Re: Behavior of Array[]

• To: mathgroup at smc.vnet.net
• Subject: [mg19461] Re: [mg19444] Behavior of Array[]
• From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
• Date: Sat, 28 Aug 1999 15:52:57 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Let's take an example. The command Array[a,{3,3}] assumes that a is a
function of two variables and constructs a 3 times 3 matrix (an array):

In[30]:=
Array[a, {3, 3}]
Out[30]=
{{a[1, 1], a[1, 2], a[1, 3]}, {a[2, 1], a[2, 2], a[2, 3]},

{a[3, 1], a[3, 2], a[3, 3]}}

This is exactly the same as thing that you get from

In[1]:=
Table[a[i, j], {i, 1, 3}, {j, 1, 3}]
Out[1]=
{{a[1, 1], a[1, 2], a[1, 3]}, {a[2, 1], a[2, 2], a[2, 3]},

{a[3, 1], a[3, 2], a[3, 3]}}

so I assume that will is at least  agree that each of these is as consistent
as the other.

Of course a is here a function, not an array!

Now suppose you define an array b with

In[2]:=
b = Array[a, {3, 3}]
Out[2]=
{{a[1, 1], a[1, 2], a[1, 3]}, {a[2, 1], a[2, 2], a[2, 3]},

{a[3, 1], a[3, 2], a[3, 3]}}

Now we have two objects, an array b and a function a.  You have to clearly
distinuish these two, for example the definition a=Array[a,{3,3}] will
immediately get you into an infinite loop. Thus to get the first element of
the first row of b you use the command

In[3]:=
b[[1, 1]]
Out[3]=
a[1, 1]

In words: the element of the array b in position {1,1} is the value of the
function a at (1,1).

This is, in my opinion, perfectly consistent and exactly as it should be.
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp

----------
>From: jslater at cs.wright.edu (Joseph C. Slater)
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg19461] [mg19444] Behavior of Array[]
>Date: Wed, Aug 25, 1999, 6:25 AM
>

> I've been using Mathematica for many years and one thing still puzzles me.
> Elements of the array defined by the variable 'a' can be obtained using
> a[[i,j]]=expression. However, the command Array creates arrays comprised
> of elements named in the form 'a[i,j]'. Note the single brackets.
> Everything I see in the Mathematica book about brackets says that these
> are functions. This seems inconsistant to me. Shouldn't they be listed as
> 'a[[i,j]]' until they are defined? What are the single brackets supposed
> to mean if not elements of the array 'a'?
>
> Joe Slater
>
> --
> ________________________________________________________________
> Dr. Joseph C. Slater             mailto:joseph.slater at wright.edu
> Mechanical and Materials Engineering    office:+1 (937) 775-5085
> Wright State University                    fax:+1 (937) 775-5009
> Dayton, OH 45435               http://www.cs.wright.edu/~jslater
>
>

```

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