Add is_diagonal(A::MatrixElem) (#1472)

... as alias for LinearAlgebra.isdiag -- and replacement
for the Nemo method.

docs/src/matrix.md

@@ -439,6 +439,10 @@ is_lower_triangular(::MatrixElem)
 is_upper_triangular(::MatrixElem)
 ```
 
+```@docs
+is_diagonal(::MatrixElem)
+```
+
 ```@docs
 change_base_ring(::Ring, ::MatElem{T}) where T <: RingElement
 ```

src/AbstractAlgebra.jl

@@ -37,6 +37,7 @@ import LinearAlgebra: det
 import LinearAlgebra: hessenberg
 import LinearAlgebra: ishermitian
 import LinearAlgebra: issymmetric
+import LinearAlgebra: isdiag
 import LinearAlgebra: istril
 import LinearAlgebra: istriu
 import LinearAlgebra: lu
@@ -319,8 +320,9 @@ export is_trivial
 @alias is_trivial istrivial
 
 # alternative names for some functions from LinearAlgebra
-export is_hermitian, is_symmetric, is_upper_triangular, is_lower_triangular
+export is_diagonal, is_hermitian, is_symmetric, is_upper_triangular, is_lower_triangular
 
+@alias is_diagonal isdiag
 @alias is_hermitian ishermitian
 @alias is_symmetric issymmetric
 @alias is_lower_triangular istril
@@ -909,6 +911,7 @@ export invmod
 export is_compatible
 export is_constant
 export is_degree
+export is_diagonal
 export is_divisible_by
 export is_domain_type
 export is_exact_type

src/Matrix.jl

@@ -3434,6 +3434,24 @@ function is_lower_triangular(M::MatrixElem)
     return true
 end
 
+@doc raw"""
+    is_diagonal(A::MatrixElem)
+
+Return `true` if $A$ is a diagonal matrix.
+
+Alias for `LinearAlgebra.isdiag`.
+"""
+function is_diagonal(A::MatrixElem)
+    for i = 1:ncols(A)
+        for j = 1:nrows(A)
+            if i != j && !is_zero_entry(A, j, i)
+                return false
+            end
+        end
+    end
+    return true
+end
+
 ###############################################################################
 #
 #   Can solve

test/Matrix-test.jl

@@ -1,3 +1,25 @@
+@testset "Matrix.is_diagonal" begin
+    A = [1 0 0; 0 0 1; 1 0 1]
+    @test !is_diagonal(A)
+    @test !is_diagonal(matrix(ZZ, A))
+
+    A = [1 0 0; 0 0 1; 0 0 1]
+    @test !is_diagonal(A)
+    @test !is_diagonal(matrix(ZZ, A))
+
+    A = [1 0 0; 0 0 1]
+    @test !is_diagonal(A)
+    @test !is_diagonal(matrix(ZZ, A))
+
+    A = [1 0 0; 0 1 0]
+    @test is_diagonal(A)
+    @test is_diagonal(matrix(ZZ, A))
+
+    A = [1 0 0; 0 2 0; 0 0 3]
+    @test is_diagonal(A)
+    @test is_diagonal(matrix(ZZ, A))
+end
+
 @testset "Matrix.is_lower_triangular" begin
     A = [1 0 0; 0 0 1; 1 0 1]
     @test !is_lower_triangular(A)
@@ -14,6 +36,10 @@
     A = [1 0 0; 0 1 0]
     @test is_lower_triangular(A)
     @test is_lower_triangular(matrix(ZZ, A))
+
+    A = [1 0 0; 0 2 0; 0 0 3]
+    @test is_lower_triangular(A)
+    @test is_lower_triangular(matrix(ZZ, A))
 end
 
 @testset "Matrix.is_upper_triangular" begin
@@ -32,6 +58,10 @@ end
     A = [1 0 0; 0 1 0]
     @test is_upper_triangular(A)
     @test is_upper_triangular(matrix(ZZ, A))
+
+    A = [1 0 0; 0 2 0; 0 0 3]
+    @test is_upper_triangular(A)
+    @test is_upper_triangular(matrix(ZZ, A))
 end
 
 @testset "Matrix.concat" begin