bug: `parent`: punning and piracy

[nsajko]

parent is a function defined in Base.

• AbstractAlgebra reuses the same function, parent, with completely different semantics. This is a bug and is known as type punning.

• This approach also leads to type piracy, xref issue Type piracy in AbstractAlgebra #1387.

This is quite bad, but the fix should be straightforward, while possibly somewhat breaking for dependents:

• Introduce a new function with the same name, parent, but owned by AbstractAlgebra, or by one of its submodules.

• Then dependents may need to do using AbstractAlgebra: parent to disambiguate between Base.parent and AbstractAlgebra.parent.

It might also make sense to introduce a public alias for AbstractAlgebra.parent with a different name, to help dependents with name clashes. For example, AbstractAlgebra.parent_abstractalgebra.

[fingolfin]

I don't think it would be "somewhat breaking", it would be just "breaking" for anyone using OSCAR (parent is one of our most central functions).

I'd be OK with trying to get rid of the type piracy (the types where it is used for are not used by OSCAR -- they are just there to have at least some "interesting" rings in AbstractAlgebra, i.e., pure Julia)

I am not sure I agree with your classification of "type punning" as a bug. What concrete issues does it cause?

[fingolfin]

To get rid of the type piracy, we could say good-bye to trying to treat BigInt or Rational{BigInt} as "ring element types" and replace them with, say IntegerRingElem and RationalRingElem (or so) zero-cost struct wrappers. That would also allow reducing the use of the RingElement union (which always confuses people and causes other issues). The downside is that it also would be breaking (but hopefully not for OSCAR and anything using it), and maybe other issues I can't think of right now?