Solution 6 to problem e3quant
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem e3quant
Expressions
The solution is given through the following expressions:
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
n1=0
n2=0
m1=0
m2=0
- 4*k1*m3 + m3*q1
r6=--------------------
a22
r5=0
r4=0
r2=0
r1=0
q20=0
2
8*a22*c33*k1 - a22*c33*q1 - k1*m3
q19=------------------------------------
2
a22
q18=0
q17=0
2
8*a22*c33*k1 - a22*c33*q1 - k1*m3
q16=------------------------------------
2
a22
q14=0
q13=0
q11=0
- a22*k38 + 6*b33*k1 - b33*q1 - m3*p3
q10=----------------------------------------
a22
a22*p13 - 2*k1*m3
q9=-------------------
a22
q8=0
q7= - 4*k1 + q1
q6=0
- a22*p13 + 2*k1*m3
q5=----------------------
a22
- a22*k38 + 6*b33*k1 - b33*q1 - m3*p3
q4=----------------------------------------
a22
q3=0
q2=0
2 2
a22 *k16*m3 + 2*a22*c33*k1*m3 + a22*c33*k12*m3 + b33 *k1*m3
p56=-------------------------------------------------------------
3
a22
p55=0
2 2
a22 *k16*m3 + a22*c33*k12*m3 + b33 *k1*m3
p54=-------------------------------------------
3
a22
p53=0
p52=0
p51=0
p50=0
2 2
a22 *k16*m3 + a22*c33*k12*m3 + b33 *k1*m3
p49=-------------------------------------------
3
a22
p48=0
p47=0
2
a22 *p41 + a22*c33*p3 + 2*b33*k1*m3
p46=-------------------------------------
2
a22
p45=0
p44=p41
p43=0
2
a22*c33*k12 + b33 *k1
p42=-----------------------
2
a22
a22*p13 + b33*p3 + k12*m3
p40=---------------------------
a22
p39=0
p38=0
p36=0
p35=0
p34=0
2
- 4*a22*c33*k1 - a22*c33*k12 - b33 *k1
p33=-----------------------------------------
2
a22
p32=0
p31=0
p30=0
p29=p13
2*a22*k38 - 2*b33*k1
p28=----------------------
a22
p27=0
2*k1*m3
p26=---------
a22
p25=0
p24=0
p23=p3
p22=0
p21=0
2
4*a22*c33*k1 + a22*c33*k12 + b33 *k1
p20=--------------------------------------
2
a22
p19=0
p18=0
p17=0
p16=0
p15=0
- 2*a22*k38 + 2*b33*k1
p14=-------------------------
a22
p12=0
p11=0
p10=0
p9=0
p8= - 4*k1
p7=0
2*k1*m3
p6=---------
a22
p5=0
p4=0
p2=0
p1=0
k125=0
2 2 2 2
- a22 *c33*k16 - 2*a22*c33 *k1 - a22*c33 *k12 - b33 *c33*k1
k124=--------------------------------------------------------------
3
a22
k123=0
2 2 2 2
- a22 *c33*k16 - a22*c33 *k1 - a22*c33 *k12 - b33 *c33*k1
k122=------------------------------------------------------------
3
a22
k121=0
k120=0
k119=0
k118=0
2 2 2 2
- a22 *c33*k16 - 2*a22*c33 *k1 - a22*c33 *k12 - b33 *c33*k1
k117=--------------------------------------------------------------
3
a22
k116=0
2 2 2 2
- 2*a22 *c33*k16 - 2*a22*c33 *k1 - 2*a22*c33 *k12 - 2*b33 *c33*k1
