Solution 1 to problem e3null
Remaining equations |
Expressions |
Parameters |
Inequalities |
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Back to problem e3null
Equations
The following unsolved equations remain:
2 2
0=n1 + n2
Expressions
The solution is given through the following expressions:
b22=0
b33=0
c12=0
c13=0
c22=0
c23=0
c33=0
b31*m2
m1=--------
b32
2 2
- 2*b31 *n2 - 3*b32 *n2
m3=--------------------------
a22*b32
2 4 3 2 2 3
r6=( - 4*a22*b31 *b32*m2*n2*n3*p5 + 80*b31 *n2 *p5 + 167*b31 *b32 *n2 *p5
2 2 2 4 3 4 2 3 3
- 4*b31 *b32 *n2*n3 *p5 + 87*b32 *n2 *p5 - 6*b32 *n2*n3 *p5)/(4*a22 *b32
*n3)
2 2 2 2 3 2
- 4*a22*b31 *m2*n2 *p5 + 11*b31 *b32*n2 *n3*p5 + 9*b32 *n2 *n3*p5
r5=--------------------------------------------------------------------
3 2
4*a22 *b32 *n3
3 2 2 2 3 2
r4=(4*a22*b31 *m2*n2 *p5 - 4*a22*b31*b32 *m2*n2 *p5 + 13*b31 *b32*n2 *n3*p5
3 2 3 3
+ 17*b31*b32 *n2 *n3*p5)/(8*a22 *b32 *n3)
2 2 2 2
33*b31 *n2 *p5 + 33*b32 *n2 *p5
r3=---------------------------------
2 2
4*a22 *b32
2 3 2 3
33*b31 *n2 *p5 + 33*b32 *n2 *p5
r2=---------------------------------
2 2
4*a22 *b32 *n3
3 3 2 3
- 33*b31 *n2 *p5 - 33*b31*b32 *n2 *p5
r1=----------------------------------------
2 3
4*a22 *b32 *n3
2 2 2
q19=( - 27*a22*b31 *m2*n2*p5 - 27*a22*b32 *m2*n2*p5 - 15*b31 *b32*n2*n3*p5
3 3
- 15*b32 *n2*n3*p5)/(4*a22 *b32*n3)
3 2 3
q18=( - 13*a22*b31 *m2*n2*p5 - 13*a22*b31*b32 *m2*n2*p5 + 15*b31 *b32*n2*n3*p5
3 3 2
+ 15*b31*b32 *n2*n3*p5)/(4*a22 *b32 *n3)
2 2 3
- 4*a22*b31 *m2*n2*p5 + 11*b31 *b32*n2*n3*p5 + 12*b32 *n2*n3*p5
q17=------------------------------------------------------------------
2 2
2*a22 *b32 *n3
2 2 2 2
- a22*b32*m2*n3*p5 - 5*b31 *n2 *p5 - 5*b32 *n2 *p5
q16=-----------------------------------------------------
2
a22 *b32*n3
3 2 2 2
- a22*b31*b32*m2*n3*p5 + 5*b31 *n2 *p5 + 5*b31*b32 *n2 *p5
q15=-------------------------------------------------------------
2 2
a22 *b32 *n3
2 3 4 2
q14=( - 35*a22*b31 *b32*m2*n3*p5 - 35*a22*b32 *m2*n3*p5 + 20*b31 *n2 *p5
2 2 2 4 2 3 2
+ 26*b31 *b32 *n2 *p5 + 6*b32 *n2 *p5)/(12*a22 *b32 *n3)
q13=0
2 2 2 2
5*b31 *n2 *p5 + 9*b32 *n2 *p5
q12=-------------------------------
2
4*a22 *b32*n3
q11=0
- 4*a22*b31*m2*n2*p5 + b31*b32*n2*n3*p5
q10=------------------------------------------
2
2*a22 *b32*n3
2 3 4 2
q9=( - 35*a22*b31 *b32*m2*n3*p5 - 35*a22*b32 *m2*n3*p5 + 20*b31 *n2 *p5
2 2 2 4 2 3 2
+ 26*b31 *b32 *n2 *p5 + 6*b32 *n2 *p5)/(12*a22 *b32 *n3)
3 2 2 2
- 7*b31 *n2 *p5 - 11*b31*b32 *n2 *p5
q8=---------------------------------------
2 2
4*a22 *b32 *n3
