Solution 7 to problem e3c2new
Expressions |
Parameters |
Relevance |
Back to problem e3c2new
Expressions
The solution is given through the following expressions:
a22=2*a33
b22=0
b31=0
b32=0
c12=0
c13=0
c22=0
c23=0
1 2
- ---*b33
8
c33=-------------
a33
3
- ---*b33*n1
4
m1=---------------
a33
3
- ---*b33*n2
4
m2=---------------
a33
- b33*n3
m3=-----------
a33
1 2 1 2 1 2
- ---*a33 *b33*n3*q1 + ---*b33*k1*n1 *n3 - ---*b33*k10*n1 *n3
2 2 2
r6=----------------------------------------------------------------
4
a33
1 2 1 2 1 2
r5=( - ---*a33 *b33*n2*q1 + ---*b33*k1*n1 *n2 + ---*b33*k1*n2*n3
4 4 4
1 2 1 2 4
- ---*b33*k10*n1 *n2 - ---*b33*k10*n2*n3 )/a33
4 4
1 2 1 3 1 2 1 3
r4=( - ---*a33 *b33*n1*q1 + ---*b33*k1*n1 + ---*b33*k1*n1*n3 - ---*b33*k10*n1
4 4 4 4
1 2 4
- ---*b33*k10*n1*n3 )/a33
4
2 2 3 2 3
a33 *n3*q1 - k1*n1 *n3 + k1*n3 + k10*n1 *n3 - k10*n3
r3=--------------------------------------------------------
3
a33
2 2 2 2 2
a33 *n2*q1 - k1*n1 *n2 + k1*n2*n3 + k10*n1 *n2 - k10*n2*n3
r2=--------------------------------------------------------------
3
a33
2 3 2 3 2
a33 *n1*q1 - k1*n1 + k1*n1*n3 + k10*n1 - k10*n1*n3
r1=--------------------------------------------------------
3
a33
1 2 1 2
---*b33 *k1*n2*n3 + ---*b33 *k10*n2*n3
4 8
q20=----------------------------------------
4
a33
1 2 1 2
---*b33 *k1*n1*n3 + ---*b33 *k10*n1*n3
4 8
q19=----------------------------------------
4
a33
1
- b33*k1*n2*n3 + ---*b33*k10*n2*n3
2
q17=-------------------------------------
3
a33
1
- b33*k1*n1*n3 + ---*b33*k10*n1*n3
2
q16=-------------------------------------
3
a33
1 2 2 1 2 2 1 2 2 1 2 2
q15=(----*a33 *b33 *q1 - ----*b33 *k1*n1 + ----*b33 *k1*n2 - ---*b33 *k1*n3
16 16 16 4
1 2 2 1 2 2 4
+ ----*b33 *k10*n1 + ----*b33 *k10*n2 )/a33
16 16
1 2 1 2
---*b33 *k1*n1*n2 + ---*b33 *k10*n1*n2
8 8
q14=----------------------------------------
4
a33
1
- ---*b33*k1*n2*n3
2
q13=---------------------
3
a33
1 2 1 2 1 2 2
q12=( - ---*a33 *b33*q1 + ---*b33*k1*n1 - ---*b33*k1*n2 + b33*k1*n3
2 2 2
1 2 1 2 3
- ---*b33*k10*n1 - ---*b33*k10*n3 )/a33
2 2
1
- ---*b33*k1*n1*n2
2
q11=---------------------
3
a33
1 2 2 1 2 2 1 2 2
----*a33 *b33 *q1 - ---*b33 *k1*n3 + ---*b33 *k10*n1
16 4 8
q10=--------------------------------------------------------
4
a33
1
- ---*b33*k1*n1*n3
2
q9=---------------------
3
a33
1
- ---*b33*k1*n1*n2
2
q8=---------------------
3
a33
1 2 2 1 2 1 2
- ---*a33 *b33*q1 + b33*k1*n3 - ---*b33*k10*n1 - ---*b33*k10*n3
2 2 2
q7=---------------------------------------------------------------------
3
a33
2*k1*n2*n3 - 2*k10*n2*n3
q5=--------------------------
2
a33
2*k1*n1*n3 - 2*k10*n1*n3
q4=--------------------------
2
a33
2 2 2 2 2
a33 *q1 - k1*n1 + k1*n2 + k10*n1 - k10*n2
q3=-----------------------------------------------
2
a33
2*k1*n1*n2 - 2*k10*n1*n2
q2=--------------------------
2
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n3 - ----*b33 *k1*n3 + ----*b33 *k10*n3
2 16 32
