Solution 8 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
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Expressions
The solution is given through the following expressions:
r10=0
r11=0
r12=0
3 6 3 3 4 5 3 2 7
r13=(2*a22 *n1 *n3 *r29 + 10*a22 *n1 *n3 *r29 + 16*a22 *n1 *n3 *r29
3 9 2 6 3 2 4 5
+ 8*a22 *n3 *r29 + 6*a22 *a33*n1 *n3 *r29 + 22*a22 *a33*n1 *n3 *r29
2 2 7 2 9 2 6 3
+ 24*a22 *a33*n1 *n3 *r29 + 8*a22 *a33*n3 *r29 + 6*a22*a33 *n1 *n3 *r29
2 4 5 2 2 7 4 7
+ 14*a22*a33 *n1 *n3 *r29 + 8*a22*a33 *n1 *n3 *r29 - 2*a22*n1 *n3 *r4119
2 9 11 3 6 3
- a22*n1 *n3 *r4119 + 3*a22*n3 *r4119 + 2*a33 *n1 *n3 *r29
3 4 5 4 7 2 9
+ 2*a33 *n1 *n3 *r29 - 2*a33*n1 *n3 *r4119 + a33*n1 *n3 *r4119
11 4 8 4 6 2 4 4 4
+ a33*n3 *r4119)/(2*a22 *n1 + 12*a22 *n1 *n3 + 26*a22 *n1 *n3
4 2 6 4 8 3 8 3 6 2
+ 24*a22 *n1 *n3 + 8*a22 *n3 + 8*a22 *a33*n1 + 40*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 72*a22 *a33*n1 *n3 + 56*a22 *a33*n1 *n3 + 16*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 12*a22 *a33 *n1 + 48*a22 *a33 *n1 *n3 + 68*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 40*a22 *a33 *n1 *n3 + 8*a22 *a33 *n3 + 8*a22*a33 *n1
3 6 2 3 4 4 3 2 6
+ 24*a22*a33 *n1 *n3 + 24*a22*a33 *n1 *n3 + 8*a22*a33 *n1 *n3
4 8 4 6 2 4 4 4
+ 2*a33 *n1 + 4*a33 *n1 *n3 + 2*a33 *n1 *n3 )
r14=0
r20=0
r21=0
r22=0
r23=0
r24=0
r26=0
r27=0
r28=0
r210=0
r212=0
r213=0
4 8 4 6 2 4 4 4
r214=(a22 *n1 *r29 + 7*a22 *n1 *n3 *r29 + 18*a22 *n1 *n3 *r29
4 2 6 4 8 3 8
+ 20*a22 *n1 *n3 *r29 + 8*a22 *n3 *r29 + 4*a22 *a33*n1 *r29
3 6 2 3 4 4
+ 22*a22 *a33*n1 *n3 *r29 + 42*a22 *a33*n1 *n3 *r29
3 2 6 3 8 2 2 8
+ 32*a22 *a33*n1 *n3 *r29 + 8*a22 *a33*n3 *r29 + 6*a22 *a33 *n1 *r29
2 2 6 2 2 2 4 4
+ 24*a22 *a33 *n1 *n3 *r29 + 30*a22 *a33 *n1 *n3 *r29
2 2 2 6 2 2 8 2 10
+ 12*a22 *a33 *n1 *n3 *r29 + 2*a22 *n1 *n3 *r4119 + 3*a22 *n3 *r4119
3 8 3 6 2 3 4 4
+ 4*a22*a33 *n1 *r29 + 10*a22*a33 *n1 *n3 *r29 + 6*a22*a33 *n1 *n3 *r29
4 6 2 8 10
+ 2*a22*a33*n1 *n3 *r4119 + 5*a22*a33*n1 *n3 *r4119 + a22*a33*n3 *r4119
4 8 4 6 2 2 4 6
+ a33 *n1 *r29 + a33 *n1 *n3 *r29 + 2*a33 *n1 *n3 *r4119
2 2 8 4 8 4 6 2 4 4 4
+ a33 *n1 *n3 *r4119)/(a22 *n1 + 6*a22 *n1 *n3 + 13*a22 *n1 *n3
4 2 6 4 8 3 8 3 6 2
+ 12*a22 *n1 *n3 + 4*a22 *n3 + 4*a22 *a33*n1 + 20*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 36*a22 *a33*n1 *n3 + 28*a22 *a33*n1 *n3 + 8*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 6*a22 *a33 *n1 + 24*a22 *a33 *n1 *n3 + 34*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 20*a22 *a33 *n1 *n3 + 4*a22 *a33 *n3 + 4*a22*a33 *n1
3 6 2 3 4 4 3 2 6 4 8
+ 12*a22*a33 *n1 *n3 + 12*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3 + a33 *n1
4 6 2 4 4 4
+ 2*a33 *n1 *n3 + a33 *n1 *n3 )
r215=0
r216=0
r217=0
3 5 7 3 5
r218=( - 2*a22*n1 *n3 *r4119 - 3*a22*n1*n3 *r4119 - 2*a33*n1 *n3 *r4119
7 3 6 3 4 2 3 2 4
- a33*n1*n3 *r4119)/(a22 *n1 + 5*a22 *n1 *n3 + 8*a22 *n1 *n3
3 6 2 6 2 4 2 2 2 4
+ 4*a22 *n3 + 3*a22 *a33*n1 + 11*a22 *a33*n1 *n3 + 12*a22 *a33*n1 *n3
2 6 2 6 2 4 2 2 2 4
+ 4*a22 *a33*n3 + 3*a22*a33 *n1 + 7*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3
3 6 3 4 2
+ a33 *n1 + a33 *n1 *n3 )
r219=0
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
r37=0
r38=0
r39=0
r310=0
r311=0
r312=0
r313=0
r314=0
r315=0
3
n3 *r4102
r316=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r317=0
r318=0
2 3 5 2 3 5
r319=( - a22*n1 *n3 *r4119 - a22*n3 *r4119 - a33*n1 *n3 *r4119 - a33*n3 *r4119)/
2 4 2 2 2 2 4 4 2 2
(a22 *n1 + 4*a22 *n1 *n3 + 4*a22 *n3 + 2*a22*a33*n1 + 4*a22*a33*n1 *n3
2 4
+ a33 *n1 )
r320=0
r321=0
r322=0
r323=0
r324=0
r325=0
r326=0
3
n3 *r4102
r327=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r328=0
r329=0
r330=0
r331=0
r332=0
3
- n3 *r4119
r333=---------------------------------------
2 2 2 2
a22*n1 + a22*n3 + a33*n1 + a33*n3
r334=0
r335=0
r336=0
r337=0
r338=0
r339=0
r340=0
2
n1*n3 *r4102
r341=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r342=0
3
n3 *r4102
r343=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
3 2 4 3 2
r344=( - a22*n1 *n3 *r4119 - a22*n1*n3 *r4119 - a33*n1 *n3 *r4119
4 2 4 2 2 2 2 4
- a33*n1*n3 *r4119)/(a22 *n1 + 4*a22 *n1 *n3 + 4*a22 *n3
4 2 2 2 4
+ 2*a22*a33*n1 + 4*a22*a33*n1 *n3 + a33 *n1 )
r345=0
2
n1*n3 *r4102
r346=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r347=0
r348=0
2
- n1*n3 *r4119
r349=---------------------------------------
2 2 2 2
a22*n1 + a22*n3 + a33*n1 + a33*n3
r350=0
r351=0
2
n1*n3 *r4102
r352=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
3
n3 *r4119
r353=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r354=0
2
n1*n3 *r4119
r355=-------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r40=0
r41=0
r42=0
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
r49=0
r410=0
r411=0
r412=0
r413=0