4*a22*b31*m2*n2*p5 - b31*b32*n2*n3*p5
q7=---------------------------------------
2
2*a22 *b32*n3
- n2*p5
q5=----------
a22
b31*n2*p5
q4=-----------
a22*b32
2 2 2 2 2 2
- 33*b31 *n2 *p5 - 35*b32 *n2 *p5 + 2*b32 *n3 *p5
q3=----------------------------------------------------
2
4*a22*b32 *n3
2
b31*n2 *p5
q2=------------
a22*b32*n3
2 2 2 2 2 2
- 35*b31 *n2 *p5 - 33*b32 *n2 *p5 + 2*b32 *n3 *p5
q1=----------------------------------------------------
2
4*a22*b32 *n3
p50=0
p49=0
p48=0
p47=0
p46=0
p45=0
p44=0
p43=0
2 2
3*b31 *n2*p5 + 3*b32 *n2*p5
p42=-----------------------------
2
a22 *n3
p41=0
p40=0
p39=0
3 2
3*b31 *n2*p5 + 3*b31*b32 *n2*p5
p38=---------------------------------
2
a22 *b32*n3
p37=0
2 2
7*b31 *n2*p5 + 9*b32 *n2*p5
p36=-----------------------------
a22*b32*n3
- 2*a22*m2*p5 - b32*n3*p5
p35=----------------------------
a22*n3
- a22*b31*m2*p5 - b31*b32*n3*p5
p34=----------------------------------
a22*b32*n3
2 2
3*b31 *n2*p5 + 3*b32 *n2*p5
p33=-----------------------------
a22*b32*n3
p32=0
2 2
2*b31 *n2*p5 + 2*b32 *n2*p5
p31=-----------------------------
a22*b32*n3
p30=0
p29=0
p28=0
p27=0
p26=0
p25=0
p24=0
p23=0
p22=0
p21=0
- 2*b31*n2*p5
p20=----------------
a22*n3
- m2*p5
p19=----------
n3
b31*m2*p5
p18=-----------
b32*n3
- m2*p5
p17=----------
n3
p16=0
p15=0
p14=0
p13=0
2*b31*n2*p5
p12=-------------
a22*n3
- b31*m2*p5
p11=--------------
b32*n3
p10=0
p9=0
p8=0
p7=p5
p6=0
n2*p5
p4=-------
n3
- b31*n2*p5
p3=--------------
b32*n3
n2*p5
p2=-------
n3
- b31*n2*p5
p1=--------------
b32*n3
k104=0
k103=0
k102=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
k95=0
k94=0
k93=0
k92=0
k91=0
k90=0
k89=0
k88=0
k87=0
k86=0
k85=0
k84=0
k83=0
k82=0
k81=0
k80=0
k79=0
k78=0
k77=0
k76=0
k75=0
k74=0
k73=0
k72=0
k71=0
k70=0
k69=0
k68=0
k67=0
k66=0
k65=0
- 2*b32*p5
k64=-------------
n3
- b31*p5
k63=-----------
n3
k62=0
k61=0
k60=0
k59=0
k58=0
k57=0
k56=0
k55=0
k54=0
k53=0
k52=0
k51=0
k50=0
k49=0
k48=0
k47=0
k46=0
k45=0
k44=0
k43=0
k42=0
k41=0
k40=0
k39=0
k38=0
k37=0
k36=0
k35=0
k34=0
k33=0
- b32*p5
k32=-----------
n3
b31*p5
k31=--------
n3
- b32*p5
k30=-----------
n3
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k21=0
k20=0
k19=0
k18=0
- b31*p5
k17=-----------
n3
k16=0
k14=0
k13=0
k12=0
k11=0
k10=0
k9=0
k8=0
k7=0
k6=0
- a22*p5
k5=-----------
2*n3
k4=0
- a22*p5
k3=-----------
n3
k2=0
a33=2*a22
- b31*n2
n1=-----------
b32
- a22*p5
k1=-----------
2*n3
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:
p5, b32, a22, m2, b31, n3, n2
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.
