Solution 20 to problem e3quant
Expressions |
Parameters |
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Back to problem e3quant
Expressions
The solution is given through the following expressions:
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
1 2
- ---*b33
4
c33=-------------
a22
n2=0
n3=0
1 1
- ---*a22*b33*n1 - ---*a33*b33*n1
2 2
m1=------------------------------------
2
a22 - a22*a33
m2=0
m3=0
r6=0
r5=0
r3=0
r2=0
- 2*a22*r4
r1=-------------
b33
q20=0
1 1
- ---*a22*b33*r4 + ---*a33*b33*r4
2 2
q19=------------------------------------
a22*n1
q18=0
q17=0
1 1
- ---*a22*b33*r4 + ---*a33*b33*r4
2 2
q16=------------------------------------
a22*n1
q14=0
q13=0
q11=0
2*a22*r4 - 2*a33*r4 - k38*n1
q10=------------------------------
n1
q9=0
q8=0
2
- 2*a22 *r4 + 2*a22*a33*r4
q7=-----------------------------
b33*n1
q6=0
q5=0
2*a22*r4 - 2*a33*r4 - k38*n1
q4=------------------------------
n1
q3=0
q2=0
2
- 2*a22 *r4 + 2*a22*a33*r4
q1=-----------------------------
b33*n1
p56=0
p55=0
p54=0
p53=0
1 2 1 1 2
- ---*a22 *b33*p16 + ---*a22*a33*b33*p16 - ---*b33 *k38*n1
2 2 4
p52=-------------------------------------------------------------
3 2
a22 - a22 *a33
p51=0
1 2 1 1 2
- ---*a22 *b33*p16 + ---*a22*a33*b33*p16 - ---*b33 *k38*n1
2 2 4
p50=-------------------------------------------------------------
3 2
a22 - a22 *a33
p49=0
p48=0
1 2 1 1 2
- ---*a22 *b33*p16 + ---*a22*a33*b33*p16 - ---*b33 *k38*n1
2 2 4
p47=-------------------------------------------------------------
3 2
a22 - a22 *a33
p46=0
p45=0
p44=0
1
- ---*b33*k38*n1
2
p43=-------------------
2
a22 - a22*a33
p42=0
p41=0
p40=0
p39=0
p38=0
p37=0
p36=0
p35=0
p34=0
p33=0
1
- ---*b33*k38*n1
2
p32=-------------------
2
a22 - a22*a33
p31=0
p30=0
p29=0
p28=2*k38
p27=0
p26=0
p25=0
p24=0
p23=0
p22=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
p21=-----------------------------------------
2
a22 - a22*a33
p20=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
p19=-----------------------------------------
2
a22 - a22*a33
p18=0
p17=0
- k38*n1
p15=-----------
a22 - a33
p14= - 2*k38
p13=0
p12=0
p11=0
- k38*n1
p10=-----------
a22 - a33
p9=0
p8=0
p7=0
p6=0
p5=0
- k38*n1
p4=-----------
a22 - a33
p3=0
p2=0
p1=0
k125=0
