Sagemath: `a = -1.0; (a)^(1/3)` returns a complex number

Question

Running the following snippet:

a = -1.0
show(a^(1/3))

Gives me the (unexpected) result:

0.500000000000000+0.866025403784439i

But, running the following:

show(-1.0^(1/3))

Gives me the expected result −1.00000000000000.

Is this expected behavior? Am I misunderstanding what computation I'm asking for?

Answer 1

The first version calculates the principal cube root of -1, which is a complex number.

In the second version, the expression -1.0^(1/3) is equivalent to -(1.0^(1/3)), because the unary negation operator has a lower precedence than exponentiation; so it calculates the cube root of 1, and then negates it.