Symmetrizing function arguments

• To: mathgroup at smc.vnet.net
• Subject: [mg127608] Symmetrizing function arguments
• From: Hauke Reddmann <fc3a501 at uni-hamburg.de>
• Date: Tue, 7 Aug 2012 03:01:26 -0400 (EDT)
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```I'd like to define a quasi 6j symbol which has tetrahedron
symmetry in its 6 arguments. At the moment (I'm a n00b, still :-)
I use a cheap hack:
f[a_,b_] := If[a>b,F[a,b],F[b,a]];
Bingo, f now is commutative and sorts by descending arguments,
and NOOOOO endless loops. My, am I proud of myself :-)
Needless to say, using this method to implement the symmetries
of h[a_,b_,c_,d_,e_,f] is a royal pain in the backside, as you
see with the hassle needed already for just 3 arguments...
g[a_,b_,c_]:=If[b>c,If[a>c,If[a>b,G[a,b,c],g[b,a,c]],g[c,b,a]],g[a,c,b]];
...especially considering all the subcases needed when two arguments
are equal.
Surely, you can offer a more elegant way? It more or less suffices to
bring the largest value to position 1 and the second-largest to 2 or 3
(assume a,b and c,d and e,f are the opponent edges of the tetrahedron),
but optimal would be if none of the 24 tetrahedron operations gives
a smaller lexicalic ordering even in the case of equal entries.

P.S. No, the inbuilt 6j symbol is useless - wrong Lie group :-)

--
Hauke Reddmann <:-EX8    fc3a501 at uni-hamburg.de
Out on deck the dawn arrived