Solution 50 to problem e3quant
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Expressions
The solution is given through the following expressions:
a22= - a33
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
1 2
---*b33
4
c33=----------
a33
n1=0
n3=0
m1=0
m2=0
m3=0
r6=0
r5=0
r4=0
r3=0
1
- 2*k1*n2 - ---*k12*n2
2
r2=-------------------------
a33
r1=0
q20=0
q19=
3 2 2 1 2 2 1 2 2 1 2 2
- ---*a33 *b33 *k1 + ---*a33 *b33 *k12 + ----*b33 *k1*n2 + ----*b33 *k12*n2
4 4 16 16
--------------------------------------------------------------------------------
4
a33
1 2
---*b33 *k12*n2
4
q18=-----------------
3
a33
q17=0
3 2 1 2
- ---*b33 *k1 + ---*b33 *k12
4 4
q16=-------------------------------
2
a33
q14=0
1 1
- ---*a33*k38*n2 - ---*b33*k1*n2
2 2
q13=-----------------------------------
2
a33
q11=0
3 2 2 1 2
- a33 *k38 - a33 *b33*k1 + a33 *b33*k12 + ---*b33*k1*n2
4
q10=-----------------------------------------------------------
3
a33
q9=0
q8=0
2 2 1 2 1 2
a33 *k1 + a33 *k12 + ---*k1*n2 - ---*k12*n2
4 4
q7=-----------------------------------------------
2
a33
1
---*b33*k12*n2
2
q6=----------------
2
a33
q5=0
- a33*k38 - b33*k1 + b33*k12
q4=-------------------------------
a33
k1*n2
q3=-------
a33
q2=0
q1=5*k1 + k12
p56=0
1 2 1 3 1 3
- ---*a33 *b33*k16*n2 - ---*b33 *k1*n2 + ---*b33 *k12*n2
4 8 8
p55=-----------------------------------------------------------
4
a33
p54=0
1 2 1 3 1 3
- ---*a33 *b33*k16*n2 - ---*b33 *k1*n2 + ----*b33 *k12*n2
4 4 16
p53=------------------------------------------------------------
4
a33
p52=0
p51=0
p50=0
p49=0
1 2 1 3 1 3
- ---*a33 *b33*k16*n2 - ---*b33 *k1*n2 + ----*b33 *k12*n2
4 4 16
p48=------------------------------------------------------------
4
a33
p47=0
p46=0
1 1 2 1 2
- ---*a33*b33*k38*n2 + ---*b33 *k1*n2 + ---*b33 *k12*n2
4 2 4
p45=----------------------------------------------------------
3
a33
p44=0
p43=0
2 1 2
b33 *k1 - ---*b33 *k12
4
p42=------------------------
2
a33
p41=0
p40=0
1
- ---*b33*k12*n2
4
p39=-------------------
2
a33
p38=0
p37=0
1 2 1 2
- ---*a33 *k16*n2 - ---*b33 *k1*n2
2 4
p36=-------------------------------------
3
a33
p35=0
1 2 1 1 2 1 2
- ---*a33 *k16*n2 - ---*a33*b33*k38*n2 - ---*b33 *k1*n2 + ---*b33 *k12*n2
2 4 2 8
p34=----------------------------------------------------------------------------
3
a33
1 2
---*b33 *k12
4
p33=--------------
2
a33
p32=0
1 2 1 2 1 2
