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Re: Define an antisymmetric function

• To: mathgroup at smc.vnet.net
• Subject: [mg107448] Re: Define an antisymmetric function
• From: Torsten Schoenfeld <kaffeetisch at gmx.de>
• Date: Fri, 12 Feb 2010 05:44:33 -0500 (EST)
• References: <hl0r36$uu$1@smc.vnet.net> <201002111307.IAA03558@smc.vnet.net> <hl380m$ekc$1@smc.vnet.net>

On 12.02.10 10:45, Leonid Shifrin wrote:
> ClearAll[G];
> G[a, b] := f[a, b]
> G[a, c] := g[a, c]
> G[b, c] := h[b, c]
> G[x_, y_] := -G[y, x] /;
>    Hold[G[y, x]] =!= (Hold[G[y, x]] /. Most@DownValues[G])

This actually works perfectly fine even if pattern-based definitions are 
involved!  (Pattern-based definitions appear normally in DownValues.)  I 
neglected to mention it, but G[_, _] is also supposed to act as a 
derivative in both slots, e.g. G[x_, y_^2] := 2 G[x, y] y.  Your 
approach handles this gracefully: G[x^2, y] yields -2 x G[y, x].

So, thanks a lot!  Thanks also for all the other suggestions in this 
thread; I learned many nice tricks.

• References:
  • Re: Define an antisymmetric function
    • From: Szabolcs Horvát <szhorvat@gmail.com>