Solution 17 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
2 2 3
a33 *n3*r26 + i*n2 *n3*r453 - i*n3 *r453
r10=------------------------------------------
3
a33
2 3 2
a33 *n2*r26 + i*n2 *r453 - i*n2*n3 *r453
r11=------------------------------------------
3
a33
2 3 2
i*a33 *n2*r26 - n2 *r453 + n2*n3 *r453
r12=----------------------------------------
3
a33
r13=0
r14=0
r15=0
3 3 2 2
r20=(i*a33 *m1*r26 - a33 *m2*r26 + 2*a33 *b33*n2*r26 + a33*m1*n2 *r453
2 2 2 3
+ a33*m1*n3 *r453 - i*a33*m2*n2 *r453 + i*a33*m2*n3 *r453 + a33*n2 *r494
2 2 3
+ a33*n2*n3 *r494 - 2*i*b33*n2*n3 *r453)/(2*a33 *n2)
i*a33*m2*n3*r453 + a33*n2*n3*r494 - i*b33*n2*n3*r453
r21=------------------------------------------------------
3
a33
2 2
a33*m1*n2*r453 + i*a33*m2*n2*r453 + a33*n2 *r494 - 2*i*b33*n2 *r453
r22=---------------------------------------------------------------------
3
a33
i*a33*m1*n3*r453 + i*a33*n2*n3*r494 + b33*n2*n3*r453
r23=------------------------------------------------------
3
a33
2 2
i*a33*m1*n2*r453 - a33*m2*n2*r453 + i*a33*n2 *r494 + 2*b33*n2 *r453
r24=---------------------------------------------------------------------
3
a33
i*n2*n3*r453
r27=--------------
2
a33
- n2*n3*r453
r28=---------------
2
a33
i*n2*n3*r453
r210=--------------
2
a33
2 2
- i*a33 *r26 - n3 *r453
r212=--------------------------
2
a33
r213=0
r214=0
- n2*n3*r453
r215=---------------
2
a33
2 2 2
i*a33 *r26 - 2*n2 *r453 + n3 *r453
r216=------------------------------------
2
a33
2
- 2*i*n2 *r453
r217=-----------------
2
a33
r218=0
r219=0
r220=0
r30=(i*a33*m1*n3*r494 - a33*m2*n3*r494 + 2*a33*n2*n3*r422 + 2*b33*n2*n3*r494
2
+ 2*c12*n2*n3*r453)/(2*a33 *n2)
2 2 2 2 2
r31=( - a33 *m1*m2*r453 + i*a33 *m1*n2*r494 - i*a33 *m2 *r453 - a33 *m2*n2*r494
2 2
+ 2*a33 *n2 *r422 + a33*b33*m1*n2*r453 + 3*i*a33*b33*m2*n2*r453
2 2 2 2 3
+ 2*a33*b33*n2 *r494 + 2*a33*c12*n2 *r453 - 2*i*b33 *n2 *r453)/(2*a33 *n2)
n3*r422
r32=---------
a33
n2*r422
r33=---------
a33
2 2 2 2 2
r34=( - a33 *m1 *r453 - i*a33 *m1*m2*r453 - a33 *m1*n2*r494 - i*a33 *m2*n2*r494
2 2
+ 2*i*a33 *n2 *r422 + 3*i*a33*b33*m1*n2*r453 - a33*b33*m2*n2*r453
2 2 2 2 3
+ 2*i*a33*b33*n2 *r494 + 2*i*a33*c12*n2 *r453 + 2*b33 *n2 *r453)/(2*a33
*n2)
2*i*c12*n3*r453
r35=-----------------
2
a33
i*a33*n2*r422 + 2*i*c12*n2*r453
r36=---------------------------------
2
a33
a33*n3*r422 + 2*c12*n3*r453
r37=-----------------------------
2
a33
n2*r422
r38=---------
a33
i*a33*n2*r422 + 2*i*c12*n2*r453
