Solution 3 to problem e3null
Expressions |
Parameters |
Inequalities |
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Back to problem e3null
Expressions
The solution is given through the following expressions:
a22= - a33
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
2
b33
c33=-------
4*a33
m1=0
m2=0
b33*n3
m3=--------
2*a33
2 2 2 2 2 2
4*a33 *k1*n3*p16 - 4*a33 *k10*n3*p16 - b33 *k20 *n3*q1
r6=----------------------------------------------------------
2 2
2*a33 *b33*k20
4 2 4 2 2 2 2
r5=(16*a33 *k1*n2*p16 - 16*a33 *k10*n2*p16 - 4*a33 *b33 *k20 *n2*q1
2 2 2 2 2 2 4 2
+ b33 *k1*k20 *n2*n3 - b33 *k10*k20 *n2*n3 )/(16*a33 *b33*k20 )
4 3 4 3 2 2 2
r4=( - 16*a33 *k1*p16 + 16*a33 *k10*p16 + 4*a33 *b33 *k20 *p16*q1
2 2 2 2 2 2 2 2 3
- b33 *k1*k20 *n3 *p16 + b33 *k10*k20 *n3 *p16)/(4*a33 *b33 *k20 )
4 2 4 2 2 2 2
r3=(16*a33 *k1*n3*p16 - 16*a33 *k10*n3*p16 - 4*a33 *b33 *k20 *n3*q1
2 2 3 2 2 3 3 2 2
- b33 *k1*k20 *n3 + b33 *k10*k20 *n3 )/(8*a33 *b33 *k20 )
4 2 4 2 2 2 2
r2=(16*a33 *k1*n2*p16 - 16*a33 *k10*n2*p16 - 4*a33 *b33 *k20 *n2*q1
2 2 2 2 2 2 3 2 2
- b33 *k1*k20 *n2*n3 + b33 *k10*k20 *n2*n3 )/(8*a33 *b33 *k20 )
4 3 4 3 2 2 2
r1=( - 16*a33 *k1*p16 + 16*a33 *k10*p16 + 4*a33 *b33 *k20 *p16*q1
2 2 2 2 2 2 3 3
+ b33 *k1*k20 *n3 *p16 - b33 *k10*k20 *n3 *p16)/(2*a33*b33 *k20 )
2 2
2*b33 *k1*n2*n3 + b33 *k10*n2*n3
q19=----------------------------------
4
8*a33
- 2*b33*k1*n3*p16 - b33*k10*n3*p16
q18=-------------------------------------
2
2*a33 *k20
4 2 2 2 2 2 2 2
q17=( - 16*a33 *k10*p16 - 4*a33 *b33 *k20 *q1 + 2*b33 *k1*k20 *n3
2 2 2 3 2
- b33 *k10*k20 *n3 )/(4*a33 *b33*k20 )
2*b33*k1*n2*n3 - b33*k10*n2*n3
q16=--------------------------------
3
4*a33
- 2*k1*n3*p16 + k10*n3*p16
q15=-----------------------------
a33*k20
4 2 4 2 2 2 2
q14=( - 16*a33 *k1*p16 + 16*a33 *k10*p16 + 4*a33 *b33 *k20 *q1
2 2 2 2 2 2 2 2 2 4 2
+ b33 *k1*k20 *n2 - 4*b33 *k1*k20 *n3 + b33 *k10*k20 *n2 )/(16*a33 *k20
)
- b33*k1*n2*p16 - b33*k10*n2*p16
q13=-----------------------------------
2
2*a33 *k20
b33*k1*n2*n3
q12=--------------
3
4*a33
4 2 2 2 2
- 16*a33 *k1*p16 + b33 *k1*k20 *n2
q11=---------------------------------------
3 2
4*a33 *b33*k20
- k1*n2*p16
q10=--------------
a33*k20
4 2 2 2 2 2 2 2
8*a33 *k10*p16 + a33 *b33 *k20 *q1 - b33 *k1*k20 *n3
q9=--------------------------------------------------------
4 2
4*a33 *k20
- k1*n3*p16
q8=--------------
a33*k20
- k1*n2*p16
q7=--------------
a33*k20
k1*n2*n3 - k10*n2*n3
q5=----------------------
2
2*a33
- 2*k1*n3*p16 + 2*k10*n3*p16
q4=-------------------------------
b33*k20
4 2 4 2 2 2 2
q3=( - 16*a33 *k1*p16 + 16*a33 *k10*p16 + 4*a33 *b33 *k20 *q1
2 2 2 2 2 2 2 2 2
+ b33 *k1*k20 *n2 - b33 *k10*k20 *n2 )/(4*a33 *b33 *k20 )
- 2*k1*n2*p16 + 2*k10*n2*p16
q2=-------------------------------
b33*k20
2 3
- 2*a33 *b33*k20*n3 + b33 *k1*n3
p50=-----------------------------------
4
4*a33
2 3 3
- 4*a33 *b33*k20*n2 + 2*b33 *k1*n2 + b33 *k10*n2
p49=---------------------------------------------------
4
16*a33
2 2 2
4*a33 *k20*p16 - 2*b33 *k1*p16 - b33 *k10*p16
p48=-----------------------------------------------
2
4*a33 *k20
2 2 2
- 4*a33 *k20*n3 + 10*b33 *k1*n3 - b33 *k10*n3
p47=------------------------------------------------
3
8*a33
2 2 2
- 4*a33 *k20*n2 + 2*b33 *k1*n2 - b33 *k10*n2
p46=-----------------------------------------------
3
8*a33
2 2 2
4*a33 *k20*p16 - 2*b33 *k1*p16 + b33 *k10*p16
