On 10/1/2013 2:08 AM, John Lapeyre wrote:
>
>
> I see three possible interpretations of this example
> (are there more ?) :
>
> 1. (-1)^(1/6) means one particular root of z^6=-1
> (e.g. the principal root). solve gave the
> correct answer. But perhaps solve should have
> applied rectform itself.
Not really. The triple of 3 solutions is well defined for ANY
consistent choice of a particular root. If you pick one of
the 3 solutions and you care for a particular root to be chosen,
you could choose such a root by providing an isolating box
in the complex plane. That's what an "analyst" would say.
>
> 2. the meaning of (-1)^(1/6) depends on the context.
> eg if it appears at the top-level of expressions
> in a list of three elements, then it means
> the same root in each case, maybe a specific
> root. This is obviously problematic.
You don't need 3 elements in a list. You could have sqrt(2) + sqrt(2).
If you are allowed to choose any of the square roots, each time, you
could come
up with zero.
>
> 3. (-1)^(1/6) means any one of the the six roots,
> or maybe all of them. It's up to the user to
> decide. In this case, solve gave an incorrect answer
> and this is a bug in solve.
Let r be a solution to an algebraic equation. The answer is
a function of r. That's what an algebraist would say, anyway.
RJF