Add low and high method for AbstractHyperrectangles

[mforets]

julia> using LazySets

julia> B = BallInf(ones(2), 1.0)
LazySets.BallInf{Float64}([1.0, 1.0], 1.0)

julia> low(B)
ERROR: MethodError: no method matching low(::LazySets.BallInf{Float64})
Closest candidates are:
  low(::LazySets.Hyperrectangle{N<:Real}) where N<:Real at /Users/forets/.julia/v0.6/LazySets/src/Hyperrectangle.jl:187
  low(::LazySets.Interval) at /Users/forets/.julia/v0.6/LazySets/src/Interval.jl:258

julia> high(B)
ERROR: MethodError: no method matching high(::LazySets.BallInf{Float64})
Closest candidates are:
  high(::LazySets.Hyperrectangle{N<:Real}) where N<:Real at /Users/forets/.julia/v0.6/LazySets/src/Hyperrectangle.jl:169
  high(::LazySets.Interval) at /Users/forets/.julia/v0.6/LazySets/src/Interval.jl:273

[schillic]

Should they be general methods for AbstractHyperrectangles? Then we also need them for AbstractSingleton, but there it is just a call to element(S).

[mforets]

Hmm the AbstractHyperrectangle interface already requires that the radius of the hyperrectangle (as a vector, the radius_hyperrectangle) is implemented.

If we also require that each concrete subtype defines the center, then we can define in the interface the fallback functions

function high(H::AbstractHyperrectangle{N})::Vector{N} where {N<:Real}
    return center(H) .+ radius_hyperrectangle(H)
end

function low(H::AbstractHyperrectangle{N})::Vector{N} where {N<:Real}
    return center(H) .- radius_hyperrectangle(H)
end

do you agree?

[schillic]

👍, then we can remove the implementation in Hyperrectangle.jl which is doing exactly that.