r415=0
r416=0
r417=0
r418=0
r419=0
r420=0
r421=0
r422=0
r423=0
r424=0
r425=0
r426=0
- r446
r427=---------
2
r428=0
r429=0
- r446
r430=---------
2
2 2 2 2
a22*n1 *r4102 + a22*n3 *r4102 + a33*n1 *r4102 + a33*n3 *r4102
r431=---------------------------------------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r432=0
r433=0
2 2 2 2 4 2 2 2 2 4
r434=(a22 *n1 *n3 *r4119 + a22 *n3 *r4119 - a33 *n1 *n3 *r4119 - a33 *n3 *r4119)
2 4 2 2 2 2 4 4 2 2
/(2*a22 *n1 + 8*a22 *n1 *n3 + 8*a22 *n3 + 4*a22*a33*n1 + 8*a22*a33*n1 *n3
2 4
+ 2*a33 *n1 )
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
r447=0
r448=0
r449=0
r450=0
r451=0
2 2 2 2
a22*n1 *r4102 + a22*n3 *r4102 + a33*n1 *r4102 + a33*n3 *r4102
r452=---------------------------------------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r453=0
r454=0
- r446
r455=---------
2
r456=0
r458=0
r459=0
- r446
r460=---------
2
r461=r4102
r462=0
r463=0
r464=0
r465=0
r466=r4102
r467=0
r468=0
2 2
- a22*n3 *r4119 + a33*n3 *r4119
r469=-----------------------------------------------
2 2 2 2
2*a22*n1 + 2*a22*n3 + 2*a33*n1 + 2*a33*n3
r470=0
r471=0
r472=0
r473=0
r474=0
r475=0
r476=0
r477=0
r478=0
r479=0
r480=0
r481=0
r482=0
r483=r446
r484=0
r485=0
r486=0
r487=0
2 2 2 2
a22*n1 *r4102 + a22*n3 *r4102 + a33*n1 *r4102 + a33*n3 *r4102
r488=---------------------------------------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r489=0
r490=0
r491=0
r492=0
r493=0
r494=r446
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
r4103=0
r4104=0
- r446
r4105=---------
2
r4106=0
- r446
r4107=---------
2
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
2 2 2 2
a22*n1 *r4119 + a22*n3 *r4119 + a33*n1 *r4119 + a33*n3 *r4119
r4114=---------------------------------------------------------------
2 2 2
a22*n1 + 2*a22*n3 + a33*n1
r4115=0
r4117=0
r4118=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
m3=0
m2=0
m1=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
a13=0
a12=0
2 2 2
- a22*n1 - a22*n3 - a33*n1
a11=--------------------------------
2
n3
3 7 2 3 5 4 3 3 6
r15=(2*a22 *n1 *n3 *r29 + 10*a22 *n1 *n3 *r29 + 16*a22 *n1 *n3 *r29
3 8 2 7 2 2 5 4
+ 8*a22 *n1*n3 *r29 + 6*a22 *a33*n1 *n3 *r29 + 22*a22 *a33*n1 *n3 *r29
2 3 6 2 8 2 7 2
+ 24*a22 *a33*n1 *n3 *r29 + 8*a22 *a33*n1*n3 *r29 + 6*a22*a33 *n1 *n3 *r29
2 5 4 2 3 6 5 6
+ 14*a22*a33 *n1 *n3 *r29 + 8*a22*a33 *n1 *n3 *r29 - 2*a22*n1 *n3 *r4119
3 8 10 3 7 2
- a22*n1 *n3 *r4119 + 3*a22*n1*n3 *r4119 + 2*a33 *n1 *n3 *r29
3 5 4 5 6 3 8
+ 2*a33 *n1 *n3 *r29 - 2*a33*n1 *n3 *r4119 + a33*n1 *n3 *r4119
10 4 8 4 6 2 4 4 4
+ a33*n1*n3 *r4119)/(2*a22 *n1 + 12*a22 *n1 *n3 + 26*a22 *n1 *n3
4 2 6 4 8 3 8 3 6 2
+ 24*a22 *n1 *n3 + 8*a22 *n3 + 8*a22 *a33*n1 + 40*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 72*a22 *a33*n1 *n3 + 56*a22 *a33*n1 *n3 + 16*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 12*a22 *a33 *n1 + 48*a22 *a33 *n1 *n3 + 68*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 40*a22 *a33 *n1 *n3 + 8*a22 *a33 *n3 + 8*a22*a33 *n1
3 6 2 3 4 4 3 2 6
+ 24*a22*a33 *n1 *n3 + 24*a22*a33 *n1 *n3 + 8*a22*a33 *n1 *n3
4 8 4 6 2 4 4 4
+ 2*a33 *n1 + 4*a33 *n1 *n3 + 2*a33 *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:
r29, r4119, r4102, r446, n3, n1, a33, a22
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.
{{r4119,
2 2 2 2
a22*n1 *r4119 + a22*n3 *r4119 + a33*n1 *r4119 + a33*n3 *r4119,
a22*r446 - a33*r446,
r4102,
r446,
2 2 2 2
a22*n1 *r4102 + a22*n3 *r4102 + a33*n1 *r4102 + a33*n3 *r4102,
a22*r4119 - a33*r4119,
2 4 2 2 2 2 4 4
a22 *n1 *r4102 + 2*a22 *n1 *n3 *r4102 + a22 *n3 *r4102 + 2*a22*a33*n1 *r4102
2 2 4 2 4
+ 3*a22*a33*n1 *n3 *r4102 + a22*a33*n3 *r4102 + a33 *n1 *r4102
2 2 2
+ a33 *n1 *n3 *r4102,
2 4 2 2 2 2 4 4
a22 *n1 *r4102 + 3*a22 *n1 *n3 *r4102 + 2*a22 *n3 *r4102 + 2*a22*a33*n1 *r4102
2 2 4 2 4
+ 4*a22*a33*n1 *n3 *r4102 + 2*a22*a33*n3 *r4102 + a33 *n1 *r4102
2 2 2
+ a33 *n1 *n3 *r4102,
2 2 2 2 2 2 2 2
a22 *n1 *r4119 + a22 *n3 *r4119 - a33 *n1 *r4119 - a33 *n3 *r4119},
2 2 2 2 2 2
a22 *n1 + a22 *n3 - a33 *n1 ,
2 2 2
a22*n1 + a22*n3 + a33*n1 ,
2 2 2
a22*n1 + 2*a22*n3 + a33*n1 ,
n1 + i*n3,
n1 - i*n3,
a22 + a33,
a22 - a33,
a33,
a22,
n3}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a11*n3**2 + a22*n1**2 + a22*n3**2 + a33*n1**2,
a12,
a13,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
b33,
c11,
c12,
c13,
c22,
c23,
c33,
n2,
m1,
m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2 2 2
2 - a22*n1 - a22*n3 - a33*n1 2 2
HAM=u1 *-------------------------------- + u1*n1 + u2 *a22 + u3 *a33 + u3*n3
2
n3
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
2 2 2 2 2 2 2 2
FI= - u1 *v2 - u1 *v3 + 2*u1*u2*v1*v2 + 2*u1*u3*v1*v3 - u2 *v1 - u2 *v3
2 2 2 2
+ 2*u2*u3*v2*v3 - u3 *v1 - u3 *v2
which the program can not factorize further.
