Solution 9 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
2
r10=(2*i*a33*b13 *m2*n3*r327 + 4*a33*b13*c13*n1*n3*r327
2 3 2
- 2*i*a33*b13*m2*n1*n3*r446 - 4*a33*c13*n1 *n3*r446 + b13 *n3 *r327
2 2 2 3
- b13 *n1*n3 *r446)/(2*a33 *b13 )
2 2 3
r11=(4*i*a33*b13*c13*n1 *r327 + a33*b13*m2*n1 *r446 - 4*i*a33*c13*n1 *r446
3 2 2 2 3
+ i*b13 *n1*n3*r327 - i*b13 *n1 *n3*r446)/(2*a33 *b13 )
2 2 3
r12=(4*a33*b13*c13*n1 *r327 - i*a33*b13*m2*n1 *r446 - 4*a33*c13*n1 *r446
3 2 2 2 3
+ b13 *n1*n3*r327 - b13 *n1 *n3*r446)/(2*a33 *b13 )
2
2*b13*n1*n3*r327 - n1 *n3*r446
r13=--------------------------------
2
2*a33*b13
2 3
2*i*b13*n1 *r327 - i*n1 *r446
r14=-------------------------------
2
2*a33*b13
2 3
2*b13*n1 *r327 - n1 *r446
r15=---------------------------
2
2*a33*b13
2 2 2 2
r20=(16*i*a33 *b13*c13*m2*r327 + 4*a33 *b13*m2 *r446 - 16*i*a33 *c13*m2*n1*r446
2 2
- 8*a33*b13 *c13*n3*r327 - 4*i*a33*b13 *m2*n3*r446
3 2 3 2 2 3
+ 8*a33*b13*c13*n1*n3*r446 + 2*b13 *n1 *r446 - b13 *n3 *r446)/(8*a33 *b13
)
2
r21=(8*i*a33*b13*c13*n1*r327 + 2*a33*b13*m2*n1*r446 - 4*i*a33*c13*n1 *r446
3 2 2 2
+ 2*i*b13 *n3*r327 - 3*i*b13 *n1*n3*r446)/(4*a33 *b13 )
2
n1 *r446
r22=----------
2
2*a33
2
r23=(8*a33*b13*c13*n1*r327 - 2*i*a33*b13*m2*n1*r446 - 4*a33*c13*n1 *r446
3 2 2 2
+ 2*b13 *n3*r327 - 3*b13 *n1*n3*r446)/(4*a33 *b13 )
2
- i*n1 *r446
r24=---------------
2
2*a33
2
r26=(2*i*a33*b13 *m2*r327 + 4*a33*b13*c13*n1*r327 - 2*i*a33*b13*m2*n1*r446
2 3 2 3
- 4*a33*c13*n1 *r446 + b13 *n3*r327 - b13 *n1*n3*r446)/(2*a33*b13 )
2
- i*n1 *r446
r27=---------------
2*a33*b13
2
- n1 *r446
r28=-------------
2*a33*b13
i*n1*r327
r210=-----------
a33
2 2
r212=(2*a33*b13 *m2*r327 + 4*i*a33*b13*c13*n1*r327 - 4*i*a33*c13*n1 *r446
3 2 3
+ i*b13 *n3*r327 - 2*i*b13 *n1*n3*r446)/(2*a33*b13 )
r213=0
2
- 2*b13*n1*r327 + n1 *r446
r214=-----------------------------
2
2*b13
n1*r327
r215=---------
a33
2 2
r216=( - 2*a33*b13 *m2*r327 - 4*i*a33*b13*c13*n1*r327 + 4*i*a33*c13*n1 *r446
3 2 3
- i*b13 *n3*r327 + 2*i*b13 *n1*n3*r446)/(2*a33*b13 )
r217=0
r218=0
r219=0
2
- 2*b13*n1*r327 + n1 *r446
r220=-----------------------------
2
2*b13
r30=0
2
2*a33*b13*m2*r446 + 4*i*a33*c13*n1*r446 - i*b13 *n3*r446
r31=----------------------------------------------------------
2
4*a33 *b13
2 2 2 2 2
r32=(16*a33 *b13*c13 *r327 - 8*i*a33 *b13*c13*m2*r446 - 16*a33 *c13 *n1*r446
2 4 2 3
- 4*a33*b13 *c13*n3*r446 + b13 *n1*r446)/(4*a33 *b13 )
- i*b13*c13*r327 + i*c13*n1*r446
r33=-----------------------------------
a33*b13
2
- 2*i*a33*b13*m2*r446 + 4*a33*c13*n1*r446 - b13 *n3*r446
r34=-----------------------------------------------------------
2
4*a33 *b13
- i*b13*n1*r446
r35=------------------
2
2*a33
- b13*c13*r327 + c13*n1*r446
r36=-------------------------------
a33*b13
2 2 2 2 2
r37=(16*a33 *b13*c13 *r327 - 8*i*a33 *b13*c13*m2*r446 - 16*a33 *c13 *n1*r446
2 4 2 3
- 4*a33*b13 *c13*n3*r446 - b13 *n1*r446)/(4*a33 *b13 )
