[sage-devel] Re: Fwd: axiom
On Thu, Aug 21, 2008 at 6:50 AM, mhampton [EMAIL PROTECTED] wrote: I really need to go to sleep so I won't do a top-ten, but here's a top 2: Thanks for reminding me this. It seems that people really like Mathematica, so when I graudate, I'll try to learn it and do something in it, so that I get a better feeling for how easy it is. Especially its assumptions and substitution. 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Wed, Aug 20, 2008 at 9:37 PM, mhampton [EMAIL PROTECTED] wrote: I used to really enjoy writing programs in mathematica, but maybe I'm a strange person. I only stopped in order to force myself to get fluent with Sage. I think it just depends on your background, what you are used to, and what you want to do. For symbolic calculations and programming I still miss mathematica quite often. -M. Hampton On Aug 20, 12:59 am, Fernando Perez [EMAIL PROTECTED] wrote: On Tue, Aug 19, 2008 at 1:05 PM, Ondrej Certik [EMAIL PROTECTED] wrote: but programming in Mathematica is not fun. And that would be the understatement of the week. I don't think you're strange, I was just joking a bit. Caveat: it's been years that I've *programmed* in Mathematica in a serious way (recently I've mostly used it as a fancy calculator for quickly computing integrals I'm too lazy to do by hand). But having said that, what I really found Mathematica programming to be was a very mixed experience: certain things that should be easy were unjustifiably tricky to achieve, even after consulting with local hard-core gurus. But the elegance with which you can manipulate expressions *structurally* is truly something to behold. This comes courtesy of the lisp-like facilities you have for accessing any entity, working on it as an expression tree you can manipulate with very powerful transformation rules. And there are classes of problems where that approach allows you to get pretty much exactly the solution you're after with a minimum amount of fuss, where as in more conventional languages it would be a lot of work. So there, I hope this is a slightly more reasoned reply to a topic worthy of an honest answer ;) Cheers, f --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Thu, Aug 21, 2008 at 10:47 AM, Fernando Perez [EMAIL PROTECTED] wrote: On Wed, Aug 20, 2008 at 9:37 PM, mhampton [EMAIL PROTECTED] wrote: I used to really enjoy writing programs in mathematica, but maybe I'm a strange person. I only stopped in order to force myself to get fluent with Sage. I think it just depends on your background, what you are used to, and what you want to do. For symbolic calculations and programming I still miss mathematica quite often. -M. Hampton On Aug 20, 12:59 am, Fernando Perez [EMAIL PROTECTED] wrote: On Tue, Aug 19, 2008 at 1:05 PM, Ondrej Certik [EMAIL PROTECTED] wrote: but programming in Mathematica is not fun. And that would be the understatement of the week. I don't think you're strange, I was just joking a bit. Caveat: it's been years that I've *programmed* in Mathematica in a serious way (recently I've mostly used it as a fancy calculator for quickly computing integrals I'm too lazy to do by hand). But having said that, what I really found Mathematica programming to be was a very mixed experience: certain things that should be easy were unjustifiably tricky to achieve, even after consulting with local hard-core gurus. But the elegance with which you can manipulate expressions *structurally* is truly something to behold. This comes courtesy of the lisp-like facilities you have for accessing any entity, working on it as an expression tree you can manipulate with very powerful transformation rules. And there are classes of problems where that approach allows you to get pretty much exactly the solution you're after with a minimum amount of fuss, where as in more conventional languages it would be a lot of work. So there, I hope this is a slightly more reasoned reply to a topic worthy of an honest answer ;) I need to learn Mathematica to understand what it means. In SymPy, you can do some fancy stuff as well, e.g.: In [1]: e = x*y+sin(x*y)**3 In [2]: print e x*y + sin(x*y)**3 In [3]: from sympy.utilities.iterables import postorder_traversal, preorder_traversal In [4]: postorder_traversal(e) Out[4]: generator object at 0xa53376c In [9]: print list(postorder_traversal(e)) [x, y, x*y, sin(x*y), 3, sin(x*y)**3, x, y, x*y, x*y + sin(x*y)**3] In [10]: print list(preorder_traversal(e)) [x*y + sin(x*y)**3, sin(x*y)**3, sin(x*y), x*y, x, y, 3, x*y, x, y] And here is how those two functions are implemented: def preorder_traversal(node): yield node for arg in node.args: for subtree in preorder_traversal(arg): yield subtree def postorder_traversal(node): for arg in node.args: for subtree in postorder_traversal(arg): yield subtree yield node So you can access all expressions uniformly and iterate over the expression tree in 4 lines by hand, or just calling one of the predefined functions above. I don't think this is complicated, but maybe things can be made even easier. 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Thu, Aug 21, 2008 at 12:50 AM, mhampton wrote: I really need to go to sleep so I won't do a top-ten, but here's a top 2: 1) Powerful substitutions and rules. Sage does not have anything comparable. The .subs() function is buggy even in its limited domain. There have been previous posts on sage-devel that give good examples of this. Because of the subject of this thread I feel justified in giving the following examples from Axiom: http://axiom-wiki.newsynthesis.org/ManipulatingExpressions Perhaps Sage can implement some form of pattern matching and subsitution such is done by Axiom's rewrite rules? I think that in many respects these provide a functionality similar to Mathematica. There is also a similar re-writing system in Maple (applyrule). ... On Aug 20, 11:38 pm, William Stein wrote: On Wed, Aug 20, 2008 at 9:37 PM, mhampton [EMAIL PROTECTED] wrote: I used to really enjoy writing programs in mathematica, but maybe I'm a strange person. I only stopped in order to force myself to get fluent with Sage. I think it just depends on your background, what