Solution 34 to problem e3quant
Expressions |
Parameters |
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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
1 2 1 2
- ---*b31 - ---*b32
2 2
c33=------------------------
a33
n1=0
n2=0
2 2
- a33*b32*m2 + b31 *n3 + b32 *n3
m1=-----------------------------------
a33*b31
m3=0
r6=0
2 2 2 2 2
- 3*a33 *b31*k1*m2 - 4*a33*b32*k1*m2*n3 + 4*b31 *k1*n3 + 4*b32 *k1*n3
r5=--------------------------------------------------------------------------
3
a33 *b31
2 2
3*a33*b32*k1*m2 - 3*b31 *k1*n3 - 4*b31*k1*m2*n3 - 3*b32 *k1*n3
r4=----------------------------------------------------------------
2
a33 *b31
- k1*n3
r3=----------
a33
r2=0
r1=0
q20=0
15 2 4 2 3 15 2 2 2
q19=( - ----*a33 *b31 *k1 + 4*a33 *b31 *k1*m2 - ----*a33 *b31 *b32 *k1
2 2
2 2 2 2 2 2 2 2
+ 4*a33 *b31 *k1*m2 + 4*a33 *b31*b32 *k1*m2 + 4*a33 *b32 *k1*m2
3 2 3
- 4*a33*b31 *b32*k1*n3 - 8*a33*b31 *b32*k1*m2*n3 - 4*a33*b31*b32 *k1*n3
3 4 2 2 2 2 4 2
- 8*a33*b32 *k1*m2*n3 + 4*b31 *k1*n3 + 8*b31 *b32 *k1*n3 + 4*b32 *k1*n3
4 2
)/(a33 *b31 )
q18=0
q17=0
15 2 4 2 3 15 2 2 2
q16=( - ----*a33 *b31 *k1 + 4*a33 *b31 *k1*m2 - ----*a33 *b31 *b32 *k1
2 2
2 2 2 2 2 2 2 2
+ 4*a33 *b31 *k1*m2 + 4*a33 *b31*b32 *k1*m2 + 4*a33 *b32 *k1*m2
3 2 3
- 4*a33*b31 *b32*k1*n3 - 8*a33*b31 *b32*k1*m2*n3 - 4*a33*b31*b32 *k1*n3
3 4 2 2 2 2 4 2
- 8*a33*b32 *k1*m2*n3 + 4*b31 *k1*n3 + 8*b31 *b32 *k1*n3 + 4*b32 *k1*n3
4 2
)/(a33 *b31 )
2 2
- 11*a33*b31*b32*k1 - 4*a33*b32*k1*m2 + 8*b31 *k1*n3 + 4*b32 *k1*n3
q14=----------------------------------------------------------------------
2
a33 *b31
5*a33*b31*k1 + 4*a33*k1*m2 - 4*b32*k1*n3
q13=------------------------------------------
2
a33
2
q11=( - 8*a33*b31*b32*k1 - 8*a33*b32*k1*m2 + 16*b31 *k1*n3 + 8*b31*k1*m2*n3
2 2
+ 8*b32 *k1*n3)/(a33 *b31)
q10=0
q9=0
q8=0
7 2 2
- ---*a33 *k1 - 4*k1*n3
2
q7=---------------------------
2
a33
2 2 2
q6=( - 8*a33 *b31 *k1 - 8*a33 *b31*k1*m2 - 8*a33*b31*b32*k1*n3
2 2 2 2 3
- 8*a33*b32*k1*m2*n3 + 8*b31 *k1*n3 + 8*b32 *k1*n3 )/(a33 *b31)