p45=-----------------------------------------------
2*a33*b33*k20
- b33*k20*n3
p44=---------------
2
2*a33
p43=0
2 2
2*b33 *k1*n2 + b33 *k10*n2
p42=----------------------------
3
4*a33
p41=0
p40=0
- b33*k20*n3
p39=---------------
2
2*a33
2 2 2
- 2*a33 *k20*p16 - 2*b33 *k1*p16 - b33 *k10*p16
p38=--------------------------------------------------
a33*b33*k20
p37=0
b33*k1*n3 - b33*k10*n3
p36=------------------------
2
a33
2*b33*k1*n2 - b33*k10*n2
p35=--------------------------
2
2*a33
- 6*k1*p16 + k10*p16
p34=-----------------------
k20
- b33*k1*n3
p33=--------------
2
a33
p32=0
- b33*k1*n3
p31=--------------
2
a33
- b33*k20*n2
p30=---------------
2
4*a33
p29=p16
- k20*n3
p28=-----------
2*a33
- k20*n2
p27=-----------
2*a33
2*a33*p16
p26=-----------
b33
- b33*k20*n2
p25=---------------
2
4*a33
p24=0
- 2*a33*p16
p23=--------------
b33
- b33*k10*n2
p22=---------------
2
4*a33
p21=0
p20=0
- 2*b33*k1*n2 - b33*k10*n2
p19=-----------------------------
2
4*a33
- 2*k1*p16 - k10*p16
p18=-----------------------
k20
- 2*b33*k1*n2 - b33*k10*n2
p17=-----------------------------
2
4*a33
- k20*n3
p15=-----------
2*a33
- k20*n2
p14=-----------
2*a33
k10*p16
p13=---------
k20
p12=0
2*k1*p16 + k10*p16
p11=--------------------
k20
- k10*n3
p10=-----------
2*a33
- k10*n2
p9=-----------
2*a33
2*a33*k10*p16
p8=---------------
b33*k20
- 2*k1*n3 + k10*n3
p7=---------------------
2*a33
p6=0
- 2*k1*n3 + k10*n3
p5=---------------------
2*a33
- 2*k1*n2 + k10*n2
p4=---------------------
2*a33
4*a33*k1*p16 - 2*a33*k10*p16
p3=------------------------------
b33*k20
- 2*k1*n2 + k10*n2
p2=---------------------
2*a33
4*a33*k1*p16 - 2*a33*k10*p16
p1=------------------------------
b33*k20
k104=0
k103=0
2 3
- 2*a33 *b33*k20 + b33 *k1
k102=-----------------------------
3
2*a33
k101=0
k100=0
2 2 4
2*a33 *b33 *k20 - b33 *k1
k99=---------------------------
4
8*a33
k98=0
k97=0
k96=0
k95=0
2 2 4
2*a33 *b33 *k20 - b33 *k1
k94=---------------------------
4
8*a33
k93=0
k92=0
2 2 2
4*a33 *k20 + 4*b33 *k1 - b33 *k10
k91=-----------------------------------
2
4*a33
k90=0
k89=0
2 2
2*a33 *k20 - b33 *k1
k88=----------------------
2
2*a33
k87=0
2 2
2*a33 *k20 - b33 *k1
k86=----------------------
2
2*a33
k85=0
k84=0
- b33*k20
k83=------------
a33
k82=0
k81=0
k80=0
k79=0
k78=0
k77=0
k76=2*k20
k75=0
k74=0
k73=0
k72=0
k71=0
- b33*k20
k70=------------
a33
k69=0
k68=0
k67=0
k66=0
- b33*k10
k65=------------
a33
k64=0
k63=0
- 2*b33*k1
k62=-------------
a33
k61=0
- 2*b33*k1
k60=-------------
a33
k59=0
k58=0
k57=0
k56=0
2 2 4
4*a33 *b33 *k20 - b33 *k1
k55=---------------------------
4
16*a33
k54=0
k53=0
k52=0
k51=0
2 2 4
4*a33 *b33 *k20 - b33 *k1
k50=---------------------------
4
8*a33
k49=0
k48=0
k47=0
k46=0
k45=0
k44=2*k20
k43=0
k42=k20
k41=0
k40=0
k39=0
k38=0
k37=0
k36=0
k35=0
k34=0
k33=0
k32=0
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
2 2 4
4*a33 *b33 *k20 - b33 *k1
k25=---------------------------
4
16*a33
k24=0
k23=0
k21=0
k19=0
k18=0
k17=0
k16=0
k14=0
k13=0
k12=k10
k11=0
k9=0
k8=0
k7=0
k6=0
k5=k1
k4=0
k3=2*k1
k2=0
2
- 4*a33 *p16
n1=---------------
b33*k20
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:
k20, q1, k10, k1, p16, b33, n3, n2, a33
Inequalities
In the following not identically vanishing expressions are shown.
Any auxiliary variables g00?? are used to express that at least
