make // more useful

[thofma]

Problem

As we were reminded of in oscar-system/Oscar.jl#5960, // can lead to nonsense:

julia> RR,_ = residue_ring(ZZ, 100)
(Integers modulo 100, Map: ZZ -> ZZ/(100))

julia> a = RR(9)
9

julia> parent(a)
Integers modulo 100

julia> W = parent(a//a)
Fraction field
  of integers modulo 100

julia> new_j = 10*W(1)
10

julia> inv_new_j = 1/new_j
1//10

julia> inv_new_j^2
Error showing value of type AbstractAlgebra.Generic.FracFieldElem{zzModRingElem}:
ERROR: Impossible inverse in Integers modulo 100

julia> weird = (inv_new_j)^2;

julia> is_zero(1//weird)
true

A possible solution

When we introduced the fraction fields, we did not have the total field of fractions. Nowadays, for a ring R we could do the following:

• if is_domain_type(R), do what we do now,
• if !is_domain_type(R), construct total_field_of_fractions.

[JohnAAbbott]

Good suggestion. While technically this would be a breaking change, the current behaviour is senselesss/just-plain-wrong, so it would be absurd to declare it as a breaking change.