Solution 26 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
r10=0
- m1*n1*r14
r11=--------------
2
n2
m1*r14
r12=--------
n2
n3*r14
r13=--------
n2
n1*r14
r15=--------
n2
3 2 2 3 2 2 4
r20=(4*a33 *m1 *r14 + 4*m1 *n2 *r464 - 4*m1 *n2*n3 *r464 - m1*n2 *r4117
2 2 2 3
+ m1*n2 *n3 *r4117)/(4*a33 *n2 )
r21=0
2 2 2 2 2 3
- 4*m1 *n1 *r464 + 4*m1 *n2 *r464 + m1*n1 *n2*r4117 - m1*n2 *r4117
r22=---------------------------------------------------------------------
2 2
4*a33 *n2
r23=0
2
4*m1 *n1*r464 - m1*n1*n2*r4117
r24=--------------------------------
2
2*a33 *n2
- 4*m1*n1*r464 + n1*n2*r4117
r26=-------------------------------
2
2*a33
4*m1*n1*n3*r464 - n1*n2*n3*r4117
r27=----------------------------------
2
2*a33 *n2
- 4*m1*n3*r464 + n2*n3*r4117
r28=-------------------------------
2
2*a33
r210=0
3 3 2 4
r212=( - 4*a33 *m1*r14 - 4*m1*n2 *r464 + 4*m1*n2*n3 *r464 + n2 *r4117
2 2 2 2
- n2 *n3 *r4117)/(2*a33 *n2 )
2
- 4*m1*n2*n3*r464 + n2 *n3*r4117
r213=-----------------------------------
2
2*a33 *m1
3 3 2 4
r214=( - 4*a33 *m1*r14 - 4*m1*n2 *r464 + 4*m1*n2*n3 *r464 + n2 *r4117
2 2 2
- n2 *n3 *r4117)/(4*a33 *m1*n2)
r215=0
3 2 2 2 2
r216=(4*a33 *m1*r14 + 4*m1*n1 *n2*r464 - 4*m1*n2*n3 *r464 - n1 *n2 *r4117
2 2 2 2
+ n2 *n3 *r4117)/(2*a33 *n2 )
- 4*m1*n1*r464 + n1*n2*r4117
r217=-------------------------------
2
a33
- 4*m1*n1*n3*r464 + n1*n2*n3*r4117
r218=-------------------------------------
2
2*a33 *m1
2
- 4*m1*n1*n2*r464 + n1*n2 *r4117
r219=-----------------------------------
2
2*a33 *m1
3 2 2 2 2
r220=( - 4*a33 *m1*r14 - 4*m1*n1 *n2*r464 + 4*m1*n2*n3 *r464 + n1 *n2 *r4117
2 2 2
- n2 *n3 *r4117)/(4*a33 *m1*n2)
r30=0
3 2 2
2*m1 *n1*r464 - m1 *n1*n2*r4117 - m1*n1*n2 *r446
r31=--------------------------------------------------
3
2*a33*n2
r32=0
- m1*n1*r446
r33=---------------
2*a33*n2
3 2 2
- 2*m1 *r464 + m1 *n2*r4117 + m1*n2 *r446
r34=--------------------------------------------
2
2*a33*n2
r35=0
m1*r446
r36=---------
2*a33
r37=0
- m1*n1*r446
r38=---------------
2*a33*n2
m1*r446
r39=---------
2*a33
2 2
- 2*m1 *n3*r464 + m1*n2*n3*r4117 + n2 *n3*r446
r310=-------------------------------------------------
2
2*a33*n2
m1*n1*r4116
r311=-------------
a33*n2
n3*r446
r312=---------
2*a33
- m1*r4116
r313=-------------
a33
r314=0
n3*r446
r315=---------
2*a33
- n3*r4116
r316=-------------
a33
m1*n1*r464
r317=------------
a33*n2
- m1*r464
r318=------------
a33
- n3*r464
r319=------------
a33
2 2
- 2*m1 *r464 + m1*n2*r4117 + n2 *r446
r320=----------------------------------------
2*a33*n2
r321=0
2
2*m1*n1*r4116 + n2 *r446
r322=--------------------------
2*a33*n2
r323=0
2 2
- 2*m1 *n1*r464 + m1*n1*n2*r4117 - m1*n2 *r4116
r324=--------------------------------------------------
2
a33*n2
2 2
4*m1 *r464 - 2*m1*n2*r4117 + n2 *r446
r325=---------------------------------------
2*a33*n2
- n2*r4116
r326=-------------
a33
- n3*r4116
r327=-------------
a33
2*m1*n3*r464 - n2*n3*r4117
r328=----------------------------
a33*n2
- n2*r464
r329=------------
a33
r330=0
2
- 2*m1*n1*r464 + n1*n2*r4117 - 2*n2 *r4116
r331=---------------------------------------------
2*a33*n2
6*m1*r464 - 3*n2*r4117
r332=------------------------
2*a33
2*m1*n3*r464 - n2*n3*r4117
r333=----------------------------
2*a33*m1
2
2*m1*n2*r464 - n2 *r4117
r334=--------------------------
2*a33*m1
2 2
- 2*m1 *n1*r464 + m1*n1*n2*r4117 + n1*n2 *r446