- i*b13*c13*r327 + i*c13*n1*r446
r38=-----------------------------------
a33*b13
- b13*c13*r327 + c13*n1*r446
r39=-------------------------------
a33*b13
r310=0
- i*n1*r446
r311=--------------
2*a33
2*b13*c13*r327 - 2*c13*n1*r446
r312=--------------------------------
2
b13
- n1*r446
r313=------------
2*a33
r314=0
2*b13*c13*r327 - 2*c13*n1*r446
r315=--------------------------------
2
b13
r316=0
r317=0
r318=0
r319=0
i*n1*r446
r320=-----------
a33
r321=0
- i*b13*r327 + 2*i*n1*r446
r322=-----------------------------
2*a33
r323=(8*i*a33*b13*c13*r327 + 2*a33*b13*m2*r446 - 4*i*a33*c13*n1*r446
2 2
- i*b13 *n3*r446)/(2*a33*b13 )
n1*r446
r324=---------
2*a33
- i*b13*r327 + i*n1*r446
r325=---------------------------
2*a33
r326=0
i*b13*r327 - i*n1*r446
r328=------------------------
b13
r329=0
r330= - r327
r331=0
r332=0
r333=0
r334=0
n1*r446
r335=---------
a33
r336=( - 8*i*a33*b13*c13*r327 - 2*a33*b13*m2*r446 + 4*i*a33*c13*n1*r446
2 2
+ i*b13 *n3*r446)/(2*a33*b13 )
- b13*r327 + n1*r446
r337=-----------------------
2*a33
r338=0
i*n1*r446
r339=-----------
2*a33
- b13*r327 + 2*n1*r446
r340=-------------------------
2*a33
r341=0
- i*b13*r327 + i*n1*r446
r342=---------------------------
b13
r343=r327
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
r350= - r327
r351=0
r352=0
r353=0
r354=0
r355=0
r40=0
i*c13*r446
r41=------------
a33
2 2 4
16*a33 *c13 *r446 + b13 *r446
r42=-------------------------------
2 2
8*a33 *b13
r43=0
r44=0
c13*r446
r45=----------
a33
2
- i*b13 *r446
r46=----------------
2
4*a33
r47=0
r48=0
2 2 4
16*a33 *c13 *r446 - b13 *r446
r49=-------------------------------
2 2
8*a33 *b13
r410=0
r411=0
r412=0
r413=0
r415=0
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
r446
r425=------
2
r426=0
r427=0
r428=0
r429=0
r431=0
r432=0
r433=0
i*b13*r446
r435=------------
2*a33
r436=0
i*b13*r446
r437=------------
2*a33
r438=0
2*i*c13*r446
r439=--------------
b13
r441=0
r442=0
r444=0
r445=0
r447=0
r448=0
r449=0
r450=0
r451=0
r453=0
r454=0
- r446
r455=---------
2
r456=0
r458=0
r459=0
r460=0
r461=0
r462=0
r463=0
r464=0
r465=0
r466=0
r467=0
r468=0
r469=0
b13*r446
r470=----------
2*a33
- 2*i*c13*r446
r471=-----------------
b13
r472=0
r473=0
r474=0
i*b13*r446
r475=------------
2*a33
r476=0
b13*r446
r477=----------
2*a33
r478=0
r479=0
r480=0
r481=0
r482=0
r483=r446
r484=0
r485=0
r486=0
r487=0
r488=0
r489=0
r490=0
r491=0
r492=0
r493=0
r494=0
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
- r446
r4105=---------
2
r4106=0
r4107=0
r4108=0
r4109=0
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
m3=0
m1= - i*m2
n2=i*n1
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
b23=i*b13
b22=0
b21=0
b12=0
b11=0
a23=0
a22=0
a13=0
a12=0
a11=0
b13*r446
r440=----------
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:
r446, r327, m2, n3, n1, b13, 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.
