Hi Simon
how big is M, how big is F, and is M sparse or do you have few zeros?
Kind regards
Gary
On Monday, April 15, 2013 1:17:14 PM UTC+2, Simon King wrote:
>
> Hi,
>
> On 2013-04-15, Simon King <simon...@uni-jena.de <javascript:>> wrote:
> > I have a finite set X and a set S of subsets of X. I'd like to get a
> > list (or better: an iterator) of all subsets U of S (i.e., subsets of
> > subsets) such that the union of the elements of U is equal to X.
> > Ideally, I'd like that the number of intersection points (counted with
> > multiplicity) of elements of U is ascending.
> >
> > Hence, if there is a disjoint cover of X by elements of S, then I'd like
> > to get this first, and otherwise I'd like to first get a cover that is
> "as
> > close to being disjoint as possible".
>
> I have found that one can get disjoint ("exact") covers via "dancing
> links".
>
> But let me formulate a related problem that I'd even more like to solve:
> Given a matrix M over some finite field F, I need a linear combination
> of rows of M such that the resulting row has all coefficients non-zero
> (in F). Preferably, the set of rows to be combined should be small, but
> it is not needed that it is minimal.
>
> How can this be done?
>
> Best regards,
> Simon
>
>
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