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Factorization of the Coefficient of x 9
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 .
g9=-F . c o e f f i c i e n t ( x , 9 )
g9
#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^9 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 . We t a k e t h e n e g a t i v e b e c a u s e we h a n d l e t h e s i g n i n t h e f i n a l form \
of the c h a r a c t e r i s t i c .
a1^4*a2^4*a3^4*a4^7*b1^3*b2^3*b3^3 + a1^3*a2^4*a3^4*a4^7*b1^4*b2^3*b3^3 +
a1^4*a2^3*a3^4*a4^7*b1^3*b2^4*b3^3 + a1^3*a2^3*a3^4*a4^7*b1^4*b2^4*b3^3 +
a1^4*a2^4*a3^3*a4^7*b1^3*b2^3*b3^4 + a1^3*a2^4*a3^3*a4^7*b1^4*b2^3*b3^4 +
a1^4*a2^3*a3^3*a4^7*b1^3*b2^4*b3^4 + a1^3*a2^3*a3^3*a4^7*b1^4*b2^4*b3^4 +
a1^4*a2^5*a3^5*a4^6*b1^3*b2^2*b3^2*b4 + a1^3*a2^5*a3^5*a4^6*b1^4*b2^2*b3^2*b4 +
a1^5*a2^4*a3^5*a4^6*b1^2*b2^3*b3^2*b4 + 4*a1^4*a2^4*a3^5*a4^6*b1^3*b2^3*b3^2*b4 +
4*a1^3*a2^4*a3^5*a4^6*b1^4*b2^3*b3^2*b4 + a1^2*a2^4*a3^5*a4^6*b1^5*b2^3*b3^2*b4 +
a1^5*a2^3*a3^5*a4^6*b1^2*b2^4*b3^2*b4 + 4*a1^4*a2^3*a3^5*a4^6*b1^3*b2^4*b3^2*b4 +
4*a1^3*a2^3*a3^5*a4^6*b1^4*b2^4*b3^2*b4 + a1^2*a2^3*a3^5*a4^6*b1^5*b2^4*b3^2*b4 +
a1^4*a2^2*a3^5*a4^6*b1^3*b2^5*b3^2*b4 + a1^3*a2^2*a3^5*a4^6*b1^4*b2^5*b3^2*b4 +
a1^5*a2^5*a3^4*a4^6*b1^2*b2^2*b3^3*b4 + 4*a1^4*a2^5*a3^4*a4^6*b1^3*b2^2*b3^3*b4 +
4*a1^3*a2^5*a3^4*a4^6*b1^4*b2^2*b3^3*b4 + a1^2*a2^5*a3^4*a4^6*b1^5*b2^2*b3^3*b4 +
4*a1^5*a2^4*a3^4*a4^6*b1^2*b2^3*b3^3*b4 + 13*a1^4*a2^4*a3^4*a4^6*b1^3*b2^3*b3^3*b4 +
13*a1^3*a2^4*a3^4*a4^6*b1^4*b2^3*b3^3*b4 + 4*a1^2*a2^4*a3^4*a4^6*b1^5*b2^3*b3^3*b4 +
4*a1^5*a2^3*a3^4*a4^6*b1^2*b2^4*b3^3*b4 + 13*a1^4*a2^3*a3^4*a4^6*b1^3*b2^4*b3^3*b4 +
13*a1^3*a2^3*a3^4*a4^6*b1^4*b2^4*b3^3*b4 + 4*a1^2*a2^3*a3^4*a4^6*b1^5*b2^4*b3^3*b4 +
a1^5*a2^2*a3^4*a4^6*b1^2*b2^5*b3^3*b4 + 4*a1^4*a2^2*a3^4*a4^6*b1^3*b2^5*b3^3*b4 +
4*a1^3*a2^2*a3^4*a4^6*b1^4*b2^5*b3^3*b4 + a1^2*a2^2*a3^4*a4^6*b1^5*b2^5*b3^3*b4 +
a1^5*a2^5*a3^3*a4^6*b1^2*b2^2*b3^4*b4 + 4*a1^4*a2^5*a3^3*a4^6*b1^3*b2^2*b3^4*b4 +
4*a1^3*a2^5*a3^3*a4^6*b1^4*b2^2*b3^4*b4 + a1^2*a2^5*a3^3*a4^6*b1^5*b2^2*b3^4*b4 +
4*a1^5*a2^4*a3^3*a4^6*b1^2*b2^3*b3^4*b4 + 13*a1^4*a2^4*a3^3*a4^6*b1^3*b2^3*b3^4*b4 +
13*a1^3*a2^4*a3^3*a4^6*b1^4*b2^3*b3^4*b4 + 4*a1^2*a2^4*a3^3*a4^6*b1^5*b2^3*b3^4*b4 +
4*a1^5*a2^3*a3^3*a4^6*b1^2*b2^4*b3^4*b4 + 13*a1^4*a2^3*a3^3*a4^6*b1^3*b2^4*b3^4*b4 +
13*a1^3*a2^3*a3^3*a4^6*b1^4*b2^4*b3^4*b4 + 4*a1^2*a2^3*a3^3*a4^6*b1^5*b2^4*b3^4*b4 +
a1^5*a2^2*a3^3*a4^6*b1^2*b2^5*b3^4*b4 + 4*a1^4*a2^2*a3^3*a4^6*b1^3*b2^5*b3^4*b4 +
4*a1^3*a2^2*a3^3*a4^6*b1^4*b2^5*b3^4*b4 + a1^2*a2^2*a3^3*a4^6*b1^5*b2^5*b3^4*b4 +
a1^4*a2^5*a3^2*a4^6*b1^3*b2^2*b3^5*b4 + a1^3*a2^5*a3^2*a4^6*b1^4*b2^2*b3^5*b4 +
a1^5*a2^4*a3^2*a4^6*b1^2*b2^3*b3^5*b4 + 4*a1^4*a2^4*a3^2*a4^6*b1^3*b2^3*b3^5*b4 +

1

4*a1^3*a2^4*a3^2*a4^6*b1^4*b2^3*b3^5*b4 + a1^2*a2^4*a3^2*a4^6*b1^5*b2^3*b3^5*b4 +
a1^5*a2^3*a3^2*a4^6*b1^2*b2^4*b3^5*b4 + 4*a1^4*a2^3*a3^2*a4^6*b1^3*b2^4*b3^5*b4 +
4*a1^3*a2^3*a3^2*a4^6*b1^4*b2^4*b3^5*b4 + a1^2*a2^3*a3^2*a4^6*b1^5*b2^4*b3^5*b4 +
a1^4*a2^2*a3^2*a4^6*b1^3*b2^5*b3^5*b4 + a1^3*a2^2*a3^2*a4^6*b1^4*b2^5*b3^5*b4 +
a1^4*a2^5*a3^6*a4^5*b1^3*b2^2*b3*b4^2 + a1^3*a2^5*a3^6*a4^5*b1^4*b2^2*b3*b4^2 +
a1^5*a2^4*a3^6*a4^5*b1^2*b2^3*b3*b4^2 + 4*a1^4*a2^4*a3^6*a4^5*b1^3*b2^3*b3*b4^2 +
4*a1^3*a2^4*a3^6*a4^5*b1^4*b2^3*b3*b4^2 + a1^2*a2^4*a3^6*a4^5*b1^5*b2^3*b3*b4^2 +
a1^5*a2^3*a3^6*a4^5*b1^2*b2^4*b3*b4^2 + 4*a1^4*a2^3*a3^6*a4^5*b1^3*b2^4*b3*b4^2 +
4*a1^3*a2^3*a3^6*a4^5*b1^4*b2^4*b3*b4^2 + a1^2*a2^3*a3^6*a4^5*b1^5*b2^4*b3*b4^2 +
a1^4*a2^2*a3^6*a4^5*b1^3*b2^5*b3*b4^2 + a1^3*a2^2*a3^6*a4^5*b1^4*b2^5*b3*b4^2 +
a1^4*a2^6*a3^5*a4^5*b1^3*b2*b3^2*b4^2 + a1^3*a2^6*a3^5*a4^5*b1^4*b2*b3^2*b4^2 +
3*a1^5*a2^5*a3^5*a4^5*b1^2*b2^2*b3^2*b4^2 + 10*a1^4*a2^5*a3^5*a4^5*b1^3*b2^2*b3^2*b4^2 +
10*a1^3*a2^5*a3^5*a4^5*b1^4*b2^2*b3^2*b4^2 + 3*a1^2*a2^5*a3^5*a4^5*b1^5*b2^2*b3^2*b4^2 +
a1^6*a2^4*a3^5*a4^5*b1*b2^3*b3^2*b4^2 + 10*a1^5*a2^4*a3^5*a4^5*b1^2*b2^3*b3^2*b4^2 +
27*a1^4*a2^4*a3^5*a4^5*b1^3*b2^3*b3^2*b4^2 + 27*a1^3*a2^4*a3^5*a4^5*b1^4*b2^3*b3^2*b4^2 +
10*a1^2*a2^4*a3^5*a4^5*b1^5*b2^3*b3^2*b4^2 + a1*a2^4*a3^5*a4^5*b1^6*b2^3*b3^2*b4^2 +
a1^6*a2^3*a3^5*a4^5*b1*b2^4*b3^2*b4^2 + 10*a1^5*a2^3*a3^5*a4^5*b1^2*b2^4*b3^2*b4^2 +
27*a1^4*a2^3*a3^5*a4^5*b1^3*b2^4*b3^2*b4^2 + 27*a1^3*a2^3*a3^5*a4^5*b1^4*b2^4*b3^2*b4^2 +
10*a1^2*a2^3*a3^5*a4^5*b1^5*b2^4*b3^2*b4^2 + a1*a2^3*a3^5*a4^5*b1^6*b2^4*b3^2*b4^2 +
3*a1^5*a2^2*a3^5*a4^5*b1^2*b2^5*b3^2*b4^2 + 10*a1^4*a2^2*a3^5*a4^5*b1^3*b2^5*b3^2*b4^2 +
10*a1^3*a2^2*a3^5*a4^5*b1^4*b2^5*b3^2*b4^2 + 3*a1^2*a2^2*a3^5*a4^5*b1^5*b2^5*b3^2*b4^2 +
a1^4*a2*a3^5*a4^5*b1^3*b2^6*b3^2*b4^2 + a1^3*a2*a3^5*a4^5*b1^4*b2^6*b3^2*b4^2 +
a1^5*a2^6*a3^4*a4^5*b1^2*b2*b3^3*b4^2 + 4*a1^4*a2^6*a3^4*a4^5*b1^3*b2*b3^3*b4^2 +
4*a1^3*a2^6*a3^4*a4^5*b1^4*b2*b3^3*b4^2 + a1^2*a2^6*a3^4*a4^5*b1^5*b2*b3^3*b4^2 +
a1^6*a2^5*a3^4*a4^5*b1*b2^2*b3^3*b4^2 + 10*a1^5*a2^5*a3^4*a4^5*b1^2*b2^2*b3^3*b4^2 +
27*a1^4*a2^5*a3^4*a4^5*b1^3*b2^2*b3^3*b4^2 + 27*a1^3*a2^5*a3^4*a4^5*b1^4*b2^2*b3^3*b4^2 +
10*a1^2*a2^5*a3^4*a4^5*b1^5*b2^2*b3^3*b4^2 + a1*a2^5*a3^4*a4^5*b1^6*b2^2*b3^3*b4^2 +
4*a1^6*a2^4*a3^4*a4^5*b1*b2^3*b3^3*b4^2 + 27*a1^5*a2^4*a3^4*a4^5*b1^2*b2^3*b3^3*b4^2 +
64*a1^4*a2^4*a3^4*a4^5*b1^3*b2^3*b3^3*b4^2 + 64*a1^3*a2^4*a3^4*a4^5*b1^4*b2^3*b3^3*b4^2 +
27*a1^2*a2^4*a3^4*a4^5*b1^5*b2^3*b3^3*b4^2 + 4*a1*a2^4*a3^4*a4^5*b1^6*b2^3*b3^3*b4^2 +
4*a1^6*a2^3*a3^4*a4^5*b1*b2^4*b3^3*b4^2 + 27*a1^5*a2^3*a3^4*a4^5*b1^2*b2^4*b3^3*b4^2 +
64*a1^4*a2^3*a3^4*a4^5*b1^3*b2^4*b3^3*b4^2 + 64*a1^3*a2^3*a3^4*a4^5*b1^4*b2^4*b3^3*b4^2 +
27*a1^2*a2^3*a3^4*a4^5*b1^5*b2^4*b3^3*b4^2 + 4*a1*a2^3*a3^4*a4^5*b1^6*b2^4*b3^3*b4^2 +
a1^6*a2^2*a3^4*a4^5*b1*b2^5*b3^3*b4^2 + 10*a1^5*a2^2*a3^4*a4^5*b1^2*b2^5*b3^3*b4^2 +
27*a1^4*a2^2*a3^4*a4^5*b1^3*b2^5*b3^3*b4^2 + 27*a1^3*a2^2*a3^4*a4^5*b1^4*b2^5*b3^3*b4^2 +
10*a1^2*a2^2*a3^4*a4^5*b1^5*b2^5*b3^3*b4^2 + a1*a2^2*a3^4*a4^5*b1^6*b2^5*b3^3*b4^2 +
a1^5*a2*a3^4*a4^5*b1^2*b2^6*b3^3*b4^2 + 4*a1^4*a2*a3^4*a4^5*b1^3*b2^6*b3^3*b4^2 +
4*a1^3*a2*a3^4*a4^5*b1^4*b2^6*b3^3*b4^2 + a1^2*a2*a3^4*a4^5*b1^5*b2^6*b3^3*b4^2 +
a1^5*a2^6*a3^3*a4^5*b1^2*b2*b3^4*b4^2 + 4*a1^4*a2^6*a3^3*a4^5*b1^3*b2*b3^4*b4^2 +
4*a1^3*a2^6*a3^3*a4^5*b1^4*b2*b3^4*b4^2 + a1^2*a2^6*a3^3*a4^5*b1^5*b2*b3^4*b4^2 +
a1^6*a2^5*a3^3*a4^5*b1*b2^2*b3^4*b4^2 + 10*a1^5*a2^5*a3^3*a4^5*b1^2*b2^2*b3^4*b4^2 +
27*a1^4*a2^5*a3^3*a4^5*b1^3*b2^2*b3^4*b4^2 + 27*a1^3*a2^5*a3^3*a4^5*b1^4*b2^2*b3^4*b4^2 +
10*a1^2*a2^5*a3^3*a4^5*b1^5*b2^2*b3^4*b4^2 + a1*a2^5*a3^3*a4^5*b1^6*b2^2*b3^4*b4^2 +
4*a1^6*a2^4*a3^3*a4^5*b1*b2^3*b3^4*b4^2 + 27*a1^5*a2^4*a3^3*a4^5*b1^2*b2^3*b3^4*b4^2 +
64*a1^4*a2^4*a3^3*a4^5*b1^3*b2^3*b3^4*b4^2 + 64*a1^3*a2^4*a3^3*a4^5*b1^4*b2^3*b3^4*b4^2 +
27*a1^2*a2^4*a3^3*a4^5*b1^5*b2^3*b3^4*b4^2 + 4*a1*a2^4*a3^3*a4^5*b1^6*b2^3*b3^4*b4^2 +
4*a1^6*a2^3*a3^3*a4^5*b1*b2^4*b3^4*b4^2 + 27*a1^5*a2^3*a3^3*a4^5*b1^2*b2^4*b3^4*b4^2 +
64*a1^4*a2^3*a3^3*a4^5*b1^3*b2^4*b3^4*b4^2 + 64*a1^3*a2^3*a3^3*a4^5*b1^4*b2^4*b3^4*b4^2 +
27*a1^2*a2^3*a3^3*a4^5*b1^5*b2^4*b3^4*b4^2 + 4*a1*a2^3*a3^3*a4^5*b1^6*b2^4*b3^4*b4^2 +
a1^6*a2^2*a3^3*a4^5*b1*b2^5*b3^4*b4^2 + 10*a1^5*a2^2*a3^3*a4^5*b1^2*b2^5*b3^4*b4^2 +
27*a1^4*a2^2*a3^3*a4^5*b1^3*b2^5*b3^4*b4^2 + 27*a1^3*a2^2*a3^3*a4^5*b1^4*b2^5*b3^4*b4^2 +
10*a1^2*a2^2*a3^3*a4^5*b1^5*b2^5*b3^4*b4^2 + a1*a2^2*a3^3*a4^5*b1^6*b2^5*b3^4*b4^2 +
a1^5*a2*a3^3*a4^5*b1^2*b2^6*b3^4*b4^2 + 4*a1^4*a2*a3^3*a4^5*b1^3*b2^6*b3^4*b4^2 +
4*a1^3*a2*a3^3*a4^5*b1^4*b2^6*b3^4*b4^2 + a1^2*a2*a3^3*a4^5*b1^5*b2^6*b3^4*b4^2 +
a1^4*a2^6*a3^2*a4^5*b1^3*b2*b3^5*b4^2 + a1^3*a2^6*a3^2*a4^5*b1^4*b2*b3^5*b4^2 +
3*a1^5*a2^5*a3^2*a4^5*b1^2*b2^2*b3^5*b4^2 + 10*a1^4*a2^5*a3^2*a4^5*b1^3*b2^2*b3^5*b4^2 +
10*a1^3*a2^5*a3^2*a4^5*b1^4*b2^2*b3^5*b4^2 + 3*a1^2*a2^5*a3^2*a4^5*b1^5*b2^2*b3^5*b4^2 +
a1^6*a2^4*a3^2*a4^5*b1*b2^3*b3^5*b4^2 + 10*a1^5*a2^4*a3^2*a4^5*b1^2*b2^3*b3^5*b4^2 +
27*a1^4*a2^4*a3^2*a4^5*b1^3*b2^3*b3^5*b4^2 + 27*a1^3*a2^4*a3^2*a4^5*b1^4*b2^3*b3^5*b4^2 +
10*a1^2*a2^4*a3^2*a4^5*b1^5*b2^3*b3^5*b4^2 + a1*a2^4*a3^2*a4^5*b1^6*b2^3*b3^5*b4^2 +
a1^6*a2^3*a3^2*a4^5*b1*b2^4*b3^5*b4^2 + 10*a1^5*a2^3*a3^2*a4^5*b1^2*b2^4*b3^5*b4^2 +

