[GAP Forum] how to iterate over all matrices over a finite field?

[Benoit Jacob]

Many thanks!

On Mon, Dec 14, 2015 at 9:00 AM, Sven Reichard <sven.reichard at tu-dresden.de>
wrote:

> Hello Benoit,
>
> matrices are tuples of tuples, so we can use the combinatorial
> functions. As we do not want to store the complete list of matrices we
> use an iterator.
>
> gap> n := 3;; F := GF(3);;
> gap> rows := Tuples(F, n);
> gap> matrices := IteratorOfTuples(rows, n);
> gap> for matrix in matrices do
> >      process(matrix);
> >    od;
>
> Hope this helps.
>
> If the set of rows is too large to be stored, the set of matrices is
> likely too large to be processed. However maybe there is also a way of
> avoiding storage of the rows.
>
> Sven Reichard
>
>
>
> On 12/14/2015 02:34 PM, Benoit Jacob wrote:
> > Hello,
> >
> > What would be a simple way to write a "for" loop iterating over all
> square
> > matrices of a fixed size, say NxN, over some fixed finite field GF(q) ?
> So
> > there would be q^(N^2) iterations? - of course, one could write a for
> loop
> > over integers from 1 to q^(N^2) and for each integer construct a
> > corresponding matrix, but is there a simpler way?
> >
> > Thanks,
> > Benoit
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>
>
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