Re: Why can't Mathematica tell when something is algebraically zero?
- To: mathgroup at smc.vnet.net
- Subject: [mg108158] Re: Why can't Mathematica tell when something is algebraically zero?
- From: Bill Rowe <readnews at sbcglobal.net>
- Date: Tue, 9 Mar 2010 06:25:14 -0500 (EST)
On 3/8/10 at 6:09 AM, mmdanziger at gmail.com (mmdanziger) wrote: >This isn't the first time that I've encountered something like this >in Mathematica but in my calculations I got a term like this: >r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] >Which is obviously identically zero. For some reason Simplify or >even FullSimplify can't figure this out. The problem is the expression is not zero for all possible values of r. Specifically In[3]:= r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] /. r -> I Out[3]= -2 + 2 I You can get Mathematica to do what you want by using PowerExpand which implicitly assumes reals. That is: In[4]:= r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] // PowerExpand Out[4]= 0