Solution 6 to problem over
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Expressions
The solution is given through the following expressions:
2 2 2 2 2
r10=(a33 *n1 *n3*r26 + a33 *n2 *n3*r26 - 2*m1*n1*n2 *n3*r4119
2 3 3 3 2
+ 2*m1*n1*n2 *n3*r464 + 2*m1*n1*n3 *r4119 - 2*m1*n1*n3 *r464)/(a33 *n1
3 2
+ a33 *n2 )
2 2 2 3 3 3
r11=(a33 *n1 *n2*r26 + a33 *n2 *r26 - 2*m1*n1*n2 *r4119 + 2*m1*n1*n2 *r464
2 2 3 2 3 2
+ 2*m1*n1*n2*n3 *r4119 - 2*m1*n1*n2*n3 *r464)/(a33 *n1 + a33 *n2 )
2 4 2 4 3 2 3 2
r12=(a33 *n1 *r26 - a33 *n2 *r26 - 2*m1*n1 *n2 *r4119 + 2*m1*n1 *n2 *r464
3 2 4 4
+ m1*n1 *n3 *r4119 + 2*m1*n1*n2 *r4119 - 2*m1*n1*n2 *r464
2 2 2 2 3 3
- 3*m1*n1*n2 *n3 *r4119 + 4*m1*n1*n2 *n3 *r464)/(2*a33 *n1
3 2
+ 2*a33 *n1*n2 )
2 2 2 2 2
r13=( - a33 *n1 *n3*r26 - a33 *n2 *n3*r26 + 2*m1*n1*n2 *n3*r4119
2 3 3 3
- 2*m1*n1*n2 *n3*r464 - 3*m1*n1*n3 *r4119 + 4*m1*n1*n3 *r464)/(2*a33 *m1
*n1)
2 2 2 3 3 3
r14=( - a33 *n1 *n2*r26 - a33 *n2 *r26 + 2*m1*n1*n2 *r4119 - 2*m1*n1*n2 *r464
2 2 3
- 3*m1*n1*n2*n3 *r4119 + 4*m1*n1*n2*n3 *r464)/(2*a33 *m1*n1)
2 2 2 2 2 2
r15=( - a33 *n1 *r26 - a33 *n2 *r26 + 2*m1*n1*n2 *r4119 - 2*m1*n1*n2 *r464
2 2 3
- 3*m1*n1*n3 *r4119 + 4*m1*n1*n3 *r464)/(2*a33 *m1)
2 4 2 2 2 2 4
r20=( - a33 *m1*n1 *r26 - 2*a33 *m1*n1 *n2 *r26 - a33 *m1*n2 *r26
2 5 2 5 2 3 2
- m1 *n1 *r4119 - 2*m1 *n1 *r464 + 4*m1 *n1 *n2 *r4119
2 3 2 2 3 2 2 3 2
- 2*m1 *n1 *n2 *r464 + 2*m1 *n1 *n3 *r4119 + 2*m1 *n1 *n3 *r464
2 4 2 2 2 2 2 2
+ m1 *n1*n2 *r4119 - 2*m1 *n1*n2 *n3 *r4119 + 2*m1 *n1*n2 *n3 *r464)/(
2 5 2 3 2 2 4
2*a33 *n1 + 4*a33 *n1 *n2 + 2*a33 *n1*n2 )
2 2
4*m1 *n1 *n2*n3*r4119
r21=--------------------------------------
2 4 2 2 2 2 4
a33 *n1 + 2*a33 *n1 *n2 + a33 *n2
2 4 2 4 2 2 2 2 4
r22=( - m1 *n1 *r4119 - 2*m1 *n1 *r464 + 6*m1 *n1 *n2 *r4119 - m1 *n2 *r4119
2 4 2 4 2 2 2 2 4
+ 2*m1 *n2 *r464)/(2*a33 *n1 + 4*a33 *n1 *n2 + 2*a33 *n2 )
2 3 2 3 2 2
r23=(2*m1 *n1 *n3*r4119 + 2*m1 *n1 *n3*r464 - 2*m1 *n1*n2 *n3*r4119
2 2 2 4 2 2 2 2 4
+ 2*m1 *n1*n2 *n3*r464)/(a33 *n1 + 2*a33 *n1 *n2 + a33 *n2 )
2 3 2 3 2 3
r24=(2*m1 *n1 *n2*r4119 + 2*m1 *n1 *n2*r464 - 2*m1 *n1*n2 *r4119
2 3 2 4 2 2 2 2 4
+ 2*m1 *n1*n2 *r464)/(a33 *n1 + 2*a33 *n1 *n2 + a33 *n2 )
- 2*m1*n1*n2*n3*r4119 + 2*m1*n1*n2*n3*r464
r27=---------------------------------------------
2 2 2 2
a33 *n1 + a33 *n2
2 2 2
- m1*n1 *n3*r4119 + m1*n2 *n3*r4119 - 2*m1*n2 *n3*r464
r28=---------------------------------------------------------
2 2 2 2
a33 *n1 + a33 *n2
- 2*m1*n1*n2*n3*r4119 + 2*m1*n1*n2*n3*r464
r210=---------------------------------------------
2 2 2 2
a33 *n1 + a33 *n2
2 2 2 3 3 3
r212=(a33 *n1 *n2*r26 + a33 *n2 *r26 - m1*n1 *n2*r4119 - m1*n1*n2 *r4119
2 2 2 3 2 2
+ 2*m1*n1*n2*n3 *r4119 - 2*m1*n1*n2*n3 *r464)/(a33 *n1 + a33 *n1*n2 )
n2*n3*r4119 - 2*n2*n3*r464
r213=----------------------------
2
a33
2 2 2 2 2 2
r214=(a33 *n1 *r26 + a33 *n2 *r26 - m1*n1*n2 *r4119 + 2*m1*n1*n3 *r4119
2 2
- 2*m1*n1*n3 *r464)/(2*a33 *m1*n1)
2 2
- 2*m1*n1 *n3*r4119 + 2*m1*n1 *n3*r464
r215=-----------------------------------------
2 2 2 2
a33 *n1 + a33 *n2
2 2 2 3 3 3
r216=( - a33 *n1 *n2*r26 - a33 *n2 *r26 - 2*m1*n1 *n2*r4119 + 2*m1*n1 *n2*r464
3 3 2
+ 2*m1*n1*n2 *r4119 - 2*m1*n1*n2 *r464 - 2*m1*n1*n2*n3 *r4119
2 2 3 2 2
+ 2*m1*n1*n2*n3 *r464)/(a33 *n1 + a33 *n1*n2 )
3 2 2
- m1*n1 *r4119 + 3*m1*n1*n2 *r4119 - 4*m1*n1*n2 *r464
r217=--------------------------------------------------------
2 2 2 2
a33 *n1 + a33 *n2
n1*n3*r4119 - 2*n1*n3*r464
r218=----------------------------
2
a33
n1*n2*r4119 - 2*n1*n2*r464
r219=----------------------------
2
a33
2 2 2 2 3 3
r220=(a33 *n1 *r26 + a33 *n2 *r26 + m1*n1 *r4119 - 2*m1*n1 *r464
2 2 2
- 2*m1*n1*n2 *r4119 + 2*m1*n1*n2 *r464 + 2*m1*n1*n3 *r4119
2 2
- 2*m1*n1*n3 *r464)/(2*a33 *m1*n1)
3 3 3 2 5
r30=( - 2*m1 *n1 *n3*r4119 - 6*m1 *n1*n2 *n3*r4119 + m1*n1 *n3*r483
3 2 4 6 4 2
+ 2*m1*n1 *n2 *n3*r483 + m1*n1*n2 *n3*r483)/(a33*n1 + 3*a33*n1 *n2
2 4 6
+ 3*a33*n1 *n2 + a33*n2 )
3 3 3 3 5
r31=( - 2*m1 *n1 *n2*r4119 - 6*m1 *n1*n2 *r4119 + m1*n1 *n2*r483
3 3 5 6 4 2
+ 2*m1*n1 *n2 *r483 + m1*n1*n2 *r483)/(a33*n1 + 3*a33*n1 *n2
2 4 6
+ 3*a33*n1 *n2 + a33*n2 )
3 2 5 3 2
r32=( - 4*m1 *n1*n2 *n3*r4119 + m1*n1 *n3*r483 + 2*m1*n1 *n2 *n3*r483
4 6 4 2 2 4 6
+ m1*n1*n2 *n3*r483)/(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
r33
3 3 5 3 3 5
- 4*m1 *n1*n2 *r4119 + m1*n1 *n2*r483 + 2*m1*n1 *n2 *r483 + m1*n1*n2 *r483
=-----------------------------------------------------------------------------
6 4 2 2 4 6
a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2
3 8 3 8 3 6 2
r34=( - 2*m1 *n1 *r4119 - 2*m1 *n1 *r464 - 8*m1 *n1 *n2 *r4119
3 6 2 3 4 4 3 4 4
- 8*m1 *n1 *n2 *r464 - 4*m1 *n1 *n2 *r4119 - 12*m1 *n1 *n2 *r464
3 2 6 3 2 6 3 8
+ 8*m1 *n1 *n2 *r4119 - 8*m1 *n1 *n2 *r464 + 6*m1 *n2 *r4119
3 8 10 8 2 6 4
- 2*m1 *n2 *r464 + m1*n1 *r483 + 3*m1*n1 *n2 *r483 + 2*m1*n1 *n2 *r483
4 6 2 8 10 10
- 2*m1*n1 *n2 *r483 - 3*m1*n1 *n2 *r483 - m1*n2 *r483)/(2*a33*n1
8 2 6 4 4 6 2 8
+ 10*a33*n1 *n2 + 20*a33*n1 *n2 + 20*a33*n1 *n2 + 10*a33*n1 *n2
10
+ 2*a33*n2 )
r35=0
3 2 2 3 4 6 4 2
r36=( - 4*m1 *n1 *n2 *r4119 + 4*m1 *n2 *r4119 + m1*n1 *r483 + m1*n1 *n2 *r483
2 4 6 6 4 2
- m1*n1 *n2 *r483 - m1*n2 *r483)/(2*a33*n1 + 6*a33*n1 *n2
2 4 6
+ 6*a33*n1 *n2 + 2*a33*n2 )
3 2 5 3 2
r37=( - 4*m1 *n1*n2 *n3*r4119 + m1*n1 *n3*r483 + 2*m1*n1 *n2 *n3*r483
4 6 4 2 2 4 6
+ m1*n1*n2 *n3*r483)/(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
r38
3 3 5 3 3 5
- 4*m1 *n1*n2 *r4119 + m1*n1 *n2*r483 + 2*m1*n1 *n2 *r483 + m1*n1*n2 *r483
=-----------------------------------------------------------------------------
6 4 2 2 4 6
a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2
3 2 2 3 4 6 4 2
r39=( - 4*m1 *n1 *n2 *r4119 + 4*m1 *n2 *r4119 + m1*n1 *r483 + m1*n1 *n2 *r483
2 4 6 6 4 2
- m1*n1 *n2 *r483 - m1*n2 *r483)/(2*a33*n1 + 6*a33*n1 *n2
2 4 6
+ 6*a33*n1 *n2 + 2*a33*n2 )
2 2 2 2 2 2
r310=(10*m1 *n1 *n3*r4119 - 2*m1 *n1 *n3*r464 + 6*m1 *n2 *n3*r4119
2 2 4 2 2 4
- 2*m1 *n2 *n3*r464 - n1 *n3*r483 - 2*n1 *n2 *n3*r483 - n2 *n3*r483)/(
4 2 2 4
2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2 )
r311=
2 2 2 3 4 2 3 5
8*m1 *n1 *n2*r4119 - 4*m1 *n2 *r4119 + n1 *n2*r483 + 2*n1 *n2 *r483 + n2 *r483
--------------------------------------------------------------------------------
4 2 2 4
2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2
2 2 4 2 2 4
4*m1 *n2 *n3*r4119 - n1 *n3*r483 - 2*n1 *n2 *n3*r483 - n2 *n3*r483
r312=--------------------------------------------------------------------
4 2 2 4
2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2
2 3 2 3 2 2 2 2
2*m1 *n1 *r4119 + 2*m1 *n1 *r464 - 6*m1 *n1*n2 *r4119 + 2*m1 *n1*n2 *r464
r313=---------------------------------------------------------------------------
4 2 2 4
a33*n1 + 2*a33*n1 *n2 + a33*n2
r314=0
2 2 4 2 2 4
4*m1 *n2 *n3*r4119 - n1 *n3*r483 - 2*n1 *n2 *n3*r483 - n2 *n3*r483
r315=--------------------------------------------------------------------
4 2 2 4
2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2
- 2*m1*n1*n3*r4119 + 4*m1*n1*n3*r464
r316=---------------------------------------
2 2
a33*n1 + a33*n2
2*m1*n1*n2*r464
r317=-------------------
2 2
a33*n1 + a33*n2
2 2
m1*n1 *r464 - m1*n2 *r464
r318=---------------------------
2 2
a33*n1 + a33*n2
