Solution 27 to problem e3quant
Expressions |
Parameters |
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Expressions
The solution is given through the following expressions:
a22=3*a33
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
1 2
- ----*b33
12
c33=--------------
a33
n2=0
1
- ---*b33*n1
3
m1=---------------
a33
m2=0
1
- ---*b33*n3
2
m3=---------------
a33
2 2 1 2 1 2
---*a33 *b33*k1*n3 - ---*a33 *b33*n3*q1 + ----*b33*k1*n1 *n3
3 6 72
r6=--------------------------------------------------------------
4
a33
1
- ----*b33*k1*n1*n3
72
r5=----------------------
3
a33
17 2 1 2 1 3
r4=(----*a33 *b33*k1*n1 - ----*a33 *b33*n1*q1 + -----*b33*k1*n1
36 12 144
1 2 4
+ -----*b33*k1*n1*n3 )/a33
144
1 2 1 2 1 3
---*a33 *n3*q1 - ----*k1*n1 *n3 + ----*k1*n3
2 24 24
r3=-----------------------------------------------
3
a33
1
----*k1*n1*n3
12
r2=---------------
2
a33
1 2 1 2 1 3 1 2
---*a33 *k1*n1 + ---*a33 *n1*q1 - ----*k1*n1 + ----*k1*n1*n3
6 2 24 24
r1=----------------------------------------------------------------
3
a33
1 2
----*b33 *k1*n1
54
q20=-----------------
3
a33
q19=
2 2 2 1 2 2 1 2 2 1 2 2
- ---*a33 *b33 *k1 + ----*a33 *b33 *q1 - -----*b33 *k1*n1 - ----*b33 *k1*n3
9 36 432 36
--------------------------------------------------------------------------------
4
a33
1 2
----*b33 *k1*n1*n3
27
q18=--------------------
4
a33
q17=0
q16=
2 2 2 1 2 2 1 2 2 1 2 2
- ---*a33 *b33 *k1 + ----*a33 *b33 *q1 + -----*b33 *k1*n1 - ----*b33 *k1*n3
9 36 108 36
--------------------------------------------------------------------------------
4
a33
1
---*b33*k1*n1
6
q14=---------------
2
a33
1
- ----*b33*k1*n1*n3
12
q13=----------------------
3
a33
1
- ---*b33*k1*n1
9
q11=------------------
2
a33
3 2 1 2 1 2
q10=( - a33 *k38 + 2*a33 *b33*k1 - ---*a33 *b33*q1 + ----*b33*k1*n1
3 36
1 2 3
+ ---*b33*k1*n3 )/a33
9
1 1
- ---*a33*k38*n3 + ---*b33*k1*n3
2 3
q9=-----------------------------------
2
a33
1
- ---*k1*n1
3
q8=--------------
a33
2 2 1 2
- 4*a33 *k1 + a33 *q1 - ----*k1*n1
12
q7=--------------------------------------
2
a33
1
- ---*b33*k1*n1*n3
9
q6=---------------------
3
a33
1 1
---*a33*k38*n3 - ---*b33*k1*n3
2 3
q5=--------------------------------
2
a33
3 2 1 2 1 2
q4=( - a33 *k38 + 2*a33 *b33*k1 - ---*a33 *b33*q1 - ----*b33*k1*n1
3 18
1 2 3
+ ---*b33*k1*n3 )/a33
9
1
---*k1*n1*n3
6
q3=--------------
2
a33
q2=0
1 2 1 3
- ---*a33 *b33*k16*n3 - -----*b33 *k1*n3