{b31,a33,n3,k1}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2 2 2 2
HAM=(a22 *b32*u1 + a22 *b32*u2 + 2*a22 *b32*u3 + a22*b31*b32*u3*v1
2
+ a22*b31*m2*v1 - a22*b31*n2*u1 + a22*b32 *u3*v2 + a22*b32*m2*v2
2 2
+ a22*b32*n2*u2 + a22*b32*n3*u3 - 2*b31 *n2*v3 - 3*b32 *n2*v3)/(a22*b32)
has apart from the Hamiltonian and Casimirs the following only first integral:
4 3 4 4 3 2 2 4 3 4
INT= - 12*a22 *b32 *u1 - 24*a22 *b32 *u1 *u2 - 12*a22 *b32 *u2
3 3 3 3 2
+ 24*a22 *b31*b32 *u1*u2*u3*v2 - 24*a22 *b31*b32 *u1*u3 *v3
3 3 2 3 2
- 24*a22 *b31*b32 *u2 *u3*v1 + 24*a22 *b31*b32 *m2*u1*u2*v2
3 2 3 2 2
- 24*a22 *b31*b32 *m2*u1*u3*v3 - 24*a22 *b31*b32 *m2*u2 *v1
3 2 3 3 2 2
- 24*a22 *b31*b32 *n2*u1 - 24*a22 *b31*b32 *n2*u1*u2
3 4 2 3 4 2 3 4 2
- 24*a22 *b32 *u1 *u3*v2 - 24*a22 *b32 *u2 *u3*v2 - 48*a22 *b32 *u2*u3 *v3
3 3 2 3 3 2
- 24*a22 *b32 *m2*u1 *v2 - 24*a22 *b32 *m2*u2 *v2
3 3 3 3 2 3 3 3
- 48*a22 *b32 *m2*u2*u3*v3 + 24*a22 *b32 *n2*u1 *u2 + 24*a22 *b32 *n2*u2
3 3 2 3 3 2
+ 24*a22 *b32 *n3*u1 *u3 + 24*a22 *b32 *n3*u2 *u3
2 2 2 2 2 2 2 2
+ 48*a22 *b31 *b32 *n2*u1 *v3 + 72*a22 *b31 *b32 *n2*u2 *v3
2 2 2 2 2 2
+ 168*a22 *b31 *b32 *n2*u3 *v3 - 48*a22 *b31 *b32*m2*n2*u3*v3
2 2 2 2 2 2 2 2
- 210*a22 *b31 *b32*n2 *u1 - 198*a22 *b31 *b32*n2 *u2
2 3 2 3
- 48*a22 *b31*b32 *n2*u1*u3*v2 + 48*a22 *b31*b32 *n2*u2*u3*v1
2 3 2 2
- 24*a22 *b31*b32 *n3*u1*u3*v3 - 48*a22 *b31*b32 *m2*n2*u1*v2
2 2 2 2
+ 48*a22 *b31*b32 *m2*n2*u2*v1 - 24*a22 *b31*b32 *m2*n3*u1*v3
2 2 2 2 2
+ 24*a22 *b31*b32 *n2 *u1*u2 + 24*a22 *b31*b32 *n2*n3*u1*u3
2 4 2 2 4 2 2 4 2
+ 48*a22 *b32 *n2*u1 *v3 + 72*a22 *b32 *n2*u2 *v3 + 216*a22 *b32 *n2*u3 *v3
2 4 2 3
- 24*a22 *b32 *n3*u2*u3*v3 - 24*a22 *b32 *m2*n3*u2*v3
2 3 2 2 2 3 2 2 2 3
- 198*a22 *b32 *n2 *u1 - 210*a22 *b32 *n2 *u2 - 24*a22 *b32 *n2*n3*u2*u3
2 3 2 2 2 3 2 2
+ 12*a22 *b32 *n3 *u1 + 12*a22 *b32 *n3 *u2
3 2 3
+ 72*a22*b31 *b32 *n2*u3*v1*v3 - 78*a22*b31 *b32*m2*n2*v1*v3
3 2 3 2
+ 120*a22*b31 *b32*n2 *u1*v3 - 42*a22*b31 *b32*n2 *u3*v1
3 2 3 3
+ 12*a22*b31 *m2*n2 *v1 - 198*a22*b31 *n2 *u1
2 3 2 2
+ 72*a22*b31 *b32 *n2*u3*v2*v3 - 162*a22*b31 *b32 *m2*n2*v2*v3
