Re: A combinatorial question

It turns out that subSet is a command from the package
SymmetricGroupCombinatoricFunctions (SGCF).  But there seems to be no
mention of it in HyperDoc.  Aside from this mail group, how would a user
find out about this function?

-Alasdair

On 03 Oct 2007 08:40:37 +0200, Martin Rubey < [email protected]>
wrote:
>
> > On 10/2/07, Alasdair McAndrew wrote:
> > > To experiment with a little algorithm, I need to generate all subsets
> of a
> > > set S which have fixed cardinality; for example to generate all three
> > > element subsets of {1,2,3,4,5,6,7}.  Is there an inbuilt command to do
> this
> > > in Axiom?  Or has somebody written a package to do such a thing?
>
> Well, the species package of Ralf and myself does that, of course.  But
> I'm not
> sure whether it wouldn't be overkill for your purpose.  Also, although you
> can
> use it from axiom, you need the Aldor compiler to install it.
>
> If you only need subsets, than
>
> In Aldor you'd say something like
>
>   structures(set [1,2,3,4,5,6,7])$(Combination(3)(Integer))
>
> in Axiom you would have to create the domain Combination(3)(Integer) first
> using
>
>   C3==>Interpret([parse "Combination(3)"], ACINT)
>
> since Axiom cannot deal with signatures like the above.  Furthermore,
> since
> Axiom doesn't understand Aldor's extend, you'll have to create the list of
> your
> labels as follows:
>
>   l := set([1,2,3,4,5,6,7]::ACList INT)$SetSpecies ACINT
>
> Now you can indeed say
>
>   structures(l)$C3
>
> and step through the subsets.
>
> Otherwise, and especially if you only need subsets, I'd roll my own, just
> as
> Bill did.  It depends a bit on how far you need to go.  If you google for
> "Ruskey, combinatorial generation", you'll find RuskeyCombGen.pdf which
> contains algorithms that are relatively easy to implement.
>
> (In fact, Combination from the species project currently also uses a dumb
> algorithm.)
>
> If you are interested in the species approach, please do not hesitate to
> ask
> for more explanations.
>
> Martin
>
>

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