Solution 4 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem over
Equations
The following unsolved equations remain:
4 2 2 2 2
0=4*a23 + 4*a23 *c22 - b31 *c22
2 2 2 2 2 2
0=4*a23 *b31 + 4*a23 *b33 - b31 *b33
2 2 4 2 2
0=4*b31 *c22 - b33 + 4*b33 *c22
2 4 4 2 2 4 2 2 2 6 4 2
0=16*a23 *b33 + 4*b31 *c22 - b31 *b33 - 8*b31 *b33 *c22 - b33 + 4*b33 *c22
Expressions
The solution is given through the following expressions:
1 2 2 3 1 4 2 1 4 3
r00=(---*b31 *c22 *n3 *r354 + ---*b33 *m2 *n3*r354 - ---*b33 *n3 *r354
2 8 8
1 2 2 3 3 4
+ ---*b33 *c22 *n3 *r354)/(a23 *b33 )
2
3 2 2 2 3 4 2 3 2 2 2
---*b31 *c22 *n3 *r354 - ---*b33 *n3 *r354 + ---*b33 *c22 *n3 *r354
2 8 2
r10=---------------------------------------------------------------------
3 3
a23 *b33
r11
3 2 2 3 4 3 2 2
- ---*b31 *c22 *m2*n3*r354 + ----*b33 *m2*n3*r354 - ---*b33 *c22 *m2*n3*r354
4 16 4
=-------------------------------------------------------------------------------
3 2
a23 *b33 *c22
r12=
3 3 2 2 3 4 2 3 2 2 2
- ---*b31 *c22 *n3 *r354 + ---*b31*b33 *n3 *r354 - ---*b31*b33 *c22 *n3 *r354
2 8 2
--------------------------------------------------------------------------------
3 4
a23 *b33
1 4 4 2 1 2 4 2 2
r13=(---*b31 *c22 *n3 *r354 + ---*b31 *b33 *c22 *m2 *r354
2 8
1 2 4 2 2 3 8 2
- ---*b31 *b33 *c22 *n3 *r354 + ----*b33 *n3 *r354
2 32
1 6 2 2 1 6 2 2 1 4 4 2
- ---*b33 *c22 *m2 *r354 - ---*b33 *c22 *n3 *r354 - ---*b33 *c22 *n3 *r354
8 4 2
3 6
)/(a23 *b33 *c22)
2 2 2 1 4 2 1 4 2
r14=(b31 *c22 *n3 *r354 + ---*b33 *m2 *r354 - ---*b33 *n3 *r354
4 4
2 2 2 2 4
+ b33 *c22 *n3 *r354)/(a23 *b33 )
r15=0
2 2 5 4 5 2 2
3*b31 *c22 *n3*r354 - ---*b33 *n3*r354 + ---*b33 *c22 *n3*r354
8 2
r20=----------------------------------------------------------------
3 2
a23 *b33
3 2 2 3 4 3 2 2
- ---*b31 *c22 *m2*r354 + ----*b33 *m2*r354 - ---*b33 *c22 *m2*r354
4 16 4
r21=----------------------------------------------------------------------
3
a23 *b33*c22
1 2 2
---*b31 *c22 *n3*r354
2
r22=-----------------------
3 2
a23 *b33
1 3 2 1 4 1 2 2
---*b31 *c22 *n3*r354 - ---*b31*b33 *n3*r354 + ---*b31*b33 *c22 *n3*r354
2 8 2
r23=--------------------------------------------------------------------------
3 3
a23 *b33
r24
3 3 2 3 4 3 2 2
- ---*b31 *c22 *m2*r354 + ----*b31*b33 *m2*r354 - ---*b31*b33 *c22 *m2*r354
4 16 4
=------------------------------------------------------------------------------
3 2
a23 *b33 *c22
r25
4 2 1 2 4 3 2 2 2
- 2*b31 *c22 *n3*r354 + ---*b31 *b33 *n3*r354 - ---*b31 *b33 *c22 *n3*r354
2 2
=-----------------------------------------------------------------------------
3 4
a23 *b33
4 4 5 2 4 2 2 2 4
r26=(2*b31 *c22 *n3*r354 - ---*b31 *b33 *c22 *n3*r354 - b31 *b33 *c22 *n3*r354
4
3 8 1 6 2 4 4 3
+ ----*b33 *n3*r354 - ---*b33 *c22 *n3*r354 - b33 *c22 *n3*r354)/(a23
