Solution 1 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
2 2 2
2*a33 *m2*n3*r214 - m2*n2 *n3*r4119 + 2*m2*n2 *n3*r464
r10=--------------------------------------------------------
3
a33 *n2
r11
2 2 2 2 2
2*a33 *m2*r214 - m2*n2 *r4119 + 2*m2*n2 *r464 - m2*n3 *r4119 + 2*m2*n3 *r464
=------------------------------------------------------------------------------
3
2*a33
2 2 2 2
r12=(2*a33 *m2*n1*r214 - m2*n1*n2 *r4119 + 2*m2*n1*n2 *r464 - m2*n1*n3 *r4119
2 3
+ 2*m2*n1*n3 *r464)/(2*a33 *n2)
2 2 2 3 3
- 2*a33 *n3*r214 + n2 *n3*r4119 - 2*n2 *n3*r464 - n3 *r4119 + 2*n3 *r464
r13=---------------------------------------------------------------------------
3
2*a33
2 3 3 2 2
- 2*a33 *n2*r214 + n2 *r4119 - 2*n2 *r464 - n2*n3 *r4119 + 2*n2*n3 *r464
r14=---------------------------------------------------------------------------
3
2*a33
2 2 2 2
r15=( - 2*a33 *n1*r214 + n1*n2 *r4119 - 2*n1*n2 *r464 - n1*n3 *r4119
2 3
+ 2*n1*n3 *r464)/(2*a33 )
2 2 2 2 2 2 2 2
r20=( - 2*a33 *m2 *r214 - m2 *n1 *r4119 - 2*m2 *n1 *r464 + m2 *n2 *r4119
2 2 2 2 2 2
- 2*m2 *n2 *r464 + 4*m2 *n3 *r4119)/(2*a33 *n2 )
2 2
2*m2 *n3*r4119 + 2*m2 *n3*r464
r21=--------------------------------
2
a33 *n2
2 2 2 2 2 2 2 2
- m2 *n1 *r4119 - 2*m2 *n1 *r464 + m2 *n2 *r4119 + 2*m2 *n2 *r464
r22=--------------------------------------------------------------------
2 2
2*a33 *n2
2 2
2*m2 *n1*n3*r4119 + 2*m2 *n1*n3*r464
r23=--------------------------------------
2 2
a33 *n2
2 2
m2 *n1*r4119 + 2*m2 *n1*r464
r24=------------------------------
2
a33 *n2
2 2 2 2
2*a33 *m2*r214 + 2*m2*n2 *r464 - 2*m2*n3 *r4119 + 2*m2*n3 *r464
r26=-----------------------------------------------------------------
2
a33 *n2
- m2*n3*r4119
r27=----------------
2
a33
- m2*n1*n3*r4119
r28=-------------------
2
a33 *n2
- 2*m2*n3*r4119 + 2*m2*n3*r464
r210=---------------------------------
2
a33
- m2*n1*r4119
r212=----------------
2
a33
n2*n3*r4119 - 2*n2*n3*r464
r213=----------------------------
2
a33
- 2*m2*n1*n3*r4119 + 2*m2*n1*n3*r464
r215=---------------------------------------
2
a33 *n2
- m2*n1*r4119
r216=----------------
2
a33
2 2
- m2*n1 *r4119 + m2*n2 *r4119
r217=--------------------------------
2
a33 *n2
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
2*a33 *r214 + n1 *r4119 - 2*n1 *r464 - n2 *r4119 + 2*n2 *r464
r220=---------------------------------------------------------------
2
2*a33
3 2
- 2*m2 *n3*r4119 + m2*n2 *n3*r483
r30=------------------------------------
3
a33*n2
3 3 2
- 2*m2 *r4119 - 2*m2 *r464 + m2*n2 *r483
r31=-------------------------------------------
2
2*a33*n2
m2*n3*r483
r32=------------
a33*n2
m2*r483
r33=---------
2*a33
3 3 2
- 2*m2 *n1*r4119 - 2*m2 *n1*r464 + m2*n1*n2 *r483
r34=----------------------------------------------------
3
2*a33*n2
r35=0
m2*n1*r483
r36=------------
2*a33*n2
m2*n3*r483
r37=------------
a33*n2
m2*r483
r38=---------
2*a33
m2*n1*r483
r39=------------
2*a33*n2
2 2 2
10*m2 *n3*r4119 - 2*m2 *n3*r464 - n2 *n3*r483
r310=-----------------------------------------------
2
2*a33*n2
2 2 2
4*m2 *r4119 + 4*m2 *r464 + n2 *r483
r311=-------------------------------------
