Solution 1 to problem over
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
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Equations
The following unsolved equations remain:
2 2
0=b31 + b32
Expressions
The solution is given through the following expressions:
1 2 201 4 3
r10=( - ---*a11*b31*b32 *m1*n2*n3*r498 + -----*b31 *n2 *r498
2 32
257 2 2 3 5 2 2 2 7 4 3
+ -----*b31 *b32 *n2 *r498 - ---*b31 *b32 *n2*n3 *r498 + ---*b32 *n2 *r498
32 8 4
5 4 2 3 4
- ---*b32 *n2*n3 *r498)/(a11 *b32 )
8
3 3 2 1 2 2
r11=(---*a11*b31 *m1*n2 *r498 + ---*a11*b31*b32 *m1*n2 *r498
4 4
1 2 2 3 4 2
+ ---*a11*b31*b32 *m1*n3 *r498 - ---*b31 *n2 *n3*r498
4 8
147 2 2 2 1 2 2 3
- -----*b31 *b32 *n2 *n3*r498 - ---*b31 *b32 *n3 *r498
32 8
143 4 2 1 4 3 3 4
- -----*b32 *n2 *n3*r498 - ---*b32 *n3 *r498)/(a11 *b32 )
32 8
3 2 2 1 2 2
r12=(---*a11*b31 *m1*n2 *r498 + ---*a11*b32 *m1*n2 *r498
4 4
1 2 2 99 3 2
- ---*a11*b32 *m1*n3 *r498 + ----*b31 *n2 *n3*r498
4 32
107 2 2 3 3
+ -----*b31*b32 *n2 *n3*r498)/(a11 *b32 )
32
29 3 2 29 2 2
r13=( - ----*a11*b31 *m1*n2 *r498 - ----*a11*b31*b32 *m1*n2 *r498
2 2
29 4 2 2 2 2 37 4 2
+ ----*b31 *n2 *n3*r498 - 2*b31 *b32 *n2 *n3*r498 - ----*b32 *n2 *n3*r498
4 4
1 4 3 2 5
- ---*b32 *n3 *r498)/(a11 *b32 )
4
35 2 3 35 2 3 1 2 2
- ----*b31 *n2 *r498 - ----*b32 *n2 *r498 - ---*b32 *n2*n3 *r498
4 4 4
r14=-------------------------------------------------------------------
2 3
a11 *b32
35 3 3 35 2 3 1 2 2
----*b31 *n2 *r498 + ----*b31*b32 *n2 *r498 + ---*b31*b32 *n2*n3 *r498
4 4 4
r15=------------------------------------------------------------------------
2 4
a11 *b32
1 2 2 2 1 3
r20=(---*a11 *b31 *m1 *r498 - ---*a11*b31 *m1*n3*r498
4 4
1 2 281 4 2 1 4 2
- ---*a11*b31*b32 *m1*n3*r498 + -----*b31 *n2 *r498 + ----*b31 *n3 *r498
4 128 16
567 2 2 2 3 2 2 2 885 4 2
+ -----*b31 *b32 *n2 *r498 + ----*b31 *b32 *n3 *r498 + -----*b32 *n2 *r498
64 16 128
1 4 2 3 3
+ ---*b32 *n3 *r498)/(a11 *b32 )
8
1 15 2 15 2
---*a11*b31*m1*n2*r498 - ----*b31 *n2*n3*r498 - ----*b32 *n2*n3*r498
2 16 16
r21=----------------------------------------------------------------------
3
a11 *b32
1 2 2 2 1 2 2 2 1 3
r22=(---*a11 *b31 *m1 *r498 - ---*a11 *b32 *m1 *r498 - ---*a11*b31 *m1*n3*r498
4 4 4
1 2 257 4 2 1 4 2
- ---*a11*b31*b32 *m1*n3*r498 + -----*b31 *n2 *r498 + ----*b31 *n3 *r498
4 128 16
69 2 2 2 1 2 2 2 295 4 2
+ ----*b31 *b32 *n2 *r498 + ---*b31 *b32 *n3 *r498 + -----*b32 *n2 *r498
16 8 128
1 4 2 3 3
+ ----*b32 *n3 *r498)/(a11 *b32 )
16
1 2 1 3 1 2
---*a11*b31 *m1*n2*r498 + ---*b31 *n2*n3*r498 + ---*b31*b32 *n2*n3*r498
2 8 8
r23=-------------------------------------------------------------------------
3 2
a11 *b32
1 2 1 2 1 2
- ---*a11*b31*m1 *r498 + ---*b31 *m1*n3*r498 + ---*b32 *m1*n3*r498
2 4 4
r24=---------------------------------------------------------------------
2 2
a11 *b32
1 51 2 53 2
- ---*a11*b31*m1*n2*r498 - ----*b31 *n2*n3*r498 - ----*b32 *n2*n3*r498
2 8 8
r26=-------------------------------------------------------------------------
2 2
a11 *b32
1 23 2 2 1 2 2
r27=( - ---*a11*b31*m1*n3*r498 - ----*b31 *n2 *r498 + ---*b31 *n3 *r498
2 4 4
21 2 2 2 2
- ----*b32 *n2 *r498)/(a11 *b32 )
4
1 2 19 3 2 21 2 2
r28=(---*a11*b32 *m1*n3*r498 - ----*b31 *n2 *r498 - ----*b31*b32 *n2 *r498
2 4 4
1 2 2 2 3
- ---*b31*b32 *n3 *r498)/(a11 *b32 )
4
35 2 2 35 2 2 1 2 2
- ----*b31 *n2 *r498 - ----*b32 *n2 *r498 - ---*b32 *n3 *r498
4 4 4
r29=----------------------------------------------------------------
3
a11*b32
1 217 2 2 1 2 2
r210=(---*a11*b31*m1*n3*r498 - -----*b31 *n2 *r498 - ---*b31 *n3 *r498
2 16 4
225 2 2 1 2 2 2 2
