Add is_associated

src/AbstractAlgebra.jl

@@ -871,6 +871,7 @@ export inverse_fn
 export inverse_image_fn
 export inverse_mat
 export invmod
+export is_associated
 export is_compatible
 export is_constant
 export is_degree

src/Rings.jl

@@ -44,6 +44,15 @@ function is_divisible_by(x::T, y::T) where T <: RingElem
    return divides(x, y)[1]
 end
 
+"""
+    is_associated(x::T, y::T) where T <: RingElem
+
+Check if `x` and `y` are associated, i.e. if `x` is a unit times `y`.
+"""
+function is_associated(x::T, y::T) where T <: RingElem
+   return is_divisible_by(x, y) && is_divisible_by(y, x)
+end
+
 ###############################################################################
 #
 #   Evaluation

src/julia/Integer.jl

@@ -149,6 +149,10 @@ function is_divisible_by(a::BigInt, b::UInt)
                                                     (Ref{BigInt}, UInt), a, b))
 end
 
+function is_associated(x::Integer, y::Integer)
+   return x == y || x == -y
+end
+
 ###############################################################################
 #
 #   Exact division

test/Rings-test.jl

@@ -67,3 +67,19 @@ end
   @test is_finite(GF(2))
   @test !is_finite(QQ)
 end
+
+@testset "is_associated" begin
+   F = GF(13)
+   for x in F, y in F
+      @test is_associated(x, y) == (iszero(x) == iszero(y))
+   end
+
+   Fx, x = polynomial_ring(F)
+   f = x^3 + 4x + 3
+   @test is_associated(f, f)
+   @test is_associated(f, 6*f)
+   @test is_associated(7*f, f)
+   @test !is_associated(f, 0*f)
+   @test !is_associated(0*f, f)
+   @test !is_associated(f, 2x^2-x+2)
+end