Solution 2 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
r10=0
2 2 2 2 2 2 2 2 2 4 2
r11=(a33 *m2 *n1 *r20 + m2 *n1 *n2 *r425 - m2 *n1 *n3 *r425 + n1 *n2 *r40
4 2 3 3
- n1 *n3 *r40)/(a33 *m2 )
2 2 2 3 2 2 3 3
r12=( - a33 *m2 *n1*n2*r20 - m2 *n1*n2 *r425 + m2 *n1*n2*n3 *r425 - n1 *n2 *r40
3 2 3 3
+ n1 *n2*n3 *r40)/(a33 *m2 )
2 2 2 2 2 2 2 2 3
r13=(a33 *m2 *n1 *n3*r20 + m2 *n1 *n2 *n3*r425 - m2 *n1 *n3 *r425
4 2 4 3 3 4
+ n1 *n2 *n3*r40 - n1 *n3 *r40)/(a33 *m2 )
2 2 2 2 2 3 2 2 2 4 3
r14=(a33 *m2 *n1 *n2*r20 + m2 *n1 *n2 *r425 - m2 *n1 *n2*n3 *r425 + n1 *n2 *r40
4 2 3 4
- n1 *n2*n3 *r40)/(a33 *m2 )
2 2 3 2 3 2 2 3 2 5 2
r15=(a33 *m2 *n1 *r20 + m2 *n1 *n2 *r425 - m2 *n1 *n3 *r425 + n1 *n2 *r40
5 2 3 4
- n1 *n3 *r40)/(a33 *m2 )
r21=0
2 2 2 2 4 2 2
m2 *n1 *r425 - m2 *n2 *r425 + n1 *r40 - n1 *n2 *r40
r22=-----------------------------------------------------
2 2
a33 *m2
r23=0
2 3
- 2*m2 *n1*n2*r425 - 2*n1 *n2*r40
r24=------------------------------------
2 2
a33 *m2
2 2 4
- 2*m2 *n1 *n2*r425 - 2*n1 *n2*r40
r26=-------------------------------------
2 3
a33 *m2
2 2 4
2*m2 *n1 *n3*r425 + 2*n1 *n3*r40
r27=----------------------------------
2 3
a33 *m2
2 3
- 2*m2 *n1*n2*n3*r425 - 2*n1 *n2*n3*r40
r28=------------------------------------------
2 3
a33 *m2
r210=0
2*n1*r20
r212=----------
m2
2 2 4
2*m2 *n1 *n2*n3*r425 + 2*n1 *n2*n3*r40
r213=----------------------------------------
2 4
a33 *m2
r215=0
2 2 2 3 2 2 5
r216=( - 2*a33 *m2 *n1*r20 + 2*m2 *n1 *r425 - 2*m2 *n1*n2 *r425 + 2*n1 *r40
3 2 2 3
- 2*n1 *n2 *r40)/(a33 *m2 )
2 2 4
- 4*m2 *n1 *n2*r425 - 4*n1 *n2*r40
r217=-------------------------------------
2 3
a33 *m2
2 3 5
2*m2 *n1 *n3*r425 + 2*n1 *n3*r40
r218=----------------------------------
2 4
a33 *m2
2 3 5
2*m2 *n1 *n2*r425 + 2*n1 *n2*r40
r219=----------------------------------
2 4
a33 *m2
r220
2 2 2 2 4 2 2 2 6 4 2
- a33 *m2 *n1 *r20 + m2 *n1 *r425 - m2 *n1 *n2 *r425 + n1 *r40 - n1 *n2 *r40
=-------------------------------------------------------------------------------
2 4
a33 *m2
r30=0
2 2
m2 *r425 + 2*n1 *r40
r31=----------------------
a33*m2
r32=0
3 2
- m2 *r464 - m2*n1 *r425
r33=---------------------------
2
a33*n1
2 2
- m2 *n2*r425 - 2*n1 *n2*r40
r34=-------------------------------
a33*m2*n1
r35=0
3 2
m2 *n2*r464 + m2*n1 *n2*r425
r36=------------------------------
3
a33*n1
r37=0
3 2
- m2 *r464 - m2*n1 *r425
r38=---------------------------
2
a33*n1
3 2
m2 *n2*r464 + m2*n1 *n2*r425
r39=------------------------------
3
a33*n1
2 2
m2 *n3*r425 + 2*n1 *n3*r40
r310=----------------------------
2
a33*m2
2 2
m2 *n2*r464 + n1 *n2*r425
r311=---------------------------
2
a33*n1
2 2
- m2 *n3*r464 - n1 *n3*r425
r312=------------------------------
2
a33*n1
4 2 2 4
- 2*m2 *r464 - 4*m2 *n1 *r425 - 4*n1 *r40
r313=--------------------------------------------
2
a33*m2 *n1
r314=0
2 2
- m2 *n3*r464 - n1 *n3*r425
r315=------------------------------
2
a33*n1
r316=0
- m2*r464
r317=------------
a33
m2*n2*r464
r318=------------
a33*n1
- n3*r464
r319=------------
a33
2 2
m2 *n2*r425 + 2*n1 *n2*r40
r320=----------------------------
2
a33*m2
r323=0
4 2 2 4
- 3*m2 *n2*r464 - 5*m2 *n1 *n2*r425 - 4*n1 *n2*r40
r325=-----------------------------------------------------
2 2
a33*m2 *n1
4 2 2 4
m2 *r464 + 2*m2 *n1 *r425 + 2*n1 *r40
r326=---------------------------------------
3
a33*m2
4 2 2 4
2*m2 *n3*r464 + 4*m2 *n1 *n3*r425 + 4*n1 *n3*r40