p56=-------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n2 - ----*b33 *k1*n2 + ----*b33 *k10*n2
4 32 32
p55=-------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n1 - ----*b33 *k1*n1 + ----*b33 *k10*n1
4 32 32
p54=-------------------------------------------------------------
4
a33
2 3 2
a33 *k26*n3 - ---*b33 *k1*n3
8
p53=------------------------------
3
a33
2 1 2
a33 *k26*n2 + ---*b33 *k1*n2
8
p52=------------------------------
3
a33
2 1 2
a33 *k26*n1 + ---*b33 *k1*n1
8
p51=------------------------------
3
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n3 - ---*b33 *k1*n3 + ----*b33 *k10*n3
2 8 32
p50=------------------------------------------------------------
4
a33
p49=0
1 1 2 1 2
- ---*a33*b33*k23*n2 - ---*b33 *k1*n2 - ---*b33 *k10*n2
4 4 8
p48=----------------------------------------------------------
3
a33
p47=0
p46=0
1 2 1 3 1 3
- ---*a33 *b33*k26*n3 - ---*b33 *k1*n3 + ----*b33 *k10*n3
2 8 32
p45=------------------------------------------------------------
4
a33
1 1 2 1 2
- ---*a33*b33*k23*n1 - ---*b33 *k1*n1 - ---*b33 *k10*n1
4 4 8
p44=----------------------------------------------------------
3
a33
p43=0
p42=0
- a33*k23*n3 + b33*k1*n3 - b33*k10*n3
p41=----------------------------------------
2
a33
1
- a33*k23*n2 + b33*k1*n2 - ---*b33*k10*n2
2
p40=--------------------------------------------
2
a33
1
- a33*k23*n1 + b33*k1*n1 - ---*b33*k10*n1
2
p39=--------------------------------------------
2
a33
- b33*k1*n3
p38=--------------
2
a33
p37=0
- b33*k1*n3
p36=--------------
2
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n2 - ----*b33 *k1*n2 + ----*b33 *k10*n2
4 16 64
p35=-------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n1 - ----*b33 *k1*n1 + ----*b33 *k10*n1
4 16 64
p34=-------------------------------------------------------------
4
a33
2 1 2 1 2
a33 *k26*n3 + ---*b33 *k1*n3 - ----*b33 *k10*n3
4 16
p33=-------------------------------------------------
3
a33
2 1 1 2 1 2
a33 *k26*n2 - ---*a33*b33*k23*n2 + ---*b33 *k1*n2 - ----*b33 *k10*n2
4 4 16
p32=----------------------------------------------------------------------
3
a33
2 1 2 1 2
a33 *k26*n1 + ---*b33 *k1*n1 - ----*b33 *k10*n1
4 16
p31=-------------------------------------------------
3
a33
1 2 1 3 1 3
- ---*a33 *b33*k26*n2 - ----*b33 *k1*n2 + ----*b33 *k10*n2
4 16 64
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
- k23*n3
p25=-----------
a33
p24=0
1 1
- a33*k23*n2 - ---*b33*k1*n2 - ---*b33*k10*n2
2 4
p23=------------------------------------------------
2
a33
- k23*n1
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 16 64
p20=-------------------------------------------------------------
4
a33
2 1 2 1 2
a33 *k26*n3 + ---*b33 *k1*n3 - ----*b33 *k10*n3
4 16
p19=-------------------------------------------------
3
a33
2 1 2 1 2
a33 *k26*n2 + ---*b33 *k1*n2 - ----*b33 *k10*n2
4 16
p18=-------------------------------------------------
3
a33
2 1 1 2 1 2