16 2
5
*b33 *c22)
4 2 1 2 4 1 2 2 2
r27=( - b31 *c22 *m2*r354 + ---*b31 *b33 *m2*r354 + ---*b31 *b33 *c22 *m2*r354
4 2
1 6 1 4 2 3 4
- ---*b33 *m2*r354 + ---*b33 *c22 *m2*r354)/(a23 *b33 )
8 2
5 4 1 3 4 2
r28=( - 2*b31 *c22 *n3*r354 - ---*b31 *b33 *c22 *n3*r354
4
3 2 4 3 8 6 2
+ b31 *b33 *c22 *n3*r354 + ----*b31*b33 *n3*r354 - b31*b33 *c22 *n3*r354
16
4 4 3 6
+ b31*b33 *c22 *n3*r354)/(a23 *b33 *c22)
1 2 4 3 4 2 3 2 4
r29=(---*a23 *b33 *n3*r354 - ---*b31 *c22 *n3*r354 + ----*b31 *b33 *n3*r354
2 4 16
3 6 3 4 2 3 4
- ----*b33 *n3*r354 + ---*b33 *c22 *n3*r354)/(a23 *b33 )
16 4
2 2 1 4 2 2
4*b31 *c22 *n3*r354 - ---*b33 *n3*r354 + 2*b33 *c22 *n3*r354
2
r210=--------------------------------------------------------------
2 3
a23 *b33
2 2 3 4 2 2
- 2*b31 *c22 *m2*r354 + ---*b33 *m2*r354 - b33 *c22 *m2*r354
8
r211=---------------------------------------------------------------
2 2
a23 *b33 *c22
3 2 4 2 2
- 4*b31 *c22 *n3*r354 + b31*b33 *n3*r354 - 2*b31*b33 *c22 *n3*r354
r212=---------------------------------------------------------------------
2 4
a23 *b33
3 2 2 3 4 3 2 2
- ---*b31 *c22 *n3*r354 + ---*b33 *n3*r354 - ---*b33 *c22 *n3*r354
2 8 2
r213=---------------------------------------------------------------------
2 2
a23 *b33 *c22
1
---*n3*r354
2
r214=-------------
a23
1
---*b31*m2*r354
4
r215=-----------------
2
a23
b31*c22*n3*r354
r216=-----------------
2
a23 *b33
1
- ---*b33*m2*r354
4
r217=--------------------
2
a23
r218=0
r219=0
1
---*n3*r354
2
r220=-------------
a23
3 2 2 3 4 3 2 2
---*b31 *c22 *r354 - ---*b33 *r354 + ---*b33 *c22 *r354
2 8 2
r30=---------------------------------------------------------
3
a23 *b33
r31=0
r32=0
r33=0
3 2 3 4 2 2
3*b31 *c22 *r354 - ---*b31*b33 *r354 + 3*b31*b33 *c22 *r354
4
r34=-------------------------------------------------------------
3 2
a23 *b33
r35=0
r36=0
3 4 2 3 2 4 3 2 2 2
---*b31 *c22 *r354 - ---*b31 *b33 *r354 + ---*b31 *b33 *c22 *r354
2 8 2
r37=-------------------------------------------------------------------
3 3
a23 *b33
r38=0
r39=0
3 4 4 7 2 4 2 3 8
r310=(---*b31 *c22 *r354 - ---*b31 *b33 *c22 *r354 + ----*b33 *r354
2 8 32
3 4 4 3 4
- ---*b33 *c22 *r354)/(a23 *b33 *c22)
2
r311=0
1 4 3 1 2 2 3
- ---*b31 *c22 *r354 + ---*b31 *b33 *c22 *r354
2 2
r312=-------------------------------------------------
3 4
a23 *b33
5 4 5 3 4 2 3 8
r313=(2*b31 *c22 *r354 - ---*b31 *b33 *c22 *r354 + ----*b31*b33 *r354
4 16
1 6 2 4 4 3 5
- ---*b31*b33 *c22 *r354 - 2*b31*b33 *c22 *r354)/(a23 *b33 *c22)
4
r314=0
3 4 2 3 2 4 1 2 2 2
- ---*b31 *c22 *r354 + ----*b31 *b33 *r354 - ---*b31 *b33 *c22 *r354
8 32 4
r315=-----------------------------------------------------------------------
3 2
a23 *b33 *c22
1 2 4 3 4 2 3 2 4
r316=(---*a23 *b33 *r354 - ---*b31 *c22 *r354 + ----*b31 *b33 *r354
