RangeEnclosures

[blegat]

We could use RangeEnclosures for computing the abstraction.
It has an interface with a list of solvers so if our abstraction based solvers are parametrized by a AbstractEnclosureAlgorithm then they automatically support any alogrithm implementing the RangeEnclosures API !
It's still only for scalar output but in their paper, they say vector output is planned, let's keep an eye on it !
If what we still want to use what we are currently doing by default, we could implement it as a solver and have it as default solver.

cc @schillic @mforets @lucaferranti

[schillic]

Just a heads up that this already works with the default algorithm if you can deal with tuple outputs:

# 1D input, 2D output

julia> f(x) = (x, 2x);

julia> X = interval(1..2)
[1.0, 2.0]

julia> enclose(f, X)
(Interval{Float64}(1.0, 2.0), Interval{Float64}(2.0, 4.0))

# 2D input, 2D output

julia> g((x, y)) = (x, 2y);

julia> Y = IntervalBox(1..2, 3..4)
[1.0, 2.0] × [3.0, 4.0]

julia> enclose(g, Y)
(Interval{Float64}(1.0, 2.0), Interval{Float64}(6.0, 8.0))

[schillic]

I also just added a PR for better support of vector outputs, at least for some of the solvers, in JuliaReach/RangeEnclosures.jl#175. But it may require some discussions before that gets in.