Solution 21 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
i*m3*r212
r10=-----------
b33
r11=0
r12=0
r13=0
r14=0
r15=0
2
2*b33*c12*r212 + 2*i*b33*c33*r212 + m3 *r494
r20=----------------------------------------------
2
2*b33
- i*m2*r212 + m2*r26
r21=-----------------------
n3
r22=0
- m2*r212 - i*m2*r26
r23=-----------------------
n3
r24=0
r27=0
r28=0
r210=0
r213=0
r214=0
r215=0
r216= - r212
r217=0
r218=0
r219=0
r220=0
2 2
r30=( - b33 *c12*r212 - i*b33 *c12*r26 + b33*m3*n3*r422 - i*c12*m3*n3*r494
2
+ c33*m3*n3*r494)/(b33 *n3)
- c12*m2*r212 - i*c12*m2*r26 - i*c33*m2*r212 + c33*m2*r26
r31=------------------------------------------------------------
m3*n3
m3*r422
r32=---------
b33
r33=0
i*c12*m2*r212 - c12*m2*r26 - c33*m2*r212 - i*c33*m2*r26
r34=---------------------------------------------------------
m3*n3
- 2*i*c12*r212 + 2*c12*r26
r35=-----------------------------
n3
r36=0
- 2*b33*c12*r212 - 2*i*b33*c12*r26 + m3*n3*r422
r37=--------------------------------------------------
b33*n3
r38=0
r39=0
r310
2
- b33*c12*r212 - i*b33*c12*r26 - i*b33*c33*r212 + b33*c33*r26 + i*m3 *r448
=-----------------------------------------------------------------------------
b33*m3
- i*b33*m2*r212 + b33*m2*r26
r311=-------------------------------
m3*n3
r312=0
- b33*m2*r212 - i*b33*m2*r26
r313=-------------------------------
m3*n3
r314=0
r315=0
- i*a33*m3*r212 + a33*m3*r26 - i*b33*n3*r212 + b33*n3*r26
r316=------------------------------------------------------------
m3*n3
r317=0
r318=0
r319=0
r320=0
i*m3*r448 - m3*r494
r321=---------------------
b33
r322=0
- i*m3*r494
r323=--------------
b33
- b33*m2*r212 - i*b33*m2*r26
r324=-------------------------------
m3*n3
i*b33*m2*r212 - b33*m2*r26
r325=----------------------------
m3*n3
r326=0
r327=0
- b33*r212 - i*b33*r26
r328=-------------------------
m3
r329=0
r330=0
r331=0
r332=0
r333=0
r334=0
r335=0
i*m3*r494
r336=-----------
b33
b33*m2*r212 + i*b33*m2*r26
r337=----------------------------
m3*n3
i*m3*r448 - m3*r494
r338=---------------------
b33
- i*b33*m2*r212 + b33*m2*r26
r339=-------------------------------
m3*n3
r340=0
r341=0
b33*r212 + i*b33*r26
r342=----------------------
m3
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
2 2 2 2 2
r40=(2*i*b33 *c12 *r212 - 2*b33 *c12 *r26 - 2*b33 *c12*c33*r212
2
- 2*i*b33 *c12*c33*r26 - 2*i*b33*c12*m3*n3*r422 + 2*b33*c33*m3*n3*r422
2 2 2
- c12 *m3*n3*r494 - 2*i*c12*c33*m3*n3*r494 + c33 *m3*n3*r494)/(2*b33 *m3
*n3)
r41=0
- i*c12*r422 + c33*r422
r42=--------------------------
b33
r43=0
r44=0
r45=0
2 2
- 2*c12 *r212 - 2*i*c12 *r26 - 2*i*c12*c33*r212 + 2*c12*c33*r26
r46=------------------------------------------------------------------
m3*n3
r47=0
r48=0
