Re: Help in defining nearly orderless function

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1981] Re: Help in defining nearly orderless function
• From: Roman Maeder <maeder at inf.ethz.ch>
• Date: Mon, 4 Sep 1995 22:21:59 -0400
• Organization: Computer Science, ETH Zurich

```Vlad.Fridkin at manuel.anu.edu.au said:
> On the up and up in mathematica I got stuck  with trying to define a
> function

> f[a,b,c,d]

> that satisfies the symmetries:

> f[a,b,c,d] = f[b,a,c,d]

> and

> f[a,b,c,d] = f[a,b,d,c]

Such symmetries are best realized with conditional rules:

In[1]:= f[a_, b_, c_, d_] /; !OrderedQ[{a, b}] := f[b, a, c, d]

In[2]:= f[a_, b_, c_, d_] /; !OrderedQ[{c, d}] := f[a, b, d, c]

In[4]:= f[x, y, u, v] - f[y, x, v, u]

Out[4]= 0

----
Roman Maeder
Theoretical Computer Science
ETH Zentrum, IFW
8092 Zurich
Switzerland

```

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