{n3,r440,a33,b13}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a11,
a12,
a13,
a22,
a23,
b11,
b12,
b21,
b22,
- i*b13 + b23,
b31,
b32,
b33,
c11,
4*a33*c12 + i*b13**2,
2*a33*c22 - b13**2,
- i*c13 + c23,
4*a33*c33 - b13**2,
- i*n1 + n2,
m1 + i*m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=u1*v3*b13 + u1*n1 + i*u2*v3*b13 + i*u2*n1 + u3 *a33 + u3*n3
2 2 2
- i*v1*v2*b13 v2 *b13
+ ----------------- + 2*v1*v3*c13 - i*v1*m2 + ---------- + 2*i*v2*v3*c13
2*a33 2*a33
2 2
v3 *b13
+ v2*m2 + ----------
4*a33
has apart from the Hamiltonian and Casimirs the following 2 first integrals:
2 2 2 2 2 2 2
FI= - 2*u1 *v3*a33 *b13 - 2*u1 *a33 *b13*n1 + 2*u1*u3*v1*a33 *b13
2 2 2 3 2 3
- 2*i*u1*u3*v2*a33 *b13 - u1*v1 *a33*b13 - u1*v2 *a33*b13
2
- 8*i*u1*v2*v3*a33 *b13*c13
2 2 2
+ u1*v2*( - 2*a33 *b13*m2 - 4*i*a33 *c13*n1 - i*a33*b13 *n3)
2 2 2 2 2
+ 2*u1*v3*a33*b13 *n1 + 2*u1*a33*b13*n1 - 2*u2 *v3*a33 *b13
2 2 2 2 2 2
- 2*u2 *a33 *b13*n1 + 2*i*u2*u3*v1*a33 *b13 + 2*u2*u3*v2*a33 *b13
2 3 2
- i*u2*v1 *a33*b13 + 8*i*u2*v1*v3*a33 *b13*c13
2 2 2
+ u2*v1*(2*a33 *b13*m2 + 4*i*a33 *c13*n1 + i*a33*b13 *n3)
2 3 2 2
- i*u2*v2 *a33*b13 + 2*i*u2*v3*a33*b13 *n1 + 2*i*u2*a33*b13*n1
2 2 2 2
+ 4*u3*v1 *a33 *b13*c13 + 4*u3*v2 *a33 *b13*c13
2 2 2
+ u3*v3*(2*i*a33 *b13*m2 + 4*a33 *c13*n1 + a33*b13 *n3) + 2*u3*a33*b13*n1*n3
3 2 2 2 2 2 2
- 2*v1 *a33*b13 *c13 - 2*i*v1 *v2*a33*b13 *c13 + 8*v1 *v3*a33 *c13
2 2 3
- 2*v1*v2 *a33*b13 *c13 + v1*v3*(4*a33*b13*c13*n1 + b13 *n3)
2 2 3 2
+ v1*(4*a33*c13*n1 + b13 *n1*n3) - 2*i*v2 *a33*b13 *c13
2 2 2 3
+ 8*v2 *v3*a33 *c13 + v2*v3*(4*i*a33*b13*c13*n1 + i*b13 *n3)
2 2
+ v2*(4*i*a33*c13*n1 + i*b13 *n1*n3)
2 2
+ v3 *(4*i*a33 *c13*m2 - 2*a33*b13*c13*n3)
2 2
+ v3*(2*i*a33*b13*m2*n3 + 4*a33*c13*n1*n3 + b13 *n3 )
= a product of the elements of: {2,
2 2 2 2 2 2 2
- u1 *v3*a33 *b13 - u1 *a33 *b13*n1 + u1*u3*v1*a33 *b13
2 3 2 3
2 2 - u1*v1 *a33*b13 - u1*v2 *a33*b13
- i*u1*u3*v2*a33 *b13 + -------------------- + --------------------
