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From: Murray Eisenberg on 1 Jan 2010 05:35 OK, so what, in an earlier post today, I suggested needed to be said in the docs is said there, although not in quite so direct a form ("What you see is not what is acted upon", as stated by Alexander Elkins). The issue, it seems, is how and when one finds such principles in the docs. Presumably the Virtual Book that's part of the Documentation Center would readily lead one to that tutorial. And it's there, to be sure -- but not so easy to find: Core Language > Patterns > Patterns for some Common Types of Expressions Part of the difficulty in finding such things in the Documentation Center may be the granularity of the documentation (as contrasted with the now-defunct, printed "The Mathematica Book" -- if I may be permitted to beat a dead horse). Norbert P. wrote: > > ... as you can read in tutorial/ > PatternsForSomeCommonTypesOfExpression: > "Especially for some common kinds of expressions, the standard > output format used by Mathematica is not particularly close to the > full internal form. But it is the internal form that you must use in > setting up patterns. " -- Murray Eisenberg murray(a)math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
From: Richard Fateman on 1 Jan 2010 05:39 Leonid Shifrin wrote: .... > > I think that there are not many more objects in Mathematica which are as > tricky as <I> or Infinity in terms of pattern-matching. I agree. That's why it can be fixed. Here's a beginning of a short list for the "we're not just talking syntactic replacement-- version of substitution": If the user says -i --> i, then do Complex[a_,-b_] -> Complex[a,b]. If the user says x^2 --> y, then do x^(-2)-> 1/y also. I assume this list can be enlarged somewhat, and could even be left open-ended by user option of some sort. [e.g. should x^2--> y also change x^3 to x*y? or to y^(3/2) or ....] ..... > It would perhaps be nice if such > cases were more systematically documented, but they have nothing to do with > bugs, You are right if you mean "bug in Mathematica implementation of intended design" (this is not such a bug). But there is another concept: "bug in Mathematica design, contrary to reasonable mathematical expectation" (this IS such a bug).
From: Noqsi on 2 Jan 2010 05:04 On Jan 1, 3:39 am, Richard Fateman <fate...(a)cs.berkeley.edu> wrote: > Leonid Shifrin wrote: > > ... > > > > > I think that there are not many more objects in Mathematica which are a= s > > tricky as <I> or Infinity in terms of pattern-matching. > > I agree. > That's why it can be fixed. > > Here's a beginning of a short list for the "we're not just talking > syntactic replacement-- version of substitution": > > If the user says -i --> i, then do Complex[a_,-b_] -> Complex[= a,b]. > If the user says x^2 --> y, then do x^(-2)-> 1/y also. > > I assume this list can be enlarged somewhat, and could even be left > open-ended by user option of some sort. [e.g. should x^2--> y also > change x^3 to x*y? or to y^(3/2) or ....] No! The language should not attempt to outsmart the user. What you're proposing would be the nastiest sort of bug, changing simple, predictable behavior into something that would play out in incomprehensible ways. Syntactic replacement is very, very useful and should not be polluted by attempts to read the user's mind. The principle here has always been "You want to see what a rule will really do? Look at FullForm." Perhaps the documentation should highlight this better, but this behavior is NOT A BUG.
From: Leonid Shifrin on 2 Jan 2010 05:06 Regarding this issue, I think I entirely agree with what David Bailey and other people said: I don't consider replacement rules as a mathematical tool for end users, but rather as an inner layer of Mathematica, which is also exposed for flexibility / convenience and intended primarily to be used by the more advanced users. In this way, they can implement some missing functionality themselves at their own risk without the need to wait for a new Mathematica release. It is stated in the documentation that rule substitution is purely syntax-based, and therefore not guaranteed to always make sense. I don't see how this by itself makes the design inconsistent: either you are the end-user without advanced Mathematica skills and then you have to stick to the built-in commands like Conjugate designed specifically to deal with the problem (complex conjugation here), or you use the lower-level tools like replacement rules but then you are on your own - the system will blindly do the replacements according to the syntax of your rules, and it is then your responsibility to use them correctly. What I would agree with is that the documentation could have made this borderline more clear-cut. But I don't think that this is a problem on the level of design. Regards, Leonid On Fri, Jan 1, 2010 at 2:39 AM, Richard Fateman <fateman(a)cs.berkeley.edu>wrote: > Leonid Shifrin wrote: > ... > > > > > I think that there are not many more objects in Mathematica which are as > > tricky as <I> or Infinity in terms of pattern-matching. > > > I agree. > That's why it can be fixed. > > Here's a beginning of a short list for the "we're not just talking > syntactic replacement-- version of substitution": > > If the user says -i --> i, then do Complex[a_,-b_] -> Complex[a,b]. > If the user says x^2 --> y, then do x^(-2)-> 1/y also. > > I assume this list can be enlarged somewhat, and could even be left > open-ended by user option of some sort. [e.g. should x^2--> y also > change x^3 to x*y? or to y^(3/2) or ....] > > .... > > > It would perhaps be nice if such > > cases were more systematically documented, but they have nothing to do > with > > bugs, > > You are right if you mean "bug in Mathematica implementation of > intended design" (this is not such a bug). > > But there is another concept: > "bug in Mathematica design, contrary to reasonable mathematical > expectation" > (this IS such a bug). > >
From: Andrzej Kozlowski on 2 Jan 2010 05:08
On 31 Dec 2009, at 17:18, Leonid Shifrin wrote: > I think that there are not many more objects in Mathematica which are as > tricky as <I> or Infinity in terms of pattern-matching. Another obvious case that can be included is Rational, e.g. Head[2/3] Rational Head[Unevaluated[2/3]] Times Head[a/b] Times AtomQ[2/3] True AtomQ[a/b] False Rational works essentially the same way as Complex. It's perfectly consistent, fully justified, and certainly will never be changed. Andrzej Kozlowski |