Solution 7 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
2*m1*n3*r214
r10=--------------
a33*n1
m2*r15
r11=--------
n1
a33*m1*r15 + 2*m1*n1*r214
r12=---------------------------
a33*n1
n3*r15
r13=--------
n1
r14=0
3 2 2 2 2 2 2 2
r20=( - a33 *m1 *n1*r15 - a33 *m1 *n1 *r214 - a33 *m1 *n3 *r214
2 2 2 2 2 2 2 4 2 2 2
- a33 *m2 *n3 *r214 - m1 *n1 *n3 *r4119 + 2*m1 *n3 *r4119)/(a33 *n1 *n3 )
3 2 2
2*a33 *m1*m2*r15 + 2*a33 *m1*m2*n1*r214 - m1*m2*n1*n3 *r4119
r21=--------------------------------------------------------------
2 2
a33 *n1 *n3
3 2 3 2 2 2 2 2
r22=( - a33 *m1 *r15 - a33 *m2 *r15 - a33 *m1 *n1*r214 - a33 *m2 *n1*r214
2 2 2 2
- m1 *n1*n3 *r4119)/(a33 *n1*n3 )
3 2 2 2 2 2
2*a33 *m1 *r15 + 2*a33 *m1 *n1*r214 + 3*m1 *n1*n3 *r4119
r23=----------------------------------------------------------
2 2
a33 *n1 *n3
- m1*m2*r4119
r24=----------------
2
a33
3 2 2
2*a33 *m1*r15 + 4*a33 *m1*n1*r214 - m1*n1*n3 *r4119
r26=-----------------------------------------------------
2 2
a33 *n1
- 2*a33*m2*r15 - 2*m2*n1*r214
r27=--------------------------------
n1*n3
- m1*n3*r4119
r28=----------------
2
a33
r210=0
- 2*m2*r214
r212=--------------
n1
r213=0
3 2 2
2*a33 *m1*r15 + 2*a33 *m1*n1*r214 - m1*n1*n3 *r4119
r215=-----------------------------------------------------
2
a33 *n1*n3
2 2
- 2*a33*m2*n1*r15 - 2*m2*n1 *r214 + 2*m2*n3 *r214
r216=----------------------------------------------------
2
n1*n3
- m1*n1*r4119
r217=----------------
2
a33
- 2*a33*r15 - 2*n1*r214
r218=--------------------------
n3
r219=0
2 2
- a33*n1*r15 - n1 *r214 + n3 *r214
r220=-------------------------------------
2
n3
3 2 2 2
- 2*m1 *n3*r4119 + 2*m1 *n1*n3*r4116 - 2*m1*m2 *n3*r4119 - m1*n1 *n3*r446
r30=----------------------------------------------------------------------------
3
a33*n1
3 2 3 3 2 2
r31=( - 2*a33 *m1 *m2*r15 - 2*a33 *m2 *r15 - 2*a33 *m1 *m2*n1*r214
2 3 2 2 2 2
- 2*a33 *m2 *n1*r214 + m1 *m2*n1*n3 *r4119 - 2*m1*m2*n1 *n3 *r4116
3 2 3 2 3 2
+ m2 *n1*n3 *r4119 + m2*n1 *n3 *r446)/(2*a33*n1 *n3 )
2
2*m1 *n3*r4116 - m1*n1*n3*r446
r32=--------------------------------
2
a33*n1
- 2*m1*m2*r4116 + m2*n1*r446
r33=-------------------------------
2*a33*n1
3 3 3 2 2 3
r34=( - 2*a33 *m1 *r15 - 2*a33 *m1*m2 *r15 - 2*a33 *m1 *n1*r214
2 2 3 2 2 2 2
- 2*a33 *m1*m2 *n1*r214 - 3*m1 *n1*n3 *r4119 + 2*m1 *n1 *n3 *r4116
2 2 3 2 3 2
- 3*m1*m2 *n1*n3 *r4119 - m1*n1 *n3 *r446)/(2*a33*n1 *n3 )
r35=0
2
2*m1 *r4116 - m1*n1*r446
r36=--------------------------
2*a33*n1
2
2*m1 *n3*r4116 - m1*n1*n3*r446
r37=--------------------------------
2
a33*n1
- 2*m1*m2*r4116 + m2*n1*r446
r38=-------------------------------
2*a33*n1
2
2*m1 *r4116 - m1*n1*r446
r39=--------------------------
2*a33*n1
3 2 3 2 2 2
r310=( - 2*a33 *m1 *r15 - 2*a33 *m2 *r15 - 2*a33 *m1 *n1*r214
2 2 2 2 2 2
- 2*a33 *m2 *n1*r214 + 9*m1 *n1*n3 *r4119 + 2*m1*n1 *n3 *r4116
2 2 3 2 3
+ m2 *n1*n3 *r4119 + n1 *n3 *r446)/(2*a33*n1 *n3)
3 2 2
r311=(2*a33 *m1*m2*r15 + 2*a33 *m1*m2*n1*r214 - m1*m2*n1*n3 *r4119
2 2 2 2
- m2*n1 *n3 *r4116)/(a33*n1 *n3 )
- 2*m1*n3*r4116 + n1*n3*r446
r312=-------------------------------
2*a33*n1
r313
3 2 2 2 2 2 2 2
2*a33 *m1 *r15 + 2*a33 *m1 *n1*r214 + 3*m1 *n1*n3 *r4119 + m1*n1 *n3 *r4116
=-----------------------------------------------------------------------------
2 2
a33*n1 *n3
r314=0
- 2*m1*n3*r4116 + n1*n3*r446
r315=-------------------------------
2*a33*n1
3 2 2 2
4*a33 *m1*r15 + 4*a33 *m1*n1*r214 - n1 *n3 *r4116
r316=---------------------------------------------------
2
a33*n1 *n3
3 2 2
- 2*a33 *m2*r15 - 2*a33 *m2*n1*r214 - m2*n1*n3 *r4119
r317=--------------------------------------------------------
2
2*a33*n1*n3
3 2 2
2*a33 *m1*r15 + 2*a33 *m1*n1*r214 + m1*n1*n3 *r4119
r318=-----------------------------------------------------
2
2*a33*n1*n3
3 2 2
- 2*a33 *r15 - 2*a33 *n1*r214 - n1*n3 *r4119
r319=-----------------------------------------------
2*a33*n1*n3
r320=0
2*m1*n3*r4116
r321=---------------
a33*n1
- m2*r4116
r322=-------------
a33
- 4*m1*m2*n3*r4119
r323=---------------------
2
a33*n1
r324
3 2 2 2 2 2 2 2
