Defining two functions at once?

• To: mathgroup at smc.vnet.net
• Subject: [mg70730] Defining two functions at once?
• From: AES <siegman at stanford.edu>
• Date: Wed, 25 Oct 2006 01:39:55 -0400 (EDT)
• Organization: Stanford University

```I want to define two functions at once, where both of their values
depend on the same two variables, and both of their values come out of a
single two-dimensional FindRoot which I'd rather not evaluate twice.

The following approach seems to work fine for a *single* function

f[x_, y_] := Module[{},
myEqns = {f1 - g1 == x1 + 3y1, f1 + g1 == 2x1 - 7y1};
myValues = {x1 -> x, y1 -> y};
mySolns = FindRoot[ myEqns /. myValues, {f1, 0} , {g1, 0}];
f1 /. mySolns]

But if I try to define two functions at once by replacing the first and
last lines with

{f[x_, y_], g[x_,y_]} := Module[{},
myEqns = {f1 - g1 == x1 + 3y1, f1 + g1 == 2x1 - 7y1};
myValues = {x1 -> x, y1 -> y};
mySolns = FindRoot[ myEqns /. myValues, {f1, 0} , {g1, 0}];
{f1, g1} /. mySolns]

I get a message about "shapes not being the same".  In fact, if I just
make the first and last lines even a single element list, e.g.

{f[x_, y_]} := Module[{},
myEqns = {f1 - g1 == x1 + 3y1, f1 + g1 == 2x1 - 7y1};
myValues = {x1 -> x, y1 -> y};
mySolns = FindRoot[ myEqns /. myValues, {f1, 0} , {g1, 0}];
{f1} /. mySolns]

this doesn't work either.

If a module supposedly returns the result of its (compound) expression,
and the final term in that expression is a list, shouldn't the final
example work?  More important (to me anyway): Is there a simple way to
define two functions that use a shared FindRoot evaluation in a way that
(a) evaluates the FindRoot only once, and (b) involves only a single
compound expression of some sort?

```

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