Solution 3 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
2 2 3 3
a33 *n1*n3*r26 - m1*n2 *n3*r4119 + 2*m1*n3 *r4119 - 2*m1*n3 *r464
r10=-------------------------------------------------------------------
3
a33 *n1
2 3 2
a33 *n1*n2*r26 - m1*n2 *r4119 + m1*n2*n3 *r4119
r11=-------------------------------------------------
3
2*a33 *n1
2 2 2
a33 *n1*r26 - m1*n2 *r4119 + m1*n3 *r4119
r12=-------------------------------------------
3
2*a33
2 2 3 3
- a33 *n1*n3*r26 + m1*n2 *n3*r4119 - 3*m1*n3 *r4119 + 4*m1*n3 *r464
r13=----------------------------------------------------------------------
3
2*a33 *m1
2 3 2 2
- a33 *n1*n2*r26 + m1*n2 *r4119 - 3*m1*n2*n3 *r4119 + 4*m1*n2*n3 *r464
r14=-------------------------------------------------------------------------
3
2*a33 *m1
2 2 2 2 2
- a33 *n1 *r26 + m1*n1*n2 *r4119 - 3*m1*n1*n3 *r4119 + 4*m1*n1*n3 *r464
r15=--------------------------------------------------------------------------
3
2*a33 *m1
2 2 2 2 2 2 2
r20=( - a33 *m1*n1*r26 - m1 *n1 *r4119 - 2*m1 *n1 *r464 + m1 *n2 *r4119
2 2 2 2 2 2
+ 2*m1 *n3 *r4119 + 2*m1 *n3 *r464)/(2*a33 *n1 )
2 2
2*m1 *n2*n3*r4119 + 2*m1 *n2*n3*r464
r21=--------------------------------------
2 2
a33 *n1
2 2 2 2 2 2 2 2
- m1 *n1 *r4119 - 2*m1 *n1 *r464 + m1 *n2 *r4119 + 2*m1 *n2 *r464
r22=--------------------------------------------------------------------
2 2
2*a33 *n1
2 2
2*m1 *n3*r4119 + 2*m1 *n3*r464
r23=--------------------------------
2
a33 *n1
2 2
m1 *n2*r4119 + 2*m1 *n2*r464
r24=------------------------------
2
a33 *n1
- m1*n2*n3*r4119
r27=-------------------
2
a33 *n1
- m1*n3*r4119
r28=----------------
2
a33
- 2*m1*n2*n3*r4119 + 2*m1*n2*n3*r464
r210=---------------------------------------
2
a33 *n1
- m1*n2*r4119
r212=----------------
2
a33
n2*n3*r4119 - 2*n2*n3*r464
r213=----------------------------
2
a33
2 2 2 2
a33 *n1*r26 - 2*m1*n2 *r464 + 2*m1*n3 *r4119 - 2*m1*n3 *r464
r214=--------------------------------------------------------------
2
2*a33 *m1
- 2*m1*n3*r4119 + 2*m1*n3*r464
r215=---------------------------------
2
a33
- m1*n2*r4119
r216=----------------
2
a33
2 2
- m1*n1 *r4119 + m1*n2 *r4119
r217=--------------------------------
2
a33 *n1
n1*n3*r4119 - 2*n1*n3*r464
r218=----------------------------
2
a33
n1*n2*r4119 - 2*n1*n2*r464
r219=----------------------------
2
a33
2 2 2 2 2
r220=(a33 *n1*r26 + m1*n1 *r4119 - 2*m1*n1 *r464 - m1*n2 *r4119 + 2*m1*n3 *r4119
2 2
- 2*m1*n3 *r464)/(2*a33 *m1)
3 2
- 2*m1 *n3*r4119 - m1*n1 *n3*r494
r30=------------------------------------
3
a33*n1
3 3 2
- 2*m1 *n2*r4119 - 2*m1 *n2*r464 - m1*n1 *n2*r494
r31=----------------------------------------------------
3
2*a33*n1
- m1*n3*r494
r32=---------------
a33*n1
- m1*n2*r494
r33=---------------
2*a33*n1
3 3 2
- 2*m1 *r4119 - 2*m1 *r464 - m1*n1 *r494
r34=-------------------------------------------
2
2*a33*n1
r35=0
- m1*r494
r36=------------
2*a33
- m1*n3*r494
r37=---------------
a33*n1
- m1*n2*r494
r38=---------------
2*a33*n1
- m1*r494
r39=------------
2*a33
2 2 2 2
10*m1 *n3*r4119 - 2*m1 *n3*r464 + 2*n1 *n3*r446 - n1 *n3*r494
r310=---------------------------------------------------------------
2
2*a33*n1
2 2 2 2
