Solution 9 to problem over
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Expressions
The solution is given through the following expressions:
2 2 2 2 2 3 4
r10=( - 2*a33 *m2*n2 *r214 + 4*a33 *m2*n3 *r214 + a33 *n2 *r26 - 2*m2*n2 *r464
2 2 3
+ 2*m2*n2 *n3 *r464)/(2*a33 *n2*n3)
2 2 2 2 2 3 2 2
r11=( - 2*a33 *m2*n2 *r214 + 2*a33 *m2*n3 *r214 + a33 *n2 *r26 + a33 *n2*n3 *r26
4 4 3 2
- 2*m2*n2 *r464 + 2*m2*n3 *r464)/(4*a33 *n3 )
2 2 2 2 2 3
r12=(2*a33 *m1*m2*n2 *r214 - 6*a33 *m1*m2*n3 *r214 - a33 *m1*n2 *r26
2 2 4 2 2
+ a33 *m1*n2*n3 *r26 + 2*m1*m2*n2 *r464 - 4*m1*m2*n2 *n3 *r464
4 3 2
+ 2*m1*m2*n3 *r464)/(4*a33 *m2*n3 )
2 2 2 2 2 3 2 2
r13=(2*a33 *m2*n2 *r214 - 6*a33 *m2*n3 *r214 - a33 *n2 *r26 + a33 *n2*n3 *r26
4 2 2 4 3
+ 2*m2*n2 *r464 - 4*m2*n2 *n3 *r464 + 2*m2*n3 *r464)/(4*a33 *m2*n3)
2 3 2 2 2 4
r14=(2*a33 *m2*n2 *r214 - 6*a33 *m2*n2*n3 *r214 - a33 *n2 *r26
2 2 2 5 3 2 4
+ a33 *n2 *n3 *r26 + 2*m2*n2 *r464 - 4*m2*n2 *n3 *r464 + 2*m2*n2*n3 *r464)
3 2
/(4*a33 *m2*n3 )
r15=0
2 2 2 2 2 2 2 2 2
r20=( - 4*a33 *m1 *n3 *r214 + 2*a33 *m2 *n2 *r214 + 4*a33 *m2 *n3 *r214
2 3 2 2 2 4
- a33 *m2*n2 *r26 - 4*a33 *m2*n2*n3 *r26 + 2*m2 *n2 *r464
2 2 2 2 4 2 2 2
+ 6*m2 *n2 *n3 *r464 + 8*m2 *n3 *r464)/(4*a33 *n2 *n3 )
2 2 2 2 2 2 2
2*a33 *m2 *r214 - a33 *m2*n2*r26 + 2*m2 *n2 *r464 + 4*m2 *n3 *r464
r21=--------------------------------------------------------------------
2
a33 *n2*n3
2 2 2 2 2 3 2 2
r22=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 + 2*a33 *m2 *r214 - a33 *m2 *n2*r26
2 2 2 2 3 2 3 2
- 2*m1 *m2*n2 *r464 + 2*m1 *m2*n3 *r464 + 2*m2 *n2 *r464 + 6*m2 *n3 *r464)
2 2
/(4*a33 *m2*n3 )
2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464
r23=----------------------------------------------------------
2
a33 *n2*n3
r24
2 2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464 - 2*m1*m2*n3 *r464
=-----------------------------------------------------------------------------
2 2
2*a33 *n3
2 2 2 2
- 2*a33 *m2*r214 + a33 *n2*r26 - 2*m2*n2 *r464 - 2*m2*n3 *r464
r27=-----------------------------------------------------------------
2
2*a33 *n3
2 2 2 2
2*a33 *m1*m2*r214 - a33 *m1*n2*r26 + 2*m1*m2*n2 *r464 - 2*m1*m2*n3 *r464
r28=--------------------------------------------------------------------------
2
2*a33 *m2*n3
2 2 2
- 2*a33 *m2*r214 + a33 *n2*r26 - 2*m2*n2 *r464
r210=-------------------------------------------------
2
a33 *n3
2*m1*r214
r212=-----------
n2
2 2 2 3 2
2*a33 *m2*n2*r214 - a33 *n2 *r26 + 2*m2*n2 *r464 - 2*m2*n2*n3 *r464
r213=---------------------------------------------------------------------
2
2*a33 *m2*n3
r215=0
2 2 2 2 2 3
r216=(2*a33 *m1*m2*n2 *r214 - 4*a33 *m1*m2*n3 *r214 - a33 *m1*n2 *r26
4 2 2 2 2
+ 2*m1*m2*n2 *r464 - 2*m1*m2*n2 *n3 *r464)/(2*a33 *m2*n2*n3 )
2 2 2 3 2
2*a33 *m2*n2*r214 - a33 *n2 *r26 + 2*m2*n2 *r464 + 2*m2*n2*n3 *r464
r217=---------------------------------------------------------------------
2 2
2*a33 *n3
r218=0
r219=0
2 2 2 2 2 3 4
r220=( - 2*a33 *m2*n2 *r214 + 4*a33 *m2*n3 *r214 + a33 *n2 *r26 - 2*m2*n2 *r464
2 2 2 2
+ 2*m2*n2 *n3 *r464)/(4*a33 *m2*n3 )
2 2 2 2 2 3 2 2
r30=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 - 2*a33 *m2 *r214 + a33 *m2 *n2*r26
2 2 2 2 3 2 3 2
- 2*m1 *m2*n2 *r464 - 2*m1 *m2*n3 *r464 - 2*m2 *n2 *r464 - 2*m2 *n3 *r464
3 2 3
+ n2 *n3 *r417)/(a33*n2 *n3)
2 2 2 2 2 3 2 2
r31=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 - 2*a33 *m2 *r214 + a33 *m2 *n2*r26
2 2 2 2 3 2 3 2
- 2*m1 *m2*n2 *r464 - 4*m1 *m2*n3 *r464 - 2*m2 *n2 *r464 - 4*m2 *n3 *r464
3 2 2 2
+ n2 *n3 *r417)/(2*a33*n2 *n3 )
n3*r417
r32=---------
a33
n2*r417
r33=---------
2*a33
2 3 2 3 2 3
r34=(2*a33 *m1 *m2*r214 - a33 *m1 *n2*r26 + 2*a33 *m1*m2 *r214
2 2 3 2 3 2
- a33 *m1*m2 *n2*r26 + 2*m1 *m2*n2 *r464 + 2*m1*m2 *n2 *r464
3 2 2 2
- m1*n2 *n3 *r417)/(2*a33*m2*n2 *n3 )
r35=0
- m1*n2*r417
r36=---------------
2*a33*m2
n3*r417
r37=---------
a33
n2*r417
r38=---------
2*a33
- m1*n2*r417
r39=---------------
2*a33*m2
2 2 2 2 2 3
r310=(2*a33 *m1 *m2*r214 - a33 *m1 *n2*r26 + 10*a33 *m2 *r214
2 2 2 2 3 2
- 5*a33 *m2 *n2*r26 + 2*m1 *m2*n2 *r464 + 10*m2 *n2 *r464
3 2 3 2 2
+ 8*m2 *n3 *r464 - n2 *n3 *r417)/(2*a33*m2*n2 *n3)
2 3 2 2 3 2 3 2
r311=(4*a33 *m2 *r214 - 2*a33 *m2 *n2*r26 + 4*m2 *n2 *r464 + 8*m2 *n3 *r464
3 2 2
+ n2 *n3 *r417)/(2*a33*m2*n2*n3 )
- n2*n3*r417
r312=---------------
2*a33*m2
r313
2 2 2 2
- 4*a33 *m1*m2*r214 + 2*a33 *m1*n2*r26 - 4*m1*m2*n2 *r464 - 4*m1*m2*n3 *r464
=-------------------------------------------------------------------------------
2
a33*n2*n3
r314=0
- n2*n3*r417
r315=---------------
2*a33*m2
2 2 2 2
- 2*a33 *m2*r214 + a33 *n2*r26 - 2*m2*n2 *r464 + 2*m2*n3 *r464
r316=-----------------------------------------------------------------
a33*n2*n3
m2*r464
r317=---------
a33
- m1*r464
r318=------------
a33
- n3*r464
r319=------------
a33
2 2 2 2 2 3 2 2
r320=(2*a33 *m1 *m2*r214 - a33 *m1 *n2*r26 + 2*a33 *m2 *r214 - a33 *m2 *n2*r26
2 2 3 2 3 2 2
+ 2*m1 *m2*n2 *r464 + 2*m2 *n2 *r464 - n2 *n3 *r417)/(2*a33*m2*n2*n3 )
r323
2 2 2 2
4*a33 *m1*m2*r214 - 2*a33 *m1*n2*r26 + 4*m1*m2*n2 *r464 + 4*m1*m2*n3 *r464
=----------------------------------------------------------------------------
2
a33*n2 *n3
r325
2 2 2 2 2 2 3 2
- 4*a33 *m1 *m2*r214 + 2*a33 *m1 *n2*r26 - 4*m1 *m2*n2 *r464 - n2 *n3 *r417
=------------------------------------------------------------------------------
2
2*a33*m2*n2*n3
2 2 2 2
- 6*a33 *m2*r214 + 3*a33 *n2*r26 - 6*m2*n2 *r464 - 4*m2*n3 *r464
r326=-------------------------------------------------------------------
2
2*a33*n3
2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464
r328=----------------------------------------------------------
a33*m2*n2*n3
- n2*r464
r329=------------
a33
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r330=--------------------------------------------------------------
a33*n2*n3
2 2 2
- 6*a33 *m1*m2*r214 + 3*a33 *m1*n2*r26 - 6*m1*m2*n2 *r464
r332=------------------------------------------------------------
2
2*a33*m2*n3
2 2 2
- 2*a33 *m2*r214 + a33 *n2*r26 - 2*m2*n2 *r464
r333=-------------------------------------------------
2*a33*m2*n3
2 2 2 3
- 2*a33 *m2*n2*r214 + a33 *n2 *r26 - 2*m2*n2 *r464
r334=-----------------------------------------------------
2
2*a33*m2*n3
r335=0
r336
2 2 2 2
- 4*a33 *m1*m2*r214 + 2*a33 *m1*n2*r26 - 4*m1*m2*n2 *r464 - 4*m1*m2*n3 *r464
=-------------------------------------------------------------------------------
2
a33*n2 *n3
r337
2 2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464 - 4*m1*m2*n3 *r464
=-----------------------------------------------------------------------------
2
a33*n2*n3
r338=0
2 2 2 2 2 2 3 2
