Solution 16 to problem e3c2new
Expressions |
Parameters |
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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
n3=0
m1=0
m2=0
m3=0
r6=0
1 2 1 2 1 2
- ---*a33 *b33*n2*q1 + ----*b33*k1*n1 *n2 - ----*b33*k10*n1 *n2
4 16 16
r5=------------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*n1*q1 + ----*b33*k1*n1 - ----*b33*k10*n1
4 16 16
r4=------------------------------------------------------------
4
a33
r3=0
1 2 1 2 1 2
- ---*a33 *n2*q1 + ---*k1*n1 *n2 - ---*k10*n1 *n2
2 8 8
r2=----------------------------------------------------
3
a33
1 2 1 3 1 3
- ---*a33 *n1*q1 + ---*k1*n1 - ---*k10*n1
2 8 8
r1=----------------------------------------------
3
a33
q20=0
q19=0
q17=0
q16=0
1 2 2 1 2 2 1 2 2 1 2 2
q15=(---*a33 *b33 *q1 - ----*b33 *k1*n1 + ----*b33 *k1*n2 + ----*b33 *k10*n1
4 16 16 16
1 2 2 4
+ ----*b33 *k10*n2 )/a33
16
1 2 1 2
---*b33 *k1*n1*n2 + ---*b33 *k10*n1*n2
8 8
q14=----------------------------------------
4
a33
q13=0
2 1 2 1 2 1 2
a33 *b33*q1 - ---*b33*k1*n1 + ---*b33*k1*n2 + ---*b33*k10*n1
4 4 4
q12=-----------------------------------------------------------------
3
a33
1
---*b33*k1*n1*n2
4
q11=------------------
3
a33
1 2 2 1 2 2
---*a33 *b33 *q1 + ---*b33 *k10*n1
4 8
q10=-------------------------------------
4
a33
q9=0
1
---*b33*k1*n1*n2
4
q8=------------------
3
a33
2 1 2
a33 *b33*q1 + ---*b33*k10*n1
4
q7=-------------------------------
3
a33
q5=0
q4=0
2 1 2 1 2 1 2 1 2
a33 *q1 - ---*k1*n1 + ---*k1*n2 + ---*k10*n1 - ---*k10*n2
4 4 4 4
q3=---------------------------------------------------------------
2
a33
1 1
---*k1*n1*n2 - ---*k10*n1*n2
2 2
q2=------------------------------
2
a33
p56=0
1 2 1 3 1 3
- ---*a33 *b33*k26*n2 - ---*b33 *k1*n2 + ---*b33 *k10*n2
4 8 8
p55=-----------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n1 - ---*b33 *k1*n1 + ---*b33 *k10*n1
4 8 8
p54=-----------------------------------------------------------
4
a33
p53=0
1 2 1 2
- ---*a33 *k26*n2 - ---*b33 *k1*n2
2 4
p52=-------------------------------------
3
a33
1 2 1 2
- ---*a33 *k26*n1 - ---*b33 *k1*n1
2 4
p51=-------------------------------------
3
a33
p50=0
p49=0
1 1 2 1 2
- ---*a33*b33*k23*n2 + ---*b33 *k1*n2 + ---*b33 *k10*n2
4 2 4
