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) >