2 2
2
- 4*i*u1*v2*v3*a33 *b13*c13
2 2 2
- 2*a33 *b13*m2 - 4*i*a33 *c13*n1 - i*a33*b13 *n3
+ u1*v2*----------------------------------------------------
2
2 2 2 2 2 2 2
+ u1*v3*a33*b13 *n1 + u1*a33*b13*n1 - u2 *v3*a33 *b13 - u2 *a33 *b13*n1
2 3
2 2 2 2 - i*u2*v1 *a33*b13
+ i*u2*u3*v1*a33 *b13 + u2*u3*v2*a33 *b13 + ----------------------
2
2
+ 4*i*u2*v1*v3*a33 *b13*c13
2 2 2
2*a33 *b13*m2 + 4*i*a33 *c13*n1 + i*a33*b13 *n3
+ u2*v1*-------------------------------------------------
2
2 3
- i*u2*v2 *a33*b13 2 2
+ ---------------------- + i*u2*v3*a33*b13 *n1 + i*u2*a33*b13*n1
2
2 2 2 2
+ 2*u3*v1 *a33 *b13*c13 + 2*u3*v2 *a33 *b13*c13
2 2 2
2*i*a33 *b13*m2 + 4*a33 *c13*n1 + a33*b13 *n3
+ u3*v3*----------------------------------------------- + u3*a33*b13*n1*n3
2
3 2 2 2 2 2 2
- v1 *a33*b13 *c13 - i*v1 *v2*a33*b13 *c13 + 4*v1 *v3*a33 *c13
3
2 2 4*a33*b13*c13*n1 + b13 *n3
- v1*v2 *a33*b13 *c13 + v1*v3*----------------------------
2
2 2
4*a33*c13*n1 + b13 *n1*n3 3 2 2 2 2
+ v1*---------------------------- - i*v2 *a33*b13 *c13 + 4*v2 *v3*a33 *c13
2
3
4*i*a33*b13*c13*n1 + i*b13 *n3
+ v2*v3*--------------------------------
2
2 2
4*i*a33*c13*n1 + i*b13 *n1*n3
+ v2*--------------------------------
2
2 2
+ v3 *(2*i*a33 *c13*m2 - a33*b13*c13*n3)
2 2
2*i*a33*b13*m2*n3 + 4*a33*c13*n1*n3 + b13 *n3
+ v3*------------------------------------------------}
2
{HAM,FI} = 0
2 2 2 3 2 2 2 2 3
FI= - 4*u1 *v3 *a33 *b13 + 4*u1 *a33 *b13*n1 + 8*u1*u3*v1*v3*a33 *b13
2 2 2 4 2 3
+ 8*i*u1*u3*v2*a33 *b13 *n1 + 4*u1*v1 *v3*a33*b13 + 8*u1*v1 *a33*b13 *n1
4 3 2 3
+ 4*i*u1*v1*v2*v3*a33*b13 + 4*i*u1*v1*v2*a33*b13 *n1 + 4*u1*v2 *a33*b13 *n1
2 2 2
- 16*i*u1*v2*v3 *a33 *b13 *c13
2 2 2 3
+ u1*v2*v3*( - 8*a33 *b13 *m2 + 16*i*a33 *b13*c13*n1 + 4*i*a33*b13 *n3)
2 2 2 3 4
+ u1*v2*(16*i*a33 *c13*n1 + 8*i*a33*b13 *n1*n3) + 4*u1*v3 *a33*b13
2 3 3 2 2 2 3
+ 8*u1*v3 *a33*b13 *n1 - 4*u1*a33*b13*n1 - 4*u2 *v3 *a33 *b13
2 2 2 2 2 2 3
