AW: [GAP Forum] GAP and rings?

[Ecker Juergen]

Dear Keith.
 
Your observation is correct. The functions for rings that I have implemented in my diploma thesis are not available in the sonata near-ring package. The main reason is that the representation of near rings is not the same as the one used for rings in GAP. Also, the questions asked in nearring theory differ from those in ring theory (the situation is much like with rings and fields). I am sorry to say that my old functions for rings have also never been updated for GAP4, since my focus has changed to near rings.
 
Best regards,
Juergen

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Von: forum-bounces at gap-system.org im Auftrag von R. Keith Dennis
Gesendet: Mo 23.07.2007 00:52
An: forum at gap-system.org
Betreff: [GAP Forum] GAP and rings?



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

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