Solution 3 to problem e3quant
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem e3quant
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
1 2
---*b33
4
c33=----------
a33
m1=0
m2=0
1
---*b33*n3
2
m3=------------
a33
r6=
2 1 2 1 2 1 2
2*a33 *b33*k1*n3 - ---*a33 *b33*n3*q1 + ---*b33*k1*n1 *n3 - ---*b33*k12*n1 *n3
2 8 8
--------------------------------------------------------------------------------
4
a33
5 2 1 2 1 2
r5=(---*a33 *b33*k1*n2 + ---*a33 *b33*k12*n2 - ---*a33 *b33*n2*q1
4 4 4
1 1 1 2
+ ---*a33*b33*k1*n1*n3 - ---*a33*b33*k12*n1*n3 + ----*b33*k1*n1 *n2
8 8 16
1 2 1 2 1 2 4
+ ----*b33*k1*n2*n3 - ----*b33*k12*n1 *n2 - ----*b33*k12*n2*n3 )/a33
16 16 16
5 2 1 2 1 2
r4=(---*a33 *b33*k1*n1 + ---*a33 *b33*k12*n1 - ---*a33 *b33*n1*q1
4 4 4
1 1 1 3
- ---*a33*b33*k1*n2*n3 + ---*a33*b33*k12*n2*n3 + ----*b33*k1*n1
8 8 16
1 2 1 3 1 2 4
+ ----*b33*k1*n1*n3 - ----*b33*k12*n1 - ----*b33*k12*n1*n3 )/a33
16 16 16
1 2 1 1 1 2
r3=( - ---*a33 *n3*q1 - ---*a33*k1*n1*n2 + ---*a33*k12*n1*n2 + ---*k1*n1 *n3
2 4 4 8
1 3 1 2 1 3 3
- ---*k1*n3 - ---*k12*n1 *n3 + ---*k12*n3 )/a33
8 8 8
1 2 1 2 1 1
r2=(---*a33 *k1*n2 - ---*a33 *n2*q1 + ---*a33*k1*n1*n3 - ---*a33*k12*n1*n3
2 2 4 4
1 2 1 2 1 2 1 2 3
+ ---*k1*n1 *n2 - ---*k1*n2*n3 - ---*k12*n1 *n2 + ---*k12*n2*n3 )/a33
8 8 8 8
1 2 1 2 1 2 1
r1=( - ---*a33 *k1*n1 + ---*a33 *k12*n1 - ---*a33 *n1*q1 - ---*a33*k1*n2*n3
2 2 2 4
1 1 3 1 2 1 3
+ ---*a33*k12*n2*n3 + ---*k1*n1 - ---*k1*n1*n3 - ---*k12*n1
4 8 8 8
1 2 3
+ ---*k12*n1*n3 )/a33
8
1 2 1 2 1 2
- ---*a33*b33 *k12*n1 + ---*b33 *k1*n2*n3 + ---*b33 *k12*n2*n3
4 4 8
q20=-----------------------------------------------------------------
4
a33
2 2 1 2 2 1 2 2 1 2 2
q19=( - 2*a33 *b33 *k1 + ---*a33 *b33 *q1 - ----*b33 *k1*n1 + ----*b33 *k1*n2
4 16 16
1 2 2 1 2 2 1 2 2 4
- ---*b33 *k1*n3 + ----*b33 *k12*n1 + ----*b33 *k12*n2 )/a33
4 16 16
1 2 1 2 1 2
---*a33*b33 *k12*n2 + ---*b33 *k1*n1*n3 + ---*b33 *k12*n1*n3
4 4 8
q18=--------------------------------------------------------------
4
a33
1 2 1 2
---*b33 *k1*n1*n2 + ---*b33 *k12*n1*n2
8 8
q17=----------------------------------------
4
a33
2 2 1 2 2 1 2 2 1 2 2
- 2*a33 *b33 *k1 + ---*a33 *b33 *q1 - ---*b33 *k1*n3 + ---*b33 *k12*n1
4 4 8
q16=---------------------------------------------------------------------------
4
a33
1 1
---*a33*b33*k1*n1 + ---*b33*k1*n2*n3
2 4
q14=--------------------------------------
3
a33
1 2 1 1
- ---*a33 *k38*n2 - ---*a33*b33*k1*n2 + ---*b33*k1*n1*n3
2 2 4
q13=-----------------------------------------------------------
3
a33
1 1 1
- ---*a33*b33*k12*n1 + ---*b33*k1*n2*n3 - ---*b33*k12*n2*n3
2 2 4
q11=--------------------------------------------------------------
3
a33
3 2 2 1 2 1 2
q10=( - a33 *k38 - 6*a33 *b33*k1 + a33 *b33*q1 - ---*b33*k1*n1 + ---*b33*k1*n2
4 4
1 2 1 2 1 2 3
- ---*b33*k1*n3 + ---*b33*k12*n1 + ---*b33*k12*n3 )/a33
2 4 4
1 2 1
---*a33 *k38*n3 + a33*b33*k1*n3 + ---*b33*k1*n1*n2
2 4
q9=----------------------------------------------------
3
a33
1 1
a33*k1*n1 - a33*k12*n1 + ---*k1*n2*n3 - ---*k12*n2*n3
2 2
q8=-------------------------------------------------------
2
a33
q7
2 2 1 2 1 2 1 2 1 2
- 4*a33 *k1 + a33 *q1 - ---*k1*n1 + ---*k1*n2 + ---*k12*n1 - ---*k12*n2
4 4 4 4
=------------------------------------------------------------------------------
2
a33
1 1 1
---*a33*b33*k12*n2 + ---*b33*k1*n1*n3 - ---*b33*k12*n1*n3
2 2 4
q6=-----------------------------------------------------------
3
a33
1 2 1
- ---*a33 *k38*n3 - a33*b33*k1*n3 + ---*b33*k1*n1*n2
2 4
q5=-------------------------------------------------------
3
a33
3 2 2 1 2 1 2
q4=( - a33 *k38 - 6*a33 *b33*k1 + a33 *b33*q1 - ---*b33*k1*n3 + ---*b33*k12*n1
2 4
1 2 3
+ ---*b33*k12*n3 )/a33
4
1 1
a33*k1*n2 + ---*k1*n1*n3 - ---*k12*n1*n3
2 2
q3=------------------------------------------
2
a33
1 1
---*k1*n1*n2 - ---*k12*n1*n2
2 2
q2=------------------------------
2
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n3 - ---*b33 *k1*n3 + ---*b33 *k12*n3
2 4 8
p56=-----------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n2 - ---*b33 *k1*n2 + ---*b33 *k12*n2
4 8 8
p55=-----------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n3 - ---*b33 *k1*n3 + ---*b33 *k12*n3
2 2 8
p54=-----------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n2 - ---*b33 *k1*n2 + ----*b33 *k12*n2
4 4 16
p53=------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n1 - ---*b33 *k1*n1 + ---*b33 *k12*n1
4 8 8
p52=-----------------------------------------------------------
4
a33
p51=0
1 2 1 3 1 3
- ---*a33 *b33*k16*n1 - ---*b33 *k1*n1 + ----*b33 *k12*n1
4 4 16
p50=------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n3 - ---*b33 *k1*n3 + ---*b33 *k12*n3
2 2 8
p49=-----------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n2 - ---*b33 *k1*n2 + ----*b33 *k12*n2
4 4 16
p48=------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k16*n1 - ---*b33 *k1*n1 + ----*b33 *k12*n1
4 4 16
p47=------------------------------------------------------------
4
a33
1 2 3 2
- ---*a33 *k16*n3 + ---*b33 *k1*n3
2 4
p46=-------------------------------------
3
a33
1 1 2 1 2
- ---*a33*b33*k38*n2 + ---*b33 *k1*n2 + ---*b33 *k12*n2
4 2 4
p45=----------------------------------------------------------
3
a33
1 2 1 2 1 2
- ---*a33 *k16*n3 - ---*b33 *k1*n3 + ---*b33 *k12*n3
2 2 8
p44=-------------------------------------------------------
3
a33
1 1 2 1 2
- ---*a33*b33*k38*n1 + ---*b33 *k1*n1 + ---*b33 *k12*n1
4 2 4
p43=----------------------------------------------------------
