Re: Mathematica cannot simplify a product of UnitStep functions

• To: mathgroup at smc.vnet.net
• Subject: [mg55136] Re: [mg55118] Mathematica cannot simplify a product of UnitStep functions
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Mon, 14 Mar 2005 03:43:36 -0500 (EST)
• Reply-to: hanlonr at cox.net
• Sender: owner-wri-mathgroup at wolfram.com

```Works fine in v5.1.1

\$Version

5.1 for Mac OS X (January 27, 2005)

e1=UnitStep[x-y];e2=UnitStep[x-z];

Simplify[{e1,e2,e1*e2},x<y<z]

{0,0,0}

FullSimplify[{e1,e2,e1*e2},x<y<z]

{0,0,0}

FunctionExpand[{e1,e2,e1*e2},x<y<z]

{0,0,0}

Bob Hanlon

>
> From: Alain Cochard <alain at geophysik.uni-muenchen.de>
To: mathgroup at smc.vnet.net
> Date: 2005/03/13 Sun AM 04:57:37 EST
> To: mathgroup at smc.vnet.net
> Subject: [mg55136] [mg55118] Mathematica cannot simplify a product of UnitStep
functions
>
> 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
>
>
>

```

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