Add AlgebraicSet and BasicSemialgebraicSet

Author: blegat

src/MultivariatePolynomials.jl

@@ -14,6 +14,8 @@ include("comp.jl")
 include("alg.jl")
 include("diff.jl")
 include("subs.jl")
+include("algebraicset.jl")
+
 include("show.jl")
 
 end # module

src/algebraicset.jl

@@ -0,0 +1,41 @@
+export AlgebraicSet, BasicSemialgebraicSet, addequality!, addinequality!
+# Semialgebraic set described by polynomials with coefficients in T
+abstract AbstractSemialgebraicSet{T}
+
+addequality!{T}(S::AbstractSemialgebraicSet{T}, p) = addequality!(S, VecPolynomial{T}(p))
+addinequality!{T}(S::AbstractSemialgebraicSet{T}, p) = addinequality!(S, VecPolynomial{T}(p))
+
+abstract AbstractBasicSemialgebraicSet{T} <: AbstractSemialgebraicSet{T}
+abstract AbstractAlgebraicSet{T} <: AbstractBasicSemialgebraicSet{T}
+
+addinequality!{T}(S::AbstractAlgebraicSet{T}, p) = throw(ArgumentError("Cannot add inequality to an algebraic set"))
+
+type AlgebraicSet{T} <: AbstractAlgebraicSet{T}
+    p::Vector{VecPolynomial{T}}
+end
+function (::Type{AlgebraicSet{T}}){T}()
+    AlgebraicSet{T}(VecPolynomial{T}[])
+end
+
+
+function Base.convert{T,U}(::Type{AlgebraicSet{T}}, V::AlgebraicSet{U})
+    AlgebraicSet{T}(Vector{VecPolynomial{T}}(V.p))
+end
+
+addequality!{T}(V::AlgebraicSet{T}, p::VecPolynomial{T}) = push!(V.p, p)
+
+type BasicSemialgebraicSet{T} <: AbstractBasicSemialgebraicSet{T}
+    V::AlgebraicSet{T}
+    p::Vector{VecPolynomial{T}}
+end
+function (::Type{BasicSemialgebraicSet{T}}){T}()
+    BasicSemialgebraicSet{T}(AlgebraicSet{T}(), VecPolynomial{T}[])
+end
+
+
+function Base.convert{T,U}(::Type{BasicSemialgebraicSet{T}}, S::BasicSemialgebraicSet{U})
+    BasicSemialgebraicSet{T}(convert(AlgebraicSet{T}, S.V), Vector{VecPolynomial{T}}(S.p))
+end
+
+addequality!{T}(S::BasicSemialgebraicSet{T}, p::VecPolynomial{T}) = addequality!(S.V, p)
+addinequality!{T}(S::BasicSemialgebraicSet{T}, p::VecPolynomial{T}) = push!(S.p, p)

test/algebraicset.jl

@@ -0,0 +1,17 @@
+facts("Algebraic set") do
+    @polyvar x y
+    V = AlgebraicSet{Int}()
+    @fact_throws ArgumentError addinequality!(V, x*y)
+    S = BasicSemialgebraicSet{Int}()
+    addequality!(S, x)
+    addinequality!(S, x^2*y)
+    addequality!(S, 2*x^2*y)
+    @fact typeof(Int32(2)*x^2*y) --> Term{Int32}
+    addequality!(S, Int32(2)*x^2*y)
+    addinequality!(S, 1.0x^2*y)
+    addequality!(S, (6//3)*x^2*y+y)
+    @fact_throws InexactError addinequality!(S, 1.5x^2*y)
+    S = BasicSemialgebraicSet{Float64}(S)
+    @fact typeof(S) --> BasicSemialgebraicSet{Float64}
+    addinequality!(S, 1.5x+y)
+end

test/runtests.jl

@@ -9,6 +9,8 @@ include("comp.jl")
 include("alg.jl")
 include("diff.jl")
 include("subs.jl")
+include("algebraicset.jl")
+
 #include("show.jl")
 
 FactCheck.exitstatus()