Solution 47 to problem e3quant
Expressions |
Parameters |
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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
n3=0
1
----*b33*n1
12
m1=-------------
a33
1
----*b33*n2
12
m2=-------------
a33
m3=0
r6=0
5 2 1 2 1 2
r5=(----*a33 *b33*k1*n2 + ----*a33 *b33*k12*n2 - ----*a33 *b33*n2*q1
12 12 12
1 2 1 2 4
+ -----*b33*k1*n1 *n2 - -----*b33*k12*n1 *n2)/a33
108 108
5 2 1 2 1 2
r4=(----*a33 *b33*k1*n1 + ----*a33 *b33*k12*n1 - ----*a33 *b33*n1*q1
12 12 12
1 3 1 3 4
+ -----*b33*k1*n1 - -----*b33*k12*n1 )/a33
108 108
1 1
- ---*k1*n1*n2 + ---*k12*n1*n2
9 9
r3=---------------------------------
2
a33
1 2 1 2 1 2 1 2
---*a33 *k1*n2 - ---*a33 *n2*q1 + ----*k1*n1 *n2 - ----*k12*n1 *n2
3 3 27 27
r2=--------------------------------------------------------------------
3
a33
1 2 1 2 1 2 1 3
r1=( - ---*a33 *k1*n1 + ---*a33 *k12*n1 - ---*a33 *n1*q1 + ----*k1*n1
3 3 3 27
1 3 3
- ----*k12*n1 )/a33
27
1 2
- ----*b33 *k12*n1
24
q20=---------------------
3
a33
1 2 2 1 2 2 1 2 2
q19=( - ---*a33 *b33 *k1 + ----*a33 *b33 *q1 - -----*b33 *k1*n1
2 16 144
1 2 2 1 2 2 1 2 2 4
+ -----*b33 *k1*n2 + -----*b33 *k12*n1 + -----*b33 *k12*n2 )/a33
144 144 144
1 2
----*b33 *k12*n2
24
q18=------------------
3
a33
1 2 1 2
----*b33 *k1*n1*n2 + ----*b33 *k12*n1*n2
72 72
q17=------------------------------------------
4
a33
1 2 2 1 2 2 1 2 2
- ---*a33 *b33 *k1 + ----*a33 *b33 *q1 + ----*b33 *k12*n1
2 16 72
q16=-------------------------------------------------------------
4
a33
1
---*b33*k1*n1
6
q14=---------------
2
a33
1 1
- ---*a33*k38*n2 - ---*b33*k1*n2
3 6
q13=-----------------------------------
2
a33
1
- ---*b33*k12*n1
6
q11=-------------------
2
a33
3 2 1 2 1 2
q10=( - a33 *k38 - 3*a33 *b33*k1 + ---*a33 *b33*q1 - ----*b33*k1*n1
2 18
1 2 1 2 3
+ ----*b33*k1*n2 + ----*b33*k12*n1 )/a33
18 18
1
----*b33*k1*n1*n2
18
q9=-------------------
3
a33
2 2
---*k1*n1 - ---*k12*n1
3 3
q8=------------------------
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
9 9 9 9
=------------------------------------------------------------------------------
2
a33
1
---*b33*k12*n2
6
q6=----------------
2
a33
1
----*b33*k1*n1*n2
18
q5=-------------------
3
a33
3 2 1 2 1 2
- a33 *k38 - 3*a33 *b33*k1 + ---*a33 *b33*q1 + ----*b33*k12*n1
2 18
q4=------------------------------------------------------------------
3
a33
2
---*k1*n2
3
q3=-----------
a33
2 2
---*k1*n1*n2 - ---*k12*n1*n2
9 9
q2=------------------------------
2
a33
p56=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n2 - ----*b33 *k1*n2 + ----*b33 *k12*n2
12 96 96
p55=--------------------------------------------------------------
4
a33
p54=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n2 - ----*b33 *k1*n2 + -----*b33 *k12*n2
12 48 192
