Re: More /.{I->-1} craziness

*To*: mathgroup at smc.vnet.net*Subject*: [mg106156] Re: More /.{I->-1} craziness*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Sun, 3 Jan 2010 03:41:22 -0500 (EST)*References*: <200912300915.EAA17299@smc.vnet.net> <hhhmn8$o9t$1@smc.vnet.net>*Reply-to*: drmajorbob at yahoo.com

I think the way we enter and understand InputForm is syntax; FullForm is the way they're stored internally. So Mathematica's pattern matching isn't what I'd call syntactical... unless you mean "syntactical on a hidden (though discoverable) level". Bobby On Sat, 02 Jan 2010 04:06:32 -0600, Leonid Shifrin <lshifr at gmail.com> wrote: > 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 at 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). >> >> > -- DrMajorBob at yahoo.com