{HAM,FI} = 0
2 3 7 2 3 5 4 3 3 6 3 8
FI=u1 *v1*(a22 *n1 *n3 + 4*a22 *n1 *n3 + 5*a22 *n1 *n3 + 2*a22 *n1*n3
2 7 2 2 5 4 2 3 6
+ 3*a22 *a33*n1 *n3 + 10*a22 *a33*n1 *n3 + 11*a22 *a33*n1 *n3
2 8 2 7 2 2 5 4
+ 4*a22 *a33*n1*n3 + 3*a22*a33 *n1 *n3 + 8*a22*a33 *n1 *n3
2 3 6 2 8 3 7 2
+ 7*a22*a33 *n1 *n3 + 2*a22*a33 *n1*n3 + a33 *n1 *n3
3 5 4 3 3 6 2 4 8
+ 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u1*u2 *v1*(a22 *n1
4 6 2 4 4 4 4 2 6 4 8
+ 6*a22 *n1 *n3 + 13*a22 *n1 *n3 + 12*a22 *n1 *n3 + 4*a22 *n3
3 8 3 6 2 3 4 4
+ 4*a22 *a33*n1 + 20*a22 *a33*n1 *n3 + 36*a22 *a33*n1 *n3
3 2 6 3 8 2 2 8
+ 28*a22 *a33*n1 *n3 + 8*a22 *a33*n3 + 6*a22 *a33 *n1
2 2 6 2 2 2 4 4 2 2 2 6
+ 24*a22 *a33 *n1 *n3 + 34*a22 *a33 *n1 *n3 + 20*a22 *a33 *n1 *n3
2 2 8 3 8 3 6 2
+ 4*a22 *a33 *n3 + 4*a22*a33 *n1 + 12*a22*a33 *n1 *n3
3 4 4 3 2 6 4 8 4 6 2
+ 12*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3 + a33 *n1 + 2*a33 *n1 *n3
4 4 4 3 7 2 3 5 4
+ a33 *n1 *n3 ) + u1*u2*v2*(a22 *n1 *n3 + 4*a22 *n1 *n3
3 3 6 3 8 2 7 2
+ 5*a22 *n1 *n3 + 2*a22 *n1*n3 + 3*a22 *a33*n1 *n3
2 5 4 2 3 6 2 8
+ 10*a22 *a33*n1 *n3 + 11*a22 *a33*n1 *n3 + 4*a22 *a33*n1*n3
2 7 2 2 5 4 2 3 6
+ 3*a22*a33 *n1 *n3 + 8*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3
2 8 3 7 2 3 5 4 3 3 6
+ 2*a22*a33 *n1*n3 + a33 *n1 *n3 + 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u1
2 4 8 4 6 2 4 4 4 4 2 6
*u3 *v1*(a22 *n1 + 5*a22 *n1 *n3 + 9*a22 *n1 *n3 + 7*a22 *n1 *n3
4 8 3 8 3 6 2
+ 2*a22 *n3 + 4*a22 *a33*n1 + 18*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 30*a22 *a33*n1 *n3 + 22*a22 *a33*n1 *n3 + 6*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 6*a22 *a33 *n1 + 24*a22 *a33 *n1 *n3 + 36*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 24*a22 *a33 *n1 *n3 + 6*a22 *a33 *n3 + 4*a22*a33 *n1
3 6 2 3 4 4 3 2 6
+ 14*a22*a33 *n1 *n3 + 18*a22*a33 *n1 *n3 + 10*a22*a33 *n1 *n3
3 8 4 8 4 6 2 4 4 4
+ 2*a22*a33 *n3 + a33 *n1 + 3*a33 *n1 *n3 + 3*a33 *n1 *n3
4 2 6 3 6 3 3 4 5
+ a33 *n1 *n3 ) + u1*u3*v1*(a22 *n1 *n3 + 4*a22 *n1 *n3
3 2 7 3 9 2 6 3 2 4 5
+ 5*a22 *n1 *n3 + 2*a22 *n3 + 3*a22 *a33*n1 *n3 + 10*a22 *a33*n1 *n3
2 2 7 2 9 2 6 3
+ 11*a22 *a33*n1 *n3 + 4*a22 *a33*n3 + 3*a22*a33 *n1 *n3
2 4 5 2 2 7 2 9 3 6 3
+ 8*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3 + 2*a22*a33 *n3 + a33 *n1 *n3
3 4 5 3 2 7 3 7 2
+ 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u1*u3*v3*(a22 *n1 *n3
3 5 4 3 3 6 3 8 2 7 2
+ 4*a22 *n1 *n3 + 5*a22 *n1 *n3 + 2*a22 *n1*n3 + 3*a22 *a33*n1 *n3
2 5 4 2 3 6 2 8
+ 10*a22 *a33*n1 *n3 + 11*a22 *a33*n1 *n3 + 4*a22 *a33*n1*n3
2 7 2 2 5 4 2 3 6
+ 3*a22*a33 *n1 *n3 + 8*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3
2 8 3 7 2 3 5 4 3 3 6 3
+ 2*a22*a33 *n1*n3 + a33 *n1 *n3 + 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u2
4 8 4 6 2 4 4 4 4 2 6
*v2*(a22 *n1 + 6*a22 *n1 *n3 + 13*a22 *n1 *n3 + 12*a22 *n1 *n3
4 8 3 8 3 6 2
+ 4*a22 *n3 + 4*a22 *a33*n1 + 20*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 36*a22 *a33*n1 *n3 + 28*a22 *a33*n1 *n3 + 8*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 6*a22 *a33 *n1 + 24*a22 *a33 *n1 *n3 + 34*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 20*a22 *a33 *n1 *n3 + 4*a22 *a33 *n3 + 4*a22*a33 *n1
3 6 2 3 4 4 3 2 6
+ 12*a22*a33 *n1 *n3 + 12*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3
4 8 4 6 2 4 4 4 2 4 8
+ a33 *n1 + 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u2 *u3*v3*(a22 *n1
4 6 2 4 4 4 4 2 6 4 8
+ 6*a22 *n1 *n3 + 13*a22 *n1 *n3 + 12*a22 *n1 *n3 + 4*a22 *n3
3 8 3 6 2 3 4 4
+ 4*a22 *a33*n1 + 20*a22 *a33*n1 *n3 + 36*a22 *a33*n1 *n3
3 2 6 3 8 2 2 8
+ 28*a22 *a33*n1 *n3 + 8*a22 *a33*n3 + 6*a22 *a33 *n1
2 2 6 2 2 2 4 4 2 2 2 6
+ 24*a22 *a33 *n1 *n3 + 34*a22 *a33 *n1 *n3 + 20*a22 *a33 *n1 *n3
2 2 8 3 8 3 6 2
+ 4*a22 *a33 *n3 + 4*a22*a33 *n1 + 12*a22*a33 *n1 *n3
3 4 4 3 2 6 4 8 4 6 2
+ 12*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3 + a33 *n1 + 2*a33 *n1 *n3
4 4 4 2 4 8 4 6 2 4 4 4
+ a33 *n1 *n3 ) + u2*u3 *v2*(a22 *n1 + 5*a22 *n1 *n3 + 9*a22 *n1 *n3
4 2 6 4 8 3 8 3 6 2
+ 7*a22 *n1 *n3 + 2*a22 *n3 + 4*a22 *a33*n1 + 18*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 30*a22 *a33*n1 *n3 + 22*a22 *a33*n1 *n3 + 6*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 6*a22 *a33 *n1 + 24*a22 *a33 *n1 *n3 + 36*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 24*a22 *a33 *n1 *n3 + 6*a22 *a33 *n3 + 4*a22*a33 *n1