p53=---------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ----*a33 *b33*k16*n1 - ----*b33 *k1*n1 + ----*b33 *k12*n1
12 96 96
p52=--------------------------------------------------------------
4
a33
p51=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n1 - ----*b33 *k1*n1 + -----*b33 *k12*n1
12 48 192
p50=---------------------------------------------------------------
4
a33
p49=0
1 2 1 3 1 3
- ----*a33 *b33*k16*n2 - ----*b33 *k1*n2 + -----*b33 *k12*n2
12 48 192
p48=---------------------------------------------------------------
4
a33
1 2 1 3 1 3
- ----*a33 *b33*k16*n1 - ----*b33 *k1*n1 + -----*b33 *k12*n1
12 48 192
p47=---------------------------------------------------------------
4
a33
p46=0
1 1 2 1 2
- ----*a33*b33*k38*n2 + ----*b33 *k1*n2 + ----*b33 *k12*n2
12 12 24
p45=-------------------------------------------------------------
3
a33
p44=0
1 1 2 1 2
- ----*a33*b33*k38*n1 + ----*b33 *k1*n1 + ----*b33 *k12*n1
12 12 24
p43=-------------------------------------------------------------
3
a33
1 2 1 2
---*b33 *k1 - ----*b33 *k12
4 16
p42=-----------------------------
2
a33
p41=0
p40=0
1
- ----*b33*k12*n2
12
p39=--------------------
2
a33
1
- ----*b33*k12*n1
12
p38=--------------------
2
a33
p37=0
1 2 1 2
- ---*a33 *k16*n2 - ----*b33 *k1*n2
3 24
p36=--------------------------------------
3
a33
p35=0
p34
1 2 1 1 2 1 2
- ---*a33 *k16*n2 - ----*a33*b33*k38*n2 - ----*b33 *k1*n2 + ----*b33 *k12*n2
3 12 12 48
=-------------------------------------------------------------------------------
3
a33
1 2
----*b33 *k12
16
p33=---------------
2
a33
1
- ----*b33*k38*n1
12
p32=--------------------
2
a33
1 2 1 2 1 2
- ---*a33 *k16*n2 - ----*b33 *k1*n2 + ----*b33 *k12*n2
3 12 48
p31=---------------------------------------------------------
3
a33
1 1 1
---*a33*k38*n2 + ---*b33*k1*n2 - ---*b33*k12*n2
3 3 6
p30=-------------------------------------------------
2
a33
p29=0
2*a33*k38 + b33*k1
p28=--------------------
a33
1
- ---*k12*n2
3
p27=---------------
a33
p26=0
1 1 1
---*a33*k38*n2 - ---*b33*k1*n2 - ----*b33*k12*n2
3 6 12
p25=--------------------------------------------------
2
a33
1 1
- ---*b33*k1*n1 - ----*b33*k12*n1
6 12
p24=------------------------------------
2
a33
p23=0
2 1
- ---*k1*n2 + ---*k12*n2
3 3
p22=---------------------------
a33
1 2 1 2
- ---*a33 *k16*n1 - ----*b33 *k1*n1
3 24
p21=--------------------------------------
3
a33
1 2
- ----*b33 *k12
16
p20=------------------
2
a33
1 2 1 2 1 2
- ---*a33 *k16*n1 - ----*b33 *k1*n1 + ----*b33 *k12*n1
3 12 48
p19=---------------------------------------------------------
3
a33
p18=0
1
- ----*b33*k38*n2
12
p17=--------------------
2
a33
p16
1 2 1 1 2 1 2
- ---*a33 *k16*n1 - ----*a33*b33*k38*n1 - ----*b33 *k1*n1 + ----*b33 *k12*n1
3 12 12 48
