Solution 6 to problem over
Expressions |
Parameters |
Inequalities |
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Expressions
The solution is given through the following expressions:
3 3 3
- 2*a33 *m2*n3*r14 - m2*n2*n3 *r4119 + 2*m2*n2*n3 *r464
r10=----------------------------------------------------------
3 2
a33 *n2
3 2 2
- a33 *m2*r14 - m2*n2*n3 *r4119 + 2*m2*n2*n3 *r464
r11=-----------------------------------------------------
3
a33 *n2
m1*r14
r12=--------
n2
n3*r14
r13=--------
n2
r15=0
3 2 3 2 2 3 2 3
r20=(2*a33 *m1 *r14 + 2*a33 *m2 *r14 - m1 *n2 *r4119 + 2*m1 *n2 *r464
2 2 2 2 2 2
+ m1 *n2*n3 *r4119 - 2*m1 *n2*n3 *r464 + 5*m2 *n2*n3 *r4119
2 2 2 3
- 2*m2 *n2*n3 *r464)/(2*a33 *n2 )
2 2
2*m2 *n3*r4119 + 2*m2 *n3*r464
r21=--------------------------------
2
a33 *n2
2 2 2 2
- m1 *r4119 + 2*m1 *r464 + m2 *r4119 + 2*m2 *r464
r22=----------------------------------------------------
2
2*a33
- 2*m1*m2*n3*r4119 + 2*m1*m2*n3*r464
r23=---------------------------------------
2
a33 *n2
- m1*m2*r4119
r24=----------------
2
a33
3 3 2 2
- 2*a33 *m2*r14 + m2*n2 *r4119 - 3*m2*n2*n3 *r4119 + 4*m2*n2*n3 *r464
r26=------------------------------------------------------------------------
2 2
a33 *n2
- m2*n3*r4119
r27=----------------
2
a33
m1*n3*r4119 - 2*m1*n3*r464
r28=----------------------------
2
a33
- 2*m2*n3*r4119 + 2*m2*n3*r464
r210=---------------------------------
2
a33
3 3 3 2
r212=( - 2*a33 *m1*r14 + m1*n2 *r4119 - 2*m1*n2 *r464 - m1*n2*n3 *r4119
2 2 2
+ 2*m1*n2*n3 *r464)/(a33 *n2 )
n2*n3*r4119 - 2*n2*n3*r464
r213=----------------------------
2
a33
3 3 3 2 2
- 2*a33 *r14 + n2 *r4119 - 2*n2 *r464 - n2*n3 *r4119 + 2*n2*n3 *r464
r214=-----------------------------------------------------------------------
2
2*a33 *n2
r215=0
3 2 2
2*a33 *m1*r14 + m1*n2*n3 *r4119 - 2*m1*n2*n3 *r464
r216=----------------------------------------------------
2 2
a33 *n2
m2*n2*r4119
r217=-------------
2
a33
r218=0
r219=0
3 2 2
- 2*a33 *r14 - n2*n3 *r4119 + 2*n2*n3 *r464
r220=----------------------------------------------
2
2*a33 *n2
2 3 2 2
- 2*m1 *m2*n3*r4119 - 2*m2 *n3*r4119 + 2*m2 *n2*n3*r4116 - m2*n2 *n3*r446
r30=----------------------------------------------------------------------------
3
a33*n2
2 2 3 3
r31=( - 2*m1 *m2*r4119 - 2*m1 *m2*r464 - 2*m2 *r4119 - 2*m2 *r464
2 2 2
+ 2*m2 *n2*r4116 - m2*n2 *r446)/(2*a33*n2 )
2
2*m2 *n3*r4116 - m2*n2*n3*r446
r32=--------------------------------
2
a33*n2
2
2*m2 *r4116 - m2*n2*r446
r33=--------------------------
2*a33*n2
3 3 2 2
r34=(2*m1 *r4119 - 2*m1 *r464 + 2*m1*m2 *r4119 - 2*m1*m2 *r464
2 2
- 2*m1*m2*n2*r4116 + m1*n2 *r446)/(2*a33*n2 )
r35=0
- 2*m1*m2*r4116 + m1*n2*r446
r36=-------------------------------
2*a33*n2
2
2*m2 *n3*r4116 - m2*n2*n3*r446
r37=--------------------------------
2
a33*n2
2
2*m2 *r4116 - m2*n2*r446
r38=--------------------------
2*a33*n2
- 2*m1*m2*r4116 + m1*n2*r446
r39=-------------------------------
2*a33*n2
2 2 2 2
r310=(2*m1 *n3*r4119 - 2*m1 *n3*r464 + 10*m2 *n3*r4119 - 2*m2 *n3*r464
2 2
+ 2*m2*n2*n3*r4116 + n2 *n3*r446)/(2*a33*n2 )
2 2
2*m2 *r4119 + 2*m2 *r464 + m2*n2*r4116
r311=----------------------------------------
a33*n2
- 2*m2*n3*r4116 + n2*n3*r446
r312=-------------------------------
2*a33*n2
- 2*m1*m2*r4119 + 2*m1*m2*r464 - m1*n2*r4116
r313=-----------------------------------------------
a33*n2
r314=0
- 2*m2*n3*r4116 + n2*n3*r446
r315=-------------------------------
2*a33*n2
- 2*m2*n3*r4119 + 4*m2*n3*r464 - n2*n3*r4116
r316=-----------------------------------------------
a33*n2
m2*r464
r317=---------
a33
- m1*r464
r318=------------
a33
- n3*r464
r319=------------