q5=0
q4=0
q3=0
q2=0
1 2 2
---*a33 *k1 - 4*k1*n3
2
q1=------------------------
2
a33
p56=0
2 2
- 4*b31 *k1*m2 - 4*b32 *k1*m2
p55=--------------------------------
3
a33
p54=0
p53=0
2 3 4 2 2
p52=(4*a33*b31 *b32*k1*m2 + 4*a33*b32 *k1*m2 - 4*b31 *k1*n3 - 8*b31 *b32 *k1*n3
4 4
- 4*b32 *k1*n3)/(a33 *b31)
p51=0
p50=0
p49=0
p48=0
p47=0
2 2
- 4*b31 *k1*n3 - 4*b32 *k1*n3
p46=--------------------------------
3
a33
p45=0
p44=0
p43=0
p42=0
p41=0
p40=0
4*b31*k1
p39=----------
a33
4*b32*k1
p38=----------
a33
p37=0
p36=0
2 2
8*b31 *k1*n3 + 8*b32 *k1*n3
p35=-----------------------------
3
a33
p34=0
2 2
12*b31 *k1 + 12*b32 *k1
p33=-------------------------
2
a33
p32=0
p31=0
8*a33*b31*k1 + 8*b32*k1*n3
p30=----------------------------
2
a33
p29=0
p28=0
p27=0
p26=0
- 8*b31*k1 - 4*k1*m2
p25=-----------------------
a33
2 2
- 8*a33*b31*b32*k1 - 4*a33*b32*k1*m2 + 4*b31 *k1*n3 + 4*b32 *k1*n3
p24=---------------------------------------------------------------------
2
a33 *b31
- 4*k1*n3
p23=------------
a33
p22=0
p21=0
2 2
- 12*b31 *k1 - 12*b32 *k1
p20=----------------------------
2
a33
p19=0
2 2
8*b31 *k1*n3 + 8*b32 *k1*n3
p18=-----------------------------
3
a33
p17=0
p16=0
- 8*a33*b32*k1 + 8*b31*k1*n3
p15=-------------------------------
2
a33
p14=0
p13=0
p12=0
p11=0
2 2
16*a33*b31*b32*k1 + 8*a33*b32*k1*m2 - 8*b31 *k1*n3 - 8*b32 *k1*n3
p10=-------------------------------------------------------------------
2
a33 *b31
- 16*b31*k1 - 8*k1*m2
p9=------------------------
a33
p8= - 4*k1
p7=0
p6=0
8*b31*k1 + 4*k1*m2
p5=--------------------
a33
2 2
8*a33*b31*b32*k1 + 4*a33*b32*k1*m2 - 4*b31 *k1*n3 - 4*b32 *k1*n3
p4=------------------------------------------------------------------
2
a33 *b31
- 4*k1*n3
p3=------------
a33
p2=0
p1=0
k125=0
4 2 2 4
- 2*b31 *k1 - 4*b31 *b32 *k1 - 2*b32 *k1
k124=-------------------------------------------
4
a33
k123=0
4 2 2 4
- b31 *k1 - 2*b31 *b32 *k1 - b32 *k1
k122=---------------------------------------
4
a33
k121=0
k120=0
k119=0
k118=0
4 2 2 4