2 4 16
3 6 3 4 2 3 3
- ----*b33 *r354 + ---*b33 *c22 *r354)/(a23 *b33 )
16 4
r317=0
1 2 4 3 5 2 3 3 4
r318=(---*a23 *b31*b33 *r354 - ---*b31 *c22 *r354 + ----*b31 *b33 *r354
2 4 16
3 6 3 4 2 3 4
- ----*b31*b33 *r354 + ---*b31*b33 *c22 *r354)/(a23 *b33 )
16 4
1 2 2 4 1 2 6 3 6 3
r319=(---*a23 *b31 *b33 *c22*r354 - ---*a23 *b33 *c22*r354 - ---*b31 *c22 *r354
2 2 8
3 4 4 3 4 2 3
+ ----*b31 *b33 *c22*r354 + ---*b31 *b33 *c22 *r354
32 8
3 2 6 3 2 4 3 3 8
- ----*b31 *b33 *c22*r354 + ---*b31 *b33 *c22 *r354 + ----*b33 *c22*r354
16 8 32
3 6 3 3 6
- ---*b33 *c22 *r354)/(a23 *b33 )
8
2 2 3 4 2 2
3*b31 *c22 *r354 - ---*b33 *r354 + 3*b33 *c22 *r354
4
r320=-----------------------------------------------------
2 2
a23 *b33
r321=0
2 2
- b31 *c22 *r354
r322=-------------------
2 2
a23 *b33
3 2 3 4 2 2
4*b31 *c22 *r354 - ---*b31*b33 *r354 + 4*b31*b33 *c22 *r354
4
r323=-------------------------------------------------------------
2 3
a23 *b33
r324=0
r325=0
3 2 2 3 4 3 2 2
- ---*b31 *c22 *r354 + ---*b33 *r354 - ---*b33 *c22 *r354
2 8 2
r326=------------------------------------------------------------
2
a23 *b33*c22
r327=0
3 3 2 3 4 3 2 2
- ---*b31 *c22 *r354 + ---*b31*b33 *r354 - ---*b31*b33 *c22 *r354
2 8 2
r328=--------------------------------------------------------------------
2 2
a23 *b33 *c22
2 4 3 4 2 3 2 4 3 6
r329=(a23 *b33 *r354 - ---*b31 *c22 *r354 + ---*b31 *b33 *r354 - ---*b33 *r354
2 8 8
3 4 2 2 4
+ ---*b33 *c22 *r354)/(a23 *b33 )
2
1
---*b33*r354
2
r330=--------------
a23
r331=0
1
---*b31*r354
2
r332=--------------
a23
2 2 3 4 2 2
- b31 *c22 *r354 + ---*b33 *r354 - 2*b33 *c22 *r354
8
r333=------------------------------------------------------
2
a23*b33 *c22
r334=r354
r335=0
1
---*b31*c22*r354
2
r336=------------------
2
a23
r337=0
r338=0
1 2
---*b31 *c22*r354
2
r339=-------------------
2
a23 *b33
r340=0
r341=0
r342=0
r343=0
r344=0
r345=0
r346=0
r347=0
r348=0
r349=0
1
---*b33*r354
2
r350=--------------
a23
r351=0
1
---*b31*r354
2
r352=--------------
a23
1 2 1 2
---*b31 *c22*r354 - ---*b33 *c22*r354
2 2
r353=---------------------------------------
2
a23*b33
r355=0
- 2*c22*n3
m3=-------------
b33
2*b31*c22*n3
m1=--------------
2
b33
2 2
b31 *c22 + b33 *c22
c11=---------------------
2
b33
b32=0
2 2
b31 *c22 - b33 *c22
a33=---------------------
2
b33
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:
r354, n3, m2, c22, b33, b31, a23
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.
2 2
{8*a23 - b31 ,c22,r354,a23,b31,b33,m2}
Relevance for the application:
Modulo the following equations:
4 2 2 2 2
0=4*a23 + 4*a23 *c22 - b31 *c22
2 2 2 2 2 2
0=4*a23 *b31 + 4*a23 *b33 - b31 *b33
2 2 4 2 2
0=4*b31 *c22 - b33 + 4*b33 *c22
2 4 4 2 2 4 2 2 2 6 4 2