r328=--------------------------------------------------
3
a33*m2 *n1
- n2*r464
r329=------------
a33
r330=0
4 2 2 4
3*m2 *n2*r464 + 6*m2 *n1 *n2*r425 + 6*n1 *n2*r40
r332=--------------------------------------------------
3
a33*m2 *n1
4 2 2 4
- m2 *n3*r464 - 2*m2 *n1 *n3*r425 - 2*n1 *n3*r40
r333=---------------------------------------------------
4
a33*m2
4 2 2 4
- m2 *n2*r464 - 2*m2 *n1 *n2*r425 - 2*n1 *n2*r40
r334=---------------------------------------------------
4
a33*m2
2 3
m2 *n1*r425 + 2*n1 *r40
r335=-------------------------
2
a33*m2
r336=0
4 2 2 4
- 3*m2 *r464 - 5*m2 *n1 *r425 - 4*n1 *r40
r337=--------------------------------------------
2
a33*m2 *n1
r338=0
4 2 2 4
3*m2 *n2*r464 + 5*m2 *n1 *n2*r425 + 4*n1 *n2*r40
r339=--------------------------------------------------
2 2
a33*m2 *n1
4 2 2 4
- 3*m2 *r464 - 5*m2 *n1 *r425 - 4*n1 *r40
r340=--------------------------------------------
2
a33*m2 *n1
4 2 2 4
2*m2 *n2*r464 + 4*m2 *n1 *n2*r425 + 4*n1 *n2*r40
r341=--------------------------------------------------
3
a33*m2 *n1
4 2 2 4
- 2*m2 *n3*r464 - 4*m2 *n1 *n3*r425 - 4*n1 *n3*r40
r342=-----------------------------------------------------
3
a33*m2 *n1
r343=0
- n1*r464
r344=------------
a33
r345=0
4 2 2 4
3*m2 *r464 + 6*m2 *n1 *r425 + 6*n1 *r40
r347=-----------------------------------------
3
a33*m2
r348=0
4 2 3 5
- m2 *n1*r464 - 2*m2 *n1 *r425 - 2*n1 *r40
r349=---------------------------------------------
4
a33*m2
r350=0
4 2 2 4
- 3*m2 *r464 - 6*m2 *n1 *r425 - 6*n1 *r40
r351=--------------------------------------------
3
a33*m2
4 2 2 4
3*m2 *n2*r464 + 6*m2 *n1 *n2*r425 + 6*n1 *n2*r40
r352=--------------------------------------------------
3
a33*m2 *n1
4 2 2 4
- m2 *n3*r464 - 2*m2 *n1 *n3*r425 - 2*n1 *n3*r40
r353=---------------------------------------------------
4
a33*m2
4 2 2 4
- m2 *n2*r464 - 2*m2 *n1 *n2*r425 - 2*n1 *n2*r40
r354=---------------------------------------------------
4
a33*m2
4 2 3 5
- m2 *n1*r464 - 2*m2 *n1 *r425 - 2*n1 *r40
r355=---------------------------------------------
4
a33*m2
r41=0
4 2 2
- m2 *r464 - m2 *n1 *r425
r42=----------------------------
4
n1
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
4 2 2
- m2 *r464 - m2 *n1 *r425
r49=----------------------------
4
n1
r410=0
r411=0
r412=0
r413=0
r415=0
r416=0
r417=0
r418=0
r419=0
3 2
2*m2 *r464 + 2*m2*n1 *r425
r420=----------------------------
3
n1
r421=0
r422=0
r423=0
r424=0
r426=0
r427=0
r428=0
r429=0
r431=0
r432=0
r433=0
r435=0
4 2 2 4
2*m2 *r464 + 2*m2 *n1 *r425 + 4*n1 *r40
r439=-----------------------------------------
3
m2*n1
r442=0
3 2
- 2*m2 *r464 - 2*m2*n1 *r425
r444=-------------------------------
3
n1
r445=0
r448=0
r450=0
r451=0
- 2*m2*r464
r453=--------------
n1
r454=0
4 2 2 4
- m2 *r464 - m2 *n1 *r425 - 2*n1 *r40
r455=----------------------------------------
2 2
m2 *n1
r458=0
4 2 2 4
5*m2 *r464 + 5*m2 *n1 *r425 + 4*n1 *r40
r460=-----------------------------------------
2 2
m2 *n1
r461=0
r463=0
r465=0
4 2 2 4
- 4*m2 *r464 - 4*m2 *n1 *r425 - 4*n1 *r40
r467=--------------------------------------------
3
m2 *n1
r468=0
4 2 2 4
m2 *r464 + m2 *n1 *r425 + n1 *r40
r469=-----------------------------------
4
m2
r470=0
4 2 2 4
- 2*m2 *r464 - 2*m2 *n1 *r425 - 4*n1 *r40
r471=--------------------------------------------
3
m2*n1
r472=0
3 2
2*m2 *r464 + 2*m2*n1 *r425
r473=----------------------------
3
n1
r474=0
r475=0
r476=0
r477=0
3 2
4*m2 *r464 + 4*m2*n1 *r425