- n3*r464
r319=------------
a33
2 2 2 2 2 3 2 3
r320=(2*m1 *n1 *n2*r4119 - 2*m1 *n1 *n2*r464 + 6*m1 *n2 *r4119 - 2*m1 *n2 *r464
4 2 3 5 4 2 2
- n1 *n2*r483 - 2*n1 *n2 *r483 - n2 *r483)/(2*a33*n1 + 4*a33*n1 *n2
4
+ 2*a33*n2 )
2
4*m1 *n1*n2*n3*r4119
r323=-----------------------------------
4 2 2 4
a33*n1 + 2*a33*n1 *n2 + a33*n2
2 2 2 2 2 3 4
r325=(4*m1 *n1 *n2*r4119 + 4*m1 *n1 *n2*r464 + 4*m1 *n2 *r464 - n1 *n2*r483
2 3 5 4 2 2 4
- 2*n1 *n2 *r483 - n2 *r483)/(2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2 )
- 4*m1*n1*n2*r4119 + 2*m1*n1*n2*r464
r326=---------------------------------------
2 2
a33*n1 + a33*n2
- 2*m1*n2*n3*r4119 + 2*m1*n2*n3*r464
r328=---------------------------------------
2 2
a33*n1 + a33*n2
- n2*r464
r329=------------
a33
2*m1*n1*n3*r4119
r330=-------------------
2 2
a33*n1 + a33*n2
2 2 2 2
m1*n1 *r4119 + m1*n1 *r464 - 3*m1*n2 *r4119 + 3*m1*n2 *r464
r332=-------------------------------------------------------------
2 2
a33*n1 + a33*n2
- n3*r4119 + n3*r464
r333=-----------------------
a33
- n2*r4119 + n2*r464
r334=-----------------------
a33
2 3 2 3 2 2 2 2
r335=(2*m1 *n1 *r4119 - 2*m1 *n1 *r464 + 6*m1 *n1*n2 *r4119 - 2*m1 *n1*n2 *r464
5 3 2 4 4 2 2
- n1 *r483 - 2*n1 *n2 *r483 - n1*n2 *r483)/(2*a33*n1 + 4*a33*n1 *n2
4
+ 2*a33*n2 )
2
- 4*m1 *n1*n2*n3*r4119
r336=-----------------------------------
4 2 2 4
a33*n1 + 2*a33*n1 *n2 + a33*n2
2 2 5 3 2 4
- 4*m1 *n1*n2 *r4119 - n1 *r483 - 2*n1 *n2 *r483 - n1*n2 *r483
r337=-----------------------------------------------------------------
4 2 2 4
2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2
r338=0
2 2 2 2 2 3 4
r339=( - 4*m1 *n1 *n2*r4119 - 4*m1 *n1 *n2*r464 - 4*m1 *n2 *r464 + n1 *n2*r483
2 3 5 4 2 2 4
+ 2*n1 *n2 *r483 + n2 *r483)/(2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2 )
2 2 5 3 2 4
- 4*m1 *n1*n2 *r4119 - n1 *r483 - 2*n1 *n2 *r483 - n1*n2 *r483
r340=-----------------------------------------------------------------
4 2 2 4
2*a33*n1 + 4*a33*n1 *n2 + 2*a33*n2
- 2*m1*r4119 + 2*m1*r464
r341=---------------------------
a33
2*m1*n2*n3*r4119 - 2*m1*n2*n3*r464
r342=------------------------------------
2 2
a33*n1 + a33*n2
r343=0
- n1*r464
r344=------------
a33
r345=0
- 4*m1*n1*n2*r4119 + 2*m1*n1*n2*r464
r347=---------------------------------------
2 2
a33*n1 + a33*n2
r348=0
- n1*r4119 + n1*r464
r349=-----------------------
a33
2*m1*n1*n3*r4119
r350=-------------------
2 2
a33*n1 + a33*n2
4*m1*n1*n2*r4119 - 2*m1*n1*n2*r464
r351=------------------------------------
2 2
a33*n1 + a33*n2
2 2 2 2
m1*n1 *r4119 + m1*n1 *r464 - 3*m1*n2 *r4119 + 3*m1*n2 *r464
r352=-------------------------------------------------------------
2 2
a33*n1 + a33*n2
- n3*r4119 + n3*r464
r353=-----------------------
a33
- n2*r4119 + n2*r464
r354=-----------------------
a33
- n1*r4119 + n1*r464
r355=-----------------------
a33
4 6 4 4 2 4 2 4
r40=(m1 *n1 *r4119 + 7*m1 *n1 *n2 *r4119 + 11*m1 *n1 *n2 *r4119
4 6 2 8 2 6 2 2 4 4
+ 5*m1 *n2 *r4119 - m1 *n1 *r483 - 4*m1 *n1 *n2 *r483 - 6*m1 *n1 *n2 *r483
2 2 6 2 8 10 8 2 6 4
- 4*m1 *n1 *n2 *r483 - m1 *n2 *r483)/(2*n1 + 10*n1 *n2 + 20*n1 *n2
4 6 2 8 10
+ 20*n1 *n2 + 10*n1 *n2 + 2*n2 )
r41=0
4 2 2 4 2 2 2 2 4
4*m1 *n2 *r4119 - m1 *n1 *r483 - 2*m1 *n1 *n2 *r483 - m1 *n2 *r483
r42=--------------------------------------------------------------------
6 4 2 2 4 6
2*n1 + 6*n1 *n2 + 6*n1 *n2 + 2*n2
r43=0
r44=0
r45=0
r46=0
r47=0
r48=0
4 2 2 4 2 2 2 2 4
4*m1 *n2 *r4119 - m1 *n1 *r483 - 2*m1 *n1 *n2 *r483 - m1 *n2 *r483
r49=--------------------------------------------------------------------
6 4 2 2 4 6
2*n1 + 6*n1 *n2 + 6*n1 *n2 + 2*n2
r410=0
r411=0
r412=0
r413=0
3 3 3 2 5 3 2
r415=( - 2*m1 *n1 *r4119 - 6*m1 *n1*n2 *r4119 + m1*n1 *r483 + 2*m1*n1 *n2 *r483
4 6 4 2 2 4 6
+ m1*n1*n2 *r483)/(n1 + 3*n1 *n2 + 3*n1 *n2 + n2 )
r416=0
3 2 5 3 2 4
- 4*m1 *n1*n2 *r4119 + m1*n1 *r483 + 2*m1*n1 *n2 *r483 + m1*n1*n2 *r483
r417=--------------------------------------------------------------------------
6 4 2 2 4 6
n1 + 3*n1 *n2 + 3*n1 *n2 + n2
r418=0
r419=0
3 3 4 2 3 5
4*m1 *n2 *r4119 - m1*n1 *n2*r483 - 2*m1*n1 *n2 *r483 - m1*n2 *r483
r420=--------------------------------------------------------------------
6 4 2 2 4 6
n1 + 3*n1 *n2 + 3*n1 *n2 + n2
r421=0
3 2 5 3 2 4
- 4*m1 *n1*n2 *r4119 + m1*n1 *r483 + 2*m1*n1 *n2 *r483 + m1*n1*n2 *r483
r422=--------------------------------------------------------------------------
6 4 2 2 4 6
n1 + 3*n1 *n2 + 3*n1 *n2 + n2
r423=0
r424=0
2 2 2 2 2 2 2 2
r425=(4*m1 *n1 *r4119 - 2*m1 *n1 *r464 - 4*m1 *n2 *r4119 - 2*m1 *n2 *r464
4 2 2 4 4 2 2 4
+ n1 *r483 + 2*n1 *n2 *r483 + n2 *r483)/(2*n1 + 4*n1 *n2 + 2*n2 )
r426=0
r427=0
r428=0
r429=0
2*m1*n1*r464
r431=--------------
2 2
n1 + n2
r432=0
r433=0
r435=0
3 2 3 3 4
r439=( - 2*m1 *n1 *n2*r4119 - 6*m1 *n2 *r4119 + m1*n1 *n2*r483
2 3 5 6 4 2 2 4 6
+ 2*m1*n1 *n2 *r483 + m1*n2 *r483)/(n1 + 3*n1 *n2 + 3*n1 *n2 + n2 )
r442=0
3 3 4 2 3 5
- 4*m1 *n2 *r4119 + m1*n1 *n2*r483 + 2*m1*n1 *n2 *r483 + m1*n2 *r483
r444=-----------------------------------------------------------------------
6 4 2 2 4 6
n1 + 3*n1 *n2 + 3*n1 *n2 + n2
r445=0
2
4*m1 *n1*n2*r4119
r448=-----------------------
4 2 2 4
n1 + 2*n1 *n2 + n2
r450=0
r451=0
2*m1*n2*r464
r453=--------------
2 2
n1 + n2
r454=0
r455
2 2 2 2 4 2 2 4
- 2*m1 *n1 *r4119 - 6*m1 *n2 *r4119 + n1 *r483 + 2*n1 *n2 *r483 + n2 *r483
=-----------------------------------------------------------------------------
4 2 2 4
2*n1 + 4*n1 *n2 + 2*n2
r458=0
r483
r460=------
2
2*m1*n1*r4119
r461=---------------
2 2
n1 + n2
r463=0
r465=0
2*m1*n2*r4119
r467=---------------
2 2
n1 + n2
r468=0
r4119
r469=-------
2
r470=0
3 2 3 3 4 2 3
r471=(2*m1 *n1 *n2*r4119 + 6*m1 *n2 *r4119 - m1*n1 *n2*r483 - 2*m1*n1 *n2 *r483
5 6 4 2 2 4 6
- m1*n2 *r483)/(n1 + 3*n1 *n2 + 3*n1 *n2 + n2 )
r472=0
3 3 4 2 3 5
4*m1 *n2 *r4119 - m1*n1 *n2*r483 - 2*m1*n1 *n2 *r483 - m1*n2 *r483
r473=--------------------------------------------------------------------
6 4 2 2 4 6
n1 + 3*n1 *n2 + 3*n1 *n2 + n2
r474=0
r475=0
r476=0
r477=0
3 3 4 2 3 5
8*m1 *n2 *r4119 - 2*m1*n1 *n2*r483 - 4*m1*n1 *n2 *r483 - 2*m1*n2 *r483
r478=------------------------------------------------------------------------
6 4 2 2 4 6
n1 + 3*n1 *n2 + 3*n1 *n2 + n2
r479=0
r480=0
2
- 4*m1 *n1*n2*r4119
r481=-----------------------
4 2 2 4
n1 + 2*n1 *n2 + n2
r482=0
r484=0
r485=0
r486=0
- 2*m1*n2*r464
r487=-----------------
2 2
n1 + n2
r488=0
r489=0
r490=0
r493=0
r495=0
2*m1*n2*r4119
r496=---------------
2 2
n1 + n2
r498=0
r499=0
r4100=0
r4102=0
r4103=0
r4104=0
r4105
2 2 2 2 4 2 2 4
- 2*m1 *n1 *r4119 - 6*m1 *n2 *r4119 + n1 *r483 + 2*n1 *n2 *r483 + n2 *r483
=-----------------------------------------------------------------------------
4 2 2 4
2*n1 + 4*n1 *n2 + 2*n2
r4106=0
r483
r4107=------
2
r4108=0
r4109=0
r4110=r483
2*m1*n1*r4119
r4111=---------------
2 2
n1 + n2
r4112=0
r4113=0
r4114=r464
r4115=0
4*m1*n2*r4119
r4117=---------------
2 2
n1 + n2
r4118=0
r4120=0
- 2*m1*n2*r4119
r4121=------------------
2 2
n1 + n2
r4122=0
r4123=0
r4124=0
r4119
r4125=-------
2
m3=0
m2=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
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, r4119, r483, r464, n3, m1, n1, 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.
