p := (a+b+c)^4
4
P := (a + b + c)
expand
4 3 3 2 2 2 2 2 3 2
a + 4 a b + 4 a c + 6 a b + 12 a b c + 6 a c + 4 a b + 12 a b c
2 3 4 3 2 2 3 4
+ 12 a b c + 4 a c + b + 4 b c + 6 b c + 4 b c + c
d := dif(p,a)
d
D := -- P
da
3 2 2 2 3 2 2
4 a + 12 a (b + c) + 12 a (b + 2 b c + c ) + 4 b + 12 b c + 12 b c
3
+ 4 c
d d d 4 3 3 2 2 2 2 2 3
-- -- -- a + 4 a b + 4 a c + 6 a b + 12 a b c + 6 a c + 4 a b
db db da
2 2 3 4 3 2 2 3 4
+ 12 a b c + 12 a b c + 4 a c + b + 4 b c + 6 b c + 4 b c + c
24 a + 24 b + 24 c
i := int(d,a)
I := D da
4 3 2 2 2 3 2 2
a + 4 a (b + c) + 6 a (b + 2 b c + c ) + a (4 b + 12 b c + 12 b c
3
+ 4 c )
i - p
I - P
4 3 2 2 3 4
- (b + 4 b c + 6 b c + 4 b c + c )
(a^2-b^2)/(a^2-2 a b+b^2)
2 2
a - b
-----------------
2 2
a - 2 a b + b
a + b
-------
a - b
g := 34 x^19-91 x+70 x^7-25 x^16+20 x^3-86
f := g (64 x^34-21 x^47-126 x^8-46 x^5-16 x^60-81)
h := g (72 x^60-25 x^25-19 x^23-22 x^39-83 x^52+54 x^10+81)
f/h nestačila paměť