one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3
means that either p4 or p3 or both are non-vanishing.
{b33,a33,n2}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
3 2 2 2 2
HAM=( - 16*a33 *p16*u1 - 4*a33 *b33*k20*u1 - 4*a33 *b33*k20*u2
2 2 2
+ 4*a33 *b33*k20*u3 + 4*a33*b33 *k20*u3*v3 + 4*a33*b33*k20*n2*u2
3 2 2
+ 4*a33*b33*k20*n3*u3 + b33 *k20*v3 + 2*b33 *k20*n3*v3)/(4*a33*b33*k20)
has apart from the Hamiltonian and Casimirs the following first integrals:
7 3 6 2 2 6 3
INT= - 128*a33 *p16 *u1 - 64*a33 *b33*k20*p16 *u2 - 64*a33 *b33*p16 *v1
5 2 3 2 5 2 3 2
+ 32*a33 *b33 *k20 *p16*u1*v2 + 32*a33 *b33 *k20 *p16*u1*v3
5 2 3 5 2 3
- 32*a33 *b33 *k20 *p16*u2*v1*v2 - 32*a33 *b33 *k20 *p16*u3*v1*v3
5 2 2 3 5 2 2 2
+ 64*a33 *b33 *k20 *p16*u1 + 64*a33 *b33 *k20 *p16*u1*u2
5 2 2 5 2
- 64*a33 *b33 *k20*p16 *u2*v2 + 32*a33 *b33*k20*n2*p16 *u2
5 2 4 3 4 2 2
+ 32*a33 *b33*k20*n3*p16 *u3 + 16*a33 *b33 *k20 *u1 *v2
4 3 4 2 2 4 3 4 2 2
+ 16*a33 *b33 *k20 *u1 *v3 + 16*a33 *b33 *k20 *u2 *v1
4 3 4 2 2 4 3 4 2 2
+ 32*a33 *b33 *k20 *u2 *v2 + 16*a33 *b33 *k20 *u2 *v3
4 3 4 4 3 4 2 2
+ 32*a33 *b33 *k20 *u2*u3*v2*v3 + 16*a33 *b33 *k20 *u3 *v3
4 3 3 3 4 3 3 2
+ 16*a33 *b33 *k20 *p16*v1 + 16*a33 *b33 *k20 *p16*v1*v2
4 3 3 2 4 3 3 4
+ 16*a33 *b33 *k20 *p16*v1*v3 + 16*a33 *b33 *k20 *u1
4 3 3 2 2 4 3 3 4
+ 32*a33 *b33 *k20 *u1 *u2 + 16*a33 *b33 *k20 *u2
4 3 2 4 3 2
- 32*a33 *b33 *k20 *p16*u1*u2*v2 - 96*a33 *b33 *k20 *p16*u1*u3*v3
4 3 2 2 4 3 2 2
+ 32*a33 *b33 *k20 *p16*u2 *v1 - 16*a33 *b33 *k20*p16 *v2
4 2 2 4 2 2
- 32*a33 *b33 *k20 *n2*p16*u1*u2 - 32*a33 *b33 *k20 *n3*p16*u1*u3
4 2 2 4 2 2
+ 16*a33 *b33 *k20*n2*p16 *v2 + 32*a33 *b33 *k20*n3*p16 *v3
3 4 4 2 3 4 4 2
- 16*a33 *b33 *k20 *u3*v1 *v3 - 16*a33 *b33 *k20 *u3*v2 *v3
3 4 4 3 3 4 3 2
- 16*a33 *b33 *k20 *u3*v3 - 32*a33 *b33 *k20 *u1 *u3*v3
3 4 3 2 3 4 2 2
- 32*a33 *b33 *k20 *u2 *u3*v3 - 16*a33 *b33 *k20 *p16*u1*v3
3 4 2 3 3 4 2
- 32*a33 *b33 *k20 *p16*u3*v1*v3 - 8*a33 *b33 *k20 *n2*u2*v1
3 3 4 2 3 3 4 2
- 8*a33 *b33 *k20 *n2*u2*v2 - 8*a33 *b33 *k20 *n2*u2*v3
3 3 4 2 3 3 4 2
- 8*a33 *b33 *k20 *n3*u3*v1 - 8*a33 *b33 *k20 *n3*u3*v2
3 3 4 2 3 3 3 2
- 8*a33 *b33 *k20 *n3*u3*v3 - 16*a33 *b33 *k20 *n2*u1 *u2
3 3 3 3 3 3 3 2
- 16*a33 *b33 *k20 *n2*u2 - 16*a33 *b33 *k20 *n3*u1 *u3
3 3 3 2 3 3 2
- 16*a33 *b33 *k20 *n3*u2 *u3 - 16*a33 *b33 *k20 *n2*p16*u1*v2
3 3 2 3 3 2
- 16*a33 *b33 *k20 *n2*p16*u2*v1 - 32*a33 *b33 *k20 *n3*p16*u1*v3
3 3 2 3 2 2 2
- 16*a33 *b33 *k20 *n3*p16*u3*v1 + 8*a33 *b33 *k20 *n3 *p16*u1
2 5 4 4 2 5 4 2 2
+ 4*a33 *b33 *k20 *v1 + 8*a33 *b33 *k20 *v1 *v2
2 5 4 2 2 2 5 4 4
+ 4*a33 *b33 *k20 *v1 *v3 + 4*a33 *b33 *k20 *v2
2 5 4 2 2 2 5 3 2 2
+ 4*a33 *b33 *k20 *v2 *v3 - 8*a33 *b33 *k20 *u1 *v3
2 5 3 2 2 2 5 3 2 2
- 8*a33 *b33 *k20 *u2 *v3 + 16*a33 *b33 *k20 *u3 *v3
2 5 2 2 2 4 4 2
- 8*a33 *b33 *k20 *p16*v1*v3 - 4*a33 *b33 *k20 *n2*v1 *v2
2 4 4 3 2 4 4 2
- 4*a33 *b33 *k20 *n2*v2 - 4*a33 *b33 *k20 *n2*v2*v3
2 4 4 2 2 4 4 2
- 8*a33 *b33 *k20 *n3*v1 *v3 - 8*a33 *b33 *k20 *n3*v2 *v3
2 4 4 3 2 4 3 2
- 8*a33 *b33 *k20 *n3*v3 - 8*a33 *b33 *k20 *n2*u1 *v2
2 4 3 2 2 4 3
- 8*a33 *b33 *k20 *n2*u2 *v2 + 16*a33 *b33 *k20 *n2*u2*u3*v3
2 4 3 2 2 4 3 2
- 16*a33 *b33 *k20 *n3*u1 *v3 - 16*a33 *b33 *k20 *n3*u2 *v3
2 4 3 2 2 4 2
+ 16*a33 *b33 *k20 *n3*u3 *v3 - 8*a33 *b33 *k20 *n2*p16*v1*v2
2 4 2 2 3 3 2 2
- 16*a33 *b33 *k20 *n3*p16*v1*v3 + 4*a33 *b33 *k20 *n2 *u2
2 3 3 2 3 2 2