- 2*b31 *k1 - 4*b31 *b32 *k1 - 2*b32 *k1
k117=-------------------------------------------
4
a33
k116=0
4 2 2 4
- 2*b31 *k1 - 4*b31 *b32 *k1 - 2*b32 *k1
k115=-------------------------------------------
4
a33
k114=0
k113=0
4 2 2 4
- b31 *k1 - 2*b31 *b32 *k1 - b32 *k1
k112=---------------------------------------
4
a33
2 3
- 4*b31 *b32*k1 - 4*b32 *k1
k110=------------------------------
3
a33
k109=0
k108=0
3 2
- 4*b31 *k1 - 4*b31*b32 *k1
k107=------------------------------
3
a33
k106=0
k105=0
k104=0
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
k95=0
k94=0
k93=0
k91=0
k90=0
k89=0
k88=0
k87=0
k86=0
k85=0
k84=0
k83=0
k82=0
k81=0
2 2
8*b31 *k1 + 8*b32 *k1
k80=-----------------------
2
a33
k79=0
k78=0
k77=0
k76=0
k75=0
k74=0
k73=0
k72=0
2 2
- 2*b31 *k1 - 2*b32 *k1
k71=--------------------------
2
a33
k70=0
k69=0
k68=0
k67=0
k66=0
k65=0
- 4*b32*k1
k64=-------------
a33
4*b31*k1
k63=----------
a33
k62=0
k61=0
k59=0
k58=0
k57=k1
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
2 2
8*b31 *k1 + 8*b32 *k1
k43=-----------------------
2
a33
k42=0
k41=0
k40=0
k39=0
k38=0
k37=0
k36=0
k35=0
k34=0
k33=0
k32=0
k31=0
k30=0
- 8*b31*k1
k29=-------------
a33
- 8*b32*k1
k28=-------------
a33
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
2 2
- 2*b31 *k1 - 2*b32 *k1
k21=--------------------------
2
a33
k20=0
k19=0
k18=0
k17=0
k16=0
k15=0
4*b32*k1
k14=----------
a33
- 4*b31*k1
k13=-------------
a33
k12=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:
n3,m2,k1,b32,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
HAM=(a33 *b31*u1 + a33 *b31*u2 + 2*a33 *b31*u3 + 2*a33*b31 *u3*v1
+ 2*a33*b31*b32*u3*v2 + 2*a33*b31*m2*v2 + 2*a33*b31*n3*u3
3 2 2 2 2 2
- 2*a33*b32*m2*v1 - b31 *v3 + 2*b31 *n3*v1 - b31*b32 *v3 + 2*b32 *n3*v1)
/(2*a33*b31)
4 2 4 4 2 2 4 2 2
INT=(k1*(2*a33 *b31 *u1 + 4*a33 *b31 *u1 *u2*u3 + a33 *b31 *u1
4 2 2 4 2 2 4 2
+ 2*a33 *b31 *u1*u2*v2 - 8*a33 *b31 *u1*u3 - 7*a33 *b31 *u1*v1
3 3 2 3 3 3 3 3 2
+ 16*a33 *b31 *u1 *u3 - 8*a33 *b31 *u1*u3 - 16*a33 *b31 *u1*u3*v1
