Add VariableInSetRef and is_variable_in_set

[odow]

Closes #3951

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (812a073) to head (189c1f2).
Report is 3 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff            @@
##            master     #3955   +/-   ##
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  Coverage   100.00%   100.00%           
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  Files           43        43           
  Lines         6054      6085   +31     
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+ Hits          6054      6085   +31     

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[odow]

So thoughts on the naming of these?

[odow]

Nightly is failing because it seems to have lost the ability to infer
https://github.com/jump-dev/MutableArithmetics.jl/blob/cc1be0edc797c3dff5fadbd33371b6c3aec0e158/src/reduce.jl#L42-L52

function fused_map_reduce(op::F, args::Vararg{Any,N}) where {F<:Function,N}
    _check_same_length(args...)
    T = promote_map_reduce(op, _concrete_eltype.(args)...)
    accumulator = neutral_element(reduce_op(op), T)
    buffer = buffer_for(op, T, eltype.(args)...)
    for I in zip(eachindex.(args)...)
        accumulator =
            buffered_operate!!(buffer, op, accumulator, getindex.(args, I)...)
    end
    return accumulator
end

which is kinda-not-surprising. It's pretty weird code that relies on splatting and types and stuff.

[joaquimg]

I mostly like this PR very much.
Name seems fine.

My only concern is the little inconsistency on the macro variable parameters.

All(?) explicit parameters like Bin (binary=true), Int (integer=trey), Bounds (lower...)
Have their own BinaryRef, IntegerRef, LowerBoundRef...

Except for PSD, although we do not have (posdef=true).
As a user I might expect PositiveSemidefiniteSetRef.

Maybe the solution for this is to acknowledge that the PSD key is legacy and remove is almost everywhere in the docs, and only keep it is the variable macro doc with a strong recommendation for the "set =" syntax.

[blegat]

Yes, the PSD is mostly legacy and in PSDCone() should be used

[odow]

The reason we don't have PSDRef is that it is not trivially inferable from the variable index in the way that scalar variable constraints are just the index of the variable.

I don't have strong opinions on PSD. I agree that it's a magic symbol though that doesn't actually exist which makes it hard for new users to reason about. I'll draft a PR that removes PSD from the docs and we can decide what to do.