Working with Real variables
- To: mathgroup at smc.vnet.net
- Subject: [mg34208] Working with Real variables
- From: bghiggins at ucdavis.edu (Brian Higgins)
- Date: Thu, 9 May 2002 05:16:22 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Dear MathGroup,
I am interested in evaluating multiple integrals involving Abs[x-y]
terms where x and y are real variables. I was interested in using the
ReIm package or Ted Ersek's SwitchableRealOnly package
To set the tone I started with the following simple example using a
traditional approach that relies on standard Mathematica functions
Simplify[Integrate[Abs[x - y], {y, 0, 1}], Element[{x, y} ,Reals]
which gives
(1/2)*((-(-1 + x))*Abs[-1 + x] + x*Abs[x])
This is effectively the same result what I would get by doing the
integration by hand. So far so good. I then try the ReIm package
In[1]:=<< Algebra`ReIm`
In[2]:=x /: Im[x] = 0; y/:Im[y]=0;
In[4]:=Integrate[Abs[x - y], {y, 0, 1}]
Out[4]=(Sqrt[(-1 + x)^2] - 2*Sqrt[(-1 + x)^2]*x)/(2*(1 - x))
This does not evaluate to the above result. If I use the
SwitchableRealOnly package I get the same result found by the ReIm
package. Is this a bug, or am I missing something crucial. when using
these packages.
Thanks in advance for any help/suggestions
Brian