Solution 7 to problem over
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Expressions
The solution is given through the following expressions:
r10=0
r11=0
3 3
6*a22*b11*n1*r217 + 22*n1 *r483 - 22*n1 *r494
r12=-----------------------------------------------
2
9*a22 *b11
r13=0
r14=0
3 3
6*a22*b11*n1*r217 + 16*n1 *r483 - 16*n1 *r494
r15=-----------------------------------------------
2
3*a22*b11
2 2
- 3*a22*b11*r217 - 5*n1 *r483 + 5*n1 *r494
r20=---------------------------------------------
2
12*a22
r21=0
2 2
a22*b11*r217 + 3*n1 *r483 - 3*n1 *r494
r22=----------------------------------------
2
12*a22
r23=0
r24=0
2 2
- 4*n1 *r483 + 4*n1 *r494
r26=----------------------------
3*a22*b11
r27=0
r28=0
2 2
- 3*a22*b11*r217 - 5*n1 *r483 + 5*n1 *r494
r29=---------------------------------------------
2
3*b11
r210=0
r212=0
r213=0
2 2
3*a22*b11*r217 + 9*n1 *r483 - 9*n1 *r494
r214=------------------------------------------
2
b11
r215=0
r216=0
r218=0
r219=0
r30=0
r31=0
r32=0
r33=0
4*b11*n1*r446 - 3*b11*n1*r483 - 13*b11*n1*r494
r34=------------------------------------------------
2
36*a22
r35=0
4*b11*n1*r446 - 9*b11*n1*r483 - 7*b11*n1*r494
r36=-----------------------------------------------
2
36*a22
r37=0
r38=0
2*b11*n1*r446 - 7*b11*n1*r483 - b11*n1*r494
r39=---------------------------------------------
2
18*a22
r310=0
r311=0
r312=0
- 2*n1*r446 + 2*n1*r483
r313=--------------------------
3*a22
r314=0
r315=0
r316=0
r317=0
n1*r483 - n1*r494
r318=-------------------
3*b11
r319=0
r320=0
r321=0
r322=0
r323=0
- 2*n1*r446 + 2*n1*r494
r324=--------------------------
3*a22
r325=0
r326=0
r327=0
r328=0
r329=0
r330=0
r331=0
- 3*n1*r483 + 3*n1*r494
r332=--------------------------
b11
r333=0
r334=0
- 16*n1*r446 + 9*n1*r483 + 7*n1*r494
r335=---------------------------------------
24*a22
r336=0
- 16*n1*r446 + 9*n1*r483 + 7*n1*r494
r337=---------------------------------------
24*a22
r338=0
r339=0
- 8*n1*r446 - 3*n1*r483 + 11*n1*r494
r340=---------------------------------------
6*a22
- 2*n1*r446 + 2*n1*r483
r341=--------------------------
b11
r342=0
r343=0
- a22*n1*r483 + a22*n1*r494
r344=------------------------------
2
2*b11
r345=0
- 2*n1*r446 + 2*n1*r494
r346=--------------------------
b11
r347=0
r348=0
- 9*a22*n1*r483 + 9*a22*n1*r494
r349=----------------------------------
2
2*b11
r350=0
r351=0
- 2*n1*r446 + 2*n1*r494
r352=--------------------------
b11
r353=0
r354=0
- 3*a22*n1*r483 + 3*a22*n1*r494
r355=----------------------------------
2
2*b11
2 2 2
- 4*b11 *r446 + 19*b11 *r483 + 13*b11 *r494
r40=----------------------------------------------
2
288*a22
r41=0
2 2 2
- 18*b11 *r446 + 19*b11 *r483 + 21*b11 *r494
r42=-----------------------------------------------
2
72*a22
r43=0
2 2 2
- 68*b11 *r446 + 65*b11 *r483 + 63*b11 *r494
r44=-----------------------------------------------
2
288*a22
r45=0
r46=0
r47=0
r48=0
2 2 2
- 2*b11 *r446 + 17*b11 *r483 - b11 *r494
r49=-------------------------------------------
