FUNCTION :  qseries[findhomcombo] - tries to express a q-series as a 
                                    homogeneous polynomial of degree n of 
                                    a given list of q-series.

CALLING SEQUENCE :  findhomcombo(L,q,n,topshift,etaoption)
    
PARAMETERS :   L   - list of q-series
               q   - variable           
               n   - positive integer
               topshift - integer greater than -20      
               etaoption - yes, no

GLOBAL VARIABLE : X

SYNOPSIS :   
   
findhomcombo(f,L,q,n,topshift,etatoption) returns a set of potential 
set of linear combinations from L for the given q-series f.
The value of topshift is usually taken to be zero. Howeverm if
it appears that spurious relations are being generated then a higher
value of topshift should be taken.

If etaoption=yes then each function in the combination is %converted%
into an eta-product.

NOTE: There is a global variable X that is reassigned each time the
function is called. This variable is used to display the combinations.
If the list L is linearly dependent more than one linear combination
may be returned.

EXAMPLES :   

> with(qseries):
> f := sum((n^2-5*trunc((n^2+2)/5))
       *q^n*((q^n)^4+26*(q^n)^3+66*(q^n)^2+26*q^n+1)
       /(1-q^n)^6,n=1..50):
> B1 := etaq(q,1,50)^5/etaq(q,5,50):
> B2 := q*etaq(q,5,50)^5/etaq(q,1,50):
> findhomcombo(f,[B1,B2],q,3,0,yes);
                                 # of terms , 25

              -----possible linear combinations of degree------, 3

                                                                        15
                 3         9                9         3       eta(5 tau)
      {eta(5 tau)  eta(tau)  + 40 eta(5 tau)  eta(tau)  + 335 ------------}
                                                                        3
                                                                eta(tau)

                         2                    2           3
                    {X[1]  X[2] + 40 X[1] X[2]  + 335 X[2] }


> g := sum((n^2-5*trunc((n^2+2)/5))*q^n/(1-q^n)^2,n=1..50):
> findhomcombo(g,[B1,B2],q,1,0,no);

                                 # of terms , 23

              -----possible linear combinations of degree------, 1

                                     {X[2]}
> 

DISCUSSION :

From the session above it appears that                                      
                                                                        15
                 3         9                9         3       eta(5 tau)
f  =   eta(5 tau)  eta(tau)  + 40 eta(5 tau)  eta(tau)  + 335 ------------ 
                                                                        3
                                                                eta(tau)

and
                         5
               eta(5 tau)
      g  =    -----------.
                eta(tau)


SEE  ALSO :  findhom, findnonhom