handle new dim property for Ideals + few simplification in dimension

Author: rprebet

src/algorithms/dimension.jl

@@ -18,17 +18,17 @@ julia> dimension(I)
 ```
 """
 function dimension(I::Ideal{T}) where T <: MPolyRingElem
-    
+
     gb = get(I.gb, 0, groebner_basis(I, complete_reduction = true))
     R = parent(first(gb))
-    res = [trues(ngens(R))]
 
+    res = [trues(ngens(R))]
     lead_exps = (_drl_lead_exp).(gb)
-    for lexp in lead_exps 
+    for lexp in lead_exps
         to_del = Int[]
         new_miss = BitVector[]
+        nz_exps_inds = findall(!iszero, lexp)
         for (i, mis) in enumerate(res)
-            nz_exps_inds = findall(e -> !iszero(e), lexp)
             ind_var_inds = findall(mis)
             if issubset(nz_exps_inds, ind_var_inds)
                 for j in nz_exps_inds
@@ -44,10 +44,7 @@ function dimension(I::Ideal{T}) where T <: MPolyRingElem
         unique!(res)
     end
 
-    length(res) == 0 && return -1
-    max_length = maximum(mis -> length(findall(mis)), res)
-    
-    I.dim = max_length
+    I.dim = isempty(res) ? -1 : maximum(length ∘ findall, res)
     return I.dim
 end
 
@@ -57,6 +54,6 @@ end
 
 function _drl_lead_exp(p::MPolyRingElem)
     exps = collect(Nemo.exponent_vectors(p))
-    _, i = findmax((u -> _drl_exp_vector(u)).(exps))
+    _, i = findmax(_drl_exp_vector, exps)
     return exps[i]
 end

src/algorithms/solvers.jl

@@ -126,12 +126,14 @@ function _core_msolve(
     if jl_dim > 0
         error("Dimension of ideal is greater than zero, no solutions provided.")
     end
+    I.dim = 0
 
     # get rational parametrization
     jl_len  = Base.unsafe_wrap(Array, res_len[], jl_ld)
     nterms  = 0
 
     if jl_dquot == 0
+        I.dim = -1
         C,x = polynomial_ring(QQ,"x")
         I.rat_param = RationalParametrization(Symbol[], ZZRingElem[], C(-1), C(-1), PolyRingElem[])
         I.real_sols = QQFieldElem[]

src/types.jl

@@ -27,7 +27,7 @@ end
 
 mutable struct Ideal{T <: MPolyRingElem}
     gens::Vector{T}
-    dim::Int
+    dim::Union{Int, Nothing}
     gb::Dict{Int, Vector{T}}
     inter_sols::Vector{Vector{Vector{QQFieldElem}}}
     real_sols::Vector{Vector{QQFieldElem}}
@@ -37,9 +37,8 @@ mutable struct Ideal{T <: MPolyRingElem}
     function Ideal(F::Vector{T}) where {T <: MPolyRingElem}
         I = new{T}()
         I.gens = F
-        I.dim  = -1
         I.gb   = Dict()
-
+        I.dim  = nothing
         return I
     end
 end

test/algorithms/dimension.jl

@@ -2,11 +2,14 @@
     R, (x,y) = polynomial_ring(QQ,["x","y"])
     I =  Ideal([x^2,x*y])
     @test isone(dimension(I))
+    @test isone(I.dim)
 
     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 iszero(dimension(I))
+    @test iszero(I.dim)
 
     I = Ideal([R(1)])
     @test dimension(I) == -1
+    @test I.dim == -1
 end

test/algorithms/groebner-bases.jl

@@ -16,7 +16,7 @@
          z^4 + 38*z^3 + 95*z^2 + 95*z
         ]
     @test G == H
-    
+
     I = Ideal([x+2*y+2*z-1, x^2+2*y^2+2*z^2-x, 2*x*y+2*y*z-y])
     G = groebner_basis(I, eliminate=2, intersect=false)
     H = MPolyRingElem[

test/algorithms/solvers.jl

@@ -26,6 +26,7 @@
     @test inter_sols == real_solutions(I, interval=true)
     @test rat_sols == rational_solutions(I)
     @test I.real_sols == real_solutions(I)
+    @test iszero(I.dim)
 
     C, x = polynomial_ring(QQ, "x")
     elim  = 128304*x^8 - 93312*x^7 + 15552*x^6 + 3144*x^5 - 1120*x^4 + 36*x^3 + 15*x^2 - x
@@ -55,11 +56,13 @@
     I = Ideal([x1^2-x2, x1*x3-x4, x2*x4-12, x4^3-x3^2])
     real_solutions(I)
     @test I.rat_param.vars == Symbol[]
+    @test I.dim == -1
 
     I = Ideal([x1^2-x2, x1*x3, x2-12])
 	@test_throws ErrorException real_solutions(I)
     @test_throws ErrorException real_solutions(I, interval=true)
 	@test_throws ErrorException rational_solutions(I)
+    @test isnothing(I.dim)
 
     R, (x, y) = polynomial_ring(QQ,["x","y"])
     # issue 54