2
144*a22
r410=0
2 2 2
- 34*b11 *r446 + 29*b11 *r483 + 35*b11 *r494
r411=-----------------------------------------------
2
144*a22
r412=0
r413=0
- 5*b11*r446 + 5*b11*r483 + 8*b11*r494
r415=-----------------------------------------
12*a22
r416=0
- 9*b11*r446 + 9*b11*r483 + 8*b11*r494
r417=-----------------------------------------
12*a22
r418=0
r419=0
r420=0
r421=0
- 2*b11*r446 + 2*b11*r483 + 2*b11*r494
r422=-----------------------------------------
3*a22
r423=0
r424=0
8*r446 - 3*r483 - 5*r494
r425=--------------------------
6
r426=0
10*r446 - 9*r483 - 7*r494
r427=---------------------------
12
r428=0
r429=0
10*r446 - 5*r483 - 11*r494
r430=----------------------------
12
a22*r446 - a22*r483
r431=---------------------
b11
r432=0
r433=0
2 2
a22 *r483 - a22 *r494
r434=-----------------------
2
2*b11
r435=0
b11*r446 - b11*r494
r436=---------------------
4*a22
r437=0
- b11*r446 + b11*r494
r438=------------------------
12*a22
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
r447=0
r448=0
r449=0
r450=0
r451=0
a22*r446 - a22*r494
r452=---------------------
b11
r453=0
r454=0
- 2*r446 + r483 - r494
r455=-------------------------
4
r456=0
r458=0
r459=0
- 2*r446 - 3*r483 + 3*r494
r460=-----------------------------
4
- 3*a22*r446 + 3*a22*r483
r461=----------------------------
b11
r462=0
r463=0
r464=0
r465=0
- 3*a22*r446 + 3*a22*r494
r466=----------------------------
b11
r467=0
r468=0
2 2
- 9*a22 *r483 + 9*a22 *r494
r469=------------------------------
2
2*b11
r470=0
r471=0
r472=0
r473=0
- 7*b11*r446 + 6*b11*r483 + 7*b11*r494
r474=-----------------------------------------
12*a22
r475=0
- 11*b11*r446 + 9*b11*r483 + 8*b11*r494
r476=------------------------------------------
12*a22
r477=0
r478=0
- 10*b11*r446 + 5*b11*r483 + 11*b11*r494
r479=-------------------------------------------
12*a22
r480=0
r481=0
r482=0
r484=0
r485=0
r486=0
r487=0
a22*r446 - a22*r483
r488=---------------------
b11
r489=0
r490=0
r491=0
r492=0
r493=0
r495=0
r496=0
r497=0
r498=0
r499=0
r4100=0
r4101=0
- 3*a22*r446 + 3*a22*r494
r4102=----------------------------
b11
r4103=0
r4104=0
8*r446 - 5*r483 - 11*r494
r4105=---------------------------
16
r4106=0
8*r446 - 9*r483 - 7*r494
r4107=--------------------------
16
r4108=0
r4109=0
r4111=0
r4112=0
r4113=0
2 2
3*a22 *r483 - 3*a22 *r494
r4114=---------------------------
2
4*b11
r4115=0
r4117=0
r4118=0
2 2
- 9*a22 *r483 + 9*a22 *r494
r4119=------------------------------
2
4*b11
r4120=0
r4121=0
- 3*a22*r483 + 3*a22*r494
r4122=----------------------------
4*b11
r4123=0
r4124=0
m3=0
m2=0
m1=0
n3=0
n2=0
2
- b11
c33=---------
36*a22
c23=0
2
b11
c22=-------
4*a22
c13=0
c12=0
c11=0
2*b11
b33=-------
3
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
a33= - a22
a23=0
a13=0
a12=0
- a22
a11=--------
2
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:
r217, r494, r483, r446, n1, b11, 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.
