FUNCTION : printtype1 - print a Type 1 identity
CALLING SEQUENCE : latexprinttype1(L, eqn, num)
PARAMETERS : L - list [p,a,c1,N,B]
eqn,num - positive integers
GLOBAL VARIABLES : _F
SYNOPSIS :
Print type 1 identity with equation number (eqn.num).
EXAMPLES :
> with(qseries):
> with(thetaids):
> with(ramarobinsids):
> G:=j->1/GetaL([1],10,j):H:=j->1/GetaL([3],10,j):
> GM:=j->1/MGetaL([1],10,j): HM:=j->1/MGetaL([3],10,j):
> GE:=j->-GetaLEXP([1],10,j):HE:=j->-GetaLEXP([3],10,j):
> proveit:=true: xprint:=false:
> ramtype1:=findtype1(6);
*** There were NO errors. Each term was modular function on
Gamma1(60). Also -mintotord=40. To prove the identity
we need to check up to O(q^(42)).
To be on the safe side we check up to O(q^(160)).
*** The identity below is PROVED!
[6, 1, -1]
3
eta(30 tau) eta(12 tau) eta(5 tau) eta(4 tau)
_G(6) _H(1) - _G(1) _H(6) = ------------------------------------------------
2 2
eta(60 tau) eta(15 tau) eta(10 tau) eta(6 tau)
ramtype1 := [[6, 1, -1]]
> L:=PROVEDFL1[1];
L := [6, 1, -1, 60, -40]
> printtype1(L,3, 1);
3
eta(30 tau) eta(12 tau) eta(5 tau) eta(4 tau)
G(6) H(1) - G(1) H(6) = ------------------------------------------------,
2 2
eta(60 tau) eta(15 tau) eta(10 tau) eta(6 tau)
Gamma[1](60), -B = 40, (3.1)
DISCUSSION :
SEE ALSO :
findtype1,
printtype1, printtype2, printtype3, printtype4,
printtype5, printtype6, printtype7, printtype8,
printtype9, printtype10, printtypelist