4*a33 *m1 *m2*r214 - 2*a33 *m1 *n2*r26 + 4*m1 *m2*n2 *r464 + n2 *n3 *r417
r339=---------------------------------------------------------------------------
2
2*a33*m2*n2*n3
r340
2 2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464 - 4*m1*m2*n3 *r464
=-----------------------------------------------------------------------------
2
a33*n2*n3
2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464
r341=----------------------------------------------------------
2
a33*m2*n3
2 2 2
2*a33 *m1*m2*r214 - a33 *m1*n2*r26 + 2*m1*m2*n2 *r464
r342=-------------------------------------------------------
a33*m2*n2*n3
r343=0
r344=0
r345=0
2 2 2 2
- 2*a33 *m2*r214 + a33 *n2*r26 - 2*m2*n2 *r464 - 4*m2*n3 *r464
r347=-----------------------------------------------------------------
2
2*a33*n3
r348=0
r349=0
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r350=--------------------------------------------------------------
a33*n2*n3
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 4*m2*n3 *r464
r351=--------------------------------------------------------------
2
2*a33*n3
2 2 2
- 6*a33 *m1*m2*r214 + 3*a33 *m1*n2*r26 - 6*m1*m2*n2 *r464
r352=------------------------------------------------------------
2
2*a33*m2*n3
2 2 2
- 2*a33 *m2*r214 + a33 *n2*r26 - 2*m2*n2 *r464
r353=-------------------------------------------------
2*a33*m2*n3
2 2 2 3
- 2*a33 *m2*n2*r214 + a33 *n2 *r26 - 2*m2*n2 *r464
r354=-----------------------------------------------------
2
2*a33*m2*n3
r355=0
2 4 2 4 2 2 3
r40=(2*a33 *m1 *m2*r214 - a33 *m1 *n2*r26 + 4*a33 *m1 *m2 *r214
2 2 2 2 5 2 4
- 2*a33 *m1 *m2 *n2*r26 + 2*a33 *m2 *r214 - a33 *m2 *n2*r26
4 2 4 2 2 3 2
+ 2*m1 *m2*n2 *r464 + 2*m1 *m2*n3 *r464 + 4*m1 *m2 *n2 *r464
2 3 2 2 3 2 5 2
+ 4*m1 *m2 *n3 *r464 - 2*m1 *n2 *n3 *r417 + 2*m2 *n2 *r464
5 2 2 3 2 4 2
+ 2*m2 *n3 *r464 - 2*m2 *n2 *n3 *r417)/(4*m2*n2 *n3 )
r41=0
2 2
- m1 *r417 - m2 *r417
r42=------------------------
2*m2*n2
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
2 2
- m1 *r417 - m2 *r417
r49=------------------------
2*m2*n2
r410=0
r411=0
r412=0
r413=0
2 2 2 2 2 3
r415=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 - 2*a33 *m2 *r214
2 2 2 2 2 2
+ a33 *m2 *n2*r26 - 2*m1 *m2*n2 *r464 - 2*m1 *m2*n3 *r464
3 2 3 2 3 2 3 2
- 2*m2 *n2 *r464 - 2*m2 *n3 *r464 + n2 *n3 *r417)/(n2 *n3 )
r416=0
r418=0
r419=0
- m1*r417
r420=------------
m2
r421=0
r422=r417
r423=0
r424=0
2 3 2 2 2 2 3 2
r425=(4*a33 *m2 *r214 - 2*a33 *m2 *n2*r26 - 2*m1 *m2*n3 *r464 + 4*m2 *n2 *r464
3 2 3 2 2 2
+ 2*m2 *n3 *r464 + n2 *n3 *r417)/(2*m2*n2 *n3 )
r426=0
r427=0
r428=0
r429=0
2*m2*r464
r431=-----------
n2
r432=0
r433=0
r435=0
2 3 2 3 2 3
r439=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 - 2*a33 *m1*m2 *r214
2 2 3 2 3 2
+ a33 *m1*m2 *n2*r26 - 2*m1 *m2*n2 *r464 - 2*m1 *m2*n3 *r464
3 2 3 2 3 2 3 2
- 2*m1*m2 *n2 *r464 - 2*m1*m2 *n3 *r464 + m1*n2 *n3 *r417)/(m2*n2 *n3 )
r442=0
m1*r417
r444=---------
m2
r445=0
r448
2 2 2 2
4*a33 *m1*m2*r214 - 2*a33 *m1*n2*r26 + 4*m1*m2*n2 *r464 + 4*m1*m2*n3 *r464
=----------------------------------------------------------------------------
2 2
n2 *n3
r450=0
r451=0
2*m1*r464
r453=-----------
n2
r454=0
2 2 2 2 2 3
r455=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 - 2*a33 *m2 *r214
2 2 2 2 2 2
+ a33 *m2 *n2*r26 - 2*m1 *m2*n2 *r464 - 2*m1 *m2*n3 *r464
3 2 3 2 3 2 2 2
- 2*m2 *n2 *r464 - 2*m2 *n3 *r464 + n2 *n3 *r417)/(2*m2*n2 *n3 )
r458=0
2 2 2 2 2 2
r460=(4*a33 *m1 *m2*r214 - 2*a33 *m1 *n2*r26 + 4*m1 *m2*n2 *r464
2 2 3 2 2 2
+ 4*m1 *m2*n3 *r464 + n2 *n3 *r417)/(2*m2*n2 *n3 )
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r461=--------------------------------------------------------------
2
n2*n3
r463=0
r465=0
2 2 2 2
2*a33 *m1*m2*r214 - a33 *m1*n2*r26 + 2*m1*m2*n2 *r464 + 2*m1*m2*n3 *r464
r467=--------------------------------------------------------------------------
2
m2*n2*n3
r468=0
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r469=--------------------------------------------------------------
2
4*m2*n3
r470=0
2 3 2 3 2 3
r471=(2*a33 *m1 *m2*r214 - a33 *m1 *n2*r26 + 2*a33 *m1*m2 *r214
2 2 3 2 3 2
- a33 *m1*m2 *n2*r26 + 2*m1 *m2*n2 *r464 + 2*m1 *m2*n3 *r464
3 2 3 2 3 2 3 2
+ 2*m1*m2 *n2 *r464 + 2*m1*m2 *n3 *r464 - m1*n2 *n3 *r417)/(m2*n2 *n3 )
r472=0
- m1*r417
r473=------------
m2
r474=0
r475=0
r476=0
r477=0
- 2*m1*r417
r478=--------------
m2
r479=0
r480=0
r481
2 2 2 2
- 4*a33 *m1*m2*r214 + 2*a33 *m1*n2*r26 - 4*m1*m2*n2 *r464 - 4*m1*m2*n3 *r464
=-------------------------------------------------------------------------------
2 2
n2 *n3
r482=0
r484=0
r485=0
r486=0
- 2*m1*r464
r487=--------------
n2
r488=0
r489=0
r490=0
r493=0
r495=0
2 2 2 2
2*a33 *m1*m2*r214 - a33 *m1*n2*r26 + 2*m1*m2*n2 *r464 + 2*m1*m2*n3 *r464
r496=--------------------------------------------------------------------------
2
m2*n2*n3
r498=0
r499=0
r4100=0
r4102=0
r4103=0
r4104=0
2 2 2 2 2 3
r4105=( - 2*a33 *m1 *m2*r214 + a33 *m1 *n2*r26 - 2*a33 *m2 *r214
2 2 2 2 2 2
+ a33 *m2 *n2*r26 - 2*m1 *m2*n2 *r464 - 2*m1 *m2*n3 *r464
3 2 3 2 3 2 2 2
- 2*m2 *n2 *r464 - 2*m2 *n3 *r464 + n2 *n3 *r417)/(2*m2*n2 *n3 )
r4106=0
2 2 2 2 2 2
r4107=(4*a33 *m1 *m2*r214 - 2*a33 *m1 *n2*r26 + 4*m1 *m2*n2 *r464
2 2 3 2 2 2
+ 4*m1 *m2*n3 *r464 + n2 *n3 *r417)/(2*m2*n2 *n3 )
r4108=0
r4109=0
2 2 2 2 2 2
r4110=(4*a33 *m1 *m2*r214 - 2*a33 *m1 *n2*r26 + 4*m1 *m2*n2 *r464
2 2 3 2 2 2
+ 4*m1 *m2*n3 *r464 + n2 *n3 *r417)/(m2*n2 *n3 )
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r4111=--------------------------------------------------------------
2
n2*n3
r4112=0
r4113=0
r4114=r464
r4115=0
r4117
2 2 2 2
4*a33 *m1*m2*r214 - 2*a33 *m1*n2*r26 + 4*m1*m2*n2 *r464 + 4*m1*m2*n3 *r464
=----------------------------------------------------------------------------
2
m2*n2*n3
r4118=0
r4120=0
r4121
2 2 2 2
- 2*a33 *m1*m2*r214 + a33 *m1*n2*r26 - 2*m1*m2*n2 *r464 - 2*m1*m2*n3 *r464
=-----------------------------------------------------------------------------
2
m2*n2*n3
r4122=0
r4123=0
r4124=0
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r4125=--------------------------------------------------------------
2
4*m2*n3
m3=0
n1=0
c33=0
c23=0
c22=0
c13=0
c12=0
c11=0
b33=0
b32=0
b31=0
b23=0
b22=0
b21=0
b13=0
b12=0
b11=0
a23=0
a22=0
a13=0
a12=0
a11=0
2 2 2 2
2*a33 *m2*r214 - a33 *n2*r26 + 2*m2*n2 *r464 + 2*m2*n3 *r464
r4119=--------------------------------------------------------------
2
2*m2*n3
2 2 2 2 2 2
r483=(4*a33 *m1 *m2*r214 - 2*a33 *m1 *n2*r26 + 4*m1 *m2*n2 *r464
2 2 3 2 2 2
+ 4*m1 *m2*n3 *r464 + n2 *n3 *r417)/(m2*n2 *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:
r26, r417, r214, r464, m2, n3, m1, n2, a33
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.
{m1,n2,a33}
Relevance for the application:
The new Hamiltonian in form of a list of vanishing expressions:
{a11,
a12,
a13,
a22,
a23,
b11,
b12,
b13,
b21,
b22,
b23,
b31,
b32,
b33,
c11,
c12,
c13,
c22,
c23,
c33,
n1,
m3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=u2*n2 + u3 *a33 + u3*n3 + v1*m1 + v2*m2
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
4 3 6 3 4 2 3 3 5 3 3 2
FI=u1 *(a33 *n2 + a33 *n2 *n3 ) + u1 *v2*( - 4*a33 *m1*n2 - 4*a33 *m1*n2 *n3 )
2 2 3 6 3 4 2
+ u1 *u2 *(2*a33 *n2 + 2*a33 *n2 *n3 )
2 3 5 3 3 2 2 2 7
+ u1 *u2*v1*(8*a33 *m1*n2 + 8*a33 *m1*n2 *n3 ) - 2*u1 *u2*a33 *n2
2 2 3 4 2 2 3 5 3 3 2
+ 2*u1 *u3 *a33 *n2 *n3 + u1 *u3*v3*(4*a33 *m2*n2 + 4*a33 *m2*n2 *n3 )
2 2 6 2 2 3 2 4 3 2 2 2
- 2*u1 *u3*a33 *n2 *n3 + u1 *v1 *(8*a33 *m1 *n2 + 8*a33 *m1 *n2 *n3 )
2 2 6 2 2 3 2 4 3 2 2 2
- 6*u1 *v1*a33 *m1*n2 + u1 *v2 *(4*a33 *m1 *n2 + 4*a33 *m1 *n2 *n3 )
2 2 6 2 4 2 2 2 3 2 4
+ u1 *v2*(2*a33 *m2*n2 + 4*a33 *m2*n2 *n3 ) + u1 *v3 *( - 2*a33 *m1 *n2
3 2 2 2 3 2 4 3 2 2 2
- 2*a33 *m1 *n2 *n3 - 2*a33 *m2 *n2 - 2*a33 *m2 *n2 *n3 )
2 2 5 2 3 3
+ u1 *v3*(4*a33 *m2*n2 *n3 + 4*a33 *m2*n2 *n3 )
2 8 6 2
+ u1 *( - a33*n2 + a33*n2 *n3 )
3 5 3 3 2
+ u1*u2*u3*v3*(4*a33 *m1*n2 + 4*a33 *m1*n2 *n3 )
2 6 2 4 2
+ u1*u2*v1*( - 2*a33 *m2*n2 - 4*a33 *m2*n2 *n3 )
2 3 3 2
- 4*u1*u3 *v2*a33 *m1*n2 *n3
3 2 4 3 2 2 2
+ u1*u3*v1*v3*(8*a33 *m1 *n2 + 8*a33 *m1 *n2 *n3 )
3 4 3 2 2
+ u1*u3*v2*v3*( - 8*a33 *m1*m2*n2 - 8*a33 *m1*m2*n2 *n3 )
2 5 2 6
+ 4*u1*u3*v2*a33 *m1*n2 *n3 - 4*u1*u3*v3*a33 *m1*n2
2 2 5 2 3 2
+ u1*v1 *( - 4*a33 *m1*m2*n2 - 8*a33 *m1*m2*n2 *n3 )
2 2 5 7 5 2
+ 4*u1*v1*v2*a33 *m1 *n2 + u1*v1*(2*a33*m2*n2 + 2*a33*m2*n2 *n3 )
2 2 5 2 3 2 2
+ u1*v2 *( - 4*a33 *m1*m2*n2 - 8*a33 *m1*m2*n2 *n3 ) + u1*v2*v3 *(
3 3 3 3 3 2 3 2 3
4*a33 *m1 *n2 + 4*a33 *m1 *n2*n3 + 4*a33 *m1*m2 *n2
3 2 2
+ 4*a33 *m1*m2 *n2*n3 )
2 4 2 2 3
+ u1*v2*v3*( - 8*a33 *m1*m2*n2 *n3 - 8*a33 *m1*m2*n2 *n3 )
7 5 2 4 3 6 3 4 2
+ u1*v2*(2*a33*m1*n2 - 2*a33*m1*n2 *n3 ) + u2 *(a33 *n2 + a33 *n2 *n3 )
3 3 5 3 3 2 3 2 7
+ u2 *v1*(4*a33 *m1*n2 + 4*a33 *m1*n2 *n3 ) - 2*u2 *a33 *n2
2 2 3 4 2 2 3 5 3 3 2
+ 2*u2 *u3 *a33 *n2 *n3 + u2 *u3*v3*(4*a33 *m2*n2 + 4*a33 *m2*n2 *n3 )
2 2 6 2 2 3 2 4 3 2 2 2
- 2*u2 *u3*a33 *n2 *n3 + u2 *v1 *(4*a33 *m1 *n2 + 4*a33 *m1 *n2 *n3 )
2 2 6 2 2 3 2 4 3 2 2 2
- 6*u2 *v1*a33 *m1*n2 + u2 *v3 *( - 2*a33 *m1 *n2 - 2*a33 *m1 *n2 *n3
3 2 4 3 2 2 2
- 2*a33 *m2 *n2 - 2*a33 *m2 *n2 *n3 )
2 2 5 2 3 3
+ u2 *v3*(4*a33 *m2*n2 *n3 + 4*a33 *m2*n2 *n3 )
2 3 3 2 2 2 5 2
+ 4*u2*u3 *v1*a33 *m1*n2 *n3 - 2*u2*u3 *a33 *n2 *n3
3 4 3 2 2
+ u2*u3*v1*v3*(8*a33 *m1*m2*n2 + 8*a33 *m1*m2*n2 *n3 )
2 5
- 4*u2*u3*v1*a33 *m1*n2 *n3
2 6 2 4 2
+ u2*u3*v3*( - 6*a33 *m2*n2 - 4*a33 *m2*n2 *n3 )
7 5 3 2 2 2 5 2
+ u2*u3*(2*a33*n2 *n3 - 2*a33*n2 *n3 ) - 4*u2*v1 *a33 *m1 *n2 + u2*v1*v3 *(
3 3 3 3 3 2 3 2 3
- 4*a33 *m1 *n2 - 4*a33 *m1 *n2*n3 - 4*a33 *m1*m2 *n2
3 2 2
- 4*a33 *m1*m2 *n2*n3 )
2 4 2 2 3
+ u2*v1*v3*(8*a33 *m1*m2*n2 *n3 + 8*a33 *m1*m2*n2 *n3 )
2 2 2 5 2 2 5 6
+ u2*v3 *(2*a33 *m1 *n2 + 2*a33 *m2 *n2 ) - 4*u2*v3*a33*m2*n2 *n3
9 7 2 5 4 3 3 3 2
+ u2*(n2 - 2*n2 *n3 + n2 *n3 ) + 4*u3 *v3*a33 *m2*n2 *n3
3 2 4 3 2 2 4 2 2 2 4 2
- 2*u3 *a33 *n2 *n3 - 2*u3 *v1*a33 *m1*n2 *n3 + 2*u3 *v2*a33 *m2*n2 *n3
2 2 3 2 2 2 3 2 4 3 2 2 2
+ u3 *v3 *( - 2*a33 *m1 *n2 *n3 + 4*a33 *m2 *n2 + 2*a33 *m2 *n2 *n3 )
2 2 5 2 3 3
+ u3 *v3*( - 4*a33 *m2*n2 *n3 + 4*a33 *m2*n2 *n3 )
2 5 2 3 2
+ u3*v1*v3*( - 8*a33 *m1*m2*n2 - 8*a33 *m1*m2*n2 *n3 )
6 4 3
+ u3*v1*(2*a33*m1*n2 *n3 - 2*a33*m1*n2 *n3 )
2 2 5 2 2 3 2
+ u3*v2*v3*(4*a33 *m2 *n2 + 8*a33 *m2 *n2 *n3 )
6 4 3 3
