Solution 15 to problem e3null
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Expressions |
Parameters |
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Equations
The following unsolved equations remain:
2 2
0=b31 + b32
Expressions
The solution is given through the following expressions:
1
a22=---*a33
2
b22=0
b33=0
c12=0
c13=0
c22=0
c23=0
c33=0
1
- ---*a33*m3
2
n1=---------------
b31
1
---*a33*b32*m3
2
n2=----------------
2
b31
7 3 8 2
- ----*b31 *n3 - ---*b31*b32 *n3
18 9
m1=-----------------------------------
2
a33*b32
7 2 8 2
- ----*b31 *n3 - ---*b32 *n3
18 9
m2=-------------------------------
a33*b32
2 2 1 2
---*b31 *m3 - ---*b32 *m3
3 3
m3=---------------------------
2
b31
1253 2 2 4 3 1253 2 6 3
r6=(------*a33 *b31 *b32 *k1*m3 + ------*a33 *b32 *k1*m3
239 239
2548 8 2 10492 6 2 2
+ ------*b31 *k1*m3*n3 - -------*b31 *b32 *k1*m3*n3
6453 6453
64396 4 4 2 3 6 2
+ -------*b31 *b32 *k1*m3*n3 )/(a33 *b31 *b32 )
6453
119 4 2 451 2 2 2 4 4 2
- -----*b31 *k1*m3 *n3 - -----*b31 *b32 *k1*m3 *n3 - ----*b32 *k1*m3 *n3
54 54 27
r5=---------------------------------------------------------------------------
2 4
a33 *b31 *b32
49 4 2 127 2 2 2 250 4 2
----*b31 *k1*m3 *n3 - -----*b31 *b32 *k1*m3 *n3 - -----*b32 *k1*m3 *n3
54 54 27
r4=------------------------------------------------------------------------
2 3 2
a33 *b31 *b32
2 2 2 2
7*b31 *k1*m3 *n3 + 7*b32 *k1*m3 *n3
r3=-------------------------------------
4
a33*b31
7 2 3 7 3 3
---*b31 *b32*k1*m3 + ---*b32 *k1*m3
2 2
r2=---------------------------------------
6
b31
7 2 3 7 2 3
- ---*b31 *k1*m3 - ---*b32 *k1*m3
2 2
r1=--------------------------------------
5
b31
28 4 92 2 2 64 4
----*b31 *k1*m3*n3 + ----*b31 *b32 *k1*m3*n3 + ----*b32 *k1*m3*n3
27 27 27
q19=-------------------------------------------------------------------
3 2
a33 *b31 *b32
28 4 92 2 2 64 4
- ----*b31 *k1*m3*n3 - ----*b31 *b32 *k1*m3*n3 - ----*b32 *k1*m3*n3
27 27 27
q18=----------------------------------------------------------------------
3 2
a33 *b31*b32
49 2 4 2 221 2 2 2 2
q16=( - ----*a33 *b31 *k1*m3 - -----*a33 *b31 *b32 *k1*m3
27 27
172 2 4 2 28 6 2 64 4 2 2 3
- -----*a33 *b32 *k1*m3 - ----*b31 *k1*n3 - ----*b31 *b32 *k1*n3 )/(a33
27 9 9
4
*b31 *b32)
49 2 4 2 221 2 2 2 2
q15=( - ----*a33 *b31 *k1*m3 - -----*a33 *b31 *b32 *k1*m3
27 27
172 2 4 2 28 6 2 64 4 2 2 3
- -----*a33 *b32 *k1*m3 - ----*b31 *k1*n3 - ----*b31 *b32 *k1*n3 )/(a33
27 9 9
3 2
*b31 *b32 )
49 6 2 140 4 2 2 107 2 4 2