- 2*a33 *m2 *r15 - 2*a33 *m2 *n1*r214 + m1*n1 *n3 *r4116 + m2 *n1*n3 *r4119
=------------------------------------------------------------------------------
2 2
a33*n1 *n3
3 2 2
- 2*a33 *m1*m2*r15 - 2*a33 *m1*m2*n1*r214 - 3*m1*m2*n1*n3 *r4119
r325=-------------------------------------------------------------------
2 2
a33*n1 *n3
r326=0
- n3*r4116
r327=-------------
a33
3 2 2
- 2*a33 *m2*r15 - 2*a33 *m2*n1*r214 + m2*n1*n3 *r4119
r328=--------------------------------------------------------
2
a33*n1 *n3
r329=0
2*m1*n3*r4119
r330=---------------
a33*n1
3 2 2
2*a33 *m2*r15 + 2*a33 *m2*n1*r214 - m2*n1*n3 *r4119
r331=-----------------------------------------------------
2
2*a33*n1*n3
3 2 2
2*a33 *m1*r15 + 2*a33 *m1*n1*r214 + 3*m1*n1*n3 *r4119
r332=-------------------------------------------------------
2
2*a33*n1*n3
3 2 2
2*a33 *r15 + 2*a33 *n1*r214 - n1*n3 *r4119
r333=--------------------------------------------
2*a33*n1*n3
r334=0
3 2 3 2 2 2
r335=( - 2*a33 *m1 *r15 - 2*a33 *m2 *r15 - 2*a33 *m1 *n1*r214
2 2 2 2 2 2
- 2*a33 *m2 *n1*r214 + m1 *n1*n3 *r4119 - 2*m1*n1 *n3 *r4116
2 2 3 2 2 2
+ m2 *n1*n3 *r4119 + n1 *n3 *r446)/(2*a33*n1 *n3 )
4*m1*m2*n3*r4119
r336=------------------
2
a33*n1
3 2 2 2 2 2
r337=(4*a33 *m2 *r15 + 4*a33 *m2 *n1*r214 - 2*m1*n1 *n3 *r4116
2 2 3 2 2 2
- 2*m2 *n1*n3 *r4119 + n1 *n3 *r446)/(2*a33*n1 *n3 )
2*m1*n3*r4116
r338=---------------
a33*n1
3 2 2
r339=(2*a33 *m1*m2*r15 + 2*a33 *m1*m2*n1*r214 + 3*m1*m2*n1*n3 *r4119
2 2 2 2
- m2*n1 *n3 *r4116)/(a33*n1 *n3 )
n1*r446
r340=---------
2*a33
3 2 2 2 2
2*a33 *m1*r15 + 2*a33 *m1*n1*r214 - m1*n1*n3 *r4119 - n1 *n3 *r4116
r341=---------------------------------------------------------------------
2
a33*n1*n3
3 2 2
2*a33 *m2*r15 + 2*a33 *m2*n1*r214 - m2*n1*n3 *r4119
r342=-----------------------------------------------------
2
a33*n1 *n3
- n3*r4116
r343=-------------
a33
3 2 2
- 2*a33 *r15 - 2*a33 *n1*r214 - n1*n3 *r4119
r344=-----------------------------------------------
2
2*a33*n3
r345=0
- n1*r4116
r346=-------------
a33
3 2 2
- 2*a33 *m2*r15 - 2*a33 *m2*n1*r214 + m2*n1*n3 *r4119
r347=--------------------------------------------------------
2
a33*n1*n3
r348=0
3 2 2
2*a33 *r15 + 2*a33 *n1*r214 - n1*n3 *r4119
r349=--------------------------------------------
2
2*a33*n3
2*m1*n3*r4119
r350=---------------
a33*n1
3 2 2
6*a33 *m2*r15 + 6*a33 *m2*n1*r214 - 3*m2*n1*n3 *r4119
r351=-------------------------------------------------------
2
2*a33*n1*n3
3 2 2 2 2
2*a33 *m1*r15 + 2*a33 *m1*n1*r214 + 3*m1*n1*n3 *r4119 - 2*n1 *n3 *r4116
r352=-------------------------------------------------------------------------
2
2*a33*n1*n3
3 2 2
2*a33 *r15 + 2*a33 *n1*r214 - n1*n3 *r4119
r353=--------------------------------------------
2*a33*n1*n3
r354=0
3 2 2
2*a33 *r15 + 2*a33 *n1*r214 - n1*n3 *r4119
r355=--------------------------------------------
2
2*a33*n3
4 3 2 2 2 2
r40=(m1 *r4119 - 2*m1 *n1*r4116 + 2*m1 *m2 *r4119 + m1 *n1 *r446
2 4 2 2 4
- 2*m1*m2 *n1*r4116 + m2 *r4119 + m2 *n1 *r446)/(2*n1 )
r41=0
3 2 2 2
- 2*m1 *r4116 + m1 *n1*r446 - 2*m1*m2 *r4116 + m2 *n1*r446
r42=-------------------------------------------------------------
3
2*n1
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
3 2 2 2
- 2*m1 *r4116 + m1 *n1*r446 - 2*m1*m2 *r4116 + m2 *n1*r446
r49=-------------------------------------------------------------
3
2*n1
r410=0
r411=0
r412=0
r413=0
r415
3 2 2 2 2
- 2*m1 *r4119 + m1 *n1*r4116 - 2*m1*m2 *r4119 - m1*n1 *r446 - m2 *n1*r4116
=-----------------------------------------------------------------------------
3
n1
r416=0
2
2*m1 *r4116 - m1*n1*r446
r417=--------------------------
2
n1
r418=0
r419=0
r420=0
r421=0
2
2*m1 *r4116 - m1*n1*r446
r422=--------------------------
2
n1
r423=0
r424=0
3 2 3 2 2 2
r425=( - 2*a33 *m1 *r15 - 2*a33 *m2 *r15 - 2*a33 *m1 *n1*r214
2 2 2 2 2 2
- 2*a33 *m2 *n1*r214 + 3*m1 *n1*n3 *r4119 + 2*m1*n1 *n3 *r4116
2 2 3 2 3 2
- m2 *n1*n3 *r4119 + n1 *n3 *r446)/(2*n1 *n3 )
r426=0
r427=0
r428=0
r429=0
3 2 2
2*a33 *m1*r15 + 2*a33 *m1*n1*r214 + m1*n1*n3 *r4119
r431=-----------------------------------------------------
2 2