r39=---------------------------------
2
a33
r310=( - a33*m1*n3*r453 - i*a33*m2*n3*r453 + 2*a33*n2*n3*r446 + 2*a33*n2*n3*r494
2
+ 2*i*b33*n2*n3*r453)/(2*a33 *n2)
i*a33*m2*r453 + a33*n2*r446 + a33*n2*r494 - i*b33*n2*r453
r311=-----------------------------------------------------------
2
a33
r312=0
i*a33*m1*r453 + i*a33*n2*r446 + i*a33*n2*r494 + b33*n2*r453
r313=-------------------------------------------------------------
2
a33
r314=0
r315=0
2*i*n3*r453
r316=-------------
a33
i*n2*r453
r317=-----------
a33
- n2*r453
r318=------------
a33
r319=0
- a33*m1*r453 - i*a33*m2*r453 + 2*i*b33*n2*r453
r320=--------------------------------------------------
2
2*a33
n3*r446
r321=---------
a33
n2*r446
r322=---------
a33
- i*n3*r494
r323=--------------
a33
a33*m2*r453 + i*a33*n2*r446 - i*a33*n2*r494 - b33*n2*r453
r324=-----------------------------------------------------------
2
a33
a33*m1*r453 + a33*n2*r494 - i*b33*n2*r453
r325=-------------------------------------------
2
a33
i*n2*r453
r326=-----------
a33
r327=0
n3*r453
r328=---------
a33
r329=0
r330=0
r331=0
n2*r453
r332=---------
a33
r333=0
r334=0
- i*a33*m1*r453 + a33*m2*r453 - 2*b33*n2*r453
r335=------------------------------------------------
2
2*a33
i*n3*r494
r336=-----------
a33
- a33*m2*r453 + i*a33*n2*r494 + b33*n2*r453
r337=----------------------------------------------
2
a33
n3*r446
r338=---------
a33
- a33*m1*r453 + a33*n2*r446 - a33*n2*r494 + i*b33*n2*r453
r339=------------------------------------------------------------
2
a33
i*n2*r446
r340=-----------
a33
- n2*r453
r341=------------
a33
- n3*r453
r342=------------
a33
r343=0
r344=0
r345=0
- n2*r453
r346=------------
a33
i*n2*r453
r347=-----------
a33
r348=0
r349=0
r350=0
- i*n2*r453
r351=--------------
a33
r352=0
r353=0
r354=0
r355=0
2 2 2 2
r40=( - a33 *m1 *r494 - 2*i*a33 *m1*m2*r494 + 4*i*a33 *m1*n2*r422
2 2 2
+ a33 *m2 *r494 - 4*a33 *m2*n2*r422 + 4*i*a33*b33*m1*n2*r494
2
- 4*a33*b33*m2*n2*r494 + 8*a33*b33*n2 *r422 + 4*i*a33*c12*m1*n2*r453
2 2 2 2 2
- 4*a33*c12*m2*n2*r453 + 4*b33 *n2 *r494 + 8*b33*c12*n2 *r453)/(8*a33 *n2
)
r41=0
i*a33*m1*r422 - a33*m2*r422 + 2*b33*n2*r422
r42=---------------------------------------------
2*a33*n2
r43=0
r44=0
r45=0
- a33*c12*m1*r453 - i*a33*c12*m2*r453 + 2*i*b33*c12*n2*r453
r46=--------------------------------------------------------------
2
a33 *n2
r47=0
r48=0
2 2
r49=(i*a33 *m1*r422 - a33 *m2*r422 + 2*a33*b33*n2*r422 + 2*i*a33*c12*m1*r453
2