a33 *k26*n1 - ---*a33*b33*k23*n1 + ---*b33 *k1*n1 - ----*b33 *k10*n1
4 4 16
p17=----------------------------------------------------------------------
3
a33
1
- ---*b33*k10*n1
4
p16=-------------------
2
a33
p15=0
- k23*n3
p14=-----------
a33
1 1
- ---*b33*k1*n1 - ---*b33*k10*n1
2 4
p13=-----------------------------------
2
a33
- k23*n2
p12=-----------
a33
1 1
- a33*k23*n1 - ---*b33*k1*n1 - ---*b33*k10*n1
2 4
p11=------------------------------------------------
2
a33
k10*n3
p10=--------
a33
k10*n2
p9=--------
a33
k10*n1
p8=--------
a33
2*k1*n3 - k10*n3
p7=------------------
a33
p6=0
2*k1*n3 - k10*n3
p5=------------------
a33
2*k1*n2 - k10*n2
p4=------------------
a33
2*k1*n1 - k10*n1
p3=------------------
a33
2*k1*n2 - k10*n2
p2=------------------
a33
2*k1*n1 - k10*n1
p1=------------------
a33
k125=0
k124=0
k122=0
k121=0
1 2 2 1 4 1 4
----*a33 *b33 *k26 + -----*b33 *k1 - -----*b33 *k10
16 128 256
k120=-----------------------------------------------------
4
a33
k119=0
k118=0
1 2 1 3 1 3
- ---*a33 *b33*k26 - ----*b33 *k1 + ----*b33 *k10
2 16 32
k117=----------------------------------------------------
3
a33
k116=0
1 2 2 1 4 1 4
----*a33 *b33 *k26 + -----*b33 *k1 - -----*b33 *k10
16 128 256
k115=-----------------------------------------------------
4
a33
k114=0
k113=0
1 2 1 3 1 3
- ---*a33 *b33*k26 - ----*b33 *k1 + ----*b33 *k10
2 16 32
k112=----------------------------------------------------
3
a33
k110=0
k109=0
2 1 2 1 2
a33 *k26 + ---*b33 *k1 - ----*b33 *k10
8 16
k108=----------------------------------------
2
a33
k107=0
2 1 2 1 2
a33 *k26 + ---*b33 *k1 - ----*b33 *k10
8 16
k106=----------------------------------------
2
a33
k105=0
k104=0
1 3
----*b33 *k1
16
k103=--------------
3
a33
k102=0
k101=0
k100=0
k99=0
k98=0
k97=0
k96=0
1 2 1 2
- ---*b33 *k1 + ---*b33 *k10
2 8
k95=-------------------------------
2
a33
k94=0
k93=0
k92=0
k91=0
k90=0
1 3
----*b33 *k1
16
k89=--------------
3
a33
k88=0
k87=0
k86=0
k85=0
1 2 1 2
- ---*b33 *k1 + ---*b33 *k10
2 8
k84=-------------------------------
2
a33
k83=0
k82=0
k81=0
1
a33*k23 + ---*b33*k10
2
k80=-----------------------
a33
k79=0
k78=0
b33*k1
k77=--------
a33
k76=0
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
16 256 256
k70=-----------------------------------------------------
4
a33
k69=0
k68=0
1 2 1 3 1 3
- ---*a33 *b33*k26 - ----*b33 *k1 + ----*b33 *k10
2 16 32
k67=----------------------------------------------------
3
a33
k66=0
1 2 2 3 4 1 4
---*a33 *b33 *k26 + -----*b33 *k1 - -----*b33 *k10
8 128 128
k65=----------------------------------------------------
4
a33
k64=0
k63=0
1 2 1 3 1 3
- ---*a33 *b33*k26 - ----*b33 *k1 + ----*b33 *k10
2 16 32
k62=----------------------------------------------------
3
a33
k61=0
k60=0
k59=0
k58=k26
k57=0
2 1 2 1 2
a33 *k26 + ---*b33 *k1 - ----*b33 *k10
4 16
k56=----------------------------------------
2
a33
k55=0
k54=0
1 2 1 3 1 3
- ---*a33 *b33*k26 - ----*b33 *k1 + ----*b33 *k10
2 16 32
