Hi Bill, On Tue, Aug 19, 2008 at 8:14 PM, Bill Page <[EMAIL PROTECTED]> wrote: >> 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.
Thanks for answering. As William said, there are not many users of such languges like Haskell. So while those languages have their communities, for me personally this is not very viable. But of course it depends what you want. >> >> 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 see thanks. >> >>> 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? Yes, my own aim with Sympy is to just be a library to Python, that is small and hackable, but feature full and fast. Something like numpy but for symbolic stuff. That people can take and use in their programs in engineering, physics, or applied math. It should have all features of calculus in Mathematica. For example I would like to do quantum field theory in sympy. There are many nice and interesting calculations, that just cry out for being automated. I'd like to play with it in python. There are some packages for it in Mathematica, but programming in Mathematica is not fun. Ondrej --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com 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 -~----------~----~----~----~------~----~------~--~---