=-------------------------------------------------------------------------------
3
a33
1 1 1
---*a33*k38*n1 + ---*b33*k1*n1 - ---*b33*k12*n1
3 3 6
p15=-------------------------------------------------
2
a33
- 2*a33*k38 - b33*k1
p14=-----------------------
a33
p13=0
1
- ---*k12*n1
3
p12=---------------
a33
p11=0
1
---*k38*n1
3
p10=------------
a33
1
---*k38*n2
3
p9=------------
a33
p8= - 4*k1
2 1
- ---*k1*n1 + ---*k12*n1
3 3
p7=---------------------------
a33
p6=0
1 1
- ---*b33*k1*n2 - ----*b33*k12*n2
6 12
p5=------------------------------------
2
a33
1 1 1
---*a33*k38*n1 - ---*b33*k1*n1 - ----*b33*k12*n1
3 6 12
p4=--------------------------------------------------
2
a33
p3=0
2 1
- ---*k1*n2 + ---*k12*n2
3 3
p2=---------------------------
a33
2 1
- ---*k1*n1 + ---*k12*n1
3 3
p1=---------------------------
a33
k125=0
1 2 2 1 4 1 4
----*a33 *b33 *k16 + -----*b33 *k1 - -----*b33 *k12
16 128 256
k124=-----------------------------------------------------
4
a33
k123=0
1 2 2 3 4 1 4
----*a33 *b33 *k16 + -----*b33 *k1 - -----*b33 *k12
16 256 256
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
16 128 256
k117=-----------------------------------------------------
4
a33
k116=0
1 2 2 3 4 1 4
---*a33 *b33 *k16 + -----*b33 *k1 - -----*b33 *k12
8 128 128
k115=----------------------------------------------------
4
a33
k114=0
k113=0
1 2 2 3 4 1 4
----*a33 *b33 *k16 + -----*b33 *k1 - -----*b33 *k12
16 256 256
k112=-----------------------------------------------------
4
a33
k110=0
1 3
- ----*b33 *k1
16
k109=-----------------
3
a33
k108=0
k107=0
k106=0
k105=0
1 3
- ----*b33 *k1
16
k104=-----------------
3
a33
k103=0
k102=0
k100=0
k99=0
k98=0
k97=0
1
a33*k38 - ---*b33*k12
2
k95=-----------------------
a33
k94=0
k93=0
k91=0
1 2 1 3 1 3
---*a33 *b33*k16 + ----*b33 *k1 - ----*b33 *k12
2 16 32
k90=-------------------------------------------------
3
a33
k89=0
1 2 1 3 1 3
---*a33 *b33*k16 + ----*b33 *k1 - ----*b33 *k12
2 16 32
k88=-------------------------------------------------
3
a33
k87=0
k86=0
k85=0
k84=0
1 2 1 3 1 3
---*a33 *b33*k16 + ----*b33 *k1 - ----*b33 *k12
2 16 32
k83=-------------------------------------------------
3
a33
k82=0
k81=0
1 2 1 2
- ---*b33 *k1 + ---*b33 *k12
2 8
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
8 16
k71=----------------------------------------
2
a33
k70=0
k69=k16
k68=0
k67=0
2 1 2 1 2
a33 *k16 + ---*b33 *k1 - ----*b33 *k12
4 16
k66=----------------------------------------
2
a33
- 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
1 2 1 3 1 3
---*a33 *b33*k16 + ----*b33 *k1 - ----*b33 *k12
2 16 32
k52=-------------------------------------------------
3
a33
k51=0
1 2 1 3 1 3
---*a33 *b33*k16 + ----*b33 *k1 - ----*b33 *k12
2 16 32
k50=-------------------------------------------------