{a22,
b11,
n1,
a33,
2 2 2
{12*b11 *n1*r446 - 57*b11 *n1*r483 - 39*b11 *n1*r494,
2 2 2
18*b11 *r446 - 19*b11 *r483 - 21*b11 *r494,
2 2 2
68*b11 *r446 - 65*b11 *r483 - 63*b11 *r494,
2 2 2
2*b11 *r446 - 17*b11 *r483 + b11 *r494,
2 2 2
34*b11 *r446 - 29*b11 *r483 - 35*b11 *r494,
5*b11*r446 - 5*b11*r483 - 8*b11*r494,
9*b11*r446 - 9*b11*r483 - 8*b11*r494,
2*b11*r446 - 2*b11*r483 - 2*b11*r494,
8*r446 - 3*r483 - 5*r494,
10*r446 - 9*r483 - 7*r494,
10*r446 - 5*r483 - 11*r494,
2 2
9*a22 *r483 - 9*a22 *r494,
b11*r446 - b11*r494,
r446,
3*a22*r446 - 3*a22*r494,
2*r446 - r483 + r494,
2*r446 + 3*r483 - 3*r494,
a22*r446 - a22*r483,
7*b11*r446 - 6*b11*r483 - 7*b11*r494,
11*b11*r446 - 9*b11*r483 - 8*b11*r494,
10*b11*r446 - 5*b11*r483 - 11*b11*r494,
r483,
r494,
24*a22*r446 - 15*a22*r483 - 33*a22*r494,
2 2 2
24*a22 *r446 - 27*a22 *r483 - 21*a22 *r494,
3 3
9*a22 *r483 - 9*a22 *r494}}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{2*a11 + a22,
a12,
a13,
a23,
a22 + a33,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
- 2*b11 + 3*b33,
c11,
c12,
c13,
4*a22*c22 - b11**2,
c23,
36*a22*c33 + b11**2,
n2,
n3,
m1,
m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2
- u1 *a22 2 2 2*u3*v3*b11
HAM=------------ + u1*v1*b11 + u1*n1 + u2 *a22 - u3 *a22 + -------------
2 3
2 2 2 2
v2 *b11 - v3 *b11
+ ---------- + -------------
4*a22 36*a22
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
2 2 2 2 2 2 2 2
FI= - 144*u1 *v1*a22 *n1 + 36*u1 *v2 *a22 *b11 + 36*u1 *v3 *a22 *b11
2 3 2 2 3
- 216*u1*u2 *v1*a22 - 144*u1*u2*v2*a22 *n1 + 72*u1*u3 *v1*a22
2 3 2 2
- 144*u1*u3*v3*a22 *n1 - 60*u1*v1 *a22*b11 - 96*u1*v1 *a22*b11*n1
2 2 2 2 2
- 66*u1*v1*v2 *a22*b11 - 42*u1*v1*v3 *a22*b11 - 48*u1*v2 *a22*b11*n1
2 3 3 2 3
- 48*u1*v3 *a22*b11*n1 - 216*u2 *v2*a22 - 216*u2 *u3*v3*a22
2 2 2 2 2 2 2 3
- 36*u2 *v1 *a22 *b11 - 36*u2 *v3 *a22 *b11 + 72*u2*u3 *v2*a22
2 3 2
+ 72*u2*u3*v2*v3*a22 *b11 - 48*u2*v1*v2*a22*b11*n1 - 6*u2*v2 *a22*b11
2 2 3 3 2 2 2
+ 18*u2*v2*v3 *a22*b11 + 72*u3 *v3*a22 + 60*u3 *v1 *a22 *b11
2 2 2 2 2 2 2 2
+ 60*u3 *v2 *a22 *b11 + 96*u3 *v3 *a22 *b11 - 48*u3*v1 *v3*a22*b11
2 2 3 2
- 48*u3*v1*v3*a22*b11*n1 - 54*u3*v2 *v3*a22*b11 - 30*u3*v3 *a22*b11
3 2 2 2 3 2 2 3 2 2
