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Re: Expressions with ellipsis (...)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93345] Re: Expressions with ellipsis (...)
  • From: magma <maderri2 at gmail.com>
  • Date: Tue, 4 Nov 2008 06:19:35 -0500 (EST)
  • References: <gdmsbd$jv$1@smc.vnet.net> <200810240630.CAA23066@smc.vnet.net>

On Nov 2, 7:58 am, AES <sieg... at stanford.edu> wrote:
> In article <geh9sa$fb... at smc.vnet.net>, dch888 <dch... 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 ;  =8A
>          evaluates the expr_i in turn, giving the last one as t=
he 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?)
>
> _Is there_ a precise definition of the ellipsis symbol? (in English, or
> in Mathematica)  
>
> Is " ;  " technically an expression? (in Mathematica)

The ellipsis symbol has no built-in special meaning in Mathematica. It is used
in CompoundExpression documentation in the same way it is used in
English.

the semicolon ";" is NOT an "expression". It is just the INFIX form of
the CompoundExpression operator, exactly like "+" is the infix form of
Plus

CompoundExpression[a, b, c]

is equivalent to typing

a;b;c

(no semicolon at the end) and WILL display the value of c.
Instead typing

a;b;c;

(semicolon at the end) is equivalent to typing

CompoundExpression[a, b, c;Null]

and WILL NOT  display the value of c. In both cases a, b and c are
evaluated.

I do not find this "mystical" or complicated in any way.
But for most Mathematica users, the semicolon can be simply considered a
separator between statements, like similar separators in other
languages.
Actually, to be more precise, the ";" is a "separator and suppressor
of output", while a simple carriage return (the big RETURN key in the
keyboard) is the basic separator between statements. You can see this
by typing

a
b

in the same cell, one below the other (using carriage return). In this
case the evaluations are carried out sequentially and the values are
displayed. The sequence of keypressees:

a "carriage return" b

is not interpreted as

ab

or as

a multiplied by b

, but as

a and then b

So the carriage return is the pure separator of statements.

HOWEVER  ".."  (just 2 dots) HAS a built-in meaning as Repeated[] and
you can read what it means in the documentation




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