2 2
r49=(2*i*b33*c12 *r212 - 2*b33*c12 *r26 - 2*b33*c12*c33*r212
- 2*i*b33*c12*c33*r26 - i*c12*m3*n3*r422 + c33*m3*n3*r422)/(b33*m3*n3)
r410=0
r411=0
r412=0
r413=0
2 2
r415=(b33 *c12*r212 + i*b33 *c12*r26 + b33*m3*n3*r422 + c12*m3*n3*r448
+ i*c33*m3*n3*r448)/(b33*m3*n3)
r416=0
2*b33*c12*r212 + 2*i*b33*c12*r26 + m3*n3*r422
r417=-----------------------------------------------
m3*n3
r418=0
r419=0
- 2*i*b33*c12*r212 + 2*b33*c12*r26
r420=-------------------------------------
m3*n3
r421=0
r423=0
r424=0
r425=( - 2*a33*c12*r212 - 2*i*a33*c12*r26 - 2*i*a33*c33*r212 + 2*a33*c33*r26
+ 2*i*m3*n3*r448 - m3*n3*r494)/(2*m3*n3)
r426=0
r427=0
r428=0
r429=0
- i*a33*b33*r212 + a33*b33*r26
r431=---------------------------------
m3*n3
r432=0
r433=0
r435=0
2 2
r436=(2*b33 *c12*r212 + 2*i*b33 *c12*r26 + c12*m3*n3*r448 + i*c12*m3*n3*r494
+ i*c33*m3*n3*r448 - c33*m3*n3*r494)/(b33*m3*n3)
r437=0
2*b33*c12*r212 + 2*i*b33*c12*r26
r438=----------------------------------
m3*n3
2 2
r439=(i*b33 *c12*r212 - b33 *c12*r26 - i*b33*m3*n3*r422 - c12*m3*n3*r494
- i*c33*m3*n3*r494)/(b33*m3*n3)
r440=0
r442=0
2*i*b33*c12*r212 - 2*b33*c12*r26 - i*m3*n3*r422
r444=-------------------------------------------------
m3*n3
r445=0
r446=i*r448 - r494
r447=0
r449=0
r450=0
r451=0
r454=0
r455=0
r456=0
r458=0
r459=r448 + i*r494
- r494
r460=---------
2
r461=0
r462=0
r463=0
r464=0
r465=0
r466=0
r467=0
r468=0
r469=0
r470=0
2 2
r471=( - i*b33 *c12*r212 + b33 *c12*r26 + i*b33*m3*n3*r422 + c12*m3*n3*r494
+ i*c33*m3*n3*r494)/(b33*m3*n3)
r472=0
r473=i*r422
2 2
r474=(2*b33 *c12*r212 + 2*i*b33 *c12*r26 + c12*m3*n3*r448 + i*c12*m3*n3*r494
+ i*c33*m3*n3*r448 - c33*m3*n3*r494)/(b33*m3*n3)
r475=0
4*b33*c12*r212 + 4*i*b33*c12*r26
r476=----------------------------------
m3*n3
r477=0
- 2*i*b33*c12*r212 + 2*b33*c12*r26 + i*m3*n3*r422
r478=----------------------------------------------------
m3*n3
2*b33*c12*r212 + 2*i*b33*c12*r26
r479=----------------------------------
m3*n3
r480=0
r481= - r448
r482=0
r483=i*r448 - r494
r484=0
r485=0
r486=0
a33*b33*r212 + i*a33*b33*r26
r487=------------------------------
m3*n3
r488=0
r489=0
r490=0
r491=0
r492= - r448 - i*r494
r493=0
r495=r448 + i*r494
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= - r448 - i*r494
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
m1= - i*m2
n2=0
n1=0
c23=0
c22=2*i*c12
c13=0
c11=0
b32=0
b31=0
b23=0
b22=0
b13=0
b12=i*b33
b11=0
a23=0
a22=0
a13=0
a12=0
a11=0
b21= - i*b33
r441= - i*r422
- a33*b33*r212 - i*a33*b33*r26
r453=---------------------------------
m3*n3
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:
r26, r422, b33, r212, r448, r494, c33, m2, m3, n3, 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.
