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