Re: RE: RE: Re: How to integrate over a constrained domain
- To: mathgroup at smc.vnet.net
- Subject: [mg34266] Re: [mg34258] RE: [mg34246] RE: [mg34217] Re: [mg34203] How to integrate over a constrained domain
- From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
- Date: Mon, 13 May 2002 05:54:07 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
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 > Subject: [mg34266] [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 >> Subject: [mg34266] [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 > > > > > >