- 2*a33*c12*m2*r453 + 4*b33*c12*n2*r453)/(2*a33 *n2)
r410=0
r411=0
r412=0
r413=0
r415=(i*a33*m1*r446 + i*a33*m1*r494 - a33*m2*r446 - a33*m2*r494 + 2*a33*n2*r422
+ 2*b33*n2*r446 + 2*b33*n2*r494 - 2*c12*n2*r453)/(2*a33*n2)
r416=0
a33*r422 - 2*c12*r453
r417=-----------------------
a33
r418=0
r419=0
2*i*c12*r453
r420=--------------
a33
r421=0
r423=0
r424=0
r425=
- a33*m1*r453 - i*a33*m2*r453 + 2*a33*n2*r446 + a33*n2*r494 + 2*i*b33*n2*r453
--------------------------------------------------------------------------------
2*a33*n2
r426=0
r427=0
r428=0
r429=0
r432=0
r433=0
r435=0
i*a33*m1*r446 - a33*m2*r446 + 2*b33*n2*r446 - 4*c12*n2*r453
r436=-------------------------------------------------------------
2*a33*n2
r437=0
- 2*c12*r453
r438=---------------
a33
r439=(a33*m1*r494 + i*a33*m2*r494 - 2*i*a33*n2*r422 - 2*i*b33*n2*r494
- 2*i*c12*n2*r453)/(2*a33*n2)
r440=0
r442=0
- i*a33*r422 - 2*i*c12*r453
r444=------------------------------
a33
r445=0
r447=0
r448= - i*r446 - i*r494
r449=0
r450=0
r451=0
r454=0
r455=0
r456=0
r458=0
r459= - i*r446
- r494
r460=---------
2
r461=0
r462=0
r463=0
r464=0
r465=0
r466=0
r467=0
r468=0
r469=0
r470=0
r471=( - a33*m1*r494 - i*a33*m2*r494 + 2*i*a33*n2*r422 + 2*i*b33*n2*r494
+ 2*i*c12*n2*r453)/(2*a33*n2)
r472=0
r473=i*r422
i*a33*m1*r446 - a33*m2*r446 + 2*b33*n2*r446 - 4*c12*n2*r453
r474=-------------------------------------------------------------
2*a33*n2
r475=0
- 4*c12*r453
r476=---------------
a33
r477=0
i*a33*r422 + 2*i*c12*r453
r478=---------------------------
a33
- 2*c12*r453
r479=---------------
a33
r480=0
r481=i*r446 + i*r494
r482=0
r483=r446
r484=0
r485=0
r486=0
r487= - r453
r488=0
r489=0
r490=0
r491=0
r492=i*r446
r493=0
r495= - i*r446
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=0
r4106=0
- r494
r4107=---------
2
r4108=0
r4109=i*r446
r4110=0
r4111=0
r4112=0
r4113=0
r4114=0
r4115=0
r4116=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
b33*n3
m3=--------
a33
n1=i*n2
c23=0
c22=2*i*c12
c13=0
c11=0
b32=0
b31=0
b23=0
b22=0
b21= - i*b33
b13=0
b12=i*b33
b11=0
a23=0
a22=0
a13=0
a12=0
a11=0
2
i*a33*b33*m1 - a33*b33*m2 + 2*i*a33*c12*n2 + 2*b33 *n2
c33=--------------------------------------------------------
2*a33*n2
r441= - i*r422
r431=i*r453
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:
r453, r422, m1, r26, r494, r446, m2, n3, b33, n2, c12,
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.
