JA homogenizer (#3344)

* Revised interface for homogenization (old UI still there)

* Removed excess semicolon in doctest

* First revision after feedback via Slack

* Restored correct operation (was temporarily disabled for testing)

* Fixed ambiguity to do with positive grading

* New Homogenizer/Dehomogenizer UI; removed old homogenization code

* Added default values of kwargs to the doc

* Updated doc for new homogenization UI

* Fixed docstring for dehomogenizer

* Workaround for limitation in Documenter

* Improved example by printing an ideal

* Updated defn of degree(ideal) to use new homogenization UI

docs/src/CommutativeAlgebra/ideals.md

@@ -262,17 +262,31 @@ equidimensional_hull_radical(I::MPolyIdeal)
 Referring to [KR05](@cite) for definitions and technical details, we discuss homogenization and dehomogenization in the context of $\mathbb Z^m$-gradings. 
 
 ```@docs
-homogenization(f::MPolyRingElem, W::Union{ZZMatrix, Matrix{<:IntegerUnion}}, var::VarName; pos::Union{Int,Nothing}=nothing)
+homogenizer(P::MPolyRing{T}, h::VarName; pos::Int=1+ngens(P))  where T
+homogenizer(P::MPolyRing{T}, W::Union{ZZMatrix, Matrix{<:IntegerUnion}}, h::VarName; pos::Int)  where T
+dehomogenizer(H::Homogenizer)
 ```
 
-```@docs
-homogenization(f::MPolyRingElem, var::VarName; pos::Union{Int,Nothing}=nothing)
-```
+```jldoctest
+julia> P, (x, y) = polynomial_ring(QQ, ["x", "y"]);
 
-```@docs
-dehomogenization(F::MPolyDecRingElem, pos::Int)
+julia> I = ideal([x^2+y, x*y+y^2]);
+
+julia> H = homogenizer(P, "h");
+
+julia> Ih = H(I)     # homogenization of ideal I
+Ideal generated by
+  x*y + y^2
+  x^2 + y*h
+  y^3 + y^2*h
+
+julia> DH = dehomogenizer(H);
+
+julia> DH(Ih) == I   # dehomogenization of Ih
+true
 ```
 
+
 ## Ideals as Modules
 
 ```@docs

src/AlgebraicGeometry/Curves/AffinePlaneCurve.jl

@@ -318,11 +318,9 @@ end
 Return the projective closure of `C`.
 """
 function projective_closure(C::AffinePlaneCurve)
-   F = defining_equation(C)
-   K = base_ring(C)
-   T, (x, y, z) = graded_polynomial_ring(K, ["x", "y", "z"])
-   G = homogenization(F, T; pos=3)
-   D = plane_curve(G)
+  F = defining_equation(C)
+  H = homogenizer(parent(F), "z")
+  return plane_curve(H(F))
 end
 
 geometric_genus(C::AffinePlaneCurve) = geometric_genus(projective_closure(C))

src/Rings/groebner.jl

@@ -174,13 +174,16 @@ function standard_basis(I::MPolyIdeal; ordering::MonomialOrdering = default_orde
       K = iszero(characteristic(R)) && !haskey(I.gb, degrevlex(R)) ? _mod_rand_prime(I) : I
       S = base_ring(K)
       gb = groebner_assure(K, degrevlex(S))
-      K_hom = homogenization(K, "w")
-      gb_hom = IdealGens((p -> homogenization(p, base_ring(K_hom))).(gens(gb)))
+      # 2024-02-09 Next lines "blindly" updated to use new homogenization UI
+      H = homogenizer(S, "w")
+      K_hom = H(K)
+      gb_hom = IdealGens(H.(gens(gb)))
       gb_hom.isGB = true
       K_hom.gb[degrevlex(S)] = gb_hom
       singular_assure(K_hom.gb[degrevlex(S)])
       hn = hilbert_series(quo(base_ring(K_hom), K_hom)[1])[1]
-      J = homogenization(I, "w")
+      H2 = homogenizer(R, "w")
+      J = H2(I)
       weights = ones(Int, ngens(base_ring(J)))
       target_ordering = _extend_mon_order(ordering, base_ring(J))
     end
@@ -191,7 +194,8 @@ function standard_basis(I::MPolyIdeal; ordering::MonomialOrdering = default_orde
     if base_ring(I) == base_ring(J)
       I.gb[ordering] = GB
     else
-      GB_dehom_gens = [dehomogenization(p, base_ring(I), 1) for p in gens(GB)]
+      DH2 = dehomogenizer(H2)
+      GB_dehom_gens = DH2.(gens(GB))
       I.gb[ordering] = IdealGens(GB_dehom_gens, ordering, isGB = true)
     end
   elseif algorithm == :f4