Solution 8 to problem e3null
Expressions |
Parameters |
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Back to problem e3null
Expressions
The solution is given through the following expressions:
a22=3*a33
b22=0
b31=0
b32=0
- 3*a33*m2
b33=-------------
n2
c12=0
c13=0
c22=0
c23=0
3 2
- ---*a33*m2
4
c33=----------------
2
n2
m2*n1
m1=-------
n2
3
---*m2*n3
2
m3=-----------
n2
1 2 7 2
---*a33 *m2*n3*q1 - ----*k1*m2*n1 *n3
2 96
r6=---------------------------------------
3
a33 *n2
1 2 7 2 7 2
---*a33 *m2*q1 - -----*k1*m2*n1 - -----*k1*m2*n3
4 192 192
r5=----------------------------------------------------
3
a33
1 2 7 3 7 2
---*a33 *m2*n1*q1 - -----*k1*m2*n1 - -----*k1*m2*n1*n3
4 192 192
r4=----------------------------------------------------------
3
a33 *n2
1 2 7 2 7 3
---*a33 *n3*q1 - ----*k1*n1 *n3 + ----*k1*n3
2 96 96
r3=-----------------------------------------------
3
a33
1 2 7 2 7 2
---*a33 *n2*q1 - ----*k1*n1 *n2 + ----*k1*n2*n3
2 96 96
r2=--------------------------------------------------
3
a33
1 2 7 3 7 2
---*a33 *n1*q1 - ----*k1*n1 + ----*k1*n1*n3
2 96 96
r1=-----------------------------------------------
3
a33
29 2
----*k1*m2 *n3
96
q19=----------------
2
a33 *n2
29 2
----*k1*m2 *n1*n3
96
q18=-------------------
2 2
a33 *n2
2 5 2 19 2
- a33 *m2*q1 - ----*k1*m2*n1 + ----*k1*m2*n3
48 48
q17=-------------------------------------------------
2
a33 *n2
19
----*k1*m2*n3
48
q16=---------------
2
a33
19
----*k1*m2*n1*n3
48
q15=------------------
2
a33 *n2
1 2 2 7 2 2 17 2 2 1 2 2
---*a33 *m2 *q1 - -----*k1*m2 *n1 + -----*k1*m2 *n2 - ---*k1*m2 *n3
4 192 192 4
q14=------------------------------------------------------------------------
2 2
a33 *n2
17 2
----*k1*m2 *n1
96
q13=----------------
2
a33 *n2
1
---*k1*m2*n3
4
q12=--------------
2
a33
1 2 1 2
- ---*k1*m2*n1 + ---*k1*m2*n2
4 4
q11=----------------------------------
2
a33 *n2
1
---*k1*m2*n1
4
q10=--------------
2
a33
1 2 2 5 2 2 1 2 2
---*a33 *m2 *q1 + ----*k1*m2 *n1 - ---*k1*m2 *n3
4 96 4
q9=----------------------------------------------------
2 2
a33 *n2
1
---*k1*m2*n1*n3
4
q8=-----------------
2
a33 *n2
1
---*k1*m2*n1
4
q7=--------------
2
a33
7
----*k1*n2*n3
24
