[GAP Forum] GAP and rings?
Nilo de Roock
ndroock1 at gmail.com
Mon Jul 23 14:55:27 BST 2007
Hello Keith,
Sorry. I don't do much with non-cummutative rings, can't really
help you with that.
If there is an open source package supporting such rings then it's probably
included in SAGE.
kind regards,
nilo de roock
2007/7/23, R. Keith Dennis <dennis at rkd.math.cornell.edu>:
>
> Thanks for the suggestions.
>
> However, I'm not sure that any of them work in this situation:
>
> the rings I want to look at are non-commutative
>
> the characteristic is almost never 0 nor prime
>
> I believe that eliminates Macaulay2 and Singular; I'm not sure about
> Cocoa as I haven't had a chance to look at the documentation.
>
> Please let me know if I've misunderstood what can be done with these
> packages.
>
> Keith
>
> > For rings there is a wide selection of available packages.
> >
> > I can confirm that the following
> > - Macaulay2
> > - Cocoa
> > - Singular
> > all do the basic stuff really well.
> >
> > Seek and you'll find a wealth of information.
> >
> > Macaulay2 and Singular are integrated with GAP in the SAGE package,
> > which I particularly recommend.
> >
> > Kind regards,
> > nilo de roock
> >
> >
> > 2007/7/23, R. Keith Dennis <dennis at rkd.math.cornell.edu>:
> > >
> > > Dear Colleagues:
> > >
> > > I have another simple question to ask.
> > >
> > > However, I'd like to first thank everyone who has helped me thus far.
> > > In particular, I'm most grateful to Bettina Eick and Jack Schmidt for
> > > providing much more than one might hope for. Thanks!
> > >
> > > Bettina Eick showed me how to use the ANUPQ package to generate larger
> > > p-groups. In particular it was possible for me to construct the
> > > groups of order 3^7 of rank 2 & the groups of order 1024 of rank 2,
> > > which were some of the things I needed. These computations went
> > > fairly quickly; the constructions of groups of the same orders of even
> > > larger ranks seems to go much more slowly though.
> > >
> > > The GAP forum has been extremely helpful to me!
> > >
> > > I have some computations I'd like to make in a quotient ring
> > > (i.e. R/I) for R the integral group ring of a finite group. Sometimes
> > > R/I is finite, sometimes not. I can of course determine the abelian
> > > group structure of R/I, but I'd like to find ring generators of the
> > > summands & determine their multiplication, particularly in the finite
> > > case.
> > >
> > > However, I did not see any methods in GAP for working with R/I. Did I
> > > miss something? Is there a ring package available for GAP?
> > >
> > > With a google search I found a Diplomarbeit (pdf) at
> Linz: "Everything
> > > you always wanted to know about rings in GAP. (but were afraid to
> > > ask)", J"urgen Ecker (October 7, 1999). It has the source code (in
> the
> > > pdf file) of the new functions added. At first I thought that the
> > > code might be included in SONATA, but that did not seem to be the
> > > case.
> > >
> > > Ok, so that's everything I was able to determine & the question is:
> > > Is there a ring package already available (or at least some
> > > collection of programs) or do I need to develop my own?
> > >
> > > Thanks for any suggestions.
> > >
> > > Keith
> > >
> > > _______________________________________________
> > > Forum mailing list
> > > Forum at mail.gap-system.org
> > > http://mail.gap-system.org/mailman/listinfo/forum
> > >
> >
> >
> >
> > --
> > met vriendelijke groet,
> > nilo
> >
> > ------=_Part_59803_32102713.1185178714054
> > Content-Type: text/html; charset=ISO-8859-1
> > Content-Transfer-Encoding: 7bit
> > Content-Disposition: inline
> >
> > Hello Keith,<br><br>For rings there is a wide selection of available
> packages.<br><br>I can confirm that the following<br>- Macaulay2<br>-
> Cocoa<br>- Singular<br>all do the basic stuff really
> well.<br><br>Seek and you'll find a wealth of information.
> >
> <br><br>Macaulay2 and Singular are integrated with GAP in the SAGE package, which I particularly recommend.<br><br>Kind regards,<br>nilo de roock <br><br><br><div><span
> class="gmail_quote">2007/7/23, R. Keith Dennis <<a href="mailto:
> dennis at rkd.math.cornell.edu">
> > dennis at rkd.math.cornell.edu</a>>:</span><blockquote
> class="gmail_quote" style="margin-top: 0; margin-right: 0; margin-bottom: 0;
> margin-left: 0; margin-left: 0.80ex; border-left-color: #cccccc;
> border-left-width: 1px; border-left-style: solid; padding-left: 1ex">
> > Dear Colleagues:<br><br>I have another simple question to
> ask.<br><br>However, I'd like to first thank everyone who has helped me
> thus far.<br>In particular, I'm most grateful to Bettina Eick and Jack
> Schmidt for<br>
> > providing much more than one might hope
> for. Thanks!<br><br>Bettina Eick showed me how to use the ANUPQ
> package to generate larger<br>p-groups. In particular it was
> possible for me to construct the<br>groups of order 3^7 of rank 2 & the
> groups of order 1024 of rank 2,
> > <br>which were some of the things I needed. These
> computations went<br>fairly quickly; the constructions of groups of the same
> orders of even<br>larger ranks seems to go much more slowly
> though.<br><br>The GAP forum has been extremely helpful to me!
> > <br><br>I have some computations I'd like to make in a quotient
> ring<br>(i.e. R/I) for R the integral group ring of a finite
> group. Sometimes<br>R/I is finite, sometimes not. I
> can of course determine the abelian<br>
> > group structure of R/I, but I'd like to find ring generators of
> the<br>summands & determine their multiplication, particularly in the
> finite<br>case.<br><br>However, I did not see any methods in GAP for working
> with R/I. Did I
> > <br>miss something? Is there a ring package available for
> GAP?<br><br>With a google search I found a Diplomarbeit (pdf) at
> Linz: "Everything<br>you always wanted to know about rings
> in GAP. (but were afraid to<br>ask)", J"urgen Ecker (October 7,
> 1999). It has the source code (in the
> > <br>pdf file) of the new functions added. At first I thought
> that the<br>code might be included in SONATA, but that did not seem to be
> the<br>case.<br><br>Ok, so that's everything I was able to determine
> & the question is:
> > <br>Is there a ring package already available (or at least
> some<br>collection of programs) or do I need to develop my
> own?<br><br>Thanks for any
> suggestions.<br><br>Keith<br><br>_______________________________________________
> > <br>Forum mailing list<br><a href="mailto:Forum at mail.gap-system.org">
> Forum at mail.gap-system.org</a><br><a href="
> http://mail.gap-system.org/mailman/listinfo/forum">
> http://mail.gap-system.org/mailman/listinfo/forum</a><br></blockquote>
> > </div><br><br clear="all"><br>-- <br>met vriendelijke groet,<br>nilo
> >
> > ------=_Part_59803_32102713.1185178714054--
> >
>
--
met vriendelijke groet,
nilo
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