Question: radical into RootOf

Hello people in mapleprimes,

I am reading Introduction to Maple. There, the following input and output appear.

> convert((-8)^(1/3), RootOf);
1+RootOf(_Z^2 + 3, index = 1)

I think, which implies



with the solution alpha of alpha^2+3=0, beta above is expressed as 1+alpha.

But, probably from my understanding being wrong, I can't understand why this becomes so.

So, though this is about mathematics, not about maple, if possible, can I ask you to teach me why

convert((-8)^(1/3), RootOf) brings 1+RootOf(_Z^2 + 3, index = 1)?

Thanks in advance.


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