I am happy with that. After all: sage: a=3 sage: a.sqrt() sqrt(3)
works like this since the extend parameter defaults to True. Compare: sage: a.sqrt(extend=False) ... ValueError: square root of 3 not an integer John On 14 June 2010 16:24, William Stein <wst...@gmail.com> wrote: > 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 > -- 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