3 6 2 3 4 4 3 2 6
+ 14*a22*a33 *n1 *n3 + 18*a22*a33 *n1 *n3 + 10*a22*a33 *n1 *n3
3 8 4 8 4 6 2 4 4 4
+ 2*a22*a33 *n3 + a33 *n1 + 3*a33 *n1 *n3 + 3*a33 *n1 *n3
4 2 6 3 6 3 3 4 5
+ a33 *n1 *n3 ) + u2*u3*v2*(a22 *n1 *n3 + 4*a22 *n1 *n3
3 2 7 3 9 2 6 3 2 4 5
+ 5*a22 *n1 *n3 + 2*a22 *n3 + 3*a22 *a33*n1 *n3 + 10*a22 *a33*n1 *n3
2 2 7 2 9 2 6 3
+ 11*a22 *a33*n1 *n3 + 4*a22 *a33*n3 + 3*a22*a33 *n1 *n3
2 4 5 2 2 7 2 9 3 6 3
+ 8*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3 + 2*a22*a33 *n3 + a33 *n1 *n3
3 4 5 3 2 7 3 4 8 4 6 2
+ 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u3 *v3*(a22 *n1 + 5*a22 *n1 *n3
4 4 4 4 2 6 4 8 3 8
+ 9*a22 *n1 *n3 + 7*a22 *n1 *n3 + 2*a22 *n3 + 4*a22 *a33*n1
3 6 2 3 4 4 3 2 6
+ 18*a22 *a33*n1 *n3 + 30*a22 *a33*n1 *n3 + 22*a22 *a33*n1 *n3
3 8 2 2 8 2 2 6 2
+ 6*a22 *a33*n3 + 6*a22 *a33 *n1 + 24*a22 *a33 *n1 *n3
2 2 4 4 2 2 2 6 2 2 8
+ 36*a22 *a33 *n1 *n3 + 24*a22 *a33 *n1 *n3 + 6*a22 *a33 *n3
3 8 3 6 2 3 4 4
+ 4*a22*a33 *n1 + 14*a22*a33 *n1 *n3 + 18*a22*a33 *n1 *n3
3 2 6 3 8 4 8 4 6 2
+ 10*a22*a33 *n1 *n3 + 2*a22*a33 *n3 + a33 *n1 + 3*a33 *n1 *n3
4 4 4 4 2 6 2 3 6 3 3 4 5
+ 3*a33 *n1 *n3 + a33 *n1 *n3 ) + u3 *v3*(a22 *n1 *n3 + 4*a22 *n1 *n3
3 2 7 3 9 2 6 3 2 4 5
+ 5*a22 *n1 *n3 + 2*a22 *n3 + 3*a22 *a33*n1 *n3 + 10*a22 *a33*n1 *n3
2 2 7 2 9 2 6 3
+ 11*a22 *a33*n1 *n3 + 4*a22 *a33*n3 + 3*a22*a33 *n1 *n3
2 4 5 2 2 7 2 9 3 6 3
+ 8*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3 + 2*a22*a33 *n3 + a33 *n1 *n3
3 4 5 3 2 7
+ 2*a33 *n1 *n3 + a33 *n1 *n3 )
= a product of the elements of: {n1 - i*n3,
n1 - i*n3,
n1 + i*n3,
n1 + i*n3,
a22 + a33,
a22 + a33,
u1*v1 + u2*v2 + u3*v3,
2 2 2
a22*n1 + 2*a22*n3 + a33*n1 ,
2 2 2 2 2
u1*n1*n3 + u2 *(a22*n1 + 2*a22*n3 + a33*n1 )
2 2 2 2 2 3
+ u3 *(a22*n1 + a22*n3 + a33*n1 + a33*n3 ) + u3*n3 }
{HAM,FI} = 0
3 3 7 2 3 5 4 3 3 6 3 8
FI=u1 *(2*a22 *n1 *n3 + 8*a22 *n1 *n3 + 10*a22 *n1 *n3 + 4*a22 *n1*n3
2 7 2 2 5 4 2 3 6
+ 6*a22 *a33*n1 *n3 + 20*a22 *a33*n1 *n3 + 22*a22 *a33*n1 *n3
2 8 2 7 2 2 5 4
+ 8*a22 *a33*n1*n3 + 6*a22*a33 *n1 *n3 + 16*a22*a33 *n1 *n3
2 3 6 2 8 3 7 2
+ 14*a22*a33 *n1 *n3 + 4*a22*a33 *n1*n3 + 2*a33 *n1 *n3
3 5 4 3 3 6 2 2 4 8
+ 4*a33 *n1 *n3 + 2*a33 *n1 *n3 ) + u1 *u2 *(2*a22 *n1
4 6 2 4 4 4 4 2 6 4 8
+ 12*a22 *n1 *n3 + 26*a22 *n1 *n3 + 24*a22 *n1 *n3 + 8*a22 *n3
3 8 3 6 2 3 4 4
+ 8*a22 *a33*n1 + 40*a22 *a33*n1 *n3 + 72*a22 *a33*n1 *n3
3 2 6 3 8 2 2 8
+ 56*a22 *a33*n1 *n3 + 16*a22 *a33*n3 + 12*a22 *a33 *n1
2 2 6 2 2 2 4 4 2 2 2 6
+ 48*a22 *a33 *n1 *n3 + 68*a22 *a33 *n1 *n3 + 40*a22 *a33 *n1 *n3
2 2 8 3 8 3 6 2
+ 8*a22 *a33 *n3 + 8*a22*a33 *n1 + 24*a22*a33 *n1 *n3
3 4 4 3 2 6 4 8 4 6 2
+ 24*a22*a33 *n1 *n3 + 8*a22*a33 *n1 *n3 + 2*a33 *n1 + 4*a33 *n1 *n3
4 4 4 2 2 4 8 4 6 2
+ 2*a33 *n1 *n3 ) + u1 *u3 *(2*a22 *n1 + 10*a22 *n1 *n3
4 4 4 4 2 6 4 8 3 8
+ 18*a22 *n1 *n3 + 14*a22 *n1 *n3 + 4*a22 *n3 + 8*a22 *a33*n1
3 6 2 3 4 4 3 2 6
+ 36*a22 *a33*n1 *n3 + 60*a22 *a33*n1 *n3 + 44*a22 *a33*n1 *n3
3 8 2 2 8 2 2 6 2
+ 12*a22 *a33*n3 + 12*a22 *a33 *n1 + 48*a22 *a33 *n1 *n3
2 2 4 4 2 2 2 6 2 2 8
+ 72*a22 *a33 *n1 *n3 + 48*a22 *a33 *n1 *n3 + 12*a22 *a33 *n3
3 8 3 6 2 3 4 4
+ 8*a22*a33 *n1 + 28*a22*a33 *n1 *n3 + 36*a22*a33 *n1 *n3
3 2 6 3 8 4 8 4 6 2
+ 20*a22*a33 *n1 *n3 + 4*a22*a33 *n3 + 2*a33 *n1 + 6*a33 *n1 *n3
4 4 4 4 2 6 2 3 6 3
+ 6*a33 *n1 *n3 + 2*a33 *n1 *n3 ) + u1 *u3*(2*a22 *n1 *n3
3 4 5 3 2 7 3 9 2 6 3
+ 8*a22 *n1 *n3 + 10*a22 *n1 *n3 + 4*a22 *n3 + 6*a22 *a33*n1 *n3
2 4 5 2 2 7 2 9
+ 20*a22 *a33*n1 *n3 + 22*a22 *a33*n1 *n3 + 8*a22 *a33*n3
2 6 3 2 4 5 2 2 7
+ 6*a22*a33 *n1 *n3 + 16*a22*a33 *n1 *n3 + 14*a22*a33 *n1 *n3
2 9 3 6 3 3 4 5 3 2 7
+ 4*a22*a33 *n3 + 2*a33 *n1 *n3 + 4*a33 *n1 *n3 + 2*a33 *n1 *n3 ) + u1
2 3 7 2 3 5 4 3 3 6 3 8
*u2 *( - 2*a22 *n1 *n3 - 10*a22 *n1 *n3 - 16*a22 *n1 *n3 - 8*a22 *n1*n3
2 7 2 2 5 4 2 3 6
- 6*a22 *a33*n1 *n3 - 22*a22 *a33*n1 *n3 - 24*a22 *a33*n1 *n3
2 8 2 7 2 2 5 4
- 8*a22 *a33*n1*n3 - 6*a22*a33 *n1 *n3 - 14*a22*a33 *n1 *n3
2 3 6 3 7 2 3 5 4 2
- 8*a22*a33 *n1 *n3 - 2*a33 *n1 *n3 - 2*a33 *n1 *n3 ) + u1*u3 *(
3 7 2 3 5 4 3 3 6 3 8
