[GAP Forum] Running through subspaces over finite field

[Rudolf Zlabinger]

Dear Arturo,

to your last question, whether the order of elements of collections of 
different calls to Iterator are fixed:

"If this is a collection C but not a list then iter iterates over the 
elements of C in an unspecified order, which may change for repeated calls 
of Iterator."  (Reference Manual...Iterators)

So a fixed order is not guaranted by description of Iterator.

All the best, Rudolf

----- Original Message ----- 
From: "Arturo Magidin" <magidin at member.ams.org>
To: "GAP Forum" <forum at gap-system.org>
Sent: Tuesday, June 12, 2007 5:09 PM
Subject: Re: [GAP Forum] Running through subspaces over finite field


> On Mon, 11 Jun 2007, Rudolf Zlabinger wrote:
>
>> Dear Arturo Magidin,
>>
>> if I understood right, you want to handle a collection:
>>
>> gap> v:=GF(3)^10;
>> ( GF(3)^10 )
>> gap> subspaces:=Subspaces(v,8);
>> Subspaces( ( GF(3)^10 ), 8 )
>> gap> IsCollection(subspaces);
>> true
>> gap>
>>
>> For collections that are not lists, the default method is IteratorList(
>> Enumerator( C ) ).  (Reference Manual.... Iterators)
>>
>> Normally you would use enum:=Enumerator(subspaces), and then set 
>> enum[xxx] to your desired element, but Enumerator(subspaces) runs out of 
>> time and out of storage. Whereas you can process an Enumerator in the 
>> same way as a list, an Iterator only is usable step by step, therefore 
>> the definition of an Iterator is unsignificant to time and storage 
>> independent from the magnitude of the collection.
>>
>> The problem now is, that Enumerator doesnt run for the magnitude of your 
>> collection, and an Iterator cannot be preset to a predefined element.
>
> I was afraid of that.
>
>> The best I see, is, that an Iterator remembers the last element called by 
>> NextIterator, so you can remember different states by different 
>> variables, you have to use ShallowCopy to get a different Object::
>
> That's fine. I don't really need to "remember" more than one object at a 
> time, so that is not really a problem.
>
> On a related topic, then. Is the order in which the subspaces iterate 
> fixed, or can it change with different calls of an iterator for 
> Subspaces(V,k)?
>
> If it is fixed, could someone point me in the direction of the algorithm 
> used to iterate through them?
>
> Thanks,
>
> Arturo
>
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