On Jun 22, 4:44 pm, John H Palmieri <[email protected]> wrote: > 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.
Don't they at least know about complex numbers?! Or are we talking about some dark ages situation when complex numbers were considered a heresy? :–) I don't thing Sage should suffer from bad decisions made by designers of stupidifying curricula... A way out is to make a dumbstudentLA.spkg (hopefully, optional :)) where one can make matrices do whatever is needed ––– even dance like paperclips in MS Word... > 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. Over R? Over C? >From my limited experience in tutoring linear algebra to undergrads, I only saw confusion when eigenvalues were required to be in R. I would never go for this in any class I teach myself; I would always say that we allow any root of det(A-xI) to occur, not only real one. Dima > > -- > 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