k53=----------------------------------------------------
3
a33
k52=0
k51=0
k50=0
k49=0
k48=0
1 2 1 2
- ---*b33 *k1 + ---*b33 *k10
2 8
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
16 256 256
k35=-----------------------------------------------------
4
a33
k34=0
k33=0
1 2 1 3 1 3
- ---*a33 *b33*k26 - ----*b33 *k1 + ----*b33 *k10
2 16 32
k32=----------------------------------------------------
3
a33
k30=0
k29=0
2 1 2 1 2
a33 *k26 + ---*b33 *k1 - ----*b33 *k10
4 16
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:
n3,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=(16*a33 *u1 + 16*a33 *u2 + 8*a33 *u3 + 8*a33*b33*u3*v3 + 8*a33*n1*u1
2 2
+ 8*a33*n2*u2 + 8*a33*n3*u3 - b33 *v3 - 6*b33*n1*v1 - 6*b33*n2*v2
- 8*b33*n3*v3)/(8*a33)
4 4 4 2 2 4 4
INT=(256*a33 *k1*u1 + 512*a33 *k1*u1 *u2 + 256*a33 *k1*u2
4 2 2 4 2 2 4 2
+ 256*a33 *k10*u1 *u3 + 256*a33 *k10*u2 *u3 + 256*a33 *k23*u1*u3 *v1
4 2 4 3 4 2 2
+ 256*a33 *k23*u2*u3 *v2 + 256*a33 *k23*u3 *v3 + 256*a33 *k26*u1 *v1
4 2 2 4 2 2 4 2 2
+ 256*a33 *k26*u1 *v2 + 256*a33 *k26*u1 *v3 + 256*a33 *k26*u2 *v1
4 2 2 4 2 2 4 2
+ 256*a33 *k26*u2 *v2 + 256*a33 *k26*u2 *v3 + 256*a33 *q1*u1
4 2 3 2 3 2
+ 256*a33 *q1*u2 + 256*a33 *b33*k1*u1 *u3*v3 + 256*a33 *b33*k1*u2 *u3*v3
3 3 3 3
+ 128*a33 *b33*k10*u3 *v3 - 128*a33 *b33*k26*u1*v1
3 2 3 2
- 128*a33 *b33*k26*u1*v1*v2 - 128*a33 *b33*k26*u1*v1*v3
3 2 3 3
- 128*a33 *b33*k26*u2*v1 *v2 - 128*a33 *b33*k26*u2*v2
3 2 3
- 128*a33 *b33*k26*u2*v2*v3 - 128*a33 *b33*q1*u1*v1
3 3 3 3 2
- 128*a33 *b33*q1*u2*v2 + 512*a33 *k1*n1*u1 + 512*a33 *k1*n1*u1*u2
3 2 3 3 3 2
+ 512*a33 *k1*n2*u1 *u2 + 512*a33 *k1*n2*u2 + 512*a33 *k1*n3*u1 *u3
3 2 3 3 3 2
+ 512*a33 *k1*n3*u2 *u3 - 256*a33 *k10*n1*u1 - 256*a33 *k10*n1*u1*u2
3 2 3 2 3 3
+ 256*a33 *k10*n1*u1*u3 - 256*a33 *k10*n2*u1 *u2 - 256*a33 *k10*n2*u2
3 2 3 2 3 2
+ 256*a33 *k10*n2*u2*u3 - 256*a33 *k10*n3*u1 *u3 - 256*a33 *k10*n3*u2 *u3
3 3 3 2 3
+ 256*a33 *k10*n3*u3 - 256*a33 *k23*n1*u1 *v1 - 256*a33 *k23*n1*u1*u2*v2
3 3
- 256*a33 *k23*n1*u1*u3*v3 - 256*a33 *k23*n2*u1*u2*v1
3 2 3
- 256*a33 *k23*n2*u2 *v2 - 256*a33 *k23*n2*u2*u3*v3
3 3
- 256*a33 *k23*n3*u1*u3*v1 - 256*a33 *k23*n3*u2*u3*v2
3 2 3 2 3 2
- 256*a33 *k23*n3*u3 *v3 + 256*a33 *k26*n1*u1*v1 + 256*a33 *k26*n1*u1*v2
3 2 3 2 3 2
+ 256*a33 *k26*n1*u1*v3 + 256*a33 *k26*n2*u2*v1 + 256*a33 *k26*n2*u2*v2
3 2 3 2 3 2
+ 256*a33 *k26*n2*u2*v3 + 256*a33 *k26*n3*u3*v1 + 256*a33 *k26*n3*u3*v2
3 2 3 3
+ 256*a33 *k26*n3*u3*v3 + 256*a33 *n1*q1*u1 + 256*a33 *n2*q1*u2
3 2 2 2 2 2 2 2 2
+ 256*a33 *n3*q1*u3 + 64*a33 *b33 *k1*u1 *v2 + 32*a33 *b33 *k1*u1 *v3
2 2 2 2
- 128*a33 *b33 *k1*u1*u2*v1*v2 - 128*a33 *b33 *k1*u1*u3*v1*v3
2 2 2 2 2 2 2 2
+ 64*a33 *b33 *k1*u2 *v1 + 32*a33 *b33 *k1*u2 *v3
2 2 2 2 2 2
- 128*a33 *b33 *k1*u2*u3*v2*v3 - 16*a33 *b33 *k10*u1 *v2
2 2 2 2 2 2
- 16*a33 *b33 *k10*u1 *v3 + 32*a33 *b33 *k10*u1*u2*v1*v2
2 2 2 2 2 2
+ 32*a33 *b33 *k10*u1*u3*v1*v3 - 16*a33 *b33 *k10*u2 *v1
2 2 2 2 2 2