3 3 3 3 2 3 3
+ 8*a33 *b31 *u1*u3*v3 - 32*a33 *b31 *u2*u3 - 16*a33 *b31 *u2*u3*v2
3 3 2 3 3 2 3 3
+ 8*a33 *b31 *u2*v1*v2 - 16*a33 *b31 *u3 + 10*a33 *b31 *u3*v2
3 3 2 3 2
+ 16*a33 *b31 *v1 *v2 - 16*a33 *b31 *b32*u1*u3*v2
3 2 3 2 3
- 16*a33 *b31 *b32*u1*v2 + 16*a33 *b31 *b32*u2
3 2 2 2 3 2 2
- 16*a33 *b31 *b32*u2 *v1 + 8*a33 *b31 *b32*u2 *v3
3 2 3 3 2
+ 8*a33 *b31 *b32*u2*u3 - 16*a33 *b31 *b32*u2*u3*v1
3 2 3 3 2 2
+ 32*a33 *b31 *b32*u3 - 8*a33 *b31 *b32*u3*v1*v2
3 2 3 2 2
- 22*a33 *b31 *b32*v1*v2 + 8*a33 *b31 *m2*u1 *u3
3 2 2 3 2
- 16*a33 *b31 *m2*u2*u3 - 8*a33 *b31 *m2*u2*u3*v2
3 2 2 3 2 3 2
- 16*a33 *b31 *m2*u3 + 8*a33 *b31 *m2*u3*v2 - 6*a33 *b31 *m2*v2
3 2 2 3 2 2 3 2
- 8*a33 *b31 *n3*u1*u2 - 8*a33 *b31 *n3*u2 *v2 - 2*a33 *b31 *n3*u3
3 3
- 8*a33 *b31*b32*m2*u1*u3*v2 - 16*a33 *b31*b32*m2*u1*v2
3 3 3 3
+ 8*a33 *b31*b32*m2*u2 + 16*a33 *b31*b32*m2*u3
3 3 2 4 3
- 8*a33 *b31*b32*m2*v1*v2 + 6*a33 *b31*b32*m2*v1 - 4*a33 *b31 *u1 *v3
2 4 2 4 2
- 4*a33 *b31 *u1*u2*u3*v1 + 16*a33 *b31 *u1*u3 *v2
2 4 2 4 3 2 4 2
- 15*a33 *b31 *u1*v3 + 16*a33 *b31 *u3 *v3 + 24*a33 *b31 *u3*v2
2 4 3 2 4 2 3
- 24*a33 *b31 *v1 - 15*a33 *b31 *v1*v3 + 8*a33 *b31 *m2*u1*v3
2 3 2 3
+ 8*a33 *b31 *m2*v1*v3 + 8*a33 *b31 *n3*u1*u3*v2
2 3 2 3 3
+ 32*a33 *b31 *n3*u1*v2 - 8*a33 *b31 *n3*u2
2 3 2 3 3
+ 16*a33 *b31 *n3*u2*u3*v1 - 16*a33 *b31 *n3*u3
2 3 2 3 2 2 2 3
+ 16*a33 *b31 *n3*v1*v2 - 6*a33 *b31 *n3*v1 - 4*a33 *b31 *b32 *u1 *v3
2 2 2 2 2 2 2
- 4*a33 *b31 *b32 *u1*u2*u3*v1 + 16*a33 *b31 *b32 *u1*u3 *v2
2 2 2 2 2 2 3
- 15*a33 *b31 *b32 *u1*v3 + 16*a33 *b31 *b32 *u3 *v3
2 2 2 2 2 2 2 3
+ 24*a33 *b31 *b32 *u3*v2 - 24*a33 *b31 *b32 *v1
2 2 2 2 2 2
- 15*a33 *b31 *b32 *v1*v3 - 16*a33 *b31 *b32*n3*u3
2 2 2 2 2
- 8*a33 *b31 *b32*n3*u3*v2 + 16*a33 *b31 *b32*n3*v1 *v2
2 2 2 2 2 2
+ 8*a33 *b31 *m2 *u1*v3 + 8*a33 *b31 *m2 *v1*v3
2 2 2 2
+ 16*a33 *b31 *m2*n3*u1*v2 - 8*a33 *b31 *m2*n3*v1
2 2 2 2 2 2 2
- 8*a33 *b31 *n3 *u1 - 8*a33 *b31 *n3 *u1*v1
2 2 2 2
+ 8*a33 *b31*b32 *m2*u1*v3 + 8*a33 *b31*b32 *m2*v1*v3
2 2 2 2