3
a33
k49=0
k48=0
1 2 1 3 1 3
---*a33 *b33*k16 + ----*b33 *k1 - ----*b33 *k12
2 16 32
k47=-------------------------------------------------
3
a33
k46=0
k45=0
k44=0
1 2 1 2
- ---*b33 *k1 + ---*b33 *k12
2 8
k43=-------------------------------
2
a33
k42=0
k41=0
k40=0
k39=0
k37=0
k36=0
k35=0
k34=0
k33=0
1 2 1 2
- ---*b33 *k1 + ---*b33 *k12
2 8
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
8 16
k21=----------------------------------------
2
a33
k20=0
2 1 2 1 2
a33 *k16 + ---*b33 *k1 - ----*b33 *k12
4 16
k19=----------------------------------------
2
a33
k18=0
k17=0
- 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,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=( - 48*a33 *u1 - 48*a33 *u2 + 24*a33 *u3 + 24*a33*b33*u3*v3
2 2
+ 24*a33*n1*u1 + 24*a33*n2*u2 + 3*b33 *v3 + 2*b33*n1*v1 + 2*b33*n2*v2)/(
24*a33)
4 4 4 2 4 2
INT=(6912*a33 *k1*u1 + 13824*a33 *k1*u1 *u2*u3 + 6912*a33 *k1*u1*u2*v2
4 2 4 4 2
- 27648*a33 *k1*u1*u3 - 27648*a33 *k1*u1*v1 + 6912*a33 *k12*u1*v1*v2
4 2 2 4 3 4 3
+ 6912*a33 *k12*u2 *u3 + 6912*a33 *k16*u1 *v1 + 6912*a33 *k16*u1 *v3
4 4 3 4 3
+ 6912*a33 *k16*u1*u2*u3*v1 + 6912*a33 *k16*u1*v2 + 6912*a33 *k16*u2 *v1
4 3 4 2 4
+ 6912*a33 *k16*v1*v2 + 6912*a33 *k38*u1*u2 *v2 - 13824*a33 *k38*u1*u3*v1
4 4 3 4
- 6912*a33 *k38*u1*u3 + 6912*a33 *k38*u2 *v3 + 6912*a33 *k38*u2*u3*v2*v3
4 4 2 4 2
+ 13824*a33 *k38*u2*v1*v2 - 6912*a33 *k38*v1 + 6912*a33 *q1*u1
4 3 3
+ 6912*a33 *q1*u1*v1 - 6912*a33 *b33*k1*u1*u3*v1 - 20736*a33 *b33*k1*u1*u3
3 3 4
+ 6912*a33 *b33*k1*u2*v1*v2 - 6912*a33 *b33*k1*u3
3 2 2 3 2
- 6912*a33 *b33*k1*v1 *v2 - 20736*a33 *b33*k1*v1
3 3
- 3456*a33 *b33*k12*u2*u3*v2*v3 + 3456*a33 *b33*k16*u1*u2*v1*v2
3 2 3 2
+ 3456*a33 *b33*k16*u1*v1 *v2 + 3456*a33 *b33*k16*u2 *v1*v3
3 3 2
+ 3456*a33 *b33*k16*u2*u3*v1*v2 + 3456*a33 *b33*k16*u2*v1 *v3
3 3 3 3 2
+ 3456*a33 *b33*k16*v1 *v3 + 3456*a33 *b33*q1*u1*u3 + 3456*a33 *b33*q1*v1
3 3 3 3 2
- 4608*a33 *k1*n1*u1 - 2304*a33 *k1*n1*u1 - 4608*a33 *k1*n1*u2 *u3
3 3 2
+ 4608*a33 *k1*n1*u2*v1 - 4608*a33 *k1*n2*u1 *u2
3 3 2 3
- 4608*a33 *k1*n2*u1*u2*v2 + 4608*a33 *k1*n2*u2 + 2304*a33 *k1*n2*u2
3 3 3 3
+ 2304*a33 *k12*n1*u1 - 2304*a33 *k12*n1*u1*u2*v1 + 2304*a33 *k12*n1*u1
3 2 3
+ 2304*a33 *k12*n1*u2 *u3 - 4608*a33 *k12*n1*u2*v1
3 2 3
+ 2304*a33 *k12*n2*u1 *u2 + 2304*a33 *k12*n2*u1*u2*v2
3 3 2
- 2304*a33 *k12*n2*u1*v1*v2 - 2304*a33 *k16*n1*u1 *v2
3 2 3 2
- 2304*a33 *k16*n1*u3 *v1 - 2304*a33 *k16*n1*u3*v1
3 2 3 2
- 2304*a33 *k16*n2*u1 *v3 - 2304*a33 *k16*n2*u1*v2
3 2 3 3
- 2304*a33 *k16*n2*v1*v2 + 2304*a33 *k38*n1*u2
3 3 3
+ 2304*a33 *k38*n1*u2*u3*v1 + 2304*a33 *k38*n1*u3
3 2 3
+ 2304*a33 *k38*n2*u2*u3 + 2304*a33 *k38*n2*u2*u3*v2
3 3 2 3
- 2304*a33 *k38*n2*u3*v2 + 2304*a33 *k38*n2*v1 *v2 - 2304*a33 *n1*q1*u1