6 162
p56=-------------------------------------------
4
a33
p55=0
1 2 5 3
- ---*a33 *b33*k16*n3 - -----*b33 *k1*n3
6 324
p54=-------------------------------------------
4
a33
p53=0
1 2 1 3
- ----*a33 *b33*k16*n1 - -----*b33 *k1*n1
12 648
p52=--------------------------------------------
4
a33
p51=0
1 2 5 3
- ----*a33 *b33*k16*n1 - -----*b33 *k1*n1
12 648
p50=--------------------------------------------
4
a33
1 2 5 3
- ---*a33 *b33*k16*n3 - -----*b33 *k1*n3
6 324
p49=-------------------------------------------
4
a33
p48=0
1 2 5 3
- ----*a33 *b33*k16*n1 - -----*b33 *k1*n1
12 648
p47=--------------------------------------------
4
a33
1 2 1 2
---*a33 *k16*n3 - ----*b33 *k1*n3
2 12
p46=-----------------------------------
3
a33
p45=0
1 2 5 2
---*a33 *k16*n3 + -----*b33 *k1*n3
2 108
p44=------------------------------------
3
a33
1 2 2
- ----*a33*b33*k38*n1 - ----*b33 *k1*n1
12 27
p43=------------------------------------------
3
a33
5 2
----*b33 *k1
54
p42=--------------
2
a33
1 2 5 2
---*a33 *k16*n3 + -----*b33 *k1*n3
2 108
p41=------------------------------------
3
a33
1 1
- ---*a33*k38*n3 + ---*b33*k1*n3
2 9
p40=-----------------------------------
2
a33
p39=0
1
- ----*b33*k1*n1
18
p38=-------------------
2
a33
1
---*k1*n3
3
p37=-----------
a33
p36=0
p35=0
p34=0
1 2
----*b33 *k1
54
p33=--------------
2
a33
1
- ----*b33*k38*n1
12
p32=--------------------
2
a33
p31=0
p30=0
1
- ---*k38*n3
2
p29=---------------
a33
2
2*a33*k38 - ---*b33*k1
3
p28=------------------------
a33
p27=0
1
- ---*b33*k1*n3
3
p26=------------------
2
a33
p25=0
2
- ---*b33*k1*n1
9
p24=------------------
2
a33
2
---*k1*n3
3
p23=-----------
a33
p22=0
1 2 1 2
---*a33 *k16*n1 + ----*b33 *k1*n1
2 36
p21=-----------------------------------
3
a33
1 2
- ----*b33 *k1
54
p20=-----------------
2
a33
1 2 5 2
---*a33 *k16*n1 + -----*b33 *k1*n1
2 108
p19=------------------------------------
3
a33
p18=0
p17=0
1 2 1 5 2
---*a33 *k16*n1 - ----*a33*b33*k38*n1 + -----*b33 *k1*n1
2 12 108
p16=----------------------------------------------------------
3
a33
1 2
- ---*a33*k38*n1 + ---*b33*k1*n1
2 9
p15=-----------------------------------
2
a33
2
- 2*a33*k38 + ---*b33*k1
3
p14=---------------------------
a33
1
- ---*k38*n3
2
p13=---------------
a33
1
---*k1*n1
3
p12=-----------
a33
p11=0
1
- ---*k38*n1
2
p10=---------------
a33
p9=0
p8= - 4*k1
2
---*k1*n1
3
p7=-----------