2 2 2 2 2 2
- 70*a22*b31 *b32 *m2*n3*v1 - 70*a22*b31 *b32 *m2*n3*v2
2 2 2 2 2 2
- 120*a22*b31 *b32 *n2 *u2*v3 + 30*a22*b31 *b32 *n2 *u3*v2
2 2 2 2
+ 132*a22*b31 *b32 *n2*n3*u3*v3 - 24*a22*b31 *b32*m2*n2 *v2
2 2 3
- 24*a22*b31 *b32*m2*n2*n3*v3 + 198*a22*b31 *b32*n2 *u2
2 2 4
+ 198*a22*b31 *b32*n2 *n3*u3 + 72*a22*b31*b32 *n2*u3*v1*v3
3 3 2
- 78*a22*b31*b32 *m2*n2*v1*v3 + 120*a22*b31*b32 *n2 *u1*v3
3 2 3
- 66*a22*b31*b32 *n2 *u3*v1 + 12*a22*b31*b32 *n2*n3*u1*v2
3 2 2
- 12*a22*b31*b32 *n2*n3*u2*v1 - 12*a22*b31*b32 *m2*n2 *v1
2 3 5
- 198*a22*b31*b32 *n2 *u1 + 72*a22*b32 *n2*u3*v2*v3
4 4 2 4 2
- 162*a22*b32 *m2*n2*v2*v3 - 70*a22*b32 *m2*n3*v1 - 70*a22*b32 *m2*n3*v2
4 2 4 2 4
- 120*a22*b32 *n2 *u2*v3 + 54*a22*b32 *n2 *u3*v2 + 144*a22*b32 *n2*n3*u3*v3
3 3 3 2 4 2 2
+ 198*a22*b32 *n2 *u2 + 198*a22*b32 *n2 *n3*u3 + 40*b31 *b32*n2 *v1
4 2 2 4 3 3 2
+ 40*b31 *b32*n2 *v2 + 480*b31 *n2 *v3 + 90*b31 *b32 *n2*n3*v1*v3
3 2 2 3 2 2 2 3 2 2
+ 39*b31 *b32*n2 *n3*v1 + 52*b31 *b32 *n2 *v1 + 52*b31 *b32 *n2 *v2
2 3 2 2 3 2 2 2
- 90*b31 *b32 *n2*n3*v2*v3 + 1002*b31 *b32 *n2 *v3 + 66*b31 *b32 *n2 *n3*v2
2 2 2 4 3 2
- 24*b31 *b32 *n2*n3 *v3 + 90*b31*b32 *n2*n3*v1*v3 + 51*b31*b32 *n2 *n3*v1
5 2 2 5 2 2 5 4 3
+ 12*b32 *n2 *v1 + 12*b32 *n2 *v2 - 90*b32 *n2*n3*v2*v3 + 522*b32 *n2 *v3
4 2 4 2
+ 54*b32 *n2 *n3*v2 - 36*b32 *n2*n3 *v3
2 2 2 2 2 4
=3*(2*(3*(29*n2 *v3 + 3*n2*n3*v2 - 2*n3 *v3)*b32*n2 - 2*(u1 + u2 ) *a22 )
2 3
*b32 + (30*b32*v3 + 13*n2)*b31 *n2*n3*v1
2
+ (30*b32*v3 + 17*n2)*b31*b32 *n2*n3*v1
2 2 4
+ 2*(2*(v1 + v2 )*n2 - 15*n3*v2*v3)*b32 *n2)*b32
2 2 4 2
+ 40*((v1 + v2 )*b32 + 12*n2*v3)*b31 *n2 + 2*(
2 2
(26*(v1 + v2 )*n2 - 45*n3*v2*v3)*b32
2 2 2 2
+ 3*(167*n2 *v3 + 11*n2*n3*v2 - 4*n3 *v3))*b31 *b32 *n2 - 24*((
2 2 2
((u2*v2 + 2*u3*v3)*u2 + u1 *v2)*m2 - (n2*u2 + n3*u3)*(u1 + u2 )
2
+ ((u2*v2 + 2*u3*v3)*u2 + u1 *v2)*b32*u3)*b32 - (
2 2 2
((u2*v2 - u3*v3)*u1 - u2 *v1)*m2 - (u1 + u2 )*n2*u1
2 3 2
+ ((u2*v2 - u3*v3)*u1 - u2 *v1)*b32*u3)*b31)*a22 *b32 - 6*(
2 2 2 2 2
((35*u1 + 33*u2 )*n2 + 8*m2*u3*v3 - 4*(3*u2 + 7*u3 + 2*u1 )*b32*v3)
2 2 2 2 3
*b31 *n2 - 4*((3*(u2 + 3*u3 ) + 2*u1 )*n2 - n3*u2*u3)*b32 *v3 +