3 2 2 3
- 2304*a33 *n2*q1*u2 + 864*a33 *b33 *k1*u1 *v3
2 2 2 2 2
+ 864*a33 *b33 *k1*u1*u2*u3*v1 - 3456*a33 *b33 *k1*u1*u3 *v2
2 2 3 2 2
- 3456*a33 *b33 *k1*u1*v1 + 1728*a33 *b33 *k1*u1*v1*v3
2 2 3 2 2
+ 1728*a33 *b33 *k1*u1*v2 - 3456*a33 *b33 *k1*u1*v3
2 2 3 2 2 3
+ 1728*a33 *b33 *k1*u2 *v1 - 3456*a33 *b33 *k1*u3 *v3
2 2 2 2 3
- 3456*a33 *b33 *k1*v1*v3 - 432*a33 *b33 *k12*u1 *v3
2 2 2 2 2
- 432*a33 *b33 *k12*u1*u2*u3*v1 + 864*a33 *b33 *k12*u1*u3 *v2
2 2 3 2 2
+ 864*a33 *b33 *k12*u1*v1 - 432*a33 *b33 *k12*u1*v1*v3
2 2 3 2 2 3
- 432*a33 *b33 *k12*u1*v2 - 432*a33 *b33 *k12*u2 *v1
2 2 3 2 2 2
+ 864*a33 *b33 *k12*u3 *v3 + 432*a33 *b33 *k12*u3*v2
2 2 3 2 2 2
- 432*a33 *b33 *k12*v1 + 432*a33 *b33 *k16*u1*v1*v3
2 2 2 2 2 3
+ 432*a33 *b33 *k16*u2*v2*v3 + 432*a33 *b33 *k16*u2*v3
2 2 2 2 2 2 3
+ 864*a33 *b33 *k16*v1 *v3 + 432*a33 *b33 *k16*v1*v3
2 2 2 2
+ 432*a33 *b33 *q1*u1*v3 + 432*a33 *b33 *q1*v1*v3
2 2 3
- 1152*a33 *b33*k1*n1*u1*u3*v2 - 1152*a33 *b33*k1*n1*u2
2 2
+ 2304*a33 *b33*k1*n1*u2*u3*v1 + 1152*a33 *b33*k1*n1*v1*v2
2 2 2
+ 2880*a33 *b33*k1*n1*v1 - 1152*a33 *b33*k1*n2*u1 *u3
2 2
- 1152*a33 *b33*k1*n2*u2*u3*v2 - 1152*a33 *b33*k1*n2*u3*v2
2 2 2
+ 2304*a33 *b33*k1*n2*v1 *v2 + 2880*a33 *b33*k1*n2*v2
2 2
- 576*a33 *b33*k12*n1*u1*u3*v2 - 1152*a33 *b33*k12*n1*u1*v2
2 3 2 2
- 576*a33 *b33*k12*n1*u2 - 576*a33 *b33*k12*n1*u2 *v3
2 2
- 1152*a33 *b33*k12*n1*u2*u3*v1 + 576*a33 *b33*k12*n1*v1
2 2 2
- 576*a33 *b33*k12*n2*u1 *u3 - 576*a33 *b33*k12*n2*u1*u3*v3
2 2 2
- 576*a33 *b33*k12*n2*u2*u3*v2 + 1152*a33 *b33*k12*n2*u3
2 2 2
- 1152*a33 *b33*k12*n2*v1 *v2 + 576*a33 *b33*k12*n2*v2
2 2 2
- 576*a33 *b33*k16*n1*u2*v2*v3 - 576*a33 *b33*k16*n1*u2*v3
2 2 2
- 576*a33 *b33*k16*n1*v2 *v3 - 576*a33 *b33*k16*n2*u3*v2*v3
2 2 2 2
- 576*a33 *b33*k16*n2*u3*v3 - 576*a33 *b33*k16*n2*v2*v3
2 2 2
- 576*a33 *b33*k38*n1*u2*v1*v3 - 576*a33 *b33*k38*n1*u2*v2
2 2 2 2
- 576*a33 *b33*k38*n1*u3 *v1 - 576*a33 *b33*k38*n2*u1*v1
2 2 2 2
- 576*a33 *b33*k38*n2*v1 *v3 - 576*a33 *b33*k38*n2*v1*v2
2 2 2 2
- 576*a33 *b33*n1*q1*v1 - 576*a33 *b33*n2*q1*v2 - 768*a33 *k1*n1 *u1*v1
2 2 2 2
+ 1536*a33 *k1*n1*n2*u1*u2 - 768*a33 *k1*n1*n2*u3 + 768*a33 *k1*n2 *u1*v1
2 2 2
+ 768*a33 *k12*n1 *u1*v1 - 1536*a33 *k12*n1*n2*u1*u2
2 2 2
+ 768*a33 *k12*n1*n2*u3 - 768*a33 *k12*n2 *u1*v1
3 3 2
+ 432*a33*b33 *k1*u1*u2*v1*v2 - 432*a33*b33 *k1*u1*u3*v3
3 2 3 2
+ 432*a33*b33 *k1*u1*v1 *v2 + 432*a33*b33 *k1*u2 *v1*v3
3 3 2
+ 432*a33*b33 *k1*u2*u3*v1*v2 + 432*a33*b33 *k1*u2*v1 *v3
3 3 3 2
+ 432*a33*b33 *k1*v1 *v3 - 432*a33*b33 *k1*v1*v2 *v3
3 3 2
- 216*a33*b33 *k12*u1*u2*v1*v2 - 216*a33*b33 *k12*u1*v1 *v2
3 2 3
- 216*a33*b33 *k12*u2 *v1*v3 - 216*a33*b33 *k12*u2*u3*v1*v2
3 2 3 3
- 216*a33*b33 *k12*u2*v1 *v3 - 216*a33*b33 *k12*v1 *v3
2 2 2
