Solution 18 to problem e3c2new
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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
n3=0
1 1
- ---*a22*b33*n1 - ---*a33*b33*n1
2 2
m1=------------------------------------
2
a22 - a22*a33
1 1
- ---*a22*b33*n2 - ---*a33*b33*n2
2 2
m2=------------------------------------
2
a22 - a22*a33
m3=0
r6=0
1 2 1 1 2
- ---*a22 *b33*n2*q1 + ---*a22*a33*b33*n2*q1 + ---*b33*k1*n1 *n2
2 2 4
r5=-------------------------------------------------------------------
4 3 2 2
a22 - 2*a22 *a33 + a22 *a33
1 2 1 1 3
- ---*a22 *b33*n1*q1 + ---*a22*a33*b33*n1*q1 + ---*b33*k1*n1
2 2 4
r4=----------------------------------------------------------------
4 3 2 2
a22 - 2*a22 *a33 + a22 *a33
r3=0
3 2 2 1 2
r2=(a22 *n2*q1 - 2*a22 *a33*n2*q1 + a22*a33 *n2*q1 - ---*a22*k1*n1 *n2
2
1 2 4 3 2 2 3
+ ---*a33*k1*n1 *n2)/(a22 - 3*a22 *a33 + 3*a22 *a33 - a22*a33 )
2
3 2 2 1 3
r1=(a22 *n1*q1 - 2*a22 *a33*n1*q1 + a22*a33 *n1*q1 - ---*a22*k1*n1
2
1 3 4 3 2 2 3
+ ---*a33*k1*n1 )/(a22 - 3*a22 *a33 + 3*a22 *a33 - a22*a33 )
2
q20=0
q19=0
q17=0
q16=0
1 3 2 1 2 2 1 2 2
q15=(---*a22 *b33 *q1 - ---*a22 *a33*b33 *q1 + ---*a22*a33 *b33 *q1
4 2 4
1 2 2 3 2 2 1 2 2
- ---*a22*b33 *k1*n1 + ---*a22*b33 *k1*n2 + ---*a33*b33 *k1*n1
8 8 8
1 2 2 5 4 3 2
+ ---*a33*b33 *k1*n2 )/(a22 - 2*a22 *a33 + a22 *a33 )
8
3 2 1 2
---*a22*b33 *k1*n1*n2 + ---*a33*b33 *k1*n1*n2
4 4
q14=-----------------------------------------------
5 4 3 2
a22 - 2*a22 *a33 + a22 *a33
q13=0
3 2 2 1 2
q12=( - a22 *b33*q1 + 2*a22 *a33*b33*q1 - a22*a33 *b33*q1 + ---*a22*b33*k1*n1
2
2 1 2 4 3 2 2
- a22*b33*k1*n2 - ---*a33*b33*k1*n1 )/(a22 - 2*a22 *a33 + a22 *a33 )
2
- b33*k1*n1*n2
q11=------------------------------
3 2 2
a22 - 2*a22 *a33 + a22*a33
1 3 2 1 2 2 1 2 2
q10=(---*a22 *b33 *q1 - ---*a22 *a33*b33 *q1 + ---*a22*a33 *b33 *q1
4 2 4
1 2 2 1 2 2 5 4
+ ---*a22*b33 *k1*n1 + ---*a33*b33 *k1*n1 )/(a22 - 2*a22 *a33
4 4
3 2
+ a22 *a33 )
q9=0
- b33*k1*n1*n2
q8=------------------------------
3 2 2
a22 - 2*a22 *a33 + a22*a33
3 2 2 1 2
q7=( - a22 *b33*q1 + 2*a22 *a33*b33*q1 - a22*a33 *b33*q1 - ---*a22*b33*k1*n1
2
1 2 4 3 2 2
- ---*a33*b33*k1*n1 )/(a22 - 2*a22 *a33 + a22 *a33 )
2
q5=0
q4=0
3 2 2 1 2 1 2
q3=(a22 *q1 - 2*a22 *a33*q1 + a22*a33 *q1 - ---*a22*k1*n1 + ---*a22*k1*n2
2 2
1 2 1 2 3 2 2
+ ---*a33*k1*n1 - ---*a33*k1*n2 )/(a22 - 2*a22 *a33 + a22*a33 )
2 2
k1*n1*n2
q2=----------------
2
a22 - a22*a33
p56=0
1 5 4 1 3 2
p55=( - ---*a22 *b33*k26*n2 + a22 *a33*b33*k26*n2 - ---*a22 *a33 *b33*k26*n2
2 2
1 3 3 3 2 3 3 2 3
- ---*a22 *b33 *k1*n2 + ---*a22 *a33*b33 *k1*n2 - ---*a22*a33 *b33 *k1*n2
8 8 8
1 3 3 7 6 5 2 4 3
+ ---*a33 *b33 *k1*n2)/(a22 - 3*a22 *a33 + 3*a22 *a33 - a22 *a33 )
8
1 6 3 5 3 4 2
p54=( - ---*a22 *b33*k26*n1 + ---*a22 *a33*b33*k26*n1 - ---*a22 *a33 *b33*k26*n1
2 2 2
1 4 3 1 3 3 1 3 3
- ---*a22 *b33 *k1*n1 + ---*a22 *a33 *b33*k26*n1 + ---*a22 *a33*b33 *k1*n1
8 2 2
3 2 2 3 1 3 3 1 4 3
- ---*a22 *a33 *b33 *k1*n1 + ---*a22*a33 *b33 *k1*n1 - ---*a33 *b33 *k1*n1
4 2 8
8 7 6 2 5 3 4 4
)/(a22 - 4*a22 *a33 + 6*a22 *a33 - 4*a22 *a33 + a22 *a33 )
p53=0
4 3 2 2 1 2 2
p52=(a22 *k26*n2 - 2*a22 *a33*k26*n2 + a22 *a33 *k26*n2 + ---*a22 *b33 *k1*n2
2
2 1 2 2 5 4
- a22*a33*b33 *k1*n2 + ---*a33 *b33 *k1*n2)/(a22 - 3*a22 *a33
2
3 2 2 3
+ 3*a22 *a33 - a22 *a33 )
3 2 1 2 1 2
a22 *k26*n1 - a22 *a33*k26*n1 + ---*a22*b33 *k1*n1 - ---*a33*b33 *k1*n1
2 2
p51=-------------------------------------------------------------------------
4 3 2 2
a22 - 2*a22 *a33 + a22 *a33
p50=0
p49=0
1 3 1 2 5 2 2
p48=( - ---*a22 *b33*k23*n2 + ---*a22 *a33*b33*k23*n2 - ---*a22 *b33 *k1*n2
2 2 4
2 1 2 2 5 4 3 2
+ a22*a33*b33 *k1*n2 + ---*a33 *b33 *k1*n2)/(a22 - 2*a22 *a33 + a22 *a33
4
)
p47=0
p46=0
p45=0
1 2 5 2 1 2
- ---*a22 *b33*k23*n1 - ---*a22*b33 *k1*n1 - ---*a33*b33 *k1*n1
2 4 4
p44=------------------------------------------------------------------
4 3
a22 - a22 *a33
p43=0
p42=0
p41=0
3 2 3 2
p40=( - a22 *k23*n2 + a22 *a33*k23*n2 + ---*a22 *b33*k1*n2 - 2*a22*a33*b33*k1*n2
2
1 2 4 3 2 2
+ ---*a33 *b33*k1*n2)/(a22 - 2*a22 *a33 + a22 *a33 )
2
3 2 3 2
p39=( - a22 *k23*n1 + a22 *a33*k23*n1 + ---*a22 *b33*k1*n1 - 2*a22*a33*b33*k1*n1
2
1 2 4 3 2 2
+ ---*a33 *b33*k1*n1)/(a22 - 2*a22 *a33 + a22 *a33 )
2
p38=0
p37=0
p36=0
1 5 4 1 3 2
p35=( - ---*a22 *b33*k26*n2 + a22 *a33*b33*k26*n2 - ---*a22 *a33 *b33*k26*n2