q5=---------------
2
a33
7
----*k1*n1*n3
24
q4=---------------
2
a33
2 7 2 7 2
a33 *q1 - ----*k1*n1 + ----*k1*n2
48 48
q3=-------------------------------------
2
a33
7
----*k1*n1*n2
24
q2=---------------
2
a33
2 1 3
a33*m2*n2 *p15 - ---*k1*m2 *n3
4
p50=--------------------------------
3
a33*n2
1 2 29 3
---*a33*m2*n2 *p15 - -----*k1*m2 *n3
2 192
p49=--------------------------------------
2
a33*n2 *n3
1 2 29 3
---*a33*m2*n1*n2 *p15 - -----*k1*m2 *n1*n3
2 192
p48=--------------------------------------------
3
a33*n2 *n3
2 115 2
a33*n2 *p15 - -----*k1*m2 *n3
96
p47=-------------------------------
2
a33*n2
2 19 2
a33*n2 *p15 - ----*k1*m2 *n3
96
p46=------------------------------
a33*n2*n3
2 19 2
a33*n1*n2 *p15 - ----*k1*m2 *n1*n3
96
p45=------------------------------------
2
a33*n2 *n3
m2*p15
p44=--------
n2
p43=0
29 2
- ----*k1*m2
48
p42=----------------
a33*n2
p41=0
p40=0
m2*p15
p39=--------
n2
2 29 2
- a33*n1*n2 *p15 - ----*k1*m2 *n1*n3
48
p38=---------------------------------------
2
a33*n2 *n3
p37=0
7
- ----*k1*m2*n3
12
p36=------------------
a33*n2
19
- ----*k1*m2
24
p35=---------------
a33
67
- ----*k1*m2*n1
48
p34=------------------
a33*n2
k1*m2*n3
p33=----------
a33*n2
p32=0
k1*m2*n3
p31=----------
a33*n2
1
---*m2*p15
2
p30=------------
n3
1
---*m2*n1*p15
2
p29=---------------
n2*n3
p28=p15
n2*p15
p27=--------
n3
n1*p15
p26=--------
n3
1
---*m2*p15
2
p25=------------
n3
p24=0
- n1*p15
p23=-----------
n3
5
----*k1*m2
48
p22=------------
a33
p21=0
p20=0
29
----*k1*m2
48
p19=------------
a33
29
- ----*k1*m2*n1
48
p18=------------------
a33*n2
29
----*k1*m2
48
p17=------------
a33
1
---*m2*n1*p15
2
p16=---------------
n2*n3
n2*p15
p14=--------
n3
5
----*k1*m2*n1
48
p13=---------------
a33*n2
p12=0
29
----*k1*m2*n1
48
p11=---------------
a33*n2
5
----*k1*n3
24
p10=------------
a33
5
----*k1*n2
24
p9=------------
a33
5
----*k1*n1
24
p8=------------
a33
19
----*k1*n3
24
p7=------------
a33
p6=0
19
----*k1*n3
24
p5=------------
a33
19
----*k1*n2
24
p4=------------
a33
19
----*k1*n1
24
p3=------------
a33
19
----*k1*n2
24
p2=------------
a33
19
----*k1*n1
24
p1=------------
a33
k104=0
k103=0
2 1 3
- 2*a33*m2*n2 *p15 + ---*k1*m2 *n3
2