q14=( - ----*b31 *k1*n3 - -----*b31 *b32 *k1*n3 - -----*b31 *b32 *k1*n3
81 27 9
592 6 2 4 4
- -----*b32 *k1*n3 )/(a33 *b32 )
81
q13=0
2 2 3 2
3*b31 *b32*k1*m3 - b32 *k1*m3
q12=---------------------------------
4
a33*b31
q11=0
28 2 100 2
- ----*b31 *k1*m3*n3 - -----*b32 *k1*m3*n3
9 9
q10=---------------------------------------------
2
a33 *b31*b32
49 6 2 140 4 2 2 107 2 4 2
q9=( - ----*b31 *k1*n3 - -----*b31 *b32 *k1*n3 - -----*b31 *b32 *k1*n3
81 27 9
592 6 2 4 4
- -----*b32 *k1*n3 )/(a33 *b32 )
81
2 2 2 2
- b31 *k1*m3 + 3*b32 *k1*m3
q8=--------------------------------
3
a33*b31
28 2 100 2
----*b31 *k1*m3*n3 + -----*b32 *k1*m3*n3
9 9
q7=------------------------------------------
2
a33 *b31*b32
4*b32*k1*m3*n3
q5=----------------
2
a33*b31
- 4*k1*m3*n3
q4=---------------
a33*b31
7 2 2 2 5 2 2 2 4 2
- ---*a33 *b31 *k1*m3 - ---*a33 *b32 *k1*m3 - 4*b31 *k1*n3
2 2
q3=----------------------------------------------------------------
2 4
a33 *b31
2
- 2*b32*k1*m3
q2=-----------------
3
b31
5 2 2 2 7 2 2 2 4 2
- ---*a33 *b31 *k1*m3 - ---*a33 *b32 *k1*m3 - 4*b31 *k1*n3
2 2
q1=----------------------------------------------------------------
2 4
a33 *b31
p50=0
p49=0
p48=0
p47=0
p46=0
p45=0
p44=0
p43=0
8 2 8 3
- ---*b31 *b32*k1*m3 - ---*b32 *k1*m3
3 3
p42=----------------------------------------
2 2
a33 *b31
p41=0
p40=0
p39=0
8 2 8 2
---*b31 *k1*m3 + ---*b32 *k1*m3
3 3
p38=---------------------------------
2
a33 *b31
p37=0
2 2
4*b31 *k1*m3 - 4*b32 *k1*m3
p36=-----------------------------
2
a33*b31
28 2 8 2
- ----*b31 *k1*n3 + ---*b32 *k1*n3
9 9
p35=-------------------------------------
2
a33 *b32
14 3 40 2
- ----*b31 *k1*n3 + ----*b31*b32 *k1*n3
9 9
p34=------------------------------------------
2 2
a33 *b32
4 2 4 2
- ---*b31 *k1*m3 - ---*b32 *k1*m3
3 3
p33=------------------------------------
2
a33*b31
p32=0
4 2 4 2
- ---*b31 *k1*m3 - ---*b32 *k1*m3
3 3
p31=------------------------------------
2
a33*b31
p30=0
p29=0
p28=0
p27=0
p26=0
p25=0
p24=0
p23=0
p22=0
p21=0
8*b32*k1*m3
p20=-------------
a33*b31
14 2 32 2
- ----*b31 *k1*n3 - ----*b32 *k1*n3
9 9
p19=--------------------------------------
2
a33 *b32
14 3 32 2
----*b31 *k1*n3 + ----*b31*b32 *k1*n3
9 9
p18=---------------------------------------
2 2
a33 *b32
14 2 32 2
- ----*b31 *k1*n3 - ----*b32 *k1*n3
9 9
p17=--------------------------------------
2
a33 *b32
p16=0
p15=0
p14=0
p13=0
- 8*b32*k1*m3
p12=----------------
a33*b31
14 3 32 2
- ----*b31 *k1*n3 - ----*b31*b32 *k1*n3
