RegionIntersection/RegionUnion do not promote mixed real types

[tobydriscoll]

Summary

RegionIntersection and RegionUnion cannot combine regions whose real-type parameters differ (e.g. a Float64 region with a BigFloat region).

Details

In src/regions.jl, both structs declare their fields with the same type parameter as the struct, and there is no promoting constructor:

struct RegionIntersection{T} <: AbstractRegion{T}
    one::AbstractRegion{T}
    two::AbstractRegion{T}
end

The corresponding operations are only defined for matching T:

function intersect(R1::AbstractRegion{T}, R2::AbstractRegion{T}) where {T}
    return RegionIntersection(R1, R2)
end

RegionUnion / union have the same shape.

As a result, R_f64 ∩ R_big (and the union equivalent) raises a MethodError because there is no method accepting two different real types. There is an existing # TODO: promote different floating types to common type comment near the struct definitions.

Proposed fix

Add a constructor / method that promotes the two regions to a common real type (via promote_type and convert_real_type) before storing them, so that the stored field types are consistent with the struct's T parameter. Apply to both RegionIntersection/intersect and RegionUnion/union.

Notes

This was previously tracked in a todo.txt file, which has since been removed in favor of GitHub issues.