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

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Thu, Dec 24, 2009 at 11:30:07AM +0000, John Cremona wrote:
> 2009/12/24 Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>:
> > 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.

Your suggestion is good, thought matker in the PARI development branch will
automatically call FpM_ker if the matrix is filled with intmod. However the
interface of FpM_ker can be more convenient and less wasteful.
The development branch also include a function F2m_ker for matrix over GF(2)
(which is used internally by FpM_ker) but it use a different input format
(one bit per entry).

Cheers,
Bill.