a33
1
- ---*b33*k1*n3
3
p6=------------------
2
a33
p5=0
1 2
- ---*a33*k38*n1 - ---*b33*k1*n1
2 9
p4=-----------------------------------
2
a33
2
---*k1*n3
3
p3=-----------
a33
p2=0
2
---*k1*n1
3
p1=-----------
a33
k125=0
1 2 2 1 4
----*a33 *b33 *k16 + -----*b33 *k1
36 972
k124=------------------------------------
4
a33
k123=0
1 2 2 7 4
----*a33 *b33 *k16 + ------*b33 *k1
36 3888
k122=-------------------------------------
4
a33
k121=0
k120=0
k119=0
k118=0
1 2 2 1 4
----*a33 *b33 *k16 + -----*b33 *k1
36 972
k117=------------------------------------
4
a33
k116=0
1 2 2 7 4
----*a33 *b33 *k16 + ------*b33 *k1
18 1944
k115=-------------------------------------
4
a33
k114=0
k113=0
1 2 2 7 4
----*a33 *b33 *k16 + ------*b33 *k1
36 3888
k112=-------------------------------------
4
a33
k110=0
1 3
----*b33 *k1
54
k109=--------------
3
a33
k108=0
k107=0
k106=0
k105=0
1 3
----*b33 *k1
54
k104=--------------
3
a33
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
2
a33*k38 + ---*b33*k1
9
k95=----------------------
a33
k94=0
k93=0
k91=0
1 2 1 3
- ---*a33 *b33*k16 - ----*b33 *k1
3 81
k90=------------------------------------
3
a33
k89=0
1 2 1 3
- ---*a33 *b33*k16 - ----*b33 *k1
3 81
k88=------------------------------------
3
a33
k87=0
k86=0
k85=0
k84=0
1 2 1 3
- ---*a33 *b33*k16 - ----*b33 *k1
3 81
k83=------------------------------------
3
a33
k82=0
k81=0
5 2
- ----*b33 *k1
27
k80=-----------------
2
a33
k79=0
k78=0
k77=0
k76=0
k75=0
k74=k38
k73=0
k72=0
2 1 2
a33 *k16 + ----*b33 *k1
27
k71=-------------------------
2
a33
k70=0
k69=k16
k68=0
k67=0
2 5 2
a33 *k16 + ----*b33 *k1
54
k66=-------------------------
2
a33
2
---*b33*k1
3
k65=------------
a33
k64=0
k63=0
2
k62=---*k1
3
k61=0
k59=0
k58=0
k57=k1
k56=0
k55=0
k54=0
k53=0
1 2 1 3
- ---*a33 *b33*k16 - ----*b33 *k1
3 81
k52=------------------------------------
3
a33
k51=0
1 2 1 3
- ---*a33 *b33*k16 - ----*b33 *k1
3 81
k50=------------------------------------
3
a33
k49=0
k48=0
1 2 1 3
- ---*a33 *b33*k16 - ----*b33 *k1
3 81
k47=------------------------------------
3
a33
k46=0
k45=0
k44=0
5 2
- ----*b33 *k1
27
k43=-----------------
2
a33
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
5 2
- ----*b33 *k1
27
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
a33 *k16 + ----*b33 *k1
27
k21=-------------------------
2
a33
k20=0
2 5 2
a33 *k16 + ----*b33 *k1
54
k19=-------------------------
