Solution 13 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
2 2
2*a33*b13*m2*n3*r328 - 4*a33*c13*n2*n3*r328 + i*b13 *n3 *r328
r10=---------------------------------------------------------------
2 2
2*a33 *b13
2 2 2
- 4*a33*c13*n2 *r328 + 2*a33*m2*n2 *r425 + i*b13 *n2*n3*r328
r11=---------------------------------------------------------------
2 2
2*a33 *b13
2 2 2
- 4*i*a33*c13*n2 *r328 + 2*i*a33*m2*n2 *r425 - b13 *n2*n3*r328
r12=-----------------------------------------------------------------
2 2
2*a33 *b13
2
- b13*n2*n3*r328 + n2 *n3*r425
r13=---------------------------------
2
a33*b13
2 3
- b13*n2 *r328 + n2 *r425
r14=----------------------------
2
a33*b13
2 3
- i*b13*n2 *r328 + i*n2 *r425
r15=--------------------------------
2
a33*b13
2 2 2
r20=(8*a33 *c13*m2*r328 - 4*a33 *m2 *r425 - 4*i*a33*b13*c13*n3*r328
2 2 2 2 2 2
- 4*i*a33*b13*m2*n3*r425 + 2*b13 *n2 *r425 + b13 *n3 *r425)/(4*a33 *b13 )
2
r21=(4*i*a33*b13*c13*n2*r328 - 2*i*a33*b13*m2*n2*r425 - 4*i*a33*c13*n2 *r425
3 2 2 2
+ b13 *n3*r328 + b13 *n2*n3*r425)/(2*a33 *b13 )
2
n2 *r425
r22=----------
2
a33
2
r23=( - 4*a33*b13*c13*n2*r328 + 2*a33*b13*m2*n2*r425 + 4*a33*c13*n2 *r425
3 2 2 2
+ i*b13 *n3*r328 + i*b13 *n2*n3*r425)/(2*a33 *b13 )
2
i*n2 *r425
r24=------------
2
a33
2
2*a33*b13*m2*r328 - 4*a33*c13*n2*r328 + i*b13 *n3*r328
r26=--------------------------------------------------------
2
2*a33*b13
2
i*n2 *r425
r27=------------
a33*b13
2
- n2 *r425
r28=-------------
a33*b13
2
i*b13*n2*r328 - 2*i*n2 *r425
r210=------------------------------
a33*b13
r212=(2*i*a33*b13*m2*r328 + 4*i*a33*c13*n2*r328 - 4*i*a33*m2*n2*r425
2 2
+ b13 *n3*r328 + 2*b13*n2*n3*r425)/(2*a33*b13 )
r213=0
2
b13*n2*r328 - n2 *r425
r214=------------------------
2
b13
2
- b13*n2*r328 + 2*n2 *r425
r215=-----------------------------
a33*b13
r216=( - 2*i*a33*b13*m2*r328 - 4*i*a33*c13*n2*r328 + 4*i*a33*m2*n2*r425
2 2
- b13 *n3*r328 - 2*b13*n2*n3*r425)/(2*a33*b13 )
r217=0
r218=0
r219=0
2
b13*n2*r328 - n2 *r425
r220=------------------------
2
b13
r30=0
2
- 2*a33*b13*m2*r425 - 4*a33*c13*n2*r425 - i*b13 *n3*r425
r31=-----------------------------------------------------------
2
2*a33 *b13
2 2 2
r32=(8*i*a33 *c13 *r328 - 8*i*a33 *c13*m2*r425 + 4*a33*b13*c13*n3*r425
3 2 2
- i*b13 *n2*r425)/(2*a33 *b13 )
- c13*r328
r33=-------------
a33
2
- 2*i*a33*b13*m2*r425 - 4*i*a33*c13*n2*r425 + b13 *n3*r425
