From 0004eaafb3ac8097294f741cc9796036d3656ec0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 28 Feb 2024 12:36:31 +0100
Subject: [PATCH] Add `is_associated`

---
 src/AbstractAlgebra.jl |  1 +
 src/Rings.jl           |  9 +++++++++
 src/julia/Integer.jl   |  4 ++++
 test/Rings-test.jl     | 16 ++++++++++++++++
 4 files changed, 30 insertions(+)

diff --git a/src/AbstractAlgebra.jl b/src/AbstractAlgebra.jl
index da5d59d619..0fe7cd1dd9 100644
--- a/src/AbstractAlgebra.jl
+++ b/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
diff --git a/src/Rings.jl b/src/Rings.jl
index cc02013e26..0b3929006f 100644
--- a/src/Rings.jl
+++ b/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
diff --git a/src/julia/Integer.jl b/src/julia/Integer.jl
index 4db4e9d093..07f0b079fb 100644
--- a/src/julia/Integer.jl
+++ b/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
diff --git a/test/Rings-test.jl b/test/Rings-test.jl
index a790decd07..f4b2f89fe5 100644
--- a/test/Rings-test.jl
+++ b/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