+ 8*a33 *b33 *k20 *n2*n3*u2*u3 - 4*a33 *b33 *k20 *n3 *p16*v1
6 3 3 5 3 2
+ 8*a33*b33 *k20 *u3*v3 + 4*a33*b33 *k20 *n2*u2*v3
5 3 5 3 2
+ 8*a33*b33 *k20 *n2*u3*v2*v3 + 20*a33*b33 *k20 *n3*u3*v3
4 3 2 4 3
+ 4*a33*b33 *k20 *n2 *u2*v2 + 8*a33*b33 *k20 *n2*n3*u2*v3
4 3 4 3 2
+ 4*a33*b33 *k20 *n2*n3*u3*v2 + 8*a33*b33 *k20 *n3 *u3*v3
3 3 2 3 3 3 7 3 4
- 2*a33*b33 *k20 *n2*n3 *u2 - 2*a33*b33 *k20 *n3 *u3 - b33 *k20 *v1
7 3 2 2 7 3 2 2 7 3 4
- 2*b33 *k20 *v1 *v2 - 2*b33 *k20 *v1 *v3 - b33 *k20 *v2
7 3 2 2 6 3 2 6 3 3
- 2*b33 *k20 *v2 *v3 + 2*b33 *k20 *n2*v2*v3 + 4*b33 *k20 *n3*v3
5 3 2 2 5 3 5 3 2 2
+ b33 *k20 *n2 *v2 + 4*b33 *k20 *n2*n3*v2*v3 - 4*b33 *k20 *n3 *v1
5 3 2 2 4 3 2
- 4*b33 *k20 *n3 *v2 + b33 *k20 *n2*n3 *v2
7 3 4 3 2
= - (128*a33 *p16 *u1 - b33 *k20 *n2*n3 *v2
2 2 2 2 2 7 3
+ (v1 + v2 + 2*v3 )*(v1 + v2 )*b33 *k20
6 3 2
- 2*(n2*v2 + 2*n3*v3)*b33 *k20 *v3
2 6 2
+ 64*(k20*u2 + p16*v1)*a33 *b33*p16
2 2 2 5 3
- ((n2*v2 + 4*n3*v3)*n2*v2 - 4*(v1 + v2 )*n3 )*b33 *k20 - 32*((
2 2
2*((u1 + u2 )*k20*u1 - p16*u2*v2)
2 2 2
- ((u2*v2 + u3*v3)*v1 - (v2 + v3 )*u1)*k20 )*b33
5
+ (n2*u2 + n3*u3)*p16)*a33 *b33*k20*p16 - 2*(
2 3 3
(2*(n2*v2 + 2*n3*v3)*b33 - n3 )*(n2*u2 + n3*u3) + 4*b33 *u3*v3
2 3 3
+ 2*((u2*v3 + 2*u3*v2)*n2 + 5*n3*u3*v3)*b33 *v3)*a33*b33 *k20 + 4*(
2 2 2 2
(2*(u2 - 2*u3 + u1 )*k20*v3
2 2 2 2 2 2 2 2
- ((v1 + v2 + v3 )*(v1 + v2 )*k20 - 2*p16*v1*v3 ))*b33
2
- ((n2*u2 + 2*n3*u3)*k20*n2*u2 - n3 *p16*v1) + (2*(
2
((u2*v2 - 2*u3*v3)*u2 + u1 *v2)*n2
2
+ 2*((u2 + u3)*(u2 - u3) + u1 )*n3*v3)*k20
2 2 2 2
+ ((v2 + v3 + v1 )*k20 + 2*p16*v1)*(n2*v2 + 2*n3*v3))*b33)
2 3 2 2 2
*a33 *b33 *k20 + 8*(2*(2*(u1 + u2 )*k20*u3 + (u1*v3 + 2*u3*v1)*p16
2 2 2 2 2 2
+ (v2 + v3 + v1 )*k20 *u3)*b33 *v3 - n3 *p16*u1 + (
2 2 2 2 2
((v2 + v3 + v1 )*k20 + 2*(u1 + u2 ))*(n2*u2 + n3*u3)*k20
3
+ 2*((u1*v2 + u2*v1)*n2 + (2*u1*v3 + u3*v1)*n3)*p16)*b33)*a33
2 2 2 2
*b33 *k20 + 16*(((2*((u2*v2 + 3*u3*v3)*u1 - u2 *v1)*k20 + p16*v2 )*p16
2 2 2 2 2 2 2
- ((v2 + v3 + v1 )*p16*v1 + (u1 + u2 ) )*k20 - (
2 2 2
(2*u2*v2 + u3*v3)*u3*v3 + (v2 + v3 )*u1
2 2 2 2 3
+ (2*v2 + v3 + v1 )*u2 )*k20 )*b33
4 2
+ (2*(n2*u2 + n3*u3)*k20*u1 - (n2*v2 + 2*n3*v3)*p16)*p16)*a33 *b33
*k20)
7 3 6 2 2 6 3
INT=128*a33 *p16 *u1 + 64*a33 *b33*k20*p16 *u2 + 64*a33 *b33*p16 *v1
5 2 3 2 5 2 3 2
+ 32*a33 *b33 *k20 *p16*u1*v2 + 32*a33 *b33 *k20 *p16*u1*v3
5 2 3 5 2 3
- 32*a33 *b33 *k20 *p16*u2*v1*v2 - 32*a33 *b33 *k20 *p16*u3*v1*v3
5 2 2 3 5 2 2 2
- 32*a33 *b33 *k20 *p16*u1 - 32*a33 *b33 *k20 *p16*u1*u2
5 2 2 2 5 2 2
+ 32*a33 *b33 *k20 *p16*u1*u3 - 64*a33 *b33 *k20*p16 *u3*v3
5 2 5 2
- 32*a33 *b33*k20*n2*p16 *u2 - 32*a33 *b33*k20*n3*p16 *u3
4 3 4 2 2 4 3 4 2 2
+ 16*a33 *b33 *k20 *u1 *v2 + 16*a33 *b33 *k20 *u1 *v3
4 3 4 2 2 4 3 4 2 2
+ 16*a33 *b33 *k20 *u2 *v1 + 32*a33 *b33 *k20 *u2 *v2
4 3 4 2 2 4 3 4
+ 16*a33 *b33 *k20 *u2 *v3 + 32*a33 *b33 *k20 *u2*u3*v2*v3
4 3 4 2 2 4 3 3 3
+ 16*a33 *b33 *k20 *u3 *v3 + 16*a33 *b33 *k20 *p16*v1
4 3 3 2 4 3 3 2
+ 16*a33 *b33 *k20 *p16*v1*v2 + 16*a33 *b33 *k20 *p16*v1*v3
4 3 3 2 2 4 3 3 2 2
+ 16*a33 *b33 *k20 *u1 *u3 + 16*a33 *b33 *k20 *u2 *u3
4 3 2 4 3 2
- 16*a33 *b33 *k20 *p16*u1*u2*v2 + 16*a33 *b33 *k20 *p16*u1*u3*v3
4 3 2 2 4 3 2 2
+ 16*a33 *b33 *k20 *p16*u2 *v1 + 16*a33 *b33 *k20 *p16*u3 *v1
4 3 2 2 4 3 2 2
+ 32*a33 *b33 *k20*p16 *v1 + 16*a33 *b33 *k20*p16 *v2
4 2 2 4 2 2
+ 32*a33 *b33 *k20 *n2*p16*u1*u2 + 32*a33 *b33 *k20 *n3*p16*u1*u3