- ---*a33 *k16*n2 - ---*b33 *k1*n2 + ---*b33 *k12*n2
2 2 8
p31=-------------------------------------------------------
3
a33
1 1
---*a33*k38*n2 + b33*k1*n2 - ---*b33*k12*n2
2 2
p30=---------------------------------------------
2
a33
p29=0
2*a33*k38 + 2*b33*k1
p28=----------------------
a33
1
- ---*k12*n2
2
p27=---------------
a33
p26=0
1 1 1
---*a33*k38*n2 - ---*b33*k1*n2 - ---*b33*k12*n2
2 2 4
p25=-------------------------------------------------
2
a33
p24=0
p23=0
1
- k1*n2 + ---*k12*n2
2
p22=-----------------------
a33
p21=0
1 2
- ---*b33 *k12
4
p20=-----------------
2
a33
p19=0
p18=0
1
- ---*b33*k38*n2
4
p17=-------------------
2
a33
p16=0
p15=0
- 2*a33*k38 - 2*b33*k1
p14=-------------------------
a33
p13=0
p12=0
p11=0
p10=0
1
---*k38*n2
2
p9=------------
a33
p8= - 4*k1
p7=0
p6=0
1 1
- ---*b33*k1*n2 - ---*b33*k12*n2
2 4
p5=-----------------------------------
2
a33
p4=0
p3=0
1
- k1*n2 + ---*k12*n2
2
p2=-----------------------
a33
p1=0
k125=0
1 2 2 1 4 1 4
---*a33 *b33 *k16 + ---*b33 *k1 - ----*b33 *k12
4 8 16
k124=-------------------------------------------------
4
a33
k123=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + ----*b33 *k1 - ----*b33 *k12
4 16 16
k122=--------------------------------------------------
4
a33
k121=0
k120=0
k119=0
k118=0
1 2 2 1 4 1 4
---*a33 *b33 *k16 + ---*b33 *k1 - ----*b33 *k12
4 8 16
k117=-------------------------------------------------
4
a33
k116=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + ---*b33 *k1 - ---*b33 *k12
2 8 8
k115=------------------------------------------------
4
a33
k114=0
k113=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + ----*b33 *k1 - ----*b33 *k12
4 16 16
k112=--------------------------------------------------
4
a33
k110=0
1 3
- ---*b33 *k1
2
k109=----------------
3
a33
k108=0
k107=0
k106=0
k105=0
1 3
- ---*b33 *k1
2
k104=----------------
3
a33
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
a33*k38 - b33*k12
k95=-------------------
a33
k94=0
k93=0
k91=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k90=-------------------------------------------
3
a33
k89=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k88=-------------------------------------------
3
a33
k87=0
k86=0
k85=0
k84=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k83=-------------------------------------------
3
a33
k82=0
k81=0
2 1 2
- 2*b33 *k1 + ---*b33 *k12
2
k80=-----------------------------