4*m1 *n2*r4119 + 4*m1 *n2*r464 + n1 *n2*r446 - n1 *n2*r494
r311=------------------------------------------------------------
2
2*a33*n1
n3*r494
r312=---------
2*a33
2 2 2 2
4*m1 *r4119 + 4*m1 *r464 + n1 *r446 - n1 *r494
r313=------------------------------------------------
2*a33*n1
r314=0
n3*r494
r315=---------
2*a33
2 2 2 2
- 4*m1 *n3*r4119 + 8*m1 *n3*r464 - n1 *n3*r446 + n1 *n3*r494
r316=---------------------------------------------------------------
2*a33*m1*n1
m1*n2*r464
r317=------------
a33*n1
m1*r464
r318=---------
a33
- n3*r464
r319=------------
a33
2 2 2
2*m1 *n2*r4119 - 2*m1 *n2*r464 + n1 *n2*r494
r320=----------------------------------------------
2
2*a33*n1
n3*r446 - n3*r494
r321=-------------------
a33
n2*r446
r322=---------
2*a33
r323=0
n1*r446 - n1*r494
r324=-------------------
2*a33
n2*r494
r325=---------
2*a33
2 2 2 2
- 4*m1 *n2*r4119 + 4*m1 *n2*r464 - n1 *n2*r446 + n1 *n2*r494
r326=---------------------------------------------------------------
2*a33*m1*n1
- n1*n3*r446 + n1*n3*r494
r327=----------------------------
2*a33*m1
r328=0
- n2*r464
r329=------------
a33
2*m1*n3*r4119
r330=---------------
a33*n1
2 2 2 2
2*m1 *n2*r4119 + 2*m1 *n2*r464 - n1 *n2*r446 + n1 *n2*r494
r331=------------------------------------------------------------
2*a33*m1*n1
m1*r4119 + m1*r464
r332=--------------------
a33
- n3*r4119 + n3*r464
r333=-----------------------
a33
- n2*r4119 + n2*r464
r334=-----------------------
a33
2 2 2
2*m1 *r4119 - 2*m1 *r464 + n1 *r494
r335=-------------------------------------
2*a33*n1
r336=0
n1*r494
r337=---------
2*a33
n3*r446 - n3*r494
r338=-------------------
a33
n2*r446 - n2*r494
r339=-------------------
2*a33
n1*r446
r340=---------
2*a33
2 2 2 2
- 4*m1 *r4119 + 4*m1 *r464 - n1 *r446 + n1 *r494
r341=---------------------------------------------------
2*a33*m1
r342=0
- n1*n3*r446 + n1*n3*r494
r343=----------------------------
2*a33*m1
- n1*r464
r344=------------
a33
r345=0
2 2
- n1 *r446 + n1 *r494
r346=------------------------
2*a33*m1
- n1*n2*r446 + n1*n2*r494
r347=----------------------------
2*a33*m1
r348=0
- n1*r4119 + n1*r464
r349=-----------------------
a33
2*m1*n3*r4119
r350=---------------
a33*n1
m1*n2*r4119 + m1*n2*r464
r351=--------------------------
a33*n1
2 2 2 2
2*m1 *r4119 + 2*m1 *r464 - n1 *r446 + n1 *r494
r352=------------------------------------------------
2*a33*m1
- n3*r4119 + n3*r464
r353=-----------------------
a33
- n2*r4119 + n2*r464
r354=-----------------------
a33
- n1*r4119 + n1*r464
r355=-----------------------
a33
4 2 2
m1 *r4119 + m1 *n1 *r494
r40=--------------------------
4
2*n1
r41=0
2
m1 *r494
r42=----------
2
2*n1
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
2
m1 *r494
r49=----------
2
2*n1
r410=0
r411=0
r412=0
r413=0
3 2 2
- 4*m1 *r4119 - m1*n1 *r446 - m1*n1 *r494
r415=--------------------------------------------
3
2*n1
r416=0
- m1*r494
r417=------------
n1
r418=0
r419=0
r420=0
r421=0
- m1*r494
r422=------------
n1
r423=0
r424=0
2 2 2 2
4*m1 *r4119 - 2*m1 *r464 + 2*n1 *r446 - n1 *r494
r425=--------------------------------------------------
2
2*n1
r426=0
r427=0
r428=0
r429=0
2*m1*r464
r431=-----------
n1
r432=0
r433=0
