Use `Set` in `UnionDomain` to avoid redundancy and ordering about domainsets.jl HOT 4 CLOSED

This has been implemented in approxfun-support, foolishly, since it's just going to make things harder... but it's definitely the right approach I think: I can't see any reason for UnionDomain to benefit from having a Tuple or Vector of domains over a Set.

from domainsets.jl.

Indeed, foolish: I reverted iit in approxfun-support, since ApproxFun's PiecewiseSpace needs to have an ordering in order to interpret the coefficients, and in places in the code it assumes this ordering is consistent with the ordering of UnionDomain.

I might try making this change again as it still feels "right" for it to be a Set. ApproxFun can work around this by calling domain.(s.spaces) instead of domain(s).domains.

from domainsets.jl.

JuliaLang/julia#23746 also makes working with Sets annoying, however

from domainsets.jl.

Currently, the type of the list of domains is a parameter (DD), so it can be chosen freely. The idea was to allow both tuples and vectors: a tuple would be fully typed, making the union domain fast. The vector could allow for a long list of subdomains, but it would be fast only if they all had the same type. Yet, I don't think we ever relied on a UnionDomain being fast.

Set sounds like it would make the code shorter and clearer, which is good. I think we currently also have some code that enumerates over the subdomains, but I'd be surprised if the ordering matters anywhere - it shouldn't and if it does we can fix it.

from domainsets.jl.