Allow AbstractVectors as input for initial (oscar-system#4027)

* TropicalGeometry: fixes initial issue oscar-system#4025 * TropicalGeometry: allow point_vector as input for initial * TropicalGeometry: removing unused optional perturbation input * Update src/TropicalGeometry/initial.jl Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com> --------- Co-authored-by: Benjamin Lorenz <benlorenz@users.noreply.github.com>
HechtiDerLachs · Sep 13, 2024 · a292f65 · a292f65
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diff --git a/docs/src/TropicalGeometry/groebner_theory.md b/docs/src/TropicalGeometry/groebner_theory.md
@@ -19,6 +19,6 @@ groebner_basis(I::MPolyIdeal, nu::TropicalSemiringMap, w::Vector{<:Union{QQField
 
 ## Initial forms and initial ideals
 ```@docs
-initial(f::MPolyRingElem, nu::TropicalSemiringMap, w::Vector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}})
-initial(I::MPolyIdeal, nu::TropicalSemiringMap, w::Vector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}; skip_groebner_basis_computation::Bool=false)
+initial(f::MPolyRingElem, nu::TropicalSemiringMap, w::AbstractVector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}})
+initial(I::MPolyIdeal, nu::TropicalSemiringMap, w::AbstractVector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}; skip_groebner_basis_computation::Bool=false)
 ```
diff --git a/src/TropicalGeometry/initial.jl b/src/TropicalGeometry/initial.jl
@@ -5,7 +5,7 @@
 ################################################################################
 
 @doc raw"""
-    initial(f::MPolyRingElem, nu::TropicalSemiringMap, w::Vector; perturbation::Vector=[])
+    initial(f::MPolyRingElem, nu::TropicalSemiringMap, w::Vector)
 
 Return the initial form of `f` with respect to the tropical semiring map `nu` and weight vector `w`.
 
@@ -46,29 +46,19 @@ x + y + 1
 
 ```
 """
-function initial(f::MPolyRingElem, nu::TropicalSemiringMap, w::Vector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}; perturbation::Union{Nothing,Vector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}}=nothing)
-
+function initial(f::MPolyRingElem, nu::TropicalSemiringMap, w::AbstractVector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}})
     ###
     # Evaluate the tropicalization of f and all its terms at w,
     # mark the terms which attain the evaluated value
     ###
     coeffs = collect(coefficients(f))
     expvs = collect(exponents(f))
-    tropTermsEvaluated = [nu(c)*dot(w,alpha) for (c,alpha) in zip(coeffs,expvs)]
+    tropTermsEvaluated = [nu(c)*tropical_semiring(nu)(dot(w,alpha)) for (c,alpha) in zip(coeffs,expvs)]
     tropPolyEvaluated = sum(tropTermsEvaluated)
     termsAttainingValue = findall(isequal(tropPolyEvaluated),tropTermsEvaluated)
     coeffs = coeffs[termsAttainingValue]
     expvs = expvs[termsAttainingValue]
 
-    # if perturbation passed, further filter the marked terms
-    if !isnothing(perturbation)
-        tropTermsEvaluated = [tropical_semiring(nu)(dot(w,alpha)) for (c,alpha) in zip(coeffs,expvs)]
-        tropPolyEvaluated = sum(tropTermsEvaluated)
-        termsAttainingValue = findall(isequal(tropPolyEvaluated),tropTermsEvaluated)
-        coeffs = coeffs[termsAttainingValue]
-        expvs = expvs[termsAttainingValue]
-    end
-
     ###
     # Construct the initial form
     ###
@@ -110,7 +100,7 @@ Ideal generated by
   -2*x^2*y + 3*y^3
 ```
 """
-function initial(I::MPolyIdeal, nu::TropicalSemiringMap, w::Vector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}; skip_groebner_basis_computation::Bool=false)
-    G = (skip_groebner_basis_computation ? gens(G) : groebner_basis(I,nu,w))
+function initial(I::MPolyIdeal, nu::TropicalSemiringMap, w::AbstractVector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}; skip_groebner_basis_computation::Bool=false)
+    G = (skip_groebner_basis_computation ? gens(I) : groebner_basis(I,nu,w))
     return ideal(initial.(G,Ref(nu),Ref(w)))
 end