I think so, but my defn of number theory may differ from yours. I asked the Axiom developers for a "killer app" - a really unique and cool application to some mathematical problem. My vote would go to Martin Rubey's GUESS (of course, if I knew Axiom better I may vote for something else). GUESS will (for example) take 4 or 5 terms of the Fibonacci sequence and return the 3-term recursion equation. However, it also works with sequences of polynomials, for example. As Martin says, it is complementary to Sloane online integer sequence database. There are analogous programs (gfun in Maple) but they are slower and less general. See http://front.math.ucdavis.edu/math.CO/0702086 (or the latest wiki entry for my Axiom column) for details. AFAIK, the full functionality of GUESS is not available anywhere else but in Axiom.
Generally speaking, Maple, Mma, Maxima allow you to ignore types and so you can do symbolic computations and programming with symbolic expressions easily. Axiom's language Aldor (which GUESS is written in) allows you do do similar things *but* Aldor gets translated to Lisp then to C then compiled, so it is really fast. I got a ton of useful information from Bill Page and Martin Rubey in our various emails. Unfortunately, I don't understand much of it due to my lack of understanding of Axiom. But I tried to summarize the gist of much of their suggestions in the wiki article. I am appreciating that Axiom serves a very important and very useful role for very advanced mathematical programmers due to properties of its language. ++++++++++++++++++++++++++++++++++++++++++++++++++ William Stein wrote: > On 3/24/07, David Joyner <[EMAIL PROTECTED]> wrote: >> Hello: >> I've posted a short survey of Axiom on the wiki: >> http://modular.math.washington.edu:9001/Axiom_as_an_OSCAS >> If there are any comments, I'd be happy to hear them. Please be as >> critical as you want! It is a draft of an article to appear >> in SIGSAM Bull. > > Thanks -- that's a very nice survey article. > > I have to admit, though, that I don't feel like the main > question I personally have, and have always had, about Axiom is > answered. And I'm not sure if your article should answer this, > since your article is aimed at SIGSAM readers. But since you've > just dived into Axiom, maybe you know. > > QUESTION: Can Axiom do anything at all relevant to number theory > or arithmetic geometry better than MAGMA or SAGE? > > By better, I mean *faster*, irregardless of interface and easy > of use issues. Does Axiom it implement any number > theory or arithmetic geometry algorithms that are not implemented > in MAGMA or SAGE? > > William > > > > --~--~---------~--~----~------------~-------~--~----~ 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-forum URLs: http://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