2

27*a1^4*a2^3*a3^2*a4^5*b1^3*b2^4*b3^5*b4^2 + 27*a1^3*a2^3*a3^2*a4^5*b1^4*b2^4*b3^5*b4^2 +
10*a1^2*a2^3*a3^2*a4^5*b1^5*b2^4*b3^5*b4^2 + a1*a2^3*a3^2*a4^5*b1^6*b2^4*b3^5*b4^2 +
3*a1^5*a2^2*a3^2*a4^5*b1^2*b2^5*b3^5*b4^2 + 10*a1^4*a2^2*a3^2*a4^5*b1^3*b2^5*b3^5*b4^2 +
10*a1^3*a2^2*a3^2*a4^5*b1^4*b2^5*b3^5*b4^2 + 3*a1^2*a2^2*a3^2*a4^5*b1^5*b2^5*b3^5*b4^2 +
a1^4*a2*a3^2*a4^5*b1^3*b2^6*b3^5*b4^2 + a1^3*a2*a3^2*a4^5*b1^4*b2^6*b3^5*b4^2 +
a1^4*a2^5*a3*a4^5*b1^3*b2^2*b3^6*b4^2 + a1^3*a2^5*a3*a4^5*b1^4*b2^2*b3^6*b4^2 +
a1^5*a2^4*a3*a4^5*b1^2*b2^3*b3^6*b4^2 + 4*a1^4*a2^4*a3*a4^5*b1^3*b2^3*b3^6*b4^2 +
4*a1^3*a2^4*a3*a4^5*b1^4*b2^3*b3^6*b4^2 + a1^2*a2^4*a3*a4^5*b1^5*b2^3*b3^6*b4^2 +
a1^5*a2^3*a3*a4^5*b1^2*b2^4*b3^6*b4^2 + 4*a1^4*a2^3*a3*a4^5*b1^3*b2^4*b3^6*b4^2 +
4*a1^3*a2^3*a3*a4^5*b1^4*b2^4*b3^6*b4^2 + a1^2*a2^3*a3*a4^5*b1^5*b2^4*b3^6*b4^2 +
a1^4*a2^2*a3*a4^5*b1^3*b2^5*b3^6*b4^2 + a1^3*a2^2*a3*a4^5*b1^4*b2^5*b3^6*b4^2 +
a1^4*a2^4*a3^7*a4^4*b1^3*b2^3*b4^3 + a1^3*a2^4*a3^7*a4^4*b1^4*b2^3*b4^3 +
a1^4*a2^3*a3^7*a4^4*b1^3*b2^4*b4^3 + a1^3*a2^3*a3^7*a4^4*b1^4*b2^4*b4^3 +
a1^5*a2^5*a3^6*a4^4*b1^2*b2^2*b3*b4^3 + 4*a1^4*a2^5*a3^6*a4^4*b1^3*b2^2*b3*b4^3 +
4*a1^3*a2^5*a3^6*a4^4*b1^4*b2^2*b3*b4^3 + a1^2*a2^5*a3^6*a4^4*b1^5*b2^2*b3*b4^3 +
4*a1^5*a2^4*a3^6*a4^4*b1^2*b2^3*b3*b4^3 + 13*a1^4*a2^4*a3^6*a4^4*b1^3*b2^3*b3*b4^3 +
13*a1^3*a2^4*a3^6*a4^4*b1^4*b2^3*b3*b4^3 + 4*a1^2*a2^4*a3^6*a4^4*b1^5*b2^3*b3*b4^3 +
4*a1^5*a2^3*a3^6*a4^4*b1^2*b2^4*b3*b4^3 + 13*a1^4*a2^3*a3^6*a4^4*b1^3*b2^4*b3*b4^3 +
13*a1^3*a2^3*a3^6*a4^4*b1^4*b2^4*b3*b4^3 + 4*a1^2*a2^3*a3^6*a4^4*b1^5*b2^4*b3*b4^3 +
a1^5*a2^2*a3^6*a4^4*b1^2*b2^5*b3*b4^3 + 4*a1^4*a2^2*a3^6*a4^4*b1^3*b2^5*b3*b4^3 +
4*a1^3*a2^2*a3^6*a4^4*b1^4*b2^5*b3*b4^3 + a1^2*a2^2*a3^6*a4^4*b1^5*b2^5*b3*b4^3 +
a1^5*a2^6*a3^5*a4^4*b1^2*b2*b3^2*b4^3 + 4*a1^4*a2^6*a3^5*a4^4*b1^3*b2*b3^2*b4^3 +
4*a1^3*a2^6*a3^5*a4^4*b1^4*b2*b3^2*b4^3 + a1^2*a2^6*a3^5*a4^4*b1^5*b2*b3^2*b4^3 +
a1^6*a2^5*a3^5*a4^4*b1*b2^2*b3^2*b4^3 + 10*a1^5*a2^5*a3^5*a4^4*b1^2*b2^2*b3^2*b4^3 +
27*a1^4*a2^5*a3^5*a4^4*b1^3*b2^2*b3^2*b4^3 + 27*a1^3*a2^5*a3^5*a4^4*b1^4*b2^2*b3^2*b4^3 +
10*a1^2*a2^5*a3^5*a4^4*b1^5*b2^2*b3^2*b4^3 + a1*a2^5*a3^5*a4^4*b1^6*b2^2*b3^2*b4^3 +
4*a1^6*a2^4*a3^5*a4^4*b1*b2^3*b3^2*b4^3 + 27*a1^5*a2^4*a3^5*a4^4*b1^2*b2^3*b3^2*b4^3 +
64*a1^4*a2^4*a3^5*a4^4*b1^3*b2^3*b3^2*b4^3 + 64*a1^3*a2^4*a3^5*a4^4*b1^4*b2^3*b3^2*b4^3 +
27*a1^2*a2^4*a3^5*a4^4*b1^5*b2^3*b3^2*b4^3 + 4*a1*a2^4*a3^5*a4^4*b1^6*b2^3*b3^2*b4^3 +
4*a1^6*a2^3*a3^5*a4^4*b1*b2^4*b3^2*b4^3 + 27*a1^5*a2^3*a3^5*a4^4*b1^2*b2^4*b3^2*b4^3 +
64*a1^4*a2^3*a3^5*a4^4*b1^3*b2^4*b3^2*b4^3 + 64*a1^3*a2^3*a3^5*a4^4*b1^4*b2^4*b3^2*b4^3 +
27*a1^2*a2^3*a3^5*a4^4*b1^5*b2^4*b3^2*b4^3 + 4*a1*a2^3*a3^5*a4^4*b1^6*b2^4*b3^2*b4^3 +
a1^6*a2^2*a3^5*a4^4*b1*b2^5*b3^2*b4^3 + 10*a1^5*a2^2*a3^5*a4^4*b1^2*b2^5*b3^2*b4^3 +
27*a1^4*a2^2*a3^5*a4^4*b1^3*b2^5*b3^2*b4^3 + 27*a1^3*a2^2*a3^5*a4^4*b1^4*b2^5*b3^2*b4^3 +
10*a1^2*a2^2*a3^5*a4^4*b1^5*b2^5*b3^2*b4^3 + a1*a2^2*a3^5*a4^4*b1^6*b2^5*b3^2*b4^3 +
a1^5*a2*a3^5*a4^4*b1^2*b2^6*b3^2*b4^3 + 4*a1^4*a2*a3^5*a4^4*b1^3*b2^6*b3^2*b4^3 +
4*a1^3*a2*a3^5*a4^4*b1^4*b2^6*b3^2*b4^3 + a1^2*a2*a3^5*a4^4*b1^5*b2^6*b3^2*b4^3 +
a1^4*a2^7*a3^4*a4^4*b1^3*b3^3*b4^3 + a1^3*a2^7*a3^4*a4^4*b1^4*b3^3*b4^3 +
4*a1^5*a2^6*a3^4*a4^4*b1^2*b2*b3^3*b4^3 + 13*a1^4*a2^6*a3^4*a4^4*b1^3*b2*b3^3*b4^3 +
13*a1^3*a2^6*a3^4*a4^4*b1^4*b2*b3^3*b4^3 + 4*a1^2*a2^6*a3^4*a4^4*b1^5*b2*b3^3*b4^3 +
4*a1^6*a2^5*a3^4*a4^4*b1*b2^2*b3^3*b4^3 + 27*a1^5*a2^5*a3^4*a4^4*b1^2*b2^2*b3^3*b4^3 +
64*a1^4*a2^5*a3^4*a4^4*b1^3*b2^2*b3^3*b4^3 + 64*a1^3*a2^5*a3^4*a4^4*b1^4*b2^2*b3^3*b4^3 +
27*a1^2*a2^5*a3^4*a4^4*b1^5*b2^2*b3^3*b4^3 + 4*a1*a2^5*a3^4*a4^4*b1^6*b2^2*b3^3*b4^3 +
a1^7*a2^4*a3^4*a4^4*b2^3*b3^3*b4^3 + 13*a1^6*a2^4*a3^4*a4^4*b1*b2^3*b3^3*b4^3 +
64*a1^5*a2^4*a3^4*a4^4*b1^2*b2^3*b3^3*b4^3 + 138*a1^4*a2^4*a3^4*a4^4*b1^3*b2^3*b3^3*b4^3 +
138*a1^3*a2^4*a3^4*a4^4*b1^4*b2^3*b3^3*b4^3 + 64*a1^2*a2^4*a3^4*a4^4*b1^5*b2^3*b3^3*b4^3 +
13*a1*a2^4*a3^4*a4^4*b1^6*b2^3*b3^3*b4^3 + a2^4*a3^4*a4^4*b1^7*b2^3*b3^3*b4^3 +
a1^7*a2^3*a3^4*a4^4*b2^4*b3^3*b4^3 + 13*a1^6*a2^3*a3^4*a4^4*b1*b2^4*b3^3*b4^3 +
64*a1^5*a2^3*a3^4*a4^4*b1^2*b2^4*b3^3*b4^3 + 138*a1^4*a2^3*a3^4*a4^4*b1^3*b2^4*b3^3*b4^3 +
138*a1^3*a2^3*a3^4*a4^4*b1^4*b2^4*b3^3*b4^3 + 64*a1^2*a2^3*a3^4*a4^4*b1^5*b2^4*b3^3*b4^3 +
13*a1*a2^3*a3^4*a4^4*b1^6*b2^4*b3^3*b4^3 + a2^3*a3^4*a4^4*b1^7*b2^4*b3^3*b4^3 +
4*a1^6*a2^2*a3^4*a4^4*b1*b2^5*b3^3*b4^3 + 27*a1^5*a2^2*a3^4*a4^4*b1^2*b2^5*b3^3*b4^3 +
64*a1^4*a2^2*a3^4*a4^4*b1^3*b2^5*b3^3*b4^3 + 64*a1^3*a2^2*a3^4*a4^4*b1^4*b2^5*b3^3*b4^3 +
27*a1^2*a2^2*a3^4*a4^4*b1^5*b2^5*b3^3*b4^3 + 4*a1*a2^2*a3^4*a4^4*b1^6*b2^5*b3^3*b4^3 +
4*a1^5*a2*a3^4*a4^4*b1^2*b2^6*b3^3*b4^3 + 13*a1^4*a2*a3^4*a4^4*b1^3*b2^6*b3^3*b4^3 +
13*a1^3*a2*a3^4*a4^4*b1^4*b2^6*b3^3*b4^3 + 4*a1^2*a2*a3^4*a4^4*b1^5*b2^6*b3^3*b4^3 +
a1^4*a3^4*a4^4*b1^3*b2^7*b3^3*b4^3 + a1^3*a3^4*a4^4*b1^4*b2^7*b3^3*b4^3 +
a1^4*a2^7*a3^3*a4^4*b1^3*b3^4*b4^3 + a1^3*a2^7*a3^3*a4^4*b1^4*b3^4*b4^3 +
4*a1^5*a2^6*a3^3*a4^4*b1^2*b2*b3^4*b4^3 + 13*a1^4*a2^6*a3^3*a4^4*b1^3*b2*b3^4*b4^3 +
13*a1^3*a2^6*a3^3*a4^4*b1^4*b2*b3^4*b4^3 + 4*a1^2*a2^6*a3^3*a4^4*b1^5*b2*b3^4*b4^3 +
4*a1^6*a2^5*a3^3*a4^4*b1*b2^2*b3^4*b4^3 + 27*a1^5*a2^5*a3^3*a4^4*b1^2*b2^2*b3^4*b4^3 +