r478=----------------------------
3
n1
r479=0
r480=0
r481=0
r482=0
r484=0
r485=0
r486=0
2*m2*r464
r487=-----------
n1
r488=0
r489=0
r490=0
r493=0
r495=0
r498=0
r499=0
r4100=0
r4102=0
r4103=0
r4104=0
4 2 2 4
- m2 *r464 - m2 *n1 *r425 - 2*n1 *r40
r4105=----------------------------------------
2 2
m2 *n1
r4106=0
4 2 2 4
5*m2 *r464 + 5*m2 *n1 *r425 + 4*n1 *r40
r4107=-----------------------------------------
2 2
m2 *n1
r4108=0
r4109=0
4 2 2 4
10*m2 *r464 + 10*m2 *n1 *r425 + 8*n1 *r40
r4110=-------------------------------------------
2 2
m2 *n1
r4111=0
r4112=0
r4113=0
r4114=r464
r4115=0
4 2 2 4
- 8*m2 *r464 - 8*m2 *n1 *r425 - 8*n1 *r40
r4117=--------------------------------------------
3
m2 *n1
r4118=0
4 2 2 4
2*m2 *r464 + 2*m2 *n1 *r425 + 2*n1 *r40
r4119=-----------------------------------------
4
m2
r4120=0
4 2 2 4
4*m2 *r464 + 4*m2 *n1 *r425 + 4*n1 *r40
r4121=-----------------------------------------
3
m2 *n1
r4122=0
r4123=0
r4124=0
4 2 2 4
m2 *r464 + m2 *n1 *r425 + n1 *r40
r4125=-----------------------------------
4
m2
m3=0
- m2*n2
m1=----------
n1
c33=0
c23=0
c22=0
c13=0
c12=0
c11=0
b33=0
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
b11=0
a23=0
a22=0
a13=0
a12=0
a11=0
4 2 2 4
- 4*m2 *r464 - 4*m2 *n1 *r425 - 4*n1 *r40
r496=--------------------------------------------
3
m2 *n1
2
- n1 *r20
r214=------------
2
m2
4 2 2 4
10*m2 *r464 + 10*m2 *n1 *r425 + 8*n1 *r40
r483=-------------------------------------------
2 2
m2 *n1
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:
r40, r20, r425, r464, n3, m2, n1, 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,a33,n1 + i*n2,n1 - i*n2,m2,n3}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a11,
a12,
a13,
a22,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
b33,
c11,
c12,
c13,
c22,
c23,
c33,
m1*n1 + m2*n2,
m3}$
The system of equations related to the Hamiltonian HAM:
2 - v1*m2*n2
HAM=u1*n1 + u2*n2 + u3 *a33 + u3*n3 + ------------- + v2*m2
n1
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
4 4 3 3 3 5 2 2 4
FI=u1 *a33*n1 + 4*u1 *v2*a33*m2*n1 - u1 *n1 + 2*u1 *u2 *a33*n1
2 3 2 4 2 2 4 2 4
- 8*u1 *u2*v1*a33*m2*n1 - u1 *u2*n1 *n2 + u1 *u3 *a33*n1 - u1 *u3*n1 *n3
2 2 2 2 2 3 2 2 2 2
+ 10*u1 *v1 *a33*m2 *n1 + 3*u1 *v1*m2*n1 *n2 + 5*u1 *v2 *a33*m2 *n1
2 4 2 2 2 2 2 5
- 3*u1 *v2*m2*n1 - u1 *v3 *a33*m2 *n1 - u1*u2 *n1
3 4 2 3
- 4*u1*u2*u3*v3*a33*m2*n1 + 3*u1*u2*v1*m2*n1 + 2*u1*u3 *v2*a33*m2*n1
2 5 2 2 3
- u1*u3 *n1 + 10*u1*u3*v1*v3*a33*m2 *n1 - 2*u1*u3*v2*m2*n1 *n3
3 2 3 2 2 3
+ 2*u1*u3*v3*m2*n1 *n2 + 4*u1*v1 *v2*a33*m2 *n1 - 3*u1*v1 *m2 *n1
2 2 3 3 2 2 3
+ 3*u1*v1*v2*m2 *n1 *n2 + 2*u1*v2 *a33*m2 *n1 - 3*u1*v2 *m2 *n1
2 3 4 4 3 3 3 4
- 2*u1*v2*v3 *a33*m2 *n1 + u2 *a33*n1 - 4*u2 *v1*a33*m2*n1 - u2 *n1 *n2
2 2 4 2 4 2 2 2 2
+ u2 *u3 *a33*n1 - u2 *u3*n1 *n3 + 5*u2 *v1 *a33*m2 *n1
2 3 2 2 2 2 2 3
+ 3*u2 *v1*m2*n1 *n2 - u2 *v3 *a33*m2 *n1 - 2*u2*u3 *v1*a33*m2*n1
2 4 3 4
- u2*u3 *n1 *n2 + 2*u2*u3*v1*m2*n1 *n3 + u2*u3*v3*m2*n1
3 3 2 2 2 2 3
- 2*u2*v1 *a33*m2 *n1 - 3*u2*v1 *m2 *n1 *n2 + 2*u2*v1*v3 *a33*m2 *n1
3 4 2 3 2 4 2 2 2
- u3 *n1 *n3 + u3 *v1*m2*n1 *n2 - u3 *v2*m2*n1 - u3*v1 *m2 *n1 *n3
3 2 3 2 2 2
+ 2*u3*v1*v2*v3*a33*m2 *n1 - 2*u3*v1*v3*m2 *n1 - u3*v2 *m2 *n1 *n3
2 2 3 3 2 3 2 2 2 4
+ u3*v2*v3*m2 *n1 *n2 + v1 *m2 *n1*n2 - v1 *v2*m2 *n1 - v1 *v3 *a33*m2
2 3 3 3 2 2 2 4
+ v1*v2 *m2 *n1*n2 - v2 *m2 *n1 - v2 *v3 *a33*m2
which the program can not factorize further.