3
a33
2 1 2
b33 *k1 - ---*b33 *k12
4
p42=------------------------
2
a33
1 2 1 2 1 2
- ---*a33 *k16*n3 - ---*b33 *k1*n3 + ---*b33 *k12*n3
2 2 8
p41=-------------------------------------------------------
3
a33
1
---*a33*k38*n3 + b33*k1*n3 - b33*k12*n3
2
p40=-----------------------------------------
2
a33
1
- ---*b33*k12*n2
4
p39=-------------------
2
a33
1
- ---*b33*k12*n1
4
p38=-------------------
2
a33
1
- ---*k12*n3
2
p37=---------------
a33
1 2 1 2
- ---*a33 *k16*n2 - ---*b33 *k1*n2
2 4
p36=-------------------------------------
3
a33
p35=0
1 2 1 1 2 1 2
- ---*a33 *k16*n2 - ---*a33*b33*k38*n2 - ---*b33 *k1*n2 + ---*b33 *k12*n2
2 4 2 8
p34=----------------------------------------------------------------------------
3
a33
1 2
---*b33 *k12
4
p33=--------------
2
a33
1
- ---*b33*k38*n1
4
p32=-------------------
2
a33
1 2 1 2 1 2
- ---*a33 *k16*n2 - ---*b33 *k1*n2 + ---*b33 *k12*n2
2 2 8
p31=-------------------------------------------------------
3
a33
1 1
---*a33*k38*n2 + b33*k1*n2 - ---*b33*k12*n2
2 2
p30=---------------------------------------------
2
a33
1
---*k38*n3
2
p29=------------
a33
2*a33*k38 + 2*b33*k1
p28=----------------------
a33
1
- ---*k12*n2
2
p27=---------------
a33
- b33*k1*n3
p26=--------------
2
a33
1 1 1
---*a33*k38*n2 - ---*b33*k1*n2 - ---*b33*k12*n2
2 2 4
p25=-------------------------------------------------
2
a33
1 1
- ---*b33*k1*n1 - ---*b33*k12*n1
2 4
p24=-----------------------------------
2
a33
1
- k1*n3 + ---*k12*n3
2
p23=-----------------------
a33
1
- k1*n2 + ---*k12*n2
2
p22=-----------------------
a33
1 2 1 2
- ---*a33 *k16*n1 - ---*b33 *k1*n1
2 4
p21=-------------------------------------
3
a33
1 2
- ---*b33 *k12
4
p20=-----------------
2
a33
1 2 1 2 1 2
- ---*a33 *k16*n1 - ---*b33 *k1*n1 + ---*b33 *k12*n1
2 2 8
p19=-------------------------------------------------------
3
a33
p18=0
1
- ---*b33*k38*n2
4
p17=-------------------
2
a33
1 2 1 1 2 1 2
- ---*a33 *k16*n1 - ---*a33*b33*k38*n1 - ---*b33 *k1*n1 + ---*b33 *k12*n1
2 4 2 8
p16=----------------------------------------------------------------------------
3
a33
1 1
---*a33*k38*n1 + b33*k1*n1 - ---*b33*k12*n1
2 2
p15=---------------------------------------------
2
a33
- 2*a33*k38 - 2*b33*k1
p14=-------------------------
a33
1
---*k38*n3
2
p13=------------
a33
1
- ---*k12*n1
2
p12=---------------
a33
p11=0
1
---*k38*n1
2
p10=------------
a33
1
---*k38*n2
2
p9=------------
a33
p8= - 4*k1
1
- k1*n1 + ---*k12*n1
2
p7=-----------------------
a33
- b33*k1*n3
p6=--------------
2
a33
1 1
- ---*b33*k1*n2 - ---*b33*k12*n2
2 4
p5=-----------------------------------
2
a33
1 1 1
---*a33*k38*n1 - ---*b33*k1*n1 - ---*b33*k12*n1
2 2 4
p4=-------------------------------------------------
2
a33
1
- k1*n3 + ---*k12*n3
2
p3=-----------------------
a33
1
- k1*n2 + ---*k12*n2
2
p2=-----------------------
a33
1
- k1*n1 + ---*k12*n1
2
p1=-----------------------
a33
k125=0
1 2 2 1 4 1 4
---*a33 *b33 *k16 + ---*b33 *k1 - ----*b33 *k12
4 8 16
k124=-------------------------------------------------
4
a33
k123=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + ----*b33 *k1 - ----*b33 *k12
4 16 16
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
4 8 16
k117=-------------------------------------------------
4
a33
k116=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + ---*b33 *k1 - ---*b33 *k12
2 8 8
k115=------------------------------------------------
4
a33
k114=0
k113=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + ----*b33 *k1 - ----*b33 *k12
4 16 16
k112=--------------------------------------------------
4
a33
k110=0
1 3
- ---*b33 *k1
2
k109=----------------
3
a33
k108=0
k107=0
k106=0
k105=0
1 3
- ---*b33 *k1
2
k104=----------------
3
a33
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
a33*k38 - b33*k12
k95=-------------------
a33
k94=0
k93=0
k91=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k90=-------------------------------------------
3
a33
k89=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k88=-------------------------------------------
3
a33
k87=0
k86=0
k85=0
k84=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k83=-------------------------------------------
3
a33
k82=0
k81=0
2 1 2
- 2*b33 *k1 + ---*b33 *k12
2
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
2 4
k71=---------------------------------------
2
a33
k70=0
k69=k16
k68=0
k67=0
2 2 1 2
a33 *k16 + b33 *k1 - ---*b33 *k12
4
k66=-----------------------------------
2
a33
- 2*b33*k1
k65=-------------
a33
k64=0
k63=0
k62=k12
k61=0
k59=0
k58=0
k57=k1
k56=0
k55=0
k54=0
k53=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k52=-------------------------------------------
3
a33
k51=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k50=-------------------------------------------
3
a33
k49=0
k48=0
2 1 3 1 3
a33 *b33*k16 + ---*b33 *k1 - ---*b33 *k12
2 4
k47=-------------------------------------------
3
a33
k46=0
k45=0
k44=0
2 1 2
- 2*b33 *k1 + ---*b33 *k12
2
k43=-----------------------------
2
a33
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
2 1 2
- 2*b33 *k1 + ---*b33 *k12
2
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
2 4
k21=---------------------------------------
2
a33
k20=0
2 2 1 2
a33 *k16 + b33 *k1 - ---*b33 *k12
4
k19=-----------------------------------
2
a33
k18=0
k17=0
- 2*b33*k1
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:
q1, k38, k16, k12, k1, n1, 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.
