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MathGroup Archive 1994

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Re: function definition

  • To: mathgroup at christensen.cybernetics.net
  • Subject: Re: function definition
  • From: Richard Mercer <richard at rmercer.wright.edu>
  • Date: Fri, 21 Oct 1994 12:43:09 -0400

>  Can anyone explain the principle for function definition
>  that yields the following:
   ...
>  f2[x_] := x + 3
>  f2[y_] := y + 4
   ...
>  David Kramer  


Sorry, David, but that's how it works! 


Seriously, there are very strong advantages to maintaining multiple function  
definitions for a single symbol, although not in this particular case. What Mma  
does is maintain all definitions with different variables, unfortunately
y_ is considered to be different than x_. This is useful e.g. if you have
f[x_Rational]:= and f[y_Integer]:=
as then you can define different behaviors for different inputs, i.e.  
"overload" the symbol f.

There are also some disadvantages, mostly that it can be very confusing for  
non-experts. In my calcE package (designed to make life with Mma easier for  
students, novices, and people with other things to do), I include a Define[__]  
command that automatically clears all previous definitions for the symbol being  
defined.
e.g. in your situation 

Define[f[y] = y+4] 

would result in
??f
f2[y_] := y + 4

and the standard syntax is still available when you actually want to overload a  
symbol.
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Wright State University                    513-429-2179 fax
Dayton, OH 45435                           NeXTmail welcome!
richard at rmercer.wright.edu        or       rmercer at desire.wright.edu
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