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Re: A Sum-like notation for iteration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg102349] Re: A Sum-like notation for iteration
  • From: pfalloon <pfalloon at gmail.com>
  • Date: Thu, 6 Aug 2009 06:31:53 -0400 (EDT)
  • References: <h5bk7g$hn3$1@smc.vnet.net>

On Aug 5, 7:43 pm, c... at gregosetroianos.mat.br wrote:
> Peter,
>
> >>I for one would be *horrified* to see such constructs included by
> >>default in the system.
>
> You misunderstood my post. I did not suggest this 2D notation as a defaul=
t.
> I said that MakeExpression should accept (parse) it. (The parsing of boxe=
s
> is done by MakeExpression.)
>
> I do not see any "horror" in this notation. To me (and to many) it appear=
s
> utterly natural. I have seen more horrible things than this. For example,
> Einstein summation convention, Frege's notations and ... the result (whic=
h
> is not "recognized universally")
>
> RowBox[{UnderoverscriptBox["\[Sum]", RowBox[{"x", "=", "1"}],
>    RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]], "f"}]
>
> returned by
>
> MakeBoxes[Sum[f, {x, {a, b}}], TraditionalForm]
>
> in Mathematica 6.
>
> It seems you would be dismayed with the very interesting work done by Bru=
no
> Buchberger on his "logicographic symbols" (implemented in Mathematica for
> his Theorema Project and -- "reinventing the wheel" -- without using the
> Notation package).
>
> Carlos Cesar de Araujo
> Gregos & Troianos Educacionalwww.gregosetroianos.mat.br
> Belo Horizonte, MG, Brasil
> (31) 3283-1122

Hi again,

A couple of comments:

1. The example you give doesn't make sense to me: I'm unable to
reproduce the output given the input (MakeBoxes[...]) and, more
importantly I think, I don't see what is meant by it. Did you simply
mean the sum of f[x] from x=a to x=b, for which I get the completely
universal summation representation (note that f should have x as
argument or else it doesn't really make sense):

In[344]:= Sum[f[x], {x, a, b}]
Out[344]= \!\(\*UnderoverscriptBox[\(\[Sum]\), \(x = a\), \(b\)]\(f[x]
\)\)

Or did you mean the sum over the specific values a and b, which
evaluates directly and so the question of formatting becomes moot:

In[345]:= Sum[f[x], {x, {a, b}}]
Out[345]= f[a]+f[b]


2. I accept that *horror* is an excessive reaction to your proposal,
perhaps *distaste* is more accurate. In my view, the issue of what
notations and formats to allow in the system by default (by "default",
I mean "available within the system" not necessarily returned as
default output) is a thorny one. So far, I think Wolfram have done a
pretty good job of "walking the tightrope" when deciding what
notations to include. As you may be aware, the issue is particularly
relevant to mathematical special functions, where often there are
conflicting notations in use in the mathematical community, and much
care has been taken to choose the most appropriate one. In the case of
Table, there is no standard mathematical notation to draw on, and it's
not clear that the need is compelling enough to justify introducing a
new one.

3. To return to your original post, I think the phrase "and, of
course, in full generality (and due embellishments for list iterators
and steps)" glosses over some significant complications. For instance,
how do we format something like Table[f[x], {x, 1, 100, 2}]? Or,
worse, Table[f[x], {x, {1,2,3,4,5}}]? Whatever solution is chosen, the
point is that it is no longer "intuitive", at least not in the sense
that one could readily guess what it should look like.

4. I am only vaguely familiar with the Theorema project, so I can't
really give my opinion on that. But let me emphasize that I'm not
seeking to disparage the general goal of developing new notations, I'm
simply saying that in many cases it wouldn't be appropriate to
incorporate them into the main system.

Cheers,
Peter.


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