- -----*b32 *n2 *r498 - ---*b32 *n3 *r498)/(a11 *b32 )
16 4
3 1
---*a11*m1*n2*r498 - ---*b31*n2*n3*r498
2 4
r212=-----------------------------------------
2
a11 *b32
r213=0
2 2 2 2
b31 *n2 *r498 + b32 *n2 *r498
r214=-------------------------------
3
a11*b32
r215
1 2 201 3 2 209 2 2
- ---*a11*b32 *m1*n3*r498 + -----*b31 *n2 *r498 + -----*b31*b32 *n2 *r498
2 16 16
=----------------------------------------------------------------------------
2 3
a11 *b32
3 2 3 3 1 2
---*a11*b31 *m1*n2*r498 - ---*b31 *n2*n3*r498 - ---*b31*b32 *n2*n3*r498
2 4 2
r216=-------------------------------------------------------------------------
2 3
a11 *b32
3 2 3 2
- ---*b31 *n2*n3*r498 - ---*b32 *n2*n3*r498
2 2
r217=----------------------------------------------
2 2
a11 *b32
r218=0
r219=0
67 2 75 3 1 4
r30=( - ----*a11*b31 *b32*n2*r455 - ----*a11*b32 *n2*r455 + ---*b31 *n2*r498
8 8 8
1 2 2 3 2
+ ---*b31 *b32 *n2*r498)/(a11 *b32 )
8
1 2 1 2
- a11*b31*m1*r455 + ---*b31 *n3*r455 + ---*b32 *n3*r455
2 2
r31=----------------------------------------------------------
2
a11 *b32
67 2 75 2 5 2
r32=( - ----*a11*b31 *n2*r455 - ----*a11*b32 *n2*r455 - ----*b31 *b32*n2*r498
8 8 16
5 3 3
- ----*b32 *n2*r498)/(a11 *b32)
16
1 2 1 2
- a11*b31*m1*r455 + ---*b31 *n3*r455 + ---*b32 *n3*r455
2 2
r33=----------------------------------------------------------
2
a11 *b32
m1*r455
r34=---------
a11
r35=0
m1*r455
r36=---------
a11
67 2 75 3 5 4
r37=( - ----*a11*b31 *b32*n2*r455 - ----*a11*b32 *n2*r455 + ----*b31 *n2*r498
8 8 16
5 2 2 3 2
+ ----*b31 *b32 *n2*r498)/(a11 *b32 )
16
1 2 1 2
- a11*b31*m1*r455 + ---*b31 *n3*r455 + ---*b32 *n3*r455
2 2
r38=----------------------------------------------------------
2
a11 *b32
m1*r455
r39=---------
a11
n3*r455
r310=---------
a11
9 2 2
- ---*b31 *n2*r498 - 5*b32 *n2*r498
2
r311=--------------------------------------
2
a11 *b32
r312=
1 1 2 1 2
- ---*a11*b31*m1*r498 + a11*b32*n3*r455 + ---*b31 *n3*r498 + ---*b32 *n3*r498
2 4 4
--------------------------------------------------------------------------------
2
a11 *b32
39 3 43 2
- ----*b31 *n2*r498 - ----*b31*b32 *n2*r498
8 8
r313=----------------------------------------------
2 2
a11 *b32
1 2 1 2 1 3
r314=( - ---*a11*b31 *m1*r498 + ---*a11*b32 *m1*r498 + ---*b31 *n3*r498
2 2 4
1 2 2 2
+ ---*b31*b32 *n3*r498)/(a11 *b32 )
4
1
---*b31*m1*r498 + b32*n3*r455
2
r315=-------------------------------
a11*b32
69 2 77 2
- ----*b31 *n2*r498 - ----*b32 *n2*r498
8 8
r316=------------------------------------------
2
a11*b32
1 2 2
- a11*b31*m1*r498 + ---*b31 *n3*r498 + b32 *n3*r498
2
r317=------------------------------------------------------
2
a11*b32
1
a11*m1*r498 + ---*b31*n3*r498
2
r318=-------------------------------
a11*b32
n3*r498
r319=---------
b32
n2*r455
r320=---------
a11
1 2 1 2
- ---*b31 *n3*r498 - ---*b32 *n3*r498
4 4
r321=----------------------------------------
2
a11 *b32
5 2 5 2
a11*b32*n2*r455 + ---*b31 *n2*r498 + ---*b32 *n2*r498
8 8
r322=-------------------------------------------------------
2
a11 *b32
r323=0
r324=0
3 2 3 2
a11*b32*n2*r455 + ---*b31 *n2*r498 + ---*b32 *n2*r498
8 8
r325=-------------------------------------------------------
2
a11 *b32
1
- ---*n3*r498
2
r326=----------------
a11
7 2 9 2
- ---*b31 *n2*r498 - ---*b32 *n2*r498
4 4
r327=----------------------------------------
2
a11*b32
3
---*b31*n2*r498
2
r328=-----------------
a11*b32
n2*r498
r329=---------
b32
1 2
---*b31 *n2*r498
2
r330=------------------
2
a11*b32
1 2 1 2
- a11*b31*m1*r498 + ---*b31 *n3*r498 + ---*b32 *n3*r498
2 2
r331=----------------------------------------------------------
2
a11*b32