n1 *n3
r432=0
r433=0
r435=0
2 2
- m1 *r4116 - m2 *r4116
r436=--------------------------
2
n1
r437=0
r438=0
2 3 2
2*m1 *m2*r4119 - 2*m1*m2*n1*r4116 + 2*m2 *r4119 + m2*n1 *r446
r439=---------------------------------------------------------------
3
n1
r440=0
- 2*m1*m2*r4116 + m2*n1*r446
r441=-------------------------------
2
n1
r442=0
- 2*m1*m2*r4116 + m2*n1*r446
r444=-------------------------------
2
n1
r445=0
r447=0
- 4*m1*m2*r4119 - 2*m2*n1*r4116
r448=----------------------------------
2
n1
r449=0
r450=0
r451=0
3 2 2
- 2*a33 *m2*r15 - 2*a33 *m2*n1*r214 - m2*n1*n3 *r4119
r453=--------------------------------------------------------
2 2
n1 *n3
r454=0
2 2 2
- 2*m1 *r4119 + 2*m1*n1*r4116 - 2*m2 *r4119 - n1 *r446
r455=---------------------------------------------------------
2
2*n1
r456=0
r458=0
- 2*m2*r4116
r459=---------------
n1
2 2
2*m1*n1*r4116 + 4*m2 *r4119 - n1 *r446
r460=----------------------------------------
2
2*n1
2*m1*r4119 + n1*r4116
r461=-----------------------
n1
r462=0
r463=0
r465=0
r466=r4116
- 2*m2*r4119
r467=---------------
n1
r468=0
r4119
r469=-------
2
r470=0
2 3 2
- 2*m1 *m2*r4119 + 2*m1*m2*n1*r4116 - 2*m2 *r4119 - m2*n1 *r446
r471=------------------------------------------------------------------
3
n1
r472=0
2*m1*m2*r4116 - m2*n1*r446
r473=----------------------------
2
n1
2 2
- m1 *r4116 - m2 *r4116
r474=--------------------------
2
n1
r475=0
r476=0
r477=0
2*m1*m2*r4116 - m2*n1*r446
r478=----------------------------
2
n1
r479=0
r480=0
4*m1*m2*r4119 + 2*m2*n1*r4116
r481=-------------------------------
2
n1
r482=0
r483=r446
r484=0
r485=0
r486=0
3 2 2
2*a33 *m2*r15 + 2*a33 *m2*n1*r214 + m2*n1*n3 *r4119
r487=-----------------------------------------------------
2 2
n1 *n3
r488=0
r489=0
r490=0
r491=0
2*m2*r4116
r492=------------
n1
r493=0
- 2*m2*r4116
r495=---------------
n1
r496=0
r497=0
r498=0
r499=0
r4100=0
2*m2*r4119
r4101=------------
n1
r4102=r4116
r4103=0
r4104=0
2 2 2
- 2*m1 *r4119 + 2*m1*n1*r4116 - 2*m2 *r4119 - n1 *r446
r4105=---------------------------------------------------------
2
2*n1
r4106=0
2 2
2*m1*n1*r4116 + 4*m2 *r4119 - n1 *r446
r4107=----------------------------------------
2
2*n1
r4108=0
2*m2*r4116
r4109=------------
n1
r4110=0
2*m1*r4119 + n1*r4116
r4111=-----------------------
n1
r4112=0
r4113=0
3 2 2
2*a33 *r15 + 2*a33 *n1*r214 + n1*n3 *r4119
r4114=--------------------------------------------
2
2*n1*n3
r4115=0
- 2*m2*r4119
r4117=---------------
n1
r4118=0
r4120=0
2*m2*r4119
r4121=------------
n1
r4122=r4116
r4123=0
r4124=0
r4119
r4125=-------
2
m3=0
n2=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
2 2
- 2*m1*n1*r4116 - 4*m2 *r4119 + n1 *r446
r494=-------------------------------------------
2
n1
3 2 2
2*a33 *r15 + 2*a33 *n1*r214 + n1*n3 *r4119
r464=--------------------------------------------
2
2*n1*n3
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:
r4119, r4116, r214, r15, r446, m1, n3, m2, n1, 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,m2}
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,
n2,
m3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=u1*n1 + u3 *a33 + u3*n3 + v1*m1 + v2*m2
has apart from the Hamiltonian and Casimirs the following 5 first integrals:
2 2 2 2 2 2 2
FI= - u1 *v2 *a33*n1 - u1 *v3 *a33*n1 + 2*u1*u2*v1*v2*a33*n1
2 2 2 3
+ 2*u1*u3*v1*v3*a33*n1 - 2*u1*v1 *v2*a33*m2*n1 + u1*v1 *n1
3 2 3 2 2 3
- 2*u1*v2 *a33*m2*n1 + u1*v2 *n1 - 2*u1*v2*v3 *a33*m2*n1 + u1*v3 *n1
2 2 2 2 2 2 2
- u2 *v1 *a33*n1 - u2 *v3 *a33*n1 + 2*u2*u3*v2*v3*a33*n1
3 2 2
+ 2*u2*v1 *a33*m2*n1 + 2*u2*v1*v2 *a33*m2*n1 + 2*u2*v1*v3 *a33*m2*n1
2 2 2 2 2 2
+ u3 *v3 *a33*n1 - 2*u3*v1 *v3*a33*m1*n1 + u3*v1 *n1 *n3
2 2 2 3 2 2
- 2*u3*v2 *v3*a33*m1*n1 + u3*v2 *n1 *n3 - 2*u3*v3 *a33*m1*n1 + u3*v3 *n1 *n3
3 2 2 2 2 2 2 2
- v1 *m1*n1 + v1 *v2*m2*n1 + v1 *v3 *(a33*m1 + a33*m2 )
2 2 2 2 2 3 2
- 2*v1 *v3*m1*n1*n3 - v1*v2 *m1*n1 - v1*v3 *m1*n1 + v2 *m2*n1
2 2 2 2 2 2 2
+ v2 *v3 *(a33*m1 + a33*m2 ) - 2*v2 *v3*m1*n1*n3 + v2*v3 *m2*n1
4 2 2 3
+ v3 *(a33*m1 + a33*m2 ) - 2*v3 *m1*n1*n3
which the program can not factorize further.