r335=-------------------------------------------------
2
2*a33*n2
r336=0
2 2
4*m1 *n1*r464 - 2*m1*n1*n2*r4117 + n1*n2 *r446
r337=------------------------------------------------
2
2*a33*n2
r338=0
2
- 2*m1 *r464 + m1*n1*r4116 + m1*n2*r4117
r339=-------------------------------------------
a33*n2
- 2*m1*r4116 + n1*r446
r340=-------------------------
2*a33
- n1*r4116
r341=-------------
a33
- 2*m1*n3*r464 + n2*n3*r4117
r342=-------------------------------
a33*n2
- n3*r4116
r343=-------------
a33
- n1*r464
r344=------------
a33
r345=0
- 2*m1*r464 - n1*r4116 + n2*r4117
r346=------------------------------------
a33
2
2*m1*n1*r464 - n1*n2*r4117 - n2 *r4116
r347=----------------------------------------
a33*n2
r348=0
2*m1*n1*r464 - n1*n2*r4117
r349=----------------------------
2*a33*m1
r350=0
- 6*m1*n1*r464 + 3*n1*n2*r4117
r351=---------------------------------
2*a33*n2
2*m1*r464 - 2*n1*r4116 - n2*r4117
r352=-----------------------------------
2*a33
2*m1*n3*r464 - n2*n3*r4117
r353=----------------------------
2*a33*m1
2
2*m1*n2*r464 - n2 *r4117
r354=--------------------------
2*a33*m1
2*m1*n1*r464 - n1*n2*r4117
r355=----------------------------
2*a33*m1
3 2
m1 *r4117 + 2*m1 *n2*r446
r40=---------------------------
3
4*n2
r41=0
2
m1 *r446
r42=----------
2
2*n2
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
2
m1 *r446
r49=----------
2
2*n2
r410=0
r411=0
r412=0
r413=0
2
- m1 *r4116
r415=--------------
2
n2
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
2 2
- 2*m1 *r464 + n2 *r446
r425=--------------------------
2
2*n2
r426=0
r427=0
r428=0
r429=0
r431=0
r432=0
r433=0
r435=0
2
- m1 *r4116
r436=--------------
2
n2
r437=0
r438=0
2
- m1 *r4117 - m1*n2*r446
r439=---------------------------
2
n2
r440=0
- m1*r446
r441=------------
n2
r442=0
- m1*r446
r444=------------
n2
r445=0
r447=0
2*m1*r4116
r448=------------
n2
r449=0
r450=0
r451=0
2*m1*r464
r453=-----------
n2
r454=0
- m1*r4117 - n2*r446
r455=-----------------------
2*n2
r456=0
r458=0
2*m1*r4116
r459=------------
n2
2*m1*r4117 - n2*r446
r460=----------------------
2*n2
r461=r4116
r462=0
r463=0
r465=0
r466=r4116
r467=r4117
r468=0
n2*r4117
r469=----------
4*m1
r470=0
2
m1 *r4117 + m1*n2*r446
r471=------------------------
2
n2
r472=0
m1*r446
r473=---------
n2
2
- m1 *r4116
r474=--------------
2
n2
r475=0
r476=0
r477=0
m1*r446
r478=---------
n2
r479=0
r480=0
- 2*m1*r4116
r481=---------------
n2
r482=0
r483=r446
r484=0
r485=0
r486=0
- 2*m1*r464
r487=--------------
n2
r488=0
r489=0
r490=0
r491=0
- 2*m1*r4116
r492=---------------
n2
r493=0
- 2*m1*r4117 + n2*r446
r494=-------------------------
n2
2*m1*r4116
r495=------------
n2
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101= - r4117
r4102=r4116
r4103=0
r4104=0
- m1*r4117 - n2*r446
r4105=-----------------------
2*n2
r4106=0
2*m1*r4117 - n2*r446
r4107=----------------------
2*n2
r4108=0
- 2*m1*r4116
r4109=---------------
n2
r4110=0
r4111=r4116
r4112=0
r4113=0
r4114=r464
r4115=0
r4118=0
n2*r4117
r4119=----------
2*m1
r4120=0
r4121= - r4117
r4122=r4116
r4123=0
r4124=0
n2*r4117
r4125=----------
4*m1
m3=0
- m1*n1
m2=----------
n2
c33=0
c23=0
c22=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
a22=0
a13=0
a12=0
a11=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:
r14, r4117, r4116, r446, r464, m1, n3, n1, n2, 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.
