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.