3

64*a1^4*a2^5*a3^3*a4^4*b1^3*b2^2*b3^4*b4^3 + 64*a1^3*a2^5*a3^3*a4^4*b1^4*b2^2*b3^4*b4^3 +
27*a1^2*a2^5*a3^3*a4^4*b1^5*b2^2*b3^4*b4^3 + 4*a1*a2^5*a3^3*a4^4*b1^6*b2^2*b3^4*b4^3 +
a1^7*a2^4*a3^3*a4^4*b2^3*b3^4*b4^3 + 13*a1^6*a2^4*a3^3*a4^4*b1*b2^3*b3^4*b4^3 +
64*a1^5*a2^4*a3^3*a4^4*b1^2*b2^3*b3^4*b4^3 + 138*a1^4*a2^4*a3^3*a4^4*b1^3*b2^3*b3^4*b4^3 +
138*a1^3*a2^4*a3^3*a4^4*b1^4*b2^3*b3^4*b4^3 + 64*a1^2*a2^4*a3^3*a4^4*b1^5*b2^3*b3^4*b4^3 +
13*a1*a2^4*a3^3*a4^4*b1^6*b2^3*b3^4*b4^3 + a2^4*a3^3*a4^4*b1^7*b2^3*b3^4*b4^3 +
a1^7*a2^3*a3^3*a4^4*b2^4*b3^4*b4^3 + 13*a1^6*a2^3*a3^3*a4^4*b1*b2^4*b3^4*b4^3 +
64*a1^5*a2^3*a3^3*a4^4*b1^2*b2^4*b3^4*b4^3 + 138*a1^4*a2^3*a3^3*a4^4*b1^3*b2^4*b3^4*b4^3 +
138*a1^3*a2^3*a3^3*a4^4*b1^4*b2^4*b3^4*b4^3 + 64*a1^2*a2^3*a3^3*a4^4*b1^5*b2^4*b3^4*b4^3 +
13*a1*a2^3*a3^3*a4^4*b1^6*b2^4*b3^4*b4^3 + a2^3*a3^3*a4^4*b1^7*b2^4*b3^4*b4^3 +
4*a1^6*a2^2*a3^3*a4^4*b1*b2^5*b3^4*b4^3 + 27*a1^5*a2^2*a3^3*a4^4*b1^2*b2^5*b3^4*b4^3 +
64*a1^4*a2^2*a3^3*a4^4*b1^3*b2^5*b3^4*b4^3 + 64*a1^3*a2^2*a3^3*a4^4*b1^4*b2^5*b3^4*b4^3 +
27*a1^2*a2^2*a3^3*a4^4*b1^5*b2^5*b3^4*b4^3 + 4*a1*a2^2*a3^3*a4^4*b1^6*b2^5*b3^4*b4^3 +
4*a1^5*a2*a3^3*a4^4*b1^2*b2^6*b3^4*b4^3 + 13*a1^4*a2*a3^3*a4^4*b1^3*b2^6*b3^4*b4^3 +
13*a1^3*a2*a3^3*a4^4*b1^4*b2^6*b3^4*b4^3 + 4*a1^2*a2*a3^3*a4^4*b1^5*b2^6*b3^4*b4^3 +
a1^4*a3^3*a4^4*b1^3*b2^7*b3^4*b4^3 + a1^3*a3^3*a4^4*b1^4*b2^7*b3^4*b4^3 +
a1^5*a2^6*a3^2*a4^4*b1^2*b2*b3^5*b4^3 + 4*a1^4*a2^6*a3^2*a4^4*b1^3*b2*b3^5*b4^3 +
4*a1^3*a2^6*a3^2*a4^4*b1^4*b2*b3^5*b4^3 + a1^2*a2^6*a3^2*a4^4*b1^5*b2*b3^5*b4^3 +
a1^6*a2^5*a3^2*a4^4*b1*b2^2*b3^5*b4^3 + 10*a1^5*a2^5*a3^2*a4^4*b1^2*b2^2*b3^5*b4^3 +
27*a1^4*a2^5*a3^2*a4^4*b1^3*b2^2*b3^5*b4^3 + 27*a1^3*a2^5*a3^2*a4^4*b1^4*b2^2*b3^5*b4^3 +
10*a1^2*a2^5*a3^2*a4^4*b1^5*b2^2*b3^5*b4^3 + a1*a2^5*a3^2*a4^4*b1^6*b2^2*b3^5*b4^3 +
4*a1^6*a2^4*a3^2*a4^4*b1*b2^3*b3^5*b4^3 + 27*a1^5*a2^4*a3^2*a4^4*b1^2*b2^3*b3^5*b4^3 +
64*a1^4*a2^4*a3^2*a4^4*b1^3*b2^3*b3^5*b4^3 + 64*a1^3*a2^4*a3^2*a4^4*b1^4*b2^3*b3^5*b4^3 +
27*a1^2*a2^4*a3^2*a4^4*b1^5*b2^3*b3^5*b4^3 + 4*a1*a2^4*a3^2*a4^4*b1^6*b2^3*b3^5*b4^3 +
4*a1^6*a2^3*a3^2*a4^4*b1*b2^4*b3^5*b4^3 + 27*a1^5*a2^3*a3^2*a4^4*b1^2*b2^4*b3^5*b4^3 +
64*a1^4*a2^3*a3^2*a4^4*b1^3*b2^4*b3^5*b4^3 + 64*a1^3*a2^3*a3^2*a4^4*b1^4*b2^4*b3^5*b4^3 +
27*a1^2*a2^3*a3^2*a4^4*b1^5*b2^4*b3^5*b4^3 + 4*a1*a2^3*a3^2*a4^4*b1^6*b2^4*b3^5*b4^3 +
a1^6*a2^2*a3^2*a4^4*b1*b2^5*b3^5*b4^3 + 10*a1^5*a2^2*a3^2*a4^4*b1^2*b2^5*b3^5*b4^3 +
27*a1^4*a2^2*a3^2*a4^4*b1^3*b2^5*b3^5*b4^3 + 27*a1^3*a2^2*a3^2*a4^4*b1^4*b2^5*b3^5*b4^3 +
10*a1^2*a2^2*a3^2*a4^4*b1^5*b2^5*b3^5*b4^3 + a1*a2^2*a3^2*a4^4*b1^6*b2^5*b3^5*b4^3 +
a1^5*a2*a3^2*a4^4*b1^2*b2^6*b3^5*b4^3 + 4*a1^4*a2*a3^2*a4^4*b1^3*b2^6*b3^5*b4^3 +
4*a1^3*a2*a3^2*a4^4*b1^4*b2^6*b3^5*b4^3 + a1^2*a2*a3^2*a4^4*b1^5*b2^6*b3^5*b4^3 +
a1^5*a2^5*a3*a4^4*b1^2*b2^2*b3^6*b4^3 + 4*a1^4*a2^5*a3*a4^4*b1^3*b2^2*b3^6*b4^3 +
4*a1^3*a2^5*a3*a4^4*b1^4*b2^2*b3^6*b4^3 + a1^2*a2^5*a3*a4^4*b1^5*b2^2*b3^6*b4^3 +
4*a1^5*a2^4*a3*a4^4*b1^2*b2^3*b3^6*b4^3 + 13*a1^4*a2^4*a3*a4^4*b1^3*b2^3*b3^6*b4^3 +
13*a1^3*a2^4*a3*a4^4*b1^4*b2^3*b3^6*b4^3 + 4*a1^2*a2^4*a3*a4^4*b1^5*b2^3*b3^6*b4^3 +
4*a1^5*a2^3*a3*a4^4*b1^2*b2^4*b3^6*b4^3 + 13*a1^4*a2^3*a3*a4^4*b1^3*b2^4*b3^6*b4^3 +
13*a1^3*a2^3*a3*a4^4*b1^4*b2^4*b3^6*b4^3 + 4*a1^2*a2^3*a3*a4^4*b1^5*b2^4*b3^6*b4^3 +
a1^5*a2^2*a3*a4^4*b1^2*b2^5*b3^6*b4^3 + 4*a1^4*a2^2*a3*a4^4*b1^3*b2^5*b3^6*b4^3 +
4*a1^3*a2^2*a3*a4^4*b1^4*b2^5*b3^6*b4^3 + a1^2*a2^2*a3*a4^4*b1^5*b2^5*b3^6*b4^3 +
a1^4*a2^4*a4^4*b1^3*b2^3*b3^7*b4^3 + a1^3*a2^4*a4^4*b1^4*b2^3*b3^7*b4^3 +
a1^4*a2^3*a4^4*b1^3*b2^4*b3^7*b4^3 + a1^3*a2^3*a4^4*b1^4*b2^4*b3^7*b4^3 +
a1^4*a2^4*a3^7*a4^3*b1^3*b2^3*b4^4 + a1^3*a2^4*a3^7*a4^3*b1^4*b2^3*b4^4 +
a1^4*a2^3*a3^7*a4^3*b1^3*b2^4*b4^4 + a1^3*a2^3*a3^7*a4^3*b1^4*b2^4*b4^4 +
a1^5*a2^5*a3^6*a4^3*b1^2*b2^2*b3*b4^4 + 4*a1^4*a2^5*a3^6*a4^3*b1^3*b2^2*b3*b4^4 +
4*a1^3*a2^5*a3^6*a4^3*b1^4*b2^2*b3*b4^4 + a1^2*a2^5*a3^6*a4^3*b1^5*b2^2*b3*b4^4 +
4*a1^5*a2^4*a3^6*a4^3*b1^2*b2^3*b3*b4^4 + 13*a1^4*a2^4*a3^6*a4^3*b1^3*b2^3*b3*b4^4 +
13*a1^3*a2^4*a3^6*a4^3*b1^4*b2^3*b3*b4^4 + 4*a1^2*a2^4*a3^6*a4^3*b1^5*b2^3*b3*b4^4 +
4*a1^5*a2^3*a3^6*a4^3*b1^2*b2^4*b3*b4^4 + 13*a1^4*a2^3*a3^6*a4^3*b1^3*b2^4*b3*b4^4 +
13*a1^3*a2^3*a3^6*a4^3*b1^4*b2^4*b3*b4^4 + 4*a1^2*a2^3*a3^6*a4^3*b1^5*b2^4*b3*b4^4 +
a1^5*a2^2*a3^6*a4^3*b1^2*b2^5*b3*b4^4 + 4*a1^4*a2^2*a3^6*a4^3*b1^3*b2^5*b3*b4^4 +
4*a1^3*a2^2*a3^6*a4^3*b1^4*b2^5*b3*b4^4 + a1^2*a2^2*a3^6*a4^3*b1^5*b2^5*b3*b4^4 +
a1^5*a2^6*a3^5*a4^3*b1^2*b2*b3^2*b4^4 + 4*a1^4*a2^6*a3^5*a4^3*b1^3*b2*b3^2*b4^4 +
4*a1^3*a2^6*a3^5*a4^3*b1^4*b2*b3^2*b4^4 + a1^2*a2^6*a3^5*a4^3*b1^5*b2*b3^2*b4^4 +
a1^6*a2^5*a3^5*a4^3*b1*b2^2*b3^2*b4^4 + 10*a1^5*a2^5*a3^5*a4^3*b1^2*b2^2*b3^2*b4^4 +
27*a1^4*a2^5*a3^5*a4^3*b1^3*b2^2*b3^2*b4^4 + 27*a1^3*a2^5*a3^5*a4^3*b1^4*b2^2*b3^2*b4^4 +
10*a1^2*a2^5*a3^5*a4^3*b1^5*b2^2*b3^2*b4^4 + a1*a2^5*a3^5*a4^3*b1^6*b2^2*b3^2*b4^4 +
4*a1^6*a2^4*a3^5*a4^3*b1*b2^3*b3^2*b4^4 + 27*a1^5*a2^4*a3^5*a4^3*b1^2*b2^3*b3^2*b4^4 +
64*a1^4*a2^4*a3^5*a4^3*b1^3*b2^3*b3^2*b4^4 + 64*a1^3*a2^4*a3^5*a4^3*b1^4*b2^3*b3^2*b4^4 +
27*a1^2*a2^4*a3^5*a4^3*b1^5*b2^3*b3^2*b4^4 + 4*a1*a2^4*a3^5*a4^3*b1^6*b2^3*b3^2*b4^4 +
4*a1^6*a2^3*a3^5*a4^3*b1*b2^4*b3^2*b4^4 + 27*a1^5*a2^3*a3^5*a4^3*b1^2*b2^4*b3^2*b4^4 +

