Sorry, Jason, I didn't get it. What would you propose to use in
function lambert_W(x::Number)
...
end
to allow dual and to forbid complex numbers? Or is it some additional test
in the body of the function.
Thanks, Hans Werner
On Wednesday, January 22, 2014 6:31:51 PM UTC+1, Jason Merrill wrote:
>
> On Wednesday, January 22, 2014 4:25:38 AM UTC-8, Stefan Karpinski wrote:
>>
>> I wonder if Dual shouldn't be a subtype of Real. Of course, you can
>> probably have Dual complex numbers as well, but maybe those can be
>> Complex{Dual} in that case.
>>
>
> Complex{Dual} and Dual{Complex} are equally sensible notions. As long as
> du and im commute, they're the same thing. Neither of them are "real"
> numbers in the mathematical sense.
>
> I wanted to make PowerSeries work over complex numbers, but ended up
> restricting them to a Real field for now because the type issues got
> confusing. It would be nice if we had a more precise way to talk about the
> relationship between algebraic number types like this.
>
> Sage is written by number theorists and has an interesting approach to
> defining mathematical objects over various fields. I haven't taken the time
> to understand exactly how their system works, though.
>