+ 4*u2 *a33 *b13*n1 - 8*i*u2*u3*v1*a33 *b13 *n1 + 8*u2*u3*v2*v3*a33 *b13
2 3 4 3
+ 4*i*u2*v1 *a33*b13 *n1 + 4*u2*v1*v2*v3*a33*b13 + 4*u2*v1*v2*a33*b13 *n1
2 2 2
+ 16*i*u2*v1*v3 *a33 *b13 *c13
2 2 2 3
+ u2*v1*v3*(8*a33 *b13 *m2 - 16*i*a33 *b13*c13*n1 - 4*i*a33*b13 *n3)
2 2 2 2 4
+ u2*v1*( - 16*i*a33 *c13*n1 - 8*i*a33*b13 *n1*n3) + 4*i*u2*v2 *v3*a33*b13
2 3 3 4 2 3
+ 8*i*u2*v2 *a33*b13 *n1 + 4*i*u2*v3 *a33*b13 + 8*i*u2*v3 *a33*b13 *n1
3 2 2 2 3 2 2
- 4*i*u2*a33*b13*n1 + 4*u3 *v3 *a33 *b13 - 16*u3*v1 *a33 *b13*c13*n1
3 2 2 2 2
- 4*u3*v1*v3*a33*b13 *n1 - 4*u3*v1*a33*b13 *n1 - 16*u3*v2 *a33 *b13*c13*n1
3 2 2
- 4*i*u3*v2*v3*a33*b13 *n1 - 4*i*u3*v2*a33*b13 *n1
2 2 2 2
+ u3*v3*( - 8*i*a33 *b13*m2*n1 - 16*a33 *c13*n1 - 4*a33*b13 *n1*n3)
2 3 2 2 2
- 4*u3*a33*b13*n1 *n3 + 8*v1 *a33*b13 *c13*n1 + 8*i*v1 *v2*a33*b13 *c13*n1
2 2 2 2 5 2
+ v1 *v3 *(16*a33 *b13*c13 - b13 ) + v1 *v3
2 2 2 2 4
*( - 16*i*a33 *b13*c13*m2 - 32*a33 *c13 *n1 - 8*a33*b13 *c13*n3 - 2*b13 *n1)
2 2 2 5 4
+ 8*v1*v2 *a33*b13 *c13*n1 - 2*i*v1*v2*v3 *b13 - 4*i*v1*v2*v3*b13 *n1
3 2 3 3
- 4*i*v1*v2*b13 *n1 + 8*v1*v3 *a33*b13 *c13
2 3 2 4
+ v1*v3 *( - 4*i*a33*b13 *m2 + 8*a33*b13 *c13*n1 - 2*b13 *n3)
2 2 3
+ v1*v3*( - 4*i*a33*b13 *m2*n1 - 8*a33*b13*c13*n1 - 6*b13 *n1*n3)
2 3 2 2
+ v1*( - 4*i*a33*b13*m2*n1 - 16*a33*c13*n1 - 4*b13 *n1 *n3)
3 2 2 2 2 2 5 2
+ 8*i*v2 *a33*b13 *c13*n1 + v2 *v3 *(16*a33 *b13*c13 + b13 ) + v2 *v3
2 2 2 2 4
*( - 16*i*a33 *b13*c13*m2 - 32*a33 *c13 *n1 - 8*a33*b13 *c13*n3 + 2*b13 *n1)
2 3 2 3 3
+ 4*v2 *b13 *n1 + 8*i*v2*v3 *a33*b13 *c13
2 3 2 4
+ v2*v3 *(4*a33*b13 *m2 + 8*i*a33*b13 *c13*n1 - 2*i*b13 *n3)
2 2 3
+ v2*v3*(4*a33*b13 *m2*n1 - 8*i*a33*b13*c13*n1 - 6*i*b13 *n1*n3)
2 3 2 2 2
+ v2*(4*a33*b13*m2*n1 - 16*i*a33*c13*n1 - 4*i*b13 *n1 *n3) + v3 *(
2 2 2 2
4*a33 *b13*m2 - 16*i*a33 *c13*m2*n1 - 4*i*a33*b13 *m2*n3
3 2 3 2
+ 8*a33*b13*c13*n1*n3 + 2*b13 *n1 - b13 *n3 )
2 2 2
