TropicalGeometry: exponentiation for tropical polynomials

Author: YueRen

src/TropicalGeometry/TropicalGeometry.jl

@@ -5,6 +5,7 @@
 ###############################################################################
 include("semiring.jl")
 include("semiring_map.jl")
+include("semiring_mpoly.jl")
 include("matrix.jl")
 include("poly.jl")
 include("homogenization.jl")

src/TropicalGeometry/semiring_mpoly.jl

@@ -0,0 +1,17 @@
+################################################################################
+#
+#  Functionality for multivariate polynomials over tropical semirings
+#  (alternatives for generic functions that do not work over tropical semirings)
+#
+################################################################################
+
+# exponentiation has to be in multiple functions, otherwise calls become ambiguous
+#   due to ^(a::AbstractAlgebra.Generic.MPoly{T}, b::Int64) where T<:RingElement
+#   in AbstractAlgebra/src/generic/MPoly.jl:2257
+function Base.:(^)(a::Generic.MPoly{<:TropicalSemiringElem}, n::Int)
+    @req n>=0 "polynomial exponentiation with negative exponent"
+    return Generic.pow_rmul(a,n)
+end
+function Base.:(^)(a::Generic.MPoly{<:TropicalSemiringElem}, n::ZZRingElem)
+    return Generic.pow_rmul(a,Int(n))
+end

test/TropicalGeometry/semiring.jl

@@ -26,6 +26,12 @@
         @testset "characteristic" begin
             @test characteristic(T) == 0
         end
+
+        @testset "polynomial exponentiation" begin
+            Tx, x = polynomial_ring(T, 1)
+            f = x[1]^4 + 3*x[1]
+            @test f^3 == f*f*f
+        end
     end
 
 end