TropicalGeometry: fix tropical_variety_prime_singular

src/Oscar.jl

@@ -178,6 +178,11 @@ function __init__()
       Pkg.is_manifest_current(dirname(Base.active_project())))
     @warn "Project dependencies might have changed, please run `]up` or `]resolve`."
   end
+
+  # Temporary workaround to allow access to Singular's tropicalVariety command
+  # see https://github.com/oscar-system/Oscar.jl/issues/5392
+  Singular.libSingular.load_library("tropical.lib")
+  Singular.call_interpreter("proc tropicalVariety_as_string(ideal I, list #) { if(size(#)==0) { return(string(tropicalVariety(I))); }; return(string(tropicalVariety(I,#[1]))); }")
 end
 
 const PROJECT_TOML = Pkg.TOML.parsefile(joinpath(@__DIR__, "..", "Project.toml"))

src/TropicalGeometry/variety.jl

@@ -221,7 +221,6 @@ julia> vertices(TropI_3)
 ```
 """
 function tropical_variety(I::MPolyIdeal, nu::TropicalSemiringMap=tropical_semiring_map(coefficient_ring(I)); weighted_polyhedral_complex_only::Bool=false, skip_saturation::Bool=false, skip_decomposition::Bool=false)
-
     if !skip_saturation
         ###
         # If saturation requested, saturate `I`

src/TropicalGeometry/variety_prime.jl

@@ -19,16 +19,13 @@ function tropical_variety_prime(I::MPolyIdeal, nu::TropicalSemiringMap; weighted
     return dehomogenize_post_tropicalization(TropIh)
 end
 
+
 # trivial valuation
 function tropical_variety_prime_singular(I::MPolyIdeal, nu::TropicalSemiringMap{QQField,Nothing,<:Union{typeof(min),typeof(max)}}; weighted_polyhedral_complex_only::Bool=false)
-    R = base_ring(I)
-    singularCommand = join(["ring r=0,("*join(string.(symbols(R)),",")*"),dp;",
-                            "ideal I = "*join(string.(gens(I)), ",")*";",
-                            "if (!defined(tropicalVariety)) { LIB \"tropical.lib\"; };",
-                            "fan TropI = tropicalVariety(I);",
-                            "string TropIString = string(TropI);"])
-    Singular.call_interpreter(singularCommand)
-    TropIString = Singular.lookup_library_symbol("Top", "TropIString")
+
+    sI = Oscar.singular_generators(I)
+    TropIString = Singular.low_level_caller("tropical", "tropicalVariety_as_string", sI)
+
     Sigma = gfan_fan_string_to_oscar_complex(TropIString,convention(nu)==max,false)
     TropI = compute_weights_and_construct_tropical_variety(Sigma,I,nu)
     if !weighted_polyhedral_complex_only
@@ -38,8 +35,23 @@ function tropical_variety_prime_singular(I::MPolyIdeal, nu::TropicalSemiringMap{
     return TropI
 end
 
+# Given a polynomial ring S, return a map into an isomorphic polynomial ring S->R
+# but with variables renamed to be Singular compatible.
+# The new names are x1, ..., xn if nvars(R)<10, x01, ..., x10 if nvar(R)<100, etc.
+# zero padding is necessary because Singular interpreter does not like variable names
+# that are substrings of other variable names.
+function hom_rename_variables_singular_compatible(S::MPolyRing)
+    n = nvars(S)
+    l = ndigits(n)
+    newVarNames = [Symbol(:x, lpad(string(i), l, '0')) for i in 1:n]
+    R,x = polynomial_ring(base_ring(S), newVarNames)
+    return hom(S,R,x)
+end
+
 # p-adic valuation
 function tropical_variety_prime_singular(I::MPolyIdeal, nu::TropicalSemiringMap{QQField,ZZRingElem,<:Union{typeof(min),typeof(max)}}; weighted_polyhedral_complex_only::Bool=false)
+    phi = hom_rename_variables_singular_compatible(base_ring(I))
+    I = phi(I)
     R = base_ring(I)
     singularCommand = join(["ring r=0,("*join(string.(symbols(R)),",")*"),dp;",
                             "ideal I = "*join(string.(gens(I)), ",")*";",
@@ -121,7 +133,6 @@ function gfan_fan_string_to_oscar_complex(input_string::String, negateFan::Bool=
         coneIncidences = [ vcat(incidence,[originIndex]) for incidence in coneIncidences ]
         return polyhedral_complex(IncidenceMatrix(coneIncidences), rayGenerators, rayIndices, linealityGenerators)
     end
-
 end
 
 

test/TropicalGeometry/variety.jl

@@ -81,5 +81,8 @@
         @test f_vector(TropV) == [1,3]
 
         # general ideals, see doctests
+        I = grassmann_pluecker_ideal(2, 5)
+        TropI = tropical_variety(I; skip_saturation=true, skip_decomposition=true)
+        @test f_vector(TropI) == [0, 0, 0, 0, 0, 1, 10, 15]
     end
 end