4 2 2 4 2 2
- 16*a33 *b33 *k20*n2*p16 *v2 - 32*a33 *b33 *k20*n3*p16 *v3
3 4 4 2 3 4 4 2
- 16*a33 *b33 *k20 *u3*v1 *v3 - 16*a33 *b33 *k20 *u3*v2 *v3
3 4 4 3 3 4 3 3
- 16*a33 *b33 *k20 *u3*v3 - 16*a33 *b33 *k20 *u3 *v3
3 4 2 2 3 4 2
+ 8*a33 *b33 *k20 *p16*u1*v3 - 16*a33 *b33 *k20 *p16*u3*v1*v3
3 3 4 2 3 3 4 2
- 8*a33 *b33 *k20 *n2*u2*v1 - 8*a33 *b33 *k20 *n2*u2*v2
3 3 4 2 3 3 4 2
- 8*a33 *b33 *k20 *n2*u2*v3 - 8*a33 *b33 *k20 *n3*u3*v1
3 3 4 2 3 3 4 2
- 8*a33 *b33 *k20 *n3*u3*v2 - 8*a33 *b33 *k20 *n3*u3*v3
3 3 3 2 3 3 3 3
+ 8*a33 *b33 *k20 *n2*u1 *u2 + 8*a33 *b33 *k20 *n2*u2
3 3 3 2 3 3 3 2
- 8*a33 *b33 *k20 *n2*u2*u3 + 8*a33 *b33 *k20 *n3*u1 *u3
3 3 3 2 3 3 3 3
+ 8*a33 *b33 *k20 *n3*u2 *u3 - 8*a33 *b33 *k20 *n3*u3
3 3 2 3 2 2 2
+ 16*a33 *b33 *k20 *n3*p16*u1*v3 - 8*a33 *b33 *k20 *n3 *p16*u1
2 5 4 4 2 5 4 2 2
+ 4*a33 *b33 *k20 *v1 + 8*a33 *b33 *k20 *v1 *v2
2 5 4 2 2 2 5 4 4
+ 4*a33 *b33 *k20 *v1 *v3 + 4*a33 *b33 *k20 *v2
2 5 4 2 2 2 5 3 2 2
+ 4*a33 *b33 *k20 *v2 *v3 - 4*a33 *b33 *k20 *u3 *v3
2 5 2 2 2 4 4 2
- 4*a33 *b33 *k20 *p16*v1*v3 - 4*a33 *b33 *k20 *n2*v1 *v2
2 4 4 3 2 4 4 2
- 4*a33 *b33 *k20 *n2*v2 - 4*a33 *b33 *k20 *n2*v2*v3
2 4 4 2 2 4 4 2
- 8*a33 *b33 *k20 *n3*v1 *v3 - 8*a33 *b33 *k20 *n3*v2 *v3
2 4 4 3 2 4 3 2
- 8*a33 *b33 *k20 *n3*v3 - 4*a33 *b33 *k20 *n2*u1 *v2
2 4 3 2 2 4 3
- 4*a33 *b33 *k20 *n2*u2 *v2 - 8*a33 *b33 *k20 *n2*u2*u3*v3
2 4 3 2 2 4 3 2
- 4*a33 *b33 *k20 *n2*u3 *v2 - 16*a33 *b33 *k20 *n3*u3 *v3
2 4 2 2 4 2
- 8*a33 *b33 *k20 *n2*p16*v1*v2 - 8*a33 *b33 *k20 *n3*p16*v1*v3
2 3 3 2 2 2 3 3
- 4*a33 *b33 *k20 *n2 *u2 - 8*a33 *b33 *k20 *n2*n3*u2*u3
2 3 2 2 5 3 2
+ 4*a33 *b33 *k20 *n3 *p16*v1 - 2*a33*b33 *k20 *n2*u2*v3
5 3 5 3 2
+ 4*a33*b33 *k20 *n2*u3*v2*v3 - 2*a33*b33 *k20 *n3*u3*v3
4 3 4 3 2
- 4*a33*b33 *k20 *n2*n3*u2*v3 - 4*a33*b33 *k20 *n3 *u3*v3
3 3 2 3 3 3 6 3 2
+ 2*a33*b33 *k20 *n2*n3 *u2 + 2*a33*b33 *k20 *n3 *u3 + b33 *k20 *n2*v2*v3
5 3 2 2 5 3 4 3 2
+ b33 *k20 *n2 *v2 + 2*b33 *k20 *n2*n3*v2*v3 - b33 *k20 *n2*n3 *v2
4 3 7 3
=(b33*v3 + n3)*(b33*v3 - n3)*b33 *k20 *n2*v2 + 128*a33 *p16 *u1
5 3 2 6 2
+ (n2*v2 + 2*n3*v3)*b33 *k20 *n2*v2 + 64*(k20*u2 + p16*v1)*a33 *b33*p16 -
2
2*(((u2*v3 - 2*u3*v2)*n2 + n3*u3*v3)*b33 *v3
3 3
+ (2*b33*v3 - n3)*(n2*u2 + n3*u3)*n3)*a33*b33 *k20 - 32*((
2
((u2 + u3)*(u2 - u3) + u1 )*k20*u1 + 2*p16*u3*v3
2 2 2
+ ((u2*v2 + u3*v3)*v1 - (v2 + v3 )*u1)*k20 )*b33
5
+ (n2*u2 + n3*u3)*p16)*a33 *b33*k20*p16 - 4*((
2 2 2 2
((u2 *v2 + 2*u2*u3*v3 + u3 *v2 + u1 *v2)*n2 + 4*n3*u3 *v3)*k20
2 2 2 2
+ (v2 + v3 + v1 )*(n2*v2 + 2*n3*v3)*k20 + 2*(n2*v2 + n3*v3)*p16*v1
)*b33
2 2 2 2 2 2 2 2 2
+ ((k20*u3 + p16*v1)*v3 - (v1 + v2 + v3 )*(v1 + v2 )*k20 )*b33
2 2 3 2
+ (n2*u2 + 2*n3*u3)*k20*n2*u2 - n3 *p16*v1)*a33 *b33 *k20 + 8*(
3 2 2 2 2 2
((u1*v3 - 2*u3*v1)*p16 - 2*k20*u3 - 2*(v2 + v3 + v1 )*k20 *u3)*b33 *v3
2 2 2 2 2
- n3 *p16*u1 - ((v2 + v3 + v1 )*(n2*u2 + n3*u3)*k20 - 2*n3*p16*u1*v3
2 3 2
- ((u2 + u3)*(u2 - u3) + u1 )*(n2*u2 + n3*u3)*k20)*b33)*a33 *b33
2 2 2 2 2
*k20 + 16*(((((u2 + u3 )*v1 - (u2*v2 - u3*v3)*u1)*k20 + (2*v1 + v2 )*p16)
2 2 2 2 2 2 2
*p16 + ((v2 + v3 + v1 )*p16*v1 + (u1 + u2 )*u3 )*k20 + (
2 2 2
(2*u2*v2 + u3*v3)*u3*v3 + (v2 + v3 )*u1
2 2 2 2 3
+ (2*v2 + v3 + v1 )*u2 )*k20 )*b33
4
+ (2*(n2*u2 + n3*u3)*k20*u1 - (n2*v2 + 2*n3*v3)*p16)*p16)*a33
2
*b33 *k20
3 2 3 2 3
INT=8*a33 *k20*p16*u1*v2 + 8*a33 *k20*p16*u1*v3 - 8*a33 *k20*p16*u2*v1*v2