a33
r320=
2 2 2 2 2
2*m1 *r4119 - 2*m1 *r464 + 2*m2 *r4119 - 2*m2 *r464 - 2*m2*n2*r4116 + n2 *r446
--------------------------------------------------------------------------------
2*a33*n2
2*m2*n3*r4116
r321=---------------
a33*n2
n2*r446
r322=---------
2*a33
4*m1*m2*n3*r4119
r323=------------------
2
a33*n2
2*m1*m2*r4119 + 2*m1*m2*r464 - m1*n2*r4116
r324=--------------------------------------------
a33*n2
2 2 2
- 4*m1 *r4119 + 4*m1 *r464 - 2*m2*n2*r4116 + n2 *r446
r325=--------------------------------------------------------
2*a33*n2
- 2*m2*r4119 + 2*m2*r464 - n2*r4116
r326=--------------------------------------
a33
- n3*r4116
r327=-------------
a33
- 2*m1*n3*r4119 + 2*m1*n3*r464
r328=---------------------------------
a33*n2
- n2*r464
r329=------------
a33
2*m2*n3*r4119
r330=---------------
a33*n2
m2*r4119 + m2*r464 - n2*r4116
r331=-------------------------------
a33
- 3*m1*r4119 + 3*m1*r464
r332=---------------------------
a33
- n3*r4119 + n3*r464
r333=-----------------------
a33
- n2*r4119 + n2*r464
r334=-----------------------
a33
r335=0
- 4*m1*m2*n3*r4119
r336=---------------------
2
a33*n2
- 2*m1*m2*r4119 - 2*m1*m2*r464
r337=---------------------------------
a33*n2
2*m2*n3*r4116
r338=---------------
a33*n2
2 2
2*m1 *r4119 - 2*m1 *r464 + m2*n2*r4116
r339=----------------------------------------
a33*n2
- m1*r4116
r340=-------------
a33
r341=0
2*m1*n3*r4119 - 2*m1*n3*r464
r342=------------------------------
a33*n2
- n3*r4116
r343=-------------
a33
r344=0
r345=0
2*m1*r4119 - 2*m1*r464
r346=------------------------
a33
- n2*r4116
r347=-------------
a33
r348=0
r349=0
2*m2*n3*r4119
r350=---------------
a33*n2
m2*r4119 + m2*r464
r351=--------------------
a33
- m1*r4119 + m1*r464
r352=-----------------------
a33
- n3*r4119 + n3*r464
r353=-----------------------
a33
- n2*r4119 + n2*r464
r354=-----------------------
a33
r355=0
4 2 2 2 2 2 4
r40=(m1 *r4119 + 2*m1 *m2 *r4119 - 2*m1 *m2*n2*r4116 + m1 *n2 *r446 + m2 *r4119
3 2 2 4
- 2*m2 *n2*r4116 + m2 *n2 *r446)/(2*n2 )
r41=0
2 2 3 2
- 2*m1 *m2*r4116 + m1 *n2*r446 - 2*m2 *r4116 + m2 *n2*r446
r42=-------------------------------------------------------------
3
2*n2
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
2 2 3 2
- 2*m1 *m2*r4116 + m1 *n2*r446 - 2*m2 *r4116 + m2 *n2*r446
r49=-------------------------------------------------------------
3
2*n2
r410=0
r411=0
r412=0
r413=0
r415
2 2 3 2 2
- 2*m1 *m2*r4119 - m1 *n2*r4116 - 2*m2 *r4119 + m2 *n2*r4116 - m2*n2 *r446
=-----------------------------------------------------------------------------
3
n2
r416=0
2
2*m2 *r4116 - m2*n2*r446
r417=--------------------------
2
n2
r418=0
r419=0
r420=0
r421=0
2
2*m2 *r4116 - m2*n2*r446
r422=--------------------------
2
n2
r423=0
r424=0
2 2 2 2
- 2*m1 *r464 + 4*m2 *r4119 - 2*m2 *r464 + 2*m2*n2*r4116 + n2 *r446
r425=---------------------------------------------------------------------
2
2*n2
r426=0
r427=0
r428=0
r429=0
2*m2*r464
r431=-----------
n2
r432=0
r433=0
r435=0
2 2
- m1 *r4116 - m2 *r4116
r436=--------------------------
2
n2
r437=0
r438=0
3 2 2
- 2*m1 *r4119 - 2*m1*m2 *r4119 + 2*m1*m2*n2*r4116 - m1*n2 *r446
r439=------------------------------------------------------------------
3
n2
r440=0
2*m1*m2*r4116 - m1*n2*r446
r441=----------------------------
2
n2
r442=0
2*m1*m2*r4116 - m1*n2*r446
r444=----------------------------
2
n2
r445=0
r447=0
4*m1*m2*r4119 + 2*m1*n2*r4116
r448=-------------------------------
2
n2
r449=0
r450=0
r451=0
2*m1*r464
r453=-----------
n2
r454=0
2 2 2
- 2*m1 *r4119 - 2*m2 *r4119 + 2*m2*n2*r4116 - n2 *r446
r455=---------------------------------------------------------