2
a33
k18=0
k17=0
2
---*b33*k1
3
k15=------------
a33
k14=0
k13=0
2
k12=---*k1
3
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:
q1,k38,k16,k1,b33,n3,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=(36*a33 *u1 + 36*a33 *u2 + 12*a33 *u3 + 12*a33*b33*u3*v3 + 12*a33*n1*u1
2 2
+ 12*a33*n3*u3 - b33 *v3 - 4*b33*n1*v1 - 6*b33*n3*v3)/(12*a33)
4 4 4 2 4 2
INT=(3888*a33 *k1*u1 + 7776*a33 *k1*u1 *u2*u3 + 3888*a33 *k1*u1*u2*v2
4 2 4 2 4
- 15552*a33 *k1*u1*u3 + 2592*a33 *k1*u1*v1*v2 - 15552*a33 *k1*u1*v1
4 2 2 4 3 4 3
+ 2592*a33 *k1*u2 *u3 + 3888*a33 *k16*u1 *v1 + 3888*a33 *k16*u1 *v3
4 4 3 4 3
+ 3888*a33 *k16*u1*u2*u3*v1 + 3888*a33 *k16*u1*v2 + 3888*a33 *k16*u2 *v1
4 3 4 2 4
+ 3888*a33 *k16*v1*v2 + 3888*a33 *k38*u1*u2 *v2 - 7776*a33 *k38*u1*u3*v1
4 4 3 4
- 3888*a33 *k38*u1*u3 + 3888*a33 *k38*u2 *v3 + 3888*a33 *k38*u2*u3*v2*v3
4 4 2 4 2
+ 7776*a33 *k38*u2*v1*v2 - 3888*a33 *k38*v1 + 3888*a33 *q1*u1
4 3 3
+ 3888*a33 *q1*u1*v1 + 2592*a33 *b33*k1*u1*u3*v1 + 7776*a33 *b33*k1*u1*u3
3 3
+ 864*a33 *b33*k1*u2*u3*v2*v3 - 2592*a33 *b33*k1*u2*v1*v2
3 4 3 2 2 3 2
+ 2592*a33 *b33*k1*u3 + 2592*a33 *b33*k1*v1 *v2 + 7776*a33 *b33*k1*v1
3 3 2
- 1296*a33 *b33*k16*u1*u2*v1*v2 - 1296*a33 *b33*k16*u1*v1 *v2
3 2 3
- 1296*a33 *b33*k16*u2 *v1*v3 - 1296*a33 *b33*k16*u2*u3*v1*v2
3 2 3 3
- 1296*a33 *b33*k16*u2*v1 *v3 - 1296*a33 *b33*k16*v1 *v3
3 3 2 3 3
- 1296*a33 *b33*q1*u1*u3 - 1296*a33 *b33*q1*v1 + 2592*a33 *k1*n1*u1
3 3 3 2
+ 1296*a33 *k1*n1*u1*u2*v1 + 648*a33 *k1*n1*u1 + 2592*a33 *k1*n1*u2 *u3
3 3 2
- 1296*a33 *k1*n1*u2*v1 + 2592*a33 *k1*n3*u1*u2
3 3 2
+ 1296*a33 *k1*n3*u1*u2*v3 + 2592*a33 *k1*n3*u2 *v2
3 2 3 2
+ 1944*a33 *k16*n1*u1 *v2 + 1944*a33 *k16*n1*u3 *v1
3 2 3
+ 1944*a33 *k16*n1*u3*v1 + 1944*a33 *k16*n3*u1*v2*v3
3 2 3
+ 1944*a33 *k16*n3*u3 *v3 + 1944*a33 *k16*n3*u3*v1*v3
3 3 3 3 3
- 1944*a33 *k38*n1*u2 - 1944*a33 *k38*n1*u2*u3*v1 - 1944*a33 *k38*n1*u3
3 2 3
- 1944*a33 *k38*n3*u2 *v1 - 1944*a33 *k38*n3*u2*u3*v3
3 3
+ 1944*a33 *k38*n3*u2*u3 - 1944*a33 *k38*n3*u3*v1*v2
3 3 3
- 1944*a33 *k38*n3*u3*v1 + 1944*a33 *n1*q1*u1 + 1944*a33 *n3*q1*u3
2 2 3 2 2
+ 144*a33 *b33 *k1*u1 *v3 + 144*a33 *b33 *k1*u1*u2*u3*v1
2 2 2 2 2 3
- 720*a33 *b33 *k1*u1*u3 *v2 - 720*a33 *b33 *k1*u1*v1
2 2 2 2 3
+ 360*a33 *b33 *k1*u1*v1*v3 + 360*a33 *b33 *k1*u1*v2
2 2 2 2 3
- 864*a33 *b33 *k1*u1*v3 + 360*a33 *b33 *k1*u2 *v1
2 2 3 2 2 2 2 2 3