{n1,n2,a33,n1 + i*n2,n1 - i*n2,m1}
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,
m2,
m3}$
The system of equations related to the Hamiltonian HAM:
2
HAM=u1*n1 + u2*n2 + u3 *a33 + u3*n3 + v1*m1
has apart from the Hamiltonian and Casimirs the following 4 first integrals:
3 2 3 2 2 2 2 2 2 3
FI=u1 *(a33 *n1 + a33 *n1*n2 ) + u1 *u2*(a33 *n1 *n2 + a33 *n2 )
2 2 3 2 3 2 2 2 2 2 2
+ u1 *u3 *(a33 *n1 + a33 *n2 ) + u1 *u3*(a33 *n1 *n3 + a33 *n2 *n3)
2 2 2 2 2 2 2
+ u1 *v1*(a33 *m1*n1 + 3*a33 *m1*n2 ) - 2*u1 *v2*a33 *m1*n1*n2
2 4 2 2 4 2 2
+ u1 *( - a33*n1 - a33*n1 *n3 + a33*n2 - a33*n2 *n3 )
2 2 3 2 2 2
+ u1*u2 *(a33 *n1 + a33 *n1*n2 ) + 2*u1*u2*v1*a33 *m1*n1*n2
3 3 2 3
+ u1*u2*( - 2*a33*n1 *n2 - 2*a33*n1*n2 ) - 2*u1*u3 *v2*a33 *m1*n2
2 2 3 2 2 2
+ u1*u3 *( - a33 *n1 - a33 *n1*n2 ) - 2*u1*u3*v2*a33 *m1*n2*n3
2 2 2 2
+ u1*u3*v3*(2*a33 *m1*n1 + 2*a33 *m1*n2 )
3 2 2 2
+ u1*u3*( - 2*a33*n1 *n3 - 2*a33*n1*n2 *n3) - 2*u1*v1*v2*a33 *m1 *n2
2
- 4*u1*v1*a33*m1*n1*n2
2 3 2
+ u1*v2*(2*a33*m1*n1 *n2 - 2*a33*m1*n2 + 2*a33*m1*n2*n3 )
2 2 2 2
- u1*v3 *a33 *m1 *n1 + 2*u1*v3*a33*m1*n1 *n3
3 2 3 2 4 2 2
+ u1*( - n1 *n2 + 2*n1 *n3 - n1*n2 + 2*n1*n2 *n3 )
3 2 2 2 3 2 2 3 2 3 2
+ u2 *(a33 *n1 *n2 + a33 *n2 ) + u2 *u3 *(a33 *n1 + a33 *n2 )
2 2 2 2 2 2 2 2 2 2
+ u2 *u3*(a33 *n1 *n3 + a33 *n2 *n3) + u2 *v1*(a33 *m1*n1 + 3*a33 *m1*n2 )
2 2 2 2 2 2 3
+ u2 *( - a33*n1 *n3 - a33*n2 *n3 ) + 2*u2*u3 *v1*a33 *m1*n2
2 2 2 2 3 2
+ u2*u3 *( - a33 *n1 *n2 - a33 *n2 ) + 2*u2*u3*v1*a33 *m1*n2*n3
2 2 3
+ 2*u2*u3*v3*a33 *m1*n1*n2 + u2*u3*( - 2*a33*n1 *n2*n3 - 2*a33*n2 *n3)
2 2 2 2 2 2 2
+ 2*u2*v1 *a33 *m1 *n2 - 2*u2*v1*a33*m1*n2*n3 - u2*v3 *a33 *m1 *n2
2 3 2 2 5 3 2
+ 2*u2*v3*a33*m1*n1*n2*n3 + u2*( - n1 *n2 + 2*n1 *n2*n3 - n2 + 2*n2 *n3 )
3 3 3 2 2 2 2
+ 2*u3 *v3*a33 *m1*n1 + u3 *( - a33 *n1 *n3 - a33 *n2 *n3)
2 2 2 2 2 2 2
+ u3 *v1*(a33 *m1*n1 - a33 *m1*n2 ) + 2*u3 *v2*a33 *m1*n1*n2
2 2 3 2 2 2 2 2
- u3 *v3 *a33 *m1 + 4*u3 *v3*a33 *m1*n1*n3 + 2*u3*v1*v3*a33 *m1 *n1
2 2 2 2
- 2*u3*v1*a33*m1*n2 *n3 + 2*u3*v2*a33*m1*n1*n2*n3 - u3*v3 *a33 *m1 *n3
2 2 2 3 4 2 3
+ u3*( - n1 *n2 *n3 + 2*n1 *n3 - n2 *n3 + 2*n2 *n3 )
2 2 2 3 2
+ 2*v1*v2*a33*m1 *n1*n2 - v1*v3 *a33 *m1 + 2*v1*v3*a33*m1 *n1*n3
2 2 4 2 2
+ v1*(m1*n1 *n2 - m1*n2 + 2*m1*n2 *n3 )
2 2 2 2 2 3 2
+ v2 *( - a33*m1 *n1 + a33*m1 *n2 ) + v2*(2*m1*n1*n2 - 2*m1*n1*n2*n3 )
2 2 2 2 2 2 3
+ v3 *( - a33*m1 *n1 + a33*m1 *n3 ) + v3*(2*m1*n1*n2 *n3 - 2*m1*n1*n3 )
which the program can not factorize further.
{HAM,FI} = {4,
n2,
n2,
a33,
a33,
u1*v1 + u2*v2 + u3*v3,
m1,
u2*n3 - u3*n2
u2*u3*a33 + ------- + ----------}
2 2
2 2 6 4 2 2 4 6
FI=u1 *v1 *(2*a33*n1 + 6*a33*n1 *n2 + 6*a33*n1 *n2 + 2*a33*n2 )
2 2 6 4 2 2 4 6
+ u1 *v2 *(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
2 2 6 4 2 2 4 6
+ u1 *v3 *(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
6 4 2 2 4 6
+ u1*u3*v1*v3*(2*a33*n1 + 6*a33*n1 *n2 + 6*a33*n1 *n2 + 2*a33*n2 )
2 4 2 3 5
+ u1*v1 *v2*( - 4*a33*m1*n1 *n2 - 8*a33*m1*n1 *n2 - 4*a33*m1*n2 )
2 7 5 2 3 4 6
+ u1*v1 *( - n1 - 3*n1 *n2 - 3*n1 *n2 - n1*n2 )
6 4 3 2 5 7
+ u1*v1*v2*(n1 *n2 + 3*n1 *n2 + 3*n1 *n2 + n2 )
3 4 2 3 5
+ u1*v2 *( - 2*a33*m1*n1 *n2 - 4*a33*m1*n1 *n2 - 2*a33*m1*n2 )
2 7 5 2 3 4 6
+ u1*v2 *( - n1 - 3*n1 *n2 - 3*n1 *n2 - n1*n2 )
2 4 2 3 5
+ u1*v2*v3 *( - 2*a33*m1*n1 *n2 - 4*a33*m1*n1 *n2 - 2*a33*m1*n2 )
2 7 5 2 3 4 6
+ u1*v3 *( - n1 - 3*n1 *n2 - 3*n1 *n2 - n1*n2 )
2 2 6 4 2 2 4 6
+ u2 *v1 *(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
2 2 6 4 2 2 4 6
+ u2 *v3 *(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
3 4 2 3 5
+ u2*v1 *(2*a33*m1*n1 *n2 + 4*a33*m1*n1 *n2 + 2*a33*m1*n2 )
2 6 4 3 2 5 7
+ u2*v1 *( - n1 *n2 - 3*n1 *n2 - 3*n1 *n2 - n2 )
2 4 2 3 5
+ u2*v1*v3 *(2*a33*m1*n1 *n2 + 4*a33*m1*n1 *n2 + 2*a33*m1*n2 )
2 6 4 3 2 5 7
+ u2*v3 *( - n1 *n2 - 3*n1 *n2 - 3*n1 *n2 - n2 )
2 2 6 4 2 2 4 6
+ u3 *v3 *(a33*n1 + 3*a33*n1 *n2 + 3*a33*n1 *n2 + a33*n2 )
2 5 3 2 4
+ u3*v1 *v3*(2*a33*m1*n1 + 4*a33*m1*n1 *n2 + 2*a33*m1*n1*n2 )
2 6 4 2 2 4 6
+ u3*v1 *( - n1 *n3 - 3*n1 *n2 *n3 - 3*n1 *n2 *n3 - n2 *n3)
4 2 3 5
+ u3*v1*v2*v3*( - 2*a33*m1*n1 *n2 - 4*a33*m1*n1 *n2 - 2*a33*m1*n2 )
2 5 3 2 4
+ u3*v2 *v3*(2*a33*m1*n1 + 4*a33*m1*n1 *n2 + 2*a33*m1*n1*n2 )
2 6 4 2 2 4 6
+ u3*v2 *( - n1 *n3 - 3*n1 *n2 *n3 - 3*n1 *n2 *n3 - n2 *n3)
6 4 3 2 5 7
+ u3*v2*v3*(n1 *n2 + 3*n1 *n2 + 3*n1 *n2 + n2 )
3 5 3 2 4
+ u3*v3 *(2*a33*m1*n1 + 4*a33*m1*n1 *n2 + 2*a33*m1*n1*n2 )
2 6 4 2 2 4 6
+ u3*v3 *( - n1 *n3 - 3*n1 *n2 *n3 - 3*n1 *n2 *n3 - n2 *n3)
3 6 4 2 2 4 6
+ v1 *(m1*n1 + m1*n1 *n2 - m1*n1 *n2 - m1*n2 )
2 5 3 3 5
+ v1 *v2*(2*m1*n1 *n2 + 4*m1*n1 *n2 + 2*m1*n1*n2 )
2 2 2 4 2 2 2 2 4
+ v1 *v3 *( - a33*m1 *n1 - 2*a33*m1 *n1 *n2 - a33*m1 *n2 )
2 5 3 2 4
+ v1 *v3*(2*m1*n1 *n3 + 4*m1*n1 *n2 *n3 + 2*m1*n1*n2 *n3)
2 6 4 2 2 4 6
+ v1*v2 *(m1*n1 + m1*n1 *n2 - m1*n1 *n2 - m1*n2 )
2 6 4 2 2 4 6
+ v1*v3 *(m1*n1 + m1*n1 *n2 - m1*n1 *n2 - m1*n2 )
3 5 3 3 5
+ v2 *(2*m1*n1 *n2 + 4*m1*n1 *n2 + 2*m1*n1*n2 )
2 2 2 4 2 2 2 2 4
+ v2 *v3 *( - a33*m1 *n1 - 2*a33*m1 *n1 *n2 - a33*m1 *n2 )
2 5 3 2 4
+ v2 *v3*(2*m1*n1 *n3 + 4*m1*n1 *n2 *n3 + 2*m1*n1*n2 *n3)
2 5 3 3 5
+ v2*v3 *(2*m1*n1 *n2 + 4*m1*n1 *n2 + 2*m1*n1*n2 )
4 2 4 2 2 2 2 4
+ v3 *( - a33*m1 *n1 - 2*a33*m1 *n1 *n2 - a33*m1 *n2 )
3 5 3 2 4
+ v3 *(2*m1*n1 *n3 + 4*m1*n1 *n2 *n3 + 2*m1*n1*n2 *n3)