+ u3*v2*( - 2*a33*m2*n2 *n3 - 2*a33*m2*n2 *n3 ) + u3*v3 *(
3 2 3 3 2 2 3 3 3
- 4*a33 *m1 *m2*n2 - 4*a33 *m1 *m2*n2*n3 - 4*a33 *m2 *n2
3 3 2
- 4*a33 *m2 *n2*n3 )
2 2 2 4 2 2 4 2 2 2 3
+ u3*v3 *(2*a33 *m1 *n2 *n3 + 10*a33 *m2 *n2 *n3 + 8*a33 *m2 *n2 *n3 )
8 6 3 4 5
+ u3*(n2 *n3 - 2*n2 *n3 + n2 *n3 )
6 4 2
+ v1*v2*( - 2*a33*m1*m2*n2 - 2*a33*m1*m2*n2 *n3 )
2 2 3 4 2 2 4 5
+ v1*v3 *(2*a33 *m1 *n2 + 2*a33 *m1*m2 *n2 ) - 4*v1*v3*a33*m1*m2*n2 *n3
8 6 2 4 4
+ v1*(m1*n2 - 2*m1*n2 *n3 + m1*n2 *n3 )
2 2 6 2 4 2 2 6 2 4 2
+ v2 *( - a33*m1 *n2 + a33*m1 *n2 *n3 + a33*m2 *n2 + 3*a33*m2 *n2 *n3 ) +
2 2 2 4 2 2 2 2 2 3 4
v2*v3 *( - 2*a33 *m1 *m2*n2 - 4*a33 *m1 *m2*n2 *n3 - 2*a33 *m2 *n2
2 3 2 2
- 4*a33 *m2 *n2 *n3 )
2 5 2 3 3 8 4 4
+ v2*v3*(4*a33*m2 *n2 *n3 + 8*a33*m2 *n2 *n3 ) + v2*( - m2*n2 + m2*n2 *n3 )
4 3 4 2 3 4 2 3 2 2 2 3 2 2 2
+ v3 *(a33 *m1 *n2 + a33 *m1 *n3 + 2*a33 *m1 *m2 *n2 + 2*a33 *m1 *m2 *n3
3 4 2 3 4 2 3 2 2 3
+ a33 *m2 *n2 + a33 *m2 *n3 ) + v3 *( - 4*a33 *m1 *m2*n2 *n3
2 2 3 2 3 3 2 3 3
- 4*a33 *m1 *m2*n2*n3 - 4*a33 *m2 *n2 *n3 - 4*a33 *m2 *n2*n3 )
2 2 6 2 4 2 2 2 4
+ v3 *(a33*m2 *n2 + 3*a33*m2 *n2 *n3 + 4*a33*m2 *n2 *n3 )
7 5 3
+ v3*( - 2*m2*n2 *n3 + 2*m2*n2 *n3 )
Stop of a subroutine.
Number of garbage collections exceeds max_gc_fac.
The factorization crashed!
which the program can not factorize further.
{HAM,FI} = {16,
n2,
n2,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
2 3 2 2
2 - a33 *m1*n2 - a33 *m1*n2*n3
u1 *u3*---------------------------------
2
3 3
2 - a33*m1*n2 *n3 - a33*m1*n2*n3
+ u1 *----------------------------------
4
2 2 2 2 2 2
+ u1*u3*v2*(a33 *m1 *n2 + a33 *m1 *n3 )
4 2 2
a33*m2*n2 + 2*a33*m2*n2 *n3
+ u1*u3*-------------------------------
4
2 2 2 3
a33*m1 *n2 *n3 + a33*m1 *n3
+ u1*v2*------------------------------
2
2 3 2 2
- a33*m1 *n2 - a33*m1 *n2*n3
+ u1*v3*---------------------------------
4
4 2 3
m2*n2 *n3 + 2*m2*n2 *n3
+ u1*--------------------------
8
2 3 2 2
2 a33 *m1*n2 + a33 *m1*n2*n3
+ u2 *u3*------------------------------
2
3 3
2 a33*m1*n2 *n3 + a33*m1*n2*n3
+ u2 *-------------------------------
4
2 2 2 2 2 2
+ u2*u3*v1*(a33 *m1 *n2 + a33 *m1 *n3 )
4 2 2
- 3*a33*m1*n2 - a33*m1*n2 *n3
+ u2*u3*----------------------------------
4
2 2 2 3
a33*m1 *n2 *n3 + a33*m1 *n3
+ u2*v1*------------------------------
2
3 2 4
- a33*m1*m2*n2 - a33*m1*m2*n2*n3 - u2*m1*n2 *n3
+ u2*v3*------------------------------------- + -----------------
4 4
2 3 2 2
- a33*m1 *n2 - a33*m1 *n2*n3
+ u3*v1*---------------------------------
2
3 2 5
- a33*m1*m2*n2 - 2*a33*m1*m2*n2*n3 u3*m1*n2
+ u3*v2*--------------------------------------- + -----------
2 4
2 2 2 2
- a33*m1 *m2*n2 - a33*m1 *m2*n3
+ v1*v3*------------------------------------
2
3 3
- m1*m2*n2 *n3 - 2*m1*m2*n2*n3
+ v2*----------------------------------
4
4 2 2
3*m1*m2*n2 + 2*m1*m2*n2 *n3
+ v3*-------------------------------}
8
4 3 4 3 3 3 2 2 3 4
FI=u1 *a33 *n2 - 4*u1 *v2*a33 *m1*n2 + 2*u1 *u2 *a33 *n2
2 3 3 2 2 5 2 3 3
+ 8*u1 *u2*v1*a33 *m1*n2 - 2*u1 *u2*a33 *n2 + 4*u1 *u3*v3*a33 *m2*n2
2 2 4 2 2 3 2 2 2 2 4
- 2*u1 *u3*a33 *n2 *n3 + 8*u1 *v1 *a33 *m1 *n2 - 6*u1 *v1*a33 *m1*n2
2 2 3 2 2 2 2 4
+ 4*u1 *v2 *a33 *m1 *n2 + 2*u1 *v2*a33 *m2*n2
2 2 3 2 2 3 2 2 2 2 3
+ u1 *v3 *( - 2*a33 *m1 *n2 - 2*a33 *m2 *n2 ) + 4*u1 *v3*a33 *m2*n2 *n3
2 6 4 2 3 3
+ u1 *( - a33*n2 + 2*a33*n2 *n3 ) + 4*u1*u2*u3*v3*a33 *m1*n2
2 4 3 2 2
- 2*u1*u2*v1*a33 *m2*n2 + 8*u1*u3*v1*v3*a33 *m1 *n2
3 2 2 3
- 8*u1*u3*v2*v3*a33 *m1*m2*n2 + 4*u1*u3*v2*a33 *m1*n2 *n3
2 4 2 2 3 2 2 3
- 4*u1*u3*v3*a33 *m1*n2 - 4*u1*v1 *a33 *m1*m2*n2 + 4*u1*v1*v2*a33 *m1 *n2
5 2 2 3