4

64*a1^4*a2^3*a3^5*a4^3*b1^3*b2^4*b3^2*b4^4 + 64*a1^3*a2^3*a3^5*a4^3*b1^4*b2^4*b3^2*b4^4 +
27*a1^2*a2^3*a3^5*a4^3*b1^5*b2^4*b3^2*b4^4 + 4*a1*a2^3*a3^5*a4^3*b1^6*b2^4*b3^2*b4^4 +
a1^6*a2^2*a3^5*a4^3*b1*b2^5*b3^2*b4^4 + 10*a1^5*a2^2*a3^5*a4^3*b1^2*b2^5*b3^2*b4^4 +
27*a1^4*a2^2*a3^5*a4^3*b1^3*b2^5*b3^2*b4^4 + 27*a1^3*a2^2*a3^5*a4^3*b1^4*b2^5*b3^2*b4^4 +
10*a1^2*a2^2*a3^5*a4^3*b1^5*b2^5*b3^2*b4^4 + a1*a2^2*a3^5*a4^3*b1^6*b2^5*b3^2*b4^4 +
a1^5*a2*a3^5*a4^3*b1^2*b2^6*b3^2*b4^4 + 4*a1^4*a2*a3^5*a4^3*b1^3*b2^6*b3^2*b4^4 +
4*a1^3*a2*a3^5*a4^3*b1^4*b2^6*b3^2*b4^4 + a1^2*a2*a3^5*a4^3*b1^5*b2^6*b3^2*b4^4 +
a1^4*a2^7*a3^4*a4^3*b1^3*b3^3*b4^4 + a1^3*a2^7*a3^4*a4^3*b1^4*b3^3*b4^4 +
4*a1^5*a2^6*a3^4*a4^3*b1^2*b2*b3^3*b4^4 + 13*a1^4*a2^6*a3^4*a4^3*b1^3*b2*b3^3*b4^4 +
13*a1^3*a2^6*a3^4*a4^3*b1^4*b2*b3^3*b4^4 + 4*a1^2*a2^6*a3^4*a4^3*b1^5*b2*b3^3*b4^4 +
4*a1^6*a2^5*a3^4*a4^3*b1*b2^2*b3^3*b4^4 + 27*a1^5*a2^5*a3^4*a4^3*b1^2*b2^2*b3^3*b4^4 +
64*a1^4*a2^5*a3^4*a4^3*b1^3*b2^2*b3^3*b4^4 + 64*a1^3*a2^5*a3^4*a4^3*b1^4*b2^2*b3^3*b4^4 +
27*a1^2*a2^5*a3^4*a4^3*b1^5*b2^2*b3^3*b4^4 + 4*a1*a2^5*a3^4*a4^3*b1^6*b2^2*b3^3*b4^4 +
a1^7*a2^4*a3^4*a4^3*b2^3*b3^3*b4^4 + 13*a1^6*a2^4*a3^4*a4^3*b1*b2^3*b3^3*b4^4 +
64*a1^5*a2^4*a3^4*a4^3*b1^2*b2^3*b3^3*b4^4 + 138*a1^4*a2^4*a3^4*a4^3*b1^3*b2^3*b3^3*b4^4 +
138*a1^3*a2^4*a3^4*a4^3*b1^4*b2^3*b3^3*b4^4 + 64*a1^2*a2^4*a3^4*a4^3*b1^5*b2^3*b3^3*b4^4 +
13*a1*a2^4*a3^4*a4^3*b1^6*b2^3*b3^3*b4^4 + a2^4*a3^4*a4^3*b1^7*b2^3*b3^3*b4^4 +
a1^7*a2^3*a3^4*a4^3*b2^4*b3^3*b4^4 + 13*a1^6*a2^3*a3^4*a4^3*b1*b2^4*b3^3*b4^4 +
64*a1^5*a2^3*a3^4*a4^3*b1^2*b2^4*b3^3*b4^4 + 138*a1^4*a2^3*a3^4*a4^3*b1^3*b2^4*b3^3*b4^4 +
138*a1^3*a2^3*a3^4*a4^3*b1^4*b2^4*b3^3*b4^4 + 64*a1^2*a2^3*a3^4*a4^3*b1^5*b2^4*b3^3*b4^4 +
13*a1*a2^3*a3^4*a4^3*b1^6*b2^4*b3^3*b4^4 + a2^3*a3^4*a4^3*b1^7*b2^4*b3^3*b4^4 +
4*a1^6*a2^2*a3^4*a4^3*b1*b2^5*b3^3*b4^4 + 27*a1^5*a2^2*a3^4*a4^3*b1^2*b2^5*b3^3*b4^4 +
64*a1^4*a2^2*a3^4*a4^3*b1^3*b2^5*b3^3*b4^4 + 64*a1^3*a2^2*a3^4*a4^3*b1^4*b2^5*b3^3*b4^4 +
27*a1^2*a2^2*a3^4*a4^3*b1^5*b2^5*b3^3*b4^4 + 4*a1*a2^2*a3^4*a4^3*b1^6*b2^5*b3^3*b4^4 +
4*a1^5*a2*a3^4*a4^3*b1^2*b2^6*b3^3*b4^4 + 13*a1^4*a2*a3^4*a4^3*b1^3*b2^6*b3^3*b4^4 +
13*a1^3*a2*a3^4*a4^3*b1^4*b2^6*b3^3*b4^4 + 4*a1^2*a2*a3^4*a4^3*b1^5*b2^6*b3^3*b4^4 +
a1^4*a3^4*a4^3*b1^3*b2^7*b3^3*b4^4 + a1^3*a3^4*a4^3*b1^4*b2^7*b3^3*b4^4 +
a1^4*a2^7*a3^3*a4^3*b1^3*b3^4*b4^4 + a1^3*a2^7*a3^3*a4^3*b1^4*b3^4*b4^4 +
4*a1^5*a2^6*a3^3*a4^3*b1^2*b2*b3^4*b4^4 + 13*a1^4*a2^6*a3^3*a4^3*b1^3*b2*b3^4*b4^4 +
13*a1^3*a2^6*a3^3*a4^3*b1^4*b2*b3^4*b4^4 + 4*a1^2*a2^6*a3^3*a4^3*b1^5*b2*b3^4*b4^4 +
4*a1^6*a2^5*a3^3*a4^3*b1*b2^2*b3^4*b4^4 + 27*a1^5*a2^5*a3^3*a4^3*b1^2*b2^2*b3^4*b4^4 +
64*a1^4*a2^5*a3^3*a4^3*b1^3*b2^2*b3^4*b4^4 + 64*a1^3*a2^5*a3^3*a4^3*b1^4*b2^2*b3^4*b4^4 +
27*a1^2*a2^5*a3^3*a4^3*b1^5*b2^2*b3^4*b4^4 + 4*a1*a2^5*a3^3*a4^3*b1^6*b2^2*b3^4*b4^4 +
a1^7*a2^4*a3^3*a4^3*b2^3*b3^4*b4^4 + 13*a1^6*a2^4*a3^3*a4^3*b1*b2^3*b3^4*b4^4 +
64*a1^5*a2^4*a3^3*a4^3*b1^2*b2^3*b3^4*b4^4 + 138*a1^4*a2^4*a3^3*a4^3*b1^3*b2^3*b3^4*b4^4 +
138*a1^3*a2^4*a3^3*a4^3*b1^4*b2^3*b3^4*b4^4 + 64*a1^2*a2^4*a3^3*a4^3*b1^5*b2^3*b3^4*b4^4 +
13*a1*a2^4*a3^3*a4^3*b1^6*b2^3*b3^4*b4^4 + a2^4*a3^3*a4^3*b1^7*b2^3*b3^4*b4^4 +
a1^7*a2^3*a3^3*a4^3*b2^4*b3^4*b4^4 + 13*a1^6*a2^3*a3^3*a4^3*b1*b2^4*b3^4*b4^4 +
64*a1^5*a2^3*a3^3*a4^3*b1^2*b2^4*b3^4*b4^4 + 138*a1^4*a2^3*a3^3*a4^3*b1^3*b2^4*b3^4*b4^4 +
138*a1^3*a2^3*a3^3*a4^3*b1^4*b2^4*b3^4*b4^4 + 64*a1^2*a2^3*a3^3*a4^3*b1^5*b2^4*b3^4*b4^4 +
13*a1*a2^3*a3^3*a4^3*b1^6*b2^4*b3^4*b4^4 + a2^3*a3^3*a4^3*b1^7*b2^4*b3^4*b4^4 +
4*a1^6*a2^2*a3^3*a4^3*b1*b2^5*b3^4*b4^4 + 27*a1^5*a2^2*a3^3*a4^3*b1^2*b2^5*b3^4*b4^4 +
64*a1^4*a2^2*a3^3*a4^3*b1^3*b2^5*b3^4*b4^4 + 64*a1^3*a2^2*a3^3*a4^3*b1^4*b2^5*b3^4*b4^4 +
27*a1^2*a2^2*a3^3*a4^3*b1^5*b2^5*b3^4*b4^4 + 4*a1*a2^2*a3^3*a4^3*b1^6*b2^5*b3^4*b4^4 +
4*a1^5*a2*a3^3*a4^3*b1^2*b2^6*b3^4*b4^4 + 13*a1^4*a2*a3^3*a4^3*b1^3*b2^6*b3^4*b4^4 +
13*a1^3*a2*a3^3*a4^3*b1^4*b2^6*b3^4*b4^4 + 4*a1^2*a2*a3^3*a4^3*b1^5*b2^6*b3^4*b4^4 +
a1^4*a3^3*a4^3*b1^3*b2^7*b3^4*b4^4 + a1^3*a3^3*a4^3*b1^4*b2^7*b3^4*b4^4 +
a1^5*a2^6*a3^2*a4^3*b1^2*b2*b3^5*b4^4 + 4*a1^4*a2^6*a3^2*a4^3*b1^3*b2*b3^5*b4^4 +
4*a1^3*a2^6*a3^2*a4^3*b1^4*b2*b3^5*b4^4 + a1^2*a2^6*a3^2*a4^3*b1^5*b2*b3^5*b4^4 +
a1^6*a2^5*a3^2*a4^3*b1*b2^2*b3^5*b4^4 + 10*a1^5*a2^5*a3^2*a4^3*b1^2*b2^2*b3^5*b4^4 +
27*a1^4*a2^5*a3^2*a4^3*b1^3*b2^2*b3^5*b4^4 + 27*a1^3*a2^5*a3^2*a4^3*b1^4*b2^2*b3^5*b4^4 +
10*a1^2*a2^5*a3^2*a4^3*b1^5*b2^2*b3^5*b4^4 + a1*a2^5*a3^2*a4^3*b1^6*b2^2*b3^5*b4^4 +
4*a1^6*a2^4*a3^2*a4^3*b1*b2^3*b3^5*b4^4 + 27*a1^5*a2^4*a3^2*a4^3*b1^2*b2^3*b3^5*b4^4 +
64*a1^4*a2^4*a3^2*a4^3*b1^3*b2^3*b3^5*b4^4 + 64*a1^3*a2^4*a3^2*a4^3*b1^4*b2^3*b3^5*b4^4 +
27*a1^2*a2^4*a3^2*a4^3*b1^5*b2^3*b3^5*b4^4 + 4*a1*a2^4*a3^2*a4^3*b1^6*b2^3*b3^5*b4^4 +
4*a1^6*a2^3*a3^2*a4^3*b1*b2^4*b3^5*b4^4 + 27*a1^5*a2^3*a3^2*a4^3*b1^2*b2^4*b3^5*b4^4 +
64*a1^4*a2^3*a3^2*a4^3*b1^3*b2^4*b3^5*b4^4 + 64*a1^3*a2^3*a3^2*a4^3*b1^4*b2^4*b3^5*b4^4 +
27*a1^2*a2^3*a3^2*a4^3*b1^5*b2^4*b3^5*b4^4 + 4*a1*a2^3*a3^2*a4^3*b1^6*b2^4*b3^5*b4^4 +
a1^6*a2^2*a3^2*a4^3*b1*b2^5*b3^5*b4^4 + 10*a1^5*a2^2*a3^2*a4^3*b1^2*b2^5*b3^5*b4^4 +
27*a1^4*a2^2*a3^2*a4^3*b1^3*b2^5*b3^5*b4^4 + 27*a1^3*a2^2*a3^2*a4^3*b1^4*b2^5*b3^5*b4^4 +
10*a1^2*a2^2*a3^2*a4^3*b1^5*b2^5*b3^5*b4^4 + a1*a2^2*a3^2*a4^3*b1^6*b2^5*b3^5*b4^4 +