r34=-------------------------------------------------------------
2
2*a33 *b13
b13*n2*r425
r35=-------------
2
a33
- i*c13*r328
r36=---------------
a33
2 2 2
r37=(8*i*a33 *c13 *r328 - 8*i*a33 *c13*m2*r425 + 4*a33*b13*c13*n3*r425
3 2 2
+ i*b13 *n2*r425)/(2*a33 *b13 )
- c13*r328
r38=-------------
a33
- i*c13*r328
r39=---------------
a33
r310=0
2*i*c13*r328
r312=--------------
b13
2*i*n2*r425
r313=-------------
a33
r314=0
2*i*c13*r328
r315=--------------
b13
- i*b13*r328 + 2*i*n2*r425
r316=-----------------------------
b13
r317=0
r318=0
r319=0
- 2*n2*r425
r320=--------------
a33
r323
2
4*a33*b13*c13*r328 - 2*a33*b13*m2*r425 - 4*a33*c13*n2*r425 - i*b13 *n3*r425
=-----------------------------------------------------------------------------
2
a33*b13
- b13*r328
r325=-------------
2*a33
r326=0
r329=0
- i*b13*r328 + 2*i*n2*r425
r330=-----------------------------
b13
r332=0
r333=0
r334=0
- 2*i*n2*r425
r335=----------------
a33
r336=
2
- 4*a33*b13*c13*r328 + 2*a33*b13*m2*r425 + 4*a33*c13*n2*r425 + i*b13 *n3*r425
--------------------------------------------------------------------------------
2
a33*b13
- i*b13*r328
r337=---------------
2*a33
r338=0
b13*r328
r339=----------
2*a33
- i*b13*r328
r340=---------------
2*a33
r341=0
r342= - r328
r343=0
r344=0
r345=0
r347=0
r348=0
r349=0
- i*b13*r328 + 2*i*n2*r425
r350=-----------------------------
b13
r351=0
r352=0
r353=0
r354=0
r355=0
r40=0
2*i*c13*r425
r41=--------------
a33
2 2 4
- 16*a33 *c13 *r425 - b13 *r425
r42=----------------------------------
2 2
4*a33 *b13
r43=0
r44=0
- 2*c13*r425
r45=---------------
a33
2
- i*b13 *r425
r46=----------------
2
2*a33
r47=0
r48=0
2 2 4
- 16*a33 *c13 *r425 + b13 *r425
r49=----------------------------------
2 2
4*a33 *b13
r410=0
r411=0
r412=0
r413=0
r415=0
- i*b13*r425
r416=---------------
a33
r417=0
r418=0
b13*r425
r419=----------
a33
r420=0
r421=0
r422=0
r423=0
r424=0
r426=0
r427=0
r428=0
r429=0
r431=0
r432=0
r433=0
i*b13*r425
r435=------------
a33
r442=0
r444=0
r445=0
r448=0
r450=0
r451=0
r453=0
r454=0
r455=r425
r458=0
r460=0
r461=0
r463=0
r464=0
r465=0
r467=0
r468=0
r469=0
- b13*r425
r470=-------------
a33
- 4*i*c13*r425
r471=-----------------
b13
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r478=0
r479=0
r480=0
r481=0
r482=0
r483=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
r4105=r425