2 2 2 2 2
(2*(2*(m2*v3 + n2*u3)*u2 - (u1 + u2 )*n3)*n3 + (33*u1 + 35*u2 )*n2 )
2
*b32 + 4*((2*(u1*v2 - u2*v1)*n2 + n3*u1*v3)*m2 - (n2*u2 + n3*u3)*n2*u1
2
+ (2*(u1*v2 - u2*v1)*n2 + n3*u1*v3)*b32*u3)*b31*b32)*a22 *b32 - 2*(((
3*((20*u2*v3 - 9*u3*v2)*n2 - 24*n3*u3*v3)*n2
2 2
+ (35*(v1 + v2 )*n3 + 81*n2*v2*v3)*m2)*b32
2 3
- 9*(11*(n2*u2 + n3*u3)*n2 + 4*b32 *u3*v2*v3)*n2)*b32 - 3*(
2
(2*m2*v1 - 33*n2*u1)*n2 + 12*b32 *u3*v1*v3
3
+ ((20*u1*v3 - 7*u3*v1)*n2 - 13*m2*v1*v3)*b32)*b31 *n2 - 3*(
((20*u1*v3 - 11*u3*v1)*n2 - 13*m2*v1*v3 + 2*(u1*v2 - u2*v1)*n3)*b32
2 2
- ((2*m2*v1 + 33*n2*u1)*n2 - 12*b32 *u3*v1*v3))*b31*b32 *n2 - (
2
3*(33*(n2*u2 + n3*u3)*n2 - 4*(n2*v2 + n3*v3)*m2 + 12*b32 *u3*v2*v3)*n2
- (3*(5*(4*u2*v3 - u3*v2)*n2 - 22*n3*u3*v3)*n2
2 2 2
+ (35*(v1 + v2 )*n3 + 81*n2*v2*v3)*m2)*b32)*b31 *b32)*a22
And again in machine readable form:
HAM=(a22**2*b32*u1**2 + a22**2*b32*u2**2 + 2*a22**2*b32*u3**2 + a22*b31*b32*u3*
v1 + a22*b31*m2*v1 - a22*b31*n2*u1 + a22*b32**2*u3*v2 + a22*b32*m2*v2 + a22*b32*
n2*u2 + a22*b32*n3*u3 - 2*b31**2*n2*v3 - 3*b32**2*n2*v3)/(a22*b32)$
INT= - 12*a22**4*b32**3*u1**4 - 24*a22**4*b32**3*u1**2*u2**2 - 12*a22**4*b32**3*
u2**4 + 24*a22**3*b31*b32**3*u1*u2*u3*v2 - 24*a22**3*b31*b32**3*u1*u3**2*v3 - 24
*a22**3*b31*b32**3*u2**2*u3*v1 + 24*a22**3*b31*b32**2*m2*u1*u2*v2 - 24*a22**3*
b31*b32**2*m2*u1*u3*v3 - 24*a22**3*b31*b32**2*m2*u2**2*v1 - 24*a22**3*b31*b32**2
*n2*u1**3 - 24*a22**3*b31*b32**2*n2*u1*u2**2 - 24*a22**3*b32**4*u1**2*u3*v2 - 24
*a22**3*b32**4*u2**2*u3*v2 - 48*a22**3*b32**4*u2*u3**2*v3 - 24*a22**3*b32**3*m2*
u1**2*v2 - 24*a22**3*b32**3*m2*u2**2*v2 - 48*a22**3*b32**3*m2*u2*u3*v3 + 24*a22
**3*b32**3*n2*u1**2*u2 + 24*a22**3*b32**3*n2*u2**3 + 24*a22**3*b32**3*n3*u1**2*
u3 + 24*a22**3*b32**3*n3*u2**2*u3 + 48*a22**2*b31**2*b32**2*n2*u1**2*v3 + 72*a22
**2*b31**2*b32**2*n2*u2**2*v3 + 168*a22**2*b31**2*b32**2*n2*u3**2*v3 - 48*a22**2
*b31**2*b32*m2*n2*u3*v3 - 210*a22**2*b31**2*b32*n2**2*u1**2 - 198*a22**2*b31**2*
b32*n2**2*u2**2 - 48*a22**2*b31*b32**3*n2*u1*u3*v2 + 48*a22**2*b31*b32**3*n2*u2*
u3*v1 - 24*a22**2*b31*b32**3*n3*u1*u3*v3 - 48*a22**2*b31*b32**2*m2*n2*u1*v2 + 48
