Fix degree_complex (#292)

* Fix degree_complex

More consistent behavior of degree_complex and halfdegree
Make assertions into actual checks

* Add example for degree_complex/halfdegree to docstring

* Extend examples

src/complex.jl

@@ -214,26 +214,68 @@ end
 # Also give complex-valued degree definitions. We choose not to overwrite degree, as this will lead to issues in monovecs
 # and their sorting. So now there are two ways to calculate degrees: strictly by considering all variables independently,
 # and also by looking at their complex structure.
+for fn in (:degree_complex, :halfdegree)
+    @eval function $fn(t::AbstractTermLike)
+        realdeg = 0
+        cpdeg = 0
+        conjdeg = 0
+        for (var, exp) in powers(t)
+            if isreal(var)
+                realdeg += exp
+                (isrealpart(var) || isimagpart(var)) && error(
+                    "Cannot calculate complex degrees when real or imaginary parts are present",
+                )
+            else
+                if isconj(var)
+                    conjdeg += exp
+                else
+                    cpdeg += exp
+                end
+            end
+        end
+        return $(
+            fn === :degree_complex ? :(realdeg) : :(div(realdeg, 2, RoundUp))
+        ) + max(cpdeg, conjdeg)
+    end
+end
+
 """
     degree_complex(t::AbstractTermLike)
 
 Return the _total complex degree_ of the monomial of the term `t`, i.e., the maximum of the total degree of the declared
 variables in `t` and the total degree of the conjugate variables in `t`.
 To be well-defined, the monomial must not contain real parts or imaginary parts of variables.
+If `x₁` and `x₂` are real-valued variables and `z₁` and `z₂` are complex-valued,
+- `degree_complex(x₁^2 * x₂^3) = 5`
+- `degree_complex(z₁^3 * conj(z₁)^4) = max(3, 4) = 4` and `degree_complex(z₁^4 * conj(z₁)^3) = max(4, 3) = 4`
+- `degree_complex(z₁^3 * z₂ * conj(z₁)^2 * conj(z₂)^4) = max(4, 6) = 6` and
+  `degree_complex(z₁^4 * z₂ * conj(z₁) * conj(z₂)^3) = max(5, 4) = 5`
+- `degree_complex(x₁^2 * x₂^3 * z₁^3 * z₂ * conj(z₁)^2 * conj(z₂)^4) = 5 + max(4, 6) = 11`
+"""
+degree_complex(t::AbstractTermLike)
+
+"""
+    halfdegree(t::AbstractTermLike)
+
+Return the equivalent of `ceil(degree(t)/2)`` for real-valued terms or `degree_complex(t)` for terms with only complex
+variables; however, respect any mixing between complex and real-valued variables.
+To be well-defined, the monomial must not contain real parts or imaginary parts of variables.
+If `x₁` and `x₂` are real-valued variables and `z₁` and `z₂` are complex-valued,
+- `halfdegree(x₁^2 * x₂^3) = ⌈5/2⌉ = 3`
+- `halfdegree(z₁^3 * conj(z₁)^4) = max(3, 4) = 4` and `halfdegree(z₁^4 * conj(z₁)^3) = max(4, 3) = 4`
+- `halfdegree(z₁^3 * z₂ * conj(z₁)^2 * conj(z₂)^4) = max(4, 6) = 6` and
+  `halfdegree(z₁^4 * z₂ * conj(z₁) * conj(z₂)^3) = max(5, 4) = 5`
+- `halfdegree(x₁^2 * x₂^3 * z₁^3 * z₂ * conj(z₁)^2 * conj(z₂)^4) = ⌈5/2⌉ + max(4, 6) = 9`
+"""
+halfdegree(t::AbstractTermLike)
 
+"""
     degree_complex(t::AbstractTermLike, v::AbstractVariable)
 
 Returns the exponent of the variable `v` or its conjugate in the monomial of the term `t`, whatever is larger.
 
 See also [`isconj`](@ref).
 """
-function degree_complex(t::AbstractTermLike)
-    vars = variables(t)
-    @assert(!any(isrealpart, vars) && !any(isimagpart, vars))
-    grouping = isconj.(vars)
-    exps = exponents(t)
-    return max(sum(exps[grouping]), sum(exps[map(!, grouping)]))
-end
 function degree_complex(t::AbstractTermLike, var::AbstractVariable)
     return degree_complex(monomial(t), var)
 end
@@ -243,7 +285,9 @@ function degree_complex(m::AbstractMonomial, v::AbstractVariable)
     deg_c = 0
     c_v = conj(v)
     for (var, exp) in powers(m)
-        @assert(!isrealpart(var) && !isimagpart(var))
+        (isrealpart(var) || isimagpart(var)) && error(
+            "Cannot calculate complex degrees when real or imaginary parts are present",
+        )
         if var == v
             deg += exp
         elseif var == c_v
@@ -253,31 +297,6 @@ function degree_complex(m::AbstractMonomial, v::AbstractVariable)
     return max(deg, deg_c)
 end
 
-"""
-    halfdegree(t::AbstractTermLike)
-
-Return the equivalent of `ceil(degree(t)/2)`` for real-valued terms or `degree_complex(t)` for terms with only complex
-variables; however, respect any mixing between complex and real-valued variables.
-"""
-function halfdegree(t::AbstractTermLike)
-    realdeg = 0
-    cpdeg = 0
-    conjdeg = 0
-    for (var, exp) in powers(t)
-        if isreal(var)
-            realdeg += exp
-        else
-            if isconj(var)
-                conjdeg += exp
-            else
-                @assert(!isrealpart(var) && !isimagpart(var))
-                cpdeg += exp
-            end
-        end
-    end
-    return ((realdeg + 1) >> 1) + max(cpdeg, conjdeg)
-end
-
 """
     mindegree_complex(p::Union{AbstractPolynomialLike, AbstractVector{<:AbstractTermLike}})
 

test/complex.jl

@@ -64,8 +64,11 @@
     @test degree_complex(x * y^2 * conj(y)^3) == 3
     @test degree_complex(x * y^2 * conj(y)^3, x) == 1
     @test degree_complex(x * y^2 * conj(y)^3, y) == 3
+    @test degree_complex(a^5 * x * y^2 * conj(y)^4) == 9
+    @test degree_complex(a^5 * x * y^2 * conj(y)^2) == 8
     @test halfdegree(x * y^2 * conj(y^3)) == 3
-    @test halfdegree(x * a^5 * conj(y)) == 4
+    @test halfdegree(x * a^5 * conj(y^2)) == 5
+    @test halfdegree(x^2 * a^5 * conj(y^2)) == 5
     @test ordinary_variable([x, y, conj(x), a, real(x), imag(y)]) == [x, y, a]
 
     @test subs(4x + 8y^2 - 6x^3, [x, y] => [2 + 4im, 9 - im]) ==