0=16*a23 *b33 + 4*b31 *c22 - b31 *b33 - 8*b31 *b33 *c22 - b33 + 4*b33 *c22
the system of equations related to the Hamiltonian HAM:
2 2 2 2 2 3
HAM=(2*u2*u3*a23*b33 + u3 *(b31 *c22 - b33 *c22) + u3*v1*b31*b33 + u3*v3*b33
2 2 2 2 2 2
+ u3*b33 *n3 + v1 *(b31 *c22 + b33 *c22) + 2*v1*b31*c22*n3 + v2 *b33 *c22
2 2
+ v2*b33 *m2 - 2*v3*b33*c22*n3)/b33
has apart from the Hamiltonian and Casimirs only the following first integral:
2 3 6
FI=32*u1 *u2*u3*a23 *b33 *c22
2 2 2 2 4 2 2 6 2
+ u1 *u3 *(16*a23 *b31 *b33 *c22 - 16*a23 *b33 *c22 )
2 2 6 2 2 7
+ 16*u1 *u3*v1*a23 *b31*b33 *c22 + 16*u1 *u3*v3*a23 *b33 *c22
2 2 6 2 5 2
+ 16*u1 *u3*a23 *b33 *c22*n3 + 16*u1*u3*v1*v2*a23*b31 *b33 *c22
7 6 2
- 8*u1*u3*v1*a23*b33 *c22*m2 + 16*u1*u3*v2*v3*a23*b31*b33 *c22
5 2 6
+ 32*u1*u3*v2*a23*b31*b33 *c22 *n3 + 8*u1*u3*v3*a23*b31*b33 *c22*m2
3 3 6
+ 32*u2 *u3*a23 *b33 *c22
2 2 2 2 4 2 2 8 2 6 2
+ u2 *u3 *( - 32*a23 *b31 *b33 *c22 + 12*a23 *b33 - 64*a23 *b33 *c22 )
2 2 6 2 2 7
+ 16*u2 *u3*v1*a23 *b31*b33 *c22 + 16*u2 *u3*v3*a23 *b33 *c22
2 2 6 3 3 6
+ 16*u2 *u3*a23 *b33 *c22*n3 + u2*u3 *(32*a23 *b33 *c22
4 2 3 2 6 8
- 48*a23*b31 *b33 *c22 + 12*a23*b31 *b33 *c22 - 12*a23*b33 *c22
6 3 2
+ 48*a23*b33 *c22 ) + u2*u3 *v1
3 4 2 8 6 2
*( - 48*a23*b31 *b33 *c22 + 12*a23*b31*b33 - 48*a23*b31*b33 *c22 )
2 2 5 2 9 7 2
+ u2*u3 *v3*( - 48*a23*b31 *b33 *c22 + 12*a23*b33 - 48*a23*b33 *c22 ) + u2
2 2 4 2 8 6 2
*u3 *( - 48*a23*b31 *b33 *c22 *n3 + 12*a23*b33 *n3 - 48*a23*b33 *c22 *n3) +
u2*u3*v1*v3
3 3 3 7 5 3
*(128*a23*b31 *b33 *c22 - 24*a23*b31*b33 *c22 + 128*a23*b31*b33 *c22 ) + u2
3 2 3 6
*u3*v1*( - 128*a23*b31 *b33 *c22 *n3 + 32*a23*b31*b33 *c22*n3
4 3 2 2 4 3
- 64*a23*b31*b33 *c22 *n3) - 32*u2*u3*v2 *a23*b31 *b33 *c22 + u2*u3
2 4 2 8 6 2
*v2*( - 64*a23*b31 *b33 *c22 *m2 + 12*a23*b33 *m2 - 32*a23*b33 *c22 *m2)
2 2 4 3 8 6 3
+ u2*u3*v3 *(96*a23*b31 *b33 *c22 - 24*a23*b33 *c22 + 96*a23*b33 *c22 ) +
u2*u3*v3
2 3 3 7 5 3
*(128*a23*b31 *b33 *c22 *n3 - 16*a23*b33 *c22*n3 + 64*a23*b33 *c22 *n3) + u2
2 2 3 2 6 2 6 2
*u3*(32*a23*b31 *b33 *c22 *n3 + 8*a23*b33 *c22*m2 - 8*a23*b33 *c22*n3
4 3 2 4 2 2 4 2
+ 32*a23*b33 *c22 *n3 ) + u3 *(16*a23 *b31 *b33 *c22
2 6 2 6 4 4 4 2 4 2 4
- 16*a23 *b33 *c22 - 12*b31 *c22 + 3*b31 *b33 *c22 + 12*b31 *b33 *c22
2 6 2 2 4 4 8 2 6 4
- 6*b31 *b33 *c22 + 12*b31 *b33 *c22 + 3*b33 *c22 - 12*b33 *c22 ) +
3 2 6 5 2 3 3 6
u3 *v1*(16*a23 *b31*b33 *c22 - 24*b31 *b33 *c22 + 6*b31 *b33 *c22
8 6 3 3 2 7
- 6*b31*b33 *c22 + 24*b31*b33 *c22 ) + u3 *v3*(16*a23 *b33 *c22
4 3 3 2 7 9 7 3 3
- 24*b31 *b33 *c22 + 6*b31 *b33 *c22 - 6*b33 *c22 + 24*b33 *c22 ) + u3 *
2 6 4 2 3 2 6
(16*a23 *b33 *c22*n3 - 24*b31 *b33 *c22 *n3 + 6*b31 *b33 *c22*n3
8 6 3
- 6*b33 *c22*n3 + 24*b33 *c22 *n3)
2 2 4 4 2 2 8 2 6 2 2
+ u3 *v1 *( - 12*b31 *b33 *c22 + 3*b31 *b33 - 8*b31 *b33 *c22 ) + u3 *v1