{HAM,FI} = {4,
- u1*v1 - u2*v2 - u3*v3,
n1,
m2,
2 2 2 2 2 2
- 2*u1 *u3*a33 *n1 - u1 *a33*n1 *n3 - 5*u1*u3*v2*a33 *m2*n1
3
3*u1*u3*a33*n1 - 5*u1*v2*a33*m2*n1*n3
+ ----------------- + -------------------------
2 2
3
u1*n1 *n3 2 2 2
+ u1*v3*a33*m2*n1*n2 + ----------- + 2*u2 *u3*a33 *n1
4
2 2 2 2
+ u2 *a33*n1 *n3 - 5*u2*u3*v1*a33 *m2*n1 - 2*u2*u3*a33*n1 *n2
2
- 5*u2*v1*a33*m2*n1*n3 - u2*v3*a33*m2*n1
+ ------------------------- + ---------------------
2 2
2
- u2*n1 *n2*n3 2 2 2 5*u3*v1*a33*m2*n1*n2
+ ----------------- + u3*v1 *a33 *m2 + ----------------------
2 2
2 4 2 2
2 2 2 3*u3*v2*a33*m2*n1 - n1 + 2*n1 *n2
- u3*v2 *a33 *m2 + -------------------- + u3*--------------------
2 4
2 2 2
v1 *a33*m2 *n3 3*v1*v3*a33*m2 *n1 v1*m2*n1*n2*n3
+ ---------------- + -------------------- + ----------------
2 2 4
2 2 2
- v2 *a33*m2 *n3 v2*m2*n1 *n3
+ ------------------- + --------------}
2 2
4 3 4 3 3 3 3 2 5 2 2 3 4
FI=u1 *a33 *n1 + 4*u1 *v2*a33 *m2*n1 - 2*u1 *a33 *n1 + 2*u1 *u2 *a33 *n1
2 3 3 2 2 4 2 2 4
- 8*u1 *u2*v1*a33 *m2*n1 - 2*u1 *u2*a33 *n1 *n2 - 2*u1 *u3*a33 *n1 *n3
2 2 3 2 2 2 2 3 2 2 3 2 2
+ 10*u1 *v1 *a33 *m2 *n1 + 6*u1 *v1*a33 *m2*n1 *n2 + 5*u1 *v2 *a33 *m2 *n1
2 2 4 2 2 3 2 2 2 6 4 2
- 6*u1 *v2*a33 *m2*n1 - u1 *v3 *a33 *m2 *n1 + u1 *(a33*n1 - a33*n1 *n2 )
2 2 5 3 3 2 4
- 2*u1*u2 *a33 *n1 - 4*u1*u2*u3*v3*a33 *m2*n1 + 6*u1*u2*v1*a33 *m2*n1
5 3 2 2
+ 2*u1*u2*a33*n1 *n2 + 10*u1*u3*v1*v3*a33 *m2 *n1
2 3 2 3 5
- 4*u1*u3*v2*a33 *m2*n1 *n3 + 4*u1*u3*v3*a33 *m2*n1 *n2 + 2*u1*u3*a33*n1 *n3
2 3 3 2 2 2 3
+ 4*u1*v1 *v2*a33 *m2 *n1 - 5*u1*v1 *a33 *m2 *n1
2 2 2 4 3 3 3
+ 5*u1*v1*v2*a33 *m2 *n1 *n2 - 4*u1*v1*a33*m2*n1 *n2 + 2*u1*v2 *a33 *m2 *n1
2 2 2 3 2 3 3
- 5*u1*v2 *a33 *m2 *n1 - 2*u1*v2*v3 *a33 *m2 *n1
5 3 2 2 2 2 3
+ u1*v2*(2*a33*m2*n1 - 2*a33*m2*n1 *n2 ) + u1*v3 *a33 *m2 *n1
5 2 5 2 4 3 4 3 3 3
+ u1*(n1 *n2 - n1 *n3 ) + u2 *a33 *n1 - 4*u2 *v1*a33 *m2*n1
3 2 4 2 2 4 2 2 3 2 2
- 2*u2 *a33 *n1 *n2 - 2*u2 *u3*a33 *n1 *n3 + 5*u2 *v1 *a33 *m2 *n1
2 2 3 2 2 3 2 2 2 3
+ 6*u2 *v1*a33 *m2*n1 *n2 - u2 *v3 *a33 *m2 *n1 + 4*u2*u3*v1*a33 *m2*n1 *n3
2 4 4 3 3 3
+ 2*u2*u3*v3*a33 *m2*n1 + 2*u2*u3*a33*n1 *n2*n3 - 2*u2*v1 *a33 *m2 *n1
