Why won't the prime graph correctly?

[Gilles]

(05-23-2019 06:59 PM)toml_12953 Wrote:  

(05-23-2019 03:42 PM)Nigel (UK) Wrote:  HP Prime: (-1)^(1/3) gives an error in Home mode (only integral powers of negative numbers allowed) and a complex result in CAS mode.

On my Prime in Home mode I get 0.500000000001+0.866025403784*i

I have "Allow complex output from real input" checked in settings.

I think that's the correct behavior. It's old for me but my teachers always teached me that the |C set is a superset of |R (wich is a superset of |Q, which is superset of Z, wich is superset of |N). From a mathematical point of view, you can have no solution in |R and one (or more) solution in |C, but you cant have a principal solution in |R wich is different in |C : it is not consistant. It will be like to get a different result in |N and in |R: a nonsense. But i'm not mathematician and I'm interested of mathematicien point of view. Perhaps i'm wrong.

Edit : the graph of the NSPIRE (up), are inconsistant in this point of view.