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MathGroup Archive 2006

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Re: Plot3D question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70650] Re: Plot3D question
  • From: Bill Rowe <readnewsciv at sbcglobal.net>
  • Date: Sun, 22 Oct 2006 01:19:43 -0400 (EDT)

On 10/21/06 at 5:14 AM, dimmechan at yahoo.com (dimitris) wrote:

>I would like to know why the Plot3D function does not complain about
>the following command (note there is a singularity at y=0)

>Plot3D[Sin[x]/y, {x, -10, 10}, {y, -10, 10}]

>whereas it does complain (a lot!) about the following

>Plot3D[Sin[x]/y, {x, -10, 10}, {y, -10, 10}]

The two lines of code above appear identical and both work for 
me on

In[12]:=
$Version

Out[12]=
5.2 for Mac OS X (June 20, 2005)

But clearly the reason any Mathematica routine fails to complain 
about a singularity is that Mathematica simply doesn't sample 
the function at the singularity. Whether Mathematica samples a 
function at a given point is determined by a number of variables 
including, the range for the variable, the version of 
Mathematica and the machine it is running on. And for Plot which 
uses the adaptive sampling routine, the settings for 
PlotDivision and MaxBend also have an effect.

I've found it is quite difficult to predict whether the plot 
routines in Mathematica will or will not sample a function at a 
singularity. The only way I have found to get predictability is 
to specifically trap the singularity in the function definition.
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