r332=0
n3*r498
r333=---------
b32
n2*r498
r334=---------
b32
- b31*n2*r455
r335=----------------
a11*b32
r336=0
3 3 3 2
- a11*b31*b32*n2*r455 - ---*b31 *n2*r498 - ---*b31*b32 *n2*r498
8 8
r337=------------------------------------------------------------------
2 2
a11 *b32
1 2 1 2
- ---*b31 *n3*r498 - ---*b32 *n3*r498
4 4
r338=----------------------------------------
2
a11 *b32
r339=0
5 3 5 2
- a11*b31*b32*n2*r455 - ---*b31 *n2*r498 - ---*b31*b32 *n2*r498
8 8
r340=------------------------------------------------------------------
2 2
a11 *b32
1
- ---*b31*n3*r498
2
r341=--------------------
a11*b32
3
- ---*b31*n2*r498
2
r342=--------------------
a11*b32
17 2 19 2
- ----*b31 *n2*r498 - ----*b32 *n2*r498
4 4
r343=------------------------------------------
2
a11*b32
- b31*n2*r498
r344=----------------
2
b32
r345=0
m1*r498
r346=---------
b32
1 2 1 2
- a11*b31*m1*r498 + ---*b31 *n3*r498 + ---*b32 *n3*r498
2 2
r347=----------------------------------------------------------
2
a11*b32
r348=0
- b31*n2*r498
r349=----------------
2
b32
1
- ---*n2*r498
2
r350=----------------
a11
r351=0
m1*r498
r352=---------
b32
n3*r498
r353=---------
b32
n2*r498
r354=---------
b32
- b31*n2*r498
r355=----------------
2
b32
1 2 1 2
- ---*b31 *r455 - ---*b32 *r455
4 4
r40=----------------------------------
2
a11
r41=0
1 2 1 2
- ---*b31 *r455 - ---*b32 *r455
4 4
r42=----------------------------------
2
a11
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
1 2 1 2
- ---*b31 *r455 - ---*b32 *r455
4 4
r49=----------------------------------
2
a11
r410=0
r411=0
r412=0
r413=0
r415=0
b32*r455
r416=----------
a11
r417=0
b32*r455
r418=----------
a11
b31*r455
r419=----------
a11
r420=0
b31*r455
r421=----------
a11
r422=0
b32*r455
r423=----------
a11
b31*r455
r424=----------
a11
1 2 1 2
a11*b32*r455 - ---*b31 *r498 - ---*b32 *r498
4 4
r425=----------------------------------------------
a11*b32
r426=0
1
2*a11*r455 + ---*b32*r498
4
r427=---------------------------
a11
r428=0
1
---*b31*r498
2
r429=--------------
a11
1 2
2*a11*b32*r455 + ---*b31 *r498
4
r430=--------------------------------
a11*b32
r431=0
r432=r498
b31*r498
r433=----------
b32
a11*r498
r434=----------
b32
r435=0
r436=0
r437=0
r438=0
r439=0
r440=0
r441=0
r442=0
r444=0
r445=0
1 2 1 2
- 2*a11*b32*r455 - ---*b31 *r498 - ---*b32 *r498
2 2
r446=---------------------------------------------------
a11*b32
r447=0
r448=0
r449=0
r450=0
r451=0
r452=0
r453=0
r454=0
r456=0
r458=0
r459=0
r460=r455
r461=0
r462=r498
r463=0
a11*r498
r464=----------
b32
r465=0
r466=0
r467=0
r468=0
r469=0
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
1 2 1 2
- 2*a11*b32*r455 - ---*b31 *r498 - ---*b32 *r498
2 2
r483=---------------------------------------------------
a11*b32
r484=0
r485=0
r486=0
r487=0
r488=0
r489=0
r490=0
r491=0
r492=0
r493=0
r494= - 2*r455
r495=0
r496=0
b31*r498
r497=----------
b32
r499=0
r4100=0
r4101=0
r4102=0
r4103=0
r4104=0
r4105=r455
r4106=0
r4107=r455
r4108=0
r4109=0
r4111=0
r4112=0
b31*r498
r4113=----------
b32
a11*r498
r4114=----------
b32
r4115=0
r4117=0
r4118=0
r4119=0
r4120=0
r4121=0
r4122=0
r4123=0
r4124=0
67 2 75 2
- ----*b31 *n2 - ----*b32 *n2
8 8
m3=--------------------------------
a11*b32
1 2 1 2
- a11*b31*m1 + ---*b31 *n3 + ---*b32 *n3
2 2
m2=-------------------------------------------
a11*b32
- b31*n2
n1=-----------
b32
1 2 1 2
- ---*b31 - ---*b32
4 4
c33=------------------------
a11
c23=0
c22=0
c13=0
c12=0
b33=0
b22=0
a33=2*a11
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:
r455, r498, m1, n3, b31, n2, b32, a11
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.