{n2,a33}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{ - i*a33*b33*m1 + a33*b33*m2 - 2*i*a33*c12*n2 + 2*a33*c33*n2 - 2*b33**2*n2,
a11,
a12,
a13,
a22,
a23,
b11,
b12 - i*b33,
b13,
b21 + i*b33,
b22,
b23,
b31,
b32,
c11,
c13,
- 2*i*c12 + c22,
c23,
n1 - i*n2,
a33*m3 - b33*n3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=i*u1*v2*b33 + i*u1*n2 - i*u2*v1*b33 + u2*n2 + u3 *a33 + u3*v3*b33 + u3*n3
2
+ 2*v1*v2*c12 + v1*m1 + 2*i*v2 *c12 + v2*m2
2
2 i*a33*b33*m1 - a33*b33*m2 + 2*i*a33*c12*n2 + 2*b33 *n2
+ v3 *--------------------------------------------------------
2*a33*n2
v3*b33*n3
+ -----------
a33
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
2 2 2
FI=2*i*u1 *v1*v2*a33*n2 - 2*i*u1*u2*v1 *a33*n2 + 2*i*u1*u2*v2 *a33*n2
2 2
+ 2*u1*u3*v1*v3*a33*n2 + 2*i*u1*u3*v2*v3*a33*n2 + 2*i*u1*v1 *n2
2 2
+ 2*u1*v1*v2*n2 + u1*v1*v3 *(i*a33*m1 - a33*m2 + 2*b33*n2)
2
+ 2*u1*v1*v3*n2*n3 - 2*i*u2 *v1*v2*a33*n2 - 2*i*u2*u3*v1*v3*a33*n2
2 2 2
+ 2*u2*u3*v2*v3*a33*n2 + 2*i*u2*v1*v2*n2 + 2*u2*v2 *n2
2
+ u2*v2*v3 *(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*u2*v2*v3*n2*n3
2 2 2 2
+ 2*u3 *v3 *a33*n2 + 2*i*u3*v1*v3*n2 + 2*u3*v2*v3*n2
3 2
+ u3*v3 *(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*u3*v3 *n2*n3
= a product of the elements of: {i,
u1*v1 + u2*v2 + u3*v3,
2 2
2*u1*v2*a33*n2 - 2*u2*v1*a33*n2 - 2*i*u3*v3*a33*n2 + 2*v1*n2 - 2*i*v2*n2
2
+ v3 *(a33*m1 + i*a33*m2 - 2*i*b33*n2) - 2*i*v3*n2*n3}
{HAM,FI} = 0
2 2 2 2 2 2 2 2
FI= - 4*u1 *v2 *a33 *n2 + 8*u1*u2*v1*v2*a33 *n2 + 8*i*u1*u3*v2*v3*a33 *n2
3 2 3
- 8*u1*v1*v2*a33*n2 + 8*i*u1*v2 *a33*n2
2 2 2 2
+ u1*v2*v3 *( - 4*a33 *m1*n2 - 4*i*a33 *m2*n2 + 8*i*a33*b33*n2 )
2 2 2 2 2 2 2
+ 8*i*u1*v2*v3*a33*n2 *n3 - 4*u2 *v1 *a33 *n2 - 8*i*u2*u3*v1*v3*a33 *n2
2 3 3
+ 8*u2*v1 *a33*n2 - 8*i*u2*v1*v2*a33*n2
2 2 2 2
+ u2*v1*v3 *(4*a33 *m1*n2 + 4*i*a33 *m2*n2 - 8*i*a33*b33*n2 )
2 2 2 2 2 3
- 8*i*u2*v1*v3*a33*n2 *n3 + 4*u3 *v3 *a33 *n2 + 8*i*u3*v1*v3*a33*n2
3
+ 8*u3*v2*v3*a33*n2
3 2 2 2
+ u3*v3 *(4*i*a33 *m1*n2 - 4*a33 *m2*n2 + 8*a33*b33*n2 )
2 2 4
+ 8*u3*v3 *a33*n2 *n3 + 8*i*v1*v2*n2
2 2 2 3 3
+ v1*v3 *( - 4*a33*m1*n2 - 4*i*a33*m2*n2 + 8*i*b33*n2 ) + 8*i*v1*v3*n2 *n3
2 4 2 2 2 3
+ 8*v2 *n2 + v2*v3 *(4*i*a33*m1*n2 - 4*a33*m2*n2 + 8*b33*n2 )
3 4 2 2 2 2 2
+ 8*v2*v3*n2 *n3 + v3 *( - a33 *m1 - 2*i*a33 *m1*m2 + a33 *m2
2 2
+ 4*i*a33*b33*m1*n2 - 4*a33*b33*m2*n2 + 4*b33 *n2 )
3 2
+ v3 *(4*i*a33*m1*n2*n3 - 4*a33*m2*n2*n3 + 8*b33*n2 *n3)
2 4 2 2
+ v3 *(4*n2 + 4*n2 *n3 )
which the program can not factorize further.