k115=--------------------------------------------------------------------
3
a22
k114=0
k113=0
2 2 2 2
- a22 *c33*k16 - a22*c33 *k1 - a22*c33 *k12 - b33 *c33*k1
k112=------------------------------------------------------------
3
a22
k110=0
- 2*b33*c33*k1
k109=-----------------
2
a22
k108=0
k107=0
k106=0
k105=0
- 2*b33*c33*k1
k104=-----------------
2
a22
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
a22*k38 + b33*k12
k95=-------------------
a22
k94=0
k93=0
k91=0
2 3
- a22 *b33*k16 - 2*a22*b33*c33*k1 - a22*b33*c33*k12 - b33 *k1
k90=----------------------------------------------------------------
3
a22
k89=0
2 3
- a22 *b33*k16 - 2*a22*b33*c33*k1 - a22*b33*c33*k12 - b33 *k1
k88=----------------------------------------------------------------
3
a22
k87=0
k86=0
k85=0
k84=0
2 3
- a22 *b33*k16 - 2*a22*b33*c33*k1 - a22*b33*c33*k12 - b33 *k1
k83=----------------------------------------------------------------
3
a22
k82=0
k81=0
2
- 2*a22*c33*k12 - 2*b33 *k1
k80=------------------------------
2
a22
k79=0
k78=0
k77=0
k76=0
k75=0
k74=k38
k73=0
k72=0
2 2
a22 *k16 + 2*a22*c33*k1 + a22*c33*k12 + b33 *k1
k71=-------------------------------------------------
2
a22
k70=0
k69=k16
k68=0
k67=0
2 2
a22 *k16 + a22*c33*k12 + b33 *k1
k66=----------------------------------
2
a22
2*b33*k1
k65=----------
a22
k64=0
k63=0
k62=k12
k61=0
k59=0
k58=0
k57=k1
k56=0
k55=0
k54=0
k53=0
2 3
- a22 *b33*k16 - 2*a22*b33*c33*k1 - a22*b33*c33*k12 - b33 *k1
k52=----------------------------------------------------------------
3
a22
k51=0
2 3
- a22 *b33*k16 - 2*a22*b33*c33*k1 - a22*b33*c33*k12 - b33 *k1
k50=----------------------------------------------------------------
3
a22
k49=0
k48=0
2 3
- a22 *b33*k16 - 2*a22*b33*c33*k1 - a22*b33*c33*k12 - b33 *k1
k47=----------------------------------------------------------------
3
a22
k46=0
k45=0
k44=0
2
- 2*a22*c33*k12 - 2*b33 *k1
k43=------------------------------
2
a22
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
2
- 2*a22*c33*k12 - 2*b33 *k1
k32=------------------------------
2
a22
k31=0
k30=0
k29=0
k28=0
k27=0
k26=0
k25=0
k24=0
k23=0
k22=0
2 2
a22 *k16 + 2*a22*c33*k1 + a22*c33*k12 + b33 *k1
k21=-------------------------------------------------
2
a22
k20=0
2 2
a22 *k16 + a22*c33*k12 + b33 *k1
k19=----------------------------------
2
a22
k18=0
k17=0
2*b33*k1
k15=----------
a22
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:
c33, n3, m3, r3, q1, p41, p37, p13, p3, k38, k16, k12,
k1, b33, a33, a22
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.
