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Factorization of the Coefficient of x 8
Sean Trendell
10/16/2017

var ( 'x , a1 , a2 , a3 , a4 , b1 , b2 , b3 , b4 , p1 , p2 , p3 , p4 , q1 , q2 , q3 , q4 ' )
w0 = SR . w i l d ( 0 )
s a g e _ s e r v e r .MAX_STDOUT_SIZE=250000
s a g e _ s e r v e r .MAX_OUTPUT=250000
#This d e f i n e s our v a r i a b l e s , s e t s up our w i l d c a r d and i n c r e a s e s max output f o r \
t h e program .
(x, a1, a2, a3, a4, b1, b2, b3, b4, p1, p2, p3, p4, q1, q2, q3, q4)
E=(x - a1 * a2 * a3 * a4 ) * ( x - a1 * a2 * a3 *b4 ) * ( x - a1 * a2 *b3* a4 ) * ( x - a1 * a2 *b3*b4 ) * ( x - a1 *b2* a3 *\
a4 ) * ( x - a1 *b2* a3 *b4 ) * ( x - a1 *b2*b3* a4 ) * ( x - a1 *b2*b3*b4 ) * ( x - b1* a2 * a3 * a4 ) * ( x - b1* a2\
* a3 *b4 ) * ( x - b1* a2 *b3* a4 ) * ( x - b1* a2 *b3*b4 ) * ( x - b1*b2* a3 * a4 ) * ( x - b1*b2* a3 *b4 ) * ( x - \
b1*b2*b3* a4 ) * ( x - b1*b2*b3*b4 )
F=E . expand ( )
#M u l t i p l i c a t i o n o f t h e c h a r a c t e r i s t i c f u n c t i o n , t h i s i s not show do t o l e n g t h .
f 8=F . c o e f f i c i e n t ( x , 8 )
f8
#Ga th er in g o f t h e c o e f f i c i e n t f o r x^8 from our e x p a n s i o n o f t h e c h a r a c t e r i s t i c \
f u n c t i o n . The g e n e r a l way we work t h i s out i s f i r s t s e p a r a t e t h e c o e f f i c i e n t \
by t h e n u m e r i c a l p a r t o f each term then s e p a r a t e i t f u r t h e r i n t o managable \
g ro u p s t h a t have c l e a r s u b s t i t u t i o n .
a1^4*a2^4*a3^4*a4^8*b1^4*b2^4*b3^4 + a1^5*a2^5*a3^5*a4^7*b1^3*b2^3*b3^3*b4 +
2*a1^4*a2^5*a3^5*a4^7*b1^4*b2^3*b3^3*b4 + a1^3*a2^5*a3^5*a4^7*b1^5*b2^3*b3^3*b4 +
2*a1^5*a2^4*a3^5*a4^7*b1^3*b2^4*b3^3*b4 + 4*a1^4*a2^4*a3^5*a4^7*b1^4*b2^4*b3^3*b4 +
2*a1^3*a2^4*a3^5*a4^7*b1^5*b2^4*b3^3*b4 + a1^5*a2^3*a3^5*a4^7*b1^3*b2^5*b3^3*b4 +
2*a1^4*a2^3*a3^5*a4^7*b1^4*b2^5*b3^3*b4 + a1^3*a2^3*a3^5*a4^7*b1^5*b2^5*b3^3*b4 +
2*a1^5*a2^5*a3^4*a4^7*b1^3*b2^3*b3^4*b4 + 4*a1^4*a2^5*a3^4*a4^7*b1^4*b2^3*b3^4*b4 +
2*a1^3*a2^5*a3^4*a4^7*b1^5*b2^3*b3^4*b4 + 4*a1^5*a2^4*a3^4*a4^7*b1^3*b2^4*b3^4*b4 +
8*a1^4*a2^4*a3^4*a4^7*b1^4*b2^4*b3^4*b4 + 4*a1^3*a2^4*a3^4*a4^7*b1^5*b2^4*b3^4*b4 +
2*a1^5*a2^3*a3^4*a4^7*b1^3*b2^5*b3^4*b4 + 4*a1^4*a2^3*a3^4*a4^7*b1^4*b2^5*b3^4*b4 +
2*a1^3*a2^3*a3^4*a4^7*b1^5*b2^5*b3^4*b4 + a1^5*a2^5*a3^3*a4^7*b1^3*b2^3*b3^5*b4 +
2*a1^4*a2^5*a3^3*a4^7*b1^4*b2^3*b3^5*b4 + a1^3*a2^5*a3^3*a4^7*b1^5*b2^3*b3^5*b4 +
2*a1^5*a2^4*a3^3*a4^7*b1^3*b2^4*b3^5*b4 + 4*a1^4*a2^4*a3^3*a4^7*b1^4*b2^4*b3^5*b4 +
2*a1^3*a2^4*a3^3*a4^7*b1^5*b2^4*b3^5*b4 + a1^5*a2^3*a3^3*a4^7*b1^3*b2^5*b3^5*b4 +
2*a1^4*a2^3*a3^3*a4^7*b1^4*b2^5*b3^5*b4 + a1^3*a2^3*a3^3*a4^7*b1^5*b2^5*b3^5*b4 +
a1^4*a2^6*a3^6*a4^6*b1^4*b2^2*b3^2*b4^2 + 2*a1^5*a2^5*a3^6*a4^6*b1^3*b2^3*b3^2*b4^2 +
4*a1^4*a2^5*a3^6*a4^6*b1^4*b2^3*b3^2*b4^2 + 2*a1^3*a2^5*a3^6*a4^6*b1^5*b2^3*b3^2*b4^2 +
a1^6*a2^4*a3^6*a4^6*b1^2*b2^4*b3^2*b4^2 + 4*a1^5*a2^4*a3^6*a4^6*b1^3*b2^4*b3^2*b4^2 +
8*a1^4*a2^4*a3^6*a4^6*b1^4*b2^4*b3^2*b4^2 + 4*a1^3*a2^4*a3^6*a4^6*b1^5*b2^4*b3^2*b4^2 +
a1^2*a2^4*a3^6*a4^6*b1^6*b2^4*b3^2*b4^2 + 2*a1^5*a2^3*a3^6*a4^6*b1^3*b2^5*b3^2*b4^2 +
4*a1^4*a2^3*a3^6*a4^6*b1^4*b2^5*b3^2*b4^2 + 2*a1^3*a2^3*a3^6*a4^6*b1^5*b2^5*b3^2*b4^2 +
a1^4*a2^2*a3^6*a4^6*b1^4*b2^6*b3^2*b4^2 + 2*a1^5*a2^6*a3^5*a4^6*b1^3*b2^2*b3^3*b4^2 +
4*a1^4*a2^6*a3^5*a4^6*b1^4*b2^2*b3^3*b4^2 + 2*a1^3*a2^6*a3^5*a4^6*b1^5*b2^2*b3^3*b4^2 +
2*a1^6*a2^5*a3^5*a4^6*b1^2*b2^3*b3^3*b4^2 + 12*a1^5*a2^5*a3^5*a4^6*b1^3*b2^3*b3^3*b4^2 +
20*a1^4*a2^5*a3^5*a4^6*b1^4*b2^3*b3^3*b4^2 + 12*a1^3*a2^5*a3^5*a4^6*b1^5*b2^3*b3^3*b4^2 +
2*a1^2*a2^5*a3^5*a4^6*b1^6*b2^3*b3^3*b4^2 + 4*a1^6*a2^4*a3^5*a4^6*b1^2*b2^4*b3^3*b4^2 +
20*a1^5*a2^4*a3^5*a4^6*b1^3*b2^4*b3^3*b4^2 + 32*a1^4*a2^4*a3^5*a4^6*b1^4*b2^4*b3^3*b4^2 +
20*a1^3*a2^4*a3^5*a4^6*b1^5*b2^4*b3^3*b4^2 + 4*a1^2*a2^4*a3^5*a4^6*b1^6*b2^4*b3^3*b4^2 +

