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Re: PowerExpand

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63560] Re: PowerExpand
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 5 Jan 2006 03:12:29 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <dpg0ro$pl2$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Blimbaum, Jerry CIV NSWC PC wrote:
> Just want to make a comment.....Normally PowerExpand is looked upon as a
> culprit because for the general case it leads to wrong
> results......However, I had an interesting case where I tried
> 
> Siimplify[expr, m>0]  ....expr was of 2 basic  forms (although really
> more complicated then this, but this shows the basic idea)
> 
>    .....Sqrt[-m^2 (a^2+b^2)]  and   Sqrt[m^2 (a^2+b^2)] 
> 
> With Simplify Mathematica cranked and cranked and cranked  with no
> output.....So , in  frustration,  I tried PowerExpand and a second later
> it performed the same operation with surprising ease and the result was
> exactly what i was trying to get...
> 
> If I try the basic expressions  , then Simplify took m out of the Square
> Root sign  for the Sqrt[m^2 (a^2+b^2)]   but  not  for Sqrt[-m^2
> (a^2+b^2)] 
> 
> 
> jerry blimbaum
> 
> 
Hi Jerry,

Here what I get on my laptop in a fraction of second:

In[1]:=
Simplify[Sqrt[m^2*(a^2 + b^2)]]

Out[1]=
        2    2   2
Sqrt[(a  + b ) m ]

In[2]:=
Simplify[Sqrt[m^2*(a^2 + b^2)], m > 0]

Out[2]=
       2    2
Sqrt[a  + b ] m

In[3]:=
PowerExpand[Sqrt[m^2*(a^2 + b^2)]]

Out[3]=
       2    2
Sqrt[a  + b ] m

In[4]:=
Simplify[Sqrt[(-m^2)*(a^2 + b^2)]]

Out[4]=
         2    2   2
Sqrt[-(a  + b ) m ]

In[5]:=
Simplify[Sqrt[(-m^2)*(a^2 + b^2)], m > 0]

Out[5]=
         2    2   2
Sqrt[-(a  + b ) m ]

In[6]:=
PowerExpand[Sqrt[(-m^2)*(a^2 + b^2)]]

Out[6]=
         2    2
I Sqrt[a  + b ] m

In[7]:=
$Version

Out[7]=
5.2 for Microsoft Windows (June 20, 2005)

Best regards,
/J.M.


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