functions: add arg._eval_rewrite_as_sign helper

https://functions.wolfram.com/ComplexComponents/Arg/27/01/05/
diofant · Feb 23, 2023 · 2d0df3f · 2d0df3f
1 parent 6273afc
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diff --git a/diofant/functions/elementary/complexes.py b/diofant/functions/elementary/complexes.py
@@ -572,6 +572,9 @@ def _eval_rewrite_as_atan2(self, arg):
         x, y = re(self.args[0]), im(self.args[0])
         return atan2(y, x)
 
+    def _eval_rewrite_as_sign(self, arg):
+        return -I*log(sign(arg))
+
 
 class conjugate(Function):
     """Returns the complex conjugate of an argument.

diff --git a/diofant/tests/functions/test_complexes.py b/diofant/tests/functions/test_complexes.py
@@ -545,6 +545,8 @@ def test_arg():
     e = (p + 1) + I*(p**2 - 1)
     assert arg(e).args[0] == e
 
+    assert arg(x).rewrite(sign) == -I*log(sign(x))
+
 
 def test_arg_rewrite():
     assert arg(1 + I) == atan2(1, 1)