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