Re: [Axiom-mail] Elliptic curve factoring

[Ralf Hemmecke]

On 07/10/2007 04:22 PM, Bill Page wrote:
> Now, Ralf, don't you go scaring people away by suggesting that we
> expect even more from them than just working with Axiom - that is hard
> enough as it is! ;-)

I apologize. It was not my intention.

> Seriously, I think we can develop such documentation as we go. From my
> point of view, doing this via the Axiom Wiki makes it very easy.

Bill, I actually was going to suggest that in my following mail, but I 
had other stuff to do and so it did not make it to the list. I would 
have suggested to use the literate axiom sources that you have put on 
MathAction. Whoever is interested in that intfact.spad project, could 
work there. And yes, there is a lot of work to do documenting the 
algebra code. My comment was actually meant to encourage to write a bit 
more documentation for new functionality than there is for current .spad 
files. Alasdair, I hope you understand, that you are probably the person 
who understands best your own code and the theory behind. Please make it 
public and help in documenting it properly. Not everything must be done 
by yourself, it is only that you are the one with the biggest knowledge 
about that subject.

Ralf

> Regards,
> Bill Page.
>
> On 7/10/07, Alasdair McAndrew wrote:
> > Err, no, I haven't written it up in pamphlet style at all... my 
> > version of
> > Axiom (Timestamp: Wednesday June 21, 2006 at 03:45:56) doesn't seem to 
> > come
> > with any pamphlets.  The '*.spad.dvi" files just contain the text of the
> > *.spad files presented as dvi files.  All I really want to do is to 
> > extend
> > the methods in intfact.spad to include ecm - which the file itself
> > recommends.
> >
> > -Alasdair
> >
> >
> > On 7/10/07, Ralf Hemmecke wrote:
> > > Why don't you put it just online and send the URL. I hope you have at
> > > least tried to write that up in a pamphlet style way?
> > >
> > > Ralf
> > >
> > > On 07/10/2007 03:08 PM, Alasdair McAndrew wrote:
> > > > I have written some highly unoptimized code for factoring integers 
> > using
> > > > Lenstra's elliptic curve method, with the "birthday paradox" phase 
> > two
> > > > developed by Richard Brent.  Even at this stage, it can factor the
> > > > seventh Fermat number 2^2^7+1 in 352 seconds, as opposed to 1877 
> > seconds
> > > > by the in-built factoring method.  If anybody is interesting in
> > > > developing this code further, do let me know.