{n1 - n2,
n1 + n2,
n1,
n2,
a33,
n3,
b33,
4 4 4 4
64*a33 *k1*v120 - 16*a33 *k1*w071 - 32*a33 *k1*w121 - 16*a33 *k1*w127
4 4 4 4
- 16*a33 *k12*w066 - 16*a33 *k12*w116 - 16*a33 *k16*w057 - 16*a33 *k16*w059
4 4 4 4
- 16*a33 *k16*w062 - 16*a33 *k16*w107 - 16*a33 *k16*w109 - 16*a33 *k16*w112
4 4 4 4
- 32*a33 *k38*v100 + 32*a33 *k38*v114 - 16*a33 *k38*w033 - 16*a33 *k38*w054
4 3 3
- 16*a33 *k38*w090 - 32*a33 *b33*k1*v100 + 32*a33 *b33*k1*v114
3 3 3
+ 32*a33 *b33*k1*w063 + 32*a33 *b33*k1*w113 + 16*a33 *b33*k12*w033
3 3 3
- 16*a33 *b33*k16*w038 - 16*a33 *b33*k16*w040 - 16*a33 *b33*k16*w045
3 3 3
- 16*a33 *b33*k16*w076 - 16*a33 *b33*k16*w078 - 16*a33 *b33*k16*w081
3 3 3
+ 16*a33 *k1*n1*v121 + 16*a33 *k1*n1*v127 + 16*a33 *k1*n2*v106
3 3 3
+ 16*a33 *k1*n2*v126 + 16*a33 *k1*n3*v105 + 16*a33 *k1*n3*v125
3 3 3
+ 8*a33 *k12*n1*v116 - 8*a33 *k12*n1*v121 - 8*a33 *k12*n1*v127
3 3 3
+ 8*a33 *k12*n2*v101 - 8*a33 *k12*n2*v106 - 8*a33 *k12*n2*v126
3 3 3
+ 8*a33 *k12*n3*v091 - 8*a33 *k12*n3*v105 - 8*a33 *k12*n3*v125
3 3 3
+ 8*a33 *k16*n1*v107 + 8*a33 *k16*n1*v109 + 8*a33 *k16*n1*v112
3 3 3
+ 8*a33 *k16*n2*v092 + 8*a33 *k16*n2*v094 + 8*a33 *k16*n2*v097
3 3 3
+ 8*a33 *k16*n3*v082 + 8*a33 *k16*n3*v084 + 8*a33 *k16*n3*v087
3 3 3
- 8*a33 *k38*n1*v113 - 8*a33 *k38*n1*v118 - 8*a33 *k38*n1*v124
3 3 3
- 8*a33 *k38*n2*v098 - 8*a33 *k38*n2*v103 - 8*a33 *k38*n2*v119
3 3 3
- 8*a33 *k38*n3*v088 - 8*a33 *k38*n3*v099 - 8*a33 *k38*n3*v115
2 2 2 2 2 2
- 16*a33 *b33 *k1*v086 + 32*a33 *b33 *k1*w048 - 8*a33 *b33 *k1*w057
2 2 2 2 2 2
- 16*a33 *b33 *k1*w062 + 32*a33 *b33 *k1*w085 + 32*a33 *b33 *k1*w096
2 2 2 2 2 2
- 8*a33 *b33 *k1*w107 - 16*a33 *b33 *k1*w109 + 4*a33 *b33 *k12*v086
2 2 2 2 2 2
- 4*a33 *b33 *k12*v095 + 4*a33 *b33 *k12*v108 - 8*a33 *b33 *k12*w048
2 2 2 2 2 2
+ 4*a33 *b33 *k12*w057 + 4*a33 *b33 *k12*w062 - 8*a33 *b33 *k12*w085
2 2 2 2 2 2
- 8*a33 *b33 *k12*w096 + 4*a33 *b33 *k12*w107 + 4*a33 *b33 *k12*w109
2 2 2 2 2 2
- 4*a33 *b33 *k16*w004 - 4*a33 *b33 *k16*w006 - 4*a33 *b33 *k16*w011
2 2 2 2 2
- 8*a33 *b33 *k16*w013 - 4*a33 *b33 *k16*w016 + 8*a33 *b33*k1*n1*v104
2 2 2
- 16*a33 *b33*k1*n1*v113 + 8*a33 *b33*k1*n1*v124 - 16*a33 *b33*k1*n2*v098
2 2 2
+ 8*a33 *b33*k1*n2*v103 + 8*a33 *b33*k1*n2*v123 - 16*a33 *b33*k1*n3*v088
2 2 2
+ 16*a33 *b33*k1*n3*v102 + 16*a33 *b33*k1*n3*v122 + 4*a33 *b33*k12*n1*v090
2 2 2
+ 4*a33 *b33*k12*n1*v104 + 8*a33 *b33*k12*n1*v113 + 4*a33 *b33*k12*n1*v124
2 2 2
+ 4*a33 *b33*k12*n2*v089 + 8*a33 *b33*k12*n2*v098 + 4*a33 *b33*k12*n2*v103
2 2 2
+ 4*a33 *b33*k12*n2*v123 + 16*a33 *b33*k12*n3*v088 + 4*a33 *b33*k16*n1*v076
2 2 2
+ 4*a33 *b33*k16*n1*v078 + 4*a33 *b33*k16*n1*v081 + 4*a33 *b33*k16*n2*v073
2 2 2
+ 4*a33 *b33*k16*n2*v075 + 4*a33 *b33*k16*n2*v080 + 8*a33 *b33*k16*n3*v072
2 2 2
+ 8*a33 *b33*k16*n3*v074 + 8*a33 *b33*k16*n3*v079 + 4*a33 *b33*k38*n1*v085
2 2 2
+ 4*a33 *b33*k38*n1*v096 + 4*a33 *b33*k38*n1*v112 + 4*a33 *b33*k38*n2*v083
2 2 3
+ 4*a33 *b33*k38*n2*v094 + 4*a33 *b33*k38*n2*v111 + 8*a33*b33 *k1*w019
3 3 3
+ 8*a33*b33 *k1*w024 - 8*a33*b33 *k1*w038 - 8*a33*b33 *k1*w040
3 3 3
- 8*a33*b33 *k1*w045 - 8*a33*b33 *k1*w076 - 8*a33*b33 *k1*w078
3 3 3
- 8*a33*b33 *k1*w081 + 4*a33*b33 *k12*w038 + 4*a33*b33 *k12*w040
3 3 3
+ 4*a33*b33 *k12*w045 + 4*a33*b33 *k12*w076 + 4*a33*b33 *k12*w078
3 2 2
+ 4*a33*b33 *k12*w081 - 8*a33*b33 *k1*n1*v085 + 4*a33*b33 *k1*n1*v107
2 2 2
+ 8*a33*b33 *k1*n1*v109 + 8*a33*b33 *k1*n1*v112 - 8*a33*b33 *k1*n2*v083
2 2 2
+ 4*a33*b33 *k1*n2*v092 + 8*a33*b33 *k1*n2*v094 + 8*a33*b33 *k1*n2*v097
2 2 2
- 12*a33*b33 *k1*n3*v082 + 8*a33*b33 *k1*n3*v084 + 8*a33*b33 *k1*n3*v087