- 720*a33 *b33 *k1*u3 *v3 + 72*a33 *b33 *k1*u3*v2 - 72*a33 *b33 *k1*v1
2 2 2 2 2
- 864*a33 *b33 *k1*v1*v3 + 108*a33 *b33 *k16*u1*v1*v3
2 2 2 2 2 3
+ 108*a33 *b33 *k16*u2*v2*v3 + 108*a33 *b33 *k16*u2*v3
2 2 2 2 2 2 3
+ 216*a33 *b33 *k16*v1 *v3 + 108*a33 *b33 *k16*v1*v3
2 2 2 2
+ 108*a33 *b33 *q1*u1*v3 + 108*a33 *b33 *q1*v1*v3
2 2
- 864*a33 *b33*k1*n1*u1*u3*v2 - 432*a33 *b33*k1*n1*u1*v2
2 3 2 2
- 864*a33 *b33*k1*n1*u2 - 216*a33 *b33*k1*n1*u2 *v3
2 2
+ 864*a33 *b33*k1*n1*u2*u3*v1 + 648*a33 *b33*k1*n1*v1*v2
2 2
+ 1836*a33 *b33*k1*n1*v1 - 1296*a33 *b33*k1*n3*u1*u2*u3
2 2
+ 432*a33 *b33*k1*n3*u2*u3*v3 - 1296*a33 *b33*k1*n3*u2*u3
2 2 2
- 1296*a33 *b33*k1*n3*u3 *v2 + 1296*a33 *b33*k1*n3*u3*v1
2 2
+ 2592*a33 *b33*k1*n3*v3 - 324*a33 *b33*k16*n1*u2*v2*v3
2 2 2 2
- 324*a33 *b33*k16*n1*u2*v3 - 324*a33 *b33*k16*n1*v2 *v3
2 2 2
- 648*a33 *b33*k16*n3*v1*v2*v3 - 648*a33 *b33*k16*n3*v1*v3
2 3 2
- 648*a33 *b33*k16*n3*v3 - 324*a33 *b33*k38*n1*u2*v1*v3
2 2 2 2
- 324*a33 *b33*k38*n1*u2*v2 - 324*a33 *b33*k38*n1*u3 *v1
2 2 2 2
- 324*a33 *b33*n1*q1*v1 - 648*a33 *b33*n3*q1*v3 - 324*a33 *k1*n1 *u1*v1
2 2 2
+ 648*a33 *k1*n1*n3*u2 + 324*a33 *k1*n1*n3*u2
3 3 2
- 48*a33*b33 *k1*u1*u2*v1*v2 + 72*a33*b33 *k1*u1*u3*v3
3 2 3 2
- 48*a33*b33 *k1*u1*v1 *v2 - 48*a33*b33 *k1*u2 *v1*v3
3 3 2
- 48*a33*b33 *k1*u2*u3*v1*v2 - 48*a33*b33 *k1*u2*v1 *v3
3 3 3 2
- 48*a33*b33 *k1*v1 *v3 + 72*a33*b33 *k1*v1*v2 *v3
2 2 2
+ 108*a33*b33 *k1*n1*u1 *v2 - 288*a33*b33 *k1*n1*u2*v1*v3
2 2 2 2
+ 180*a33*b33 *k1*n1*u3 *v1 + 180*a33*b33 *k1*n1*u3*v1
2 2
+ 72*a33*b33 *k1*n1*v2*v3 - 324*a33*b33 *k1*n3*u1*v2*v3
2 2 2
+ 180*a33*b33 *k1*n3*u3 *v3 + 180*a33*b33 *k1*n3*u3*v1*v3
2 2 2
- 216*a33*b33*k1*n1 *u1*u3 + 108*a33*b33*k1*n1 *v1
2
- 432*a33*b33*k1*n1*n3*u3 - 324*a33*b33*k1*n1*n3*u3*v2
2
- 54*a33*b33*k1*n1*n3*v2 + 432*a33*b33*k1*n3 *u1*u3
2 2 3 2
+ 432*a33*b33*k1*n3 *v1 - 162*a33*k1*n1 *u1 - 162*a33*k1*n1 *n3*u3
2 3 4 2
+ 162*a33*k1*n1*n3 *u1 + 162*a33*k1*n3 *u3 + 7*b33 *k1*u1*v1*v3
4 2 4 3 4 2 2
+ 4*b33 *k1*u2*v2*v3 + 7*b33 *k1*u2*v3 + 14*b33 *k1*v1 *v3
4 3 3 3 2
+ 4*b33 *k1*v1*v3 - 30*b33 *k1*n1*u2*v2*v3 - 6*b33 *k1*n1*u2*v3
3 2 3 3 2
- 30*b33 *k1*n1*v2 *v3 - 60*b33 *k1*n3*v1*v2*v3 - 60*b33 *k1*n3*v1*v3
3 3 2 2 2 2
- 24*b33 *k1*n3*v3 + 36*b33 *k1*n1 *u1*v3 - 9*b33 *k1*n1 *v1*v3
2 2 2 2 2
+ 144*b33 *k1*n1*n3*u3*v3 - 108*b33 *k1*n3 *u1*v3 - 108*b33 *k1*n3 *v1*v3
3 2 2 4
+ 27*b33*k1*n1 *v1 + 54*b33*k1*n1 *n3*v3 + 27*b33*k1*n1*n3 *v1)/(3888*a33
