Third root of the zero element of the real numbers fails

[HechtiDerLachs]

Try this:

CC = ComplexField(128)
RR = parent(abs(one(CC)))
a = zero(RR)
root(a, 3)

For me the result is nan. This seems to only happen for the third root. root(a, 2) is fine, for instance.

[thofma]

@fredrik-johansson, do you have an idea what is happening here? This is just calling arb_root:

julia> RR = ArbField(64)
Real Field with 64 bits of precision and error bounds

julia> a = zero(ArbField(64))
0

julia> for i in 1:10; @show i, root(a, UInt(i)); end;
(i, root(a, UInt(i))) = (1, 0)
(i, root(a, UInt(i))) = (2, 0)
(i, root(a, UInt(i))) = (3, nan)
(i, root(a, UInt(i))) = (4, 0)
(i, root(a, UInt(i))) = (5, nan)
(i, root(a, UInt(i))) = (6, nan)
(i, root(a, UInt(i))) = (7, nan)
(i, root(a, UInt(i))) = (8, nan)
(i, root(a, UInt(i))) = (9, nan)
(i, root(a, UInt(i))) = (10, nan)

[fredrik-johansson]

Yeah, in some cases the root function uses the formula exp(log(x)/n), but it should then first check for x = 0.

[thofma]

Thanks! I will probably do an is_zero check in Nemo for now.

[HechtiDerLachs]

Good to have this clarified. But what about the case when !(x== 0) but contains_zero(x)==true? Then log(x) is also ill-defined, isn't it? I'm a bit worried that is_zero might not be the correct thing to check.

[thofma]

Hm, the check in Nemo is not quite correct. At the moment it is

x < 0 && throw(DomainError("x must be positive"))

but it should be

is_zero(x) && return x
!isnonnegative(x) && throw(DomainError("x must be positive"))

Or maybe we should only check is_zero and let it return nan whenever it wants to.