{b31,n2,r498,a11,b32}
Relevance for the application:
Modulo the following equation:
2 2
0=b31 + b32
the system of equations related to the Hamiltonian HAM:
2 2 2 2
HAM=(u1 *a11 *b32 - u1*a11*b31*n2 + u2 *a11 *b32 + u2*a11*b32*n2
2 2 2
+ 2*u3 *a11 *b32 + u3*v1*a11*b31*b32 + u3*v2*a11*b32 + u3*a11*b32*n3
1 2 1 2
+ v1*a11*b32*m1 + v2*( - a11*b31*m1 + ---*b31 *n3 + ---*b32 *n3)
2 2
2 1 2 1 3 67 2 75 2
+ v3 *( - ---*b31 *b32 - ---*b32 ) + v3*( - ----*b31 *n2 - ----*b32 *n2))/
4 4 8 8
(a11*b32)
has apart from the Hamiltonian and Casimirs the following 2 first integrals:
3 3 3 2 3 4 2 2 4 4
FI= - u1 *a11 *b31*b32 *n2 + u1 *u2*a11 *b32 *n2 + u1 *u3 *a11 *b32
2 3 4 2 3 4 2 3 4
+ u1 *u3*v1*a11 *b31*b32 + u1 *u3*a11 *b32 *n3 + u1 *v1*a11 *b32 *m1
1 2 2 5 2 3 3 3 5
- ---*u1 *v3*a11 *b32 *n2 - u1*u2 *a11 *b31*b32 *n2 + u1*u2*u3*v1*a11 *b32
2
3 4
+ u1*u2*u3*v2*a11 *b31*b32
3 3 1 2 2 3 1 2 5
+ u1*u2*v1*( - a11 *b31*b32 *m1 + ---*a11 *b31 *b32 *n3 + ---*a11 *b32 *n3)
2 2
3 4 2 3 3
+ u1*u2*v2*a11 *b32 *m1 - u1*u3 *a11 *b31*b32 *n2
1 2 2 4 1 2 6
+ u1*u3*v1*v3*( - ---*a11 *b31 *b32 - ---*a11 *b32 )
2 2
17 2 2 3 19 2 5
+ u1*u3*v1*( - ----*a11 *b31 *b32 *n2 - ----*a11 *b32 *n2)
4 4
3 2 4 1 2 4
- ---*u1*u3*v2*a11 *b31*b32 *n2 - ---*u1*u3*v3*a11 *b31*b32 *n3
2 2
2 5 3 3 5 5
+ u1*v1 *( - ---*a11*b31 *b32 *n2 - ---*a11*b31*b32 *n2)
8 8
1 2 4 1 6
+ u1*v1*v3*( - ---*a11*b31 *b32 *n3 - ---*a11*b32 *n3)
4 4
3 2 3 3 5
+ u1*v1*( - ---*a11*b31 *b32 *n2*n3 - ---*a11*b32 *n2*n3)
2 2
2 3 3 3 3 5
+ u1*v2 *( - ---*a11*b31 *b32 *n2 - ---*a11*b31*b32 *n2) + u1*v2*(
8 8
3 2 2 2 3 3 2
---*a11 *b31 *b32 *m1*n2 - ---*a11*b31 *b32 *n2*n3
2 4
1 4
- ---*a11*b31*b32 *n2*n3) + u1*v3
2
1 2 4 201 3 2 2 209 4 2
*( - ---*a11 *b32 *m1*n3 + -----*a11*b31 *b32 *n2 + -----*a11*b31*b32 *n2 )
2 16 16
+ u1
35 3 3 35 3 3 1 3 2
*(----*a11*b31 *b32*n2 + ----*a11*b31*b32 *n2 + ---*a11*b31*b32 *n2*n3 )
4 4 4
3 3 4 2 2 4 4 2 3 5
+ u2 *a11 *b32 *n2 + u2 *u3 *a11 *b32 + u2 *u3*v2*a11 *b32
2 3 4
+ u2 *u3*a11 *b32 *n3
2 3 3 1 2 2 3 1 2 5
+ u2 *v2*( - a11 *b31*b32 *m1 + ---*a11 *b31 *b32 *n3 + ---*a11 *b32 *n3)
2 2
1 2 2 2 3 2 2 2 2 2 2 4 2
+ ---*u2 *v3*a11 *b31 *b32 *n2 + u2 *(a11 *b31 *b32 *n2 + a11 *b32 *n2 )
2
2 3 4 3 2 4
+ u2*u3 *a11 *b32 *n2 + ---*u2*u3*v1*a11 *b31*b32 *n2
2
1 2 2 4 1 2 6
+ u2*u3*v2*v3*( - ---*a11 *b31 *b32 - ---*a11 *b32 )
2 2
7 2 2 3 9 2 5
+ u2*u3*v2*( - ---*a11 *b31 *b32 *n2 - ---*a11 *b32 *n2)
4 4
1 2 5
- ---*u2*u3*v3*a11 *b32 *n3
2
2 3 2 4 3 6
+ u2*v1 *(---*a11*b31 *b32 *n2 + ---*a11*b32 *n2)
8 8
3 2 4 1 4
+ u2*v1*(---*a11 *b32 *m1*n2 - ---*a11*b31*b32 *n2*n3)
2 4
2 5 2 4 5 6
+ u2*v2 *(---*a11*b31 *b32 *n2 + ---*a11*b32 *n2)
8 8
1 2 4 1 6
+ u2*v2*v3*( - ---*a11*b31 *b32 *n3 - ---*a11*b32 *n3) + u2*v3*(
4 4
1 2 3 217 2 3 2 1 2 3 2
---*a11 *b31*b32 *m1*n3 - -----*a11*b31 *b32 *n2 - ---*a11*b31 *b32 *n3
2 16 4
225 5 2 1 5 2