k102=-------------------------------------
3
n2 *n3
k101=0
k100=0
1 2 2 1 4
---*a33*m2 *n2 *p15 - ---*k1*m2 *n3
2 8
k99=-------------------------------------
4
n2 *n3
k98=0
k97=0
k96=0
k95=0
1 2 2 1 4
---*a33*m2 *n2 *p15 - ---*k1*m2 *n3
2 8
k94=-------------------------------------
4
n2 *n3
k93=0
k92=0
2 43 2
2*a33*n2 *p15 + ----*k1*m2 *n3
48
k91=--------------------------------
2
n2 *n3
k90=0
k89=0
2 1 2
2*a33*n2 *p15 - ---*k1*m2 *n3
2
k88=-------------------------------
2
n2 *n3
k87=0
2 1 2
2*a33*n2 *p15 - ---*k1*m2 *n3
2
k86=-------------------------------
2
n2 *n3
k85=0
k84=0
- 2*a33*m2*p15
k83=-----------------
n2*n3
k82=0
k81=0
k80=0
k79=0
k78=0
k77=0
4*a33*p15
k76=-----------
n3
k75=0
k74=0
k73=0
k72=0
k71=0
- 2*a33*m2*p15
k70=-----------------
n2*n3
k69=0
k68=0
k67=0
k66=0
5
- ----*k1*m2
12
k65=---------------
n2
k64=0
k63=0
- 2*k1*m2
k62=------------
n2
k61=0
- 2*k1*m2
k60=------------
n2
k59=0
k58=0
k57=0
k56=0
1 2 2 1 4
---*a33*m2 *n2 *p15 - ----*k1*m2 *n3
2 16
k55=--------------------------------------
4
n2 *n3
k54=0
k53=0
k52=0
k51=0
2 2 1 4
a33*m2 *n2 *p15 - ---*k1*m2 *n3
8
k50=---------------------------------
4
n2 *n3
k49=0
k48=0
k47=0
k46=0
k45=0
4*a33*p15
k44=-----------
n3
k43=0
2*a33*p15
k42=-----------
n3
k41=0
k40=0
k39=0
k38=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
1 2 2 1 4
---*a33*m2 *n2 *p15 - ----*k1*m2 *n3
2 16
k25=--------------------------------------
4
n2 *n3
k24=0
k23=0
k21=0
2*a33*p15
k20=-----------
n3
k19=0
k18=0
k17=0
k16=0
k14=0
k13=0
5
k12=----*k1
12
k11=0
5
k10=----*k1
12
k9=0
k8=0
k7=0
k6=0
k5=k1
k4=0
k3=2*k1
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:
q1,p15,m2,k1,n1,n3,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=( - 3*a33*m2 *v3 - 12*a33*m2*n2*u3*v3 + 12*a33*n2 *u1 + 12*a33*n2 *u2
2 2 2
+ 4*a33*n2 *u3 + 4*m2*n1*n2*v1 + 4*m2*n2 *v2 + 6*m2*n2*n3*v3
2 3 2 2
+ 4*n1*n2 *u1 + 4*n2 *u2 + 4*n2 *n3*u3)/(4*n2 )
4 2 2 4 4 2 2 2 2
INT=(96*a33 *m2 *n2 *p15*v1 + 192*a33 *m2 *n2 *p15*v1 *v2
4 2 2 2 2 4 2 2 4
+ 96*a33 *m2 *n2 *p15*v1 *v3 + 96*a33 *m2 *n2 *p15*v2
4 2 2 2 2 4 3 2
+ 96*a33 *m2 *n2 *p15*v2 *v3 - 384*a33 *m2*n2 *p15*u3*v1 *v3
4 3 2 4 3 3
