either characteristic or equality test in localizations of quotients is lying

[thofma]

@HechtiDerLachs For the ring

julia> Qxyz, (x, y, z) = QQ["x", "y", "z"];

julia> I = ideal(Qxyz, x^2 - x, x * y);

julia> Q, = quo(Qxyz, I);

julia> L, = localization(Q, powers_of_element(x) * powers_of_element(x - 1));

I get

julia> iszero(one(L))
true

julia> characteristic(L)
0

Any idea what could be wrong?

P.S.: I got this from an example in the geometry tests, while looking for usages of the zero ring.

[thofma]

I guess the multiplicative set contains zero, so the characteristic is wrong.

[fingolfin]

yeah, this method is overly optimistic:

characteristic(W::AbsLocalizedRing) = characteristic(base_ring(W))