- -----*a11*b32 *n2 - ---*a11*b32 *n3 )
16 4
35 2 2 3 35 4 3 1 4 2
+ u2*( - ----*a11*b31 *b32 *n2 - ----*a11*b32 *n2 - ---*a11*b32 *n2*n3 )
4 4 4
4 4 4 3 3 4 3 3 5 3 3 4
+ u3 *a11 *b32 + u3 *v1*a11 *b31*b32 + u3 *v2*a11 *b32 + u3 *a11 *b32 *n3
1 2 2 2 2 4 1 2 2 5
+ ---*u3 *v1 *a11 *b31 *b32 + ---*u3 *v1*v2*a11 *b31*b32
4 2
2 3 4 1 2 4 1 2 2 2 6
+ u3 *v1*(a11 *b32 *m1 + ---*a11 *b31*b32 *n3) + ---*u3 *v2 *a11 *b32
2 4
2 3 3 1 2 2 3 2 5
+ u3 *v2*( - a11 *b31*b32 *m1 + ---*a11 *b31 *b32 *n3 + a11 *b32 *n3)
2
2 2 1 2 2 4 1 2 6
+ u3 *v3 *( - ---*a11 *b31 *b32 - ---*a11 *b32 )
4 4
2 69 2 2 3 77 2 5
+ u3 *v3*( - ----*a11 *b31 *b32 *n2 - ----*a11 *b32 *n2)
8 8
2 35 2 2 2 2 35 2 4 2 1 2 4 2
+ u3 *( - ----*a11 *b31 *b32 *n2 - ----*a11 *b32 *n2 - ---*a11 *b32 *n3 )
4 4 4
1 2 2 4 1 2 2 3
+ ---*u3*v1 *a11 *b31*b32 *m1 + u3*v1*v2*( - ---*a11 *b31 *b32 *m1
2 2
1 2 5 1 3 3 1 5
+ ---*a11 *b32 *m1 + ---*a11*b31 *b32 *n3 + ---*a11*b31*b32 *n3)
2 4 4
39 3 3 43 5
+ u3*v1*v3*( - ----*a11*b31 *b32 *n2 - ----*a11*b31*b32 *n2) + u3*v1*(
8 8
1 2 4 19 3 2 2 21 4 2
---*a11 *b32 *m1*n3 - ----*a11*b31 *b32 *n2 - ----*a11*b31*b32 *n2
2 4 4
1 4 2
- ---*a11*b31*b32 *n3 )
4
2 1 2 4 1 2 4 1 6
+ u3*v2 *( - ---*a11 *b31*b32 *m1 + ---*a11*b31 *b32 *n3 + ---*a11*b32 *n3)
2 4 4
9 2 4 6
+ u3*v2*v3*( - ---*a11*b31 *b32 *n2 - 5*a11*b32 *n2) + u3*v2*(
2
1 2 3 23 2 3 2
- ---*a11 *b31*b32 *m1*n3 - ----*a11*b31 *b32 *n2
2 4
1 2 3 2 21 5 2
+ ---*a11*b31 *b32 *n3 - ----*a11*b32 *n2 ) + u3*v3*(
4 4
1 2 3 51 2 3
- ---*a11 *b31*b32 *m1*n2 - ----*a11*b31 *b32 *n2*n3
2 8
53 5 29 2 3 2
- ----*a11*b32 *n2*n3) + u3*( - ----*a11 *b31 *m1*n2
8 2
29 2 2 2 29 4 2
- ----*a11 *b31*b32 *m1*n2 + ----*a11*b31 *n2 *n3
2 4
2 2 2 37 4 2 1 4 3
- 2*a11*b31 *b32 *n2 *n3 - ----*a11*b32 *n2 *n3 - ---*a11*b32 *n3 )
4 4
2 5 4 3 5 2 5
+ v1 *v3*(----*b31 *b32 *n2 + ----*b31 *b32 *n2) + v1*v2
16 16
1 2 3 2 1 2 3 1 5
*( - ---*a11 *b31*b32 *m1 + ---*a11*b31 *b32 *m1*n3 + ---*a11*b32 *m1*n3)
2 4 4
1 2 3 1 3 3 1 5
+ v1*v3*(---*a11*b31 *b32 *m1*n2 + ---*b31 *b32 *n2*n3 + ---*b31*b32 *n2*n3)
2 8 8
3 2 2 2 1 4 2 1 4 2
+ v1*(---*a11*b31 *b32 *m1*n2 + ---*a11*b32 *m1*n2 - ---*a11*b32 *m1*n3
4 4 4
99 3 2 2 107 4 2
+ ----*b31 *b32 *n2 *n3 + -----*b31*b32 *n2 *n3)
32 32
2 5 2 5 5 7 2 1 2 2 2 2
+ v2 *v3*( - ----*b31 *b32 *n2 - ----*b32 *n2) + v2 *(---*a11 *b31 *b32 *m1
16 16 4
1 2 4 2 1 3 2 1 4
- ---*a11 *b32 *m1 - ---*a11*b31 *b32 *m1*n3 - ---*a11*b31*b32 *m1*n3
4 4 4
257 4 2 2 1 4 2 2 69 2 4 2
+ -----*b31 *b32 *n2 + ----*b31 *b32 *n3 + ----*b31 *b32 *n2
128 16 16
1 2 4 2 295 6 2 1 6 2
+ ---*b31 *b32 *n3 + -----*b32 *n2 + ----*b32 *n3 )
8 128 16
1 4 15 2 4 15 6
+ v2*v3*(---*a11*b31*b32 *m1*n2 - ----*b31 *b32 *n2*n3 - ----*b32 *n2*n3) +
2 16 16
3 3 2 1 3 2
v2*(---*a11*b31 *b32*m1*n2 + ---*a11*b31*b32 *m1*n2
4 4
1 3 2 3 4 2 147 2 3 2
+ ---*a11*b31*b32 *m1*n3 - ---*b31 *b32*n2 *n3 - -----*b31 *b32 *n2 *n3
4 8 32
