Re: Piecewise vs. /; ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg104035] Re: Piecewise vs. /; ?*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Fri, 16 Oct 2009 07:20:25 -0400 (EDT)*References*: <hashpc$qu8$1@smc.vnet.net> <hav19a$4gr$1@smc.vnet.net> <hb70d0$8uj$1@smc.vnet.net>

On 2009.10.15. 13:17, Dan Dubin wrote: > Folks -- > > I would respectfully disagree with the idea that /; is more general > than Piecewise. The example given, a function that returns a > different value in the morning than the evening, is simply a > time-dependent function that could be constructed using Piecewise, as > in > > f[x_,h_] = Piecewise[{{x, h< 12}, {-x, h>= 12}}]; > > and called via > > f[x,DateList[[4]]] > > > In fact, it seems to me that any difference in the way that > Mathematica interprets Piecewise and conditionals should be removed > from later editions of Mathematica, since as far as I can see the > difference between them is merely a Mathematica-specific matter of > the mechanics of how the expressions are evaluated with little (or > no?) utility, that causes considerable confusion among new users. I > don't see any benefit in this distinction, but feel free to convince > me otherwise! > Piecewise[] is explicitly designed to be used to represent a mathematical concept, piecewise functions. Mathematical operations, like D[], can be applied to it. For example, D[Piecewise[{{1, x > 0}}, 0], x] /; can be used with patterns (or, as a more special use, with := definitions or Module). It cannot be used to compose a standalone mathematical expression like Piecewise can. Actually Piecewise[] is much closer to Which[] than to /;. But again, Which[] is a programming construct, not something that is meant to be used as a mathematical expression. The following does not work as expected from a mathematical point of view: D[Which[x > 0, 1, True, 0], x] There are many differences between how these three types of expressions are (or are not) evaluated, making Piecewise[] suitable for mathematical use, but unwieldy for programming/pattern matching use. The overlap between programming and mathematical use of some constructs (for example, "functions") can already cause confusion in Mathematica. I can see how a programming use of Piecewise could be forced... but I think that it was a good decision to try to separate these two kinds of uses in this case.