Solution 18 to problem e3quant
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
a22=4*a33
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
1 2
- ----*b33
16
c33=--------------
a33
n2=0
n3=0
5
- ----*b33*n1
24
m1=----------------
a33
m2=0
m3=0
r6=0
r5=0
5 2 1 2 1 2
r4=(----*a33 *b33*k1*n1 + ----*a33 *b33*k12*n1 - ----*a33 *b33*n1*q1
24 24 24
1 3 1 3 4
+ -----*b33*k1*n1 - -----*b33*k12*n1 )/a33
216 216
r3=0
r2=0
r1=
1 2 1 2 1 2 1 3 1 3
---*a33 *k1*n1 - ---*a33 *k12*n1 + ---*a33 *n1*q1 - ----*k1*n1 + ----*k12*n1
3 3 3 27 27
--------------------------------------------------------------------------------
3
a33
1 2
----*b33 *k12*n1
96
q20=------------------
3
a33
1 2 2 1 2 2 1 2 2
q19=( - ---*a33 *b33 *k1 + ----*a33 *b33 *q1 - -----*b33 *k1*n1
8 64 576
1 2 2 4
+ -----*b33 *k12*n1 )/a33
576
q18=0
q17=0
1 2 2 1 2 2 1 2 2
- ---*a33 *b33 *k1 + ----*a33 *b33 *q1 + -----*b33 *k12*n1
8 64 288
q16=--------------------------------------------------------------
4
a33
1
----*b33*k1*n1
12
q14=----------------
2
a33
q13=0
1
- ----*b33*k12*n1
12
q11=--------------------
2
a33
3 3 2 1 2 1 2
q10=( - a33 *k38 + ---*a33 *b33*k1 - ---*a33 *b33*q1 + ----*b33*k1*n1
2 4 36
1 2 3
- ----*b33*k12*n1 )/a33
36
q9=0
2 2
- ---*k1*n1 + ---*k12*n1
3 3
q8=---------------------------
a33
2 2 1 2 1 2
- 4*a33 *k1 + a33 *q1 - ---*k1*n1 + ---*k12*n1
9 9
q7=---------------------------------------------------
2
a33
q6=0
q5=0
3 3 2 1 2 1 2
- a33 *k38 + ---*a33 *b33*k1 - ---*a33 *b33*q1 - ----*b33*k12*n1
2 4 36
q4=--------------------------------------------------------------------
3
a33
q3=0
q2=0
p56=0
p55=0
p54=0
p53=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n1 - -----*b33 *k1*n1 + -----*b33 *k12*n1
24 768 768
p52=----------------------------------------------------------------
4
a33
p51=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n1 - -----*b33 *k1*n1 + ------*b33 *k12*n1
24 384 1536
p50=-----------------------------------------------------------------
4
a33
p49=0
p48=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n1 - -----*b33 *k1*n1 + ------*b33 *k12*n1
24 384 1536
p47=-----------------------------------------------------------------
4
a33
p46=0
p45=0
p44=0
1 1 2 1 2
- ----*a33*b33*k38*n1 - ----*b33 *k1*n1 - ----*b33 *k12*n1
24 48 96
p43=-------------------------------------------------------------
3
a33
1 2 1 2