= a product of the elements of: { - n1 + i*n2,
n1 - i*n2,
n1 + i*n2,
n1 + i*n2,
2 2 2 2 2 2 2 2
u1 *v1 *( - 2*a33*n1 - 2*a33*n2 ) + u1 *v2 *( - a33*n1 - a33*n2 )
2 2 2 2 2 2
+ u1 *v3 *( - a33*n1 - a33*n2 ) + u1*u3*v1*v3*( - 2*a33*n1 - 2*a33*n2 )
2 2 3 2 2 3
+ 4*u1*v1 *v2*a33*m1*n2 + u1*v1 *(n1 + n1*n2 ) + u1*v1*v2*( - n1 *n2 - n2 )
3 2 3 2 2
+ 2*u1*v2 *a33*m1*n2 + u1*v2 *(n1 + n1*n2 ) + 2*u1*v2*v3 *a33*m1*n2
2 3 2 2 2 2 2
+ u1*v3 *(n1 + n1*n2 ) + u2 *v1 *( - a33*n1 - a33*n2 )
2 2 2 2 3
+ u2 *v3 *( - a33*n1 - a33*n2 ) - 2*u2*v1 *a33*m1*n2
2 2 3 2 2 2 3
+ u2*v1 *(n1 *n2 + n2 ) - 2*u2*v1*v3 *a33*m1*n2 + u2*v3 *(n1 *n2 + n2 )
2 2 2 2 2
+ u3 *v3 *( - a33*n1 - a33*n2 ) - 2*u3*v1 *v3*a33*m1*n1
2 2 2 2
+ u3*v1 *(n1 *n3 + n2 *n3) + 2*u3*v1*v2*v3*a33*m1*n2 - 2*u3*v2 *v3*a33*m1*n1
2 2 2 2 3 3
+ u3*v2 *(n1 *n3 + n2 *n3) + u3*v2*v3*( - n1 *n2 - n2 ) - 2*u3*v3 *a33*m1*n1
2 2 2 3 2 2 2
+ u3*v3 *(n1 *n3 + n2 *n3) + v1 *( - m1*n1 + m1*n2 ) - 2*v1 *v2*m1*n1*n2
2 2 2 2 2 2 2
+ v1 *v3 *a33*m1 - 2*v1 *v3*m1*n1*n3 + v1*v2 *( - m1*n1 + m1*n2 )
2 2 2 3 2 2 2
+ v1*v3 *( - m1*n1 + m1*n2 ) - 2*v2 *m1*n1*n2 + v2 *v3 *a33*m1
2 2 4 2 3
- 2*v2 *v3*m1*n1*n3 - 2*v2*v3 *m1*n1*n2 + v3 *a33*m1 - 2*v3 *m1*n1*n3}
{HAM,FI} = {4,
n1 - i*n2,
n1 - i*n2,
n1 + i*n2,
n1 + i*n2,
u1*v1 + u2*v2 + u3*v3,
2 2
2 2 2 2 a33*n1 *n3 + a33*n2 *n3
u1*u3*v2*(a33 *n1 + a33 *n2 ) + u1*v2*-------------------------
2
2 2
2 2 2 2 a33*n1 *n3 + a33*n2 *n3
+ u2*u3*v1*(a33 *n1 + a33 *n2 ) + u2*v1*-------------------------
2
3 2
- a33*n1 - a33*n1*n2 2 2
+ u2*v3*------------------------- + u3*v1 *a33 *m1*n2
2
2 3
- a33*n1 *n2 - a33*n2 2 2
+ u3*v1*------------------------- - u3*v2 *a33 *m1*n2
2
3 2 2
- a33*n1 - a33*n1*n2 v1 *a33*m1*n2*n3
+ u3*v2*------------------------- + ------------------
2 2
2 3
- v1*v3*a33*m1*n1*n2 - n1 *n2*n3 - n2 *n3
+ ----------------------- + v1*-----------------------
2 4
2 2
- v2 *a33*m1*n2*n3 - v2*v3*a33*m1*n1
+ --------------------- + ---------------------
2 2
3 3
n1 *n2 + n1*n2
+ v3*-----------------}
4
4 3 6 3 4 2 3 2 4 3 6
FI=u1 *(a33 *n1 + 3*a33 *n1 *n2 + 3*a33 *n1 *n2 + a33 *n2 )
3 3 4 3 2 3 3 5
+ u1 *v2*( - 4*a33 *m1*n1 *n2 - 8*a33 *m1*n1 *n2 - 4*a33 *m1*n2 )
3 2 7 2 5 2 2 3 4 2 6
+ u1 *( - 2*a33 *n1 - 6*a33 *n1 *n2 - 6*a33 *n1 *n2 - 2*a33 *n1*n2 )
2 2 3 6 3 4 2 3 2 4 3 6
+ u1 *u2 *(2*a33 *n1 + 6*a33 *n1 *n2 + 6*a33 *n1 *n2 + 2*a33 *n2 )
2 3 4 3 2 3 3 5
+ u1 *u2*v1*(8*a33 *m1*n1 *n2 + 16*a33 *m1*n1 *n2 + 8*a33 *m1*n2 )
2 2 6 2 4 3 2 2 5 2 7
+ u1 *u2*( - 2*a33 *n1 *n2 - 6*a33 *n1 *n2 - 6*a33 *n1 *n2 - 2*a33 *n2 )
2 3 5 3 3 2 3 4 2
+ u1 *u3*v3*(4*a33 *m1*n1 + 8*a33 *m1*n1 *n2 + 4*a33 *m1*n1*n2 ) + u1 *u3
2 6 2 4 2 2 2 4 2 6
*( - 2*a33 *n1 *n3 - 6*a33 *n1 *n2 *n3 - 6*a33 *n1 *n2 *n3 - 2*a33 *n2 *n3) +
2
u1 *v1
2 6 2 4 2 2 2 4 2 6
*(2*a33 *m1*n1 - 2*a33 *m1*n1 *n2 - 10*a33 *m1*n1 *n2 - 6*a33 *m1*n2 )
2 2 5 2 3 3 2 5
+ u1 *v2*(8*a33 *m1*n1 *n2 + 16*a33 *m1*n1 *n2 + 8*a33 *m1*n1*n2 )
2 2 3 2 4 3 2 2 2 3 2 4
+ u1 *v3 *( - 2*a33 *m1 *n1 - 8*a33 *m1 *n1 *n2 - 6*a33 *m1 *n2 )
2 2 5 2 3 2 2 4
+ u1 *v3*(4*a33 *m1*n1 *n3 + 8*a33 *m1*n1 *n2 *n3 + 4*a33 *m1*n1*n2 *n3) +
2 8 6 2 6 2 4 4
u1 *(a33*n1 + a33*n1 *n2 + 2*a33*n1 *n3 - 3*a33*n1 *n2
4 2 2 2 6 2 4 2 8
+ 6*a33*n1 *n2 *n3 - 5*a33*n1 *n2 + 6*a33*n1 *n2 *n3 - 2*a33*n2
6 2
+ 2*a33*n2 *n3 )
2 2 7 2 5 2 2 3 4 2 6
+ u1*u2 *( - 2*a33 *n1 - 6*a33 *n1 *n2 - 6*a33 *n1 *n2 - 2*a33 *n1*n2 )
3 4 3 2 3 3 5
+ u1*u2*u3*v3*(4*a33 *m1*n1 *n2 + 8*a33 *m1*n1 *n2 + 4*a33 *m1*n2 )
2 5 2 3 3 2 5
+ u1*u2*v1*( - 8*a33 *m1*n1 *n2 - 16*a33 *m1*n1 *n2 - 8*a33 *m1*n1*n2 )
7 5 3 3 5 7
+ u1*u2*(2*a33*n1 *n2 + 6*a33*n1 *n2 + 6*a33*n1 *n2 + 2*a33*n1*n2 )
3 2 3 3 2 3
+ u1*u3*v2*v3*( - 8*a33 *m1 *n1 *n2 - 8*a33 *m1 *n1*n2 )
2 4 2 2 3 2 5
+ u1*u3*v2*(4*a33 *m1*n1 *n2*n3 + 8*a33 *m1*n1 *n2 *n3 + 4*a33 *m1*n2 *n3) +
u1*u3*v3
2 6 2 4 2 2 2 4 2 6
*( - 4*a33 *m1*n1 - 12*a33 *m1*n1 *n2 - 12*a33 *m1*n1 *n2 - 4*a33 *m1*n2 )
+ u1*u3
7 5 2 3 4 6
*(2*a33*n1 *n3 + 6*a33*n1 *n2 *n3 + 6*a33*n1 *n2 *n3 + 2*a33*n1*n2 *n3)
2 3 3 3
+ 16*u1*v1 *v2*a33 *m1 *n2
2 2 2 3 2 2 2 4
+ u1*v1 *( - 4*a33 *m1 *n1 *n2 - 4*a33 *m1 *n1*n2 )
2 2 4 2 2 2 3
+ u1*v1*v2*( - 4*a33 *m1 *n1 *n2 - 4*a33 *m1 *n1 *n2 ) + u1*v1
7 5 2 3 4 6
*( - 2*a33*m1*n1 + 2*a33*m1*n1 *n2 + 10*a33*m1*n1 *n2 + 6*a33*m1*n1*n2 )
3 3 3 3 2 2 2 3 2 2 2 4
+ 8*u1*v2 *a33 *m1 *n2 + u1*v2 *( - 4*a33 *m1 *n1 *n2 - 4*a33 *m1 *n1*n2 )
2 3 3 2 3 3 3
+ u1*v2*v3 *(4*a33 *m1 *n1 *n2 + 12*a33 *m1 *n2 )
2 2 3 2 2 3
+ u1*v2*v3*( - 8*a33 *m1 *n1 *n2*n3 - 8*a33 *m1 *n1*n2 *n3) + u1*v2*(
6 4 3 4 2
- 4*a33*m1*n1 *n2 - 4*a33*m1*n1 *n2 - 4*a33*m1*n1 *n2*n3
2 5 2 3 2 7
+ 4*a33*m1*n1 *n2 - 8*a33*m1*n1 *n2 *n3 + 4*a33*m1*n2
5 2
- 4*a33*m1*n2 *n3 )
2 2 2 5 2 2 3 2 2 2 4
+ u1*v3 *(2*a33 *m1 *n1 + 8*a33 *m1 *n1 *n2 + 6*a33 *m1 *n1*n2 )
6 4 2 2 4
+ u1*v3*( - 4*a33*m1*n1 *n3 - 8*a33*m1*n1 *n2 *n3 - 4*a33*m1*n1 *n2 *n3) +
7 2 7 2 5 4 5 2 2 3 6
u1*(2*n1 *n2 - 3*n1 *n3 + 6*n1 *n2 - 9*n1 *n2 *n3 + 6*n1 *n2
3 4 2 8 6 2
- 9*n1 *n2 *n3 + 2*n1*n2 - 3*n1*n2 *n3 )
4 3 6 3 4 2 3 2 4 3 6
+ u2 *(a33 *n1 + 3*a33 *n1 *n2 + 3*a33 *n1 *n2 + a33 *n2 )
3 3 4 3 2 3 3 5
+ u2 *v1*(4*a33 *m1*n1 *n2 + 8*a33 *m1*n1 *n2 + 4*a33 *m1*n2 )
3 2 6 2 4 3 2 2 5 2 7
+ u2 *( - 2*a33 *n1 *n2 - 6*a33 *n1 *n2 - 6*a33 *n1 *n2 - 2*a33 *n2 )