3 3 3 3 3
{4*a22 *k1*v120 - a22 *k1*w071 - 2*a22 *k1*w121 - a22 *k1*w127 - a22 *k12*w066
3 3 3 3
- a22 *k12*w116 - a22 *k16*w057 - a22 *k16*w059 - a22 *k16*w062
3 3 3 3
- a22 *k16*w107 - a22 *k16*w109 - a22 *k16*w112 - 2*a22 *k38*v100
3 3 3 3
+ 2*a22 *k38*v114 - a22 *k38*w033 - a22 *k38*w054 - a22 *k38*w090
3 3 3 3 3
- a22 *p13*v088 - a22 *p13*v099 - a22 *p13*v115 - a22 *p3*v105 - a22 *p3*v125
3 3 3 3
- a22 *p37*v091 - a22 *p41*v082 - a22 *p41*v084 - a22 *p41*v087
2 2 2
+ 2*a22 *b33*k1*v100 - 2*a22 *b33*k1*v114 - 2*a22 *b33*k1*w063
2 2 2
- 2*a22 *b33*k1*w113 - a22 *b33*k12*w033 + a22 *b33*k16*w038
2 2 2
+ a22 *b33*k16*w040 + a22 *b33*k16*w045 + a22 *b33*k16*w076
2 2 2
+ a22 *b33*k16*w078 + a22 *b33*k16*w081 - a22 *b33*p3*v088
2 2 2
+ 4*a22 *c33*k1*v095 - 4*a22 *c33*k1*v108 - 2*a22 *c33*k1*w057
2 2 2
- 2*a22 *c33*k1*w107 - a22 *c33*k12*v086 + a22 *c33*k12*v095
2 2 2
- a22 *c33*k12*v108 + 2*a22 *c33*k12*w048 - a22 *c33*k12*w057
2 2 2
- a22 *c33*k12*w062 + 2*a22 *c33*k12*w085 + 2*a22 *c33*k12*w096
2 2 2
- a22 *c33*k12*w107 - a22 *c33*k12*w109 + a22 *c33*k16*w004
2 2 2
+ a22 *c33*k16*w006 + a22 *c33*k16*w011 + 2*a22 *c33*k16*w013
2 2 2 2
+ a22 *c33*k16*w016 - a22 *c33*p3*v082 - 2*a22 *k1*m3*v102 - 2*a22 *k1*m3*v122
2 2 2 2
- a22 *k12*m3*v088 - a22 *k16*m3*v072 - a22 *k16*m3*v074 - a22 *k16*m3*v079
2 2 2 2
- a22*b33 *k1*v086 + a22*b33 *k1*v095 - a22*b33 *k1*v108 + 2*a22*b33 *k1*w048
2 2 2
- a22*b33 *k1*w057 - a22*b33 *k1*w062 + 2*a22*b33 *k1*w085
2 2 2
+ 2*a22*b33 *k1*w096 - a22*b33 *k1*w107 - a22*b33 *k1*w109
+ 2*a22*b33*c33*k1*w019 + 2*a22*b33*c33*k1*w024 + 2*a22*b33*c33*k1*w038
+ 2*a22*b33*c33*k1*w040 + 2*a22*b33*c33*k1*w045 + 2*a22*b33*c33*k1*w076
+ 2*a22*b33*c33*k1*w078 + 2*a22*b33*c33*k1*w081 + a22*b33*c33*k12*w038
+ a22*b33*c33*k12*w040 + a22*b33*c33*k12*w045 + a22*b33*c33*k12*w076
+ a22*b33*c33*k12*w078 + a22*b33*c33*k12*w081 - 2*a22*b33*k1*m3*v082
2 2 2
+ 2*a22*c33 *k1*w004 + a22*c33 *k1*w006 + 2*a22*c33 *k1*w011