2*a33*n2
- n3*r483
r312=------------
2*a33
2 2
2*m2 *n1*r4119 + 2*m2 *n1*r464
r313=--------------------------------
2
a33*n2
r314=0
- n3*r483
r315=------------
2*a33
- 2*m2*n3*r4119 + 4*m2*n3*r464
r316=---------------------------------
a33*n2
m2*r464
r317=---------
a33
m2*n1*r464
r318=------------
a33*n2
- n3*r464
r319=------------
a33
2 2 2
2*m2 *r4119 - 2*m2 *r464 - n2 *r483
r320=-------------------------------------
2*a33*n2
r323=0
- n2*r483
r325=------------
2*a33
- 3*m2*r4119 + m2*r464
r326=-------------------------
a33
r328=0
- n2*r464
r329=------------
a33
2*m2*n3*r4119
r330=---------------
a33*n2
m2*n1*r4119 + m2*n1*r464
r332=--------------------------
a33*n2
- n3*r4119 + n3*r464
r333=-----------------------
a33
- n2*r4119 + n2*r464
r334=-----------------------
a33
2 2 2
2*m2 *n1*r4119 - 2*m2 *n1*r464 - n1*n2 *r483
r335=----------------------------------------------
2
2*a33*n2
r336=0
- n1*r483
r337=------------
2*a33
r338=0
n2*r483
r339=---------
2*a33
- n1*r483
r340=------------
2*a33
- 2*m2*n1*r4119 + 2*m2*n1*r464
r341=---------------------------------
a33*n2
r342=0
r343=0
- n1*r464
r344=------------
a33
r345=0
- m2*r4119 - m2*r464
r347=-----------------------
a33
r348=0
- n1*r4119 + n1*r464
r349=-----------------------
a33
2*m2*n3*r4119
r350=---------------
a33*n2
m2*r4119 + m2*r464
r351=--------------------
a33
m2*n1*r4119 + m2*n1*r464
r352=--------------------------
a33*n2
- n3*r4119 + n3*r464
r353=-----------------------
a33
- n2*r4119 + n2*r464
r354=-----------------------
a33
- n1*r4119 + n1*r464
r355=-----------------------
a33
4 2 2
m2 *r4119 - m2 *n2 *r483
r40=--------------------------
4
2*n2
r41=0
2
- m2 *r483
r42=-------------
2
2*n2
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
2
- m2 *r483
r49=-------------
2
2*n2
r410=0
r411=0
r412=0
r413=0
3 2
- 2*m2 *r4119 + m2*n2 *r483
r415=------------------------------
3
n2
r416=0
m2*r483
r417=---------
n2
r418=0
r419=0
r420=0
r421=0
m2*r483
r422=---------
n2
r423=0
r424=0
2 2 2
4*m2 *r4119 - 2*m2 *r464 + n2 *r483
r425=-------------------------------------
2
2*n2
r426=0
r427=0
r428=0
r429=0
2*m2*r464
r431=-----------
n2
r432=0
r433=0
r435=0
r439=0
r442=0
r444=0
r445=0
r448=0
r450=0
r451=0
r453=0
r454=0
2 2
- 2*m2 *r4119 + n2 *r483
r455=---------------------------
2
2*n2
r458=0
r483
r460=------
2
r463=0
r465=0
r467=0
r468=0
r4119
r469=-------
2
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r478=0
r479=0
r480=0
r481=0
r482=0
r484=0
r485=0
r486=0
r487=0
r488=0
r489=0
r490=0
r493=0
r495=0
r496=0
r498=0
r499=0
r4100=0
r4102=0
r4103=0
r4104=0
2 2
- 2*m2 *r4119 + n2 *r483
r4105=---------------------------
2
2*n2
r4106=0
r483
r4107=------
2
r4108=0
r4109=0
r4110=r483
2*m2*r4119
r4111=------------
n2
r4112=0
r4113=0
r4114=r464
r4115=0
r4117=0
r4118=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4119
r4125=-------
2
m3=0
m2*n1
m1=-------
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
2*m2*r4119
r461=------------
n2
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, r214, r483, r464, n3, m2, 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.
