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Re: negative pattern matching anyone?

• To: mathgroup at smc.vnet.net
• Subject: [mg43775] Re: negative pattern matching anyone?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Sat, 4 Oct 2003 02:04:53 -0400 (EDT)
• Organization: The University of Western Australia
• References: <blcqqj$p8h$1@smc.vnet.net> <blgio6$fvm$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <blgio6$fvm$1 at smc.vnet.net>,
 Paul Abbott <paul at physics.uwa.edu.au> wrote:

> > Then, is there a way to match both -3 and -a with the same pattern?
> 
> Yes -- use Sign:
> 
>    h[x_] := Abs[-x] /; Sign[x] == -1
>    h[x_] := x^2

I forgot to mention that also you need to declare a to be positive:

   h[x_] := Abs[-x] /; Sign[x] == -1
   h[x_] := x^2

   Sign[a] ^= 1;

   h[-3]
   3

   h[-a]
   Abs[a]

   h[a]
   a^2

To me it doesn't make sense for h[-x] to evaluate to Abs[x] unless x is 
positive and, a priori, this is not known. Indeed, it would probably be 
better to define

   Clear[h]
   h[x_] := Abs[-x] /; Sign[x] == -1
   h[x_] := x^2 /; Sign[x] == 1

so that h[x] and h[-x] remain unevaluated unless Sign[x] is declared.
   
Finally, what is the application? There are possibly other better ways 
to approach such problems.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
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