+ v3*( - 8*i*a33*b13*m2*n1*n3 - 16*a33*c13*n1 *n3 - 4*b13 *n1*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=u1*v3*b13 + u1*n1 + i*u2*v3*b13 + i*u2*n1 + 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= - 2*u1**2*v3*a33**2*b13**2 - 2*u1**2*a33**2*b13*n1 + 2*u1*u3*v1*a33**2*b13**
2 - 2*i*u1*u3*v2*a33**2*b13**2 - u1*v1**2*a33*b13**3 - u1*v2**2*a33*b13**3 - 8*i
*u1*v2*v3*a33**2*b13*c13 + u1*v2*( - 2*a33**2*b13*m2 - 4*i*a33**2*c13*n1 - i*a33
*b13**2*n3) + 2*u1*v3*a33*b13**2*n1 + 2*u1*a33*b13*n1**2 - 2*u2**2*v3*a33**2*b13
**2 - 2*u2**2*a33**2*b13*n1 + 2*i*u2*u3*v1*a33**2*b13**2 + 2*u2*u3*v2*a33**2*b13
**2 - i*u2*v1**2*a33*b13**3 + 8*i*u2*v1*v3*a33**2*b13*c13 + u2*v1*(2*a33**2*b13*
m2 + 4*i*a33**2*c13*n1 + i*a33*b13**2*n3) - i*u2*v2**2*a33*b13**3 + 2*i*u2*v3*
a33*b13**2*n1 + 2*i*u2*a33*b13*n1**2 + 4*u3*v1**2*a33**2*b13*c13 + 4*u3*v2**2*
a33**2*b13*c13 + u3*v3*(2*i*a33**2*b13*m2 + 4*a33**2*c13*n1 + a33*b13**2*n3) + 2
*u3*a33*b13*n1*n3 - 2*v1**3*a33*b13**2*c13 - 2*i*v1**2*v2*a33*b13**2*c13 + 8*v1
**2*v3*a33**2*c13**2 - 2*v1*v2**2*a33*b13**2*c13 + v1*v3*(4*a33*b13*c13*n1 + b13
**3*n3) + v1*(4*a33*c13*n1**2 + b13**2*n1*n3) - 2*i*v2**3*a33*b13**2*c13 + 8*v2
**2*v3*a33**2*c13**2 + v2*v3*(4*i*a33*b13*c13*n1 + i*b13**3*n3) + v2*(4*i*a33*
c13*n1**2 + i*b13**2*n1*n3) + v3**2*(4*i*a33**2*c13*m2 - 2*a33*b13*c13*n3) + v3*
(2*i*a33*b13*m2*n3 + 4*a33*c13*n1*n3 + b13**2*n3**2)$
FI= - 4*u1**2*v3**2*a33**2*b13**3 + 4*u1**2*a33**2*b13*n1**2 + 8*u1*u3*v1*v3*a33
**2*b13**3 + 8*i*u1*u3*v2*a33**2*b13**2*n1 + 4*u1*v1**2*v3*a33*b13**4 + 8*u1*v1
**2*a33*b13**3*n1 + 4*i*u1*v1*v2*v3*a33*b13**4 + 4*i*u1*v1*v2*a33*b13**3*n1 + 4*
u1*v2**2*a33*b13**3*n1 - 16*i*u1*v2*v3**2*a33**2*b13**2*c13 + u1*v2*v3*( - 8*a33
**2*b13**2*m2 + 16*i*a33**2*b13*c13*n1 + 4*i*a33*b13**3*n3) + u1*v2*(16*i*a33**2
*c13*n1**2 + 8*i*a33*b13**2*n1*n3) + 4*u1*v3**3*a33*b13**4 + 8*u1*v3**2*a33*b13
**3*n1 - 4*u1*a33*b13*n1**3 - 4*u2**2*v3**2*a33**2*b13**3 + 4*u2**2*a33**2*b13*
n1**2 - 8*i*u2*u3*v1*a33**2*b13**2*n1 + 8*u2*u3*v2*v3*a33**2*b13**3 + 4*i*u2*v1