{b21,a33}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{b21 + i*b33,
a11,
a12,
a13,
a22,
a23,
b11,
b12 - i*b33,
b13,
b22,
b23,
b31,
b32,
c11,
c13,
- 2*i*c12 + c22,
c23,
n1,
n2,
m1 + i*m2}$
The system of equations related to the Hamiltonian HAM:
2
HAM=i*u1*v2*b33 - i*u2*v1*b33 + u3 *a33 + u3*v3*b33 + u3*n3 + 2*v1*v2*c12
2 2
- i*v1*m2 + 2*i*v2 *c12 + v2*m2 + v3 *c33 + v3*m3
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
2 2 2 2 2 2 2
FI= - 2*i*u1 *v1*v2*b33 - u1 *v2 *b33 + 2*i*u1*u2*v1 *b33
2 2 2 2
+ 2*u1*u2*v1*v2*b33 - 2*i*u1*u2*v2 *b33 - 2*u1*u3*v1*v3*b33
2
+ u1*v1*v3 *(2*i*b33*c12 - 2*b33*c33) - 2*u1*v1*v3*b33*m3
2 2 2 2
+ u1*v2*v3 *(2*b33*c12 + 2*i*b33*c33) + 2*i*u1*v2*v3*b33*m3 - u2 *v1 *b33
2 2 2
+ 2*i*u2 *v1*v2*b33 - 2*u2*u3*v2*v3*b33
2
+ u2*v1*v3 *( - 2*b33*c12 - 2*i*b33*c33) - 2*i*u2*v1*v3*b33*m3
2 2 2 2
+ u2*v2*v3 *(2*i*b33*c12 - 2*b33*c33) - 2*u2*v2*v3*b33*m3 - u3 *v3 *b33
4 2 2 3
+ v3 *( - c12 - 2*i*c12*c33 + c33 ) + v3 *( - 2*i*c12*m3 + 2*c33*m3)
2 2
+ v3 *m3
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
FI= - u1 *v1*v2*b33 + u1*u2*v1 *b33 - u1*u2*v2 *b33 + i*u1*u3*v1*v3*b33
2 2
- u1*u3*v2*v3*b33 + u1*v1*v3 *(c12 + i*c33) + i*u1*v1*v3*m3 + u2 *v1*v2*b33
2
+ u2*u3*v1*v3*b33 + i*u2*u3*v2*v3*b33 + u2*v2*v3 *(c12 + i*c33)
2 2 3 2
+ i*u2*v2*v3*m3 + i*u3 *v3 *b33 + u3*v3 *(c12 + i*c33) + i*u3*v3 *m3
= a product of the elements of: { - u1*v1 - u2*v2 - u3*v3,
2
u1*v2*b33 - u2*v1*b33 - i*u3*v3*b33 + v3 *( - c12 - i*c33) - i*v3*m3}
{HAM,FI} = 0
2 2 2 3 2
FI=u1*u3 *v2*a33*b33 + u1*u3*v2*b33 *n3 + 2*u1*v1 *b33 *c12
2 2 2 2 2
- 2*i*u1*v1 *v2*b33 *c12 + 4*u1*v1*v2 *b33 *c12 - i*u1*v1*v2*b33 *m2
2 2 2 2 2 2
+ 2*u1*v1*v3 *b33 *c12 + u1*v2 *b33 *m2 - i*u1*v2*v3 *b33 *c12
2 2 2
- u1*v2*b33*m3*n3 - u2*u3 *v1*a33*b33 - u2*u3*v1*b33 *n3
3 2 2 2 2
+ 2*i*u2*v1 *b33 *c12 + i*u2*v1 *b33 *m2 - u2*v1*v2*b33 *m2
2 2 3 2
+ i*u2*v1*v3 *b33 *c12 + u2*v1*b33*m3*n3 + 2*u2*v2 *b33 *c12
2 2 3 2
+ 2*u2*v2*v3 *b33 *c12 - i*u3 *v3*a33*b33
2 2
+ u3 *v3 *( - a33*b33*c12 - i*a33*b33*c33)
2 2 2
+ u3 *v3*( - i*a33*b33*m3 - i*b33 *n3) - 2*i*u3*v1*v2*v3*b33 *c12
2 2 2 2
- u3*v1*v3*b33 *m2 + 2*u3*v2 *v3*b33 *c12 - i*u3*v2*v3*b33 *m2
3 2 2
+ u3*v3 *b33 *c12 + u3*v3 *( - b33*c12*n3 - i*b33*c33*n3)
2 2 2 2
+ v1 *v3 *(2*i*b33*c12 - 2*b33*c12*c33) - 2*v1 *v3*b33*c12*m3
2 2
+ v1*v2*v3 *( - 2*b33*c12 - 2*i*b33*c12*c33) - 2*i*v1*v2*v3*b33*c12*m3
2
+ v1*v3 *(i*b33*c12*m2 - b33*c33*m2) - v1*v3*b33*m2*m3
2
+ v2*v3 *( - b33*c12*m2 - i*b33*c33*m2) - i*v2*v3*b33*m2*m3
4 2 3
+ v3 *(i*b33*c12 - b33*c12*c33) - v3 *b33*c12*m3
2 2
+ v3 *(c12*m3*n3 + i*c33*m3*n3) + i*v3*m3 *n3
which the program can not factorize further.