r4106=0
r4107=0
r4108=0
r4109=0
r4110=0
r4111=0
r4112=0
r4113=0
r4114=0
r4115=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
r4125=0
m3=0
m1=i*m2
n1=i*n2
2
b13
c33=-------
4*a33
c23= - i*c13
2
b13
c22=-------
2*a33
2
i*b13
c12=--------
4*a33
c11=0
b33=0
b32=0
b31=0
b22=0
b21=0
b12=0
b11=0
a23=0
a22=0
a13=0
a12=0
a11=0
b23= - i*b13
4*i*c13*r425
r439=--------------
b13
b13*r328 + 4*n2*r425
r311=----------------------
2*a33
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:
r328, r425, b13, m2, n3, n2, c13, 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,b23}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{i*b13 + b23,
a11,
a12,
a13,
a22,
a23,
b11,
b12,
b21,
b22,
b31,
b32,
b33,
c11,
4*a33*c12 - i*b13**2,
2*a33*c22 - b13**2,
i*c13 + c23,
4*a33*c33 - b13**2,
n1 - i*n2,
m1 - i*m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2
2 i*v1*v2*b13
HAM=u1*v3*b13 + i*u1*n2 - i*u2*v3*b13 + u2*n2 + u3 *a33 + u3*n3 + --------------
2*a33
2 2 2 2
v2 *b13 v3 *b13
+ 2*v1*v3*c13 + i*v1*m2 + ---------- - 2*i*v2*v3*c13 + v2*m2 + ----------
2*a33 4*a33
has apart from the Hamiltonian and Casimirs the following 2 first integrals:
2 2 2 2 2 2 2 2 2
FI=4*u1 *v3 *a33 *b13 + 8*i*u1 *v3*a33 *b13*n2 - 4*u1 *a33 *n2
2 2
- 16*i*u1*v2*v3 *a33 *b13*c13
2 2 2
+ u1*v2*v3*(8*a33 *b13*m2 + 16*a33 *c13*n2 + 4*i*a33*b13 *n3)
2 3 3
+ u1*v2*(8*i*a33 *m2*n2 - 4*a33*b13*n2*n3) - 4*u1*v3 *a33*b13
2 2 2 3
- 8*i*u1*v3 *a33*b13 *n2 + 8*u1*v3*a33*b13*n2 + 4*i*u1*a33*n2
2 2 2 2 2 2 2 2 2
+ 4*u2 *v3 *a33 *b13 + 8*i*u2 *v3*a33 *b13*n2 - 4*u2 *a33 *n2
2 2
+ 16*i*u2*v1*v3 *a33 *b13*c13
2 2 2
+ u2*v1*v3*( - 8*a33 *b13*m2 - 16*a33 *c13*n2 - 4*i*a33*b13 *n3)
2 3 3
+ u2*v1*( - 8*i*a33 *m2*n2 + 4*a33*b13*n2*n3) + 4*i*u2*v3 *a33*b13
2 2 2 3
- 8*u2*v3 *a33*b13 *n2 - 8*i*u2*v3*a33*b13*n2 + 4*u2*a33*n2
2 2 2 2 2 2 2 3
+ 4*u3 *v3 *a33 *b13 + 8*i*u3 *v3*a33 *b13*n2 + 4*u3*v1*v3 *a33*b13
2 2 2 3
+ 8*i*u3*v1*v3*a33*b13 *n2 - 4*u3*v1*a33*b13*n2 - 4*i*u3*v2*v3 *a33*b13
2 2 2
+ 8*u3*v2*v3*a33*b13 *n2 + 4*i*u3*v2*a33*b13*n2 + 4*u3*a33*n2 *n3
2 2 2 2 4
+ v1 *v3 *( - 16*a33 *c13 + b13 )
2 2 3
+ v1 *v3*( - 16*i*a33 *c13*m2 + 8*a33*b13*c13*n3 + 2*i*b13 *n2)
2 4 3 2 2
- 2*i*v1*v2*v3 *b13 + 4*v1*v2*v3*b13 *n2 + 4*i*v1*v2*b13 *n2
3 2
- 8*v1*v3 *a33*b13 *c13
2 2 3
+ v1*v3 *( - 4*i*a33*b13 *m2 - 8*i*a33*b13*c13*n2 + 2*b13 *n3)
2 2
