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Re: Options in self-defined functions

	Meader's book on Programming in Mathematica offers a very 
informative discussion on defining options, here is the gist of it.  
Lets say we are defining a function f which takes one argument and we 
want it to have an option called Opt.  We first define the default taking 
into consideration that we may want to add more options later.

Options[f] = {Opt->defaultval};

Next we define the function with a line to extract the default value from 
Options[f] or to take a user defined value if they input one, and finally 
include some expression involving the value of Opt and the argument of 
our function which was the reason we wanted to define a function in the 
first place.

f[x_,opts___Rule] := 
	opt = Opt /. {opts} /. Options[f];
	expression involving opt and x

Note that the triple underscore pattern object opts___Rule is neccessarry 
because we want to allow the user to give no option setting if they so 
choose, and of course we only want to allow options of the form lhs -> rhs 
after the first argument.  Here is a more concrete example, power[x] squaring 
x by default but allowing us to change exponent if we want to.

Options[power] = {exponent->2};

power[x_,opts___Rule] := 
	exp = exponent /. {opts} /. Options[power];

.                                         R              
L                                         E               
I             Anthony Rebello             |       
V              Knox  College              T                           
E             Math Department             H                 
|                                         E              
L                                         |      

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