2 2 2
- 4*a33*b33 *k12*n1*v085 - 2*a33*b33 *k12*n1*v109 - 2*a33*b33 *k12*n1*v112
2 2 2
- 4*a33*b33 *k12*n2*v083 - 2*a33*b33 *k12*n2*v094 - 2*a33*b33 *k12*n2*v097
2 2 4
- 2*a33*b33 *k12*n3*v084 - 2*a33*b33 *k12*n3*v087 - 2*b33 *k1*w004
4 4 4 4
- 3*b33 *k1*w006 - 2*b33 *k1*w011 - 6*b33 *k1*w013 - 3*b33 *k1*w016
4 4 4 4
+ b33 *k12*w004 + b33 *k12*w006 + b33 *k12*w011 + 2*b33 *k12*w013
4 3 3 3
+ b33 *k12*w016 + 2*b33 *k1*n1*v076 + 4*b33 *k1*n1*v078 + 4*b33 *k1*n1*v081
3 3 3
+ 2*b33 *k1*n2*v073 + 4*b33 *k1*n2*v075 + 4*b33 *k1*n2*v080
3 3 3
+ 4*b33 *k1*n3*v072 + 8*b33 *k1*n3*v074 + 8*b33 *k1*n3*v079
3 3 3
- 2*b33 *k12*n1*v076 - b33 *k12*n1*v078 - b33 *k12*n1*v081
3 3 3
- 2*b33 *k12*n2*v073 - b33 *k12*n2*v075 - b33 *k12*n2*v080
3 3 3
- 2*b33 *k12*n3*v072 - 2*b33 *k12*n3*v074 - 2*b33 *k12*n3*v079}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2 2 2 2
HAM=( - 4*a33 *u1 - 4*a33 *u2 + 4*a33 *u3 + 4*a33*b33*u3*v3 + 4*a33*n1*u1
2 2
+ 4*a33*n2*u2 + 4*a33*n3*u3 + b33 *v3 + 2*b33*n3*v3)/(4*a33)
has apart from the Hamiltonian and Casimirs the following first integrals:
4 4 4 2 4 2 4 2
INT=16*a33 *u1 + 32*a33 *u1 *u2*u3 + 16*a33 *u1*u2*v2 - 64*a33 *u1*u3
4 3 3
- 64*a33 *u1*v1 - 32*a33 *b33*u1*u3*v1 - 96*a33 *b33*u1*u3
3 3 4 3 2 2
+ 32*a33 *b33*u2*v1*v2 - 32*a33 *b33*u3 - 32*a33 *b33*v1 *v2
3 2 3 3 3 3 2
- 96*a33 *b33*v1 - 16*a33 *n1*u1 - 8*a33 *n1*u1 - 16*a33 *n1*u2 *u3
3 3 2 3
+ 16*a33 *n1*u2*v1 - 16*a33 *n2*u1 *u2 - 16*a33 *n2*u1*u2*v2
3 2 3 3 2 3 2
+ 16*a33 *n2*u2 + 8*a33 *n2*u2 - 16*a33 *n3*u1*u2 - 16*a33 *n3*u2 *v2
2 2 3 2 2 2 2 2
+ 8*a33 *b33 *u1 *v3 + 8*a33 *b33 *u1*u2*u3*v1 - 32*a33 *b33 *u1*u3 *v2
2 2 3 2 2 2 2 3
- 32*a33 *b33 *u1*v1 + 16*a33 *b33 *u1*v1*v3 + 16*a33 *b33 *u1*v2
2 2 2 2 3 2 2 3
- 32*a33 *b33 *u1*v3 + 16*a33 *b33 *u2 *v1 - 32*a33 *b33 *u3 *v3
2 2 2 2 3
- 32*a33 *b33 *v1*v3 - 8*a33 *b33*n1*u1*u3*v2 - 8*a33 *b33*n1*u2
2 2 2
+ 16*a33 *b33*n1*u2*u3*v1 + 8*a33 *b33*n1*v1*v2 + 20*a33 *b33*n1*v1
2 2 2 2
- 8*a33 *b33*n2*u1 *u3 - 8*a33 *b33*n2*u2*u3*v2 - 8*a33 *b33*n2*u3*v2
2 2 2 2
+ 16*a33 *b33*n2*v1 *v2 + 20*a33 *b33*n2*v2 - 16*a33 *b33*n3*u1*u2*u3
2 2 2 2
+ 16*a33 *b33*n3*u2*u3*v3 - 16*a33 *b33*n3*u2*u3 - 16*a33 *b33*n3*u3 *v2
2 2 2 2
+ 16*a33 *b33*n3*u3*v1 + 32*a33 *b33*n3*v3 - 4*a33 *n1 *u1*v1
2 2 2 2 2
+ 8*a33 *n1*n2*u1*u2 - 4*a33 *n1*n2*u3 + 8*a33 *n1*n3*u2 + 4*a33 *n1*n3*u2
2 2 2 2
+ 4*a33 *n2 *u1*v1 - 4*a33 *n2*n3*u1 + 8*a33 *n2*n3*u2*v1
3 3 2 3 2
+ 8*a33*b33 *u1*u2*v1*v2 - 8*a33*b33 *u1*u3*v3 + 8*a33*b33 *u1*v1 *v2
3 2 3 3 2
+ 8*a33*b33 *u2 *v1*v3 + 8*a33*b33 *u2*u3*v1*v2 + 8*a33*b33 *u2*v1 *v3
3 3 3 2 2 2
+ 8*a33*b33 *v1 *v3 - 8*a33*b33 *v1*v2 *v3 - 4*a33*b33 *n1*u1 *v2
2 2 2 2 2
+ 8*a33*b33 *n1*u2*v1*v3 - 8*a33*b33 *n1*u3 *v1 - 8*a33*b33 *n1*u3*v1
2 2 2 2 2 2
- 4*a33*b33 *n2*u1 *v3 - 8*a33*b33 *n2*u1*v2 + 8*a33*b33 *n2*v1 *v3
2 2 2 2 2
- 8*a33*b33 *n2*v1*v2 + 12*a33*b33 *n3*u1*v2*v3 - 8*a33*b33 *n3*u3 *v3
2 2 2
- 8*a33*b33 *n3*u3*v1*v3 - 4*a33*b33*n1 *v1 + 4*a33*b33*n1*n2*u2*u3
2
+ 4*a33*b33*n1*n2*u3*v1 + 8*a33*b33*n1*n3*u3 + 4*a33*b33*n1*n3*u3*v2
2 2
+ 2*a33*b33*n1*n3*v2 + 4*a33*b33*n2 *v1 + 8*a33*b33*n2*n3*u1*v2
2
+ 4*a33*b33*n2*n3*v1*v2 - 2*a33*b33*n2*n3*v1 - 8*a33*b33*n3 *u1*u3
2 2 3 2 2
- 8*a33*b33*n3 *v1 + 2*a33*n1 *u1 + 2*a33*n1 *n2*u2 + 2*a33*n1 *n3*u3
2 2 3 4 2
- 2*a33*n1*n3 *u1 - 2*a33*n2*n3 *u2 - 2*a33*n3 *u3 + 3*b33 *u1*v1*v3
4 2 4 3 4 2 2 4 3
+ 2*b33 *u2*v2*v3 + 3*b33 *u2*v3 + 6*b33 *v1 *v3 + 2*b33 *v1*v3
3 3 2 3 2
- 4*b33 *n1*u2*v2*v3 - 2*b33 *n1*u2*v3 - 4*b33 *n1*v2 *v3
3 3 2 3 2
- 4*b33 *n2*u3*v2*v3 - 4*b33 *n2*u3*v3 - 2*b33 *n2*v2*v3
3 3 2 3 3 2 2