{n1,a33,n1 + i*n2,n1 - i*n2,n3}
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*n2 - m2*n1,
m3}$
The system of equations related to the Hamiltonian HAM:
2 v1*m2*n1
HAM=u1*n1 + u2*n2 + u3 *a33 + u3*n3 + ---------- + v2*m2
n2
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
3 2 3 2 2 4 2 2 3 3 2 2 3
FI=u1 *a33 *n1*n2 + u1 *u2*a33 *n2 + u1 *u3 *a33 *n2 + u1 *u3*a33 *n2 *n3
2 2 2 2 2 3
+ u1 *v1*a33 *m2*n1*n2 + u1 *v2*a33 *m2*n2
2 2 3 5 2 2 3 2 3
+ u1 *( - a33*n1 *n2 + a33*n2 ) + u1*u2 *a33 *n1*n2 - u1*u2*v1*a33 *m2*n2
4 2 2 3 2 2
- 2*u1*u2*a33*n1*n2 - u1*u3 *a33 *n1*n2 + 2*u1*u3*v3*a33 *m2*n1*n2
3 2 2 2 2
- 2*u1*u3*a33*n1*n2 *n3 - u1*v3 *a33 *m2 *n1*n2 + 2*u1*v3*a33*m2*n1*n2 *n3
5 3 2 3 2 4 2 2 3 3
+ u1*( - n1*n2 + n1*n2 *n3 ) + u2 *a33 *n2 + u2 *u3 *a33 *n2
2 2 3 2 2 2 2 2 4
+ u2 *u3*a33 *n2 *n3 + u2 *v1*a33 *m2*n1*n2 - u2*u3 *a33 *n2
2 3 4 2 2 2 2
+ u2*u3*v3*a33 *m2*n2 - 2*u2*u3*a33*n2 *n3 - u2*v3 *a33 *m2 *n2
3 6 4 2 3 3 2
+ 2*u2*v3*a33*m2*n2 *n3 + u2*( - n2 + n2 *n3 ) + 2*u3 *v3*a33 *m2*n2
3 2 3 2 2 2 2 2 3
- u3 *a33 *n2 *n3 + u3 *v1*a33 *m2*n1*n2 + u3 *v2*a33 *m2*n2
2 2 3 2 2 2 2 2 2
- u3 *v3 *a33 *m2 *n2 + 4*u3 *v3*a33 *m2*n2 *n3 + 2*u3*v1*v3*a33 *m2 *n1*n2
2 2 2 2 2 2
+ 2*u3*v2*v3*a33 *m2 *n2 - u3*v3 *a33 *m2 *n2*n3
4 2 2 5 3 3
+ u3*v3*(2*a33*m2*n2 + 2*a33*m2*n2 *n3 ) + u3*( - n2 *n3 + n2 *n3 )
2 2 2 2 3 2
+ 2*v1*v2*a33*m2 *n1*n2 - v1*v3 *a33 *m2 *n1 + 2*v1*v3*a33*m2 *n1*n2*n3
4 2 2 2 2 2 2 3
+ v1*(m2*n1*n2 + m2*n1*n2 *n3 ) + v2 *( - a33*m2 *n1 *n2 + a33*m2 *n2 )
2 2 3 2 2 5 3 2
- v2*v3 *a33 *m2 *n2 + 2*v2*v3*a33*m2 *n2 *n3 + v2*(m2*n2 + m2*n2 *n3 )
2 2 2 2 3 4
+ v3 *( - a33*m2 *n1 *n2 - a33*m2 *n2 ) + 2*v3*m2*n2 *n3
which the program can not factorize further.
