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Mathematica cannot simplify a product of UnitStep functions

• To: mathgroup at smc.vnet.net
• Subject: [mg55118] Mathematica cannot simplify a product of UnitStep functions
• From: Alain Cochard <alain at geophysik.uni-muenchen.de>
• Date: Sun, 13 Mar 2005 04:57:37 -0500 (EST)
• Reply-to: alain at geophysik.uni-muenchen.de
• Sender: owner-wri-mathgroup at wolfram.com

Consider the following:

    Mathematica 4.0 for Linux
    Copyright 1988-1999 Wolfram Research, Inc.
     -- Motif graphics initialized -- 

    In[1]:= e1=UnitStep[x-y]; e2=UnitStep[x-z]; 

    In[2]:= FullSimplify[{e1,e2,e1*e2},x<y<z]

    Out[2]= {0, 0, UnitStep[x - y, x - z]}

I find it strange that it cannot simplify the product to 0.  Is there
something mathematically profound here, implying that the true result
is indeed not 0?? (At least I hope it's not something trivial!)
Assuming the answer is no, is there a smarter/more elegant way to
perform the simplification than the workaround I found, which is to
simplify each term and multiply them.

Thanks in advance.
AC

• Follow-Ups:
  • Re: Mathematica cannot simplify a product of UnitStep functions
    • From: yehuda ben-shimol <bsyehuda@gmail.com>