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Re: Re: Why can't Mathematica tell when something is algebraically zero?

• To: mathgroup at smc.vnet.net
• Subject: [mg108200] Re: [mg108167] Re: Why can't Mathematica tell when something is algebraically zero?
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 10 Mar 2010 01:46:44 -0500 (EST)
• References: <hn2ltj$3kt$1@smc.vnet.net> <201003091126.GAA07255@smc.vnet.net>

On 9 Mar 2010, at 12:26, Simon wrote:

>
>
> In fact it can do better than that, and tell you exactly when it is
> zero:
>
> In[2]:= Reduce[r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] ==
> 0, Reals]
> Out[2]= r <= -1 || r > 0
>

Well, actually, this does not mean what you think it means. The way to do it is:

Reduce[r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] == 0 &&
  Element[r, Reals], r]

and then you will see that Reduce can't do it. In fact

 r^2 Sqrt[(r^3 + r + 2)/r] - Sqrt[r^3 (r^3 + r + 2)] /.
 r -> -1/2

 0

Andrzej Kozlowski

• References:
  • Re: Why can't Mathematica tell when something is algebraically zero?
    • From: Simon <simonjtyler@gmail.com>