Fallback implementation for inclusion between polytopic sets

[mforets]

julia> typeof.([Rt, Tg])

2-element Array{DataType,1}:
 Zonotope{Float64}                                                         
 MinkowskiSum{Float64,Singleton{Float64,Array{Float64,1}},BallInf{Float64}}

julia> Rt ⊆ Tg

MethodError: no method matching iterate(::MinkowskiSum{Float64,Singleton{Float64,Array{Float64,1}},BallInf{Float64}})
Closest candidates are:
  iterate(!Matched::Core.SimpleVector) at essentials.jl:604
  iterate(!Matched::Core.SimpleVector, !Matched::Any) at essentials.jl:604
  iterate(!Matched::ExponentialBackOff) at error.jl:214
  ...

Stacktrace:
 [1] in(::Array{Float64,1}, ::MinkowskiSum{Float64,Singleton{Float64,Array{Float64,1}},BallInf{Float64}}) at ./operators.jl:1055
 [2] ∉(::Array{Float64,1}, ::MinkowskiSum{Float64,Singleton{Float64,Array{Float64,1}},BallInf{Float64}}) at ./operators.jl:1068
 [3] issubset at /home/mforets/.julia/dev/LazySets/src/ConcreteOperations/issubset.jl:229 [inlined]
 [4] issubset(::Zonotope{Float64}, ::MinkowskiSum{Float64,Singleton{Float64,Array{Float64,1}},BallInf{Float64}}) at /home/mforets/.julia/dev/LazySets/src/ConcreteOperations/issubset.jl:226
 [5] top-level scope at In[187]:1

but

julia> Tg_poly = HPolytope(constraints_list(Tg));
julia>Rt_poly = HPolytope(constraints_list(Rt));
julia>Rt_poly ⊆ Tg_poly 

true

cc: @dfcaporale, @SebastianGuadalupe

[schillic]

The problem is in the membership (see the top of the stack trace).

[mforets]

True, dispatch is trying to use the function the uses the vertices (this one). However, in general it is more efficient and less error-prone to use the support function (this function) which is triggered if one swaps the containment check.

I would add an algorithm choice for ⊆(P::AbstractPolytope{N}, S::LazySet{N}), such that algorithm='vertices' and algorithm='constraints' allows to choose the method, letting the constraints algorithm to be the default one.

[mforets]

For a new method to handle the computation in [1] of the stack trace, i've opened #1793.

[schillic]

I would add an algorithm choice for ⊆(P::AbstractPolytope{N}, S::LazySet{N}), such that algorithm='vertices' and algorithm='constraints' allows to choose the method, letting the constraints algorithm to be the default one.

Sounds good.