Solution 1 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
2 2
0=a12 + a13
Expressions
The solution is given through the following expressions:
1 2 1
- a12*a13*m1*n3*r214 + ---*a12*b11*n3 *r214 + ---*a13*b11*n2*n3*r214
6 6
r10=-----------------------------------------------------------------------
2 3
a12*a13 *n3 - a13 *n2
1 2 1 2 3
---*a12 *b11*n2*n3*r214 + ---*a12*a13*b11*n2 *r214 + a13 *m1*n2*r214
6 6
r11=----------------------------------------------------------------------
2 2 3
a12 *a13 *n3 - a12*a13 *n2
1 2 1 3
---*a12 *b11*n1*n3*r214 + ---*a12*a13*b11*n1*n2*r214 + a13 *m1*n1*r214
6 6
r12=------------------------------------------------------------------------
2 2 3
a12 *a13 *n3 - a12*a13 *n2
r13=0
r14=0
r15=0
1 3 2 1 2 2
r20=(----*a12 *b11 *n3*r214 - ----*a12 *a13*b11 *n2*r214
36 18
1 2 2 1 3 2 4
+ ----*a12*a13 *b11 *n3*r214 - ----*a13 *b11 *n2*r214)/(a12*a13 *n3
36 18
5
- a13 *n2)
1 2 2 1 2 2
----*a12 *b11 *r214 + ----*a13 *b11 *r214
18 18
r21=-------------------------------------------
3
a12*a13
1 2
- ----*a12*b11 *n1*r214
18
r23=--------------------------
2 3
a12*a13 *n3 - a13 *n2
1 2
- ----*b11 *n1*r214
18
r24=----------------------
2
a12*a13*n3 - a13 *n2
1 4 2 1 3 2
r25=( - ---*a12 *b11 *n3*r214 + ----*a12 *a13*b11 *n2*r214
9 36
1 2 3 1 2 2 2
+ ---*a12 *a13 *b11*m1*r214 - ----*a12 *a13 *b11 *n3*r214
6 36
1 3 2 1 5 2 4
+ ---*a12*a13 *b11 *n2*r214 + ---*a13 *b11*m1*r214)/(a12 *a13 *n3
9 2
5
- a12*a13 *n2)
r26=0
1
- ---*b11*n1*r214
3
r27=--------------------
a12*n3 - a13*n2
1
---*a12*b11*n3*r214
3
r28=----------------------
2
a12*a13*n3 - a13 *n2
r29=r214
1
---*b11*n1*r214
3
r210=-----------------
a12*n3 - a13*n2
1
---*a12*b11*n2*r214
3
r212=----------------------
2
a12*a13*n3 - a13 *n2
r213=0
1 2
---*a12*b11*n2*r214 + 2*a13 *m1*r214
3
r215=--------------------------------------
2
a12 *n3 - a12*a13*n2
1
2*a13*m1*r214 - ---*b11*n3*r214
3
r216=---------------------------------
a12*n3 - a13*n2
r217=0
r219=0
r220=r214
r30=0
r31=0
r32=0
r33=0
r34=0
r35=0
r36=0
1 3
- ----*a12*b11 *r214
54
r37=-----------------------
2 3
a12*a13 *n3 - a13 *n2
1 3
- ----*b11 *r214
54
r38=----------------------
2
a12*a13*n3 - a13 *n2
r39=0
r310=r338
r311=r339
r312=0
1 3 2 3 1 2 2
r313=( - ---*a12 *b11 *r214 + a12*a13 *n3*r340 - ---*a12*a13 *b11 *r214