+ 8*v1 *b11 *n1 - 17*v1 *v2 *b11 - v1 *v3 *b11 + 8*v1*v2 *b11 *n1
2 2 4 3 2 2 3 4 3
+ 8*v1*v3 *b11 *n1 - 17*v2 *b11 - 18*v2 *v3 *b11 - v3 *b11
= a product of the elements of: {216,
2 2 2 2 2 2 2 2
- 2*u1 *v1*a22 *n1 u1 *v2 *a22 *b11 u1 *v3 *a22 *b11
--------------------- + ------------------ + ------------------
3 6 6
2 2 3
2 3 - 2*u1*u2*v2*a22 *n1 u1*u3 *v1*a22
- u1*u2 *v1*a22 + ----------------------- + ----------------
3 3
2 3 2
- 2*u1*u3*v3*a22 *n1 - 5*u1*v1 *a22*b11
+ ----------------------- + ----------------------
3 18
2 2 2
- 4*u1*v1 *a22*b11*n1 - 11*u1*v1*v2 *a22*b11
+ ------------------------ + --------------------------
9 36
2 2 2
- 7*u1*v1*v3 *a22*b11 - 2*u1*v2 *a22*b11*n1
+ ------------------------- + ------------------------
36 9
2
- 2*u1*v3 *a22*b11*n1 3 3 2 3
+ ------------------------ - u2 *v2*a22 - u2 *u3*v3*a22
9
2 2 2 2 2 2 2 3
- u2 *v1 *a22 *b11 - u2 *v3 *a22 *b11 u2*u3 *v2*a22
+ --------------------- + --------------------- + ----------------
6 6 3
2 3 2
u2*u3*v2*v3*a22 *b11 - 2*u2*v1*v2*a22*b11*n1 - u2*v2 *a22*b11
+ ---------------------- + -------------------------- + --------------------
3 9 36
2 2 3 3 2 2 2
u2*v2*v3 *a22*b11 u3 *v3*a22 5*u3 *v1 *a22 *b11
+ -------------------- + ------------- + --------------------
12 3 18
2 2 2 2 2 2 2 2
5*u3 *v2 *a22 *b11 4*u3 *v3 *a22 *b11 - 2*u3*v1 *v3*a22*b11
+ -------------------- + -------------------- + -------------------------
18 9 9
2 2
- 2*u3*v1*v3*a22*b11*n1 - u3*v2 *v3*a22*b11
+ -------------------------- + -----------------------
9 4
3 2 3 2 2 2 3
- 5*u3*v3 *a22*b11 v1 *b11 *n1 - 17*v1 *v2 *b11
+ ---------------------- + ------------- + --------------------
36 27 216
2 2 3 2 2 2 2 4 3
- v1 *v3 *b11 v1*v2 *b11 *n1 v1*v3 *b11 *n1 - 17*v2 *b11
+ ----------------- + ---------------- + ---------------- + ----------------
216 27 27 216
2 2 3 4 3
- v2 *v3 *b11 - v3 *b11
+ ----------------- + -------------}
12 216
{HAM,FI} = 0
3 3 3 3 2 2 4
FI= - 216*u1 *v1*a22 *b11 - 432*u1 *a22 *n1 - 648*u1 *u2 *a22
2 2 4 2 2 2 2 2 2 2 2
+ 216*u1 *u3 *a22 - 162*u1 *v2 *a22 *b11 - 90*u1 *v3 *a22 *b11
2 3 2 3 2 3
- 1296*u1*u2 *a22 *n1 - 288*u1*u3 *v1*a22 *b11 - 144*u1*u3 *a22 *n1
2 2 2 3 3
