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Allow AbstractVectors as input for initial #4027

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merged 4 commits into from
Aug 20, 2024
Merged

Allow AbstractVectors as input for initial #4027

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6b48af3
TropicalGeometry: fixes initial issue
YueRen Aug 19, 2024
18b65a7
TropicalGeometry: allow point_vector as input for initial
YueRen Aug 19, 2024
92289bc
TropicalGeometry: removing unused optional perturbation input
YueRen Aug 19, 2024
8a2755c
Update src/TropicalGeometry/initial.jl
YueRen Aug 20, 2024
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4 changes: 2 additions & 2 deletions docs/src/TropicalGeometry/groebner_theory.md
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Expand Up @@ -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)
```
18 changes: 4 additions & 14 deletions src/TropicalGeometry/initial.jl
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Expand Up @@ -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`.

Expand Down Expand Up @@ -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
###
Expand Down Expand Up @@ -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)
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)))
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end
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