- 16*a33 *b33 *k10*u2 *v3 + 32*a33 *b33 *k10*u2*u3*v2*v3
2 2 4 2 2 2 2
+ 16*a33 *b33 *k26*v1 + 32*a33 *b33 *k26*v1 *v2
2 2 2 2 2 2 4
+ 16*a33 *b33 *k26*v1 *v3 + 16*a33 *b33 *k26*v2
2 2 2 2 2 2 2 2 2 2
+ 16*a33 *b33 *k26*v2 *v3 + 16*a33 *b33 *q1*v1 + 16*a33 *b33 *q1*v2
2 2 2
- 128*a33 *b33*k1*n1*u1 *v1 + 256*a33 *b33*k1*n1*u1*u3*v3
2 2 2 2
- 128*a33 *b33*k1*n1*u2 *v1 - 128*a33 *b33*k1*n2*u1 *v2
2 2 2
- 128*a33 *b33*k1*n2*u2 *v2 + 256*a33 *b33*k1*n2*u2*u3*v3
2 2 2 2
- 256*a33 *b33*k1*n3*u1 *v3 - 256*a33 *b33*k1*n3*u2 *v3
2 2 2 2
+ 256*a33 *b33*k1*n3*u3 *v3 - 64*a33 *b33*k10*n1*u1 *v1
2 2 2
- 128*a33 *b33*k10*n1*u1*u3*v3 - 64*a33 *b33*k10*n1*u2 *v1
2 2 2 2
- 64*a33 *b33*k10*n1*u3 *v1 - 64*a33 *b33*k10*n2*u1 *v2
2 2 2
- 64*a33 *b33*k10*n2*u2 *v2 - 128*a33 *b33*k10*n2*u2*u3*v3
2 2 2 2
- 64*a33 *b33*k10*n2*u3 *v2 - 256*a33 *b33*k10*n3*u3 *v3
2 2 2
- 64*a33 *b33*k23*n1*u1*v1 - 64*a33 *b33*k23*n1*u2*v1*v2
2 2
- 64*a33 *b33*k23*n1*u3*v1*v3 - 64*a33 *b33*k23*n2*u1*v1*v2
2 2 2
- 64*a33 *b33*k23*n2*u2*v2 - 64*a33 *b33*k23*n2*u3*v2*v3
2 3 2 2
- 64*a33 *b33*k26*n1*v1 - 64*a33 *b33*k26*n1*v1*v2
2 2 2 2
- 64*a33 *b33*k26*n1*v1*v3 - 64*a33 *b33*k26*n2*v1 *v2
2 3 2 2
- 64*a33 *b33*k26*n2*v2 - 64*a33 *b33*k26*n2*v2*v3
2 2 2 2
- 128*a33 *b33*k26*n3*v1 *v3 - 128*a33 *b33*k26*n3*v2 *v3
2 3 2 2
- 128*a33 *b33*k26*n3*v3 - 64*a33 *b33*n1*q1*v1 - 64*a33 *b33*n2*q1*v2
2 2 2 2 2
- 128*a33 *b33*n3*q1*v3 - 256*a33 *k1*n1 *u2 + 512*a33 *k1*n1*n2*u1*u2
2 2 2 2 2
+ 512*a33 *k1*n1*n3*u1*u3 + 256*a33 *k1*n2 *u2 + 512*a33 *k1*n2*n3*u2*u3
2 2 2 2
+ 256*a33 *k10*n1 *u2 - 512*a33 *k10*n1*n2*u1*u2
2 2 2 2
- 512*a33 *k10*n1*n3*u1*u3 - 256*a33 *k10*n2 *u2
2 3 3
- 512*a33 *k10*n2*n3*u2*u3 - 16*a33*b33 *k1*u1*v1
3 2 3 2
- 16*a33*b33 *k1*u1*v1*v2 - 16*a33*b33 *k1*u1*v1*v3
3 2 3 3
- 16*a33*b33 *k1*u2*v1 *v2 - 16*a33*b33 *k1*u2*v2
3 2 3 2
- 16*a33*b33 *k1*u2*v2*v3 + 16*a33*b33 *k1*u3*v1 *v3
3 2 3 3
+ 16*a33*b33 *k1*u3*v2 *v3 + 8*a33*b33 *k10*u1*v1
3 2 3 2
+ 8*a33*b33 *k10*u1*v1*v2 + 8*a33*b33 *k10*u1*v1*v3
3 2 3 3
+ 8*a33*b33 *k10*u2*v1 *v2 + 8*a33*b33 *k10*u2*v2
3 2 2 2
+ 8*a33*b33 *k10*u2*v2*v3 + 64*a33*b33 *k1*n1*u1*v1
2 2 2 2
+ 64*a33*b33 *k1*n1*u1*v2 + 32*a33*b33 *k1*n1*u1*v3
2 2 2
- 64*a33*b33 *k1*n1*u3*v1*v3 + 64*a33*b33 *k1*n2*u2*v1
2 2 2 2
+ 64*a33*b33 *k1*n2*u2*v2 + 32*a33*b33 *k1*n2*u2*v3
2 2 2
- 64*a33*b33 *k1*n2*u3*v2*v3 + 64*a33*b33 *k1*n3*u3*v1
2 2 2 2
+ 64*a33*b33 *k1*n3*u3*v2 - 96*a33*b33 *k1*n3*u3*v3
2 2 2 2
- 16*a33*b33 *k10*n1*u1*v1 - 16*a33*b33 *k10*n1*u1*v2
2 2 2
- 32*a33*b33 *k10*n1*u3*v1*v3 - 16*a33*b33 *k10*n2*u2*v1
2 2 2
- 16*a33*b33 *k10*n2*u2*v2 - 32*a33*b33 *k10*n2*u3*v2*v3
2 2 2 2
- 16*a33*b33 *k10*n3*u3*v1 - 16*a33*b33 *k10*n3*u3*v2
2
+ 128*a33*b33*k1*n1 *u2*v2 - 128*a33*b33*k1*n1*n2*u1*v2
- 128*a33*b33*k1*n1*n2*u2*v1 - 256*a33*b33*k1*n1*n3*u1*v3
2
- 128*a33*b33*k1*n1*n3*u3*v1 - 128*a33*b33*k1*n2 *u2*v2
- 256*a33*b33*k1*n2*n3*u2*v3 - 128*a33*b33*k1*n2*n3*u3*v2
2 2
+ 256*a33*b33*k1*n3 *u1*v1 + 256*a33*b33*k1*n3 *u2*v2