----*b33 *k1 - ----*b33 *k12
16 64
p42=------------------------------
2
a33
p41=0
p40=0
p39=0
1
- ----*b33*k12*n1
24
p38=--------------------
2
a33
p37=0
p36=0
p35=0
p34=0
1 2
----*b33 *k12
64
p33=---------------
2
a33
1
- ----*b33*k38*n1
24
p32=--------------------
2
a33
p31=0
p30=0
p29=0
1
2*a33*k38 - ---*b33*k1
2
p28=------------------------
a33
p27=0
p26=0
p25=0
1 1
- ----*b33*k1*n1 - ----*b33*k12*n1
12 24
p24=-------------------------------------
2
a33
p23=0
p22=0
1 2 1 2
---*a33 *k16*n1 + ----*b33 *k1*n1
3 96
p21=-----------------------------------
3
a33
1 2
- ----*b33 *k12
64
p20=------------------
2
a33
1 2 1 2 1 2
---*a33 *k16*n1 + ----*b33 *k1*n1 - -----*b33 *k12*n1
3 48 192
p19=-------------------------------------------------------
3
a33
p18=0
p17=0
p16
1 2 1 1 2 1 2
---*a33 *k16*n1 - ----*a33*b33*k38*n1 + ----*b33 *k1*n1 - -----*b33 *k12*n1
3 24 48 192
=-----------------------------------------------------------------------------
3
a33
1 1 1
- ---*a33*k38*n1 + ---*b33*k1*n1 - ----*b33*k12*n1
3 6 12
p15=-----------------------------------------------------
2
a33
1
- 2*a33*k38 + ---*b33*k1
2
p14=---------------------------
a33
p13=0
1
---*k12*n1
3
p12=------------
a33
p11=0
1
- ---*k38*n1
3
p10=---------------
a33
p9=0
p8= - 4*k1
2 1
---*k1*n1 - ---*k12*n1
3 3
p7=------------------------
a33
p6=0
p5=0
1 1 1
- ---*a33*k38*n1 - ----*b33*k1*n1 - ----*b33*k12*n1
3 12 24
p4=------------------------------------------------------
2
a33
p3=0
p2=0
2 1
---*k1*n1 - ---*k12*n1
3 3
p1=------------------------
a33
k125=0
1 2 2 1 4 1 4
----*a33 *b33 *k16 + ------*b33 *k1 - ------*b33 *k12
64 2048 4096
k124=-------------------------------------------------------
4
a33
k123=0
1 2 2 3 4 1 4
----*a33 *b33 *k16 + ------*b33 *k1 - ------*b33 *k12
64 4096 4096
k122=-------------------------------------------------------
4
a33
k121=0
k120=0
k119=0
k118=0
1 2 2 1 4 1 4
----*a33 *b33 *k16 + ------*b33 *k1 - ------*b33 *k12
64 2048 4096
k117=-------------------------------------------------------
4
a33
k116=0
1 2 2 3 4 1 4
----*a33 *b33 *k16 + ------*b33 *k1 - ------*b33 *k12
32 2048 2048
k115=-------------------------------------------------------
4
a33
k114=0
k113=0
1 2 2 3 4 1 4
----*a33 *b33 *k16 + ------*b33 *k1 - ------*b33 *k12
64 4096 4096
k112=-------------------------------------------------------
4
a33
k110=0
1 3
-----*b33 *k1
128