{HAM,FI} = {2,
n2,
n2,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
m2,
u1*n2*n3 - u3*n1*n2 - v3*m2*n1
u1*u3*a33*n2 + ---------- + ------------- + -------------}
2 2 2
2 2 2 2 2 2 2 2 2 2
FI=2*u1 *v1 *a33*n2 + u1 *v2 *a33*n2 + u1 *v3 *a33*n2 + 2*u1*u3*v1*v3*a33*n2
2 2 3 2 2 2 2
- u1*v1 *n1*n2 + u1*v1*v2*n2 - u1*v2 *n1*n2 - u1*v3 *n1*n2
2 2 2 2 2 2 2 3 2 3
+ u2 *v1 *a33*n2 + u2 *v3 *a33*n2 - u2*v1 *n2 - u2*v3 *n2
2 2 2 2 2 2
+ u3 *v3 *a33*n2 + 2*u3*v1 *v3*a33*m2*n2 - u3*v1 *n2 *n3
2 2 2 3 3
+ 2*u3*v2 *v3*a33*m2*n2 - u3*v2 *n2 *n3 + u3*v2*v3*n2 + 2*u3*v3 *a33*m2*n2
2 2 3 2 2 2 2 2
- u3*v3 *n2 *n3 + v1 *m2*n1*n2 + v1 *v2*m2*n2 - v1 *v3 *a33*m2
2 2 2 3 2
+ 2*v1 *v3*m2*n2*n3 + v1*v2 *m2*n1*n2 + v1*v3 *m2*n1*n2 + v2 *m2*n2
2 2 2 2 2 2 4 2
- v2 *v3 *a33*m2 + 2*v2 *v3*m2*n2*n3 + v2*v3 *m2*n2 - v3 *a33*m2
3
+ 2*v3 *m2*n2*n3
which the program can not factorize further.
{HAM,FI} = {4,
u1*v1 + u2*v2 + u3*v3,
n2,
2 u1*v2*a33*n2*n3 2
u1*u3*v2*a33 *n2 + ----------------- + u2*u3*v1*a33 *n2
2
2
u2*v1*a33*n2*n3 - u2*v3*a33*n1*n2 - u3*v1*a33*n2
+ ----------------- + -------------------- + ------------------
2 2 2
2
- u3*v2*a33*n1*n2 - v1*n2 *n3 - v2*v3*a33*m2*n1
+ -------------------- + -------------- + --------------------
2 4 2
2
v3*n1*n2
+ -----------}
4
2 2 2 2 2 3
FI=u1 *a33*n2 - u1*n1*n2 + u2 *a33*n2 - u2*n2 + 2*u3*v3*a33*m2*n2
2 2 2 2
- u3*n2 *n3 + v1*m2*n1*n2 + v2*m2*n2 - v3 *a33*m2 + 2*v3*m2*n2*n3
which the program can not factorize further.
