[GAP Forum] GAP and rings?
R. Keith Dennis
dennis at rkd.math.cornell.edu
Mon Jul 23 13:36:46 BST 2007
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
>
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> 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
>
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>
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