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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