k109=---------------
3
a33
k108=0
k107=0
k106=0
k105=0
1 3
-----*b33 *k1
128
k104=---------------
3
a33
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
1
a33*k38 + ---*b33*k12
4
k95=-----------------------
a33
k94=0
k93=0
k91=0
1 2 1 3 1 3
- ---*a33 *b33*k16 - -----*b33 *k1 + -----*b33 *k12
4 128 256
k90=------------------------------------------------------
3
a33
k89=0
1 2 1 3 1 3
- ---*a33 *b33*k16 - -----*b33 *k1 + -----*b33 *k12
4 128 256
k88=------------------------------------------------------
3
a33
k87=0
k86=0
k85=0
k84=0
1 2 1 3 1 3
- ---*a33 *b33*k16 - -----*b33 *k1 + -----*b33 *k12
4 128 256
k83=------------------------------------------------------
3
a33
k82=0
k81=0
1 2 1 2
- ---*b33 *k1 + ----*b33 *k12
8 32
k80=--------------------------------
2
a33
k79=0
k78=0
k77=0
k76=0
k75=0
k74=k38
k73=0
k72=0
2 1 2 1 2
a33 *k16 + ----*b33 *k1 - ----*b33 *k12
32 64
k71=-----------------------------------------
2
a33
k70=0
k69=k16
k68=0
k67=0
2 1 2 1 2
a33 *k16 + ----*b33 *k1 - ----*b33 *k12
16 64
k66=-----------------------------------------
2
a33
1
---*b33*k1
2
k65=------------
a33
k64=0
k63=0
k62=k12
k61=0
k59=0
k58=0
k57=k1
k56=0
k55=0
k54=0
k53=0
1 2 1 3 1 3
- ---*a33 *b33*k16 - -----*b33 *k1 + -----*b33 *k12
4 128 256
k52=------------------------------------------------------
3
a33
k51=0
1 2 1 3 1 3
- ---*a33 *b33*k16 - -----*b33 *k1 + -----*b33 *k12
4 128 256
k50=------------------------------------------------------
3
a33
k49=0
k48=0
1 2 1 3 1 3
- ---*a33 *b33*k16 - -----*b33 *k1 + -----*b33 *k12
4 128 256
k47=------------------------------------------------------
3
a33
k46=0
k45=0
k44=0
1 2 1 2
- ---*b33 *k1 + ----*b33 *k12
8 32
k43=--------------------------------
2
a33
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
1 2 1 2
- ---*b33 *k1 + ----*b33 *k12
8 32
k32=--------------------------------
2
a33
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
2 1 2 1 2
a33 *k16 + ----*b33 *k1 - ----*b33 *k12
32 64
k21=-----------------------------------------
2
a33
k20=0
2 1 2 1 2
a33 *k16 + ----*b33 *k1 - ----*b33 *k12
16 64
k19=-----------------------------------------
2
a33
k18=0
k17=0
1
---*b33*k1
2
k15=------------
a33
k14=0
k13=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:
b33,q1,k38,k16,k12,k1,n1,a33
Relevance for the application:
The following expression INT is a first