2 3 5 3 3 2 3 4 2
+ u2 *u3*v3*(4*a33 *m1*n1 + 8*a33 *m1*n1 *n2 + 4*a33 *m1*n1*n2 ) + u2 *u3
2 6 2 4 2 2 2 4 2 6
*( - 2*a33 *n1 *n3 - 6*a33 *n1 *n2 *n3 - 6*a33 *n1 *n2 *n3 - 2*a33 *n2 *n3) +
2
u2 *v1
2 6 2 4 2 2 2 4 2 6
*(2*a33 *m1*n1 - 2*a33 *m1*n1 *n2 - 10*a33 *m1*n1 *n2 - 6*a33 *m1*n2 )
2 2 3 2 4 3 2 2 2 3 2 4
+ u2 *v3 *( - 2*a33 *m1 *n1 - 8*a33 *m1 *n1 *n2 - 6*a33 *m1 *n2 )
2 2 5 2 3 2 2 4
+ u2 *v3*(4*a33 *m1*n1 *n3 + 8*a33 *m1*n1 *n2 *n3 + 4*a33 *m1*n1*n2 *n3) +
2 6 2 6 2 4 4 4 2 2
u2 *( - a33*n1 *n2 + 2*a33*n1 *n3 - 3*a33*n1 *n2 + 6*a33*n1 *n2 *n3
2 6 2 4 2 8 6 2
- 3*a33*n1 *n2 + 6*a33*n1 *n2 *n3 - a33*n2 + 2*a33*n2 *n3 )
3 2 3 3 2 3
+ u2*u3*v1*v3*(8*a33 *m1 *n1 *n2 + 8*a33 *m1 *n1*n2 ) + u2*u3*v1
2 4 2 2 3 2 5
*( - 4*a33 *m1*n1 *n2*n3 - 8*a33 *m1*n1 *n2 *n3 - 4*a33 *m1*n2 *n3)
2 5 2 3 3 2 5
+ u2*u3*v3*( - 8*a33 *m1*n1 *n2 - 16*a33 *m1*n1 *n2 - 8*a33 *m1*n1*n2 ) +
6 4 3 2 5 7
u2*u3*(2*a33*n1 *n2*n3 + 6*a33*n1 *n2 *n3 + 6*a33*n1 *n2 *n3 + 2*a33*n2 *n3)
3 3 3 3 2 2 2 4 2 2 2 3
- 8*u2*v1 *a33 *m1 *n2 + u2*v1 *(4*a33 *m1 *n1 *n2 + 4*a33 *m1 *n1 *n2 )
2 3 3 2 3 3 3
+ u2*v1*v3 *( - 4*a33 *m1 *n1 *n2 - 12*a33 *m1 *n2 )
2 2 3 2 2 3
+ u2*v1*v3*(8*a33 *m1 *n1 *n2*n3 + 8*a33 *m1 *n1*n2 *n3) + u2*v1*(
6 4 3 4 2
- 2*a33*m1*n1 *n2 - 6*a33*m1*n1 *n2 + 4*a33*m1*n1 *n2*n3
2 5 2 3 2 7
- 6*a33*m1*n1 *n2 + 8*a33*m1*n1 *n2 *n3 - 2*a33*m1*n2
5 2
+ 4*a33*m1*n2 *n3 )
2 2 2 4 2 2 2 3 2 2 5
+ u2*v3 *(2*a33 *m1 *n1 *n2 + 8*a33 *m1 *n1 *n2 + 6*a33 *m1 *n2 )
5 3 3 5
+ u2*v3*( - 4*a33*m1*n1 *n2*n3 - 8*a33*m1*n1 *n2 *n3 - 4*a33*m1*n1*n2 *n3) +
6 3 6 2 4 5 4 3 2 2 7
u2*(2*n1 *n2 - 3*n1 *n2*n3 + 6*n1 *n2 - 9*n1 *n2 *n3 + 6*n1 *n2
2 5 2 9 7 2
- 9*n1 *n2 *n3 + 2*n2 - 3*n2 *n3 )
2 2 3 2 4 3 2 4
+ u3 *v3 *(4*a33 *m1 *n1 - 4*a33 *m1 *n2 )
2 2 5 2 3 2 2 4
+ u3 *v3*( - 4*a33 *m1*n1 *n3 - 8*a33 *m1*n1 *n2 *n3 - 4*a33 *m1*n1*n2 *n3)
2 3 3 2
- 8*u3*v1 *v3*a33 *m1 *n1*n2
2 2 2 2 2 2 2 4
+ u3*v1 *(4*a33 *m1 *n1 *n2 *n3 + 4*a33 *m1 *n2 *n3)
3 3 3
+ 8*u3*v1*v2*v3*a33 *m1 *n2
2 2 5 2 2 3 2 2 2 4
+ u3*v1*v3*(4*a33 *m1 *n1 - 8*a33 *m1 *n1 *n2 - 12*a33 *m1 *n1*n2 ) + u3
6 4 2 2 4
*v1*( - 2*a33*m1*n1 *n3 - 2*a33*m1*n1 *n2 *n3 + 2*a33*m1*n1 *n2 *n3
6 2 3 3 2
+ 2*a33*m1*n2 *n3) - 8*u3*v2 *v3*a33 *m1 *n1*n2
2 2 2 2 2 2 2 4
+ u3*v2 *(4*a33 *m1 *n1 *n2 *n3 + 4*a33 *m1 *n2 *n3)
2 2 4 2 2 2 3 2 2 5
+ u3*v2*v3*(8*a33 *m1 *n1 *n2 + 4*a33 *m1 *n1 *n2 - 4*a33 *m1 *n2 )
5 3 3 5
+ u3*v2*( - 4*a33*m1*n1 *n2*n3 - 8*a33*m1*n1 *n2 *n3 - 4*a33*m1*n1*n2 *n3)
3 3 3 3 3 3 2
+ u3*v3 *( - 4*a33 *m1 *n1 - 12*a33 *m1 *n1*n2 )
2 2 2 4 2 2 2 2 2 2 4
+ u3*v3 *(10*a33 *m1 *n1 *n3 + 16*a33 *m1 *n1 *n2 *n3 + 6*a33 *m1 *n2 *n3) +
6 2 6 3 4 4 4 2 3 2 6
u3*(2*n1 *n2 *n3 - 3*n1 *n3 + 6*n1 *n2 *n3 - 9*n1 *n2 *n3 + 6*n1 *n2 *n3
2 4 3 8 6 3
- 9*n1 *n2 *n3 + 2*n2 *n3 - 3*n2 *n3 )
3 2 3 2 2 2 3 4 2 2 3 3
+ v1 *( - 4*a33 *m1 *n1 *n2 + 4*a33 *m1 *n2 ) - 8*v1 *v2*a33 *m1 *n1*n2
2 2 3 4 2 2 2 3 2
+ 4*v1 *v3 *a33 *m1 *n2 - 8*v1 *v3*a33 *m1 *n1*n2 *n3
2 2 3 2 2 2 3 4
+ v1*v2 *( - 4*a33 *m1 *n1 *n2 + 4*a33 *m1 *n2 )
2 5 2 5
+ v1*v2*(4*a33*m1 *n1 *n2 - 4*a33*m1 *n1*n2 )
2 2 3 4 2 3 2 2 2 3 4
+ v1*v3 *( - 2*a33 *m1 *n1 - 4*a33 *m1 *n1 *n2 + 6*a33 *m1 *n2 )
2 5 2 4 6 2
+ v1*v3*(4*a33*m1 *n1 *n3 - 4*a33*m1 *n1*n2 *n3) + v1*( - 2*m1*n1 *n2
6 2 4 4 4 2 2 2 6
+ m1*n1 *n3 - 2*m1*n1 *n2 - m1*n1 *n2 *n3 + 2*m1*n1 *n2
2 4 2 8 6 2 3 2 3 3
- 5*m1*n1 *n2 *n3 + 2*m1*n2 - 3*m1*n2 *n3 ) - 8*v2 *a33 *m1 *n1*n2
2 2 3 4 2 2 2 3 2
+ 4*v2 *v3 *a33 *m1 *n2 - 8*v2 *v3*a33 *m1 *n1*n2 *n3
2 2 6 2 4 2 2 2 4 2 6
+ v2 *( - a33*m1 *n1 + 5*a33*m1 *n1 *n2 + 5*a33*m1 *n1 *n2 - a33*m1 *n2 )
2 2 3 3 2 3 3
+ v2*v3 *( - 4*a33 *m1 *n1 *n2 - 12*a33 *m1 *n1*n2 )
2 4 2 2 3 5 3
+ v2*v3*(8*a33*m1 *n1 *n2*n3 + 8*a33*m1 *n1 *n2 *n3) + v2*( - 4*m1*n1 *n2
5 2 3 5 3 3 2 7
+ 4*m1*n1 *n2*n3 - 8*m1*n1 *n2 + 8*m1*n1 *n2 *n3 - 4*m1*n1*n2
5 2 4 3 4 2 3 4 2
+ 4*m1*n1*n2 *n3 ) + v3 *(a33 *m1 *n1 + 5*a33 *m1 *n2 )
3 2 3 3 2 3 2 2 2 6
+ v3 *( - 4*a33 *m1 *n1 *n3 - 12*a33 *m1 *n1*n2 *n3) + v3 *( - a33*m1 *n1
2 4 2 2 4 2 2 2 4 2 6
+ 3*a33*m1 *n1 *n2 + 2*a33*m1 *n1 *n3 + 5*a33*m1 *n1 *n2 + a33*m1 *n2
2 4 2 5 2 5 3
- 2*a33*m1 *n2 *n3 ) + v3*( - 4*m1*n1 *n2 *n3 + 4*m1*n1 *n3
3 4 3 2 3 6 4 3
- 8*m1*n1 *n2 *n3 + 8*m1*n1 *n2 *n3 - 4*m1*n1*n2 *n3 + 4*m1*n1*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,
- a33,
a33,
u1*v1 + u2*v2 + u3*v3,
n2,
m1,
2 4 2 2 2 2 4
2 a33 *n1 + 2*a33 *n1 *n2 + a33 *n2
u1 *u3*--------------------------------------
2
4 2 2 4
2 a33*n1 *n3 + 2*a33*n1 *n2 *n3 + a33*n2 *n3
+ u1 *--------------------------------------------
4
5 3 2 4
- 3*a33*n1 - 6*a33*n1 *n2 - 3*a33*n1*n2
+ u1*u3*---------------------------------------------
4
4 4
- a33*m1*n1 + a33*m1*n2
+ u1*v3*----------------------------
4
5 3 2 4
- n1 *n3 - 2*n1 *n2 *n3 - n1*n2 *n3
+ u1*--------------------------------------
4
2 4 2 2 2 2 4
2 - a33 *n1 - 2*a33 *n1 *n2 - a33 *n2
+ u2 *u3*-----------------------------------------
2
4 2 2 4
2 - a33*n1 *n3 - 2*a33*n1 *n2 *n3 - a33*n2 *n3
+ u2 *-----------------------------------------------
4
4 2 3 5
3*a33*n1 *n2 + 6*a33*n1 *n2 + 3*a33*n2
+ u2*u3*------------------------------------------
4
3 3
- a33*m1*n1 *n2 - a33*m1*n1*n2
+ u2*v3*----------------------------------
2
4 2 3 5
n1 *n2*n3 + 2*n1 *n2 *n3 + n2 *n3 2 2 2 2