- 8*b33 *n3*v1*v2*v3 - 8*b33 *n3*v1*v3 - 4*b33 *n3*v3 - b33 *n1 *v1*v3
2 2 2 2
+ 2*b33 *n1*n2*u2*v3 + 4*b33 *n1*n3*u3*v3 + b33 *n2 *v1*v3
2 2 2 2 2 3
+ 4*b33 *n2*n3*v2*v3 - 4*b33 *n3 *u1*v3 - 4*b33 *n3 *v1*v3 + b33*n1 *v1
2 2 2 2
+ b33*n1 *n2*v2 + 2*b33*n1 *n3*v3 + b33*n1*n3 *v1 + b33*n2*n3 *v2
3 2 3
=(((2*(3*v1 + v3) + 3*u1)*v1 + (2*v2 + 3*v3)*u2)*b33 *v3 + n1 *v1
2 2 2
+ n1*n3 *v1 + n2*n3 *v2 + (n2*v2 + 2*n3*v3)*n1 )*b33
2 2 2 4
- 16*(4*(u3 + v1) - u2*v2 - (u1 + 2*u2*u3)*u1)*a33 *u1 - 2*(
2
(2*(v2 + v3)*u3 + v2*v3)*n2 + 2*(2*(v2 + v3)*v1 + v3 )*n3
2 3
+ ((2*v2 + v3)*u2 + 2*v2 )*n1)*b33 *v3 +
2 2
((n2*v1 + 4*n3*v2)*n2 - n1 *v1 - 4*(u1 + v1)*n3 + 2*(n2*u2 + 2*n3*u3)*n1)
2
*b33 *v3 - 8*(((2*(u1 + v2)*u1 - (2*u2 + 1))*n2 + 2*(u1 + v2)*n3*u2)*u2
2
+ ((2*u1 + 1)*u1 + 2*(u2*u3 - v1)*u2)*n1
4 2 2 3
- 4*(u2*v1*v2 - u3 - (v2 + 3)*v1 - (v1 + 3)*u1*u3)*b33)*a33 + 2*(4*(
2
(((v1 + v2)*(v1 - v2) + u2 )*v3 + (u3*v2 + v1*v3)*u2)*v1
2 2 3
- (u3*v3 - v1 *v2 - u2*v1*v2)*u1)*b33
+ (n1*u1 + n2*u2 + n3*u3)*(n1 + n3)*(n1 - n3) - 2*(
2 2
((u1*v3 + 2*v2 )*u1 - 2*(v1*v3 - v2 )*v1)*n2
+ (2*(u3 + v1)*u3 - 3*u1*v2)*n3*v3
2 2
+ (2*((u3 + v1)*u3 - u2*v3)*v1 + u1 *v2)*n1)*b33 - (
2 2 2
2*((n1 + n2)*(n1 - n2)*v1 + 2*(u1*u3 + v1 )*n3 )
- ((2*v2 - 1)*v1 + 4*u1*v2)*n2*n3
2
- (2*(u2 + v1)*n2*u3 + (4*u3 + 2*u3*v2 + v2)*n3)*n1)*b33)*a33 - 4*(2
2 3 2
*((2*((2*v1 - v3)*v1 - (v2 - 2*v3) + 2*u3 *v2) - u2*u3*v1)*u1
3 3 3 2
+ 2*(2*(u3 + v1)*v3 - u2 *v1) - u1 *v3)*b33
+ (n1 + n2)*(n1 - n2)*u1*v1 + (u1 - 2*u2*v1)*n2*n3
- ((2*u1*u2 - u3)*n2 + (2*u2 + 1)*n3*u2)*n1 + (
2
(2*((u2 - 2*u3*v1)*u2 + u1*u3*v2) - (2*v2 + 5)*v1)*n1
2
+ 4*(u3 *v2 - u3*v1 - 2*v3 + u1*u2*u3 - (v3 - 1)*u2*u3)*n3
2 2 2
- ((4*v1 + 5 - 2*u3 - 2*u2*u3)*v2 - 2*u1 *u3)*n2)*b33)*a33
4 2 4 2 2 3
INT=16*a33 *u1*v1*v2 + 16*a33 *u2 *u3 - 16*a33 *b33*u2*u3*v2*v3
3 3 3 3 3 2
+ 8*a33 *n1*u1 - 8*a33 *n1*u1*u2*v1 + 8*a33 *n1*u1 + 8*a33 *n1*u2 *u3
3 3 2 3
- 16*a33 *n1*u2*v1 + 8*a33 *n2*u1 *u2 + 8*a33 *n2*u1*u2*v2
3 3 2 3
- 8*a33 *n2*u1*v1*v2 + 8*a33 *n3*u1*u2 - 8*a33 *n3*u1*u2*v3
3 2 2 2 3 2 2
+ 8*a33 *n3*u2 *v2 - 4*a33 *b33 *u1 *v3 - 4*a33 *b33 *u1*u2*u3*v1
2 2 2 2 2 3 2 2
+ 8*a33 *b33 *u1*u3 *v2 + 8*a33 *b33 *u1*v1 - 4*a33 *b33 *u1*v1*v3
2 2 3 2 2 3 2 2 3
- 4*a33 *b33 *u1*v2 - 4*a33 *b33 *u2 *v1 + 8*a33 *b33 *u3 *v3
2 2 2 2 2 3 2
+ 4*a33 *b33 *u3*v2 - 4*a33 *b33 *v1 - 4*a33 *b33*n1*u1*u3*v2
2 2 3 2 2
- 8*a33 *b33*n1*u1*v2 - 4*a33 *b33*n1*u2 - 4*a33 *b33*n1*u2 *v3
2 2 2 2
- 8*a33 *b33*n1*u2*u3*v1 + 4*a33 *b33*n1*v1 - 4*a33 *b33*n2*u1 *u3
2 2 2 2
- 4*a33 *b33*n2*u1*u3*v3 - 4*a33 *b33*n2*u2*u3*v2 + 8*a33 *b33*n2*u3
2 2 2 2
- 8*a33 *b33*n2*v1 *v2 + 4*a33 *b33*n2*v2 - 16*a33 *b33*n3*u2*u3*v3
2 2 2 2
+ 4*a33 *n1 *u1*v1 - 8*a33 *n1*n2*u1*u2 + 4*a33 *n1*n2*u3
2 2 2 2 2 2
- 8*a33 *n1*n3*u2 - 4*a33 *n1*n3*u2 - 4*a33 *n2 *u1*v1 + 4*a33 *n2*n3*u1
2 3 3 2
- 8*a33 *n2*n3*u2*v1 - 4*a33*b33 *u1*u2*v1*v2 - 4*a33*b33 *u1*v1 *v2
3 2 3 3 2
- 4*a33*b33 *u2 *v1*v3 - 4*a33*b33 *u2*u3*v1*v2 - 4*a33*b33 *u2*v1 *v3
3 3 2 2 2
- 4*a33*b33 *v1 *v3 + 4*a33*b33 *n1*u2*v1*v3 + 2*a33*b33 *n1*u3 *v1
2 2 2 2 2
+ 2*a33*b33 *n1*u3*v1 - 4*a33*b33 *n1*v2*v3 + 2*a33*b33 *n2*u1*v2
2 2 2 2 2
+ 4*a33*b33 *n2*u3*v3 + 4*a33*b33 *n2*v1 *v3 + 2*a33*b33 *n2*v1*v2
2 2 2 2
+ 2*a33*b33 *n3*u3 *v3 + 2*a33*b33 *n3*u3*v1*v3 + 4*a33*b33*n1 *u1*u3
2 2 2
+ 4*a33*b33*n1 *v1 - 4*a33*b33*n1*n3*u3 - 2*a33*b33*n1*n3*v2
2
- 4*a33*b33*n2*n3*u1*v2 + 2*a33*b33*n2*n3*v1 + 4*a33*b33*n3 *u1*u3
2 2 3 2 2
+ 4*a33*b33*n3 *v1 - 2*a33*n1 *u1 - 2*a33*n1 *n2*u2 - 2*a33*n1 *n3*u3
2 2 3 4 2
+ 2*a33*n1*n3 *u1 + 2*a33*n2*n3 *u2 + 2*a33*n3 *u3 - b33 *u1*v1*v3