2 2 2 2 2 3 3
- 5*u2*v1 *a33 *m2 *n1 *n2 + 2*u2*v1*v3 *a33 *m2 *n1
2 2 2 2 4 3 4 2 2 2 3 2 2
+ u2*v3 *a33 *m2 *n1 *n2 + u2*(n1 *n2 - n1 *n2*n3 ) + u3 *v3 *a33 *m2 *n1
2 2 2 2 3 3
- u3*v1 *a33 *m2 *n1 *n3 + 2*u3*v1*v2*v3*a33 *m2 *n1
2 2 3 3
- 4*u3*v1*v3*a33 *m2 *n1 - 2*u3*v1*a33*m2*n1 *n2*n3
2 2 2 2 2 2 2 4
- u3*v2 *a33 *m2 *n1 *n3 + u3*v2*v3*a33 *m2 *n1 *n2 + 2*u3*v2*a33*m2*n1 *n3
2 2 2 2 4 4 2 4 3
+ u3*v3 *a33 *m2 *n1 *n3 - 2*u3*v3*a33*m2*n1 *n2 + u3*(n1 *n2 *n3 - n1 *n3 )
3 2 3 2 2 3 2 2 2 3 4
+ v1 *a33 *m2 *n1*n2 - v1 *v2*a33 *m2 *n1 - v1 *v3 *a33 *m2
2 2 3 2 3 2 2 3
+ v1*v2 *a33 *m2 *n1*n2 - 2*v1*v2*a33*m2 *n1 *n2 - v1*v3 *a33 *m2 *n1*n2
3 3 3 2 3 2 3 2 2 2 3 4
+ v1*( - m2*n1 *n2 + m2*n1 *n2*n3 ) - v2 *a33 *m2 *n1 - v2 *v3 *a33 *m2
2 2 4 2 2 2 2 2 3 2
+ v2 *(a33*m2 *n1 - a33*m2 *n1 *n2 ) + v2*v3 *a33 *m2 *n1
4 2 4 2
+ v2*(m2*n1 *n2 - m2*n1 *n3 )
Stop of a subroutine.
Number of garbage collections exceeds max_gc_fac.
The factorization crashed!
which the program can not factorize further.
{HAM,FI} = {4,
- a33,
a33,
u1*v1 + u2*v2 + u3*v3,
n1,
m2,
2 2 2 2 2 2
- 2*u1 *u3*a33 *n1 - u1 *a33*n1 *n3 - 5*u1*u3*v2*a33 *m2*n1
3 - 5*u1*v2*a33*m2*n1*n3
+ 2*u1*u3*a33*n1 + ------------------------- + u1*v3*a33*m2*n1*n2
2
3
u1*n1 *n3 2 2 2 2 2
+ ----------- + 2*u2 *u3*a33 *n1 + u2 *a33*n1 *n3
2
2 2
- 5*u2*u3*v1*a33 *m2*n1 - 3*u2*u3*a33*n1 *n2
2
- 5*u2*v1*a33*m2*n1*n3 - u2*v3*a33*m2*n1 2
+ ------------------------- + --------------------- - u2*n1 *n2*n3
2 2
2 2 2 5*u3*v1*a33*m2*n1*n2 2 2 2
+ u3*v1 *a33 *m2 + ---------------------- - u3*v2 *a33 *m2
2
2 4 2 2 2 2
5*u3*v2*a33*m2*n1 - n1 + 2*n1 *n2 v1 *a33*m2 *n3
+ -------------------- + u3*-------------------- + ----------------
2 2 2
2 2 2
3*v1*v3*a33*m2 *n1 v1*m2*n1*n2*n3 - v2 *a33*m2 *n3
+ -------------------- + ---------------- + -------------------
2 4 2
2
2 v3*m2*n1 *n2
+ v2*m2*n1 *n3 + --------------}
4
2 2 3 2 2
FI= - u1 *a33*n1 - 2*u1*v2*a33*m2*n1 + u1*n1 - u2 *a33*n1 + 2*u2*v1*a33*m2*n1
2 2 2 2 2
+ u2*n1 *n2 + u3*n1 *n3 - v1*m2*n1*n2 + v2*m2*n1 + v3 *a33*m2
which the program can not factorize further.