r435=0
- m1*r446 + m1*r494
r436=----------------------
2*n1
r437=0
r438=0
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*m1 *r4119 - n1 *r494
r455=---------------------------
2
2*n1
r456=0
r458=0
r459=0
- r494
r460=---------
2
2 2 2
4*m1 *r4119 + n1 *r446 - n1 *r494
r461=-----------------------------------
2*m1*n1
r462=0
r463=0
r465=0
n1*r446 - n1*r494
r466=-------------------
2*m1
r467=0
r468=0
r4119
r469=-------
2
r470=0
r471=0
r472=0
r473=0
- m1*r446 + m1*r494
r474=----------------------
2*n1
r475=0
r476=0
r477=0
r478=0
r479=0
r480=0
r481=0
r482=0
r483=r446
r484=0
r485=0
r486=0
r487=0
r488=0
r489=0
r490=0
r491=0
r492=0
r493=0
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
n1*r446 - n1*r494
r4102=-------------------
2*m1
r4103=0
r4104=0
2 2
- 2*m1 *r4119 - n1 *r494
r4105=---------------------------
2
2*n1
r4106=0
- r494
r4107=---------
2
r4108=0
r4109=0
r4110=0
r4112=0
r4113=0
r4114=r464
r4115=0
n1*r446 - n1*r494
r4116=-------------------
2*m1
r4117=0
r4118=0
r4120=0
r4121=0
n1*r446 - n1*r494
r4122=-------------------
2*m1
r4123=0
r4124=0
r4119
r4125=-------
2
m3=0
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
m1*n2
m2=-------
n1
2 2 2
4*m1 *r4119 + n1 *r446 - n1 *r494
r4111=-----------------------------------
2*m1*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:
r4119, m1, r26, r494, r446, r464, 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.
{a33,n1,n1 + i*n2,n1 - i*n2,n1 - n2,n1 + n2,m1}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{ - m1*n2 + m2*n1,
a11,
a12,
a13,
a22,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
b33,
c11,
c12,
c13,
c22,
c23,
c33,
m3}$
The system of equations related to the Hamiltonian HAM:
2 v2*m1*n2
HAM=u1*n1 + u2*n2 + u3 *a33 + u3*n3 + v1*m1 + ----------
n1
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
3 2 4 2 2 3 2 2 3 3 2 2 3
FI=u1 *a33 *n1 + u1 *u2*a33 *n1 *n2 + u1 *u3 *a33 *n1 + u1 *u3*a33 *n1 *n3
2 2 3 2 2 2
+ u1 *v1*a33 *m1*n1 + u1 *v2*a33 *m1*n1 *n2
2 5 3 2 2 2 4 4
+ u1 *( - a33*n1 - a33*n1 *n3 ) + u1*u2 *a33 *n1 - 2*u1*u2*a33*n1 *n2
2 2 4 2 3 4
- u1*u3 *a33 *n1 + 2*u1*u3*v3*a33 *m1*n1 - 2*u1*u3*a33*n1 *n3
2 2 2 2 3 4 2
- u1*v3 *a33 *m1 *n1 + 2*u1*v3*a33*m1*n1 *n3 + 2*u1*n1 *n3
3 2 3 2 2 3 3 2 2 3
+ u2 *a33 *n1 *n2 + u2 *u3 *a33 *n1 + u2 *u3*a33 *n1 *n3
2 2 3 2 2 2
+ u2 *v1*a33 *m1*n1 + u2 *v2*a33 *m1*n1 *n2
2 3 2 3 2 2 2 3
+ u2 *( - a33*n1 *n2 - a33*n1 *n3 ) - u2*u3 *a33 *n1 *n2
2 2 3 2 2 2
+ 2*u2*u3*v3*a33 *m1*n1 *n2 - 2*u2*u3*a33*n1 *n2*n3 - u2*v3 *a33 *m1 *n1*n2
2 3 2 3 3 2
+ 2*u2*v3*a33*m1*n1 *n2*n3 + 2*u2*n1 *n2*n3 + 2*u3 *v3*a33 *m1*n1
3 2 3 2 2 3 2 2 2
- u3 *a33 *n1 *n3 + u3 *v1*a33 *m1*n1 + u3 *v2*a33 *m1*n1 *n2
2 2 3 2 2 2 2 2 2 2
- u3 *v3 *a33 *m1 *n1 + 4*u3 *v3*a33 *m1*n1 *n3 + 2*u3*v1*v3*a33 *m1 *n1
2 2 2 2 2 3 3
+ 2*u3*v2*v3*a33 *m1 *n1*n2 - u3*v3 *a33 *m1 *n1*n3 + 2*u3*n1 *n3
2 2 2 2 3 2 2
+ 2*v1*v2*a33*m1 *n1 *n2 - v1*v3 *a33 *m1 *n1 + 2*v1*v3*a33*m1 *n1 *n3
2 2 3 2 2 2 2 3
+ v2 *( - a33*m1 *n1 + a33*m1 *n1*n2 ) - v2*v3 *a33 *m1 *n2
2 2 2 3 2 2
+ 2*v2*v3*a33*m1 *n1*n2*n3 + v3 *( - a33*m1 *n1 + a33*m1 *n1*n3 )
2 3
- 2*v3*m1*n1 *n3
which the program can not factorize further.