2 2
7 3 3 15 2 3
- ----*a22 *b33 *k1*n2 + ----*a22 *a33*b33 *k1*n2
16 16
9 2 3 1 3 3 7 6
- ----*a22*a33 *b33 *k1*n2 + ----*a33 *b33 *k1*n2)/(a22 - 3*a22 *a33
16 16
5 2 4 3
+ 3*a22 *a33 - a22 *a33 )
1 4 1 3 7 2 3
p34=( - ---*a22 *b33*k26*n1 + ---*a22 *a33*b33*k26*n1 - ----*a22 *b33 *k1*n1
2 2 16
1 3 1 2 3 6 5
+ ---*a22*a33*b33 *k1*n1 - ----*a33 *b33 *k1*n1)/(a22 - 2*a22 *a33
2 16
4 2
+ a22 *a33 )
p33=0
5 4 1 4 3 2
p32=(a22 *k26*n2 - 2*a22 *a33*k26*n2 - ---*a22 *b33*k23*n2 + a22 *a33 *k26*n2
2
3 7 3 2 1 2 2
+ a22 *a33*b33*k23*n2 + ---*a22 *b33 *k1*n2 - ---*a22 *a33 *b33*k23*n2
8 2
15 2 2 9 2 2 1 3 2
- ----*a22 *a33*b33 *k1*n2 + ---*a22*a33 *b33 *k1*n2 - ---*a33 *b33 *k1*n2
8 8 8
6 5 4 2 3 3
)/(a22 - 3*a22 *a33 + 3*a22 *a33 - a22 *a33 )
4 3 7 2 2 2
p31=(a22 *k26*n1 - a22 *a33*k26*n1 + ---*a22 *b33 *k1*n1 - a22*a33*b33 *k1*n1
8
1 2 2 5 4 3 2
+ ---*a33 *b33 *k1*n1)/(a22 - 2*a22 *a33 + a22 *a33 )
8
1 5 4 1 3 2
p30=( - ---*a22 *b33*k26*n2 + a22 *a33*b33*k26*n2 - ---*a22 *a33 *b33*k26*n2
2 2
7 3 3 15 2 3
- ----*a22 *b33 *k1*n2 + ----*a22 *a33*b33 *k1*n2
16 16
9 2 3 1 3 3 7 6
- ----*a22*a33 *b33 *k1*n2 + ----*a33 *b33 *k1*n2)/(a22 - 3*a22 *a33
16 16
5 2 4 3
+ 3*a22 *a33 - a22 *a33 )
p29=0
1
- ---*b33*k23*n1
2
p28=-------------------
2
a22 - a22*a33
1
- ---*b33*k23*n2
2
p27=-------------------
2
a22 - a22*a33
1 1
- ---*a22*b33*k1*n2 - ---*a33*b33*k1*n2
4 4
p26=------------------------------------------
3 2
a22 - a22 *a33
p25=0
p24=0
3 2 5 2
p23=( - a22 *k23*n2 + a22 *a33*k23*n2 - ---*a22 *b33*k1*n2 + a22*a33*b33*k1*n2
4
1 2 4 3 2 2
+ ---*a33 *b33*k1*n2)/(a22 - 2*a22 *a33 + a22 *a33 )
4
- k23*n1
p22=-----------
a22 - a33
5 1
- ---*a22*b33*k1*n2 - ---*a33*b33*k1*n2
4 4
p21=------------------------------------------
3 2
a22 - a22 *a33
1 3 7 3 1 3
- ---*a22 *b33*k26*n1 - ----*a22*b33 *k1*n1 + ----*a33*b33 *k1*n1
2 16 16
p20=--------------------------------------------------------------------
5 4
a22 - a22 *a33
p19=0
5 4 3 2 7 3 2
p18=(a22 *k26*n2 - 2*a22 *a33*k26*n2 + a22 *a33 *k26*n2 + ---*a22 *b33 *k1*n2
8
15 2 2 9 2 2 1 3 2
- ----*a22 *a33*b33 *k1*n2 + ---*a22*a33 *b33 *k1*n2 - ---*a33 *b33 *k1*n2
8 8 8
6 5 4 2 3 3
)/(a22 - 3*a22 *a33 + 3*a22 *a33 - a22 *a33 )
p17
3 1 2 7 2 1 2
a22 *k26*n1 - ---*a22 *b33*k23*n1 + ---*a22*b33 *k1*n1 - ---*a33*b33 *k1*n1
2 8 8
=-----------------------------------------------------------------------------
4 3
a22 - a22 *a33
1 1
- ---*a22*b33*k1*n1 - ---*a33*b33*k1*n1
4 4
p16=------------------------------------------
3 2
a22 - a22 *a33
p15=0
p14=0
5 1
- ---*a22*b33*k1*n1 - ---*a33*b33*k1*n1
4 4
p13=------------------------------------------
3 2
a22 - a22 *a33
- k23*n2
p12=-----------
a22 - a33
3 2 5 2
p11=( - a22 *k23*n1 + a22 *a33*k23*n1 - ---*a22 *b33*k1*n1 + a22*a33*b33*k1*n1
4
1 2 4 3 2 2
+ ---*a33 *b33*k1*n1)/(a22 - 2*a22 *a33 + a22 *a33 )
4
p10=0
1 1
---*a22*k1*n2 + ---*a33*k1*n2
2 2
p9=-------------------------------
2
a22 - a22*a33
1 1
---*a22*k1*n1 + ---*a33*k1*n1
2 2
p8=-------------------------------
2
a22 - a22*a33
p7=0
p6=0
p5=0
3 1
---*a22*k1*n2 - ---*a33*k1*n2
2 2
p4=-------------------------------
2
a22 - a22*a33
3 1
---*a22*k1*n1 - ---*a33*k1*n1
2 2
p3=-------------------------------
2
a22 - a22*a33
3 1
---*a22*k1*n2 - ---*a33*k1*n2
2 2
p2=-------------------------------
2
a22 - a22*a33
3 1
---*a22*k1*n1 - ---*a33*k1*n1
2 2
p1=-------------------------------
2
a22 - a22*a33
k125=0
k124=0
k122=0
k121=0
1 3 2 3 4 1 4
---*a22 *b33 *k26 + ----*a22*b33 *k1 - ----*a33*b33 *k1
4 32 32
k120=---------------------------------------------------------
5
a22
k119=0
k118=0
3 3 3 1 3
- a22 *b33*k26 - ---*a22*b33 *k1 + ---*a33*b33 *k1
8 8
k117=-----------------------------------------------------
4
a22
k116=0
1 3 2 3 4 1 4
---*a22 *b33 *k26 + ----*a22*b33 *k1 - ----*a33*b33 *k1
4 32 32
k115=---------------------------------------------------------
5
a22
k114=0
k113=0
3 3 3 1 3
- a22 *b33*k26 - ---*a22*b33 *k1 + ---*a33*b33 *k1
8 8
k112=-----------------------------------------------------
4
a22
k110=0
k109=0
3 3 2 1 2
a22 *k26 + ---*a22*b33 *k1 - ---*a33*b33 *k1
8 8
k108=----------------------------------------------
3
a22
k107=0
3 3 2 1 2
a22 *k26 + ---*a22*b33 *k1 - ---*a33*b33 *k1
8 8
k106=----------------------------------------------
3
a22
k105=0
k104=0
1 3