{HAM,FI} = 0
2 2
FI=2*i*u1*v2*a33*n2 - 2*i*u2*v1*a33*n2 + 2*u3*v3*a33*n2 + 2*i*v1*n2 + 2*v2*n2
2
+ v3 *(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*v3*n2*n3
= a product of the elements of: {i,
2 2
2*u1*v2*a33*n2 - 2*u2*v1*a33*n2 - 2*i*u3*v3*a33*n2 + 2*v1*n2 - 2*i*v2*n2
2
+ v3 *(a33*m1 + i*a33*m2 - 2*i*b33*n2) - 2*i*v3*n2*n3}
{HAM,FI} = 0
2 3 2
FI=2*i*u1*v1 *v2*a33*n2 + 2*i*u1*v2 *a33*n2 + 2*i*u1*v2*v3 *a33*n2
3 2 2
- 2*i*u2*v1 *a33*n2 - 2*i*u2*v1*v2 *a33*n2 - 2*i*u2*v1*v3 *a33*n2
2 2 3 3 2
+ 2*u3*v1 *v3*a33*n2 + 2*u3*v2 *v3*a33*n2 + 2*u3*v3 *a33*n2 + 2*i*v1 *n2
2 2 2 2 2
+ 2*v1 *v2*n2 + v1 *v3 *(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*v1 *v3*n2*n3
2 2 2 2 3 2
+ 2*i*v1*v2 *n2 + 2*i*v1*v3 *n2 + 2*v2 *n2
2 2 2 2 2
+ v2 *v3 *(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*v2 *v3*n2*n3 + 2*v2*v3 *n2
4 3
+ v3 *(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*v3 *n2*n3
= a product of the elements of: {i,
2 2 2
v1 + v2 + v3 ,
2 2
2*u1*v2*a33*n2 - 2*u2*v1*a33*n2 - 2*i*u3*v3*a33*n2 + 2*v1*n2 - 2*i*v2*n2
2
+ v3 *(a33*m1 + i*a33*m2 - 2*i*b33*n2) - 2*i*v3*n2*n3}
{HAM,FI} = 0
2 2 2 2 2 2 2
FI= - 2*i*u1 *v2*a33 *n2 + 2*i*u1*u2*v1*a33 *n2 - 2*u1*u2*v2*a33 *n2
2 3 2 2 2
- 2*u1*u3 *v2*a33 *n2 - 2*u1*u3*v2*a33 *n2*n3 - 2*u1*u3*v3*a33 *n2
3 2 2 2 2 2
- 4*u1*v1 *a33 *c12*n2 + 4*i*u1*v1 *v2*a33 *c12*n2 - 8*u1*v1*v2 *a33 *c12*n2
2 2 2 2
+ u1*v1*v2*( - 2*a33 *m1*n2 + 2*i*a33*b33*n2 ) - 4*u1*v1*v3 *a33 *c12*n2
3 2 2 2
- 4*i*u1*v1*a33*n2 + u1*v2 *( - 2*a33 *m2*n2 + 2*a33*b33*n2 )
2 2 3 2
+ 2*i*u1*v2*v3 *a33 *c12*n2 + u1*v2*( - 4*a33*n2 + 2*a33*n2*n3 )
2 2 2 2 2
+ u1*v3 *( - i*a33 *m1*n2 + a33 *m2*n2 - 2*a33*b33*n2 ) - 2*u1*v3*a33*n2 *n3
2 2 2 2 3 2
+ 2*u2 *v1*a33 *n2 + 2*u2*u3 *v1*a33 *n2 + 2*u2*u3*v1*a33 *n2*n3
2 2 3 2
+ 2*i*u2*u3*v3*a33 *n2 - 4*i*u2*v1 *a33 *c12*n2
2 2 2
+ u2*v1 *(2*a33 *m1*n2 - 2*i*a33*b33*n2 )
2 2 2 2
+ u2*v1*v2*(2*a33 *m2*n2 - 2*a33*b33*n2 ) - 2*i*u2*v1*v3 *a33 *c12*n2
2 3 2 2 2
- 2*u2*v1*a33*n2*n3 - 4*u2*v2 *a33 *c12*n2 - 4*u2*v2*v3 *a33 *c12*n2
2 2 2 2
+ u2*v3 *( - a33 *m1*n2 - i*a33 *m2*n2 + 2*i*a33*b33*n2 )
2 3 3 2 2 2
+ 2*i*u2*v3*a33*n2 *n3 + 2*i*u3 *v3*a33 *n2 - 2*u3 *v1*a33 *n2
