> Well, the rule seems clear: the expression for (say) Y involves every 
> coordinate except Y itself. I never realised it actually matters which 
> order you put them in...

Your initial algorithm would fail even the most basic test of the cross 
product:

x cross y = z
y cross z = x
z cross x = y

where x = (1,0,0), y = (0,1,0), z = (0,0,1)

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