1

2*a1^6*a2^3*a3^5*a4^6*b1^2*b2^5*b3^3*b4^2 + 12*a1^5*a2^3*a3^5*a4^6*b1^3*b2^5*b3^3*b4^2 +
20*a1^4*a2^3*a3^5*a4^6*b1^4*b2^5*b3^3*b4^2 + 12*a1^3*a2^3*a3^5*a4^6*b1^5*b2^5*b3^3*b4^2 +
2*a1^2*a2^3*a3^5*a4^6*b1^6*b2^5*b3^3*b4^2 + 2*a1^5*a2^2*a3^5*a4^6*b1^3*b2^6*b3^3*b4^2 +
4*a1^4*a2^2*a3^5*a4^6*b1^4*b2^6*b3^3*b4^2 + 2*a1^3*a2^2*a3^5*a4^6*b1^5*b2^6*b3^3*b4^2 +
a1^6*a2^6*a3^4*a4^6*b1^2*b2^2*b3^4*b4^2 + 4*a1^5*a2^6*a3^4*a4^6*b1^3*b2^2*b3^4*b4^2 +
8*a1^4*a2^6*a3^4*a4^6*b1^4*b2^2*b3^4*b4^2 + 4*a1^3*a2^6*a3^4*a4^6*b1^5*b2^2*b3^4*b4^2 +
a1^2*a2^6*a3^4*a4^6*b1^6*b2^2*b3^4*b4^2 + 4*a1^6*a2^5*a3^4*a4^6*b1^2*b2^3*b3^4*b4^2 +
20*a1^5*a2^5*a3^4*a4^6*b1^3*b2^3*b3^4*b4^2 + 32*a1^4*a2^5*a3^4*a4^6*b1^4*b2^3*b3^4*b4^2 +
20*a1^3*a2^5*a3^4*a4^6*b1^5*b2^3*b3^4*b4^2 + 4*a1^2*a2^5*a3^4*a4^6*b1^6*b2^3*b3^4*b4^2 +
8*a1^6*a2^4*a3^4*a4^6*b1^2*b2^4*b3^4*b4^2 + 32*a1^5*a2^4*a3^4*a4^6*b1^3*b2^4*b3^4*b4^2 +
52*a1^4*a2^4*a3^4*a4^6*b1^4*b2^4*b3^4*b4^2 + 32*a1^3*a2^4*a3^4*a4^6*b1^5*b2^4*b3^4*b4^2 +
8*a1^2*a2^4*a3^4*a4^6*b1^6*b2^4*b3^4*b4^2 + 4*a1^6*a2^3*a3^4*a4^6*b1^2*b2^5*b3^4*b4^2 +
20*a1^5*a2^3*a3^4*a4^6*b1^3*b2^5*b3^4*b4^2 + 32*a1^4*a2^3*a3^4*a4^6*b1^4*b2^5*b3^4*b4^2 +
20*a1^3*a2^3*a3^4*a4^6*b1^5*b2^5*b3^4*b4^2 + 4*a1^2*a2^3*a3^4*a4^6*b1^6*b2^5*b3^4*b4^2 +
a1^6*a2^2*a3^4*a4^6*b1^2*b2^6*b3^4*b4^2 + 4*a1^5*a2^2*a3^4*a4^6*b1^3*b2^6*b3^4*b4^2 +
8*a1^4*a2^2*a3^4*a4^6*b1^4*b2^6*b3^4*b4^2 + 4*a1^3*a2^2*a3^4*a4^6*b1^5*b2^6*b3^4*b4^2 +
a1^2*a2^2*a3^4*a4^6*b1^6*b2^6*b3^4*b4^2 + 2*a1^5*a2^6*a3^3*a4^6*b1^3*b2^2*b3^5*b4^2 +
4*a1^4*a2^6*a3^3*a4^6*b1^4*b2^2*b3^5*b4^2 + 2*a1^3*a2^6*a3^3*a4^6*b1^5*b2^2*b3^5*b4^2 +
2*a1^6*a2^5*a3^3*a4^6*b1^2*b2^3*b3^5*b4^2 + 12*a1^5*a2^5*a3^3*a4^6*b1^3*b2^3*b3^5*b4^2 +
20*a1^4*a2^5*a3^3*a4^6*b1^4*b2^3*b3^5*b4^2 + 12*a1^3*a2^5*a3^3*a4^6*b1^5*b2^3*b3^5*b4^2 +
2*a1^2*a2^5*a3^3*a4^6*b1^6*b2^3*b3^5*b4^2 + 4*a1^6*a2^4*a3^3*a4^6*b1^2*b2^4*b3^5*b4^2 +
20*a1^5*a2^4*a3^3*a4^6*b1^3*b2^4*b3^5*b4^2 + 32*a1^4*a2^4*a3^3*a4^6*b1^4*b2^4*b3^5*b4^2 +
20*a1^3*a2^4*a3^3*a4^6*b1^5*b2^4*b3^5*b4^2 + 4*a1^2*a2^4*a3^3*a4^6*b1^6*b2^4*b3^5*b4^2 +
2*a1^6*a2^3*a3^3*a4^6*b1^2*b2^5*b3^5*b4^2 + 12*a1^5*a2^3*a3^3*a4^6*b1^3*b2^5*b3^5*b4^2 +
20*a1^4*a2^3*a3^3*a4^6*b1^4*b2^5*b3^5*b4^2 + 12*a1^3*a2^3*a3^3*a4^6*b1^5*b2^5*b3^5*b4^2 +
2*a1^2*a2^3*a3^3*a4^6*b1^6*b2^5*b3^5*b4^2 + 2*a1^5*a2^2*a3^3*a4^6*b1^3*b2^6*b3^5*b4^2 +
4*a1^4*a2^2*a3^3*a4^6*b1^4*b2^6*b3^5*b4^2 + 2*a1^3*a2^2*a3^3*a4^6*b1^5*b2^6*b3^5*b4^2 +
a1^4*a2^6*a3^2*a4^6*b1^4*b2^2*b3^6*b4^2 + 2*a1^5*a2^5*a3^2*a4^6*b1^3*b2^3*b3^6*b4^2 +
4*a1^4*a2^5*a3^2*a4^6*b1^4*b2^3*b3^6*b4^2 + 2*a1^3*a2^5*a3^2*a4^6*b1^5*b2^3*b3^6*b4^2 +
a1^6*a2^4*a3^2*a4^6*b1^2*b2^4*b3^6*b4^2 + 4*a1^5*a2^4*a3^2*a4^6*b1^3*b2^4*b3^6*b4^2 +
8*a1^4*a2^4*a3^2*a4^6*b1^4*b2^4*b3^6*b4^2 + 4*a1^3*a2^4*a3^2*a4^6*b1^5*b2^4*b3^6*b4^2 +
a1^2*a2^4*a3^2*a4^6*b1^6*b2^4*b3^6*b4^2 + 2*a1^5*a2^3*a3^2*a4^6*b1^3*b2^5*b3^6*b4^2 +
4*a1^4*a2^3*a3^2*a4^6*b1^4*b2^5*b3^6*b4^2 + 2*a1^3*a2^3*a3^2*a4^6*b1^5*b2^5*b3^6*b4^2 +
a1^4*a2^2*a3^2*a4^6*b1^4*b2^6*b3^6*b4^2 + a1^5*a2^5*a3^7*a4^5*b1^3*b2^3*b3*b4^3 +
2*a1^4*a2^5*a3^7*a4^5*b1^4*b2^3*b3*b4^3 + a1^3*a2^5*a3^7*a4^5*b1^5*b2^3*b3*b4^3 +
2*a1^5*a2^4*a3^7*a4^5*b1^3*b2^4*b3*b4^3 + 4*a1^4*a2^4*a3^7*a4^5*b1^4*b2^4*b3*b4^3 +
2*a1^3*a2^4*a3^7*a4^5*b1^5*b2^4*b3*b4^3 + a1^5*a2^3*a3^7*a4^5*b1^3*b2^5*b3*b4^3 +
2*a1^4*a2^3*a3^7*a4^5*b1^4*b2^5*b3*b4^3 + a1^3*a2^3*a3^7*a4^5*b1^5*b2^5*b3*b4^3 +
2*a1^5*a2^6*a3^6*a4^5*b1^3*b2^2*b3^2*b4^3 + 4*a1^4*a2^6*a3^6*a4^5*b1^4*b2^2*b3^2*b4^3 +
2*a1^3*a2^6*a3^6*a4^5*b1^5*b2^2*b3^2*b4^3 + 2*a1^6*a2^5*a3^6*a4^5*b1^2*b2^3*b3^2*b4^3 +
12*a1^5*a2^5*a3^6*a4^5*b1^3*b2^3*b3^2*b4^3 + 20*a1^4*a2^5*a3^6*a4^5*b1^4*b2^3*b3^2*b4^3 +
12*a1^3*a2^5*a3^6*a4^5*b1^5*b2^3*b3^2*b4^3 + 2*a1^2*a2^5*a3^6*a4^5*b1^6*b2^3*b3^2*b4^3 +
4*a1^6*a2^4*a3^6*a4^5*b1^2*b2^4*b3^2*b4^3 + 20*a1^5*a2^4*a3^6*a4^5*b1^3*b2^4*b3^2*b4^3 +
32*a1^4*a2^4*a3^6*a4^5*b1^4*b2^4*b3^2*b4^3 + 20*a1^3*a2^4*a3^6*a4^5*b1^5*b2^4*b3^2*b4^3 +
4*a1^2*a2^4*a3^6*a4^5*b1^6*b2^4*b3^2*b4^3 + 2*a1^6*a2^3*a3^6*a4^5*b1^2*b2^5*b3^2*b4^3 +
12*a1^5*a2^3*a3^6*a4^5*b1^3*b2^5*b3^2*b4^3 + 20*a1^4*a2^3*a3^6*a4^5*b1^4*b2^5*b3^2*b4^3 +
12*a1^3*a2^3*a3^6*a4^5*b1^5*b2^5*b3^2*b4^3 + 2*a1^2*a2^3*a3^6*a4^5*b1^6*b2^5*b3^2*b4^3 +
2*a1^5*a2^2*a3^6*a4^5*b1^3*b2^6*b3^2*b4^3 + 4*a1^4*a2^2*a3^6*a4^5*b1^4*b2^6*b3^2*b4^3 +
2*a1^3*a2^2*a3^6*a4^5*b1^5*b2^6*b3^2*b4^3 + a1^5*a2^7*a3^5*a4^5*b1^3*b2*b3^3*b4^3 +
2*a1^4*a2^7*a3^5*a4^5*b1^4*b2*b3^3*b4^3 + a1^3*a2^7*a3^5*a4^5*b1^5*b2*b3^3*b4^3 +
2*a1^6*a2^6*a3^5*a4^5*b1^2*b2^2*b3^3*b4^3 + 12*a1^5*a2^6*a3^5*a4^5*b1^3*b2^2*b3^3*b4^3 +
20*a1^4*a2^6*a3^5*a4^5*b1^4*b2^2*b3^3*b4^3 + 12*a1^3*a2^6*a3^5*a4^5*b1^5*b2^2*b3^3*b4^3 +
2*a1^2*a2^6*a3^5*a4^5*b1^6*b2^2*b3^3*b4^3 + a1^7*a2^5*a3^5*a4^5*b1*b2^3*b3^3*b4^3 +
12*a1^6*a2^5*a3^5*a4^5*b1^2*b2^3*b3^3*b4^3 + 46*a1^5*a2^5*a3^5*a4^5*b1^3*b2^3*b3^3*b4^3 +
70*a1^4*a2^5*a3^5*a4^5*b1^4*b2^3*b3^3*b4^3 + 46*a1^3*a2^5*a3^5*a4^5*b1^5*b2^3*b3^3*b4^3 +
12*a1^2*a2^5*a3^5*a4^5*b1^6*b2^3*b3^3*b4^3 + a1*a2^5*a3^5*a4^5*b1^7*b2^3*b3^3*b4^3 +
2*a1^7*a2^4*a3^5*a4^5*b1*b2^4*b3^3*b4^3 + 20*a1^6*a2^4*a3^5*a4^5*b1^2*b2^4*b3^3*b4^3 +
70*a1^5*a2^4*a3^5*a4^5*b1^3*b2^4*b3^3*b4^3 + 104*a1^4*a2^4*a3^5*a4^5*b1^4*b2^4*b3^3*b4^3 +
70*a1^3*a2^4*a3^5*a4^5*b1^5*b2^4*b3^3*b4^3 + 20*a1^2*a2^4*a3^5*a4^5*b1^6*b2^4*b3^3*b4^3 +
2*a1*a2^4*a3^5*a4^5*b1^7*b2^4*b3^3*b4^3 + a1^7*a2^3*a3^5*a4^5*b1*b2^5*b3^3*b4^3 +
12*a1^6*a2^3*a3^5*a4^5*b1^2*b2^5*b3^3*b4^3 + 46*a1^5*a2^3*a3^5*a4^5*b1^3*b2^5*b3^3*b4^3 +