---*b33 *k1
2
k103=-------------
3
a22
k102=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
7 2 1 2
- ---*a22*b33 *k1 + ---*a33*b33 *k1
4 4
k95=--------------------------------------
3
a22
k94=0
k93=0
k92=0
k91=0
k90=0
1 3
---*b33 *k1
2
k89=-------------
3
a22
k88=0
k87=0
k86=0
k85=0
7 2 1 2
- ---*a22*b33 *k1 + ---*a33*b33 *k1
4 4
k84=--------------------------------------
3
a22
k83=0
k82=0
k81=0
2 1 1
a22 *k23 + ---*a22*b33*k1 + ---*a33*b33*k1
2 2
k80=--------------------------------------------
2
a22
k79=0
k78=0
2*b33*k1
k77=----------
a22
k76=0
2*b33*k1
k75=----------
a22
k74=0
k73=0
k72=0
k71=0
1 3 2 5 4 1 4
---*a22 *b33 *k26 + ----*a22*b33 *k1 - ----*a33*b33 *k1
4 32 32
k70=---------------------------------------------------------
5
a22
k69=0
k68=0
3 3 3 1 3
- a22 *b33*k26 - ---*a22*b33 *k1 + ---*a33*b33 *k1
8 8
k67=-----------------------------------------------------
4
a22
k66=0
1 3 2 5 4 1 4
---*a22 *b33 *k26 + ----*a22*b33 *k1 - ----*a33*b33 *k1
2 16 16
k65=---------------------------------------------------------
5
a22
k64=0
k63=0
3 3 3 1 3
- a22 *b33*k26 - ---*a22*b33 *k1 + ---*a33*b33 *k1
8 8
k62=-----------------------------------------------------
4
a22
k61=0
k60=0
k59=0
k58=k26
k57=0
3 7 2 1 2
a22 *k26 + ---*a22*b33 *k1 - ---*a33*b33 *k1
8 8
k56=----------------------------------------------
3
a22
k55=0
k54=0
3 3 3 1 3
- a22 *b33*k26 - ---*a22*b33 *k1 + ---*a33*b33 *k1
8 8
k53=-----------------------------------------------------
4
a22
k52=0
k51=0
k50=0
k49=0
k48=0
7 2 1 2
- ---*a22*b33 *k1 + ---*a33*b33 *k1
4 4
k47=--------------------------------------
3
a22
k46=0
k45=0
k44=k23
k43=0
k42=0
k41=0
k40=0
k38=0
k37=0
k36=0
1 3 2 5 4 1 4
---*a22 *b33 *k26 + ----*a22*b33 *k1 - ----*a33*b33 *k1
4 32 32
k35=---------------------------------------------------------
5
a22
k34=0
k33=0
3 3 3 1 3
- a22 *b33*k26 - ---*a22*b33 *k1 + ---*a33*b33 *k1
8 8
k32=-----------------------------------------------------
4
a22
k30=0
k29=0
3 7 2 1 2
a22 *k26 + ---*a22*b33 *k1 - ---*a33*b33 *k1
8 8
k28=----------------------------------------------
3
a22
k27=0
k25=0
k24=0
k22=0
k21=0
k20=0
k19=0
k18=0
k17=0
k16=0
k14=0
k13=0
1 1
---*a22*k1 + ---*a33*k1
2 2
k12=-------------------------
a22
k11=0
1 1
---*a22*k1 + ---*a33*k1
2 2
k10=-------------------------
a22
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,k26,k23,n1,k1,b33,n2,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 2
+ 4*a22 *b33*u3*v3 + 4*a22 *n1*u1 + 4*a22 *n2*u2 - 4*a22*a33 *u3
2 2
- 4*a22*a33*b33*u3*v3 - 4*a22*a33*n1*u1 - 4*a22*a33*n2*u2 - a22*b33 *v3
2 2
- 2*a22*b33*n1*v1 - 2*a22*b33*n2*v2 + a33*b33 *v3 - 2*a33*b33*n1*v1
- 2*a33*b33*n2*v2)/(4*a22*(a22 - a33))
7 4 7 2 2 7 2 2 7 4
INT=(32*a22 *k1*u1 + 64*a22 *k1*u1 *u2 + 16*a22 *k1*u1 *u3 + 32*a22 *k1*u2
7 2 2 7 2 7 2
+ 16*a22 *k1*u2 *u3 + 32*a22 *k23*u1*u3 *v1 + 32*a22 *k23*u2*u3 *v2
7 3 7 2 2 7 2 2
+ 32*a22 *k23*u3 *v3 + 32*a22 *k26*u1 *v1 + 32*a22 *k26*u1 *v2
7 2 2 7 2 2 7 2 2
+ 32*a22 *k26*u1 *v3 + 32*a22 *k26*u2 *v1 + 32*a22 *k26*u2 *v2
7 2 2 7 2 7 2
+ 32*a22 *k26*u2 *v3 + 32*a22 *q1*u1 + 32*a22 *q1*u2
6 4 6 2 2 6 2 2
- 64*a22 *a33*k1*u1 - 128*a22 *a33*k1*u1 *u2 - 16*a22 *a33*k1*u1 *u3
6 4 6 2 2 6 2
- 64*a22 *a33*k1*u2 - 16*a22 *a33*k1*u2 *u3 - 64*a22 *a33*k23*u1*u3 *v1
6 2 6 3
- 64*a22 *a33*k23*u2*u3 *v2 - 64*a22 *a33*k23*u3 *v3
6 2 2 6 2 2
- 64*a22 *a33*k26*u1 *v1 - 64*a22 *a33*k26*u1 *v2
6 2 2 6 2 2
- 64*a22 *a33*k26*u1 *v3 - 64*a22 *a33*k26*u2 *v1
6 2 2 6 2 2 6 2
- 64*a22 *a33*k26*u2 *v2 - 64*a22 *a33*k26*u2 *v3 - 64*a22 *a33*q1*u1
6 2 6 2 6 2
- 64*a22 *a33*q1*u2 + 64*a22 *b33*k1*u1 *u3*v3 + 64*a22 *b33*k1*u2 *u3*v3
6 3 6 3
+ 16*a22 *b33*k1*u3 *v3 - 32*a22 *b33*k26*u1*v1
6 2 6 2
- 32*a22 *b33*k26*u1*v1*v2 - 32*a22 *b33*k26*u1*v1*v3
6 2 6 3
- 32*a22 *b33*k26*u2*v1 *v2 - 32*a22 *b33*k26*u2*v2
6 2 6 6
- 32*a22 *b33*k26*u2*v2*v3 - 32*a22 *b33*q1*u1*v1 - 32*a22 *b33*q1*u2*v2
6 3 6 2 6 2
+ 48*a22 *k1*n1*u1 + 48*a22 *k1*n1*u1*u2 + 16*a22 *k1*n1*u1*u3
6 2 6 3 6 2
+ 48*a22 *k1*n2*u1 *u2 + 48*a22 *k1*n2*u2 + 16*a22 *k1*n2*u2*u3
6 2 6
- 32*a22 *k23*n1*u1 *v1 - 32*a22 *k23*n1*u1*u2*v2
6 6
- 32*a22 *k23*n1*u1*u3*v3 - 32*a22 *k23*n2*u1*u2*v1
6 2 6 6 2
- 32*a22 *k23*n2*u2 *v2 - 32*a22 *k23*n2*u2*u3*v3 + 32*a22 *k26*n1*u1*v1
6 2 6 2 6 2
+ 32*a22 *k26*n1*u1*v2 + 32*a22 *k26*n1*u1*v3 + 32*a22 *k26*n2*u2*v1
