       Re: Re: Finding the periphery of a region

• To: mathgroup at smc.vnet.net
• Subject: [mg72096] Re: [mg72005] Re: Finding the periphery of a region
• From: Daniel Huber <dh at metrohm.ch>
• Date: Mon, 11 Dec 2006 04:55:33 -0500 (EST)
• References: <el8ufm\$st3\$1@smc.vnet.net> <200612081117.GAA20172@smc.vnet.net> <6DA7D258-EA36-456E-A8F7-B4CBE82001B8@mimuw.edu.pl>

```Hi Andrzej,
thank's a lot for the interesting example. Note that (0,0) is an
isolated point. The question is, if an isolated  point belong's to the
boundary of an area. I think this is up to how we define "boundary". I
Daniel

Andrzej Kozlowski wrote:
> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> It's well known fact in real algebraic geometry that this does not
> work in general. Here is a well known example example (also included
> in my response to the OP):
>
> x^3 - x^2 - y^2 > 0 && x < 10
>
> The boundary is not x^3 - x^2 - y^2 >= 0 && x <= 10
>
> This can be seen also on a picture:
>
>
> <<Graphics`InequalityGraphics`
>
>
> InequalityPlot[x^3-x^2-y^2>0&&x<10,{x},{y}]
>
> You can see that the point {0,0} which lies on x^3 - x^2 - y^2 == 0
> is not on the boundary of the region.
>
> Andrzej Kozlowski
>
>
> On 8 Dec 2006, at 20:17, dh wrote:
>
>>
>>
>> Hi,
>>
>> try replacing inequalities by equalities. This should work fine as long
>>
>> as you do not have intersecting regions. E.g.:
>>
>> x^2+y^2<100  ==> x^2+y^2=100, obviously a circle
>>
>> (5<=x<=25 and -10<=y<=10)  ===>( x==5&&-10<=y<=10) ||
>>
>> (x==25&&-10<=y<=10) || (5<=x<=25&&y==-10)  || (5<=x<=25&&y==10), four
>>
>> line segements.
>>
>> Daniel
>>
>>
>>
>> Bonny Banerjee wrote:
>>
>>> I have a region specified by a logical combination of equatlities and
>>
>>> inequalities. For example, r(x,y) is a region defined as follows:
>>
>>>
>>
>>> r(x,y) = x^2+y^2<100 or (5<=x<=25 and -10<=y<=10)
>>
>>>
>>
>>> How do I obtain the periphery of r(x,y)? I am only interested in finite
>>
>>> regions i.e. x or y never extends to infinity.
>>
>>>
>>
>>> Thanks,
>>
>>> Bonny.
>>
>>>
>>
>>>
>>
>>
>
>
>

--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh at metrohm.ch>
Internet:<http://www.metrohm.ch>

```

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