- 2*a22 *n1 *n3 - 6*a22 *n1 *n3 - 6*a22 *n1 *n3 - 2*a22 *n1*n3
2 7 2 2 5 4 2 3 6
- 6*a22 *a33*n1 *n3 - 18*a22 *a33*n1 *n3 - 18*a22 *a33*n1 *n3
2 8 2 7 2 2 5 4
- 6*a22 *a33*n1*n3 - 6*a22*a33 *n1 *n3 - 18*a22*a33 *n1 *n3
2 3 6 2 8 3 7 2
- 18*a22*a33 *n1 *n3 - 6*a22*a33 *n1*n3 - 2*a33 *n1 *n3
3 5 4 3 3 6 3 8
- 6*a33 *n1 *n3 - 6*a33 *n1 *n3 - 2*a33 *n1*n3 ) + u1*u3*(
2 5 5 2 3 7 2 9 5 5
- 4*a22 *n1 *n3 - 10*a22 *n1 *n3 - 6*a22 *n1*n3 - 8*a22*a33*n1 *n3
3 7 9 2 5 5 2 3 7
- 16*a22*a33*n1 *n3 - 8*a22*a33*n1*n3 - 4*a33 *n1 *n3 - 6*a33 *n1 *n3
2 9 5 6 3 8 10
- 2*a33 *n1*n3 ) + u1*( - 2*a22*n1 *n3 - a22*n1 *n3 + 3*a22*n1*n3
5 6 3 8 10 4 4 6 2
- 2*a33*n1 *n3 + a33*n1 *n3 + a33*n1*n3 ) + u2 *( - a22 *n1 *n3
4 4 4 4 2 6 4 8 3 6 2
- 5*a22 *n1 *n3 - 8*a22 *n1 *n3 - 4*a22 *n3 - 2*a22 *a33*n1 *n3
3 4 4 3 2 6 2 2 4 4
- 6*a22 *a33*n1 *n3 - 4*a22 *a33*n1 *n3 + 4*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 6 2
+ 8*a22 *a33 *n1 *n3 + 4*a22 *a33 *n3 + 2*a22*a33 *n1 *n3
3 4 4 3 2 6 4 6 2 4 4 4
+ 6*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3 + a33 *n1 *n3 + a33 *n1 *n3 )
2 3 6 3 3 4 5 3 2 7 3 9
+ u2 *u3*( - 2*a22 *n1 *n3 - 10*a22 *n1 *n3 - 16*a22 *n1 *n3 - 8*a22 *n3
2 6 3 2 4 5 2 2 7
- 6*a22 *a33*n1 *n3 - 22*a22 *a33*n1 *n3 - 24*a22 *a33*n1 *n3
2 9 2 6 3 2 4 5
- 8*a22 *a33*n3 - 6*a22*a33 *n1 *n3 - 14*a22*a33 *n1 *n3
2 2 7 3 6 3 3 4 5 2
- 8*a22*a33 *n1 *n3 - 2*a33 *n1 *n3 - 2*a33 *n1 *n3 ) + u2 *(
2 2 8 2 10 4 6 2 8
4*a22 *n1 *n3 + 6*a22 *n3 + 4*a22*a33*n1 *n3 + 10*a22*a33*n1 *n3
10 2 4 6 2 2 8 4 4 6 2
+ 2*a22*a33*n3 + 4*a33 *n1 *n3 + 2*a33 *n1 *n3 ) + u3 *(a22 *n1 *n3
4 4 4 4 2 6 4 8 3 6 2
+ 3*a22 *n1 *n3 + 3*a22 *n1 *n3 + a22 *n3 + 2*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 6*a22 *a33*n1 *n3 + 6*a22 *a33*n1 *n3 + 2*a22 *a33*n3
3 6 2 3 4 4 3 2 6
- 2*a22*a33 *n1 *n3 - 6*a22*a33 *n1 *n3 - 6*a22*a33 *n1 *n3
3 8 4 6 2 4 4 4 4 2 6
- 2*a22*a33 *n3 - a33 *n1 *n3 - 3*a33 *n1 *n3 - 3*a33 *n1 *n3
4 8 3 3 6 3 3 4 5 3 2 7
- a33 *n3 ) + u3 *( - 2*a22 *n1 *n3 - 6*a22 *n1 *n3 - 6*a22 *n1 *n3
3 9 2 6 3 2 4 5
- 2*a22 *n3 - 6*a22 *a33*n1 *n3 - 18*a22 *a33*n1 *n3
2 2 7 2 9 2 6 3
- 18*a22 *a33*n1 *n3 - 6*a22 *a33*n3 - 6*a22*a33 *n1 *n3
2 4 5 2 2 7 2 9
- 18*a22*a33 *n1 *n3 - 18*a22*a33 *n1 *n3 - 6*a22*a33 *n3
3 6 3 3 4 5 3 2 7 3 9
- 2*a33 *n1 *n3 - 6*a33 *n1 *n3 - 6*a33 *n1 *n3 - 2*a33 *n3 ) + u3*(
4 7 2 9 11 4 7 2 9
- 2*a22*n1 *n3 - a22*n1 *n3 + 3*a22*n3 - 2*a33*n1 *n3 + a33*n1 *n3
11
+ a33*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} = 0
3 7 2 3 5 4 3 3 6 3 8
FI=u1*(a22 *n1 *n3 + 5*a22 *n1 *n3 + 8*a22 *n1 *n3 + 4*a22 *n1*n3
2 7 2 2 5 4 2 3 6
+ 3*a22 *a33*n1 *n3 + 11*a22 *a33*n1 *n3 + 12*a22 *a33*n1 *n3
2 8 2 7 2 2 5 4
+ 4*a22 *a33*n1*n3 + 3*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3
2 3 6 3 7 2 3 5 4 2 4 8
+ 4*a22*a33 *n1 *n3 + a33 *n1 *n3 + a33 *n1 *n3 ) + u2 *(a22 *n1
4 6 2 4 4 4 4 2 6 4 8
+ 7*a22 *n1 *n3 + 18*a22 *n1 *n3 + 20*a22 *n1 *n3 + 8*a22 *n3
3 8 3 6 2 3 4 4
+ 4*a22 *a33*n1 + 22*a22 *a33*n1 *n3 + 42*a22 *a33*n1 *n3
3 2 6 3 8 2 2 8
+ 32*a22 *a33*n1 *n3 + 8*a22 *a33*n3 + 6*a22 *a33 *n1
2 2 6 2 2 2 4 4 2 2 2 6
+ 24*a22 *a33 *n1 *n3 + 30*a22 *a33 *n1 *n3 + 12*a22 *a33 *n1 *n3
3 8 3 6 2 3 4 4 4 8
+ 4*a22*a33 *n1 + 10*a22*a33 *n1 *n3 + 6*a22*a33 *n1 *n3 + a33 *n1
4 6 2 2 4 8 4 6 2 4 4 4
+ a33 *n1 *n3 ) + u3 *(a22 *n1 + 6*a22 *n1 *n3 + 13*a22 *n1 *n3
4 2 6 4 8 3 8 3 6 2
+ 12*a22 *n1 *n3 + 4*a22 *n3 + 4*a22 *a33*n1 + 20*a22 *a33*n1 *n3
3 4 4 3 2 6 3 8
+ 36*a22 *a33*n1 *n3 + 28*a22 *a33*n1 *n3 + 8*a22 *a33*n3
2 2 8 2 2 6 2 2 2 4 4
+ 6*a22 *a33 *n1 + 24*a22 *a33 *n1 *n3 + 34*a22 *a33 *n1 *n3
2 2 2 6 2 2 8 3 8
+ 20*a22 *a33 *n1 *n3 + 4*a22 *a33 *n3 + 4*a22*a33 *n1
3 6 2 3 4 4 3 2 6
+ 12*a22*a33 *n1 *n3 + 12*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3
4 8 4 6 2 4 4 4 3 6 3
+ a33 *n1 + 2*a33 *n1 *n3 + a33 *n1 *n3 ) + u3*(a22 *n1 *n3
3 4 5 3 2 7 3 9 2 6 3
+ 5*a22 *n1 *n3 + 8*a22 *n1 *n3 + 4*a22 *n3 + 3*a22 *a33*n1 *n3
2 4 5 2 2 7 2 9
+ 11*a22 *a33*n1 *n3 + 12*a22 *a33*n1 *n3 + 4*a22 *a33*n3
2 6 3 2 4 5 2 2 7
+ 3*a22*a33 *n1 *n3 + 7*a22*a33 *n1 *n3 + 4*a22*a33 *n1 *n3
3 6 3 3 4 5
+ a33 *n1 *n3 + a33 *n1 *n3 )
2 2 2
= a product of the elements of: {a22*n1 + 2*a22*n3 + a33*n1 ,
2 2 2
a22*n1 + 2*a22*n3 + a33*n1 ,
n1 - i*n3,