6 2 6 2 6
+ 32*a22 *k26*n2*u2*v2 + 32*a22 *k26*n2*u2*v3 + 32*a22 *n1*q1*u1
6 5 2 4 5 2 2 2
+ 32*a22 *n2*q1*u2 + 32*a22 *a33 *k1*u1 + 64*a22 *a33 *k1*u1 *u2
5 2 2 2 5 2 4 5 2 2 2
- 16*a22 *a33 *k1*u1 *u3 + 32*a22 *a33 *k1*u2 - 16*a22 *a33 *k1*u2 *u3
5 2 2 5 2 2
+ 32*a22 *a33 *k23*u1*u3 *v1 + 32*a22 *a33 *k23*u2*u3 *v2
5 2 3 5 2 2 2
+ 32*a22 *a33 *k23*u3 *v3 + 32*a22 *a33 *k26*u1 *v1
5 2 2 2 5 2 2 2
+ 32*a22 *a33 *k26*u1 *v2 + 32*a22 *a33 *k26*u1 *v3
5 2 2 2 5 2 2 2
+ 32*a22 *a33 *k26*u2 *v1 + 32*a22 *a33 *k26*u2 *v2
5 2 2 2 5 2 2 5 2 2
+ 32*a22 *a33 *k26*u2 *v3 + 32*a22 *a33 *q1*u1 + 32*a22 *a33 *q1*u2
5 2 5 2
- 128*a22 *a33*b33*k1*u1 *u3*v3 - 128*a22 *a33*b33*k1*u2 *u3*v3
5 3 5 3
- 16*a22 *a33*b33*k1*u3 *v3 + 64*a22 *a33*b33*k26*u1*v1
5 2 5 2
+ 64*a22 *a33*b33*k26*u1*v1*v2 + 64*a22 *a33*b33*k26*u1*v1*v3
5 2 5 3
+ 64*a22 *a33*b33*k26*u2*v1 *v2 + 64*a22 *a33*b33*k26*u2*v2
5 2 5
+ 64*a22 *a33*b33*k26*u2*v2*v3 + 64*a22 *a33*b33*q1*u1*v1
5 5 3
+ 64*a22 *a33*b33*q1*u2*v2 - 64*a22 *a33*k1*n1*u1
5 2 5 2
- 64*a22 *a33*k1*n1*u1*u2 - 64*a22 *a33*k1*n2*u1 *u2
5 3 5 2
- 64*a22 *a33*k1*n2*u2 + 32*a22 *a33*k23*n1*u1 *v1
5 5
+ 32*a22 *a33*k23*n1*u1*u2*v2 + 32*a22 *a33*k23*n1*u1*u3*v3
5 5 2
+ 32*a22 *a33*k23*n2*u1*u2*v1 + 32*a22 *a33*k23*n2*u2 *v2
5 5 2
+ 32*a22 *a33*k23*n2*u2*u3*v3 - 32*a22 *a33*k26*n1*u1*v1
5 2 5 2
- 32*a22 *a33*k26*n1*u1*v2 - 32*a22 *a33*k26*n1*u1*v3
5 2 5 2
- 32*a22 *a33*k26*n2*u2*v1 - 32*a22 *a33*k26*n2*u2*v2
5 2 5 5
- 32*a22 *a33*k26*n2*u2*v3 - 32*a22 *a33*n1*q1*u1 - 32*a22 *a33*n2*q1*u2
5 2 2 2 5 2 2 2
+ 28*a22 *b33 *k1*u1 *v2 + 12*a22 *b33 *k1*u1 *v3
5 2 5 2
- 56*a22 *b33 *k1*u1*u2*v1*v2 - 56*a22 *b33 *k1*u1*u3*v1*v3
5 2 2 2 5 2 2 2
+ 28*a22 *b33 *k1*u2 *v1 + 12*a22 *b33 *k1*u2 *v3
5 2 5 2 4
- 56*a22 *b33 *k1*u2*u3*v2*v3 + 8*a22 *b33 *k26*v1
5 2 2 2 5 2 2 2 5 2 4
+ 16*a22 *b33 *k26*v1 *v2 + 8*a22 *b33 *k26*v1 *v3 + 8*a22 *b33 *k26*v2
5 2 2 2 5 2 2 5 2 2
+ 8*a22 *b33 *k26*v2 *v3 + 8*a22 *b33 *q1*v1 + 8*a22 *b33 *q1*v2
5 2 5
- 40*a22 *b33*k1*n1*u1 *v1 + 48*a22 *b33*k1*n1*u1*u3*v3
5 2 5 2
- 40*a22 *b33*k1*n1*u2 *v1 - 8*a22 *b33*k1*n1*u3 *v1
5 2 5 2
- 40*a22 *b33*k1*n2*u1 *v2 - 40*a22 *b33*k1*n2*u2 *v2
5 5 2
+ 48*a22 *b33*k1*n2*u2*u3*v3 - 8*a22 *b33*k1*n2*u3 *v2
5 2 5
- 16*a22 *b33*k23*n1*u1*v1 - 16*a22 *b33*k23*n1*u2*v1*v2
5 5
- 16*a22 *b33*k23*n1*u3*v1*v3 - 16*a22 *b33*k23*n2*u1*v1*v2
5 2 5
- 16*a22 *b33*k23*n2*u2*v2 - 16*a22 *b33*k23*n2*u3*v2*v3
5 3 5 2
- 16*a22 *b33*k26*n1*v1 - 16*a22 *b33*k26*n1*v1*v2
5 2 5 2
- 16*a22 *b33*k26*n1*v1*v3 - 16*a22 *b33*k26*n2*v1 *v2
5 3 5 2
- 16*a22 *b33*k26*n2*v2 - 16*a22 *b33*k26*n2*v2*v3
5 5 5 2 2
- 16*a22 *b33*n1*q1*v1 - 16*a22 *b33*n2*q1*v2 - 16*a22 *k1*n1 *u2
5 5 2 2 4 3 2 2
+ 32*a22 *k1*n1*n2*u1*u2 + 16*a22 *k1*n2 *u2 + 16*a22 *a33 *k1*u1 *u3
4 3 2 2 4 2 2
+ 16*a22 *a33 *k1*u2 *u3 + 64*a22 *a33 *b33*k1*u1 *u3*v3
4 2 2 4 2 3
+ 64*a22 *a33 *b33*k1*u2 *u3*v3 - 16*a22 *a33 *b33*k1*u3 *v3
4 2 3 4 2 2
- 32*a22 *a33 *b33*k26*u1*v1 - 32*a22 *a33 *b33*k26*u1*v1*v2
4 2 2 4 2 2
- 32*a22 *a33 *b33*k26*u1*v1*v3 - 32*a22 *a33 *b33*k26*u2*v1 *v2
4 2 3 4 2 2
- 32*a22 *a33 *b33*k26*u2*v2 - 32*a22 *a33 *b33*k26*u2*v2*v3
4 2 4 2
- 32*a22 *a33 *b33*q1*u1*v1 - 32*a22 *a33 *b33*q1*u2*v2
4 2 3 4 2 2
+ 16*a22 *a33 *k1*n1*u1 + 16*a22 *a33 *k1*n1*u1*u2
4 2 2 4 2 2
- 16*a22 *a33 *k1*n1*u1*u3 + 16*a22 *a33 *k1*n2*u1 *u2
4 2 3 4 2 2
+ 16*a22 *a33 *k1*n2*u2 - 16*a22 *a33 *k1*n2*u2*u3
4 2 2 2 4 2 2 2
- 60*a22 *a33*b33 *k1*u1 *v2 - 28*a22 *a33*b33 *k1*u1 *v3
4 2 4 2
+ 120*a22 *a33*b33 *k1*u1*u2*v1*v2 + 120*a22 *a33*b33 *k1*u1*u3*v1*v3
4 2 2 2 4 2 2 2
- 60*a22 *a33*b33 *k1*u2 *v1 - 28*a22 *a33*b33 *k1*u2 *v3
4 2 4 2 4
+ 120*a22 *a33*b33 *k1*u2*u3*v2*v3 - 16*a22 *a33*b33 *k26*v1
4 2 2 2 4 2 2 2
- 32*a22 *a33*b33 *k26*v1 *v2 - 16*a22 *a33*b33 *k26*v1 *v3
4 2 4 4 2 2 2
- 16*a22 *a33*b33 *k26*v2 - 16*a22 *a33*b33 *k26*v2 *v3
4 2 2 4 2 2
- 16*a22 *a33*b33 *q1*v1 - 16*a22 *a33*b33 *q1*v2
4 2 4
+ 32*a22 *a33*b33*k1*n1*u1 *v1 - 64*a22 *a33*b33*k1*n1*u1*u3*v3
4 2 4 2
+ 32*a22 *a33*b33*k1*n1*u2 *v1 + 32*a22 *a33*b33*k1*n2*u1 *v2
4 2 4
+ 32*a22 *a33*b33*k1*n2*u2 *v2 - 64*a22 *a33*b33*k1*n2*u2*u3*v3
4 2 4
+ 16*a22 *a33*b33*k23*n1*u1*v1 + 16*a22 *a33*b33*k23*n1*u2*v1*v2
4 4
+ 16*a22 *a33*b33*k23*n1*u3*v1*v3 + 16*a22 *a33*b33*k23*n2*u1*v1*v2
4 2 4