9 9
p11=------------------------------------------
2 2
a33 *b32
p10=0
p9=0
p8=0
- 4*k1*n3
p7=------------
a33
p6=0
- 4*k1*n3
p5=------------
a33
- 2*b32*k1*m3
p4=----------------
2
b31
2*k1*m3
p3=---------
b31
- 2*b32*k1*m3
p2=----------------
2
b31
2*k1*m3
p1=---------
b31
k104=0
k103=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
k95=0
k94=0
k93=0
k92=0
k90=0
k89=0
k88=0
k87=0
k86=0
k85=0
k84=0
k83=0
k82=0
k81=0
k80=0
k79=0
k78=0
k77=0
k76=0
k75=0
k74=0
k73=0
k72=0
k71=0
k70=0
k69=0
k68=0
k67=0
k66=0
k65=0
8*b32*k1
k64=----------
a33
4*b31*k1
k63=----------
a33
k62=0
k61=0
k60=0
k59=0
k58=0
k57=0
k56=0
k55=0
k54=0
k53=0
k52=0
k51=0
k50=0
k49=0
k48=0
k47=0
k46=0
k45=0
k44=0
k43=0
k42=0
k41=0
k40=0
k39=0
k38=0
k37=0
k36=0
k35=0
k34=0
k33=0
4*b32*k1
k32=----------
a33
- 4*b31*k1
k31=-------------
a33
4*b32*k1
k30=----------
a33
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k21=0
k20=0
k19=0
k18=0
4*b31*k1
k17=----------
a33
k16=0
k14=0
k13=0
k12=0
k11=0
k10=0
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:
n3,m3,b32,k1,b31,a33
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2 2 2 2 2 2 2 2 2 2
HAM=(9*a33 *b31 *b32 *u1 + 9*a33 *b31 *b32 *u2 + 18*a33 *b31 *b32 *u3
2 2 2 3 3 2
- 9*a33 *b31*b32 *m3*u1 + 9*a33 *b32 *m3*u2 + 18*a33*b31 *b32 *u3*v1
2 3 2 2 2 2
+ 18*a33*b31 *b32 *u3*v2 + 12*a33*b31 *b32 *m3*v3 + 18*a33*b31 *b32 *n3*u3
4 5 4 3 2
- 6*a33*b32 *m3*v3 - 7*b31 *n3*v1 - 7*b31 *b32*n3*v2 - 16*b31 *b32 *n3*v1
2 3 2 2
- 16*b31 *b32 *n3*v2)/(18*a33*b31 *b32 )
4 6 4 4 4 6 4 2 2
INT=(k1*(38718*a33 *b31 *b32 *u1 + 77436*a33 *b31 *b32 *u1 *u2
4 6 4 4 4 5 4 3
+ 38718*a33 *b31 *b32 *u2 + 77436*a33 *b31 *b32 *m3*u1
4 5 4 2 4 4 5 2
+ 77436*a33 *b31 *b32 *m3*u1*u2 - 77436*a33 *b31 *b32 *m3*u1 *u2
4 4 5 3 4 4 4 2 2
- 77436*a33 *b31 *b32 *m3*u2 - 96795*a33 *b31 *b32 *m3 *u1
4 4 4 2 2 4 3 5 2
- 135513*a33 *b31 *b32 *m3 *u2 - 77436*a33 *b31 *b32 *m3 *u1*u2
4 3 4 3 4 2 6 2 2
- 135513*a33 *b31 *b32 *m3 *u1 - 135513*a33 *b31 *b32 *m3 *u1
4 2 6 2 2 4 2 5 3
- 96795*a33 *b31 *b32 *m3 *u2 + 135513*a33 *b31 *b32 *m3 *u2
4 6 3 4 7 3
- 135513*a33 *b31*b32 *m3 *u1 + 135513*a33 *b32 *m3 *u2
3 7 4 3 7 4 2
- 154872*a33 *b31 *b32 *u1*u2*u3*v2 + 154872*a33 *b31 *b32 *u1*u3 *v3
3 7 4 2 3 7 2 2
+ 154872*a33 *b31 *b32 *u2 *u3*v1 - 70266*a33 *b31 *b32 *m3 *u1*v3
3 6 5 2 3 6 5 2
+ 154872*a33 *b31 *b32 *u1 *u3*v2 + 154872*a33 *b31 *b32 *u2 *u3*v2
3 6 5 2 3 6 4 2
+ 309744*a33 *b31 *b32 *u2*u3 *v3 - 51624*a33 *b31 *b32 *m3*u1 *v3
