On Sun, May 18, 2008 at 11:50 AM, Alec Mihailovs <[EMAIL PROTECTED]> wrote: > > I am trying to promote SAGE at Mapleprimes (in various threads).
Thank you! > In addition to > > http://www.mapleprimes.com/forum/a110375 > > where Mike Hansen posted a comment at the end of the thread, there is a > question from Alejandro Jakubi in > > http://www.mapleprimes.com/forum/clairautsyoungstheorem > > He asked whether SAGE is using Maxima or Axiom for calculus. Sage does not use Axiom for anything. Sage uses Maxima as a backend for a lot of Calculus right now. In the long run it will likely use Maxima less and new faster more modern code that it is in the pipeline (this is work being funded by Google, but not as part of Google Summer of Code). It will be interesting to see how all of these physics/mathematicians/etc. assumptions will play out in Sage as compared to how they played out in Maple. It is likely in Sage that we'll have for calculus a global proof=True and proof=False mode, like we have with number fields, linear algebra, etc. With proof=False, assumptions about partial commuting, functions being continuous, etc., like maple makes, would be in force. The default unless explicitly changed would be proof=True. One could see everywhere in the source where the proof flag is used, hence see precisely what assumptions are being made in a computation... > I am not a SAGE developer (just a happy user), and I could say something > wrong about that. Could somebody post there explaining that, please? Please feel free to post my remark there. I don't have account. > Also, it would be nice to see another response in A110375 thread to keep in > on the top of Recent posts list (that's what many people use - in the menu > from the left hand side.) I'm not sure what to say except I agree with all the posts in that thread. Somebody could post a precise table of timings comparing Sage, Mathematica, Maple, and Pari, say, all on a common architecture. That would fit in the thread. > > Thank you, > Alec Mihailovs I enjoyed reading this story that you posted in one of the threads: "That reminded me something that V.I. Arnold said in one of his books. He noticed in one of physical books that it was said about the derivative that it is a mathematical approximation to the slope of the tangent line. When he talked with the author of that book and told him that it _is_ the slope - not an approimation to it, he said - only from mathematician's point of view. In real life (f(x+t)-f(x))/t has sense only for t not less than, if I recall correctly, 10^(-16), and for that value it gives the real slope, and smaller values don't make physical sense because Newtonian physics doesn't work on such small distances and quantum mechanics should be used there instead (with completely different formulas). So the limit that mathematician's use is only approximation to the real slope. Also, he said, you mathematicians write a lot of other wrong things - for example, that the graph of y=exp(-x^2) doesn't intersect the x-axis while everybody can see that they intersect and not that far from 0, and for x=10 nobody can insert even an atom between them." --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