{HAM,FI} = 0
4 3 4 3 3 3 3 2 5 2 2 3 4
FI=u1 *a33 *n1 + 4*u1 *v2*a33 *m2*n1 - 2*u1 *a33 *n1 + 2*u1 *u2 *a33 *n1
2 3 3 2 2 4 2 2 4
- 8*u1 *u2*v1*a33 *m2*n1 - 2*u1 *u2*a33 *n1 *n2 - 2*u1 *u3*a33 *n1 *n3
2 2 3 2 2 2 2 3 2 2 3 2 2
+ 8*u1 *v1 *a33 *m2 *n1 + 6*u1 *v1*a33 *m2*n1 *n2 + 4*u1 *v2 *a33 *m2 *n1
2 2 4 2 2 3 2 2
- 6*u1 *v2*a33 *m2*n1 - 2*u1 *v3 *a33 *m2 *n1
2 6 4 2 2 2 5
+ u1 *(a33*n1 - a33*n1 *n2 ) - 2*u1*u2 *a33 *n1
3 3 2 4 5
- 4*u1*u2*u3*v3*a33 *m2*n1 + 6*u1*u2*v1*a33 *m2*n1 + 2*u1*u2*a33*n1 *n2
3 2 2 2 3
+ 8*u1*u3*v1*v3*a33 *m2 *n1 - 4*u1*u3*v2*a33 *m2*n1 *n3
2 3 5 2 2 2 3
+ 4*u1*u3*v3*a33 *m2*n1 *n2 + 2*u1*u3*a33*n1 *n3 - 4*u1*v1 *a33 *m2 *n1
2 2 2 4 2 2 2 3
+ 4*u1*v1*v2*a33 *m2 *n1 *n2 - 4*u1*v1*a33*m2*n1 *n2 - 4*u1*v2 *a33 *m2 *n1
2 3 3 5 3 2
- 4*u1*v2*v3 *a33 *m2 *n1 + u1*v2*(2*a33*m2*n1 - 2*a33*m2*n1 *n2 )
2 2 2 3 5 2 5 2 4 3 4
+ 2*u1*v3 *a33 *m2 *n1 + u1*(n1 *n2 - n1 *n3 ) + u2 *a33 *n1
3 3 3 3 2 4 2 2 4
- 4*u2 *v1*a33 *m2*n1 - 2*u2 *a33 *n1 *n2 - 2*u2 *u3*a33 *n1 *n3
2 2 3 2 2 2 2 3 2 2 3 2 2
+ 4*u2 *v1 *a33 *m2 *n1 + 6*u2 *v1*a33 *m2*n1 *n2 - 2*u2 *v3 *a33 *m2 *n1
2 3 2 4 4
+ 4*u2*u3*v1*a33 *m2*n1 *n3 + 2*u2*u3*v3*a33 *m2*n1 + 2*u2*u3*a33*n1 *n2*n3
2 2 2 2 2 3 3
- 4*u2*v1 *a33 *m2 *n1 *n2 + 4*u2*v1*v3 *a33 *m2 *n1
2 2 2 2 4 3 4 2
+ 2*u2*v3 *a33 *m2 *n1 *n2 + u2*(n1 *n2 - n1 *n2*n3 )
2 2 3 3 4
- 4*u3*v1*v3*a33 *m2 *n1 - 2*u3*v1*a33*m2*n1 *n2*n3 + 2*u3*v2*a33*m2*n1 *n3
2 2 2 2 4
+ 2*u3*v3 *a33 *m2 *n1 *n3 - 2*u3*v3*a33*m2*n1 *n2
4 2 4 3 2 3
+ u3*(n1 *n2 *n3 - n1 *n3 ) - 2*v1*v2*a33*m2 *n1 *n2
2 2 3 3 3 3 2
- 2*v1*v3 *a33 *m2 *n1*n2 + v1*( - m2*n1 *n2 + m2*n1 *n2*n3 )
2 2 4 2 2 2 2 2 3 2
+ v2 *(a33*m2 *n1 - a33*m2 *n1 *n2 ) + 2*v2*v3 *a33 *m2 *n1
4 2 4 2 4 3 4
+ v2*(m2*n1 *n2 - m2*n1 *n3 ) + v3 *a33 *m2
which the program can not factorize further.
{HAM,FI} = {16,
n1,
n1,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
m2,
2 2 2
u1 *u3*a33 *n1 u1 *a33*n1*n3 2
---------------- + --------------- + u1*u3*v2*a33 *m2
2 4
2
- u1*u3*a33*n1 u1*v2*a33*m2*n3 - u1*v3*a33*m2*n2
+ ------------------ + ----------------- + --------------------
2 2 4
2 2 2 2
- u1*n1 *n3 - u2 *u3*a33 *n1 - u2 *a33*n1*n3
+ -------------- + ------------------- + ------------------
8 2 4
2 3*u2*u3*a33*n1*n2 u2*v1*a33*m2*n3
+ u2*u3*v1*a33 *m2 + ------------------- + -----------------
4 2
u2*v3*a33*m2*n1 u2*n1*n2*n3 - u3*v1*a33*m2*n2
+ ----------------- + ------------- + --------------------
4 4 2
3 2 2
- u3*v2*a33*m2*n1 n1 - 2*n1*n2 - v1*v3*a33*m2
+ -------------------- + u3*---------------- + ------------------
2 8 2
- v2*m2*n1*n3 - v3*m2*n1*n2
+ ---------------- + ----------------}
4 8
And again in machine readable form:
HAM=u1*n1 + u2*n2 + u3**2*a33 + u3*n3 + ( - v1*m2*n2)/n1 + v2*m2$