2 2 2
+ 2*a22*c33 *k1*w013 + a22*c33 *k1*w016 + a22*c33 *k12*w004
2 2 2
+ a22*c33 *k12*w006 + a22*c33 *k12*w011 + 2*a22*c33 *k12*w013
2
+ a22*c33 *k12*w016 - 2*a22*c33*k1*m3*v072 - a22*c33*k12*m3*v072
3 3
- a22*c33*k12*m3*v074 - a22*c33*k12*m3*v079 + b33 *k1*w038 + b33 *k1*w040
3 3 3 3 2
+ b33 *k1*w045 + b33 *k1*w076 + b33 *k1*w078 + b33 *k1*w081 + b33 *c33*k1*w004
2 2 2 2
+ b33 *c33*k1*w006 + b33 *c33*k1*w011 + 2*b33 *c33*k1*w013 + b33 *c33*k1*w016
2 2 2
- b33 *k1*m3*v072 - b33 *k1*m3*v074 - b33 *k1*m3*v079,
b33,
a33,
a22 - a33,
a22,
a22 - 4*a33}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2 2
HAM=a22*u1 + a22*u2 + a33*u3 + b33*u3*v3 + c33*v3 + m3*v3 + n3*u3
has apart from the Hamiltonian and Casimirs the following first integrals:
3 4 3 2 3 2 3 2 3
INT=a22 *u1 + 2*a22 *u1 *u2*u3 + a22 *u1*u2*v2 - 4*a22 *u1*u3 - 4*a22 *u1*v1
2 2 2
+ 2*a22 *b33*u1*u3*v1 + 6*a22 *b33*u1*u3 - 2*a22 *b33*u2*v1*v2
2 4 2 2 2 2 2 2 3
+ 2*a22 *b33*u3 + 2*a22 *b33*v1 *v2 + 6*a22 *b33*v1 + 2*a22 *c33*u1 *v3
2 2 2 2
+ 2*a22 *c33*u1*u2*u3*v1 + 8*a22 *c33*u1*v3 - 4*a22 *c33*u3*v2
2 3 2 2 2
+ 4*a22 *c33*v1 + 8*a22 *c33*v1*v3 + 2*a22 *m3*u1*u2*u3 + 2*a22 *m3*u2*u3
2 2 2 2 2 3
+ 2*a22 *m3*u3 *v2 - 2*a22 *m3*u3*v1 - 4*a22 *m3*v3 + a22*b33 *u1 *v3
2 2 2 2 3
+ a22*b33 *u1*u2*u3*v1 - 2*a22*b33 *u1*u3 *v2 - 2*a22*b33 *u1*v1
2 2 3 2 3 2 3
+ a22*b33 *u1*v1*v3 + a22*b33 *u1*v2 + a22*b33 *u2 *v1 - 2*a22*b33 *u3 *v3
2 2 2 3
- a22*b33 *u3*v2 + a22*b33 *v1 - 2*a22*b33*c33*u1*u2*v1*v2
2 2
- 2*a22*b33*c33*u1*u3*v3 - 2*a22*b33*c33*u1*v1 *v2
2
- 2*a22*b33*c33*u2 *v1*v3 - 2*a22*b33*c33*u2*u3*v1*v2
2 3 2
- 2*a22*b33*c33*u2*v1 *v3 - 2*a22*b33*c33*v1 *v3 - 2*a22*b33*c33*v1*v2 *v3
2 2 2 2
+ 2*a22*b33*m3*u1*v2*v3 - a22*c33 *u1*v1*v3 - 2*a22*c33 *u2*v2*v3
2 3 2 2 2 2 3
- a22*c33 *u2*v3 - 2*a22*c33 *v1 *v3 - 2*a22*c33 *v1*v3
3 2 2 3
+ 2*a22*c33*m3*v3 - a22*m3 *u1*v3 - a22*m3 *v1*v3 - b33 *u1*u2*v1*v2
3 2 3 2 3 3 2
- b33 *u1*v1 *v2 - b33 *u2 *v1*v3 - b33 *u2*u3*v1*v2 - b33 *u2*v1 *v3