+ 288*u1*u3*v1*v3*a22 *b11 + 576*u1*u3*v3*a22 *b11*n1 + 120*u1*v1 *a22*b11
2 2 2 3 2 3
- 144*u1*v1 *a22*b11 *n1 + 216*u1*v1*v2 *a22*b11 + 144*u1*v1*v3 *a22*b11
2 2 2 2 3
+ 108*u1*v2 *a22*b11 *n1 + 108*u1*v3 *a22*b11 *n1 + 1536*u1*a22*n1
4 4 2 3 2 2 2 2
- 1296*u2 *a22 + 864*u2 *u3*v3*a22 *b11 - 216*u2 *v1 *a22 *b11
2 2 2 2 2 2 2 2 2
- 864*u2 *v1*a22 *b11*n1 + 72*u2 *v3 *a22 *b11 + 2592*u2 *a22 *n1
4 4 3 3 2 2 2 2
+ 144*u3 *a22 - 288*u3 *v3*a22 *b11 - 120*u3 *v1 *a22 *b11
2 2 2 2 2 2 2 2 2 2
+ 96*u3 *v1*a22 *b11*n1 - 216*u3 *v2 *a22 *b11 - 144*u3 *v3 *a22 *b11
2 2 2 2 3 2
- 480*u3 *a22 *n1 + 192*u3*v1 *v3*a22*b11 + 192*u3*v1*v3*a22*b11 *n1
2 3 3 3 2
+ 216*u3*v2 *v3*a22*b11 + 120*u3*v3 *a22*b11 - 384*u3*v3*a22*b11*n1
3 3 2 2 4 2 2 4 2 3
- 112*v1 *b11 *n1 + 58*v1 *v2 *b11 + 34*v1 *v3 *b11 - 72*v1*v2 *b11 *n1
2 3 3 4 4 2 2 4
- 24*v1*v3 *b11 *n1 + 704*v1*b11*n1 + 65*v2 *b11 + 76*v2 *v3 *b11
2 2 2 4 4 2 2 2
+ 72*v2 *b11 *n1 + 19*v3 *b11 - 120*v3 *b11 *n1
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 3 3 3 2 2 4 2 2 4
FI=216*u1 *v1*a22 *b11 + 432*u1 *a22 *n1 + 648*u1 *u2 *a22 - 216*u1 *u3 *a22
2 2 2 2 2 2 2 2 2 2
+ 576*u1 *v1*a22 *b11*n1 - 126*u1 *v2 *a22 *b11 - 198*u1 *v3 *a22 *b11
2 3 2 3 2 2
+ 864*u1*u2 *v1*a22 *b11 + 1296*u1*u2 *a22 *n1 + 288*u1*u2*v1*v2*a22 *b11
2 2 3 3 3
+ 576*u1*u2*v2*a22 *b11*n1 + 144*u1*u3 *a22 *n1 + 264*u1*v1 *a22*b11
2 2 2 3 2 3
+ 528*u1*v1 *a22*b11 *n1 + 192*u1*v1*v2 *a22*b11 + 168*u1*v1*v3 *a22*b11
2 2 2 2 3
+ 84*u1*v2 *a22*b11 *n1 + 84*u1*v3 *a22*b11 *n1 - 1536*u1*a22*n1
4 4 3 3 2 2 2 2
+ 1296*u2 *a22 + 864*u2 *v2*a22 *b11 + 216*u2 *v1 *a22 *b11
2 2 2 2 2 2 2 2 2
+ 864*u2 *v1*a22 *b11*n1 - 72*u2 *v3 *a22 *b11 - 2592*u2 *a22 *n1
2 3 2 3 3
- 288*u2*u3 *v2*a22 *b11 + 192*u2*v1*v2*a22*b11 *n1 + 24*u2*v2 *a22*b11
2 3 4 4 2 2 2 2
- 72*u2*v2*v3 *a22*b11 - 144*u3 *a22 - 264*u3 *v1 *a22 *b11
2 2 2 2 2 2 2 2 2 2
- 96*u3 *v1*a22 *b11*n1 - 168*u3 *v2 *a22 *b11 - 240*u3 *v3 *a22 *b11
2 2 2 2 3 2 3
+ 480*u3 *a22 *n1 + 192*u3*v1 *v3*a22*b11 + 192*u3*v2 *v3*a22*b11
3 3 2 3 3
+ 192*u3*v3 *a22*b11 + 384*u3*v3*a22*b11*n1 - 16*v1 *b11 *n1
2 2 4 2 2 4 2 3 2 3
+ 70*v1 *v2 *b11 - 2*v1 *v3 *b11 - 56*v1*v2 *b11 *n1 - 104*v1*v3 *b11 *n1
3 4 4 2 2 4 2 2 2
