From fd5346df35cdf3657459973888041813589bb903 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Sat, 2 Nov 2024 15:13:21 -0500
Subject: [PATCH 1/8] Fix and test lcm([1//2, 1//2]) == 1//1

---
 base/intfuncs.jl | 3 ++-
 test/intfuncs.jl | 7 +++++++
 2 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index e8d4b65305be7..6874a919bc04e 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -150,7 +150,8 @@ gcd(a::T, b::T) where T<:Real = throw(MethodError(gcd, (a,b)))
 lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))
 
 gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
-lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc; init=one(eltype(abc)))
+lcm(abc::AbstractArray{<:Integer}) = reduce(lcm, abc; init=one(eltype(abc)))
+lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc) # lcm has no identity over the reals.
 
 function gcd(abc::AbstractArray{<:Integer})
     a = zero(eltype(abc))
diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index 6f1bde69dddfe..325df5fd4ab24 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -191,6 +191,13 @@ end
 
         @test lcm(T[2, 4, 6]) ⟷ T(12)
     end
+
+    # Issue #55379
+    @test lcm([1//2; 1//2]) === lcm([1//2, 1//2]) === lcm(1//2, 1//2) === 1//2
+    @test gcd(Int[]) === 0
+    @test lcm(Int[]) === 1
+    @test gcd(Rational{Int}[]) === 0//1
+    @test_throws ArgumentError lcm(Rational{Int}[])
 end
 
 ⟷(a::Tuple{T, T, T}, b::Tuple{T, T, T}) where T <: Union{Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128} = a === b

From 4f06ad09c7f266a43c35c3e10d01d91394e7d9a7 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Mon, 4 Nov 2024 07:28:00 -0600
Subject: [PATCH 2/8] restore `lcm(Rational{Int}[]) === 1//1`

---
 base/intfuncs.jl | 3 +--
 test/intfuncs.jl | 2 +-
 2 files changed, 2 insertions(+), 3 deletions(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index 6874a919bc04e..d230a1da0ea0f 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -150,8 +150,7 @@ gcd(a::T, b::T) where T<:Real = throw(MethodError(gcd, (a,b)))
 lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))
 
 gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
-lcm(abc::AbstractArray{<:Integer}) = reduce(lcm, abc; init=one(eltype(abc)))
-lcm(abc::AbstractArray{<:Real}) = reduce(lcm, abc) # lcm has no identity over the reals.
+lcm(abc::AbstractArray{<:Real}) = isempty(abc) ? one(eltype(abc)) : reduce(lcm, abc) # lcm(Rational[]) is not an identity
 
 function gcd(abc::AbstractArray{<:Integer})
     a = zero(eltype(abc))
diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index 325df5fd4ab24..ddf105a328da7 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -197,7 +197,7 @@ end
     @test gcd(Int[]) === 0
     @test lcm(Int[]) === 1
     @test gcd(Rational{Int}[]) === 0//1
-    @test_throws ArgumentError lcm(Rational{Int}[])
+    @test lcm(Rational{Int}[]) === 1//1
 end
 
 ⟷(a::Tuple{T, T, T}, b::Tuple{T, T, T}) where T <: Union{Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128} = a === b

From 232402d1bbd65fbe9611621c0881ebfb047b0e98 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Mon, 4 Nov 2024 11:11:57 -0600
Subject: [PATCH 3/8] Fix `lcm([-1])`

---
 base/intfuncs.jl | 8 +++++++-
 1 file changed, 7 insertions(+), 1 deletion(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index d230a1da0ea0f..bc5d7b2844641 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -150,7 +150,13 @@ gcd(a::T, b::T) where T<:Real = throw(MethodError(gcd, (a,b)))
 lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))
 
 gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
-lcm(abc::AbstractArray{<:Real}) = isempty(abc) ? one(eltype(abc)) : reduce(lcm, abc) # lcm(Rational[]) is not an identity
+function lcm(abc::AbstractArray{<:Real})
+    # Setting init=one(eltype(abc)) is buggy for Rationals.
+    l = length(abc)
+    l == 0 && return one(eltype(abc))
+    l == 1 && return abs(only(abc))
+    return reduce(lcm, abc)
+end
 
 function gcd(abc::AbstractArray{<:Integer})
     a = zero(eltype(abc))

From 79d3f770bcb13ce810d1cb7798713c4e68a30523 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Mon, 4 Nov 2024 11:12:34 -0600
Subject: [PATCH 4/8] Update comment

---
 base/intfuncs.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index bc5d7b2844641..ae7cd016fe245 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -151,7 +151,7 @@ lcm(a::T, b::T) where T<:Real = throw(MethodError(lcm, (a,b)))
 
 gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
 function lcm(abc::AbstractArray{<:Real})
-    # Setting init=one(eltype(abc)) is buggy for Rationals.
+    # Using reduce with init=one(eltype(abc)) is buggy for Rationals.
     l = length(abc)
     l == 0 && return one(eltype(abc))
     l == 1 && return abs(only(abc))

From 2ef55d8fbef398a5c34ddcd989b4a2a9c13ae2a6 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Tue, 31 Dec 2024 07:24:31 -0600
Subject: [PATCH 5/8] Make `lcm(Rational[])` throw.