1 2 2 1 2 1 3
---*a22 *b33 *p16 - ---*a22*a33*b33 *p16 + ---*b33 *k38*n1
4 4 8
k124=------------------------------------------------------------
3
a22 *n1
k123=0
1 2 2 1 2 1 3
---*a22 *b33 *p16 - ---*a22*a33*b33 *p16 + ---*b33 *k38*n1
4 4 8
k122=------------------------------------------------------------
3
a22 *n1
k121=0
k120=0
k119=0
k118=0
1 2 2 1 2 1 3
---*a22 *b33 *p16 - ---*a22*a33*b33 *p16 + ---*b33 *k38*n1
4 4 8
k117=------------------------------------------------------------
3
a22 *n1
k116=0
1 2 2 1 2 1 3
---*a22 *b33 *p16 - ---*a22*a33*b33 *p16 + ---*b33 *k38*n1
2 2 4
k115=------------------------------------------------------------
3
a22 *n1
k114=0
k113=0
1 2 2 1 2 1 3
---*a22 *b33 *p16 - ---*a22*a33*b33 *p16 + ---*b33 *k38*n1
4 4 8
k112=------------------------------------------------------------
3
a22 *n1
k110=0
k109=0
k108=0
k107=0
k106=0
k105=0
k104=0
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
k95=k38
k94=0
k93=0
k91=0
2 1 2
- a22 *b33*p16 + a22*a33*b33*p16 - ---*b33 *k38*n1
2
k90=-----------------------------------------------------
2
a22 *n1
k89=0
2 1 2
- a22 *b33*p16 + a22*a33*b33*p16 - ---*b33 *k38*n1
2
k88=-----------------------------------------------------
2
a22 *n1
k87=0
k86=0
k85=0
k84=0
2 1 2
- a22 *b33*p16 + a22*a33*b33*p16 - ---*b33 *k38*n1
2
k83=-----------------------------------------------------
2
a22 *n1
k82=0
k81=0
k80=0
k79=0
k78=0
k77=0
k76=0
k75=0
k74=k38
k73=0
k72=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
k71=-----------------------------------------
a22*n1
k70=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
k69=-----------------------------------------
a22*n1
k68=0
k67=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
k66=-----------------------------------------
a22*n1
k65=0
k64=0
k63=0
k62=0
k61=0
k59=0
k58=0
k57=0
k56=0
k55=0
k54=0
k53=0
2 1 2
- a22 *b33*p16 + a22*a33*b33*p16 - ---*b33 *k38*n1
2
k52=-----------------------------------------------------
2
a22 *n1
k51=0
2 1 2
- a22 *b33*p16 + a22*a33*b33*p16 - ---*b33 *k38*n1
2
k50=-----------------------------------------------------
2
a22 *n1
k49=0
k48=0
2 1 2
- a22 *b33*p16 + a22*a33*b33*p16 - ---*b33 *k38*n1
2
