FUNCTION :  printtype4 -  print a Type 4 identity
                

CALLING SEQUENCE :  printtype4(L, eqn, num)                 

PARAMETERS :  L - list [p,a,c1,N,B]
             eqn,num - positive integers

GLOBAL VARIABLES : _F

SYNOPSIS :   
   Prints  identity for
  G*(p) H*(a) + c1 G*(a) H*(p)                             
  with equation number (eqn.num)
   

EXAMPLES :   


>  with(qseries):
>  with(thetaids):
>  with(ramarobinsids):
>  G:=j->1/GetaL([1],12,j): H:=j->1/GetaL([5],12,j):
>  GM:=j->1/MGetaL([1],12,j): HM:=j->1/MGetaL([5],12,j):
>  GE:=j->-GetaLEXP([1],12,j): HE:=j->-GetaLEXP([5],12,j):
>  proveit:=true: xprint:=false:
>  findtype4(6);
*** There were NO errors.  Each term was modular function on
    Gamma1(48). Also -mintotord=24. To prove the identity
    we need to  check up to O(q^(26)).
    To be on the safe side we check up to O(q^(120)).
*** The identity below is PROVED!
[2, 1, -1]
                                                        3
                                  eta(48 tau) eta(8 tau)  eta(6 tau) eta(tau)
 _GM(2) _HM(1) - _GM(1) _HM(2) = ----------------------------------------------
                                            3
                                 eta(24 tau)  eta(16 tau) eta(4 tau) eta(2 tau)

"n=", 5
                                  [[2, 1, -1]]

>  L:=PROVEDFL4[1];
                            L := [2, 1, -1, 48, -24]

>  printtype4(L,3, 4);
                                                   3
                             eta(48 tau) eta(8 tau)  eta(6 tau) eta(tau)
G*(2) H*(1) - G*(1) H*(2) = ----------------------------------------------,
                                       3
                            eta(24 tau)  eta(16 tau) eta(4 tau) eta(2 tau)

    Gamma[1](48), -B = 24,     (3.4)


DISCUSSION :

SEE ALSO :  

findtype1,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypeL1