Re: Poor choice in PiecewiseExpand ?

• To: mathgroup at smc.vnet.net
• Subject: [mg107553] Re: [mg107550] Poor choice in PiecewiseExpand ?
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Wed, 17 Feb 2010 07:00:53 -0500 (EST)

```If you intend for it to be zero outside the interval, then define the function in that manner.

f[x_] = PiecewiseExpand[Piecewise[{{Ceiling[x], 0 <= x <= 3}}]]

f /@ Range[-1, 4, .5]

{0,0,0,1,1,2,2,3,3,0,0}

Bob Hanlon

---- Jack L Goldberg 1 <jackgold at umich.edu> wrote:

=============
Hi Folks,

I am running ver. 7.01.0 on a MackBookPro using OS 10.6.2.

In[1]  PiecewiseExpand[Ceiling[x], 0 <= x <= 3]

For clarity, I write the piecewise output in the form of a "Which"
command.  It DOES NOT display as "Which", of course.

Out[1]  Which[1, 1 <= x < 2, 2, 2 <= x <= 3, 3, x >= 3, 0, True]

My beef (confusion) is with the values given in Out[1] when x > 3.
(This issue arises in Floor[x] and other such functions.)  Why is the
value 3 ?  Since the assumption is that x lies in [0,3], giving a
value of x outside this interval should result in an error message.
No?.  By the way, the value returned for x = -1 is zero so clearly(?)
Mathematica decided to make this function continuous with the values at the
end points of the assumed interval, where possible.  Is this a
documented feature of PiecewiseExpand?  Is it even a good idea?

I can live with this "feature" by the way.  I just wish I hadn't had
to discovered it after spending much time fooling around with
PiecewiseExpand in other code that I am writing.

My own feeling is that outside the assumed region, PiecewiseExpand
should return  0 if anything.

Jack

```

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