*a22**2*b31*b32**2*m2*n2*u2*v1 - 24*a22**2*b31*b32**2*m2*n3*u1*v3 + 24*a22**2*
b31*b32**2*n2**2*u1*u2 + 24*a22**2*b31*b32**2*n2*n3*u1*u3 + 48*a22**2*b32**4*n2*
u1**2*v3 + 72*a22**2*b32**4*n2*u2**2*v3 + 216*a22**2*b32**4*n2*u3**2*v3 - 24*a22
**2*b32**4*n3*u2*u3*v3 - 24*a22**2*b32**3*m2*n3*u2*v3 - 198*a22**2*b32**3*n2**2*
u1**2 - 210*a22**2*b32**3*n2**2*u2**2 - 24*a22**2*b32**3*n2*n3*u2*u3 + 12*a22**2
*b32**3*n3**2*u1**2 + 12*a22**2*b32**3*n3**2*u2**2 + 72*a22*b31**3*b32**2*n2*u3*
v1*v3 - 78*a22*b31**3*b32*m2*n2*v1*v3 + 120*a22*b31**3*b32*n2**2*u1*v3 - 42*a22*
b31**3*b32*n2**2*u3*v1 + 12*a22*b31**3*m2*n2**2*v1 - 198*a22*b31**3*n2**3*u1 +
72*a22*b31**2*b32**3*n2*u3*v2*v3 - 162*a22*b31**2*b32**2*m2*n2*v2*v3 - 70*a22*
b31**2*b32**2*m2*n3*v1**2 - 70*a22*b31**2*b32**2*m2*n3*v2**2 - 120*a22*b31**2*
b32**2*n2**2*u2*v3 + 30*a22*b31**2*b32**2*n2**2*u3*v2 + 132*a22*b31**2*b32**2*n2
*n3*u3*v3 - 24*a22*b31**2*b32*m2*n2**2*v2 - 24*a22*b31**2*b32*m2*n2*n3*v3 + 198*
a22*b31**2*b32*n2**3*u2 + 198*a22*b31**2*b32*n2**2*n3*u3 + 72*a22*b31*b32**4*n2*
u3*v1*v3 - 78*a22*b31*b32**3*m2*n2*v1*v3 + 120*a22*b31*b32**3*n2**2*u1*v3 - 66*
a22*b31*b32**3*n2**2*u3*v1 + 12*a22*b31*b32**3*n2*n3*u1*v2 - 12*a22*b31*b32**3*
n2*n3*u2*v1 - 12*a22*b31*b32**2*m2*n2**2*v1 - 198*a22*b31*b32**2*n2**3*u1 + 72*
a22*b32**5*n2*u3*v2*v3 - 162*a22*b32**4*m2*n2*v2*v3 - 70*a22*b32**4*m2*n3*v1**2
- 70*a22*b32**4*m2*n3*v2**2 - 120*a22*b32**4*n2**2*u2*v3 + 54*a22*b32**4*n2**2*
u3*v2 + 144*a22*b32**4*n2*n3*u3*v3 + 198*a22*b32**3*n2**3*u2 + 198*a22*b32**3*n2
**2*n3*u3 + 40*b31**4*b32*n2**2*v1**2 + 40*b31**4*b32*n2**2*v2**2 + 480*b31**4*
n2**3*v3 + 90*b31**3*b32**2*n2*n3*v1*v3 + 39*b31**3*b32*n2**2*n3*v1 + 52*b31**2*
b32**3*n2**2*v1**2 + 52*b31**2*b32**3*n2**2*v2**2 - 90*b31**2*b32**3*n2*n3*v2*v3
+ 1002*b31**2*b32**2*n2**3*v3 + 66*b31**2*b32**2*n2**2*n3*v2 - 24*b31**2*b32**2
*n2*n3**2*v3 + 90*b31*b32**4*n2*n3*v1*v3 + 51*b31*b32**3*n2**2*n3*v1 + 12*b32**5
*n2**2*v1**2 + 12*b32**5*n2**2*v2**2 - 90*b32**5*n2*n3*v2*v3 + 522*b32**4*n2**3*
v3 + 54*b32**4*n2**2*n3*v2 - 36*b32**4*n2*n3**2*v3$