On Fri, Jun 24, 2011 at 7:48 PM, Rob Beezer <[email protected]> wrote: > Hi Gonzalo, > > Thanks for your comments. > > On Jun 24, 8:06 am, Gonzalo Tornaria <[email protected]> wrote: >> What's wrong with: > > Nothing - except there are no vector spaces in sight. I'd like to > retain the exposure to vector spaces (eigenspaces) without going as > far as Galois theory. They are a nice lead-in to invariant subspaces, > which would be a central topic for a second course. > >> And what if the output of "B.eigenspaces_right()" is a bit confusing? >> I'd argue that's actually a feature, because it will make the student >> *think* about it, get a glimpse of some interesting mathematics, and >> maybe open a door to a new world. > > I agree entirely with the sentiment. The students I teach have had a > minimum of two semesters of calculus, and afterwards are expected to > be ready for real analysis and abstract algebra. Many do not major in > mathematics, but are from physics, computer science and economics. My > course is different from many, in that we do not have an engineering > college, so we don't serve that audience. > > I'll play the experience card - I've taught this course about 30 > times. My experience tells me that if the only way to get an > eigenspace of matrix over QQ is to take a detour into roots of > irreducible polynomials, then I will just skip it entirely. It just > goes too far down a road that I don't find beneficial for the vast > majority of the students at that point - they are already struggling > with ideas like matrix representations of linear transformations. > With the Galois conjugate version optionally available, it will still > be there via a keyword to challenge students (or inform our own > research). > > I am just now about to implement optionally promoting a QQ matrix to a > QQbar matrix when the eigenvalues lie outside QQ, to obtain an > alternate format for output, as described above. I don't think there > will be any disagreement with making that available. The question > will be - what should the default be? So far, there is a +2\epsilon > in favor of the QQbar version replacing the Galois conjugate version. >
I'll add my vote for that. John > Rob > > -- > 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 > -- 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
