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Re: ? ? ? ! ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8305] Re: [mg8223] ? ? ? ! ?
  • From: jpk at max.mpae.gwdg.de
  • Date: Sun, 24 Aug 1997 04:46:50 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

> From me at talmanl.mscd.edu Wed Aug 20 05:35:00 1997
> Date: Tue, 19 Aug 1997 21:12:03 -0400
> From: Lou Talman <me at talmanl.mscd.edu>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg8305] [mg8223] ? ? ? ! ?
> 
> Can anyone explain what v3.0 of Mathematica thinks it's doing when it
> executes
> 
>      Plot[Abs'[x], {x, -3/10, 3/10}]
> 
> ???
> 
> Note the prime:  The first argument of Plot was Abs'[x], not Abs[x].
> 
> The strange behavior I see appears both on a PowerMac 7200/120 running
> Mac OS 7.5.3 and on a Wintel box running Windoze 95, so I presume that 
> it isn't platform dependent--or at least, not fully so.
> 
> --Lou Talman
> 
Hi Lou,

Mma does not know that Abs'[x]==Sign[x] and during the Plot[] command it
make a numerical approximation. At x==0 the derivative of Abs doesn't exist
and the numerical approximation fails and give wrong results
with

Unprotect[Derivative]
Derivative[1][Abs][x_]:=Sign[x]
Protect[Derivative]

You will get what You want.

Hope that helps
Jens


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