{HAM,FI} = 0
3 2 3 2 2 3 2 2 2 2 2 2 2
FI=u1 *a33 *n1 + u1 *u3 *a33 *n1 + u1 *u3*a33 *n1 *n3 + u1 *v1*a33 *m1*n1
2 2 2 2 4 2 2 3
+ 3*u1 *v2*a33 *m2*n1 - u1 *a33*n1 + u1*u2 *a33 *n1
2 2 2 3 2 2 3
- 2*u1*u2*v1*a33 *m2*n1 + 2*u1*u3 *v2*a33 *m2*n1 - u1*u3 *a33 *n1
2 2 2 3
+ 2*u1*u3*v2*a33 *m2*n1*n3 + 2*u1*u3*v3*a33 *m1*n1 - 2*u1*u3*a33*n1 *n3
2 2 2 2 3
+ 2*u1*v1*v2*a33 *m1*m2*n1 + 2*u1*v2 *a33 *m2 *n1 - 2*u1*v2*a33*m2*n1
2 2 2 2 2 2 3 2
+ u1*v3 *( - a33 *m1 *n1 - a33 *m2 *n1) + 2*u1*v3*a33*m1*n1 *n3 + u1*n1 *n3
2 2 3 2 2 2 2 2 2 2
+ u2 *u3 *a33 *n1 + u2 *u3*a33 *n1 *n3 + u2 *v1*a33 *m1*n1
2 2 2 2 3 2
+ u2 *v2*a33 *m2*n1 - 2*u2*u3 *v1*a33 *m2*n1 - 2*u2*u3*v1*a33 *m2*n1*n3
2 2 2 2 3 3
- 2*u2*v1 *a33 *m1*m2*n1 - 2*u2*v1*v2*a33 *m2 *n1 + 2*u3 *v3*a33 *m1*n1
3 2 2 2 2 2 2 2 2
- u3 *a33 *n1 *n3 + u3 *v1*a33 *m1*n1 - u3 *v2*a33 *m2*n1
2 2 3 2 3 2 2 2
+ u3 *v3 *( - a33 *m1 - a33 *m2 ) + 4*u3 *v3*a33 *m1*n1*n3
2 2 2 2
+ 2*u3*v1*v3*a33 *m1 *n1 + 2*u3*v2*v3*a33 *m1*m2*n1 - 2*u3*v2*a33*m2*n1 *n3
2 2 2 2 2 2 2 3
+ u3*v3 *( - a33 *m1 *n3 - a33 *m2 *n3) + 2*u3*v3*a33*m1*n1*n3 + u3*n1 *n3
2 2 3 2 2 2 2 2
+ v1*v3 *( - a33 *m1 - a33 *m1*m2 ) + 2*v1*v3*a33*m1 *n1*n3 + v1*m1*n1 *n3
2 2 2 2 2 2 2 2 2 3
+ v2 *( - a33*m1 *n1 - a33*m2 *n1 ) + v2*v3 *( - a33 *m1 *m2 - a33 *m2 )
2 2 2 2 2
+ 2*v2*v3*a33*m1*m2*n1*n3 + v2*m2*n1 *n3 - v3 *a33*m1 *n1
which the program can not factorize further.
{HAM,FI} = 0
3 2 3 2 2 3 2 2 2 2 2 2 2
FI=u1 *a33 *n1 + u1 *u3 *a33 *n1 + u1 *u3*a33 *n1 *n3 + u1 *v1*a33 *m1*n1
2 2 2 2 4 2 2 2 2 3
+ 3*u1 *v2*a33 *m2*n1 + u1 *( - a33*n1 + a33*n1 *n3 ) + u1*u2 *a33 *n1
2 2 2 3 2 2 3
- 2*u1*u2*v1*a33 *m2*n1 + 2*u1*u3 *v2*a33 *m2*n1 - u1*u3 *a33 *n1
2 2 2 3
+ 2*u1*u3*v2*a33 *m2*n1*n3 + 2*u1*u3*v3*a33 *m1*n1 - 2*u1*u3*a33*n1 *n3
2 2 2 2
+ 2*u1*v1*v2*a33 *m1*m2*n1 + 2*u1*v2 *a33 *m2 *n1
3 2
+ u1*v2*( - 2*a33*m2*n1 + 2*a33*m2*n1*n3 )
2 2 2 2 2 2
+ u1*v3 *( - a33 *m1 *n1 - a33 *m2 *n1) + 2*u1*v3*a33*m1*n1 *n3
2 2 3 2 2 2 2 2 2 2
+ u2 *u3 *a33 *n1 + u2 *u3*a33 *n1 *n3 + u2 *v1*a33 *m1*n1
2 2 2 2 2 2 2 3
+ u2 *v2*a33 *m2*n1 + u2 *a33*n1 *n3 - 2*u2*u3 *v1*a33 *m2*n1
2 2 2 2 2
- 2*u2*u3*v1*a33 *m2*n1*n3 - 2*u2*v1 *a33 *m1*m2*n1 - 2*u2*v1*v2*a33 *m2 *n1
2 3 3 3 2 2
- 2*u2*v1*a33*m2*n1*n3 + 2*u3 *v3*a33 *m1*n1 - u3 *a33 *n1 *n3
2 2 2 2 2 2 2 2 3 2 3 2
+ u3 *v1*a33 *m1*n1 - u3 *v2*a33 *m2*n1 + u3 *v3 *( - a33 *m1 - a33 *m2 )
2 2 2 2 2
+ 4*u3 *v3*a33 *m1*n1*n3 + 2*u3*v1*v3*a33 *m1 *n1 + 2*u3*v2*v3*a33 *m1*m2*n1
2 2 2 2 2 2
- 2*u3*v2*a33*m2*n1 *n3 + u3*v3 *( - a33 *m1 *n3 - a33 *m2 *n3)
2 2 2 3 2 2
+ 4*u3*v3*a33*m1*n1*n3 + v1*v3 *( - a33 *m1 - a33 *m1*m2 )
2 2 2
+ 2*v1*v3*a33*m1 *n1*n3 + 2*v1*m1*n1 *n3
2 2 2 2 2 2 2 2 2 3
+ v2 *( - a33*m1 *n1 - a33*m2 *n1 ) + v2*v3 *( - a33 *m1 *m2 - a33 *m2 )
2 2 2 2 2 2 2
+ 2*v2*v3*a33*m1*m2*n1*n3 + v3 *( - a33*m1 *n1 - a33*m1 *n3 - a33*m2 *n3 )
3
+ 2*v3*m1*n1*n3
which the program can not factorize further.