p48=----------------------------------------------------------
3
a33
p47=0
p46=0
p45=0
1 1 2 1 2
- ---*a33*b33*k23*n1 + ---*b33 *k1*n1 + ---*b33 *k10*n1
4 2 4
p44=----------------------------------------------------------
3
a33
p43=0
p42=0
p41=0
1 1
---*a33*k23*n2 + b33*k1*n2 - ---*b33*k10*n2
2 2
p40=---------------------------------------------
2
a33
1 1
---*a33*k23*n1 + b33*k1*n1 - ---*b33*k10*n1
2 2
p39=---------------------------------------------
2
a33
p38=0
p37=0
p36=0
1 2 1 3 1 3
- ---*a33 *b33*k26*n2 - ---*b33 *k1*n2 + ----*b33 *k10*n2
4 4 16
p35=------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n1 - ---*b33 *k1*n1 + ----*b33 *k10*n1
4 4 16
p34=------------------------------------------------------------
4
a33
p33=0
1 2 1 1 2 1 2
- ---*a33 *k26*n2 - ---*a33*b33*k23*n2 - ---*b33 *k1*n2 + ---*b33 *k10*n2
2 4 2 8
p32=----------------------------------------------------------------------------
3
a33
1 2 1 2 1 2
- ---*a33 *k26*n1 - ---*b33 *k1*n1 + ---*b33 *k10*n1
2 2 8
p31=-------------------------------------------------------
3
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n2 - ---*b33 *k1*n2 + ----*b33 *k10*n2
4 4 16
p30=------------------------------------------------------------
4
a33
p29=0
1
- ---*b33*k23*n1
4
p28=-------------------
2
a33
1
- ---*b33*k23*n2
4
p27=-------------------
2
a33
1
- ---*b33*k10*n2
4
p26=-------------------
2
a33
p25=0
p24=0
1 1 1
---*a33*k23*n2 - ---*b33*k1*n2 - ---*b33*k10*n2
2 2 4
p23=-------------------------------------------------
2
a33
1
---*k23*n1
2
p22=------------
a33
1 1
- ---*b33*k1*n2 - ---*b33*k10*n2
2 4
p21=-----------------------------------
2
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n1 - ---*b33 *k1*n1 + ----*b33 *k10*n1
4 4 16
p20=------------------------------------------------------------
4
a33
p19=0
1 2 1 2 1 2
- ---*a33 *k26*n2 - ---*b33 *k1*n2 + ---*b33 *k10*n2
2 2 8
p18=-------------------------------------------------------
3
a33
1 2 1 1 2 1 2
- ---*a33 *k26*n1 - ---*a33*b33*k23*n1 - ---*b33 *k1*n1 + ---*b33 *k10*n1
2 4 2 8
p17=----------------------------------------------------------------------------
3
a33
1
- ---*b33*k10*n1
4
p16=-------------------
2
a33
p15=0
p14=0
1 1
- ---*b33*k1*n1 - ---*b33*k10*n1
2 4
p13=-----------------------------------
