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)
>