Types in Mathematica, a practical example

*To*: mathgroup at smc.vnet.net*Subject*: [mg62800] Types in Mathematica, a practical example*From*: "Ingolf Dahl" <ingolf.dahl at telia.com>*Date*: Mon, 5 Dec 2005 13:41:04 -0500 (EST)*Organization*: Goteborg University*Reply-to*: <ingolf.dahl at telia.com>*Sender*: owner-wri-mathgroup at wolfram.com

To MathGroup, I am not an advocate for strong typing in Mathematica, but consider the following simple example: I want to see if two matrices are equal. One of them was the result from some equation, and is given inside a rule. Then I write some code similar to this: a = {{1, 2}, {3, 4}}; x - a /. {x -> a} I of course hope to get a matrix filled by zeroes, but if x is undefined, the following is returned: {{{{0, 1}, {2, 3}}, {{-1, 0}, {1, 2}}}, {{{-2, -1}, {0, 1}}, {{-3, -2}, {-1, 0}}}} First x was assumed to be a number, and (x - a) was evaluated. Then x was substituted by the matrix a. No bug in Mathematica, but it was not what I wanted as user. It is easy to make such a mistake in the programming. Of course there are many ways to get around this problem, but is there any reasonably simple way to "type" x to be a list of lists without specifying the elements, in such a way that the above example works? I could do ReleaseHold[Hold[x - a] /. {x -> a}] but then we are not in the "typing business" any longer. I think this question illuminates one aspect of the typing issue in Mathematica. I remember that I as a newbie looked for ways to declare matrices, in such a way that I later could specify matrix elements one-by-one, without initializing them first. I soon learned that there are other ways to achieve similar results, but still I do not see any good reason why I cannot force Mathematica to give the following response from x-a, if x in some way is declared to be a 2x2 list of lists: {{x[[1,1]] - 1, x[[1,2]] - 2},{x[[2,1]] - 3, x[[2,2]] - 4}} I am not allowed to Unset or Clear any part of a list either. Why not? Ingolf Dahl Sweden

**Follow-Ups**:**Re: Types in Mathematica, a practical example***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Types in Mathematica, a practical example***From:*Sseziwa Mukasa <mukasa@jeol.com>

**Re: Types in Mathematica, a practical example***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**Re: Types in Mathematica, a practical example***From:*Pratik Desai <pdesai1@umbc.edu>

**Re: Types in Mathematica, a practical example***From:*Kristen W Carlson <carlsonkw@Gmail.com>