{HAM,FI} = 0
3 3 2 3 2 3
FI=u1 *v1*a33*n1 + u1 *u2*v2*a33*n1 + u1 *u3*v3*a33*n1
2 2 2 4 2 2 2
+ 2*u1 *v1*v2*a33*m2*n1 - u1 *v1*n1 + u1 *v2 *a33*m1*n1
2 2 2 2 3 2 2
+ u1 *v3 *a33*m1*n1 + u1*u2 *v1*a33*n1 - 2*u1*u2*v1 *a33*m2*n1
2 2 2 4
- 2*u1*u2*v1*v2*a33*m1*n1 + 2*u1*u2*v2 *a33*m2*n1 - u1*u2*v2*n1
3 2 4
- u1*u3*v1*n1 *n3 + 2*u1*u3*v2*v3*a33*m2*n1 - u1*u3*v3*n1
2 3
+ 2*u1*v1 *v2*a33*m1*m2*n1 - u1*v1*v2*m2*n1
2 2 2 2
+ u1*v1*v3 *( - a33*m1 *n1 - a33*m2 *n1) + 2*u1*v1*v3*m1*n1 *n3
3 2 3 2
+ 2*u1*v2 *a33*m1*m2*n1 - u1*v2 *m1*n1 + 2*u1*v2*v3 *a33*m1*m2*n1
2 3 3 3 2 3 2 2 2
- u1*v3 *m1*n1 + u2 *v2*a33*n1 + u2 *u3*v3*a33*n1 + u2 *v1 *a33*m1*n1
2 2 2 2 2 2
- 2*u2 *v1*v2*a33*m2*n1 + u2 *v3 *a33*m1*n1 - 2*u2*u3*v1*v3*a33*m2*n1
3 3 2
- u2*u3*v2*n1 *n3 - 2*u2*v1 *a33*m1*m2*n1 - 2*u2*v1*v2 *a33*m1*m2*n1
3 2 2 3
+ u2*v1*v2*m1*n1 - 2*u2*v1*v3 *a33*m1*m2*n1 - u2*v2 *m2*n1
2 2 2 2
+ u2*v2*v3 *( - a33*m1 *n1 - a33*m2 *n1) + 2*u2*v2*v3*m1*n1 *n3
2 2 2 2 3 2 2
+ u3 *v3 *a33*m1*n1 - u3 *v3*n1 *n3 + 2*u3*v1 *v3*a33*m1 *n1
2 2 3 2 2
- u3*v1 *m1*n1 *n3 + u3*v1*v3*m1*n1 + 2*u3*v2 *v3*a33*m1 *n1
2 2 3 3 2 2
- u3*v2 *m1*n1 *n3 - u3*v2*v3*m2*n1 + u3*v3 *(a33*m1 *n1 - a33*m2 *n1)
2 2 3 2 2 2 2
+ u3*v3 *m1*n1 *n3 + v1 *m1 *n1 - v1 *v2*m1*m2*n1
2 2 3 2 2 2 2 2 2
+ v1 *v3 *( - a33*m1 - a33*m1*m2 ) + 2*v1 *v3*m1 *n1*n3 + v1*v2 *m1 *n1
2 2 2 3 2 2 2 3 2
+ v1*v3 *m1 *n1 - v2 *m1*m2*n1 + v2 *v3 *( - a33*m1 - a33*m1*m2 )
2 2 2 2 4 3 2
+ 2*v2 *v3*m1 *n1*n3 - v2*v3 *m1*m2*n1 + v3 *( - a33*m1 - a33*m1*m2 )
3 2
+ 2*v3 *m1 *n1*n3
which the program can not factorize further.
{HAM,FI} = 0
4 2 4 3 2 3 3 5 2 2 2 4
FI=u1 *a33 *n1 + 4*u1 *v2*a33 *m2*n1 - u1 *a33*n1 + 2*u1 *u2 *a33 *n1
2 2 3 2 2 2 4 2 2 3
- 4*u1 *u2*v1*a33 *m2*n1 + u1 *u3 *a33 *n1 + 4*u1 *u3*v3*a33 *m1*n1
2 4 2 4 2 2 2 2 2
- u1 *u3*a33*n1 *n3 + 3*u1 *v1*a33*m1*n1 + 4*u1 *v2 *a33 *m2 *n1
2 4 2 2 2 2 2 2 2 2
- 3*u1 *v2*a33*m2*n1 + u1 *v3 *( - 2*a33 *m1 *n1 - 2*a33 *m2 *n1 )
2 3 2 2 3 2 5
+ 4*u1 *v3*a33*m1*n1 *n3 + 4*u1*u2 *v2*a33 *m2*n1 - u1*u2 *a33*n1
2 2 2 4
- 8*u1*u2*v1*v2*a33 *m2 *n1 + 2*u1*u2*v1*a33*m2*n1
2 2 3 2 5 2 2
+ 2*u1*u3 *v2*a33 *m2*n1 - u1*u3 *a33*n1 + 8*u1*u3*v2*v3*a33 *m1*m2*n1
3 4
- 2*u1*u3*v2*a33*m2*n1 *n3 - 2*u1*u3*v3*a33*m1*n1
3 5 2 2 3
+ 6*u1*v1*v2*a33*m1*m2*n1 - 2*u1*v1*m1*n1 - 2*u1*v2 *a33*m2 *n1
2 2 2 2 3
+ u1*v2*v3 *( - 4*a33 *m1 *m2*n1 - 4*a33 *m2 *n1)
2 2 2 3 2 3
+ 8*u1*v2*v3*a33*m1*m2*n1 *n3 + u1*v3 *(a33*m1 *n1 + a33*m2 *n1 )
4 4 2 4 3 2 3 2 2 2 4
- 2*u1*v3*m1*n1 *n3 + u2 *a33 *n1 - 4*u2 *v1*a33 *m2*n1 + u2 *u3 *a33 *n1
2 2 3 2 4 2 2 2 2 2
+ 4*u2 *u3*v3*a33 *m1*n1 - u2 *u3*a33*n1 *n3 + 4*u2 *v1 *a33 *m2 *n1
2 4 2 4
+ 3*u2 *v1*a33*m1*n1 - u2 *v2*a33*m2*n1
2 2 2 2 2 2 2 2 2 3
+ u2 *v3 *( - 2*a33 *m1 *n1 - 2*a33 *m2 *n1 ) + 4*u2 *v3*a33*m1*n1 *n3
2 2 3 2 2
- 2*u2*u3 *v1*a33 *m2*n1 - 8*u2*u3*v1*v3*a33 *m1*m2*n1
3 2 3 2 3