2
2*n2
r456=0
r458=0
2*m1*r4116
r459=------------
n2
2 2
4*m1 *r4119 + 2*m2*n2*r4116 - n2 *r446
r460=----------------------------------------
2
2*n2
2*m2*r4119 + n2*r4116
r461=-----------------------
n2
r462=0
r463=0
r465=0
r466=r4116
2*m1*r4119
r467=------------
n2
r468=0
1
r469=---*r4119
2
r470=0
3 2 2
2*m1 *r4119 + 2*m1*m2 *r4119 - 2*m1*m2*n2*r4116 + m1*n2 *r446
r471=---------------------------------------------------------------
3
n2
r472=0
- 2*m1*m2*r4116 + m1*n2*r446
r473=-------------------------------
2
n2
2 2
- m1 *r4116 - m2 *r4116
r474=--------------------------
2
n2
r475=0
r476=0
r477=0
- 2*m1*m2*r4116 + m1*n2*r446
r478=-------------------------------
2
n2
r479=0
r480=0
- 4*m1*m2*r4119 - 2*m1*n2*r4116
r481=----------------------------------
2
n2
r482=0
r483=r446
r484=0
r485=0
r486=0
- 2*m1*r464
r487=--------------
n2
r488=0
r489=0
r490=0
r491=0
- 2*m1*r4116
r492=---------------
n2
r493=0
2 2
- 4*m1 *r4119 - 2*m2*n2*r4116 + n2 *r446
r494=-------------------------------------------
2
n2
2*m1*r4116
r495=------------
n2
r496=0
r497=0
r498=0
r499=0
r4100=0
- 2*m1*r4119
r4101=---------------
n2
r4102=r4116
r4103=0
r4104=0
2 2 2
- 2*m1 *r4119 - 2*m2 *r4119 + 2*m2*n2*r4116 - n2 *r446
r4105=---------------------------------------------------------
2
2*n2
r4106=0
2 2
4*m1 *r4119 + 2*m2*n2*r4116 - n2 *r446
r4107=----------------------------------------
2
2*n2
r4108=0
- 2*m1*r4116
r4109=---------------
n2
r4110=0
2*m2*r4119 + n2*r4116
r4111=-----------------------
n2
r4112=0
r4113=0
r4114=r464
r4115=0
2*m1*r4119
r4117=------------
n2
r4118=0
r4120=0
- 2*m1*r4119
r4121=---------------
n2
r4122=r4116
r4123=0
r4124=0
1
r4125=---*r4119
2
m3=0
n1=0
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
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:
r14, r4119, r4116, r446, r464, m1, m2, 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.
{a33,n2,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,
n1,
m3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=u2*n2 + u3 *a33 + u3*n3 + v1*m1 + v2*m2
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
2 2 3 2 2 3 2 2 2 2 2 2 2
FI=u1 *u2*a33 *n2 + u1 *u3 *a33 *n2 + u1 *u3*a33 *n2 *n3 + u1 *v1*a33 *m1*n2
2 2 2 2 2 2 2 2
+ u1 *v2*a33 *m2*n2 + u1 *a33*n2 *n3 - 2*u1*u2*v2*a33 *m1*n2
2 3 2 2 2
- 2*u1*u3 *v2*a33 *m1*n2 - 2*u1*u3*v2*a33 *m1*n2*n3 - 2*u1*v1*v2*a33 *m1 *n2
2 2 2 3 2 3
- 2*u1*v2 *a33 *m1*m2*n2 - 2*u1*v2*a33*m1*n2*n3 + u2 *a33 *n2
2 2 3 2 2 2 2 2 2 2
+ u2 *u3 *a33 *n2 + u2 *u3*a33 *n2 *n3 + 3*u2 *v1*a33 *m1*n2
2 2 2 2 4 2 2
+ u2 *v2*a33 *m2*n2 + u2 *( - a33*n2 + a33*n2 *n3 )
2 3 2 2 3 2
+ 2*u2*u3 *v1*a33 *m1*n2 - u2*u3 *a33 *n2 + 2*u2*u3*v1*a33 *m1*n2*n3
2 2 3 2 2 2
+ 2*u2*u3*v3*a33 *m2*n2 - 2*u2*u3*a33*n2 *n3 + 2*u2*v1 *a33 *m1 *n2
2 3 2
+ 2*u2*v1*v2*a33 *m1*m2*n2 + u2*v1*( - 2*a33*m1*n2 + 2*a33*m1*n2*n3 )
2 2 2 2 2 2
+ u2*v3 *( - a33 *m1 *n2 - a33 *m2 *n2) + 2*u2*v3*a33*m2*n2 *n3
3 3 3 2 2 2 2 2
+ 2*u3 *v3*a33 *m2*n2 - u3 *a33 *n2 *n3 - u3 *v1*a33 *m1*n2
2 2 2 2 2 3 2 3 2
+ u3 *v2*a33 *m2*n2 + u3 *v3 *( - a33 *m1 - a33 *m2 )
2 2 2 2
+ 4*u3 *v3*a33 *m2*n2*n3 + 2*u3*v1*v3*a33 *m1*m2*n2 - 2*u3*v1*a33*m1*n2 *n3
2 2 2 2 2 2 2
+ 2*u3*v2*v3*a33 *m2 *n2 + u3*v3 *( - a33 *m1 *n3 - a33 *m2 *n3)
2 2 2 3 2 2
+ 4*u3*v3*a33*m2*n2*n3 + v1*v3 *( - a33 *m1 - a33 *m1*m2 )
2 2 2 2 2
+ 2*v1*v3*a33*m1*m2*n2*n3 + v2 *(a33*m1 *n2 + a33*m2 *n2 )
2 2 2 2 3 2
+ v2*v3 *( - a33 *m1 *m2 - a33 *m2 ) + 2*v2*v3*a33*m2 *n2*n3
2 2 2 2 2 2 2 2 2
+ 2*v2*m2*n2 *n3 + v3 *(a33*m1 *n2 - a33*m1 *n3 - a33*m2 *n3 )
3
+ 2*v3*m2*n2*n3
which the program can not factorize further.
