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.