+ v1*v3*(4*a33*b13*m2*n2 + 8*a33*c13*n2 + 2*i*b13 *n2*n3)
2 2 2 2 2 4
+ 4*i*v1*a33*m2*n2 + v2 *v3 *( - 16*a33 *c13 - b13 )
2 2 3
+ v2 *v3*( - 16*i*a33 *c13*m2 + 8*a33*b13*c13*n3 - 2*i*b13 *n2)
2 2 2 3 2
+ 4*v2 *b13 *n2 + 8*i*v2*v3 *a33*b13 *c13
2 2 3
+ v2*v3 *( - 4*a33*b13 *m2 - 8*a33*b13*c13*n2 - 2*i*b13 *n3)
2 2
+ v2*v3*( - 4*i*a33*b13*m2*n2 - 8*i*a33*c13*n2 + 2*b13 *n2*n3)
2
+ 4*v2*a33*m2*n2
2 2 2 2 2 2 2
+ v3 *( - 4*a33 *m2 - 4*i*a33*b13*m2*n3 + 2*b13 *n2 + b13 *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} = { - 8*i,
u1*v1 + u2*v2 + u3*v3,
b13,
v3*b13 + i*n2,
a33,
u1*v3*a33*b13 + i*u1*a33*n2 - i*u2*v3*a33*b13 + u2*a33*n2
2*i*a33*m2 - b13*n3
+ 2*v1*v3*a33*c13 + v1*--------------------- - 2*i*v2*v3*a33*c13
2
2*a33*m2 + i*b13*n3
+ v2*---------------------}
2
2 2 2 2 2 2 2
FI= - 2*i*u1 *v3*a33 *b13 + 2*u1 *a33 *b13*n2 - 2*u1*u3*v2*a33 *b13
2 3 3 2 3
- i*u1*v1 *a33*b13 + u1*v1*v2*a33*b13 - i*u1*v2 *a33*b13
2
- 8*u1*v2*v3*a33 *b13*c13
2 2 2
+ u1*v2*( - 2*i*a33 *b13*m2 - 4*i*a33 *c13*n2 - a33*b13 *n3)
2 2 2 2 2
- 2*u1*v3*a33*b13 *n2 - 2*i*u1*a33*b13*n2 - 2*i*u2 *v3*a33 *b13
2 2 2 2 2 3
+ 2*u2 *a33 *b13*n2 + 2*u2*u3*v1*a33 *b13 - u2*v1 *a33*b13
2
+ 8*u2*v1*v3*a33 *b13*c13
2 2 2
+ u2*v1*(2*i*a33 *b13*m2 + 4*i*a33 *c13*n2 + a33*b13 *n3)
2 2 2 2 2
+ 2*i*u2*v3*a33*b13 *n2 - 2*u2*a33*b13*n2 - 2*i*u3 *v3*a33 *b13
2 2 2 2 3
+ 4*i*u3*v1 *a33 *b13*c13 + 4*i*u3*v2 *a33 *b13*c13 + u3*v2*v3*a33*b13
2 2 2
+ u3*v3*(2*a33 *b13*m2 - 4*a33 *c13*n2 + i*a33*b13 *n3) - 2*u3*a33*b13*n2*n3
3 2 2 2 2 2 2
- 2*i*v1 *a33*b13 *c13 - 2*v1 *v2*a33*b13 *c13 + 8*i*v1 *v3*a33 *c13
2 2 3
- 2*i*v1*v2 *a33*b13 *c13 + v1*v3*( - 4*a33*b13*c13*n2 + i*b13 *n3)
2 2 3 2
+ v1*( - 4*i*a33*c13*n2 - b13 *n2*n3) - 2*v2 *a33*b13 *c13
2 2 2 3
+ 8*i*v2 *v3*a33 *c13 + v2*v3*(4*i*a33*b13*c13*n2 + b13 *n3)
2 2
+ v2*( - 4*a33*c13*n2 + i*b13 *n2*n3)
2 2
+ v3 *(4*a33 *c13*m2 - 2*i*a33*b13*c13*n3)
2 2
+ v3*(2*a33*b13*m2*n3 - 4*a33*c13*n2*n3 + i*b13 *n3 )
= a product of the elements of: { - 2*i,
2 2 2 2 2 2 2
u1 *v3*a33 *b13 + i*u1 *a33 *b13*n2 - i*u1*u3*v2*a33 *b13
2 3 3 2 3
u1*v1 *a33*b13 i*u1*v1*v2*a33*b13 u1*v2 *a33*b13
+ ----------------- + --------------------- + -----------------
2 2 2
2
- 4*i*u1*v2*v3*a33 *b13*c13
2 2 2
2*a33 *b13*m2 + 4*a33 *c13*n2 - i*a33*b13 *n3
+ u1*v2*-----------------------------------------------
2
2 2 2 2 2
