FUNCTION :  qseries[zqfactor] - Convert (z,q)-series into (z,q)-product
                

CALLING SEQUENCE :  zqfactor(F,z,q)
                    zqfactor(F,z,N)
                    

PARAMETERS :   F  -  q-series with coeffients that are polynomials in z
               z  -  variable (name)
               N -   positive integer (optional, default=1000)

GLOBAL VARIABLES : 

SYNOPSIS :   

 zqfactor(F,z,q) tries to convert F into a product of terms
 (1 - a[i,j] z^i q^j) where each a[i,j] is an integer.
 Here N is the max number of terms (default is 1000 but can be assigned).

 WARNING: This function does not work all the time.
          Sometimes it finds the correct (z,q)-product - see example below.
          But at times it will fail to find a reasonable product even
          though one may exist.
   
EXAMPLES :   

>  with(qseries):
>  L1:=tripleprod(-z^2*q^3,q^4,20):
>  L2:=tripleprod(-z^2*q,q^4,20):
>  g:=L1-L2/z:
>  zqfactor(g,z,q,10);
                                                          /      2 \
                                              2        2  |     q  |         3        3
(1 - 1/z) (1 - z q) (1 - q) (1 - q/z) (1 - z q ) (1 - q ) |1 - ----| (1 - z q ) (1 - q )
                                                          \     z  /

    /      3 \                     /      4 \                     /      5 \
    |     q  |         4        4  |     q  |         5        5  |     q  |         6
    |1 - ----| (1 - z q ) (1 - q ) |1 - ----| (1 - z q ) (1 - q ) |1 - ----| (1 - z q )
    \     z  /                     \     z  /                     \     z  /

             /      6 \                     /      7 \                     /      8 \
          6  |     q  |         7        7  |     q  |         8        8  |     q  |
    (1 - q ) |1 - ----| (1 - z q ) (1 - q ) |1 - ----| (1 - z q ) (1 - q ) |1 - ----|
             \     z  /                     \     z  /                     \     z  /

                        /      9 \                       /     10\
            9        9  |     q  |         10        10  |    q  |
    (1 - z q ) (1 - q ) |1 - ----| (1 - z q  ) (1 - q  ) |1 - ---|
                        \     z  /                       \     z /

DISCUSSION :

SEE ALSO :  qfactor