2
a33
k79=0
k78=0
k77=0
k76=0
k75=0
k74=k38
k73=0
k72=0
2 1 2 1 2
a33 *k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k71=---------------------------------------
2
a33
k70=0
k69=k16
k68=0
k67=0
2 2 1 2
a33 *k16 + b33 *k1 - ---*b33 *k12
4
k66=-----------------------------------
2
a33
- 2*b33*k1
k65=-------------
a33
k64=0
k63=0
k62=k12
k61=0
k59=0
k58=0
k57=k1
k56=0
k55=0
k54=0
k53=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k52=-------------------------------------------
3
a33
k51=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k50=-------------------------------------------
3
a33
k49=0
k48=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k47=-------------------------------------------
3
a33
k46=0
k45=0
k44=0
2 1 2
- 2*b33 *k1 + ---*b33 *k12
2
k43=-----------------------------
2
a33
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
2 1 2
- 2*b33 *k1 + ---*b33 *k12
2
k32=-----------------------------
2
a33
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
2 1 2 1 2
a33 *k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k21=---------------------------------------
2
a33
k20=0
2 2 1 2
a33 *k16 + b33 *k1 - ---*b33 *k12
4
k19=-----------------------------------
2
a33
k18=0
k17=0
- 2*b33*k1
k15=-------------
a33
k14=0
k13=0
k11=0
k10=0
k9=0
k8=0
k7=2*k1
k6=0
k5=0
k4=0
k3=0
k2=0
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:
k38,k16,k12,k1,b33,n2,a33
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2 2 2 2
HAM=( - 4*a33 *u1 - 4*a33 *u2 + 4*a33 *u3 + 4*a33*b33*u3*v3 + 4*a33*n2*u2
2 2
+ b33 *v3 )/(4*a33)
4 4 4 2 4 2
INT=(16*a33 *k1*u1 + 32*a33 *k1*u1 *u2*u3 + 80*a33 *k1*u1
4 2 4 2 4
+ 16*a33 *k1*u1*u2*v2 - 64*a33 *k1*u1*u3 + 16*a33 *k1*u1*v1
4 2 4 2 4
+ 16*a33 *k12*u1 + 16*a33 *k12*u1*v1*v2 + 16*a33 *k12*u1*v1
4 2 2 4 3 4 3
+ 16*a33 *k12*u2 *u3 + 16*a33 *k16*u1 *v1 + 16*a33 *k16*u1 *v3
4 4 3 4 3
+ 16*a33 *k16*u1*u2*u3*v1 + 16*a33 *k16*u1*v2 + 16*a33 *k16*u2 *v1
4 3 4 2 4
+ 16*a33 *k16*v1*v2 + 16*a33 *k38*u1*u2 *v2 - 32*a33 *k38*u1*u3*v1
4 4 3 4
- 16*a33 *k38*u1*u3 + 16*a33 *k38*u2 *v3 + 16*a33 *k38*u2*u3*v2*v3
4 4 2 3
+ 32*a33 *k38*u2*v1*v2 - 16*a33 *k38*v1 - 32*a33 *b33*k1*u1*u3*v1
3 3 3 4
- 16*a33 *b33*k1*u1*u3 + 32*a33 *b33*k1*u2*v1*v2 - 32*a33 *b33*k1*u3
3 2 2 3 2 3
- 32*a33 *b33*k1*v1 *v2 - 16*a33 *b33*k1*v1 + 16*a33 *b33*k12*u1*u3
3 3 2
- 16*a33 *b33*k12*u2*u3*v2*v3 + 16*a33 *b33*k12*v1
