Re: Symmetrizing function arguments

*To*: mathgroup at smc.vnet.net*Subject*: [mg127620] Re: Symmetrizing function arguments*From*: Sseziwa Mukasa <mukasa at gmail.com>*Date*: Wed, 8 Aug 2012 03:14:44 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20120807070126.D06C1662F@smc.vnet.net>

You could just sort the arguments: h[{a_,b_},{c_,d_},{e_,f_}]:= Your code here... h[a_,b_,c_,d_,e_,f_]:=h[Sort[{a,b}],Sort[{c,d}],Sort[{e,f}]] or h[a_,b_,c_,d_,e_,f_]:=h[Sort[{a,b},Greater],Sort[{c,d},Greater],Sort[{e,f},Greater]] On Aug 7, 2012, at 3:01 AM, Hauke Reddmann wrote: > 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 > Your grey sweater oversized > The rooftops glimmered before our eyes >

**References**:**Symmetrizing function arguments***From:*Hauke Reddmann <fc3a501@uni-hamburg.de>