- i*u1*v3*a33*b13 *n2 + u1*a33*b13*n2 + u2 *v3*a33 *b13
2 3
2 2 2 2 - i*u2*v1 *a33*b13
+ i*u2 *a33 *b13*n2 + i*u2*u3*v1*a33 *b13 + ----------------------
2
2
+ 4*i*u2*v1*v3*a33 *b13*c13
2 2 2
- 2*a33 *b13*m2 - 4*a33 *c13*n2 + i*a33*b13 *n3
+ u2*v1*--------------------------------------------------
2
2 2 2 2 2
- u2*v3*a33*b13 *n2 - i*u2*a33*b13*n2 + u3 *v3*a33 *b13
3
2 2 2 2 i*u3*v2*v3*a33*b13
- 2*u3*v1 *a33 *b13*c13 - 2*u3*v2 *a33 *b13*c13 + ---------------------
2
2 2 2
2*i*a33 *b13*m2 - 4*i*a33 *c13*n2 - a33*b13 *n3
+ u3*v3*-------------------------------------------------
2
3 2 2 2
- i*u3*a33*b13*n2*n3 + v1 *a33*b13 *c13 - i*v1 *v2*a33*b13 *c13
2 2 2 2 2
- 4*v1 *v3*a33 *c13 + v1*v2 *a33*b13 *c13
3
- 4*i*a33*b13*c13*n2 - b13 *n3
+ v1*v3*---------------------------------
2
2 2
4*a33*c13*n2 - i*b13 *n2*n3 3 2
+ v1*------------------------------ - i*v2 *a33*b13 *c13
2
3
2 2 2 - 4*a33*b13*c13*n2 + i*b13 *n3
- 4*v2 *v3*a33 *c13 + v2*v3*---------------------------------
2
2 2
- 4*i*a33*c13*n2 - b13 *n2*n3
+ v2*---------------------------------
2
2 2
+ v3 *(2*i*a33 *c13*m2 + a33*b13*c13*n3)
2 2
2*i*a33*b13*m2*n3 - 4*i*a33*c13*n2*n3 - b13 *n3
+ v3*--------------------------------------------------}
2
{HAM,FI} = {2,
- b13,
b13,
u1*v1 + u2*v2 + u3*v3,
a33,
u1*v3*a33*b13 + i*u1*a33*n2 - i*u2*v3*a33*b13 + u2*a33*n2
2 2
- v1 *b13 2
+ u3*v1*a33*b13 + ------------- + i*v1*v2*b13 + 2*v1*v3*a33*c13
2
2 2
2*i*a33*m2 + b13*n3 v2 *b13
+ v1*--------------------- + ---------- - 2*i*v2*v3*a33*c13
2 2
2 2
- v3 *b13 - i*v3*b13*n2
+ v2*a33*m2 + ------------- + ----------------}
2 2
And again in machine readable form:
HAM=u1*v3*b13 + i*u1*n2 - i*u2*v3*b13 + u2*n2 + u3**2*a33 + u3*n3 + (i*v1*v2*b13
**2)/(2*a33) + 2*v1*v3*c13 + i*v1*m2 + (v2**2*b13**2)/(2*a33) - 2*i*v2*v3*c13 +
v2*m2 + (v3**2*b13**2)/(4*a33)$
FI=4*u1**2*v3**2*a33**2*b13**2 + 8*i*u1**2*v3*a33**2*b13*n2 - 4*u1**2*a33**2*n2
**2 - 16*i*u1*v2*v3**2*a33**2*b13*c13 + u1*v2*v3*(8*a33**2*b13*m2 + 16*a33**2*
c13*n2 + 4*i*a33*b13**2*n3) + u1*v2*(8*i*a33**2*m2*n2 - 4*a33*b13*n2*n3) - 4*u1*
v3**3*a33*b13**3 - 8*i*u1*v3**2*a33*b13**2*n2 + 8*u1*v3*a33*b13*n2**2 + 4*i*u1*
a33*n2**3 + 4*u2**2*v3**2*a33**2*b13**2 + 8*i*u2**2*v3*a33**2*b13*n2 - 4*u2**2*
a33**2*n2**2 + 16*i*u2*v1*v3**2*a33**2*b13*c13 + u2*v1*v3*( - 8*a33**2*b13*m2 -
16*a33**2*c13*n2 - 4*i*a33*b13**2*n3) + u2*v1*( - 8*i*a33**2*m2*n2 + 4*a33*b13*