+ 2*u1*v1*a33*m2*n2 - 4*u1*v2 *a33 *m1*m2*n2
2 3 3 3 2
+ u1*v2*v3 *(4*a33 *m1 *n2 + 4*a33 *m1*m2 *n2)
2 2 5 3 2
- 8*u1*v2*v3*a33 *m1*m2*n2 *n3 + u1*v2*(2*a33*m1*n2 - 4*a33*m1*n2 *n3 )
4 3 4 3 3 3 3 2 5
+ u2 *a33 *n2 + 4*u2 *v1*a33 *m1*n2 - 2*u2 *a33 *n2
2 3 3 2 2 4 2 2 3 2 2
+ 4*u2 *u3*v3*a33 *m2*n2 - 2*u2 *u3*a33 *n2 *n3 + 4*u2 *v1 *a33 *m1 *n2
2 2 4 2 2 3 2 2 3 2 2
- 6*u2 *v1*a33 *m1*n2 + u2 *v3 *( - 2*a33 *m1 *n2 - 2*a33 *m2 *n2 )
2 2 3 2 4 2 3 2
+ 4*u2 *v3*a33 *m2*n2 *n3 + 2*u2 *a33*n2 *n3 + 8*u2*u3*v1*v3*a33 *m1*m2*n2
2 3 2 4 5
- 4*u2*u3*v1*a33 *m1*n2 *n3 - 6*u2*u3*v3*a33 *m2*n2 + 2*u2*u3*a33*n2 *n3
2 2 2 3 2 3 3 3 2
- 4*u2*v1 *a33 *m1 *n2 + u2*v1*v3 *( - 4*a33 *m1 *n2 - 4*a33 *m1*m2 *n2)
2 2 3 2
+ 8*u2*v1*v3*a33 *m1*m2*n2 *n3 + 4*u2*v1*a33*m1*n2 *n3
2 2 2 3 2 2 3 4
+ u2*v3 *(2*a33 *m1 *n2 + 2*a33 *m2 *n2 ) - 4*u2*v3*a33*m2*n2 *n3
7 5 2 2 2 3 2 2 2 2 3
+ u2*(n2 - 3*n2 *n3 ) + 4*u3 *v3 *a33 *m2 *n2 - 4*u3 *v3*a33 *m2*n2 *n3
2 3 4
- 8*u3*v1*v3*a33 *m1*m2*n2 + 2*u3*v1*a33*m1*n2 *n3
2 2 3 4
+ 4*u3*v2*v3*a33 *m2 *n2 - 2*u3*v2*a33*m2*n2 *n3
3 3 2 3 3
+ u3*v3 *( - 4*a33 *m1 *m2*n2 - 4*a33 *m2 *n2)
2 2 2 2 2 2 2 6 4 3
+ u3*v3 *(2*a33 *m1 *n2 *n3 + 10*a33 *m2 *n2 *n3) + u3*(n2 *n3 - 3*n2 *n3 )
4 2 2 3 2 2 2 2
- 2*v1*v2*a33*m1*m2*n2 + v1*v3 *(2*a33 *m1 *n2 + 2*a33 *m1*m2 *n2 )
3 6 4 2
- 4*v1*v3*a33*m1*m2*n2 *n3 + v1*(m1*n2 - 3*m1*n2 *n3 )
2 2 4 2 4
+ v2 *( - a33*m1 *n2 + a33*m2 *n2 )
2 2 2 2 2 3 2 2 3
+ v2*v3 *( - 2*a33 *m1 *m2*n2 - 2*a33 *m2 *n2 ) + 4*v2*v3*a33*m2 *n2 *n3
6 4 2 4 3 4 3 2 2 3 4
+ v2*( - m2*n2 + m2*n2 *n3 ) + v3 *(a33 *m1 + 2*a33 *m1 *m2 + a33 *m2 )
3 2 2 2 3
+ v3 *( - 4*a33 *m1 *m2*n2*n3 - 4*a33 *m2 *n2*n3)
2 2 2 2 2 4 2 2 2
+ v3 *( - 2*a33*m1 *n2 *n3 + a33*m2 *n2 + 2*a33*m2 *n2 *n3 )
5 3 3
+ v3*( - 2*m2*n2 *n3 + 4*m2*n2 *n3 )
which the program can not factorize further.
{HAM,FI} = {16,
n2,
n2,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
2 2 2
- u1 *u3*a33 *m1*n2 - u1 *a33*m1*n2*n3 2 2
---------------------- + --------------------- + u1*u3*v2*a33 *m1
2 4
2 2 2
u1*u3*a33*m2*n2 u1*v2*a33*m1 *n3 - u1*v3*a33*m1 *n2
+ ------------------ + ------------------ + ---------------------
4 2 4
2 2 2 2
u1*m2*n2 *n3 u2 *u3*a33 *m1*n2 u2 *a33*m1*n2*n3
+ -------------- + ------------------- + ------------------
8 2 4
2 2
2 2 - 3*u2*u3*a33*m1*n2 u2*v1*a33*m1 *n3
+ u2*u3*v1*a33 *m1 + ----------------------- + ------------------
4 2
2
- u2*v3*a33*m1*m2*n2 - u2*m1*n2 *n3
+ ----------------------- + -----------------
4 4
2 3
- u3*v1*a33*m1 *n2 - u3*v2*a33*m1*m2*n2 u3*m1*n2
+ --------------------- + ----------------------- + -----------
2 2 4
2 2
- v1*v3*a33*m1 *m2 - v2*m1*m2*n2*n3 3*v3*m1*m2*n2
+ --------------------- + ------------------- + ----------------}
2 4 8
2 2 2 2 2 2 2 2 2 2
FI=2*u1 *v1 *a33*n2 + u1 *v2 *a33*n2 + u1 *v3 *a33*n2 + 2*u1*u3*v1*v3*a33*n2
2 3 3
- 4*u1*v1 *v2*a33*m1*n2 + u1*v1*v2*n2 - 2*u1*v2 *a33*m1*n2
2 2 2 2 2 2 2
- 2*u1*v2*v3 *a33*m1*n2 + u2 *v1 *a33*n2 + u2 *v3 *a33*n2
3 2 3 2 2 3
+ 2*u2*v1 *a33*m1*n2 - u2*v1 *n2 + 2*u2*v1*v3 *a33*m1*n2 - u2*v3 *n2
2 2 2 2 2 2
+ u3 *v3 *a33*n2 + 2*u3*v1 *v3*a33*m2*n2 - u3*v1 *n2 *n3
2 2 2
- 2*u3*v1*v2*v3*a33*m1*n2 + 2*u3*v2 *v3*a33*m2*n2 - u3*v2 *n2 *n3
3 3 2 2 3 2
+ u3*v2*v3*n2 + 2*u3*v3 *a33*m2*n2 - u3*v3 *n2 *n3 - v1 *m1*n2
2 2 2 2 2 2 2
+ v1 *v2*m2*n2 + v1 *v3 *( - a33*m1 - a33*m2 ) + 2*v1 *v3*m2*n2*n3
2 2 2 2 3 2
- v1*v2 *m1*n2 - v1*v3 *m1*n2 + v2 *m2*n2
2 2 2 2 2 2 2
+ v2 *v3 *( - a33*m1 - a33*m2 ) + 2*v2 *v3*m2*n2*n3 + v2*v3 *m2*n2
4 2 2 3
+ v3 *( - a33*m1 - a33*m2 ) + 2*v3 *m2*n2*n3
which the program can not factorize further.
