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

• To: mathgroup at smc.vnet.net
• Subject: [mg54067] Re: [mg54037] Summary: Which[] as Textbook Input, Plot[] Questions
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Wed, 9 Feb 2005 09:27:50 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200502081031.FAA17755@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```You would like Mathematica 5.1, which introduces the new function
Piecewise.  You could enter your function like this:

f[x_] := Piecewise[{{Sin[x]/x, x != 0}, {1, x == 0}}]

Then the result of evaluating

f[x]

would be a display of exactly the kind you want, with the large left
brace (albeit no commas).  And then you could plot as usual:

Plot[f[x], {x, -Pi, Pi}]

By the way, it's unclear why you expressed your piecewise definition
with three clauses, instead of just two:

Which[x != 0, Sin[x]/x, x == 0, 1]

Matt 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)?

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

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