9 3
4 3 4
- a13 *n2*r340)/(a12*a13 *n3 - a13 *n2)
1 2 2
---*a12 *b11 *r214
9
r314=-----------------------
2 3
a12*a13 *n3 - a13 *n2
r315=0
2
- ---*a12*b11*r214 + a12*n3*r343 - a13*n2*r343
3
r316=-------------------------------------------------
a12*n3 - a13*n2
r317=0
r318=0
r319=0
r320=0
r321=r338
r322=r339
1 2 2
- ---*a12 *b11 *r214
9
r323=-----------------------
2 3
a12*a13 *n3 - a13 *n2
1 3 2 3 1 2 2
r324=( - ---*a12 *b11 *r214 + a12*a13 *n3*r340 - ---*a12*a13 *b11 *r214
9 3
4 3 4
- a13 *n2*r340)/(a12*a13 *n3 - a13 *n2)
r325=0
2
- ---*a12*b11*r214 + a12*n3*r343 - a13*n2*r343
3
r327=-------------------------------------------------
a12*n3 - a13*n2
r328=0
r329=0
r330=0
r331=r326
r332=0
r333=0
r334=0
1 3 2
- ---*a12 *b11 *r214
9
r335=-----------------------
3 4
a12*a13 *n3 - a13 *n2
r336=0
1 2
---*a12*b11 *r214
9
r337=----------------------
2
a12*a13*n3 - a13 *n2
r342=0
r344=0
r345=0
r346=r341
2
a12*n3*r326 - ---*a13*b11*r214 - a13*n2*r326
3
r347=----------------------------------------------
a12*n3 - a13*n2
r348=0
r349=0
2
- ---*a12*b11*r214
3
r350=---------------------
a12*n3 - a13*n2
2
---*a13*b11*r214
3
r351=------------------
a12*n3 - a13*n2
r352=r341
r353=0
r354=0
r355=0
1
- ---*b11*n1
6
m3=---------------
a13
1
---*a12*b11*n1
6
m2=----------------
2
a13
c33=0
c23=0
c22=0
1 2
- ----*b11
36
c13=--------------
a13
1 2
- ----*b11
36
c12=--------------
a12
b33=0
b31=0
b21=0
b13=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:
r340, r338, r339, r341, r343, r326, r214, m1, n2, n3,
b11, n1, a12, a13
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.
{a12*n3 - a13*n2,a12,a13,r214}
Relevance for the application:
Modulo the following equation:
2 2
0=a12 + a13
the system of equations related to the Hamiltonian HAM:
2 2 3 2 2
HAM=(2*u1*u2*a12 *a13 + 2*u1*u3*a12*a13 + u1*v1*a12*a13 *b11 + u1*a12*a13 *n1
2 2 1 2 2
+ u2*a12*a13 *n2 + u3*a12*a13 *n3 - ----*v1*v2*a13 *b11
18
1 2 2 1 2
- ----*v1*v3*a12*a13*b11 + v1*a12*a13 *m1 + ---*v2*a12 *b11*n1
18 6
1 2
- ---*v3*a12*a13*b11*n1)/(a12*a13 )
6
has apart from the Hamiltonian and Casimirs the following 7 first integrals:
2 2 5 2 2 2 4
FI=---*u1 *v2*a12*a13 *b11 - ---*u1 *v3*a12 *a13 *b11
3 3
2 2 4 5 2 5
+ u1 *(a12 *a13 *n3 - a12*a13 *n2) - ---*u1*u2*v1*a12*a13 *b11
3
1 2 2 3 2 5 1 4
