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