Misc tweaks...

* Correct behavior when only one complex variable has been given
* Add "ComplexExpand" to CHANGES.rst
* More ComplexExpand doctests
* Correct url links

CHANGES.rst

@@ -104,6 +104,7 @@ New Builtins
 #. ``$PythonImplementation``
 #. ``Accuracy``
 #. ``ClebschGordan``
+#. ``ComplexExpand`` (@yzrun)
 #. ``Curl`` (2-D and 3-D vector forms only)
 #. ``DiscretePlot``
 #. ``Kurtosis``

mathics/builtin/numbers/hyperbolic.py

@@ -251,24 +251,47 @@ class ArcTanh(_MPMathFunction):
 
 class ComplexExpand(SympyFunction):
     """
-    <url>
-    :SymPy:
-    https://docs.sympy.org/latest/modules/core.html#sympy.core.expr.Expr.expand
-    :WMA:
-    https://reference.wolfram.com/language/ref/ExpandComplex.html</url>)
+        (<url>
+        :SymPy:
+        https://docs.sympy.org/latest/
+    modules/core.html#sympy.core.expr.Expr.expand</url>, <url>:WMA:
+        https://reference.wolfram.com/language/ref/ComplexExpand.html
+        </url>)
 
-    <dl>
-      <dt>'ComplexExpand[$expr$]'
-      <dd>expands $expr$ assuming that all variables are real.
-    </dl>
+        <dl>
+          <dt>'ComplexExpand[$expr$]'
+          <dd>expands $expr$ assuming that all variables are real.
+        </dl>
+
+        Note: we get equivalent, but different results from WMA:
+
+        >> ComplexExpand[3^(I x)]
+         = 3 ^ (-Im[x]) Re[3 ^ (I Re[x])] + I Im[3 ^ (I Re[x])] 3 ^ (-Im[x])
+
+        Assume that both and are real:
+        >> ComplexExpand[Sin[x + I y]]
+         = Cosh[y] Sin[x] + I Cos[x] Sinh[y]
+
+        Take $x$ to be complex:
+
+        >> ComplexExpand[Sin[x], x]
+         = Cosh[Im[x]] Sin[Re[x]] + I Cos[Re[x]] Sinh[Im[x]]
+
+        Polynomials:
+        >> ComplexExpand[Re[z^5 - 2 z^3 - z + 1], z]
+         = 1 + Re[z] ^ 5 - 2 Re[z] ^ 3 - Re[z] - 10 Im[z] ^ 2 Re[z] ^ 3 + 5 Im[z] ^ 4 Re[z] + 6 Im[z] ^ 2 Re[z]
 
-    Note: we get equivalent, but different results from WMA:
+        Trigonometric and hyperbolic functions
+        >> ComplexExpand[Cos[x + I y] + Tanh[z], {z}]
+         = Cos[x] Cosh[y] - I Sin[x] Sinh[y] + Cosh[Re[z]] Sinh[Re[z]] / (Cos[Im[z]] ^ 2 + Sinh[Re[z]] ^ 2) + I Cos[Im[z]] Sin[Im[z]] / (Cos[Im[z]] ^ 2 + Sinh[Re[z]] ^ 2)
 
-    >> ComplexExpand[3^(I x)]
-     = 3 ^ (-Im[x]) Re[3 ^ (I Re[x])] + I Im[3 ^ (I Re[x])] 3 ^ (-Im[x])
+        Exponential and logarithmic functions:
+        >> ComplexExpand[Abs[2^z Log[2 z]], z]
+         = Abs[I Arg[Re[z] + I Im[z]] + Log[4 Im[z] ^ 2 + 4 Re[z] ^ 2] / 2] 2 ^ Re[z]
 
-    >> ComplexExpand[Sin[x + I y]]
-     = Cosh[y] Sin[x] + I Cos[x] Sinh[y]
+        Specify that a variable is take to be complex:
+        >> ComplexExpand[Re[2 z^3 - z + 1], z]
+         = 1 - Re[z] + 2 Re[z] ^ 3 - 6 Im[z] ^ 2 Re[z]
     """
 
     summary_text = "expand a complex expression of real variables"

mathics/eval/hyperbolic.py

@@ -8,7 +8,10 @@
 
 def eval_ComplexExpand(expr, vars):
     sympy_expr = expr.to_sympy()
-    sympy_vars = {v.to_sympy() for v in vars.elements}
+    if hasattr(vars, "elements"):
+        sympy_vars = {v.to_sympy() for v in vars.elements}
+    else:
+        sympy_vars = {vars.to_sympy()}
     # All vars are assumed to be real
     replaces = [
         (fs, SympySymbol(fs.name, real=True))