{HAM,FI} = 0
2 3 2 3
FI=i*u1*v1 *v2*b33 + i*u1*v2 *b33 + i*u1*v2*v3 *b33 - i*u2*v1 *b33
2 2 2 2
- i*u2*v1*v2 *b33 - i*u2*v1*v3 *b33 + u3*v1 *v3*b33 + u3*v2 *v3*b33
3 2 2 2
+ u3*v3 *b33 + v1 *v3 *( - i*c12 + c33) + v1 *v3*m3
2 2 2 4 3
+ v2 *v3 *( - i*c12 + c33) + v2 *v3*m3 + v3 *( - i*c12 + c33) + v3 *m3
= a product of the elements of: {i,
2 2 2
v1 + v2 + v3 ,
2
u1*v2*b33 - u2*v1*b33 - i*u3*v3*b33 + v3 *( - c12 - i*c33) - i*v3*m3}
{HAM,FI} = 0
2 3
FI=i*u1*u3 *v2*a33*b33 + i*u1*u3*v2*b33*n3 + 2*i*u1*v1 *b33*c12
2 2
+ 2*u1*v1 *v2*b33*c12 + 4*i*u1*v1*v2 *b33*c12 + u1*v1*v2*b33*m2
2 2 2
+ 2*i*u1*v1*v3 *b33*c12 + i*u1*v2 *b33*m2 + u1*v2*v3 *b33*c12
2 3 2
- i*u2*u3 *v1*a33*b33 - i*u2*u3*v1*b33*n3 - 2*u2*v1 *b33*c12 - u2*v1 *b33*m2
2 3
- i*u2*v1*v2*b33*m2 - u2*v1*v3 *b33*c12 + 2*i*u2*v2 *b33*c12
2 3 2 2
+ 2*i*u2*v2*v3 *b33*c12 + u3 *v3*a33*b33 + u3 *v3 *( - i*a33*c12 + a33*c33)
2
+ u3 *v3*(a33*m3 + b33*n3) + 2*u3*v1*v2*v3*b33*c12 - i*u3*v1*v3*b33*m2
2 3
+ 2*i*u3*v2 *v3*b33*c12 + u3*v2*v3*b33*m2 + i*u3*v3 *b33*c12
2
+ u3*v3 *( - i*c12*n3 + c33*n3) + u3*v3*m3*n3
2 2 2 2
+ v1 *v3 *( - 2*c12 - 2*i*c12*c33) - 2*i*v1 *v3*c12*m3
2 2
+ v1*v2*v3 *( - 2*i*c12 + 2*c12*c33) + 2*v1*v2*v3*c12*m3
2
+ v1*v3 *( - c12*m2 - i*c33*m2) - i*v1*v3*m2*m3
2 4 2
+ v2*v3 *( - i*c12*m2 + c33*m2) + v2*v3*m2*m3 + v3 *( - c12 - i*c12*c33)
3
- i*v3 *c12*m3
= a product of the elements of: {i,
2 3
u1*u3 *v2*a33*b33 + u1*u3*v2*b33*n3 + 2*u1*v1 *b33*c12
2 2
- 2*i*u1*v1 *v2*b33*c12 + 4*u1*v1*v2 *b33*c12 - i*u1*v1*v2*b33*m2
2 2 2
+ 2*u1*v1*v3 *b33*c12 + u1*v2 *b33*m2 - i*u1*v2*v3 *b33*c12
2 3 2
- u2*u3 *v1*a33*b33 - u2*u3*v1*b33*n3 + 2*i*u2*v1 *b33*c12 + i*u2*v1 *b33*m2
2 3
- u2*v1*v2*b33*m2 + i*u2*v1*v3 *b33*c12 + 2*u2*v2 *b33*c12
2 3 2 2
+ 2*u2*v2*v3 *b33*c12 - i*u3 *v3*a33*b33 + u3 *v3 *( - a33*c12 - i*a33*c33)
2
+ u3 *v3*( - i*a33*m3 - i*b33*n3) - 2*i*u3*v1*v2*v3*b33*c12
2 3