+ u2*----------------------------------- + u3*v1 *a33 *m1 *n2
4
3 3
2 2 2 2 a33*m1*n1 *n2 + a33*m1*n1*n2
- u3*v2 *a33 *m1 *n2 + u3*v2*-------------------------------
2
6 4 2 2 4 6 2 2 2
n1 + n1 *n2 - n1 *n2 - n2 v1 *a33*m1 *n2 *n3
+ u3*------------------------------- + --------------------
4 2
2 2 2 2 4
- v1*v3*a33*m1 *n1*n2 - m1*n1 *n2 *n3 - m1*n2 *n3
+ ------------------------- + v1*------------------------------
2 4
2 2 2 2 2
- v2 *a33*m1 *n2 *n3 - v2*v3*a33*m1 *n1 *n2
+ ----------------------- + -------------------------
2 2
3 3 5 3 2
m1*n1 *n2*n3 + m1*n1*n2 *n3 m1*n1 + m1*n1 *n2
+ v2*----------------------------- + v3*---------------------}
2 4
2 8 6 2 4 4 2 6 8
FI=u1 *(a33*n1 + 4*a33*n1 *n2 + 6*a33*n1 *n2 + 4*a33*n1 *n2 + a33*n2 ) + u1
6 4 3 2 5 7
*v2*( - 2*a33*m1*n1 *n2 - 6*a33*m1*n1 *n2 - 6*a33*m1*n1 *n2 - 2*a33*m1*n2 )
9 7 2 5 4 3 6 8
+ u1*( - n1 - 4*n1 *n2 - 6*n1 *n2 - 4*n1 *n2 - n1*n2 )
2 8 6 2 4 4 2 6 8
+ u2 *(a33*n1 + 4*a33*n1 *n2 + 6*a33*n1 *n2 + 4*a33*n1 *n2 + a33*n2 ) +
6 4 3 2 5 7
u2*v1*(2*a33*m1*n1 *n2 + 6*a33*m1*n1 *n2 + 6*a33*m1*n1 *n2 + 2*a33*m1*n2 )
8 6 3 4 5 2 7 9
+ u2*( - n1 *n2 - 4*n1 *n2 - 6*n1 *n2 - 4*n1 *n2 - n2 ) + u3*v3
7 5 2 3 4 6
*(2*a33*m1*n1 + 6*a33*m1*n1 *n2 + 6*a33*m1*n1 *n2 + 2*a33*m1*n1*n2 )
8 6 2 4 4 2 6 8
+ u3*( - n1 *n3 - 4*n1 *n2 *n3 - 6*n1 *n2 *n3 - 4*n1 *n2 *n3 - n2 *n3)
8 6 2 2 6 8
+ v1*(m1*n1 + 2*m1*n1 *n2 - 2*m1*n1 *n2 - m1*n2 )
7 5 3 3 5 7
+ v2*(2*m1*n1 *n2 + 6*m1*n1 *n2 + 6*m1*n1 *n2 + 2*m1*n1*n2 )
2 2 6 2 4 2 2 2 4 2 6
+ v3 *( - a33*m1 *n1 - 3*a33*m1 *n1 *n2 - 3*a33*m1 *n1 *n2 - a33*m1 *n2 )
7 5 2 3 4 6
+ v3*(2*m1*n1 *n3 + 6*m1*n1 *n2 *n3 + 6*m1*n1 *n2 *n3 + 2*m1*n1*n2 *n3)
= a product of the elements of: { - n1 + i*n2,
n1 - i*n2,
n1 - i*n2,
n1 + i*n2,
n1 + i*n2,
n1 + i*n2,
2 2 2 3 2
u1 *( - a33*n1 - a33*n2 ) + 2*u1*v2*a33*m1*n2 + u1*(n1 + n1*n2 )
2 2 2 2 3
+ u2 *( - a33*n1 - a33*n2 ) - 2*u2*v1*a33*m1*n2 + u2*(n1 *n2 + n2 )
2 2 2 2
- 2*u3*v3*a33*m1*n1 + u3*(n1 *n3 + n2 *n3) + v1*( - m1*n1 + m1*n2 )
2 2
- 2*v2*m1*n1*n2 + v3 *a33*m1 - 2*v3*m1*n1*n3}
{HAM,FI} = 0
And again in machine readable form:
HAM=u1*n1 + u2*n2 + u3**2*a33 + u3*n3 + v1*m1$
FI=u1**3*(a33**2*n1**3 + a33**2*n1*n2**2) + u1**2*u2*(a33**2*n1**2*n2 + a33**2*
n2**3) + u1**2*u3**2*(a33**3*n1**2 + a33**3*n2**2) + u1**2*u3*(a33**2*n1**2*n3 +
a33**2*n2**2*n3) + u1**2*v1*(a33**2*m1*n1**2 + 3*a33**2*m1*n2**2) - 2*u1**2*v2*
a33**2*m1*n1*n2 + u1**2*( - a33*n1**4 - a33*n1**2*n3**2 + a33*n2**4 - a33*n2**2*
n3**2) + u1*u2**2*(a33**2*n1**3 + a33**2*n1*n2**2) + 2*u1*u2*v1*a33**2*m1*n1*n2
+ u1*u2*( - 2*a33*n1**3*n2 - 2*a33*n1*n2**3) - 2*u1*u3**2*v2*a33**3*m1*n2 + u1*
u3**2*( - a33**2*n1**3 - a33**2*n1*n2**2) - 2*u1*u3*v2*a33**2*m1*n2*n3 + u1*u3*
v3*(2*a33**2*m1*n1**2 + 2*a33**2*m1*n2**2) + u1*u3*( - 2*a33*n1**3*n3 - 2*a33*n1
*n2**2*n3) - 2*u1*v1*v2*a33**2*m1**2*n2 - 4*u1*v1*a33*m1*n1*n2**2 + u1*v2*(2*a33
*m1*n1**2*n2 - 2*a33*m1*n2**3 + 2*a33*m1*n2*n3**2) - u1*v3**2*a33**2*m1**2*n1 +
2*u1*v3*a33*m1*n1**2*n3 + u1*( - n1**3*n2**2 + 2*n1**3*n3**2 - n1*n2**4 + 2*n1*
n2**2*n3**2) + u2**3*(a33**2*n1**2*n2 + a33**2*n2**3) + u2**2*u3**2*(a33**3*n1**
2 + a33**3*n2**2) + u2**2*u3*(a33**2*n1**2*n3 + a33**2*n2**2*n3) + u2**2*v1*(a33
**2*m1*n1**2 + 3*a33**2*m1*n2**2) + u2**2*( - a33*n1**2*n3**2 - a33*n2**2*n3**2)
+ 2*u2*u3**2*v1*a33**3*m1*n2 + u2*u3**2*( - a33**2*n1**2*n2 - a33**2*n2**3) + 2
*u2*u3*v1*a33**2*m1*n2*n3 + 2*u2*u3*v3*a33**2*m1*n1*n2 + u2*u3*( - 2*a33*n1**2*
n2*n3 - 2*a33*n2**3*n3) + 2*u2*v1**2*a33**2*m1**2*n2 - 2*u2*v1*a33*m1*n2*n3**2 -
u2*v3**2*a33**2*m1**2*n2 + 2*u2*v3*a33*m1*n1*n2*n3 + u2*( - n1**2*n2**3 + 2*n1
**2*n2*n3**2 - n2**5 + 2*n2**3*n3**2) + 2*u3**3*v3*a33**3*m1*n1 + u3**3*( - a33
**2*n1**2*n3 - a33**2*n2**2*n3) + u3**2*v1*(a33**2*m1*n1**2 - a33**2*m1*n2**2) +
2*u3**2*v2*a33**2*m1*n1*n2 - u3**2*v3**2*a33**3*m1**2 + 4*u3**2*v3*a33**2*m1*n1
*n3 + 2*u3*v1*v3*a33**2*m1**2*n1 - 2*u3*v1*a33*m1*n2**2*n3 + 2*u3*v2*a33*m1*n1*
n2*n3 - u3*v3**2*a33**2*m1**2*n3 + u3*( - n1**2*n2**2*n3 + 2*n1**2*n3**3 - n2**4
*n3 + 2*n2**2*n3**3) + 2*v1*v2*a33*m1**2*n1*n2 - v1*v3**2*a33**2*m1**3 + 2*v1*v3
*a33*m1**2*n1*n3 + v1*(m1*n1**2*n2**2 - m1*n2**4 + 2*m1*n2**2*n3**2) + v2**2*( -
a33*m1**2*n1**2 + a33*m1**2*n2**2) + v2*(2*m1*n1*n2**3 - 2*m1*n1*n2*n3**2) + v3
**2*( - a33*m1**2*n1**2 + a33*m1**2*n3**2) + v3*(2*m1*n1*n2**2*n3 - 2*m1*n1*n3**
3)$
FI=u1**2*v1**2*(2*a33*n1**6 + 6*a33*n1**4*n2**2 + 6*a33*n1**2*n2**4 + 2*a33*n2**
6) + u1**2*v2**2*(a33*n1**6 + 3*a33*n1**4*n2**2 + 3*a33*n1**2*n2**4 + a33*n2**6)
+ u1**2*v3**2*(a33*n1**6 + 3*a33*n1**4*n2**2 + 3*a33*n1**2*n2**4 + a33*n2**6) +
u1*u3*v1*v3*(2*a33*n1**6 + 6*a33*n1**4*n2**2 + 6*a33*n1**2*n2**4 + 2*a33*n2**6)
+ u1*v1**2*v2*( - 4*a33*m1*n1**4*n2 - 8*a33*m1*n1**2*n2**3 - 4*a33*m1*n2**5) +
u1*v1**2*( - n1**7 - 3*n1**5*n2**2 - 3*n1**3*n2**4 - n1*n2**6) + u1*v1*v2*(n1**6
*n2 + 3*n1**4*n2**3 + 3*n1**2*n2**5 + n2**7) + u1*v2**3*( - 2*a33*m1*n1**4*n2 -
4*a33*m1*n1**2*n2**3 - 2*a33*m1*n2**5) + u1*v2**2*( - n1**7 - 3*n1**5*n2**2 - 3*
n1**3*n2**4 - n1*n2**6) + u1*v2*v3**2*( - 2*a33*m1*n1**4*n2 - 4*a33*m1*n1**2*n2
**3 - 2*a33*m1*n2**5) + u1*v3**2*( - n1**7 - 3*n1**5*n2**2 - 3*n1**3*n2**4 - n1*
n2**6) + u2**2*v1**2*(a33*n1**6 + 3*a33*n1**4*n2**2 + 3*a33*n1**2*n2**4 + a33*n2
