add iscall() to the functions real() conj() and imag(); add adjoint(::Symbolic{Number}) method; tests for real and complex syms

Author: ChristophHotter

src/methods.jl

@@ -160,11 +160,36 @@ for f in [identity, one, zero, *, +, -]
 end
 
 promote_symtype(::typeof(Base.real), T::Type{<:Number}) = Real
-Base.real(s::Symbolic{<:Number}) = islike(s, Real) ? s : term(real, s)
 promote_symtype(::typeof(Base.conj), T::Type{<:Number}) = T
-Base.conj(s::Symbolic{<:Number}) = islike(s, Real) ? s : term(conj, s)
 promote_symtype(::typeof(Base.imag), T::Type{<:Number}) = Real
-Base.imag(s::Symbolic{<:Number}) = islike(s, Real) ? zero(symtype(s)) : term(imag, s)
+function Base.real(s::Symbolic{<:Number}) 
+    if iscall(s) 
+        f = operation(s)
+        args = map(real, arguments(s))
+        return f(args...)
+    else
+        islike(s, Real) ? s : term(real, s)
+    end
+end
+function Base.conj(s::Symbolic{<:Number}) 
+    if iscall(s) 
+        f = operation(s)
+        args = map(conj, arguments(s))
+        return f(args...)
+    else
+        islike(s, Real) ? s : term(conj, s)
+    end
+end
+function Base.imag(s::Symbolic{<:Number}) 
+    if iscall(s) 
+        f = operation(s)
+        args = map(imag, arguments(s))
+        return f(args...)
+    else
+        islike(s, Real) ? zero(symtype(s)) : term(imag, s)
+    end
+end
+Base.adjoint(s::Symbolic{<:Number}) = conj(s)
 
 ## Booleans
 

test/basics.jl

@@ -354,3 +354,14 @@ end
     end
     @test repr(sin(x) + sin(x)) == "sin(x) + sin(x)"
 end
+
+@testset "real and complex" begin
+    @syms x y z::Real
+    @test isequal(conj(x*y*z), conj(x)*conj(y)*z)
+    @test isequal(conj(x*y*z + y), conj(x)*conj(y)*z + conj(y))
+    @test isequal(real(x*y*z + y), real(x)*real(y)*z + real(y))
+    @test isequal(imag(x*y*z + y), imag(y))
+    @test isequal(imag(x*y*z + y), imag(y))
+    @test isequal(conj(exp(1im*x)*y), conj(exp(1im*x))*conj(y))
+    @test isequal(adjoint(x*y*z), conj(x)*conj(y)*z)    
+end