{HAM,FI} = 0
4 3 4 3 2 4 2 2 3 4 2 2 5
FI=u1 *a33 *n2 - 2*u1 *a33 *n1*n2 + 2*u1 *u2 *a33 *n2 - 2*u1 *u2*a33 *n2
2 3 3 2 2 4 2 2 3
+ 4*u1 *u3*v3*a33 *m2*n2 - 2*u1 *u3*a33 *n2 *n3 + 2*u1 *v1*a33 *m2*n1*n2
2 2 4 2 2 3 2 2 2 2 3
+ 2*u1 *v2*a33 *m2*n2 - 2*u1 *v3 *a33 *m2 *n2 + 4*u1 *v3*a33 *m2*n2 *n3
2 2 4 6 2 2 4
+ u1 *(a33*n1 *n2 - a33*n2 ) - 2*u1*u2 *a33 *n1*n2
2 4 5 2 3
- 2*u1*u2*v1*a33 *m2*n2 + 2*u1*u2*a33*n1*n2 - 4*u1*u3*v3*a33 *m2*n1*n2
4 2 3 5
+ 2*u1*u3*a33*n1*n2 *n3 + u1*v1*( - 2*a33*m2*n1 *n2 + 2*a33*m2*n2 )
4 2 2 2 2
- 2*u1*v2*a33*m2*n1*n2 + 2*u1*v3 *a33 *m2 *n1*n2
3 6 4 2 4 3 4
- 4*u1*v3*a33*m2*n1*n2 *n3 + u1*(n1*n2 - n1*n2 *n3 ) + u2 *a33 *n2
3 2 5 2 3 3 2 2 4
- 2*u2 *a33 *n2 + 4*u2 *u3*v3*a33 *m2*n2 - 2*u2 *u3*a33 *n2 *n3
2 2 3 2 2 3 2 2 2 2 3
+ 2*u2 *v1*a33 *m2*n1*n2 - 2*u2 *v3 *a33 *m2 *n2 + 4*u2 *v3*a33 *m2*n2 *n3
2 4 5 4
- 6*u2*u3*v3*a33 *m2*n2 + 2*u2*u3*a33*n2 *n3 - 2*u2*v1*a33*m2*n1*n2
2 2 2 3 4 7 5 2
+ 2*u2*v3 *a33 *m2 *n2 - 4*u2*v3*a33*m2*n2 *n3 + u2*(n2 - n2 *n3 )
2 2 3 2 2 2 2 3
+ 4*u3 *v3 *a33 *m2 *n2 - 4*u3 *v3*a33 *m2*n2 *n3
2 2 2 3
+ 4*u3*v1*v3*a33 *m2 *n1*n2 - 2*u3*v1*a33*m2*n1*n2 *n3
2 2 3 4 3 3 3
+ 4*u3*v2*v3*a33 *m2 *n2 - 2*u3*v2*a33*m2*n2 *n3 - 4*u3*v3 *a33 *m2 *n2
2 2 2 2 3 2 6 4 3
+ 10*u3*v3 *a33 *m2 *n2 *n3 - 4*u3*v3*a33*m2*n2 *n3 + u3*(n2 *n3 - n2 *n3 )
2 3 2 2 3
+ 2*v1*v2*a33*m2 *n1*n2 - 2*v1*v3 *a33 *m2 *n1*n2
2 2 5 3 2
+ 4*v1*v3*a33*m2 *n1*n2 *n3 + v1*( - m2*n1*n2 - m2*n1*n2 *n3 )
2 2 2 2 2 4 2 2 3 2
+ v2 *( - a33*m2 *n1 *n2 + a33*m2 *n2 ) - 2*v2*v3 *a33 *m2 *n2
2 3 6 4 2 4 3 4
+ 4*v2*v3*a33*m2 *n2 *n3 + v2*( - m2*n2 - m2*n2 *n3 ) + v3 *a33 *m2
3 2 3
- 4*v3 *a33 *m2 *n2*n3
2 2 2 2 2 4 2 2 2
+ v3 *( - a33*m2 *n1 *n2 + a33*m2 *n2 + 4*a33*m2 *n2 *n3 )
5
- 2*v3*m2*n2 *n3
which the program can not factorize further.
