Solution 22 to problem over
Expressions |
Parameters |
Inequalities |
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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 2
FI=2*i*u1 *v1*v2*b33 - u1 *v2 *b33 - 2*i*u1*u2*v1 *b33 + 2*u1*u2*v1*v2*b33
2 2 2
+ 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 2 2
+ v3 *( - c12 + 2*i*c12*c33 + c33 ) + v3 *(2*i*c12*m3 + 2*c33*m3) + v3 *m3
= a product of the elements of: {2*i,
2
u1*v2*b33 - u2*v1*b33 + i*u3*v3*b33 + v3 *( - c12 + i*c33) + i*v3*m3,
i*u1*v2*b33 - i*u2*v1*b33 u3*v3*b33
u1*v1*b33 + ------------- + ---------------- + u2*v2*b33 + -----------
2 2 2
2 - i*c12 - c33 - v3*m3
+ v3 *---------------- + ----------}
2 2
{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 2 2
+ u3*v3 *b33 + v1 *v3 *(i*c12 + c33) + v1 *v3*m3 + v2 *v3 *(i*c12 + c33)
2 4 3
+ 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 2
+ v1*v3 *( - c12*m2 + i*c33*m2) + i*v1*v3*m2*m3 + v2*v3 *(i*c12*m2 + c33*m2)
4 2 3
+ v2*v3*m2*m3 + v3 *( - c12 + i*c12*c33) + 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 - u3*v1*v3*b33*m2
2 3
+ 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
+ v1*v3 *( - i*c12*m2 - c33*m2) - v1*v3*m2*m3
2 4 2
+ v2*v3 *( - c12*m2 + i*c33*m2) + i*v2*v3*m2*m3 + v3 *( - i*c12 - c12*c33)
3
- 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$