3 3 2 2 2 2 2 3
- b33 *v1 *v3 - b33 *c33*u1*v1*v3 - b33 *c33*u2*v2*v3 - b33 *c33*u2*v3
2 2 2 2 3 2 2 2
- 2*b33 *c33*v1 *v3 - b33 *c33*v1*v3 + b33 *m3*v1*v2*v3 + b33 *m3*v1*v3
2 3
+ b33 *m3*v3
2 2 3
= - (((u2 + v1 )*v3 + (u3*v2 + v1*v3)*u2 + (u2 + v1)*u1*v2)*b33 *v1
2 2 2 3
+ (4*(u3 + v1) - u2*v2 - (u1 + 2*u2*u3)*u1)*a22 *u1 +
2
(((2*v1 + v3 + u1)*v1 + (v2 + v3)*u2)*c33*v3 - ((v2 + v3)*v1 + v3 )*m3)
2 4 2 2
*b33 *v3 + 2*((u2*v1*v2 - u3 - (v2 + 3)*v1 - (v1 + 3)*u1*u3)*b33
2
- (u3 *v2 - u3*v1 - 2*v3 + u2*u3 + u1*u2*u3)*m3
2 2 3
- (2*((v1 + 2*v3)*v1 - u3*v2 ) + u1 *v3 + (u2*u3*v1 + 4*v3)*u1)*c33
2 3 2 3 3 3
)*a22 + ((2*u3 *v3 + u3*v2 - v1 - u2 *v1 - u1 *v3
3 3 2 2
+ (2*v1 - v1*v3 - v2 + 2*u3 *v2 - u2*u3*v1)*u1)*b33 + (
2
((2*(v1 + v3) + u1)*v1 + (2*v2 + v3)*u2)*c33 *v3
2
+ ((u1 + v1)*m3 - 2*c33*v3 )*m3)*v3 + 2*((
2 2 2
((v1 + v2 + u2 )*v3 + (u3*v2 + v1*v3)*u2)*v1
2 2
+ (u3*v3 + v1 *v2 + u2*v1*v2)*u1)*c33 - m3*u1*v2*v3)*b33)*a22
)
2 2 2 2 2 3
INT=a22 *u1*v1*v2 + a22 *u2 *u3 + a22*b33*u2*u3*v2*v3 + a22*c33*u1 *v3
2 3
+ a22*c33*u1*u2*u3*v1 - 2*a22*c33*u1*u3 *v2 - 2*a22*c33*u1*v1
3 3 3
+ a22*c33*u1*v1*v3 + a22*c33*u1*v2 + a22*c33*u2 *v1 - 2*a22*c33*u3 *v3
2 3
- a22*c33*u3*v2 + a22*c33*v1 + a22*m3*u2*u3*v3 - b33*c33*u1*u2*v1*v2
2 2
- b33*c33*u1*v1 *v2 - b33*c33*u2 *v1*v3 - b33*c33*u2*u3*v1*v2
2 3 2 2 2 2
- b33*c33*u2*v1 *v3 - b33*c33*v1 *v3 - c33 *u1*v1*v3 - c33 *u2*v2*v3
2 3 2 2 2 2 3
- c33 *u2*v3 - 2*c33 *v1 *v3 - c33 *v1*v3 + c33*m3*v1*v2*v3
2 3
+ c33*m3*v1*v3 + c33*m3*v3
3 2 3 3 3
= - (((2*u3 *v3 + u3*v2 - v1 - u2 *v1 - u1 *v3
3 3 2
+ (2*v1 - v1*v3 - v2 + 2*u3 *v2 - u2*u3*v1)*u1)*c33
- (b33*v2 + m3)*u2*u3*v3)*a22
2 2
+ ((2*v1 + v3 + u1)*v1 + (v2 + v3)*u2)*c33 *v3
2 2 2 2 2
- (((v2 + v3)*v1 + v3 )*c33*m3*v3 + (u1*v1*v2 + u2 *u3 )*a22 )
2 2
+ ((u2 + v1 )*v3 + (u3*v2 + v1*v3)*u2 + (u2 + v1)*u1*v2)*b33*c33*v1)
3 3 3 3
INT=a22*u1 *v1 + a22*u1 *v3 + a22*u1*u2*u3*v1 + a22*u1*v2 + a22*u2 *v1
3 2 2