{HAM,FI} = {4,
n2,
n2,
n2,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
m2,
u1*n2*n3 - u3*n1*n2 - v3*m2*n1
u1*u3*a33*n2 + ---------- + ------------- + -------------}
2 2 2
And again in machine readable form:
HAM=u1*n1 + u2*n2 + u3**2*a33 + u3*n3 + (v1*m2*n1)/n2 + v2*m2$
FI=u1**3*a33**2*n1*n2**3 + u1**2*u2*a33**2*n2**4 + u1**2*u3**2*a33**3*n2**3 + u1
**2*u3*a33**2*n2**3*n3 + u1**2*v1*a33**2*m2*n1*n2**2 + u1**2*v2*a33**2*m2*n2**3
+ u1**2*( - a33*n1**2*n2**3 + a33*n2**5) + u1*u2**2*a33**2*n1*n2**3 - u1*u2*v1*
a33**2*m2*n2**3 - 2*u1*u2*a33*n1*n2**4 - u1*u3**2*a33**2*n1*n2**3 + 2*u1*u3*v3*
a33**2*m2*n1*n2**2 - 2*u1*u3*a33*n1*n2**3*n3 - u1*v3**2*a33**2*m2**2*n1*n2 + 2*
u1*v3*a33*m2*n1*n2**2*n3 + u1*( - n1*n2**5 + n1*n2**3*n3**2) + u2**3*a33**2*n2**
4 + u2**2*u3**2*a33**3*n2**3 + u2**2*u3*a33**2*n2**3*n3 + u2**2*v1*a33**2*m2*n1*
n2**2 - u2*u3**2*a33**2*n2**4 + u2*u3*v3*a33**2*m2*n2**3 - 2*u2*u3*a33*n2**4*n3
- u2*v3**2*a33**2*m2**2*n2**2 + 2*u2*v3*a33*m2*n2**3*n3 + u2*( - n2**6 + n2**4*
n3**2) + 2*u3**3*v3*a33**3*m2*n2**2 - u3**3*a33**2*n2**3*n3 + u3**2*v1*a33**2*m2
*n1*n2**2 + u3**2*v2*a33**2*m2*n2**3 - u3**2*v3**2*a33**3*m2**2*n2 + 4*u3**2*v3*
a33**2*m2*n2**2*n3 + 2*u3*v1*v3*a33**2*m2**2*n1*n2 + 2*u3*v2*v3*a33**2*m2**2*n2
**2 - u3*v3**2*a33**2*m2**2*n2*n3 + u3*v3*(2*a33*m2*n2**4 + 2*a33*m2*n2**2*n3**2
) + u3*( - n2**5*n3 + n2**3*n3**3) + 2*v1*v2*a33*m2**2*n1*n2**2 - v1*v3**2*a33**
2*m2**3*n1 + 2*v1*v3*a33*m2**2*n1*n2*n3 + v1*(m2*n1*n2**4 + m2*n1*n2**2*n3**2) +
v2**2*( - a33*m2**2*n1**2*n2 + a33*m2**2*n2**3) - v2*v3**2*a33**2*m2**3*n2 + 2*
v2*v3*a33*m2**2*n2**2*n3 + v2*(m2*n2**5 + m2*n2**3*n3**2) + v3**2*( - a33*m2**2*
n1**2*n2 - a33*m2**2*n2**3) + 2*v3*m2*n2**4*n3$
FI=2*u1**2*v1**2*a33*n2**2 + u1**2*v2**2*a33*n2**2 + u1**2*v3**2*a33*n2**2 + 2*
u1*u3*v1*v3*a33*n2**2 - u1*v1**2*n1*n2**2 + u1*v1*v2*n2**3 - u1*v2**2*n1*n2**2 -
u1*v3**2*n1*n2**2 + u2**2*v1**2*a33*n2**2 + u2**2*v3**2*a33*n2**2 - u2*v1**2*n2
**3 - u2*v3**2*n2**3 + u3**2*v3**2*a33*n2**2 + 2*u3*v1**2*v3*a33*m2*n2 - u3*v1**
2*n2**2*n3 + 2*u3*v2**2*v3*a33*m2*n2 - u3*v2**2*n2**2*n3 + u3*v2*v3*n2**3 + 2*u3
*v3**3*a33*m2*n2 - u3*v3**2*n2**2*n3 + v1**3*m2*n1*n2 + v1**2*v2*m2*n2**2 - v1**
