EXAMPLE (8)
===========
Define the function T(r,n) as on page 20 of the notes
for Chapter 5.
Using the qfactor function find a formula for T(r,n).

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> read "FUNCS.txt":
> 
> T:=proc(r,j)
> 	option remember:
> 	local x,k:
> 	if j=0 or j=1 then
> 	   RETURN( (j-1)^2 ):
> 	else
> 	   x:=-add(qbin(q,k,r+2*k)*T(r+2*k,j-2*k),k=1..floor(j/2)):
> 	   RETURN(expand(x)):
> 	fi:
> end:
> 	
>  T(0,2);
                                     -q - 1

>  T(1,2);
                                    2
                                  -q  - q - 1

>  T(2,2);
                                  3    2
                                -q  - q  - q - 1

>  T(0,4);
                                      3
                                     q  + q

>  T(1,4);
                              5    4    3    2
                             q  + q  + q  + q  + q

>  T(2,4);
                       7    6      5    4      3    2
                      q  + q  + 2 q  + q  + 2 q  + q  + q

>  T(3,4);
                     6    8    2      3      4      5      7    9
              q + 2 q  + q  + q  + 2 q  + 2 q  + 2 q  + 2 q  + q

>  qfactor(T(0,4));
                                           4
                                   q (1 - q )
                                   ----------
                                          2
                                     1 - q

>  qfactor(T(1,4));
                                           5
                                   q (1 - q )
                                   ----------
                                     1 - q

>  qfactor(T(2,4));
                                      3        6
                              q (1 - q ) (1 - q )
                              -------------------
                                             2
                               (1 - q) (1 - q )

>  qfactor(T(3,4));
                                      4        7
                              q (1 - q ) (1 - q )
                              -------------------
                                     2
                               (1 - q ) (1 - q)

>  qfactor(T(4,4));
                                      5        8
                              q (1 - q ) (1 - q )
                              -------------------
                                     2
                               (1 - q ) (1 - q)

>  qfactor( aqprod(q,q,3)*T(0,6) );
                                        2   3       6
                         -(1 - q) (1 - q ) q  (1 - q )

>  qfactor( aqprod(q,q,3)*T(1,6) );
                                2        3   3       7
                         -(1 - q ) (1 - q ) q  (1 - q )

>  qfactor( aqprod(q,q,3)*T(2,6) );
                                3   3       4        8
                         -(1 - q ) q  (1 - q ) (1 - q )

>  qfactor( aqprod(q,q,3)*T(3,6) );
                           3       4        5        9
                         -q  (1 - q ) (1 - q ) (1 - q )

>  
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