2 2
{m2,n1 - 2*n2 ,m1,a33,r464,n2,n1,n1 + i*n2,n1 - i*n2}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a11,
a12,
a13,
a22,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
b33,
c11,
c12,
c13,
c22,
c23,
c33,
m1*n1 + m2*n2,
m3}$
The system of equations related to the Hamiltonian HAM:
2 - v2*m1*n1
HAM=u1*n1 + u2*n2 + u3 *a33 + u3*n3 + v1*m1 + -------------
n2
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
3 3 2 4 2 2 2 3 2 3
FI=u1 *a33*n1*n2 + u1 *u2*a33*n2 + u1 *u3 *a33 *n2 + u1 *u3*a33*n2 *n3
2 3 2 2 2 2 3 3 2
+ u1 *v1*a33*m1*n2 - 3*u1 *v2*a33*m1*n1*n2 + u1 *( - n1 *n2 + n2 *n3 )
2 3 2 3
+ u1*u2 *a33*n1*n2 + 2*u1*u2*v1*a33*m1*n1*n2 - 2*u1*u2*v2*a33*m1*n2
4 2 2 2 2 3
- 2*u1*u2*n1*n2 - 2*u1*u3 *v2*a33 *m1*n2 - u1*u3 *a33*n1*n2
2 3 2 2
- 2*u1*u3*v2*a33*m1*n2 *n3 - 2*u1*u3*n1*n2 *n3 - 2*u1*v1*v2*a33*m1 *n2
3 2 2
- 4*u1*v1*m1*n1*n2 + 2*u1*v2 *a33*m1 *n1*n2
2 2 2 2 2 2 3 4
+ u1*v2*(2*m1*n1 *n2 - 2*m1*n2 *n3 ) - u1*v3 *a33*m1 *n1*n2 + u2 *a33*n2
2 2 2 3 2 3 2 3
+ u2 *u3 *a33 *n2 + u2 *u3*a33*n2 *n3 + 3*u2 *v1*a33*m1*n2
2 2 2 5 3 2 2 2 2
- u2 *v2*a33*m1*n1*n2 + u2 *( - n2 + n2 *n3 ) + 2*u2*u3 *v1*a33 *m1*n2
2 4 2 4
- u2*u3 *a33*n2 + 2*u2*u3*v1*a33*m1*n2 *n3 - 2*u2*u3*n2 *n3
2 2 2 2
+ 2*u2*v1 *a33*m1 *n2 - 2*u2*v1*v2*a33*m1 *n1*n2
4 2 2 2 2 2 3 3
+ u2*v1*( - 2*m1*n2 + 2*m1*n2 *n3 ) - u2*v3 *a33*m1 *n2 - u3 *a33*n2 *n3
2 3 2 2 2 2 2 2
- u3 *v1*a33*m1*n2 + u3 *v2*a33*m1*n1*n2 - u3 *v3 *a33 *m1 *n2
3 2 2 2
- 2*u3*v1*m1*n2 *n3 + 2*u3*v2*m1*n1*n2 *n3 - u3*v3 *a33*m1 *n2*n3
3 2 2 2 3
- 2*u3*v3*m1*n1*n2 + 2*v1*v2*m1 *n1*n2 - v1*v3 *a33*m1 *n2
2 2 2 2 3 2 3
+ v2 *( - m1 *n1 *n2 + m1 *n2 ) + v2*v3 *a33*m1 *n1
2 2 3 2 2
+ v3 *(m1 *n2 - m1 *n2*n3 )
which the program can not factorize further.