{HAM,FI} = 0
2 2 2 2 2 2 2
FI= - u1 *v2 *a33*n2 - u1 *v3 *a33*n2 + 2*u1*u2*v1*v2*a33*n2
2 2 3
+ 2*u1*u3*v1*v3*a33*n2 + 2*u1*v1 *v2*a33*m1*n2 + 2*u1*v2 *a33*m1*n2
2 2 2 2 2 2 2
+ 2*u1*v2*v3 *a33*m1*n2 - u2 *v1 *a33*n2 - u2 *v3 *a33*n2
2 3 2 3
+ 2*u2*u3*v2*v3*a33*n2 - 2*u2*v1 *a33*m1*n2 + u2*v1 *n2
2 2 2 3 2 3
- 2*u2*v1*v2 *a33*m1*n2 - 2*u2*v1*v3 *a33*m1*n2 + u2*v2 *n2 + u2*v3 *n2
2 2 2 2 2 2
+ u3 *v3 *a33*n2 - 2*u3*v1 *v3*a33*m2*n2 + u3*v1 *n2 *n3
2 2 2 3 2 2
- 2*u3*v2 *v3*a33*m2*n2 + u3*v2 *n2 *n3 - 2*u3*v3 *a33*m2*n2 + u3*v3 *n2 *n3
3 2 2 2 2 2 2 2
+ v1 *m1*n2 - v1 *v2*m2*n2 + v1 *v3 *(a33*m1 + a33*m2 )
2 2 2 2 2 3 2
- 2*v1 *v3*m2*n2*n3 + v1*v2 *m1*n2 + v1*v3 *m1*n2 - v2 *m2*n2
2 2 2 2 2 2 2
+ v2 *v3 *(a33*m1 + a33*m2 ) - 2*v2 *v3*m2*n2*n3 - v2*v3 *m2*n2
4 2 2 3
+ v3 *(a33*m1 + a33*m2 ) - 2*v3 *m2*n2*n3
which the program can not factorize further.
{HAM,FI} = 0
3 3 2 3 2 3
FI=u1 *v1*a33*n2 + u1 *u2*v2*a33*n2 + u1 *u3*v3*a33*n2
2 2 2 2 2 2 2 2
- 2*u1 *v1*v2*a33*m1*n2 + u1 *v2 *a33*m2*n2 + u1 *v3 *a33*m2*n2
2 3 2 2 2
+ u1*u2 *v1*a33*n2 + 2*u1*u2*v1 *a33*m1*n2 - 2*u1*u2*v1*v2*a33*m2*n2
4 2 2 3
- u1*u2*v1*n2 - 2*u1*u2*v2 *a33*m1*n2 - u1*u3*v1*n2 *n3
2 2 2 3
- 2*u1*u3*v2*v3*a33*m1*n2 - 2*u1*v1 *v2*a33*m1*m2*n2 - u1*v1 *m1*n2
3 2 2 2
+ u1*v1*v2*m2*n2 + u1*v1*v3 *( - a33*m1 *n2 - a33*m2 *n2)
2 3 2
+ 2*u1*v1*v3*m2*n2 *n3 - 2*u1*v2 *a33*m1*m2*n2 - 2*u1*v2*v3 *a33*m1*m2*n2
3 3 2 3 2 2 2
+ u2 *v2*a33*n2 + u2 *u3*v3*a33*n2 + u2 *v1 *a33*m2*n2
2 2 2 4 2 2 2
+ 2*u2 *v1*v2*a33*m1*n2 - u2 *v2*n2 + u2 *v3 *a33*m2*n2
2 3 4
+ 2*u2*u3*v1*v3*a33*m1*n2 - u2*u3*v2*n2 *n3 - u2*u3*v3*n2
3 2 3 2
+ 2*u2*v1 *a33*m1*m2*n2 - u2*v1 *m2*n2 + 2*u2*v1*v2 *a33*m1*m2*n2
3 2
- u2*v1*v2*m1*n2 + 2*u2*v1*v3 *a33*m1*m2*n2
2 2 2 2
+ u2*v2*v3 *( - a33*m1 *n2 - a33*m2 *n2) + 2*u2*v2*v3*m2*n2 *n3
2 3 2 2 2 2 3
- u2*v3 *m2*n2 + u3 *v3 *a33*m2*n2 - u3 *v3*n2 *n3
2 2 2 2 3
+ 2*u3*v1 *v3*a33*m2 *n2 - u3*v1 *m2*n2 *n3 - u3*v1*v3*m1*n2
2 2 2 2 3
+ 2*u3*v2 *v3*a33*m2 *n2 - u3*v2 *m2*n2 *n3 + u3*v2*v3*m2*n2
3 2 2 2 2 3 2
+ u3*v3 *( - a33*m1 *n2 + a33*m2 *n2) + u3*v3 *m2*n2 *n3 - v1 *m1*m2*n2
2 2 2 2 2 2 3 2 2
+ v1 *v2*m2 *n2 + v1 *v3 *( - a33*m1 *m2 - a33*m2 ) + 2*v1 *v3*m2 *n2*n3
2 2 2 2 3 2 2
- v1*v2 *m1*m2*n2 - v1*v3 *m1*m2*n2 + v2 *m2 *n2
2 2 2 3 2 2 2 2 2
+ v2 *v3 *( - a33*m1 *m2 - a33*m2 ) + 2*v2 *v3*m2 *n2*n3 + v2*v3 *m2 *n2
4 2 3 3 2
+ v3 *( - a33*m1 *m2 - a33*m2 ) + 2*v3 *m2 *n2*n3
which the program can not factorize further.