5

a1^5*a2*a3^2*a4^3*b1^2*b2^6*b3^5*b4^4 + 4*a1^4*a2*a3^2*a4^3*b1^3*b2^6*b3^5*b4^4 +
4*a1^3*a2*a3^2*a4^3*b1^4*b2^6*b3^5*b4^4 + a1^2*a2*a3^2*a4^3*b1^5*b2^6*b3^5*b4^4 +
a1^5*a2^5*a3*a4^3*b1^2*b2^2*b3^6*b4^4 + 4*a1^4*a2^5*a3*a4^3*b1^3*b2^2*b3^6*b4^4 +
4*a1^3*a2^5*a3*a4^3*b1^4*b2^2*b3^6*b4^4 + a1^2*a2^5*a3*a4^3*b1^5*b2^2*b3^6*b4^4 +
4*a1^5*a2^4*a3*a4^3*b1^2*b2^3*b3^6*b4^4 + 13*a1^4*a2^4*a3*a4^3*b1^3*b2^3*b3^6*b4^4 +
13*a1^3*a2^4*a3*a4^3*b1^4*b2^3*b3^6*b4^4 + 4*a1^2*a2^4*a3*a4^3*b1^5*b2^3*b3^6*b4^4 +
4*a1^5*a2^3*a3*a4^3*b1^2*b2^4*b3^6*b4^4 + 13*a1^4*a2^3*a3*a4^3*b1^3*b2^4*b3^6*b4^4 +
13*a1^3*a2^3*a3*a4^3*b1^4*b2^4*b3^6*b4^4 + 4*a1^2*a2^3*a3*a4^3*b1^5*b2^4*b3^6*b4^4 +
a1^5*a2^2*a3*a4^3*b1^2*b2^5*b3^6*b4^4 + 4*a1^4*a2^2*a3*a4^3*b1^3*b2^5*b3^6*b4^4 +
4*a1^3*a2^2*a3*a4^3*b1^4*b2^5*b3^6*b4^4 + a1^2*a2^2*a3*a4^3*b1^5*b2^5*b3^6*b4^4 +
a1^4*a2^4*a4^3*b1^3*b2^3*b3^7*b4^4 + a1^3*a2^4*a4^3*b1^4*b2^3*b3^7*b4^4 +
a1^4*a2^3*a4^3*b1^3*b2^4*b3^7*b4^4 + a1^3*a2^3*a4^3*b1^4*b2^4*b3^7*b4^4 +
a1^4*a2^5*a3^6*a4^2*b1^3*b2^2*b3*b4^5 + a1^3*a2^5*a3^6*a4^2*b1^4*b2^2*b3*b4^5 +
a1^5*a2^4*a3^6*a4^2*b1^2*b2^3*b3*b4^5 + 4*a1^4*a2^4*a3^6*a4^2*b1^3*b2^3*b3*b4^5 +
4*a1^3*a2^4*a3^6*a4^2*b1^4*b2^3*b3*b4^5 + a1^2*a2^4*a3^6*a4^2*b1^5*b2^3*b3*b4^5 +
a1^5*a2^3*a3^6*a4^2*b1^2*b2^4*b3*b4^5 + 4*a1^4*a2^3*a3^6*a4^2*b1^3*b2^4*b3*b4^5 +
4*a1^3*a2^3*a3^6*a4^2*b1^4*b2^4*b3*b4^5 + a1^2*a2^3*a3^6*a4^2*b1^5*b2^4*b3*b4^5 +
a1^4*a2^2*a3^6*a4^2*b1^3*b2^5*b3*b4^5 + a1^3*a2^2*a3^6*a4^2*b1^4*b2^5*b3*b4^5 +
a1^4*a2^6*a3^5*a4^2*b1^3*b2*b3^2*b4^5 + a1^3*a2^6*a3^5*a4^2*b1^4*b2*b3^2*b4^5 +
3*a1^5*a2^5*a3^5*a4^2*b1^2*b2^2*b3^2*b4^5 + 10*a1^4*a2^5*a3^5*a4^2*b1^3*b2^2*b3^2*b4^5 +
10*a1^3*a2^5*a3^5*a4^2*b1^4*b2^2*b3^2*b4^5 + 3*a1^2*a2^5*a3^5*a4^2*b1^5*b2^2*b3^2*b4^5 +
a1^6*a2^4*a3^5*a4^2*b1*b2^3*b3^2*b4^5 + 10*a1^5*a2^4*a3^5*a4^2*b1^2*b2^3*b3^2*b4^5 +
27*a1^4*a2^4*a3^5*a4^2*b1^3*b2^3*b3^2*b4^5 + 27*a1^3*a2^4*a3^5*a4^2*b1^4*b2^3*b3^2*b4^5 +
10*a1^2*a2^4*a3^5*a4^2*b1^5*b2^3*b3^2*b4^5 + a1*a2^4*a3^5*a4^2*b1^6*b2^3*b3^2*b4^5 +
a1^6*a2^3*a3^5*a4^2*b1*b2^4*b3^2*b4^5 + 10*a1^5*a2^3*a3^5*a4^2*b1^2*b2^4*b3^2*b4^5 +
27*a1^4*a2^3*a3^5*a4^2*b1^3*b2^4*b3^2*b4^5 + 27*a1^3*a2^3*a3^5*a4^2*b1^4*b2^4*b3^2*b4^5 +
10*a1^2*a2^3*a3^5*a4^2*b1^5*b2^4*b3^2*b4^5 + a1*a2^3*a3^5*a4^2*b1^6*b2^4*b3^2*b4^5 +
3*a1^5*a2^2*a3^5*a4^2*b1^2*b2^5*b3^2*b4^5 + 10*a1^4*a2^2*a3^5*a4^2*b1^3*b2^5*b3^2*b4^5 +
10*a1^3*a2^2*a3^5*a4^2*b1^4*b2^5*b3^2*b4^5 + 3*a1^2*a2^2*a3^5*a4^2*b1^5*b2^5*b3^2*b4^5 +
a1^4*a2*a3^5*a4^2*b1^3*b2^6*b3^2*b4^5 + a1^3*a2*a3^5*a4^2*b1^4*b2^6*b3^2*b4^5 +
a1^5*a2^6*a3^4*a4^2*b1^2*b2*b3^3*b4^5 + 4*a1^4*a2^6*a3^4*a4^2*b1^3*b2*b3^3*b4^5 +
4*a1^3*a2^6*a3^4*a4^2*b1^4*b2*b3^3*b4^5 + a1^2*a2^6*a3^4*a4^2*b1^5*b2*b3^3*b4^5 +
a1^6*a2^5*a3^4*a4^2*b1*b2^2*b3^3*b4^5 + 10*a1^5*a2^5*a3^4*a4^2*b1^2*b2^2*b3^3*b4^5 +
27*a1^4*a2^5*a3^4*a4^2*b1^3*b2^2*b3^3*b4^5 + 27*a1^3*a2^5*a3^4*a4^2*b1^4*b2^2*b3^3*b4^5 +
10*a1^2*a2^5*a3^4*a4^2*b1^5*b2^2*b3^3*b4^5 + a1*a2^5*a3^4*a4^2*b1^6*b2^2*b3^3*b4^5 +
4*a1^6*a2^4*a3^4*a4^2*b1*b2^3*b3^3*b4^5 + 27*a1^5*a2^4*a3^4*a4^2*b1^2*b2^3*b3^3*b4^5 +
64*a1^4*a2^4*a3^4*a4^2*b1^3*b2^3*b3^3*b4^5 + 64*a1^3*a2^4*a3^4*a4^2*b1^4*b2^3*b3^3*b4^5 +
27*a1^2*a2^4*a3^4*a4^2*b1^5*b2^3*b3^3*b4^5 + 4*a1*a2^4*a3^4*a4^2*b1^6*b2^3*b3^3*b4^5 +
4*a1^6*a2^3*a3^4*a4^2*b1*b2^4*b3^3*b4^5 + 27*a1^5*a2^3*a3^4*a4^2*b1^2*b2^4*b3^3*b4^5 +
64*a1^4*a2^3*a3^4*a4^2*b1^3*b2^4*b3^3*b4^5 + 64*a1^3*a2^3*a3^4*a4^2*b1^4*b2^4*b3^3*b4^5 +
27*a1^2*a2^3*a3^4*a4^2*b1^5*b2^4*b3^3*b4^5 + 4*a1*a2^3*a3^4*a4^2*b1^6*b2^4*b3^3*b4^5 +
a1^6*a2^2*a3^4*a4^2*b1*b2^5*b3^3*b4^5 + 10*a1^5*a2^2*a3^4*a4^2*b1^2*b2^5*b3^3*b4^5 +
27*a1^4*a2^2*a3^4*a4^2*b1^3*b2^5*b3^3*b4^5 + 27*a1^3*a2^2*a3^4*a4^2*b1^4*b2^5*b3^3*b4^5 +
10*a1^2*a2^2*a3^4*a4^2*b1^5*b2^5*b3^3*b4^5 + a1*a2^2*a3^4*a4^2*b1^6*b2^5*b3^3*b4^5 +
a1^5*a2*a3^4*a4^2*b1^2*b2^6*b3^3*b4^5 + 4*a1^4*a2*a3^4*a4^2*b1^3*b2^6*b3^3*b4^5 +
4*a1^3*a2*a3^4*a4^2*b1^4*b2^6*b3^3*b4^5 + a1^2*a2*a3^4*a4^2*b1^5*b2^6*b3^3*b4^5 +
a1^5*a2^6*a3^3*a4^2*b1^2*b2*b3^4*b4^5 + 4*a1^4*a2^6*a3^3*a4^2*b1^3*b2*b3^4*b4^5 +
4*a1^3*a2^6*a3^3*a4^2*b1^4*b2*b3^4*b4^5 + a1^2*a2^6*a3^3*a4^2*b1^5*b2*b3^4*b4^5 +
a1^6*a2^5*a3^3*a4^2*b1*b2^2*b3^4*b4^5 + 10*a1^5*a2^5*a3^3*a4^2*b1^2*b2^2*b3^4*b4^5 +
27*a1^4*a2^5*a3^3*a4^2*b1^3*b2^2*b3^4*b4^5 + 27*a1^3*a2^5*a3^3*a4^2*b1^4*b2^2*b3^4*b4^5 +
10*a1^2*a2^5*a3^3*a4^2*b1^5*b2^2*b3^4*b4^5 + a1*a2^5*a3^3*a4^2*b1^6*b2^2*b3^4*b4^5 +
4*a1^6*a2^4*a3^3*a4^2*b1*b2^3*b3^4*b4^5 + 27*a1^5*a2^4*a3^3*a4^2*b1^2*b2^3*b3^4*b4^5 +
64*a1^4*a2^4*a3^3*a4^2*b1^3*b2^3*b3^4*b4^5 + 64*a1^3*a2^4*a3^3*a4^2*b1^4*b2^3*b3^4*b4^5 +
27*a1^2*a2^4*a3^3*a4^2*b1^5*b2^3*b3^4*b4^5 + 4*a1*a2^4*a3^3*a4^2*b1^6*b2^3*b3^4*b4^5 +
4*a1^6*a2^3*a3^3*a4^2*b1*b2^4*b3^4*b4^5 + 27*a1^5*a2^3*a3^3*a4^2*b1^2*b2^4*b3^4*b4^5 +
64*a1^4*a2^3*a3^3*a4^2*b1^3*b2^4*b3^4*b4^5 + 64*a1^3*a2^3*a3^3*a4^2*b1^4*b2^4*b3^4*b4^5 +
27*a1^2*a2^3*a3^3*a4^2*b1^5*b2^4*b3^4*b4^5 + 4*a1*a2^3*a3^3*a4^2*b1^6*b2^4*b3^4*b4^5 +
a1^6*a2^2*a3^3*a4^2*b1*b2^5*b3^4*b4^5 + 10*a1^5*a2^2*a3^3*a4^2*b1^2*b2^5*b3^4*b4^5 +
27*a1^4*a2^2*a3^3*a4^2*b1^3*b2^5*b3^4*b4^5 + 27*a1^3*a2^2*a3^3*a4^2*b1^4*b2^5*b3^4*b4^5 +
10*a1^2*a2^2*a3^3*a4^2*b1^5*b2^5*b3^4*b4^5 + a1*a2^2*a3^3*a4^2*b1^6*b2^5*b3^4*b4^5 +
a1^5*a2*a3^3*a4^2*b1^2*b2^6*b3^4*b4^5 + 4*a1^4*a2*a3^3*a4^2*b1^3*b2^6*b3^4*b4^5 +