n1 + i*n3,
a22 + a33,
2 2 2 2 2
u1*n1*n3 + u2 *(a22*n1 + 2*a22*n3 + a33*n1 )
2 2 2 2 2 3
+ u3 *(a22*n1 + a22*n3 + a33*n1 + a33*n3 ) + u3*n3 }
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*( - a22*n1**2 - a22*n3**2 - a33*n1**2)/n3**2 + u1*n1 + u2**2*a22 + u3
**2*a33 + u3*n3$
FI= - u1**2*v2**2 - u1**2*v3**2 + 2*u1*u2*v1*v2 + 2*u1*u3*v1*v3 - u2**2*v1**2 -
u2**2*v3**2 + 2*u2*u3*v2*v3 - u3**2*v1**2 - u3**2*v2**2$
FI=u1**2*v1*(a22**3*n1**7*n3**2 + 4*a22**3*n1**5*n3**4 + 5*a22**3*n1**3*n3**6 +
2*a22**3*n1*n3**8 + 3*a22**2*a33*n1**7*n3**2 + 10*a22**2*a33*n1**5*n3**4 + 11*
a22**2*a33*n1**3*n3**6 + 4*a22**2*a33*n1*n3**8 + 3*a22*a33**2*n1**7*n3**2 + 8*
a22*a33**2*n1**5*n3**4 + 7*a22*a33**2*n1**3*n3**6 + 2*a22*a33**2*n1*n3**8 + a33
**3*n1**7*n3**2 + 2*a33**3*n1**5*n3**4 + a33**3*n1**3*n3**6) + u1*u2**2*v1*(a22
**4*n1**8 + 6*a22**4*n1**6*n3**2 + 13*a22**4*n1**4*n3**4 + 12*a22**4*n1**2*n3**6
+ 4*a22**4*n3**8 + 4*a22**3*a33*n1**8 + 20*a22**3*a33*n1**6*n3**2 + 36*a22**3*
a33*n1**4*n3**4 + 28*a22**3*a33*n1**2*n3**6 + 8*a22**3*a33*n3**8 + 6*a22**2*a33
**2*n1**8 + 24*a22**2*a33**2*n1**6*n3**2 + 34*a22**2*a33**2*n1**4*n3**4 + 20*a22
**2*a33**2*n1**2*n3**6 + 4*a22**2*a33**2*n3**8 + 4*a22*a33**3*n1**8 + 12*a22*a33
**3*n1**6*n3**2 + 12*a22*a33**3*n1**4*n3**4 + 4*a22*a33**3*n1**2*n3**6 + a33**4*
n1**8 + 2*a33**4*n1**6*n3**2 + a33**4*n1**4*n3**4) + u1*u2*v2*(a22**3*n1**7*n3**
2 + 4*a22**3*n1**5*n3**4 + 5*a22**3*n1**3*n3**6 + 2*a22**3*n1*n3**8 + 3*a22**2*
a33*n1**7*n3**2 + 10*a22**2*a33*n1**5*n3**4 + 11*a22**2*a33*n1**3*n3**6 + 4*a22
**2*a33*n1*n3**8 + 3*a22*a33**2*n1**7*n3**2 + 8*a22*a33**2*n1**5*n3**4 + 7*a22*
a33**2*n1**3*n3**6 + 2*a22*a33**2*n1*n3**8 + a33**3*n1**7*n3**2 + 2*a33**3*n1**5
*n3**4 + a33**3*n1**3*n3**6) + u1*u3**2*v1*(a22**4*n1**8 + 5*a22**4*n1**6*n3**2
+ 9*a22**4*n1**4*n3**4 + 7*a22**4*n1**2*n3**6 + 2*a22**4*n3**8 + 4*a22**3*a33*n1
**8 + 18*a22**3*a33*n1**6*n3**2 + 30*a22**3*a33*n1**4*n3**4 + 22*a22**3*a33*n1**
2*n3**6 + 6*a22**3*a33*n3**8 + 6*a22**2*a33**2*n1**8 + 24*a22**2*a33**2*n1**6*n3
**2 + 36*a22**2*a33**2*n1**4*n3**4 + 24*a22**2*a33**2*n1**2*n3**6 + 6*a22**2*a33
**2*n3**8 + 4*a22*a33**3*n1**8 + 14*a22*a33**3*n1**6*n3**2 + 18*a22*a33**3*n1**4
*n3**4 + 10*a22*a33**3*n1**2*n3**6 + 2*a22*a33**3*n3**8 + a33**4*n1**8 + 3*a33**
4*n1**6*n3**2 + 3*a33**4*n1**4*n3**4 + a33**4*n1**2*n3**6) + u1*u3*v1*(a22**3*n1
**6*n3**3 + 4*a22**3*n1**4*n3**5 + 5*a22**3*n1**2*n3**7 + 2*a22**3*n3**9 + 3*a22
**2*a33*n1**6*n3**3 + 10*a22**2*a33*n1**4*n3**5 + 11*a22**2*a33*n1**2*n3**7 + 4*
a22**2*a33*n3**9 + 3*a22*a33**2*n1**6*n3**3 + 8*a22*a33**2*n1**4*n3**5 + 7*a22*
a33**2*n1**2*n3**7 + 2*a22*a33**2*n3**9 + a33**3*n1**6*n3**3 + 2*a33**3*n1**4*n3
**5 + a33**3*n1**2*n3**7) + u1*u3*v3*(a22**3*n1**7*n3**2 + 4*a22**3*n1**5*n3**4
+ 5*a22**3*n1**3*n3**6 + 2*a22**3*n1*n3**8 + 3*a22**2*a33*n1**7*n3**2 + 10*a22**
2*a33*n1**5*n3**4 + 11*a22**2*a33*n1**3*n3**6 + 4*a22**2*a33*n1*n3**8 + 3*a22*
a33**2*n1**7*n3**2 + 8*a22*a33**2*n1**5*n3**4 + 7*a22*a33**2*n1**3*n3**6 + 2*a22
*a33**2*n1*n3**8 + a33**3*n1**7*n3**2 + 2*a33**3*n1**5*n3**4 + a33**3*n1**3*n3**
6) + u2**3*v2*(a22**4*n1**8 + 6*a22**4*n1**6*n3**2 + 13*a22**4*n1**4*n3**4 + 12*
a22**4*n1**2*n3**6 + 4*a22**4*n3**8 + 4*a22**3*a33*n1**8 + 20*a22**3*a33*n1**6*
n3**2 + 36*a22**3*a33*n1**4*n3**4 + 28*a22**3*a33*n1**2*n3**6 + 8*a22**3*a33*n3
**8 + 6*a22**2*a33**2*n1**8 + 24*a22**2*a33**2*n1**6*n3**2 + 34*a22**2*a33**2*n1
**4*n3**4 + 20*a22**2*a33**2*n1**2*n3**6 + 4*a22**2*a33**2*n3**8 + 4*a22*a33**3*
n1**8 + 12*a22*a33**3*n1**6*n3**2 + 12*a22*a33**3*n1**4*n3**4 + 4*a22*a33**3*n1
**2*n3**6 + a33**4*n1**8 + 2*a33**4*n1**6*n3**2 + a33**4*n1**4*n3**4) + u2**2*u3
*v3*(a22**4*n1**8 + 6*a22**4*n1**6*n3**2 + 13*a22**4*n1**4*n3**4 + 12*a22**4*n1
**2*n3**6 + 4*a22**4*n3**8 + 4*a22**3*a33*n1**8 + 20*a22**3*a33*n1**6*n3**2 + 36
*a22**3*a33*n1**4*n3**4 + 28*a22**3*a33*n1**2*n3**6 + 8*a22**3*a33*n3**8 + 6*a22
**2*a33**2*n1**8 + 24*a22**2*a33**2*n1**6*n3**2 + 34*a22**2*a33**2*n1**4*n3**4 +
20*a22**2*a33**2*n1**2*n3**6 + 4*a22**2*a33**2*n3**8 + 4*a22*a33**3*n1**8 + 12*
a22*a33**3*n1**6*n3**2 + 12*a22*a33**3*n1**4*n3**4 + 4*a22*a33**3*n1**2*n3**6 +
a33**4*n1**8 + 2*a33**4*n1**6*n3**2 + a33**4*n1**4*n3**4) + u2*u3**2*v2*(a22**4*