{HAM,FI} = 0
2 2 2 2 2 2 2
FI= - u1 *v2 *a33*n2 - u1 *v3 *a33*n2 + 2*u1*u2*v1*v2*a33*n2
2 2 2 2
+ 2*u1*u3*v1*v3*a33*n2 + 2*u1*v1 *v2*a33*m1*n2 + u1*v1 *n1*n2
3 2 2 2 2 2
+ 2*u1*v2 *a33*m1*n2 + u1*v2 *n1*n2 + 2*u1*v2*v3 *a33*m1*n2 + u1*v3 *n1*n2
2 2 2 2 2 2 2
- u2 *v1 *a33*n2 - u2 *v3 *a33*n2 + 2*u2*u3*v2*v3*a33*n2
3 2 3 2
- 2*u2*v1 *a33*m1*n2 + u2*v1 *n2 - 2*u2*v1*v2 *a33*m1*n2
2 2 3 2 3 2 2 2
- 2*u2*v1*v3 *a33*m1*n2 + u2*v2 *n2 + u2*v3 *n2 + u3 *v3 *a33*n2
2 2 2 2 2 2 3 2
+ u3*v1 *n2 *n3 + u3*v2 *n2 *n3 + u3*v3 *n2 *n3 + v1 *m1*n2
2 2 2 2 2 2 2 2
- v1 *v2*m1*n1*n2 + v1 *v3 *a33*m1 + v1*v2 *m1*n2 + v1*v3 *m1*n2
3 2 2 2 2 4 2
- v2 *m1*n1*n2 + v2 *v3 *a33*m1 - v2*v3 *m1*n1*n2 + v3 *a33*m1
which the program can not factorize further.
{HAM,FI} = 0
3 2 2 2 2 2
FI=u1 *v1*a33*n2 + u1 *u2*v2*a33*n2 + u1 *u3*v3*a33*n2
2 2 2 2 2
- 2*u1 *v1*v2*a33*m1*n2 - u1 *v1*n1*n2 + u1*u2 *v1*a33*n2
2 3 2
+ 2*u1*u2*v1 *a33*m1*n2 - u1*u2*v1*n2 - 2*u1*u2*v2 *a33*m1*n2
2 2
- u1*u2*v2*n1*n2 - u1*u3*v1*n2 *n3 - 2*u1*u3*v2*v3*a33*m1*n2
2 2 2 2 2
- u1*u3*v3*n1*n2 - u1*v1 *m1*n2 + u1*v1*v2*m1*n1*n2 - u1*v1*v3 *a33*m1
3 2 2 2 2 2 3
+ u2 *v2*a33*n2 + u2 *u3*v3*a33*n2 + 2*u2 *v1*v2*a33*m1*n2 - u2 *v2*n2
2 3 2
+ 2*u2*u3*v1*v3*a33*m1*n2 - u2*u3*v2*n2 *n3 - u2*u3*v3*n2 - u2*v1*v2*m1*n2
2 2 2 2 2 2
+ u2*v2 *m1*n1*n2 - u2*v2*v3 *a33*m1 - u3 *v3*n2 *n3 - u3*v1*v3*m1*n2
3 2
+ u3*v2*v3*m1*n1*n2 - u3*v3 *a33*m1
= a product of the elements of: { - u1*v1 - u2*v2 - u3*v3,
2 2 2 2 2
- u1 *a33*n2 + 2*u1*v2*a33*m1*n2 + u1*n1*n2 - u2 *a33*n2
3 2 2
- 2*u2*v1*a33*m1*n2 + u2*n2 + u3*n2 *n3 + v1*m1*n2 - v2*m1*n1*n2
2 2
+ v3 *a33*m1 }
{HAM,FI} = 0
4 2 4 3 2 3 3 4 2 2 2 4