2 2 2 2 2 3 3 2
+ 2*i*u3 *v2*a33 *n2 + u3 *v3 *( - a33 *m1 - i*a33 *m2 + 2*i*a33 *b33*n2)
2 2 2
+ 4*i*u3 *v3*a33 *n2*n3 + 4*i*u3*v1*v2*v3*a33 *c12*n2
2 2 2
+ u3*v1*v3*(2*i*a33 *m1*n2 + 2*a33*b33*n2 ) - 2*u3*v1*a33*n2 *n3
2 2 2 2
- 4*u3*v2 *v3*a33 *c12*n2 + u3*v2*v3*(2*i*a33 *m2*n2 - 2*i*a33*b33*n2 )
2 3 2
+ 2*i*u3*v2*a33*n2 *n3 - 2*u3*v3 *a33 *c12*n2
2 2 2
+ u3*v3 *( - a33 *m1*n3 - i*a33 *m2*n3 + 2*i*a33*b33*n2*n3)
3 2
+ 4*i*v1 *a33*c12*n2
2 2 2 2
+ v1 *v3 *(2*i*a33 *c12*m1 - 2*a33 *c12*m2 + 4*a33*b33*c12*n2)
2 2 2
+ 4*v1 *v3*a33*c12*n2*n3 + 4*i*v1*v2 *a33*c12*n2
2 2 2
+ v1*v2*v3 *( - 2*a33 *c12*m1 - 2*i*a33 *c12*m2 + 4*i*a33*b33*c12*n2)
+ 4*i*v1*v2*v3*a33*c12*n2*n3
2 2 3 2 2 2
+ v1*v2*(2*i*a33*m1*n2 - 2*a33*m2*n2 + 4*b33*n2 ) + v1*v3 *( - a33 *m1
2 2
- i*a33 *m1*m2 + 3*i*a33*b33*m1*n2 - a33*b33*m2*n2 + 2*i*a33*c12*n2
2 2 2
+ 2*b33 *n2 ) + v1*v3*(2*i*a33*m1*n2*n3 + 2*b33*n2 *n3)
4 2 2
+ v1*( - 2*n2 + 2*n2 *n3 )
2 2 2 3 2 2
+ v2 *(2*a33*m1*n2 + 2*i*a33*m2*n2 - 4*i*b33*n2 ) + v2*v3 *( - a33 *m1*m2
2 2 2
- i*a33 *m2 + a33*b33*m1*n2 + 3*i*a33*b33*m2*n2 + 2*a33*c12*n2
2 2 2
- 2*i*b33 *n2 ) + v2*v3*(2*i*a33*m2*n2*n3 - 2*i*b33*n2 *n3)
4 2 2
+ v2*(2*i*n2 - 2*i*n2 *n3 )
4 2 2 3
+ v3 *(i*a33 *c12*m1 - a33 *c12*m2 + 2*a33*b33*c12*n2) + 2*v3 *a33*c12*n2*n3
2
+ v3
2 2 2 2 2
*(a33*m1*n2 + a33*m1*n3 - i*a33*m2*n2 + i*a33*m2*n3 - 2*i*b33*n2*n3 )
3 3
+ v3*(2*i*n2 *n3 - 2*i*n2*n3 )
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
And again in machine readable form:
HAM=i*u1*v2*b33 + i*u1*n2 - i*u2*v1*b33 + u2*n2 + u3**2*a33 + u3*v3*b33 + u3*n3
+ 2*v1*v2*c12 + v1*m1 + 2*i*v2**2*c12 + v2*m2 + v3**2*(i*a33*b33*m1 - a33*b33*m2
+ 2*i*a33*c12*n2 + 2*b33**2*n2)/(2*a33*n2) + (v3*b33*n3)/a33$
FI=2*i*u1**2*v1*v2*a33*n2 - 2*i*u1*u2*v1**2*a33*n2 + 2*i*u1*u2*v2**2*a33*n2 + 2*
u1*u3*v1*v3*a33*n2 + 2*i*u1*u3*v2*v3*a33*n2 + 2*i*u1*v1**2*n2**2 + 2*u1*v1*v2*n2
**2 + u1*v1*v3**2*(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*u1*v1*v3*n2*n3 - 2*i*u2**2*
v1*v2*a33*n2 - 2*i*u2*u3*v1*v3*a33*n2 + 2*u2*u3*v2*v3*a33*n2 + 2*i*u2*v1*v2*n2**
2 + 2*u2*v2**2*n2**2 + u2*v2*v3**2*(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*u2*v2*v3*
