Implement ComplexExpand

Clean up ComplexExpand

Added test cases for ComplexExpand

Fix style

mathics/builtin/numbers/hyperbolic.py

@@ -275,6 +275,7 @@ class ComplexExpand(SympyFunction):
     sympy_name = "expand"
 
     def eval(self, expr, evaluation: Evaluation):
+        "ComplexExpand[expr_]"
         return eval_ComplexExpand(expr, ListExpression())
 
     def eval_with_complex_vars(self, expr, vars, evaluation: Evaluation):

mathics/eval/hyperbolic.py

@@ -1,10 +1,19 @@
 """
 Mathics3 builtins from mathics.core.numbers.hyperbolic
 """
+from sympy import Symbol as SympySymbol
+
 from mathics.core.convert.sympy import from_sympy
 
 
 def eval_ComplexExpand(expr, vars):
     sympy_expr = expr.to_sympy()
-    # Turn Re[x] -> x and remove Im[x] for all variables X that are not in vars.
+    sympy_vars = {v.to_sympy() for v in vars.elements}
+    # All vars are assumed to be real
+    replaces = [
+        (fs, SympySymbol(fs.name, real=True))
+        for fs in sympy_expr.free_symbols
+        if fs not in sympy_vars
+    ]
+    sympy_expr = sympy_expr.subs(replaces)
     return from_sympy(sympy_expr.expand(complex=True))

test/builtin/numbers/test_hyperbolic.py

@@ -23,3 +23,14 @@ def test_gudermannian():
         ("Gudermannian[z]", "2 ArcTan[Tanh[z / 2]]"),
     ):
         check_evaluation(str_expr, str_expected)
+
+
+def test_complexexpand():
+    for str_expr, str_expected in (
+        ("ComplexExpand[Sin[x + I y]]", "Cosh[y]*Sin[x] + I*Cos[x]*Sinh[y]"),
+        (
+            "ComplexExpand[3^(I x)]",
+            "3 ^ (-Im[x]) Re[3 ^ (I Re[x])] + I Im[3 ^ (I Re[x])] 3 ^ (-Im[x])",
+        ),
+    ):
+        check_evaluation(str_expr, str_expected)