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