On Mon, Jun 14, 2010 at 8:22 AM, Rob Beezer <goo...@beezer.cotse.net> wrote: > On Jun 14, 6:12 am, mmarco <mma...@unizar.es> wrote: >> So, what do you think? > > Sure, but can the default remain extend = True and maintain your > desire for correctness?
It has to. I think it would be a very bad idea to change the default behavior, since that would massively break backwards compatibility. > If a student has to read examples to get complex eigenvalues out of a > real (or rational) matrix, the utility of Sage for teacing > introductory linear algebra will be greatly diminished. We have > confronted this with echelon form for matrices defined with integer > entries. Prior to the introduction of the rref() command, only > echelon_form() was available and it refused to divide rows by integers > if the matrix was (inadvertently) defined over the integers. Now > rref() works over the fraction field, thus stepping up automatically > to a larger field. > > When I teach a first course in linear algebra I specify the field as > the complex numbers, to avoid this ambiguity once we get to > eigenvalues. But as a practical matter, I compute over the rationals > (or even just the integers!) for the first two-thirds of the course. > Any notion of a field extension is way out-of-bounds, while I give > them just a taste of the simplicity of being algebraically closed. I > fear that the subtleties of extend = False will be an impediment to > teaching and perhaps lost on more applied users who might > "accidentally" have a matrix with rational entries. > +1 > Rob > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- William Stein Professor of Mathematics University of Washington http://wstein.org -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
