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? 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. 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