**6) + u2**2*v3**2*(a33*n1**6 + 3*a33*n1**4*n2**2 + 3*a33*n1**2*n2**4 + a33*n2**
6) + u2*v1**3*(2*a33*m1*n1**4*n2 + 4*a33*m1*n1**2*n2**3 + 2*a33*m1*n2**5) + u2*
v1**2*( - n1**6*n2 - 3*n1**4*n2**3 - 3*n1**2*n2**5 - n2**7) + u2*v1*v3**2*(2*a33
*m1*n1**4*n2 + 4*a33*m1*n1**2*n2**3 + 2*a33*m1*n2**5) + u2*v3**2*( - n1**6*n2 -
3*n1**4*n2**3 - 3*n1**2*n2**5 - n2**7) + u3**2*v3**2*(a33*n1**6 + 3*a33*n1**4*n2
**2 + 3*a33*n1**2*n2**4 + a33*n2**6) + u3*v1**2*v3*(2*a33*m1*n1**5 + 4*a33*m1*n1
**3*n2**2 + 2*a33*m1*n1*n2**4) + u3*v1**2*( - n1**6*n3 - 3*n1**4*n2**2*n3 - 3*n1
**2*n2**4*n3 - n2**6*n3) + u3*v1*v2*v3*( - 2*a33*m1*n1**4*n2 - 4*a33*m1*n1**2*n2
**3 - 2*a33*m1*n2**5) + u3*v2**2*v3*(2*a33*m1*n1**5 + 4*a33*m1*n1**3*n2**2 + 2*
a33*m1*n1*n2**4) + u3*v2**2*( - n1**6*n3 - 3*n1**4*n2**2*n3 - 3*n1**2*n2**4*n3 -
n2**6*n3) + u3*v2*v3*(n1**6*n2 + 3*n1**4*n2**3 + 3*n1**2*n2**5 + n2**7) + u3*v3
**3*(2*a33*m1*n1**5 + 4*a33*m1*n1**3*n2**2 + 2*a33*m1*n1*n2**4) + u3*v3**2*( -
n1**6*n3 - 3*n1**4*n2**2*n3 - 3*n1**2*n2**4*n3 - n2**6*n3) + v1**3*(m1*n1**6 +
m1*n1**4*n2**2 - m1*n1**2*n2**4 - m1*n2**6) + v1**2*v2*(2*m1*n1**5*n2 + 4*m1*n1
**3*n2**3 + 2*m1*n1*n2**5) + v1**2*v3**2*( - a33*m1**2*n1**4 - 2*a33*m1**2*n1**2
*n2**2 - a33*m1**2*n2**4) + v1**2*v3*(2*m1*n1**5*n3 + 4*m1*n1**3*n2**2*n3 + 2*m1
*n1*n2**4*n3) + v1*v2**2*(m1*n1**6 + m1*n1**4*n2**2 - m1*n1**2*n2**4 - m1*n2**6)
+ v1*v3**2*(m1*n1**6 + m1*n1**4*n2**2 - m1*n1**2*n2**4 - m1*n2**6) + v2**3*(2*
m1*n1**5*n2 + 4*m1*n1**3*n2**3 + 2*m1*n1*n2**5) + v2**2*v3**2*( - a33*m1**2*n1**
4 - 2*a33*m1**2*n1**2*n2**2 - a33*m1**2*n2**4) + v2**2*v3*(2*m1*n1**5*n3 + 4*m1*
n1**3*n2**2*n3 + 2*m1*n1*n2**4*n3) + v2*v3**2*(2*m1*n1**5*n2 + 4*m1*n1**3*n2**3
+ 2*m1*n1*n2**5) + v3**4*( - a33*m1**2*n1**4 - 2*a33*m1**2*n1**2*n2**2 - a33*m1
**2*n2**4) + v3**3*(2*m1*n1**5*n3 + 4*m1*n1**3*n2**2*n3 + 2*m1*n1*n2**4*n3)$
FI=u1**4*(a33**3*n1**6 + 3*a33**3*n1**4*n2**2 + 3*a33**3*n1**2*n2**4 + a33**3*n2
**6) + u1**3*v2*( - 4*a33**3*m1*n1**4*n2 - 8*a33**3*m1*n1**2*n2**3 - 4*a33**3*m1
*n2**5) + u1**3*( - 2*a33**2*n1**7 - 6*a33**2*n1**5*n2**2 - 6*a33**2*n1**3*n2**4
- 2*a33**2*n1*n2**6) + u1**2*u2**2*(2*a33**3*n1**6 + 6*a33**3*n1**4*n2**2 + 6*
a33**3*n1**2*n2**4 + 2*a33**3*n2**6) + u1**2*u2*v1*(8*a33**3*m1*n1**4*n2 + 16*
a33**3*m1*n1**2*n2**3 + 8*a33**3*m1*n2**5) + u1**2*u2*( - 2*a33**2*n1**6*n2 - 6*
a33**2*n1**4*n2**3 - 6*a33**2*n1**2*n2**5 - 2*a33**2*n2**7) + u1**2*u3*v3*(4*a33
**3*m1*n1**5 + 8*a33**3*m1*n1**3*n2**2 + 4*a33**3*m1*n1*n2**4) + u1**2*u3*( - 2*
a33**2*n1**6*n3 - 6*a33**2*n1**4*n2**2*n3 - 6*a33**2*n1**2*n2**4*n3 - 2*a33**2*
n2**6*n3) + u1**2*v1*(2*a33**2*m1*n1**6 - 2*a33**2*m1*n1**4*n2**2 - 10*a33**2*m1
*n1**2*n2**4 - 6*a33**2*m1*n2**6) + u1**2*v2*(8*a33**2*m1*n1**5*n2 + 16*a33**2*
m1*n1**3*n2**3 + 8*a33**2*m1*n1*n2**5) + u1**2*v3**2*( - 2*a33**3*m1**2*n1**4 -
8*a33**3*m1**2*n1**2*n2**2 - 6*a33**3*m1**2*n2**4) + u1**2*v3*(4*a33**2*m1*n1**5
*n3 + 8*a33**2*m1*n1**3*n2**2*n3 + 4*a33**2*m1*n1*n2**4*n3) + u1**2*(a33*n1**8 +
a33*n1**6*n2**2 + 2*a33*n1**6*n3**2 - 3*a33*n1**4*n2**4 + 6*a33*n1**4*n2**2*n3
**2 - 5*a33*n1**2*n2**6 + 6*a33*n1**2*n2**4*n3**2 - 2*a33*n2**8 + 2*a33*n2**6*n3
**2) + u1*u2**2*( - 2*a33**2*n1**7 - 6*a33**2*n1**5*n2**2 - 6*a33**2*n1**3*n2**4
- 2*a33**2*n1*n2**6) + u1*u2*u3*v3*(4*a33**3*m1*n1**4*n2 + 8*a33**3*m1*n1**2*n2
**3 + 4*a33**3*m1*n2**5) + u1*u2*v1*( - 8*a33**2*m1*n1**5*n2 - 16*a33**2*m1*n1**
3*n2**3 - 8*a33**2*m1*n1*n2**5) + u1*u2*(2*a33*n1**7*n2 + 6*a33*n1**5*n2**3 + 6*
a33*n1**3*n2**5 + 2*a33*n1*n2**7) + u1*u3*v2*v3*( - 8*a33**3*m1**2*n1**3*n2 - 8*
a33**3*m1**2*n1*n2**3) + u1*u3*v2*(4*a33**2*m1*n1**4*n2*n3 + 8*a33**2*m1*n1**2*
n2**3*n3 + 4*a33**2*m1*n2**5*n3) + u1*u3*v3*( - 4*a33**2*m1*n1**6 - 12*a33**2*m1
*n1**4*n2**2 - 12*a33**2*m1*n1**2*n2**4 - 4*a33**2*m1*n2**6) + u1*u3*(2*a33*n1**
7*n3 + 6*a33*n1**5*n2**2*n3 + 6*a33*n1**3*n2**4*n3 + 2*a33*n1*n2**6*n3) + 16*u1*
v1**2*v2*a33**3*m1**3*n2**3 + u1*v1**2*( - 4*a33**2*m1**2*n1**3*n2**2 - 4*a33**2
*m1**2*n1*n2**4) + u1*v1*v2*( - 4*a33**2*m1**2*n1**4*n2 - 4*a33**2*m1**2*n1**2*
n2**3) + u1*v1*( - 2*a33*m1*n1**7 + 2*a33*m1*n1**5*n2**2 + 10*a33*m1*n1**3*n2**4
+ 6*a33*m1*n1*n2**6) + 8*u1*v2**3*a33**3*m1**3*n2**3 + u1*v2**2*( - 4*a33**2*m1
**2*n1**3*n2**2 - 4*a33**2*m1**2*n1*n2**4) + u1*v2*v3**2*(4*a33**3*m1**3*n1**2*
n2 + 12*a33**3*m1**3*n2**3) + u1*v2*v3*( - 8*a33**2*m1**2*n1**3*n2*n3 - 8*a33**2
*m1**2*n1*n2**3*n3) + u1*v2*( - 4*a33*m1*n1**6*n2 - 4*a33*m1*n1**4*n2**3 - 4*a33
*m1*n1**4*n2*n3**2 + 4*a33*m1*n1**2*n2**5 - 8*a33*m1*n1**2*n2**3*n3**2 + 4*a33*
m1*n2**7 - 4*a33*m1*n2**5*n3**2) + u1*v3**2*(2*a33**2*m1**2*n1**5 + 8*a33**2*m1
**2*n1**3*n2**2 + 6*a33**2*m1**2*n1*n2**4) + u1*v3*( - 4*a33*m1*n1**6*n3 - 8*a33
*m1*n1**4*n2**2*n3 - 4*a33*m1*n1**2*n2**4*n3) + u1*(2*n1**7*n2**2 - 3*n1**7*n3**
2 + 6*n1**5*n2**4 - 9*n1**5*n2**2*n3**2 + 6*n1**3*n2**6 - 9*n1**3*n2**4*n3**2 +
2*n1*n2**8 - 3*n1*n2**6*n3**2) + u2**4*(a33**3*n1**6 + 3*a33**3*n1**4*n2**2 + 3*
a33**3*n1**2*n2**4 + a33**3*n2**6) + u2**3*v1*(4*a33**3*m1*n1**4*n2 + 8*a33**3*
m1*n1**2*n2**3 + 4*a33**3*m1*n2**5) + u2**3*( - 2*a33**2*n1**6*n2 - 6*a33**2*n1
**4*n2**3 - 6*a33**2*n1**2*n2**5 - 2*a33**2*n2**7) + u2**2*u3*v3*(4*a33**3*m1*n1
**5 + 8*a33**3*m1*n1**3*n2**2 + 4*a33**3*m1*n1*n2**4) + u2**2*u3*( - 2*a33**2*n1
**6*n3 - 6*a33**2*n1**4*n2**2*n3 - 6*a33**2*n1**2*n2**4*n3 - 2*a33**2*n2**6*n3)
+ u2**2*v1*(2*a33**2*m1*n1**6 - 2*a33**2*m1*n1**4*n2**2 - 10*a33**2*m1*n1**2*n2