+ a22*v1*v2 - b33*u1*u2*v1*v2 - b33*u1*v1 *v2 - b33*u2 *v1*v3
2 3 2
- b33*u2*u3*v1*v2 - b33*u2*v1 *v3 - b33*v1 *v3 - c33*u1*v1*v3
2 3 2 2 3
- c33*u2*v2*v3 - c33*u2*v3 - 2*c33*v1 *v3 - c33*v1*v3 + m3*v1*v2*v3
2 3
+ m3*v1*v3 + m3*v3
3 3 3 3 3
=(u1 *v1 + u1 *v3 + u2 *v1 + v1*v2 + (u2*u3*v1 + v2 )*u1)*a22
2 2
+ ((v2 + v3)*v1 + v3 )*m3*v3 - ((2*v1 + v3 + u1)*v1 + (v2 + v3)*u2)*c33*v3
2 2
- ((u2 + v1 )*v3 + (u3*v2 + v1*v3)*u2 + (u2 + v1)*u1*v2)*b33*v1
2 3 2
INT=u1*u2 *v2 - 2*u1*u3*v1 - u1*u3 + u2 *v3 + u2*u3*v2*v3 + 2*u2*v1*v2 - v1
3 2 2
=u2 *v3 - v1 + (u3*v3 + 2*v1)*u2*v2 - ((2*v1 + 1)*u3 - u2 *v2)*u1
2 2 2
INT=a22*u1*u2 + a22*u2 *v2 + b33*u2*u3*v3 + c33*u1*v2*v3 - m3*u1*u3 - m3*v1
2 2
=(b33*u2*u3 + c33*u1*v2)*v3 + (u1 + v2)*a22*u2 - (u1*u3 + v1 )*m3
2
INT=u2 *v1 + u2*u3*v3 - u2*u3 + u3*v1*v2 + u3*v1
=((v3 - 1)*u3 + u2*v1)*u2 + (v2 + 1)*u3*v1
INT=u1*u2*v3
=u1*u2*v3
2
INT=v3*(u1*v2 + u3 + u3*v1)
=((u3 + v1)*u3 + u1*v2)*v3
2 2
INT=a22*u1 + a22*u1*v1 - b33*u1*u3 - b33*v1 - c33*u1*v3 - c33*v1*v3 + m3*v3
2
=(a22*u1 - c33*v3)*(u1 + v1) + m3*v3 - (u1*u3 + v1 )*b33
INT=u3
=u3
And again in machine readable form:
HAM=a22*u1**2 + a22*u2**2 + a33*u3**2 + b33*u3*v3 + c33*v3**2 + m3*v3 + n3*u3$
INT=a22**3*u1**4 + 2*a22**3*u1**2*u2*u3 + a22**3*u1*u2*v2**2 - 4*a22**3*u1*u3**2
- 4*a22**3*u1*v1 + 2*a22**2*b33*u1*u3*v1 + 6*a22**2*b33*u1*u3 - 2*a22**2*b33*u2
*v1*v2 + 2*a22**2*b33*u3**4 + 2*a22**2*b33*v1**2*v2**2 + 6*a22**2*b33*v1**2 + 2*
a22**2*c33*u1**3*v3 + 2*a22**2*c33*u1*u2*u3*v1 + 8*a22**2*c33*u1*v3 - 4*a22**2*
c33*u3*v2**2 + 4*a22**2*c33*v1**3 + 8*a22**2*c33*v1*v3 + 2*a22**2*m3*u1*u2*u3 +
2*a22**2*m3*u2*u3 + 2*a22**2*m3*u3**2*v2 - 2*a22**2*m3*u3*v1 - 4*a22**2*m3*v3 +
a22*b33**2*u1**3*v3 + a22*b33**2*u1*u2*u3*v1 - 2*a22*b33**2*u1*u3**2*v2 - 2*a22*
b33**2*u1*v1**3 + a22*b33**2*u1*v1*v3 + a22*b33**2*u1*v2**3 + a22*b33**2*u2**3*
v1 - 2*a22*b33**2*u3**3*v3 - a22*b33**2*u3*v2**2 + a22*b33**2*v1**3 - 2*a22*b33*