+ ---*u1*v2 *a12 *a13 *b11 + u1*v2*(2*a12*a13 *m1 - ---*a12*a13 *b11*n3)
9 3
1 2 4 2 1 4 6
- ---*u1*v3 *a12 *a13*b11 + u1*v3*(---*a12*a13 *b11*n2 + 2*a13 *m1)
9 3
2 2 4 5 2 2 4
+ u2 *(a12 *a13 *n3 - a12*a13 *n2) - ---*u2*u3*v2*a12 *a13 *b11
3
1 4 2 1 2 3 2
+ u2*v1*v2*( - ---*a12 *a13*b11 - ---*a12 *a13 *b11 )
9 3
1 3 2 2 1 2 3
- ---*u2*v1*v3*a12 *a13 *b11 + ---*u2*v1*a12 *a13 *b11*n2
9 3
1 4 2 2 2 4
+ ---*u2*v3*a12*a13 *b11*n1 - ---*u3 *v3*a12 *a13 *b11
3 3
2 2 4 5 1 3 2 2
+ u3 *(a12 *a13 *n3 - a12*a13 *n2) + ---*u3*v1*v2*a12 *a13 *b11
9
1 4 2 1 2 3 2
+ u3*v1*v3*( - ---*a12 *a13*b11 - ---*a12 *a13 *b11 )
9 3
1 2 3 1 4
+ ---*u3*v1*a12 *a13 *b11*n3 - ---*u3*v2*a12*a13 *b11*n1
3 3
1 2 3 3 1 2 2 2 3 2
- ----*v1 *v2*a12*a13 *b11 - ----*v1 *v3*a12 *a13 *b11 + v1 *(
54 54
1 4 2 1 3 2 1 2 3
- ---*a12 *b11 *n3 + ----*a12 *a13*b11 *n2 + ---*a12 *a13 *b11*m1
9 36 6
1 2 2 2 1 3 2 1 5
- ----*a12 *a13 *b11 *n3 + ---*a12*a13 *b11 *n2 + ---*a13 *b11*m1)
36 9 2
1 3 2 1 2 2 2
- ----*v1*v2*a12*a13 *b11 *n1 - ----*v1*v3*a12 *a13 *b11 *n1
18 18
1 2 2 1 3 5
+ v1*(---*a12 *a13 *b11*n1*n3 + ---*a12*a13 *b11*n1*n2 + a13 *m1*n1) + v2*v3
6 6
1 3 2 1 2 2 2 1 3 2
*(----*a12 *a13*b11 *n3 - ----*a12 *a13 *b11 *n2 + ----*a12*a13 *b11 *n3
18 18 18
1 4 2
- ----*a13 *b11 *n2)
18
1 2 2 1 3 2 5 2
+ v2*(---*a12 *a13 *b11*n2*n3 + ---*a12*a13 *b11*n2 + a13 *m1*n2) + v3 *(
6 6
1 4 2 1 3 2 1 2 2 2
----*a12 *b11 *n3 - ----*a12 *a13*b11 *n2 + ----*a12 *a13 *b11 *n3
36 18 36
1 3 2
- ----*a12*a13 *b11 *n2)
18
2 3 1 2 2 2 1 3
+ v3*( - a12 *a13 *m1*n3 + ---*a12 *a13 *b11*n3 + ---*a12*a13 *b11*n2*n3)
6 6
4 3 9 4 2 9
{HAM,FI} = - ---*u1 *v1*a13 *b11 - ---*u1 *u2*v2*a13 *b11
3 3
4 2 9 4 2 7 2
- ---*u1 *u3*v3*a13 *b11 - ---*u1 *v1*v2*a12*a13 *b11
3 9
2 2 8 2 2 2 7
+ ---*u1 *v1*v3*a13 *b11 + ---*u1 *v1*a12*a13 *b11*n2
9 3
4 2 9 4 8
+ ---*u1*u2 *v1*a13 *b11 - ---*u1*u2*u3*v1*a12*a13 *b11
3 3
2 2 7 2 2 7
- ---*u1*u2*v1 *a12*a13 *b11 - ---*u1*u2*v1*a12*a13 *b11*n1
3 3
4 2 7 2 2 8 2
- ---*u1*u2*v2 *a12*a13 *b11 + ---*u1*u2*v2*v3*a13 *b11
9 9
2 7 4 7 2
+ ---*u1*u2*v2*a12*a13 *b11*n2 - ---*u1*u3*v2*v3*a12*a13 *b11
3 9
2 2 8 2 2 7
+ ---*u1*u3*v3 *a13 *b11 + ---*u1*u3*v3*a12*a13 *b11*n2
9 3
1 3 7 3 1 2 7 2
- ----*u1*v1 *a13 *b11 - ---*u1*v1 *a13 *b11 *n1
27 9
1 2 7 3 1 6 3