FI=u1 *a33 *n2 - 4*u1 *v2*a33 *m1*n2 - 2*u1 *a33*n1*n2 + 2*u1 *u2 *a33 *n2
2 2 3 2 5 2 4
+ 4*u1 *u2*v1*a33 *m1*n2 - 2*u1 *u2*a33*n2 - 2*u1 *u3*a33*n2 *n3
2 4 2 2 2 2 2 2 3
- 2*u1 *v1*a33*m1*n2 + 4*u1 *v2 *a33 *m1 *n2 + 6*u1 *v2*a33*m1*n1*n2
2 2 2 2 2 2 2 4 4 2 2 2 3
- 2*u1 *v3 *a33 *m1 *n2 + u1 *(n1 *n2 - n2 *n3 ) - 4*u1*u2 *v2*a33 *m1*n2
2 4 2 2 2
- 2*u1*u2 *a33*n1*n2 - 8*u1*u2*v1*v2*a33 *m1 *n2
3 4 5
- 4*u1*u2*v1*a33*m1*n1*n2 + 4*u1*u2*v2*a33*m1*n2 + 2*u1*u2*n1*n2
3 4 2 3
+ 4*u1*u3*v2*a33*m1*n2 *n3 + 2*u1*u3*n1*n2 *n3 + 4*u1*v1*v2*a33*m1 *n2
4 2 2 2 2 2 3
+ 4*u1*v1*m1*n1*n2 - 4*u1*v2 *a33*m1 *n1*n2 + 4*u1*v2*v3 *a33 *m1 *n2
2 3 3 2 2 2 2
+ u1*v2*( - 2*m1*n1 *n2 + 2*m1*n2 *n3 ) + 2*u1*v3 *a33*m1 *n1*n2
4 2 4 3 2 3 3 5 2 4
+ u2 *a33 *n2 + 4*u2 *v1*a33 *m1*n2 - 2*u2 *a33*n2 - 2*u2 *u3*a33*n2 *n3
2 2 2 2 2 2 4 2 3
+ 4*u2 *v1 *a33 *m1 *n2 - 6*u2 *v1*a33*m1*n2 + 2*u2 *v2*a33*m1*n1*n2
2 2 2 2 2 2 6 4 2 3
- 2*u2 *v3 *a33 *m1 *n2 + u2 *(n2 - n2 *n3 ) - 4*u2*u3*v1*a33*m1*n2 *n3
5 2 2 3 2 2
+ 2*u2*u3*n2 *n3 - 4*u2*v1 *a33*m1 *n2 + 4*u2*v1*v2*a33*m1 *n1*n2
2 2 3 5 3 2
- 4*u2*v1*v3 *a33 *m1 *n2 + u2*v1*(2*m1*n2 - 2*m1*n2 *n3 )
2 2 3 4 3
+ 2*u2*v3 *a33*m1 *n2 + 2*u3*v1*m1*n2 *n3 - 2*u3*v2*m1*n1*n2 *n3
2 2 2 4 2 3
+ 2*u3*v3 *a33*m1 *n2 *n3 + 2*u3*v3*m1*n1*n2 - 2*v1*v2*m1 *n1*n2
2 3 2 2 2 2 2 2 4
+ 2*v1*v3 *a33*m1 *n2 + v2 *(m1 *n1 *n2 - m1 *n2 )
2 3 4 2 4 2 2 4 2 2 2
- 2*v2*v3 *a33*m1 *n1*n2 + v3 *a33 *m1 + v3 *( - m1 *n2 + m1 *n2 *n3 )
which the program can not factorize further.
{HAM,FI} = 0
2 2 2 2 2
FI= - u1 *a33*n2 + 2*u1*v2*a33*m1*n2 + u1*n1*n2 - u2 *a33*n2
3 2 2
- 2*u2*v1*a33*m1*n2 + u2*n2 + u3*n2 *n3 + v1*m1*n2 - v2*m1*n1*n2
2 2
+ v3 *a33*m1
which the program can not factorize further.
