I'm not sure Keith is a sage-devel subscriber but also I only cc'd the list one of the last posts in the thread. The original post describes what he wants. Here is a piece of it:
... 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 +++++++++++++++++++++++++++++++++++++++++ On 7/23/07, William Stein <[EMAIL PROTECTED]> wrote: > > Keith, > > Could you be more precise about what computations you want > to do in a quotient of a noncommutative group ring? Do you just > want to do basic arithmetic? Do you need to check equality? > Do you need abstract structure statements? > > -- William > > > On 7/23/07, Martin Albrecht <[EMAIL PROTECTED]> wrote: > > To whom it may concern, > > > > there is plural: http://www.singular.uni-kl.de/Manual/latest/sing_349.htm > > > > which is shipped with SAGE (though, the interface hasn't been worked on) > > > > sage: singular.lib('ncalg.lib') > > sage: a = singular.makeUsl2() > > sage: W = singular.ring(0,'(x,d)','dp') > > sage: singular.Weyl() > > `sage2` > > sage: S = a + W > > sage: singular.set_ring(S) > > sage: S > > > > // characteristic : 0 > > // number of vars : 5 > > // block 1 : ordering dp > > // : names e f h > > // block 2 : ordering dp > > // : names x d > > // block 3 : ordering C > > // noncommutative relations: > > // fe=e*f-h > > // he=e*h+2*e > > // hf=f*h-2*f > > // dx=x*d+1 > > > > or in terms of SINGULAR/PLURAL directly: > > > > LIB "ncalg.lib"; > > def a = makeUsl2(); // U(sl_2) in e,f,h presentation > > ring W = 0,(x,d),dp; > > Weyl(); // 1st Weyl algebra in x,d > > def S = a+W; > > setring S; > > S; > > ==> // characteristic : 0 > > ==> // number of vars : 5 > > ==> // block 1 : ordering dp > > ==> // : names e f h > > ==> // block 2 : ordering dp > > ==> // : names x d > > ==> // block 3 : ordering C > > ==> // noncommutative relations: > > ==> // fe=ef-h > > ==> // he=eh+2e > > ==> // hf=fh-2f > > ==> // dx=xd+1 > > > > Martin > > > > PS: I don't know much about non-commutative algebra, so I wouldn't know if > > your favorite ring is supported by PLURAL. > > > > > > -- > > name: Martin Albrecht > > _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 > > _www: http://www.informatik.uni-bremen.de/~malb > > _jab: [EMAIL PROTECTED] > > > > > > > > > > > > -- > William Stein > Associate Professor of Mathematics > University of Washington > http://www.williamstein.org > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