k47=-----------------------------------------------------
2
a22 *n1
k46=0
k45=0
k44=0
k43=0
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
k32=0
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
k21=-----------------------------------------
a22*n1
k20=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
k19=-----------------------------------------
a22*n1
k18=0
k17=0
2 1
a22 *p16 - a22*a33*p16 + ---*b33*k38*n1
2
k16=-----------------------------------------
a22*n1
k15=0
k14=0
k13=0
k12=0
k11=0
k10=0
k9=0
k8=0
k7=0
k6=0
k5=0
k4=0
k3=0
k2=0
k1=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:
b33,r4,p16,k38,n1,a33,a22
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
3 2 3 2 2 2 2 2 2 2
HAM=(4*a22 *u1 + 4*a22 *u2 - 4*a22 *a33*u1 - 4*a22 *a33*u2 + 4*a22 *a33*u3
2 2 2 2
+ 4*a22 *b33*u3*v3 + 4*a22 *n1*u1 - 4*a22*a33 *u3 - 4*a22*a33*b33*u3*v3
2 2 2 2
- 4*a22*a33*n1*u1 - a22*b33 *v3 - 2*a22*b33*n1*v1 + a33*b33 *v3
- 2*a33*b33*n1*v1)/(4*a22*(a22 - a33))
6 2 6 5 2
INT=( - 16*a22 *r4*u1 - 16*a22 *r4*u1*v1 + 32*a22 *a33*r4*u1
5 5 3 5 3
+ 32*a22 *a33*r4*u1*v1 + 8*a22 *b33*p16*u1 *v1 + 8*a22 *b33*p16*u1 *v3
5 5 3
+ 8*a22 *b33*p16*u1*u2*u3*v1 + 8*a22 *b33*p16*u1*v2
5 3 5 3 5
+ 8*a22 *b33*p16*u2 *v1 + 8*a22 *b33*p16*v1*v2 + 16*a22 *b33*r4*u1*u3
5 2 5 4 2 2
+ 16*a22 *b33*r4*v1 - 16*a22 *n1*r4*u1 - 16*a22 *a33 *r4*u1
4 2 4 3
- 16*a22 *a33 *r4*u1*v1 - 16*a22 *a33*b33*p16*u1 *v1
4 3 4
- 16*a22 *a33*b33*p16*u1 *v3 - 16*a22 *a33*b33*p16*u1*u2*u3*v1
4 3 4 3
- 16*a22 *a33*b33*p16*u1*v2 - 16*a22 *a33*b33*p16*u2 *v1
4 3 4
- 16*a22 *a33*b33*p16*v1*v2 - 32*a22 *a33*b33*r4*u1*u3
4 2 4
- 32*a22 *a33*b33*r4*v1 + 16*a22 *a33*n1*r4*u1
4 2 4 2 2
- 8*a22 *b33 *p16*u1*u2*v1*v2 - 8*a22 *b33 *p16*u1*v1 *v2
4 2 2 4 2
- 8*a22 *b33 *p16*u2 *v1*v3 - 8*a22 *b33 *p16*u2*u3*v1*v2
4 2 2 4 2 3
- 8*a22 *b33 *p16*u2*v1 *v3 - 8*a22 *b33 *p16*v1 *v3
4 2 4 2
- 4*a22 *b33 *r4*u1*v3 - 4*a22 *b33 *r4*v1*v3
4 2 4
+ 8*a22 *b33*k38*n1*u1*u2 *v2 - 16*a22 *b33*k38*n1*u1*u3*v1
4 4 3
- 8*a22 *b33*k38*n1*u1*u3 + 8*a22 *b33*k38*n1*u2 *v3
4 4
+ 8*a22 *b33*k38*n1*u2*u3*v2*v3 + 16*a22 *b33*k38*n1*u2*v1*v2
4 2 4 2
- 8*a22 *b33*k38*n1*v1 + 8*a22 *b33*n1*p16*u1 *v2
4 2 4 2
+ 8*a22 *b33*n1*p16*u3 *v1 + 8*a22 *b33*n1*p16*u3*v1
4 3 2 3