n1**8 + 5*a22**4*n1**6*n3**2 + 9*a22**4*n1**4*n3**4 + 7*a22**4*n1**2*n3**6 + 2*
a22**4*n3**8 + 4*a22**3*a33*n1**8 + 18*a22**3*a33*n1**6*n3**2 + 30*a22**3*a33*n1
**4*n3**4 + 22*a22**3*a33*n1**2*n3**6 + 6*a22**3*a33*n3**8 + 6*a22**2*a33**2*n1
**8 + 24*a22**2*a33**2*n1**6*n3**2 + 36*a22**2*a33**2*n1**4*n3**4 + 24*a22**2*
a33**2*n1**2*n3**6 + 6*a22**2*a33**2*n3**8 + 4*a22*a33**3*n1**8 + 14*a22*a33**3*
n1**6*n3**2 + 18*a22*a33**3*n1**4*n3**4 + 10*a22*a33**3*n1**2*n3**6 + 2*a22*a33
**3*n3**8 + a33**4*n1**8 + 3*a33**4*n1**6*n3**2 + 3*a33**4*n1**4*n3**4 + a33**4*
n1**2*n3**6) + u2*u3*v2*(a22**3*n1**6*n3**3 + 4*a22**3*n1**4*n3**5 + 5*a22**3*n1
**2*n3**7 + 2*a22**3*n3**9 + 3*a22**2*a33*n1**6*n3**3 + 10*a22**2*a33*n1**4*n3**
5 + 11*a22**2*a33*n1**2*n3**7 + 4*a22**2*a33*n3**9 + 3*a22*a33**2*n1**6*n3**3 +
8*a22*a33**2*n1**4*n3**5 + 7*a22*a33**2*n1**2*n3**7 + 2*a22*a33**2*n3**9 + a33**
3*n1**6*n3**3 + 2*a33**3*n1**4*n3**5 + a33**3*n1**2*n3**7) + u3**3*v3*(a22**4*n1
**8 + 5*a22**4*n1**6*n3**2 + 9*a22**4*n1**4*n3**4 + 7*a22**4*n1**2*n3**6 + 2*a22
**4*n3**8 + 4*a22**3*a33*n1**8 + 18*a22**3*a33*n1**6*n3**2 + 30*a22**3*a33*n1**4
*n3**4 + 22*a22**3*a33*n1**2*n3**6 + 6*a22**3*a33*n3**8 + 6*a22**2*a33**2*n1**8
+ 24*a22**2*a33**2*n1**6*n3**2 + 36*a22**2*a33**2*n1**4*n3**4 + 24*a22**2*a33**2
*n1**2*n3**6 + 6*a22**2*a33**2*n3**8 + 4*a22*a33**3*n1**8 + 14*a22*a33**3*n1**6*
n3**2 + 18*a22*a33**3*n1**4*n3**4 + 10*a22*a33**3*n1**2*n3**6 + 2*a22*a33**3*n3
**8 + a33**4*n1**8 + 3*a33**4*n1**6*n3**2 + 3*a33**4*n1**4*n3**4 + a33**4*n1**2*
n3**6) + u3**2*v3*(a22**3*n1**6*n3**3 + 4*a22**3*n1**4*n3**5 + 5*a22**3*n1**2*n3
**7 + 2*a22**3*n3**9 + 3*a22**2*a33*n1**6*n3**3 + 10*a22**2*a33*n1**4*n3**5 + 11
*a22**2*a33*n1**2*n3**7 + 4*a22**2*a33*n3**9 + 3*a22*a33**2*n1**6*n3**3 + 8*a22*
a33**2*n1**4*n3**5 + 7*a22*a33**2*n1**2*n3**7 + 2*a22*a33**2*n3**9 + a33**3*n1**
6*n3**3 + 2*a33**3*n1**4*n3**5 + a33**3*n1**2*n3**7)$
FI=u1**3*(2*a22**3*n1**7*n3**2 + 8*a22**3*n1**5*n3**4 + 10*a22**3*n1**3*n3**6 +
4*a22**3*n1*n3**8 + 6*a22**2*a33*n1**7*n3**2 + 20*a22**2*a33*n1**5*n3**4 + 22*
a22**2*a33*n1**3*n3**6 + 8*a22**2*a33*n1*n3**8 + 6*a22*a33**2*n1**7*n3**2 + 16*
a22*a33**2*n1**5*n3**4 + 14*a22*a33**2*n1**3*n3**6 + 4*a22*a33**2*n1*n3**8 + 2*
a33**3*n1**7*n3**2 + 4*a33**3*n1**5*n3**4 + 2*a33**3*n1**3*n3**6) + u1**2*u2**2*
(2*a22**4*n1**8 + 12*a22**4*n1**6*n3**2 + 26*a22**4*n1**4*n3**4 + 24*a22**4*n1**
2*n3**6 + 8*a22**4*n3**8 + 8*a22**3*a33*n1**8 + 40*a22**3*a33*n1**6*n3**2 + 72*
a22**3*a33*n1**4*n3**4 + 56*a22**3*a33*n1**2*n3**6 + 16*a22**3*a33*n3**8 + 12*
a22**2*a33**2*n1**8 + 48*a22**2*a33**2*n1**6*n3**2 + 68*a22**2*a33**2*n1**4*n3**
4 + 40*a22**2*a33**2*n1**2*n3**6 + 8*a22**2*a33**2*n3**8 + 8*a22*a33**3*n1**8 +
24*a22*a33**3*n1**6*n3**2 + 24*a22*a33**3*n1**4*n3**4 + 8*a22*a33**3*n1**2*n3**6
+ 2*a33**4*n1**8 + 4*a33**4*n1**6*n3**2 + 2*a33**4*n1**4*n3**4) + u1**2*u3**2*(
2*a22**4*n1**8 + 10*a22**4*n1**6*n3**2 + 18*a22**4*n1**4*n3**4 + 14*a22**4*n1**2
*n3**6 + 4*a22**4*n3**8 + 8*a22**3*a33*n1**8 + 36*a22**3*a33*n1**6*n3**2 + 60*
a22**3*a33*n1**4*n3**4 + 44*a22**3*a33*n1**2*n3**6 + 12*a22**3*a33*n3**8 + 12*
a22**2*a33**2*n1**8 + 48*a22**2*a33**2*n1**6*n3**2 + 72*a22**2*a33**2*n1**4*n3**
4 + 48*a22**2*a33**2*n1**2*n3**6 + 12*a22**2*a33**2*n3**8 + 8*a22*a33**3*n1**8 +
28*a22*a33**3*n1**6*n3**2 + 36*a22*a33**3*n1**4*n3**4 + 20*a22*a33**3*n1**2*n3
**6 + 4*a22*a33**3*n3**8 + 2*a33**4*n1**8 + 6*a33**4*n1**6*n3**2 + 6*a33**4*n1**
4*n3**4 + 2*a33**4*n1**2*n3**6) + u1**2*u3*(2*a22**3*n1**6*n3**3 + 8*a22**3*n1**
4*n3**5 + 10*a22**3*n1**2*n3**7 + 4*a22**3*n3**9 + 6*a22**2*a33*n1**6*n3**3 + 20
*a22**2*a33*n1**4*n3**5 + 22*a22**2*a33*n1**2*n3**7 + 8*a22**2*a33*n3**9 + 6*a22
*a33**2*n1**6*n3**3 + 16*a22*a33**2*n1**4*n3**5 + 14*a22*a33**2*n1**2*n3**7 + 4*
a22*a33**2*n3**9 + 2*a33**3*n1**6*n3**3 + 4*a33**3*n1**4*n3**5 + 2*a33**3*n1**2*
n3**7) + u1*u2**2*( - 2*a22**3*n1**7*n3**2 - 10*a22**3*n1**5*n3**4 - 16*a22**3*
n1**3*n3**6 - 8*a22**3*n1*n3**8 - 6*a22**2*a33*n1**7*n3**2 - 22*a22**2*a33*n1**5
*n3**4 - 24*a22**2*a33*n1**3*n3**6 - 8*a22**2*a33*n1*n3**8 - 6*a22*a33**2*n1**7*
n3**2 - 14*a22*a33**2*n1**5*n3**4 - 8*a22*a33**2*n1**3*n3**6 - 2*a33**3*n1**7*n3
