FUNCTION : Gamma1ModFunc - Checks whether the generalized eta-quotient
corresponding to the geta-list L is a
modular function of Gamma[1](N)
CALLING SEQUENCE : Gamma1ModFunc(L,N)
PARAMETERS : L - (geta)-list produced by GETAP2getalist
and corresponds to a generalized eta-quotient
on Gamma[1](N).
N - positive integer
GLOBAL VARIABLES : xprint (default=false)
SYNOPSIS : Checks whether the generalized eta-quotient
corresponding to the geta-list L is a modular function
of Gamma[1](N). It returns 1 if it is a modular function
otherwise it returns 0. It also prints diagnostics.
This function is needed in the proc provemodfuncid.
If xprint is true then extra info is printed.
EXAMPLES :
> with(thetaids):
> Gamma1ModFunc();
-------------------------------------------------------------
Gamma1ModFunc(L,N)
L is a getalist; i.e. L=[[b1,a1,c1],....]
and assumes each a1, a2, etc is not zero.
Let G be the corresponding generalized eta-function.
Checks whether G is a modular function of Gamma[1](N).
Returns 1 if it is a modular function otherwise 0.
It also prints diagnostics.
-------------------------------------------------------------
> eprod := GETA(40,3)^2/GETA(40,4)^5*GETA(40,5)^4/GETA(40,6)^3
*GETA(40,7)^2*GETA(40,8)^2/GETA(40,10)^2*GETA(40,13)^2
/GETA(40,14)^3*GETA(40,15)^4/GETA(40,16)^4*GETA(40,17)^2
/GETA(40,20)/GETA(20,1)^2*GETA(20,2)^3/GETA(20,3)^2
*GETA(20,4)*GETA(20,6)^3/GETA(20,7)^2*GETA(20,8)
/GETA(20,9)^2;
> L2:=GETAP2getalist(eprod);
L2 := [[40, 3, 2], [40, 4, -5], [40, 5, 4], [40, 6, -3], [40, 7, 2],
[40, 8, 2], [40, 10, -2], [40, 13, 2], [40, 14, -3], [40, 15, 4],
[40, 16, -4], [40, 17, 2], [40, 20, -1], [20, 1, -2], [20, 2, 3],
[20, 3, -2], [20, 4, 1], [20, 6, 3], [20, 7, -2], [20, 8, 1],
[20, 9, -2]]
> Gamma1ModFunc(L2,40);
1
> xprint:=true:
> Gamma1ModFunc(L2,40);
* starting Gamma1ModFunc with L=[[40, 3, 2], [40, 4, -5], [40, 5, 4],
[40, 6, -3], [40, 7, 2], [40, 8, 2], [40, 10, -2], [40, 13, 2],
[40, 14, -3], [40, 15, 4], [40, 16, -4], [40, 17, 2], [40, 20, -1],
[20, 1, -2], [20, 2, 3], [20, 3, -2], [20, 4, 1], [20, 6, 3], [20, 7, -2],
[20, 8, 1], [20, 9, -2]] and N=40
All n are divisors of 40
val0=0
which is even.
valinf=2
which is even.
It IS a modfunc on Gamma1(40)
DISCUSSION : We see that the generalized eta-quotient eprod is
a Modular Function on Gamma[1](40).
SEE ALSO : 2getalist,
provemodfuncid