---------- Forwarded message ---------- From: Ondrej Certik <[EMAIL PROTECTED]> Date: Tue, Aug 19, 2008 at 4:23 AM Subject: Re: axiom To: Bill Page <[EMAIL PROTECTED]>
Yes, please post it to sage-devel and I'll reply there. I wasn't sure what your reply would be, so I started offlist. :) Ondrej On Tue, Aug 19, 2008 at 1:54 AM, Bill Page <[EMAIL PROTECTED]> wrote: > Ondrej, > > I would be glad (with your permission) to post this question and my > reply on-list somewhere - sage-devel if you prefer. > > On Mon, Aug 18, 2008 at 6:50 PM, Ondrej Certik wrote: >> Hi Bill, >> >> since you know both Python and Aldor or Axiom and now you know >> Sage quite a bit, do you think Aldor or the Axiom style of things >> (domains) is viable? I know it's not 100% equivalent to Python and >> it can be fast with Aldor. >> > > Yes, certainly I think Axiom domains are viable. Another way of asking > this question is: if static strongly typed language with first-order > polymorphic dependent types is viable? I think this has been answered > in the positive by other experiments besides Axiom such as the ML > series of languages and Haskell. Axiom (and Aldor) however does have a > slightly different angle on the object-oriented part of the language > by introducing the concept of 'category'. Categories are named subsets > of domains. Categories allow a kind of generic programming that seems > quite suitable to mathematical algorithms but I think this part of the > design is less proven. So a better form of your question might be: Is > the Axiom concept of 'category' viable? The existence of the Axiom > library (and some of the libraries available in Aldor) provide some > positive evidence, but I do not consider it proven. > > The Sage concept of 'parent' is an attempt to capture similar generic > relationships that are represented by categories in Axiom, but I do > not like the fact that this concept needs to be added on to Sage > rather than being supported by some more fundamental feature of > Python, e.g. Python meta-types. > >> What are your personal goals with Axiom (and forks)? >> > > My personal goals do shift a little over time but currently I am > mostly focused on the goal of using many algebraic notions from > mathematical category theory (not the same as the notion of category > in Axiom), in computer algebra. Ultimately, like you I want to be able > to use computer algebra in theoretical physics but perhaps my goals > are a little more abstract. > > http://axiom-wiki.newsynthesis.org/CategoryTheoryAndAxiom > >> I don't know how to judge it. I was looking at fricas mailinglist, >> currently it has 59 members. Sympy list has 172 members. But >> these numbers can easily change, so it imho doesn't say much. >> > > What do you mean by "judge"? Are you trying to consider which of Sympy > or FriCAS is more "viable"? I think you first have to define more > exactly what you mean, e.g. viable for what purposes etc. You have > previously argued that the simply popularity of a language like Python > trumps any technical advantage that FriCAS may or may not have. I do > accept that as largely true. On the other hand Python would *not* be > my language of choice for doing more abstract things in category > theory. > >> Sympy compared to fricas is really stupid, it cannot do many things. > > Probably it is more accurate to compare Sympy to some of the libraries > that are available in Aldor, e.g. 'libAlgebra' and 'BasicMath'. These > libraries also "cannot do many things" but they attempt to do at least > a small number of things reasonably well. FriCAS likewise has the > Axiom library but it is not so easily separable from the rest of the > Axiom environment and interpreter (some people might call it: "the > Axiom ecosystem"). So maybe it is better to compare FriCAS to Sage > and/or Maxima etc. As I understand it Sympy does not attempt to become > such an "ecosystem" but rather just a rather more lightweight library > for Python programmers. Right? > >> So this means that there is a big barrier for people who would like >> to use fricas, even its advanced features doesn't seem to track >> attention. >> > > If you mean that the type system of FriCAS is a big barrier, then I > agree. On the other hand, depending on what you want to do with FriCAS > this might be an essential advantage. > >> So I am just interested in your opinions on this. >> > > Thank you. I am also interested to know other people's opinions on this issue. > > Regards, > Bill Page. > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