**2 - 2*a33**3*n1**5*n3**4) + u1*u3**2*( - 2*a22**3*n1**7*n3**2 - 6*a22**3*n1**5
*n3**4 - 6*a22**3*n1**3*n3**6 - 2*a22**3*n1*n3**8 - 6*a22**2*a33*n1**7*n3**2 -
18*a22**2*a33*n1**5*n3**4 - 18*a22**2*a33*n1**3*n3**6 - 6*a22**2*a33*n1*n3**8 -
6*a22*a33**2*n1**7*n3**2 - 18*a22*a33**2*n1**5*n3**4 - 18*a22*a33**2*n1**3*n3**6
- 6*a22*a33**2*n1*n3**8 - 2*a33**3*n1**7*n3**2 - 6*a33**3*n1**5*n3**4 - 6*a33**
3*n1**3*n3**6 - 2*a33**3*n1*n3**8) + u1*u3*( - 4*a22**2*n1**5*n3**5 - 10*a22**2*
n1**3*n3**7 - 6*a22**2*n1*n3**9 - 8*a22*a33*n1**5*n3**5 - 16*a22*a33*n1**3*n3**7
- 8*a22*a33*n1*n3**9 - 4*a33**2*n1**5*n3**5 - 6*a33**2*n1**3*n3**7 - 2*a33**2*
n1*n3**9) + u1*( - 2*a22*n1**5*n3**6 - a22*n1**3*n3**8 + 3*a22*n1*n3**10 - 2*a33
*n1**5*n3**6 + a33*n1**3*n3**8 + a33*n1*n3**10) + u2**4*( - a22**4*n1**6*n3**2 -
5*a22**4*n1**4*n3**4 - 8*a22**4*n1**2*n3**6 - 4*a22**4*n3**8 - 2*a22**3*a33*n1
**6*n3**2 - 6*a22**3*a33*n1**4*n3**4 - 4*a22**3*a33*n1**2*n3**6 + 4*a22**2*a33**
2*n1**4*n3**4 + 8*a22**2*a33**2*n1**2*n3**6 + 4*a22**2*a33**2*n3**8 + 2*a22*a33
**3*n1**6*n3**2 + 6*a22*a33**3*n1**4*n3**4 + 4*a22*a33**3*n1**2*n3**6 + a33**4*
n1**6*n3**2 + a33**4*n1**4*n3**4) + u2**2*u3*( - 2*a22**3*n1**6*n3**3 - 10*a22**
3*n1**4*n3**5 - 16*a22**3*n1**2*n3**7 - 8*a22**3*n3**9 - 6*a22**2*a33*n1**6*n3**
3 - 22*a22**2*a33*n1**4*n3**5 - 24*a22**2*a33*n1**2*n3**7 - 8*a22**2*a33*n3**9 -
6*a22*a33**2*n1**6*n3**3 - 14*a22*a33**2*n1**4*n3**5 - 8*a22*a33**2*n1**2*n3**7
- 2*a33**3*n1**6*n3**3 - 2*a33**3*n1**4*n3**5) + u2**2*(4*a22**2*n1**2*n3**8 +
6*a22**2*n3**10 + 4*a22*a33*n1**4*n3**6 + 10*a22*a33*n1**2*n3**8 + 2*a22*a33*n3
**10 + 4*a33**2*n1**4*n3**6 + 2*a33**2*n1**2*n3**8) + u3**4*(a22**4*n1**6*n3**2
+ 3*a22**4*n1**4*n3**4 + 3*a22**4*n1**2*n3**6 + a22**4*n3**8 + 2*a22**3*a33*n1**
6*n3**2 + 6*a22**3*a33*n1**4*n3**4 + 6*a22**3*a33*n1**2*n3**6 + 2*a22**3*a33*n3
**8 - 2*a22*a33**3*n1**6*n3**2 - 6*a22*a33**3*n1**4*n3**4 - 6*a22*a33**3*n1**2*
n3**6 - 2*a22*a33**3*n3**8 - a33**4*n1**6*n3**2 - 3*a33**4*n1**4*n3**4 - 3*a33**
4*n1**2*n3**6 - a33**4*n3**8) + u3**3*( - 2*a22**3*n1**6*n3**3 - 6*a22**3*n1**4*
n3**5 - 6*a22**3*n1**2*n3**7 - 2*a22**3*n3**9 - 6*a22**2*a33*n1**6*n3**3 - 18*
a22**2*a33*n1**4*n3**5 - 18*a22**2*a33*n1**2*n3**7 - 6*a22**2*a33*n3**9 - 6*a22*
a33**2*n1**6*n3**3 - 18*a22*a33**2*n1**4*n3**5 - 18*a22*a33**2*n1**2*n3**7 - 6*
a22*a33**2*n3**9 - 2*a33**3*n1**6*n3**3 - 6*a33**3*n1**4*n3**5 - 6*a33**3*n1**2*
n3**7 - 2*a33**3*n3**9) + u3*( - 2*a22*n1**4*n3**7 - a22*n1**2*n3**9 + 3*a22*n3
**11 - 2*a33*n1**4*n3**7 + a33*n1**2*n3**9 + a33*n3**11)$
FI=u1*(a22**3*n1**7*n3**2 + 5*a22**3*n1**5*n3**4 + 8*a22**3*n1**3*n3**6 + 4*a22
**3*n1*n3**8 + 3*a22**2*a33*n1**7*n3**2 + 11*a22**2*a33*n1**5*n3**4 + 12*a22**2*
a33*n1**3*n3**6 + 4*a22**2*a33*n1*n3**8 + 3*a22*a33**2*n1**7*n3**2 + 7*a22*a33**
2*n1**5*n3**4 + 4*a22*a33**2*n1**3*n3**6 + a33**3*n1**7*n3**2 + a33**3*n1**5*n3
**4) + u2**2*(a22**4*n1**8 + 7*a22**4*n1**6*n3**2 + 18*a22**4*n1**4*n3**4 + 20*
a22**4*n1**2*n3**6 + 8*a22**4*n3**8 + 4*a22**3*a33*n1**8 + 22*a22**3*a33*n1**6*
n3**2 + 42*a22**3*a33*n1**4*n3**4 + 32*a22**3*a33*n1**2*n3**6 + 8*a22**3*a33*n3
**8 + 6*a22**2*a33**2*n1**8 + 24*a22**2*a33**2*n1**6*n3**2 + 30*a22**2*a33**2*n1
**4*n3**4 + 12*a22**2*a33**2*n1**2*n3**6 + 4*a22*a33**3*n1**8 + 10*a22*a33**3*n1
**6*n3**2 + 6*a22*a33**3*n1**4*n3**4 + a33**4*n1**8 + a33**4*n1**6*n3**2) + u3**
2*(a22**4*n1**8 + 6*a22**4*n1**6*n3**2 + 13*a22**4*n1**4*n3**4 + 12*a22**4*n1**2
*n3**6 + 4*a22**4*n3**8 + 4*a22**3*a33*n1**8 + 20*a22**3*a33*n1**6*n3**2 + 36*
a22**3*a33*n1**4*n3**4 + 28*a22**3*a33*n1**2*n3**6 + 8*a22**3*a33*n3**8 + 6*a22
**2*a33**2*n1**8 + 24*a22**2*a33**2*n1**6*n3**2 + 34*a22**2*a33**2*n1**4*n3**4 +
20*a22**2*a33**2*n1**2*n3**6 + 4*a22**2*a33**2*n3**8 + 4*a22*a33**3*n1**8 + 12*
a22*a33**3*n1**6*n3**2 + 12*a22*a33**3*n1**4*n3**4 + 4*a22*a33**3*n1**2*n3**6 +
a33**4*n1**8 + 2*a33**4*n1**6*n3**2 + a33**4*n1**4*n3**4) + u3*(a22**3*n1**6*n3
**3 + 5*a22**3*n1**4*n3**5 + 8*a22**3*n1**2*n3**7 + 4*a22**3*n3**9 + 3*a22**2*
a33*n1**6*n3**3 + 11*a22**2*a33*n1**4*n3**5 + 12*a22**2*a33*n1**2*n3**7 + 4*a22
**2*a33*n3**9 + 3*a22*a33**2*n1**6*n3**3 + 7*a22*a33**2*n1**4*n3**5 + 4*a22*a33
**2*n1**2*n3**7 + a33**3*n1**6*n3**3 + a33**3*n1**4*n3**5)$