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Re: Piecewise functions

• To: mathgroup at smc.vnet.net
• Subject: [mg8953] Re: [mg8876] Piecewise functions
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Mon, 6 Oct 1997 01:59:21 -0400
• Sender: owner-wri-mathgroup at wolfram.com

Venkateswara Rao Ayyadevara <va2a+ at andrew.cmu.edu>
mg8876] Piecewise functions

> I would like to know how to represent piecewise linear functions in
> Mathematica.  I tried searching on-line help but could not find  
any > info regarding this.

Venkat,
In addition to the ways given by Stephen Luttrell in [mg8906] you  
might like to try the following.

f[x_] := Which[ x<=0,-x,True,x];

This can be extended:

?Which
"Which[test1, value1, test2, value2, ... ] evaluates each of the  
testi in  turn, returning the value of the valuei corresponding to  
the first one that yields True."

This and the Dirac function approach allow the function f to be  
differentiated by using f' or, for example, D[f[x],x]. This is not  
possible with case by case definition as

g[x_]:=-x/;x\[LessEqual]0
g[x_]:=x/;x\[GreaterEqual]0

Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk/training.html
voice:+44 (0)116 2714198
fax: +44 (0)116 2718642
Leicester,  UK