3 3 2
+ 16*a33 *b33*k16*u1*u2*v1*v2 + 16*a33 *b33*k16*u1*v1 *v2
3 2 3
+ 16*a33 *b33*k16*u2 *v1*v3 + 16*a33 *b33*k16*u2*u3*v1*v2
3 2 3 3
+ 16*a33 *b33*k16*u2*v1 *v3 + 16*a33 *b33*k16*v1 *v3
3 2 3 3 2
- 16*a33 *k1*n2*u1 *u2 - 16*a33 *k1*n2*u1*u2*v2 + 16*a33 *k1*n2*u2
3 3 2 3
- 32*a33 *k1*n2*u2 + 8*a33 *k12*n2*u1 *u2 + 8*a33 *k12*n2*u1*u2*v2
3 3 3 2
- 8*a33 *k12*n2*u1*v1*v2 - 8*a33 *k12*n2*u2 - 8*a33 *k16*n2*u1 *v3
3 2 3 2 3 2
- 8*a33 *k16*n2*u1*v2 - 8*a33 *k16*n2*v1*v2 + 8*a33 *k38*n2*u2*u3
3 3 3 2
+ 8*a33 *k38*n2*u2*u3*v2 - 8*a33 *k38*n2*u3*v2 + 8*a33 *k38*n2*v1 *v2
2 2 3 2 2
+ 8*a33 *b33 *k1*u1 *v3 + 8*a33 *b33 *k1*u1*u2*u3*v1
2 2 2 2 2 3
- 32*a33 *b33 *k1*u1*u3 *v2 - 32*a33 *b33 *k1*u1*v1
2 2 2 2 3
+ 16*a33 *b33 *k1*u1*v1*v3 + 16*a33 *b33 *k1*u1*v2
2 2 2 2 3 2 2 3
- 12*a33 *b33 *k1*u1*v3 + 16*a33 *b33 *k1*u2 *v1 - 32*a33 *b33 *k1*u3 *v3
2 2 2 2 3
- 12*a33 *b33 *k1*v1*v3 - 4*a33 *b33 *k12*u1 *v3
2 2 2 2 2
- 4*a33 *b33 *k12*u1*u2*u3*v1 + 8*a33 *b33 *k12*u1*u3 *v2
2 2 3 2 2
+ 8*a33 *b33 *k12*u1*v1 - 4*a33 *b33 *k12*u1*v1*v3
2 2 3 2 2 2 2 3
- 4*a33 *b33 *k12*u1*v2 + 4*a33 *b33 *k12*u1*v3 - 4*a33 *b33 *k12*u2 *v1
2 2 3 2 2 2 2 2 3
+ 8*a33 *b33 *k12*u3 *v3 + 4*a33 *b33 *k12*u3*v2 - 4*a33 *b33 *k12*v1
2 2 2 2 2
+ 4*a33 *b33 *k12*v1*v3 + 4*a33 *b33 *k16*u1*v1*v3
2 2 2 2 2 3
+ 4*a33 *b33 *k16*u2*v2*v3 + 4*a33 *b33 *k16*u2*v3
2 2 2 2 2 2 3
+ 8*a33 *b33 *k16*v1 *v3 + 4*a33 *b33 *k16*v1*v3
2 2 2
- 8*a33 *b33*k1*n2*u1 *u3 - 8*a33 *b33*k1*n2*u2*u3*v2
2 2 2
- 8*a33 *b33*k1*n2*u3*v2 + 16*a33 *b33*k1*n2*v1 *v2
2 2 2
- 4*a33 *b33*k12*n2*u1 *u3 - 4*a33 *b33*k12*n2*u1*u3*v3
2 2 2
- 4*a33 *b33*k12*n2*u2*u3*v2 + 8*a33 *b33*k12*n2*u3
2 2 2
- 8*a33 *b33*k12*n2*v1 *v2 - 4*a33 *b33*k16*n2*u3*v2*v3
2 2 2 2
- 4*a33 *b33*k16*n2*u3*v3 - 4*a33 *b33*k16*n2*v2*v3
2 2 2 2
- 4*a33 *b33*k38*n2*u1*v1 - 4*a33 *b33*k38*n2*v1 *v3
2 2 2 2 2 2
- 4*a33 *b33*k38*n2*v1*v2 + 4*a33 *k1*n2 *u1*v1 - 4*a33 *k12*n2 *u1*v1
3 3 2
+ 8*a33*b33 *k1*u1*u2*v1*v2 - 8*a33*b33 *k1*u1*u3*v3
3 2 3 2
+ 8*a33*b33 *k1*u1*v1 *v2 + 8*a33*b33 *k1*u2 *v1*v3
3 3 2
+ 8*a33*b33 *k1*u2*u3*v1*v2 + 8*a33*b33 *k1*u2*v1 *v3
3 3 3 2
+ 8*a33*b33 *k1*v1 *v3 - 8*a33*b33 *k1*v1*v2 *v3
3 3 2
- 4*a33*b33 *k12*u1*u2*v1*v2 - 4*a33*b33 *k12*u1*v1 *v2
3 2 3
- 4*a33*b33 *k12*u2 *v1*v3 - 4*a33*b33 *k12*u2*u3*v1*v2
3 2 3 3
- 4*a33*b33 *k12*u2*v1 *v3 - 4*a33*b33 *k12*v1 *v3
2 2 2 2
- 4*a33*b33 *k1*n2*u1 *v3 - 8*a33*b33 *k1*n2*u1*v2
