On Wednesday, June 22, 2011 7:37:11 AM UTC-7, Dima Pasechnik wrote: > > > > On Jun 21, 9:59 pm, Rob Beezer <[email protected]> wrote: > > I think I have one more big push left in me as I try to tidy up linear > > algebra in Sage to make it even more useful for students studying the > > subject for the first time. Eigen-stuff is on my radar. Some > > behaviors that I find problematic, most vexing first. > > > > 1. Eigenspaces > > > > sage: A = matrix(QQ, [[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]]) > > sage: A.eigenspaces_right() > > [ > > (a0, Vector space of degree 4 and dimension 2 over Number Field in a0 > > with defining polynomial x^2 + 1 > > User basis matrix: > > [ 1 -a0 0 0] > > [ 0 0 1 -a0]) > > ] > > > > It is real impressive that we can do computations in QQbar and get > > Galois conjugates and all, but there is no possible way to explain > > this to a student who is fresh out of calculus. > what about > sage: A = matrix(QQbar, [[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]]) > sage: A.eigenspaces_right() >
As Rob basically said in the last sentence that you quoted, you don't want to have to use QQbar when you're teaching a sophomore-level linear algebra class, populated by science and engineering majors: the students there don't have any idea what QQbar is; they don't even know what a field is. Students will want to be able to do A = matrix([[0,-1,0,0],[1,0,0,0],[0,0,0,-1],[0,0,1,0]]) # no field explicitly specified and then compute eigenvalues, eigenspaces, etc. -- John -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