3 6 4 2 3 6 4 2
- 51624*a33 *b31 *b32 *m3*u2 *v3 + 154872*a33 *b31 *b32 *m3*u3 *v3
3 6 4 2 3 6 4 2
- 154872*a33 *b31 *b32 *n3*u1 *u3 - 154872*a33 *b31 *b32 *n3*u2 *u3
3 6 3 2 3 5 5
- 70266*a33 *b31 *b32 *m3 *u2*v3 + 309744*a33 *b31 *b32 *m3*u1*u3*v2
3 5 5 3 5 4 2
- 309744*a33 *b31 *b32 *m3*u2*u3*v1 - 316914*a33 *b31 *b32 *m3 *u1*v3
3 5 4 2 3 5 4
- 38718*a33 *b31 *b32 *m3 *u3*v1 - 154872*a33 *b31 *b32 *m3*n3*u1*u3
3 4 6 2 3 4 6 2
- 51624*a33 *b31 *b32 *m3*u1 *v3 - 51624*a33 *b31 *b32 *m3*u2 *v3
3 4 6 2 3 4 5 2
- 154872*a33 *b31 *b32 *m3*u3 *v3 - 316914*a33 *b31 *b32 *m3 *u2*v3
3 4 5 2 3 4 5
+ 116154*a33 *b31 *b32 *m3 *u3*v2 + 154872*a33 *b31 *b32 *m3*n3*u2*u3
3 4 4 2 3 3 6 2
+ 271026*a33 *b31 *b32 *m3 *n3*u3 - 246648*a33 *b31 *b32 *m3 *u1*v3
3 3 6 2 3 2 7 2
+ 116154*a33 *b31 *b32 *m3 *u3*v1 - 246648*a33 *b31 *b32 *m3 *u2*v3
3 2 7 2 3 2 6 3
- 38718*a33 *b31 *b32 *m3 *u3*v2 + 202986*a33 *b31 *b32 *m3 *v3
3 2 6 2 3 8 3
+ 271026*a33 *b31 *b32 *m3 *n3*u3 + 202986*a33 *b32 *m3 *v3
2 9 2 2 9 2
+ 60228*a33 *b31 *b32 *n3*u1*u2*v2 - 60228*a33 *b31 *b32 *n3*u1*u3*v3
2 9 2 2 2 8 3 2
- 60228*a33 *b31 *b32 *n3*u2 *v1 - 60228*a33 *b31 *b32 *n3*u1 *v2
2 8 3 2 2 8 3
- 60228*a33 *b31 *b32 *n3*u2 *v2 - 120456*a33 *b31 *b32 *n3*u2*u3*v3
2 7 4
+ 103248*a33 *b31 *b32 *m3*u3*v1*v3
2 7 4
+ 137664*a33 *b31 *b32 *n3*u1*u2*v2
2 7 4 2 7 4 2
+ 172080*a33 *b31 *b32 *n3*u1*u3*v3 - 137664*a33 *b31 *b32 *n3*u2 *v1
2 7 3
- 120456*a33 *b31 *b32 *m3*n3*u1*v2
2 7 3 2 7 2 2
+ 120456*a33 *b31 *b32 *m3*n3*u2*v1 + 35133*a33 *b31 *b32 *m3 *n3*v1
2 6 5 2 6 5 2
- 103248*a33 *b31 *b32 *m3*u3*v2*v3 - 137664*a33 *b31 *b32 *n3*u1 *v2
2 6 5 2 2 6 5
- 137664*a33 *b31 *b32 *n3*u2 *v2 + 34416*a33 *b31 *b32 *n3*u2*u3*v3
2 6 4 2 2 2 6 4 2 2
- 154872*a33 *b31 *b32 *n3 *u1 - 154872*a33 *b31 *b32 *n3 *u2
2 6 3 2 2 5 6
- 85323*a33 *b31 *b32 *m3 *n3*v2 + 103248*a33 *b31 *b32 *m3*u3*v1*v3
2 5 5
- 430200*a33 *b31 *b32 *m3*n3*u1*v2
2 5 5 2 5 4 2
+ 430200*a33 *b31 *b32 *m3*n3*u2*v1 - 91059*a33 *b31 *b32 *m3 *n3*v1
2 4 7 2 4 5 2
- 103248*a33 *b31 *b32 *m3*u3*v2*v3 - 323367*a33 *b31 *b32 *m3 *n3*v2
2 3 6 2 2 2 7 2
- 358500*a33 *b31 *b32 *m3 *n3*v1 - 5736*a33 *b31 *b32 *m3 *n3*v2
9 2 9 2 2
- 40152*a33*b31 *b32 *m3*n3*v1*v3 - 120456*a33*b31 *b32 *n3 *u1*v3
8 3 8 3 2
+ 40152*a33*b31 *b32 *m3*n3*v2*v3 - 120456*a33*b31 *b32 *n3 *u2*v3
8 2 2 7 4
+ 15288*a33*b31 *b32 *m3*n3 *v3 - 131928*a33*b31 *b32 *m3*n3*v1*v3
7 4 2 6 5
- 275328*a33*b31 *b32 *n3 *u1*v3 + 131928*a33*b31 *b32 *m3*n3*v2*v3