integral for the Hamiltonian HAM:
2 2 2 2 2 2
HAM=(192*a33 *u1 + 192*a33 *u2 + 48*a33 *u3 + 48*a33*b33*u3*v3 + 48*a33*n1*u1
2 2
- 3*b33 *v3 - 10*b33*n1*v1)/(48*a33)
4 4 4 2 4 2
INT=(110592*a33 *k1*u1 + 221184*a33 *k1*u1 *u2*u3 + 110592*a33 *k1*u1*u2*v2
4 2 4 4 2
- 442368*a33 *k1*u1*u3 - 442368*a33 *k1*u1*v1 + 110592*a33 *k12*u1*v1*v2
4 2 2 4 3
+ 110592*a33 *k12*u2 *u3 + 110592*a33 *k16*u1 *v1
4 3 4
+ 110592*a33 *k16*u1 *v3 + 110592*a33 *k16*u1*u2*u3*v1
4 3 4 3 4 3
+ 110592*a33 *k16*u1*v2 + 110592*a33 *k16*u2 *v1 + 110592*a33 *k16*v1*v2
4 2 4
+ 110592*a33 *k38*u1*u2 *v2 - 221184*a33 *k38*u1*u3*v1
4 4 3
- 110592*a33 *k38*u1*u3 + 110592*a33 *k38*u2 *v3
4 4
+ 110592*a33 *k38*u2*u3*v2*v3 + 221184*a33 *k38*u2*v1*v2
4 2 4 2 4
- 110592*a33 *k38*v1 + 110592*a33 *q1*u1 + 110592*a33 *q1*u1*v1
3 3
+ 55296*a33 *b33*k1*u1*u3*v1 + 165888*a33 *b33*k1*u1*u3
3 3 4
- 55296*a33 *b33*k1*u2*v1*v2 + 55296*a33 *b33*k1*u3
3 2 2 3 2
+ 55296*a33 *b33*k1*v1 *v2 + 165888*a33 *b33*k1*v1
3 3
+ 27648*a33 *b33*k12*u2*u3*v2*v3 - 27648*a33 *b33*k16*u1*u2*v1*v2
3 2 3 2
- 27648*a33 *b33*k16*u1*v1 *v2 - 27648*a33 *b33*k16*u2 *v1*v3
3 3 2
- 27648*a33 *b33*k16*u2*u3*v1*v2 - 27648*a33 *b33*k16*u2*v1 *v3
3 3 3
- 27648*a33 *b33*k16*v1 *v3 - 27648*a33 *b33*q1*u1*u3
3 2 3 3 3
- 27648*a33 *b33*q1*v1 + 73728*a33 *k1*n1*u1 + 36864*a33 *k1*n1*u1
3 2 3 3 3
+ 73728*a33 *k1*n1*u2 *u3 - 73728*a33 *k1*n1*u2*v1 - 36864*a33 *k12*n1*u1
3 3
+ 36864*a33 *k12*n1*u1*u2*v1 - 36864*a33 *k12*n1*u1
3 2 3
- 36864*a33 *k12*n1*u2 *u3 + 73728*a33 *k12*n1*u2*v1
3 2 3 2
+ 36864*a33 *k16*n1*u1 *v2 + 36864*a33 *k16*n1*u3 *v1
3 2 3 3
+ 36864*a33 *k16*n1*u3*v1 - 36864*a33 *k38*n1*u2
3 3 3 3
- 36864*a33 *k38*n1*u2*u3*v1 - 36864*a33 *k38*n1*u3 + 36864*a33 *n1*q1*u1
2 2 3 2 2
+ 3456*a33 *b33 *k1*u1 *v3 + 3456*a33 *b33 *k1*u1*u2*u3*v1
2 2 2 2 2 3
- 13824*a33 *b33 *k1*u1*u3 *v2 - 13824*a33 *b33 *k1*u1*v1
2 2 2 2 3
+ 6912*a33 *b33 *k1*u1*v1*v3 + 6912*a33 *b33 *k1*u1*v2
2 2 2 2 3
- 13824*a33 *b33 *k1*u1*v3 + 6912*a33 *b33 *k1*u2 *v1
2 2 3 2 2
- 13824*a33 *b33 *k1*u3 *v3 - 13824*a33 *b33 *k1*v1*v3
2 2 3 2 2
- 1728*a33 *b33 *k12*u1 *v3 - 1728*a33 *b33 *k12*u1*u2*u3*v1
2 2 2 2 2 3
+ 3456*a33 *b33 *k12*u1*u3 *v2 + 3456*a33 *b33 *k12*u1*v1
2 2 2 2 3
- 1728*a33 *b33 *k12*u1*v1*v3 - 1728*a33 *b33 *k12*u1*v2
2 2 3 2 2 3
- 1728*a33 *b33 *k12*u2 *v1 + 3456*a33 *b33 *k12*u3 *v3
2 2 2 2 2 3
+ 1728*a33 *b33 *k12*u3*v2 - 1728*a33 *b33 *k12*v1