+ ----*u1*v1*v2 *a13 *b11 + ----*u1*v1*v2*v3*a12*a13 *b11
27 27
2 7 1 6 2
+ u1*v1*v2*( - ---*a12*a13 *b11*m1 + ---*a12*a13 *b11 *n3)
3 9
1 6 2 4 3 9
- ---*u1*v1*v3*a12*a13 *b11 *n2 + ---*u2 *v2*a13 *b11
9 3
4 2 8 4 2 9
- ---*u2 *u3*v2*a12*a13 *b11 + ---*u2 *u3*v3*a13 *b11
3 3
2 2 7 2 2 2 7
- ---*u2 *v1*v2*a12*a13 *b11 - ---*u2 *v2*a12*a13 *b11*n1
3 3
4 2 8 2 7 2
- ---*u2*u3 *v3*a12*a13 *b11 - ---*u2*u3*v1*v3*a12*a13 *b11
3 3
2 7 1 2 7 3
- ---*u2*u3*v3*a12*a13 *b11*n1 - ----*u2*v1 *v2*a13 *b11
3 27
1 7 2 1 3 7 3
- ---*u2*v1*v2*a13 *b11 *n1 + ----*u2*v2 *a13 *b11
9 27
1 2 6 3
+ ----*u2*v2 *v3*a12*a13 *b11
27
2 2 7 1 6 2
+ u2*v2 *( - ---*a12*a13 *b11*m1 + ---*a12*a13 *b11 *n3)
3 9
1 6 2 1 2 7 3
- ---*u2*v2*v3*a12*a13 *b11 *n2 - ----*u3*v1 *v3*a13 *b11
9 27
1 7 2 1 2 7 3
- ---*u3*v1*v3*a13 *b11 *n1 + ----*u3*v2 *v3*a13 *b11
9 27
1 2 6 3
+ ----*u3*v2*v3 *a12*a13 *b11
27
2 7 1 6 2
+ u3*v2*v3*( - ---*a12*a13 *b11*m1 + ---*a12*a13 *b11 *n3)
3 9
1 2 6 2
- ---*u3*v3 *a12*a13 *b11 *n2
9
2
FI=u1*u2*v1 + u2 *v2 + u2*u3*v3
3 2 2 2 2 2
{HAM,FI} = - 2*u1 *v1*a12*a13 - 2*u1 *u2*v2*a12*a13 - 2*u1 *u3*v3*a12*a13
2 2 3
+ u1 *v1*v3*a12*a13*b11 - u1 *v1*a12*a13*n3 - 2*u1*u2*u3*v1*a13
+ u1*u2*v2*v3*a12*a13*b11 - u1*u2*v2*a12*a13*n3
2 2 2
+ 2*u1*u3 *v1*a12*a13 + u1*u3*v1 *a12*a13*b11 + u1*u3*v1*a12*a13*n1
2 1 3 2
+ u1*u3*v3 *a12*a13*b11 - u1*u3*v3*a12*a13*n3 + ----*u1*v1 *a12*b11
18
1 2 1 2
+ ---*u1*v1 *a12*b11*n1 - ----*u1*v1*v2*v3*a13*b11
6 18
1 2 2 2 3
- ----*u1*v1*v3 *a12*b11 + u1*v1*v3*a12*a13*m1 - 2*u2 *u3*v2*a13
18
2 2 2 3
+ 2*u2*u3 *v2*a12*a13 - 2*u2*u3 *v3*a13 + u2*u3*v1*v2*a12*a13*b11
1 2 2
+ u2*u3*v2*a12*a13*n1 + ----*u2*v1 *v2*a12*b11
18
1 1 2 2
+ ---*u2*v1*v2*a12*b11*n1 - ----*u2*v2 *v3*a13*b11
6 18
1 2 2 3 2
- ----*u2*v2*v3 *a12*b11 + u2*v2*v3*a12*a13*m1 + 2*u3 *v3*a12*a13
18
2 2
+ u3 *v1*v3*a12*a13*b11 + u3 *v3*a12*a13*n1
1 2 2 1
+ ----*u3*v1 *v3*a12*b11 + ---*u3*v1*v3*a12*b11*n1
18 6
1 2 2 1 3 2 2
- ----*u3*v2*v3 *a13*b11 - ----*u3*v3 *a12*b11 + u3*v3 *a12*a13*m1
18 18
2
FI=u1*u3*v1 + u2*u3*v2 + u3 *v3
3 4 2 4 2 4
{HAM,FI} = - 2*u1 *v1*a13 - 2*u1 *u2*v2*a13 - 2*u1 *u3*v3*a13
2 2 2 2 2 4
- u1 *v1*v2*a12*a13 *b11 + u1 *v1*a12*a13 *n2 + 2*u1*u2 *v1*a13
3 2 2
- 2*u1*u2*u3*v1*a12*a13 - u1*u2*v1 *a12*a13 *b11
2 2 2
- u1*u2*v1*a12*a13 *n1 - u1*u2*v2 *a12*a13 *b11
