Implement issymmetric and ishermitian (#324)

* Implement issymmetric and ishermitian

* Add tests

* Add comment

* Fix format

* Bump compat of DP

Author: blegat

src/operators.jl

@@ -434,6 +434,8 @@ function LinearAlgebra.hermitian(v::AbstractPolynomialLike, ::Symbol)
     )
     return v
 end
+# This is the same implementation as `LinearAlgebra.ishermitian(::Number)`
+LinearAlgebra.ishermitian(p::AbstractPolynomialLike) = p == conj(p)
 
 LinearAlgebra.transpose(v::AbstractVariable) = v
 LinearAlgebra.transpose(m::AbstractMonomial) = m
@@ -458,6 +460,7 @@ LinearAlgebra.dot(p::AbstractPolynomialLike, x) = p' * x
 
 LinearAlgebra.symmetric_type(PT::Type{<:_APL}) = PT
 LinearAlgebra.symmetric(p::_APL, ::Symbol) = p
+LinearAlgebra.issymmetric(::_APL) = true
 
 # Amazingly, this works! Thanks, StaticArrays.jl!
 """

test/Project.toml

@@ -10,5 +10,5 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 TypedPolynomials = "afbbf031-7a57-5f58-a1b9-b774a0fad08d"
 
 [compat]
-DynamicPolynomials = "0.5"
+DynamicPolynomials = "0.6"
 TypedPolynomials = "0.4"

test/commutative/complex.jl

@@ -82,4 +82,25 @@
         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