Re: Why can't Mathematica tell when something is algebraically zero?
- To: mathgroup at smc.vnet.net
- Subject: [mg108151] Re: Why can't Mathematica tell when something is algebraically zero?
- From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
- Date: Tue, 9 Mar 2010 06:23:57 -0500 (EST)
- References: <hn2ltj$3kt$1@smc.vnet.net>
Your expression does not generally equal zero: In[12]:= r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] /. r -> I Out[12]= -2 + 2 I PowerExpand does the job: In[18]:= PowerExpand[ r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)]] Out[18]= 0 Cheers -- Sjoerd On Mar 8, 1:09 pm, mmdanziger <mmdanzi... at gmail.com> 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. Once you get dependent on > Mathematica these things are pretty disturbing...you forget about your > own knowledge because the program tells you that things are > different. Then you sit there like an idiot checking an algebraic > identity that any beginning precalc student should be able to solve no > problem. > > Is there any way to get Mathematica to "wake up" to these things? It > has such a powerful algebraic engine for most things, why can't it see > something simple like the above? Do you really have to manually > override and tell the program when things should be zero? > > For the time being I'll just sift through and test things by hand but > I can't believe that there isn't a better way. > > Best, > md