1 2 3 3 143 5 2 1 5 3
- ---*b31 *b32 *n3 - -----*b32 *n2 *n3 - ---*b32 *n3 )
8 32 8
3 1 4 3 1 2 5 2 1 2 2 2 2
+ v3 *(---*b31 *b32 *n2 + ---*b31 *b32 *n2) + v3 *(---*a11 *b31 *b32 *m1
8 8 4
1 3 2 1 4 281 4 2 2
- ---*a11*b31 *b32 *m1*n3 - ---*a11*b31*b32 *m1*n3 + -----*b31 *b32 *n2
4 4 128
1 4 2 2 567 2 4 2 3 2 4 2
+ ----*b31 *b32 *n3 + -----*b31 *b32 *n2 + ----*b31 *b32 *n3
16 64 16
885 6 2 1 6 2 1 3
+ -----*b32 *n2 + ---*b32 *n3 ) + v3*( - ---*a11*b31*b32 *m1*n2*n3
128 8 2
201 4 3 257 2 3 3 5 2 3 2
+ -----*b31 *b32*n2 + -----*b31 *b32 *n2 - ---*b31 *b32 *n2*n3
32 32 8
7 5 3 5 5 2
+ ---*b32 *n2 - ---*b32 *n2*n3 )
4 8
{HAM,FI} = 0
2 2 2 2 2 2 2
FI=u1 *v2 *a11 *b32 + u1 *v3 *a11 *b32 - 2*u1*u2*v1*v2*a11 *b32
2 2 2
- 2*u1*u3*v1*v3*a11 *b32 - u1*v1 *a11*b31*n2 - u1*v2 *a11*b31*n2
2 2 2 2 2 2 2
- u1*v3 *a11*b31*n2 + u2 *v1 *a11 *b32 + u2 *v3 *a11 *b32
2 2 2
- 2*u2*u3*v2*v3*a11 *b32 + u2*v1 *a11*b32*n2 + u2*v2 *a11*b32*n2
2 2 2 2 2 2 2
+ u2*v3 *a11*b32*n2 + 2*u3 *v1 *a11 *b32 + 2*u3 *v2 *a11 *b32
2 2 2 3 2 2
+ u3 *v3 *a11 *b32 + u3*v1 *a11*b31*b32 + u3*v1 *v2*a11*b32
2 2 2
+ u3*v1 *a11*b32*n3 + u3*v1*v2 *a11*b31*b32 + u3*v1*v3 *a11*b31*b32
3 2 2 2 2
+ u3*v2 *a11*b32 + u3*v2 *a11*b32*n3 + u3*v2*v3 *a11*b32
2 3
+ u3*v3 *a11*b32*n3 + v1 *a11*b32*m1
2 1 2 1 2
+ v1 *v2*( - a11*b31*m1 + ---*b31 *n3 + ---*b32 *n3)
2 2
2 2 1 2 1 3
+ v1 *v3 *( - ---*b31 *b32 - ---*b32 )
4 4
2 67 2 75 2 2
+ v1 *v3*( - ----*b31 *n2 - ----*b32 *n2) + v1*v2 *a11*b32*m1
8 8
2 3 1 2 1 2
+ v1*v3 *a11*b32*m1 + v2 *( - a11*b31*m1 + ---*b31 *n3 + ---*b32 *n3)
2 2
2 2 1 2 1 3
+ v2 *v3 *( - ---*b31 *b32 - ---*b32 )
4 4
2 67 2 75 2
+ v2 *v3*( - ----*b31 *n2 - ----*b32 *n2)
8 8
2 1 2 1 2
+ v2*v3 *( - a11*b31*m1 + ---*b31 *n3 + ---*b32 *n3)
2 2
4 1 2 1 3 3 67 2 75 2
+ v3 *( - ---*b31 *b32 - ---*b32 ) + v3 *( - ----*b31 *n2 - ----*b32 *n2)
4 4 8 8
{HAM,FI} = 0
And again in machine readable form:
HAM=(u1**2*a11**2*b32 - u1*a11*b31*n2 + u2**2*a11**2*b32 + u2*a11*b32*n2 + 2*u3
**2*a11**2*b32 + u3*v1*a11*b31*b32 + u3*v2*a11*b32**2 + u3*a11*b32*n3 + v1*a11*
b32*m1 + v2*( - a11*b31*m1 + 1/2*b31**2*n3 + 1/2*b32**2*n3) + v3**2*( - 1/4*b31
**2*b32 - 1/4*b32**3) + v3*( - 67/8*b31**2*n2 - 75/8*b32**2*n2))/(a11*b32)$
FI= - u1**3*a11**3*b31*b32**3*n2 + u1**2*u2*a11**3*b32**4*n2 + u1**2*u3**2*a11**
4*b32**4 + u1**2*u3*v1*a11**3*b31*b32**4 + u1**2*u3*a11**3*b32**4*n3 + u1**2*v1*
a11**3*b32**4*m1 - 1/2*u1**2*v3*a11**2*b32**5*n2 - u1*u2**2*a11**3*b31*b32**3*n2
+ u1*u2*u3*v1*a11**3*b32**5 + u1*u2*u3*v2*a11**3*b31*b32**4 + u1*u2*v1*( - a11
**3*b31*b32**3*m1 + 1/2*a11**2*b31**2*b32**3*n3 + 1/2*a11**2*b32**5*n3) + u1*u2*
v2*a11**3*b32**4*m1 - u1*u3**2*a11**3*b31*b32**3*n2 + u1*u3*v1*v3*( - 1/2*a11**2
*b31**2*b32**4 - 1/2*a11**2*b32**6) + u1*u3*v1*( - 17/4*a11**2*b31**2*b32**3*n2
- 19/4*a11**2*b32**5*n2) - 3/2*u1*u3*v2*a11**2*b31*b32**4*n2 - 1/2*u1*u3*v3*a11