5 4 3 5 2 9 7 2
*v3*(64*b31 *b33*c22 - 40*b31 *b33 *c22 + 6*b31*b33 - 8*b31*b33 *c22
5 4 2 5 4 3 4 2
- 64*b31*b33 *c22 ) + u3 *v1*( - 64*b31 *c22 *n3 - 8*b31 *b33 *c22 *n3
3 2 4 8 6 2
+ 32*b31 *b33 *c22 *n3 + 6*b31*b33 *n3 - 32*b31*b33 *c22 *n3
4 4
+ 32*b31*b33 *c22 *n3)
2 2 4 2 4 2 4 4 2
+ u3 *v2 *( - 16*b31 *b33 *c22 + 16*b31 *b33 *c22 ) + u3 *v2*(
4 2 3 2 6 2 4 3
- 32*b31 *b33 *c22 *m2 + 8*b31 *b33 *c22*m2 + 16*b31 *b33 *c22 *m2
8 6 3
- 4*b33 *c22*m2 + 16*b33 *c22 *m2)
2 2 4 2 4 2 6 2 10 6 4
+ u3 *v3 *(48*b31 *b33 *c22 - 28*b31 *b33 *c22 + 3*b33 - 48*b33 *c22 ) +
2 4 4 2 5 2 2 3 4
u3 *v3*(64*b31 *b33*c22 *n3 - 40*b31 *b33 *c22 *n3 - 32*b31 *b33 *c22 *n3
9 7 2 5 4 2
+ 6*b33 *n3 - 16*b33 *c22 *n3 - 32*b33 *c22 *n3) + u3 *(
4 4 2 2 4 2 2 2 4 2 2
16*b31 *c22 *n3 + 4*b31 *b33 *c22 *m2 - 16*b31 *b33 *c22 *n3
8 2 6 2 2 6 2 2 4 4 2
+ 3*b33 *n3 - 4*b33 *c22 *m2 - 8*b33 *c22 *n3 - 16*b33 *c22 *n3 )
2 4 3 3 2 7 2 5 3
+ u3*v1 *v3*(48*b31 *b33 *c22 - 12*b31 *b33 *c22 + 48*b31 *b33 *c22 ) + u3
2 4 2 3 2 6 2 4 3
*v1 *( - 64*b31 *b33 *c22 *n3 + 16*b31 *b33 *c22*n3 - 48*b31 *b33 *c22 *n3)
3 4 2 8 6 2
+ u3*v1*v2*( - 24*b31 *b33 *c22 *m2 + 6*b31*b33 *m2 - 24*b31*b33 *c22 *m2)
2 3 4 3 8 6 3
+ u3*v1*v3 *(96*b31 *b33 *c22 - 24*b31*b33 *c22 + 96*b31*b33 *c22 )
3 3 3 7 5 3
+ u3*v1*v3*(16*b31 *b33 *c22 *n3 - 4*b31*b33 *c22*n3 + 16*b31*b33 *c22 *n3)
+ u3*v1
3 2 3 2 6 2 4 3 2
*( - 48*b31 *b33 *c22 *n3 + 12*b31*b33 *c22*n3 - 48*b31*b33 *c22 *n3 )
2 2 4 3
+ 16*u3*v2 *b31 *b33 *c22 *n3
2 5 2 9 7 2
+ u3*v2*v3*( - 24*b31 *b33 *c22 *m2 + 6*b33 *m2 - 24*b33 *c22 *m2)
2 4 2 8 6 2
+ u3*v2*( - 24*b31 *b33 *c22 *m2*n3 + 6*b33 *m2*n3 - 24*b33 *c22 *m2*n3)
3 2 5 3 9 7 3
+ u3*v3 *(48*b31 *b33 *c22 - 12*b33 *c22 + 48*b33 *c22 )
2 2 4 3 8 6 3
+ u3*v3 *(96*b31 *b33 *c22 *n3 - 20*b33 *c22*n3 + 80*b33 *c22 *n3)
2 3 3 2 7 2 5 3 2
+ u3*v3*(48*b31 *b33 *c22 *n3 - 12*b33 *c22*n3 + 48*b33 *c22 *n3 ) + u3*(
2 2 3 3 6 2 6 3
16*b31 *b33 *c22 *n3 + 4*b33 *c22*m2 *n3 - 4*b33 *c22*n3
4 3 3
+ 16*b33 *c22 *n3 )
= a product of the elements of: {u3,
2 3 6 2 2 2 4 2 2 6 2
32*u1 *u2*a23 *b33 *c22 + u1 *u3*(16*a23 *b31 *b33 *c22 - 16*a23 *b33 *c22 )
2 2 6 2 2 7
+ 16*u1 *v1*a23 *b31*b33 *c22 + 16*u1 *v3*a23 *b33 *c22
2 2 6 2 5 2
+ 16*u1 *a23 *b33 *c22*n3 + 16*u1*v1*v2*a23*b31 *b33 *c22
7 6 2
- 8*u1*v1*a23*b33 *c22*m2 + 16*u1*v2*v3*a23*b31*b33 *c22
5 2 6
+ 32*u1*v2*a23*b31*b33 *c22 *n3 + 8*u1*v3*a23*b31*b33 *c22*m2
3 3 6
+ 32*u2 *a23 *b33 *c22
2 2 2 4 2 2 8 2 6 2
+ u2 *u3*( - 32*a23 *b31 *b33 *c22 + 12*a23 *b33 - 64*a23 *b33 *c22 )
2 2 6 2 2 7
+ 16*u2 *v1*a23 *b31*b33 *c22 + 16*u2 *v3*a23 *b33 *c22
2 2 6 2 3 6 4 2 3
+ 16*u2 *a23 *b33 *c22*n3 + u2*u3 *(32*a23 *b33 *c22 - 48*a23*b31 *b33 *c22
2 6 8 6 3