2 2
- 128*a33*b33*k10*n1 *u1*v1 - 128*a33*b33*k10*n1 *u2*v2
+ 128*a33*b33*k10*n1*n3*u1*v3 + 128*a33*b33*k10*n2*n3*u2*v3
2 2
- 128*a33*b33*k10*n3 *u1*v1 - 128*a33*b33*k10*n3 *u2*v2
3 2 2
- 256*a33*k1*n1 *u1 - 256*a33*k1*n1 *n2*u2 - 256*a33*k1*n1 *n3*u3
2 2 3
+ 256*a33*k1*n1*n3 *u1 + 256*a33*k1*n2*n3 *u2 + 256*a33*k1*n3 *u3
3 2 2
+ 256*a33*k10*n1 *u1 + 256*a33*k10*n1 *n2*u2 + 256*a33*k10*n1 *n3*u3
2 2 3
- 256*a33*k10*n1*n3 *u1 - 256*a33*k10*n2*n3 *u2 - 256*a33*k10*n3 *u3
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
- b33 *k10*v2 - b33 *k10*v2 *v3 - 16*b33 *k1*n1*v1
3 2 3 2 3 2
- 16*b33 *k1*n1*v1*v2 - 8*b33 *k1*n1*v1*v3 - 16*b33 *k1*n2*v1 *v2
3 3 3 2 3 2
- 16*b33 *k1*n2*v2 - 8*b33 *k1*n2*v2*v3 - 32*b33 *k1*n3*v1 *v3
3 2 3 3 3 3
- 32*b33 *k1*n3*v2 *v3 - 16*b33 *k1*n3*v3 + 4*b33 *k10*n1*v1
3 2 3 2 3 2
+ 4*b33 *k10*n1*v1*v2 + 8*b33 *k10*n1*v1*v3 + 4*b33 *k10*n2*v1 *v2
3 3 3 2 3 2
+ 4*b33 *k10*n2*v2 + 8*b33 *k10*n2*v2*v3 + 8*b33 *k10*n3*v1 *v3
3 2 3 3 2 2 2
+ 8*b33 *k10*n3*v2 *v3 + 8*b33 *k10*n3*v3 - 16*b33 *k1*n1 *v2
2 2 2 2 2
+ 32*b33 *k1*n1*n2*v1*v2 + 64*b33 *k1*n1*n3*v1*v3 + 16*b33 *k1*n2 *v2
2 2 2 2 2 2 2
+ 64*b33 *k1*n2*n3*v2*v3 - 64*b33 *k1*n3 *v1 - 64*b33 *k1*n3 *v2
2 2 2 2 2 2 2
+ 32*b33 *k10*n1 *v1 + 16*b33 *k10*n1 *v2 + 32*b33 *k10*n1*n2*v1*v2
2 2 2 2 2
+ 32*b33 *k10*n1*n3*v1*v3 + 16*b33 *k10*n2 *v2 + 32*b33 *k10*n2*n3*v2*v3
3 2 2
+ 64*b33*k1*n1 *v1 + 64*b33*k1*n1 *n2*v2 + 128*b33*k1*n1 *n3*v3
2 2 3
+ 64*b33*k1*n1*n3 *v1 + 64*b33*k1*n2*n3 *v2 - 64*b33*k10*n1 *v1
2 2 2
- 64*b33*k10*n1 *n2*v2 - 128*b33*k10*n1 *n3*v3 - 64*b33*k10*n1*n3 *v1
2 4
- 64*b33*k10*n2*n3 *v2)/(256*a33 )
And again in machine readable form:
HAM=(16*a33**2*u1**2 + 16*a33**2*u2**2 + 8*a33**2*u3**2 + 8*a33*b33*u3*v3 + 8*
a33*n1*u1 + 8*a33*n2*u2 + 8*a33*n3*u3 - b33**2*v3**2 - 6*b33*n1*v1 - 6*b33*n2*v2
- 8*b33*n3*v3)/(8*a33)$
INT=(256*a33**4*k1*u1**4 + 512*a33**4*k1*u1**2*u2**2 + 256*a33**4*k1*u2**4 + 256
*a33**4*k10*u1**2*u3**2 + 256*a33**4*k10*u2**2*u3**2 + 256*a33**4*k23*u1*u3**2*
v1 + 256*a33**4*k23*u2*u3**2*v2 + 256*a33**4*k23*u3**3*v3 + 256*a33**4*k26*u1**2
*v1**2 + 256*a33**4*k26*u1**2*v2**2 + 256*a33**4*k26*u1**2*v3**2 + 256*a33**4*
k26*u2**2*v1**2 + 256*a33**4*k26*u2**2*v2**2 + 256*a33**4*k26*u2**2*v3**2 + 256*
a33**4*q1*u1**2 + 256*a33**4*q1*u2**2 + 256*a33**3*b33*k1*u1**2*u3*v3 + 256*a33
**3*b33*k1*u2**2*u3*v3 + 128*a33**3*b33*k10*u3**3*v3 - 128*a33**3*b33*k26*u1*v1
**3 - 128*a33**3*b33*k26*u1*v1*v2**2 - 128*a33**3*b33*k26*u1*v1*v3**2 - 128*a33
**3*b33*k26*u2*v1**2*v2 - 128*a33**3*b33*k26*u2*v2**3 - 128*a33**3*b33*k26*u2*v2
*v3**2 - 128*a33**3*b33*q1*u1*v1 - 128*a33**3*b33*q1*u2*v2 + 512*a33**3*k1*n1*u1
**3 + 512*a33**3*k1*n1*u1*u2**2 + 512*a33**3*k1*n2*u1**2*u2 + 512*a33**3*k1*n2*
u2**3 + 512*a33**3*k1*n3*u1**2*u3 + 512*a33**3*k1*n3*u2**2*u3 - 256*a33**3*k10*
n1*u1**3 - 256*a33**3*k10*n1*u1*u2**2 + 256*a33**3*k10*n1*u1*u3**2 - 256*a33**3*