{HAM,FI} = 0
3 2 2 2 2 2 2 3
FI=u1 *v1*a33*n1 + u1 *u2*v2*a33*n1 + u1 *u3*v3*a33*n1 - u1 *v1*n1
2 2 2 3
+ u1*u2 *v1*a33*n1 - u1*u2*v1*n1 *n2 - u1*u2*v2*n1
2 3 2 2
+ 2*u1*u3*v1*v3*a33*m1*n1 - u1*u3*v1*n1 *n3 - u1*u3*v3*n1 + u1*v1 *m1*n1
2 2
+ u1*v1*v2*m1*n1*n2 - u1*v1*v3 *a33*m1 + 2*u1*v1*v3*m1*n1*n3
3 2 2 2 2 2
+ u2 *v2*a33*n1 + u2 *u3*v3*a33*n1 - u2 *v2*n1 *n2
2 2
+ 2*u2*u3*v2*v3*a33*m1*n1 - u2*u3*v2*n1 *n3 - u2*u3*v3*n1 *n2
2 2 2 2
+ u2*v1*v2*m1*n1 + u2*v2 *m1*n1*n2 - u2*v2*v3 *a33*m1
2 2 2 2
+ 2*u2*v2*v3*m1*n1*n3 + 2*u3 *v3 *a33*m1*n1 - u3 *v3*n1 *n3
2 3 2 2
+ u3*v1*v3*m1*n1 + u3*v2*v3*m1*n1*n2 - u3*v3 *a33*m1 + 2*u3*v3 *m1*n1*n3
= a product of the elements of: { - u1*v1 - u2*v2 - u3*v3,
2 2 3 2 2 2
- u1 *a33*n1 + u1*n1 - u2 *a33*n1 + u2*n1 *n2 - 2*u3*v3*a33*m1*n1
2 2 2 2
+ u3*n1 *n3 - v1*m1*n1 - v2*m1*n1*n2 + v3 *a33*m1 - 2*v3*m1*n1*n3}
{HAM,FI} = 0
3 3 2 3 2 3 2 4
FI= - u1 *v1*a33*n1 - u1 *u2*v2*a33*n1 - u1 *u3*v3*a33*n1 + u1 *v1*n1
2 2 2 2 2 2 2 3
- u1 *v2 *a33*m1*n1 - u1 *v3 *a33*m1*n1 - u1*u2 *v1*a33*n1
2 3 4
+ 2*u1*u2*v1*v2*a33*m1*n1 + u1*u2*v1*n1 *n2 + u1*u2*v2*n1
3 4 2 2 2
+ u1*u3*v1*n1 *n3 + u1*u3*v3*n1 - u1*v1*v2*m1*n1 *n2 + u1*v1*v3 *a33*m1 *n1
2 2 3 2 3 3 3
- 2*u1*v1*v3*m1*n1 *n3 + u1*v2 *m1*n1 + u1*v3 *m1*n1 - u2 *v2*a33*n1
2 3 2 2 2 2 3
- u2 *u3*v3*a33*n1 - u2 *v1 *a33*m1*n1 + u2 *v2*n1 *n2
2 2 2 3 3 2 2
- u2 *v3 *a33*m1*n1 + u2*u3*v2*n1 *n3 + u2*u3*v3*n1 *n2 + u2*v1 *m1*n1 *n2
3 2 2 2
- u2*v1*v2*m1*n1 + u2*v2*v3 *a33*m1 *n1 - 2*u2*v2*v3*m1*n1 *n3
2 2 2 2 2 2 3
+ u2*v3 *m1*n1 *n2 - u3 *v3 *a33*m1*n1 + u3 *v3*n1 *n3
2 2 2 2 3
- 2*u3*v1 *v3*a33*m1 *n1 + u3*v1 *m1*n1 *n3 - u3*v1*v3*m1*n1
2 2 2 2 2
- 2*u3*v2 *v3*a33*m1 *n1 + u3*v2 *m1*n1 *n3 - u3*v2*v3*m1*n1 *n2
3 2 2 2 3 2 2 2 2
- u3*v3 *a33*m1 *n1 - u3*v3 *m1*n1 *n3 - v1 *m1 *n1 - v1 *v2*m1 *n1*n2
2 2 3 2 2 2 2 2 2 2 2
+ v1 *v3 *a33*m1 - 2*v1 *v3*m1 *n1*n3 - v1*v2 *m1 *n1 - v1*v3 *m1 *n1