+ 2*u2*u3*v1*a33*m2*n1 *n3 - 6*u2*v1 *a33*m1*m2*n1 + 2*u2*v1*v2*a33*m2 *n1
2 2 2 2 3 2
+ u2*v1*v3 *(4*a33 *m1 *m2*n1 + 4*a33 *m2 *n1) - 8*u2*v1*v3*a33*m1*m2*n1 *n3
3 2 3 3 4 2 4
+ 2*u3 *v3*a33 *m1*n1 - u3 *a33*n1 *n3 + u3 *v1*a33*m1*n1
2 4 2 2 2 2 2 2 2 2
- u3 *v2*a33*m2*n1 + u3 *v3 *(3*a33 *m1 *n1 - a33 *m2 *n1 )
2 3 4 3
+ 6*u3*v1*v3*a33*m1 *n1 - 2*u3*v1*m1*n1 *n3 - 2*u3*v2*v3*a33*m1*m2*n1
3 2 3 2 2
+ u3*v3 *( - 4*a33 *m1 *n1 - 4*a33 *m1*m2 *n1)
2 2 2 2 2 3 2
+ u3*v3 *(9*a33*m1 *n1 *n3 + a33*m2 *n1 *n3) - 2*u3*v3*m1*n1 *n3
4 2 3 2 2 2
- 2*v1*v2*m1*m2*n1 + v1*v3 *( - 3*a33*m1 *n1 - 3*a33*m1*m2 *n1 )
2 3 2 2 4 2 2 2 3 2
+ 6*v1*v3*m1 *n1 *n3 - 2*v2 *m1 *n1 + v2*v3 *(a33*m1 *m2*n1 + a33*m2 *n1 )
3 4 2 4 2 2 2 2 4
- 2*v2*v3*m1*m2*n1 *n3 + v3 *(a33 *m1 + 2*a33 *m1 *m2 + a33 *m2 )
3 3 2
+ v3 *( - 4*a33*m1 *n1*n3 - 4*a33*m1*m2 *n1*n3)
2 2 4 2 2 2
+ v3 *( - 2*m1 *n1 + 4*m1 *n1 *n3 )
which the program can not factorize further.
{HAM,FI} = 0
And again in machine readable form:
HAM=u1*n1 + u3**2*a33 + u3*n3 + v1*m1 + v2*m2$
FI= - u1**2*v2**2*a33*n1**2 - u1**2*v3**2*a33*n1**2 + 2*u1*u2*v1*v2*a33*n1**2 +
2*u1*u3*v1*v3*a33*n1**2 - 2*u1*v1**2*v2*a33*m2*n1 + u1*v1**2*n1**3 - 2*u1*v2**3*
a33*m2*n1 + u1*v2**2*n1**3 - 2*u1*v2*v3**2*a33*m2*n1 + u1*v3**2*n1**3 - u2**2*v1
**2*a33*n1**2 - u2**2*v3**2*a33*n1**2 + 2*u2*u3*v2*v3*a33*n1**2 + 2*u2*v1**3*a33
*m2*n1 + 2*u2*v1*v2**2*a33*m2*n1 + 2*u2*v1*v3**2*a33*m2*n1 + u3**2*v3**2*a33*n1
**2 - 2*u3*v1**2*v3*a33*m1*n1 + u3*v1**2*n1**2*n3 - 2*u3*v2**2*v3*a33*m1*n1 + u3
*v2**2*n1**2*n3 - 2*u3*v3**3*a33*m1*n1 + u3*v3**2*n1**2*n3 - v1**3*m1*n1**2 + v1
**2*v2*m2*n1**2 + v1**2*v3**2*(a33*m1**2 + a33*m2**2) - 2*v1**2*v3*m1*n1*n3 - v1
*v2**2*m1*n1**2 - v1*v3**2*m1*n1**2 + v2**3*m2*n1**2 + v2**2*v3**2*(a33*m1**2 +
a33*m2**2) - 2*v2**2*v3*m1*n1*n3 + v2*v3**2*m2*n1**2 + v3**4*(a33*m1**2 + a33*m2
**2) - 2*v3**3*m1*n1*n3$
FI=u1**3*a33**2*n1**3 + u1**2*u3**2*a33**3*n1**2 + u1**2*u3*a33**2*n1**2*n3 + u1
**2*v1*a33**2*m1*n1**2 + 3*u1**2*v2*a33**2*m2*n1**2 - u1**2*a33*n1**4 + u1*u2**2
*a33**2*n1**3 - 2*u1*u2*v1*a33**2*m2*n1**2 + 2*u1*u3**2*v2*a33**3*m2*n1 - u1*u3
**2*a33**2*n1**3 + 2*u1*u3*v2*a33**2*m2*n1*n3 + 2*u1*u3*v3*a33**2*m1*n1**2 - 2*
u1*u3*a33*n1**3*n3 + 2*u1*v1*v2*a33**2*m1*m2*n1 + 2*u1*v2**2*a33**2*m2**2*n1 - 2
*u1*v2*a33*m2*n1**3 + u1*v3**2*( - a33**2*m1**2*n1 - a33**2*m2**2*n1) + 2*u1*v3*
a33*m1*n1**2*n3 + u1*n1**3*n3**2 + u2**2*u3**2*a33**3*n1**2 + u2**2*u3*a33**2*n1
**2*n3 + u2**2*v1*a33**2*m1*n1**2 + u2**2*v2*a33**2*m2*n1**2 - 2*u2*u3**2*v1*a33
**3*m2*n1 - 2*u2*u3*v1*a33**2*m2*n1*n3 - 2*u2*v1**2*a33**2*m1*m2*n1 - 2*u2*v1*v2
*a33**2*m2**2*n1 + 2*u3**3*v3*a33**3*m1*n1 - u3**3*a33**2*n1**2*n3 + u3**2*v1*
a33**2*m1*n1**2 - u3**2*v2*a33**2*m2*n1**2 + u3**2*v3**2*( - a33**3*m1**2 - a33