{HAM,FI} = {4,
u1*v1 + u2*v2 + u3*v3,
n2,
n3
u3*a33 + ----,
2
2
2 - v1*n2 2
u1*v2*a33*n2 + u2*v1*a33*n2 + v1 *a33*m1 + ----------- - v2 *a33*m1}
2
4 3 4 3 3 3 2 2 3 4
FI= - u1 *a33 *n2 + 4*u1 *v2*a33 *m1*n2 - 2*u1 *u2 *a33 *n2
2 3 3 2 2 5 2 3 3
- 8*u1 *u2*v1*a33 *m1*n2 + 2*u1 *u2*a33 *n2 - 4*u1 *u3*v3*a33 *m2*n2
2 2 4 2 2 3 2 2 2 2 4
+ 2*u1 *u3*a33 *n2 *n3 - 8*u1 *v1 *a33 *m1 *n2 + 6*u1 *v1*a33 *m1*n2
2 2 3 2 2 2 2 4
- 4*u1 *v2 *a33 *m1 *n2 - 2*u1 *v2*a33 *m2*n2
2 2 3 2 2 3 2 2 2 2 3
+ u1 *v3 *(2*a33 *m1 *n2 + 2*a33 *m2 *n2 ) - 4*u1 *v3*a33 *m2*n2 *n3
2 6 3 3 2 4
+ u1 *a33*n2 - 4*u1*u2*u3*v3*a33 *m1*n2 + 2*u1*u2*v1*a33 *m2*n2
3 2 2 3 2
- 8*u1*u3*v1*v3*a33 *m1 *n2 + 8*u1*u3*v2*v3*a33 *m1*m2*n2
2 3 2 4
- 4*u1*u3*v2*a33 *m1*n2 *n3 + 4*u1*u3*v3*a33 *m1*n2
2 2 3 2 2 3 5
+ 4*u1*v1 *a33 *m1*m2*n2 - 4*u1*v1*v2*a33 *m1 *n2 - 2*u1*v1*a33*m2*n2
2 2 3 2 3 3 3 2
+ 4*u1*v2 *a33 *m1*m2*n2 + u1*v2*v3 *( - 4*a33 *m1 *n2 - 4*a33 *m1*m2 *n2)
2 2 5 4 3 4
+ 8*u1*v2*v3*a33 *m1*m2*n2 *n3 - 2*u1*v2*a33*m1*n2 - u2 *a33 *n2
3 3 3 3 2 5 2 3 3
- 4*u2 *v1*a33 *m1*n2 + 2*u2 *a33 *n2 - 4*u2 *u3*v3*a33 *m2*n2
2 2 4 2 2 3 2 2 2 2 4
+ 2*u2 *u3*a33 *n2 *n3 - 4*u2 *v1 *a33 *m1 *n2 + 6*u2 *v1*a33 *m1*n2
2 2 3 2 2 3 2 2 2 2 3
+ u2 *v3 *(2*a33 *m1 *n2 + 2*a33 *m2 *n2 ) - 4*u2 *v3*a33 *m2*n2 *n3
3 2 2 3
- 8*u2*u3*v1*v3*a33 *m1*m2*n2 + 4*u2*u3*v1*a33 *m1*n2 *n3
2 4 5 2 2 2 3
+ 6*u2*u3*v3*a33 *m2*n2 - 2*u2*u3*a33*n2 *n3 + 4*u2*v1 *a33 *m1 *n2
2 3 3 3 2
+ u2*v1*v3 *(4*a33 *m1 *n2 + 4*a33 *m1*m2 *n2)
2 2 2 2 2 3 2 2 3
- 8*u2*v1*v3*a33 *m1*m2*n2 *n3 + u2*v3 *( - 2*a33 *m1 *n2 - 2*a33 *m2 *n2 )
4 7 5 2 2 2 3 2 2
+ 4*u2*v3*a33*m2*n2 *n3 + u2*( - n2 + n2 *n3 ) - 4*u3 *v3 *a33 *m2 *n2
2 2 3 2 3
+ 4*u3 *v3*a33 *m2*n2 *n3 + 8*u3*v1*v3*a33 *m1*m2*n2
4 2 2 3 4
- 2*u3*v1*a33*m1*n2 *n3 - 4*u3*v2*v3*a33 *m2 *n2 + 2*u3*v2*a33*m2*n2 *n3
3 3 2 3 3
+ u3*v3 *(4*a33 *m1 *m2*n2 + 4*a33 *m2 *n2)
2 2 2 2 2 2 2
+ u3*v3 *( - 2*a33 *m1 *n2 *n3 - 10*a33 *m2 *n2 *n3)
3 2 6 4 3 4
+ 4*u3*v3*a33*m2*n2 *n3 + u3*( - n2 *n3 + n2 *n3 ) + 2*v1*v2*a33*m1*m2*n2
2 2 3 2 2 2 2 3
+ v1*v3 *( - 2*a33 *m1 *n2 - 2*a33 *m1*m2 *n2 ) + 4*v1*v3*a33*m1*m2*n2 *n3
6 4 2 2 2 4 2 4
+ v1*( - m1*n2 + m1*n2 *n3 ) + v2 *(a33*m1 *n2 - a33*m2 *n2 )
2 2 2 2 2 3 2 2 3
+ v2*v3 *(2*a33 *m1 *m2*n2 + 2*a33 *m2 *n2 ) - 4*v2*v3*a33*m2 *n2 *n3
6 4 2 4 3 4 3 2 2 3 4
+ v2*(m2*n2 + m2*n2 *n3 ) + v3 *( - a33 *m1 - 2*a33 *m1 *m2 - a33 *m2 )
3 2 2 2 3
+ v3 *(4*a33 *m1 *m2*n2*n3 + 4*a33 *m2 *n2*n3)
2 2 4 2 2 2 5
+ v3 *( - a33*m2 *n2 - 4*a33*m2 *n2 *n3 ) + 2*v3*m2*n2 *n3
which the program can not factorize further.
{HAM,FI} = {16,
- n2,
n2,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
2 2 2
- u1 *u3*a33 *m1*n2 - u1 *a33*m1*n2*n3 2 2
---------------------- + --------------------- + u1*u3*v2*a33 *m1
2 4
2 2 2
u1*u3*a33*m2*n2 u1*v2*a33*m1 *n3 - u1*v3*a33*m1 *n2
+ ------------------ + ------------------ + ---------------------
4 2 4
2 2 2 2
u1*m2*n2 *n3 u2 *u3*a33 *m1*n2 u2 *a33*m1*n2*n3
+ -------------- + ------------------- + ------------------
8 2 4
2 2
2 2 - 3*u2*u3*a33*m1*n2 u2*v1*a33*m1 *n3
+ u2*u3*v1*a33 *m1 + ----------------------- + ------------------
4 2
2
- u2*v3*a33*m1*m2*n2 - u2*m1*n2 *n3
+ ----------------------- + -----------------
4 4
2 3
- u3*v1*a33*m1 *n2 - u3*v2*a33*m1*m2*n2 u3*m1*n2
+ --------------------- + ----------------------- + -----------
2 2 4
2 2
- v1*v3*a33*m1 *m2 - v2*m1*m2*n2*n3 3*v3*m1*m2*n2
+ --------------------- + ------------------- + ----------------}
2 4 8
And again in machine readable form:
HAM=u2*n2 + u3**2*a33 + u3*n3 + v1*m1 + v2*m2$
FI=u1**4*(a33**3*n2**6 + a33**3*n2**4*n3**2) + u1**3*v2*( - 4*a33**3*m1*n2**5 -
4*a33**3*m1*n2**3*n3**2) + u1**2*u2**2*(2*a33**3*n2**6 + 2*a33**3*n2**4*n3**2) +
u1**2*u2*v1*(8*a33**3*m1*n2**5 + 8*a33**3*m1*n2**3*n3**2) - 2*u1**2*u2*a33**2*
n2**7 + 2*u1**2*u3**2*a33**3*n2**4*n3**2 + u1**2*u3*v3*(4*a33**3*m2*n2**5 + 4*
a33**3*m2*n2**3*n3**2) - 2*u1**2*u3*a33**2*n2**6*n3 + u1**2*v1**2*(8*a33**3*m1**
2*n2**4 + 8*a33**3*m1**2*n2**2*n3**2) - 6*u1**2*v1*a33**2*m1*n2**6 + u1**2*v2**2
*(4*a33**3*m1**2*n2**4 + 4*a33**3*m1**2*n2**2*n3**2) + u1**2*v2*(2*a33**2*m2*n2
**6 + 4*a33**2*m2*n2**4*n3**2) + u1**2*v3**2*( - 2*a33**3*m1**2*n2**4 - 2*a33**3
*m1**2*n2**2*n3**2 - 2*a33**3*m2**2*n2**4 - 2*a33**3*m2**2*n2**2*n3**2) + u1**2*
v3*(4*a33**2*m2*n2**5*n3 + 4*a33**2*m2*n2**3*n3**3) + u1**2*( - a33*n2**8 + a33*
n2**6*n3**2) + u1*u2*u3*v3*(4*a33**3*m1*n2**5 + 4*a33**3*m1*n2**3*n3**2) + u1*u2
*v1*( - 2*a33**2*m2*n2**6 - 4*a33**2*m2*n2**4*n3**2) - 4*u1*u3**2*v2*a33**3*m1*
n2**3*n3**2 + u1*u3*v1*v3*(8*a33**3*m1**2*n2**4 + 8*a33**3*m1**2*n2**2*n3**2) +