+ 16*a22 *a33*b33*k23*n2*u2*v2 + 16*a22 *a33*b33*k23*n2*u3*v2*v3
4 3 4 2
+ 16*a22 *a33*b33*k26*n1*v1 + 16*a22 *a33*b33*k26*n1*v1*v2
4 2 4 2
+ 16*a22 *a33*b33*k26*n1*v1*v3 + 16*a22 *a33*b33*k26*n2*v1 *v2
4 3 4 2
+ 16*a22 *a33*b33*k26*n2*v2 + 16*a22 *a33*b33*k26*n2*v2*v3
4 4
+ 16*a22 *a33*b33*n1*q1*v1 + 16*a22 *a33*b33*n2*q1*v2
4 2 2 4
+ 16*a22 *a33*k1*n1 *u2 - 32*a22 *a33*k1*n1*n2*u1*u2
4 2 2 4 3 3
- 16*a22 *a33*k1*n2 *u2 - 12*a22 *b33 *k1*u1*v1
4 3 2 4 3 2
- 12*a22 *b33 *k1*u1*v1*v2 - 12*a22 *b33 *k1*u1*v1*v3
4 3 2 4 3 3
- 12*a22 *b33 *k1*u2*v1 *v2 - 12*a22 *b33 *k1*u2*v2
4 3 2 4 3 2
- 12*a22 *b33 *k1*u2*v2*v3 + 16*a22 *b33 *k1*u3*v1 *v3
4 3 2 4 2 2
+ 16*a22 *b33 *k1*u3*v2 *v3 + 28*a22 *b33 *k1*n1*u1*v1
4 2 2 4 2 2
+ 28*a22 *b33 *k1*n1*u1*v2 + 16*a22 *b33 *k1*n1*u1*v3
4 2 4 2 2
- 40*a22 *b33 *k1*n1*u3*v1*v3 + 28*a22 *b33 *k1*n2*u2*v1
4 2 2 4 2 2
+ 28*a22 *b33 *k1*n2*u2*v2 + 16*a22 *b33 *k1*n2*u2*v3
4 2 4 2
- 40*a22 *b33 *k1*n2*u3*v2*v3 - 16*a22 *b33*k1*n1 *u1*v1
4 2 4
+ 16*a22 *b33*k1*n1 *u2*v2 - 32*a22 *b33*k1*n1*n2*u1*v2
4 4 2
- 32*a22 *b33*k1*n1*n2*u2*v1 - 32*a22 *b33*k1*n2 *u2*v2
4 3 4 2 3 3 3
- 16*a22 *k1*n1 *u1 - 16*a22 *k1*n1 *n2*u2 + 16*a22 *a33 *b33*k1*u3 *v3
3 2 2 2 2 3 2 2 2 2
+ 36*a22 *a33 *b33 *k1*u1 *v2 + 20*a22 *a33 *b33 *k1*u1 *v3
3 2 2 3 2 2
- 72*a22 *a33 *b33 *k1*u1*u2*v1*v2 - 72*a22 *a33 *b33 *k1*u1*u3*v1*v3
3 2 2 2 2 3 2 2 2 2
+ 36*a22 *a33 *b33 *k1*u2 *v1 + 20*a22 *a33 *b33 *k1*u2 *v3
3 2 2 3 2 2 4
- 72*a22 *a33 *b33 *k1*u2*u3*v2*v3 + 8*a22 *a33 *b33 *k26*v1
3 2 2 2 2 3 2 2 2 2
+ 16*a22 *a33 *b33 *k26*v1 *v2 + 8*a22 *a33 *b33 *k26*v1 *v3
3 2 2 4 3 2 2 2 2
+ 8*a22 *a33 *b33 *k26*v2 + 8*a22 *a33 *b33 *k26*v2 *v3
3 2 2 2 3 2 2 2
+ 8*a22 *a33 *b33 *q1*v1 + 8*a22 *a33 *b33 *q1*v2
3 2 2 3 2
+ 8*a22 *a33 *b33*k1*n1*u1 *v1 + 16*a22 *a33 *b33*k1*n1*u1*u3*v3
3 2 2 3 2 2
+ 8*a22 *a33 *b33*k1*n1*u2 *v1 + 8*a22 *a33 *b33*k1*n1*u3 *v1
3 2 2 3 2 2
+ 8*a22 *a33 *b33*k1*n2*u1 *v2 + 8*a22 *a33 *b33*k1*n2*u2 *v2
3 2 3 2 2
+ 16*a22 *a33 *b33*k1*n2*u2*u3*v3 + 8*a22 *a33 *b33*k1*n2*u3 *v2
3 3 3 3 3 2
+ 28*a22 *a33*b33 *k1*u1*v1 + 28*a22 *a33*b33 *k1*u1*v1*v2
3 3 2 3 3 2
+ 28*a22 *a33*b33 *k1*u1*v1*v3 + 28*a22 *a33*b33 *k1*u2*v1 *v2
3 3 3 3 3 2
+ 28*a22 *a33*b33 *k1*u2*v2 + 28*a22 *a33*b33 *k1*u2*v2*v3
3 3 2 3 3 2
- 32*a22 *a33*b33 *k1*u3*v1 *v3 - 32*a22 *a33*b33 *k1*u3*v2 *v3
3 2 2 3 2 2
- 32*a22 *a33*b33 *k1*n1*u1*v1 - 32*a22 *a33*b33 *k1*n1*u1*v2
3 2 2 3 2
- 16*a22 *a33*b33 *k1*n1*u1*v3 + 32*a22 *a33*b33 *k1*n1*u3*v1*v3
3 2 2 3 2 2
- 32*a22 *a33*b33 *k1*n2*u2*v1 - 32*a22 *a33*b33 *k1*n2*u2*v2
3 2 2 3 2
- 16*a22 *a33*b33 *k1*n2*u2*v3 + 32*a22 *a33*b33 *k1*n2*u3*v2*v3
3 2 3 2
- 16*a22 *a33*b33*k1*n1 *u1*v1 - 16*a22 *a33*b33*k1*n1 *u2*v2
3 4 4 3 4 2 2 3 4 2 2
+ 5*a22 *b33 *k1*v1 + 10*a22 *b33 *k1*v1 *v2 + 3*a22 *b33 *k1*v1 *v3
3 4 4 3 4 2 2 3 3 3
+ 5*a22 *b33 *k1*v2 + 3*a22 *b33 *k1*v2 *v3 - 14*a22 *b33 *k1*n1*v1
3 3 2 3 3 2
- 14*a22 *b33 *k1*n1*v1*v2 - 4*a22 *b33 *k1*n1*v1*v3
3 3 2 3 3 3
- 14*a22 *b33 *k1*n2*v1 *v2 - 14*a22 *b33 *k1*n2*v2
3 3 2 3 2 2 2
- 4*a22 *b33 *k1*n2*v2*v3 + 8*a22 *b33 *k1*n1 *v1
3 2 2 2 3 2
- 4*a22 *b33 *k1*n1 *v2 + 24*a22 *b33 *k1*n1*n2*v1*v2
3 2 2 2 3 3 3 2
+ 12*a22 *b33 *k1*n2 *v2 + 8*a22 *b33*k1*n1 *v1 + 8*a22 *b33*k1*n1 *n2*v2
2 3 2 2 2 2 3 2 2 2
- 4*a22 *a33 *b33 *k1*u1 *v2 - 4*a22 *a33 *b33 *k1*u1 *v3
2 3 2 2 3 2
+ 8*a22 *a33 *b33 *k1*u1*u2*v1*v2 + 8*a22 *a33 *b33 *k1*u1*u3*v1*v3
2 3 2 2 2 2 3 2 2 2
- 4*a22 *a33 *b33 *k1*u2 *v1 - 4*a22 *a33 *b33 *k1*u2 *v3
2 3 2 2 2 3 3
+ 8*a22 *a33 *b33 *k1*u2*u3*v2*v3 - 20*a22 *a33 *b33 *k1*u1*v1
2 2 3 2 2 2 3 2
- 20*a22 *a33 *b33 *k1*u1*v1*v2 - 20*a22 *a33 *b33 *k1*u1*v1*v3
2 2 3 2 2 2 3 3
- 20*a22 *a33 *b33 *k1*u2*v1 *v2 - 20*a22 *a33 *b33 *k1*u2*v2
2 2 3 2 2 2 3 2
- 20*a22 *a33 *b33 *k1*u2*v2*v3 + 16*a22 *a33 *b33 *k1*u3*v1 *v3
2 2 3 2 2 2 2 2
+ 16*a22 *a33 *b33 *k1*u3*v2 *v3 + 4*a22 *a33 *b33 *k1*n1*u1*v1
2 2 2 2 2 2 2
+ 4*a22 *a33 *b33 *k1*n1*u1*v2 + 8*a22 *a33 *b33 *k1*n1*u3*v1*v3
2 2 2 2 2 2 2 2
+ 4*a22 *a33 *b33 *k1*n2*u2*v1 + 4*a22 *a33 *b33 *k1*n2*u2*v2
2 2 2 2 4 4
+ 8*a22 *a33 *b33 *k1*n2*u3*v2*v3 - 11*a22 *a33*b33 *k1*v1
2 4 2 2 2 4 2 2
- 22*a22 *a33*b33 *k1*v1 *v2 - 7*a22 *a33*b33 *k1*v1 *v3
2 4 4 2 4 2 2
- 11*a22 *a33*b33 *k1*v2 - 7*a22 *a33*b33 *k1*v2 *v3
2 3 3 2 3 2
+ 16*a22 *a33*b33 *k1*n1*v1 + 16*a22 *a33*b33 *k1*n1*v1*v2
2 3 2 2 3 2