FI=u1**4*a33*n1**4 + 4*u1**3*v2*a33*m2*n1**3 - u1**3*n1**5 + 2*u1**2*u2**2*a33*
n1**4 - 8*u1**2*u2*v1*a33*m2*n1**3 - u1**2*u2*n1**4*n2 + u1**2*u3**2*a33*n1**4 -
u1**2*u3*n1**4*n3 + 10*u1**2*v1**2*a33*m2**2*n1**2 + 3*u1**2*v1*m2*n1**3*n2 + 5
*u1**2*v2**2*a33*m2**2*n1**2 - 3*u1**2*v2*m2*n1**4 - u1**2*v3**2*a33*m2**2*n1**2
- u1*u2**2*n1**5 - 4*u1*u2*u3*v3*a33*m2*n1**3 + 3*u1*u2*v1*m2*n1**4 + 2*u1*u3**
2*v2*a33*m2*n1**3 - u1*u3**2*n1**5 + 10*u1*u3*v1*v3*a33*m2**2*n1**2 - 2*u1*u3*v2
*m2*n1**3*n3 + 2*u1*u3*v3*m2*n1**3*n2 + 4*u1*v1**2*v2*a33*m2**3*n1 - 3*u1*v1**2*
m2**2*n1**3 + 3*u1*v1*v2*m2**2*n1**2*n2 + 2*u1*v2**3*a33*m2**3*n1 - 3*u1*v2**2*
m2**2*n1**3 - 2*u1*v2*v3**2*a33*m2**3*n1 + u2**4*a33*n1**4 - 4*u2**3*v1*a33*m2*
n1**3 - u2**3*n1**4*n2 + u2**2*u3**2*a33*n1**4 - u2**2*u3*n1**4*n3 + 5*u2**2*v1
**2*a33*m2**2*n1**2 + 3*u2**2*v1*m2*n1**3*n2 - u2**2*v3**2*a33*m2**2*n1**2 - 2*
u2*u3**2*v1*a33*m2*n1**3 - u2*u3**2*n1**4*n2 + 2*u2*u3*v1*m2*n1**3*n3 + u2*u3*v3
*m2*n1**4 - 2*u2*v1**3*a33*m2**3*n1 - 3*u2*v1**2*m2**2*n1**2*n2 + 2*u2*v1*v3**2*
a33*m2**3*n1 - u3**3*n1**4*n3 + u3**2*v1*m2*n1**3*n2 - u3**2*v2*m2*n1**4 - u3*v1
**2*m2**2*n1**2*n3 + 2*u3*v1*v2*v3*a33*m2**3*n1 - 2*u3*v1*v3*m2**2*n1**3 - u3*v2
**2*m2**2*n1**2*n3 + u3*v2*v3*m2**2*n1**2*n2 + v1**3*m2**3*n1*n2 - v1**2*v2*m2**
3*n1**2 - v1**2*v3**2*a33*m2**4 + v1*v2**2*m2**3*n1*n2 - v2**3*m2**3*n1**2 - v2
**2*v3**2*a33*m2**4$
FI=u1**4*a33**3*n1**4 + 4*u1**3*v2*a33**3*m2*n1**3 - 2*u1**3*a33**2*n1**5 + 2*u1
**2*u2**2*a33**3*n1**4 - 8*u1**2*u2*v1*a33**3*m2*n1**3 - 2*u1**2*u2*a33**2*n1**4
*n2 - 2*u1**2*u3*a33**2*n1**4*n3 + 10*u1**2*v1**2*a33**3*m2**2*n1**2 + 6*u1**2*
v1*a33**2*m2*n1**3*n2 + 5*u1**2*v2**2*a33**3*m2**2*n1**2 - 6*u1**2*v2*a33**2*m2*
n1**4 - u1**2*v3**2*a33**3*m2**2*n1**2 + u1**2*(a33*n1**6 - a33*n1**4*n2**2) - 2
*u1*u2**2*a33**2*n1**5 - 4*u1*u2*u3*v3*a33**3*m2*n1**3 + 6*u1*u2*v1*a33**2*m2*n1
**4 + 2*u1*u2*a33*n1**5*n2 + 10*u1*u3*v1*v3*a33**3*m2**2*n1**2 - 4*u1*u3*v2*a33
**2*m2*n1**3*n3 + 4*u1*u3*v3*a33**2*m2*n1**3*n2 + 2*u1*u3*a33*n1**5*n3 + 4*u1*v1
**2*v2*a33**3*m2**3*n1 - 5*u1*v1**2*a33**2*m2**2*n1**3 + 5*u1*v1*v2*a33**2*m2**2
*n1**2*n2 - 4*u1*v1*a33*m2*n1**4*n2 + 2*u1*v2**3*a33**3*m2**3*n1 - 5*u1*v2**2*
a33**2*m2**2*n1**3 - 2*u1*v2*v3**2*a33**3*m2**3*n1 + u1*v2*(2*a33*m2*n1**5 - 2*
a33*m2*n1**3*n2**2) + u1*v3**2*a33**2*m2**2*n1**3 + u1*(n1**5*n2**2 - n1**5*n3**
2) + u2**4*a33**3*n1**4 - 4*u2**3*v1*a33**3*m2*n1**3 - 2*u2**3*a33**2*n1**4*n2 -
2*u2**2*u3*a33**2*n1**4*n3 + 5*u2**2*v1**2*a33**3*m2**2*n1**2 + 6*u2**2*v1*a33
**2*m2*n1**3*n2 - u2**2*v3**2*a33**3*m2**2*n1**2 + 4*u2*u3*v1*a33**2*m2*n1**3*n3
+ 2*u2*u3*v3*a33**2*m2*n1**4 + 2*u2*u3*a33*n1**4*n2*n3 - 2*u2*v1**3*a33**3*m2**
3*n1 - 5*u2*v1**2*a33**2*m2**2*n1**2*n2 + 2*u2*v1*v3**2*a33**3*m2**3*n1 + u2*v3