6

4*a1^3*a2*a3^3*a4^2*b1^4*b2^6*b3^4*b4^5 + a1^2*a2*a3^3*a4^2*b1^5*b2^6*b3^4*b4^5 +
a1^4*a2^6*a3^2*a4^2*b1^3*b2*b3^5*b4^5 + a1^3*a2^6*a3^2*a4^2*b1^4*b2*b3^5*b4^5 +
3*a1^5*a2^5*a3^2*a4^2*b1^2*b2^2*b3^5*b4^5 + 10*a1^4*a2^5*a3^2*a4^2*b1^3*b2^2*b3^5*b4^5 +
10*a1^3*a2^5*a3^2*a4^2*b1^4*b2^2*b3^5*b4^5 + 3*a1^2*a2^5*a3^2*a4^2*b1^5*b2^2*b3^5*b4^5 +
a1^6*a2^4*a3^2*a4^2*b1*b2^3*b3^5*b4^5 + 10*a1^5*a2^4*a3^2*a4^2*b1^2*b2^3*b3^5*b4^5 +
27*a1^4*a2^4*a3^2*a4^2*b1^3*b2^3*b3^5*b4^5 + 27*a1^3*a2^4*a3^2*a4^2*b1^4*b2^3*b3^5*b4^5 +
10*a1^2*a2^4*a3^2*a4^2*b1^5*b2^3*b3^5*b4^5 + a1*a2^4*a3^2*a4^2*b1^6*b2^3*b3^5*b4^5 +
a1^6*a2^3*a3^2*a4^2*b1*b2^4*b3^5*b4^5 + 10*a1^5*a2^3*a3^2*a4^2*b1^2*b2^4*b3^5*b4^5 +
27*a1^4*a2^3*a3^2*a4^2*b1^3*b2^4*b3^5*b4^5 + 27*a1^3*a2^3*a3^2*a4^2*b1^4*b2^4*b3^5*b4^5 +
10*a1^2*a2^3*a3^2*a4^2*b1^5*b2^4*b3^5*b4^5 + a1*a2^3*a3^2*a4^2*b1^6*b2^4*b3^5*b4^5 +
3*a1^5*a2^2*a3^2*a4^2*b1^2*b2^5*b3^5*b4^5 + 10*a1^4*a2^2*a3^2*a4^2*b1^3*b2^5*b3^5*b4^5 +
10*a1^3*a2^2*a3^2*a4^2*b1^4*b2^5*b3^5*b4^5 + 3*a1^2*a2^2*a3^2*a4^2*b1^5*b2^5*b3^5*b4^5 +
a1^4*a2*a3^2*a4^2*b1^3*b2^6*b3^5*b4^5 + a1^3*a2*a3^2*a4^2*b1^4*b2^6*b3^5*b4^5 +
a1^4*a2^5*a3*a4^2*b1^3*b2^2*b3^6*b4^5 + a1^3*a2^5*a3*a4^2*b1^4*b2^2*b3^6*b4^5 +
a1^5*a2^4*a3*a4^2*b1^2*b2^3*b3^6*b4^5 + 4*a1^4*a2^4*a3*a4^2*b1^3*b2^3*b3^6*b4^5 +
4*a1^3*a2^4*a3*a4^2*b1^4*b2^3*b3^6*b4^5 + a1^2*a2^4*a3*a4^2*b1^5*b2^3*b3^6*b4^5 +
a1^5*a2^3*a3*a4^2*b1^2*b2^4*b3^6*b4^5 + 4*a1^4*a2^3*a3*a4^2*b1^3*b2^4*b3^6*b4^5 +
4*a1^3*a2^3*a3*a4^2*b1^4*b2^4*b3^6*b4^5 + a1^2*a2^3*a3*a4^2*b1^5*b2^4*b3^6*b4^5 +
a1^4*a2^2*a3*a4^2*b1^3*b2^5*b3^6*b4^5 + a1^3*a2^2*a3*a4^2*b1^4*b2^5*b3^6*b4^5 +
a1^4*a2^5*a3^5*a4*b1^3*b2^2*b3^2*b4^6 + a1^3*a2^5*a3^5*a4*b1^4*b2^2*b3^2*b4^6 +
a1^5*a2^4*a3^5*a4*b1^2*b2^3*b3^2*b4^6 + 4*a1^4*a2^4*a3^5*a4*b1^3*b2^3*b3^2*b4^6 +
4*a1^3*a2^4*a3^5*a4*b1^4*b2^3*b3^2*b4^6 + a1^2*a2^4*a3^5*a4*b1^5*b2^3*b3^2*b4^6 +
a1^5*a2^3*a3^5*a4*b1^2*b2^4*b3^2*b4^6 + 4*a1^4*a2^3*a3^5*a4*b1^3*b2^4*b3^2*b4^6 +
4*a1^3*a2^3*a3^5*a4*b1^4*b2^4*b3^2*b4^6 + a1^2*a2^3*a3^5*a4*b1^5*b2^4*b3^2*b4^6 +
a1^4*a2^2*a3^5*a4*b1^3*b2^5*b3^2*b4^6 + a1^3*a2^2*a3^5*a4*b1^4*b2^5*b3^2*b4^6 +
a1^5*a2^5*a3^4*a4*b1^2*b2^2*b3^3*b4^6 + 4*a1^4*a2^5*a3^4*a4*b1^3*b2^2*b3^3*b4^6 +
4*a1^3*a2^5*a3^4*a4*b1^4*b2^2*b3^3*b4^6 + a1^2*a2^5*a3^4*a4*b1^5*b2^2*b3^3*b4^6 +
4*a1^5*a2^4*a3^4*a4*b1^2*b2^3*b3^3*b4^6 + 13*a1^4*a2^4*a3^4*a4*b1^3*b2^3*b3^3*b4^6 +
13*a1^3*a2^4*a3^4*a4*b1^4*b2^3*b3^3*b4^6 + 4*a1^2*a2^4*a3^4*a4*b1^5*b2^3*b3^3*b4^6 +
4*a1^5*a2^3*a3^4*a4*b1^2*b2^4*b3^3*b4^6 + 13*a1^4*a2^3*a3^4*a4*b1^3*b2^4*b3^3*b4^6 +
13*a1^3*a2^3*a3^4*a4*b1^4*b2^4*b3^3*b4^6 + 4*a1^2*a2^3*a3^4*a4*b1^5*b2^4*b3^3*b4^6 +
a1^5*a2^2*a3^4*a4*b1^2*b2^5*b3^3*b4^6 + 4*a1^4*a2^2*a3^4*a4*b1^3*b2^5*b3^3*b4^6 +
4*a1^3*a2^2*a3^4*a4*b1^4*b2^5*b3^3*b4^6 + a1^2*a2^2*a3^4*a4*b1^5*b2^5*b3^3*b4^6 +
a1^5*a2^5*a3^3*a4*b1^2*b2^2*b3^4*b4^6 + 4*a1^4*a2^5*a3^3*a4*b1^3*b2^2*b3^4*b4^6 +
4*a1^3*a2^5*a3^3*a4*b1^4*b2^2*b3^4*b4^6 + a1^2*a2^5*a3^3*a4*b1^5*b2^2*b3^4*b4^6 +
4*a1^5*a2^4*a3^3*a4*b1^2*b2^3*b3^4*b4^6 + 13*a1^4*a2^4*a3^3*a4*b1^3*b2^3*b3^4*b4^6 +
13*a1^3*a2^4*a3^3*a4*b1^4*b2^3*b3^4*b4^6 + 4*a1^2*a2^4*a3^3*a4*b1^5*b2^3*b3^4*b4^6 +
4*a1^5*a2^3*a3^3*a4*b1^2*b2^4*b3^4*b4^6 + 13*a1^4*a2^3*a3^3*a4*b1^3*b2^4*b3^4*b4^6 +
13*a1^3*a2^3*a3^3*a4*b1^4*b2^4*b3^4*b4^6 + 4*a1^2*a2^3*a3^3*a4*b1^5*b2^4*b3^4*b4^6 +
a1^5*a2^2*a3^3*a4*b1^2*b2^5*b3^4*b4^6 + 4*a1^4*a2^2*a3^3*a4*b1^3*b2^5*b3^4*b4^6 +
4*a1^3*a2^2*a3^3*a4*b1^4*b2^5*b3^4*b4^6 + a1^2*a2^2*a3^3*a4*b1^5*b2^5*b3^4*b4^6 +
a1^4*a2^5*a3^2*a4*b1^3*b2^2*b3^5*b4^6 + a1^3*a2^5*a3^2*a4*b1^4*b2^2*b3^5*b4^6 +
a1^5*a2^4*a3^2*a4*b1^2*b2^3*b3^5*b4^6 + 4*a1^4*a2^4*a3^2*a4*b1^3*b2^3*b3^5*b4^6 +
4*a1^3*a2^4*a3^2*a4*b1^4*b2^3*b3^5*b4^6 + a1^2*a2^4*a3^2*a4*b1^5*b2^3*b3^5*b4^6 +
a1^5*a2^3*a3^2*a4*b1^2*b2^4*b3^5*b4^6 + 4*a1^4*a2^3*a3^2*a4*b1^3*b2^4*b3^5*b4^6 +
4*a1^3*a2^3*a3^2*a4*b1^4*b2^4*b3^5*b4^6 + a1^2*a2^3*a3^2*a4*b1^5*b2^4*b3^5*b4^6 +
a1^4*a2^2*a3^2*a4*b1^3*b2^5*b3^5*b4^6 + a1^3*a2^2*a3^2*a4*b1^4*b2^5*b3^5*b4^6 +
a1^4*a2^4*a3^4*b1^3*b2^3*b3^3*b4^7 + a1^3*a2^4*a3^4*b1^4*b2^3*b3^3*b4^7 +
a1^4*a2^3*a3^4*b1^3*b2^4*b3^3*b4^7 + a1^3*a2^3*a3^4*b1^4*b2^4*b3^3*b4^7 +
a1^4*a2^4*a3^3*b1^3*b2^3*b3^4*b4^7 + a1^3*a2^4*a3^3*b1^4*b2^3*b3^4*b4^7 +
a1^4*a2^3*a3^3*b1^3*b2^4*b3^4*b4^7 + a1^3*a2^3*a3^3*b1^4*b2^4*b3^4*b4^7
g9 . f a c t o r ( )
#This i s an i n i t i a l f a c t o r i n g t o t r y and make t h i n g s e a s i e r .
(a1^3*a2^3*a3^3*a4^6*b1^3*b2^3*b3^3 + a1^3*a2^4*a3^4*a4^5*b1^3*b2^2*b3^2*b4 +
a1^4*a2^3*a3^4*a4^5*b1^2*b2^3*b3^2*b4 + 2*a1^3*a2^3*a3^4*a4^5*b1^3*b2^3*b3^2*b4 +
a1^2*a2^3*a3^4*a4^5*b1^4*b2^3*b3^2*b4 + a1^3*a2^2*a3^4*a4^5*b1^3*b2^4*b3^2*b4 +
a1^4*a2^4*a3^3*a4^5*b1^2*b2^2*b3^3*b4 + 2*a1^3*a2^4*a3^3*a4^5*b1^3*b2^2*b3^3*b4 +
a1^2*a2^4*a3^3*a4^5*b1^4*b2^2*b3^3*b4 + 2*a1^4*a2^3*a3^3*a4^5*b1^2*b2^3*b3^3*b4 +
3*a1^3*a2^3*a3^3*a4^5*b1^3*b2^3*b3^3*b4 + 2*a1^2*a2^3*a3^3*a4^5*b1^4*b2^3*b3^3*b4 +