+ 12*a23*b31 *b33 *c22 - 12*a23*b33 *c22 + 48*a23*b33 *c22 ) + u2*u3*v1
3 4 2 8 6 2
*( - 48*a23*b31 *b33 *c22 + 12*a23*b31*b33 - 48*a23*b31*b33 *c22 )
2 5 2 9 7 2
+ u2*u3*v3*( - 48*a23*b31 *b33 *c22 + 12*a23*b33 - 48*a23*b33 *c22 )
2 4 2 8 6 2
+ u2*u3*( - 48*a23*b31 *b33 *c22 *n3 + 12*a23*b33 *n3 - 48*a23*b33 *c22 *n3)
+ u2*v1*v3
3 3 3 7 5 3
*(128*a23*b31 *b33 *c22 - 24*a23*b31*b33 *c22 + 128*a23*b31*b33 *c22 ) + u2
3 2 3 6
*v1*( - 128*a23*b31 *b33 *c22 *n3 + 32*a23*b31*b33 *c22*n3
4 3 2 2 4 3
- 64*a23*b31*b33 *c22 *n3) - 32*u2*v2 *a23*b31 *b33 *c22
2 4 2 8 6 2
+ u2*v2*( - 64*a23*b31 *b33 *c22 *m2 + 12*a23*b33 *m2 - 32*a23*b33 *c22 *m2)
2 2 4 3 8 6 3
+ u2*v3 *(96*a23*b31 *b33 *c22 - 24*a23*b33 *c22 + 96*a23*b33 *c22 ) + u2
2 3 3 7 5 3
*v3*(128*a23*b31 *b33 *c22 *n3 - 16*a23*b33 *c22*n3 + 64*a23*b33 *c22 *n3) +
2 2 3 2 6 2 6 2
u2*(32*a23*b31 *b33 *c22 *n3 + 8*a23*b33 *c22*m2 - 8*a23*b33 *c22*n3
4 3 2 3 2 2 4 2
+ 32*a23*b33 *c22 *n3 ) + u3 *(16*a23 *b31 *b33 *c22
2 6 2 6 4 4 4 2 4 2 4
- 16*a23 *b33 *c22 - 12*b31 *c22 + 3*b31 *b33 *c22 + 12*b31 *b33 *c22
2 6 2 2 4 4 8 2 6 4
- 6*b31 *b33 *c22 + 12*b31 *b33 *c22 + 3*b33 *c22 - 12*b33 *c22 ) +
2 2 6 5 2 3 3 6
u3 *v1*(16*a23 *b31*b33 *c22 - 24*b31 *b33 *c22 + 6*b31 *b33 *c22
8 6 3 2 2 7
- 6*b31*b33 *c22 + 24*b31*b33 *c22 ) + u3 *v3*(16*a23 *b33 *c22
4 3 3 2 7 9 7 3 2
- 24*b31 *b33 *c22 + 6*b31 *b33 *c22 - 6*b33 *c22 + 24*b33 *c22 ) + u3 *
2 6 4 2 3 2 6
(16*a23 *b33 *c22*n3 - 24*b31 *b33 *c22 *n3 + 6*b31 *b33 *c22*n3
8 6 3
- 6*b33 *c22*n3 + 24*b33 *c22 *n3)
2 4 4 2 2 8 2 6 2
+ u3*v1 *( - 12*b31 *b33 *c22 + 3*b31 *b33 - 8*b31 *b33 *c22 ) + u3*v1*v3*
5 4 3 5 2 9 7 2
(64*b31 *b33*c22 - 40*b31 *b33 *c22 + 6*b31*b33 - 8*b31*b33 *c22
5 4 5 4 3 4 2
- 64*b31*b33 *c22 ) + u3*v1*( - 64*b31 *c22 *n3 - 8*b31 *b33 *c22 *n3
3 2 4 8 6 2
+ 32*b31 *b33 *c22 *n3 + 6*b31*b33 *n3 - 32*b31*b33 *c22 *n3
4 4
+ 32*b31*b33 *c22 *n3)
2 4 2 4 2 4 4
+ u3*v2 *( - 16*b31 *b33 *c22 + 16*b31 *b33 *c22 ) + u3*v2*(
4 2 3 2 6 2 4 3
- 32*b31 *b33 *c22 *m2 + 8*b31 *b33 *c22*m2 + 16*b31 *b33 *c22 *m2
8 6 3
- 4*b33 *c22*m2 + 16*b33 *c22 *m2)
2 4 2 4 2 6 2 10 6 4
+ u3*v3 *(48*b31 *b33 *c22 - 28*b31 *b33 *c22 + 3*b33 - 48*b33 *c22 ) +
4 4 2 5 2 2 3 4
u3*v3*(64*b31 *b33*c22 *n3 - 40*b31 *b33 *c22 *n3 - 32*b31 *b33 *c22 *n3
9 7 2 5 4
+ 6*b33 *n3 - 16*b33 *c22 *n3 - 32*b33 *c22 *n3) + u3*(
4 4 2 2 4 2 2 2 4 2 2
16*b31 *c22 *n3 + 4*b31 *b33 *c22 *m2 - 16*b31 *b33 *c22 *n3
8 2 6 2 2 6 2 2 4 4 2
+ 3*b33 *n3 - 4*b33 *c22 *m2 - 8*b33 *c22 *n3 - 16*b33 *c22 *n3 )
2 4 3 3 2 7 2 5 3
+ v1 *v3*(48*b31 *b33 *c22 - 12*b31 *b33 *c22 + 48*b31 *b33 *c22 )
2 4 2 3 2 6 2 4 3
+ v1 *( - 64*b31 *b33 *c22 *n3 + 16*b31 *b33 *c22*n3 - 48*b31 *b33 *c22 *n3)
3 4 2 8 6 2
+ v1*v2*( - 24*b31 *b33 *c22 *m2 + 6*b31*b33 *m2 - 24*b31*b33 *c22 *m2)
