I had my doubts and did some quick research
German Wikipedia states that it's disputed, if the cube root of a negative real number was defined.°
I couldn't find it in English sources in the hurry, but I suppose it's the old problem of having functions which fulfill certain qualities like reversibility in order to play well with the whole mathematical model.
In the end you'll have to handle two definitions of odd roots.
Hence your approach to define your own sub cube_root() looks fine for me. :)
°) https://de.wikipedia.org/wiki/Wurzel_(Mathematik)#Wurzeln_aus_negativen_Zahlen
Bezüglich der ungeraden Wurzeln aus negativen Zahlen werden folgende Positionen vertreten:
- Wurzeln aus negativen Zahlen sind generell nicht definiert ...
- Wurzeln aus negativen Zahlen sind definiert ...
update
Here the google translate for the laziest of lazy ...
Regarding the odd roots of negative numbers, the following positions are held:
- Roots of negative numbers are generally undefined...
- Roots of negative numbers are defined...
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