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Nested Lists, Definition and Evaluation.

• To: mathgroup at smc.vnet.net
• Subject: [mg59729] Nested Lists, Definition and Evaluation.
• From: "Alexander" <beginning.physst at mail.ru>
• Date: Fri, 19 Aug 2005 04:31:51 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello!

Here is simple example of defining list:

b = Table[Symbol["a" <> ToString[i] <> ToString[j]], {i, 2}, {j, 2}];
a11 = IdentityMatrix[2];
b[[1,1]][[1,1]]

Output will be number 1.

Then we type another command:
b[[1,1]][[1,1]]=2

wich cause error message.

If we type ?b the structure of b can be seen:
Global`b
b = {{a11, a12}, {a21, a22}}

And I wonder, how to change elements of aij from b? It's interesing
question about how mathematica think things and how evaluate them.

So, the questions are:
1) Why code above produce error message?
2) What difference between b[[1,1]][[1,1]] and
b[[1,1,1,1]] notation?

Here is an example concerning the second  question:
This code doesn't produce an error:

a11 = IdentityMatrix[2];
b = Table[Symbol["a" <> ToString[
    i] <> ToString[j]], {i, 2}, {j, 2}];
b[[1, 1, 1, 1]] = 3

but this does:

a11 = IdentityMatrix[2];
b = Table[Symbol["a" <> ToString[
    i] <> ToString[j]], {i, 2}, {j, 2}];
b[[1, 1]][[1, 1]] = 3

Why?

Sorry for my obscure speech, and thanks for your answers!

• Follow-Ups:
  • format of "Solve" output
    • From: Ed Peschko <esp5@mdssdev05.comp.pge.com>
  • Re: Nested Lists, Definition and Evaluation.
    • From: "benshimo@bgumail.bgu.ac.il" <bsyehuda@gmail.com>