+ 8*a22 *a33*b33 *k1*n1*v1*v3 + 16*a22 *a33*b33 *k1*n2*v1 *v2
2 3 3 2 3 2
+ 16*a22 *a33*b33 *k1*n2*v2 + 8*a22 *a33*b33 *k1*n2*v2*v3
2 2 2 2 2 2 2 2
+ 8*a22 *a33*b33 *k1*n1 *v1 + 4*a22 *a33*b33 *k1*n1 *v2
2 2 2 2 2 2
+ 8*a22 *a33*b33 *k1*n1*n2*v1*v2 + 4*a22 *a33*b33 *k1*n2 *v2
3 3 3 3 3 2
+ 4*a22*a33 *b33 *k1*u1*v1 + 4*a22*a33 *b33 *k1*u1*v1*v2
3 3 2 3 3 2
+ 4*a22*a33 *b33 *k1*u1*v1*v3 + 4*a22*a33 *b33 *k1*u2*v1 *v2
3 3 3 3 3 2
+ 4*a22*a33 *b33 *k1*u2*v2 + 4*a22*a33 *b33 *k1*u2*v2*v3
2 4 4 2 4 2 2
+ 7*a22*a33 *b33 *k1*v1 + 14*a22*a33 *b33 *k1*v1 *v2
2 4 2 2 2 4 4
+ 5*a22*a33 *b33 *k1*v1 *v3 + 7*a22*a33 *b33 *k1*v2
2 4 2 2 2 3 3
+ 5*a22*a33 *b33 *k1*v2 *v3 - 2*a22*a33 *b33 *k1*n1*v1
2 3 2 2 3 2
- 2*a22*a33 *b33 *k1*n1*v1*v2 - 4*a22*a33 *b33 *k1*n1*v1*v3
2 3 2 2 3 3
- 2*a22*a33 *b33 *k1*n2*v1 *v2 - 2*a22*a33 *b33 *k1*n2*v2
2 3 2 3 4 4 3 4 2 2
- 4*a22*a33 *b33 *k1*n2*v2*v3 - a33 *b33 *k1*v1 - 2*a33 *b33 *k1*v1 *v2
3 4 2 2 3 4 4 3 4 2 2 5
- a33 *b33 *k1*v1 *v3 - a33 *b33 *k1*v2 - a33 *b33 *k1*v2 *v3 )/(32*a22
2 2
*(a22 - 2*a22*a33 + 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**2*n2*u2 - 4*
a22*a33**2*u3**2 - 4*a22*a33*b33*u3*v3 - 4*a22*a33*n1*u1 - 4*a22*a33*n2*u2 - a22
*b33**2*v3**2 - 2*a22*b33*n1*v1 - 2*a22*b33*n2*v2 + a33*b33**2*v3**2 - 2*a33*b33
*n1*v1 - 2*a33*b33*n2*v2)/(4*a22*(a22 - a33))$
INT=(32*a22**7*k1*u1**4 + 64*a22**7*k1*u1**2*u2**2 + 16*a22**7*k1*u1**2*u3**2 +
32*a22**7*k1*u2**4 + 16*a22**7*k1*u2**2*u3**2 + 32*a22**7*k23*u1*u3**2*v1 + 32*
a22**7*k23*u2*u3**2*v2 + 32*a22**7*k23*u3**3*v3 + 32*a22**7*k26*u1**2*v1**2 + 32
*a22**7*k26*u1**2*v2**2 + 32*a22**7*k26*u1**2*v3**2 + 32*a22**7*k26*u2**2*v1**2
+ 32*a22**7*k26*u2**2*v2**2 + 32*a22**7*k26*u2**2*v3**2 + 32*a22**7*q1*u1**2 +
32*a22**7*q1*u2**2 - 64*a22**6*a33*k1*u1**4 - 128*a22**6*a33*k1*u1**2*u2**2 - 16
*a22**6*a33*k1*u1**2*u3**2 - 64*a22**6*a33*k1*u2**4 - 16*a22**6*a33*k1*u2**2*u3
**2 - 64*a22**6*a33*k23*u1*u3**2*v1 - 64*a22**6*a33*k23*u2*u3**2*v2 - 64*a22**6*
a33*k23*u3**3*v3 - 64*a22**6*a33*k26*u1**2*v1**2 - 64*a22**6*a33*k26*u1**2*v2**2
- 64*a22**6*a33*k26*u1**2*v3**2 - 64*a22**6*a33*k26*u2**2*v1**2 - 64*a22**6*a33
*k26*u2**2*v2**2 - 64*a22**6*a33*k26*u2**2*v3**2 - 64*a22**6*a33*q1*u1**2 - 64*
a22**6*a33*q1*u2**2 + 64*a22**6*b33*k1*u1**2*u3*v3 + 64*a22**6*b33*k1*u2**2*u3*
v3 + 16*a22**6*b33*k1*u3**3*v3 - 32*a22**6*b33*k26*u1*v1**3 - 32*a22**6*b33*k26*
u1*v1*v2**2 - 32*a22**6*b33*k26*u1*v1*v3**2 - 32*a22**6*b33*k26*u2*v1**2*v2 - 32
*a22**6*b33*k26*u2*v2**3 - 32*a22**6*b33*k26*u2*v2*v3**2 - 32*a22**6*b33*q1*u1*
v1 - 32*a22**6*b33*q1*u2*v2 + 48*a22**6*k1*n1*u1**3 + 48*a22**6*k1*n1*u1*u2**2 +
16*a22**6*k1*n1*u1*u3**2 + 48*a22**6*k1*n2*u1**2*u2 + 48*a22**6*k1*n2*u2**3 +
16*a22**6*k1*n2*u2*u3**2 - 32*a22**6*k23*n1*u1**2*v1 - 32*a22**6*k23*n1*u1*u2*v2
- 32*a22**6*k23*n1*u1*u3*v3 - 32*a22**6*k23*n2*u1*u2*v1 - 32*a22**6*k23*n2*u2**
2*v2 - 32*a22**6*k23*n2*u2*u3*v3 + 32*a22**6*k26*n1*u1*v1**2 + 32*a22**6*k26*n1*
u1*v2**2 + 32*a22**6*k26*n1*u1*v3**2 + 32*a22**6*k26*n2*u2*v1**2 + 32*a22**6*k26
*n2*u2*v2**2 + 32*a22**6*k26*n2*u2*v3**2 + 32*a22**6*n1*q1*u1 + 32*a22**6*n2*q1*
u2 + 32*a22**5*a33**2*k1*u1**4 + 64*a22**5*a33**2*k1*u1**2*u2**2 - 16*a22**5*a33
**2*k1*u1**2*u3**2 + 32*a22**5*a33**2*k1*u2**4 - 16*a22**5*a33**2*k1*u2**2*u3**2
+ 32*a22**5*a33**2*k23*u1*u3**2*v1 + 32*a22**5*a33**2*k23*u2*u3**2*v2 + 32*a22
**5*a33**2*k23*u3**3*v3 + 32*a22**5*a33**2*k26*u1**2*v1**2 + 32*a22**5*a33**2*
k26*u1**2*v2**2 + 32*a22**5*a33**2*k26*u1**2*v3**2 + 32*a22**5*a33**2*k26*u2**2*
v1**2 + 32*a22**5*a33**2*k26*u2**2*v2**2 + 32*a22**5*a33**2*k26*u2**2*v3**2 + 32
*a22**5*a33**2*q1*u1**2 + 32*a22**5*a33**2*q1*u2**2 - 128*a22**5*a33*b33*k1*u1**
2*u3*v3 - 128*a22**5*a33*b33*k1*u2**2*u3*v3 - 16*a22**5*a33*b33*k1*u3**3*v3 + 64
*a22**5*a33*b33*k26*u1*v1**3 + 64*a22**5*a33*b33*k26*u1*v1*v2**2 + 64*a22**5*a33
*b33*k26*u1*v1*v3**2 + 64*a22**5*a33*b33*k26*u2*v1**2*v2 + 64*a22**5*a33*b33*k26
*u2*v2**3 + 64*a22**5*a33*b33*k26*u2*v2*v3**2 + 64*a22**5*a33*b33*q1*u1*v1 + 64*
a22**5*a33*b33*q1*u2*v2 - 64*a22**5*a33*k1*n1*u1**3 - 64*a22**5*a33*k1*n1*u1*u2
**2 - 64*a22**5*a33*k1*n2*u1**2*u2 - 64*a22**5*a33*k1*n2*u2**3 + 32*a22**5*a33*
k23*n1*u1**2*v1 + 32*a22**5*a33*k23*n1*u1*u2*v2 + 32*a22**5*a33*k23*n1*u1*u3*v3
+ 32*a22**5*a33*k23*n2*u1*u2*v1 + 32*a22**5*a33*k23*n2*u2**2*v2 + 32*a22**5*a33*