4 2 4 3 4 2 2 4 3
- b33 *u2*v2*v3 - b33 *u2*v3 - 2*b33 *v1 *v3 - b33 *v1*v3
3 3 2 3 2 3
+ b33 *n1*u2*v2*v3 + 2*b33 *n1*u2*v3 + b33 *n1*v2 *v3 + b33 *n2*u3*v2*v3
3 2 3 2 3 3 2
+ b33 *n2*u3*v3 + 2*b33 *n2*v2*v3 + 2*b33 *n3*v1*v2*v3 + 2*b33 *n3*v1*v3
3 3 2 2 2 2 2
+ 2*b33 *n3*v3 + 2*b33 *n1 *u1*v3 + b33 *n1 *v1*v3 + 2*b33 *n1*n2*u2*v3
2 2 2 2 3
+ 2*b33 *n1*n3*u3*v3 + b33 *n2 *v1*v3 + 2*b33 *n2*n3*v2*v3 - b33*n1 *v1
2 2 2 2
- b33*n1 *n2*v2 - 2*b33*n1 *n3*v3 - b33*n1*n3 *v1 - b33*n2*n3 *v2
3 2 2 2
= - ((n1 *v1 + n1*n3 *v1 + n2*n3 *v2 + (n2*v2 + 2*n3*v3)*n1 )*b33
2 2 2 4
- 16*(u1*v1*v2 + u2 *u3 )*a33
4 2
+ ((2*v1 + v3 + u1)*v1 + (v2 + v3)*u2)*b33 *v3 -
2 2
((n2*v1 + 2*n3*v2)*n2 + (2*u1 + v1)*n1 + 2*(n2*u2 + n3*u3)*n1)*b33 *v3
2
- (((v2 + v3)*u3 + 2*v2*v3)*n2 + 2*((v2 + v3)*v1 + v3 )*n3
2 3
+ ((v2 + 2*v3)*u2 + v2 )*n1)*b33 *v3 - 8*(
(((u2 - v3)*u1 + u2*v2)*n3 - 2*b33*u3*v2*v3)*u2
+ ((u2 - v1)*v2 + u1*u2)*n2*u1
3 3 3
+ ((u2*u3 - 2*v1)*u2 + u1 - (u2*v1 - 1)*u1)*n1)*a33 - 4*((2*u3 *v3
2 3 3 3
+ u3*v2 - v1 - u2 *v1 - u1 *v3
3 3 2 2
+ (2*v1 - v1*v3 - v2 + 2*u3 *v2 - u2*u3*v1)*u1)*b33
+ (n1 + n2)*(n1 - n2)*u1*v1 + (u1 - 2*u2*v1)*n2*n3
- ((2*u1*u2 - u3)*n2 + (2*u2 + 1)*n3*u2)*n1 - (
2 2
((2*v1 - 1)*v2 - 2*u3 + u2*u3*v2 + (u1 + v3)*u1*u3)*n2
3 2
+ (u2 + u2 *v3 + 2*u2*u3*v1 - v1 + (u3 + 2)*u1*v2)*n1
2
+ 4*n3*u2*u3*v3)*b33)*a33 + 2*(
2 2 3
2*((u2 + v1 )*v3 + (u3*v2 + v1*v3)*u2 + (u2 + v1)*u1*v2)*b33 *v1
+ (n1*u1 + n2*u2 + n3*u3)*(n1 + n3)*(n1 - n3) + (
2
((2*u1*v2 - v1)*n2 + (2*u3 + v2)*n1)*n3
2 2 2
- 2*(n1 + n3 )*(u1*u3 + v1 ))*b33 - (
2 2
(u3 *v1 + u3*v1 - 2*v2*v3 + 2*u2*v1*v3)*n1 + (u3 + v1)*n3*u3*v3
2 2 2
+ ((2*v1*v3 + v2 )*v1 + 2*u3*v3 + u1*v2 )*n2)*b33 )*a33)
2 3 2 3 2 2 3
INT=4*a33 *u1 *v1 + 4*a33 *u1 *v3 + 4*a33 *u1*u2*u3*v1 + 4*a33 *u1*v2
2 3 2 3
+ 4*a33 *u2 *v1 + 4*a33 *v1*v2 + 4*a33*b33*u1*u2*v1*v2
2 2
+ 4*a33*b33*u1*v1 *v2 + 4*a33*b33*u2 *v1*v3 + 4*a33*b33*u2*u3*v1*v2
2 3 2
+ 4*a33*b33*u2*v1 *v3 + 4*a33*b33*v1 *v3 - 2*a33*n1*u1 *v2
2 2 2 2
- 2*a33*n1*u3 *v1 - 2*a33*n1*u3*v1 - 2*a33*n2*u1 *v3 - 2*a33*n2*u1*v2
2 2
- 2*a33*n2*v1*v2 - 2*a33*n3*u1*v2*v3 - 2*a33*n3*u3 *v3 - 2*a33*n3*u3*v1*v3
2 2 2 2 2 3 2 2 2
+ b33 *u1*v1*v3 + b33 *u2*v2*v3 + b33 *u2*v3 + 2*b33 *v1 *v3
2 3 2 2
+ b33 *v1*v3 - b33*n1*u2*v2*v3 - b33*n1*u2*v3 - b33*n1*v2 *v3
2 2
- b33*n2*u3*v2*v3 - b33*n2*u3*v3 - b33*n2*v2*v3 - 2*b33*n3*v1*v2*v3
2 3
- 2*b33*n3*v1*v3 - 2*b33*n3*v3
2 2 2
= - (2*(((u3 + v1)*u3 + u1*v2)*n3*v3 + (u1 *v3 + u1*v2 + v1*v2 )*n2
2
+ ((u3 + v1)*u3*v1 + u1 *v2)*n1
2 2
- 2*((u2 + v1 )*v3 + (u3*v2 + v1*v3)*u2 + (u2 + v1)*u1*v2)*b33*v1)
2 2
*a33 - (((2*v1 + v3 + u1)*v1 + (v2 + v3)*u2)*b33 *v3 + 4
3 3 3 3 3 2
*(u1 *v1 + u1 *v3 + u2 *v1 + v1*v2 + (u2*u3*v1 + v2 )*u1)*a33
2
- (((v2 + v3)*u3 + v2*v3)*n2 + 2*((v2 + v3)*v1 + v3 )*n3
2
+ ((v2 + v3)*u2 + v2 )*n1)*b33*v3))
2 2 2 2 2 3
INT=4*a33 *u1*u2 *v2 - 8*a33 *u1*u3*v1 - 4*a33 *u1*u3 + 4*a33 *u2 *v3
2 2 2 2 3
+ 4*a33 *u2*u3*v2*v3 + 8*a33 *u2*v1*v2 - 4*a33 *v1 + 2*a33*n1*u2
3 2
+ 2*a33*n1*u2*u3*v1 + 2*a33*n1*u3 + 2*a33*n2*u2*u3 + 2*a33*n2*u2*u3*v2
2 2
- 2*a33*n2*u3*v2 + 2*a33*n2*v1 *v2 + 2*a33*n3*u2 *v1 + 2*a33*n3*u2*u3*v3
- 2*a33*n3*u2*u3 + 2*a33*n3*u3*v1*v2 + 2*a33*n3*u3*v1 - b33*n1*u2*v1*v3
2 2 2 2
- b33*n1*u2*v2 - b33*n1*u3 *v1 - b33*n2*u1*v1 - b33*n2*v1 *v3
2
- b33*n2*v1*v2
3 2 2 2
=4*(u2 *v3 - v1 + (u3*v3 + 2*v1)*u2*v2 - ((2*v1 + 1)*u3 - u2 *v2)*u1)*a33
2 2 2
- (((v1*v3 + v2 )*u2 + u3 *v1)*n1 + (v1*v3 + v2 + u1*v1)*n2*v1)*b33 - 2*(
2 3 3
((u3 - v1 )*v2 - (u3 + v2)*u2*u3)*n2 - (u2 + u2*u3*v1 + u3 )*n1
- (((v3 - 1)*u3 + u2*v1)*u2 + (v2 + 1)*u3*v1)*n3)*a33