)
And again in machine readable form:
HAM=(36*a33**2*u1**2 + 36*a33**2*u2**2 + 12*a33**2*u3**2 + 12*a33*b33*u3*v3 + 12
*a33*n1*u1 + 12*a33*n3*u3 - b33**2*v3**2 - 4*b33*n1*v1 - 6*b33*n3*v3)/(12*a33)$
INT=(3888*a33**4*k1*u1**4 + 7776*a33**4*k1*u1**2*u2*u3 + 3888*a33**4*k1*u1*u2*v2
**2 - 15552*a33**4*k1*u1*u3**2 + 2592*a33**4*k1*u1*v1*v2**2 - 15552*a33**4*k1*u1
*v1 + 2592*a33**4*k1*u2**2*u3**2 + 3888*a33**4*k16*u1**3*v1 + 3888*a33**4*k16*u1
**3*v3 + 3888*a33**4*k16*u1*u2*u3*v1 + 3888*a33**4*k16*u1*v2**3 + 3888*a33**4*
k16*u2**3*v1 + 3888*a33**4*k16*v1*v2**3 + 3888*a33**4*k38*u1*u2**2*v2 - 7776*a33
**4*k38*u1*u3*v1 - 3888*a33**4*k38*u1*u3 + 3888*a33**4*k38*u2**3*v3 + 3888*a33**
4*k38*u2*u3*v2*v3 + 7776*a33**4*k38*u2*v1*v2 - 3888*a33**4*k38*v1**2 + 3888*a33
**4*q1*u1**2 + 3888*a33**4*q1*u1*v1 + 2592*a33**3*b33*k1*u1*u3*v1 + 7776*a33**3*
b33*k1*u1*u3 + 864*a33**3*b33*k1*u2*u3*v2*v3 - 2592*a33**3*b33*k1*u2*v1*v2 +
2592*a33**3*b33*k1*u3**4 + 2592*a33**3*b33*k1*v1**2*v2**2 + 7776*a33**3*b33*k1*
v1**2 - 1296*a33**3*b33*k16*u1*u2*v1*v2 - 1296*a33**3*b33*k16*u1*v1**2*v2 - 1296
*a33**3*b33*k16*u2**2*v1*v3 - 1296*a33**3*b33*k16*u2*u3*v1*v2 - 1296*a33**3*b33*
k16*u2*v1**2*v3 - 1296*a33**3*b33*k16*v1**3*v3 - 1296*a33**3*b33*q1*u1*u3 - 1296
*a33**3*b33*q1*v1**2 + 2592*a33**3*k1*n1*u1**3 + 1296*a33**3*k1*n1*u1*u2*v1 +
648*a33**3*k1*n1*u1 + 2592*a33**3*k1*n1*u2**2*u3 - 1296*a33**3*k1*n1*u2*v1 +
2592*a33**3*k1*n3*u1*u2**2 + 1296*a33**3*k1*n3*u1*u2*v3 + 2592*a33**3*k1*n3*u2**
2*v2 + 1944*a33**3*k16*n1*u1**2*v2 + 1944*a33**3*k16*n1*u3**2*v1 + 1944*a33**3*
k16*n1*u3*v1**2 + 1944*a33**3*k16*n3*u1*v2*v3 + 1944*a33**3*k16*n3*u3**2*v3 +
1944*a33**3*k16*n3*u3*v1*v3 - 1944*a33**3*k38*n1*u2**3 - 1944*a33**3*k38*n1*u2*
u3*v1 - 1944*a33**3*k38*n1*u3**3 - 1944*a33**3*k38*n3*u2**2*v1 - 1944*a33**3*k38
*n3*u2*u3*v3 + 1944*a33**3*k38*n3*u2*u3 - 1944*a33**3*k38*n3*u3*v1*v2 - 1944*a33
**3*k38*n3*u3*v1 + 1944*a33**3*n1*q1*u1 + 1944*a33**3*n3*q1*u3 + 144*a33**2*b33
**2*k1*u1**3*v3 + 144*a33**2*b33**2*k1*u1*u2*u3*v1 - 720*a33**2*b33**2*k1*u1*u3
**2*v2 - 720*a33**2*b33**2*k1*u1*v1**3 + 360*a33**2*b33**2*k1*u1*v1*v3 + 360*a33
**2*b33**2*k1*u1*v2**3 - 864*a33**2*b33**2*k1*u1*v3 + 360*a33**2*b33**2*k1*u2**3
*v1 - 720*a33**2*b33**2*k1*u3**3*v3 + 72*a33**2*b33**2*k1*u3*v2**2 - 72*a33**2*
b33**2*k1*v1**3 - 864*a33**2*b33**2*k1*v1*v3 + 108*a33**2*b33**2*k16*u1*v1*v3**2