2
a33
1
---*k23*n2
2
p12=------------
a33
1 1 1
---*a33*k23*n1 - ---*b33*k1*n1 - ---*b33*k10*n1
2 2 4
p11=-------------------------------------------------
2
a33
p10=0
1
- ---*k10*n2
2
p9=---------------
a33
1
- ---*k10*n1
2
p8=---------------
a33
p7=0
p6=0
p5=0
1
- k1*n2 + ---*k10*n2
2
p4=-----------------------
a33
1
- k1*n1 + ---*k10*n1
2
p3=-----------------------
a33
1
- k1*n2 + ---*k10*n2
2
p2=-----------------------
a33
1
- k1*n1 + ---*k10*n1
2
p1=-----------------------
a33
k125=0
k124=0
k122=0
k121=0
1 2 2 1 4 1 4
---*a33 *b33 *k26 + ---*b33 *k1 - ----*b33 *k10
4 8 16
k120=-------------------------------------------------
4
a33
k119=0
k118=0
2 1 3 1 3
a33 *b33*k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k117=-------------------------------------------
3
a33
k116=0
1 2 2 1 4 1 4
---*a33 *b33 *k26 + ---*b33 *k1 - ----*b33 *k10
4 8 16
k115=-------------------------------------------------
4
a33
k114=0
k113=0
2 1 3 1 3
a33 *b33*k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k112=-------------------------------------------
3
a33
k110=0
k109=0
2 1 2 1 2
a33 *k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k108=---------------------------------------
2
a33
k107=0
2 1 2 1 2
a33 *k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k106=---------------------------------------
2
a33
k105=0
k104=0
1 3
- ---*b33 *k1
2
k103=----------------
3
a33
k102=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
2 1 2
- 2*b33 *k1 + ---*b33 *k10
2
k95=-----------------------------
2
a33
k94=0
k93=0
k92=0
k91=0
k90=0
1 3
- ---*b33 *k1
2
k89=----------------
3
a33
k88=0
k87=0
k86=0
k85=0
2 1 2
- 2*b33 *k1 + ---*b33 *k10
2
k84=-----------------------------
2
a33
k83=0
k82=0
k81=0
a33*k23 - b33*k10
k80=-------------------
a33
k79=0
k78=0
- 2*b33*k1
k77=-------------
a33
k76=0
- 2*b33*k1
k75=-------------
a33
k74=0
k73=0
k72=0
k71=0
1 2 2 3 4 1 4
---*a33 *b33 *k26 + ----*b33 *k1 - ----*b33 *k10
4 16 16
k70=--------------------------------------------------
4
a33
k69=0
k68=0
2 1 3 1 3
a33 *b33*k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k67=-------------------------------------------
3
a33
k66=0
1 2 2 3 4 1 4
---*a33 *b33 *k26 + ---*b33 *k1 - ---*b33 *k10
2 8 8