n2*n3 + 2*u3**2*v3**2*a33*n2 + 2*i*u3*v1*v3*n2**2 + 2*u3*v2*v3*n2**2 + u3*v3**3*
(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*u3*v3**2*n2*n3$
FI= - 4*u1**2*v2**2*a33**2*n2**2 + 8*u1*u2*v1*v2*a33**2*n2**2 + 8*i*u1*u3*v2*v3*
a33**2*n2**2 - 8*u1*v1*v2*a33*n2**3 + 8*i*u1*v2**2*a33*n2**3 + u1*v2*v3**2*( - 4
*a33**2*m1*n2 - 4*i*a33**2*m2*n2 + 8*i*a33*b33*n2**2) + 8*i*u1*v2*v3*a33*n2**2*
n3 - 4*u2**2*v1**2*a33**2*n2**2 - 8*i*u2*u3*v1*v3*a33**2*n2**2 + 8*u2*v1**2*a33*
n2**3 - 8*i*u2*v1*v2*a33*n2**3 + u2*v1*v3**2*(4*a33**2*m1*n2 + 4*i*a33**2*m2*n2
- 8*i*a33*b33*n2**2) - 8*i*u2*v1*v3*a33*n2**2*n3 + 4*u3**2*v3**2*a33**2*n2**2 +
8*i*u3*v1*v3*a33*n2**3 + 8*u3*v2*v3*a33*n2**3 + u3*v3**3*(4*i*a33**2*m1*n2 - 4*
a33**2*m2*n2 + 8*a33*b33*n2**2) + 8*u3*v3**2*a33*n2**2*n3 + 8*i*v1*v2*n2**4 + v1
*v3**2*( - 4*a33*m1*n2**2 - 4*i*a33*m2*n2**2 + 8*i*b33*n2**3) + 8*i*v1*v3*n2**3*
n3 + 8*v2**2*n2**4 + v2*v3**2*(4*i*a33*m1*n2**2 - 4*a33*m2*n2**2 + 8*b33*n2**3)
+ 8*v2*v3*n2**3*n3 + v3**4*( - a33**2*m1**2 - 2*i*a33**2*m1*m2 + a33**2*m2**2 +
4*i*a33*b33*m1*n2 - 4*a33*b33*m2*n2 + 4*b33**2*n2**2) + v3**3*(4*i*a33*m1*n2*n3
- 4*a33*m2*n2*n3 + 8*b33*n2**2*n3) + v3**2*(4*n2**4 + 4*n2**2*n3**2)$
FI=2*i*u1*v2*a33*n2 - 2*i*u2*v1*a33*n2 + 2*u3*v3*a33*n2 + 2*i*v1*n2**2 + 2*v2*n2
**2 + v3**2*(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*v3*n2*n3$
FI=2*i*u1*v1**2*v2*a33*n2 + 2*i*u1*v2**3*a33*n2 + 2*i*u1*v2*v3**2*a33*n2 - 2*i*
u2*v1**3*a33*n2 - 2*i*u2*v1*v2**2*a33*n2 - 2*i*u2*v1*v3**2*a33*n2 + 2*u3*v1**2*
v3*a33*n2 + 2*u3*v2**2*v3*a33*n2 + 2*u3*v3**3*a33*n2 + 2*i*v1**3*n2**2 + 2*v1**2
*v2*n2**2 + v1**2*v3**2*(i*a33*m1 - a33*m2 + 2*b33*n2) + 2*v1**2*v3*n2*n3 + 2*i*
v1*v2**2*n2**2 + 2*i*v1*v3**2*n2**2 + 2*v2**3*n2**2 + v2**2*v3**2*(i*a33*m1 -
a33*m2 + 2*b33*n2) + 2*v2**2*v3*n2*n3 + 2*v2*v3**2*n2**2 + v3**4*(i*a33*m1 - a33
*m2 + 2*b33*n2) + 2*v3**3*n2*n3$
FI= - 2*i*u1**2*v2*a33**2*n2**2 + 2*i*u1*u2*v1*a33**2*n2**2 - 2*u1*u2*v2*a33**2*
n2**2 - 2*u1*u3**2*v2*a33**3*n2 - 2*u1*u3*v2*a33**2*n2*n3 - 2*u1*u3*v3*a33**2*n2
**2 - 4*u1*v1**3*a33**2*c12*n2 + 4*i*u1*v1**2*v2*a33**2*c12*n2 - 8*u1*v1*v2**2*
a33**2*c12*n2 + u1*v1*v2*( - 2*a33**2*m1*n2 + 2*i*a33*b33*n2**2) - 4*u1*v1*v3**2
