Add tests

Author: blegat

src/operators.jl

@@ -434,7 +434,7 @@ function LinearAlgebra.hermitian(v::AbstractPolynomialLike, ::Symbol)
     )
     return v
 end
-LinearAlgebra.ishermitian(::AbstractPolynomialLike) = isreal(v)
+LinearAlgebra.ishermitian(p::AbstractPolynomialLike) = p == conj(p)
 
 LinearAlgebra.transpose(v::AbstractVariable) = v
 LinearAlgebra.transpose(m::AbstractMonomial) = m

test/commutative/complex.jl

@@ -82,4 +82,23 @@
         4x + 8y^2 - 6x^3,
         [x, real(y)] => [2 + 4im, 9 + 0 * x^0],
     ) == 1184 + 112im + 144im * imag(y) - 8imag(y)^2
+
+    @testset "Symmetric and Hermitian" begin
+        p = a + 1
+        P = typeof(p)
+        @test LinearAlgebra.symmetric_type(P) == P
+        @test LinearAlgebra.issymmetric(p)
+        @test LinearAlgebra.symmetric(p, :U) === p
+        @test LinearAlgebra.symmetric(p, :L) === p
+        @test LinearAlgebra.hermitian_type(P) == P
+        @test LinearAlgebra.ishermitian(p)
+        @test LinearAlgebra.hermitian(p, :U) === p
+        @test LinearAlgebra.hermitian(p, :L) === p
+        @test !LinearAlgebra.ishermitian(a + im)
+        q = x + 1
+        @test !LinearAlgebra.ishermitian(q)
+        err = ErrorException("Complex-valued polynomials cannot be interpreted as hermitian scalars")
+        @test_throws err LinearAlgebra.hermitian(q, :U)
+        @test_throws err LinearAlgebra.hermitian(q, :L)
+    end
 end