Variables of the set

[blegat]

The variables on which a semialgebraic set is currently not defined.
We should add a field containing the ordered list of variables that is by default the union of the variables of all the polynomials defining the set but which can be set to something else.

Current behavior:

julia> using SemialgebraicSets

julia> using DynamicPolynomials

julia> @polyvar x y
(x, y)

julia> S = @set x >= 0 && y >= 0;

julia> variables(S)
ERROR: MethodError: no method matching variables(::BasicSemialgebraicSet{Float64,Polynomial{true,Float64},AlgebraicSet{Float64,Polynomial{true,Float64},Buchberger,SemialgebraicSets.SolverUsingMultiplicationMatrices{SemialgebraicSets.GröbnerBasisMultiplicationMatricesAlgorithm,ReorderedSchurMultiplicationMatricesSolver{Int64,Random.MersenneTwister}}}})
Closest candidates are:
  variables(::SemialgebraicSets.PolynomialIdeal) at /home/blegat/.julia/packages/SemialgebraicSets/64a8D/src/ideal.jl:32
  variables(::Union{AbstractArray{#s26,N} where N where #s26<:(Union{Monomial{C}, PolyVar{C}, Polynomial{C,T} where T, Term{C,T} where T} where C), Union{Monomial{C}, PolyVar{C}, Polynomial{C,T} where T, Term{C,T} where T} where C}) at /home/blegat/.julia/dev/DynamicPolynomials/src/DynamicPolynomials.jl:33
Stacktrace:
 [1] top-level scope at none:0

julia> nvariables(S)
ERROR: MethodError: no method matching nvariables(::BasicSemialgebraicSet{Float64,Polynomial{true,Float64},AlgebraicSet{Float64,Polynomial{true,Float64},Buchberger,SemialgebraicSets.SolverUsingMultiplicationMatrices{SemialgebraicSets.GröbnerBasisMultiplicationMatricesAlgorithm,ReorderedSchurMultiplicationMatricesSolver{Int64,Random.MersenneTwister}}}})
Closest candidates are:
  nvariables(::Union{AbstractArray{#s26,N} where N where #s26<:(Union{Monomial{C}, PolyVar{C}, Polynomial{C,T} where T, Term{C,T} where T} where C), Union{Monomial{C}, PolyVar{C}, Polynomial{C,T} where T, Term{C,T} where T} where C}) at /home/blegat/.julia/dev/DynamicPolynomials/src/DynamicPolynomials.jl:34
  nvariables(::Union{AbstractVariable, Type{#s13} where #s13<:AbstractVariable}) at /home/blegat/.julia/dev/MultivariatePolynomials/src/monomial.jl:38
Stacktrace:
 [1] top-level scope at none:0

julia> variables(S.p)
2-element Array{PolyVar{true},1}:
 x
 y

julia> S.variables
ERROR: type BasicSemialgebraicSet has no field variables

Desired behavior:

julia> using SemialgebraicSets

julia> using DynamicPolynomials

julia> @polyvar x y
(x, y)

julia> S = @set x >= 0 && y >= 0;

julia> variables(S)
2-element Array{PolyVar{true},1}:
 x
 y

julia> nvariables(S)
2

cc @tweisser