Created: Oct. 11, 2002.

                          This version: Oct. 11, 2002

``
              CLD: A Maple package to automatically conjecture and

              rigorously prove explicit evaluations for Hankel and

         Topelitz determinants that evaluate to super-nice expressions

                              using Dodgson's rule



             Written by Doron Zeilberger, zeilberg@math.rutgers.edu



                          It accompanies the article:

            "Liebe Opa Paul: Ich Bin Auch Ein Experimental Scientist"

                       available from Zeilberger's website

``
                Please report bugs to zeilberg@math.rutgers.edu

``
              The most current version of this  package and paper

                               are  available from

                     http://www.math.rutgers.edu/~zeilberg/

       For a list of the IMPORTANT procedures type ezra();, for help with

                a specific procedure, type ezra(procedure_name);

                 For a list of ALL  procedures, type, ezra1();



                           This is the Terse Version

                 This does Ambdeberhan and Ekhad's determinant

                       conjectured by Kuperberg and Propp

                            EvalH(r!*(m-r)!,n,r,4);

    (n - 1) (-m - 3 + n) (n - 1 + r) (n - 3 - m + r)
[-------------------------------------------------------,
                                                       2
 (2 n - 3 - m + r) (2 n - 5 - m + r) (-4 + 2 n + r - m)

          (n - 1 + r) (n - 3 - m + r)       (n - 1 + r) (n - 3 - m + r)
    - ------------------------------------, ---------------------------]
      (2 n - 3 - m + r) (-4 + 2 n + r - m)   (r - 1) (2 n - 3 - m + r)

                      It took, 36.959, seconds of CPU time

                        This does MacMahon's determinant

                             EvalT(1/(m+r)!,n,r,4);

                      n - 1            1          m + r - 1
                 [-------------, -------------, -------------]
                  m - 1 + r + n  m - 1 + r + n  m - 1 + r + n

                       It took, .640, seconds of CPU time

                        This does Hilbert's determinant

                   2            2                                2
            (n - 1)  (n - 1 + r)                      (n - 1 + r)
[-------------------------------------------, ----------------------------,
                                           2  (2 n - 1 + r) (-2 + 2 n + r)
 (2 n - 1 + r) (2 n - 3 + r) (-2 + 2 n + r)

                   2
        (n - 1 + r)
    ---------------------]
    (r - 1) (2 n - 1 + r)

                             EvalH(1/(r+1),n,r,4);

                       It took, .411, seconds of CPU time