**2*b31*b32**4*n3 + u1*v1**2*( - 5/8*a11*b31**3*b32**3*n2 - 5/8*a11*b31*b32**5*
n2) + u1*v1*v3*( - 1/4*a11*b31**2*b32**4*n3 - 1/4*a11*b32**6*n3) + u1*v1*( - 3/2
*a11*b31**2*b32**3*n2*n3 - 3/2*a11*b32**5*n2*n3) + u1*v2**2*( - 3/8*a11*b31**3*
b32**3*n2 - 3/8*a11*b31*b32**5*n2) + u1*v2*(3/2*a11**2*b31**2*b32**2*m1*n2 - 3/4
*a11*b31**3*b32**2*n2*n3 - 1/2*a11*b31*b32**4*n2*n3) + u1*v3*( - 1/2*a11**2*b32
**4*m1*n3 + 201/16*a11*b31**3*b32**2*n2**2 + 209/16*a11*b31*b32**4*n2**2) + u1*(
35/4*a11*b31**3*b32*n2**3 + 35/4*a11*b31*b32**3*n2**3 + 1/4*a11*b31*b32**3*n2*n3
**2) + u2**3*a11**3*b32**4*n2 + u2**2*u3**2*a11**4*b32**4 + u2**2*u3*v2*a11**3*
b32**5 + u2**2*u3*a11**3*b32**4*n3 + u2**2*v2*( - a11**3*b31*b32**3*m1 + 1/2*a11
**2*b31**2*b32**3*n3 + 1/2*a11**2*b32**5*n3) + 1/2*u2**2*v3*a11**2*b31**2*b32**3
*n2 + u2**2*(a11**2*b31**2*b32**2*n2**2 + a11**2*b32**4*n2**2) + u2*u3**2*a11**3
*b32**4*n2 + 3/2*u2*u3*v1*a11**2*b31*b32**4*n2 + u2*u3*v2*v3*( - 1/2*a11**2*b31
**2*b32**4 - 1/2*a11**2*b32**6) + u2*u3*v2*( - 7/4*a11**2*b31**2*b32**3*n2 - 9/4
*a11**2*b32**5*n2) - 1/2*u2*u3*v3*a11**2*b32**5*n3 + u2*v1**2*(3/8*a11*b31**2*
b32**4*n2 + 3/8*a11*b32**6*n2) + u2*v1*(3/2*a11**2*b32**4*m1*n2 - 1/4*a11*b31*
b32**4*n2*n3) + u2*v2**2*(5/8*a11*b31**2*b32**4*n2 + 5/8*a11*b32**6*n2) + u2*v2*
v3*( - 1/4*a11*b31**2*b32**4*n3 - 1/4*a11*b32**6*n3) + u2*v3*(1/2*a11**2*b31*b32
**3*m1*n3 - 217/16*a11*b31**2*b32**3*n2**2 - 1/4*a11*b31**2*b32**3*n3**2 - 225/
16*a11*b32**5*n2**2 - 1/4*a11*b32**5*n3**2) + u2*( - 35/4*a11*b31**2*b32**2*n2**
3 - 35/4*a11*b32**4*n2**3 - 1/4*a11*b32**4*n2*n3**2) + u3**4*a11**4*b32**4 + u3
**3*v1*a11**3*b31*b32**4 + u3**3*v2*a11**3*b32**5 + u3**3*a11**3*b32**4*n3 + 1/4
*u3**2*v1**2*a11**2*b31**2*b32**4 + 1/2*u3**2*v1*v2*a11**2*b31*b32**5 + u3**2*v1
*(a11**3*b32**4*m1 + 1/2*a11**2*b31*b32**4*n3) + 1/4*u3**2*v2**2*a11**2*b32**6 +
u3**2*v2*( - a11**3*b31*b32**3*m1 + 1/2*a11**2*b31**2*b32**3*n3 + a11**2*b32**5
*n3) + u3**2*v3**2*( - 1/4*a11**2*b31**2*b32**4 - 1/4*a11**2*b32**6) + u3**2*v3*
( - 69/8*a11**2*b31**2*b32**3*n2 - 77/8*a11**2*b32**5*n2) + u3**2*( - 35/4*a11**
2*b31**2*b32**2*n2**2 - 35/4*a11**2*b32**4*n2**2 - 1/4*a11**2*b32**4*n3**2) + 1/
2*u3*v1**2*a11**2*b31*b32**4*m1 + u3*v1*v2*( - 1/2*a11**2*b31**2*b32**3*m1 + 1/2
*a11**2*b32**5*m1 + 1/4*a11*b31**3*b32**3*n3 + 1/4*a11*b31*b32**5*n3) + u3*v1*v3
*( - 39/8*a11*b31**3*b32**3*n2 - 43/8*a11*b31*b32**5*n2) + u3*v1*(1/2*a11**2*b32
**4*m1*n3 - 19/4*a11*b31**3*b32**2*n2**2 - 21/4*a11*b31*b32**4*n2**2 - 1/4*a11*
b31*b32**4*n3**2) + u3*v2**2*( - 1/2*a11**2*b31*b32**4*m1 + 1/4*a11*b31**2*b32**
4*n3 + 1/4*a11*b32**6*n3) + u3*v2*v3*( - 9/2*a11*b31**2*b32**4*n2 - 5*a11*b32**6
*n2) + u3*v2*( - 1/2*a11**2*b31*b32**3*m1*n3 - 23/4*a11*b31**2*b32**3*n2**2 + 1/
4*a11*b31**2*b32**3*n3**2 - 21/4*a11*b32**5*n2**2) + u3*v3*( - 1/2*a11**2*b31*
b32**3*m1*n2 - 51/8*a11*b31**2*b32**3*n2*n3 - 53/8*a11*b32**5*n2*n3) + u3*( - 29
