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