k23*n2*u2*u3*v3 - 32*a22**5*a33*k26*n1*u1*v1**2 - 32*a22**5*a33*k26*n1*u1*v2**2
- 32*a22**5*a33*k26*n1*u1*v3**2 - 32*a22**5*a33*k26*n2*u2*v1**2 - 32*a22**5*a33*
k26*n2*u2*v2**2 - 32*a22**5*a33*k26*n2*u2*v3**2 - 32*a22**5*a33*n1*q1*u1 - 32*
a22**5*a33*n2*q1*u2 + 28*a22**5*b33**2*k1*u1**2*v2**2 + 12*a22**5*b33**2*k1*u1**
2*v3**2 - 56*a22**5*b33**2*k1*u1*u2*v1*v2 - 56*a22**5*b33**2*k1*u1*u3*v1*v3 + 28
*a22**5*b33**2*k1*u2**2*v1**2 + 12*a22**5*b33**2*k1*u2**2*v3**2 - 56*a22**5*b33
**2*k1*u2*u3*v2*v3 + 8*a22**5*b33**2*k26*v1**4 + 16*a22**5*b33**2*k26*v1**2*v2**
2 + 8*a22**5*b33**2*k26*v1**2*v3**2 + 8*a22**5*b33**2*k26*v2**4 + 8*a22**5*b33**
2*k26*v2**2*v3**2 + 8*a22**5*b33**2*q1*v1**2 + 8*a22**5*b33**2*q1*v2**2 - 40*a22
**5*b33*k1*n1*u1**2*v1 + 48*a22**5*b33*k1*n1*u1*u3*v3 - 40*a22**5*b33*k1*n1*u2**
2*v1 - 8*a22**5*b33*k1*n1*u3**2*v1 - 40*a22**5*b33*k1*n2*u1**2*v2 - 40*a22**5*
b33*k1*n2*u2**2*v2 + 48*a22**5*b33*k1*n2*u2*u3*v3 - 8*a22**5*b33*k1*n2*u3**2*v2
- 16*a22**5*b33*k23*n1*u1*v1**2 - 16*a22**5*b33*k23*n1*u2*v1*v2 - 16*a22**5*b33*
k23*n1*u3*v1*v3 - 16*a22**5*b33*k23*n2*u1*v1*v2 - 16*a22**5*b33*k23*n2*u2*v2**2
- 16*a22**5*b33*k23*n2*u3*v2*v3 - 16*a22**5*b33*k26*n1*v1**3 - 16*a22**5*b33*k26
*n1*v1*v2**2 - 16*a22**5*b33*k26*n1*v1*v3**2 - 16*a22**5*b33*k26*n2*v1**2*v2 -
16*a22**5*b33*k26*n2*v2**3 - 16*a22**5*b33*k26*n2*v2*v3**2 - 16*a22**5*b33*n1*q1
*v1 - 16*a22**5*b33*n2*q1*v2 - 16*a22**5*k1*n1**2*u2**2 + 32*a22**5*k1*n1*n2*u1*
u2 + 16*a22**5*k1*n2**2*u2**2 + 16*a22**4*a33**3*k1*u1**2*u3**2 + 16*a22**4*a33
**3*k1*u2**2*u3**2 + 64*a22**4*a33**2*b33*k1*u1**2*u3*v3 + 64*a22**4*a33**2*b33*
k1*u2**2*u3*v3 - 16*a22**4*a33**2*b33*k1*u3**3*v3 - 32*a22**4*a33**2*b33*k26*u1*
v1**3 - 32*a22**4*a33**2*b33*k26*u1*v1*v2**2 - 32*a22**4*a33**2*b33*k26*u1*v1*v3
**2 - 32*a22**4*a33**2*b33*k26*u2*v1**2*v2 - 32*a22**4*a33**2*b33*k26*u2*v2**3 -
32*a22**4*a33**2*b33*k26*u2*v2*v3**2 - 32*a22**4*a33**2*b33*q1*u1*v1 - 32*a22**
4*a33**2*b33*q1*u2*v2 + 16*a22**4*a33**2*k1*n1*u1**3 + 16*a22**4*a33**2*k1*n1*u1
*u2**2 - 16*a22**4*a33**2*k1*n1*u1*u3**2 + 16*a22**4*a33**2*k1*n2*u1**2*u2 + 16*
a22**4*a33**2*k1*n2*u2**3 - 16*a22**4*a33**2*k1*n2*u2*u3**2 - 60*a22**4*a33*b33
**2*k1*u1**2*v2**2 - 28*a22**4*a33*b33**2*k1*u1**2*v3**2 + 120*a22**4*a33*b33**2
*k1*u1*u2*v1*v2 + 120*a22**4*a33*b33**2*k1*u1*u3*v1*v3 - 60*a22**4*a33*b33**2*k1
*u2**2*v1**2 - 28*a22**4*a33*b33**2*k1*u2**2*v3**2 + 120*a22**4*a33*b33**2*k1*u2
*u3*v2*v3 - 16*a22**4*a33*b33**2*k26*v1**4 - 32*a22**4*a33*b33**2*k26*v1**2*v2**
2 - 16*a22**4*a33*b33**2*k26*v1**2*v3**2 - 16*a22**4*a33*b33**2*k26*v2**4 - 16*
a22**4*a33*b33**2*k26*v2**2*v3**2 - 16*a22**4*a33*b33**2*q1*v1**2 - 16*a22**4*
a33*b33**2*q1*v2**2 + 32*a22**4*a33*b33*k1*n1*u1**2*v1 - 64*a22**4*a33*b33*k1*n1
*u1*u3*v3 + 32*a22**4*a33*b33*k1*n1*u2**2*v1 + 32*a22**4*a33*b33*k1*n2*u1**2*v2
+ 32*a22**4*a33*b33*k1*n2*u2**2*v2 - 64*a22**4*a33*b33*k1*n2*u2*u3*v3 + 16*a22**
4*a33*b33*k23*n1*u1*v1**2 + 16*a22**4*a33*b33*k23*n1*u2*v1*v2 + 16*a22**4*a33*
b33*k23*n1*u3*v1*v3 + 16*a22**4*a33*b33*k23*n2*u1*v1*v2 + 16*a22**4*a33*b33*k23*
n2*u2*v2**2 + 16*a22**4*a33*b33*k23*n2*u3*v2*v3 + 16*a22**4*a33*b33*k26*n1*v1**3
+ 16*a22**4*a33*b33*k26*n1*v1*v2**2 + 16*a22**4*a33*b33*k26*n1*v1*v3**2 + 16*
a22**4*a33*b33*k26*n2*v1**2*v2 + 16*a22**4*a33*b33*k26*n2*v2**3 + 16*a22**4*a33*
b33*k26*n2*v2*v3**2 + 16*a22**4*a33*b33*n1*q1*v1 + 16*a22**4*a33*b33*n2*q1*v2 +
16*a22**4*a33*k1*n1**2*u2**2 - 32*a22**4*a33*k1*n1*n2*u1*u2 - 16*a22**4*a33*k1*
n2**2*u2**2 - 12*a22**4*b33**3*k1*u1*v1**3 - 12*a22**4*b33**3*k1*u1*v1*v2**2 -
12*a22**4*b33**3*k1*u1*v1*v3**2 - 12*a22**4*b33**3*k1*u2*v1**2*v2 - 12*a22**4*
b33**3*k1*u2*v2**3 - 12*a22**4*b33**3*k1*u2*v2*v3**2 + 16*a22**4*b33**3*k1*u3*v1
**2*v3 + 16*a22**4*b33**3*k1*u3*v2**2*v3 + 28*a22**4*b33**2*k1*n1*u1*v1**2 + 28*
a22**4*b33**2*k1*n1*u1*v2**2 + 16*a22**4*b33**2*k1*n1*u1*v3**2 - 40*a22**4*b33**
2*k1*n1*u3*v1*v3 + 28*a22**4*b33**2*k1*n2*u2*v1**2 + 28*a22**4*b33**2*k1*n2*u2*
v2**2 + 16*a22**4*b33**2*k1*n2*u2*v3**2 - 40*a22**4*b33**2*k1*n2*u3*v2*v3 - 16*
a22**4*b33*k1*n1**2*u1*v1 + 16*a22**4*b33*k1*n1**2*u2*v2 - 32*a22**4*b33*k1*n1*
n2*u1*v2 - 32*a22**4*b33*k1*n1*n2*u2*v1 - 32*a22**4*b33*k1*n2**2*u2*v2 - 16*a22
**4*k1*n1**3*u1 - 16*a22**4*k1*n1**2*n2*u2 + 16*a22**3*a33**3*b33*k1*u3**3*v3 +
36*a22**3*a33**2*b33**2*k1*u1**2*v2**2 + 20*a22**3*a33**2*b33**2*k1*u1**2*v3**2
