Re: [q-lang-users] Exponentiation operator

[Rob H. <hub...@gm...>]

I would prefer either:

(1) Always a float, or
(2) A value of a type as simple as possible (up to the simplicity of the 
arguments perhaps): thus Int if possible, otherwise Rational if 
possible, otherwise Real if possible, otherwise (perhaps) Complex (e.g. 
(-1)^(1/2) would be complex).

That is, I think either
(1) no attempt at all should be made to return an exact value in a 
suitable type; a Float should be returned where possible (i.e. where 
defined and Real), or
(2) a thorough attempt should be made.

With (2), I would like to see (1 over 100)^(1 over 2) return (1 over 10).

I would also expect the algorithm for (2) know that (N over 1) is an 
integer.

On the other hand, I would not expect the algorithm to recognise that 
e.g. 0.5 = 1/2. It's fair for the algorithm to assume that a value 
expressed in a given inexact type can not be expressed exactly as a 
simpler type.

[Perhaps there should be operators to do both.]

When both (1) and (2) produce values, those values should be "equal" (in 
some sense; the problem is of course that you can't rely on testing 
equality of floats). That's quite a tall order as X^(1/N) has N complex 
values, so great care would need to be taken in choosing the "principal 
value".

One possibility for the algorithm is to (a) first find a complex value, 
then (b) attempt a series of simplifications somehow.

That doesn't really answer the question does it??

Rob.