I have the following question(s): I have an “Algebra-With-One” $R$ as a subalgebra of a full matrix algebra in GAP. Furthermore, I have 5 primitive orthogonal idempotents $e_1,…,e_5$, which sum up to $1_R$ (the identity matrix). I would like to compute the projective indecomposable modules $P_1=e_1R,…,P_5=e_5R$ with GAP (or another computer programm (e.g. SAGE) which […]
I asked a question the other day: Multidimensional Hensel lifting which @Hurkyl kindly and very elegantly answered. A follow-on from this is that I have tried to implement exactly the “algorithm” implicit in his answer in order to solve my problem on SAGE, but without much success. Has anyone out there had any success with […]
I am using Octave (3.6) on Ubuntu 10.0.4 LTS. I want to do some research involving symbolic math. I was thinking of downloading sage (I just found about it today) – but thought I’d better ask in here – at least, I’m already familiar with Octave.
I am attempting to teach number theory from John Stillwell’s Elements of Number Theory in the upcoming semester. There are two sections (5.7 and 5.8) which describe the diagrammatic method for the derivation of primitive vectors which ultimately lead to a healthy understanding of values which the quadratic form $x^2-ny^2$ may attain for fixed $n$ […]