+ 8*a22 *b33*n1*r4*v1 + 8*a22 *a33 *b33*p16*u1 *v1
3 2 3 3 2
+ 8*a22 *a33 *b33*p16*u1 *v3 + 8*a22 *a33 *b33*p16*u1*u2*u3*v1
3 2 3 3 2 3
+ 8*a22 *a33 *b33*p16*u1*v2 + 8*a22 *a33 *b33*p16*u2 *v1
3 2 3 3 2
+ 8*a22 *a33 *b33*p16*v1*v2 + 16*a22 *a33 *b33*r4*u1*u3
3 2 2 3 2
+ 16*a22 *a33 *b33*r4*v1 + 16*a22 *a33*b33 *p16*u1*u2*v1*v2
3 2 2 3 2 2
+ 16*a22 *a33*b33 *p16*u1*v1 *v2 + 16*a22 *a33*b33 *p16*u2 *v1*v3
3 2 3 2 2
+ 16*a22 *a33*b33 *p16*u2*u3*v1*v2 + 16*a22 *a33*b33 *p16*u2*v1 *v3
3 2 3 3 2
+ 16*a22 *a33*b33 *p16*v1 *v3 + 8*a22 *a33*b33 *r4*u1*v3
3 2 3 2
+ 8*a22 *a33*b33 *r4*v1*v3 - 8*a22 *a33*b33*k38*n1*u1*u2 *v2
3 3
+ 16*a22 *a33*b33*k38*n1*u1*u3*v1 + 8*a22 *a33*b33*k38*n1*u1*u3
3 3 3
- 8*a22 *a33*b33*k38*n1*u2 *v3 - 8*a22 *a33*b33*k38*n1*u2*u3*v2*v3
3 3 2
- 16*a22 *a33*b33*k38*n1*u2*v1*v2 + 8*a22 *a33*b33*k38*n1*v1
3 2 3 2
- 8*a22 *a33*b33*n1*p16*u1 *v2 - 8*a22 *a33*b33*n1*p16*u3 *v1
3 2 3
- 8*a22 *a33*b33*n1*p16*u3*v1 - 8*a22 *a33*b33*n1*r4*v1
3 3 2 3 3 2
+ 2*a22 *b33 *p16*u1*v1*v3 + 2*a22 *b33 *p16*u2*v2*v3
3 3 3 3 3 2 2
+ 2*a22 *b33 *p16*u2*v3 + 4*a22 *b33 *p16*v1 *v3
3 3 3 3 2 3
+ 2*a22 *b33 *p16*v1*v3 + 4*a22 *b33 *k38*n1*u1 *v1
3 2 3 3 2
+ 4*a22 *b33 *k38*n1*u1 *v3 + 4*a22 *b33 *k38*n1*u1*u2*u3*v1
3 2 3 3 2 3
+ 4*a22 *b33 *k38*n1*u1*v2 + 4*a22 *b33 *k38*n1*u2 *v1
3 2 3 3 2
+ 4*a22 *b33 *k38*n1*v1*v2 - 4*a22 *b33 *n1*p16*u2*v2*v3
3 2 2 3 2 2
- 4*a22 *b33 *n1*p16*u2*v3 - 4*a22 *b33 *n1*p16*v2 *v3
3 2 3 3 2
- 8*a22 *b33*k38*n1 *u2 - 8*a22 *b33*k38*n1 *u2*u3*v1
3 2 3 2 2 2
- 8*a22 *b33*k38*n1 *u3 - 8*a22 *a33 *b33 *p16*u1*u2*v1*v2
2 2 2 2 2 2 2 2
- 8*a22 *a33 *b33 *p16*u1*v1 *v2 - 8*a22 *a33 *b33 *p16*u2 *v1*v3
2 2 2 2 2 2 2
- 8*a22 *a33 *b33 *p16*u2*u3*v1*v2 - 8*a22 *a33 *b33 *p16*u2*v1 *v3
2 2 2 3 2 2 2
- 8*a22 *a33 *b33 *p16*v1 *v3 - 4*a22 *a33 *b33 *r4*u1*v3
2 2 2 2 3 2
- 4*a22 *a33 *b33 *r4*v1*v3 - 4*a22 *a33*b33 *p16*u1*v1*v3
2 3 2 2 3 3
- 4*a22 *a33*b33 *p16*u2*v2*v3 - 4*a22 *a33*b33 *p16*u2*v3
2 3 2 2 2 3 3
- 8*a22 *a33*b33 *p16*v1 *v3 - 4*a22 *a33*b33 *p16*v1*v3
2 2 3 2 2 3
- 4*a22 *a33*b33 *k38*n1*u1 *v1 - 4*a22 *a33*b33 *k38*n1*u1 *v3
2 2 2 2 3
- 4*a22 *a33*b33 *k38*n1*u1*u2*u3*v1 - 4*a22 *a33*b33 *k38*n1*u1*v2
2 2 3 2 2 3