+ 108*a33**2*b33**2*k16*u2*v2*v3**2 + 108*a33**2*b33**2*k16*u2*v3**3 + 216*a33
**2*b33**2*k16*v1**2*v3**2 + 108*a33**2*b33**2*k16*v1*v3**3 + 108*a33**2*b33**2*
q1*u1*v3 + 108*a33**2*b33**2*q1*v1*v3 - 864*a33**2*b33*k1*n1*u1*u3*v2 - 432*a33
**2*b33*k1*n1*u1*v2 - 864*a33**2*b33*k1*n1*u2**3 - 216*a33**2*b33*k1*n1*u2**2*v3
+ 864*a33**2*b33*k1*n1*u2*u3*v1 + 648*a33**2*b33*k1*n1*v1*v2 + 1836*a33**2*b33*
k1*n1*v1 - 1296*a33**2*b33*k1*n3*u1*u2*u3 + 432*a33**2*b33*k1*n3*u2*u3*v3 - 1296
*a33**2*b33*k1*n3*u2*u3 - 1296*a33**2*b33*k1*n3*u3**2*v2 + 1296*a33**2*b33*k1*n3
*u3*v1 + 2592*a33**2*b33*k1*n3*v3 - 324*a33**2*b33*k16*n1*u2*v2*v3 - 324*a33**2*
b33*k16*n1*u2*v3**2 - 324*a33**2*b33*k16*n1*v2**2*v3 - 648*a33**2*b33*k16*n3*v1*
v2*v3 - 648*a33**2*b33*k16*n3*v1*v3**2 - 648*a33**2*b33*k16*n3*v3**3 - 324*a33**
2*b33*k38*n1*u2*v1*v3 - 324*a33**2*b33*k38*n1*u2*v2**2 - 324*a33**2*b33*k38*n1*
u3**2*v1 - 324*a33**2*b33*n1*q1*v1 - 648*a33**2*b33*n3*q1*v3 - 324*a33**2*k1*n1
**2*u1*v1 + 648*a33**2*k1*n1*n3*u2**2 + 324*a33**2*k1*n1*n3*u2 - 48*a33*b33**3*
k1*u1*u2*v1*v2 + 72*a33*b33**3*k1*u1*u3*v3**2 - 48*a33*b33**3*k1*u1*v1**2*v2 -
48*a33*b33**3*k1*u2**2*v1*v3 - 48*a33*b33**3*k1*u2*u3*v1*v2 - 48*a33*b33**3*k1*
u2*v1**2*v3 - 48*a33*b33**3*k1*v1**3*v3 + 72*a33*b33**3*k1*v1*v2**2*v3 + 108*a33
*b33**2*k1*n1*u1**2*v2 - 288*a33*b33**2*k1*n1*u2*v1*v3 + 180*a33*b33**2*k1*n1*u3
**2*v1 + 180*a33*b33**2*k1*n1*u3*v1**2 + 72*a33*b33**2*k1*n1*v2*v3 - 324*a33*b33
**2*k1*n3*u1*v2*v3 + 180*a33*b33**2*k1*n3*u3**2*v3 + 180*a33*b33**2*k1*n3*u3*v1*
v3 - 216*a33*b33*k1*n1**2*u1*u3 + 108*a33*b33*k1*n1**2*v1**2 - 432*a33*b33*k1*n1
*n3*u3**2 - 324*a33*b33*k1*n1*n3*u3*v2 - 54*a33*b33*k1*n1*n3*v2 + 432*a33*b33*k1
*n3**2*u1*u3 + 432*a33*b33*k1*n3**2*v1**2 - 162*a33*k1*n1**3*u1 - 162*a33*k1*n1
**2*n3*u3 + 162*a33*k1*n1*n3**2*u1 + 162*a33*k1*n3**3*u3 + 7*b33**4*k1*u1*v1*v3
**2 + 4*b33**4*k1*u2*v2*v3**2 + 7*b33**4*k1*u2*v3**3 + 14*b33**4*k1*v1**2*v3**2
+ 4*b33**4*k1*v1*v3**3 - 30*b33**3*k1*n1*u2*v2*v3 - 6*b33**3*k1*n1*u2*v3**2 - 30
*b33**3*k1*n1*v2**2*v3 - 60*b33**3*k1*n3*v1*v2*v3 - 60*b33**3*k1*n3*v1*v3**2 -
24*b33**3*k1*n3*v3**3 + 36*b33**2*k1*n1**2*u1*v3 - 9*b33**2*k1*n1**2*v1*v3 + 144
*b33**2*k1*n1*n3*u3*v3 - 108*b33**2*k1*n3**2*u1*v3 - 108*b33**2*k1*n3**2*v1*v3 +
27*b33*k1*n1**3*v1 + 54*b33*k1*n1**2*n3*v3 + 27*b33*k1*n1*n3**2*v1)/(3888*a33**
4)$