Hi, I am trying to work with group rings of the form Q[G], where Q is the field of rational numbers and G is a finite (not necessarily abelian) group. To create the group G, I have tried to express the group G as a quotient of a free group, using some of the techniques mentioned here <http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html>. To be concrete, I have created a public worksheet here <https://cloud.sagemath.com/projects/f274d380-1d9f-43bd-9626-db40c33ce49d/files/group-rings.sagews>, where I have tried to work with Q[G], where G is a non-abelian group of order 125. The group G is expressed as a quotient of the free group on e, f, where the relations are {e^5, f^25, efe^{-1}f^{-6}}. (I believe this works since the output of the command G.order() is 125).
I am ultimately interested in doing computations over group rings: for eg, let's say I am trying to compute xy + zwu, where x,y,z,w,u are elements of the group ring. It would really be helpful to obtain these computations in their simplest forms. However, when I try to do some computations, even some simple ones involving the group elements, the expressions don't simplify and I cannot figure out a way to simplify them automatically. For eg the element e^5 does not get simplified to 1. I would like to work with complicated expressions and it will really help to obtain some workaround. Any help would be great. Thank you. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