**3*m2**2) + 4*u3**2*v3*a33**2*m1*n1*n3 + 2*u3*v1*v3*a33**2*m1**2*n1 + 2*u3*v2*
v3*a33**2*m1*m2*n1 - 2*u3*v2*a33*m2*n1**2*n3 + u3*v3**2*( - a33**2*m1**2*n3 -
a33**2*m2**2*n3) + 2*u3*v3*a33*m1*n1*n3**2 + u3*n1**2*n3**3 + v1*v3**2*( - a33**
2*m1**3 - a33**2*m1*m2**2) + 2*v1*v3*a33*m1**2*n1*n3 + v1*m1*n1**2*n3**2 + v2**2
*( - a33*m1**2*n1**2 - a33*m2**2*n1**2) + v2*v3**2*( - a33**2*m1**2*m2 - a33**2*
m2**3) + 2*v2*v3*a33*m1*m2*n1*n3 + v2*m2*n1**2*n3**2 - v3**2*a33*m1**2*n1**2$
FI=u1**3*a33**2*n1**3 + u1**2*u3**2*a33**3*n1**2 + u1**2*u3*a33**2*n1**2*n3 + u1
**2*v1*a33**2*m1*n1**2 + 3*u1**2*v2*a33**2*m2*n1**2 + u1**2*( - a33*n1**4 + a33*
n1**2*n3**2) + u1*u2**2*a33**2*n1**3 - 2*u1*u2*v1*a33**2*m2*n1**2 + 2*u1*u3**2*
v2*a33**3*m2*n1 - u1*u3**2*a33**2*n1**3 + 2*u1*u3*v2*a33**2*m2*n1*n3 + 2*u1*u3*
v3*a33**2*m1*n1**2 - 2*u1*u3*a33*n1**3*n3 + 2*u1*v1*v2*a33**2*m1*m2*n1 + 2*u1*v2
**2*a33**2*m2**2*n1 + u1*v2*( - 2*a33*m2*n1**3 + 2*a33*m2*n1*n3**2) + u1*v3**2*(
- a33**2*m1**2*n1 - a33**2*m2**2*n1) + 2*u1*v3*a33*m1*n1**2*n3 + u2**2*u3**2*
a33**3*n1**2 + u2**2*u3*a33**2*n1**2*n3 + u2**2*v1*a33**2*m1*n1**2 + u2**2*v2*
a33**2*m2*n1**2 + u2**2*a33*n1**2*n3**2 - 2*u2*u3**2*v1*a33**3*m2*n1 - 2*u2*u3*
v1*a33**2*m2*n1*n3 - 2*u2*v1**2*a33**2*m1*m2*n1 - 2*u2*v1*v2*a33**2*m2**2*n1 - 2
*u2*v1*a33*m2*n1*n3**2 + 2*u3**3*v3*a33**3*m1*n1 - u3**3*a33**2*n1**2*n3 + u3**2
*v1*a33**2*m1*n1**2 - u3**2*v2*a33**2*m2*n1**2 + u3**2*v3**2*( - a33**3*m1**2 -
a33**3*m2**2) + 4*u3**2*v3*a33**2*m1*n1*n3 + 2*u3*v1*v3*a33**2*m1**2*n1 + 2*u3*
v2*v3*a33**2*m1*m2*n1 - 2*u3*v2*a33*m2*n1**2*n3 + u3*v3**2*( - a33**2*m1**2*n3 -
a33**2*m2**2*n3) + 4*u3*v3*a33*m1*n1*n3**2 + v1*v3**2*( - a33**2*m1**3 - a33**2
*m1*m2**2) + 2*v1*v3*a33*m1**2*n1*n3 + 2*v1*m1*n1**2*n3**2 + v2**2*( - a33*m1**2
*n1**2 - a33*m2**2*n1**2) + v2*v3**2*( - a33**2*m1**2*m2 - a33**2*m2**3) + 2*v2*
v3*a33*m1*m2*n1*n3 + v3**2*( - a33*m1**2*n1**2 - a33*m1**2*n3**2 - a33*m2**2*n3
**2) + 2*v3*m1*n1*n3**3$
FI=u1**3*v1*a33*n1**3 + u1**2*u2*v2*a33*n1**3 + u1**2*u3*v3*a33*n1**3 + 2*u1**2*
v1*v2*a33*m2*n1**2 - u1**2*v1*n1**4 + u1**2*v2**2*a33*m1*n1**2 + u1**2*v3**2*a33
*m1*n1**2 + u1*u2**2*v1*a33*n1**3 - 2*u1*u2*v1**2*a33*m2*n1**2 - 2*u1*u2*v1*v2*
a33*m1*n1**2 + 2*u1*u2*v2**2*a33*m2*n1**2 - u1*u2*v2*n1**4 - u1*u3*v1*n1**3*n3 +
2*u1*u3*v2*v3*a33*m2*n1**2 - u1*u3*v3*n1**4 + 2*u1*v1**2*v2*a33*m1*m2*n1 - u1*
v1*v2*m2*n1**3 + u1*v1*v3**2*( - a33*m1**2*n1 - a33*m2**2*n1) + 2*u1*v1*v3*m1*n1
**2*n3 + 2*u1*v2**3*a33*m1*m2*n1 - u1*v2**2*m1*n1**3 + 2*u1*v2*v3**2*a33*m1*m2*
n1 - u1*v3**2*m1*n1**3 + u2**3*v2*a33*n1**3 + u2**2*u3*v3*a33*n1**3 + u2**2*v1**
2*a33*m1*n1**2 - 2*u2**2*v1*v2*a33*m2*n1**2 + u2**2*v3**2*a33*m1*n1**2 - 2*u2*u3
*v1*v3*a33*m2*n1**2 - u2*u3*v2*n1**3*n3 - 2*u2*v1**3*a33*m1*m2*n1 - 2*u2*v1*v2**
2*a33*m1*m2*n1 + u2*v1*v2*m1*n1**3 - 2*u2*v1*v3**2*a33*m1*m2*n1 - u2*v2**2*m2*n1