2 2 2 2
+ 8*a33*b33 *k1*n2*v1 *v3 - 8*a33*b33 *k1*n2*v1*v2
2 2 2
+ 2*a33*b33 *k12*n2*u1*v2 + 4*a33*b33 *k12*n2*u3*v3
2 2 2 2
+ 4*a33*b33 *k12*n2*v1 *v3 + 2*a33*b33 *k12*n2*v1*v2
2 2 4 2 4 2
+ 4*a33*b33*k1*n2 *v1 + 3*b33 *k1*u1*v1*v3 + 2*b33 *k1*u2*v2*v3
4 3 4 2 2 4 3
+ 3*b33 *k1*u2*v3 + 6*b33 *k1*v1 *v3 + 2*b33 *k1*v1*v3
4 2 4 2 4 3
- b33 *k12*u1*v1*v3 - b33 *k12*u2*v2*v3 - b33 *k12*u2*v3
4 2 2 4 3 3
- 2*b33 *k12*v1 *v3 - b33 *k12*v1*v3 - 4*b33 *k1*n2*u3*v2*v3
3 2 3 2 3
- 4*b33 *k1*n2*u3*v3 - 2*b33 *k1*n2*v2*v3 + b33 *k12*n2*u3*v2*v3
3 2 3 2 2 2
+ b33 *k12*n2*u3*v3 + 2*b33 *k12*n2*v2*v3 + b33 *k1*n2 *v1*v3
2 2 4
+ b33 *k12*n2 *v1*v3)/(16*a33 )
And again in machine readable form:
HAM=( - 4*a33**2*u1**2 - 4*a33**2*u2**2 + 4*a33**2*u3**2 + 4*a33*b33*u3*v3 + 4*
a33*n2*u2 + b33**2*v3**2)/(4*a33)$
INT=(16*a33**4*k1*u1**4 + 32*a33**4*k1*u1**2*u2*u3 + 80*a33**4*k1*u1**2 + 16*a33
**4*k1*u1*u2*v2**2 - 64*a33**4*k1*u1*u3**2 + 16*a33**4*k1*u1*v1 + 16*a33**4*k12*
u1**2 + 16*a33**4*k12*u1*v1*v2**2 + 16*a33**4*k12*u1*v1 + 16*a33**4*k12*u2**2*u3
**2 + 16*a33**4*k16*u1**3*v1 + 16*a33**4*k16*u1**3*v3 + 16*a33**4*k16*u1*u2*u3*
v1 + 16*a33**4*k16*u1*v2**3 + 16*a33**4*k16*u2**3*v1 + 16*a33**4*k16*v1*v2**3 +
16*a33**4*k38*u1*u2**2*v2 - 32*a33**4*k38*u1*u3*v1 - 16*a33**4*k38*u1*u3 + 16*
a33**4*k38*u2**3*v3 + 16*a33**4*k38*u2*u3*v2*v3 + 32*a33**4*k38*u2*v1*v2 - 16*
a33**4*k38*v1**2 - 32*a33**3*b33*k1*u1*u3*v1 - 16*a33**3*b33*k1*u1*u3 + 32*a33**
3*b33*k1*u2*v1*v2 - 32*a33**3*b33*k1*u3**4 - 32*a33**3*b33*k1*v1**2*v2**2 - 16*
a33**3*b33*k1*v1**2 + 16*a33**3*b33*k12*u1*u3 - 16*a33**3*b33*k12*u2*u3*v2*v3 +
16*a33**3*b33*k12*v1**2 + 16*a33**3*b33*k16*u1*u2*v1*v2 + 16*a33**3*b33*k16*u1*
v1**2*v2 + 16*a33**3*b33*k16*u2**2*v1*v3 + 16*a33**3*b33*k16*u2*u3*v1*v2 + 16*
a33**3*b33*k16*u2*v1**2*v3 + 16*a33**3*b33*k16*v1**3*v3 - 16*a33**3*k1*n2*u1**2*
u2 - 16*a33**3*k1*n2*u1*u2*v2 + 16*a33**3*k1*n2*u2**2 - 32*a33**3*k1*n2*u2 + 8*
a33**3*k12*n2*u1**2*u2 + 8*a33**3*k12*n2*u1*u2*v2 - 8*a33**3*k12*n2*u1*v1*v2 - 8
*a33**3*k12*n2*u2 - 8*a33**3*k16*n2*u1**2*v3 - 8*a33**3*k16*n2*u1*v2**2 - 8*a33
**3*k16*n2*v1*v2**2 + 8*a33**3*k38*n2*u2*u3**2 + 8*a33**3*k38*n2*u2*u3*v2 - 8*
a33**3*k38*n2*u3*v2 + 8*a33**3*k38*n2*v1**2*v2 + 8*a33**2*b33**2*k1*u1**3*v3 + 8
*a33**2*b33**2*k1*u1*u2*u3*v1 - 32*a33**2*b33**2*k1*u1*u3**2*v2 - 32*a33**2*b33