---
 base/intfuncs.jl | 5 ++++-
 test/intfuncs.jl | 2 +-
 2 files changed, 5 insertions(+), 2 deletions(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index ae7cd016fe245..69b7f0386ce01 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -153,7 +153,10 @@ gcd(abc::AbstractArray{<:Real}) = reduce(gcd, abc; init=zero(eltype(abc)))
 function lcm(abc::AbstractArray{<:Real})
     # Using reduce with init=one(eltype(abc)) is buggy for Rationals.
     l = length(abc)
-    l == 0 && return one(eltype(abc))
+    if l == 0
+        eltype(abc) <: Integer && return one(eltype(abc))
+        throw(ArgumentError("lcm has no identity over $(eltype(abc))"))
+    end
     l == 1 && return abs(only(abc))
     return reduce(lcm, abc)
 end
diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index ddf105a328da7..5375e1ea55cb3 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -197,7 +197,7 @@ end
     @test gcd(Int[]) === 0
     @test lcm(Int[]) === 1
     @test gcd(Rational{Int}[]) === 0//1
-    @test lcm(Rational{Int}[]) === 1//1
+    @test_throws ArgumentError("lcm has no identity on Rational{Int}") lcm(Rational{Int}[])
 end
 
 ⟷(a::Tuple{T, T, T}, b::Tuple{T, T, T}) where T <: Union{Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128} = a === b

From 42c2f825a38f3f0cd152cced648ca3b2f6d2ed93 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Tue, 31 Dec 2024 09:08:56 -0600
Subject: [PATCH 6/8] Fix tests

---
 base/intfuncs.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index 4771e2594373b..13a5007e4c74b 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -155,7 +155,7 @@ function lcm(abc::AbstractArray{<:Real})
     l = length(abc)
     if l == 0
         eltype(abc) <: Integer && return one(eltype(abc))
-        throw(ArgumentError("lcm has no identity over $(eltype(abc))"))
+        throw(ArgumentError("lcm has no identity for $(eltype(abc))"))
     end
     l == 1 && return abs(only(abc))
     return reduce(lcm, abc)

From e296436e752c1169d89ecda3e474762f34e8b577 Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Tue, 31 Dec 2024 12:49:16 -0600
Subject: [PATCH 7/8] Fix typo

---
 test/intfuncs.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index 5375e1ea55cb3..25795bbf8cf6a 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -197,7 +197,7 @@ end
     @test gcd(Int[]) === 0
     @test lcm(Int[]) === 1
     @test gcd(Rational{Int}[]) === 0//1
-    @test_throws ArgumentError("lcm has no identity on Rational{Int}") lcm(Rational{Int}[])
+    @test_throws ArgumentError("lcm has no identity for Rational{Int}") lcm(Rational{Int}[])
 end
 
 ⟷(a::Tuple{T, T, T}, b::Tuple{T, T, T}) where T <: Union{Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128} = a === b

From 9e71fd9ac62110ebd3378d9e6ebe82c8ce6950ba Mon Sep 17 00:00:00 2001
From: Lilith Orion Hafner <lilithhafner@gmail.com>
Date: Wed, 1 Jan 2025 07:20:55 -0600
Subject: [PATCH 8/8] Interpolate in tests

---
 test/intfuncs.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/intfuncs.jl b/test/intfuncs.jl
index 25795bbf8cf6a..38f29344d2f30 100644
--- a/test/intfuncs.jl
+++ b/test/intfuncs.jl
@@ -197,7 +197,7 @@ end
     @test gcd(Int[]) === 0
     @test lcm(Int[]) === 1
     @test gcd(Rational{Int}[]) === 0//1
-    @test_throws ArgumentError("lcm has no identity for Rational{Int}") lcm(Rational{Int}[])
+    @test_throws ArgumentError("lcm has no identity for Rational{$Int}") lcm(Rational{Int}[])
 end
 
 ⟷(a::Tuple{T, T, T}, b::Tuple{T, T, T}) where T <: Union{Int8, UInt8, Int16, UInt16, Int32, UInt32, Int64, UInt64, Int128, UInt128} = a === b