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?
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- From: Daniel Lichtblau <danl@wolfram.com>
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