On Thu, Aug 21, 2008 at 11:28 PM, David Philp <[EMAIL PROTECTED]> wrote:
>
>
> On 22/08/2008, at 3:34 PM, William Stein wrote:
>
>>
>> On Thu, Aug 21, 2008 at 9:41 PM, Arnaud Bergeron
>> <[EMAIL PROTECTED]> wrote:
>>>
>>>>>> data /. x_?(# < 0 &) -> 0 (this is perhaps not the killer example)
>>>>>
>>>>> What does that do?
>>>>
>>>> /. is the pattern replacement operator, _ is a placeholder pattern
>>>> that matches anything, x_ gives this placeholder a name so you can
>>>> use
>>>> it later, ? filters the matches (in this case, everything matches)
>>>> with the pure function # < 0&, which takes one argument and returns
>>>> true if the argument is less than 0, and the -> 0 part says anything
>>>> that made it through the filter gets set to 0. So
>>>>
>>>> In[40]:= data = {-1, 2, 3};
>>>> In[41]:= data /. x_?(# < 0 &) -> 0
>> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>
>> Just out of curiosity, what words do you say in your head
>> when you read In[41]?
>
> Keep in mind that it is a Lisp-like expression. That means there has
> to be some intracranial translation into lisp-like nested
> expressions. If there is a flamewar to be had, it is probably about
> the relative merits of Lisp-like languages. I am not at all
There's not going to be any flamewars in this thread.
> interested in proving that Mathematica is better than language X, I am
> only pointing out features that I think are worth studying.
Many thanks for explaining this in detail below. It was a superb
explanation.
>
> Start small:
>
> data /. x->y
> means "data, replacing all occurrences of x with y".
>
> x_?( # < 0&) is a pattern somewhat like in ocaml. It reads like this
> "any item x, such that when the test 'argument is less than zero' is
> applied, returns True"
>
> So line 41 reads:
> data, replacing all (/.) items (x_) that are less than zero (?(#<0&) )
> with (->) zero.
>
> More strictly, though, the -> indicates a rule, whose full form is:
> Rule[ x_?(#<0&), 0]
>
> The "x" is strictly unnecessary, but it is simpler to understand.
>
> If you had more than one rule, you would read it differently:
> data /. { a -> 2, b -> 3}
> "data, transformed by replacing a with 2 and b with 3"
>
> Can one do the same with Arnaud's python version?
>
>> I would like to understand what
>> people are thinking when they find an expression like that
>> easy to read and appealing.
>
> It is neat because I can write it from left to right, and I think
> about the object to be manipulated before the operations.
>
>> When I look at Arnaud's python version:
>>
>>> sage: data = [-1, 2, 3]
>>> sage: [(0 if d < 0 else d) for d in data]
>>
>> I read "the list got from data where the negative
>> entries are replaced by 0", or maybe more literally
>> "the list made by taking each entry d of data and
>> putting 0 if it is negative else putting d."
>
> The unappealing thing is the emphasis on "the list". No such
> requirement in Mathematica: "data" could just as well be Cos[8 x].
>
> snip.
>
>> I could certainly see a place in sage for something
>> like this:
>>
>> sage: data = [-1, 2, 3]
>> sage: data = ma_eval('data /. x_?(# < 0 &) -> 0')
>> sage: data
>> [0, 2, 3]
>>
>> where ma_eval is a function that evaluates a mathematica-style
>> expression in the scope of the current Sage
>> session, and returns the result as a Python object.
>> It's something that could be totally ignored by most users,
>> but something people who understand the power of
>> Mathematica might find very useful. Anyway, that's why
>> this thread is I think potentially interesting.
>
> I would be scared of getting sued into oblivion. I would have a
> lawyer look at the Mathematica EULA before even thinking about it.
> "WRI is the holder of ... including without limitation... structure,
> sequence, organization, "look and feel", programming language and
> compilation of command names." I hope one can't own such things but I
> don't want a legal fight.
If I were afraid, then Sage would be nowhere today.
> Otherwise, I agree. A mathematica-like parser would be useful.
> Though I'd be surprised if the concepts map across well enough for it
> to be anything other than an ugly hack.
Why?
>
> D
>
>
> ==================================
> David J Philp
> Postdoctoral Fellow
> National Centre for Epidemiology and Population Health
> Building 62, cnr Mills Rd & Eggleston Rd
> The Australian National University
> Canberra ACT 0200 Australia
>
> T: +61 2 6125 8260
> F: +61 2 6125 0740
> M: 0423 535 397
> W: http://nceph.anu.edu.au/
>
> CRICOS Provider #00120C
>
>
>
>
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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