- 704*v1*b11*n1 + 63*v2 *b11 + 84*v2 *v3 *b11 - 72*v2 *b11 *n1
4 4 2 2 2
+ 13*v3 *b11 + 120*v3 *b11 *n1
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
2 2 2 2
FI=12*u1*v1*a22*b11 + 24*u1*a22*n1 + 36*u2 *a22 - 12*u3 *a22 + 8*v1*b11*n1
2 2 2 2
+ v2 *b11 - 3*v3 *b11
= a product of the elements of: {36,
2 2
u1*v1*a22*b11 2*u1*a22*n1 2 2 - u3 *a22 2*v1*b11*n1
--------------- + ------------- + u2 *a22 + ------------- + -------------
3 3 3 9
2 2 2 2
v2 *b11 - v3 *b11
+ ---------- + -------------}
36 12
{HAM,FI} = 0
And again in machine readable form:
HAM=( - u1**2*a22)/2 + u1*v1*b11 + u1*n1 + u2**2*a22 - u3**2*a22 + (2*u3*v3*b11)
/3 + (v2**2*b11**2)/(4*a22) + ( - v3**2*b11**2)/(36*a22)$
FI= - 144*u1**2*v1*a22**2*n1 + 36*u1**2*v2**2*a22**2*b11 + 36*u1**2*v3**2*a22**2
*b11 - 216*u1*u2**2*v1*a22**3 - 144*u1*u2*v2*a22**2*n1 + 72*u1*u3**2*v1*a22**3 -
144*u1*u3*v3*a22**2*n1 - 60*u1*v1**3*a22*b11**2 - 96*u1*v1**2*a22*b11*n1 - 66*
u1*v1*v2**2*a22*b11**2 - 42*u1*v1*v3**2*a22*b11**2 - 48*u1*v2**2*a22*b11*n1 - 48
*u1*v3**2*a22*b11*n1 - 216*u2**3*v2*a22**3 - 216*u2**2*u3*v3*a22**3 - 36*u2**2*
v1**2*a22**2*b11 - 36*u2**2*v3**2*a22**2*b11 + 72*u2*u3**2*v2*a22**3 + 72*u2*u3*
v2*v3*a22**2*b11 - 48*u2*v1*v2*a22*b11*n1 - 6*u2*v2**3*a22*b11**2 + 18*u2*v2*v3
**2*a22*b11**2 + 72*u3**3*v3*a22**3 + 60*u3**2*v1**2*a22**2*b11 + 60*u3**2*v2**2
*a22**2*b11 + 96*u3**2*v3**2*a22**2*b11 - 48*u3*v1**2*v3*a22*b11**2 - 48*u3*v1*
v3*a22*b11*n1 - 54*u3*v2**2*v3*a22*b11**2 - 30*u3*v3**3*a22*b11**2 + 8*v1**3*b11
**2*n1 - 17*v1**2*v2**2*b11**3 - v1**2*v3**2*b11**3 + 8*v1*v2**2*b11**2*n1 + 8*
v1*v3**2*b11**2*n1 - 17*v2**4*b11**3 - 18*v2**2*v3**2*b11**3 - v3**4*b11**3$
FI= - 216*u1**3*v1*a22**3*b11 - 432*u1**3*a22**3*n1 - 648*u1**2*u2**2*a22**4 +
216*u1**2*u3**2*a22**4 - 162*u1**2*v2**2*a22**2*b11**2 - 90*u1**2*v3**2*a22**2*
b11**2 - 1296*u1*u2**2*a22**3*n1 - 288*u1*u3**2*v1*a22**3*b11 - 144*u1*u3**2*a22
**3*n1 + 288*u1*u3*v1*v3*a22**2*b11**2 + 576*u1*u3*v3*a22**2*b11*n1 + 120*u1*v1
**3*a22*b11**3 - 144*u1*v1**2*a22*b11**2*n1 + 216*u1*v1*v2**2*a22*b11**3 + 144*
u1*v1*v3**2*a22*b11**3 + 108*u1*v2**2*a22*b11**2*n1 + 108*u1*v3**2*a22*b11**2*n1
+ 1536*u1*a22*n1**3 - 1296*u2**4*a22**4 + 864*u2**2*u3*v3*a22**3*b11 - 216*u2**