- 384*a33 *m2*n2 *p15*u3*v2 *v3 - 384*a33 *m2*n2 *p15*u3*v3
4 4 2 2 4 4 2 2
+ 384*a33 *n2 *p15*u1 *v2 + 384*a33 *n2 *p15*u1 *v3
4 4 2 2 4 4 2 2
+ 384*a33 *n2 *p15*u2 *v1 + 768*a33 *n2 *p15*u2 *v2
4 4 2 2 4 4
+ 384*a33 *n2 *p15*u2 *v3 + 768*a33 *n2 *p15*u2*u3*v2*v3
4 4 2 2 3 4 4
+ 384*a33 *n2 *p15*u3 *v3 - 12*a33 *k1*m2 *n3*v1
3 4 2 2 3 4 2 2
- 24*a33 *k1*m2 *n3*v1 *v2 - 24*a33 *k1*m2 *n3*v1 *v3
3 4 4 3 4 2 2
- 12*a33 *k1*m2 *n3*v2 - 24*a33 *k1*m2 *n3*v2 *v3
3 3 3 3 2 2 2 2
+ 96*a33 *k1*m2 *n2*n3*u3*v3 - 96*a33 *k1*m2 *n2 *n3*u1 *v3
3 2 2 2 2 3 2 2 2 2
- 96*a33 *k1*m2 *n2 *n3*u2 *v3 + 172*a33 *k1*m2 *n2 *n3*u3 *v3
3 3 2 3 3 2
- 384*a33 *k1*m2*n2 *n3*u1 *u3*v3 - 384*a33 *k1*m2*n2 *n3*u2 *u3*v3
3 3 3 3 4 4
- 80*a33 *k1*m2*n2 *n3*u3 *v3 + 192*a33 *k1*n2 *n3*u1
3 4 2 2 3 4 2 2
+ 384*a33 *k1*n2 *n3*u1 *u2 + 80*a33 *k1*n2 *n3*u1 *u3
3 4 4 3 4 2 2
+ 192*a33 *k1*n2 *n3*u2 + 80*a33 *k1*n2 *n3*u2 *u3
3 2 2 2 3 2 2 2
+ 48*a33 *m2 *n2 *n3*q1*v1 + 48*a33 *m2 *n2 *n3*q1*v2
3 3 3 3 3 2
+ 96*a33 *m2*n1*n2 *p15*v1 + 96*a33 *m2*n1*n2 *p15*v1*v2
3 3 2 3 4 2
+ 96*a33 *m2*n1*n2 *p15*v1*v3 + 96*a33 *m2*n2 *p15*v1 *v2
3 4 3 3 4 2
+ 96*a33 *m2*n2 *p15*v2 + 96*a33 *m2*n2 *p15*v2*v3
3 3 2 3 3 2
+ 192*a33 *m2*n2 *n3*p15*v1 *v3 + 192*a33 *m2*n2 *n3*p15*v2 *v3
3 3 3 3 3
+ 192*a33 *m2*n2 *n3*p15*v3 - 192*a33 *m2*n2 *n3*q1*u3*v3
3 4 2 3 4 2
+ 192*a33 *n1*n2 *p15*u1*v2 + 192*a33 *n1*n2 *p15*u1*v3
3 4 3 4
- 192*a33 *n1*n2 *p15*u2*v1*v2 - 192*a33 *n1*n2 *p15*u3*v1*v3
3 5 2 3 5 2
+ 192*a33 *n2 *p15*u2*v1 + 192*a33 *n2 *p15*u2*v2
3 5 2 3 4 2
+ 192*a33 *n2 *p15*u2*v3 + 192*a33 *n2 *n3*p15*u3*v1
3 4 2 3 4 2
+ 192*a33 *n2 *n3*p15*u3*v2 + 192*a33 *n2 *n3*p15*u3*v3
3 4 2 3 4 2
+ 192*a33 *n2 *n3*q1*u1 + 192*a33 *n2 *n3*q1*u2
2 3 2 2 3 2 2
- 29*a33 *k1*m2 *n1*n2*n3*v1*v3 - 29*a33 *k1*m2 *n2 *n3*v2*v3
2 3 2 3 2 2 2 2
- 48*a33 *k1*m2 *n2*n3 *v3 - 38*a33 *k1*m2 *n1*n2 *n3*u1*v3
2 2 2 2 2 3 2
- 116*a33 *k1*m2 *n1*n2 *n3*u3*v1*v3 - 38*a33 *k1*m2 *n2 *n3*u2*v3
2 2 3 2 2 2 2 2
- 116*a33 *k1*m2 *n2 *n3*u3*v2*v3 - 230*a33 *k1*m2 *n2 *n3 *u3*v3
2 3 2 3
- 116*a33 *k1*m2*n1*n2 *n3*u1*u2*v2 - 268*a33 *k1*m2*n1*n2 *n3*u1*u3*v3
2 3 2 2 3 2
+ 116*a33 *k1*m2*n1*n2 *n3*u2 *v1 + 20*a33 *k1*m2*n1*n2 *n3*u3 *v1
