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.
