MathGroup Archive 2002

[Date Index] [Thread Index] [Author Index]

Search the Archive

RE: RE: RE: Re: How to integrate over a constrained domain

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34278] RE: [mg34258] RE: [mg34246] RE: [mg34217] Re: [mg34203] How to integrate over a constrained domain
  • From: "DrBob" <majort at cox-internet.com>
  • Date: Mon, 13 May 2002 05:54:26 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

>>Boole --- another undocumented feature.   Sigh...

That's all I said originally, and I stand by it.  Boole is undocumented.

I don't mean to quibble over trivialities, but if I sigh, and mention
that something isn't documented, why quibble with me in return?

It doesn't seem too much to ask to put ALL standard package functions in
the Master Index.  I don't think there's a defensible reason for
excluding ANY of them, and including them all seems easier than deciding
WHICH ones to include.

>>there is also a lot more to Boole than turning True/False into 1/0 !

No, it does just that, and nothing else.  (According to the
documentation you've pointed out, and everything Mathematica tells me.)
If there's more to it, how can we tell?

Bobby

-----Original Message-----
From: Andrzej Kozlowski [mailto:andrzej at platon.c.u-tokyo.ac.jp] 
To: mathgroup at smc.vnet.net
Subject: [mg34278] Re: [mg34258] RE: [mg34246] RE: [mg34217] Re: [mg34203] How to
integrate over a constrained domain

In the case of Mathematica it's quite hard for functions to get into the

Kernel, and even many of those that make it end up in  Developer, 
Experimental or even Internal contexts. Those included in Standard 
Packages are considered either not of sufficiently universal interest or

just not good enough to qualify. Some of them are not programmed by 
people at Wolfram and some don't even work properly!
Also, there is also a lot more to Boole than turning True/False into 
1/0 ! It is quite trivial to define a function that would do that 
without needing to load the add on package Calculus`Integration` but it 
will do nothing useful for you. This function needs the rest of the 
package to work. And the main tool of this package package is the 
function GenericCylindricalDecomposition (which I used in my answer to 
the same problem, having forgotten all about Boole). It is this function

that does all the hard work, but it itself has so far made it only into 
the Experimental context, so one could hardly expect a function that 
depends on it to do better.

Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/


On Sunday, May 12, 2002, at 04:26  PM, DrBob wrote:

>>> It's NOT undocumented -- in the Help Browser, go to Add-ons,
Standard
> Packages, Calculus, Integration.
>
> OK, but there's no particular reason for a function that turns
> True/False into 1/0 to be (a) part of an add-on, (b) related to
> Calculus, or (c) involved specifically in Integration.  Why would I
look
> for it there?
>
> That's what I call "undocumented"... you can find it only if you've
> ALREADY found it... and didn't forget where.
>
> It should be mentioned in the documentation of True, False, TrueQ, If,
> etc.  It's also conceptually related to UnitStep, DiracDelta, etc.
>
> And yes, definitely, it should be in the Master Index!
>
> Bobby
>
> -----Original Message-----
> From: Murray Eisenberg [mailto:murraye at attbi.com]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg34278] [mg34258] Re: [mg34246] RE: [mg34217] Re: [mg34203] How to 
> integrate over
> a constrained domain
>
> It's NOT undocumented -- in the Help Browser, go to Add-ons, Standard
> Packages, Calculus, Integration.
>
> However, it IS missing from the Master Index!
>
> DrBob wrote:
>>
>> Boole --- another undocumented feature.   Sigh...
>>
>> Bobby
>>
>> -----Original Message-----
>> From: BobHanlon at aol.com [mailto:BobHanlon at aol.com]
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
>> Subject: [mg34278] [mg34258] [mg34246] [mg34217] Re: [mg34203] How to integrate

>> over a
> constrained
>> domain
>>
>> In a message dated 5/9/02 6:42:13 AM, maciej at maciejsobczak.com
writes:
>>
>>> Let's say I have a set on a (x,y) plane given by:
>>>
>>> x^2 + y^2 < r^2
>>>
>>> and I want to compute its area.
>>> Yes, I know its Pi*r^2, but I want Mathematica tell me.
>>>
>>> As a generalization, I want to integrate over a domain given by one
> or
>>> more
>>> inequalities.
>>> The problem above can be solved like this:
>>>
>>> Integrate[1, {x, -r, r}, {y, -Sqrt[r^2-x^2], Sqrt[r^2-x^2]}]
>>> Simplify[%, {r>0}]
>>>
>>> which gives
>>>
>>> Pi r^2
>>>
>>> That's nice, but requires solving the inequality for y, which is not
>> always
>>> viable.
>>>
>>> It would be nice to have syntax like:
>>>
>>> Integrate[1, {x, y}, {x^2 + y^2 < r^2}]
>>>
>>> but it does not work (of course).
>>>
>>> How can I achieve what I want?
>>
>> For specific numeric values it is easy
>>
>> Needs["Calculus`Integration`"];
>>
>> Table[{r,
>>
>>     Integrate[Boole[ x^2+y^2<r^2] ,
>>
>>       {x,-r,r}, {y,-r,r}]},
>>
>>   {r,0,5}]
>>
>> {{0, 0}, {1, Pi}, {2, 4*Pi}, {3, 9*Pi}, {4, 16*Pi},
>>
>>   {5, 25*Pi}}
>>
>> Bob Hanlon
>> Chantilly, VA  USA
>
> --
> 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
> Amherst, MA 01375
>
>
>
>
>
>




  • Prev by Date: Re: Re: Tough Limit
  • Next by Date: Numerical solutions to problems in theory of optimal control
  • Previous by thread: Re: RE: RE: Re: How to integrate over a constrained domain
  • Next by thread: Re: RE: RE: RE: Re: How to integrate over a constrained domain