{HAM,FI} = 0
And again in machine readable form:
HAM=u1*n1 + u2*n2 + u3**2*a33 + u3*n3 + v1*m1 + ( - v2*m1*n1)/n2$
FI=u1**3*a33*n1*n2**3 + u1**2*u2*a33*n2**4 + u1**2*u3**2*a33**2*n2**3 + u1**2*u3
*a33*n2**3*n3 + u1**2*v1*a33*m1*n2**3 - 3*u1**2*v2*a33*m1*n1*n2**2 + u1**2*( -
n1**2*n2**3 + n2**3*n3**2) + u1*u2**2*a33*n1*n2**3 + 2*u1*u2*v1*a33*m1*n1*n2**2
- 2*u1*u2*v2*a33*m1*n2**3 - 2*u1*u2*n1*n2**4 - 2*u1*u3**2*v2*a33**2*m1*n2**2 -
u1*u3**2*a33*n1*n2**3 - 2*u1*u3*v2*a33*m1*n2**2*n3 - 2*u1*u3*n1*n2**3*n3 - 2*u1*
v1*v2*a33*m1**2*n2**2 - 4*u1*v1*m1*n1*n2**3 + 2*u1*v2**2*a33*m1**2*n1*n2 + u1*v2
*(2*m1*n1**2*n2**2 - 2*m1*n2**2*n3**2) - u1*v3**2*a33*m1**2*n1*n2 + u2**3*a33*n2
**4 + u2**2*u3**2*a33**2*n2**3 + u2**2*u3*a33*n2**3*n3 + 3*u2**2*v1*a33*m1*n2**3
- u2**2*v2*a33*m1*n1*n2**2 + u2**2*( - n2**5 + n2**3*n3**2) + 2*u2*u3**2*v1*a33
**2*m1*n2**2 - u2*u3**2*a33*n2**4 + 2*u2*u3*v1*a33*m1*n2**2*n3 - 2*u2*u3*n2**4*
n3 + 2*u2*v1**2*a33*m1**2*n2**2 - 2*u2*v1*v2*a33*m1**2*n1*n2 + u2*v1*( - 2*m1*n2
**4 + 2*m1*n2**2*n3**2) - u2*v3**2*a33*m1**2*n2**2 - u3**3*a33*n2**3*n3 - u3**2*
v1*a33*m1*n2**3 + u3**2*v2*a33*m1*n1*n2**2 - u3**2*v3**2*a33**2*m1**2*n2 - 2*u3*
v1*m1*n2**3*n3 + 2*u3*v2*m1*n1*n2**2*n3 - u3*v3**2*a33*m1**2*n2*n3 - 2*u3*v3*m1*
n1*n2**3 + 2*v1*v2*m1**2*n1*n2**2 - v1*v3**2*a33*m1**3*n2 + v2**2*( - m1**2*n1**
2*n2 + m1**2*n2**3) + v2*v3**2*a33*m1**3*n1 + v3**2*(m1**2*n2**3 - m1**2*n2*n3**
2)$
FI= - u1**2*v2**2*a33*n2**2 - u1**2*v3**2*a33*n2**2 + 2*u1*u2*v1*v2*a33*n2**2 +
2*u1*u3*v1*v3*a33*n2**2 + 2*u1*v1**2*v2*a33*m1*n2 + u1*v1**2*n1*n2**2 + 2*u1*v2
**3*a33*m1*n2 + u1*v2**2*n1*n2**2 + 2*u1*v2*v3**2*a33*m1*n2 + u1*v3**2*n1*n2**2
- u2**2*v1**2*a33*n2**2 - u2**2*v3**2*a33*n2**2 + 2*u2*u3*v2*v3*a33*n2**2 - 2*u2
*v1**3*a33*m1*n2 + u2*v1**2*n2**3 - 2*u2*v1*v2**2*a33*m1*n2 - 2*u2*v1*v3**2*a33*
m1*n2 + u2*v2**2*n2**3 + u2*v3**2*n2**3 + u3**2*v3**2*a33*n2**2 + u3*v1**2*n2**2
*n3 + u3*v2**2*n2**2*n3 + u3*v3**2*n2**2*n3 + v1**3*m1*n2**2 - v1**2*v2*m1*n1*n2
+ v1**2*v3**2*a33*m1**2 + v1*v2**2*m1*n2**2 + v1*v3**2*m1*n2**2 - v2**3*m1*n1*
n2 + v2**2*v3**2*a33*m1**2 - v2*v3**2*m1*n1*n2 + v3**4*a33*m1**2$
FI=u1**3*v1*a33*n2**2 + u1**2*u2*v2*a33*n2**2 + u1**2*u3*v3*a33*n2**2 - 2*u1**2*
v1*v2*a33*m1*n2 - u1**2*v1*n1*n2**2 + u1*u2**2*v1*a33*n2**2 + 2*u1*u2*v1**2*a33*
