FUNCTION :   getaprodcuspORDS - ORD of generalized-etaproduct at each cusp


CALLING SEQUENCE :  getaprodcuspORDS(L,cusps,wids)                               
                    

PARAMETERS :  L - (geta)-list produced by GETAP2getalist
              cusps - Set of inequivalent cusps for Gamma[1](N).
              wids  - List of corresponding widths.

GLOBAL VARIABLES : toterror - total ORD (should be zero)

SYNOPSIS :   Let G be a generalized-etaproduct corresponding to the    
             getalist L. This proc calculates ORD(G,z) with respect to 
             Gamma[1](N) for each cusp z in cusps. Here cusps is a list
             of inequivalent cusps of Gamma[1](N) and wids is the list 
             of their corresponding widths. The cusp at infinity is    
             repesented by oo. The total ORD should be 0.              
             Global var toterror = total ORD (for error-checking).     
   
EXAMPLES :   

> cusps40:=cuspmake1(40):
> cusps40:=cusps40 minus {[1,0]}:   
> cusps40:=convert(cusps40,list):
> wids40:=map(x->cuspwid1(x[1],x[2],40),cusps40):
> wids40:=[1,op(wids40)]:
> CUSPS40:=map(x->x[1]/x[2],cusps40):
> CUSPS40:=[oo,op(CUSPS40)]:
> 
> 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]]

> getaprodcuspORDS(gltmp,CUSPS40,wids40);
                                 %Cusp ords: %

[[oo, 0], [0, 0], [1/3, 0], [1/7, 0], [1/9, 0], [1/11, 0], [1/13, 0], [1/17, 0],

    [1/19, 0], [1/2, 0], [1/6, 0], [1/14, 0], [1/18, 0], [1/4, -2], [3/4, -2],

    [1/12, -2], [7/12, -2], [1/5, 3], [3/5, 0], [2/5, 0], [4/5, 3], [1/15, 3],

     13
    [--, 0], [7/15, 0], [4/15, 3], [1/8, 1], [3/8, 1], [7/8, 1], [5/8, 1],
     15

                                      13
    [1/16, 1], [3/16, 1], [7/16, 1], [--, 1], [1/10, -4], [3/10, -2],
                                      16

    [7/10, -2], [9/10, -4], [1/20, 0], [3/20, -2], [7/20, -2], [9/20, 0],

                                      11       13       17       19
    [3/40, 1], [7/40, 1], [9/40, 0], [--, 0], [--, 1], [--, 1], [--, 0]]
                                      40       40       40       40

                               %TOTAL ORD = %, 0

[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, 3, 0, 0, 3, 3, 0, 0, 3,

    1, 1, 1, 1, 1, 1, 1, 1, -4, -2, -2, -4, 0, -2, -2, 0, 1, 1, 0, 0, 1, 1, 0]


DISCUSSION :

SEE ALSO :