{HAM,FI} = 0
4 3 4 3 3 3 2 2 3 4
FI=u1 *a33 *n2 - 4*u1 *v2*a33 *m1*n2 + 2*u1 *u2 *a33 *n2
2 3 3 2 2 5 2 3 3
+ 4*u1 *u2*v1*a33 *m1*n2 - 2*u1 *u2*a33 *n2 + 4*u1 *u3*v3*a33 *m2*n2
2 2 4 2 2 4 2 2 3 2 2
- 2*u1 *u3*a33 *n2 *n3 - 2*u1 *v1*a33 *m1*n2 + 4*u1 *v2 *a33 *m1 *n2
2 2 4 2 2 3 2 2 3 2 2
+ 2*u1 *v2*a33 *m2*n2 + u1 *v3 *( - 2*a33 *m1 *n2 - 2*a33 *m2 *n2 )
2 2 3 2 4 2 2 3 3
+ 4*u1 *v3*a33 *m2*n2 *n3 - u1 *a33*n2 *n3 - 4*u1*u2 *v2*a33 *m1*n2
3 2 2 2 4
- 8*u1*u2*v1*v2*a33 *m1 *n2 + 4*u1*u2*v2*a33 *m1*n2
3 2 2 3
- 8*u1*u3*v2*v3*a33 *m1*m2*n2 + 4*u1*u3*v2*a33 *m1*n2 *n3
2 2 3 5 2 2 3
+ 4*u1*v1*v2*a33 *m1 *n2 + 2*u1*v1*a33*m2*n2 - 4*u1*v2 *a33 *m1*m2*n2
2 3 3 3 2
+ u1*v2*v3 *(4*a33 *m1 *n2 + 4*a33 *m1*m2 *n2)
2 2 3 2 4 3 4
- 8*u1*v2*v3*a33 *m1*m2*n2 *n3 + 2*u1*v2*a33*m1*n2 *n3 + u2 *a33 *n2
3 3 3 3 2 5 2 3 3
+ 4*u2 *v1*a33 *m1*n2 - 2*u2 *a33 *n2 + 4*u2 *u3*v3*a33 *m2*n2
2 2 4 2 2 3 2 2 2 2 4
- 2*u2 *u3*a33 *n2 *n3 + 4*u2 *v1 *a33 *m1 *n2 - 6*u2 *v1*a33 *m1*n2
2 2 4 2 2 3 2 2 3 2 2
+ 2*u2 *v2*a33 *m2*n2 + u2 *v3 *( - 2*a33 *m1 *n2 - 2*a33 *m2 *n2 )
2 2 3 2 6 4 2
+ 4*u2 *v3*a33 *m2*n2 *n3 + u2 *(a33*n2 - a33*n2 *n3 )
3 2 2 3
+ 8*u2*u3*v1*v3*a33 *m1*m2*n2 - 4*u2*u3*v1*a33 *m1*n2 *n3
2 4 5 2 2 2 3
- 4*u2*u3*v3*a33 *m2*n2 + 2*u2*u3*a33*n2 *n3 - 4*u2*v1 *a33 *m1 *n2
2 3
+ 4*u2*v1*v2*a33 *m1*m2*n2
2 3 3 3 2
+ u2*v1*v3 *( - 4*a33 *m1 *n2 - 4*a33 *m1*m2 *n2)
2 2 5 3 2
+ 8*u2*v1*v3*a33 *m1*m2*n2 *n3 + u2*v1*(2*a33*m1*n2 - 2*a33*m1*n2 *n3 )
2 2 2 3 2 2 3 4
+ u2*v3 *(2*a33 *m1 *n2 + 2*a33 *m2 *n2 ) - 4*u2*v3*a33*m2*n2 *n3
2 2 3 2 2 2 2 3
+ 4*u3 *v3 *a33 *m2 *n2 - 4*u3 *v3*a33 *m2*n2 *n3
2 3 4
- 4*u3*v1*v3*a33 *m1*m2*n2 + 2*u3*v1*a33*m1*n2 *n3
2 2 3 4
+ 4*u3*v2*v3*a33 *m2 *n2 - 2*u3*v2*a33*m2*n2 *n3
3 3 2 3 3
+ u3*v3 *( - 4*a33 *m1 *m2*n2 - 4*a33 *m2 *n2)
2 2 2 2 2 2 2
+ u3*v3 *(2*a33 *m1 *n2 *n3 + 10*a33 *m2 *n2 *n3)
5 3 2 4
+ u3*v3*(2*a33*m2*n2 - 6*a33*m2*n2 *n3 ) - 2*v1*v2*a33*m1*m2*n2
2 2 3 2 2 2 2 3
+ v1*v3 *(2*a33 *m1 *n2 + 2*a33 *m1*m2 *n2 ) - 4*v1*v3*a33*m1*m2*n2 *n3
2 2 4 2 4
+ v2 *( - a33*m1 *n2 + a33*m2 *n2 )
2 2 2 2 2 3 2 2 3
+ v2*v3 *( - 2*a33 *m1 *m2*n2 - 2*a33 *m2 *n2 ) + 4*v2*v3*a33*m2 *n2 *n3
4 2 4 3 4 3 2 2 3 4
- 2*v2*m2*n2 *n3 + v3 *(a33 *m1 + 2*a33 *m1 *m2 + a33 *m2 )
3 2 2 2 3
+ v3 *( - 4*a33 *m1 *m2*n2*n3 - 4*a33 *m2 *n2*n3)
2 2 4 2 2 2 2 2 2
+ v3 *( - a33*m1 *n2 + a33*m1 *n2 *n3 + 5*a33*m2 *n2 *n3 )
3 3
- 2*v3*m2*n2 *n3
which the program can not factorize further.