- 288*a33*b33 *k1*n1*u1 *v2 + 576*a33*b33 *k1*n1*u2*v1*v3
2 2 2 2
- 576*a33*b33 *k1*n1*u3 *v1 - 576*a33*b33 *k1*n1*u3*v1
2 2 2 2
- 288*a33*b33 *k1*n2*u1 *v3 - 576*a33*b33 *k1*n2*u1*v2
2 2 2 2
+ 576*a33*b33 *k1*n2*v1 *v3 - 576*a33*b33 *k1*n2*v1*v2
2 2 2
+ 288*a33*b33 *k12*n1*u2*v1*v3 + 144*a33*b33 *k12*n1*u3 *v1
2 2 2
+ 144*a33*b33 *k12*n1*u3*v1 - 288*a33*b33 *k12*n1*v2*v3
2 2 2
+ 144*a33*b33 *k12*n2*u1*v2 + 288*a33*b33 *k12*n2*u3*v3
2 2 2 2
+ 288*a33*b33 *k12*n2*v1 *v3 + 144*a33*b33 *k12*n2*v1*v2
2 2
- 384*a33*b33*k1*n1 *v1 + 384*a33*b33*k1*n1*n2*u2*u3
2 2
+ 384*a33*b33*k1*n1*n2*u3*v1 + 384*a33*b33*k1*n2 *v1
2 2 2 3
+ 384*a33*b33*k12*n1 *u1*u3 + 384*a33*b33*k12*n1 *v1 + 256*a33*k1*n1 *u1
2 3 2
+ 256*a33*k1*n1 *n2*u2 - 256*a33*k12*n1 *u1 - 256*a33*k12*n1 *n2*u2
4 2 4 2 4 3
+ 81*b33 *k1*u1*v1*v3 + 54*b33 *k1*u2*v2*v3 + 81*b33 *k1*u2*v3
4 2 2 4 3 4 2
+ 162*b33 *k1*v1 *v3 + 54*b33 *k1*v1*v3 - 27*b33 *k12*u1*v1*v3
4 2 4 3 4 2 2
- 27*b33 *k12*u2*v2*v3 - 27*b33 *k12*u2*v3 - 54*b33 *k12*v1 *v3
4 3 3 3 2
- 27*b33 *k12*v1*v3 - 144*b33 *k1*n1*u2*v2*v3 - 72*b33 *k1*n1*u2*v3
3 2 3 3 2
- 144*b33 *k1*n1*v2 *v3 - 144*b33 *k1*n2*u3*v2*v3 - 144*b33 *k1*n2*u3*v3
3 2 3 3 2
- 72*b33 *k1*n2*v2*v3 + 36*b33 *k12*n1*u2*v2*v3 + 72*b33 *k12*n1*u2*v3
3 2 3 3 2
+ 36*b33 *k12*n1*v2 *v3 + 36*b33 *k12*n2*u3*v2*v3 + 36*b33 *k12*n2*u3*v3
3 2 2 2 2
+ 72*b33 *k12*n2*v2*v3 - 48*b33 *k1*n1 *v1*v3 + 96*b33 *k1*n1*n2*u2*v3
2 2 2 2 2 2
+ 48*b33 *k1*n2 *v1*v3 + 96*b33 *k12*n1 *u1*v3 + 48*b33 *k12*n1 *v1*v3
2 2 2 3
+ 96*b33 *k12*n1*n2*u2*v3 + 48*b33 *k12*n2 *v1*v3 + 64*b33*k1*n1 *v1
2 3 2
+ 64*b33*k1*n1 *n2*v2 - 64*b33*k12*n1 *v1 - 64*b33*k12*n1 *n2*v2)/(6912
4
*a33 )
And again in machine readable form:
HAM=( - 48*a33**2*u1**2 - 48*a33**2*u2**2 + 24*a33**2*u3**2 + 24*a33*b33*u3*v3 +
24*a33*n1*u1 + 24*a33*n2*u2 + 3*b33**2*v3**2 + 2*b33*n1*v1 + 2*b33*n2*v2)/(24*
a33)$
INT=(6912*a33**4*k1*u1**4 + 13824*a33**4*k1*u1**2*u2*u3 + 6912*a33**4*k1*u1*u2*
v2**2 - 27648*a33**4*k1*u1*u3**2 - 27648*a33**4*k1*u1*v1 + 6912*a33**4*k12*u1*v1
*v2**2 + 6912*a33**4*k12*u2**2*u3**2 + 6912*a33**4*k16*u1**3*v1 + 6912*a33**4*
k16*u1**3*v3 + 6912*a33**4*k16*u1*u2*u3*v1 + 6912*a33**4*k16*u1*v2**3 + 6912*a33
**4*k16*u2**3*v1 + 6912*a33**4*k16*v1*v2**3 + 6912*a33**4*k38*u1*u2**2*v2 -
13824*a33**4*k38*u1*u3*v1 - 6912*a33**4*k38*u1*u3 + 6912*a33**4*k38*u2**3*v3 +
6912*a33**4*k38*u2*u3*v2*v3 + 13824*a33**4*k38*u2*v1*v2 - 6912*a33**4*k38*v1**2
+ 6912*a33**4*q1*u1**2 + 6912*a33**4*q1*u1*v1 - 6912*a33**3*b33*k1*u1*u3*v1 -
20736*a33**3*b33*k1*u1*u3 + 6912*a33**3*b33*k1*u2*v1*v2 - 6912*a33**3*b33*k1*u3
**4 - 6912*a33**3*b33*k1*v1**2*v2**2 - 20736*a33**3*b33*k1*v1**2 - 3456*a33**3*
b33*k12*u2*u3*v2*v3 + 3456*a33**3*b33*k16*u1*u2*v1*v2 + 3456*a33**3*b33*k16*u1*