k65=------------------------------------------------
4
a33
k64=0
k63=0
2 1 3 1 3
a33 *b33*k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k62=-------------------------------------------
3
a33
k61=0
k60=0
k59=0
k58=k26
k57=0
2 2 1 2
a33 *k26 + b33 *k1 - ---*b33 *k10
4
k56=-----------------------------------
2
a33
k55=0
k54=0
2 1 3 1 3
a33 *b33*k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k53=-------------------------------------------
3
a33
k52=0
k51=0
k50=0
k49=0
k48=0
2 1 2
- 2*b33 *k1 + ---*b33 *k10
2
k47=-----------------------------
2
a33
k46=0
k45=0
k44=k23
k43=0
k42=0
k41=0
k40=0
k38=0
k37=0
k36=0
1 2 2 3 4 1 4
---*a33 *b33 *k26 + ----*b33 *k1 - ----*b33 *k10
4 16 16
k35=--------------------------------------------------
4
a33
k34=0
k33=0
2 1 3 1 3
a33 *b33*k26 + ---*b33 *k1 - ---*b33 *k10
2 4
k32=-------------------------------------------
3
a33
k30=0
k29=0
2 2 1 2
a33 *k26 + b33 *k1 - ---*b33 *k10
4
k28=-----------------------------------
2
a33
k27=0
k25=0
k24=0
k22=0
k21=0
k20=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
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,k26,k23,k1,k10,n1,b33,n2,a33
Relevance for the application:
The following expression INT is a first
integral for 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 + b33 *v3 )/(4*a33)
4 4 4 2 2 4 4 4 2 2
INT=(16*a33 *k1*u1 + 32*a33 *k1*u1 *u2 + 16*a33 *k1*u2 + 16*a33 *k10*u1 *u3
4 2 2 4 2 4 2
+ 16*a33 *k10*u2 *u3 + 16*a33 *k23*u1*u3 *v1 + 16*a33 *k23*u2*u3 *v2
4 3 4 2 2 4 2 2
+ 16*a33 *k23*u3 *v3 + 16*a33 *k26*u1 *v1 + 16*a33 *k26*u1 *v2
4 2 2 4 2 2 4 2 2
+ 16*a33 *k26*u1 *v3 + 16*a33 *k26*u2 *v1 + 16*a33 *k26*u2 *v2
4 2 2 4 2 4 2
+ 16*a33 *k26*u2 *v3 + 16*a33 *q1*u1 + 16*a33 *q1*u2
3 2 3 2
- 32*a33 *b33*k1*u1 *u3*v3 - 32*a33 *b33*k1*u2 *u3*v3
3 3 3 3
- 16*a33 *b33*k10*u3 *v3 + 16*a33 *b33*k26*u1*v1
3 2 3 2
+ 16*a33 *b33*k26*u1*v1*v2 + 16*a33 *b33*k26*u1*v1*v3
3 2 3 3
+ 16*a33 *b33*k26*u2*v1 *v2 + 16*a33 *b33*k26*u2*v2
3 2 3 3
+ 16*a33 *b33*k26*u2*v2*v3 + 16*a33 *b33*q1*u1*v1 + 16*a33 *b33*q1*u2*v2
3 3 3 2 3 2
- 16*a33 *k1*n1*u1 - 16*a33 *k1*n1*u1*u2 - 16*a33 *k1*n2*u1 *u2
3 3 3 3 3 2
- 16*a33 *k1*n2*u2 + 8*a33 *k10*n1*u1 + 8*a33 *k10*n1*u1*u2
3 2 3 2 3 3
- 8*a33 *k10*n1*u1*u3 + 8*a33 *k10*n2*u1 *u2 + 8*a33 *k10*n2*u2