{HAM,FI} = 0
2 2 2 2 3
FI= - u1 *a33*n2 + 2*u1*v2*a33*m1*n2 - u2 *a33*n2 - 2*u2*v1*a33*m1*n2 + u2*n2
2 2 2
- 2*u3*v3*a33*m2*n2 + u3*n2 *n3 + v1*m1*n2 - v2*m2*n2
2 2 2
+ v3 *(a33*m1 + a33*m2 ) - 2*v3*m2*n2*n3
which the program can not factorize further.
{HAM,FI} = 0
And again in machine readable form:
HAM=u2*n2 + u3**2*a33 + u3*n3 + v1*m1 + v2*m2$
FI=u1**2*u2*a33**2*n2**3 + u1**2*u3**2*a33**3*n2**2 + u1**2*u3*a33**2*n2**2*n3 +
u1**2*v1*a33**2*m1*n2**2 + u1**2*v2*a33**2*m2*n2**2 + u1**2*a33*n2**2*n3**2 - 2
*u1*u2*v2*a33**2*m1*n2**2 - 2*u1*u3**2*v2*a33**3*m1*n2 - 2*u1*u3*v2*a33**2*m1*n2
*n3 - 2*u1*v1*v2*a33**2*m1**2*n2 - 2*u1*v2**2*a33**2*m1*m2*n2 - 2*u1*v2*a33*m1*
n2*n3**2 + u2**3*a33**2*n2**3 + u2**2*u3**2*a33**3*n2**2 + u2**2*u3*a33**2*n2**2
*n3 + 3*u2**2*v1*a33**2*m1*n2**2 + u2**2*v2*a33**2*m2*n2**2 + u2**2*( - a33*n2**
4 + a33*n2**2*n3**2) + 2*u2*u3**2*v1*a33**3*m1*n2 - u2*u3**2*a33**2*n2**3 + 2*u2
*u3*v1*a33**2*m1*n2*n3 + 2*u2*u3*v3*a33**2*m2*n2**2 - 2*u2*u3*a33*n2**3*n3 + 2*
u2*v1**2*a33**2*m1**2*n2 + 2*u2*v1*v2*a33**2*m1*m2*n2 + u2*v1*( - 2*a33*m1*n2**3
+ 2*a33*m1*n2*n3**2) + u2*v3**2*( - a33**2*m1**2*n2 - a33**2*m2**2*n2) + 2*u2*
v3*a33*m2*n2**2*n3 + 2*u3**3*v3*a33**3*m2*n2 - u3**3*a33**2*n2**2*n3 - u3**2*v1*
a33**2*m1*n2**2 + u3**2*v2*a33**2*m2*n2**2 + u3**2*v3**2*( - a33**3*m1**2 - a33
**3*m2**2) + 4*u3**2*v3*a33**2*m2*n2*n3 + 2*u3*v1*v3*a33**2*m1*m2*n2 - 2*u3*v1*
a33*m1*n2**2*n3 + 2*u3*v2*v3*a33**2*m2**2*n2 + u3*v3**2*( - a33**2*m1**2*n3 -
a33**2*m2**2*n3) + 4*u3*v3*a33*m2*n2*n3**2 + v1*v3**2*( - a33**2*m1**3 - a33**2*
m1*m2**2) + 2*v1*v3*a33*m1*m2*n2*n3 + v2**2*(a33*m1**2*n2**2 + a33*m2**2*n2**2)
+ v2*v3**2*( - a33**2*m1**2*m2 - a33**2*m2**3) + 2*v2*v3*a33*m2**2*n2*n3 + 2*v2*
m2*n2**2*n3**2 + v3**2*(a33*m1**2*n2**2 - a33*m1**2*n3**2 - a33*m2**2*n3**2) + 2
*v3*m2*n2*n3**3$
FI= - u1**2*v2**2*a33*n2**2 - u1**2*v3**2*a33*n2**2 + 2*u1*u2*v1*v2*a33*n2**2 +
2*u1*u3*v1*v3*a33*n2**2 + 2*u1*v1**2*v2*a33*m1*n2 + 2*u1*v2**3*a33*m1*n2 + 2*u1*
v2*v3**2*a33*m1*n2 - u2**2*v1**2*a33*n2**2 - u2**2*v3**2*a33*n2**2 + 2*u2*u3*v2*
v3*a33*n2**2 - 2*u2*v1**3*a33*m1*n2 + u2*v1**2*n2**3 - 2*u2*v1*v2**2*a33*m1*n2 -
2*u2*v1*v3**2*a33*m1*n2 + u2*v2**2*n2**3 + u2*v3**2*n2**3 + u3**2*v3**2*a33*n2