2

70*a1^4*a2^3*a3^5*a4^5*b1^4*b2^5*b3^3*b4^3 + 46*a1^3*a2^3*a3^5*a4^5*b1^5*b2^5*b3^3*b4^3 +
12*a1^2*a2^3*a3^5*a4^5*b1^6*b2^5*b3^3*b4^3 + a1*a2^3*a3^5*a4^5*b1^7*b2^5*b3^3*b4^3 +
2*a1^6*a2^2*a3^5*a4^5*b1^2*b2^6*b3^3*b4^3 + 12*a1^5*a2^2*a3^5*a4^5*b1^3*b2^6*b3^3*b4^3 +
20*a1^4*a2^2*a3^5*a4^5*b1^4*b2^6*b3^3*b4^3 + 12*a1^3*a2^2*a3^5*a4^5*b1^5*b2^6*b3^3*b4^3 +
2*a1^2*a2^2*a3^5*a4^5*b1^6*b2^6*b3^3*b4^3 + a1^5*a2*a3^5*a4^5*b1^3*b2^7*b3^3*b4^3 +
2*a1^4*a2*a3^5*a4^5*b1^4*b2^7*b3^3*b4^3 + a1^3*a2*a3^5*a4^5*b1^5*b2^7*b3^3*b4^3 +
2*a1^5*a2^7*a3^4*a4^5*b1^3*b2*b3^4*b4^3 + 4*a1^4*a2^7*a3^4*a4^5*b1^4*b2*b3^4*b4^3 +
2*a1^3*a2^7*a3^4*a4^5*b1^5*b2*b3^4*b4^3 + 4*a1^6*a2^6*a3^4*a4^5*b1^2*b2^2*b3^4*b4^3 +
20*a1^5*a2^6*a3^4*a4^5*b1^3*b2^2*b3^4*b4^3 + 32*a1^4*a2^6*a3^4*a4^5*b1^4*b2^2*b3^4*b4^3 +
20*a1^3*a2^6*a3^4*a4^5*b1^5*b2^2*b3^4*b4^3 + 4*a1^2*a2^6*a3^4*a4^5*b1^6*b2^2*b3^4*b4^3 +
2*a1^7*a2^5*a3^4*a4^5*b1*b2^3*b3^4*b4^3 + 20*a1^6*a2^5*a3^4*a4^5*b1^2*b2^3*b3^4*b4^3 +
70*a1^5*a2^5*a3^4*a4^5*b1^3*b2^3*b3^4*b4^3 + 104*a1^4*a2^5*a3^4*a4^5*b1^4*b2^3*b3^4*b4^3 +
70*a1^3*a2^5*a3^4*a4^5*b1^5*b2^3*b3^4*b4^3 + 20*a1^2*a2^5*a3^4*a4^5*b1^6*b2^3*b3^4*b4^3 +
2*a1*a2^5*a3^4*a4^5*b1^7*b2^3*b3^4*b4^3 + 4*a1^7*a2^4*a3^4*a4^5*b1*b2^4*b3^4*b4^3 +
32*a1^6*a2^4*a3^4*a4^5*b1^2*b2^4*b3^4*b4^3 + 104*a1^5*a2^4*a3^4*a4^5*b1^3*b2^4*b3^4*b4^3 +
152*a1^4*a2^4*a3^4*a4^5*b1^4*b2^4*b3^4*b4^3 + 104*a1^3*a2^4*a3^4*a4^5*b1^5*b2^4*b3^4*b4^3
+ 32*a1^2*a2^4*a3^4*a4^5*b1^6*b2^4*b3^4*b4^3 + 4*a1*a2^4*a3^4*a4^5*b1^7*b2^4*b3^4*b4^3 +
2*a1^7*a2^3*a3^4*a4^5*b1*b2^5*b3^4*b4^3 + 20*a1^6*a2^3*a3^4*a4^5*b1^2*b2^5*b3^4*b4^3 +
70*a1^5*a2^3*a3^4*a4^5*b1^3*b2^5*b3^4*b4^3 + 104*a1^4*a2^3*a3^4*a4^5*b1^4*b2^5*b3^4*b4^3 +
70*a1^3*a2^3*a3^4*a4^5*b1^5*b2^5*b3^4*b4^3 + 20*a1^2*a2^3*a3^4*a4^5*b1^6*b2^5*b3^4*b4^3 +
2*a1*a2^3*a3^4*a4^5*b1^7*b2^5*b3^4*b4^3 + 4*a1^6*a2^2*a3^4*a4^5*b1^2*b2^6*b3^4*b4^3 +
20*a1^5*a2^2*a3^4*a4^5*b1^3*b2^6*b3^4*b4^3 + 32*a1^4*a2^2*a3^4*a4^5*b1^4*b2^6*b3^4*b4^3 +
20*a1^3*a2^2*a3^4*a4^5*b1^5*b2^6*b3^4*b4^3 + 4*a1^2*a2^2*a3^4*a4^5*b1^6*b2^6*b3^4*b4^3 +
2*a1^5*a2*a3^4*a4^5*b1^3*b2^7*b3^4*b4^3 + 4*a1^4*a2*a3^4*a4^5*b1^4*b2^7*b3^4*b4^3 +
2*a1^3*a2*a3^4*a4^5*b1^5*b2^7*b3^4*b4^3 + a1^5*a2^7*a3^3*a4^5*b1^3*b2*b3^5*b4^3 +
2*a1^4*a2^7*a3^3*a4^5*b1^4*b2*b3^5*b4^3 + a1^3*a2^7*a3^3*a4^5*b1^5*b2*b3^5*b4^3 +
2*a1^6*a2^6*a3^3*a4^5*b1^2*b2^2*b3^5*b4^3 + 12*a1^5*a2^6*a3^3*a4^5*b1^3*b2^2*b3^5*b4^3 +
20*a1^4*a2^6*a3^3*a4^5*b1^4*b2^2*b3^5*b4^3 + 12*a1^3*a2^6*a3^3*a4^5*b1^5*b2^2*b3^5*b4^3 +
2*a1^2*a2^6*a3^3*a4^5*b1^6*b2^2*b3^5*b4^3 + a1^7*a2^5*a3^3*a4^5*b1*b2^3*b3^5*b4^3 +
12*a1^6*a2^5*a3^3*a4^5*b1^2*b2^3*b3^5*b4^3 + 46*a1^5*a2^5*a3^3*a4^5*b1^3*b2^3*b3^5*b4^3 +
70*a1^4*a2^5*a3^3*a4^5*b1^4*b2^3*b3^5*b4^3 + 46*a1^3*a2^5*a3^3*a4^5*b1^5*b2^3*b3^5*b4^3 +
12*a1^2*a2^5*a3^3*a4^5*b1^6*b2^3*b3^5*b4^3 + a1*a2^5*a3^3*a4^5*b1^7*b2^3*b3^5*b4^3 +
2*a1^7*a2^4*a3^3*a4^5*b1*b2^4*b3^5*b4^3 + 20*a1^6*a2^4*a3^3*a4^5*b1^2*b2^4*b3^5*b4^3 +
70*a1^5*a2^4*a3^3*a4^5*b1^3*b2^4*b3^5*b4^3 + 104*a1^4*a2^4*a3^3*a4^5*b1^4*b2^4*b3^5*b4^3 +
70*a1^3*a2^4*a3^3*a4^5*b1^5*b2^4*b3^5*b4^3 + 20*a1^2*a2^4*a3^3*a4^5*b1^6*b2^4*b3^5*b4^3 +
2*a1*a2^4*a3^3*a4^5*b1^7*b2^4*b3^5*b4^3 + a1^7*a2^3*a3^3*a4^5*b1*b2^5*b3^5*b4^3 +
12*a1^6*a2^3*a3^3*a4^5*b1^2*b2^5*b3^5*b4^3 + 46*a1^5*a2^3*a3^3*a4^5*b1^3*b2^5*b3^5*b4^3 +
70*a1^4*a2^3*a3^3*a4^5*b1^4*b2^5*b3^5*b4^3 + 46*a1^3*a2^3*a3^3*a4^5*b1^5*b2^5*b3^5*b4^3 +
12*a1^2*a2^3*a3^3*a4^5*b1^6*b2^5*b3^5*b4^3 + a1*a2^3*a3^3*a4^5*b1^7*b2^5*b3^5*b4^3 +
2*a1^6*a2^2*a3^3*a4^5*b1^2*b2^6*b3^5*b4^3 + 12*a1^5*a2^2*a3^3*a4^5*b1^3*b2^6*b3^5*b4^3 +
20*a1^4*a2^2*a3^3*a4^5*b1^4*b2^6*b3^5*b4^3 + 12*a1^3*a2^2*a3^3*a4^5*b1^5*b2^6*b3^5*b4^3 +
2*a1^2*a2^2*a3^3*a4^5*b1^6*b2^6*b3^5*b4^3 + a1^5*a2*a3^3*a4^5*b1^3*b2^7*b3^5*b4^3 +
2*a1^4*a2*a3^3*a4^5*b1^4*b2^7*b3^5*b4^3 + a1^3*a2*a3^3*a4^5*b1^5*b2^7*b3^5*b4^3 +
2*a1^5*a2^6*a3^2*a4^5*b1^3*b2^2*b3^6*b4^3 + 4*a1^4*a2^6*a3^2*a4^5*b1^4*b2^2*b3^6*b4^3 +
2*a1^3*a2^6*a3^2*a4^5*b1^5*b2^2*b3^6*b4^3 + 2*a1^6*a2^5*a3^2*a4^5*b1^2*b2^3*b3^6*b4^3 +
12*a1^5*a2^5*a3^2*a4^5*b1^3*b2^3*b3^6*b4^3 + 20*a1^4*a2^5*a3^2*a4^5*b1^4*b2^3*b3^6*b4^3 +
12*a1^3*a2^5*a3^2*a4^5*b1^5*b2^3*b3^6*b4^3 + 2*a1^2*a2^5*a3^2*a4^5*b1^6*b2^3*b3^6*b4^3 +
4*a1^6*a2^4*a3^2*a4^5*b1^2*b2^4*b3^6*b4^3 + 20*a1^5*a2^4*a3^2*a4^5*b1^3*b2^4*b3^6*b4^3 +
32*a1^4*a2^4*a3^2*a4^5*b1^4*b2^4*b3^6*b4^3 + 20*a1^3*a2^4*a3^2*a4^5*b1^5*b2^4*b3^6*b4^3 +
4*a1^2*a2^4*a3^2*a4^5*b1^6*b2^4*b3^6*b4^3 + 2*a1^6*a2^3*a3^2*a4^5*b1^2*b2^5*b3^6*b4^3 +
12*a1^5*a2^3*a3^2*a4^5*b1^3*b2^5*b3^6*b4^3 + 20*a1^4*a2^3*a3^2*a4^5*b1^4*b2^5*b3^6*b4^3 +
12*a1^3*a2^3*a3^2*a4^5*b1^5*b2^5*b3^6*b4^3 + 2*a1^2*a2^3*a3^2*a4^5*b1^6*b2^5*b3^6*b4^3 +
2*a1^5*a2^2*a3^2*a4^5*b1^3*b2^6*b3^6*b4^3 + 4*a1^4*a2^2*a3^2*a4^5*b1^4*b2^6*b3^6*b4^3 +
2*a1^3*a2^2*a3^2*a4^5*b1^5*b2^6*b3^6*b4^3 + a1^5*a2^5*a3*a4^5*b1^3*b2^3*b3^7*b4^3 +
2*a1^4*a2^5*a3*a4^5*b1^4*b2^3*b3^7*b4^3 + a1^3*a2^5*a3*a4^5*b1^5*b2^3*b3^7*b4^3 +
2*a1^5*a2^4*a3*a4^5*b1^3*b2^4*b3^7*b4^3 + 4*a1^4*a2^4*a3*a4^5*b1^4*b2^4*b3^7*b4^3 +
2*a1^3*a2^4*a3*a4^5*b1^5*b2^4*b3^7*b4^3 + a1^5*a2^3*a3*a4^5*b1^3*b2^5*b3^7*b4^3 +
2*a1^4*a2^3*a3*a4^5*b1^4*b2^5*b3^7*b4^3 + a1^3*a2^3*a3*a4^5*b1^5*b2^5*b3^7*b4^3 +
a1^4*a2^4*a3^8*a4^4*b1^4*b2^4*b4^4 + 2*a1^5*a2^5*a3^7*a4^4*b1^3*b2^3*b3*b4^4 +
4*a1^4*a2^5*a3^7*a4^4*b1^4*b2^3*b3*b4^4 + 2*a1^3*a2^5*a3^7*a4^4*b1^5*b2^3*b3*b4^4 +
4*a1^5*a2^4*a3^7*a4^4*b1^3*b2^4*b3*b4^4 + 8*a1^4*a2^4*a3^7*a4^4*b1^4*b2^4*b3*b4^4 +