**2*k1*u1*v1**3 + 16*a33**2*b33**2*k1*u1*v1*v3 + 16*a33**2*b33**2*k1*u1*v2**3 -
12*a33**2*b33**2*k1*u1*v3 + 16*a33**2*b33**2*k1*u2**3*v1 - 32*a33**2*b33**2*k1*
u3**3*v3 - 12*a33**2*b33**2*k1*v1*v3 - 4*a33**2*b33**2*k12*u1**3*v3 - 4*a33**2*
b33**2*k12*u1*u2*u3*v1 + 8*a33**2*b33**2*k12*u1*u3**2*v2 + 8*a33**2*b33**2*k12*
u1*v1**3 - 4*a33**2*b33**2*k12*u1*v1*v3 - 4*a33**2*b33**2*k12*u1*v2**3 + 4*a33**
2*b33**2*k12*u1*v3 - 4*a33**2*b33**2*k12*u2**3*v1 + 8*a33**2*b33**2*k12*u3**3*v3
+ 4*a33**2*b33**2*k12*u3*v2**2 - 4*a33**2*b33**2*k12*v1**3 + 4*a33**2*b33**2*
k12*v1*v3 + 4*a33**2*b33**2*k16*u1*v1*v3**2 + 4*a33**2*b33**2*k16*u2*v2*v3**2 +
4*a33**2*b33**2*k16*u2*v3**3 + 8*a33**2*b33**2*k16*v1**2*v3**2 + 4*a33**2*b33**2
*k16*v1*v3**3 - 8*a33**2*b33*k1*n2*u1**2*u3 - 8*a33**2*b33*k1*n2*u2*u3*v2 - 8*
a33**2*b33*k1*n2*u3*v2 + 16*a33**2*b33*k1*n2*v1**2*v2 - 4*a33**2*b33*k12*n2*u1**
2*u3 - 4*a33**2*b33*k12*n2*u1*u3*v3 - 4*a33**2*b33*k12*n2*u2*u3*v2 + 8*a33**2*
b33*k12*n2*u3**2 - 8*a33**2*b33*k12*n2*v1**2*v2 - 4*a33**2*b33*k16*n2*u3*v2*v3 -
4*a33**2*b33*k16*n2*u3*v3**2 - 4*a33**2*b33*k16*n2*v2*v3**2 - 4*a33**2*b33*k38*
n2*u1*v1**2 - 4*a33**2*b33*k38*n2*v1**2*v3 - 4*a33**2*b33*k38*n2*v1*v2**2 + 4*
a33**2*k1*n2**2*u1*v1 - 4*a33**2*k12*n2**2*u1*v1 + 8*a33*b33**3*k1*u1*u2*v1*v2 -
8*a33*b33**3*k1*u1*u3*v3**2 + 8*a33*b33**3*k1*u1*v1**2*v2 + 8*a33*b33**3*k1*u2
**2*v1*v3 + 8*a33*b33**3*k1*u2*u3*v1*v2 + 8*a33*b33**3*k1*u2*v1**2*v3 + 8*a33*
b33**3*k1*v1**3*v3 - 8*a33*b33**3*k1*v1*v2**2*v3 - 4*a33*b33**3*k12*u1*u2*v1*v2
- 4*a33*b33**3*k12*u1*v1**2*v2 - 4*a33*b33**3*k12*u2**2*v1*v3 - 4*a33*b33**3*k12
*u2*u3*v1*v2 - 4*a33*b33**3*k12*u2*v1**2*v3 - 4*a33*b33**3*k12*v1**3*v3 - 4*a33*
b33**2*k1*n2*u1**2*v3 - 8*a33*b33**2*k1*n2*u1*v2**2 + 8*a33*b33**2*k1*n2*v1**2*
v3 - 8*a33*b33**2*k1*n2*v1*v2**2 + 2*a33*b33**2*k12*n2*u1*v2**2 + 4*a33*b33**2*
k12*n2*u3*v3 + 4*a33*b33**2*k12*n2*v1**2*v3 + 2*a33*b33**2*k12*n2*v1*v2**2 + 4*
a33*b33*k1*n2**2*v1**2 + 3*b33**4*k1*u1*v1*v3**2 + 2*b33**4*k1*u2*v2*v3**2 + 3*
b33**4*k1*u2*v3**3 + 6*b33**4*k1*v1**2*v3**2 + 2*b33**4*k1*v1*v3**3 - b33**4*k12
*u1*v1*v3**2 - b33**4*k12*u2*v2*v3**2 - b33**4*k12*u2*v3**3 - 2*b33**4*k12*v1**2
*v3**2 - b33**4*k12*v1*v3**3 - 4*b33**3*k1*n2*u3*v2*v3 - 4*b33**3*k1*n2*u3*v3**2
- 2*b33**3*k1*n2*v2*v3**2 + b33**3*k12*n2*u3*v2*v3 + b33**3*k12*n2*u3*v3**2 + 2
*b33**3*k12*n2*v2*v3**2 + b33**2*k1*n2**2*v1*v3 + b33**2*k12*n2**2*v1*v3)/(16*
a33**4)$