**2 - 2*u3*v1**2*v3*a33*m2*n2 + u3*v1**2*n2**2*n3 - 2*u3*v2**2*v3*a33*m2*n2 + u3
*v2**2*n2**2*n3 - 2*u3*v3**3*a33*m2*n2 + u3*v3**2*n2**2*n3 + v1**3*m1*n2**2 - v1
**2*v2*m2*n2**2 + v1**2*v3**2*(a33*m1**2 + a33*m2**2) - 2*v1**2*v3*m2*n2*n3 + v1
*v2**2*m1*n2**2 + v1*v3**2*m1*n2**2 - v2**3*m2*n2**2 + v2**2*v3**2*(a33*m1**2 +
a33*m2**2) - 2*v2**2*v3*m2*n2*n3 - v2*v3**2*m2*n2**2 + v3**4*(a33*m1**2 + a33*m2
**2) - 2*v3**3*m2*n2*n3$
FI=u1**3*v1*a33*n2**3 + u1**2*u2*v2*a33*n2**3 + u1**2*u3*v3*a33*n2**3 - 2*u1**2*
v1*v2*a33*m1*n2**2 + u1**2*v2**2*a33*m2*n2**2 + u1**2*v3**2*a33*m2*n2**2 + u1*u2
**2*v1*a33*n2**3 + 2*u1*u2*v1**2*a33*m1*n2**2 - 2*u1*u2*v1*v2*a33*m2*n2**2 - u1*
u2*v1*n2**4 - 2*u1*u2*v2**2*a33*m1*n2**2 - u1*u3*v1*n2**3*n3 - 2*u1*u3*v2*v3*a33
*m1*n2**2 - 2*u1*v1**2*v2*a33*m1*m2*n2 - u1*v1**2*m1*n2**3 + u1*v1*v2*m2*n2**3 +
u1*v1*v3**2*( - a33*m1**2*n2 - a33*m2**2*n2) + 2*u1*v1*v3*m2*n2**2*n3 - 2*u1*v2
**3*a33*m1*m2*n2 - 2*u1*v2*v3**2*a33*m1*m2*n2 + u2**3*v2*a33*n2**3 + u2**2*u3*v3
*a33*n2**3 + u2**2*v1**2*a33*m2*n2**2 + 2*u2**2*v1*v2*a33*m1*n2**2 - u2**2*v2*n2
**4 + u2**2*v3**2*a33*m2*n2**2 + 2*u2*u3*v1*v3*a33*m1*n2**2 - u2*u3*v2*n2**3*n3
- u2*u3*v3*n2**4 + 2*u2*v1**3*a33*m1*m2*n2 - u2*v1**2*m2*n2**3 + 2*u2*v1*v2**2*
a33*m1*m2*n2 - u2*v1*v2*m1*n2**3 + 2*u2*v1*v3**2*a33*m1*m2*n2 + u2*v2*v3**2*( -
a33*m1**2*n2 - a33*m2**2*n2) + 2*u2*v2*v3*m2*n2**2*n3 - u2*v3**2*m2*n2**3 + u3**
2*v3**2*a33*m2*n2**2 - u3**2*v3*n2**3*n3 + 2*u3*v1**2*v3*a33*m2**2*n2 - u3*v1**2
*m2*n2**2*n3 - u3*v1*v3*m1*n2**3 + 2*u3*v2**2*v3*a33*m2**2*n2 - u3*v2**2*m2*n2**
2*n3 + u3*v2*v3*m2*n2**3 + u3*v3**3*( - a33*m1**2*n2 + a33*m2**2*n2) + u3*v3**2*
m2*n2**2*n3 - v1**3*m1*m2*n2**2 + v1**2*v2*m2**2*n2**2 + v1**2*v3**2*( - a33*m1
**2*m2 - a33*m2**3) + 2*v1**2*v3*m2**2*n2*n3 - v1*v2**2*m1*m2*n2**2 - v1*v3**2*
m1*m2*n2**2 + v2**3*m2**2*n2**2 + v2**2*v3**2*( - a33*m1**2*m2 - a33*m2**3) + 2*
v2**2*v3*m2**2*n2*n3 + v2*v3**2*m2**2*n2**2 + v3**4*( - a33*m1**2*m2 - a33*m2**3
) + 2*v3**3*m2**2*n2*n3$
FI=u1**4*a33**3*n2**4 - 4*u1**3*v2*a33**3*m1*n2**3 + 2*u1**2*u2**2*a33**3*n2**4
+ 4*u1**2*u2*v1*a33**3*m1*n2**3 - 2*u1**2*u2*a33**2*n2**5 + 4*u1**2*u3*v3*a33**3
*m2*n2**3 - 2*u1**2*u3*a33**2*n2**4*n3 - 2*u1**2*v1*a33**2*m1*n2**4 + 4*u1**2*v2
**2*a33**3*m1**2*n2**2 + 2*u1**2*v2*a33**2*m2*n2**4 + u1**2*v3**2*( - 2*a33**3*
m1**2*n2**2 - 2*a33**3*m2**2*n2**2) + 4*u1**2*v3*a33**2*m2*n2**3*n3 - u1**2*a33*