6 5 2 6 4 2
- 275328*a33*b31 *b32 *n3 *u2*v3 - 62952*a33*b31 *b32 *m3*n3 *v3
5 6 4 7
- 91776*a33*b31 *b32 *m3*n3*v1*v3 + 91776*a33*b31 *b32 *m3*n3*v2*v3
4 6 2 12 2 2
+ 386376*a33*b31 *b32 *m3*n3 *v3 - 23422*b31 *n3 *v1
12 2 2 10 2 2 2
- 23422*b31 *n3 *v2 - 200760*b31 *b32 *n3 *v1
10 2 2 2 8 4 2 2
- 200760*b31 *b32 *n3 *v2 - 460314*b31 *b32 *n3 *v1
8 4 2 2 6 6 2 2
- 460314*b31 *b32 *n3 *v2 - 282976*b31 *b32 *n3 *v1
6 6 2 2 4 6 4
- 282976*b31 *b32 *n3 *v2 ))/(38718*a33 *b31 *b32 )
And again in machine readable form:
HAM=(9*a33**2*b31**2*b32**2*u1**2 + 9*a33**2*b31**2*b32**2*u2**2 + 18*a33**2*b31
**2*b32**2*u3**2 - 9*a33**2*b31*b32**2*m3*u1 + 9*a33**2*b32**3*m3*u2 + 18*a33*
b31**3*b32**2*u3*v1 + 18*a33*b31**2*b32**3*u3*v2 + 12*a33*b31**2*b32**2*m3*v3 +
18*a33*b31**2*b32**2*n3*u3 - 6*a33*b32**4*m3*v3 - 7*b31**5*n3*v1 - 7*b31**4*b32*
n3*v2 - 16*b31**3*b32**2*n3*v1 - 16*b31**2*b32**3*n3*v2)/(18*a33*b31**2*b32**2)$
INT=(k1*(38718*a33**4*b31**6*b32**4*u1**4 + 77436*a33**4*b31**6*b32**4*u1**2*u2
**2 + 38718*a33**4*b31**6*b32**4*u2**4 + 77436*a33**4*b31**5*b32**4*m3*u1**3 +
77436*a33**4*b31**5*b32**4*m3*u1*u2**2 - 77436*a33**4*b31**4*b32**5*m3*u1**2*u2
- 77436*a33**4*b31**4*b32**5*m3*u2**3 - 96795*a33**4*b31**4*b32**4*m3**2*u1**2 -
135513*a33**4*b31**4*b32**4*m3**2*u2**2 - 77436*a33**4*b31**3*b32**5*m3**2*u1*
u2 - 135513*a33**4*b31**3*b32**4*m3**3*u1 - 135513*a33**4*b31**2*b32**6*m3**2*u1
**2 - 96795*a33**4*b31**2*b32**6*m3**2*u2**2 + 135513*a33**4*b31**2*b32**5*m3**3
*u2 - 135513*a33**4*b31*b32**6*m3**3*u1 + 135513*a33**4*b32**7*m3**3*u2 - 154872
*a33**3*b31**7*b32**4*u1*u2*u3*v2 + 154872*a33**3*b31**7*b32**4*u1*u3**2*v3 +
154872*a33**3*b31**7*b32**4*u2**2*u3*v1 - 70266*a33**3*b31**7*b32**2*m3**2*u1*v3
+ 154872*a33**3*b31**6*b32**5*u1**2*u3*v2 + 154872*a33**3*b31**6*b32**5*u2**2*
u3*v2 + 309744*a33**3*b31**6*b32**5*u2*u3**2*v3 - 51624*a33**3*b31**6*b32**4*m3*
u1**2*v3 - 51624*a33**3*b31**6*b32**4*m3*u2**2*v3 + 154872*a33**3*b31**6*b32**4*
m3*u3**2*v3 - 154872*a33**3*b31**6*b32**4*n3*u1**2*u3 - 154872*a33**3*b31**6*b32
**4*n3*u2**2*u3 - 70266*a33**3*b31**6*b32**3*m3**2*u2*v3 + 309744*a33**3*b31**5*
b32**5*m3*u1*u3*v2 - 309744*a33**3*b31**5*b32**5*m3*u2*u3*v1 - 316914*a33**3*b31
**5*b32**4*m3**2*u1*v3 - 38718*a33**3*b31**5*b32**4*m3**2*u3*v1 - 154872*a33**3*
b31**5*b32**4*m3*n3*u1*u3 - 51624*a33**3*b31**4*b32**6*m3*u1**2*v3 - 51624*a33**
3*b31**4*b32**6*m3*u2**2*v3 - 154872*a33**3*b31**4*b32**6*m3*u3**2*v3 - 316914*
