But I was talking about mathematical definitions and these are CS standards.

For instance: pure math has no big notion of floating point numbers.

Personally I'm fine with allowing root($x,$o) with $x<0 and $o odd integer in a computer.

But I could imagine reasons in the realm of mathematical modeling of functions to consider them undefined.

> the second argument has a non-integer value

I'd say because there is no way to express 1/$o loss free as binary floating point number ('$o odd integer')

update

see also https://en.wikipedia.org/wiki/Cube_root#Complex_numbers

With this definition, the principal cube root of a negative number is a complex number, and for instance 3√−8 will not be −2, but rather 1 + i√3.