*a33**2*c12*n2 - 4*i*u1*v1*a33*n2**3 + u1*v2**2*( - 2*a33**2*m2*n2 + 2*a33*b33*
n2**2) + 2*i*u1*v2*v3**2*a33**2*c12*n2 + u1*v2*( - 4*a33*n2**3 + 2*a33*n2*n3**2)
+ u1*v3**2*( - i*a33**2*m1*n2 + a33**2*m2*n2 - 2*a33*b33*n2**2) - 2*u1*v3*a33*
n2**2*n3 + 2*u2**2*v1*a33**2*n2**2 + 2*u2*u3**2*v1*a33**3*n2 + 2*u2*u3*v1*a33**2
*n2*n3 + 2*i*u2*u3*v3*a33**2*n2**2 - 4*i*u2*v1**3*a33**2*c12*n2 + u2*v1**2*(2*
a33**2*m1*n2 - 2*i*a33*b33*n2**2) + u2*v1*v2*(2*a33**2*m2*n2 - 2*a33*b33*n2**2)
- 2*i*u2*v1*v3**2*a33**2*c12*n2 - 2*u2*v1*a33*n2*n3**2 - 4*u2*v2**3*a33**2*c12*
n2 - 4*u2*v2*v3**2*a33**2*c12*n2 + u2*v3**2*( - a33**2*m1*n2 - i*a33**2*m2*n2 +
2*i*a33*b33*n2**2) + 2*i*u2*v3*a33*n2**2*n3 + 2*i*u3**3*v3*a33**3*n2 - 2*u3**2*
v1*a33**2*n2**2 + 2*i*u3**2*v2*a33**2*n2**2 + u3**2*v3**2*( - a33**3*m1 - i*a33
**3*m2 + 2*i*a33**2*b33*n2) + 4*i*u3**2*v3*a33**2*n2*n3 + 4*i*u3*v1*v2*v3*a33**2
*c12*n2 + u3*v1*v3*(2*i*a33**2*m1*n2 + 2*a33*b33*n2**2) - 2*u3*v1*a33*n2**2*n3 -
4*u3*v2**2*v3*a33**2*c12*n2 + u3*v2*v3*(2*i*a33**2*m2*n2 - 2*i*a33*b33*n2**2) +
2*i*u3*v2*a33*n2**2*n3 - 2*u3*v3**3*a33**2*c12*n2 + u3*v3**2*( - a33**2*m1*n3 -
i*a33**2*m2*n3 + 2*i*a33*b33*n2*n3) + 4*i*v1**3*a33*c12*n2**2 + v1**2*v3**2*(2*
i*a33**2*c12*m1 - 2*a33**2*c12*m2 + 4*a33*b33*c12*n2) + 4*v1**2*v3*a33*c12*n2*n3
+ 4*i*v1*v2**2*a33*c12*n2**2 + v1*v2*v3**2*( - 2*a33**2*c12*m1 - 2*i*a33**2*c12
*m2 + 4*i*a33*b33*c12*n2) + 4*i*v1*v2*v3*a33*c12*n2*n3 + v1*v2*(2*i*a33*m1*n2**2
- 2*a33*m2*n2**2 + 4*b33*n2**3) + v1*v3**2*( - a33**2*m1**2 - i*a33**2*m1*m2 +
3*i*a33*b33*m1*n2 - a33*b33*m2*n2 + 2*i*a33*c12*n2**2 + 2*b33**2*n2**2) + v1*v3*
(2*i*a33*m1*n2*n3 + 2*b33*n2**2*n3) + v1*( - 2*n2**4 + 2*n2**2*n3**2) + v2**2*(2
*a33*m1*n2**2 + 2*i*a33*m2*n2**2 - 4*i*b33*n2**3) + v2*v3**2*( - a33**2*m1*m2 -
i*a33**2*m2**2 + a33*b33*m1*n2 + 3*i*a33*b33*m2*n2 + 2*a33*c12*n2**2 - 2*i*b33**
2*n2**2) + v2*v3*(2*i*a33*m2*n2*n3 - 2*i*b33*n2**2*n3) + v2*(2*i*n2**4 - 2*i*n2
**2*n3**2) + v3**4*(i*a33**2*c12*m1 - a33**2*c12*m2 + 2*a33*b33*c12*n2) + 2*v3**
3*a33*c12*n2*n3 + v3**2*(a33*m1*n2**2 + a33*m1*n3**2 - i*a33*m2*n2**2 + i*a33*m2
*n3**2 - 2*i*b33*n2*n3**2) + v3*(2*i*n2**3*n3 - 2*i*n2*n3**3)$