From aef52636f3a3f5b93568ef1afaeb13a1de80ef36 Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Sun, 22 Dec 2024 18:01:03 +0100
Subject: [PATCH] Add conformance tests for is_unit & is_nilpotent

Also improve is_nilpotent for matrices / matrix ring elements
to work if the base ring is trivial.
---
 src/Matrix.jl                   |  4 +--
 test/Rings-conformance-tests.jl | 43 ++++++++++++++++++++++++++++++---
 2 files changed, 42 insertions(+), 5 deletions(-)

diff --git a/src/Matrix.jl b/src/Matrix.jl
index 51f1d885b..cc224a5df 100644
--- a/src/Matrix.jl
+++ b/src/Matrix.jl
@@ -3876,13 +3876,13 @@ Return if `A` is nilpotent, i.e. if there exists a natural number $k$
 such that $A^k = 0$. If `A` is not square an exception is raised.
 """
 function is_nilpotent(A::MatrixElem{T}) where {T <: RingElement}
-  is_domain_type(T) || error("Only supported over integral domains")
   !is_square(A) && error("Dimensions don't match in is_nilpotent")
+  is_zero(A) && return true
+  is_domain_type(T) || error("Only supported over integral domains")
   is_zero(tr(A)) || return false
   n = nrows(A)
   A = deepcopy(A)
   i = 1
-  is_zero(A) && return true
   while i < n
     i *= 2
     A = mul!(A, A, A)
diff --git a/test/Rings-conformance-tests.jl b/test/Rings-conformance-tests.jl
index 3e45769ee..0088b0449 100644
--- a/test/Rings-conformance-tests.jl
+++ b/test/Rings-conformance-tests.jl
@@ -315,14 +315,49 @@ function test_NCRing_interface(R::AbstractAlgebra.NCRing; reps = 50)
          end
       end
 
-      @testset "Basic functions" begin
+      @testset "Basic properties" begin
          @test iszero(R())       # R() is supposed to construct 0 ?
          @test iszero(zero(R))
          @test isone(one(R))
          @test iszero(R(0))
          @test isone(R(1))
-         @test isone(R(0)) || !is_unit(R(0))
+
          @test is_unit(R(1))
+         if is_trivial(R)
+            @test isone(R(0))
+            @test iszero(R(1))
+            @test R(0) == R(1)
+         else
+            @test !is_unit(R(0))
+            for i in 1:reps
+               a = test_elem(R)::T
+               @test is_unit(a) == is_unit(a^2)
+            end
+         end
+
+         # test is_nilpotent if it is supported
+         try
+            f = is_nilpotent(R(1))
+            @test is_nilpotent(R(0))
+            if is_trivial(R)
+               @test is_nilpotent(R(1))
+            else
+               @test !is_unit(R(0))
+               @test !is_nilpotent(R(1))
+               for i in 1:reps
+                  a = test_elem(R)::T
+                  @test !(is_unit(a) && is_nilpotent(a))
+                  @test is_nilpotent(a) == is_nilpotent(a^2)
+                  if is_domain_type(typeof(a))
+                     @test is_nilpotent(a) == is_zero(a)
+                  end
+               end
+            end
+         catch
+         end
+      end
+
+      @testset "hash, deepcopy, equality, printing, parent" begin
          for i in 1:reps
             a = test_elem(R)::T
             @test hash(a) isa UInt
@@ -330,11 +365,13 @@ function test_NCRing_interface(R::AbstractAlgebra.NCRing; reps = 50)
             @test !ismutable(a) || a !== A
             @test equality(a, A)
             @test hash(a) == hash(A)
-            @test parent(a) === parent(A)
+            @test parent(a) === R
             @test sprint(show, "text/plain", a) isa String
          end
          @test sprint(show, "text/plain", R) isa String
+      end
 
+      @testset "Basic arithmetic" begin
          for i in 1:reps
             a = test_elem(R)::T
             b = test_elem(R)::T