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Tropicalization of polynomial ideals

Introduction

Tropical varieties can arise as tropicalizations of polynomial ideals. For a general introduction, see

For algorithmic details, see

Main function

tropical_variety — Function
tropical_variety(I::MPolyIdeal, nu::Union{TropicalSemiringMap,Nothing}=nothing; weighted_polyhedral_complex_only::Bool=false, skip_saturation::Bool=false, skip_primary_decomposition::Bool=false)

Return the tropicalization of I with respect to nu as a Vector{TropicalVariety}. If nu==nothing, will compute with respect to the trivial valuation and min convention. If weighted_polyhedral_complex_only==true, will not cache any additional information. If skip_saturation==true, will not saturate I with respect to the product of all variables. If skip_primary_decomposition==true, will not decompose I.

Warning

tropical_variety is currently under development and only works for ideals that primary decompose into principal, linear, and binomial ideals.

Examples

julia> R,(x,y) = QQ[:x, :y];

julia> I = ideal([(x^2+y)*(x+y^2)*(x+y)]);

julia> tropical_variety(I)
3-element Vector{TropicalVariety}:
 Min tropical variety
 Min tropical variety
 Min tropical variety
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