3 2 2 2 3 2 2 2 2
- v2 *m1 *n1*n2 + v2 *v3 *a33*m1 - 2*v2 *v3*m1 *n1*n3 - v2*v3 *m1 *n1*n2
4 3 3 2
+ v3 *a33*m1 - 2*v3 *m1 *n1*n3
which the program can not factorize further.
{HAM,FI} = 0
2 2 3 2 2 2
FI=u1 *a33*n1 - u1*n1 + u2 *a33*n1 - u2*n1 *n2 + 2*u3*v3*a33*m1*n1
2 2 2 2
- u3*n1 *n3 + v1*m1*n1 + v2*m1*n1*n2 - v3 *a33*m1 + 2*v3*m1*n1*n3
which the program can not factorize further.
{HAM,FI} = 0
4 3 4 3 2 5 2 2 3 4 2 2 4
FI=u1 *a33 *n1 - 2*u1 *a33 *n1 + 2*u1 *u2 *a33 *n1 - 2*u1 *u2*a33 *n1 *n2
2 3 3 2 2 4 2 2 4
+ 4*u1 *u3*v3*a33 *m1*n1 - 2*u1 *u3*a33 *n1 *n3 + 2*u1 *v1*a33 *m1*n1
2 2 3 2 2 3 2 2 2 2 3
+ 2*u1 *v2*a33 *m1*n1 *n2 - 2*u1 *v3 *a33 *m1 *n1 + 4*u1 *v3*a33 *m1*n1 *n3
2 6 4 2 4 2 2 2 5
+ u1 *(a33*n1 - a33*n1 *n2 + 2*a33*n1 *n3 ) - 2*u1*u2 *a33 *n1
5 2 4 5
+ 2*u1*u2*a33*n1 *n2 - 4*u1*u3*v3*a33 *m1*n1 + 2*u1*u3*a33*n1 *n3
5 3 2 4
+ u1*v1*( - 2*a33*m1*n1 + 2*a33*m1*n1 *n2 ) - 2*u1*v2*a33*m1*n1 *n2
2 2 2 3 4 5 2 5 2
+ 2*u1*v3 *a33 *m1 *n1 - 4*u1*v3*a33*m1*n1 *n3 + u1*(n1 *n2 - 3*n1 *n3 )
4 3 4 3 2 4 2 3 3
+ u2 *a33 *n1 - 2*u2 *a33 *n1 *n2 + 4*u2 *u3*v3*a33 *m1*n1
2 2 4 2 2 4 2 2 3
- 2*u2 *u3*a33 *n1 *n3 + 2*u2 *v1*a33 *m1*n1 + 2*u2 *v2*a33 *m1*n1 *n2
2 2 3 2 2 2 2 3 2 4 2
- 2*u2 *v3 *a33 *m1 *n1 + 4*u2 *v3*a33 *m1*n1 *n3 + 2*u2 *a33*n1 *n3
2 3 4 4
- 4*u2*u3*v3*a33 *m1*n1 *n2 + 2*u2*u3*a33*n1 *n2*n3 - 2*u2*v1*a33*m1*n1 *n2
2 2 2 2 3
+ 2*u2*v3 *a33 *m1 *n1 *n2 - 4*u2*v3*a33*m1*n1 *n2*n3
4 3 4 2 2 2 3 2 2
+ u2*(n1 *n2 - 3*n1 *n2*n3 ) + 4*u3 *v3 *a33 *m1 *n1
2 2 3 2 2 3 4
- 4*u3 *v3*a33 *m1*n1 *n3 + 4*u3*v1*v3*a33 *m1 *n1 - 2*u3*v1*a33*m1*n1 *n3
2 2 2 3
+ 4*u3*v2*v3*a33 *m1 *n1 *n2 - 2*u3*v2*a33*m1*n1 *n2*n3
3 3 3 2 2 2 2
- 4*u3*v3 *a33 *m1 *n1 + 10*u3*v3 *a33 *m1 *n1 *n3
4 2 4 3 2 3
+ u3*(n1 *n2 *n3 - 3*n1 *n3 ) + 2*v1*v2*a33*m1 *n1 *n2
2 2 3 2 2 3
- 2*v1*v3 *a33 *m1 *n1 + 4*v1*v3*a33*m1 *n1 *n3
4 2 4 2 2 2 4 2 2 2