u1*u3*v2*v3*( - 8*a33**3*m1*m2*n2**4 - 8*a33**3*m1*m2*n2**2*n3**2) + 4*u1*u3*v2*
a33**2*m1*n2**5*n3 - 4*u1*u3*v3*a33**2*m1*n2**6 + u1*v1**2*( - 4*a33**2*m1*m2*n2
**5 - 8*a33**2*m1*m2*n2**3*n3**2) + 4*u1*v1*v2*a33**2*m1**2*n2**5 + u1*v1*(2*a33
*m2*n2**7 + 2*a33*m2*n2**5*n3**2) + u1*v2**2*( - 4*a33**2*m1*m2*n2**5 - 8*a33**2
*m1*m2*n2**3*n3**2) + u1*v2*v3**2*(4*a33**3*m1**3*n2**3 + 4*a33**3*m1**3*n2*n3**
2 + 4*a33**3*m1*m2**2*n2**3 + 4*a33**3*m1*m2**2*n2*n3**2) + u1*v2*v3*( - 8*a33**
2*m1*m2*n2**4*n3 - 8*a33**2*m1*m2*n2**2*n3**3) + u1*v2*(2*a33*m1*n2**7 - 2*a33*
m1*n2**5*n3**2) + u2**4*(a33**3*n2**6 + a33**3*n2**4*n3**2) + u2**3*v1*(4*a33**3
*m1*n2**5 + 4*a33**3*m1*n2**3*n3**2) - 2*u2**3*a33**2*n2**7 + 2*u2**2*u3**2*a33
**3*n2**4*n3**2 + u2**2*u3*v3*(4*a33**3*m2*n2**5 + 4*a33**3*m2*n2**3*n3**2) - 2*
u2**2*u3*a33**2*n2**6*n3 + u2**2*v1**2*(4*a33**3*m1**2*n2**4 + 4*a33**3*m1**2*n2
**2*n3**2) - 6*u2**2*v1*a33**2*m1*n2**6 + u2**2*v3**2*( - 2*a33**3*m1**2*n2**4 -
2*a33**3*m1**2*n2**2*n3**2 - 2*a33**3*m2**2*n2**4 - 2*a33**3*m2**2*n2**2*n3**2)
+ u2**2*v3*(4*a33**2*m2*n2**5*n3 + 4*a33**2*m2*n2**3*n3**3) + 4*u2*u3**2*v1*a33
**3*m1*n2**3*n3**2 - 2*u2*u3**2*a33**2*n2**5*n3**2 + u2*u3*v1*v3*(8*a33**3*m1*m2
*n2**4 + 8*a33**3*m1*m2*n2**2*n3**2) - 4*u2*u3*v1*a33**2*m1*n2**5*n3 + u2*u3*v3*
( - 6*a33**2*m2*n2**6 - 4*a33**2*m2*n2**4*n3**2) + u2*u3*(2*a33*n2**7*n3 - 2*a33
*n2**5*n3**3) - 4*u2*v1**2*a33**2*m1**2*n2**5 + u2*v1*v3**2*( - 4*a33**3*m1**3*
n2**3 - 4*a33**3*m1**3*n2*n3**2 - 4*a33**3*m1*m2**2*n2**3 - 4*a33**3*m1*m2**2*n2
*n3**2) + u2*v1*v3*(8*a33**2*m1*m2*n2**4*n3 + 8*a33**2*m1*m2*n2**2*n3**3) + u2*
v3**2*(2*a33**2*m1**2*n2**5 + 2*a33**2*m2**2*n2**5) - 4*u2*v3*a33*m2*n2**6*n3 +
u2*(n2**9 - 2*n2**7*n3**2 + n2**5*n3**4) + 4*u3**3*v3*a33**3*m2*n2**3*n3**2 - 2*
u3**3*a33**2*n2**4*n3**3 - 2*u3**2*v1*a33**2*m1*n2**4*n3**2 + 2*u3**2*v2*a33**2*
m2*n2**4*n3**2 + u3**2*v3**2*( - 2*a33**3*m1**2*n2**2*n3**2 + 4*a33**3*m2**2*n2
**4 + 2*a33**3*m2**2*n2**2*n3**2) + u3**2*v3*( - 4*a33**2*m2*n2**5*n3 + 4*a33**2
*m2*n2**3*n3**3) + u3*v1*v3*( - 8*a33**2*m1*m2*n2**5 - 8*a33**2*m1*m2*n2**3*n3**
2) + u3*v1*(2*a33*m1*n2**6*n3 - 2*a33*m1*n2**4*n3**3) + u3*v2*v3*(4*a33**2*m2**2
*n2**5 + 8*a33**2*m2**2*n2**3*n3**2) + u3*v2*( - 2*a33*m2*n2**6*n3 - 2*a33*m2*n2
**4*n3**3) + u3*v3**3*( - 4*a33**3*m1**2*m2*n2**3 - 4*a33**3*m1**2*m2*n2*n3**2 -
4*a33**3*m2**3*n2**3 - 4*a33**3*m2**3*n2*n3**2) + u3*v3**2*(2*a33**2*m1**2*n2**
4*n3 + 10*a33**2*m2**2*n2**4*n3 + 8*a33**2*m2**2*n2**2*n3**3) + u3*(n2**8*n3 - 2
*n2**6*n3**3 + n2**4*n3**5) + v1*v2*( - 2*a33*m1*m2*n2**6 - 2*a33*m1*m2*n2**4*n3
**2) + v1*v3**2*(2*a33**2*m1**3*n2**4 + 2*a33**2*m1*m2**2*n2**4) - 4*v1*v3*a33*
m1*m2*n2**5*n3 + v1*(m1*n2**8 - 2*m1*n2**6*n3**2 + m1*n2**4*n3**4) + v2**2*( -
a33*m1**2*n2**6 + a33*m1**2*n2**4*n3**2 + a33*m2**2*n2**6 + 3*a33*m2**2*n2**4*n3
**2) + v2*v3**2*( - 2*a33**2*m1**2*m2*n2**4 - 4*a33**2*m1**2*m2*n2**2*n3**2 - 2*
a33**2*m2**3*n2**4 - 4*a33**2*m2**3*n2**2*n3**2) + v2*v3*(4*a33*m2**2*n2**5*n3 +
8*a33*m2**2*n2**3*n3**3) + v2*( - m2*n2**8 + m2*n2**4*n3**4) + v3**4*(a33**3*m1
**4*n2**2 + a33**3*m1**4*n3**2 + 2*a33**3*m1**2*m2**2*n2**2 + 2*a33**3*m1**2*m2
**2*n3**2 + a33**3*m2**4*n2**2 + a33**3*m2**4*n3**2) + v3**3*( - 4*a33**2*m1**2*
m2*n2**3*n3 - 4*a33**2*m1**2*m2*n2*n3**3 - 4*a33**2*m2**3*n2**3*n3 - 4*a33**2*m2
**3*n2*n3**3) + v3**2*(a33*m2**2*n2**6 + 3*a33*m2**2*n2**4*n3**2 + 4*a33*m2**2*
n2**2*n3**4) + v3*( - 2*m2*n2**7*n3 + 2*m2*n2**5*n3**3)$
FI=u1**4*a33**3*n2**4 - 4*u1**3*v2*a33**3*m1*n2**3 + 2*u1**2*u2**2*a33**3*n2**4
+ 8*u1**2*u2*v1*a33**3*m1*n2**3 - 2*u1**2*u2*a33**2*n2**5 + 4*u1**2*u3*v3*a33**3
*m2*n2**3 - 2*u1**2*u3*a33**2*n2**4*n3 + 8*u1**2*v1**2*a33**3*m1**2*n2**2 - 6*u1
**2*v1*a33**2*m1*n2**4 + 4*u1**2*v2**2*a33**3*m1**2*n2**2 + 2*u1**2*v2*a33**2*m2
*n2**4 + u1**2*v3**2*( - 2*a33**3*m1**2*n2**2 - 2*a33**3*m2**2*n2**2) + 4*u1**2*
v3*a33**2*m2*n2**3*n3 + u1**2*( - a33*n2**6 + 2*a33*n2**4*n3**2) + 4*u1*u2*u3*v3
*a33**3*m1*n2**3 - 2*u1*u2*v1*a33**2*m2*n2**4 + 8*u1*u3*v1*v3*a33**3*m1**2*n2**2
- 8*u1*u3*v2*v3*a33**3*m1*m2*n2**2 + 4*u1*u3*v2*a33**2*m1*n2**3*n3 - 4*u1*u3*v3
*a33**2*m1*n2**4 - 4*u1*v1**2*a33**2*m1*m2*n2**3 + 4*u1*v1*v2*a33**2*m1**2*n2**3
+ 2*u1*v1*a33*m2*n2**5 - 4*u1*v2**2*a33**2*m1*m2*n2**3 + u1*v2*v3**2*(4*a33**3*
m1**3*n2 + 4*a33**3*m1*m2**2*n2) - 8*u1*v2*v3*a33**2*m1*m2*n2**2*n3 + u1*v2*(2*
a33*m1*n2**5 - 4*a33*m1*n2**3*n3**2) + u2**4*a33**3*n2**4 + 4*u2**3*v1*a33**3*m1
*n2**3 - 2*u2**3*a33**2*n2**5 + 4*u2**2*u3*v3*a33**3*m2*n2**3 - 2*u2**2*u3*a33**
2*n2**4*n3 + 4*u2**2*v1**2*a33**3*m1**2*n2**2 - 6*u2**2*v1*a33**2*m1*n2**4 + u2
