Re: Limiting range of variables when defining funxtions of several
- To: mathgroup at smc.vnet.net
- Subject: [mg74707] Re: Limiting range of variables when defining funxtions of several
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Sun, 1 Apr 2007 04:18:43 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <eukv3v$3hr$1@smc.vnet.net>
Michelasso wrote:
> Hello everybody,
> my problem is that I would like to plot a 3d graphic of a function of
> two variables, restricted to domain D={(x,y): x>= 0, y>=0, y <= 1-x}.
>
> I thought to define the function in this way:
> test[x_,y_/; y <= 1-x]:= x+y
>
> but this seems not to work, while it works for functions of one
> variable, i.e.:
> test2[x_/; x<= 1]:= 3x
>
> So, am I doing some syntax error, or is there some other kind of
> problems with my definition?
You should use the Boole function [1] to define a function over a
region. For instance,
In[1]:=
Clear[test]
test[x_, y_] := (x + y)*Boole[x >= 0 && y >= 0 && y <= 1 - x]
Plot3D[test[x, y], {x, -2, 2}, {y, -2, 2}];
[...graphic deleted...]
Regards,
Jean-Marc
[1] http://documents.wolfram.com/mathematica/functions/Boole
[2] _The Mathematica Book_, "3.5.9 Integrals over Regions",
http://documents.wolfram.com/mathematica/book/section-3.5.9