UniversalCyclotomicField elements considered real

[gagern]

This is certainly wrong:

sage: UCF.<E> = UniversalCyclotomicField()
sage: E3 = E(3)
sage: E3
E(3)
sage: N(E3)
-0.500000000000000 + 0.866025403784439*I
sage: real(E3)
E(3)
sage: imag(E3)
0

This is probably due to the fact that real and imag aren't methods of this class, even though conjugate seems to work correctly.

sage: E3.conjugate()
E(3)^2
sage: conjugate(E3)
E(3)^2
sage: (E3 + E3.conjugate())/2
-1/2
sage: (E3 - E3.conjugate())/(2*E(4))
-1/2*E(12)^7 + 1/2*E(12)^11

So I'd say these methods should be implemented, building on conjugate. Perhaps the functions will pick the methods up if they do exist, even though #17116 makes me far from certain on this point right now.

Furthermore, if asked explicitely then these objects know that they are not real:

sage: E3.is_real()
False

So the real function might want to call such an is_real method if it exists, and make sure not to simply return its argument if that method returns False.

Component: number fields

Issue created by migration from https://trac.sagemath.org/ticket/17117

[videlec]

comment:2

Hello,

In #18152, I reimplemented the universal cyclotomic field using libgap (faster and more reliable). In that version the issue disappears. My goal would be to close this ticket as "won't fix" as soon as #18152 would be reviewed.

Vincent

[fchapoton]

comment:3

now works with libgap version