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Re: Indefinite numbers of arguments in a function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87844] Re: Indefinite numbers of arguments in a function
  • From: Albert Retey <awnl at arcor.net>
  • Date: Fri, 18 Apr 2008 07:10:16 -0400 (EDT)
  • References: <fu9fnt$c91$1@smc.vnet.net>

Patrick Klitzke wrote:
> Hello everybody,
> Is it possible to define a function in Mathematica, where the numbers of 
> arguments does not matter?
> 
> I know the function Plus is defined like that:
> 
> I call the function with two arguments( for example Plus[5,3]) or I can 
> call the function with five arguments (for example
> Plus[1,6,4,6,8]).
> 
> How can i define a function in Mathematica like that? I know I can 
> define for ever number of arguments a function like that:
> MyPlus[a_,b_]:=a+b
> MyPlus[a_,b_,c_]:=a+b+c
> MyPlus[a_,b_,c_,d_]:=a+b+c+d
> MyPlus[a_,b_,c_,d_,e_]:=a+b+c+d+e
> 
> I also know that I can create a list as one argument:
> 
> MyPlus[list_List] := (
>   m = 0; For[n = 1, n < Length[list] + 1, n++, m += list[[n]] ];
>   m
>    )
> 
> 
> But since there are functions like Plus, there has to be a way to define 
> those kind of functions.
> 
> I would be very glad, if someone could give me his advice.
> 
> Best regards,
> 
> Patrick Klitzke
> 
> email:   philologos14 at gmx.de

Any symbol can have attributes which control how it behaves. The 
attribute you are looking for is Orderless:

In[3]:= SetAttributes[fff,Orderless]
In[6]:= fff[1,2,3,4]==fff[2,4,3,1]
Out[6]= True

How would you know? Check the attributes of Plus and see which fits, if 
in doubt, look them up in the documentation:

In[2]:= Attributes[Plus]
Out[2]= {Flat,Listable,NumericFunction,OneIdentity,Orderless,Protected}


hth,

albert


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