+ v1*( - m1*n1 *n2 + m1*n1 *n3 ) + v2 *( - a33*m1 *n1 + a33*m1 *n1 *n2 )
2 2 3 2 2
- 2*v2*v3 *a33 *m1 *n1*n2 + 4*v2*v3*a33*m1 *n1 *n2*n3
3 3 3 2 4 3 4 3 2 3
+ v2*( - m1*n1 *n2 + m1*n1 *n2*n3 ) + v3 *a33 *m1 - 4*v3 *a33 *m1 *n1*n3
2 2 4 2 2 2 2 2 2
+ v3 *( - a33*m1 *n1 + a33*m1 *n1 *n2 + 2*a33*m1 *n1 *n3 )
3 2 3 3
+ v3*( - 2*m1*n1 *n2 *n3 + 4*m1*n1 *n3 )
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*n2)/n1$
FI=u1**3*a33**2*n1**4 + u1**2*u2*a33**2*n1**3*n2 + u1**2*u3**2*a33**3*n1**3 + u1
**2*u3*a33**2*n1**3*n3 + u1**2*v1*a33**2*m1*n1**3 + u1**2*v2*a33**2*m1*n1**2*n2
+ u1**2*( - a33*n1**5 - a33*n1**3*n3**2) + u1*u2**2*a33**2*n1**4 - 2*u1*u2*a33*
n1**4*n2 - u1*u3**2*a33**2*n1**4 + 2*u1*u3*v3*a33**2*m1*n1**3 - 2*u1*u3*a33*n1**
4*n3 - u1*v3**2*a33**2*m1**2*n1**2 + 2*u1*v3*a33*m1*n1**3*n3 + 2*u1*n1**4*n3**2
+ u2**3*a33**2*n1**3*n2 + u2**2*u3**2*a33**3*n1**3 + u2**2*u3*a33**2*n1**3*n3 +
u2**2*v1*a33**2*m1*n1**3 + u2**2*v2*a33**2*m1*n1**2*n2 + u2**2*( - a33*n1**3*n2
**2 - a33*n1**3*n3**2) - u2*u3**2*a33**2*n1**3*n2 + 2*u2*u3*v3*a33**2*m1*n1**2*
n2 - 2*u2*u3*a33*n1**3*n2*n3 - u2*v3**2*a33**2*m1**2*n1*n2 + 2*u2*v3*a33*m1*n1**
2*n2*n3 + 2*u2*n1**3*n2*n3**2 + 2*u3**3*v3*a33**3*m1*n1**2 - u3**3*a33**2*n1**3*
n3 + u3**2*v1*a33**2*m1*n1**3 + u3**2*v2*a33**2*m1*n1**2*n2 - u3**2*v3**2*a33**3
*m1**2*n1 + 4*u3**2*v3*a33**2*m1*n1**2*n3 + 2*u3*v1*v3*a33**2*m1**2*n1**2 + 2*u3
*v2*v3*a33**2*m1**2*n1*n2 - u3*v3**2*a33**2*m1**2*n1*n3 + 2*u3*n1**3*n3**3 + 2*
v1*v2*a33*m1**2*n1**2*n2 - v1*v3**2*a33**2*m1**3*n1 + 2*v1*v3*a33*m1**2*n1**2*n3
+ v2**2*( - a33*m1**2*n1**3 + a33*m1**2*n1*n2**2) - v2*v3**2*a33**2*m1**3*n2 +
2*v2*v3*a33*m1**2*n1*n2*n3 + v3**2*( - a33*m1**2*n1**3 + a33*m1**2*n1*n3**2) - 2
*v3*m1*n1**2*n3**3$
FI=u1**3*v1*a33*n1**2 + u1**2*u2*v2*a33*n1**2 + u1**2*u3*v3*a33*n1**2 - u1**2*v1
*n1**3 + u1*u2**2*v1*a33*n1**2 - u1*u2*v1*n1**2*n2 - u1*u2*v2*n1**3 + 2*u1*u3*v1