+ 8*a33 *b31*b32 *n3*u1*u3*v2 + 16*a33 *b31*b32 *n3*u1*v2
2 2 3 2 2 3
- 8*a33 *b31*b32 *n3*u2 - 16*a33 *b31*b32 *n3*u3
2 2 2 2
+ 8*a33 *b31*b32 *n3*v1*v2 - 6*a33 *b31*b32 *n3*v1
2 2 2
- 16*a33 *b31*b32*m2*n3*u3 - 8*a33 *b31*b32*m2*n3*v2
2 2 2 2 2 2 5 2
+ 8*a33 *b32 *m2 *u1*v3 + 8*a33 *b32 *m2 *v1*v3 - 8*a33*b31 *u1*u2*v3
4 2 4 2
- 8*a33*b31 *b32*u2*u3*v3 - 8*a33*b31 *m2*v2*v3
4 4 2 4 3
- 8*a33*b31 *n3*u1*v2*v3 + 16*a33*b31 *n3*u2*v1 + 16*a33*b31 *n3*v2
3 2 2 3 2
- 8*a33*b31 *b32 *u1*u2*v3 + 8*a33*b31 *b32*m2*u2*v3
3 3
- 8*a33*b31 *b32*n3*u1*v3 - 8*a33*b31 *b32*n3*v1*v3
3 2 2 3 2 2 3 2
+ 16*a33*b31 *n3 *u3 + 8*a33*b31 *n3 *v2 - 8*a33*b31 *b32 *u2*u3*v3
2 2 2 2 2
- 8*a33*b31 *b32 *m2*v2*v3 - 8*a33*b31 *b32 *n3*u1*v2*v3
2 2 2 2 2 3
+ 16*a33*b31 *b32 *n3*u2*v1 + 16*a33*b31 *b32 *n3*v2
2 2
- 16*a33*b31 *b32*m2*n3*u1*v3 - 16*a33*b31 *b32*m2*n3*v1*v3
3 2 3
+ 8*a33*b31*b32 *m2*u2*v3 - 8*a33*b31*b32 *n3*u1*v3
3 2 2 2
- 8*a33*b31*b32 *n3*v1*v3 + 16*a33*b31*b32 *n3 *u3
2 2 3
+ 8*a33*b31*b32 *n3 *v2 - 16*a33*b32 *m2*n3*u1*v3
3 6 2 6 2
- 16*a33*b32 *m2*n3*v1*v3 - 2*b31 *u1*v1*v3 - 4*b31 *u2*v2*v3
6 3 6 2 2 6 3 5 2
- 2*b31 *u2*v3 - 4*b31 *v1 *v3 - 4*b31 *v1*v3 - 8*b31 *n3*u2*v3
4 2 2 4 2 2 4 2 3
- 4*b31 *b32 *u1*v1*v3 - 8*b31 *b32 *u2*v2*v3 - 4*b31 *b32 *u2*v3
4 2 2 2 4 2 3 4 2
- 8*b31 *b32 *v1 *v3 - 8*b31 *b32 *v1*v3 + 8*b31 *n3 *u1*v3
4 2 3 2 2 2 4 2
+ 8*b31 *n3 *v1*v3 - 16*b31 *b32 *n3*u2*v3 - 2*b31 *b32 *u1*v1*v3
2 4 2 2 4 3 2 4 2 2
- 4*b31 *b32 *u2*v2*v3 - 2*b31 *b32 *u2*v3 - 4*b31 *b32 *v1 *v3
2 4 3 2 2 2 2 2 2
- 4*b31 *b32 *v1*v3 + 16*b31 *b32 *n3 *u1*v3 + 16*b31 *b32 *n3 *v1*v3
4 2 4 2 4 2 4
- 8*b31*b32 *n3*u2*v3 + 8*b32 *n3 *u1*v3 + 8*b32 *n3 *v1*v3))/(2*a33
2
*b31 )
And again in machine readable form:
HAM=(a33**2*b31*u1**2 + a33**2*b31*u2**2 + 2*a33**2*b31*u3**2 + 2*a33*b31**2*u3*
v1 + 2*a33*b31*b32*u3*v2 + 2*a33*b31*m2*v2 + 2*a33*b31*n3*u3 - 2*a33*b32*m2*v1 -
b31**3*v3**2 + 2*b31**2*n3*v1 - b31*b32**2*v3**2 + 2*b32**2*n3*v1)/(2*a33*b31)$