2 2 2 2
INT=4*a33 *u1 + 4*a33 *u1*v1 + 4*a33*b33*u1*u3 + 4*a33*b33*v1 - 2*a33*n1*u1
2 2
- 2*a33*n2*u2 - 2*a33*n3*u3 + b33 *u1*v3 + b33 *v1*v3 - b33*n1*v1
- b33*n2*v2 - 2*b33*n3*v3
2
= - (2*(n2*u2 + n3*u3 + n1*u1 - 2*(u1*u3 + v1 )*b33)*a33
2 2
+ (n2*v2 + 2*n3*v3 + n1*v1)*b33 - (4*a33 *u1 + b33 *v3)*(u1 + v1))
And again in machine readable form:
HAM=( - 4*a33**2*u1**2 - 4*a33**2*u2**2 + 4*a33**2*u3**2 + 4*a33*b33*u3*v3 + 4*
a33*n1*u1 + 4*a33*n2*u2 + 4*a33*n3*u3 + b33**2*v3**2 + 2*b33*n3*v3)/(4*a33)$
INT=16*a33**4*u1**4 + 32*a33**4*u1**2*u2*u3 + 16*a33**4*u1*u2*v2**2 - 64*a33**4*
u1*u3**2 - 64*a33**4*u1*v1 - 32*a33**3*b33*u1*u3*v1 - 96*a33**3*b33*u1*u3 + 32*
a33**3*b33*u2*v1*v2 - 32*a33**3*b33*u3**4 - 32*a33**3*b33*v1**2*v2**2 - 96*a33**
3*b33*v1**2 - 16*a33**3*n1*u1**3 - 8*a33**3*n1*u1 - 16*a33**3*n1*u2**2*u3 + 16*
a33**3*n1*u2*v1 - 16*a33**3*n2*u1**2*u2 - 16*a33**3*n2*u1*u2*v2 + 16*a33**3*n2*
u2**2 + 8*a33**3*n2*u2 - 16*a33**3*n3*u1*u2**2 - 16*a33**3*n3*u2**2*v2 + 8*a33**
2*b33**2*u1**3*v3 + 8*a33**2*b33**2*u1*u2*u3*v1 - 32*a33**2*b33**2*u1*u3**2*v2 -
32*a33**2*b33**2*u1*v1**3 + 16*a33**2*b33**2*u1*v1*v3 + 16*a33**2*b33**2*u1*v2
**3 - 32*a33**2*b33**2*u1*v3 + 16*a33**2*b33**2*u2**3*v1 - 32*a33**2*b33**2*u3**
3*v3 - 32*a33**2*b33**2*v1*v3 - 8*a33**2*b33*n1*u1*u3*v2 - 8*a33**2*b33*n1*u2**3
+ 16*a33**2*b33*n1*u2*u3*v1 + 8*a33**2*b33*n1*v1*v2 + 20*a33**2*b33*n1*v1 - 8*
a33**2*b33*n2*u1**2*u3 - 8*a33**2*b33*n2*u2*u3*v2 - 8*a33**2*b33*n2*u3*v2 + 16*
a33**2*b33*n2*v1**2*v2 + 20*a33**2*b33*n2*v2 - 16*a33**2*b33*n3*u1*u2*u3 + 16*
a33**2*b33*n3*u2*u3*v3 - 16*a33**2*b33*n3*u2*u3 - 16*a33**2*b33*n3*u3**2*v2 + 16
*a33**2*b33*n3*u3*v1 + 32*a33**2*b33*n3*v3 - 4*a33**2*n1**2*u1*v1 + 8*a33**2*n1*
n2*u1*u2 - 4*a33**2*n1*n2*u3 + 8*a33**2*n1*n3*u2**2 + 4*a33**2*n1*n3*u2 + 4*a33
**2*n2**2*u1*v1 - 4*a33**2*n2*n3*u1 + 8*a33**2*n2*n3*u2*v1 + 8*a33*b33**3*u1*u2*
v1*v2 - 8*a33*b33**3*u1*u3*v3**2 + 8*a33*b33**3*u1*v1**2*v2 + 8*a33*b33**3*u2**2
*v1*v3 + 8*a33*b33**3*u2*u3*v1*v2 + 8*a33*b33**3*u2*v1**2*v3 + 8*a33*b33**3*v1**
3*v3 - 8*a33*b33**3*v1*v2**2*v3 - 4*a33*b33**2*n1*u1**2*v2 + 8*a33*b33**2*n1*u2*
v1*v3 - 8*a33*b33**2*n1*u3**2*v1 - 8*a33*b33**2*n1*u3*v1**2 - 4*a33*b33**2*n2*u1
**2*v3 - 8*a33*b33**2*n2*u1*v2**2 + 8*a33*b33**2*n2*v1**2*v3 - 8*a33*b33**2*n2*
v1*v2**2 + 12*a33*b33**2*n3*u1*v2*v3 - 8*a33*b33**2*n3*u3**2*v3 - 8*a33*b33**2*
n3*u3*v1*v3 - 4*a33*b33*n1**2*v1**2 + 4*a33*b33*n1*n2*u2*u3 + 4*a33*b33*n1*n2*u3
*v1 + 8*a33*b33*n1*n3*u3**2 + 4*a33*b33*n1*n3*u3*v2 + 2*a33*b33*n1*n3*v2 + 4*a33
*b33*n2**2*v1**2 + 8*a33*b33*n2*n3*u1*v2 + 4*a33*b33*n2*n3*v1*v2 - 2*a33*b33*n2*
n3*v1 - 8*a33*b33*n3**2*u1*u3 - 8*a33*b33*n3**2*v1**2 + 2*a33*n1**3*u1 + 2*a33*
n1**2*n2*u2 + 2*a33*n1**2*n3*u3 - 2*a33*n1*n3**2*u1 - 2*a33*n2*n3**2*u2 - 2*a33*
n3**3*u3 + 3*b33**4*u1*v1*v3**2 + 2*b33**4*u2*v2*v3**2 + 3*b33**4*u2*v3**3 + 6*
b33**4*v1**2*v3**2 + 2*b33**4*v1*v3**3 - 4*b33**3*n1*u2*v2*v3 - 2*b33**3*n1*u2*
v3**2 - 4*b33**3*n1*v2**2*v3 - 4*b33**3*n2*u3*v2*v3 - 4*b33**3*n2*u3*v3**2 - 2*
b33**3*n2*v2*v3**2 - 8*b33**3*n3*v1*v2*v3 - 8*b33**3*n3*v1*v3**2 - 4*b33**3*n3*
v3**3 - b33**2*n1**2*v1*v3 + 2*b33**2*n1*n2*u2*v3 + 4*b33**2*n1*n3*u3*v3 + b33**
2*n2**2*v1*v3 + 4*b33**2*n2*n3*v2*v3 - 4*b33**2*n3**2*u1*v3 - 4*b33**2*n3**2*v1*
v3 + b33*n1**3*v1 + b33*n1**2*n2*v2 + 2*b33*n1**2*n3*v3 + b33*n1*n3**2*v1 + b33*
n2*n3**2*v2$
INT=16*a33**4*u1*v1*v2**2 + 16*a33**4*u2**2*u3**2 - 16*a33**3*b33*u2*u3*v2*v3 +
8*a33**3*n1*u1**3 - 8*a33**3*n1*u1*u2*v1 + 8*a33**3*n1*u1 + 8*a33**3*n1*u2**2*u3
- 16*a33**3*n1*u2*v1 + 8*a33**3*n2*u1**2*u2 + 8*a33**3*n2*u1*u2*v2 - 8*a33**3*
