Re: Types in Mathematica, a practical example

*To*: mathgroup at smc.vnet.net*Subject*: [mg62835] Re: [mg62800] Types in Mathematica, a practical example*From*: Pratik Desai <pdesai1 at umbc.edu>*Date*: Tue, 6 Dec 2005 00:05:04 -0500 (EST)*References*: <200512051841.NAA21133@smc.vnet.net> <4394B78F.4050809@umbc.edu> <4394C2F2.2030305@umbc.edu>*Sender*: owner-wri-mathgroup at wolfram.com

Pratik Desai wrote: > 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 > > :-[ > > > But this might MatEQ[m_?MatrixQ, n_?MatrixQ] := ( Dimensions[m] === Dimensions[n]) && (Flatten[m] === Flatten[n]) s1 = {{1, 2, 3}, {4, 5, 6}} s2 = {{1, 2}, {3, 4}, {5, 6}} s3 = {{1, 2, 3}, {4, 5, 6}} MatEQ[s1,s2] >>False MatEQ[s1,s3] >>True

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

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

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

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

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