2 4 2 2 4 2
+ 116*a33 *k1*m2*n2 *n3*u1 *v2 + 116*a33 *k1*m2*n2 *n3*u2 *v2
2 4 2 4 2
- 152*a33 *k1*m2*n2 *n3*u2*u3*v3 + 20*a33 *k1*m2*n2 *n3*u3 *v2
2 3 2 2 2 3 2 2
+ 192*a33 *k1*m2*n2 *n3 *u1 *v3 + 192*a33 *k1*m2*n2 *n3 *u2 *v3
2 3 2 2 2 4 3
- 112*a33 *k1*m2*n2 *n3 *u3 *v3 + 152*a33 *k1*n1*n2 *n3*u1
2 4 2 2 4 2
+ 152*a33 *k1*n1*n2 *n3*u1*u2 + 40*a33 *k1*n1*n2 *n3*u1*u3
2 5 2 2 5 3
+ 152*a33 *k1*n2 *n3*u1 *u2 + 152*a33 *k1*n2 *n3*u2
2 5 2 2 4 2 2
+ 40*a33 *k1*n2 *n3*u2*u3 + 152*a33 *k1*n2 *n3 *u1 *u3
2 4 2 2 2 4 2 3
+ 152*a33 *k1*n2 *n3 *u2 *u3 + 40*a33 *k1*n2 *n3 *u3
2 3 2 4
+ 48*a33 *m2*n1*n2 *n3*q1*v1 + 48*a33 *m2*n2 *n3*q1*v2
2 3 2 2 4
+ 96*a33 *m2*n2 *n3 *q1*v3 + 96*a33 *n1*n2 *n3*q1*u1
2 5 2 4 2
+ 96*a33 *n2 *n3*q1*u2 + 96*a33 *n2 *n3 *q1*u3
2 2 2 2 2 2 2 2
+ 10*a33*k1*m2 *n1 *n2 *n3*v1 - 7*a33*k1*m2 *n1 *n2 *n3*v2
2 3 2 2 2
+ 34*a33*k1*m2 *n1*n2 *n3*v1*v2 + 58*a33*k1*m2 *n1*n2 *n3 *v1*v3
2 4 2 2 3 2
+ 17*a33*k1*m2 *n2 *n3*v2 + 58*a33*k1*m2 *n2 *n3 *v2*v3
2 2 3 2 2 2 3 2
- 48*a33*k1*m2 *n2 *n3 *v1 - 48*a33*k1*m2 *n2 *n3 *v2
2 3 2 3
- 48*a33*k1*m2*n1 *n2 *n3*u2*v2 - 20*a33*k1*m2*n1 *n2 *n3*u3*v3
4 4
+ 48*a33*k1*m2*n1*n2 *n3*u1*v2 + 48*a33*k1*m2*n1*n2 *n3*u2*v1
3 2 3 2
+ 76*a33*k1*m2*n1*n2 *n3 *u1*v3 + 48*a33*k1*m2*n1*n2 *n3 *u3*v1
5 4 2
+ 48*a33*k1*m2*n2 *n3*u2*v2 + 76*a33*k1*m2*n2 *n3 *u2*v3
4 2 3 3
+ 48*a33*k1*m2*n2 *n3 *u3*v2 + 76*a33*k1*m2*n2 *n3 *u3*v3
2 4 2 5
- 28*a33*k1*n1 *n2 *n3*u2 + 56*a33*k1*n1*n2 *n3*u1*u2
4 2 6 2
+ 56*a33*k1*n1*n2 *n3 *u1*u3 + 28*a33*k1*n2 *n3*u2
5 2 3 3 2 4
+ 56*a33*k1*n2 *n3 *u2*u3 - 7*k1*m2*n1 *n2 *n3*v1 - 7*k1*m2*n1 *n2 *n3*v2
2 3 2 3 3 4 3
- 14*k1*m2*n1 *n2 *n3 *v3 - 7*k1*m2*n1*n2 *n3 *v1 - 7*k1*m2*n2 *n3 *v2
3 4 2 5 2 4 2
- 14*k1*n1 *n2 *n3*u1 - 14*k1*n1 *n2 *n3*u2 - 14*k1*n1 *n2 *n3 *u3
4 3 5 3 4 4 3 4
+ 14*k1*n1*n2 *n3 *u1 + 14*k1*n2 *n3 *u2 + 14*k1*n2 *n3 *u3)/(192*a33 *n2
*n3)
And again in machine readable form:
HAM=( - 3*a33*m2**2*v3**2 - 12*a33*m2*n2*u3*v3 + 12*a33*n2**2*u1**2 + 12*a33*n2
**2*u2**2 + 4*a33*n2**2*u3**2 + 4*m2*n1*n2*v1 + 4*m2*n2**2*v2 + 6*m2*n2*n3*v3 +
4*n1*n2**2*u1 + 4*n2**3*u2 + 4*n2**2*n3*u3)/(4*n2**2)$
INT=(96*a33**4*m2**2*n2**2*p15*v1**4 + 192*a33**4*m2**2*n2**2*p15*v1**2*v2**2 +
