From 55d6c8968ba9730957f88b8be5efc7e70fca4fd0 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Lars=20G=C3=B6ttgens?= <lars.goettgens@rwth-aachen.de>
Date: Wed, 19 Jul 2023 16:02:42 +0200
Subject: [PATCH] Change `is_skewsymmetric_matrix` to `is_alternating` (#2566)

---
 docs/src/Groups/matgroup.md                | 2 +-
 src/Groups/matrices/forms.jl               | 2 +-
 src/Groups/matrices/matrix_manipulation.jl | 8 ++++----
 src/aliases.jl                             | 1 -
 src/exports.jl                             | 1 -
 test/Groups/forms.jl                       | 4 ++--
 test/Groups/operations.jl                  | 9 ++++++---
 7 files changed, 14 insertions(+), 13 deletions(-)

diff --git a/docs/src/Groups/matgroup.md b/docs/src/Groups/matgroup.md
index 92a60cb518fc..6d7cf9347cd9 100644
--- a/docs/src/Groups/matgroup.md
+++ b/docs/src/Groups/matgroup.md
@@ -83,7 +83,7 @@ lower_triangular_matrix(L)
 conjugate_transpose(x::MatElem{T}) where T <: FinFieldElem
 complement(V::AbstractAlgebra.Generic.FreeModule{T}, W::AbstractAlgebra.Generic.Submodule{T}) where T <: FieldElem
 permutation_matrix(F::Ring, Q::AbstractVector{<:IntegerUnion})
-is_skewsymmetric_matrix(B::MatElem{T}) where T <: RingElem
+is_alternating(B::MatElem)
 is_hermitian(B::MatElem{T}) where T <: FinFieldElem
 ```
 
diff --git a/src/Groups/matrices/forms.jl b/src/Groups/matrices/forms.jl
index 5651c7361989..c4af34fce75f 100644
--- a/src/Groups/matrices/forms.jl
+++ b/src/Groups/matrices/forms.jl
@@ -26,7 +26,7 @@ mutable struct SesquilinearForm{T<:RingElem}
       elseif sym==:symmetric
          @assert is_symmetric(B) "The matrix is not symmetric"
       elseif sym==:alternating
-         @assert is_skewsymmetric_matrix(B) "The matrix is not skew-symmetric"
+         @assert is_alternating(B) "The matrix does not correspond to an alternating form"
       elseif sym != :quadratic
          error("Unsupported description")
       end
diff --git a/src/Groups/matrices/matrix_manipulation.jl b/src/Groups/matrices/matrix_manipulation.jl
index 9af03cb9111c..8db452851600 100644
--- a/src/Groups/matrices/matrix_manipulation.jl
+++ b/src/Groups/matrices/matrix_manipulation.jl
@@ -160,15 +160,15 @@ permutation_matrix(F::Ring, p::PermGroupElem) = permutation_matrix(F, Vector(p))
 #
 ########################################################################
 
-# TODO: not sure whether this definition of skew-symmetric is standard (for fields of characteristic 2)
+# TODO: Move to AbstractAlgebra
 """
-    is_skewsymmetric_matrix(B::MatElem{T}) where T <: Ring
+    is_alternating(B::MatElem)
 
-Return whether the matrix `B` is skew-symmetric,
+Return whether the form corresponding to the matrix `B` is alternating,
 i.e. `B = -transpose(B)` and `B` has zeros on the diagonal.
 Return `false` if `B` is not a square matrix.
 """
-function is_skewsymmetric_matrix(B::MatElem{T}) where T <: RingElem
+function is_alternating(B::MatElem)
    n = nrows(B)
    n==ncols(B) || return false
 
diff --git a/src/aliases.jl b/src/aliases.jl
index fd51087f455a..0686c53519f8 100644
--- a/src/aliases.jl
+++ b/src/aliases.jl
@@ -61,7 +61,6 @@
 @alias issemisimple is_semisimple
 @alias issimplicial is_simplicial
 @alias issingular is_singular
-@alias isskewsymmetric_matrix is_skewsymmetric_matrix
 @alias issmooth_curve is_smooth_curve
 @alias issolvable is_solvable
 @alias issupersolvable is_supersolvable
diff --git a/src/exports.jl b/src/exports.jl
index d9ba95c888b6..4f080eab9860 100644
--- a/src/exports.jl
+++ b/src/exports.jl
@@ -802,7 +802,6 @@ export is_semisimple
 export is_simple, has_is_simple, set_is_simple
 export is_simplicial
 export is_singular
-export is_skewsymmetric_matrix
 export is_smooth
 export is_solvable, has_is_solvable, set_is_solvable
 export is_sporadic_simple, has_is_sporadic_simple, set_is_sporadic_simple
diff --git a/test/Groups/forms.jl b/test/Groups/forms.jl
index 058f51893011..f46fa4fe26b9 100644
--- a/test/Groups/forms.jl
+++ b/test/Groups/forms.jl
@@ -3,7 +3,7 @@
    F,z = FiniteField(t^2+1,"z")
 
    B = matrix(F,4,4,[0 1 0 0; 2 0 0 0; 0 0 0 z+2; 0 0 1-z 0])
-   @test is_skewsymmetric_matrix(B)
+   @test is_alternating(B)
    f = alternating_form(B)
    @test f isa SesquilinearForm
    @test gram_matrix(f)==B
@@ -473,7 +473,7 @@ end
    end
    B = Oscar.invariant_quadratic_form(G)
    @testset for g in gens(G)
-      @test is_skewsymmetric_matrix(g.elm*B*transpose(g.elm)-B)
+      @test is_alternating(g.elm*B*transpose(g.elm)-B)
    end
 
    G = GU(4,5)
diff --git a/test/Groups/operations.jl b/test/Groups/operations.jl
index 0e27ed224f99..77b7fe87f88c 100644
--- a/test/Groups/operations.jl
+++ b/test/Groups/operations.jl
@@ -80,16 +80,19 @@ end
    @test f(identity_matrix(F,6))==f(1)*identity_matrix(F,6)
    @test_throws ArgumentError conjugate_transpose(x)
    @test is_symmetric(P+transpose(P))
-   @test is_skewsymmetric_matrix(P-transpose(P))
+   @test is_skew_symmetric(P-transpose(P))
+   @test is_alternating(P-transpose(P))
 
    F,z = FiniteField(2,2)
    x=matrix(F,4,4,[1,z,0,0,0,1,z^2,z,z,0,0,1,0,0,z+1,0])
    y=x+transpose(x)
    @test is_symmetric(y)
    @test is_hermitian(x+conjugate_transpose(x))
-   @test is_skewsymmetric_matrix(y)
+   @test is_skew_symmetric(y)
+   @test is_alternating(y)
    y[1,1]=1
-   @test !is_skewsymmetric_matrix(y)
+   @test is_skew_symmetric(y)
+   @test !is_alternating(y)
    @test conjugate_transpose(x)==transpose(matrix(F,4,4,[1,z+1,0,0,0,1,z,z+1,z+1,0,0,1,0,0,z,0]))
 
 end