[GAP Forum] Question
Max Neunhoeffer
neunhoef at mcs.st-and.ac.uk
Mon Jul 19 09:34:42 BST 2010
Dear Lisette,
if you want to save typing, simply define a function making the group:
MyCycGrp := function(n)
return Group(PermList(Concatenation([2..n],[1])));
end;
(this can simply be typed in or saved in a file and read with the
"Read" command).
Then a simple
gap> MyCycGrp(100);
<permutation group with 1 generators>
gap> Size(last);
100
does the job.
I hope this helps.
Cheers,
Max.
On Mon, Jul 19, 2010 at 10:27:11AM +0200, Lisette Brillemans wrote:
> Dear Dan, dear Forum,
>
> Thank you for your reply.
> This does it indeed. But:
>
> gap> G := Group(PermList(List([1..10], i->(i mod 10)+1));
>
> is a very long and complicated line. Furthermore, what does NOT work (of
> course...) is:
>
> gap> G := SymmetricGroup(PermList(List([1..10], i->(i mod 10)+1));
>
> So I would like to ask the forum again: Is it possible to do something
> like (and how??):
>
> gap> G:=Group([1..10]);
> gap? G:=SymmetricGroup([1..10]);
>
> etc.
> (and especially with 100 instead of 10 and so.)
>
>
> with regards,
>
> Lisette
>
>
> > Dear Lisette, Dear Forum,
> >
> > On Mon, Jul 19, 2010 at 8:57 AM, Alexander Hulpke <ahulpke at gmail.com>
> > wrote:
> > Dear GAP Forum,
> >
> > On Jul 18, 2010, at 3:15 PM, Lisette Brillemans wrote:
> >
> > > Is there a command to enter a group like
> > >
> > > S:=Group((1,2,3,4,5,6,7,8,9,10)); at once.
> > >
> > > For instance a command like:
> > >
> > > S:=Group([1..10]) or so?
> >
> > If you just want a cyclic group you can use
> > CyclicGroup(IsPermGroup,10);
> >
> > Alternatively, you could use "List" to construct a list describing the
> > permutation you are interested in:
> > gap> x := List([1..10], i->(i mod 10)+1);
> > [ 2, 3, 4, 5, 6, 7, 8, 9, 10, 1 ]
> > (this list means that 1 goes to x[1]=2, 2 goes to x[2] = 3, etc. Then
> > use PermList to turn it into a permutation:
> > gap> PermList(x);
> > (1,2,3,4,5,6,7,8,9,10)
> > see http://www.gap-system.org/Manuals/doc/htm/ref/CHAP040.htm#SECT004 for the documentation for PermList. We then use Group to construct the group generated by that permutation:
> > gap> G := Group(PermList(x));
> > Group([ (1,2,3,4,5,6,7,8,9,10) ])
> > gap> Size(G);
> > 10
> >
> >
> > Hope this helps.
> >
> >
> > Kind regards,
> > Dan
> >
>
>
>
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--
Max Neunhoeffer http://www-groups.mcs.st-and.ac.uk/~neunhoef/
> > > > > > > > > > > May the Source be with you! < < < < < < < < < < < <
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