- 72*a22**3*a33**2*b33**2*k1*u1*u2*v1*v2 - 72*a22**3*a33**2*b33**2*k1*u1*u3*v1*
v3 + 36*a22**3*a33**2*b33**2*k1*u2**2*v1**2 + 20*a22**3*a33**2*b33**2*k1*u2**2*
v3**2 - 72*a22**3*a33**2*b33**2*k1*u2*u3*v2*v3 + 8*a22**3*a33**2*b33**2*k26*v1**
4 + 16*a22**3*a33**2*b33**2*k26*v1**2*v2**2 + 8*a22**3*a33**2*b33**2*k26*v1**2*
v3**2 + 8*a22**3*a33**2*b33**2*k26*v2**4 + 8*a22**3*a33**2*b33**2*k26*v2**2*v3**
2 + 8*a22**3*a33**2*b33**2*q1*v1**2 + 8*a22**3*a33**2*b33**2*q1*v2**2 + 8*a22**3
*a33**2*b33*k1*n1*u1**2*v1 + 16*a22**3*a33**2*b33*k1*n1*u1*u3*v3 + 8*a22**3*a33
**2*b33*k1*n1*u2**2*v1 + 8*a22**3*a33**2*b33*k1*n1*u3**2*v1 + 8*a22**3*a33**2*
b33*k1*n2*u1**2*v2 + 8*a22**3*a33**2*b33*k1*n2*u2**2*v2 + 16*a22**3*a33**2*b33*
k1*n2*u2*u3*v3 + 8*a22**3*a33**2*b33*k1*n2*u3**2*v2 + 28*a22**3*a33*b33**3*k1*u1
*v1**3 + 28*a22**3*a33*b33**3*k1*u1*v1*v2**2 + 28*a22**3*a33*b33**3*k1*u1*v1*v3
**2 + 28*a22**3*a33*b33**3*k1*u2*v1**2*v2 + 28*a22**3*a33*b33**3*k1*u2*v2**3 +
28*a22**3*a33*b33**3*k1*u2*v2*v3**2 - 32*a22**3*a33*b33**3*k1*u3*v1**2*v3 - 32*
a22**3*a33*b33**3*k1*u3*v2**2*v3 - 32*a22**3*a33*b33**2*k1*n1*u1*v1**2 - 32*a22
**3*a33*b33**2*k1*n1*u1*v2**2 - 16*a22**3*a33*b33**2*k1*n1*u1*v3**2 + 32*a22**3*
a33*b33**2*k1*n1*u3*v1*v3 - 32*a22**3*a33*b33**2*k1*n2*u2*v1**2 - 32*a22**3*a33*
b33**2*k1*n2*u2*v2**2 - 16*a22**3*a33*b33**2*k1*n2*u2*v3**2 + 32*a22**3*a33*b33
**2*k1*n2*u3*v2*v3 - 16*a22**3*a33*b33*k1*n1**2*u1*v1 - 16*a22**3*a33*b33*k1*n1
**2*u2*v2 + 5*a22**3*b33**4*k1*v1**4 + 10*a22**3*b33**4*k1*v1**2*v2**2 + 3*a22**
3*b33**4*k1*v1**2*v3**2 + 5*a22**3*b33**4*k1*v2**4 + 3*a22**3*b33**4*k1*v2**2*v3
**2 - 14*a22**3*b33**3*k1*n1*v1**3 - 14*a22**3*b33**3*k1*n1*v1*v2**2 - 4*a22**3*
b33**3*k1*n1*v1*v3**2 - 14*a22**3*b33**3*k1*n2*v1**2*v2 - 14*a22**3*b33**3*k1*n2
*v2**3 - 4*a22**3*b33**3*k1*n2*v2*v3**2 + 8*a22**3*b33**2*k1*n1**2*v1**2 - 4*a22
**3*b33**2*k1*n1**2*v2**2 + 24*a22**3*b33**2*k1*n1*n2*v1*v2 + 12*a22**3*b33**2*
k1*n2**2*v2**2 + 8*a22**3*b33*k1*n1**3*v1 + 8*a22**3*b33*k1*n1**2*n2*v2 - 4*a22
**2*a33**3*b33**2*k1*u1**2*v2**2 - 4*a22**2*a33**3*b33**2*k1*u1**2*v3**2 + 8*a22
**2*a33**3*b33**2*k1*u1*u2*v1*v2 + 8*a22**2*a33**3*b33**2*k1*u1*u3*v1*v3 - 4*a22
**2*a33**3*b33**2*k1*u2**2*v1**2 - 4*a22**2*a33**3*b33**2*k1*u2**2*v3**2 + 8*a22
**2*a33**3*b33**2*k1*u2*u3*v2*v3 - 20*a22**2*a33**2*b33**3*k1*u1*v1**3 - 20*a22
**2*a33**2*b33**3*k1*u1*v1*v2**2 - 20*a22**2*a33**2*b33**3*k1*u1*v1*v3**2 - 20*
a22**2*a33**2*b33**3*k1*u2*v1**2*v2 - 20*a22**2*a33**2*b33**3*k1*u2*v2**3 - 20*
a22**2*a33**2*b33**3*k1*u2*v2*v3**2 + 16*a22**2*a33**2*b33**3*k1*u3*v1**2*v3 +
16*a22**2*a33**2*b33**3*k1*u3*v2**2*v3 + 4*a22**2*a33**2*b33**2*k1*n1*u1*v1**2 +
4*a22**2*a33**2*b33**2*k1*n1*u1*v2**2 + 8*a22**2*a33**2*b33**2*k1*n1*u3*v1*v3 +
4*a22**2*a33**2*b33**2*k1*n2*u2*v1**2 + 4*a22**2*a33**2*b33**2*k1*n2*u2*v2**2 +
8*a22**2*a33**2*b33**2*k1*n2*u3*v2*v3 - 11*a22**2*a33*b33**4*k1*v1**4 - 22*a22
**2*a33*b33**4*k1*v1**2*v2**2 - 7*a22**2*a33*b33**4*k1*v1**2*v3**2 - 11*a22**2*
a33*b33**4*k1*v2**4 - 7*a22**2*a33*b33**4*k1*v2**2*v3**2 + 16*a22**2*a33*b33**3*
k1*n1*v1**3 + 16*a22**2*a33*b33**3*k1*n1*v1*v2**2 + 8*a22**2*a33*b33**3*k1*n1*v1
*v3**2 + 16*a22**2*a33*b33**3*k1*n2*v1**2*v2 + 16*a22**2*a33*b33**3*k1*n2*v2**3
+ 8*a22**2*a33*b33**3*k1*n2*v2*v3**2 + 8*a22**2*a33*b33**2*k1*n1**2*v1**2 + 4*
a22**2*a33*b33**2*k1*n1**2*v2**2 + 8*a22**2*a33*b33**2*k1*n1*n2*v1*v2 + 4*a22**2
*a33*b33**2*k1*n2**2*v2**2 + 4*a22*a33**3*b33**3*k1*u1*v1**3 + 4*a22*a33**3*b33
**3*k1*u1*v1*v2**2 + 4*a22*a33**3*b33**3*k1*u1*v1*v3**2 + 4*a22*a33**3*b33**3*k1
*u2*v1**2*v2 + 4*a22*a33**3*b33**3*k1*u2*v2**3 + 4*a22*a33**3*b33**3*k1*u2*v2*v3
**2 + 7*a22*a33**2*b33**4*k1*v1**4 + 14*a22*a33**2*b33**4*k1*v1**2*v2**2 + 5*a22
*a33**2*b33**4*k1*v1**2*v3**2 + 7*a22*a33**2*b33**4*k1*v2**4 + 5*a22*a33**2*b33
**4*k1*v2**2*v3**2 - 2*a22*a33**2*b33**3*k1*n1*v1**3 - 2*a22*a33**2*b33**3*k1*n1
*v1*v2**2 - 4*a22*a33**2*b33**3*k1*n1*v1*v3**2 - 2*a22*a33**2*b33**3*k1*n2*v1**2
*v2 - 2*a22*a33**2*b33**3*k1*n2*v2**3 - 4*a22*a33**2*b33**3*k1*n2*v2*v3**2 - a33
**3*b33**4*k1*v1**4 - 2*a33**3*b33**4*k1*v1**2*v2**2 - a33**3*b33**4*k1*v1**2*v3
**2 - a33**3*b33**4*k1*v2**4 - a33**3*b33**4*k1*v2**2*v3**2)/(32*a22**5*(a22**2
- 2*a22*a33 + a33**2))$