FUNCTION : jac2eprod - Convert a quotient of theta-functions to generalize eta-products
CALLING SEQUENCE : jac2eprod(JJ)
PARAMETERS : JJ - Quotient of theta-functions written in
in terms of JAC(a,b,infinity)
SYNOPSIS : Converts the JAC-quotient JJ into a quotient of
eta-products and generalized eta-products.
The output is in terms of EETA(b) and GETA(b,a).
EETA(b) corresponds to eta(b*tau)
GETA(b,a) corresponds to the generalized eta-function
eta[b,a](tau).
This version (7/19/13) does NOT omit the power of q.
EXAMPLES :
> with(thetaids):
> jac2eprod();
-------------------------------------------------------------
jac2eprod(JJ)
JJ is a quotient of theta functions encoded in terms of
JAC(a,b,infinity). This proc converts this quotient into
a quotient of eta-products and generalized eta-products
The output is terms of EETA(b) and GETA(b,a).
EETA(b) corresponds to eta(b*tau), and
GETA(b,a) corresponds to the generalized eta-function
eta[b,a](tau).
-------------------------------------------------------------
> JJ := JAC(1,40,infinity)/JAC(0,40,infinity)^12*JAC(2,40,infinity)
/JAC(4,40,infinity)*JAC(5,40,infinity)^2*JAC(6,40,infinity)^2
*JAC(9,40,infinity)*JAC(11,40,infinity)*JAC(14,40,infinity)^2
*JAC(15,40,infinity)^2*JAC(18,40,infinity)*JAC(19,40,infinity)
/JAC(20,40,infinity);
2
JAC(1, 40, infinity) JAC(2, 40, infinity) JAC(5, 40, infinity)
2
JAC(6, 40, infinity) JAC(9, 40, infinity) JAC(11, 40, infinity)
2 2
JAC(14, 40, infinity) JAC(15, 40, infinity)
/
JAC(18, 40, infinity) JAC(19, 40, infinity) / (
/
12
JAC(0, 40, infinity) JAC(4, 40, infinity)
JAC(20, 40, infinity))
> jac2eprod(JJ);
2 2
GETA(40, 1) GETA(40, 2) GETA(40, 5) GETA(40, 6) GETA(40, 9)
2 2
GETA(40, 11) GETA(40, 14) GETA(40, 15) GETA(40, 18)
GETA(40, 19)/(GETA(40, 4) GETA(40, 20))
>
> JJ2:=JAC(1,5,infinity)/JAC(0,5,infinity):
>
> jac2eprod(JJ2);
GETA(5, 1)
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q
DISCUSSION :
SEE ALSO :