- 4*a22 *a33*b33 *k38*n1*u2 *v1 - 4*a22 *a33*b33 *k38*n1*v1*v2
2 2 2 2 2
+ 4*a22 *a33*b33 *n1*p16*u2*v2*v3 + 4*a22 *a33*b33 *n1*p16*u2*v3
2 2 2 2 3
+ 4*a22 *a33*b33 *n1*p16*v2 *v3 - 4*a22 *b33 *k38*n1*u1*u2*v1*v2
2 3 2 2 3 2
- 4*a22 *b33 *k38*n1*u1*v1 *v2 - 4*a22 *b33 *k38*n1*u2 *v1*v3
2 3 2 3 2
- 4*a22 *b33 *k38*n1*u2*u3*v1*v2 - 4*a22 *b33 *k38*n1*u2*v1 *v3
2 3 3 2 2 2 2
- 4*a22 *b33 *k38*n1*v1 *v3 + 4*a22 *b33 *k38*n1 *u1 *v2
2 2 2 2 2 2 2
- 4*a22 *b33 *k38*n1 *u2*v1*v3 - 4*a22 *b33 *k38*n1 *u2*v2
2 2 2 2 2 3 2
+ 4*a22 *b33 *k38*n1 *u3*v1 + 2*a22*a33 *b33 *p16*u1*v1*v3
2 3 2 2 3 3
+ 2*a22*a33 *b33 *p16*u2*v2*v3 + 2*a22*a33 *b33 *p16*u2*v3
2 3 2 2 2 3 3
+ 4*a22*a33 *b33 *p16*v1 *v3 + 2*a22*a33 *b33 *p16*v1*v3
3 3 2
+ 4*a22*a33*b33 *k38*n1*u1*u2*v1*v2 + 4*a22*a33*b33 *k38*n1*u1*v1 *v2
3 2 3
+ 4*a22*a33*b33 *k38*n1*u2 *v1*v3 + 4*a22*a33*b33 *k38*n1*u2*u3*v1*v2
3 2 3 3
+ 4*a22*a33*b33 *k38*n1*u2*v1 *v3 + 4*a22*a33*b33 *k38*n1*v1 *v3
4 2 4 2
+ a22*b33 *k38*n1*u1*v1*v3 + a22*b33 *k38*n1*u2*v2*v3
4 3 4 2 2
+ a22*b33 *k38*n1*u2*v3 + 2*a22*b33 *k38*n1*v1 *v3
4 3 3 2
+ a22*b33 *k38*n1*v1*v3 - 2*a22*b33 *k38*n1 *u2*v2*v3
3 2 2 3 2 2
- 2*a22*b33 *k38*n1 *u2*v3 - 2*a22*b33 *k38*n1 *v2 *v3
4 2 4 2
- a33*b33 *k38*n1*u1*v1*v3 - a33*b33 *k38*n1*u2*v2*v3
4 3 4 2 2
- a33*b33 *k38*n1*u2*v3 - 2*a33*b33 *k38*n1*v1 *v3
4 3 3
- a33*b33 *k38*n1*v1*v3 )/(8*a22 *b33*n1*(a22 - a33))
And again in machine readable form:
HAM=(4*a22**3*u1**2 + 4*a22**3*u2**2 - 4*a22**2*a33*u1**2 - 4*a22**2*a33*u2**2 +
4*a22**2*a33*u3**2 + 4*a22**2*b33*u3*v3 + 4*a22**2*n1*u1 - 4*a22*a33**2*u3**2 -
4*a22*a33*b33*u3*v3 - 4*a22*a33*n1*u1 - a22*b33**2*v3**2 - 2*a22*b33*n1*v1 +
a33*b33**2*v3**2 - 2*a33*b33*n1*v1)/(4*a22*(a22 - a33))$
INT=( - 16*a22**6*r4*u1**2 - 16*a22**6*r4*u1*v1 + 32*a22**5*a33*r4*u1**2 + 32*
a22**5*a33*r4*u1*v1 + 8*a22**5*b33*p16*u1**3*v1 + 8*a22**5*b33*p16*u1**3*v3 + 8*
a22**5*b33*p16*u1*u2*u3*v1 + 8*a22**5*b33*p16*u1*v2**3 + 8*a22**5*b33*p16*u2**3*
v1 + 8*a22**5*b33*p16*v1*v2**3 + 16*a22**5*b33*r4*u1*u3 + 16*a22**5*b33*r4*v1**2
- 16*a22**5*n1*r4*u1 - 16*a22**4*a33**2*r4*u1**2 - 16*a22**4*a33**2*r4*u1*v1 -
16*a22**4*a33*b33*p16*u1**3*v1 - 16*a22**4*a33*b33*p16*u1**3*v3 - 16*a22**4*a33*
