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MathGroup Archive 1999

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Re: simple Simplify[] question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19787] Re: [mg19766] simple Simplify[] question
  • From: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
  • Date: Fri, 17 Sep 1999 01:36:43 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

This sort of question comes up regularly. It's nothing to do with 
Mathematica really, it's just mathematics. First of all, this
"simplification" is not valid when a is a  complex numbers:
In[1]:=
(-1 + I)^3
Out[1]=
2 + 2 I

In[2]:=
((-1 + I)^2)^(3/2)
Out[2]=
-2 - 2 I

Actually, it is not even valid when a is a real negative number:

In[3]:=
(-1)^3
Out[3]=
-1

In[4]:=
((-1)^2)^(3/2)
Out[4]=
1

If you have Mathematica 4 you can do this:
In[37]:=
 Simplify[(a^2)^(3/2), a \[Element] Reals]
Out[37]=
      3
Abs[a]

or this:

In[38]:=
 Simplify[(a^2)^(3/2), a >= 0]
Out[38]=
 3
a

If not, and you are dealing with non-negative numbers perhaps the simplest
thing to do is to write Abs[a] instead of a (and if necessary later replace
Abs[a] by a) thus:

In[8]:=
 Simplify[(Abs[a]^2)^(3/2)]  /. Abs[a] -> a
Out[8]=
 3
a


--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp
http://eri2.tuins.ac.jp


----------
>From: Ulf Saalmann <us at atom.msi.se>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg19787] [mg19766] simple Simplify[] question
>Date: Wed, Sep 15, 1999, 4:53 PM
>

>
>
>  Hello,
>
>  why gives Mathematica
>                                      2 3/2
>       Simplify[(a^2)^(3/2)]        (a )
>
>
>  and not
>                                       3
>                                     a
>
>  and how to convince Mathematica to do it?
>
>
>  Thanks
>          Ulf  (us at atom.msi.se)
> 


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