FUNCTION : vinf - 2*ORD(G,oo)
CALLING SEQUENCE : vinf(L,N)
PARAMETERS : L - (geta)-list produced by GETAP2getalist
and corresponds to a generalized eta-quotient
on Gamma[1](N).
N - positive integer
SYNOPSIS : Returns 2*ORD(G,oo) where G is the generalized eta-quotient
corresponding to the (geta)-list L with respect to the
group GAMMA[1](N).
EXAMPLES :
> with(thetaids):
> vinf();
-------------------------------------------------------------
vinf(L,N)
L is a getalist; i.e. L=[[b1,a1,c1],....]
Let G be the corresponding generalized eta-function.
vinf(L,N) returns ord(G,oo)
-------------------------------------------------------------
> JJ0:= -q/JAC(1,40,infinity)*JAC(2,40,infinity)^2/JAC(4,40,infinity)^3
> *JAC(5,40,infinity)^2*JAC(8,40,infinity)^2/JAC(9,40,infinity)
> /JAC(11,40,infinity)*JAC(15,40,infinity)^2/JAC(16,40,infinity)^2
> *JAC(18,40,infinity)^2/JAC(19,40,infinity)/JAC(20,40,infinity);
2 2 2
JJ0 := - q JAC(2, 40, infinity) JAC(5, 40, infinity) JAC(8, 40, infinity)
2 2 /
JAC(15, 40, infinity) JAC(18, 40, infinity) / (JAC(1, 40, infinity)
/
3
JAC(4, 40, infinity) JAC(9, 40, infinity) JAC(11, 40, infinity)
2
JAC(16, 40, infinity) JAC(19, 40, infinity) JAC(20, 40, infinity))
> JJ1:=rmcofnotqjac(JJ0);
2 2 2
JJ1 := q JAC(2, 40, infinity) JAC(5, 40, infinity) JAC(8, 40, infinity)
2 2 /
JAC(15, 40, infinity) JAC(18, 40, infinity) / (JAC(1, 40, infinity)
/
3
JAC(4, 40, infinity) JAC(9, 40, infinity) JAC(11, 40, infinity)
2
JAC(16, 40, infinity) JAC(19, 40, infinity) JAC(20, 40, infinity))
> GEP1:=jac2eprod(JJ1);
2 2 2 2 2 /
GEP1 := GETA(40, 2) GETA(40, 5) GETA(40, 8) GETA(40, 15) GETA(40, 18) /
/
3 2
(GETA(40, 1) GETA(40, 4) GETA(40, 9) GETA(40, 11) GETA(40, 16)
GETA(40, 19) GETA(40, 20))
> L1:=GETAP2getalist(GEP1);
L1 := [[40, 1, -1], [40, 2, 2], [40, 4, -3], [40, 5, 2], [40, 8, 2],
[40, 9, -1], [40, 11, -1], [40, 15, 2], [40, 16, -2], [40, 18, 2],
[40, 19, -1], [40, 20, -1]]
> vinf(L1,40);
2
DISCUSSION : We see that vinf(JJ0,40) = 2
which is twice power q in JJ0.
SEE ALSO : jac2eprod, GETAP2getalist, rmcofjac, v0, getaprodcuspord