3

4*a1^3*a2^4*a3^7*a4^4*b1^5*b2^4*b3*b4^4 + 2*a1^5*a2^3*a3^7*a4^4*b1^3*b2^5*b3*b4^4 +
4*a1^4*a2^3*a3^7*a4^4*b1^4*b2^5*b3*b4^4 + 2*a1^3*a2^3*a3^7*a4^4*b1^5*b2^5*b3*b4^4 +
a1^6*a2^6*a3^6*a4^4*b1^2*b2^2*b3^2*b4^4 + 4*a1^5*a2^6*a3^6*a4^4*b1^3*b2^2*b3^2*b4^4 +
8*a1^4*a2^6*a3^6*a4^4*b1^4*b2^2*b3^2*b4^4 + 4*a1^3*a2^6*a3^6*a4^4*b1^5*b2^2*b3^2*b4^4 +
a1^2*a2^6*a3^6*a4^4*b1^6*b2^2*b3^2*b4^4 + 4*a1^6*a2^5*a3^6*a4^4*b1^2*b2^3*b3^2*b4^4 +
20*a1^5*a2^5*a3^6*a4^4*b1^3*b2^3*b3^2*b4^4 + 32*a1^4*a2^5*a3^6*a4^4*b1^4*b2^3*b3^2*b4^4 +
20*a1^3*a2^5*a3^6*a4^4*b1^5*b2^3*b3^2*b4^4 + 4*a1^2*a2^5*a3^6*a4^4*b1^6*b2^3*b3^2*b4^4 +
8*a1^6*a2^4*a3^6*a4^4*b1^2*b2^4*b3^2*b4^4 + 32*a1^5*a2^4*a3^6*a4^4*b1^3*b2^4*b3^2*b4^4 +
52*a1^4*a2^4*a3^6*a4^4*b1^4*b2^4*b3^2*b4^4 + 32*a1^3*a2^4*a3^6*a4^4*b1^5*b2^4*b3^2*b4^4 +
8*a1^2*a2^4*a3^6*a4^4*b1^6*b2^4*b3^2*b4^4 + 4*a1^6*a2^3*a3^6*a4^4*b1^2*b2^5*b3^2*b4^4 +
20*a1^5*a2^3*a3^6*a4^4*b1^3*b2^5*b3^2*b4^4 + 32*a1^4*a2^3*a3^6*a4^4*b1^4*b2^5*b3^2*b4^4 +
20*a1^3*a2^3*a3^6*a4^4*b1^5*b2^5*b3^2*b4^4 + 4*a1^2*a2^3*a3^6*a4^4*b1^6*b2^5*b3^2*b4^4 +
a1^6*a2^2*a3^6*a4^4*b1^2*b2^6*b3^2*b4^4 + 4*a1^5*a2^2*a3^6*a4^4*b1^3*b2^6*b3^2*b4^4 +
8*a1^4*a2^2*a3^6*a4^4*b1^4*b2^6*b3^2*b4^4 + 4*a1^3*a2^2*a3^6*a4^4*b1^5*b2^6*b3^2*b4^4 +
a1^2*a2^2*a3^6*a4^4*b1^6*b2^6*b3^2*b4^4 + 2*a1^5*a2^7*a3^5*a4^4*b1^3*b2*b3^3*b4^4 +
4*a1^4*a2^7*a3^5*a4^4*b1^4*b2*b3^3*b4^4 + 2*a1^3*a2^7*a3^5*a4^4*b1^5*b2*b3^3*b4^4 +
4*a1^6*a2^6*a3^5*a4^4*b1^2*b2^2*b3^3*b4^4 + 20*a1^5*a2^6*a3^5*a4^4*b1^3*b2^2*b3^3*b4^4 +
32*a1^4*a2^6*a3^5*a4^4*b1^4*b2^2*b3^3*b4^4 + 20*a1^3*a2^6*a3^5*a4^4*b1^5*b2^2*b3^3*b4^4 +
4*a1^2*a2^6*a3^5*a4^4*b1^6*b2^2*b3^3*b4^4 + 2*a1^7*a2^5*a3^5*a4^4*b1*b2^3*b3^3*b4^4 +
20*a1^6*a2^5*a3^5*a4^4*b1^2*b2^3*b3^3*b4^4 + 70*a1^5*a2^5*a3^5*a4^4*b1^3*b2^3*b3^3*b4^4 +
104*a1^4*a2^5*a3^5*a4^4*b1^4*b2^3*b3^3*b4^4 + 70*a1^3*a2^5*a3^5*a4^4*b1^5*b2^3*b3^3*b4^4 +
20*a1^2*a2^5*a3^5*a4^4*b1^6*b2^3*b3^3*b4^4 + 2*a1*a2^5*a3^5*a4^4*b1^7*b2^3*b3^3*b4^4 +
4*a1^7*a2^4*a3^5*a4^4*b1*b2^4*b3^3*b4^4 + 32*a1^6*a2^4*a3^5*a4^4*b1^2*b2^4*b3^3*b4^4 +
104*a1^5*a2^4*a3^5*a4^4*b1^3*b2^4*b3^3*b4^4 + 152*a1^4*a2^4*a3^5*a4^4*b1^4*b2^4*b3^3*b4^4
+ 104*a1^3*a2^4*a3^5*a4^4*b1^5*b2^4*b3^3*b4^4 + 32*a1^2*a2^4*a3^5*a4^4*b1^6*b2^4*b3^3*b4^4
+ 4*a1*a2^4*a3^5*a4^4*b1^7*b2^4*b3^3*b4^4 + 2*a1^7*a2^3*a3^5*a4^4*b1*b2^5*b3^3*b4^4 +
20*a1^6*a2^3*a3^5*a4^4*b1^2*b2^5*b3^3*b4^4 + 70*a1^5*a2^3*a3^5*a4^4*b1^3*b2^5*b3^3*b4^4 +
104*a1^4*a2^3*a3^5*a4^4*b1^4*b2^5*b3^3*b4^4 + 70*a1^3*a2^3*a3^5*a4^4*b1^5*b2^5*b3^3*b4^4 +
20*a1^2*a2^3*a3^5*a4^4*b1^6*b2^5*b3^3*b4^4 + 2*a1*a2^3*a3^5*a4^4*b1^7*b2^5*b3^3*b4^4 +
4*a1^6*a2^2*a3^5*a4^4*b1^2*b2^6*b3^3*b4^4 + 20*a1^5*a2^2*a3^5*a4^4*b1^3*b2^6*b3^3*b4^4 +
32*a1^4*a2^2*a3^5*a4^4*b1^4*b2^6*b3^3*b4^4 + 20*a1^3*a2^2*a3^5*a4^4*b1^5*b2^6*b3^3*b4^4 +
4*a1^2*a2^2*a3^5*a4^4*b1^6*b2^6*b3^3*b4^4 + 2*a1^5*a2*a3^5*a4^4*b1^3*b2^7*b3^3*b4^4 +
4*a1^4*a2*a3^5*a4^4*b1^4*b2^7*b3^3*b4^4 + 2*a1^3*a2*a3^5*a4^4*b1^5*b2^7*b3^3*b4^4 +
a1^4*a2^8*a3^4*a4^4*b1^4*b3^4*b4^4 + 4*a1^5*a2^7*a3^4*a4^4*b1^3*b2*b3^4*b4^4 +
8*a1^4*a2^7*a3^4*a4^4*b1^4*b2*b3^4*b4^4 + 4*a1^3*a2^7*a3^4*a4^4*b1^5*b2*b3^4*b4^4 +
8*a1^6*a2^6*a3^4*a4^4*b1^2*b2^2*b3^4*b4^4 + 32*a1^5*a2^6*a3^4*a4^4*b1^3*b2^2*b3^4*b4^4 +
52*a1^4*a2^6*a3^4*a4^4*b1^4*b2^2*b3^4*b4^4 + 32*a1^3*a2^6*a3^4*a4^4*b1^5*b2^2*b3^4*b4^4 +
8*a1^2*a2^6*a3^4*a4^4*b1^6*b2^2*b3^4*b4^4 + 4*a1^7*a2^5*a3^4*a4^4*b1*b2^3*b3^4*b4^4 +
32*a1^6*a2^5*a3^4*a4^4*b1^2*b2^3*b3^4*b4^4 + 104*a1^5*a2^5*a3^4*a4^4*b1^3*b2^3*b3^4*b4^4 +
152*a1^4*a2^5*a3^4*a4^4*b1^4*b2^3*b3^4*b4^4 + 104*a1^3*a2^5*a3^4*a4^4*b1^5*b2^3*b3^4*b4^4
+ 32*a1^2*a2^5*a3^4*a4^4*b1^6*b2^3*b3^4*b4^4 + 4*a1*a2^5*a3^4*a4^4*b1^7*b2^3*b3^4*b4^4 +
a1^8*a2^4*a3^4*a4^4*b2^4*b3^4*b4^4 + 8*a1^7*a2^4*a3^4*a4^4*b1*b2^4*b3^4*b4^4 +
52*a1^6*a2^4*a3^4*a4^4*b1^2*b2^4*b3^4*b4^4 + 152*a1^5*a2^4*a3^4*a4^4*b1^3*b2^4*b3^4*b4^4 +
222*a1^4*a2^4*a3^4*a4^4*b1^4*b2^4*b3^4*b4^4 + 152*a1^3*a2^4*a3^4*a4^4*b1^5*b2^4*b3^4*b4^4
+ 52*a1^2*a2^4*a3^4*a4^4*b1^6*b2^4*b3^4*b4^4 + 8*a1*a2^4*a3^4*a4^4*b1^7*b2^4*b3^4*b4^4 +
a2^4*a3^4*a4^4*b1^8*b2^4*b3^4*b4^4 + 4*a1^7*a2^3*a3^4*a4^4*b1*b2^5*b3^4*b4^4 +
32*a1^6*a2^3*a3^4*a4^4*b1^2*b2^5*b3^4*b4^4 + 104*a1^5*a2^3*a3^4*a4^4*b1^3*b2^5*b3^4*b4^4 +
152*a1^4*a2^3*a3^4*a4^4*b1^4*b2^5*b3^4*b4^4 + 104*a1^3*a2^3*a3^4*a4^4*b1^5*b2^5*b3^4*b4^4
+ 32*a1^2*a2^3*a3^4*a4^4*b1^6*b2^5*b3^4*b4^4 + 4*a1*a2^3*a3^4*a4^4*b1^7*b2^5*b3^4*b4^4 +
8*a1^6*a2^2*a3^4*a4^4*b1^2*b2^6*b3^4*b4^4 + 32*a1^5*a2^2*a3^4*a4^4*b1^3*b2^6*b3^4*b4^4 +
52*a1^4*a2^2*a3^4*a4^4*b1^4*b2^6*b3^4*b4^4 + 32*a1^3*a2^2*a3^4*a4^4*b1^5*b2^6*b3^4*b4^4 +
8*a1^2*a2^2*a3^4*a4^4*b1^6*b2^6*b3^4*b4^4 + 4*a1^5*a2*a3^4*a4^4*b1^3*b2^7*b3^4*b4^4 +
8*a1^4*a2*a3^4*a4^4*b1^4*b2^7*b3^4*b4^4 + 4*a1^3*a2*a3^4*a4^4*b1^5*b2^7*b3^4*b4^4 +
a1^4*a3^4*a4^4*b1^4*b2^8*b3^4*b4^4 + 2*a1^5*a2^7*a3^3*a4^4*b1^3*b2*b3^5*b4^4 +
4*a1^4*a2^7*a3^3*a4^4*b1^4*b2*b3^5*b4^4 + 2*a1^3*a2^7*a3^3*a4^4*b1^5*b2*b3^5*b4^4 +
4*a1^6*a2^6*a3^3*a4^4*b1^2*b2^2*b3^5*b4^4 + 20*a1^5*a2^6*a3^3*a4^4*b1^3*b2^2*b3^5*b4^4 +
32*a1^4*a2^6*a3^3*a4^4*b1^4*b2^2*b3^5*b4^4 + 20*a1^3*a2^6*a3^3*a4^4*b1^5*b2^2*b3^5*b4^4 +
4*a1^2*a2^6*a3^3*a4^4*b1^6*b2^2*b3^5*b4^4 + 2*a1^7*a2^5*a3^3*a4^4*b1*b2^3*b3^5*b4^4 +
20*a1^6*a2^5*a3^3*a4^4*b1^2*b2^3*b3^5*b4^4 + 70*a1^5*a2^5*a3^3*a4^4*b1^3*b2^3*b3^5*b4^4 +
104*a1^4*a2^5*a3^3*a4^4*b1^4*b2^3*b3^5*b4^4 + 70*a1^3*a2^5*a3^3*a4^4*b1^5*b2^3*b3^5*b4^4 +
20*a1^2*a2^5*a3^3*a4^4*b1^6*b2^3*b3^5*b4^4 + 2*a1*a2^5*a3^3*a4^4*b1^7*b2^3*b3^5*b4^4 +

4

4*a1^7*a2^4*a3^3*a4^4*b1*b2^4*b3^5*b4^4 + 32*a1^6*a2^4*a3^3*a4^4*b1^2*b2^4*b3^5*b4^4 +
104*a1^5*a2^4*a3^3*a4^4*b1^3*b2^4*b3^5*b4^4 + 152*a1^4*a2^4*a3^3*a4^4*b1^4*b2^4*b3^5*b4^4
+ 104*a1^3*a2^4*a3^3*a4^4*b1^5*b2^4*b3^5*b4^4 + 32*a1^2*a2^4*a3^3*a4^4*b1^6*b2^4*b3^5*b4^4
+ 4*a1*a2^4*a3^3*a4^4*b1^7*b2^4*b3^5*b4^4 + 2*a1^7*a2^3*a3^3*a4^4*b1*b2^5*b3^5*b4^4 +
20*a1^6*a2^3*a3^3*a4^4*b1^2*b2^5*b3^5*b4^4 + 70*a1^5*a2^3*a3^3*a4^4*b1^3*b2^5*b3^5*b4^4 +
104*a1^4*a2^3*a3^3*a4^4*b1^4*b2^5*b3^5*b4^4 + 70*a1^3*a2^3*a3^3*a4^4*b1^5*b2^5*b3^5*b4^4 +
20*a1^2*a2^3*a3^3*a4^4*b1^6*b2^5*b3^5*b4^4 + 2*a1*a2^3*a3^3*a4^4*b1^7*b2^5*b3^5*b4^4 +
4*a1^6*a2^2*a3^3*a4^4*b1^2*b2^6*b3^5*b4^4 + 20*a1^5*a2^2*a3^3*a4^4*b1^3*b2^6*b3^5*b4^4 +
32*a1^4*a2^2*a3^3*a4^4*b1^4*b2^6*b3^5*b4^4 + 20*a1^3*a2^2*a3^3*a4^4*b1^5*b2^6*b3^5*b4^4 +
4*a1^2*a2^2*a3^3*a4^4*b1^6*b2^6*b3^5*b4^4 + 2*a1^5*a2*a3^3*a4^4*b1^3*b2^7*b3^5*b4^4 +
4*a1^4*a2*a3^3*a4^4*b1^4*b2^7*b3^5*b4^4 + 2*a1^3*a2*a3^3*a4^4*b1^5*b2^7*b3^5*b4^4 +
a1^6*a2^6*a3^2*a4^4*b1^2*b2^2*b3^6*b4^4 + 4*a1^5*a2^6*a3^2*a4^4*b1^3*b2^2*b3^6*b4^4 +
8*a1^4*a2^6*a3^2*a4^4*b1^4*b2^2*b3^6*b4^4 + 4*a1^3*a2^6*a3^2*a4^4*b1^5*b2^2*b3^6*b4^4 +
a1^2*a2^6*a3^2*a4^4*b1^6*b2^2*b3^6*b4^4 + 4*a1^6*a2^5*a3^2*a4^4*b1^2*b2^3*b3^6*b4^4 +
20*a1^5*a2^5*a3^2*a4^4*b1^3*b2^3*b3^6*b4^4 + 32*a1^4*a2^5*a3^2*a4^4*b1^4*b2^3*b3^6*b4^4 +
20*a1^3*a2^5*a3^2*a4^4*b1^5*b2^3*b3^6*b4^4 + 4*a1^2*a2^5*a3^2*a4^4*b1^6*b2^3*b3^6*b4^4 +
8*a1^6*a2^4*a3^2*a4^4*b1^2*b2^4*b3^6*b4^4 + 32*a1^5*a2^4*a3^2*a4^4*b1^3*b2^4*b3^6*b4^4 +
52*a1^4*a2^4*a3^2*a4^4*b1^4*b2^4*b3^6*b4^4 + 32*a1^3*a2^4*a3^2*a4^4*b1^5*b2^4*b3^6*b4^4 +
8*a1^2*a2^4*a3^2*a4^4*b1^6*b2^4*b3^6*b4^4 + 4*a1^6*a2^3*a3^2*a4^4*b1^2*b2^5*b3^6*b4^4 +
20*a1^5*a2^3*a3^2*a4^4*b1^3*b2^5*b3^6*b4^4 + 32*a1^4*a2^3*a3^2*a4^4*b1^4*b2^5*b3^6*b4^4 +
20*a1^3*a2^3*a3^2*a4^4*b1^5*b2^5*b3^6*b4^4 + 4*a1^2*a2^3*a3^2*a4^4*b1^6*b2^5*b3^6*b4^4 +
a1^6*a2^2*a3^2*a4^4*b1^2*b2^6*b3^6*b4^4 + 4*a1^5*a2^2*a3^2*a4^4*b1^3*b2^6*b3^6*b4^4 +
8*a1^4*a2^2*a3^2*a4^4*b1^4*b2^6*b3^6*b4^4 + 4*a1^3*a2^2*a3^2*a4^4*b1^5*b2^6*b3^6*b4^4 +
a1^2*a2^2*a3^2*a4^4*b1^6*b2^6*b3^6*b4^4 + 2*a1^5*a2^5*a3*a4^4*b1^3*b2^3*b3^7*b4^4 +
4*a1^4*a2^5*a3*a4^4*b1^4*b2^3*b3^7*b4^4 + 2*a1^3*a2^5*a3*a4^4*b1^5*b2^3*b3^7*b4^4 +
4*a1^5*a2^4*a3*a4^4*b1^3*b2^4*b3^7*b4^4 + 8*a1^4*a2^4*a3*a4^4*b1^4*b2^4*b3^7*b4^4 +
4*a1^3*a2^4*a3*a4^4*b1^5*b2^4*b3^7*b4^4 + 2*a1^5*a2^3*a3*a4^4*b1^3*b2^5*b3^7*b4^4 +
4*a1^4*a2^3*a3*a4^4*b1^4*b2^5*b3^7*b4^4 + 2*a1^3*a2^3*a3*a4^4*b1^5*b2^5*b3^7*b4^4 +
a1^4*a2^4*a4^4*b1^4*b2^4*b3^8*b4^4 + a1^5*a2^5*a3^7*a4^3*b1^3*b2^3*b3*b4^5 +
2*a1^4*a2^5*a3^7*a4^3*b1^4*b2^3*b3*b4^5 + a1^3*a2^5*a3^7*a4^3*b1^5*b2^3*b3*b4^5 +
2*a1^5*a2^4*a3^7*a4^3*b1^3*b2^4*b3*b4^5 + 4*a1^4*a2^4*a3^7*a4^3*b1^4*b2^4*b3*b4^5 +
2*a1^3*a2^4*a3^7*a4^3*b1^5*b2^4*b3*b4^5 + a1^5*a2^3*a3^7*a4^3*b1^3*b2^5*b3*b4^5 +
2*a1^4*a2^3*a3^7*a4^3*b1^4*b2^5*b3*b4^5 + a1^3*a2^3*a3^7*a4^3*b1^5*b2^5*b3*b4^5 +
2*a1^5*a2^6*a3^6*a4^3*b1^3*b2^2*b3^2*b4^5 + 4*a1^4*a2^6*a3^6*a4^3*b1^4*b2^2*b3^2*b4^5 +
2*a1^3*a2^6*a3^6*a4^3*b1^5*b2^2*b3^2*b4^5 + 2*a1^6*a2^5*a3^6*a4^3*b1^2*b2^3*b3^2*b4^5 +
12*a1^5*a2^5*a3^6*a4^3*b1^3*b2^3*b3^2*b4^5 + 20*a1^4*a2^5*a3^6*a4^3*b1^4*b2^3*b3^2*b4^5 +
12*a1^3*a2^5*a3^6*a4^3*b1^5*b2^3*b3^2*b4^5 + 2*a1^2*a2^5*a3^6*a4^3*b1^6*b2^3*b3^2*b4^5 +
4*a1^6*a2^4*a3^6*a4^3*b1^2*b2^4*b3^2*b4^5 + 20*a1^5*a2^4*a3^6*a4^3*b1^3*b2^4*b3^2*b4^5 +
32*a1^4*a2^4*a3^6*a4^3*b1^4*b2^4*b3^2*b4^5 + 20*a1^3*a2^4*a3^6*a4^3*b1^5*b2^4*b3^2*b4^5 +
4*a1^2*a2^4*a3^6*a4^3*b1^6*b2^4*b3^2*b4^5 + 2*a1^6*a2^3*a3^6*a4^3*b1^2*b2^5*b3^2*b4^5 +
12*a1^5*a2^3*a3^6*a4^3*b1^3*b2^5*b3^2*b4^5 + 20*a1^4*a2^3*a3^6*a4^3*b1^4*b2^5*b3^2*b4^5 +
12*a1^3*a2^3*a3^6*a4^3*b1^5*b2^5*b3^2*b4^5 + 2*a1^2*a2^3*a3^6*a4^3*b1^6*b2^5*b3^2*b4^5 +
2*a1^5*a2^2*a3^6*a4^3*b1^3*b2^6*b3^2*b4^5 + 4*a1^4*a2^2*a3^6*a4^3*b1^4*b2^6*b3^2*b4^5 +
2*a1^3*a2^2*a3^6*a4^3*b1^5*b2^6*b3^2*b4^5 + a1^5*a2^7*a3^5*a4^3*b1^3*b2*b3^3*b4^5 +
2*a1^4*a2^7*a3^5*a4^3*b1^4*b2*b3^3*b4^5 + a1^3*a2^7*a3^5*a4^3*b1^5*b2*b3^3*b4^5 +
2*a1^6*a2^6*a3^5*a4^3*b1^2*b2^2*b3^3*b4^5 + 12*a1^5*a2^6*a3^5*a4^3*b1^3*b2^2*b3^3*b4^5 +
20*a1^4*a2^6*a3^5*a4^3*b1^4*b2^2*b3^3*b4^5 + 12*a1^3*a2^6*a3^5*a4^3*b1^5*b2^2*b3^3*b4^5 +
2*a1^2*a2^6*a3^5*a4^3*b1^6*b2^2*b3^3*b4^5 + a1^7*a2^5*a3^5*a4^3*b1*b2^3*b3^3*b4^5 +
12*a1^6*a2^5*a3^5*a4^3*b1^2*b2^3*b3^3*b4^5 + 46*a1^5*a2^5*a3^5*a4^3*b1^3*b2^3*b3^3*b4^5 +
70*a1^4*a2^5*a3^5*a4^3*b1^4*b2^3*b3^3*b4^5 + 46*a1^3*a2^5*a3^5*a4^3*b1^5*b2^3*b3^3*b4^5 +
12*a1^2*a2^5*a3^5*a4^3*b1^6*b2^3*b3^3*b4^5 + a1*a2^5*a3^5*a4^3*b1^7*b2^3*b3^3*b4^5 +
2*a1^7*a2^4*a3^5*a4^3*b1*b2^4*b3^3*b4^5 + 20*a1^6*a2^4*a3^5*a4^3*b1^2*b2^4*b3^3*b4^5 +
70*a1^5*a2^4*a3^5*a4^3*b1^3*b2^4*b3^3*b4^5 + 104*a1^4*a2^4*a3^5*a4^3*b1^4*b2^4*b3^3*b4^5 +
70*a1^3*a2^4*a3^5*a4^3*b1^5*b2^4*b3^3*b4^5 + 20*a1^2*a2^4*a3^5*a4^3*b1^6*b2^4*b3^3*b4^5 +
2*a1*a2^4*a3^5*a4^3*b1^7*b2^4*b3^3*b4^5 + a1^7*a2^3*a3^5*a4^3*b1*b2^5*b3^3*b4^5 +
12*a1^6*a2^3*a3^5*a4^3*b1^2*b2^5*b3^3*b4^5 + 46*a1^5*a2^3*a3^5*a4^3*b1^3*b2^5*b3^3*b4^5 +
70*a1^4*a2^3*a3^5*a4^3*b1^4*b2^5*b3^3*b4^5 + 46*a1^3*a2^3*a3^5*a4^3*b1^5*b2^5*b3^3*b4^5 +
12*a1^2*a2^3*a3^5*a4^3*b1^6*b2^5*b3^3*b4^5 + a1*a2^3*a3^5*a4^3*b1^7*b2^5*b3^3*b4^5 +
2*a1^6*a2^2*a3^5*a4^3*b1^2*b2^6*b3^3*b4^5 + 12*a1^5*a2^2*a3^5*a4^3*b1^3*b2^6*b3^3*b4^5 +
20*a1^4*a2^2*a3^5*a4^3*b1^4*b2^6*b3^3*b4^5 + 12*a1^3*a2^2*a3^5*a4^3*b1^5*b2^6*b3^3*b4^5 +
2*a1^2*a2^2*a3^5*a4^3*b1^6*b2^6*b3^3*b4^5 + a1^5*a2*a3^5*a4^3*b1^3*b2^7*b3^3*b4^5 +

