AA with complex keytype?

[Frits van Bommel]

Manfred Nowak wrote:
> For complex numbers comparisons other than == and != are not defined.

Indeed.

> AA's require classes to have comparisons defined.

Also correct.

> Why are AA's of complex numbers allowed?

For one thing, complex numbers aren't classes :P.


Seriously: AA's use the TypeInfo.compare() method to compare. For 
complex types, this is implemented as lexicographical ordering (compare 
the real parts, and return the result unless it's equal; in that case, 
return the result of comparing the imaginary parts).

The reason "<" and friends aren't defined for complex types is that 
there's no definition that makes any mathematical sense (at least, not 
more than other definitions).
Fortunately, AA's don't require the ordering to make any mathematical 
sense at all, they just need some way to decide in what order to put 
them in a binary three if a hash collision should occur. As long as the 
order is consistent[1] (a < b && b < c => a < c, that sort of thing) 
they're happy.


[1]: I'm sure there's a mathematical term for this that I can't 
currently remember.