a33**3*b31**4*b32**5*m3**2*u2*v3 + 116154*a33**3*b31**4*b32**5*m3**2*u3*v2 +
154872*a33**3*b31**4*b32**5*m3*n3*u2*u3 + 271026*a33**3*b31**4*b32**4*m3**2*n3*
u3 - 246648*a33**3*b31**3*b32**6*m3**2*u1*v3 + 116154*a33**3*b31**3*b32**6*m3**2
*u3*v1 - 246648*a33**3*b31**2*b32**7*m3**2*u2*v3 - 38718*a33**3*b31**2*b32**7*m3
**2*u3*v2 + 202986*a33**3*b31**2*b32**6*m3**3*v3 + 271026*a33**3*b31**2*b32**6*
m3**2*n3*u3 + 202986*a33**3*b32**8*m3**3*v3 + 60228*a33**2*b31**9*b32**2*n3*u1*
u2*v2 - 60228*a33**2*b31**9*b32**2*n3*u1*u3*v3 - 60228*a33**2*b31**9*b32**2*n3*
u2**2*v1 - 60228*a33**2*b31**8*b32**3*n3*u1**2*v2 - 60228*a33**2*b31**8*b32**3*
n3*u2**2*v2 - 120456*a33**2*b31**8*b32**3*n3*u2*u3*v3 + 103248*a33**2*b31**7*b32
**4*m3*u3*v1*v3 + 137664*a33**2*b31**7*b32**4*n3*u1*u2*v2 + 172080*a33**2*b31**7
*b32**4*n3*u1*u3*v3 - 137664*a33**2*b31**7*b32**4*n3*u2**2*v1 - 120456*a33**2*
b31**7*b32**3*m3*n3*u1*v2 + 120456*a33**2*b31**7*b32**3*m3*n3*u2*v1 + 35133*a33
**2*b31**7*b32**2*m3**2*n3*v1 - 103248*a33**2*b31**6*b32**5*m3*u3*v2*v3 - 137664
*a33**2*b31**6*b32**5*n3*u1**2*v2 - 137664*a33**2*b31**6*b32**5*n3*u2**2*v2 +
34416*a33**2*b31**6*b32**5*n3*u2*u3*v3 - 154872*a33**2*b31**6*b32**4*n3**2*u1**2
- 154872*a33**2*b31**6*b32**4*n3**2*u2**2 - 85323*a33**2*b31**6*b32**3*m3**2*n3
*v2 + 103248*a33**2*b31**5*b32**6*m3*u3*v1*v3 - 430200*a33**2*b31**5*b32**5*m3*
n3*u1*v2 + 430200*a33**2*b31**5*b32**5*m3*n3*u2*v1 - 91059*a33**2*b31**5*b32**4*
m3**2*n3*v1 - 103248*a33**2*b31**4*b32**7*m3*u3*v2*v3 - 323367*a33**2*b31**4*b32
**5*m3**2*n3*v2 - 358500*a33**2*b31**3*b32**6*m3**2*n3*v1 - 5736*a33**2*b31**2*
b32**7*m3**2*n3*v2 - 40152*a33*b31**9*b32**2*m3*n3*v1*v3 - 120456*a33*b31**9*b32
**2*n3**2*u1*v3 + 40152*a33*b31**8*b32**3*m3*n3*v2*v3 - 120456*a33*b31**8*b32**3
*n3**2*u2*v3 + 15288*a33*b31**8*b32**2*m3*n3**2*v3 - 131928*a33*b31**7*b32**4*m3
*n3*v1*v3 - 275328*a33*b31**7*b32**4*n3**2*u1*v3 + 131928*a33*b31**6*b32**5*m3*
n3*v2*v3 - 275328*a33*b31**6*b32**5*n3**2*u2*v3 - 62952*a33*b31**6*b32**4*m3*n3
**2*v3 - 91776*a33*b31**5*b32**6*m3*n3*v1*v3 + 91776*a33*b31**4*b32**7*m3*n3*v2*
v3 + 386376*a33*b31**4*b32**6*m3*n3**2*v3 - 23422*b31**12*n3**2*v1**2 - 23422*
b31**12*n3**2*v2**2 - 200760*b31**10*b32**2*n3**2*v1**2 - 200760*b31**10*b32**2*
n3**2*v2**2 - 460314*b31**8*b32**4*n3**2*v1**2 - 460314*b31**8*b32**4*n3**2*v2**
2 - 282976*b31**6*b32**6*n3**2*v1**2 - 282976*b31**6*b32**6*n3**2*v2**2))/(38718
*a33**4*b31**6*b32**4)$