*v3*a33*m1*n1 - u1*u3*v1*n1**2*n3 - u1*u3*v3*n1**3 + u1*v1**2*m1*n1**2 + u1*v1*
v2*m1*n1*n2 - u1*v1*v3**2*a33*m1**2 + 2*u1*v1*v3*m1*n1*n3 + u2**3*v2*a33*n1**2 +
u2**2*u3*v3*a33*n1**2 - u2**2*v2*n1**2*n2 + 2*u2*u3*v2*v3*a33*m1*n1 - u2*u3*v2*
n1**2*n3 - u2*u3*v3*n1**2*n2 + u2*v1*v2*m1*n1**2 + u2*v2**2*m1*n1*n2 - u2*v2*v3
**2*a33*m1**2 + 2*u2*v2*v3*m1*n1*n3 + 2*u3**2*v3**2*a33*m1*n1 - u3**2*v3*n1**2*
n3 + u3*v1*v3*m1*n1**2 + u3*v2*v3*m1*n1*n2 - u3*v3**3*a33*m1**2 + 2*u3*v3**2*m1*
n1*n3$
FI= - u1**3*v1*a33*n1**3 - u1**2*u2*v2*a33*n1**3 - u1**2*u3*v3*a33*n1**3 + u1**2
*v1*n1**4 - u1**2*v2**2*a33*m1*n1**2 - u1**2*v3**2*a33*m1*n1**2 - u1*u2**2*v1*
a33*n1**3 + 2*u1*u2*v1*v2*a33*m1*n1**2 + u1*u2*v1*n1**3*n2 + u1*u2*v2*n1**4 + u1
*u3*v1*n1**3*n3 + u1*u3*v3*n1**4 - u1*v1*v2*m1*n1**2*n2 + u1*v1*v3**2*a33*m1**2*
n1 - 2*u1*v1*v3*m1*n1**2*n3 + u1*v2**2*m1*n1**3 + u1*v3**2*m1*n1**3 - u2**3*v2*
a33*n1**3 - u2**2*u3*v3*a33*n1**3 - u2**2*v1**2*a33*m1*n1**2 + u2**2*v2*n1**3*n2
- u2**2*v3**2*a33*m1*n1**2 + u2*u3*v2*n1**3*n3 + u2*u3*v3*n1**3*n2 + u2*v1**2*
m1*n1**2*n2 - u2*v1*v2*m1*n1**3 + u2*v2*v3**2*a33*m1**2*n1 - 2*u2*v2*v3*m1*n1**2
*n3 + u2*v3**2*m1*n1**2*n2 - u3**2*v3**2*a33*m1*n1**2 + u3**2*v3*n1**3*n3 - 2*u3
*v1**2*v3*a33*m1**2*n1 + u3*v1**2*m1*n1**2*n3 - u3*v1*v3*m1*n1**3 - 2*u3*v2**2*
v3*a33*m1**2*n1 + u3*v2**2*m1*n1**2*n3 - u3*v2*v3*m1*n1**2*n2 - u3*v3**3*a33*m1
**2*n1 - u3*v3**2*m1*n1**2*n3 - v1**3*m1**2*n1**2 - v1**2*v2*m1**2*n1*n2 + v1**2
*v3**2*a33*m1**3 - 2*v1**2*v3*m1**2*n1*n3 - v1*v2**2*m1**2*n1**2 - v1*v3**2*m1**
2*n1**2 - v2**3*m1**2*n1*n2 + v2**2*v3**2*a33*m1**3 - 2*v2**2*v3*m1**2*n1*n3 -
v2*v3**2*m1**2*n1*n2 + v3**4*a33*m1**3 - 2*v3**3*m1**2*n1*n3$
FI=u1**2*a33*n1**2 - u1*n1**3 + u2**2*a33*n1**2 - u2*n1**2*n2 + 2*u3*v3*a33*m1*
n1 - u3*n1**2*n3 + v1*m1*n1**2 + v2*m1*n1*n2 - v3**2*a33*m1**2 + 2*v3*m1*n1*n3$
