Re: The uses of Condition (/;)

*To*: mathgroup at smc.vnet.net*Subject*: [mg82947] Re: The uses of Condition (/;)*From*: magma <maderri2 at gmail.com>*Date*: Sun, 4 Nov 2007 06:11:40 -0500 (EST)*References*: <fghcbl$k9n$1@smc.vnet.net>

On Nov 3, 9:43 am, Szabolcs Horv=E1t <szhor... at gmail.com> wrote: > According to the documentation, /; can be used in three different ways, > illustrated below: > > A. pattern /; condition = definition > > B. pattern := definition /; condition > > C. pattern := Module[{}, definition /; condition] > > Real examples for testing: > > f[x_] /; (Print["cond"]; x > 5) := (Print["def"]; x) > > g[x_] := (Print["def"]; x) /; (Print["cond"]; x > 5) > > h[x_] := Module[{}, Print["def"]; x /; (Print["cond"]; x > 5)] > > Usage C differs from A and B in that 'definition' is always evaluated, > and it is evaluated before 'condition'. But I cannot see *any* > difference in meaning between A and B. > > Is B completely redundant? Could someone show an example where an A > type and a B type definition behave differently? Is there any situation > where B can be used, but A cannot? (A is more general: it can be used > with any pattern, while B is restricted to use with SetDelayed and > similar functions.) Is B provided solely as a more readable syntax? > > Szabolcs > > P.S. Unfortunately usage C is "hidden" in the docs. IMO, since it's > *meaning* (and not only syntax) is different from that of A and B, it > deserves a more prominent place in the docs. Usage C is described in the Mathematica 6 documentation under Condition - More information (and nowhere else I think) in the form lhs:=Module[{vars},rhs/;test] They say that "this usage allows local variables to be shared between test and rhs " On the same Documentation page , under Scope, there is a concrete example of usage C. f[x_] := Module[{u}, u^2 /; ((u = x - 1) > 0)] here it is seen that the pattern (u) is a local variable. In your examples you were using x, a global variable, so no difference was apparent. In C, condition is evaluated before definition, for example (please make sure you have Remove[f] before typing this: f[x_] := Module[{u}, (Print [u]; u^2) /; ((u = x - 1) > 0)] f[3] 2 4 u only acquires a value after cond is evaluated and then def (Print [u]; u^2) will be evaluated. A and B are very similar, but A is considered a bit faster, because evaluation stops immediately if the cond is not safisfied Changing slightly topic: In the same Condition documentation page we find: {6, -7, 3, 2, -1, -2} /. x_ /; x < 0 -> w giving {6, w, 3, 2, w, w} and that 's ok. The x_ stand for the individual elements in the list But why then {6, -7, 3, 2, -1, -2} /. x_ -> w gives w instead of {w,w,w,w,w,w} ? shouldn't the x_ still stand for the individual elements in the list?

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**Re: Re: The uses of Condition (/;)***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>