**4 - 6*a33**2*m1*n2**6) + u2**2*v3**2*( - 2*a33**3*m1**2*n1**4 - 8*a33**3*m1**2
*n1**2*n2**2 - 6*a33**3*m1**2*n2**4) + u2**2*v3*(4*a33**2*m1*n1**5*n3 + 8*a33**2
*m1*n1**3*n2**2*n3 + 4*a33**2*m1*n1*n2**4*n3) + u2**2*( - a33*n1**6*n2**2 + 2*
a33*n1**6*n3**2 - 3*a33*n1**4*n2**4 + 6*a33*n1**4*n2**2*n3**2 - 3*a33*n1**2*n2**
6 + 6*a33*n1**2*n2**4*n3**2 - a33*n2**8 + 2*a33*n2**6*n3**2) + u2*u3*v1*v3*(8*
a33**3*m1**2*n1**3*n2 + 8*a33**3*m1**2*n1*n2**3) + u2*u3*v1*( - 4*a33**2*m1*n1**
4*n2*n3 - 8*a33**2*m1*n1**2*n2**3*n3 - 4*a33**2*m1*n2**5*n3) + u2*u3*v3*( - 8*
a33**2*m1*n1**5*n2 - 16*a33**2*m1*n1**3*n2**3 - 8*a33**2*m1*n1*n2**5) + u2*u3*(2
*a33*n1**6*n2*n3 + 6*a33*n1**4*n2**3*n3 + 6*a33*n1**2*n2**5*n3 + 2*a33*n2**7*n3)
- 8*u2*v1**3*a33**3*m1**3*n2**3 + u2*v1**2*(4*a33**2*m1**2*n1**4*n2 + 4*a33**2*
m1**2*n1**2*n2**3) + u2*v1*v3**2*( - 4*a33**3*m1**3*n1**2*n2 - 12*a33**3*m1**3*
n2**3) + u2*v1*v3*(8*a33**2*m1**2*n1**3*n2*n3 + 8*a33**2*m1**2*n1*n2**3*n3) + u2
*v1*( - 2*a33*m1*n1**6*n2 - 6*a33*m1*n1**4*n2**3 + 4*a33*m1*n1**4*n2*n3**2 - 6*
a33*m1*n1**2*n2**5 + 8*a33*m1*n1**2*n2**3*n3**2 - 2*a33*m1*n2**7 + 4*a33*m1*n2**
5*n3**2) + u2*v3**2*(2*a33**2*m1**2*n1**4*n2 + 8*a33**2*m1**2*n1**2*n2**3 + 6*
a33**2*m1**2*n2**5) + u2*v3*( - 4*a33*m1*n1**5*n2*n3 - 8*a33*m1*n1**3*n2**3*n3 -
4*a33*m1*n1*n2**5*n3) + u2*(2*n1**6*n2**3 - 3*n1**6*n2*n3**2 + 6*n1**4*n2**5 -
9*n1**4*n2**3*n3**2 + 6*n1**2*n2**7 - 9*n1**2*n2**5*n3**2 + 2*n2**9 - 3*n2**7*n3
**2) + u3**2*v3**2*(4*a33**3*m1**2*n1**4 - 4*a33**3*m1**2*n2**4) + u3**2*v3*( -
4*a33**2*m1*n1**5*n3 - 8*a33**2*m1*n1**3*n2**2*n3 - 4*a33**2*m1*n1*n2**4*n3) - 8
*u3*v1**2*v3*a33**3*m1**3*n1*n2**2 + u3*v1**2*(4*a33**2*m1**2*n1**2*n2**2*n3 + 4
*a33**2*m1**2*n2**4*n3) + 8*u3*v1*v2*v3*a33**3*m1**3*n2**3 + u3*v1*v3*(4*a33**2*
m1**2*n1**5 - 8*a33**2*m1**2*n1**3*n2**2 - 12*a33**2*m1**2*n1*n2**4) + u3*v1*( -
2*a33*m1*n1**6*n3 - 2*a33*m1*n1**4*n2**2*n3 + 2*a33*m1*n1**2*n2**4*n3 + 2*a33*
m1*n2**6*n3) - 8*u3*v2**2*v3*a33**3*m1**3*n1*n2**2 + u3*v2**2*(4*a33**2*m1**2*n1
**2*n2**2*n3 + 4*a33**2*m1**2*n2**4*n3) + u3*v2*v3*(8*a33**2*m1**2*n1**4*n2 + 4*
a33**2*m1**2*n1**2*n2**3 - 4*a33**2*m1**2*n2**5) + u3*v2*( - 4*a33*m1*n1**5*n2*
n3 - 8*a33*m1*n1**3*n2**3*n3 - 4*a33*m1*n1*n2**5*n3) + u3*v3**3*( - 4*a33**3*m1
**3*n1**3 - 12*a33**3*m1**3*n1*n2**2) + u3*v3**2*(10*a33**2*m1**2*n1**4*n3 + 16*
a33**2*m1**2*n1**2*n2**2*n3 + 6*a33**2*m1**2*n2**4*n3) + u3*(2*n1**6*n2**2*n3 -
3*n1**6*n3**3 + 6*n1**4*n2**4*n3 - 9*n1**4*n2**2*n3**3 + 6*n1**2*n2**6*n3 - 9*n1
**2*n2**4*n3**3 + 2*n2**8*n3 - 3*n2**6*n3**3) + v1**3*( - 4*a33**2*m1**3*n1**2*
n2**2 + 4*a33**2*m1**3*n2**4) - 8*v1**2*v2*a33**2*m1**3*n1*n2**3 + 4*v1**2*v3**2
*a33**3*m1**4*n2**2 - 8*v1**2*v3*a33**2*m1**3*n1*n2**2*n3 + v1*v2**2*( - 4*a33**
2*m1**3*n1**2*n2**2 + 4*a33**2*m1**3*n2**4) + v1*v2*(4*a33*m1**2*n1**5*n2 - 4*
a33*m1**2*n1*n2**5) + v1*v3**2*( - 2*a33**2*m1**3*n1**4 - 4*a33**2*m1**3*n1**2*
n2**2 + 6*a33**2*m1**3*n2**4) + v1*v3*(4*a33*m1**2*n1**5*n3 - 4*a33*m1**2*n1*n2
**4*n3) + v1*( - 2*m1*n1**6*n2**2 + m1*n1**6*n3**2 - 2*m1*n1**4*n2**4 - m1*n1**4
*n2**2*n3**2 + 2*m1*n1**2*n2**6 - 5*m1*n1**2*n2**4*n3**2 + 2*m1*n2**8 - 3*m1*n2
**6*n3**2) - 8*v2**3*a33**2*m1**3*n1*n2**3 + 4*v2**2*v3**2*a33**3*m1**4*n2**2 -
8*v2**2*v3*a33**2*m1**3*n1*n2**2*n3 + v2**2*( - a33*m1**2*n1**6 + 5*a33*m1**2*n1
**4*n2**2 + 5*a33*m1**2*n1**2*n2**4 - a33*m1**2*n2**6) + v2*v3**2*( - 4*a33**2*
m1**3*n1**3*n2 - 12*a33**2*m1**3*n1*n2**3) + v2*v3*(8*a33*m1**2*n1**4*n2*n3 + 8*
a33*m1**2*n1**2*n2**3*n3) + v2*( - 4*m1*n1**5*n2**3 + 4*m1*n1**5*n2*n3**2 - 8*m1
*n1**3*n2**5 + 8*m1*n1**3*n2**3*n3**2 - 4*m1*n1*n2**7 + 4*m1*n1*n2**5*n3**2) +
v3**4*(a33**3*m1**4*n1**2 + 5*a33**3*m1**4*n2**2) + v3**3*( - 4*a33**2*m1**3*n1
**3*n3 - 12*a33**2*m1**3*n1*n2**2*n3) + v3**2*( - a33*m1**2*n1**6 + 3*a33*m1**2*
n1**4*n2**2 + 2*a33*m1**2*n1**4*n3**2 + 5*a33*m1**2*n1**2*n2**4 + a33*m1**2*n2**
6 - 2*a33*m1**2*n2**4*n3**2) + v3*( - 4*m1*n1**5*n2**2*n3 + 4*m1*n1**5*n3**3 - 8
*m1*n1**3*n2**4*n3 + 8*m1*n1**3*n2**2*n3**3 - 4*m1*n1*n2**6*n3 + 4*m1*n1*n2**4*
n3**3)$
FI=u1**2*(a33*n1**8 + 4*a33*n1**6*n2**2 + 6*a33*n1**4*n2**4 + 4*a33*n1**2*n2**6
+ a33*n2**8) + u1*v2*( - 2*a33*m1*n1**6*n2 - 6*a33*m1*n1**4*n2**3 - 6*a33*m1*n1
**2*n2**5 - 2*a33*m1*n2**7) + u1*( - n1**9 - 4*n1**7*n2**2 - 6*n1**5*n2**4 - 4*
n1**3*n2**6 - n1*n2**8) + u2**2*(a33*n1**8 + 4*a33*n1**6*n2**2 + 6*a33*n1**4*n2
**4 + 4*a33*n1**2*n2**6 + a33*n2**8) + u2*v1*(2*a33*m1*n1**6*n2 + 6*a33*m1*n1**4
*n2**3 + 6*a33*m1*n1**2*n2**5 + 2*a33*m1*n2**7) + u2*( - n1**8*n2 - 4*n1**6*n2**
3 - 6*n1**4*n2**5 - 4*n1**2*n2**7 - n2**9) + u3*v3*(2*a33*m1*n1**7 + 6*a33*m1*n1
**5*n2**2 + 6*a33*m1*n1**3*n2**4 + 2*a33*m1*n1*n2**6) + u3*( - n1**8*n3 - 4*n1**
6*n2**2*n3 - 6*n1**4*n2**4*n3 - 4*n1**2*n2**6*n3 - n2**8*n3) + v1*(m1*n1**8 + 2*
m1*n1**6*n2**2 - 2*m1*n1**2*n2**6 - m1*n2**8) + v2*(2*m1*n1**7*n2 + 6*m1*n1**5*
n2**3 + 6*m1*n1**3*n2**5 + 2*m1*n1*n2**7) + v3**2*( - a33*m1**2*n1**6 - 3*a33*m1
**2*n1**4*n2**2 - 3*a33*m1**2*n1**2*n2**4 - a33*m1**2*n2**6) + v3*(2*m1*n1**7*n3
+ 6*m1*n1**5*n2**2*n3 + 6*m1*n1**3*n2**4*n3 + 2*m1*n1*n2**6*n3)$