2 2 2 2 2 2
+ 1728*a33 *b33 *k16*u1*v1*v3 + 1728*a33 *b33 *k16*u2*v2*v3
2 2 3 2 2 2 2
+ 1728*a33 *b33 *k16*u2*v3 + 3456*a33 *b33 *k16*v1 *v3
2 2 3 2 2
+ 1728*a33 *b33 *k16*v1*v3 + 1728*a33 *b33 *q1*u1*v3
2 2 2
+ 1728*a33 *b33 *q1*v1*v3 - 9216*a33 *b33*k1*n1*u1*u3*v2
2 3 2
- 9216*a33 *b33*k1*n1*u2 + 18432*a33 *b33*k1*n1*u2*u3*v1
2 2
+ 9216*a33 *b33*k1*n1*v1*v2 + 23040*a33 *b33*k1*n1*v1
2 2
- 4608*a33 *b33*k12*n1*u1*u3*v2 - 9216*a33 *b33*k12*n1*u1*v2
2 3 2 2
- 4608*a33 *b33*k12*n1*u2 - 4608*a33 *b33*k12*n1*u2 *v3
2 2
- 9216*a33 *b33*k12*n1*u2*u3*v1 + 4608*a33 *b33*k12*n1*v1
2 2 2
- 4608*a33 *b33*k16*n1*u2*v2*v3 - 4608*a33 *b33*k16*n1*u2*v3
2 2 2
- 4608*a33 *b33*k16*n1*v2 *v3 - 4608*a33 *b33*k38*n1*u2*v1*v3
2 2 2 2
- 4608*a33 *b33*k38*n1*u2*v2 - 4608*a33 *b33*k38*n1*u3 *v1
2 2 2
- 4608*a33 *b33*n1*q1*v1 - 12288*a33 *k1*n1 *u1*v1
2 2 3
+ 12288*a33 *k12*n1 *u1*v1 - 864*a33*b33 *k1*u1*u2*v1*v2
3 2 3 2
+ 864*a33*b33 *k1*u1*u3*v3 - 864*a33*b33 *k1*u1*v1 *v2
3 2 3
- 864*a33*b33 *k1*u2 *v1*v3 - 864*a33*b33 *k1*u2*u3*v1*v2
3 2 3 3
- 864*a33*b33 *k1*u2*v1 *v3 - 864*a33*b33 *k1*v1 *v3
3 2 3
+ 864*a33*b33 *k1*v1*v2 *v3 + 432*a33*b33 *k12*u1*u2*v1*v2
3 2 3 2
+ 432*a33*b33 *k12*u1*v1 *v2 + 432*a33*b33 *k12*u2 *v1*v3
3 3 2
+ 432*a33*b33 *k12*u2*u3*v1*v2 + 432*a33*b33 *k12*u2*v1 *v3
3 3 2 2
+ 432*a33*b33 *k12*v1 *v3 + 1152*a33*b33 *k1*n1*u1 *v2
2 2 2
- 2304*a33*b33 *k1*n1*u2*v1*v3 + 2304*a33*b33 *k1*n1*u3 *v1
2 2 2
+ 2304*a33*b33 *k1*n1*u3*v1 - 1152*a33*b33 *k12*n1*u2*v1*v3
2 2 2 2
- 576*a33*b33 *k12*n1*u3 *v1 - 576*a33*b33 *k12*n1*u3*v1
2 2 2
+ 1152*a33*b33 *k12*n1*v2*v3 + 3072*a33*b33*k1*n1 *v1
2 2 2
- 3072*a33*b33*k12*n1 *u1*u3 - 3072*a33*b33*k12*n1 *v1
3 3 4 2
- 4096*a33*k1*n1 *u1 + 4096*a33*k12*n1 *u1 + 81*b33 *k1*u1*v1*v3
4 2 4 3 4 2 2
+ 54*b33 *k1*u2*v2*v3 + 81*b33 *k1*u2*v3 + 162*b33 *k1*v1 *v3
4 3 4 2 4 2
+ 54*b33 *k1*v1*v3 - 27*b33 *k12*u1*v1*v3 - 27*b33 *k12*u2*v2*v3
4 3 4 2 2 4 3
- 27*b33 *k12*u2*v3 - 54*b33 *k12*v1 *v3 - 27*b33 *k12*v1*v3
3 3 2 3 2
- 288*b33 *k1*n1*u2*v2*v3 - 144*b33 *k1*n1*u2*v3 - 288*b33 *k1*n1*v2 *v3
3 3 2 3 2
+ 72*b33 *k12*n1*u2*v2*v3 + 144*b33 *k12*n1*u2*v3 + 72*b33 *k12*n1*v2 *v3
2 2 2 2 2 2
- 192*b33 *k1*n1 *v1*v3 + 384*b33 *k12*n1 *u1*v3 + 192*b33 *k12*n1 *v1*v3
3 3 4
+ 512*b33*k1*n1 *v1 - 512*b33*k12*n1 *v1)/(110592*a33 )
And again in machine readable form:
