Re: How to implement equivalent of magma NullSpace in Pari/GP

[Kevin Acres <research@research-systems.com>]

Hi,

Thanks both Bill and John for the help.  I've got what I need now.

lift(matker(M2~*Mod(1,2))~) does the job, but it seems that 
FpM_ker(M2~, 2)~ does it quicker.

Both of these directly replace the Magma NullSpace function in the 
context that I'm using it.

Once again many thanks for the help. I can get back to the snfs port once more.


Best Regards,

Kevin.


At 10:30 PM 24/12/2009, John Cremona wrote:
> 2009/12/24 Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>:
> > On Thu, Dec 24, 2009 at 08:33:41PM +1100, Kevin Acres wrote:
> >> Hi,
> >>
> >> I'm trying to implement an equivalent of the Magma NullSpace() function.
> >
> > In PARI, this is called matker().
> >
> >> For example I'd like:
> >>
> >> [0 0 0 1 0 0 1 0]
> >> [1 0 1 0 0 0 1 0]
> >> [1 1 0 0 0 0 0 1]
> >> [0 1 1 0 0 0 0 1]
> >> [0 1 1 0 0 0 0 0]
> >> [0 0 1 0 0 1 0 0]
> >>
> >> to return
> >>
> >> [0 1 0 0 0 0 0 0 1]
> >> [0 0 1 0 0 1 1 0 0]
> >
> > Really ?  If you want to compute the kernel over Z/2Z then you should do
> > matker(M*Mod(1,2)).
>
> Perhaps not "should":  from the documentation of matker,
>
>    Note:  The library function FpM_ker(x,  p),  where x has integer
> entries reduced mod p and p is
> prime,  is equivalent to,  but orders of magnitude faster than,
> matker(x*Mod(1,p)) and needs much
> less stack space. To use it under gp, type install(FpM_ker, GG) first.
>
> John
>
>
> >
> > Cheers,
> > Bill.
> >