m1*n2 - u1*u2*v1*n2**3 - 2*u1*u2*v2**2*a33*m1*n2 - u1*u2*v2*n1*n2**2 - u1*u3*v1*
n2**2*n3 - 2*u1*u3*v2*v3*a33*m1*n2 - u1*u3*v3*n1*n2**2 - u1*v1**2*m1*n2**2 + u1*
v1*v2*m1*n1*n2 - u1*v1*v3**2*a33*m1**2 + u2**3*v2*a33*n2**2 + u2**2*u3*v3*a33*n2
**2 + 2*u2**2*v1*v2*a33*m1*n2 - u2**2*v2*n2**3 + 2*u2*u3*v1*v3*a33*m1*n2 - u2*u3
*v2*n2**2*n3 - u2*u3*v3*n2**3 - u2*v1*v2*m1*n2**2 + u2*v2**2*m1*n1*n2 - u2*v2*v3
**2*a33*m1**2 - u3**2*v3*n2**2*n3 - u3*v1*v3*m1*n2**2 + u3*v2*v3*m1*n1*n2 - u3*
v3**3*a33*m1**2$
FI=u1**4*a33**2*n2**4 - 4*u1**3*v2*a33**2*m1*n2**3 - 2*u1**3*a33*n1*n2**4 + 2*u1
**2*u2**2*a33**2*n2**4 + 4*u1**2*u2*v1*a33**2*m1*n2**3 - 2*u1**2*u2*a33*n2**5 -
2*u1**2*u3*a33*n2**4*n3 - 2*u1**2*v1*a33*m1*n2**4 + 4*u1**2*v2**2*a33**2*m1**2*
n2**2 + 6*u1**2*v2*a33*m1*n1*n2**3 - 2*u1**2*v3**2*a33**2*m1**2*n2**2 + u1**2*(
n1**2*n2**4 - n2**4*n3**2) - 4*u1*u2**2*v2*a33**2*m1*n2**3 - 2*u1*u2**2*a33*n1*
n2**4 - 8*u1*u2*v1*v2*a33**2*m1**2*n2**2 - 4*u1*u2*v1*a33*m1*n1*n2**3 + 4*u1*u2*
v2*a33*m1*n2**4 + 2*u1*u2*n1*n2**5 + 4*u1*u3*v2*a33*m1*n2**3*n3 + 2*u1*u3*n1*n2
**4*n3 + 4*u1*v1*v2*a33*m1**2*n2**3 + 4*u1*v1*m1*n1*n2**4 - 4*u1*v2**2*a33*m1**2
*n1*n2**2 + 4*u1*v2*v3**2*a33**2*m1**3*n2 + u1*v2*( - 2*m1*n1**2*n2**3 + 2*m1*n2
**3*n3**2) + 2*u1*v3**2*a33*m1**2*n1*n2**2 + u2**4*a33**2*n2**4 + 4*u2**3*v1*a33
**2*m1*n2**3 - 2*u2**3*a33*n2**5 - 2*u2**2*u3*a33*n2**4*n3 + 4*u2**2*v1**2*a33**
2*m1**2*n2**2 - 6*u2**2*v1*a33*m1*n2**4 + 2*u2**2*v2*a33*m1*n1*n2**3 - 2*u2**2*
v3**2*a33**2*m1**2*n2**2 + u2**2*(n2**6 - n2**4*n3**2) - 4*u2*u3*v1*a33*m1*n2**3
*n3 + 2*u2*u3*n2**5*n3 - 4*u2*v1**2*a33*m1**2*n2**3 + 4*u2*v1*v2*a33*m1**2*n1*n2
**2 - 4*u2*v1*v3**2*a33**2*m1**3*n2 + u2*v1*(2*m1*n2**5 - 2*m1*n2**3*n3**2) + 2*
u2*v3**2*a33*m1**2*n2**3 + 2*u3*v1*m1*n2**4*n3 - 2*u3*v2*m1*n1*n2**3*n3 + 2*u3*
v3**2*a33*m1**2*n2**2*n3 + 2*u3*v3*m1*n1*n2**4 - 2*v1*v2*m1**2*n1*n2**3 + 2*v1*
v3**2*a33*m1**3*n2**2 + v2**2*(m1**2*n1**2*n2**2 - m1**2*n2**4) - 2*v2*v3**2*a33
*m1**3*n1*n2 + v3**4*a33**2*m1**4 + v3**2*( - m1**2*n2**4 + m1**2*n2**2*n3**2)$
FI= - u1**2*a33*n2**2 + 2*u1*v2*a33*m1*n2 + u1*n1*n2**2 - u2**2*a33*n2**2 - 2*u2
*v1*a33*m1*n2 + u2*n2**3 + u3*n2**2*n3 + v1*m1*n2**2 - v2*m1*n1*n2 + v3**2*a33*
m1**2$