you are used to, and what you want to do. For symbolic calculations and programming I still miss mathematica quite often. Could you remind me (yet again) of the top ten things you miss about mathematica for symbolic calculations? --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Aug 21, 2008, at 8:08 AM, Bill Page wrote: On Thu, Aug 21, 2008 at 12:50 AM, mhampton wrote: I really need to go to sleep so I won't do a top-ten, but here's a top 2: 1) Powerful substitutions and rules. Sage does not have anything comparable. The .subs() function is buggy even in its limited domain. There have been previous posts on sage-devel that give good examples of this. Because of the subject of this thread I feel justified in giving the following examples from Axiom: http://axiom-wiki.newsynthesis.org/ManipulatingExpressions Perhaps Sage can implement some form of pattern matching and subsitution such is done by Axiom's rewrite rules? I think that in many respects these provide a functionality similar to Mathematica. There is also a similar re-writing system in Maple (applyrule). I believe patter matching is something that GiNaC will get for us. - Robert --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Aug 21, 9:08 am, Bill Page [EMAIL PROTECTED] wrote: Perhaps Sage can implement some form of pattern matching and subsitution such is done by Axiom's rewrite rules? I think that in many respects these provide a functionality similar to Mathematica. There is also a similar re-writing system in Maple (applyrule). Dunno if it matters but there is also pattern matching, substitution, and expression-hacking machinery in Maxima. It's probably well within the realm of possibility to strengthen Maxima's pattern matching by importing an existing Lisp library for that purpose. I haven't looked into the details. FWIW Robert Dodier --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Tue, Aug 19, 2008 at 1:05 PM, Ondrej Certik [EMAIL PROTECTED] wrote: but programming in Mathematica is not fun. And that would be the understatement of the week. Cheers, f --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
I used to really enjoy writing programs in mathematica, but maybe I'm a strange person. I only stopped in order to force myself to get fluent with Sage. I think it just depends on your background, what you are used to, and what you want to do. For symbolic calculations and programming I still miss mathematica quite often. -M. Hampton On Aug 20, 12:59 am, Fernando Perez [EMAIL PROTECTED] wrote: On Tue, Aug 19, 2008 at 1:05 PM, Ondrej Certik [EMAIL PROTECTED] wrote: but programming in Mathematica is not fun. And that would be the understatement of the week. Cheers, f --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
On Wed, Aug 20, 2008 at 9:37 PM, mhampton [EMAIL PROTECTED] wrote: I used to really enjoy writing programs in mathematica, but maybe I'm a strange person. I only stopped in order to force myself to get fluent with Sage. I think it just depends on your background, what you are used to, and what you want to do. For symbolic calculations and programming I still miss mathematica quite often. Could you remind me (yet again) of the top ten things you miss about mathematica for symbolic calculations? -- William --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
I really need to go to sleep so I won't do a top-ten, but here's a top 2: 1) Powerful substitutions and rules. Sage does not have anything comparable. The .subs() function is buggy even in its limited domain. There have been previous posts on sage-devel that give good examples of this. 2) Implicit variable declaration - ? I'm not sure what to call this. Basically, mathematica assumes everything is in the equivalent of its symbolic ring until told otherwise. Because of problems with Sage's symbolics, I often have to explicitly declare a ring (e.g. R.x,y,z = PolynomialRing(QQ,3)), and then later when I want to do something else declare another ring. I often get headaches when adding or removing variables, changing term orders, or trying to do simplifications in which intermediate quantities don't fit the current setup (e.g. a fraction field). I am hoping that some of the coercion changes will help with some of this. Part of my problem with #2 probably doesn't make as much sense to you because Mathematica has a bias towards working in QQ, and that is what I usually care about. I am sure that if you like working over more exotic fields Sage starts to have advantages. Hope that helps, I am too tired to explain in more detail right now. Cheers, M. Hampton On Aug 20, 11:38 pm, William Stein [EMAIL PROTECTED] wrote: On Wed, Aug 20, 2008 at 9:37 PM, mhampton [EMAIL PROTECTED] wrote: I used to really enjoy writing programs in mathematica, but maybe I'm a strange person. I only stopped in order to force myself to get fluent with Sage. I think it just depends on your background, what you are used to, and what you want to do. For symbolic calculations and programming I still miss mathematica quite often. Could you remind me (yet again) of the top ten things you miss about mathematica for symbolic calculations? -- William --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
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 The popularity of these examples with end users suggests to me a lack of viability. Though of course it depends on one's goals. 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. Just to make sure credit goes where it should, the idea of parent is not a Sage concept but a Magma concept. I think the credit for it should definitely go to John Cannon et al., and certainly not to me or Sage. I think in Magma it is also not a part of the language but something that is implemented on top of the Magma language. Unlike you, I personally like that parent is not a fundamental feature of Python, but a design pattern that can be implemented on top of Python. That means one can directly use the same idea in C/C++/etc. code. -- William --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
[sage-devel] Re: Fwd: axiom
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 -~--~~~~--~~--~--~---
