Script started on Fri Mar 21 13:53:02 1997
bash$ maple
    |\^/|     Maple V Release 3 (University of Toronto)
._|\|   |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the
 \  MAPLE  /  University of Waterloo. All rights reserved. Maple and Maple V
 <____ ____>  are registered trademarks of Waterloo Maple Software.
      |       Type ? for help.
> read(`div`);

                                     4      2
                               a := x  + 3 x  + 2

                                         2
                                 b := 2 x  + 1

                                            2      4
                            rec4a := 1 + 3 x  + 2 x

                                              2
                                rec2b := 2 + x

                 gcdex(rec2b,x^3,x,'rec2b_inv_rat','dummy'), 1

                                                      2
                         rec2b_inv_rat = , 1/2 - 1/4 x

                                                2
                              rec2b_inv := 3 + x

           rec2q is expand(rem((rec4a * rec2b_inv),x^3,x)) mod 5 , 3

                                   rec2q := 3

                                           2
                                   q := 3 x

                          r is expand(a-q*b) mod 5, 2

                                     r := 2

                                       4      2
                            q*b+r = , x  + 3 x  + 2

                                     4      2
                               a =, x  + 3 x  + 2

> read('sff');

                   7    6      5       4      3      2
             f := x  + x  + 2 x  + 10 x  + 9 x  + 9 x  + 24 x + 16

                         6      5       4       3       2
           f_prime := 7 x  + 6 x  + 10 x  + 40 x  + 27 x  + 18 x + 24

                                              3
                         gcd(f,f_prime) is , x  + x + 4

                                      3
                                g := x  + x + 4

                        f1 is quo(f,g^2,x,'r') = , x + 1

                                  f1 := x + 1

                                    r is , 0

                                        3         2
                      g * g * f1 is , (x  + x + 4)  (x + 1)

                 7    6      5       4      3      2
                x  + x  + 2 x  + 10 x  + 9 x  + 9 x  + 24 x + 16

                 7    6      5       4      3      2
                x  + x  + 2 x  + 10 x  + 9 x  + 9 x  + 24 x + 16

                            gcd(diff(g,x),g) is , 1

                                     ------

                                     14      7
                             f := 4 x   + 4 x  + 1

                                            13       6
                         diff(f,x) is , 56 x   + 28 x

                              diff(f,x) mod 7 is, 0

                                                14      7
                  gcd(f,diff(f,x)mod 7) is , 4 x   + 4 x  + 1

                                           2
                          f_7th_root := 4 x  + 4 x + 1

                                                     14      7
              expand(f_7th_root ^7) mod 7   is  , 4 x   + 4 x  + 1

                                       2
                             f_7 := 4 x  + 4 x + 1

                                    8 x + 4

                                     x + 4

                       gcd(f_7,diff(f_7,x) mod 7,x) is, 1

> quit
bytes used=504160, alloc=196572, time=0.25
bash$ exit
exit

script done on Fri Mar 21 13:53:29 1997