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. -- William --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