96*a33**4*m2**2*n2**2*p15*v1**2*v3**2 + 96*a33**4*m2**2*n2**2*p15*v2**4 + 96*a33
**4*m2**2*n2**2*p15*v2**2*v3**2 - 384*a33**4*m2*n2**3*p15*u3*v1**2*v3 - 384*a33
**4*m2*n2**3*p15*u3*v2**2*v3 - 384*a33**4*m2*n2**3*p15*u3*v3**3 + 384*a33**4*n2
**4*p15*u1**2*v2**2 + 384*a33**4*n2**4*p15*u1**2*v3**2 + 384*a33**4*n2**4*p15*u2
**2*v1**2 + 768*a33**4*n2**4*p15*u2**2*v2**2 + 384*a33**4*n2**4*p15*u2**2*v3**2
+ 768*a33**4*n2**4*p15*u2*u3*v2*v3 + 384*a33**4*n2**4*p15*u3**2*v3**2 - 12*a33**
3*k1*m2**4*n3*v1**4 - 24*a33**3*k1*m2**4*n3*v1**2*v2**2 - 24*a33**3*k1*m2**4*n3*
v1**2*v3**2 - 12*a33**3*k1*m2**4*n3*v2**4 - 24*a33**3*k1*m2**4*n3*v2**2*v3**2 +
96*a33**3*k1*m2**3*n2*n3*u3*v3**3 - 96*a33**3*k1*m2**2*n2**2*n3*u1**2*v3**2 - 96
*a33**3*k1*m2**2*n2**2*n3*u2**2*v3**2 + 172*a33**3*k1*m2**2*n2**2*n3*u3**2*v3**2
- 384*a33**3*k1*m2*n2**3*n3*u1**2*u3*v3 - 384*a33**3*k1*m2*n2**3*n3*u2**2*u3*v3
- 80*a33**3*k1*m2*n2**3*n3*u3**3*v3 + 192*a33**3*k1*n2**4*n3*u1**4 + 384*a33**3
*k1*n2**4*n3*u1**2*u2**2 + 80*a33**3*k1*n2**4*n3*u1**2*u3**2 + 192*a33**3*k1*n2
**4*n3*u2**4 + 80*a33**3*k1*n2**4*n3*u2**2*u3**2 + 48*a33**3*m2**2*n2**2*n3*q1*
v1**2 + 48*a33**3*m2**2*n2**2*n3*q1*v2**2 + 96*a33**3*m2*n1*n2**3*p15*v1**3 + 96
*a33**3*m2*n1*n2**3*p15*v1*v2**2 + 96*a33**3*m2*n1*n2**3*p15*v1*v3**2 + 96*a33**
3*m2*n2**4*p15*v1**2*v2 + 96*a33**3*m2*n2**4*p15*v2**3 + 96*a33**3*m2*n2**4*p15*
v2*v3**2 + 192*a33**3*m2*n2**3*n3*p15*v1**2*v3 + 192*a33**3*m2*n2**3*n3*p15*v2**
2*v3 + 192*a33**3*m2*n2**3*n3*p15*v3**3 - 192*a33**3*m2*n2**3*n3*q1*u3*v3 + 192*
a33**3*n1*n2**4*p15*u1*v2**2 + 192*a33**3*n1*n2**4*p15*u1*v3**2 - 192*a33**3*n1*
n2**4*p15*u2*v1*v2 - 192*a33**3*n1*n2**4*p15*u3*v1*v3 + 192*a33**3*n2**5*p15*u2*
v1**2 + 192*a33**3*n2**5*p15*u2*v2**2 + 192*a33**3*n2**5*p15*u2*v3**2 + 192*a33
**3*n2**4*n3*p15*u3*v1**2 + 192*a33**3*n2**4*n3*p15*u3*v2**2 + 192*a33**3*n2**4*
n3*p15*u3*v3**2 + 192*a33**3*n2**4*n3*q1*u1**2 + 192*a33**3*n2**4*n3*q1*u2**2 -
29*a33**2*k1*m2**3*n1*n2*n3*v1*v3**2 - 29*a33**2*k1*m2**3*n2**2*n3*v2*v3**2 - 48
*a33**2*k1*m2**3*n2*n3**2*v3**3 - 38*a33**2*k1*m2**2*n1*n2**2*n3*u1*v3**2 - 116*
a33**2*k1*m2**2*n1*n2**2*n3*u3*v1*v3 - 38*a33**2*k1*m2**2*n2**3*n3*u2*v3**2 -