5

2*a1^4*a2*a3^5*a4^3*b1^4*b2^7*b3^3*b4^5 + a1^3*a2*a3^5*a4^3*b1^5*b2^7*b3^3*b4^5 +
2*a1^5*a2^7*a3^4*a4^3*b1^3*b2*b3^4*b4^5 + 4*a1^4*a2^7*a3^4*a4^3*b1^4*b2*b3^4*b4^5 +
2*a1^3*a2^7*a3^4*a4^3*b1^5*b2*b3^4*b4^5 + 4*a1^6*a2^6*a3^4*a4^3*b1^2*b2^2*b3^4*b4^5 +
20*a1^5*a2^6*a3^4*a4^3*b1^3*b2^2*b3^4*b4^5 + 32*a1^4*a2^6*a3^4*a4^3*b1^4*b2^2*b3^4*b4^5 +
20*a1^3*a2^6*a3^4*a4^3*b1^5*b2^2*b3^4*b4^5 + 4*a1^2*a2^6*a3^4*a4^3*b1^6*b2^2*b3^4*b4^5 +
2*a1^7*a2^5*a3^4*a4^3*b1*b2^3*b3^4*b4^5 + 20*a1^6*a2^5*a3^4*a4^3*b1^2*b2^3*b3^4*b4^5 +
70*a1^5*a2^5*a3^4*a4^3*b1^3*b2^3*b3^4*b4^5 + 104*a1^4*a2^5*a3^4*a4^3*b1^4*b2^3*b3^4*b4^5 +
70*a1^3*a2^5*a3^4*a4^3*b1^5*b2^3*b3^4*b4^5 + 20*a1^2*a2^5*a3^4*a4^3*b1^6*b2^3*b3^4*b4^5 +
2*a1*a2^5*a3^4*a4^3*b1^7*b2^3*b3^4*b4^5 + 4*a1^7*a2^4*a3^4*a4^3*b1*b2^4*b3^4*b4^5 +
32*a1^6*a2^4*a3^4*a4^3*b1^2*b2^4*b3^4*b4^5 + 104*a1^5*a2^4*a3^4*a4^3*b1^3*b2^4*b3^4*b4^5 +
152*a1^4*a2^4*a3^4*a4^3*b1^4*b2^4*b3^4*b4^5 + 104*a1^3*a2^4*a3^4*a4^3*b1^5*b2^4*b3^4*b4^5
+ 32*a1^2*a2^4*a3^4*a4^3*b1^6*b2^4*b3^4*b4^5 + 4*a1*a2^4*a3^4*a4^3*b1^7*b2^4*b3^4*b4^5 +
2*a1^7*a2^3*a3^4*a4^3*b1*b2^5*b3^4*b4^5 + 20*a1^6*a2^3*a3^4*a4^3*b1^2*b2^5*b3^4*b4^5 +
70*a1^5*a2^3*a3^4*a4^3*b1^3*b2^5*b3^4*b4^5 + 104*a1^4*a2^3*a3^4*a4^3*b1^4*b2^5*b3^4*b4^5 +
70*a1^3*a2^3*a3^4*a4^3*b1^5*b2^5*b3^4*b4^5 + 20*a1^2*a2^3*a3^4*a4^3*b1^6*b2^5*b3^4*b4^5 +
2*a1*a2^3*a3^4*a4^3*b1^7*b2^5*b3^4*b4^5 + 4*a1^6*a2^2*a3^4*a4^3*b1^2*b2^6*b3^4*b4^5 +
20*a1^5*a2^2*a3^4*a4^3*b1^3*b2^6*b3^4*b4^5 + 32*a1^4*a2^2*a3^4*a4^3*b1^4*b2^6*b3^4*b4^5 +
20*a1^3*a2^2*a3^4*a4^3*b1^5*b2^6*b3^4*b4^5 + 4*a1^2*a2^2*a3^4*a4^3*b1^6*b2^6*b3^4*b4^5 +
2*a1^5*a2*a3^4*a4^3*b1^3*b2^7*b3^4*b4^5 + 4*a1^4*a2*a3^4*a4^3*b1^4*b2^7*b3^4*b4^5 +
2*a1^3*a2*a3^4*a4^3*b1^5*b2^7*b3^4*b4^5 + a1^5*a2^7*a3^3*a4^3*b1^3*b2*b3^5*b4^5 +
2*a1^4*a2^7*a3^3*a4^3*b1^4*b2*b3^5*b4^5 + a1^3*a2^7*a3^3*a4^3*b1^5*b2*b3^5*b4^5 +
2*a1^6*a2^6*a3^3*a4^3*b1^2*b2^2*b3^5*b4^5 + 12*a1^5*a2^6*a3^3*a4^3*b1^3*b2^2*b3^5*b4^5 +
20*a1^4*a2^6*a3^3*a4^3*b1^4*b2^2*b3^5*b4^5 + 12*a1^3*a2^6*a3^3*a4^3*b1^5*b2^2*b3^5*b4^5 +
2*a1^2*a2^6*a3^3*a4^3*b1^6*b2^2*b3^5*b4^5 + a1^7*a2^5*a3^3*a4^3*b1*b2^3*b3^5*b4^5 +
12*a1^6*a2^5*a3^3*a4^3*b1^2*b2^3*b3^5*b4^5 + 46*a1^5*a2^5*a3^3*a4^3*b1^3*b2^3*b3^5*b4^5 +
70*a1^4*a2^5*a3^3*a4^3*b1^4*b2^3*b3^5*b4^5 + 46*a1^3*a2^5*a3^3*a4^3*b1^5*b2^3*b3^5*b4^5 +
12*a1^2*a2^5*a3^3*a4^3*b1^6*b2^3*b3^5*b4^5 + a1*a2^5*a3^3*a4^3*b1^7*b2^3*b3^5*b4^5 +
2*a1^7*a2^4*a3^3*a4^3*b1*b2^4*b3^5*b4^5 + 20*a1^6*a2^4*a3^3*a4^3*b1^2*b2^4*b3^5*b4^5 +
70*a1^5*a2^4*a3^3*a4^3*b1^3*b2^4*b3^5*b4^5 + 104*a1^4*a2^4*a3^3*a4^3*b1^4*b2^4*b3^5*b4^5 +
70*a1^3*a2^4*a3^3*a4^3*b1^5*b2^4*b3^5*b4^5 + 20*a1^2*a2^4*a3^3*a4^3*b1^6*b2^4*b3^5*b4^5 +
2*a1*a2^4*a3^3*a4^3*b1^7*b2^4*b3^5*b4^5 + a1^7*a2^3*a3^3*a4^3*b1*b2^5*b3^5*b4^5 +
12*a1^6*a2^3*a3^3*a4^3*b1^2*b2^5*b3^5*b4^5 + 46*a1^5*a2^3*a3^3*a4^3*b1^3*b2^5*b3^5*b4^5 +
70*a1^4*a2^3*a3^3*a4^3*b1^4*b2^5*b3^5*b4^5 + 46*a1^3*a2^3*a3^3*a4^3*b1^5*b2^5*b3^5*b4^5 +
12*a1^2*a2^3*a3^3*a4^3*b1^6*b2^5*b3^5*b4^5 + a1*a2^3*a3^3*a4^3*b1^7*b2^5*b3^5*b4^5 +
2*a1^6*a2^2*a3^3*a4^3*b1^2*b2^6*b3^5*b4^5 + 12*a1^5*a2^2*a3^3*a4^3*b1^3*b2^6*b3^5*b4^5 +
20*a1^4*a2^2*a3^3*a4^3*b1^4*b2^6*b3^5*b4^5 + 12*a1^3*a2^2*a3^3*a4^3*b1^5*b2^6*b3^5*b4^5 +
2*a1^2*a2^2*a3^3*a4^3*b1^6*b2^6*b3^5*b4^5 + a1^5*a2*a3^3*a4^3*b1^3*b2^7*b3^5*b4^5 +
2*a1^4*a2*a3^3*a4^3*b1^4*b2^7*b3^5*b4^5 + a1^3*a2*a3^3*a4^3*b1^5*b2^7*b3^5*b4^5 +
2*a1^5*a2^6*a3^2*a4^3*b1^3*b2^2*b3^6*b4^5 + 4*a1^4*a2^6*a3^2*a4^3*b1^4*b2^2*b3^6*b4^5 +
2*a1^3*a2^6*a3^2*a4^3*b1^5*b2^2*b3^6*b4^5 + 2*a1^6*a2^5*a3^2*a4^3*b1^2*b2^3*b3^6*b4^5 +
12*a1^5*a2^5*a3^2*a4^3*b1^3*b2^3*b3^6*b4^5 + 20*a1^4*a2^5*a3^2*a4^3*b1^4*b2^3*b3^6*b4^5 +
12*a1^3*a2^5*a3^2*a4^3*b1^5*b2^3*b3^6*b4^5 + 2*a1^2*a2^5*a3^2*a4^3*b1^6*b2^3*b3^6*b4^5 +
4*a1^6*a2^4*a3^2*a4^3*b1^2*b2^4*b3^6*b4^5 + 20*a1^5*a2^4*a3^2*a4^3*b1^3*b2^4*b3^6*b4^5 +
32*a1^4*a2^4*a3^2*a4^3*b1^4*b2^4*b3^6*b4^5 + 20*a1^3*a2^4*a3^2*a4^3*b1^5*b2^4*b3^6*b4^5 +
4*a1^2*a2^4*a3^2*a4^3*b1^6*b2^4*b3^6*b4^5 + 2*a1^6*a2^3*a3^2*a4^3*b1^2*b2^5*b3^6*b4^5 +
12*a1^5*a2^3*a3^2*a4^3*b1^3*b2^5*b3^6*b4^5 + 20*a1^4*a2^3*a3^2*a4^3*b1^4*b2^5*b3^6*b4^5 +
12*a1^3*a2^3*a3^2*a4^3*b1^5*b2^5*b3^6*b4^5 + 2*a1^2*a2^3*a3^2*a4^3*b1^6*b2^5*b3^6*b4^5 +
2*a1^5*a2^2*a3^2*a4^3*b1^3*b2^6*b3^6*b4^5 + 4*a1^4*a2^2*a3^2*a4^3*b1^4*b2^6*b3^6*b4^5 +
2*a1^3*a2^2*a3^2*a4^3*b1^5*b2^6*b3^6*b4^5 + a1^5*a2^5*a3*a4^3*b1^3*b2^3*b3^7*b4^5 +
2*a1^4*a2^5*a3*a4^3*b1^4*b2^3*b3^7*b4^5 + a1^3*a2^5*a3*a4^3*b1^5*b2^3*b3^7*b4^5 +
2*a1^5*a2^4*a3*a4^3*b1^3*b2^4*b3^7*b4^5 + 4*a1^4*a2^4*a3*a4^3*b1^4*b2^4*b3^7*b4^5 +
2*a1^3*a2^4*a3*a4^3*b1^5*b2^4*b3^7*b4^5 + a1^5*a2^3*a3*a4^3*b1^3*b2^5*b3^7*b4^5 +
2*a1^4*a2^3*a3*a4^3*b1^4*b2^5*b3^7*b4^5 + a1^3*a2^3*a3*a4^3*b1^5*b2^5*b3^7*b4^5 +
a1^4*a2^6*a3^6*a4^2*b1^4*b2^2*b3^2*b4^6 + 2*a1^5*a2^5*a3^6*a4^2*b1^3*b2^3*b3^2*b4^6 +
4*a1^4*a2^5*a3^6*a4^2*b1^4*b2^3*b3^2*b4^6 + 2*a1^3*a2^5*a3^6*a4^2*b1^5*b2^3*b3^2*b4^6 +
a1^6*a2^4*a3^6*a4^2*b1^2*b2^4*b3^2*b4^6 + 4*a1^5*a2^4*a3^6*a4^2*b1^3*b2^4*b3^2*b4^6 +
8*a1^4*a2^4*a3^6*a4^2*b1^4*b2^4*b3^2*b4^6 + 4*a1^3*a2^4*a3^6*a4^2*b1^5*b2^4*b3^2*b4^6 +
a1^2*a2^4*a3^6*a4^2*b1^6*b2^4*b3^2*b4^6 + 2*a1^5*a2^3*a3^6*a4^2*b1^3*b2^5*b3^2*b4^6 +
4*a1^4*a2^3*a3^6*a4^2*b1^4*b2^5*b3^2*b4^6 + 2*a1^3*a2^3*a3^6*a4^2*b1^5*b2^5*b3^2*b4^6 +
a1^4*a2^2*a3^6*a4^2*b1^4*b2^6*b3^2*b4^6 + 2*a1^5*a2^6*a3^5*a4^2*b1^3*b2^2*b3^3*b4^6 +
4*a1^4*a2^6*a3^5*a4^2*b1^4*b2^2*b3^3*b4^6 + 2*a1^3*a2^6*a3^5*a4^2*b1^5*b2^2*b3^3*b4^6 +

