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 would prefere to exclude it. What do you think about this? 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>

**References**:**Re: Finding the periphery of a region***From:*dh <dh@metrohm.ch>