[GAP Forum] RandomMat with really random source

[Ha T. Lam]

Dear Alexander,


On Wed, Jul 23, 2014 at 5:40 PM, Alexander Konovalov <
alexk at mcs.st-andrews.ac.uk> wrote:

> Dear Ha,
>
> On 23 Jul 2014, at 22:19, Ha T. Lam <hatlam at gmail.com> wrote:
>
> > Dear GAP forum,
> >
> > I'm trying to generate random 2x2 matrices with entries from GF(947).
> > Normally, I would just use RandomMat(2,2,GF(947)), but I want to get
> > different results every time I start GAP. I found that RandomSource( r,
> dev
> > ) from the io package (
> > http://www.gap-system.org/Manuals/pkg/io/doc/chap6.html) allows
> randomness
> > from /dev/random, but I don't know how to use it as the random source for
> > RandomMat. Any advice?
>
> This is doable - first you have to create a real random source:
>
> gap> rs:=RandomSource(IsRealRandomSource,"random");
> <a real random source>
>
> Then you may create a list of all elements of GF(947) and pick up
> elements from it using "Random":
>
> ​​
> gap> gf:=AsList(GF(947));;
> gap> Random(rs,gf);
> Z(947)^42
> gap> Random(rs,gf);
> Z(947)^817
>
> Now you may take the code for RandomMat from the library and adjust it to
> say ReallyRandomMat which will use the approach above instead of calling
> Random( GF(947) );
>
> There is a warning, however. If it may be enough for you to use dev/urandom
> instead of dev/random, then it is advised to go for the 'urandom' option.
> I remember once we were very puzzled by the slow performance of GAP on the
> server where dev/random was used to generate some random strings. It was
> not possible to reproduce the slowdown at all while using GAP
> interactively.
> Then we figured out what happened: dev/random needs some noise in the
> entropy pool, and it may block when the pool is empty to wait for some more
> events to happen. There was a plenty of events when one was sitting in
> front
> of the keyboard; however, that was not the case on the server when GAP was
> running as a daemon. So please be aware of this feature.
>
> Hope this helps,
> Alexander
> ​
>
> ​
T​hank you very much for the quick reply and the warning. I was trying to
use 'random' instead of 'urandom' and was indeed puzzled by the speed
decrease. In my code, I used
​
List(GF(947)) instead of
​
AsList(GF(947)). Do you know if this makes a difference? The manual only
tells me that AsList gives roughly the same access time to elements.

I am also worried about working with a larger prime, would this method
create an in-memory list of all the elements? Is there anyway to do a sort
of "lazy evaluation"?

Thank you,

Ha