v1**2*v2 + 3456*a33**3*b33*k16*u2**2*v1*v3 + 3456*a33**3*b33*k16*u2*u3*v1*v2 +
3456*a33**3*b33*k16*u2*v1**2*v3 + 3456*a33**3*b33*k16*v1**3*v3 + 3456*a33**3*b33
*q1*u1*u3 + 3456*a33**3*b33*q1*v1**2 - 4608*a33**3*k1*n1*u1**3 - 2304*a33**3*k1*
n1*u1 - 4608*a33**3*k1*n1*u2**2*u3 + 4608*a33**3*k1*n1*u2*v1 - 4608*a33**3*k1*n2
*u1**2*u2 - 4608*a33**3*k1*n2*u1*u2*v2 + 4608*a33**3*k1*n2*u2**2 + 2304*a33**3*
k1*n2*u2 + 2304*a33**3*k12*n1*u1**3 - 2304*a33**3*k12*n1*u1*u2*v1 + 2304*a33**3*
k12*n1*u1 + 2304*a33**3*k12*n1*u2**2*u3 - 4608*a33**3*k12*n1*u2*v1 + 2304*a33**3
*k12*n2*u1**2*u2 + 2304*a33**3*k12*n2*u1*u2*v2 - 2304*a33**3*k12*n2*u1*v1*v2 -
2304*a33**3*k16*n1*u1**2*v2 - 2304*a33**3*k16*n1*u3**2*v1 - 2304*a33**3*k16*n1*
u3*v1**2 - 2304*a33**3*k16*n2*u1**2*v3 - 2304*a33**3*k16*n2*u1*v2**2 - 2304*a33
**3*k16*n2*v1*v2**2 + 2304*a33**3*k38*n1*u2**3 + 2304*a33**3*k38*n1*u2*u3*v1 +
2304*a33**3*k38*n1*u3**3 + 2304*a33**3*k38*n2*u2*u3**2 + 2304*a33**3*k38*n2*u2*
u3*v2 - 2304*a33**3*k38*n2*u3*v2 + 2304*a33**3*k38*n2*v1**2*v2 - 2304*a33**3*n1*
q1*u1 - 2304*a33**3*n2*q1*u2 + 864*a33**2*b33**2*k1*u1**3*v3 + 864*a33**2*b33**2
*k1*u1*u2*u3*v1 - 3456*a33**2*b33**2*k1*u1*u3**2*v2 - 3456*a33**2*b33**2*k1*u1*
v1**3 + 1728*a33**2*b33**2*k1*u1*v1*v3 + 1728*a33**2*b33**2*k1*u1*v2**3 - 3456*
a33**2*b33**2*k1*u1*v3 + 1728*a33**2*b33**2*k1*u2**3*v1 - 3456*a33**2*b33**2*k1*
u3**3*v3 - 3456*a33**2*b33**2*k1*v1*v3 - 432*a33**2*b33**2*k12*u1**3*v3 - 432*
a33**2*b33**2*k12*u1*u2*u3*v1 + 864*a33**2*b33**2*k12*u1*u3**2*v2 + 864*a33**2*
b33**2*k12*u1*v1**3 - 432*a33**2*b33**2*k12*u1*v1*v3 - 432*a33**2*b33**2*k12*u1*
v2**3 - 432*a33**2*b33**2*k12*u2**3*v1 + 864*a33**2*b33**2*k12*u3**3*v3 + 432*
a33**2*b33**2*k12*u3*v2**2 - 432*a33**2*b33**2*k12*v1**3 + 432*a33**2*b33**2*k16
*u1*v1*v3**2 + 432*a33**2*b33**2*k16*u2*v2*v3**2 + 432*a33**2*b33**2*k16*u2*v3**
3 + 864*a33**2*b33**2*k16*v1**2*v3**2 + 432*a33**2*b33**2*k16*v1*v3**3 + 432*a33
**2*b33**2*q1*u1*v3 + 432*a33**2*b33**2*q1*v1*v3 - 1152*a33**2*b33*k1*n1*u1*u3*
v2 - 1152*a33**2*b33*k1*n1*u2**3 + 2304*a33**2*b33*k1*n1*u2*u3*v1 + 1152*a33**2*
b33*k1*n1*v1*v2 + 2880*a33**2*b33*k1*n1*v1 - 1152*a33**2*b33*k1*n2*u1**2*u3 -
1152*a33**2*b33*k1*n2*u2*u3*v2 - 1152*a33**2*b33*k1*n2*u3*v2 + 2304*a33**2*b33*
k1*n2*v1**2*v2 + 2880*a33**2*b33*k1*n2*v2 - 576*a33**2*b33*k12*n1*u1*u3*v2 -
1152*a33**2*b33*k12*n1*u1*v2 - 576*a33**2*b33*k12*n1*u2**3 - 576*a33**2*b33*k12*
n1*u2**2*v3 - 1152*a33**2*b33*k12*n1*u2*u3*v1 + 576*a33**2*b33*k12*n1*v1 - 576*
a33**2*b33*k12*n2*u1**2*u3 - 576*a33**2*b33*k12*n2*u1*u3*v3 - 576*a33**2*b33*k12
*n2*u2*u3*v2 + 1152*a33**2*b33*k12*n2*u3**2 - 1152*a33**2*b33*k12*n2*v1**2*v2 +
576*a33**2*b33*k12*n2*v2 - 576*a33**2*b33*k16*n1*u2*v2*v3 - 576*a33**2*b33*k16*
