FUNCTION : getaprodcuspord - invariant order of a generalized-etaproduct at a cusp
CALLING SEQUENCE : getaprodcuspord()
getaprodcuspord(L,z)
PARAMETERS : L - (geta)-list produced by GETAP2getalist
z - rational or oo (cusp)
SYNOPSIS : Let G be a generalized-etaproduct corresponding to the
getalist L. This proc calculates invariant ord(G,z) at the cusp z.
EXAMPLES :
> with(thetaids):
> getaprodcuspord();
-------------------------------------------------------------
getaprodcuspord(L,cusp)
Let G be a generalized-etaproduct corresponding to the
getalist L. This proc calculates invariant order ord(G,z)
-------------------------------------------------------------
> CW40:=CUSPSANDWIDMAKE1(40):
> jptmp:=1/JAC(3,40,infinity)*JAC(5,40,infinity)^2*JAC(6,40,infinity)^2
> /JAC(7,40,infinity)/JAC(8,40,infinity)^2/JAC(12,40,infinity)^3
> /JAC(13,40,infinity)*JAC(14,40,infinity)^2
> *JAC(15,40,infinity)^2*JAC(16,40,infinity)^2/JAC(17,40,infinity)
> /JAC(20,40,infinity):
> eptmp:=jac2eprod(jptmp);
2 2 2 2 2
eptmp := GETA(40, 5) GETA(40, 6) GETA(40, 14) GETA(40, 15) GETA(40, 16)
/ 2 3
/ (GETA(40, 3) GETA(40, 7) GETA(40, 8) GETA(40, 12) GETA(40, 13)
/
GETA(40, 17) GETA(40, 20))
> gltmp:=GETAP2getalist(eptmp);
gltmp := [[40, 3, -1], [40, 5, 2], [40, 6, 2], [40, 7, -1], [40, 8, -2],
[40, 12, -3], [40, 13, -1], [40, 14, 2], [40, 15, 2], [40, 16, 2],
[40, 17, -1], [40, 20, -1]]
> Gamma1ModFunc(gltmp,40);
1
> ORDS:=getaprodcuspORDS(gltmp,CW40[1],CW40[2]);
ORDS := [0, 0, 0, 0, -2, 3, 0, 0, 1, 0, -4, 0, -2, 0, 0, 3, 1, 0, 0, 0, 0, 0,
-2, 0, 1, -2, 1, -2, 1, 3, 3, 1, 1, -2, -2, 0, 1, -2, 1, -4, 0, 0, 0, 0, 1,
1, 1, 0]
> BMAT:=matrix(nops(CW40[1]),4):
> for j from 1 to nops(CW40[1]) do
> BMAT[j,1]:= CW40[1][j]:
> BMAT[j,2]:= getaprodcuspord(gltmp,CW40[1][j]):
> BMAT[j,3]:= CW40[2][j]:
> BMAT[j,4]:= ORDS[j]:
> od:
> op(BMAT);
[ oo 0 1 0]
[ ]
[ 0 0 40 0]
[ ]
[1/2 0 20 0]
[ ]
[1/3 0 40 0]
[ ]
[1/4 -1/5 10 -2]
[ ]
[1/5 3/8 8 3]
[ ]
[1/6 0 20 0]
[ ]
[1/7 0 40 0]
[ ]
[1/8 1/5 5 1]
[ ]
[1/9 0 40 0]
[ ]
[1/10 -1 4 -4]
[ ]
[1/11 0 40 0]
[ ]
[1/12 -1/5 10 -2]
[ ]
[1/13 0 40 0]
[ ]
[1/14 0 20 0]
[ ]
[1/15 3/8 8 3]
[ ]
[1/16 1/5 5 1]
[ ]
[1/17 0 40 0]
[ ]
[1/18 0 20 0]
[ ]
[1/19 0 40 0]
[ ]
[1/20 0 2 0]
[ ]
[2/5 0 8 0]
[ ]
[3/4 -1/5 10 -2]
[ ]
[3/5 0 8 0]
[ ]
[3/8 1/5 5 1]
[ ]
[3/10 -1/2 4 -2]
[ ]
[3/16 1/5 5 1]
[ ]
[3/20 -1 2 -2]
[ ]
[3/40 1 1 1]
[ ]
[4/5 3/8 8 3]
[ ]
[4/15 3/8 8 3]
[ ]
[5/8 1/5 5 1]
[ ]
[7/8 1/5 5 1]
[ ]
[7/10 -1/2 4 -2]
[ ]
[7/12 -1/5 10 -2]
[ ]
[7/15 0 8 0]
[ ]
[7/16 1/5 5 1]
[ ]
[7/20 -1 2 -2]
[ ]
[7/40 1 1 1]
[ ]
[9/10 -1 4 -4]
[ ]
[9/20 0 2 0]
[ ]
[9/40 0 1 0]
[ ]
[ 11 ]
[ -- 0 1 0]
[ 40 ]
[ ]
[ 13 ]
[ -- 0 8 0]
[ 15 ]
[ ]
[ 13 ]
[ -- 1/5 5 1]
[ 16 ]
[ ]
[ 13 ]
[ -- 1 1 1]
[ 40 ]
[ ]
[ 17 ]
[ -- 1 1 1]
[ 40 ]
[ ]
[ 19 ]
[ -- 0 1 0]
[ 40 ]
DISCUSSION :
The four columns of the matrix correspond to
z=cusp, ord(G,z), width(z), ORD(G,z)=ord(G,z)*width(z)
SEE ALSO : getaprodcuspORDS,
getacuspord