3 2 3 2 3
- 8*a33 *k10*n2*u2*u3 + 8*a33 *k23*n1*u1 *v1 + 8*a33 *k23*n1*u1*u2*v2
3 3 3 2
+ 8*a33 *k23*n1*u1*u3*v3 + 8*a33 *k23*n2*u1*u2*v1 + 8*a33 *k23*n2*u2 *v2
3 3 2 3 2
+ 8*a33 *k23*n2*u2*u3*v3 - 8*a33 *k26*n1*u1*v1 - 8*a33 *k26*n1*u1*v2
3 2 3 2 3 2
- 8*a33 *k26*n1*u1*v3 - 8*a33 *k26*n2*u2*v1 - 8*a33 *k26*n2*u2*v2
3 2 3 3
- 8*a33 *k26*n2*u2*v3 - 8*a33 *n1*q1*u1 - 8*a33 *n2*q1*u2
2 2 2 2 2 2 2 2
+ 16*a33 *b33 *k1*u1 *v2 + 8*a33 *b33 *k1*u1 *v3
2 2 2 2
- 32*a33 *b33 *k1*u1*u2*v1*v2 - 32*a33 *b33 *k1*u1*u3*v1*v3
2 2 2 2 2 2 2 2
+ 16*a33 *b33 *k1*u2 *v1 + 8*a33 *b33 *k1*u2 *v3
2 2 2 2 2 2
- 32*a33 *b33 *k1*u2*u3*v2*v3 - 4*a33 *b33 *k10*u1 *v2
2 2 2 2 2 2
- 4*a33 *b33 *k10*u1 *v3 + 8*a33 *b33 *k10*u1*u2*v1*v2
2 2 2 2 2 2
+ 8*a33 *b33 *k10*u1*u3*v1*v3 - 4*a33 *b33 *k10*u2 *v1
2 2 2 2 2 2
- 4*a33 *b33 *k10*u2 *v3 + 8*a33 *b33 *k10*u2*u3*v2*v3
2 2 4 2 2 2 2 2 2 2 2
+ 4*a33 *b33 *k26*v1 + 8*a33 *b33 *k26*v1 *v2 + 4*a33 *b33 *k26*v1 *v3
2 2 4 2 2 2 2 2 2 2
+ 4*a33 *b33 *k26*v2 + 4*a33 *b33 *k26*v2 *v3 + 4*a33 *b33 *q1*v1
2 2 2 2 2
+ 4*a33 *b33 *q1*v2 - 8*a33 *b33*k1*n1*u1 *v1
2 2 2
+ 16*a33 *b33*k1*n1*u1*u3*v3 - 8*a33 *b33*k1*n1*u2 *v1
2 2 2 2
- 8*a33 *b33*k1*n2*u1 *v2 - 8*a33 *b33*k1*n2*u2 *v2
2 2 2
+ 16*a33 *b33*k1*n2*u2*u3*v3 - 4*a33 *b33*k10*n1*u1 *v1
2 2 2
- 8*a33 *b33*k10*n1*u1*u3*v3 - 4*a33 *b33*k10*n1*u2 *v1
2 2 2 2
- 4*a33 *b33*k10*n1*u3 *v1 - 4*a33 *b33*k10*n2*u1 *v2
2 2 2
- 4*a33 *b33*k10*n2*u2 *v2 - 8*a33 *b33*k10*n2*u2*u3*v3
2 2 2 2
- 4*a33 *b33*k10*n2*u3 *v2 - 4*a33 *b33*k23*n1*u1*v1
2 2
- 4*a33 *b33*k23*n1*u2*v1*v2 - 4*a33 *b33*k23*n1*u3*v1*v3
2 2 2
- 4*a33 *b33*k23*n2*u1*v1*v2 - 4*a33 *b33*k23*n2*u2*v2
2 2 3
- 4*a33 *b33*k23*n2*u3*v2*v3 - 4*a33 *b33*k26*n1*v1
2 2 2 2
- 4*a33 *b33*k26*n1*v1*v2 - 4*a33 *b33*k26*n1*v1*v3
2 2 2 3
- 4*a33 *b33*k26*n2*v1 *v2 - 4*a33 *b33*k26*n2*v2
2 2 2 2
- 4*a33 *b33*k26*n2*v2*v3 - 4*a33 *b33*n1*q1*v1 - 4*a33 *b33*n2*q1*v2
2 2 2 2 2 2 2
- 4*a33 *k1*n1 *u2 + 8*a33 *k1*n1*n2*u1*u2 + 4*a33 *k1*n2 *u2
2 2 2 2 2 2 2
+ 4*a33 *k10*n1 *u2 - 8*a33 *k10*n1*n2*u1*u2 - 4*a33 *k10*n2 *u2
3 3 3 2 3 2
+ 8*a33*b33 *k1*u1*v1 + 8*a33*b33 *k1*u1*v1*v2 + 8*a33*b33 *k1*u1*v1*v3
3 2 3 3 3 2
+ 8*a33*b33 *k1*u2*v1 *v2 + 8*a33*b33 *k1*u2*v2 + 8*a33*b33 *k1*u2*v2*v3
3 2 3 2