INT=(k1*(2*a33**4*b31**2*u1**4 + 4*a33**4*b31**2*u1**2*u2*u3 + a33**4*b31**2*u1
**2 + 2*a33**4*b31**2*u1*u2*v2**2 - 8*a33**4*b31**2*u1*u3**2 - 7*a33**4*b31**2*
u1*v1 + 16*a33**3*b31**3*u1**2*u3 - 8*a33**3*b31**3*u1*u3**3 - 16*a33**3*b31**3*
u1*u3*v1**2 + 8*a33**3*b31**3*u1*u3*v3 - 32*a33**3*b31**3*u2*u3**2 - 16*a33**3*
b31**3*u2*u3*v2 + 8*a33**3*b31**3*u2*v1*v2**2 - 16*a33**3*b31**3*u3**2 + 10*a33
**3*b31**3*u3*v2 + 16*a33**3*b31**3*v1**2*v2 - 16*a33**3*b31**2*b32*u1*u3*v2 -
16*a33**3*b31**2*b32*u1*v2 + 16*a33**3*b31**2*b32*u2**3 - 16*a33**3*b31**2*b32*
u2**2*v1**2 + 8*a33**3*b31**2*b32*u2**2*v3 + 8*a33**3*b31**2*b32*u2*u3**3 - 16*
a33**3*b31**2*b32*u2*u3*v1 + 32*a33**3*b31**2*b32*u3**3 - 8*a33**3*b31**2*b32*u3
*v1*v2**2 - 22*a33**3*b31**2*b32*v1*v2 + 8*a33**3*b31**2*m2*u1**2*u3 - 16*a33**3
*b31**2*m2*u2*u3**2 - 8*a33**3*b31**2*m2*u2*u3*v2 - 16*a33**3*b31**2*m2*u3**2 +
8*a33**3*b31**2*m2*u3*v2 - 6*a33**3*b31**2*m2*v2 - 8*a33**3*b31**2*n3*u1*u2**2 -
8*a33**3*b31**2*n3*u2**2*v2 - 2*a33**3*b31**2*n3*u3 - 8*a33**3*b31*b32*m2*u1*u3
*v2 - 16*a33**3*b31*b32*m2*u1*v2 + 8*a33**3*b31*b32*m2*u2**3 + 16*a33**3*b31*b32
*m2*u3**3 - 8*a33**3*b31*b32*m2*v1*v2 + 6*a33**3*b31*b32*m2*v1 - 4*a33**2*b31**4
*u1**3*v3 - 4*a33**2*b31**4*u1*u2*u3*v1 + 16*a33**2*b31**4*u1*u3**2*v2 - 15*a33
**2*b31**4*u1*v3 + 16*a33**2*b31**4*u3**3*v3 + 24*a33**2*b31**4*u3*v2**2 - 24*
a33**2*b31**4*v1**3 - 15*a33**2*b31**4*v1*v3 + 8*a33**2*b31**3*m2*u1*v3 + 8*a33
**2*b31**3*m2*v1*v3 + 8*a33**2*b31**3*n3*u1*u3*v2 + 32*a33**2*b31**3*n3*u1*v2 -
8*a33**2*b31**3*n3*u2**3 + 16*a33**2*b31**3*n3*u2*u3*v1 - 16*a33**2*b31**3*n3*u3
**3 + 16*a33**2*b31**3*n3*v1*v2 - 6*a33**2*b31**3*n3*v1 - 4*a33**2*b31**2*b32**2
*u1**3*v3 - 4*a33**2*b31**2*b32**2*u1*u2*u3*v1 + 16*a33**2*b31**2*b32**2*u1*u3**
2*v2 - 15*a33**2*b31**2*b32**2*u1*v3 + 16*a33**2*b31**2*b32**2*u3**3*v3 + 24*a33
**2*b31**2*b32**2*u3*v2**2 - 24*a33**2*b31**2*b32**2*v1**3 - 15*a33**2*b31**2*
b32**2*v1*v3 - 16*a33**2*b31**2*b32*n3*u3**2 - 8*a33**2*b31**2*b32*n3*u3*v2 + 16