n1*u2*v3**2 - 576*a33**2*b33*k16*n1*v2**2*v3 - 576*a33**2*b33*k16*n2*u3*v2*v3 -
576*a33**2*b33*k16*n2*u3*v3**2 - 576*a33**2*b33*k16*n2*v2*v3**2 - 576*a33**2*b33
*k38*n1*u2*v1*v3 - 576*a33**2*b33*k38*n1*u2*v2**2 - 576*a33**2*b33*k38*n1*u3**2*
v1 - 576*a33**2*b33*k38*n2*u1*v1**2 - 576*a33**2*b33*k38*n2*v1**2*v3 - 576*a33**
2*b33*k38*n2*v1*v2**2 - 576*a33**2*b33*n1*q1*v1 - 576*a33**2*b33*n2*q1*v2 - 768*
a33**2*k1*n1**2*u1*v1 + 1536*a33**2*k1*n1*n2*u1*u2 - 768*a33**2*k1*n1*n2*u3 +
768*a33**2*k1*n2**2*u1*v1 + 768*a33**2*k12*n1**2*u1*v1 - 1536*a33**2*k12*n1*n2*
u1*u2 + 768*a33**2*k12*n1*n2*u3 - 768*a33**2*k12*n2**2*u1*v1 + 432*a33*b33**3*k1
*u1*u2*v1*v2 - 432*a33*b33**3*k1*u1*u3*v3**2 + 432*a33*b33**3*k1*u1*v1**2*v2 +
432*a33*b33**3*k1*u2**2*v1*v3 + 432*a33*b33**3*k1*u2*u3*v1*v2 + 432*a33*b33**3*
k1*u2*v1**2*v3 + 432*a33*b33**3*k1*v1**3*v3 - 432*a33*b33**3*k1*v1*v2**2*v3 -
216*a33*b33**3*k12*u1*u2*v1*v2 - 216*a33*b33**3*k12*u1*v1**2*v2 - 216*a33*b33**3
*k12*u2**2*v1*v3 - 216*a33*b33**3*k12*u2*u3*v1*v2 - 216*a33*b33**3*k12*u2*v1**2*
v3 - 216*a33*b33**3*k12*v1**3*v3 - 288*a33*b33**2*k1*n1*u1**2*v2 + 576*a33*b33**
2*k1*n1*u2*v1*v3 - 576*a33*b33**2*k1*n1*u3**2*v1 - 576*a33*b33**2*k1*n1*u3*v1**2
- 288*a33*b33**2*k1*n2*u1**2*v3 - 576*a33*b33**2*k1*n2*u1*v2**2 + 576*a33*b33**
2*k1*n2*v1**2*v3 - 576*a33*b33**2*k1*n2*v1*v2**2 + 288*a33*b33**2*k12*n1*u2*v1*
v3 + 144*a33*b33**2*k12*n1*u3**2*v1 + 144*a33*b33**2*k12*n1*u3*v1**2 - 288*a33*
b33**2*k12*n1*v2*v3 + 144*a33*b33**2*k12*n2*u1*v2**2 + 288*a33*b33**2*k12*n2*u3*
v3 + 288*a33*b33**2*k12*n2*v1**2*v3 + 144*a33*b33**2*k12*n2*v1*v2**2 - 384*a33*
b33*k1*n1**2*v1**2 + 384*a33*b33*k1*n1*n2*u2*u3 + 384*a33*b33*k1*n1*n2*u3*v1 +
384*a33*b33*k1*n2**2*v1**2 + 384*a33*b33*k12*n1**2*u1*u3 + 384*a33*b33*k12*n1**2
*v1**2 + 256*a33*k1*n1**3*u1 + 256*a33*k1*n1**2*n2*u2 - 256*a33*k12*n1**3*u1 -
256*a33*k12*n1**2*n2*u2 + 81*b33**4*k1*u1*v1*v3**2 + 54*b33**4*k1*u2*v2*v3**2 +
81*b33**4*k1*u2*v3**3 + 162*b33**4*k1*v1**2*v3**2 + 54*b33**4*k1*v1*v3**3 - 27*
b33**4*k12*u1*v1*v3**2 - 27*b33**4*k12*u2*v2*v3**2 - 27*b33**4*k12*u2*v3**3 - 54
*b33**4*k12*v1**2*v3**2 - 27*b33**4*k12*v1*v3**3 - 144*b33**3*k1*n1*u2*v2*v3 -
72*b33**3*k1*n1*u2*v3**2 - 144*b33**3*k1*n1*v2**2*v3 - 144*b33**3*k1*n2*u3*v2*v3
- 144*b33**3*k1*n2*u3*v3**2 - 72*b33**3*k1*n2*v2*v3**2 + 36*b33**3*k12*n1*u2*v2
*v3 + 72*b33**3*k12*n1*u2*v3**2 + 36*b33**3*k12*n1*v2**2*v3 + 36*b33**3*k12*n2*
u3*v2*v3 + 36*b33**3*k12*n2*u3*v3**2 + 72*b33**3*k12*n2*v2*v3**2 - 48*b33**2*k1*
n1**2*v1*v3 + 96*b33**2*k1*n1*n2*u2*v3 + 48*b33**2*k1*n2**2*v1*v3 + 96*b33**2*
k12*n1**2*u1*v3 + 48*b33**2*k12*n1**2*v1*v3 + 96*b33**2*k12*n1*n2*u2*v3 + 48*b33
**2*k12*n2**2*v1*v3 + 64*b33*k1*n1**3*v1 + 64*b33*k1*n1**2*n2*v2 - 64*b33*k12*n1
**3*v1 - 64*b33*k12*n1**2*n2*v2)/(6912*a33**4)$