- 8*a33*b33 *k1*u3*v1 *v3 - 8*a33*b33 *k1*u3*v2 *v3
3 3 3 2
- 4*a33*b33 *k10*u1*v1 - 4*a33*b33 *k10*u1*v1*v2
3 2 3 2
- 4*a33*b33 *k10*u1*v1*v3 - 4*a33*b33 *k10*u2*v1 *v2
3 3 3 2
- 4*a33*b33 *k10*u2*v2 - 4*a33*b33 *k10*u2*v2*v3
2 2 2 2
- 8*a33*b33 *k1*n1*u1*v1 - 8*a33*b33 *k1*n1*u1*v2
2 2 2
- 4*a33*b33 *k1*n1*u1*v3 + 8*a33*b33 *k1*n1*u3*v1*v3
2 2 2 2
- 8*a33*b33 *k1*n2*u2*v1 - 8*a33*b33 *k1*n2*u2*v2
2 2 2
- 4*a33*b33 *k1*n2*u2*v3 + 8*a33*b33 *k1*n2*u3*v2*v3
2 2 2 2
+ 2*a33*b33 *k10*n1*u1*v1 + 2*a33*b33 *k10*n1*u1*v2
2 2 2
+ 4*a33*b33 *k10*n1*u3*v1*v3 + 2*a33*b33 *k10*n2*u2*v1
2 2 2
+ 2*a33*b33 *k10*n2*u2*v2 + 4*a33*b33 *k10*n2*u3*v2*v3
2
- 4*a33*b33*k1*n1 *u2*v2 + 4*a33*b33*k1*n1*n2*u1*v2
2
+ 4*a33*b33*k1*n1*n2*u2*v1 + 4*a33*b33*k1*n2 *u2*v2
2 2 3
+ 4*a33*b33*k10*n1 *u1*v1 + 4*a33*b33*k10*n1 *u2*v2 + 2*a33*k1*n1 *u1
2 3 2
+ 2*a33*k1*n1 *n2*u2 - 2*a33*k10*n1 *u1 - 2*a33*k10*n1 *n2*u2
4 4 4 2 2 4 2 2 4 4
+ 3*b33 *k1*v1 + 6*b33 *k1*v1 *v2 + 2*b33 *k1*v1 *v3 + 3*b33 *k1*v2
4 2 2 4 4 4 2 2 4 2 2
+ 2*b33 *k1*v2 *v3 - b33 *k10*v1 - 2*b33 *k10*v1 *v2 - b33 *k10*v1 *v3
4 4 4 2 2 3 3 3 2
- b33 *k10*v2 - b33 *k10*v2 *v3 - 4*b33 *k1*n1*v1 - 4*b33 *k1*n1*v1*v2
3 2 3 2 3 3
- 2*b33 *k1*n1*v1*v3 - 4*b33 *k1*n2*v1 *v2 - 4*b33 *k1*n2*v2
3 2 3 3 3 2
- 2*b33 *k1*n2*v2*v3 + b33 *k10*n1*v1 + b33 *k10*n1*v1*v2
3 2 3 2 3 3
+ 2*b33 *k10*n1*v1*v3 + b33 *k10*n2*v1 *v2 + b33 *k10*n2*v2
3 2 2 2 2 2
+ 2*b33 *k10*n2*v2*v3 - b33 *k1*n1 *v2 + 2*b33 *k1*n1*n2*v1*v2
2 2 2 2 2 2 2 2 2
+ b33 *k1*n2 *v2 + 2*b33 *k10*n1 *v1 + b33 *k10*n1 *v2
2 2 2 2 3
+ 2*b33 *k10*n1*n2*v1*v2 + b33 *k10*n2 *v2 + b33*k1*n1 *v1
2 3 2 4
+ b33*k1*n1 *n2*v2 - b33*k10*n1 *v1 - b33*k10*n1 *n2*v2)/(16*a33 )
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 + b33**2*v3**2)/(4*a33)$
INT=(16*a33**4*k1*u1**4 + 32*a33**4*k1*u1**2*u2**2 + 16*a33**4*k1*u2**4 + 16*a33
**4*k10*u1**2*u3**2 + 16*a33**4*k10*u2**2*u3**2 + 16*a33**4*k23*u1*u3**2*v1 + 16
*a33**4*k23*u2*u3**2*v2 + 16*a33**4*k23*u3**3*v3 + 16*a33**4*k26*u1**2*v1**2 +
16*a33**4*k26*u1**2*v2**2 + 16*a33**4*k26*u1**2*v3**2 + 16*a33**4*k26*u2**2*v1**
2 + 16*a33**4*k26*u2**2*v2**2 + 16*a33**4*k26*u2**2*v3**2 + 16*a33**4*q1*u1**2 +
16*a33**4*q1*u2**2 - 32*a33**3*b33*k1*u1**2*u3*v3 - 32*a33**3*b33*k1*u2**2*u3*