3 3 2 2 2 2
- 8*a33 *k20*p16*u3*v1*v3 + 8*a33 *p16*u1 + 4*a33 *b33*k20 *u1 *v2
2 2 2 2 2 2 2 2
+ 4*a33 *b33*k20 *u1 *v3 + 4*a33 *b33*k20 *u2 *v1
2 2 2 2 2 2 2 2
+ 8*a33 *b33*k20 *u2 *v2 + 4*a33 *b33*k20 *u2 *v3
2 2 2 2 2 2
+ 8*a33 *b33*k20 *u2*u3*v2*v3 + 4*a33 *b33*k20 *u3 *v3
2 3 2 2
+ 4*a33 *b33*k20*p16*v1 + 4*a33 *b33*k20*p16*v1*v2
2 2 2 2 2 2
+ 4*a33 *b33*k20*p16*v1*v3 + 4*a33 *b33*k20*u1 + 4*a33 *b33*k20*u2
2 2 2 2 2 2 2
+ 4*a33 *b33*p16*v1 - 4*a33*b33 *k20 *u3*v1 *v3 - 4*a33*b33 *k20 *u3*v2 *v3
2 2 3 2 2 2
- 4*a33*b33 *k20 *u3*v3 - 4*a33*b33 *k20*u3*v3 - 2*a33*b33*k20 *n2*u2*v1
2 2 2 2
- 2*a33*b33*k20 *n2*u2*v2 - 2*a33*b33*k20 *n2*u2*v3
2 2 2 2
- 2*a33*b33*k20 *n3*u3*v1 - 2*a33*b33*k20 *n3*u3*v2
2 2
- 2*a33*b33*k20 *n3*u3*v3 - 2*a33*b33*k20*n2*u2 - 2*a33*b33*k20*n3*u3
3 2 4 3 2 2 2 3 2 2 2 3 2 4
+ b33 *k20 *v1 + 2*b33 *k20 *v1 *v2 + b33 *k20 *v1 *v3 + b33 *k20 *v2
3 2 2 2 3 2 3 2 2 2 2
+ b33 *k20 *v2 *v3 + b33 *k20*v1 + b33 *k20*v2 - b33 *k20 *n2*v1 *v2
2 2 3 2 2 2 2 2 2
- b33 *k20 *n2*v2 - b33 *k20 *n2*v2*v3 - 2*b33 *k20 *n3*v1 *v3
2 2 2 2 2 3 2
- 2*b33 *k20 *n3*v2 *v3 - 2*b33 *k20 *n3*v3 - b33 *k20*n2*v2
2
- 2*b33 *k20*n3*v3
2 2 2 2 2
=4*(((v2 + v3 + v1 )*p16*v1 + u1 + u2 )*k20 + p16*v1 +
2 2 2 2 2 2 2
((2*u2*v2 + u3*v3)*u3*v3 + (v2 + v3 )*u1 + (2*v2 + v3 + v1 )*u2 )
2 2
*k20 )*a33 *b33 - (
2 2 3
8*(((u2*v2 + u3*v3)*v1 - (v2 + v3 )*u1)*k20 - u1)*a33 *p16 + (
2 2 2 2
4*a33*b33*u3*v3 + 2*a33*n2*u2 + 2*a33*n3*u3 - b33 *v1 - b33 *v2
2 2 2
+ b33*n2*v2 + 2*b33*n3*v3)*(k20*v1 + k20*v2 + k20*v3 + 1)*b33*k20)
And again in machine readable form:
HAM=( - 16*a33**3*p16*u1 - 4*a33**2*b33*k20*u1**2 - 4*a33**2*b33*k20*u2**2 + 4*
a33**2*b33*k20*u3**2 + 4*a33*b33**2*k20*u3*v3 + 4*a33*b33*k20*n2*u2 + 4*a33*b33*
k20*n3*u3 + b33**3*k20*v3**2 + 2*b33**2*k20*n3*v3)/(4*a33*b33*k20)$
INT= - 128*a33**7*p16**3*u1 - 64*a33**6*b33*k20*p16**2*u2**2 - 64*a33**6*b33*p16
**3*v1 + 32*a33**5*b33**2*k20**3*p16*u1*v2**2 + 32*a33**5*b33**2*k20**3*p16*u1*
v3**2 - 32*a33**5*b33**2*k20**3*p16*u2*v1*v2 - 32*a33**5*b33**2*k20**3*p16*u3*v1
*v3 + 64*a33**5*b33**2*k20**2*p16*u1**3 + 64*a33**5*b33**2*k20**2*p16*u1*u2**2 -
64*a33**5*b33**2*k20*p16**2*u2*v2 + 32*a33**5*b33*k20*n2*p16**2*u2 + 32*a33**5*
b33*k20*n3*p16**2*u3 + 16*a33**4*b33**3*k20**4*u1**2*v2**2 + 16*a33**4*b33**3*
k20**4*u1**2*v3**2 + 16*a33**4*b33**3*k20**4*u2**2*v1**2 + 32*a33**4*b33**3*k20
**4*u2**2*v2**2 + 16*a33**4*b33**3*k20**4*u2**2*v3**2 + 32*a33**4*b33**3*k20**4*
u2*u3*v2*v3 + 16*a33**4*b33**3*k20**4*u3**2*v3**2 + 16*a33**4*b33**3*k20**3*p16*
v1**3 + 16*a33**4*b33**3*k20**3*p16*v1*v2**2 + 16*a33**4*b33**3*k20**3*p16*v1*v3
**2 + 16*a33**4*b33**3*k20**3*u1**4 + 32*a33**4*b33**3*k20**3*u1**2*u2**2 + 16*
a33**4*b33**3*k20**3*u2**4 - 32*a33**4*b33**3*k20**2*p16*u1*u2*v2 - 96*a33**4*
b33**3*k20**2*p16*u1*u3*v3 + 32*a33**4*b33**3*k20**2*p16*u2**2*v1 - 16*a33**4*
b33**3*k20*p16**2*v2**2 - 32*a33**4*b33**2*k20**2*n2*p16*u1*u2 - 32*a33**4*b33**
2*k20**2*n3*p16*u1*u3 + 16*a33**4*b33**2*k20*n2*p16**2*v2 + 32*a33**4*b33**2*k20
*n3*p16**2*v3 - 16*a33**3*b33**4*k20**4*u3*v1**2*v3 - 16*a33**3*b33**4*k20**4*u3
*v2**2*v3 - 16*a33**3*b33**4*k20**4*u3*v3**3 - 32*a33**3*b33**4*k20**3*u1**2*u3*
v3 - 32*a33**3*b33**4*k20**3*u2**2*u3*v3 - 16*a33**3*b33**4*k20**2*p16*u1*v3**2
- 32*a33**3*b33**4*k20**2*p16*u3*v1*v3 - 8*a33**3*b33**3*k20**4*n2*u2*v1**2 - 8*
