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Re: multiple outputs from a function

  • To: mathgroup at
  • Subject: [mg52834] Re: multiple outputs from a function
  • From: "John Jowett" <John.Jowett at>
  • Date: Tue, 14 Dec 2004 05:59:32 -0500 (EST)
  • Organization: CERN
  • References: <cpekeh$744$>
  • Sender: owner-wri-mathgroup at


As several people have pointed out, returning a list of values is probably
the most straightforward thing to do. It's fine as long as you know what the
elements in the list are supposed to be.

But another technique that is often useful is to return a list of rules. To
give a trivial example:

f[x_,y_]:={sum->x+y,difference->x-y,product->x y, quotient-> x/y}


{sum -> 3, difference -> -1, product -> 2, quotient -> 1/2}

These results can then be used in other expressions:



For less trivial examples see the built-in function Solve or functions like
LocationReport in the standard package Statistics`DescriptiveStatistics`.

This is a way to provide a number of "named" results without worrying about
order in the list (in some other programming languages something similar is
achieved with so-called "associative arrays").

John Jowett

"Ben Barrowes" <barrowes at> wrote in message
news:cpekeh$744$1 at
> I feel I must be missing something fundamental...
> How do you write a function (or ?) in Mathematica which produces more
> than one output?
> Let's say I have some data and I want a single function to calculate the
> mean, variance, std, etc, more than one thing and return those? I know
> that there are builtin functions for those parameters, but the point is
> I want to define functions with more than one output.
> The only examples I can find are along the lines of:
> f[x_,y_]:=x^2+y^2;
> which have only a single result.
> Is there a different structure altogether, such as a Subroutine, which
> allows multiple results from a single subunit?
> One thought I had was that because Mathematica treats everything as
> global unless defined specifically local (e.g. in a module), that
> variables used in a procedure would be accessible and would thus be a
> "result", but it seems scoping problems would arise if this was used too
> often. For example:
> In[67]:=
> t1[x_,y_]:=(a1=x^2+y;a2=x+y^2;x+y)
> In[68]:=
> t2=t1[5,6]
> Out[68]=
> 11
> In[69]:=
> a1
> Out[69]=
> 31
> In[70]:=
> a2
> Out[70]=
> 41
> Is this the accepted method for extracting multiple results from one
> function definition?
> Ben Barrowes

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