v3 - 16*a33**3*b33*k10*u3**3*v3 + 16*a33**3*b33*k26*u1*v1**3 + 16*a33**3*b33*k26
*u1*v1*v2**2 + 16*a33**3*b33*k26*u1*v1*v3**2 + 16*a33**3*b33*k26*u2*v1**2*v2 +
16*a33**3*b33*k26*u2*v2**3 + 16*a33**3*b33*k26*u2*v2*v3**2 + 16*a33**3*b33*q1*u1
*v1 + 16*a33**3*b33*q1*u2*v2 - 16*a33**3*k1*n1*u1**3 - 16*a33**3*k1*n1*u1*u2**2
- 16*a33**3*k1*n2*u1**2*u2 - 16*a33**3*k1*n2*u2**3 + 8*a33**3*k10*n1*u1**3 + 8*
a33**3*k10*n1*u1*u2**2 - 8*a33**3*k10*n1*u1*u3**2 + 8*a33**3*k10*n2*u1**2*u2 + 8
*a33**3*k10*n2*u2**3 - 8*a33**3*k10*n2*u2*u3**2 + 8*a33**3*k23*n1*u1**2*v1 + 8*
a33**3*k23*n1*u1*u2*v2 + 8*a33**3*k23*n1*u1*u3*v3 + 8*a33**3*k23*n2*u1*u2*v1 + 8
*a33**3*k23*n2*u2**2*v2 + 8*a33**3*k23*n2*u2*u3*v3 - 8*a33**3*k26*n1*u1*v1**2 -
8*a33**3*k26*n1*u1*v2**2 - 8*a33**3*k26*n1*u1*v3**2 - 8*a33**3*k26*n2*u2*v1**2 -
8*a33**3*k26*n2*u2*v2**2 - 8*a33**3*k26*n2*u2*v3**2 - 8*a33**3*n1*q1*u1 - 8*a33
**3*n2*q1*u2 + 16*a33**2*b33**2*k1*u1**2*v2**2 + 8*a33**2*b33**2*k1*u1**2*v3**2
- 32*a33**2*b33**2*k1*u1*u2*v1*v2 - 32*a33**2*b33**2*k1*u1*u3*v1*v3 + 16*a33**2*
b33**2*k1*u2**2*v1**2 + 8*a33**2*b33**2*k1*u2**2*v3**2 - 32*a33**2*b33**2*k1*u2*
u3*v2*v3 - 4*a33**2*b33**2*k10*u1**2*v2**2 - 4*a33**2*b33**2*k10*u1**2*v3**2 + 8
*a33**2*b33**2*k10*u1*u2*v1*v2 + 8*a33**2*b33**2*k10*u1*u3*v1*v3 - 4*a33**2*b33
**2*k10*u2**2*v1**2 - 4*a33**2*b33**2*k10*u2**2*v3**2 + 8*a33**2*b33**2*k10*u2*
u3*v2*v3 + 4*a33**2*b33**2*k26*v1**4 + 8*a33**2*b33**2*k26*v1**2*v2**2 + 4*a33**
2*b33**2*k26*v1**2*v3**2 + 4*a33**2*b33**2*k26*v2**4 + 4*a33**2*b33**2*k26*v2**2
*v3**2 + 4*a33**2*b33**2*q1*v1**2 + 4*a33**2*b33**2*q1*v2**2 - 8*a33**2*b33*k1*
n1*u1**2*v1 + 16*a33**2*b33*k1*n1*u1*u3*v3 - 8*a33**2*b33*k1*n1*u2**2*v1 - 8*a33
**2*b33*k1*n2*u1**2*v2 - 8*a33**2*b33*k1*n2*u2**2*v2 + 16*a33**2*b33*k1*n2*u2*u3
*v3 - 4*a33**2*b33*k10*n1*u1**2*v1 - 8*a33**2*b33*k10*n1*u1*u3*v3 - 4*a33**2*b33
*k10*n1*u2**2*v1 - 4*a33**2*b33*k10*n1*u3**2*v1 - 4*a33**2*b33*k10*n2*u1**2*v2 -
4*a33**2*b33*k10*n2*u2**2*v2 - 8*a33**2*b33*k10*n2*u2*u3*v3 - 4*a33**2*b33*k10*
n2*u3**2*v2 - 4*a33**2*b33*k23*n1*u1*v1**2 - 4*a33**2*b33*k23*n1*u2*v1*v2 - 4*
a33**2*b33*k23*n1*u3*v1*v3 - 4*a33**2*b33*k23*n2*u1*v1*v2 - 4*a33**2*b33*k23*n2*
u2*v2**2 - 4*a33**2*b33*k23*n2*u3*v2*v3 - 4*a33**2*b33*k26*n1*v1**3 - 4*a33**2*
