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Generating inverse functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3493] Generating inverse functions
  • From: "T. Daniel Crawford" <crawdad at zopyros.ccqc.uga.edu>
  • Date: Mon, 18 Mar 1996 00:56:42 -0500
  • Organization: Center for Computational Quantum Chemistry
  • Sender: owner-wri-mathgroup at wolfram.com

I was wondering if anyone out there has any advice for me on the 
construction of the inverse of a function supplied by the user.
These functions have only symbolic arguments.  For example,

The user provides us with:

func[i] = 1; func[j] = 2; func[k] = 3; func[l] = 4;

We would like to automatically construct the inverse function:

funcInverse[1] = i;
funcInverse[2] = j;
funcInverse[3] = k;
funcInverse[4] = l;

Perhaps this question has an obvious answer, but I don't see it.  Of
course, if the functions were numerical and we knew their domain and
range, we could simply generate the inverse with a loop.  In this case,
though, we don't know what domain the original function might have.  Is
there a way to use Mathematica's stored values for the original function
to build the inverse?

Thanks in advance for any help you can provide!
-Daniel
-- 
T. Daniel Crawford			Center for Computational Quantum
crawdad at otanes.ccqc.uga.edu			    Chemistry

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