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Re: Bugs in Abs and Sign !?

• To: mathgroup at smc.vnet.net
• Subject: [mg25705] Re: [mg25674] Bugs in Abs and Sign !?
• From: Tomas Garza <tgarza01 at prodigy.net.mx>
• Date: Thu, 19 Oct 2000 04:35:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I guess it's just a matter of how Abs[] works. Take

In[1]:=
Abs[x^2] // FullForm
Out[1]//FullForm=
Power[Abs[x], 2]

This says that the calculation of Abs[x^2] proceeds by taking first the 
absolute value of x, and then squaring it. This procedure gives the 
right result. However, for an arbitrary function g,

In[2]:=
g[x^2] // FullForm
Out[2]//FullForm=
g[Power[x, 2]]

i.e., first square the argument and then apply g, which is what one 
might expect. Why does Abs[] goes in a different way? That is why one 
gets

In[3]:=
Abs[x^2] /. Abs[u_] -> fnt[u]
Out[4]=
fnt[x]^2

instead of fnt[x^2]. But I wouldn't call it a bug - it's just the way 
Abs[] calculates, and it gives the right result.

Tomas Garza
Mexico City

Jack Goldberg  <jackgold at umich.edu> wrote:

> Try,
>
> Abs[x^2] /. Abs[u_] -> fnt[u]
>
> and
>
> Sign[x^2] /. Sign[u_] -> fnt[u]
>
> In each case I get  fnt[x]^2.  Shouldn't I get  fnt[x^2]? After all,
> g[x^2] /. g[u_] -> fnt[u]  returns fnt[x^2] which is what I have been 
led
> to expect from Mathematica.  I am using ver 4.01 on a PowerMac.
>
> These peculiarities are driving me crazy.  This is the fourth "bug" I 
have
> found in just 2 weeks.  Please tell me I'm wrong.