Bill Allombert on Wed, 12 Jun 2013 17:39:48 +0200

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Re: How to calculate lower degree factors of elldivpol(e,100)

On Wed, Jun 12, 2013 at 03:55:01PM +0100, Richard in Reading wrote:
> I'm interested in the lower degree factors of various divison polynomials.
> I'm very impressed with PARI's ability to calculate with and then factorize a
> polynomials with large coefficients and degrees in the thousands. I have used
> the following:
> e=ellinit("1584s1");
> f=elldivpol(e,100);
> fordiv(100,d,if(d!=100,f=f/gcd(f,elldivpol(e,d))));
> ff=factor(f);
> apply(poldegree,ff[,1]~)
> %1 = [100, 100, 200, 200, 1000, 2000]
> But this is slow. Is there a more direct way to calculate the factors of degree 100 without getting the larger factors?

First you should use Moebius inversion formula, 

Second, why do you expect the polynomial to have small degree factors ?
This is the key to find them more quickly.