a33**3*b33**3*k20**4*n2*u2*v2**2 - 8*a33**3*b33**3*k20**4*n2*u2*v3**2 - 8*a33**3
*b33**3*k20**4*n3*u3*v1**2 - 8*a33**3*b33**3*k20**4*n3*u3*v2**2 - 8*a33**3*b33**
3*k20**4*n3*u3*v3**2 - 16*a33**3*b33**3*k20**3*n2*u1**2*u2 - 16*a33**3*b33**3*
k20**3*n2*u2**3 - 16*a33**3*b33**3*k20**3*n3*u1**2*u3 - 16*a33**3*b33**3*k20**3*
n3*u2**2*u3 - 16*a33**3*b33**3*k20**2*n2*p16*u1*v2 - 16*a33**3*b33**3*k20**2*n2*
p16*u2*v1 - 32*a33**3*b33**3*k20**2*n3*p16*u1*v3 - 16*a33**3*b33**3*k20**2*n3*
p16*u3*v1 + 8*a33**3*b33**2*k20**2*n3**2*p16*u1 + 4*a33**2*b33**5*k20**4*v1**4 +
8*a33**2*b33**5*k20**4*v1**2*v2**2 + 4*a33**2*b33**5*k20**4*v1**2*v3**2 + 4*a33
**2*b33**5*k20**4*v2**4 + 4*a33**2*b33**5*k20**4*v2**2*v3**2 - 8*a33**2*b33**5*
k20**3*u1**2*v3**2 - 8*a33**2*b33**5*k20**3*u2**2*v3**2 + 16*a33**2*b33**5*k20**
3*u3**2*v3**2 - 8*a33**2*b33**5*k20**2*p16*v1*v3**2 - 4*a33**2*b33**4*k20**4*n2*
v1**2*v2 - 4*a33**2*b33**4*k20**4*n2*v2**3 - 4*a33**2*b33**4*k20**4*n2*v2*v3**2
- 8*a33**2*b33**4*k20**4*n3*v1**2*v3 - 8*a33**2*b33**4*k20**4*n3*v2**2*v3 - 8*
a33**2*b33**4*k20**4*n3*v3**3 - 8*a33**2*b33**4*k20**3*n2*u1**2*v2 - 8*a33**2*
b33**4*k20**3*n2*u2**2*v2 + 16*a33**2*b33**4*k20**3*n2*u2*u3*v3 - 16*a33**2*b33
**4*k20**3*n3*u1**2*v3 - 16*a33**2*b33**4*k20**3*n3*u2**2*v3 + 16*a33**2*b33**4*
k20**3*n3*u3**2*v3 - 8*a33**2*b33**4*k20**2*n2*p16*v1*v2 - 16*a33**2*b33**4*k20
**2*n3*p16*v1*v3 + 4*a33**2*b33**3*k20**3*n2**2*u2**2 + 8*a33**2*b33**3*k20**3*
n2*n3*u2*u3 - 4*a33**2*b33**3*k20**2*n3**2*p16*v1 + 8*a33*b33**6*k20**3*u3*v3**3
+ 4*a33*b33**5*k20**3*n2*u2*v3**2 + 8*a33*b33**5*k20**3*n2*u3*v2*v3 + 20*a33*
b33**5*k20**3*n3*u3*v3**2 + 4*a33*b33**4*k20**3*n2**2*u2*v2 + 8*a33*b33**4*k20**
3*n2*n3*u2*v3 + 4*a33*b33**4*k20**3*n2*n3*u3*v2 + 8*a33*b33**4*k20**3*n3**2*u3*
v3 - 2*a33*b33**3*k20**3*n2*n3**2*u2 - 2*a33*b33**3*k20**3*n3**3*u3 - b33**7*k20
**3*v1**4 - 2*b33**7*k20**3*v1**2*v2**2 - 2*b33**7*k20**3*v1**2*v3**2 - b33**7*
k20**3*v2**4 - 2*b33**7*k20**3*v2**2*v3**2 + 2*b33**6*k20**3*n2*v2*v3**2 + 4*b33
**6*k20**3*n3*v3**3 + b33**5*k20**3*n2**2*v2**2 + 4*b33**5*k20**3*n2*n3*v2*v3 -
4*b33**5*k20**3*n3**2*v1**2 - 4*b33**5*k20**3*n3**2*v2**2 + b33**4*k20**3*n2*n3
**2*v2$
INT=128*a33**7*p16**3*u1 + 64*a33**6*b33*k20*p16**2*u2**2 + 64*a33**6*b33*p16**3
*v1 + 32*a33**5*b33**2*k20**3*p16*u1*v2**2 + 32*a33**5*b33**2*k20**3*p16*u1*v3**
2 - 32*a33**5*b33**2*k20**3*p16*u2*v1*v2 - 32*a33**5*b33**2*k20**3*p16*u3*v1*v3
- 32*a33**5*b33**2*k20**2*p16*u1**3 - 32*a33**5*b33**2*k20**2*p16*u1*u2**2 + 32*
a33**5*b33**2*k20**2*p16*u1*u3**2 - 64*a33**5*b33**2*k20*p16**2*u3*v3 - 32*a33**
5*b33*k20*n2*p16**2*u2 - 32*a33**5*b33*k20*n3*p16**2*u3 + 16*a33**4*b33**3*k20**
4*u1**2*v2**2 + 16*a33**4*b33**3*k20**4*u1**2*v3**2 + 16*a33**4*b33**3*k20**4*u2
**2*v1**2 + 32*a33**4*b33**3*k20**4*u2**2*v2**2 + 16*a33**4*b33**3*k20**4*u2**2*
v3**2 + 32*a33**4*b33**3*k20**4*u2*u3*v2*v3 + 16*a33**4*b33**3*k20**4*u3**2*v3**
2 + 16*a33**4*b33**3*k20**3*p16*v1**3 + 16*a33**4*b33**3*k20**3*p16*v1*v2**2 +
16*a33**4*b33**3*k20**3*p16*v1*v3**2 + 16*a33**4*b33**3*k20**3*u1**2*u3**2 + 16*
a33**4*b33**3*k20**3*u2**2*u3**2 - 16*a33**4*b33**3*k20**2*p16*u1*u2*v2 + 16*a33
**4*b33**3*k20**2*p16*u1*u3*v3 + 16*a33**4*b33**3*k20**2*p16*u2**2*v1 + 16*a33**
4*b33**3*k20**2*p16*u3**2*v1 + 32*a33**4*b33**3*k20*p16**2*v1**2 + 16*a33**4*b33