HAM=(192*a33**2*u1**2 + 192*a33**2*u2**2 + 48*a33**2*u3**2 + 48*a33*b33*u3*v3 +
48*a33*n1*u1 - 3*b33**2*v3**2 - 10*b33*n1*v1)/(48*a33)$
INT=(110592*a33**4*k1*u1**4 + 221184*a33**4*k1*u1**2*u2*u3 + 110592*a33**4*k1*u1
*u2*v2**2 - 442368*a33**4*k1*u1*u3**2 - 442368*a33**4*k1*u1*v1 + 110592*a33**4*
k12*u1*v1*v2**2 + 110592*a33**4*k12*u2**2*u3**2 + 110592*a33**4*k16*u1**3*v1 +
110592*a33**4*k16*u1**3*v3 + 110592*a33**4*k16*u1*u2*u3*v1 + 110592*a33**4*k16*
u1*v2**3 + 110592*a33**4*k16*u2**3*v1 + 110592*a33**4*k16*v1*v2**3 + 110592*a33
**4*k38*u1*u2**2*v2 - 221184*a33**4*k38*u1*u3*v1 - 110592*a33**4*k38*u1*u3 +
110592*a33**4*k38*u2**3*v3 + 110592*a33**4*k38*u2*u3*v2*v3 + 221184*a33**4*k38*
u2*v1*v2 - 110592*a33**4*k38*v1**2 + 110592*a33**4*q1*u1**2 + 110592*a33**4*q1*
u1*v1 + 55296*a33**3*b33*k1*u1*u3*v1 + 165888*a33**3*b33*k1*u1*u3 - 55296*a33**3
*b33*k1*u2*v1*v2 + 55296*a33**3*b33*k1*u3**4 + 55296*a33**3*b33*k1*v1**2*v2**2 +
165888*a33**3*b33*k1*v1**2 + 27648*a33**3*b33*k12*u2*u3*v2*v3 - 27648*a33**3*
b33*k16*u1*u2*v1*v2 - 27648*a33**3*b33*k16*u1*v1**2*v2 - 27648*a33**3*b33*k16*u2
**2*v1*v3 - 27648*a33**3*b33*k16*u2*u3*v1*v2 - 27648*a33**3*b33*k16*u2*v1**2*v3
- 27648*a33**3*b33*k16*v1**3*v3 - 27648*a33**3*b33*q1*u1*u3 - 27648*a33**3*b33*
q1*v1**2 + 73728*a33**3*k1*n1*u1**3 + 36864*a33**3*k1*n1*u1 + 73728*a33**3*k1*n1
*u2**2*u3 - 73728*a33**3*k1*n1*u2*v1 - 36864*a33**3*k12*n1*u1**3 + 36864*a33**3*
k12*n1*u1*u2*v1 - 36864*a33**3*k12*n1*u1 - 36864*a33**3*k12*n1*u2**2*u3 + 73728*
a33**3*k12*n1*u2*v1 + 36864*a33**3*k16*n1*u1**2*v2 + 36864*a33**3*k16*n1*u3**2*
v1 + 36864*a33**3*k16*n1*u3*v1**2 - 36864*a33**3*k38*n1*u2**3 - 36864*a33**3*k38
*n1*u2*u3*v1 - 36864*a33**3*k38*n1*u3**3 + 36864*a33**3*n1*q1*u1 + 3456*a33**2*
b33**2*k1*u1**3*v3 + 3456*a33**2*b33**2*k1*u1*u2*u3*v1 - 13824*a33**2*b33**2*k1*
u1*u3**2*v2 - 13824*a33**2*b33**2*k1*u1*v1**3 + 6912*a33**2*b33**2*k1*u1*v1*v3 +
6912*a33**2*b33**2*k1*u1*v2**3 - 13824*a33**2*b33**2*k1*u1*v3 + 6912*a33**2*b33
**2*k1*u2**3*v1 - 13824*a33**2*b33**2*k1*u3**3*v3 - 13824*a33**2*b33**2*k1*v1*v3
- 1728*a33**2*b33**2*k12*u1**3*v3 - 1728*a33**2*b33**2*k12*u1*u2*u3*v1 + 3456*
a33**2*b33**2*k12*u1*u3**2*v2 + 3456*a33**2*b33**2*k12*u1*v1**3 - 1728*a33**2*
b33**2*k12*u1*v1*v3 - 1728*a33**2*b33**2*k12*u1*v2**3 - 1728*a33**2*b33**2*k12*
u2**3*v1 + 3456*a33**2*b33**2*k12*u3**3*v3 + 1728*a33**2*b33**2*k12*u3*v2**2 -
