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 :-[

**References**:**Types in Mathematica, a practical example***From:*"Ingolf Dahl" <ingolf.dahl@telia.com>

**Re: Re: Re: Re: Types in Mathematica thread**

**Re: Types in Mathematica**

**Re: Types in Mathematica, a practical example**

**Re: Types in Mathematica, a practical example**