Merge pull request #74 from RafaelDavidMohr/rm/dimension

Adds function for dimension computation

Author: ederc

src/AlgebraicSolving.jl

@@ -12,6 +12,7 @@ include("interfaces/nemo.jl")
 include("algorithms/groebner-bases.jl")
 include("algorithms/normal-forms.jl")
 include("algorithms/solvers.jl")
+include("algorithms/dimension.jl")
 #= siggb =#
 include("siggb/siggb.jl")
 #= examples =#

src/algorithms/dimension.jl

@@ -0,0 +1,50 @@
+@doc Markdown.doc"""
+    dimension(I::Ideal{T}) where T <: MPolyRingElem
+
+Compute the Krull dimension of a given polynomial ideal `I`.
+
+**Note**: This requires a Gröbner basis of `I`. 
+
+# Examples
+```jldoctest
+julia> using AlgebraicSolving
+
+julia> R, (x, y, z) = polynomial_ring(QQ, ["x", "y", "z"]);
+
+julia> I = Ideal([x*y,x*z,y*z]);
+
+julia> dimension(I)
+1
+```
+"""
+function dimension(I::Ideal{T}) where T <: MPolyRingElem
+    
+    gb = isempty(values(I.gb)) ? groebner_basis(I) : first(values(I.gb))
+    R = parent(first(gb))
+    res = [trues(ngens(R))]
+
+    lms = (Nemo.leading_monomial).(gb)
+    for lm in lms
+        to_del = Int[]
+        new_miss = BitVector[]
+        for (i, mis) in enumerate(res)
+            nz_exps_inds = findall(e -> !iszero(e),
+                                   first(Nemo.exponent_vectors(lm)))
+            ind_var_inds = findall(mis)
+            if issubset(nz_exps_inds, ind_var_inds)
+                for j in nz_exps_inds
+                    new_mis = copy(mis)
+                    new_mis[j] = false
+                    push!(new_miss, new_mis)
+                end
+                push!(to_del, i)
+            end
+        end
+        deleteat!(res, to_del)
+        append!(res, new_miss)
+        unique!(res)
+    end
+
+    max_length = maximum(mis -> length(findall(mis)), res)
+    return max_length
+end

src/exports.jl

@@ -1,4 +1,4 @@
 export polynomial_ring, MPolyRing, GFElem, MPolyRingElem, finite_field, GF, fpMPolyRingElem,
        characteristic, degree, ZZ, QQ, vars, nvars, ngens, ZZRingElem, QQFieldElem, QQMPolyRingElem,
        base_ring, coefficient_ring, evaluate, prime_field, sig_groebner_basis, cyclic, leading_coefficient,
-       FqMPolyRingElem
+       FqMPolyRingElem, dimension

test/algorithms/dimension.jl

@@ -0,0 +1,9 @@
+@testset "dimension" begin
+    R, (x,y) = polynomial_ring(QQ,["x","y"])
+    I =  Ideal([x^2,x*y])
+    @test isone(dimension(I))
+
+    R, (x,y,z) = polynomial_ring(GF(101),["x","y","z"])
+    I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y])
+    @test isone(dimension(I))
+end

test/runtests.jl

@@ -6,5 +6,6 @@ include("interfaces/nemo.jl")
 include("algorithms/groebner-bases.jl")
 include("algorithms/normal-forms.jl")
 include("algorithms/solvers.jl")
+include("algorithms/dimension.jl")
 include("examples/katsura.jl")
 end