v3**2*(a11**2*b33**2 - 2*a11*a22*b33**2 + a22**2*b33**2)$