6

2*a1^6*a2^5*a3^5*a4^2*b1^2*b2^3*b3^3*b4^6 + 12*a1^5*a2^5*a3^5*a4^2*b1^3*b2^3*b3^3*b4^6 +
20*a1^4*a2^5*a3^5*a4^2*b1^4*b2^3*b3^3*b4^6 + 12*a1^3*a2^5*a3^5*a4^2*b1^5*b2^3*b3^3*b4^6 +
2*a1^2*a2^5*a3^5*a4^2*b1^6*b2^3*b3^3*b4^6 + 4*a1^6*a2^4*a3^5*a4^2*b1^2*b2^4*b3^3*b4^6 +
20*a1^5*a2^4*a3^5*a4^2*b1^3*b2^4*b3^3*b4^6 + 32*a1^4*a2^4*a3^5*a4^2*b1^4*b2^4*b3^3*b4^6 +
20*a1^3*a2^4*a3^5*a4^2*b1^5*b2^4*b3^3*b4^6 + 4*a1^2*a2^4*a3^5*a4^2*b1^6*b2^4*b3^3*b4^6 +
2*a1^6*a2^3*a3^5*a4^2*b1^2*b2^5*b3^3*b4^6 + 12*a1^5*a2^3*a3^5*a4^2*b1^3*b2^5*b3^3*b4^6 +
20*a1^4*a2^3*a3^5*a4^2*b1^4*b2^5*b3^3*b4^6 + 12*a1^3*a2^3*a3^5*a4^2*b1^5*b2^5*b3^3*b4^6 +
2*a1^2*a2^3*a3^5*a4^2*b1^6*b2^5*b3^3*b4^6 + 2*a1^5*a2^2*a3^5*a4^2*b1^3*b2^6*b3^3*b4^6 +
4*a1^4*a2^2*a3^5*a4^2*b1^4*b2^6*b3^3*b4^6 + 2*a1^3*a2^2*a3^5*a4^2*b1^5*b2^6*b3^3*b4^6 +
a1^6*a2^6*a3^4*a4^2*b1^2*b2^2*b3^4*b4^6 + 4*a1^5*a2^6*a3^4*a4^2*b1^3*b2^2*b3^4*b4^6 +
8*a1^4*a2^6*a3^4*a4^2*b1^4*b2^2*b3^4*b4^6 + 4*a1^3*a2^6*a3^4*a4^2*b1^5*b2^2*b3^4*b4^6 +
a1^2*a2^6*a3^4*a4^2*b1^6*b2^2*b3^4*b4^6 + 4*a1^6*a2^5*a3^4*a4^2*b1^2*b2^3*b3^4*b4^6 +
20*a1^5*a2^5*a3^4*a4^2*b1^3*b2^3*b3^4*b4^6 + 32*a1^4*a2^5*a3^4*a4^2*b1^4*b2^3*b3^4*b4^6 +
20*a1^3*a2^5*a3^4*a4^2*b1^5*b2^3*b3^4*b4^6 + 4*a1^2*a2^5*a3^4*a4^2*b1^6*b2^3*b3^4*b4^6 +
8*a1^6*a2^4*a3^4*a4^2*b1^2*b2^4*b3^4*b4^6 + 32*a1^5*a2^4*a3^4*a4^2*b1^3*b2^4*b3^4*b4^6 +
52*a1^4*a2^4*a3^4*a4^2*b1^4*b2^4*b3^4*b4^6 + 32*a1^3*a2^4*a3^4*a4^2*b1^5*b2^4*b3^4*b4^6 +
8*a1^2*a2^4*a3^4*a4^2*b1^6*b2^4*b3^4*b4^6 + 4*a1^6*a2^3*a3^4*a4^2*b1^2*b2^5*b3^4*b4^6 +
20*a1^5*a2^3*a3^4*a4^2*b1^3*b2^5*b3^4*b4^6 + 32*a1^4*a2^3*a3^4*a4^2*b1^4*b2^5*b3^4*b4^6 +
20*a1^3*a2^3*a3^4*a4^2*b1^5*b2^5*b3^4*b4^6 + 4*a1^2*a2^3*a3^4*a4^2*b1^6*b2^5*b3^4*b4^6 +
a1^6*a2^2*a3^4*a4^2*b1^2*b2^6*b3^4*b4^6 + 4*a1^5*a2^2*a3^4*a4^2*b1^3*b2^6*b3^4*b4^6 +
8*a1^4*a2^2*a3^4*a4^2*b1^4*b2^6*b3^4*b4^6 + 4*a1^3*a2^2*a3^4*a4^2*b1^5*b2^6*b3^4*b4^6 +
a1^2*a2^2*a3^4*a4^2*b1^6*b2^6*b3^4*b4^6 + 2*a1^5*a2^6*a3^3*a4^2*b1^3*b2^2*b3^5*b4^6 +
4*a1^4*a2^6*a3^3*a4^2*b1^4*b2^2*b3^5*b4^6 + 2*a1^3*a2^6*a3^3*a4^2*b1^5*b2^2*b3^5*b4^6 +
2*a1^6*a2^5*a3^3*a4^2*b1^2*b2^3*b3^5*b4^6 + 12*a1^5*a2^5*a3^3*a4^2*b1^3*b2^3*b3^5*b4^6 +
20*a1^4*a2^5*a3^3*a4^2*b1^4*b2^3*b3^5*b4^6 + 12*a1^3*a2^5*a3^3*a4^2*b1^5*b2^3*b3^5*b4^6 +
2*a1^2*a2^5*a3^3*a4^2*b1^6*b2^3*b3^5*b4^6 + 4*a1^6*a2^4*a3^3*a4^2*b1^2*b2^4*b3^5*b4^6 +
20*a1^5*a2^4*a3^3*a4^2*b1^3*b2^4*b3^5*b4^6 + 32*a1^4*a2^4*a3^3*a4^2*b1^4*b2^4*b3^5*b4^6 +
20*a1^3*a2^4*a3^3*a4^2*b1^5*b2^4*b3^5*b4^6 + 4*a1^2*a2^4*a3^3*a4^2*b1^6*b2^4*b3^5*b4^6 +
2*a1^6*a2^3*a3^3*a4^2*b1^2*b2^5*b3^5*b4^6 + 12*a1^5*a2^3*a3^3*a4^2*b1^3*b2^5*b3^5*b4^6 +
20*a1^4*a2^3*a3^3*a4^2*b1^4*b2^5*b3^5*b4^6 + 12*a1^3*a2^3*a3^3*a4^2*b1^5*b2^5*b3^5*b4^6 +
2*a1^2*a2^3*a3^3*a4^2*b1^6*b2^5*b3^5*b4^6 + 2*a1^5*a2^2*a3^3*a4^2*b1^3*b2^6*b3^5*b4^6 +
4*a1^4*a2^2*a3^3*a4^2*b1^4*b2^6*b3^5*b4^6 + 2*a1^3*a2^2*a3^3*a4^2*b1^5*b2^6*b3^5*b4^6 +
a1^4*a2^6*a3^2*a4^2*b1^4*b2^2*b3^6*b4^6 + 2*a1^5*a2^5*a3^2*a4^2*b1^3*b2^3*b3^6*b4^6 +
4*a1^4*a2^5*a3^2*a4^2*b1^4*b2^3*b3^6*b4^6 + 2*a1^3*a2^5*a3^2*a4^2*b1^5*b2^3*b3^6*b4^6 +
a1^6*a2^4*a3^2*a4^2*b1^2*b2^4*b3^6*b4^6 + 4*a1^5*a2^4*a3^2*a4^2*b1^3*b2^4*b3^6*b4^6 +
8*a1^4*a2^4*a3^2*a4^2*b1^4*b2^4*b3^6*b4^6 + 4*a1^3*a2^4*a3^2*a4^2*b1^5*b2^4*b3^6*b4^6 +
a1^2*a2^4*a3^2*a4^2*b1^6*b2^4*b3^6*b4^6 + 2*a1^5*a2^3*a3^2*a4^2*b1^3*b2^5*b3^6*b4^6 +
4*a1^4*a2^3*a3^2*a4^2*b1^4*b2^5*b3^6*b4^6 + 2*a1^3*a2^3*a3^2*a4^2*b1^5*b2^5*b3^6*b4^6 +
a1^4*a2^2*a3^2*a4^2*b1^4*b2^6*b3^6*b4^6 + a1^5*a2^5*a3^5*a4*b1^3*b2^3*b3^3*b4^7 +
2*a1^4*a2^5*a3^5*a4*b1^4*b2^3*b3^3*b4^7 + a1^3*a2^5*a3^5*a4*b1^5*b2^3*b3^3*b4^7 +
2*a1^5*a2^4*a3^5*a4*b1^3*b2^4*b3^3*b4^7 + 4*a1^4*a2^4*a3^5*a4*b1^4*b2^4*b3^3*b4^7 +
2*a1^3*a2^4*a3^5*a4*b1^5*b2^4*b3^3*b4^7 + a1^5*a2^3*a3^5*a4*b1^3*b2^5*b3^3*b4^7 +
2*a1^4*a2^3*a3^5*a4*b1^4*b2^5*b3^3*b4^7 + a1^3*a2^3*a3^5*a4*b1^5*b2^5*b3^3*b4^7 +
2*a1^5*a2^5*a3^4*a4*b1^3*b2^3*b3^4*b4^7 + 4*a1^4*a2^5*a3^4*a4*b1^4*b2^3*b3^4*b4^7 +
2*a1^3*a2^5*a3^4*a4*b1^5*b2^3*b3^4*b4^7 + 4*a1^5*a2^4*a3^4*a4*b1^3*b2^4*b3^4*b4^7 +
8*a1^4*a2^4*a3^4*a4*b1^4*b2^4*b3^4*b4^7 + 4*a1^3*a2^4*a3^4*a4*b1^5*b2^4*b3^4*b4^7 +
2*a1^5*a2^3*a3^4*a4*b1^3*b2^5*b3^4*b4^7 + 4*a1^4*a2^3*a3^4*a4*b1^4*b2^5*b3^4*b4^7 +
2*a1^3*a2^3*a3^4*a4*b1^5*b2^5*b3^4*b4^7 + a1^5*a2^5*a3^3*a4*b1^3*b2^3*b3^5*b4^7 +
2*a1^4*a2^5*a3^3*a4*b1^4*b2^3*b3^5*b4^7 + a1^3*a2^5*a3^3*a4*b1^5*b2^3*b3^5*b4^7 +
2*a1^5*a2^4*a3^3*a4*b1^3*b2^4*b3^5*b4^7 + 4*a1^4*a2^4*a3^3*a4*b1^4*b2^4*b3^5*b4^7 +
2*a1^3*a2^4*a3^3*a4*b1^5*b2^4*b3^5*b4^7 + a1^5*a2^3*a3^3*a4*b1^3*b2^5*b3^5*b4^7 +
2*a1^4*a2^3*a3^3*a4*b1^4*b2^5*b3^5*b4^7 + a1^3*a2^3*a3^3*a4*b1^5*b2^5*b3^5*b4^7 +
a1^4*a2^4*a3^4*b1^4*b2^4*b3^4*b4^8
c02=sum ( f 8 . f i n d ( 2 *w0) )
c02
#This f i n d s a l l our terms i n f 8 t h a t have a 2 i n them and then adds them \
t o g e t h e r . The f i r s t s e t o f gro u ps we form w i l l have one o f t h e f o u r a \
v a r i a b l e s t o t h e f o r t h power and e i t h e r a s e c o n d a v a r i a b l e o r i t s \
c o r r e s p o n d i n g b v a r i a b l e t o t h e s e v e n t h power .

