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MathGroup Archive 2005

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Re: Summary: Which[] as Textbook Input, Plot[] Questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54042] Re: [mg54037] Summary: Which[] as Textbook Input, Plot[] Questions
  • From: yehuda ben-shimol <bsyehuda at gmail.com>
  • Date: Wed, 9 Feb 2005 09:27:14 -0500 (EST)
  • References: <200502081031.FAA17755@smc.vnet.net>
  • Reply-to: yehuda ben-shimol <bsyehuda at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

This is solved in Mathematica 5.1 as the Piecewise technology and is
integrated to all Mathematica functions such as Integrate, NIntegrate,
DSOlve, NDSolve etc.
In earlier versions (i.e., 5.0 and below) there is no such implementation.
yehuda


On Tue, 8 Feb 2005 05:31:22 -0500 (EST), Matt <anonmous69 at netscape.net> wrote:
> Hello,
>    I apologize if the answer to this is somewhere glaringly obvious in
> the documentation, however, after at least 4 hours pawing through both
> the hardcover Mathematica 4.0 book by Wolfram and the in-program
> Mathematica 4.1 documentation, I cannot find how I would annotate a
> function that takes on different values based upon different domains.
> To wit, something like:
> 
> Clear[f];
> f[x_] := Which[x < 0, Sin[x]/x, x == 0, 1, x > 0, Sin[x]/x];
> Plot[f[x], {x, -pi, pi}, AxesLabel -> {"x", "f[x]"};
> 
> The 'Which' function is great for actually evaluating something, but I
> was looking for something along the lines of traditional mathematical
> notation (such as one would write on a chalkboard or on a sheet of
> paper), where a large left-bracket would be used and the various
> definitions of the function for the various ranges would be
> 'constrained' by the bracket.
> 
> I'll try to illustrate what I mean, where the '|'s that I will use
> should be interpreted as a single, large left-bracket:
> 
>        | Sin(x)/x, x < 0
> f(x) = | 1, x = 0
>        | Sin(x)/x, x > 0
> 
> Is there a way to do what I'm asking in Mathematica 4.1 (or even
> above)?
> 
> As regards the Plot[] function, I'm puzzled as to why the following
> doesn't give me an error when evaluated:
> 
> Clear[g];
> g[x_] := 1/x;
> Plot[g[x], {x, -5, 5}];
> 
> It seems as though it should, considering that x at zero is undefined.
> However, Mathematica draws the graph as though the function were just
> fine.
> 
> Thanks for any light you can shed on this,
> 
> Matt
> 
>


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