k10*n2*u1**2*u2 - 256*a33**3*k10*n2*u2**3 + 256*a33**3*k10*n2*u2*u3**2 - 256*a33
**3*k10*n3*u1**2*u3 - 256*a33**3*k10*n3*u2**2*u3 + 256*a33**3*k10*n3*u3**3 - 256
*a33**3*k23*n1*u1**2*v1 - 256*a33**3*k23*n1*u1*u2*v2 - 256*a33**3*k23*n1*u1*u3*
v3 - 256*a33**3*k23*n2*u1*u2*v1 - 256*a33**3*k23*n2*u2**2*v2 - 256*a33**3*k23*n2
*u2*u3*v3 - 256*a33**3*k23*n3*u1*u3*v1 - 256*a33**3*k23*n3*u2*u3*v2 - 256*a33**3
*k23*n3*u3**2*v3 + 256*a33**3*k26*n1*u1*v1**2 + 256*a33**3*k26*n1*u1*v2**2 + 256
*a33**3*k26*n1*u1*v3**2 + 256*a33**3*k26*n2*u2*v1**2 + 256*a33**3*k26*n2*u2*v2**
2 + 256*a33**3*k26*n2*u2*v3**2 + 256*a33**3*k26*n3*u3*v1**2 + 256*a33**3*k26*n3*
u3*v2**2 + 256*a33**3*k26*n3*u3*v3**2 + 256*a33**3*n1*q1*u1 + 256*a33**3*n2*q1*
u2 + 256*a33**3*n3*q1*u3 + 64*a33**2*b33**2*k1*u1**2*v2**2 + 32*a33**2*b33**2*k1
*u1**2*v3**2 - 128*a33**2*b33**2*k1*u1*u2*v1*v2 - 128*a33**2*b33**2*k1*u1*u3*v1*
v3 + 64*a33**2*b33**2*k1*u2**2*v1**2 + 32*a33**2*b33**2*k1*u2**2*v3**2 - 128*a33
**2*b33**2*k1*u2*u3*v2*v3 - 16*a33**2*b33**2*k10*u1**2*v2**2 - 16*a33**2*b33**2*
k10*u1**2*v3**2 + 32*a33**2*b33**2*k10*u1*u2*v1*v2 + 32*a33**2*b33**2*k10*u1*u3*
v1*v3 - 16*a33**2*b33**2*k10*u2**2*v1**2 - 16*a33**2*b33**2*k10*u2**2*v3**2 + 32
*a33**2*b33**2*k10*u2*u3*v2*v3 + 16*a33**2*b33**2*k26*v1**4 + 32*a33**2*b33**2*
k26*v1**2*v2**2 + 16*a33**2*b33**2*k26*v1**2*v3**2 + 16*a33**2*b33**2*k26*v2**4
+ 16*a33**2*b33**2*k26*v2**2*v3**2 + 16*a33**2*b33**2*q1*v1**2 + 16*a33**2*b33**
2*q1*v2**2 - 128*a33**2*b33*k1*n1*u1**2*v1 + 256*a33**2*b33*k1*n1*u1*u3*v3 - 128
*a33**2*b33*k1*n1*u2**2*v1 - 128*a33**2*b33*k1*n2*u1**2*v2 - 128*a33**2*b33*k1*
n2*u2**2*v2 + 256*a33**2*b33*k1*n2*u2*u3*v3 - 256*a33**2*b33*k1*n3*u1**2*v3 -
256*a33**2*b33*k1*n3*u2**2*v3 + 256*a33**2*b33*k1*n3*u3**2*v3 - 64*a33**2*b33*
k10*n1*u1**2*v1 - 128*a33**2*b33*k10*n1*u1*u3*v3 - 64*a33**2*b33*k10*n1*u2**2*v1
- 64*a33**2*b33*k10*n1*u3**2*v1 - 64*a33**2*b33*k10*n2*u1**2*v2 - 64*a33**2*b33
*k10*n2*u2**2*v2 - 128*a33**2*b33*k10*n2*u2*u3*v3 - 64*a33**2*b33*k10*n2*u3**2*
v2 - 256*a33**2*b33*k10*n3*u3**2*v3 - 64*a33**2*b33*k23*n1*u1*v1**2 - 64*a33**2*
b33*k23*n1*u2*v1*v2 - 64*a33**2*b33*k23*n1*u3*v1*v3 - 64*a33**2*b33*k23*n2*u1*v1
*v2 - 64*a33**2*b33*k23*n2*u2*v2**2 - 64*a33**2*b33*k23*n2*u3*v2*v3 - 64*a33**2*
b33*k26*n1*v1**3 - 64*a33**2*b33*k26*n1*v1*v2**2 - 64*a33**2*b33*k26*n1*v1*v3**2
- 64*a33**2*b33*k26*n2*v1**2*v2 - 64*a33**2*b33*k26*n2*v2**3 - 64*a33**2*b33*
k26*n2*v2*v3**2 - 128*a33**2*b33*k26*n3*v1**2*v3 - 128*a33**2*b33*k26*n3*v2**2*
v3 - 128*a33**2*b33*k26*n3*v3**3 - 64*a33**2*b33*n1*q1*v1 - 64*a33**2*b33*n2*q1*
v2 - 128*a33**2*b33*n3*q1*v3 - 256*a33**2*k1*n1**2*u2**2 + 512*a33**2*k1*n1*n2*
u1*u2 + 512*a33**2*k1*n1*n3*u1*u3 + 256*a33**2*k1*n2**2*u2**2 + 512*a33**2*k1*n2
*n3*u2*u3 + 256*a33**2*k10*n1**2*u2**2 - 512*a33**2*k10*n1*n2*u1*u2 - 512*a33**2
*k10*n1*n3*u1*u3 - 256*a33**2*k10*n2**2*u2**2 - 512*a33**2*k10*n2*n3*u2*u3 - 16*