**3*k20*p16**2*v2**2 + 32*a33**4*b33**2*k20**2*n2*p16*u1*u2 + 32*a33**4*b33**2*
k20**2*n3*p16*u1*u3 - 16*a33**4*b33**2*k20*n2*p16**2*v2 - 32*a33**4*b33**2*k20*
n3*p16**2*v3 - 16*a33**3*b33**4*k20**4*u3*v1**2*v3 - 16*a33**3*b33**4*k20**4*u3*
v2**2*v3 - 16*a33**3*b33**4*k20**4*u3*v3**3 - 16*a33**3*b33**4*k20**3*u3**3*v3 +
8*a33**3*b33**4*k20**2*p16*u1*v3**2 - 16*a33**3*b33**4*k20**2*p16*u3*v1*v3 - 8*
a33**3*b33**3*k20**4*n2*u2*v1**2 - 8*a33**3*b33**3*k20**4*n2*u2*v2**2 - 8*a33**3
*b33**3*k20**4*n2*u2*v3**2 - 8*a33**3*b33**3*k20**4*n3*u3*v1**2 - 8*a33**3*b33**
3*k20**4*n3*u3*v2**2 - 8*a33**3*b33**3*k20**4*n3*u3*v3**2 + 8*a33**3*b33**3*k20
**3*n2*u1**2*u2 + 8*a33**3*b33**3*k20**3*n2*u2**3 - 8*a33**3*b33**3*k20**3*n2*u2
*u3**2 + 8*a33**3*b33**3*k20**3*n3*u1**2*u3 + 8*a33**3*b33**3*k20**3*n3*u2**2*u3
- 8*a33**3*b33**3*k20**3*n3*u3**3 + 16*a33**3*b33**3*k20**2*n3*p16*u1*v3 - 8*
a33**3*b33**2*k20**2*n3**2*p16*u1 + 4*a33**2*b33**5*k20**4*v1**4 + 8*a33**2*b33
**5*k20**4*v1**2*v2**2 + 4*a33**2*b33**5*k20**4*v1**2*v3**2 + 4*a33**2*b33**5*
k20**4*v2**4 + 4*a33**2*b33**5*k20**4*v2**2*v3**2 - 4*a33**2*b33**5*k20**3*u3**2
*v3**2 - 4*a33**2*b33**5*k20**2*p16*v1*v3**2 - 4*a33**2*b33**4*k20**4*n2*v1**2*
v2 - 4*a33**2*b33**4*k20**4*n2*v2**3 - 4*a33**2*b33**4*k20**4*n2*v2*v3**2 - 8*
a33**2*b33**4*k20**4*n3*v1**2*v3 - 8*a33**2*b33**4*k20**4*n3*v2**2*v3 - 8*a33**2
*b33**4*k20**4*n3*v3**3 - 4*a33**2*b33**4*k20**3*n2*u1**2*v2 - 4*a33**2*b33**4*
k20**3*n2*u2**2*v2 - 8*a33**2*b33**4*k20**3*n2*u2*u3*v3 - 4*a33**2*b33**4*k20**3
*n2*u3**2*v2 - 16*a33**2*b33**4*k20**3*n3*u3**2*v3 - 8*a33**2*b33**4*k20**2*n2*
p16*v1*v2 - 8*a33**2*b33**4*k20**2*n3*p16*v1*v3 - 4*a33**2*b33**3*k20**3*n2**2*
u2**2 - 8*a33**2*b33**3*k20**3*n2*n3*u2*u3 + 4*a33**2*b33**3*k20**2*n3**2*p16*v1
- 2*a33*b33**5*k20**3*n2*u2*v3**2 + 4*a33*b33**5*k20**3*n2*u3*v2*v3 - 2*a33*b33
**5*k20**3*n3*u3*v3**2 - 4*a33*b33**4*k20**3*n2*n3*u2*v3 - 4*a33*b33**4*k20**3*
n3**2*u3*v3 + 2*a33*b33**3*k20**3*n2*n3**2*u2 + 2*a33*b33**3*k20**3*n3**3*u3 +
b33**6*k20**3*n2*v2*v3**2 + b33**5*k20**3*n2**2*v2**2 + 2*b33**5*k20**3*n2*n3*v2
*v3 - b33**4*k20**3*n2*n3**2*v2$
INT=8*a33**3*k20*p16*u1*v2**2 + 8*a33**3*k20*p16*u1*v3**2 - 8*a33**3*k20*p16*u2*
v1*v2 - 8*a33**3*k20*p16*u3*v1*v3 + 8*a33**3*p16*u1 + 4*a33**2*b33*k20**2*u1**2*
v2**2 + 4*a33**2*b33*k20**2*u1**2*v3**2 + 4*a33**2*b33*k20**2*u2**2*v1**2 + 8*
a33**2*b33*k20**2*u2**2*v2**2 + 4*a33**2*b33*k20**2*u2**2*v3**2 + 8*a33**2*b33*
k20**2*u2*u3*v2*v3 + 4*a33**2*b33*k20**2*u3**2*v3**2 + 4*a33**2*b33*k20*p16*v1**
3 + 4*a33**2*b33*k20*p16*v1*v2**2 + 4*a33**2*b33*k20*p16*v1*v3**2 + 4*a33**2*b33
*k20*u1**2 + 4*a33**2*b33*k20*u2**2 + 4*a33**2*b33*p16*v1 - 4*a33*b33**2*k20**2*
u3*v1**2*v3 - 4*a33*b33**2*k20**2*u3*v2**2*v3 - 4*a33*b33**2*k20**2*u3*v3**3 - 4
*a33*b33**2*k20*u3*v3 - 2*a33*b33*k20**2*n2*u2*v1**2 - 2*a33*b33*k20**2*n2*u2*v2
**2 - 2*a33*b33*k20**2*n2*u2*v3**2 - 2*a33*b33*k20**2*n3*u3*v1**2 - 2*a33*b33*
k20**2*n3*u3*v2**2 - 2*a33*b33*k20**2*n3*u3*v3**2 - 2*a33*b33*k20*n2*u2 - 2*a33*
b33*k20*n3*u3 + b33**3*k20**2*v1**4 + 2*b33**3*k20**2*v1**2*v2**2 + b33**3*k20**
2*v1**2*v3**2 + b33**3*k20**2*v2**4 + b33**3*k20**2*v2**2*v3**2 + b33**3*k20*v1
**2 + b33**3*k20*v2**2 - b33**2*k20**2*n2*v1**2*v2 - b33**2*k20**2*n2*v2**3 -
b33**2*k20**2*n2*v2*v3**2 - 2*b33**2*k20**2*n3*v1**2*v3 - 2*b33**2*k20**2*n3*v2
**2*v3 - 2*b33**2*k20**2*n3*v3**3 - b33**2*k20*n2*v2 - 2*b33**2*k20*n3*v3$