homogenization for ideal with ZZ^m grading

docs/src/CommutativeAlgebra/ideals.md

@@ -248,11 +248,11 @@ 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::Int = 1)
+homogenization(f::MPolyRingElem, W::Union{ZZMatrix, Matrix{<:IntegerUnion}}, var::VarName; pos::Union{Int,Nothing}=nothing)
 ```
 
 ```@docs
-homogenization(f::MPolyRingElem, var::VarName, pos::Int=1)
+homogenization(f::MPolyRingElem, var::VarName; pos::Union{Int,Nothing}=nothing)
 ```
 
 ```@docs

experimental/PlaneCurve/src/AffinePlaneCurve.jl

@@ -522,7 +522,7 @@ function arithmetic_genus(C::AffinePlaneCurve)
    K = base_ring(parent(F))
    R, (x, y, z) = polynomial_ring(K, ["x", "y", "z"])
    T, _ = grade(R)
-   G = homogenization(F, T, 3)
+   G = homogenization(F, T; pos=3)
    D = ProjPlaneCurve(G)
    return arithmetic_genus(D)
 end
@@ -551,7 +551,7 @@ function geometric_genus(C::AffinePlaneCurve)
    K = base_ring(parent(F))
    R, (x, y, z) = polynomial_ring(K, ["x", "y", "z"])
    T, _ = grade(R)
-   G = homogenization(F, T, 3)
+   G = homogenization(F, T; pos=3)
    D = ProjPlaneCurve(G)
    return geometric_genus(D)
 end