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Re: Expressions with ellipsis (...)

• To: mathgroup at smc.vnet.net
• Subject: [mg93303] Re: Expressions with ellipsis (...)
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Mon, 3 Nov 2008 05:27:21 -0500 (EST)

On 11/2/08 at 1:58 AM, siegman at stanford.edu (AES) wrote:

>In article <geh9sa$fbs$1 at smc.vnet.net>, dch888
><dch888 at googlemail.com> wrote:

>>>Another answer is that Mathematica *should* understand the syntax
>>>with ellipsis-- and indeed it can with the facilities of David
>>>Park's Presentations application package.

>One has to be careful about the use and interpretation of ellipses.

>For example the Mathematica documentation for Compound Expression
>says that

>expr_1 ;  expr_2 ;  =C2=8A evaluates the expr_i in turn, giving the last
>one as the result.

>Would this statement, interpreted very literally using a precise
>definition of the ellipsis symbol, cover both

>expr_1 ;  expr_2  ;  expr_3  ;  expr_4  ;

>and

>expr_1 ;  expr_2  ;  expr_3  ;  expr_4

>or just one of these?  (Which one?)

If an ellipsis were a symbol Mathematica understood and could be
used to replace some of the parts in your examples, I would
expect your first example to be written

expr_1 ;  ...  expr_4  ;

and your second example to be written as

expr_1 ;  ...  expr_4

So there would be no ambiguity.

But I doubt even if Mathematica understood an ellipsis, these
would be allowed constructs. Consider a rather simple usage of
the ellipsis in mathematics, i.e.,

1+2+3+ ... +10+11+12

or

1,2,3, ... 12

The first would be interpreted as the sum of the first 12
natural numbers and the second a list of the first 12 natural
numbers. Neither is really a sequence of expressions as is the
case for your examples.

>_Is there_ a precise definition of the ellipsis symbol? (in English,
>or in Mathematica)

Certainly, there is a definition in English. But precision isn't
well defined when it comes to English definitions. As for
Mathematica, there should be no expectation of a definition
other than the English definition since this isn't allowed
Mathematica syntax.