Ariel Pacetti on Thu, 05 May 2005 12:25:20 +0200 |
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Re: Computing the theta function of a positive definite quadratic form? |
There is a command (in the new versions) which is qfrep. If you look at the help command:
? ?qfrepqfrep(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