1728*a33**2*b33**2*k12*v1**3 + 1728*a33**2*b33**2*k16*u1*v1*v3**2 + 1728*a33**2*
b33**2*k16*u2*v2*v3**2 + 1728*a33**2*b33**2*k16*u2*v3**3 + 3456*a33**2*b33**2*
k16*v1**2*v3**2 + 1728*a33**2*b33**2*k16*v1*v3**3 + 1728*a33**2*b33**2*q1*u1*v3
+ 1728*a33**2*b33**2*q1*v1*v3 - 9216*a33**2*b33*k1*n1*u1*u3*v2 - 9216*a33**2*b33
*k1*n1*u2**3 + 18432*a33**2*b33*k1*n1*u2*u3*v1 + 9216*a33**2*b33*k1*n1*v1*v2 +
23040*a33**2*b33*k1*n1*v1 - 4608*a33**2*b33*k12*n1*u1*u3*v2 - 9216*a33**2*b33*
k12*n1*u1*v2 - 4608*a33**2*b33*k12*n1*u2**3 - 4608*a33**2*b33*k12*n1*u2**2*v3 -
9216*a33**2*b33*k12*n1*u2*u3*v1 + 4608*a33**2*b33*k12*n1*v1 - 4608*a33**2*b33*
k16*n1*u2*v2*v3 - 4608*a33**2*b33*k16*n1*u2*v3**2 - 4608*a33**2*b33*k16*n1*v2**2
*v3 - 4608*a33**2*b33*k38*n1*u2*v1*v3 - 4608*a33**2*b33*k38*n1*u2*v2**2 - 4608*
a33**2*b33*k38*n1*u3**2*v1 - 4608*a33**2*b33*n1*q1*v1 - 12288*a33**2*k1*n1**2*u1
*v1 + 12288*a33**2*k12*n1**2*u1*v1 - 864*a33*b33**3*k1*u1*u2*v1*v2 + 864*a33*b33
**3*k1*u1*u3*v3**2 - 864*a33*b33**3*k1*u1*v1**2*v2 - 864*a33*b33**3*k1*u2**2*v1*
v3 - 864*a33*b33**3*k1*u2*u3*v1*v2 - 864*a33*b33**3*k1*u2*v1**2*v3 - 864*a33*b33
**3*k1*v1**3*v3 + 864*a33*b33**3*k1*v1*v2**2*v3 + 432*a33*b33**3*k12*u1*u2*v1*v2
+ 432*a33*b33**3*k12*u1*v1**2*v2 + 432*a33*b33**3*k12*u2**2*v1*v3 + 432*a33*b33
**3*k12*u2*u3*v1*v2 + 432*a33*b33**3*k12*u2*v1**2*v3 + 432*a33*b33**3*k12*v1**3*
v3 + 1152*a33*b33**2*k1*n1*u1**2*v2 - 2304*a33*b33**2*k1*n1*u2*v1*v3 + 2304*a33*
b33**2*k1*n1*u3**2*v1 + 2304*a33*b33**2*k1*n1*u3*v1**2 - 1152*a33*b33**2*k12*n1*
u2*v1*v3 - 576*a33*b33**2*k12*n1*u3**2*v1 - 576*a33*b33**2*k12*n1*u3*v1**2 +
1152*a33*b33**2*k12*n1*v2*v3 + 3072*a33*b33*k1*n1**2*v1**2 - 3072*a33*b33*k12*n1
**2*u1*u3 - 3072*a33*b33*k12*n1**2*v1**2 - 4096*a33*k1*n1**3*u1 + 4096*a33*k12*
n1**3*u1 + 81*b33**4*k1*u1*v1*v3**2 + 54*b33**4*k1*u2*v2*v3**2 + 81*b33**4*k1*u2
*v3**3 + 162*b33**4*k1*v1**2*v3**2 + 54*b33**4*k1*v1*v3**3 - 27*b33**4*k12*u1*v1
*v3**2 - 27*b33**4*k12*u2*v2*v3**2 - 27*b33**4*k12*u2*v3**3 - 54*b33**4*k12*v1**
2*v3**2 - 27*b33**4*k12*v1*v3**3 - 288*b33**3*k1*n1*u2*v2*v3 - 144*b33**3*k1*n1*
u2*v3**2 - 288*b33**3*k1*n1*v2**2*v3 + 72*b33**3*k12*n1*u2*v2*v3 + 144*b33**3*
k12*n1*u2*v3**2 + 72*b33**3*k12*n1*v2**2*v3 - 192*b33**2*k1*n1**2*v1*v3 + 384*
b33**2*k12*n1**2*u1*v3 + 192*b33**2*k12*n1**2*v1*v3 + 512*b33*k1*n1**3*v1 - 512*
b33*k12*n1**3*v1)/(110592*a33**4)$