7

a1^4*a2^2*a3^3*a4^5*b1^2*b2^4*b3^3*b4 + 2*a1^3*a2^2*a3^3*a4^5*b1^3*b2^4*b3^3*b4 +
a1^2*a2^2*a3^3*a4^5*b1^4*b2^4*b3^3*b4 + a1^3*a2^4*a3^2*a4^5*b1^3*b2^2*b3^4*b4 +
a1^4*a2^3*a3^2*a4^5*b1^2*b2^3*b3^4*b4 + 2*a1^3*a2^3*a3^2*a4^5*b1^3*b2^3*b3^4*b4 +
a1^2*a2^3*a3^2*a4^5*b1^4*b2^3*b3^4*b4 + a1^3*a2^2*a3^2*a4^5*b1^3*b2^4*b3^4*b4 +
a1^3*a2^4*a3^5*a4^4*b1^3*b2^2*b3*b4^2 + a1^4*a2^3*a3^5*a4^4*b1^2*b2^3*b3*b4^2 +
2*a1^3*a2^3*a3^5*a4^4*b1^3*b2^3*b3*b4^2 + a1^2*a2^3*a3^5*a4^4*b1^4*b2^3*b3*b4^2 +
a1^3*a2^2*a3^5*a4^4*b1^3*b2^4*b3*b4^2 + a1^3*a2^5*a3^4*a4^4*b1^3*b2*b3^2*b4^2 +
3*a1^4*a2^4*a3^4*a4^4*b1^2*b2^2*b3^2*b4^2 + 4*a1^3*a2^4*a3^4*a4^4*b1^3*b2^2*b3^2*b4^2 +
3*a1^2*a2^4*a3^4*a4^4*b1^4*b2^2*b3^2*b4^2 + a1^5*a2^3*a3^4*a4^4*b1*b2^3*b3^2*b4^2 +
4*a1^4*a2^3*a3^4*a4^4*b1^2*b2^3*b3^2*b4^2 + 8*a1^3*a2^3*a3^4*a4^4*b1^3*b2^3*b3^2*b4^2 +
4*a1^2*a2^3*a3^4*a4^4*b1^4*b2^3*b3^2*b4^2 + a1*a2^3*a3^4*a4^4*b1^5*b2^3*b3^2*b4^2 +
3*a1^4*a2^2*a3^4*a4^4*b1^2*b2^4*b3^2*b4^2 + 4*a1^3*a2^2*a3^4*a4^4*b1^3*b2^4*b3^2*b4^2 +
3*a1^2*a2^2*a3^4*a4^4*b1^4*b2^4*b3^2*b4^2 + a1^3*a2*a3^4*a4^4*b1^3*b2^5*b3^2*b4^2 +
a1^4*a2^5*a3^3*a4^4*b1^2*b2*b3^3*b4^2 + 2*a1^3*a2^5*a3^3*a4^4*b1^3*b2*b3^3*b4^2 +
a1^2*a2^5*a3^3*a4^4*b1^4*b2*b3^3*b4^2 + a1^5*a2^4*a3^3*a4^4*b1*b2^2*b3^3*b4^2 +
4*a1^4*a2^4*a3^3*a4^4*b1^2*b2^2*b3^3*b4^2 + 8*a1^3*a2^4*a3^3*a4^4*b1^3*b2^2*b3^3*b4^2 +
4*a1^2*a2^4*a3^3*a4^4*b1^4*b2^2*b3^3*b4^2 + a1*a2^4*a3^3*a4^4*b1^5*b2^2*b3^3*b4^2 +
2*a1^5*a2^3*a3^3*a4^4*b1*b2^3*b3^3*b4^2 + 8*a1^4*a2^3*a3^3*a4^4*b1^2*b2^3*b3^3*b4^2 +
13*a1^3*a2^3*a3^3*a4^4*b1^3*b2^3*b3^3*b4^2 + 8*a1^2*a2^3*a3^3*a4^4*b1^4*b2^3*b3^3*b4^2 +
2*a1*a2^3*a3^3*a4^4*b1^5*b2^3*b3^3*b4^2 + a1^5*a2^2*a3^3*a4^4*b1*b2^4*b3^3*b4^2 +
4*a1^4*a2^2*a3^3*a4^4*b1^2*b2^4*b3^3*b4^2 + 8*a1^3*a2^2*a3^3*a4^4*b1^3*b2^4*b3^3*b4^2 +
4*a1^2*a2^2*a3^3*a4^4*b1^4*b2^4*b3^3*b4^2 + a1*a2^2*a3^3*a4^4*b1^5*b2^4*b3^3*b4^2 +
a1^4*a2*a3^3*a4^4*b1^2*b2^5*b3^3*b4^2 + 2*a1^3*a2*a3^3*a4^4*b1^3*b2^5*b3^3*b4^2 +
a1^2*a2*a3^3*a4^4*b1^4*b2^5*b3^3*b4^2 + a1^3*a2^5*a3^2*a4^4*b1^3*b2*b3^4*b4^2 +
3*a1^4*a2^4*a3^2*a4^4*b1^2*b2^2*b3^4*b4^2 + 4*a1^3*a2^4*a3^2*a4^4*b1^3*b2^2*b3^4*b4^2 +
3*a1^2*a2^4*a3^2*a4^4*b1^4*b2^2*b3^4*b4^2 + a1^5*a2^3*a3^2*a4^4*b1*b2^3*b3^4*b4^2 +
4*a1^4*a2^3*a3^2*a4^4*b1^2*b2^3*b3^4*b4^2 + 8*a1^3*a2^3*a3^2*a4^4*b1^3*b2^3*b3^4*b4^2 +
4*a1^2*a2^3*a3^2*a4^4*b1^4*b2^3*b3^4*b4^2 + a1*a2^3*a3^2*a4^4*b1^5*b2^3*b3^4*b4^2 +
3*a1^4*a2^2*a3^2*a4^4*b1^2*b2^4*b3^4*b4^2 + 4*a1^3*a2^2*a3^2*a4^4*b1^3*b2^4*b3^4*b4^2 +
3*a1^2*a2^2*a3^2*a4^4*b1^4*b2^4*b3^4*b4^2 + a1^3*a2*a3^2*a4^4*b1^3*b2^5*b3^4*b4^2 +
a1^3*a2^4*a3*a4^4*b1^3*b2^2*b3^5*b4^2 + a1^4*a2^3*a3*a4^4*b1^2*b2^3*b3^5*b4^2 +
2*a1^3*a2^3*a3*a4^4*b1^3*b2^3*b3^5*b4^2 + a1^2*a2^3*a3*a4^4*b1^4*b2^3*b3^5*b4^2 +
a1^3*a2^2*a3*a4^4*b1^3*b2^4*b3^5*b4^2 + a1^3*a2^3*a3^6*a4^3*b1^3*b2^3*b4^3 +
a1^4*a2^4*a3^5*a4^3*b1^2*b2^2*b3*b4^3 + 2*a1^3*a2^4*a3^5*a4^3*b1^3*b2^2*b3*b4^3 +
a1^2*a2^4*a3^5*a4^3*b1^4*b2^2*b3*b4^3 + 2*a1^4*a2^3*a3^5*a4^3*b1^2*b2^3*b3*b4^3 +
3*a1^3*a2^3*a3^5*a4^3*b1^3*b2^3*b3*b4^3 + 2*a1^2*a2^3*a3^5*a4^3*b1^4*b2^3*b3*b4^3 +
a1^4*a2^2*a3^5*a4^3*b1^2*b2^4*b3*b4^3 + 2*a1^3*a2^2*a3^5*a4^3*b1^3*b2^4*b3*b4^3 +
a1^2*a2^2*a3^5*a4^3*b1^4*b2^4*b3*b4^3 + a1^4*a2^5*a3^4*a4^3*b1^2*b2*b3^2*b4^3 +
2*a1^3*a2^5*a3^4*a4^3*b1^3*b2*b3^2*b4^3 + a1^2*a2^5*a3^4*a4^3*b1^4*b2*b3^2*b4^3 +
a1^5*a2^4*a3^4*a4^3*b1*b2^2*b3^2*b4^3 + 4*a1^4*a2^4*a3^4*a4^3*b1^2*b2^2*b3^2*b4^3 +
8*a1^3*a2^4*a3^4*a4^3*b1^3*b2^2*b3^2*b4^3 + 4*a1^2*a2^4*a3^4*a4^3*b1^4*b2^2*b3^2*b4^3 +
a1*a2^4*a3^4*a4^3*b1^5*b2^2*b3^2*b4^3 + 2*a1^5*a2^3*a3^4*a4^3*b1*b2^3*b3^2*b4^3 +
8*a1^4*a2^3*a3^4*a4^3*b1^2*b2^3*b3^2*b4^3 + 13*a1^3*a2^3*a3^4*a4^3*b1^3*b2^3*b3^2*b4^3 +
8*a1^2*a2^3*a3^4*a4^3*b1^4*b2^3*b3^2*b4^3 + 2*a1*a2^3*a3^4*a4^3*b1^5*b2^3*b3^2*b4^3 +
a1^5*a2^2*a3^4*a4^3*b1*b2^4*b3^2*b4^3 + 4*a1^4*a2^2*a3^4*a4^3*b1^2*b2^4*b3^2*b4^3 +
8*a1^3*a2^2*a3^4*a4^3*b1^3*b2^4*b3^2*b4^3 + 4*a1^2*a2^2*a3^4*a4^3*b1^4*b2^4*b3^2*b4^3 +
a1*a2^2*a3^4*a4^3*b1^5*b2^4*b3^2*b4^3 + a1^4*a2*a3^4*a4^3*b1^2*b2^5*b3^2*b4^3 +
2*a1^3*a2*a3^4*a4^3*b1^3*b2^5*b3^2*b4^3 + a1^2*a2*a3^4*a4^3*b1^4*b2^5*b3^2*b4^3 +
a1^3*a2^6*a3^3*a4^3*b1^3*b3^3*b4^3 + 2*a1^4*a2^5*a3^3*a4^3*b1^2*b2*b3^3*b4^3 +
3*a1^3*a2^5*a3^3*a4^3*b1^3*b2*b3^3*b4^3 + 2*a1^2*a2^5*a3^3*a4^3*b1^4*b2*b3^3*b4^3 +
2*a1^5*a2^4*a3^3*a4^3*b1*b2^2*b3^3*b4^3 + 8*a1^4*a2^4*a3^3*a4^3*b1^2*b2^2*b3^3*b4^3 +
13*a1^3*a2^4*a3^3*a4^3*b1^3*b2^2*b3^3*b4^3 + 8*a1^2*a2^4*a3^3*a4^3*b1^4*b2^2*b3^3*b4^3 +
2*a1*a2^4*a3^3*a4^3*b1^5*b2^2*b3^3*b4^3 + a1^6*a2^3*a3^3*a4^3*b2^3*b3^3*b4^3 +
3*a1^5*a2^3*a3^3*a4^3*b1*b2^3*b3^3*b4^3 + 13*a1^4*a2^3*a3^3*a4^3*b1^2*b2^3*b3^3*b4^3 +
19*a1^3*a2^3*a3^3*a4^3*b1^3*b2^3*b3^3*b4^3 + 13*a1^2*a2^3*a3^3*a4^3*b1^4*b2^3*b3^3*b4^3 +
3*a1*a2^3*a3^3*a4^3*b1^5*b2^3*b3^3*b4^3 + a2^3*a3^3*a4^3*b1^6*b2^3*b3^3*b4^3 +
2*a1^5*a2^2*a3^3*a4^3*b1*b2^4*b3^3*b4^3 + 8*a1^4*a2^2*a3^3*a4^3*b1^2*b2^4*b3^3*b4^3 +
13*a1^3*a2^2*a3^3*a4^3*b1^3*b2^4*b3^3*b4^3 + 8*a1^2*a2^2*a3^3*a4^3*b1^4*b2^4*b3^3*b4^3 +
2*a1*a2^2*a3^3*a4^3*b1^5*b2^4*b3^3*b4^3 + 2*a1^4*a2*a3^3*a4^3*b1^2*b2^5*b3^3*b4^3 +
3*a1^3*a2*a3^3*a4^3*b1^3*b2^5*b3^3*b4^3 + 2*a1^2*a2*a3^3*a4^3*b1^4*b2^5*b3^3*b4^3 +
a1^3*a3^3*a4^3*b1^3*b2^6*b3^3*b4^3 + a1^4*a2^5*a3^2*a4^3*b1^2*b2*b3^4*b4^3 +