2*v3**2*a33*m2**2 + 2*v1**2*v3*m2*n2*n3 + v1*v2**2*m2*n1*n2 + v1*v3**2*m2*n1*n2
+ v2**3*m2*n2**2 - v2**2*v3**2*a33*m2**2 + 2*v2**2*v3*m2*n2*n3 + v2*v3**2*m2*n2
**2 - v3**4*a33*m2**2 + 2*v3**3*m2*n2*n3$
FI=u1**2*a33*n2**2 - u1*n1*n2**2 + u2**2*a33*n2**2 - u2*n2**3 + 2*u3*v3*a33*m2*
n2 - u3*n2**2*n3 + v1*m2*n1*n2 + v2*m2*n2**2 - v3**2*a33*m2**2 + 2*v3*m2*n2*n3$
FI=u1**4*a33**3*n2**4 - 2*u1**3*a33**2*n1*n2**4 + 2*u1**2*u2**2*a33**3*n2**4 - 2
*u1**2*u2*a33**2*n2**5 + 4*u1**2*u3*v3*a33**3*m2*n2**3 - 2*u1**2*u3*a33**2*n2**4
*n3 + 2*u1**2*v1*a33**2*m2*n1*n2**3 + 2*u1**2*v2*a33**2*m2*n2**4 - 2*u1**2*v3**2
*a33**3*m2**2*n2**2 + 4*u1**2*v3*a33**2*m2*n2**3*n3 + u1**2*(a33*n1**2*n2**4 -
a33*n2**6) - 2*u1*u2**2*a33**2*n1*n2**4 - 2*u1*u2*v1*a33**2*m2*n2**4 + 2*u1*u2*
a33*n1*n2**5 - 4*u1*u3*v3*a33**2*m2*n1*n2**3 + 2*u1*u3*a33*n1*n2**4*n3 + u1*v1*(
- 2*a33*m2*n1**2*n2**3 + 2*a33*m2*n2**5) - 2*u1*v2*a33*m2*n1*n2**4 + 2*u1*v3**2
*a33**2*m2**2*n1*n2**2 - 4*u1*v3*a33*m2*n1*n2**3*n3 + u1*(n1*n2**6 - n1*n2**4*n3
**2) + u2**4*a33**3*n2**4 - 2*u2**3*a33**2*n2**5 + 4*u2**2*u3*v3*a33**3*m2*n2**3
- 2*u2**2*u3*a33**2*n2**4*n3 + 2*u2**2*v1*a33**2*m2*n1*n2**3 - 2*u2**2*v3**2*
a33**3*m2**2*n2**2 + 4*u2**2*v3*a33**2*m2*n2**3*n3 - 6*u2*u3*v3*a33**2*m2*n2**4
+ 2*u2*u3*a33*n2**5*n3 - 2*u2*v1*a33*m2*n1*n2**4 + 2*u2*v3**2*a33**2*m2**2*n2**3
- 4*u2*v3*a33*m2*n2**4*n3 + u2*(n2**7 - n2**5*n3**2) + 4*u3**2*v3**2*a33**3*m2
**2*n2**2 - 4*u3**2*v3*a33**2*m2*n2**3*n3 + 4*u3*v1*v3*a33**2*m2**2*n1*n2**2 - 2
*u3*v1*a33*m2*n1*n2**3*n3 + 4*u3*v2*v3*a33**2*m2**2*n2**3 - 2*u3*v2*a33*m2*n2**4
*n3 - 4*u3*v3**3*a33**3*m2**3*n2 + 10*u3*v3**2*a33**2*m2**2*n2**2*n3 - 4*u3*v3*
a33*m2*n2**3*n3**2 + u3*(n2**6*n3 - n2**4*n3**3) + 2*v1*v2*a33*m2**2*n1*n2**3 -
2*v1*v3**2*a33**2*m2**3*n1*n2 + 4*v1*v3*a33*m2**2*n1*n2**2*n3 + v1*( - m2*n1*n2
**5 - m2*n1*n2**3*n3**2) + v2**2*( - a33*m2**2*n1**2*n2**2 + a33*m2**2*n2**4) -
2*v2*v3**2*a33**2*m2**3*n2**2 + 4*v2*v3*a33*m2**2*n2**3*n3 + v2*( - m2*n2**6 -
m2*n2**4*n3**2) + v3**4*a33**3*m2**4 - 4*v3**3*a33**2*m2**3*n2*n3 + v3**2*( -
a33*m2**2*n1**2*n2**2 + a33*m2**2*n2**4 + 4*a33*m2**2*n2**2*n3**2) - 2*v3*m2*n2
**5*n3$