- u3*v1*v3*b33*m2 + 2*u3*v2 *v3*b33*c12 - i*u3*v2*v3*b33*m2 + u3*v3 *b33*c12
2
+ u3*v3 *( - c12*n3 - i*c33*n3) - i*u3*v3*m3*n3
2 2 2 2
+ v1 *v3 *(2*i*c12 - 2*c12*c33) - 2*v1 *v3*c12*m3
2 2
+ v1*v2*v3 *( - 2*c12 - 2*i*c12*c33) - 2*i*v1*v2*v3*c12*m3
2 2
+ v1*v3 *(i*c12*m2 - c33*m2) - v1*v3*m2*m3 + v2*v3 *( - c12*m2 - i*c33*m2)
4 2 3
- i*v2*v3*m2*m3 + v3 *(i*c12 - c12*c33) - v3 *c12*m3}
{HAM,FI} = 0
And again in machine readable form:
HAM=i*u1*v2*b33 - i*u2*v1*b33 + u3**2*a33 + u3*v3*b33 + u3*n3 + 2*v1*v2*c12 - i*
v1*m2 + 2*i*v2**2*c12 + v2*m2 + v3**2*c33 + v3*m3$
FI= - 2*i*u1**2*v1*v2*b33**2 - u1**2*v2**2*b33**2 + 2*i*u1*u2*v1**2*b33**2 + 2*
u1*u2*v1*v2*b33**2 - 2*i*u1*u2*v2**2*b33**2 - 2*u1*u3*v1*v3*b33**2 + u1*v1*v3**2
*(2*i*b33*c12 - 2*b33*c33) - 2*u1*v1*v3*b33*m3 + u1*v2*v3**2*(2*b33*c12 + 2*i*
b33*c33) + 2*i*u1*v2*v3*b33*m3 - u2**2*v1**2*b33**2 + 2*i*u2**2*v1*v2*b33**2 - 2
*u2*u3*v2*v3*b33**2 + u2*v1*v3**2*( - 2*b33*c12 - 2*i*b33*c33) - 2*i*u2*v1*v3*
b33*m3 + u2*v2*v3**2*(2*i*b33*c12 - 2*b33*c33) - 2*u2*v2*v3*b33*m3 - u3**2*v3**2
*b33**2 + v3**4*( - c12**2 - 2*i*c12*c33 + c33**2) + v3**3*( - 2*i*c12*m3 + 2*
c33*m3) + v3**2*m3**2$
FI= - u1**2*v1*v2*b33 + u1*u2*v1**2*b33 - u1*u2*v2**2*b33 + i*u1*u3*v1*v3*b33 -
u1*u3*v2*v3*b33 + u1*v1*v3**2*(c12 + i*c33) + i*u1*v1*v3*m3 + u2**2*v1*v2*b33 +
u2*u3*v1*v3*b33 + i*u2*u3*v2*v3*b33 + u2*v2*v3**2*(c12 + i*c33) + i*u2*v2*v3*m3
+ i*u3**2*v3**2*b33 + u3*v3**3*(c12 + i*c33) + i*u3*v3**2*m3$
FI=u1*u3**2*v2*a33*b33**2 + u1*u3*v2*b33**2*n3 + 2*u1*v1**3*b33**2*c12 - 2*i*u1*
v1**2*v2*b33**2*c12 + 4*u1*v1*v2**2*b33**2*c12 - i*u1*v1*v2*b33**2*m2 + 2*u1*v1*
v3**2*b33**2*c12 + u1*v2**2*b33**2*m2 - i*u1*v2*v3**2*b33**2*c12 - u1*v2*b33*m3*
n3 - u2*u3**2*v1*a33*b33**2 - u2*u3*v1*b33**2*n3 + 2*i*u2*v1**3*b33**2*c12 + i*
u2*v1**2*b33**2*m2 - u2*v1*v2*b33**2*m2 + i*u2*v1*v3**2*b33**2*c12 + u2*v1*b33*
