Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Define an antisymmetric function

• To: mathgroup at smc.vnet.net
• Subject: [mg107396] Define an antisymmetric function
• From: Torsten Schoenfeld <kaffeetisch at gmx.de>
• Date: Thu, 11 Feb 2010 06:54:28 -0500 (EST)

I'd like to define an antisymmetric function by giving its value on a 
set of known objects.  I'm having trouble enforcing antisymmetry.  Say I 
want to define G[_, _] on the objects {a, b, c}:

   G[a, b] := f[a, b]
   G[a, c] := g[a, c]
   G[b, c] := h[b, c]

If I now enforce antisymmetry simply by

   G[x_, y_] := -G[y, x]

then it mostly works (e.g., G[b, a] evaluates to -f[a, b]).  But if I 
apply G to something that is not in {a, b, c}, then I run into an 
infinite loop: G[a, f[b]] yields "$RecursionLimit::reclim: Recursion 
depth of 256 exceeded."

Ideally, I would like applications to unknown input to stay unevaluated 
(e.g., G[a, f[b]] just yields G[a, f[b]]).  How can I achieve that while 
also enforcing antisymmetry?

• Follow-Ups:
  • Re: Define an antisymmetric function
    • From: Daniel Lichtblau <danl@wolfram.com>