b33*k26*n1*v1*v2**2 - 4*a33**2*b33*k26*n1*v1*v3**2 - 4*a33**2*b33*k26*n2*v1**2*
v2 - 4*a33**2*b33*k26*n2*v2**3 - 4*a33**2*b33*k26*n2*v2*v3**2 - 4*a33**2*b33*n1*
q1*v1 - 4*a33**2*b33*n2*q1*v2 - 4*a33**2*k1*n1**2*u2**2 + 8*a33**2*k1*n1*n2*u1*
u2 + 4*a33**2*k1*n2**2*u2**2 + 4*a33**2*k10*n1**2*u2**2 - 8*a33**2*k10*n1*n2*u1*
u2 - 4*a33**2*k10*n2**2*u2**2 + 8*a33*b33**3*k1*u1*v1**3 + 8*a33*b33**3*k1*u1*v1
*v2**2 + 8*a33*b33**3*k1*u1*v1*v3**2 + 8*a33*b33**3*k1*u2*v1**2*v2 + 8*a33*b33**
3*k1*u2*v2**3 + 8*a33*b33**3*k1*u2*v2*v3**2 - 8*a33*b33**3*k1*u3*v1**2*v3 - 8*
a33*b33**3*k1*u3*v2**2*v3 - 4*a33*b33**3*k10*u1*v1**3 - 4*a33*b33**3*k10*u1*v1*
v2**2 - 4*a33*b33**3*k10*u1*v1*v3**2 - 4*a33*b33**3*k10*u2*v1**2*v2 - 4*a33*b33
**3*k10*u2*v2**3 - 4*a33*b33**3*k10*u2*v2*v3**2 - 8*a33*b33**2*k1*n1*u1*v1**2 -
8*a33*b33**2*k1*n1*u1*v2**2 - 4*a33*b33**2*k1*n1*u1*v3**2 + 8*a33*b33**2*k1*n1*
u3*v1*v3 - 8*a33*b33**2*k1*n2*u2*v1**2 - 8*a33*b33**2*k1*n2*u2*v2**2 - 4*a33*b33
**2*k1*n2*u2*v3**2 + 8*a33*b33**2*k1*n2*u3*v2*v3 + 2*a33*b33**2*k10*n1*u1*v1**2
+ 2*a33*b33**2*k10*n1*u1*v2**2 + 4*a33*b33**2*k10*n1*u3*v1*v3 + 2*a33*b33**2*k10
*n2*u2*v1**2 + 2*a33*b33**2*k10*n2*u2*v2**2 + 4*a33*b33**2*k10*n2*u3*v2*v3 - 4*
a33*b33*k1*n1**2*u2*v2 + 4*a33*b33*k1*n1*n2*u1*v2 + 4*a33*b33*k1*n1*n2*u2*v1 + 4
*a33*b33*k1*n2**2*u2*v2 + 4*a33*b33*k10*n1**2*u1*v1 + 4*a33*b33*k10*n1**2*u2*v2
+ 2*a33*k1*n1**3*u1 + 2*a33*k1*n1**2*n2*u2 - 2*a33*k10*n1**3*u1 - 2*a33*k10*n1**
2*n2*u2 + 3*b33**4*k1*v1**4 + 6*b33**4*k1*v1**2*v2**2 + 2*b33**4*k1*v1**2*v3**2
+ 3*b33**4*k1*v2**4 + 2*b33**4*k1*v2**2*v3**2 - b33**4*k10*v1**4 - 2*b33**4*k10*
v1**2*v2**2 - b33**4*k10*v1**2*v3**2 - b33**4*k10*v2**4 - b33**4*k10*v2**2*v3**2
- 4*b33**3*k1*n1*v1**3 - 4*b33**3*k1*n1*v1*v2**2 - 2*b33**3*k1*n1*v1*v3**2 - 4*
b33**3*k1*n2*v1**2*v2 - 4*b33**3*k1*n2*v2**3 - 2*b33**3*k1*n2*v2*v3**2 + b33**3*
k10*n1*v1**3 + b33**3*k10*n1*v1*v2**2 + 2*b33**3*k10*n1*v1*v3**2 + b33**3*k10*n2
*v1**2*v2 + b33**3*k10*n2*v2**3 + 2*b33**3*k10*n2*v2*v3**2 - b33**2*k1*n1**2*v2
**2 + 2*b33**2*k1*n1*n2*v1*v2 + b33**2*k1*n2**2*v2**2 + 2*b33**2*k10*n1**2*v1**2
+ b33**2*k10*n1**2*v2**2 + 2*b33**2*k10*n1*n2*v1*v2 + b33**2*k10*n2**2*v2**2 +
b33*k1*n1**3*v1 + b33*k1*n1**2*n2*v2 - b33*k10*n1**3*v1 - b33*k10*n1**2*n2*v2)/(
16*a33**4)$