a33*b33**3*k1*u1*v1**3 - 16*a33*b33**3*k1*u1*v1*v2**2 - 16*a33*b33**3*k1*u1*v1*
v3**2 - 16*a33*b33**3*k1*u2*v1**2*v2 - 16*a33*b33**3*k1*u2*v2**3 - 16*a33*b33**3
*k1*u2*v2*v3**2 + 16*a33*b33**3*k1*u3*v1**2*v3 + 16*a33*b33**3*k1*u3*v2**2*v3 +
8*a33*b33**3*k10*u1*v1**3 + 8*a33*b33**3*k10*u1*v1*v2**2 + 8*a33*b33**3*k10*u1*
v1*v3**2 + 8*a33*b33**3*k10*u2*v1**2*v2 + 8*a33*b33**3*k10*u2*v2**3 + 8*a33*b33
**3*k10*u2*v2*v3**2 + 64*a33*b33**2*k1*n1*u1*v1**2 + 64*a33*b33**2*k1*n1*u1*v2**
2 + 32*a33*b33**2*k1*n1*u1*v3**2 - 64*a33*b33**2*k1*n1*u3*v1*v3 + 64*a33*b33**2*
k1*n2*u2*v1**2 + 64*a33*b33**2*k1*n2*u2*v2**2 + 32*a33*b33**2*k1*n2*u2*v3**2 -
64*a33*b33**2*k1*n2*u3*v2*v3 + 64*a33*b33**2*k1*n3*u3*v1**2 + 64*a33*b33**2*k1*
n3*u3*v2**2 - 96*a33*b33**2*k1*n3*u3*v3**2 - 16*a33*b33**2*k10*n1*u1*v1**2 - 16*
a33*b33**2*k10*n1*u1*v2**2 - 32*a33*b33**2*k10*n1*u3*v1*v3 - 16*a33*b33**2*k10*
n2*u2*v1**2 - 16*a33*b33**2*k10*n2*u2*v2**2 - 32*a33*b33**2*k10*n2*u3*v2*v3 - 16
*a33*b33**2*k10*n3*u3*v1**2 - 16*a33*b33**2*k10*n3*u3*v2**2 + 128*a33*b33*k1*n1
**2*u2*v2 - 128*a33*b33*k1*n1*n2*u1*v2 - 128*a33*b33*k1*n1*n2*u2*v1 - 256*a33*
b33*k1*n1*n3*u1*v3 - 128*a33*b33*k1*n1*n3*u3*v1 - 128*a33*b33*k1*n2**2*u2*v2 -
256*a33*b33*k1*n2*n3*u2*v3 - 128*a33*b33*k1*n2*n3*u3*v2 + 256*a33*b33*k1*n3**2*
u1*v1 + 256*a33*b33*k1*n3**2*u2*v2 - 128*a33*b33*k10*n1**2*u1*v1 - 128*a33*b33*
k10*n1**2*u2*v2 + 128*a33*b33*k10*n1*n3*u1*v3 + 128*a33*b33*k10*n2*n3*u2*v3 -
128*a33*b33*k10*n3**2*u1*v1 - 128*a33*b33*k10*n3**2*u2*v2 - 256*a33*k1*n1**3*u1
- 256*a33*k1*n1**2*n2*u2 - 256*a33*k1*n1**2*n3*u3 + 256*a33*k1*n1*n3**2*u1 + 256
*a33*k1*n2*n3**2*u2 + 256*a33*k1*n3**3*u3 + 256*a33*k10*n1**3*u1 + 256*a33*k10*
n1**2*n2*u2 + 256*a33*k10*n1**2*n3*u3 - 256*a33*k10*n1*n3**2*u1 - 256*a33*k10*n2
*n3**2*u2 - 256*a33*k10*n3**3*u3 + 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 - 16*b33**3*k1*n1*v1**3 - 16*b33**3*k1*n1*v1*v2**2 - 8
*b33**3*k1*n1*v1*v3**2 - 16*b33**3*k1*n2*v1**2*v2 - 16*b33**3*k1*n2*v2**3 - 8*
b33**3*k1*n2*v2*v3**2 - 32*b33**3*k1*n3*v1**2*v3 - 32*b33**3*k1*n3*v2**2*v3 - 16
*b33**3*k1*n3*v3**3 + 4*b33**3*k10*n1*v1**3 + 4*b33**3*k10*n1*v1*v2**2 + 8*b33**
3*k10*n1*v1*v3**2 + 4*b33**3*k10*n2*v1**2*v2 + 4*b33**3*k10*n2*v2**3 + 8*b33**3*
k10*n2*v2*v3**2 + 8*b33**3*k10*n3*v1**2*v3 + 8*b33**3*k10*n3*v2**2*v3 + 8*b33**3
*k10*n3*v3**3 - 16*b33**2*k1*n1**2*v2**2 + 32*b33**2*k1*n1*n2*v1*v2 + 64*b33**2*
k1*n1*n3*v1*v3 + 16*b33**2*k1*n2**2*v2**2 + 64*b33**2*k1*n2*n3*v2*v3 - 64*b33**2
*k1*n3**2*v1**2 - 64*b33**2*k1*n3**2*v2**2 + 32*b33**2*k10*n1**2*v1**2 + 16*b33
**2*k10*n1**2*v2**2 + 32*b33**2*k10*n1*n2*v1*v2 + 32*b33**2*k10*n1*n3*v1*v3 + 16
*b33**2*k10*n2**2*v2**2 + 32*b33**2*k10*n2*n3*v2*v3 + 64*b33*k1*n1**3*v1 + 64*
b33*k1*n1**2*n2*v2 + 128*b33*k1*n1**2*n3*v3 + 64*b33*k1*n1*n3**2*v1 + 64*b33*k1*
n2*n3**2*v2 - 64*b33*k10*n1**3*v1 - 64*b33*k10*n1**2*n2*v2 - 128*b33*k10*n1**2*
n3*v3 - 64*b33*k10*n1*n3**2*v1 - 64*b33*k10*n2*n3**2*v2)/(256*a33**4)$