**2*a33*b13**3*n1 + 4*u2*v1*v2*v3*a33*b13**4 + 4*u2*v1*v2*a33*b13**3*n1 + 16*i*
u2*v1*v3**2*a33**2*b13**2*c13 + u2*v1*v3*(8*a33**2*b13**2*m2 - 16*i*a33**2*b13*
c13*n1 - 4*i*a33*b13**3*n3) + u2*v1*( - 16*i*a33**2*c13*n1**2 - 8*i*a33*b13**2*
n1*n3) + 4*i*u2*v2**2*v3*a33*b13**4 + 8*i*u2*v2**2*a33*b13**3*n1 + 4*i*u2*v3**3*
a33*b13**4 + 8*i*u2*v3**2*a33*b13**3*n1 - 4*i*u2*a33*b13*n1**3 + 4*u3**2*v3**2*
a33**2*b13**3 - 16*u3*v1**2*a33**2*b13*c13*n1 - 4*u3*v1*v3*a33*b13**3*n1 - 4*u3*
v1*a33*b13**2*n1**2 - 16*u3*v2**2*a33**2*b13*c13*n1 - 4*i*u3*v2*v3*a33*b13**3*n1
- 4*i*u3*v2*a33*b13**2*n1**2 + u3*v3*( - 8*i*a33**2*b13*m2*n1 - 16*a33**2*c13*
n1**2 - 4*a33*b13**2*n1*n3) - 4*u3*a33*b13*n1**2*n3 + 8*v1**3*a33*b13**2*c13*n1
+ 8*i*v1**2*v2*a33*b13**2*c13*n1 + v1**2*v3**2*(16*a33**2*b13*c13**2 - b13**5) +
v1**2*v3*( - 16*i*a33**2*b13*c13*m2 - 32*a33**2*c13**2*n1 - 8*a33*b13**2*c13*n3
- 2*b13**4*n1) + 8*v1*v2**2*a33*b13**2*c13*n1 - 2*i*v1*v2*v3**2*b13**5 - 4*i*v1
*v2*v3*b13**4*n1 - 4*i*v1*v2*b13**3*n1**2 + 8*v1*v3**3*a33*b13**3*c13 + v1*v3**2
*( - 4*i*a33*b13**3*m2 + 8*a33*b13**2*c13*n1 - 2*b13**4*n3) + v1*v3*( - 4*i*a33*
b13**2*m2*n1 - 8*a33*b13*c13*n1**2 - 6*b13**3*n1*n3) + v1*( - 4*i*a33*b13*m2*n1
**2 - 16*a33*c13*n1**3 - 4*b13**2*n1**2*n3) + 8*i*v2**3*a33*b13**2*c13*n1 + v2**
2*v3**2*(16*a33**2*b13*c13**2 + b13**5) + v2**2*v3*( - 16*i*a33**2*b13*c13*m2 -
32*a33**2*c13**2*n1 - 8*a33*b13**2*c13*n3 + 2*b13**4*n1) + 4*v2**2*b13**3*n1**2
+ 8*i*v2*v3**3*a33*b13**3*c13 + v2*v3**2*(4*a33*b13**3*m2 + 8*i*a33*b13**2*c13*
n1 - 2*i*b13**4*n3) + v2*v3*(4*a33*b13**2*m2*n1 - 8*i*a33*b13*c13*n1**2 - 6*i*
b13**3*n1*n3) + v2*(4*a33*b13*m2*n1**2 - 16*i*a33*c13*n1**3 - 4*i*b13**2*n1**2*
n3) + v3**2*(4*a33**2*b13*m2**2 - 16*i*a33**2*c13*m2*n1 - 4*i*a33*b13**2*m2*n3 +
8*a33*b13*c13*n1*n3 + 2*b13**3*n1**2 - b13**3*n3**2) + v3*( - 8*i*a33*b13*m2*n1
*n3 - 16*a33*c13*n1**2*n3 - 4*b13**2*n1*n3**2)$