Re: Computing the theta function of a positive definite quadratic form?

[Ariel Pacetti <apacetti@math.utexas.edu>]

There is a command (in the new versions) which is qfrep. If you look at 
the help command:

? ?qfrep
qfrep(x,B,{flag=0}): vector of (half) the number of vectors of norms from 
1 to B for the integral and definite quadratic form x. Binary digits of 
flag mean 1: count vectors of even norm from 1 to 2B, 2: return a 
t_VECSMALL instead of a t_VEC.

Little example;

? qfrep([1,0;0,1],100)
%1 = [2, 2, 0, 2, 4, 0, 0, 2, 2, 4, 0, 0, 4, 0, 0, 2, 4, 2, 0, 4, 0, 0, 0, 
0, 6, 4, 0, 0, 4, 0, 0, 2, 0, 4, 0, 2, 4, 0, 0, 4, 4, 0, 0, 0, 4, 0, 0, 0, 
2, 6, 0, 4, 4, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 2, 8, 0, 0, 4, 0, 0, 0, 2, 4, 
4, 0, 0, 0, 0, 0, 4, 2, 4, 0, 0, 8, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 4, 2, 
0, 6]

(note that it is implemented in all dimensions, not just quadratic forms).

Ariel


On Thu, 5 May 2005, Jonathan Hanke wrote:

> Hi,
>
> I was wondering if Pari can compute the theta function of a quadratic
> form.  There seems to have been a gp command (qfred?) which did this,
> but I can't find it in the current manual.  Thanks,
>
> 						-Jon