7

2*a1^4*a2^5*a3^5*a4^7*b1^4*b2^3*b3^3*b4 + 2*a1^5*a2^4*a3^5*a4^7*b1^3*b2^4*b3^3*b4 +
2*a1^3*a2^4*a3^5*a4^7*b1^5*b2^4*b3^3*b4 + 2*a1^4*a2^3*a3^5*a4^7*b1^4*b2^5*b3^3*b4 +
2*a1^5*a2^5*a3^4*a4^7*b1^3*b2^3*b3^4*b4 + 2*a1^3*a2^5*a3^4*a4^7*b1^5*b2^3*b3^4*b4 +
2*a1^5*a2^3*a3^4*a4^7*b1^3*b2^5*b3^4*b4 + 2*a1^3*a2^3*a3^4*a4^7*b1^5*b2^5*b3^4*b4 +
2*a1^4*a2^5*a3^3*a4^7*b1^4*b2^3*b3^5*b4 + 2*a1^5*a2^4*a3^3*a4^7*b1^3*b2^4*b3^5*b4 +
2*a1^3*a2^4*a3^3*a4^7*b1^5*b2^4*b3^5*b4 + 2*a1^4*a2^3*a3^3*a4^7*b1^4*b2^5*b3^5*b4 +
2*a1^5*a2^5*a3^6*a4^6*b1^3*b2^3*b3^2*b4^2 + 2*a1^3*a2^5*a3^6*a4^6*b1^5*b2^3*b3^2*b4^2 +
2*a1^5*a2^3*a3^6*a4^6*b1^3*b2^5*b3^2*b4^2 + 2*a1^3*a2^3*a3^6*a4^6*b1^5*b2^5*b3^2*b4^2 +
2*a1^5*a2^6*a3^5*a4^6*b1^3*b2^2*b3^3*b4^2 + 2*a1^3*a2^6*a3^5*a4^6*b1^5*b2^2*b3^3*b4^2 +
2*a1^6*a2^5*a3^5*a4^6*b1^2*b2^3*b3^3*b4^2 + 2*a1^2*a2^5*a3^5*a4^6*b1^6*b2^3*b3^3*b4^2 +
2*a1^6*a2^3*a3^5*a4^6*b1^2*b2^5*b3^3*b4^2 + 2*a1^2*a2^3*a3^5*a4^6*b1^6*b2^5*b3^3*b4^2 +
2*a1^5*a2^2*a3^5*a4^6*b1^3*b2^6*b3^3*b4^2 + 2*a1^3*a2^2*a3^5*a4^6*b1^5*b2^6*b3^3*b4^2 +
2*a1^5*a2^6*a3^3*a4^6*b1^3*b2^2*b3^5*b4^2 + 2*a1^3*a2^6*a3^3*a4^6*b1^5*b2^2*b3^5*b4^2 +
2*a1^6*a2^5*a3^3*a4^6*b1^2*b2^3*b3^5*b4^2 + 2*a1^2*a2^5*a3^3*a4^6*b1^6*b2^3*b3^5*b4^2 +
2*a1^6*a2^3*a3^3*a4^6*b1^2*b2^5*b3^5*b4^2 + 2*a1^2*a2^3*a3^3*a4^6*b1^6*b2^5*b3^5*b4^2 +
2*a1^5*a2^2*a3^3*a4^6*b1^3*b2^6*b3^5*b4^2 + 2*a1^3*a2^2*a3^3*a4^6*b1^5*b2^6*b3^5*b4^2 +
2*a1^5*a2^5*a3^2*a4^6*b1^3*b2^3*b3^6*b4^2 + 2*a1^3*a2^5*a3^2*a4^6*b1^5*b2^3*b3^6*b4^2 +
2*a1^5*a2^3*a3^2*a4^6*b1^3*b2^5*b3^6*b4^2 + 2*a1^3*a2^3*a3^2*a4^6*b1^5*b2^5*b3^6*b4^2 +
2*a1^4*a2^5*a3^7*a4^5*b1^4*b2^3*b3*b4^3 + 2*a1^5*a2^4*a3^7*a4^5*b1^3*b2^4*b3*b4^3 +
2*a1^3*a2^4*a3^7*a4^5*b1^5*b2^4*b3*b4^3 + 2*a1^4*a2^3*a3^7*a4^5*b1^4*b2^5*b3*b4^3 +
2*a1^5*a2^6*a3^6*a4^5*b1^3*b2^2*b3^2*b4^3 + 2*a1^3*a2^6*a3^6*a4^5*b1^5*b2^2*b3^2*b4^3 +
2*a1^6*a2^5*a3^6*a4^5*b1^2*b2^3*b3^2*b4^3 + 2*a1^2*a2^5*a3^6*a4^5*b1^6*b2^3*b3^2*b4^3 +
2*a1^6*a2^3*a3^6*a4^5*b1^2*b2^5*b3^2*b4^3 + 2*a1^2*a2^3*a3^6*a4^5*b1^6*b2^5*b3^2*b4^3 +
2*a1^5*a2^2*a3^6*a4^5*b1^3*b2^6*b3^2*b4^3 + 2*a1^3*a2^2*a3^6*a4^5*b1^5*b2^6*b3^2*b4^3 +
2*a1^4*a2^7*a3^5*a4^5*b1^4*b2*b3^3*b4^3 + 2*a1^6*a2^6*a3^5*a4^5*b1^2*b2^2*b3^3*b4^3 +
2*a1^2*a2^6*a3^5*a4^5*b1^6*b2^2*b3^3*b4^3 + 2*a1^7*a2^4*a3^5*a4^5*b1*b2^4*b3^3*b4^3 +
2*a1*a2^4*a3^5*a4^5*b1^7*b2^4*b3^3*b4^3 + 2*a1^6*a2^2*a3^5*a4^5*b1^2*b2^6*b3^3*b4^3 +
2*a1^2*a2^2*a3^5*a4^5*b1^6*b2^6*b3^3*b4^3 + 2*a1^4*a2*a3^5*a4^5*b1^4*b2^7*b3^3*b4^3 +
2*a1^5*a2^7*a3^4*a4^5*b1^3*b2*b3^4*b4^3 + 2*a1^3*a2^7*a3^4*a4^5*b1^5*b2*b3^4*b4^3 +
2*a1^7*a2^5*a3^4*a4^5*b1*b2^3*b3^4*b4^3 + 2*a1*a2^5*a3^4*a4^5*b1^7*b2^3*b3^4*b4^3 +
2*a1^7*a2^3*a3^4*a4^5*b1*b2^5*b3^4*b4^3 + 2*a1*a2^3*a3^4*a4^5*b1^7*b2^5*b3^4*b4^3 +
2*a1^5*a2*a3^4*a4^5*b1^3*b2^7*b3^4*b4^3 + 2*a1^3*a2*a3^4*a4^5*b1^5*b2^7*b3^4*b4^3 +
2*a1^4*a2^7*a3^3*a4^5*b1^4*b2*b3^5*b4^3 + 2*a1^6*a2^6*a3^3*a4^5*b1^2*b2^2*b3^5*b4^3 +
2*a1^2*a2^6*a3^3*a4^5*b1^6*b2^2*b3^5*b4^3 + 2*a1^7*a2^4*a3^3*a4^5*b1*b2^4*b3^5*b4^3 +
2*a1*a2^4*a3^3*a4^5*b1^7*b2^4*b3^5*b4^3 + 2*a1^6*a2^2*a3^3*a4^5*b1^2*b2^6*b3^5*b4^3 +
2*a1^2*a2^2*a3^3*a4^5*b1^6*b2^6*b3^5*b4^3 + 2*a1^4*a2*a3^3*a4^5*b1^4*b2^7*b3^5*b4^3 +
2*a1^5*a2^6*a3^2*a4^5*b1^3*b2^2*b3^6*b4^3 + 2*a1^3*a2^6*a3^2*a4^5*b1^5*b2^2*b3^6*b4^3 +
2*a1^6*a2^5*a3^2*a4^5*b1^2*b2^3*b3^6*b4^3 + 2*a1^2*a2^5*a3^2*a4^5*b1^6*b2^3*b3^6*b4^3 +
2*a1^6*a2^3*a3^2*a4^5*b1^2*b2^5*b3^6*b4^3 + 2*a1^2*a2^3*a3^2*a4^5*b1^6*b2^5*b3^6*b4^3 +
2*a1^5*a2^2*a3^2*a4^5*b1^3*b2^6*b3^6*b4^3 + 2*a1^3*a2^2*a3^2*a4^5*b1^5*b2^6*b3^6*b4^3 +
2*a1^4*a2^5*a3*a4^5*b1^4*b2^3*b3^7*b4^3 + 2*a1^5*a2^4*a3*a4^5*b1^3*b2^4*b3^7*b4^3 +
2*a1^3*a2^4*a3*a4^5*b1^5*b2^4*b3^7*b4^3 + 2*a1^4*a2^3*a3*a4^5*b1^4*b2^5*b3^7*b4^3 +
2*a1^5*a2^5*a3^7*a4^4*b1^3*b2^3*b3*b4^4 + 2*a1^3*a2^5*a3^7*a4^4*b1^5*b2^3*b3*b4^4 +
2*a1^5*a2^3*a3^7*a4^4*b1^3*b2^5*b3*b4^4 + 2*a1^3*a2^3*a3^7*a4^4*b1^5*b2^5*b3*b4^4 +
2*a1^5*a2^7*a3^5*a4^4*b1^3*b2*b3^3*b4^4 + 2*a1^3*a2^7*a3^5*a4^4*b1^5*b2*b3^3*b4^4 +
2*a1^7*a2^5*a3^5*a4^4*b1*b2^3*b3^3*b4^4 + 2*a1*a2^5*a3^5*a4^4*b1^7*b2^3*b3^3*b4^4 +
2*a1^7*a2^3*a3^5*a4^4*b1*b2^5*b3^3*b4^4 + 2*a1*a2^3*a3^5*a4^4*b1^7*b2^5*b3^3*b4^4 +
2*a1^5*a2*a3^5*a4^4*b1^3*b2^7*b3^3*b4^4 + 2*a1^3*a2*a3^5*a4^4*b1^5*b2^7*b3^3*b4^4 +
2*a1^5*a2^7*a3^3*a4^4*b1^3*b2*b3^5*b4^4 + 2*a1^3*a2^7*a3^3*a4^4*b1^5*b2*b3^5*b4^4 +
2*a1^7*a2^5*a3^3*a4^4*b1*b2^3*b3^5*b4^4 + 2*a1*a2^5*a3^3*a4^4*b1^7*b2^3*b3^5*b4^4 +
2*a1^7*a2^3*a3^3*a4^4*b1*b2^5*b3^5*b4^4 + 2*a1*a2^3*a3^3*a4^4*b1^7*b2^5*b3^5*b4^4 +
2*a1^5*a2*a3^3*a4^4*b1^3*b2^7*b3^5*b4^4 + 2*a1^3*a2*a3^3*a4^4*b1^5*b2^7*b3^5*b4^4 +
2*a1^5*a2^5*a3*a4^4*b1^3*b2^3*b3^7*b4^4 + 2*a1^3*a2^5*a3*a4^4*b1^5*b2^3*b3^7*b4^4 +
2*a1^5*a2^3*a3*a4^4*b1^3*b2^5*b3^7*b4^4 + 2*a1^3*a2^3*a3*a4^4*b1^5*b2^5*b3^7*b4^4 +
2*a1^4*a2^5*a3^7*a4^3*b1^4*b2^3*b3*b4^5 + 2*a1^5*a2^4*a3^7*a4^3*b1^3*b2^4*b3*b4^5 +
2*a1^3*a2^4*a3^7*a4^3*b1^5*b2^4*b3*b4^5 + 2*a1^4*a2^3*a3^7*a4^3*b1^4*b2^5*b3*b4^5 +
2*a1^5*a2^6*a3^6*a4^3*b1^3*b2^2*b3^2*b4^5 + 2*a1^3*a2^6*a3^6*a4^3*b1^5*b2^2*b3^2*b4^5 +
2*a1^6*a2^5*a3^6*a4^3*b1^2*b2^3*b3^2*b4^5 + 2*a1^2*a2^5*a3^6*a4^3*b1^6*b2^3*b3^2*b4^5 +
2*a1^6*a2^3*a3^6*a4^3*b1^2*b2^5*b3^2*b4^5 + 2*a1^2*a2^3*a3^6*a4^3*b1^6*b2^5*b3^2*b4^5 +
2*a1^5*a2^2*a3^6*a4^3*b1^3*b2^6*b3^2*b4^5 + 2*a1^3*a2^2*a3^6*a4^3*b1^5*b2^6*b3^2*b4^5 +
2*a1^4*a2^7*a3^5*a4^3*b1^4*b2*b3^3*b4^5 + 2*a1^6*a2^6*a3^5*a4^3*b1^2*b2^2*b3^3*b4^5 +