c33*u1*u2*v1*v2 - 2*a22*b33*c33*u1*u3*v3**2 - 2*a22*b33*c33*u1*v1**2*v2 - 2*a22*
b33*c33*u2**2*v1*v3 - 2*a22*b33*c33*u2*u3*v1*v2 - 2*a22*b33*c33*u2*v1**2*v3 - 2*
a22*b33*c33*v1**3*v3 - 2*a22*b33*c33*v1*v2**2*v3 + 2*a22*b33*m3*u1*v2*v3 - a22*
c33**2*u1*v1*v3**2 - 2*a22*c33**2*u2*v2*v3**2 - a22*c33**2*u2*v3**3 - 2*a22*c33
**2*v1**2*v3**2 - 2*a22*c33**2*v1*v3**3 + 2*a22*c33*m3*v3**3 - a22*m3**2*u1*v3 -
a22*m3**2*v1*v3 - b33**3*u1*u2*v1*v2 - b33**3*u1*v1**2*v2 - b33**3*u2**2*v1*v3
- b33**3*u2*u3*v1*v2 - b33**3*u2*v1**2*v3 - b33**3*v1**3*v3 - b33**2*c33*u1*v1*
v3**2 - b33**2*c33*u2*v2*v3**2 - b33**2*c33*u2*v3**3 - 2*b33**2*c33*v1**2*v3**2
- b33**2*c33*v1*v3**3 + b33**2*m3*v1*v2*v3 + b33**2*m3*v1*v3**2 + b33**2*m3*v3**
3$
INT=a22**2*u1*v1*v2**2 + a22**2*u2**2*u3**2 + a22*b33*u2*u3*v2*v3 + a22*c33*u1**
3*v3 + a22*c33*u1*u2*u3*v1 - 2*a22*c33*u1*u3**2*v2 - 2*a22*c33*u1*v1**3 + a22*
c33*u1*v1*v3 + a22*c33*u1*v2**3 + a22*c33*u2**3*v1 - 2*a22*c33*u3**3*v3 - a22*
c33*u3*v2**2 + a22*c33*v1**3 + a22*m3*u2*u3*v3 - b33*c33*u1*u2*v1*v2 - b33*c33*
u1*v1**2*v2 - b33*c33*u2**2*v1*v3 - b33*c33*u2*u3*v1*v2 - b33*c33*u2*v1**2*v3 -
b33*c33*v1**3*v3 - c33**2*u1*v1*v3**2 - c33**2*u2*v2*v3**2 - c33**2*u2*v3**3 - 2
*c33**2*v1**2*v3**2 - c33**2*v1*v3**3 + c33*m3*v1*v2*v3 + c33*m3*v1*v3**2 + c33*
m3*v3**3$
INT=a22*u1**3*v1 + a22*u1**3*v3 + a22*u1*u2*u3*v1 + a22*u1*v2**3 + a22*u2**3*v1
+ a22*v1*v2**3 - b33*u1*u2*v1*v2 - b33*u1*v1**2*v2 - b33*u2**2*v1*v3 - b33*u2*u3
*v1*v2 - b33*u2*v1**2*v3 - b33*v1**3*v3 - c33*u1*v1*v3**2 - c33*u2*v2*v3**2 -
c33*u2*v3**3 - 2*c33*v1**2*v3**2 - c33*v1*v3**3 + m3*v1*v2*v3 + m3*v1*v3**2 + m3
*v3**3$
INT=u1*u2**2*v2 - 2*u1*u3*v1 - u1*u3 + u2**3*v3 + u2*u3*v2*v3 + 2*u2*v1*v2 - v1
**2$
INT=a22*u1*u2**2 + a22*u2**2*v2 + b33*u2*u3*v3 + c33*u1*v2*v3 - m3*u1*u3 - m3*v1
**2$
INT=u2**2*v1 + u2*u3*v3 - u2*u3 + u3*v1*v2 + u3*v1$
INT=u1*u2*v3$
INT=v3*(u1*v2 + u3**2 + u3*v1)$
INT=a22*u1**2 + a22*u1*v1 - b33*u1*u3 - b33*v1**2 - c33*u1*v3 - c33*v1*v3 + m3*
v3$
INT=u3$