**2*v3**2*( - 2*a33**3*m1**2*n2**2 - 2*a33**3*m2**2*n2**2) + 4*u2**2*v3*a33**2*
m2*n2**3*n3 + 2*u2**2*a33*n2**4*n3**2 + 8*u2*u3*v1*v3*a33**3*m1*m2*n2**2 - 4*u2*
u3*v1*a33**2*m1*n2**3*n3 - 6*u2*u3*v3*a33**2*m2*n2**4 + 2*u2*u3*a33*n2**5*n3 - 4
*u2*v1**2*a33**2*m1**2*n2**3 + u2*v1*v3**2*( - 4*a33**3*m1**3*n2 - 4*a33**3*m1*
m2**2*n2) + 8*u2*v1*v3*a33**2*m1*m2*n2**2*n3 + 4*u2*v1*a33*m1*n2**3*n3**2 + u2*
v3**2*(2*a33**2*m1**2*n2**3 + 2*a33**2*m2**2*n2**3) - 4*u2*v3*a33*m2*n2**4*n3 +
u2*(n2**7 - 3*n2**5*n3**2) + 4*u3**2*v3**2*a33**3*m2**2*n2**2 - 4*u3**2*v3*a33**
2*m2*n2**3*n3 - 8*u3*v1*v3*a33**2*m1*m2*n2**3 + 2*u3*v1*a33*m1*n2**4*n3 + 4*u3*
v2*v3*a33**2*m2**2*n2**3 - 2*u3*v2*a33*m2*n2**4*n3 + u3*v3**3*( - 4*a33**3*m1**2
*m2*n2 - 4*a33**3*m2**3*n2) + u3*v3**2*(2*a33**2*m1**2*n2**2*n3 + 10*a33**2*m2**
2*n2**2*n3) + u3*(n2**6*n3 - 3*n2**4*n3**3) - 2*v1*v2*a33*m1*m2*n2**4 + v1*v3**2
*(2*a33**2*m1**3*n2**2 + 2*a33**2*m1*m2**2*n2**2) - 4*v1*v3*a33*m1*m2*n2**3*n3 +
v1*(m1*n2**6 - 3*m1*n2**4*n3**2) + v2**2*( - a33*m1**2*n2**4 + a33*m2**2*n2**4)
+ v2*v3**2*( - 2*a33**2*m1**2*m2*n2**2 - 2*a33**2*m2**3*n2**2) + 4*v2*v3*a33*m2
**2*n2**3*n3 + v2*( - m2*n2**6 + m2*n2**4*n3**2) + v3**4*(a33**3*m1**4 + 2*a33**
3*m1**2*m2**2 + a33**3*m2**4) + v3**3*( - 4*a33**2*m1**2*m2*n2*n3 - 4*a33**2*m2
**3*n2*n3) + v3**2*( - 2*a33*m1**2*n2**2*n3**2 + a33*m2**2*n2**4 + 2*a33*m2**2*
n2**2*n3**2) + v3*( - 2*m2*n2**5*n3 + 4*m2*n2**3*n3**3)$
FI=2*u1**2*v1**2*a33*n2**2 + u1**2*v2**2*a33*n2**2 + u1**2*v3**2*a33*n2**2 + 2*
u1*u3*v1*v3*a33*n2**2 - 4*u1*v1**2*v2*a33*m1*n2 + u1*v1*v2*n2**3 - 2*u1*v2**3*
a33*m1*n2 - 2*u1*v2*v3**2*a33*m1*n2 + u2**2*v1**2*a33*n2**2 + u2**2*v3**2*a33*n2
**2 + 2*u2*v1**3*a33*m1*n2 - u2*v1**2*n2**3 + 2*u2*v1*v3**2*a33*m1*n2 - u2*v3**2
*n2**3 + u3**2*v3**2*a33*n2**2 + 2*u3*v1**2*v3*a33*m2*n2 - u3*v1**2*n2**2*n3 - 2
*u3*v1*v2*v3*a33*m1*n2 + 2*u3*v2**2*v3*a33*m2*n2 - u3*v2**2*n2**2*n3 + u3*v2*v3*
n2**3 + 2*u3*v3**3*a33*m2*n2 - u3*v3**2*n2**2*n3 - v1**3*m1*n2**2 + v1**2*v2*m2*
n2**2 + v1**2*v3**2*( - a33*m1**2 - a33*m2**2) + 2*v1**2*v3*m2*n2*n3 - v1*v2**2*
m1*n2**2 - v1*v3**2*m1*n2**2 + v2**3*m2*n2**2 + v2**2*v3**2*( - a33*m1**2 - a33*
m2**2) + 2*v2**2*v3*m2*n2*n3 + v2*v3**2*m2*n2**2 + v3**4*( - a33*m1**2 - a33*m2
**2) + 2*v3**3*m2*n2*n3$
FI= - u1**4*a33**3*n2**4 + 4*u1**3*v2*a33**3*m1*n2**3 - 2*u1**2*u2**2*a33**3*n2
**4 - 8*u1**2*u2*v1*a33**3*m1*n2**3 + 2*u1**2*u2*a33**2*n2**5 - 4*u1**2*u3*v3*
a33**3*m2*n2**3 + 2*u1**2*u3*a33**2*n2**4*n3 - 8*u1**2*v1**2*a33**3*m1**2*n2**2
+ 6*u1**2*v1*a33**2*m1*n2**4 - 4*u1**2*v2**2*a33**3*m1**2*n2**2 - 2*u1**2*v2*a33
**2*m2*n2**4 + u1**2*v3**2*(2*a33**3*m1**2*n2**2 + 2*a33**3*m2**2*n2**2) - 4*u1
**2*v3*a33**2*m2*n2**3*n3 + u1**2*a33*n2**6 - 4*u1*u2*u3*v3*a33**3*m1*n2**3 + 2*
u1*u2*v1*a33**2*m2*n2**4 - 8*u1*u3*v1*v3*a33**3*m1**2*n2**2 + 8*u1*u3*v2*v3*a33
**3*m1*m2*n2**2 - 4*u1*u3*v2*a33**2*m1*n2**3*n3 + 4*u1*u3*v3*a33**2*m1*n2**4 + 4
*u1*v1**2*a33**2*m1*m2*n2**3 - 4*u1*v1*v2*a33**2*m1**2*n2**3 - 2*u1*v1*a33*m2*n2
**5 + 4*u1*v2**2*a33**2*m1*m2*n2**3 + u1*v2*v3**2*( - 4*a33**3*m1**3*n2 - 4*a33
**3*m1*m2**2*n2) + 8*u1*v2*v3*a33**2*m1*m2*n2**2*n3 - 2*u1*v2*a33*m1*n2**5 - u2
**4*a33**3*n2**4 - 4*u2**3*v1*a33**3*m1*n2**3 + 2*u2**3*a33**2*n2**5 - 4*u2**2*
u3*v3*a33**3*m2*n2**3 + 2*u2**2*u3*a33**2*n2**4*n3 - 4*u2**2*v1**2*a33**3*m1**2*
n2**2 + 6*u2**2*v1*a33**2*m1*n2**4 + u2**2*v3**2*(2*a33**3*m1**2*n2**2 + 2*a33**
3*m2**2*n2**2) - 4*u2**2*v3*a33**2*m2*n2**3*n3 - 8*u2*u3*v1*v3*a33**3*m1*m2*n2**
2 + 4*u2*u3*v1*a33**2*m1*n2**3*n3 + 6*u2*u3*v3*a33**2*m2*n2**4 - 2*u2*u3*a33*n2
**5*n3 + 4*u2*v1**2*a33**2*m1**2*n2**3 + u2*v1*v3**2*(4*a33**3*m1**3*n2 + 4*a33
**3*m1*m2**2*n2) - 8*u2*v1*v3*a33**2*m1*m2*n2**2*n3 + u2*v3**2*( - 2*a33**2*m1**
2*n2**3 - 2*a33**2*m2**2*n2**3) + 4*u2*v3*a33*m2*n2**4*n3 + u2*( - n2**7 + n2**5
*n3**2) - 4*u3**2*v3**2*a33**3*m2**2*n2**2 + 4*u3**2*v3*a33**2*m2*n2**3*n3 + 8*
u3*v1*v3*a33**2*m1*m2*n2**3 - 2*u3*v1*a33*m1*n2**4*n3 - 4*u3*v2*v3*a33**2*m2**2*
n2**3 + 2*u3*v2*a33*m2*n2**4*n3 + u3*v3**3*(4*a33**3*m1**2*m2*n2 + 4*a33**3*m2**
3*n2) + u3*v3**2*( - 2*a33**2*m1**2*n2**2*n3 - 10*a33**2*m2**2*n2**2*n3) + 4*u3*
v3*a33*m2*n2**3*n3**2 + u3*( - n2**6*n3 + n2**4*n3**3) + 2*v1*v2*a33*m1*m2*n2**4
+ v1*v3**2*( - 2*a33**2*m1**3*n2**2 - 2*a33**2*m1*m2**2*n2**2) + 4*v1*v3*a33*m1
*m2*n2**3*n3 + v1*( - m1*n2**6 + m1*n2**4*n3**2) + v2**2*(a33*m1**2*n2**4 - a33*
m2**2*n2**4) + v2*v3**2*(2*a33**2*m1**2*m2*n2**2 + 2*a33**2*m2**3*n2**2) - 4*v2*
v3*a33*m2**2*n2**3*n3 + v2*(m2*n2**6 + m2*n2**4*n3**2) + v3**4*( - a33**3*m1**4
- 2*a33**3*m1**2*m2**2 - a33**3*m2**4) + v3**3*(4*a33**2*m1**2*m2*n2*n3 + 4*a33
**2*m2**3*n2*n3) + v3**2*( - a33*m2**2*n2**4 - 4*a33*m2**2*n2**2*n3**2) + 2*v3*
m2*n2**5*n3$