2 2
+ u1*u2*v2*a12*a13 *n2 - u1*u3*v2*v3*a12*a13 *b11
2 1 3 2 2
+ u1*u3*v3*a12*a13 *n2 - ----*u1*v1 *a13 *b11
18
1 2 2 1 2 2 2
- ---*u1*v1 *a13 *b11*n1 + ----*u1*v1*v2 *a13 *b11
6 18
1 2 2
+ ----*u1*v1*v2*v3*a12*a13*b11 - u1*v1*v2*a12*a13 *m1
18
3 4 2 3 2 4
+ 2*u2 *v2*a13 - 2*u2 *u3*v2*a12*a13 + 2*u2 *u3*v3*a13
2 2 2 2 2 3
- u2 *v1*v2*a12*a13 *b11 - u2 *v2*a12*a13 *n1 - 2*u2*u3 *v3*a12*a13
2 2
- u2*u3*v1*v3*a12*a13 *b11 - u2*u3*v3*a12*a13 *n1
1 2 2 2 1 2
- ----*u2*v1 *v2*a13 *b11 - ---*u2*v1*v2*a13 *b11*n1
18 6
1 3 2 2 1 2 2
+ ----*u2*v2 *a13 *b11 + ----*u2*v2 *v3*a12*a13*b11
18 18
2 2 1 2 2 2
- u2*v2 *a12*a13 *m1 - ----*u3*v1 *v3*a13 *b11
18
1 2 1 2 2 2
- ---*u3*v1*v3*a13 *b11*n1 + ----*u3*v2 *v3*a13 *b11
6 18
1 2 2 2
+ ----*u3*v2*v3 *a12*a13*b11 - u3*v2*v3*a12*a13 *m1
18
2
FI=u1 *v1 + u1*u2*v2 + u1*u3*v3
2 3 2 4 2 3
{HAM,FI} = 2*u1 *u2*v1*a12*a13 + 2*u1 *u3*v1*a13 + 2*u1*u2 *v2*a12*a13
4 3 2
+ 2*u1*u2*u3*v2*a13 + 2*u1*u2*u3*v3*a12*a13 + u1*u2*v1*a12*a13 *n3
2 4 2
+ 2*u1*u3 *v3*a13 - u1*u3*v1*a12*a13 *n2
1 2 2 1 2 2 2
- ----*u1*v1 *v2*a12*a13*b11 + ----*u1*v1 *v3*a13 *b11
18 18
1 1 2
- ---*u1*v1*v2*a12*a13*b11*n1 + ---*u1*v1*v3*a13 *b11*n1
6 6
2 2 2 2
+ u2 *v2*a12*a13 *n3 - u2*u3*v2*a12*a13 *n2 + u2*u3*v3*a12*a13 *n3
1 2 2 1 2 2
- ----*u2*v1*v2 *a12*a13*b11 + ----*u2*v1*v2*v3*a13 *b11
18 18
1 2 1 2
- ---*u2*v2 *a12*a13*b11*n1 + ---*u2*v2*v3*a13 *b11*n1
6 6
2 2 1 2
- u3 *v3*a12*a13 *n2 - ----*u3*v1*v2*v3*a12*a13*b11
18
1 2 2 2 1
+ ----*u3*v1*v3 *a13 *b11 - ---*u3*v2*v3*a12*a13*b11*n1
18 6
1 2 2
+ ---*u3*v3 *a13 *b11*n1
6
2
FI=u1*v1*v2 + u2*v2 + u3*v2*v3
2 2
{HAM,FI} = - 2*u1 *v1 *a13 - 2*u1*u2*v1*v2*a13 + 2*u1*u2*v1*v3*a12
2 2 2
+ u1*v1 *v3*b11 - u1*v1 *n3 + u1*v1*v3*n1 + 2*u2 *v2*v3*a12
2
+ 2*u2*u3*v2*v3*a13 + 2*u2*u3*v3 *a12 + u2*v1*v2*v3*b11
2 2 2
- u2*v1*v2*n3 + u2*v2*v3*n1 + 2*u3 *v3 *a13 + u3*v1*v3 *b11
2
- u3*v1*v3*n3 + u3*v3 *n1
2
FI=u1*v1*v3 + u2*v2*v3 + u3*v3
2 2 2
{HAM,FI} = 2*u1 *v1 *a12 - 2*u1*u3*v1*v2*a13 + 2*u1*u3*v1*v3*a12 - u1*v1 *v2*b11
2 2 2 2
+ u1*v1 *n2 - u1*v1*v2*n1 - 2*u2 *v2 *a12 - 2*u2*u3*v2 *a13
2 2
- 2*u2*u3*v2*v3*a12 - u2*v1*v2 *b11 + u2*v1*v2*n2 - u2*v2 *n1
2
- 2*u3 *v2*v3*a13 - u3*v1*v2*v3*b11 + u3*v1*v3*n2 - u3*v2*v3*n1
2
FI=u1*v1 + u2*v1*v2 + u3*v1*v3
2 2 2
{HAM,FI} = 2*u1 *v1*v2*a13 - 2*u1 *v1*v3*a12 + 2*u1*u2*v2 *a13
