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Re: Simplify UnitStep expressions

• To: mathgroup at smc.vnet.net
• Subject: [mg69205] Re: [mg69195] Simplify UnitStep expressions
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 1 Sep 2006 18:41:05 -0400 (EDT)
• References: <200609011041.GAA25645@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

On 1 Sep 2006, at 11:41, L. Dwynn Lafleur wrote:

> The following is transcribed from a Mathematica 5.2 notebook in  
> Windows XP:
>
> In[1]:= Simplify[UnitStep[a-x/b], a-x/b > 0]
> Out[1]= 1
>
> In[2]:= Simplify[UnitStep[a-Pi/b], a-Pi/b > 0]
> Out[2]= UnitStep[a-Pi/b]
>
> Why does the second output different from the first?  I know it has
> something to do with the fact that Pi is internally defined in  
> Mathematica
> because a similar result occurs Pi is replaced with E, but what  
> logic is
> being followed?
>
> -- 
> ======================================
>  L. Dwynn Lafleur
>  Professor of Physics
>  University of Louisiana at Lafayette
>  lafleur at louisiana.edu
> ======================================
>

Curiously, if you use FullSimplify rather then Simplify you will get:


FullSimplify[UnitStep[a-Pi/b], a-Pi/b > 0]

1


The same holds if Pi is replaces by E, or indeed by explicit  
functions of E or Pi such as Pi^2, E^Pi etc. In all such cases  
FullSimplify works but Simplify does not work. Strange.

Andrzej Kozlowski	

• References:
  • Simplify UnitStep expressions
    • From: "L. Dwynn Lafleur" <lafleur@louisiana.edu>