I believe you probably mean, you want all subgroups of the permutation
group on 10 elements.
if you create a permutation group then
sage: a= SymmetricGroup(10)
sage: a.conjugacy_classes_subgroups()
will give you a list of subgroups up to conjugation
(For any subgroup S there is some group element g such that gSg^{-1}
is on that list)
For each subgroup you can also get its subgroups. Note that the above
takes quite a bit of time to compute
for the symmetric group on 10 elements though for 8 elements its not
so bad.
Not sure if this is what you want.
Josh
On Aug 5, 5:27 am, "Green Kobold" <[EMAIL PROTECTED]> wrote:
> I apologise for delaying this reply, I just got back home.
> My concern is to allow users to experiment with this script I am doing
> without requiring them to install wxpython, floatspin, numpy, pyaudiolab,
> matplotlib... Some of these have to be installed manually on SAGE's python
> interpreter. I intend to make a plain and easy "install and run". If I was
> not doing this research, I would like to try this little app but would be in
> trouble installing all externals necessary.
> I don´t want to lose group manipulation facilities because this research is
> in development and I am not really sure where we are heading, that is
> exactly why we are researching.
>
> Joshua, thanks. Here are some points about what you've came up with:
> In our current status, if I can store groups in a data bank, that would make
> the app run faster (I suppose), and would, maybe, make the final app free
> from sage, running on a python interpreter with external packages. In that
> case, I would be able to make the executable with cx_freeze. That seems
> perfect, and I don't mind having a 15Mb group bank, that is nothing for
> today's standards, imho. And, that way, I could still use SAGE for
> development, without attacking my framework. And I could make a little
> script for making a bank based executable out of a in development version.
> As far as I can see, sage permutations are functions:
> sage: list(c)[5]
> (3,5)
> sage: list(c)[5](3)
> 5
> sage: list(c)[5](5)
> 3
> sage: list(c)[5](10)
> 10
>
> i am thinking about storing groups as a set of tuples that are translated to
> these sort of functions, so I won't have to alter the script much in order
> to make the executable. I would than make a .py 'group bank' and import it
> as a module.
> As I understand, that is one option out of what you proposed.
> One true question arises:
> I would like to have all groups that acts, say, on 10 elements (groups with
> degree 10?) and list all subgroups of each of these groups. Is there a way
> that I can request this output from sage.
>
> thankful good wishes,
> gk or Renato
>
> On 7/25/07, Joshua Kantor <[EMAIL PROTECTED] > wrote:
>
>
>
> > I am guessing you are intererested in having subgroups of the
> > permutation group acting on tone rows or something along those lines.
>
> > Do you actually need to have the ability to manipulate groups in your
> > final application or are you using sage to find some set of
> > interesting groups and only intend to deal with those.
>
> > In the the latter case I think your solution number 2 is more likely
> > to be reasonable.
> > if you could write two functions.
>
> > 1. A function that takes any (finite) group and automaticallly stores
> > some easy representation (tuples representing permutations as you say)
>
> > 2. A function that can read in that file and from that apply the
> > action of the group to a set of elements.
>
> > Then you could do your experimentation in SAGE, but you could easily
> > export any group in such a way that the action of its elements could
> > by computed only using python.
>
> > If you actually need to manipulate groups and need to use GAP its more
> > complicated.
> > SAGE uses gap by actually running a gap process and piping commands in
> > and reading the response out. This involves some somewhat tricky
> > python. To use gap you would have to take this interface (or write
> > you own) and if you wanted to distribute it you would have to package
> > it all up so that gap was automatically installed and then used by
> > your python code. (this isn't too bad on linux/mac, on windows its
> > probably harder)
>
> > I'm curious why you are so concerned about it being a compiled
> > executable. Python is on most linux machines (and easy to install) and
> > on all macs. On those machines python scripts are just as executable
> > as any binary. Is this for use on windows machines?
>
> > Josh
>
> > On Jul 24, 10:10 am, "William Stein" < [EMAIL PROTECTED]> wrote:
> > > On 7/24/07, Green Kobold <[EMAIL PROTECTED]> wrote:
>
> > > > Thanks William, that was very elucidating. BTW, SAGE was very helpful
> > in
> > > > some recent developments, I indeed mentioned SAGE with some emphasis
> > on a
> > > > computer music article recently accepted (if it helps SAGE project, I
> > can
> > > > send some infos in the occasion of its publication).
>
> > > Yes, it would help SAGE greatly if you could send some info.
> > > I'll post a link or info about the publication here:
> > > http://sagemath.org/pub.html
>
> > > > back to the executable issue:
> > > > I am not very experienced with programming, actually I only know a
> > little of
> > > > python. So I can spend some weeks on a senseless plan b. I've already
> > done
> > > > some executables from python code, using cx_freeze.
>
> > > I don't know really anything more useful
> > > about making standalone executables from
> > > python, etc., code, like you're discussing, unfortunately.
> > > Sorry. I hope somebody else has some ideas.
>
> > > -- william
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