n2*n3) + 4*i*u2*v3**3*a33*b13**3 - 8*u2*v3**2*a33*b13**2*n2 - 8*i*u2*v3*a33*b13*
n2**2 + 4*u2*a33*n2**3 + 4*u3**2*v3**2*a33**2*b13**2 + 8*i*u3**2*v3*a33**2*b13*
n2 + 4*u3*v1*v3**2*a33*b13**3 + 8*i*u3*v1*v3*a33*b13**2*n2 - 4*u3*v1*a33*b13*n2
**2 - 4*i*u3*v2*v3**2*a33*b13**3 + 8*u3*v2*v3*a33*b13**2*n2 + 4*i*u3*v2*a33*b13*
n2**2 + 4*u3*a33*n2**2*n3 + v1**2*v3**2*( - 16*a33**2*c13**2 + b13**4) + v1**2*
v3*( - 16*i*a33**2*c13*m2 + 8*a33*b13*c13*n3 + 2*i*b13**3*n2) - 2*i*v1*v2*v3**2*
b13**4 + 4*v1*v2*v3*b13**3*n2 + 4*i*v1*v2*b13**2*n2**2 - 8*v1*v3**3*a33*b13**2*
c13 + v1*v3**2*( - 4*i*a33*b13**2*m2 - 8*i*a33*b13*c13*n2 + 2*b13**3*n3) + v1*v3
*(4*a33*b13*m2*n2 + 8*a33*c13*n2**2 + 2*i*b13**2*n2*n3) + 4*i*v1*a33*m2*n2**2 +
v2**2*v3**2*( - 16*a33**2*c13**2 - b13**4) + v2**2*v3*( - 16*i*a33**2*c13*m2 + 8
*a33*b13*c13*n3 - 2*i*b13**3*n2) + 4*v2**2*b13**2*n2**2 + 8*i*v2*v3**3*a33*b13**
2*c13 + v2*v3**2*( - 4*a33*b13**2*m2 - 8*a33*b13*c13*n2 - 2*i*b13**3*n3) + v2*v3
*( - 4*i*a33*b13*m2*n2 - 8*i*a33*c13*n2**2 + 2*b13**2*n2*n3) + 4*v2*a33*m2*n2**2
+ v3**2*( - 4*a33**2*m2**2 - 4*i*a33*b13*m2*n3 + 2*b13**2*n2**2 + b13**2*n3**2)
$
FI= - 2*i*u1**2*v3*a33**2*b13**2 + 2*u1**2*a33**2*b13*n2 - 2*u1*u3*v2*a33**2*b13
**2 - i*u1*v1**2*a33*b13**3 + u1*v1*v2*a33*b13**3 - i*u1*v2**2*a33*b13**3 - 8*u1
*v2*v3*a33**2*b13*c13 + u1*v2*( - 2*i*a33**2*b13*m2 - 4*i*a33**2*c13*n2 - a33*
b13**2*n3) - 2*u1*v3*a33*b13**2*n2 - 2*i*u1*a33*b13*n2**2 - 2*i*u2**2*v3*a33**2*
b13**2 + 2*u2**2*a33**2*b13*n2 + 2*u2*u3*v1*a33**2*b13**2 - u2*v1**2*a33*b13**3
+ 8*u2*v1*v3*a33**2*b13*c13 + u2*v1*(2*i*a33**2*b13*m2 + 4*i*a33**2*c13*n2 + a33
*b13**2*n3) + 2*i*u2*v3*a33*b13**2*n2 - 2*u2*a33*b13*n2**2 - 2*i*u3**2*v3*a33**2
*b13**2 + 4*i*u3*v1**2*a33**2*b13*c13 + 4*i*u3*v2**2*a33**2*b13*c13 + u3*v2*v3*
a33*b13**3 + u3*v3*(2*a33**2*b13*m2 - 4*a33**2*c13*n2 + i*a33*b13**2*n3) - 2*u3*
a33*b13*n2*n3 - 2*i*v1**3*a33*b13**2*c13 - 2*v1**2*v2*a33*b13**2*c13 + 8*i*v1**2
*v3*a33**2*c13**2 - 2*i*v1*v2**2*a33*b13**2*c13 + v1*v3*( - 4*a33*b13*c13*n2 + i
*b13**3*n3) + v1*( - 4*i*a33*c13*n2**2 - b13**2*n2*n3) - 2*v2**3*a33*b13**2*c13
+ 8*i*v2**2*v3*a33**2*c13**2 + v2*v3*(4*i*a33*b13*c13*n2 + b13**3*n3) + v2*( - 4
*a33*c13*n2**2 + i*b13**2*n2*n3) + v3**2*(4*a33**2*c13*m2 - 2*i*a33*b13*c13*n3)
+ v3*(2*a33*b13*m2*n3 - 4*a33*c13*n2*n3 + i*b13**2*n3**2)$