m3*n3 + 2*u2*v2**3*b33**2*c12 + 2*u2*v2*v3**2*b33**2*c12 - i*u3**3*v3*a33*b33**2
+ u3**2*v3**2*( - a33*b33*c12 - i*a33*b33*c33) + u3**2*v3*( - i*a33*b33*m3 - i*
b33**2*n3) - 2*i*u3*v1*v2*v3*b33**2*c12 - u3*v1*v3*b33**2*m2 + 2*u3*v2**2*v3*b33
**2*c12 - i*u3*v2*v3*b33**2*m2 + u3*v3**3*b33**2*c12 + u3*v3**2*( - b33*c12*n3 -
i*b33*c33*n3) + v1**2*v3**2*(2*i*b33*c12**2 - 2*b33*c12*c33) - 2*v1**2*v3*b33*
c12*m3 + v1*v2*v3**2*( - 2*b33*c12**2 - 2*i*b33*c12*c33) - 2*i*v1*v2*v3*b33*c12*
m3 + v1*v3**2*(i*b33*c12*m2 - b33*c33*m2) - v1*v3*b33*m2*m3 + v2*v3**2*( - b33*
c12*m2 - i*b33*c33*m2) - i*v2*v3*b33*m2*m3 + v3**4*(i*b33*c12**2 - b33*c12*c33)
- v3**3*b33*c12*m3 + v3**2*(c12*m3*n3 + i*c33*m3*n3) + i*v3*m3**2*n3$
FI=i*u1*v1**2*v2*b33 + i*u1*v2**3*b33 + i*u1*v2*v3**2*b33 - i*u2*v1**3*b33 - i*
u2*v1*v2**2*b33 - i*u2*v1*v3**2*b33 + u3*v1**2*v3*b33 + u3*v2**2*v3*b33 + u3*v3
**3*b33 + v1**2*v3**2*( - i*c12 + c33) + v1**2*v3*m3 + v2**2*v3**2*( - i*c12 +
c33) + v2**2*v3*m3 + v3**4*( - i*c12 + c33) + v3**3*m3$
FI=i*u1*u3**2*v2*a33*b33 + i*u1*u3*v2*b33*n3 + 2*i*u1*v1**3*b33*c12 + 2*u1*v1**2
*v2*b33*c12 + 4*i*u1*v1*v2**2*b33*c12 + u1*v1*v2*b33*m2 + 2*i*u1*v1*v3**2*b33*
c12 + i*u1*v2**2*b33*m2 + u1*v2*v3**2*b33*c12 - i*u2*u3**2*v1*a33*b33 - i*u2*u3*
v1*b33*n3 - 2*u2*v1**3*b33*c12 - u2*v1**2*b33*m2 - i*u2*v1*v2*b33*m2 - u2*v1*v3
**2*b33*c12 + 2*i*u2*v2**3*b33*c12 + 2*i*u2*v2*v3**2*b33*c12 + u3**3*v3*a33*b33
+ u3**2*v3**2*( - i*a33*c12 + a33*c33) + u3**2*v3*(a33*m3 + b33*n3) + 2*u3*v1*v2
*v3*b33*c12 - i*u3*v1*v3*b33*m2 + 2*i*u3*v2**2*v3*b33*c12 + u3*v2*v3*b33*m2 + i*
u3*v3**3*b33*c12 + u3*v3**2*( - i*c12*n3 + c33*n3) + u3*v3*m3*n3 + v1**2*v3**2*(
- 2*c12**2 - 2*i*c12*c33) - 2*i*v1**2*v3*c12*m3 + v1*v2*v3**2*( - 2*i*c12**2 +
2*c12*c33) + 2*v1*v2*v3*c12*m3 + v1*v3**2*( - c12*m2 - i*c33*m2) - i*v1*v3*m2*m3
+ v2*v3**2*( - i*c12*m2 + c33*m2) + v2*v3*m2*m3 + v3**4*( - c12**2 - i*c12*c33)
- i*v3**3*c12*m3$