b33*p16*u1*u2*u3*v1 - 16*a22**4*a33*b33*p16*u1*v2**3 - 16*a22**4*a33*b33*p16*u2
**3*v1 - 16*a22**4*a33*b33*p16*v1*v2**3 - 32*a22**4*a33*b33*r4*u1*u3 - 32*a22**4
*a33*b33*r4*v1**2 + 16*a22**4*a33*n1*r4*u1 - 8*a22**4*b33**2*p16*u1*u2*v1*v2 - 8
*a22**4*b33**2*p16*u1*v1**2*v2 - 8*a22**4*b33**2*p16*u2**2*v1*v3 - 8*a22**4*b33
**2*p16*u2*u3*v1*v2 - 8*a22**4*b33**2*p16*u2*v1**2*v3 - 8*a22**4*b33**2*p16*v1**
3*v3 - 4*a22**4*b33**2*r4*u1*v3 - 4*a22**4*b33**2*r4*v1*v3 + 8*a22**4*b33*k38*n1
*u1*u2**2*v2 - 16*a22**4*b33*k38*n1*u1*u3*v1 - 8*a22**4*b33*k38*n1*u1*u3 + 8*a22
**4*b33*k38*n1*u2**3*v3 + 8*a22**4*b33*k38*n1*u2*u3*v2*v3 + 16*a22**4*b33*k38*n1
*u2*v1*v2 - 8*a22**4*b33*k38*n1*v1**2 + 8*a22**4*b33*n1*p16*u1**2*v2 + 8*a22**4*
b33*n1*p16*u3**2*v1 + 8*a22**4*b33*n1*p16*u3*v1**2 + 8*a22**4*b33*n1*r4*v1 + 8*
a22**3*a33**2*b33*p16*u1**3*v1 + 8*a22**3*a33**2*b33*p16*u1**3*v3 + 8*a22**3*a33
**2*b33*p16*u1*u2*u3*v1 + 8*a22**3*a33**2*b33*p16*u1*v2**3 + 8*a22**3*a33**2*b33
*p16*u2**3*v1 + 8*a22**3*a33**2*b33*p16*v1*v2**3 + 16*a22**3*a33**2*b33*r4*u1*u3
+ 16*a22**3*a33**2*b33*r4*v1**2 + 16*a22**3*a33*b33**2*p16*u1*u2*v1*v2 + 16*a22
**3*a33*b33**2*p16*u1*v1**2*v2 + 16*a22**3*a33*b33**2*p16*u2**2*v1*v3 + 16*a22**
3*a33*b33**2*p16*u2*u3*v1*v2 + 16*a22**3*a33*b33**2*p16*u2*v1**2*v3 + 16*a22**3*
a33*b33**2*p16*v1**3*v3 + 8*a22**3*a33*b33**2*r4*u1*v3 + 8*a22**3*a33*b33**2*r4*
v1*v3 - 8*a22**3*a33*b33*k38*n1*u1*u2**2*v2 + 16*a22**3*a33*b33*k38*n1*u1*u3*v1
+ 8*a22**3*a33*b33*k38*n1*u1*u3 - 8*a22**3*a33*b33*k38*n1*u2**3*v3 - 8*a22**3*
a33*b33*k38*n1*u2*u3*v2*v3 - 16*a22**3*a33*b33*k38*n1*u2*v1*v2 + 8*a22**3*a33*
b33*k38*n1*v1**2 - 8*a22**3*a33*b33*n1*p16*u1**2*v2 - 8*a22**3*a33*b33*n1*p16*u3
**2*v1 - 8*a22**3*a33*b33*n1*p16*u3*v1**2 - 8*a22**3*a33*b33*n1*r4*v1 + 2*a22**3
*b33**3*p16*u1*v1*v3**2 + 2*a22**3*b33**3*p16*u2*v2*v3**2 + 2*a22**3*b33**3*p16*
u2*v3**3 + 4*a22**3*b33**3*p16*v1**2*v3**2 + 2*a22**3*b33**3*p16*v1*v3**3 + 4*
a22**3*b33**2*k38*n1*u1**3*v1 + 4*a22**3*b33**2*k38*n1*u1**3*v3 + 4*a22**3*b33**
2*k38*n1*u1*u2*u3*v1 + 4*a22**3*b33**2*k38*n1*u1*v2**3 + 4*a22**3*b33**2*k38*n1*
u2**3*v1 + 4*a22**3*b33**2*k38*n1*v1*v2**3 - 4*a22**3*b33**2*n1*p16*u2*v2*v3 - 4
*a22**3*b33**2*n1*p16*u2*v3**2 - 4*a22**3*b33**2*n1*p16*v2**2*v3 - 8*a22**3*b33*