8

2*a1^2*a2^6*a3^5*a4^3*b1^6*b2^2*b3^3*b4^5 + 2*a1^7*a2^4*a3^5*a4^3*b1*b2^4*b3^3*b4^5 +
2*a1*a2^4*a3^5*a4^3*b1^7*b2^4*b3^3*b4^5 + 2*a1^6*a2^2*a3^5*a4^3*b1^2*b2^6*b3^3*b4^5 +
2*a1^2*a2^2*a3^5*a4^3*b1^6*b2^6*b3^3*b4^5 + 2*a1^4*a2*a3^5*a4^3*b1^4*b2^7*b3^3*b4^5 +
2*a1^5*a2^7*a3^4*a4^3*b1^3*b2*b3^4*b4^5 + 2*a1^3*a2^7*a3^4*a4^3*b1^5*b2*b3^4*b4^5 +
2*a1^7*a2^5*a3^4*a4^3*b1*b2^3*b3^4*b4^5 + 2*a1*a2^5*a3^4*a4^3*b1^7*b2^3*b3^4*b4^5 +
2*a1^7*a2^3*a3^4*a4^3*b1*b2^5*b3^4*b4^5 + 2*a1*a2^3*a3^4*a4^3*b1^7*b2^5*b3^4*b4^5 +
2*a1^5*a2*a3^4*a4^3*b1^3*b2^7*b3^4*b4^5 + 2*a1^3*a2*a3^4*a4^3*b1^5*b2^7*b3^4*b4^5 +
2*a1^4*a2^7*a3^3*a4^3*b1^4*b2*b3^5*b4^5 + 2*a1^6*a2^6*a3^3*a4^3*b1^2*b2^2*b3^5*b4^5 +
2*a1^2*a2^6*a3^3*a4^3*b1^6*b2^2*b3^5*b4^5 + 2*a1^7*a2^4*a3^3*a4^3*b1*b2^4*b3^5*b4^5 +
2*a1*a2^4*a3^3*a4^3*b1^7*b2^4*b3^5*b4^5 + 2*a1^6*a2^2*a3^3*a4^3*b1^2*b2^6*b3^5*b4^5 +
2*a1^2*a2^2*a3^3*a4^3*b1^6*b2^6*b3^5*b4^5 + 2*a1^4*a2*a3^3*a4^3*b1^4*b2^7*b3^5*b4^5 +
2*a1^5*a2^6*a3^2*a4^3*b1^3*b2^2*b3^6*b4^5 + 2*a1^3*a2^6*a3^2*a4^3*b1^5*b2^2*b3^6*b4^5 +
2*a1^6*a2^5*a3^2*a4^3*b1^2*b2^3*b3^6*b4^5 + 2*a1^2*a2^5*a3^2*a4^3*b1^6*b2^3*b3^6*b4^5 +
2*a1^6*a2^3*a3^2*a4^3*b1^2*b2^5*b3^6*b4^5 + 2*a1^2*a2^3*a3^2*a4^3*b1^6*b2^5*b3^6*b4^5 +
2*a1^5*a2^2*a3^2*a4^3*b1^3*b2^6*b3^6*b4^5 + 2*a1^3*a2^2*a3^2*a4^3*b1^5*b2^6*b3^6*b4^5 +
2*a1^4*a2^5*a3*a4^3*b1^4*b2^3*b3^7*b4^5 + 2*a1^5*a2^4*a3*a4^3*b1^3*b2^4*b3^7*b4^5 +
2*a1^3*a2^4*a3*a4^3*b1^5*b2^4*b3^7*b4^5 + 2*a1^4*a2^3*a3*a4^3*b1^4*b2^5*b3^7*b4^5 +
2*a1^5*a2^5*a3^6*a4^2*b1^3*b2^3*b3^2*b4^6 + 2*a1^3*a2^5*a3^6*a4^2*b1^5*b2^3*b3^2*b4^6 +
2*a1^5*a2^3*a3^6*a4^2*b1^3*b2^5*b3^2*b4^6 + 2*a1^3*a2^3*a3^6*a4^2*b1^5*b2^5*b3^2*b4^6 +
2*a1^5*a2^6*a3^5*a4^2*b1^3*b2^2*b3^3*b4^6 + 2*a1^3*a2^6*a3^5*a4^2*b1^5*b2^2*b3^3*b4^6 +
2*a1^6*a2^5*a3^5*a4^2*b1^2*b2^3*b3^3*b4^6 + 2*a1^2*a2^5*a3^5*a4^2*b1^6*b2^3*b3^3*b4^6 +
2*a1^6*a2^3*a3^5*a4^2*b1^2*b2^5*b3^3*b4^6 + 2*a1^2*a2^3*a3^5*a4^2*b1^6*b2^5*b3^3*b4^6 +
2*a1^5*a2^2*a3^5*a4^2*b1^3*b2^6*b3^3*b4^6 + 2*a1^3*a2^2*a3^5*a4^2*b1^5*b2^6*b3^3*b4^6 +
2*a1^5*a2^6*a3^3*a4^2*b1^3*b2^2*b3^5*b4^6 + 2*a1^3*a2^6*a3^3*a4^2*b1^5*b2^2*b3^5*b4^6 +
2*a1^6*a2^5*a3^3*a4^2*b1^2*b2^3*b3^5*b4^6 + 2*a1^2*a2^5*a3^3*a4^2*b1^6*b2^3*b3^5*b4^6 +
2*a1^6*a2^3*a3^3*a4^2*b1^2*b2^5*b3^5*b4^6 + 2*a1^2*a2^3*a3^3*a4^2*b1^6*b2^5*b3^5*b4^6 +
2*a1^5*a2^2*a3^3*a4^2*b1^3*b2^6*b3^5*b4^6 + 2*a1^3*a2^2*a3^3*a4^2*b1^5*b2^6*b3^5*b4^6 +
2*a1^5*a2^5*a3^2*a4^2*b1^3*b2^3*b3^6*b4^6 + 2*a1^3*a2^5*a3^2*a4^2*b1^5*b2^3*b3^6*b4^6 +
2*a1^5*a2^3*a3^2*a4^2*b1^3*b2^5*b3^6*b4^6 + 2*a1^3*a2^3*a3^2*a4^2*b1^5*b2^5*b3^6*b4^6 +
2*a1^4*a2^5*a3^5*a4*b1^4*b2^3*b3^3*b4^7 + 2*a1^5*a2^4*a3^5*a4*b1^3*b2^4*b3^3*b4^7 +
2*a1^3*a2^4*a3^5*a4*b1^5*b2^4*b3^3*b4^7 + 2*a1^4*a2^3*a3^5*a4*b1^4*b2^5*b3^3*b4^7 +
2*a1^5*a2^5*a3^4*a4*b1^3*b2^3*b3^4*b4^7 + 2*a1^3*a2^5*a3^4*a4*b1^5*b2^3*b3^4*b4^7 +
2*a1^5*a2^3*a3^4*a4*b1^3*b2^5*b3^4*b4^7 + 2*a1^3*a2^3*a3^4*a4*b1^5*b2^5*b3^4*b4^7 +
2*a1^4*a2^5*a3^3*a4*b1^4*b2^3*b3^5*b4^7 + 2*a1^5*a2^4*a3^3*a4*b1^3*b2^4*b3^5*b4^7 +
2*a1^3*a2^4*a3^3*a4*b1^5*b2^4*b3^5*b4^7 + 2*a1^4*a2^3*a3^3*a4*b1^4*b2^5*b3^5*b4^7
c0212=sum ( c02 . f i n d ( a1 ^4* a2 ^7*w0) )+sum ( c02 . f i n d ( a1 ^4* b2 ^7*w0) )
c0212
c0212 . f a c t o r ( )
s0 2 1 2 = -2*(( p2^2 + 2* q2 ) ^2 - 3* q2 ^2) * ( p2^2 + 2* q2 ) * ( p3^2 + 2* q3 ) * ( p4^2 + 2* q4 ) *\
q1 ^4* q2 * q3 ^3* q4 ^3
s0 2 1 2
#This i s t h e sum o f t h e terms with a1 ^4 , and e i t h e r a2 ^7 o r b2 ^7 , i t s \
f a c t o r i z a t i o n , and i t s s u b s t i t u t i o n .
2*a1^4*a2^7*a3^5*a4^5*b1^4*b2*b3^3*b4^3 + 2*a1^4*a2*a3^5*a4^5*b1^4*b2^7*b3^3*b4^3 +
2*a1^4*a2^7*a3^3*a4^5*b1^4*b2*b3^5*b4^3 + 2*a1^4*a2*a3^3*a4^5*b1^4*b2^7*b3^5*b4^3 +
2*a1^4*a2^7*a3^5*a4^3*b1^4*b2*b3^3*b4^5 + 2*a1^4*a2*a3^5*a4^3*b1^4*b2^7*b3^3*b4^5 +
2*a1^4*a2^7*a3^3*a4^3*b1^4*b2*b3^5*b4^5 + 2*a1^4*a2*a3^3*a4^3*b1^4*b2^7*b3^5*b4^5
2*(a2^4 - a2^2*b2^2 + b2^4)*(a2^2 + b2^2)*(a3^2 + b3^2)*(a4^2 +
b4^2)*a1^4*a2*a3^3*a4^3*b1^4*b2*b3^3*b4^3
-2*((p2^2 + 2*q2)^2 - 3*q2^2)*(p2^2 + 2*q2)*(p3^2 + 2*q3)*(p4^2 + 2*q4)*q1^4*q2*q3^3*q4^3
c0213=sum ( c02 . f i n d ( a1 ^4* a3 ^7*w0) )+sum ( c02 . f i n d ( a1 ^4* b3 ^7*w0) )
c0213
c0213 . f a c t o r ( )
s0 2 1 3 = -2*(( p3^2 + 2* q3 ) ^2 - 3* q3 ^2) * ( p2^2 + 2* q2 ) * ( p3^2 + 2* q3 ) * ( p4^2 + 2* q4 ) *\
q1 ^4* q2 ^3* q3 * q4 ^3
s0 2 1 3
#This i s t h e sum o f t h e terms with a1 ^4 , and e i t h e r a3 ^7 o r b3 ^7 , i t s \
f a c t o r i z a t i o n , and i t s s u b s t i t u t i o n .

9


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