n2**4*n3**2 - 4*u1*u2**2*v2*a33**3*m1*n2**3 - 8*u1*u2*v1*v2*a33**3*m1**2*n2**2 +
4*u1*u2*v2*a33**2*m1*n2**4 - 8*u1*u3*v2*v3*a33**3*m1*m2*n2**2 + 4*u1*u3*v2*a33
**2*m1*n2**3*n3 + 4*u1*v1*v2*a33**2*m1**2*n2**3 + 2*u1*v1*a33*m2*n2**5 - 4*u1*v2
**2*a33**2*m1*m2*n2**3 + u1*v2*v3**2*(4*a33**3*m1**3*n2 + 4*a33**3*m1*m2**2*n2)
- 8*u1*v2*v3*a33**2*m1*m2*n2**2*n3 + 2*u1*v2*a33*m1*n2**3*n3**2 + u2**4*a33**3*
n2**4 + 4*u2**3*v1*a33**3*m1*n2**3 - 2*u2**3*a33**2*n2**5 + 4*u2**2*u3*v3*a33**3
*m2*n2**3 - 2*u2**2*u3*a33**2*n2**4*n3 + 4*u2**2*v1**2*a33**3*m1**2*n2**2 - 6*u2
**2*v1*a33**2*m1*n2**4 + 2*u2**2*v2*a33**2*m2*n2**4 + u2**2*v3**2*( - 2*a33**3*
m1**2*n2**2 - 2*a33**3*m2**2*n2**2) + 4*u2**2*v3*a33**2*m2*n2**3*n3 + u2**2*(a33
*n2**6 - a33*n2**4*n3**2) + 8*u2*u3*v1*v3*a33**3*m1*m2*n2**2 - 4*u2*u3*v1*a33**2
*m1*n2**3*n3 - 4*u2*u3*v3*a33**2*m2*n2**4 + 2*u2*u3*a33*n2**5*n3 - 4*u2*v1**2*
a33**2*m1**2*n2**3 + 4*u2*v1*v2*a33**2*m1*m2*n2**3 + u2*v1*v3**2*( - 4*a33**3*m1
**3*n2 - 4*a33**3*m1*m2**2*n2) + 8*u2*v1*v3*a33**2*m1*m2*n2**2*n3 + u2*v1*(2*a33
*m1*n2**5 - 2*a33*m1*n2**3*n3**2) + u2*v3**2*(2*a33**2*m1**2*n2**3 + 2*a33**2*m2
**2*n2**3) - 4*u2*v3*a33*m2*n2**4*n3 + 4*u3**2*v3**2*a33**3*m2**2*n2**2 - 4*u3**
2*v3*a33**2*m2*n2**3*n3 - 4*u3*v1*v3*a33**2*m1*m2*n2**3 + 2*u3*v1*a33*m1*n2**4*
n3 + 4*u3*v2*v3*a33**2*m2**2*n2**3 - 2*u3*v2*a33*m2*n2**4*n3 + u3*v3**3*( - 4*
a33**3*m1**2*m2*n2 - 4*a33**3*m2**3*n2) + u3*v3**2*(2*a33**2*m1**2*n2**2*n3 + 10
*a33**2*m2**2*n2**2*n3) + u3*v3*(2*a33*m2*n2**5 - 6*a33*m2*n2**3*n3**2) - 2*v1*
v2*a33*m1*m2*n2**4 + v1*v3**2*(2*a33**2*m1**3*n2**2 + 2*a33**2*m1*m2**2*n2**2) -
4*v1*v3*a33*m1*m2*n2**3*n3 + v2**2*( - a33*m1**2*n2**4 + a33*m2**2*n2**4) + v2*
v3**2*( - 2*a33**2*m1**2*m2*n2**2 - 2*a33**2*m2**3*n2**2) + 4*v2*v3*a33*m2**2*n2
**3*n3 - 2*v2*m2*n2**4*n3**2 + v3**4*(a33**3*m1**4 + 2*a33**3*m1**2*m2**2 + a33
**3*m2**4) + v3**3*( - 4*a33**2*m1**2*m2*n2*n3 - 4*a33**2*m2**3*n2*n3) + v3**2*(
- a33*m1**2*n2**4 + a33*m1**2*n2**2*n3**2 + 5*a33*m2**2*n2**2*n3**2) - 2*v3*m2*
n2**3*n3**3$
FI= - u1**2*a33*n2**2 + 2*u1*v2*a33*m1*n2 - u2**2*a33*n2**2 - 2*u2*v1*a33*m1*n2
+ u2*n2**3 - 2*u3*v3*a33*m2*n2 + u3*n2**2*n3 + v1*m1*n2**2 - v2*m2*n2**2 + v3**2
*(a33*m1**2 + a33*m2**2) - 2*v3*m2*n2*n3$