116*a33**2*k1*m2**2*n2**3*n3*u3*v2*v3 - 230*a33**2*k1*m2**2*n2**2*n3**2*u3*v3**2
- 116*a33**2*k1*m2*n1*n2**3*n3*u1*u2*v2 - 268*a33**2*k1*m2*n1*n2**3*n3*u1*u3*v3
+ 116*a33**2*k1*m2*n1*n2**3*n3*u2**2*v1 + 20*a33**2*k1*m2*n1*n2**3*n3*u3**2*v1
+ 116*a33**2*k1*m2*n2**4*n3*u1**2*v2 + 116*a33**2*k1*m2*n2**4*n3*u2**2*v2 - 152*
a33**2*k1*m2*n2**4*n3*u2*u3*v3 + 20*a33**2*k1*m2*n2**4*n3*u3**2*v2 + 192*a33**2*
k1*m2*n2**3*n3**2*u1**2*v3 + 192*a33**2*k1*m2*n2**3*n3**2*u2**2*v3 - 112*a33**2*
k1*m2*n2**3*n3**2*u3**2*v3 + 152*a33**2*k1*n1*n2**4*n3*u1**3 + 152*a33**2*k1*n1*
n2**4*n3*u1*u2**2 + 40*a33**2*k1*n1*n2**4*n3*u1*u3**2 + 152*a33**2*k1*n2**5*n3*
u1**2*u2 + 152*a33**2*k1*n2**5*n3*u2**3 + 40*a33**2*k1*n2**5*n3*u2*u3**2 + 152*
a33**2*k1*n2**4*n3**2*u1**2*u3 + 152*a33**2*k1*n2**4*n3**2*u2**2*u3 + 40*a33**2*
k1*n2**4*n3**2*u3**3 + 48*a33**2*m2*n1*n2**3*n3*q1*v1 + 48*a33**2*m2*n2**4*n3*q1
*v2 + 96*a33**2*m2*n2**3*n3**2*q1*v3 + 96*a33**2*n1*n2**4*n3*q1*u1 + 96*a33**2*
n2**5*n3*q1*u2 + 96*a33**2*n2**4*n3**2*q1*u3 + 10*a33*k1*m2**2*n1**2*n2**2*n3*v1
**2 - 7*a33*k1*m2**2*n1**2*n2**2*n3*v2**2 + 34*a33*k1*m2**2*n1*n2**3*n3*v1*v2 +
58*a33*k1*m2**2*n1*n2**2*n3**2*v1*v3 + 17*a33*k1*m2**2*n2**4*n3*v2**2 + 58*a33*
k1*m2**2*n2**3*n3**2*v2*v3 - 48*a33*k1*m2**2*n2**2*n3**3*v1**2 - 48*a33*k1*m2**2
*n2**2*n3**3*v2**2 - 48*a33*k1*m2*n1**2*n2**3*n3*u2*v2 - 20*a33*k1*m2*n1**2*n2**
3*n3*u3*v3 + 48*a33*k1*m2*n1*n2**4*n3*u1*v2 + 48*a33*k1*m2*n1*n2**4*n3*u2*v1 +
76*a33*k1*m2*n1*n2**3*n3**2*u1*v3 + 48*a33*k1*m2*n1*n2**3*n3**2*u3*v1 + 48*a33*
k1*m2*n2**5*n3*u2*v2 + 76*a33*k1*m2*n2**4*n3**2*u2*v3 + 48*a33*k1*m2*n2**4*n3**2
*u3*v2 + 76*a33*k1*m2*n2**3*n3**3*u3*v3 - 28*a33*k1*n1**2*n2**4*n3*u2**2 + 56*
a33*k1*n1*n2**5*n3*u1*u2 + 56*a33*k1*n1*n2**4*n3**2*u1*u3 + 28*a33*k1*n2**6*n3*
u2**2 + 56*a33*k1*n2**5*n3**2*u2*u3 - 7*k1*m2*n1**3*n2**3*n3*v1 - 7*k1*m2*n1**2*
n2**4*n3*v2 - 14*k1*m2*n1**2*n2**3*n3**2*v3 - 7*k1*m2*n1*n2**3*n3**3*v1 - 7*k1*
m2*n2**4*n3**3*v2 - 14*k1*n1**3*n2**4*n3*u1 - 14*k1*n1**2*n2**5*n3*u2 - 14*k1*n1
**2*n2**4*n3**2*u3 + 14*k1*n1*n2**4*n3**3*u1 + 14*k1*n2**5*n3**3*u2 + 14*k1*n2**
4*n3**4*u3)/(192*a33**3*n2**4*n3)$