       Re: Types in Mathematica, a practical example

• To: mathgroup at smc.vnet.net
• Subject: [mg62826] Re: [mg62800] Types in Mathematica, a practical example
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Tue, 6 Dec 2005 00:04:05 -0500 (EST)
• References: <200512051841.NAA21133@smc.vnet.net> <4394B78F.4050809@umbc.edu>
• Sender: owner-wri-mathgroup at wolfram.com

```Pratik Desai wrote:

> Ingolf Dahl wrote:
>
>> 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
>>
>>
>>
>>
> Hi Ingolf
> Perhaps I am missing the point, and after reading some of the posts in
> this thread I am not really sure what type actually means.
> Nevertheless based on the definition
> http://mathworld.wolfram.com/MatrixEquality.html
> Why not write a function such as this??
>
> MatEQ[m_?MatrixQ, n_?MatrixQ] := (Flatten[m] === Flatten[n])
>
>
>
>
>
>
Whoops, that will not work for obvious reasons
s1 = {{1, 2, 3}, {4, 5, 6}}
s2 = {{1, 2}, {3, 4}, {5, 6}}
MatEQ[s1,s2]
>>True

:-[

```

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