**2*a33**2*m2**2*n1**2*n2 + u2*(n1**4*n2**3 - n1**4*n2*n3**2) + u3**2*v3**2*a33
**3*m2**2*n1**2 - u3*v1**2*a33**2*m2**2*n1**2*n3 + 2*u3*v1*v2*v3*a33**3*m2**3*n1
- 4*u3*v1*v3*a33**2*m2**2*n1**3 - 2*u3*v1*a33*m2*n1**3*n2*n3 - u3*v2**2*a33**2*
m2**2*n1**2*n3 + u3*v2*v3*a33**2*m2**2*n1**2*n2 + 2*u3*v2*a33*m2*n1**4*n3 + u3*
v3**2*a33**2*m2**2*n1**2*n3 - 2*u3*v3*a33*m2*n1**4*n2 + u3*(n1**4*n2**2*n3 - n1
**4*n3**3) + v1**3*a33**2*m2**3*n1*n2 - v1**2*v2*a33**2*m2**3*n1**2 - v1**2*v3**
2*a33**3*m2**4 + v1*v2**2*a33**2*m2**3*n1*n2 - 2*v1*v2*a33*m2**2*n1**3*n2 - v1*
v3**2*a33**2*m2**3*n1*n2 + v1*( - m2*n1**3*n2**3 + m2*n1**3*n2*n3**2) - v2**3*
a33**2*m2**3*n1**2 - v2**2*v3**2*a33**3*m2**4 + v2**2*(a33*m2**2*n1**4 - a33*m2
**2*n1**2*n2**2) + v2*v3**2*a33**2*m2**3*n1**2 + v2*(m2*n1**4*n2**2 - m2*n1**4*
n3**2)$
FI= - u1**2*a33*n1**2 - 2*u1*v2*a33*m2*n1 + u1*n1**3 - u2**2*a33*n1**2 + 2*u2*v1
*a33*m2*n1 + u2*n1**2*n2 + u3*n1**2*n3 - v1*m2*n1*n2 + v2*m2*n1**2 + v3**2*a33*
m2**2$
FI=u1**4*a33**3*n1**4 + 4*u1**3*v2*a33**3*m2*n1**3 - 2*u1**3*a33**2*n1**5 + 2*u1
**2*u2**2*a33**3*n1**4 - 8*u1**2*u2*v1*a33**3*m2*n1**3 - 2*u1**2*u2*a33**2*n1**4
*n2 - 2*u1**2*u3*a33**2*n1**4*n3 + 8*u1**2*v1**2*a33**3*m2**2*n1**2 + 6*u1**2*v1
*a33**2*m2*n1**3*n2 + 4*u1**2*v2**2*a33**3*m2**2*n1**2 - 6*u1**2*v2*a33**2*m2*n1
**4 - 2*u1**2*v3**2*a33**3*m2**2*n1**2 + u1**2*(a33*n1**6 - a33*n1**4*n2**2) - 2
*u1*u2**2*a33**2*n1**5 - 4*u1*u2*u3*v3*a33**3*m2*n1**3 + 6*u1*u2*v1*a33**2*m2*n1
**4 + 2*u1*u2*a33*n1**5*n2 + 8*u1*u3*v1*v3*a33**3*m2**2*n1**2 - 4*u1*u3*v2*a33**
2*m2*n1**3*n3 + 4*u1*u3*v3*a33**2*m2*n1**3*n2 + 2*u1*u3*a33*n1**5*n3 - 4*u1*v1**
2*a33**2*m2**2*n1**3 + 4*u1*v1*v2*a33**2*m2**2*n1**2*n2 - 4*u1*v1*a33*m2*n1**4*
n2 - 4*u1*v2**2*a33**2*m2**2*n1**3 - 4*u1*v2*v3**2*a33**3*m2**3*n1 + u1*v2*(2*
a33*m2*n1**5 - 2*a33*m2*n1**3*n2**2) + 2*u1*v3**2*a33**2*m2**2*n1**3 + u1*(n1**5
*n2**2 - n1**5*n3**2) + u2**4*a33**3*n1**4 - 4*u2**3*v1*a33**3*m2*n1**3 - 2*u2**
3*a33**2*n1**4*n2 - 2*u2**2*u3*a33**2*n1**4*n3 + 4*u2**2*v1**2*a33**3*m2**2*n1**
2 + 6*u2**2*v1*a33**2*m2*n1**3*n2 - 2*u2**2*v3**2*a33**3*m2**2*n1**2 + 4*u2*u3*
v1*a33**2*m2*n1**3*n3 + 2*u2*u3*v3*a33**2*m2*n1**4 + 2*u2*u3*a33*n1**4*n2*n3 - 4
*u2*v1**2*a33**2*m2**2*n1**2*n2 + 4*u2*v1*v3**2*a33**3*m2**3*n1 + 2*u2*v3**2*a33
**2*m2**2*n1**2*n2 + u2*(n1**4*n2**3 - n1**4*n2*n3**2) - 4*u3*v1*v3*a33**2*m2**2
*n1**3 - 2*u3*v1*a33*m2*n1**3*n2*n3 + 2*u3*v2*a33*m2*n1**4*n3 + 2*u3*v3**2*a33**
2*m2**2*n1**2*n3 - 2*u3*v3*a33*m2*n1**4*n2 + u3*(n1**4*n2**2*n3 - n1**4*n3**3) -
2*v1*v2*a33*m2**2*n1**3*n2 - 2*v1*v3**2*a33**2*m2**3*n1*n2 + v1*( - m2*n1**3*n2
**3 + m2*n1**3*n2*n3**2) + v2**2*(a33*m2**2*n1**4 - a33*m2**2*n1**2*n2**2) + 2*
v2*v3**2*a33**2*m2**3*n1**2 + v2*(m2*n1**4*n2**2 - m2*n1**4*n3**2) + v3**4*a33**
3*m2**4$