*a33**2*b31**2*b32*n3*v1**2*v2 + 8*a33**2*b31**2*m2**2*u1*v3 + 8*a33**2*b31**2*
m2**2*v1*v3 + 16*a33**2*b31**2*m2*n3*u1*v2 - 8*a33**2*b31**2*m2*n3*v1 - 8*a33**2
*b31**2*n3**2*u1**2 - 8*a33**2*b31**2*n3**2*u1*v1 + 8*a33**2*b31*b32**2*m2*u1*v3
+ 8*a33**2*b31*b32**2*m2*v1*v3 + 8*a33**2*b31*b32**2*n3*u1*u3*v2 + 16*a33**2*
b31*b32**2*n3*u1*v2 - 8*a33**2*b31*b32**2*n3*u2**3 - 16*a33**2*b31*b32**2*n3*u3
**3 + 8*a33**2*b31*b32**2*n3*v1*v2 - 6*a33**2*b31*b32**2*n3*v1 - 16*a33**2*b31*
b32*m2*n3*u3**2 - 8*a33**2*b31*b32*m2*n3*v2 + 8*a33**2*b32**2*m2**2*u1*v3 + 8*
a33**2*b32**2*m2**2*v1*v3 - 8*a33*b31**5*u1*u2*v3**2 - 8*a33*b31**4*b32*u2*u3*v3
**2 - 8*a33*b31**4*m2*v2*v3**2 - 8*a33*b31**4*n3*u1*v2*v3 + 16*a33*b31**4*n3*u2*
v1**2 + 16*a33*b31**4*n3*v2**3 - 8*a33*b31**3*b32**2*u1*u2*v3**2 + 8*a33*b31**3*
b32*m2*u2*v3**2 - 8*a33*b31**3*b32*n3*u1*v3 - 8*a33*b31**3*b32*n3*v1*v3 + 16*a33
*b31**3*n3**2*u3**2 + 8*a33*b31**3*n3**2*v2 - 8*a33*b31**2*b32**3*u2*u3*v3**2 -
8*a33*b31**2*b32**2*m2*v2*v3**2 - 8*a33*b31**2*b32**2*n3*u1*v2*v3 + 16*a33*b31**
2*b32**2*n3*u2*v1**2 + 16*a33*b31**2*b32**2*n3*v2**3 - 16*a33*b31**2*b32*m2*n3*
u1*v3 - 16*a33*b31**2*b32*m2*n3*v1*v3 + 8*a33*b31*b32**3*m2*u2*v3**2 - 8*a33*b31
*b32**3*n3*u1*v3 - 8*a33*b31*b32**3*n3*v1*v3 + 16*a33*b31*b32**2*n3**2*u3**2 + 8
*a33*b31*b32**2*n3**2*v2 - 16*a33*b32**3*m2*n3*u1*v3 - 16*a33*b32**3*m2*n3*v1*v3
- 2*b31**6*u1*v1*v3**2 - 4*b31**6*u2*v2*v3**2 - 2*b31**6*u2*v3**3 - 4*b31**6*v1
**2*v3**2 - 4*b31**6*v1*v3**3 - 8*b31**5*n3*u2*v3**2 - 4*b31**4*b32**2*u1*v1*v3
**2 - 8*b31**4*b32**2*u2*v2*v3**2 - 4*b31**4*b32**2*u2*v3**3 - 8*b31**4*b32**2*
v1**2*v3**2 - 8*b31**4*b32**2*v1*v3**3 + 8*b31**4*n3**2*u1*v3 + 8*b31**4*n3**2*
v1*v3 - 16*b31**3*b32**2*n3*u2*v3**2 - 2*b31**2*b32**4*u1*v1*v3**2 - 4*b31**2*
b32**4*u2*v2*v3**2 - 2*b31**2*b32**4*u2*v3**3 - 4*b31**2*b32**4*v1**2*v3**2 - 4*
b31**2*b32**4*v1*v3**3 + 16*b31**2*b32**2*n3**2*u1*v3 + 16*b31**2*b32**2*n3**2*
v1*v3 - 8*b31*b32**4*n3*u2*v3**2 + 8*b32**4*n3**2*u1*v3 + 8*b32**4*n3**2*v1*v3))
/(2*a33**4*b31**2)$