FI=u1**4*a33**3*n1**4 - 2*u1**3*a33**2*n1**5 + 2*u1**2*u2**2*a33**3*n1**4 - 2*u1
**2*u2*a33**2*n1**4*n2 + 4*u1**2*u3*v3*a33**3*m1*n1**3 - 2*u1**2*u3*a33**2*n1**4
*n3 + 2*u1**2*v1*a33**2*m1*n1**4 + 2*u1**2*v2*a33**2*m1*n1**3*n2 - 2*u1**2*v3**2
*a33**3*m1**2*n1**2 + 4*u1**2*v3*a33**2*m1*n1**3*n3 + u1**2*(a33*n1**6 - a33*n1
**4*n2**2 + 2*a33*n1**4*n3**2) - 2*u1*u2**2*a33**2*n1**5 + 2*u1*u2*a33*n1**5*n2
- 4*u1*u3*v3*a33**2*m1*n1**4 + 2*u1*u3*a33*n1**5*n3 + u1*v1*( - 2*a33*m1*n1**5 +
2*a33*m1*n1**3*n2**2) - 2*u1*v2*a33*m1*n1**4*n2 + 2*u1*v3**2*a33**2*m1**2*n1**3
- 4*u1*v3*a33*m1*n1**4*n3 + u1*(n1**5*n2**2 - 3*n1**5*n3**2) + u2**4*a33**3*n1
**4 - 2*u2**3*a33**2*n1**4*n2 + 4*u2**2*u3*v3*a33**3*m1*n1**3 - 2*u2**2*u3*a33**
2*n1**4*n3 + 2*u2**2*v1*a33**2*m1*n1**4 + 2*u2**2*v2*a33**2*m1*n1**3*n2 - 2*u2**
2*v3**2*a33**3*m1**2*n1**2 + 4*u2**2*v3*a33**2*m1*n1**3*n3 + 2*u2**2*a33*n1**4*
n3**2 - 4*u2*u3*v3*a33**2*m1*n1**3*n2 + 2*u2*u3*a33*n1**4*n2*n3 - 2*u2*v1*a33*m1
*n1**4*n2 + 2*u2*v3**2*a33**2*m1**2*n1**2*n2 - 4*u2*v3*a33*m1*n1**3*n2*n3 + u2*(
n1**4*n2**3 - 3*n1**4*n2*n3**2) + 4*u3**2*v3**2*a33**3*m1**2*n1**2 - 4*u3**2*v3*
a33**2*m1*n1**3*n3 + 4*u3*v1*v3*a33**2*m1**2*n1**3 - 2*u3*v1*a33*m1*n1**4*n3 + 4
*u3*v2*v3*a33**2*m1**2*n1**2*n2 - 2*u3*v2*a33*m1*n1**3*n2*n3 - 4*u3*v3**3*a33**3
*m1**3*n1 + 10*u3*v3**2*a33**2*m1**2*n1**2*n3 + u3*(n1**4*n2**2*n3 - 3*n1**4*n3
**3) + 2*v1*v2*a33*m1**2*n1**3*n2 - 2*v1*v3**2*a33**2*m1**3*n1**2 + 4*v1*v3*a33*
m1**2*n1**3*n3 + v1*( - m1*n1**4*n2**2 + m1*n1**4*n3**2) + v2**2*( - a33*m1**2*
n1**4 + a33*m1**2*n1**2*n2**2) - 2*v2*v3**2*a33**2*m1**3*n1*n2 + 4*v2*v3*a33*m1
**2*n1**2*n2*n3 + v2*( - m1*n1**3*n2**3 + m1*n1**3*n2*n3**2) + v3**4*a33**3*m1**
4 - 4*v3**3*a33**2*m1**3*n1*n3 + v3**2*( - a33*m1**2*n1**4 + a33*m1**2*n1**2*n2
**2 + 2*a33*m1**2*n1**2*n3**2) + v3*( - 2*m1*n1**3*n2**2*n3 + 4*m1*n1**3*n3**3)$