2*v1**2*a22**2*b11**2 - 864*u2**2*v1*a22**2*b11*n1 + 72*u2**2*v3**2*a22**2*b11**
2 + 2592*u2**2*a22**2*n1**2 + 144*u3**4*a22**4 - 288*u3**3*v3*a22**3*b11 - 120*
u3**2*v1**2*a22**2*b11**2 + 96*u3**2*v1*a22**2*b11*n1 - 216*u3**2*v2**2*a22**2*
b11**2 - 144*u3**2*v3**2*a22**2*b11**2 - 480*u3**2*a22**2*n1**2 + 192*u3*v1**2*
v3*a22*b11**3 + 192*u3*v1*v3*a22*b11**2*n1 + 216*u3*v2**2*v3*a22*b11**3 + 120*u3
*v3**3*a22*b11**3 - 384*u3*v3*a22*b11*n1**2 - 112*v1**3*b11**3*n1 + 58*v1**2*v2
**2*b11**4 + 34*v1**2*v3**2*b11**4 - 72*v1*v2**2*b11**3*n1 - 24*v1*v3**2*b11**3*
n1 + 704*v1*b11*n1**3 + 65*v2**4*b11**4 + 76*v2**2*v3**2*b11**4 + 72*v2**2*b11**
2*n1**2 + 19*v3**4*b11**4 - 120*v3**2*b11**2*n1**2$
FI=216*u1**3*v1*a22**3*b11 + 432*u1**3*a22**3*n1 + 648*u1**2*u2**2*a22**4 - 216*
u1**2*u3**2*a22**4 + 576*u1**2*v1*a22**2*b11*n1 - 126*u1**2*v2**2*a22**2*b11**2
- 198*u1**2*v3**2*a22**2*b11**2 + 864*u1*u2**2*v1*a22**3*b11 + 1296*u1*u2**2*a22
**3*n1 + 288*u1*u2*v1*v2*a22**2*b11**2 + 576*u1*u2*v2*a22**2*b11*n1 + 144*u1*u3
**2*a22**3*n1 + 264*u1*v1**3*a22*b11**3 + 528*u1*v1**2*a22*b11**2*n1 + 192*u1*v1
*v2**2*a22*b11**3 + 168*u1*v1*v3**2*a22*b11**3 + 84*u1*v2**2*a22*b11**2*n1 + 84*
u1*v3**2*a22*b11**2*n1 - 1536*u1*a22*n1**3 + 1296*u2**4*a22**4 + 864*u2**3*v2*
a22**3*b11 + 216*u2**2*v1**2*a22**2*b11**2 + 864*u2**2*v1*a22**2*b11*n1 - 72*u2
**2*v3**2*a22**2*b11**2 - 2592*u2**2*a22**2*n1**2 - 288*u2*u3**2*v2*a22**3*b11 +
192*u2*v1*v2*a22*b11**2*n1 + 24*u2*v2**3*a22*b11**3 - 72*u2*v2*v3**2*a22*b11**3
- 144*u3**4*a22**4 - 264*u3**2*v1**2*a22**2*b11**2 - 96*u3**2*v1*a22**2*b11*n1
- 168*u3**2*v2**2*a22**2*b11**2 - 240*u3**2*v3**2*a22**2*b11**2 + 480*u3**2*a22
**2*n1**2 + 192*u3*v1**2*v3*a22*b11**3 + 192*u3*v2**2*v3*a22*b11**3 + 192*u3*v3
**3*a22*b11**3 + 384*u3*v3*a22*b11*n1**2 - 16*v1**3*b11**3*n1 + 70*v1**2*v2**2*
b11**4 - 2*v1**2*v3**2*b11**4 - 56*v1*v2**2*b11**3*n1 - 104*v1*v3**2*b11**3*n1 -
704*v1*b11*n1**3 + 63*v2**4*b11**4 + 84*v2**2*v3**2*b11**4 - 72*v2**2*b11**2*n1
**2 + 13*v3**4*b11**4 + 120*v3**2*b11**2*n1**2$
FI=12*u1*v1*a22*b11 + 24*u1*a22*n1 + 36*u2**2*a22**2 - 12*u3**2*a22**2 + 8*v1*
b11*n1 + v2**2*b11**2 - 3*v3**2*b11**2$