n2*u1*v1*v2 + 8*a33**3*n3*u1*u2**2 - 8*a33**3*n3*u1*u2*v3 + 8*a33**3*n3*u2**2*v2
- 4*a33**2*b33**2*u1**3*v3 - 4*a33**2*b33**2*u1*u2*u3*v1 + 8*a33**2*b33**2*u1*
u3**2*v2 + 8*a33**2*b33**2*u1*v1**3 - 4*a33**2*b33**2*u1*v1*v3 - 4*a33**2*b33**2
*u1*v2**3 - 4*a33**2*b33**2*u2**3*v1 + 8*a33**2*b33**2*u3**3*v3 + 4*a33**2*b33**
2*u3*v2**2 - 4*a33**2*b33**2*v1**3 - 4*a33**2*b33*n1*u1*u3*v2 - 8*a33**2*b33*n1*
u1*v2 - 4*a33**2*b33*n1*u2**3 - 4*a33**2*b33*n1*u2**2*v3 - 8*a33**2*b33*n1*u2*u3
*v1 + 4*a33**2*b33*n1*v1 - 4*a33**2*b33*n2*u1**2*u3 - 4*a33**2*b33*n2*u1*u3*v3 -
4*a33**2*b33*n2*u2*u3*v2 + 8*a33**2*b33*n2*u3**2 - 8*a33**2*b33*n2*v1**2*v2 + 4
*a33**2*b33*n2*v2 - 16*a33**2*b33*n3*u2*u3*v3 + 4*a33**2*n1**2*u1*v1 - 8*a33**2*
n1*n2*u1*u2 + 4*a33**2*n1*n2*u3 - 8*a33**2*n1*n3*u2**2 - 4*a33**2*n1*n3*u2 - 4*
a33**2*n2**2*u1*v1 + 4*a33**2*n2*n3*u1 - 8*a33**2*n2*n3*u2*v1 - 4*a33*b33**3*u1*
u2*v1*v2 - 4*a33*b33**3*u1*v1**2*v2 - 4*a33*b33**3*u2**2*v1*v3 - 4*a33*b33**3*u2
*u3*v1*v2 - 4*a33*b33**3*u2*v1**2*v3 - 4*a33*b33**3*v1**3*v3 + 4*a33*b33**2*n1*
u2*v1*v3 + 2*a33*b33**2*n1*u3**2*v1 + 2*a33*b33**2*n1*u3*v1**2 - 4*a33*b33**2*n1
*v2*v3 + 2*a33*b33**2*n2*u1*v2**2 + 4*a33*b33**2*n2*u3*v3 + 4*a33*b33**2*n2*v1**
2*v3 + 2*a33*b33**2*n2*v1*v2**2 + 2*a33*b33**2*n3*u3**2*v3 + 2*a33*b33**2*n3*u3*
v1*v3 + 4*a33*b33*n1**2*u1*u3 + 4*a33*b33*n1**2*v1**2 - 4*a33*b33*n1*n3*u3**2 -
2*a33*b33*n1*n3*v2 - 4*a33*b33*n2*n3*u1*v2 + 2*a33*b33*n2*n3*v1 + 4*a33*b33*n3**
2*u1*u3 + 4*a33*b33*n3**2*v1**2 - 2*a33*n1**3*u1 - 2*a33*n1**2*n2*u2 - 2*a33*n1
**2*n3*u3 + 2*a33*n1*n3**2*u1 + 2*a33*n2*n3**2*u2 + 2*a33*n3**3*u3 - b33**4*u1*
v1*v3**2 - b33**4*u2*v2*v3**2 - b33**4*u2*v3**3 - 2*b33**4*v1**2*v3**2 - b33**4*
v1*v3**3 + b33**3*n1*u2*v2*v3 + 2*b33**3*n1*u2*v3**2 + b33**3*n1*v2**2*v3 + b33
**3*n2*u3*v2*v3 + b33**3*n2*u3*v3**2 + 2*b33**3*n2*v2*v3**2 + 2*b33**3*n3*v1*v2*
v3 + 2*b33**3*n3*v1*v3**2 + 2*b33**3*n3*v3**3 + 2*b33**2*n1**2*u1*v3 + b33**2*n1
**2*v1*v3 + 2*b33**2*n1*n2*u2*v3 + 2*b33**2*n1*n3*u3*v3 + b33**2*n2**2*v1*v3 + 2
*b33**2*n2*n3*v2*v3 - b33*n1**3*v1 - b33*n1**2*n2*v2 - 2*b33*n1**2*n3*v3 - b33*
n1*n3**2*v1 - b33*n2*n3**2*v2$
INT=4*a33**2*u1**3*v1 + 4*a33**2*u1**3*v3 + 4*a33**2*u1*u2*u3*v1 + 4*a33**2*u1*
v2**3 + 4*a33**2*u2**3*v1 + 4*a33**2*v1*v2**3 + 4*a33*b33*u1*u2*v1*v2 + 4*a33*
b33*u1*v1**2*v2 + 4*a33*b33*u2**2*v1*v3 + 4*a33*b33*u2*u3*v1*v2 + 4*a33*b33*u2*
v1**2*v3 + 4*a33*b33*v1**3*v3 - 2*a33*n1*u1**2*v2 - 2*a33*n1*u3**2*v1 - 2*a33*n1
*u3*v1**2 - 2*a33*n2*u1**2*v3 - 2*a33*n2*u1*v2**2 - 2*a33*n2*v1*v2**2 - 2*a33*n3
*u1*v2*v3 - 2*a33*n3*u3**2*v3 - 2*a33*n3*u3*v1*v3 + b33**2*u1*v1*v3**2 + b33**2*
u2*v2*v3**2 + b33**2*u2*v3**3 + 2*b33**2*v1**2*v3**2 + b33**2*v1*v3**3 - b33*n1*
u2*v2*v3 - b33*n1*u2*v3**2 - b33*n1*v2**2*v3 - b33*n2*u3*v2*v3 - b33*n2*u3*v3**2
- b33*n2*v2*v3**2 - 2*b33*n3*v1*v2*v3 - 2*b33*n3*v1*v3**2 - 2*b33*n3*v3**3$
INT=4*a33**2*u1*u2**2*v2 - 8*a33**2*u1*u3*v1 - 4*a33**2*u1*u3 + 4*a33**2*u2**3*
v3 + 4*a33**2*u2*u3*v2*v3 + 8*a33**2*u2*v1*v2 - 4*a33**2*v1**2 + 2*a33*n1*u2**3
+ 2*a33*n1*u2*u3*v1 + 2*a33*n1*u3**3 + 2*a33*n2*u2*u3**2 + 2*a33*n2*u2*u3*v2 - 2
*a33*n2*u3*v2 + 2*a33*n2*v1**2*v2 + 2*a33*n3*u2**2*v1 + 2*a33*n3*u2*u3*v3 - 2*
a33*n3*u2*u3 + 2*a33*n3*u3*v1*v2 + 2*a33*n3*u3*v1 - b33*n1*u2*v1*v3 - b33*n1*u2*
v2**2 - b33*n1*u3**2*v1 - b33*n2*u1*v1**2 - b33*n2*v1**2*v3 - b33*n2*v1*v2**2$
INT=4*a33**2*u1**2 + 4*a33**2*u1*v1 + 4*a33*b33*u1*u3 + 4*a33*b33*v1**2 - 2*a33*
n1*u1 - 2*a33*n2*u2 - 2*a33*n3*u3 + b33**2*u1*v3 + b33**2*v1*v3 - b33*n1*v1 -
b33*n2*v2 - 2*b33*n3*v3$