2 3 4 3 8 6 3
+ v1*v3 *(96*b31 *b33 *c22 - 24*b31*b33 *c22 + 96*b31*b33 *c22 )
3 3 3 7 5 3
+ v1*v3*(16*b31 *b33 *c22 *n3 - 4*b31*b33 *c22*n3 + 16*b31*b33 *c22 *n3)
3 2 3 2 6 2 4 3 2
+ v1*( - 48*b31 *b33 *c22 *n3 + 12*b31*b33 *c22*n3 - 48*b31*b33 *c22 *n3 )
2 2 4 3
+ 16*v2 *b31 *b33 *c22 *n3
2 5 2 9 7 2
+ v2*v3*( - 24*b31 *b33 *c22 *m2 + 6*b33 *m2 - 24*b33 *c22 *m2)
2 4 2 8 6 2
+ v2*( - 24*b31 *b33 *c22 *m2*n3 + 6*b33 *m2*n3 - 24*b33 *c22 *m2*n3)
3 2 5 3 9 7 3
+ v3 *(48*b31 *b33 *c22 - 12*b33 *c22 + 48*b33 *c22 )
2 2 4 3 8 6 3
+ v3 *(96*b31 *b33 *c22 *n3 - 20*b33 *c22*n3 + 80*b33 *c22 *n3)
2 3 3 2 7 2 5 3 2
+ v3*(48*b31 *b33 *c22 *n3 - 12*b33 *c22*n3 + 48*b33 *c22 *n3 )
2 2 3 3 6 2 6 3
+ 16*b31 *b33 *c22 *n3 + 4*b33 *c22*m2 *n3 - 4*b33 *c22*n3
4 3 3
+ 16*b33 *c22 *n3 }
{HAM,FI} = 0
And again in machine readable form:
HAM=(2*u2*u3*a23*b33**2 + u3**2*(b31**2*c22 - b33**2*c22) + u3*v1*b31*b33**2 +
u3*v3*b33**3 + u3*b33**2*n3 + v1**2*(b31**2*c22 + b33**2*c22) + 2*v1*b31*c22*n3
+ v2**2*b33**2*c22 + v2*b33**2*m2 - 2*v3*b33*c22*n3)/b33**2$
FI=32*u1**2*u2*u3*a23**3*b33**6*c22 + u1**2*u3**2*(16*a23**2*b31**2*b33**4*c22**
2 - 16*a23**2*b33**6*c22**2) + 16*u1**2*u3*v1*a23**2*b31*b33**6*c22 + 16*u1**2*
u3*v3*a23**2*b33**7*c22 + 16*u1**2*u3*a23**2*b33**6*c22*n3 + 16*u1*u3*v1*v2*a23*
b31**2*b33**5*c22**2 - 8*u1*u3*v1*a23*b33**7*c22*m2 + 16*u1*u3*v2*v3*a23*b31*b33
**6*c22**2 + 32*u1*u3*v2*a23*b31*b33**5*c22**2*n3 + 8*u1*u3*v3*a23*b31*b33**6*
c22*m2 + 32*u2**3*u3*a23**3*b33**6*c22 + u2**2*u3**2*( - 32*a23**2*b31**2*b33**4
*c22**2 + 12*a23**2*b33**8 - 64*a23**2*b33**6*c22**2) + 16*u2**2*u3*v1*a23**2*
b31*b33**6*c22 + 16*u2**2*u3*v3*a23**2*b33**7*c22 + 16*u2**2*u3*a23**2*b33**6*
c22*n3 + u2*u3**3*(32*a23**3*b33**6*c22 - 48*a23*b31**4*b33**2*c22**3 + 12*a23*
b31**2*b33**6*c22 - 12*a23*b33**8*c22 + 48*a23*b33**6*c22**3) + u2*u3**2*v1*( -
48*a23*b31**3*b33**4*c22**2 + 12*a23*b31*b33**8 - 48*a23*b31*b33**6*c22**2) + u2
*u3**2*v3*( - 48*a23*b31**2*b33**5*c22**2 + 12*a23*b33**9 - 48*a23*b33**7*c22**2
) + u2*u3**2*( - 48*a23*b31**2*b33**4*c22**2*n3 + 12*a23*b33**8*n3 - 48*a23*b33
**6*c22**2*n3) + u2*u3*v1*v3*(128*a23*b31**3*b33**3*c22**3 - 24*a23*b31*b33**7*
c22 + 128*a23*b31*b33**5*c22**3) + u2*u3*v1*( - 128*a23*b31**3*b33**2*c22**3*n3
+ 32*a23*b31*b33**6*c22*n3 - 64*a23*b31*b33**4*c22**3*n3) - 32*u2*u3*v2**2*a23*
b31**2*b33**4*c22**3 + u2*u3*v2*( - 64*a23*b31**2*b33**4*c22**2*m2 + 12*a23*b33
**8*m2 - 32*a23*b33**6*c22**2*m2) + u2*u3*v3**2*(96*a23*b31**2*b33**4*c22**3 -
24*a23*b33**8*c22 + 96*a23*b33**6*c22**3) + u2*u3*v3*(128*a23*b31**2*b33**3*c22
**3*n3 - 16*a23*b33**7*c22*n3 + 64*a23*b33**5*c22**3*n3) + u2*u3*(32*a23*b31**2*
b33**2*c22**3*n3**2 + 8*a23*b33**6*c22*m2**2 - 8*a23*b33**6*c22*n3**2 + 32*a23*