**3 + u2*v2*v3**2*( - a33*m1**2*n1 - a33*m2**2*n1) + 2*u2*v2*v3*m1*n1**2*n3 + u3
**2*v3**2*a33*m1*n1**2 - u3**2*v3*n1**3*n3 + 2*u3*v1**2*v3*a33*m1**2*n1 - u3*v1
**2*m1*n1**2*n3 + u3*v1*v3*m1*n1**3 + 2*u3*v2**2*v3*a33*m1**2*n1 - u3*v2**2*m1*
n1**2*n3 - u3*v2*v3*m2*n1**3 + u3*v3**3*(a33*m1**2*n1 - a33*m2**2*n1) + u3*v3**2
*m1*n1**2*n3 + v1**3*m1**2*n1**2 - v1**2*v2*m1*m2*n1**2 + v1**2*v3**2*( - a33*m1
**3 - a33*m1*m2**2) + 2*v1**2*v3*m1**2*n1*n3 + v1*v2**2*m1**2*n1**2 + v1*v3**2*
m1**2*n1**2 - v2**3*m1*m2*n1**2 + v2**2*v3**2*( - a33*m1**3 - a33*m1*m2**2) + 2*
v2**2*v3*m1**2*n1*n3 - v2*v3**2*m1*m2*n1**2 + v3**4*( - a33*m1**3 - a33*m1*m2**2
) + 2*v3**3*m1**2*n1*n3$
FI=u1**4*a33**2*n1**4 + 4*u1**3*v2*a33**2*m2*n1**3 - u1**3*a33*n1**5 + 2*u1**2*
u2**2*a33**2*n1**4 - 4*u1**2*u2*v1*a33**2*m2*n1**3 + u1**2*u3**2*a33**2*n1**4 +
4*u1**2*u3*v3*a33**2*m1*n1**3 - u1**2*u3*a33*n1**4*n3 + 3*u1**2*v1*a33*m1*n1**4
+ 4*u1**2*v2**2*a33**2*m2**2*n1**2 - 3*u1**2*v2*a33*m2*n1**4 + u1**2*v3**2*( - 2
*a33**2*m1**2*n1**2 - 2*a33**2*m2**2*n1**2) + 4*u1**2*v3*a33*m1*n1**3*n3 + 4*u1*
u2**2*v2*a33**2*m2*n1**3 - u1*u2**2*a33*n1**5 - 8*u1*u2*v1*v2*a33**2*m2**2*n1**2
+ 2*u1*u2*v1*a33*m2*n1**4 + 2*u1*u3**2*v2*a33**2*m2*n1**3 - u1*u3**2*a33*n1**5
+ 8*u1*u3*v2*v3*a33**2*m1*m2*n1**2 - 2*u1*u3*v2*a33*m2*n1**3*n3 - 2*u1*u3*v3*a33
*m1*n1**4 + 6*u1*v1*v2*a33*m1*m2*n1**3 - 2*u1*v1*m1*n1**5 - 2*u1*v2**2*a33*m2**2
*n1**3 + u1*v2*v3**2*( - 4*a33**2*m1**2*m2*n1 - 4*a33**2*m2**3*n1) + 8*u1*v2*v3*
a33*m1*m2*n1**2*n3 + u1*v3**2*(a33*m1**2*n1**3 + a33*m2**2*n1**3) - 2*u1*v3*m1*
n1**4*n3 + u2**4*a33**2*n1**4 - 4*u2**3*v1*a33**2*m2*n1**3 + u2**2*u3**2*a33**2*
n1**4 + 4*u2**2*u3*v3*a33**2*m1*n1**3 - u2**2*u3*a33*n1**4*n3 + 4*u2**2*v1**2*
a33**2*m2**2*n1**2 + 3*u2**2*v1*a33*m1*n1**4 - u2**2*v2*a33*m2*n1**4 + u2**2*v3
**2*( - 2*a33**2*m1**2*n1**2 - 2*a33**2*m2**2*n1**2) + 4*u2**2*v3*a33*m1*n1**3*
n3 - 2*u2*u3**2*v1*a33**2*m2*n1**3 - 8*u2*u3*v1*v3*a33**2*m1*m2*n1**2 + 2*u2*u3*
v1*a33*m2*n1**3*n3 - 6*u2*v1**2*a33*m1*m2*n1**3 + 2*u2*v1*v2*a33*m2**2*n1**3 +
u2*v1*v3**2*(4*a33**2*m1**2*m2*n1 + 4*a33**2*m2**3*n1) - 8*u2*v1*v3*a33*m1*m2*n1
**2*n3 + 2*u3**3*v3*a33**2*m1*n1**3 - u3**3*a33*n1**4*n3 + u3**2*v1*a33*m1*n1**4
- u3**2*v2*a33*m2*n1**4 + u3**2*v3**2*(3*a33**2*m1**2*n1**2 - a33**2*m2**2*n1**
2) + 6*u3*v1*v3*a33*m1**2*n1**3 - 2*u3*v1*m1*n1**4*n3 - 2*u3*v2*v3*a33*m1*m2*n1
**3 + u3*v3**3*( - 4*a33**2*m1**3*n1 - 4*a33**2*m1*m2**2*n1) + u3*v3**2*(9*a33*
m1**2*n1**2*n3 + a33*m2**2*n1**2*n3) - 2*u3*v3*m1*n1**3*n3**2 - 2*v1*v2*m1*m2*n1
**4 + v1*v3**2*( - 3*a33*m1**3*n1**2 - 3*a33*m1*m2**2*n1**2) + 6*v1*v3*m1**2*n1
**3*n3 - 2*v2**2*m1**2*n1**4 + v2*v3**2*(a33*m1**2*m2*n1**2 + a33*m2**3*n1**2) -
2*v2*v3*m1*m2*n1**3*n3 + v3**4*(a33**2*m1**4 + 2*a33**2*m1**2*m2**2 + a33**2*m2
**4) + v3**3*( - 4*a33*m1**3*n1*n3 - 4*a33*m1*m2**2*n1*n3) + v3**2*( - 2*m1**2*
n1**4 + 4*m1**2*n1**2*n3**2)$