What follows is a list of Maple routines for manipulation of polynomials.
collect --- collect like terms of polynomials.
factor --- factor polynomials over the rationals or
certain extension fields.
coeff,coeffs --- pick off the coefficients of a collected
polynomial.
sort --- sort a polynomial in increasing or decreasing
order.
rem,quo --- compute the remainder and quotient of two polynomials.
discrim --- compute the discriminant[3] of a polynomial.
resultant --- compute the resultant of two polynomials.
gcd --- find the Greatest Common Divisor of two polynomials.
expand --- expand products of polynomials.
The following session illustrates the usage of these.
>
> p := randpoly(x);
5 4 3 2
p := - 85 x - 55 x - 37 x - 35 x + 97 x + 50
> q := randpoly(x);
5 4 3 2
q := 79 x + 56 x + 49 x + 63 x + 57 x - 59
> p + q;
5 4 3 2
- 6 x + x + 12 x + 28 x + 154 x - 9
> p*q;
5 4 3 2
(- 85 x - 55 x - 37 x - 35 x + 97 x + 50)
5 4 3 2
(79 x + 56 x + 49 x + 63 x + 57 x - 59)
> expand(");
10 9 8 4 5 3
- 2873 x - 6715 x - 9105 x - 10168 x + 6484 x + 7216 x + 8749 x
2 6 7
+ 10744 x - 4420 x - 12887 x - 2950
> sort(");
10 9 8 7 6 5 4
- 6715 x - 9105 x - 10168 x - 12887 x - 4420 x + 7216 x + 6484 x
3 2
+ 8749 x + 10744 x - 2873 x - 2950
> factor(");
5 4 3 2
- (79 x + 56 x + 49 x + 63 x + 57 x - 59)
5 4 3 2
(85 x + 55 x + 37 x + 35 x - 97 x - 50)
> rem(p,q,x,'quotient');
415 4 1242 3 2590 2 12508 1065
--- x + ---- x + ---- x + ----- x - ----
79 79 79 79 79
> quotient;
85
- ----
79
> quo(p,q,x,'remainder');
85
- ----
79
> remainder;
415 4 1242 3 2590 2 12508 1065
--- x + ---- x + ---- x + ----- x - ----
79 79 79 79 79
> gcd(p,q);
1
>
> r := randpoly([x,a]);
5 3 2 3
r := 54 - 5 a + 99 x - 61 x - 50 x a - 12 x a
> collect(r,x);
5 3 2
99 x + (- 61 - 12 a) x - 50 x a + 54 - 5 a
> coeff(",x,3); # Pick off the coefficient of x^3.
- 61 - 12 a
> collect(r,a);
2 3 5 3
(- 5 - 50 x - 12 x ) a + 54 + 99 x - 61 x
> coeff(",x,3); # POLYNOMIALS MUST BE COLLECTED IN THE COEFF VARIABLE
Error, unable to compute coeff
> d := discrim(r,x); # The discriminant is the resultant of r and r'.
6 5 4
d := - 99 (- 54 + 5 a) (3590369280 a - 3433596969024 a - 192447722160 a
3 2
+ 21325528435565 a + 48080023745670 a - 463897100992680 a
+ 472534194797568)