2
- 2*u1*u2*v2*v3*a12 + 2*u1*u3*v2*v3*a13 - 2*u1*u3*v3 *a12
2
+ u1*v1*v2*n3 - u1*v1*v3*n2 + u2*v2 *n3 - u2*v2*v3*n2 + u3*v2*v3*n3
2
- u3*v3 *n2
And again in machine readable form:
HAM=(2*u1*u2*a12**2*a13**2 + 2*u1*u3*a12*a13**3 + u1*v1*a12*a13**2*b11 + u1*a12*
a13**2*n1 + u2*a12*a13**2*n2 + u3*a12*a13**2*n3 - 1/18*v1*v2*a13**2*b11**2 - 1/
18*v1*v3*a12*a13*b11**2 + v1*a12*a13**2*m1 + 1/6*v2*a12**2*b11*n1 - 1/6*v3*a12*
a13*b11*n1)/(a12*a13**2)$
FI=2/3*u1**2*v2*a12*a13**5*b11 - 2/3*u1**2*v3*a12**2*a13**4*b11 + u1**2*(a12**2*
a13**4*n3 - a12*a13**5*n2) - 2/3*u1*u2*v1*a12*a13**5*b11 + 1/9*u1*v2**2*a12**2*
a13**3*b11**2 + u1*v2*(2*a12*a13**5*m1 - 1/3*a12*a13**4*b11*n3) - 1/9*u1*v3**2*
a12**4*a13*b11**2 + u1*v3*(1/3*a12*a13**4*b11*n2 + 2*a13**6*m1) + u2**2*(a12**2*
a13**4*n3 - a12*a13**5*n2) - 2/3*u2*u3*v2*a12**2*a13**4*b11 + u2*v1*v2*( - 1/9*
a12**4*a13*b11**2 - 1/3*a12**2*a13**3*b11**2) - 1/9*u2*v1*v3*a12**3*a13**2*b11**
2 + 1/3*u2*v1*a12**2*a13**3*b11*n2 + 1/3*u2*v3*a12*a13**4*b11*n1 - 2/3*u3**2*v3*
a12**2*a13**4*b11 + u3**2*(a12**2*a13**4*n3 - a12*a13**5*n2) + 1/9*u3*v1*v2*a12
**3*a13**2*b11**2 + u3*v1*v3*( - 1/9*a12**4*a13*b11**2 - 1/3*a12**2*a13**3*b11**
2) + 1/3*u3*v1*a12**2*a13**3*b11*n3 - 1/3*u3*v2*a12*a13**4*b11*n1 - 1/54*v1**2*
v2*a12*a13**3*b11**3 - 1/54*v1**2*v3*a12**2*a13**2*b11**3 + v1**2*( - 1/9*a12**4
*b11**2*n3 + 1/36*a12**3*a13*b11**2*n2 + 1/6*a12**2*a13**3*b11*m1 - 1/36*a12**2*
a13**2*b11**2*n3 + 1/9*a12*a13**3*b11**2*n2 + 1/2*a13**5*b11*m1) - 1/18*v1*v2*
a12*a13**3*b11**2*n1 - 1/18*v1*v3*a12**2*a13**2*b11**2*n1 + v1*(1/6*a12**2*a13**
2*b11*n1*n3 + 1/6*a12*a13**3*b11*n1*n2 + a13**5*m1*n1) + v2*v3*(1/18*a12**3*a13*
b11**2*n3 - 1/18*a12**2*a13**2*b11**2*n2 + 1/18*a12*a13**3*b11**2*n3 - 1/18*a13
**4*b11**2*n2) + v2*(1/6*a12**2*a13**2*b11*n2*n3 + 1/6*a12*a13**3*b11*n2**2 +
a13**5*m1*n2) + v3**2*(1/36*a12**4*b11**2*n3 - 1/18*a12**3*a13*b11**2*n2 + 1/36*
a12**2*a13**2*b11**2*n3 - 1/18*a12*a13**3*b11**2*n2) + v3*( - a12**2*a13**3*m1*
n3 + 1/6*a12**2*a13**2*b11*n3**2 + 1/6*a12*a13**3*b11*n2*n3)$
FI=u1*u2*v1 + u2**2*v2 + u2*u3*v3$
FI=u1*u3*v1 + u2*u3*v2 + u3**2*v3$
FI=u1**2*v1 + u1*u2*v2 + u1*u3*v3$
FI=u1*v1*v2 + u2*v2**2 + u3*v2*v3$
FI=u1*v1*v3 + u2*v2*v3 + u3*v3**2$
FI=u1*v1**2 + u2*v1*v2 + u3*v1*v3$