For comparison with other CAS choose from: Axiom Derive Macsyma Maple Mathematica
pol:=(a+b+c) ^4;
4 3 3 2 2 2 2 2 3
pol := a + 4*a *b + 4*a *c + 6*a *b + 12*a *b*c + 6*a *c + 4*a*b
2 2 3 4 3 2 2
+ 12*a*b *c + 12*a*b*c + 4*a*c + b + 4*b *c + 6*b *c
3 4
+ 4*b*c + c
dpol:=df(pol,a);
3 2 2 2 2 3
dpol := 4*(a + 3*a *b + 3*a *c + 3*a*b + 6*a*b*c + 3*a*c + b
2 2 3
+ 3*b *c + 3*b*c + c )
df(pol,a,b,2);
24*(a + b + c)
int(dpol,a);
3 2 2 2 2 3 2
a*(a + 4*a *b + 4*a *c + 6*a*b + 12*a*b*c + 6*a*c + 4*b + 12*b *c
2 3
+ 12*b*c + 4*c )
ws-pol;
4 3 2 2 3 4
- b - 4*b *c - 6*b *c - 4*b*c - c
(a
on gcd,ezgcd;
^2-b^2)/(a^2-2*a*b+b^2);
a + b
-------
a - b
off gcd;
g := 34*x**19-91*x+70*x**7-25*x**16+20*x**3-86;
19 16 7 3
g := 34*x - 25*x + 70*x + 20*x - 91*x - 86
f1:=g * (64*x**34-21*x**47-126*x**8-46*x**5-16*x**60-81);
79 76 67 66 63 61
f1 := - 544*x + 400*x - 1120*x - 714*x + 205*x + 1456*x
60 54 53 50 48
+ 1376*x - 1470*x + 2176*x - 2020*x + 1911*x
47 41 37 35 34
+ 1806*x + 4480*x + 1280*x - 5824*x - 5504*x
27 24 21 19 16
- 4284*x + 1586*x + 1150*x - 2754*x + 2025*x
15 12 11 9 8
- 8820*x - 3220*x - 2520*x + 11466*x + 9916*x
7 6 5 3
- 5670*x + 4186*x + 3956*x - 1620*x + 7371*x + 6966
f2:=g * (72*x**60-25*x**25-19*x**23-22*x**39-83*x**52+54*x**10+81);
79 76 71 68 67 63
f2 := 2448*x - 1800*x - 2822*x + 2075*x + 5040*x + 1440*x
61 60 59 58 55
- 6552*x - 6192*x - 5810*x - 748*x - 1110*x
53 52 46 44 42
+ 7553*x + 7138*x - 1540*x - 850*x - 1086*x
41 40 39 32 30
+ 625*x + 2002*x + 2367*x - 1750*x - 1330*x
29 28 26 25 24
+ 1836*x - 500*x + 545*x + 2150*x + 1729*x
23 19 17 16 13
+ 1634*x + 2754*x + 3780*x - 2025*x + 1080*x
11 10 7 3
- 4914*x - 4644*x + 5670*x + 1620*x - 7371*x - 6966
gcd(f1,f2);
19 16 7 3
34*x - 25*x + 70*x + 20*x - 91*x - 86