From 7a20ddf299c54ed94f8ec1591f9d3cc758f2c1f0 Mon Sep 17 00:00:00 2001
From: ThomasBreuer <sam@math.rwth-aachen.de>
Date: Fri, 11 Oct 2024 16:02:56 +0200
Subject: [PATCH 1/2] allow `==` for two groups/group elements in fewer cases

If `_check_compatible` for the two groups in question returns `false`
then throw an exception.
Note that the result is not based only on the types of the arguments
but also on the groups.
---
 src/Groups/GAPGroups.jl    | 21 +++++++++++++++++++--
 test/Groups/conformance.jl |  4 ++++
 2 files changed, 23 insertions(+), 2 deletions(-)

diff --git a/src/Groups/GAPGroups.jl b/src/Groups/GAPGroups.jl
index b71cbaf8509a..2475d290d111 100644
--- a/src/Groups/GAPGroups.jl
+++ b/src/Groups/GAPGroups.jl
@@ -372,9 +372,26 @@ end
 
 Base.:*(x::GAPGroupElem, y::GAPGroupElem) = _prod(x, y)
 
-==(x::GAPGroup, y::GAPGroup) = GapObj(x) == GapObj(y)
+function ==(x::GAPGroup, y::GAPGroup)
+  _check_compatible(x, y; error = false) || throw(ArgumentError("x and y are not compatible"))
+  return GapObj(x) == GapObj(y)
+end
+
+# For two `BasicGAPGroupElem`s,
+# we allow the question for equality if their parents fit together
+# in the sense of `_check_compatible`,
+# and compare the `GapObj`s if this is the case.
+function ==(x::BasicGAPGroupElem, y::BasicGAPGroupElem)
+  _check_compatible(parent(x), parent(y); error = false) || throw(ArgumentError("parents of x and y are not compatible"))
+  return GapObj(x) == GapObj(y)
+end
 
-==(x::BasicGAPGroupElem, y::BasicGAPGroupElem ) = GapObj(x) == GapObj(y)
+# For two `GAPGroupElem`s,
+# if no specialized method is applicable then no `==` comparison is allowed.
+function ==(x::GAPGroupElem, y::GAPGroupElem)
+  _check_compatible(parent(x), parent(y); error = false) || throw(ArgumentError("parents of x and y are not compatible"))
+  throw(ArgumentError("== is not implemented for the given types"))
+end
 
 """
     one(G::GAPGroup) -> elem_type(G)
diff --git a/test/Groups/conformance.jl b/test/Groups/conformance.jl
index e92c09bf2530..dbbc4ceed9f9 100644
--- a/test/Groups/conformance.jl
+++ b/test/Groups/conformance.jl
@@ -60,6 +60,10 @@ include(joinpath(dirname(pathof(AbstractAlgebra)), "..", "test", "Groups-conform
       @test g>h || g==h || g<h
       @test isequal(g,h) || isless(g,h) || isless(h,g)
       end
+
+      F = free_group(1)
+      @test_throws ArgumentError F == G
+      @test_throws ArgumentError gen(F, 1) == g
    end
 
    @testset "Group operations" begin

From 864daad97a7bf42fe19c1162b28fe4633f9d6f0e Mon Sep 17 00:00:00 2001
From: ThomasBreuer <sam@math.rwth-aachen.de>
Date: Fri, 11 Oct 2024 17:19:40 +0200
Subject: [PATCH 2/2] address a comment

---
 src/Groups/GAPGroups.jl | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/Groups/GAPGroups.jl b/src/Groups/GAPGroups.jl
index 2475d290d111..68152aa1ddf6 100644
--- a/src/Groups/GAPGroups.jl
+++ b/src/Groups/GAPGroups.jl
@@ -373,7 +373,7 @@ end
 Base.:*(x::GAPGroupElem, y::GAPGroupElem) = _prod(x, y)
 
 function ==(x::GAPGroup, y::GAPGroup)
-  _check_compatible(x, y; error = false) || throw(ArgumentError("x and y are not compatible"))
+  _check_compatible(x, y)
   return GapObj(x) == GapObj(y)
 end
 
@@ -382,7 +382,7 @@ end
 # in the sense of `_check_compatible`,
 # and compare the `GapObj`s if this is the case.
 function ==(x::BasicGAPGroupElem, y::BasicGAPGroupElem)
-  _check_compatible(parent(x), parent(y); error = false) || throw(ArgumentError("parents of x and y are not compatible"))
+  _check_compatible(parent(x), parent(y))
   return GapObj(x) == GapObj(y)
 end