k38*n1**2*u2**3 - 8*a22**3*b33*k38*n1**2*u2*u3*v1 - 8*a22**3*b33*k38*n1**2*u3**3
- 8*a22**2*a33**2*b33**2*p16*u1*u2*v1*v2 - 8*a22**2*a33**2*b33**2*p16*u1*v1**2*
v2 - 8*a22**2*a33**2*b33**2*p16*u2**2*v1*v3 - 8*a22**2*a33**2*b33**2*p16*u2*u3*
v1*v2 - 8*a22**2*a33**2*b33**2*p16*u2*v1**2*v3 - 8*a22**2*a33**2*b33**2*p16*v1**
3*v3 - 4*a22**2*a33**2*b33**2*r4*u1*v3 - 4*a22**2*a33**2*b33**2*r4*v1*v3 - 4*a22
**2*a33*b33**3*p16*u1*v1*v3**2 - 4*a22**2*a33*b33**3*p16*u2*v2*v3**2 - 4*a22**2*
a33*b33**3*p16*u2*v3**3 - 8*a22**2*a33*b33**3*p16*v1**2*v3**2 - 4*a22**2*a33*b33
**3*p16*v1*v3**3 - 4*a22**2*a33*b33**2*k38*n1*u1**3*v1 - 4*a22**2*a33*b33**2*k38
*n1*u1**3*v3 - 4*a22**2*a33*b33**2*k38*n1*u1*u2*u3*v1 - 4*a22**2*a33*b33**2*k38*
n1*u1*v2**3 - 4*a22**2*a33*b33**2*k38*n1*u2**3*v1 - 4*a22**2*a33*b33**2*k38*n1*
v1*v2**3 + 4*a22**2*a33*b33**2*n1*p16*u2*v2*v3 + 4*a22**2*a33*b33**2*n1*p16*u2*
v3**2 + 4*a22**2*a33*b33**2*n1*p16*v2**2*v3 - 4*a22**2*b33**3*k38*n1*u1*u2*v1*v2
- 4*a22**2*b33**3*k38*n1*u1*v1**2*v2 - 4*a22**2*b33**3*k38*n1*u2**2*v1*v3 - 4*
a22**2*b33**3*k38*n1*u2*u3*v1*v2 - 4*a22**2*b33**3*k38*n1*u2*v1**2*v3 - 4*a22**2
*b33**3*k38*n1*v1**3*v3 + 4*a22**2*b33**2*k38*n1**2*u1**2*v2 - 4*a22**2*b33**2*
k38*n1**2*u2*v1*v3 - 4*a22**2*b33**2*k38*n1**2*u2*v2**2 + 4*a22**2*b33**2*k38*n1
**2*u3*v1**2 + 2*a22*a33**2*b33**3*p16*u1*v1*v3**2 + 2*a22*a33**2*b33**3*p16*u2*
v2*v3**2 + 2*a22*a33**2*b33**3*p16*u2*v3**3 + 4*a22*a33**2*b33**3*p16*v1**2*v3**
2 + 2*a22*a33**2*b33**3*p16*v1*v3**3 + 4*a22*a33*b33**3*k38*n1*u1*u2*v1*v2 + 4*
a22*a33*b33**3*k38*n1*u1*v1**2*v2 + 4*a22*a33*b33**3*k38*n1*u2**2*v1*v3 + 4*a22*
a33*b33**3*k38*n1*u2*u3*v1*v2 + 4*a22*a33*b33**3*k38*n1*u2*v1**2*v3 + 4*a22*a33*
b33**3*k38*n1*v1**3*v3 + a22*b33**4*k38*n1*u1*v1*v3**2 + a22*b33**4*k38*n1*u2*v2
*v3**2 + a22*b33**4*k38*n1*u2*v3**3 + 2*a22*b33**4*k38*n1*v1**2*v3**2 + a22*b33
**4*k38*n1*v1*v3**3 - 2*a22*b33**3*k38*n1**2*u2*v2*v3 - 2*a22*b33**3*k38*n1**2*
u2*v3**2 - 2*a22*b33**3*k38*n1**2*v2**2*v3 - a33*b33**4*k38*n1*u1*v1*v3**2 - a33
*b33**4*k38*n1*u2*v2*v3**2 - a33*b33**4*k38*n1*u2*v3**3 - 2*a33*b33**4*k38*n1*v1
**2*v3**2 - a33*b33**4*k38*n1*v1*v3**3)/(8*a22**3*b33*n1*(a22 - a33))$