/2*a11**2*b31**3*m1*n2**2 - 29/2*a11**2*b31*b32**2*m1*n2**2 + 29/4*a11*b31**4*n2
**2*n3 - 2*a11*b31**2*b32**2*n2**2*n3 - 37/4*a11*b32**4*n2**2*n3 - 1/4*a11*b32**
4*n3**3) + v1**2*v3*(5/16*b31**4*b32**3*n2 + 5/16*b31**2*b32**5*n2) + v1*v2*( -
1/2*a11**2*b31*b32**3*m1**2 + 1/4*a11*b31**2*b32**3*m1*n3 + 1/4*a11*b32**5*m1*n3
) + v1*v3*(1/2*a11*b31**2*b32**3*m1*n2 + 1/8*b31**3*b32**3*n2*n3 + 1/8*b31*b32**
5*n2*n3) + v1*(3/4*a11*b31**2*b32**2*m1*n2**2 + 1/4*a11*b32**4*m1*n2**2 - 1/4*
a11*b32**4*m1*n3**2 + 99/32*b31**3*b32**2*n2**2*n3 + 107/32*b31*b32**4*n2**2*n3)
+ v2**2*v3*( - 5/16*b31**2*b32**5*n2 - 5/16*b32**7*n2) + v2**2*(1/4*a11**2*b31
**2*b32**2*m1**2 - 1/4*a11**2*b32**4*m1**2 - 1/4*a11*b31**3*b32**2*m1*n3 - 1/4*
a11*b31*b32**4*m1*n3 + 257/128*b31**4*b32**2*n2**2 + 1/16*b31**4*b32**2*n3**2 +
69/16*b31**2*b32**4*n2**2 + 1/8*b31**2*b32**4*n3**2 + 295/128*b32**6*n2**2 + 1/
16*b32**6*n3**2) + v2*v3*(1/2*a11*b31*b32**4*m1*n2 - 15/16*b31**2*b32**4*n2*n3 -
15/16*b32**6*n2*n3) + v2*(3/4*a11*b31**3*b32*m1*n2**2 + 1/4*a11*b31*b32**3*m1*
n2**2 + 1/4*a11*b31*b32**3*m1*n3**2 - 3/8*b31**4*b32*n2**2*n3 - 147/32*b31**2*
b32**3*n2**2*n3 - 1/8*b31**2*b32**3*n3**3 - 143/32*b32**5*n2**2*n3 - 1/8*b32**5*
n3**3) + v3**3*(1/8*b31**4*b32**3*n2 + 1/8*b31**2*b32**5*n2) + v3**2*(1/4*a11**2
*b31**2*b32**2*m1**2 - 1/4*a11*b31**3*b32**2*m1*n3 - 1/4*a11*b31*b32**4*m1*n3 +
281/128*b31**4*b32**2*n2**2 + 1/16*b31**4*b32**2*n3**2 + 567/64*b31**2*b32**4*n2
**2 + 3/16*b31**2*b32**4*n3**2 + 885/128*b32**6*n2**2 + 1/8*b32**6*n3**2) + v3*(
- 1/2*a11*b31*b32**3*m1*n2*n3 + 201/32*b31**4*b32*n2**3 + 257/32*b31**2*b32**3*
n2**3 - 5/8*b31**2*b32**3*n2*n3**2 + 7/4*b32**5*n2**3 - 5/8*b32**5*n2*n3**2)$
FI=u1**2*v2**2*a11**2*b32 + u1**2*v3**2*a11**2*b32 - 2*u1*u2*v1*v2*a11**2*b32 -
2*u1*u3*v1*v3*a11**2*b32 - u1*v1**2*a11*b31*n2 - u1*v2**2*a11*b31*n2 - u1*v3**2*
a11*b31*n2 + u2**2*v1**2*a11**2*b32 + u2**2*v3**2*a11**2*b32 - 2*u2*u3*v2*v3*a11
**2*b32 + u2*v1**2*a11*b32*n2 + u2*v2**2*a11*b32*n2 + u2*v3**2*a11*b32*n2 + 2*u3
**2*v1**2*a11**2*b32 + 2*u3**2*v2**2*a11**2*b32 + u3**2*v3**2*a11**2*b32 + u3*v1
**3*a11*b31*b32 + u3*v1**2*v2*a11*b32**2 + u3*v1**2*a11*b32*n3 + u3*v1*v2**2*a11
*b31*b32 + u3*v1*v3**2*a11*b31*b32 + u3*v2**3*a11*b32**2 + u3*v2**2*a11*b32*n3 +
u3*v2*v3**2*a11*b32**2 + u3*v3**2*a11*b32*n3 + v1**3*a11*b32*m1 + v1**2*v2*( -
a11*b31*m1 + 1/2*b31**2*n3 + 1/2*b32**2*n3) + v1**2*v3**2*( - 1/4*b31**2*b32 - 1
/4*b32**3) + v1**2*v3*( - 67/8*b31**2*n2 - 75/8*b32**2*n2) + v1*v2**2*a11*b32*m1
+ v1*v3**2*a11*b32*m1 + v2**3*( - a11*b31*m1 + 1/2*b31**2*n3 + 1/2*b32**2*n3) +
v2**2*v3**2*( - 1/4*b31**2*b32 - 1/4*b32**3) + v2**2*v3*( - 67/8*b31**2*n2 - 75
/8*b32**2*n2) + v2*v3**2*( - a11*b31*m1 + 1/2*b31**2*n3 + 1/2*b32**2*n3) + v3**4
*( - 1/4*b31**2*b32 - 1/4*b32**3) + v3**3*( - 67/8*b31**2*n2 - 75/8*b32**2*n2)$