Re: Piecewise inside a Module or Block, I don't understand this behavior.

*To*: mathgroup at smc.vnet.net*Subject*: [mg83324] Re: Piecewise inside a Module or Block, I don't understand this behavior.*From*: Albert <awnl at arcor.net>*Date*: Sat, 17 Nov 2007 05:29:48 -0500 (EST)*Organization*: Arcor*References*: <fhjs9v$4vg$1@smc.vnet.net>

W. Craig Carter wrote: > Hello, > > I have a Piecewise function calculated in a module: > Here is a simplifed example of something which has a > behavior that puzzles me. > > a[c_, d_] := > Module[{e, f}, e = d^2; f = c^2; > Return[Piecewise[{e, 0 < x < 1/2}, {f, 1/2 < x <= 1}]]]; just a sidenote: Return is not necessary since the last expression within the module is returned anyway. In fact Return sometimes behaves a little different than expected, so it is better not used if there is no reason to... > a[1,2] (*doen't return what I had anticipated*) > > (*However this does*) > a[c_, d_] := > Module[{e, f}, e = d^2; f = c^2; > Return[Piecewise[{d^2, 0 < x < 1/2}, {c^2, 1/2 < x <= 1}]]]; > a[1,2] > > (*The same goes for Block, and putting an explicit Evaluate > inside the local function*) > > (*This behavior seems to be unique to Piecewise*) > a[c_, d_] := > Module[{e, f}, e = d^2; f = c^2; > Return[MyFunction[{e, 0 < x < 1/2}, {f, 1/2 < x <= 1}]]]; > a[1,2] > > I can't find anything about Piecewise, or in Module and > Block documentation that gives me a hint. > > Anyone know what is going on? > > Thanks, Craig > > PS: I have a work-around: > > aAlt[c_, d_] := > Module[{e, f}, e = d^2; f = c^2; > {{e, 0 < x < 1/2}, {f, 1/2 < x <= 1}}]; > Piecewise@aAlt[1,2] > > but, I am still curious.... > Piecewise has attributes HoldAll, so the symbols e and f are not evaluated to d^2 and c^2. When using Piecewise@aAlt[] you are effectively doing Piecewise at {{...}} which you can also do directly within the module: a[c_, d_] := Module[{e, f}, e = d^2; f = c^2; Piecewise@{{e, 0 < x < 1/2}, {f, 1/2 < x <= 1}} ]; There are other tricks to achieve what you expected to happen, you just have to find a way to put the evaluated versions of e and f into the Piecewise function. A very handy candidate for this is With: a[c_,d_]:= With[{e=d^2,f=c^2}, Piecewise[{{e,0 < x < 1/2},{f, 1/2 < x <= 1}}] ]; which I think is the cleanest way to achieve what you want. If all this seems strange to you I suggest you learn more about the evaluation process within mathematica, good starting points are the tutorials listed at the bottom of guide/EvaluationControl in the Documentation-Center. This is an advanced topic but understanding it will probably be an eye opener and make you gain much more from mathematica's power... hth, albert