On Wed, Jul 1, 2009 at 6:33 PM, William Stein<wst...@gmail.com> wrote: > > 2009/7/2 Stéfan van der Walt <ste...@sun.ac.za>: >> >> 2009/7/1 William Stein <wst...@gmail.com>: >>> Perhaps I'm missing the point, but I'm taking this as a message to >>> focus in Sage more on the algebraic/symbolic side of mathematics >>> (e.g., Magma, Maple, Mathematica) rather than the numerical side, at >>> least for the time being. I don't have a problem with that >>> personally, since that is what I do best, and where most of my >>> personal interests are. >> >> I'm joining this conversation late, so I am glad to see the >> conclusions reached so far (not to give up on numerics!). >> >> If I may highlight a distinction (maybe obvious to some) between SAGE >> and NumPy-based experiments: >> >> Sage provides a "language" for eloquently expressing >> algebraic/symbolical problems. On the other hand, NumPy is mainly a >> library (that provides a data structure with accompanying operations). >> >> This means that users of that library expect to run their code >> unmodified on any Python platform where it is available (Sage >> included). Whether this expectation is reasonable or not is up for >> debate, but I certainly found it surprising that I had to modify my >> code in order to compute things in Sage. > > Either that, or you click on the "python" switch at the top of the > notebook or type "sage -ipython", or from within Sage you type > "preparser(False)". > >> On a more practical level, it frightens me that Maxima spawns so >> easily without my even knowing, simply by refering to a certain >> variable or by using the wrong "exp". > > FYI, that is no longer the case. In Sage-4.0, we replaced Maxima by > the C++ library Ginac (http://www.ginac.de/) for all basic symbolic > manipulation. > >> That's the kind of thing that kills numerics performance! > > There is often a tension between numerics performance and correct > answers. The following is in MATLAB: > >>> format rat; >>> a = [-101, 208, 105; 76, -187, 76] >>> rref(a) > ans = > 1 0 -2567/223 > 0 1 -3839/755 > > The same echelon form in Sage: > > a = matrix(QQ, 2, [-101, 208, 105, 76, -187, 76]) > a.echelon_form() > [ 1 0 -35443/3079] > [ 0 1 -15656/3079] > > Trying the same computation on larger matrices, and one sees that > matlab is way faster than Sage. But of course the answers are > nonsense... to anybody not doing numerics. To a numerical person they > mean something, because matlab is really just doing everything with > floats, and "format rat" just makes them print as rational > approximations to those floats. > > So indeed, mixing numerics with mathematics is a very difficult > problem, and nobody really seems to have solved it to everybody's > satisfaction.
I think people need both approaches, but I why you cannot just pass an option to echelon_form() to use fast floating point numbers (besides nobody yet implementing it)? Then we can have both. Ondrej --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
