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tropical determinant via Hungarian method #3943

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Jul 18, 2024
Merged

tropical determinant via Hungarian method #3943

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fdcc031
replaced computation of tropical determinant by the 'correct' impleme…
micjoswig Jul 16, 2024
29037d9
Update src/TropicalGeometry/matrix.jl
micjoswig Jul 16, 2024
6163f3d
removed tropical determinant of a matrix whose coeffs are (tropical) …
micjoswig Jul 17, 2024
9078816
tropical determinant triggers error for non-square matrix
micjoswig Jul 17, 2024
05f98be
cleanup
micjoswig Jul 17, 2024
72d4896
cleanup
micjoswig Jul 17, 2024
91334dc
re-add tropical det for julia matrix
benlorenz Jul 18, 2024
c4125c0
cleanup project toml
benlorenz Jul 18, 2024
b99e100
Update src/TropicalGeometry/matrix.jl
benlorenz Jul 18, 2024
7d0e8c7
Update src/TropicalGeometry/matrix.jl
benlorenz Jul 18, 2024
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3 changes: 3 additions & 0 deletions Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -7,15 +7,18 @@ version = "1.2.0-DEV"
AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
AlgebraicSolving = "66b61cbe-0446-4d5d-9090-1ff510639f9d"
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Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
Pkg = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
Polymake = "d720cf60-89b5-51f5-aff5-213f193123e7"
PrettyTables = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
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19 changes: 7 additions & 12 deletions src/TropicalGeometry/matrix.jl
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Expand Up @@ -14,7 +14,9 @@
@doc raw"""
det(A::Generic.MatSpaceElem{<: TropicalSemiringElem})
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Return the tropical determinant of `A`.
Return the tropical determinant of `A`. That is, this function evaluates the tropicalization of the ordinary determinant considered as a multivariate polynomial at `A`.

That computation is equivalent to solving a linear assignment problem from combinatorial optimization. The implementation employs the Hungarian method, which is polynomial time. See Chapter 3 in [Jos21](@cite).

!!! note
This function effectively overwrites the `det` command for tropical matrices. This means that functions like `minors` will use the tropical determinant when used on a tropical matrix.
Expand All @@ -29,15 +31,8 @@ julia> det(A)
(5)
```
"""
function det(A::Generic.MatSpaceElem{R}) where {R<:Union{TropicalSemiringElem,MPolyRingElem{<:TropicalSemiringElem},PolyRingElem{<:TropicalSemiringElem}}}
detA = zero(base_ring(A))
nrows(A)!=ncols(A) && return detA # return tropical zero if matrix not square
for sigma in AbstractAlgebra.SymmetricGroup(nrows(A)) # otherwise follow Leibniz Formula
detA += prod([ A[i,sigma[i]] for i in 1:nrows(A) ])
end
return detA
end

function det(A::Matrix{R}) where {R<:Union{TropicalSemiringElem,MPolyRingElem{<:TropicalSemiringElem},PolyRingElem{<:TropicalSemiringElem}}}
return det(matrix(parent(first(A)),A))
function det(A::Generic.MatSpaceElem{<:TropicalSemiringElem})
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nrows(A)!=ncols(A) && error("Non-square matrix")
T = base_ring(A)
return T(Polymake.tropical.tdet(A))
end
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3 changes: 0 additions & 3 deletions test/TropicalGeometry/matrix.jl
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Expand Up @@ -5,9 +5,6 @@
@testset "det(A::Generic.MatSpaceElem{<:TropicalSemiringElem})" begin
A = Matrix(T[1 2; 3 5]) # (julia) matrix over tropical numbers
@test det(A) == (minOrMax==min ? T(5) : T(6))
R, (x,y) = T[:x,:y]
A = Matrix(identity_matrix(R,2)) # (julia) matrix over tropical polynomials
@test det(A) == one(R)
end
end

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