b33**4*c22**3*n3**2) + u3**4*(16*a23**2*b31**2*b33**4*c22**2 - 16*a23**2*b33**6*
c22**2 - 12*b31**6*c22**4 + 3*b31**4*b33**4*c22**2 + 12*b31**4*b33**2*c22**4 - 6
*b31**2*b33**6*c22**2 + 12*b31**2*b33**4*c22**4 + 3*b33**8*c22**2 - 12*b33**6*
c22**4) + u3**3*v1*(16*a23**2*b31*b33**6*c22 - 24*b31**5*b33**2*c22**3 + 6*b31**
3*b33**6*c22 - 6*b31*b33**8*c22 + 24*b31*b33**6*c22**3) + u3**3*v3*(16*a23**2*
b33**7*c22 - 24*b31**4*b33**3*c22**3 + 6*b31**2*b33**7*c22 - 6*b33**9*c22 + 24*
b33**7*c22**3) + u3**3*(16*a23**2*b33**6*c22*n3 - 24*b31**4*b33**2*c22**3*n3 + 6
*b31**2*b33**6*c22*n3 - 6*b33**8*c22*n3 + 24*b33**6*c22**3*n3) + u3**2*v1**2*( -
12*b31**4*b33**4*c22**2 + 3*b31**2*b33**8 - 8*b31**2*b33**6*c22**2) + u3**2*v1*
v3*(64*b31**5*b33*c22**4 - 40*b31**3*b33**5*c22**2 + 6*b31*b33**9 - 8*b31*b33**7
*c22**2 - 64*b31*b33**5*c22**4) + u3**2*v1*( - 64*b31**5*c22**4*n3 - 8*b31**3*
b33**4*c22**2*n3 + 32*b31**3*b33**2*c22**4*n3 + 6*b31*b33**8*n3 - 32*b31*b33**6*
c22**2*n3 + 32*b31*b33**4*c22**4*n3) + u3**2*v2**2*( - 16*b31**4*b33**2*c22**4 +
16*b31**2*b33**4*c22**4) + u3**2*v2*( - 32*b31**4*b33**2*c22**3*m2 + 8*b31**2*
b33**6*c22*m2 + 16*b31**2*b33**4*c22**3*m2 - 4*b33**8*c22*m2 + 16*b33**6*c22**3*
m2) + u3**2*v3**2*(48*b31**4*b33**2*c22**4 - 28*b31**2*b33**6*c22**2 + 3*b33**10
- 48*b33**6*c22**4) + u3**2*v3*(64*b31**4*b33*c22**4*n3 - 40*b31**2*b33**5*c22
**2*n3 - 32*b31**2*b33**3*c22**4*n3 + 6*b33**9*n3 - 16*b33**7*c22**2*n3 - 32*b33
**5*c22**4*n3) + u3**2*(16*b31**4*c22**4*n3**2 + 4*b31**2*b33**4*c22**2*m2**2 -
16*b31**2*b33**4*c22**2*n3**2 + 3*b33**8*n3**2 - 4*b33**6*c22**2*m2**2 - 8*b33**
6*c22**2*n3**2 - 16*b33**4*c22**4*n3**2) + u3*v1**2*v3*(48*b31**4*b33**3*c22**3
- 12*b31**2*b33**7*c22 + 48*b31**2*b33**5*c22**3) + u3*v1**2*( - 64*b31**4*b33**
2*c22**3*n3 + 16*b31**2*b33**6*c22*n3 - 48*b31**2*b33**4*c22**3*n3) + u3*v1*v2*(
- 24*b31**3*b33**4*c22**2*m2 + 6*b31*b33**8*m2 - 24*b31*b33**6*c22**2*m2) + u3*
v1*v3**2*(96*b31**3*b33**4*c22**3 - 24*b31*b33**8*c22 + 96*b31*b33**6*c22**3) +
u3*v1*v3*(16*b31**3*b33**3*c22**3*n3 - 4*b31*b33**7*c22*n3 + 16*b31*b33**5*c22**
3*n3) + u3*v1*( - 48*b31**3*b33**2*c22**3*n3**2 + 12*b31*b33**6*c22*n3**2 - 48*
b31*b33**4*c22**3*n3**2) + 16*u3*v2**2*b31**2*b33**4*c22**3*n3 + u3*v2*v3*( - 24
*b31**2*b33**5*c22**2*m2 + 6*b33**9*m2 - 24*b33**7*c22**2*m2) + u3*v2*( - 24*b31
**2*b33**4*c22**2*m2*n3 + 6*b33**8*m2*n3 - 24*b33**6*c22**2*m2*n3) + u3*v3**3*(
48*b31**2*b33**5*c22**3 - 12*b33**9*c22 + 48*b33**7*c22**3) + u3*v3**2*(96*b31**
2*b33**4*c22**3*n3 - 20*b33**8*c22*n3 + 80*b33**6*c22**3*n3) + u3*v3*(48*b31**2*
b33**3*c22**3*n3**2 - 12*b33**7*c22*n3**2 + 48*b33**5*c22**3*n3**2) + u3*(16*b31
**2*b33**2*c22**3*n3**3 + 4*b33**6*c22*m2**2*n3 - 4*b33**6*c22*n3**3 + 16*b33**4
*c22**3*n3**3)$