diff --git a/docs/src/TropicalGeometry/groebner_theory.md b/docs/src/TropicalGeometry/groebner_theory.md
index e96f1b98ed7d..f697c68affe5 100644
--- 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
index 3c07ab71c63f..32ea2dd64794 100644
--- a/src/TropicalGeometry/initial.jl
+++ b/src/TropicalGeometry/initial.jl
@@ -46,7 +46,7 @@ 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}}; perturbation::Union{Nothing,AbstractVector{<:Union{QQFieldElem,ZZRingElem,Rational,Integer}}}=nothing)
 
     ###
     # Evaluate the tropicalization of f and all its terms at w,
@@ -110,7 +110,7 @@ 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)
+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(G) : groebner_basis(I,nu,w))
     return ideal(initial.(G,Ref(nu),Ref(w)))
 end