8

2*a1^3*a2^5*a3^2*a4^3*b1^3*b2*b3^4*b4^3 + a1^2*a2^5*a3^2*a4^3*b1^4*b2*b3^4*b4^3 +
a1^5*a2^4*a3^2*a4^3*b1*b2^2*b3^4*b4^3 + 4*a1^4*a2^4*a3^2*a4^3*b1^2*b2^2*b3^4*b4^3 +
8*a1^3*a2^4*a3^2*a4^3*b1^3*b2^2*b3^4*b4^3 + 4*a1^2*a2^4*a3^2*a4^3*b1^4*b2^2*b3^4*b4^3 +
a1*a2^4*a3^2*a4^3*b1^5*b2^2*b3^4*b4^3 + 2*a1^5*a2^3*a3^2*a4^3*b1*b2^3*b3^4*b4^3 +
8*a1^4*a2^3*a3^2*a4^3*b1^2*b2^3*b3^4*b4^3 + 13*a1^3*a2^3*a3^2*a4^3*b1^3*b2^3*b3^4*b4^3 +
8*a1^2*a2^3*a3^2*a4^3*b1^4*b2^3*b3^4*b4^3 + 2*a1*a2^3*a3^2*a4^3*b1^5*b2^3*b3^4*b4^3 +
a1^5*a2^2*a3^2*a4^3*b1*b2^4*b3^4*b4^3 + 4*a1^4*a2^2*a3^2*a4^3*b1^2*b2^4*b3^4*b4^3 +
8*a1^3*a2^2*a3^2*a4^3*b1^3*b2^4*b3^4*b4^3 + 4*a1^2*a2^2*a3^2*a4^3*b1^4*b2^4*b3^4*b4^3 +
a1*a2^2*a3^2*a4^3*b1^5*b2^4*b3^4*b4^3 + a1^4*a2*a3^2*a4^3*b1^2*b2^5*b3^4*b4^3 +
2*a1^3*a2*a3^2*a4^3*b1^3*b2^5*b3^4*b4^3 + a1^2*a2*a3^2*a4^3*b1^4*b2^5*b3^4*b4^3 +
a1^4*a2^4*a3*a4^3*b1^2*b2^2*b3^5*b4^3 + 2*a1^3*a2^4*a3*a4^3*b1^3*b2^2*b3^5*b4^3 +
a1^2*a2^4*a3*a4^3*b1^4*b2^2*b3^5*b4^3 + 2*a1^4*a2^3*a3*a4^3*b1^2*b2^3*b3^5*b4^3 +
3*a1^3*a2^3*a3*a4^3*b1^3*b2^3*b3^5*b4^3 + 2*a1^2*a2^3*a3*a4^3*b1^4*b2^3*b3^5*b4^3 +
a1^4*a2^2*a3*a4^3*b1^2*b2^4*b3^5*b4^3 + 2*a1^3*a2^2*a3*a4^3*b1^3*b2^4*b3^5*b4^3 +
a1^2*a2^2*a3*a4^3*b1^4*b2^4*b3^5*b4^3 + a1^3*a2^3*a4^3*b1^3*b2^3*b3^6*b4^3 +
a1^3*a2^4*a3^5*a4^2*b1^3*b2^2*b3*b4^4 + a1^4*a2^3*a3^5*a4^2*b1^2*b2^3*b3*b4^4 +
2*a1^3*a2^3*a3^5*a4^2*b1^3*b2^3*b3*b4^4 + a1^2*a2^3*a3^5*a4^2*b1^4*b2^3*b3*b4^4 +
a1^3*a2^2*a3^5*a4^2*b1^3*b2^4*b3*b4^4 + a1^3*a2^5*a3^4*a4^2*b1^3*b2*b3^2*b4^4 +
3*a1^4*a2^4*a3^4*a4^2*b1^2*b2^2*b3^2*b4^4 + 4*a1^3*a2^4*a3^4*a4^2*b1^3*b2^2*b3^2*b4^4 +
3*a1^2*a2^4*a3^4*a4^2*b1^4*b2^2*b3^2*b4^4 + a1^5*a2^3*a3^4*a4^2*b1*b2^3*b3^2*b4^4 +
4*a1^4*a2^3*a3^4*a4^2*b1^2*b2^3*b3^2*b4^4 + 8*a1^3*a2^3*a3^4*a4^2*b1^3*b2^3*b3^2*b4^4 +
4*a1^2*a2^3*a3^4*a4^2*b1^4*b2^3*b3^2*b4^4 + a1*a2^3*a3^4*a4^2*b1^5*b2^3*b3^2*b4^4 +
3*a1^4*a2^2*a3^4*a4^2*b1^2*b2^4*b3^2*b4^4 + 4*a1^3*a2^2*a3^4*a4^2*b1^3*b2^4*b3^2*b4^4 +
3*a1^2*a2^2*a3^4*a4^2*b1^4*b2^4*b3^2*b4^4 + a1^3*a2*a3^4*a4^2*b1^3*b2^5*b3^2*b4^4 +
a1^4*a2^5*a3^3*a4^2*b1^2*b2*b3^3*b4^4 + 2*a1^3*a2^5*a3^3*a4^2*b1^3*b2*b3^3*b4^4 +
a1^2*a2^5*a3^3*a4^2*b1^4*b2*b3^3*b4^4 + a1^5*a2^4*a3^3*a4^2*b1*b2^2*b3^3*b4^4 +
4*a1^4*a2^4*a3^3*a4^2*b1^2*b2^2*b3^3*b4^4 + 8*a1^3*a2^4*a3^3*a4^2*b1^3*b2^2*b3^3*b4^4 +
4*a1^2*a2^4*a3^3*a4^2*b1^4*b2^2*b3^3*b4^4 + a1*a2^4*a3^3*a4^2*b1^5*b2^2*b3^3*b4^4 +
2*a1^5*a2^3*a3^3*a4^2*b1*b2^3*b3^3*b4^4 + 8*a1^4*a2^3*a3^3*a4^2*b1^2*b2^3*b3^3*b4^4 +
13*a1^3*a2^3*a3^3*a4^2*b1^3*b2^3*b3^3*b4^4 + 8*a1^2*a2^3*a3^3*a4^2*b1^4*b2^3*b3^3*b4^4 +
2*a1*a2^3*a3^3*a4^2*b1^5*b2^3*b3^3*b4^4 + a1^5*a2^2*a3^3*a4^2*b1*b2^4*b3^3*b4^4 +
4*a1^4*a2^2*a3^3*a4^2*b1^2*b2^4*b3^3*b4^4 + 8*a1^3*a2^2*a3^3*a4^2*b1^3*b2^4*b3^3*b4^4 +
4*a1^2*a2^2*a3^3*a4^2*b1^4*b2^4*b3^3*b4^4 + a1*a2^2*a3^3*a4^2*b1^5*b2^4*b3^3*b4^4 +
a1^4*a2*a3^3*a4^2*b1^2*b2^5*b3^3*b4^4 + 2*a1^3*a2*a3^3*a4^2*b1^3*b2^5*b3^3*b4^4 +
a1^2*a2*a3^3*a4^2*b1^4*b2^5*b3^3*b4^4 + a1^3*a2^5*a3^2*a4^2*b1^3*b2*b3^4*b4^4 +
3*a1^4*a2^4*a3^2*a4^2*b1^2*b2^2*b3^4*b4^4 + 4*a1^3*a2^4*a3^2*a4^2*b1^3*b2^2*b3^4*b4^4 +
3*a1^2*a2^4*a3^2*a4^2*b1^4*b2^2*b3^4*b4^4 + a1^5*a2^3*a3^2*a4^2*b1*b2^3*b3^4*b4^4 +
4*a1^4*a2^3*a3^2*a4^2*b1^2*b2^3*b3^4*b4^4 + 8*a1^3*a2^3*a3^2*a4^2*b1^3*b2^3*b3^4*b4^4 +
4*a1^2*a2^3*a3^2*a4^2*b1^4*b2^3*b3^4*b4^4 + a1*a2^3*a3^2*a4^2*b1^5*b2^3*b3^4*b4^4 +
3*a1^4*a2^2*a3^2*a4^2*b1^2*b2^4*b3^4*b4^4 + 4*a1^3*a2^2*a3^2*a4^2*b1^3*b2^4*b3^4*b4^4 +
3*a1^2*a2^2*a3^2*a4^2*b1^4*b2^4*b3^4*b4^4 + a1^3*a2*a3^2*a4^2*b1^3*b2^5*b3^4*b4^4 +
a1^3*a2^4*a3*a4^2*b1^3*b2^2*b3^5*b4^4 + a1^4*a2^3*a3*a4^2*b1^2*b2^3*b3^5*b4^4 +
2*a1^3*a2^3*a3*a4^2*b1^3*b2^3*b3^5*b4^4 + a1^2*a2^3*a3*a4^2*b1^4*b2^3*b3^5*b4^4 +
a1^3*a2^2*a3*a4^2*b1^3*b2^4*b3^5*b4^4 + a1^3*a2^4*a3^4*a4*b1^3*b2^2*b3^2*b4^5 +
a1^4*a2^3*a3^4*a4*b1^2*b2^3*b3^2*b4^5 + 2*a1^3*a2^3*a3^4*a4*b1^3*b2^3*b3^2*b4^5 +
a1^2*a2^3*a3^4*a4*b1^4*b2^3*b3^2*b4^5 + a1^3*a2^2*a3^4*a4*b1^3*b2^4*b3^2*b4^5 +
a1^4*a2^4*a3^3*a4*b1^2*b2^2*b3^3*b4^5 + 2*a1^3*a2^4*a3^3*a4*b1^3*b2^2*b3^3*b4^5 +
a1^2*a2^4*a3^3*a4*b1^4*b2^2*b3^3*b4^5 + 2*a1^4*a2^3*a3^3*a4*b1^2*b2^3*b3^3*b4^5 +
3*a1^3*a2^3*a3^3*a4*b1^3*b2^3*b3^3*b4^5 + 2*a1^2*a2^3*a3^3*a4*b1^4*b2^3*b3^3*b4^5 +
a1^4*a2^2*a3^3*a4*b1^2*b2^4*b3^3*b4^5 + 2*a1^3*a2^2*a3^3*a4*b1^3*b2^4*b3^3*b4^5 +
a1^2*a2^2*a3^3*a4*b1^4*b2^4*b3^3*b4^5 + a1^3*a2^4*a3^2*a4*b1^3*b2^2*b3^4*b4^5 +
a1^4*a2^3*a3^2*a4*b1^2*b2^3*b3^4*b4^5 + 2*a1^3*a2^3*a3^2*a4*b1^3*b2^3*b3^4*b4^5 +
a1^2*a2^3*a3^2*a4*b1^4*b2^3*b3^4*b4^5 + a1^3*a2^2*a3^2*a4*b1^3*b2^4*b3^4*b4^5 +
a1^3*a2^3*a3^3*b1^3*b2^3*b3^3*b4^6)*(a1 + b1)*(a2 + b2)*(a3 + b3)*(a4 + b4)
t =(a1 + b1 ) * ( a2 + b2 ) * ( a3 + b3 ) * ( a4 + b4 )
t
f 9=g9 . f a c t o r ( ) / t
f9
#This s e p a r a t e s t h e f a c t o r i z a t i o n above i n t o two p a r t s .

9


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