FUNCTION :  ETA[provemodfuncGAMMA0idBATCH] -  proving etaid as a modfunc on Gamma0(N)

CALLING SEQUENCE :  provemodfuncGAMMA0idBATCH()
                    provemodfuncGAMMA0idBATCH(etaid,N)
                    provemodfuncGAMMA0idBATCH(symid,etaid,N)
                    

PARAMETERS :  
   symid - symbolic form of the identity. 
   etaid - sum of modular functions on Gamma[0](N)           
           Each term in the sum is a eta-quotient to base N. 
       N - positive integer
                  -            

GLOBAL VARIABLES : 
    qcheck,modfunccheck, totcheck, _ORDS,jptmp,jpqd,eptmp,gltmp
    etaPRODL,GPL,COFS,conpres,CONTERMS,mintottmp,consL,MFLB
    xprint, overrideproofq,_CUSPS,noprint
    qthreshold,proveit,printlocalsymid

SYNOPSIS :   
   This is a BATCH version of provemodfuncGAMMA0id 
   It uses the global var qthreshold .
   symid = symbolic form of the identity. 
   etaid = sum of modular functions on Gamma[0](N)           
           Each term in the sum is a eta-quotient to base N. 
   CUSPS = Set of inequivalent cusps for Gamma[0](N).        
   WIDS  = List of corresponding widths.                     
   global vars (can be used for error-checking):             
   qcheck, modfunccheck, totcheck, _ORDS, jptmp, jpqd, eptmp,
   gltmp, EPRODL, GETAL, COFS, conpres, CONTERMS, mintottmp  
   

EXAMPLES :   

> with(ETA):
> provemodfuncGAMMA0idBATCH();
-------------------------------------------------------------
provemodfuncGAMMA0idBATCH(symid,etaid,N)                     
provemodfuncGAMMA0idBATCH(etaid,N)                           
   This is a BATCH version of provemodfuncGAMMA0id 
   It uses the global var qthreshold .
   symid = symbolic form of the identity. 
   etaid = sum of modular functions on Gamma[0](N)           
           Each term in the sum is a eta-quotient to base N. 
   CUSPS = Set of inequivalent cusps for Gamma[0](N).        
   WIDS  = List of corresponding widths.                     
   global vars (can be used for error-checking):             
   qcheck, modfunccheck, totcheck, _ORDS, jptmp, jpqd, eptmp,
   gltmp, EPRODL, GETAL, COFS, conpres, CONTERMS, mintottmp  
                                                             
-------------------------------------------------------------
> gpP:=[1,2,3,-2]: gpQ:=[2,2,6,-2]:
> P:=gp2etaprod(gpP):
> Q:=gp2etaprod(gpQ):
> ETAid:=P*Q+9/P/Q - (Q/P)^3 - (P/Q)^3:
> ETAidn:=etanormalid(%):
> f1:=op(2,ETAidn)/9:
> f2:=-op(3,ETAidn):
> f3:=-op(4,ETAidn):
> provemodfuncGAMMA0idBATCH(1+9*f1-f2-f3,6);
*** There were NO errors. 
*** o Each term was modular function on
      Gamma0(6). 
*** o We also checked that the total order of
      each term was zero.
To prove the identity we will need to verify if up to 
q^(3).
*** The identity below is PROVED!
                                   [1, -2, 0]

DISCUSSION :

SEE ALSO :