From 8b944a051a9b118edcd98309e5a2d651e8376b5c Mon Sep 17 00:00:00 2001
From: rocky <rb@dustyfeet.com>
Date: Sat, 28 Dec 2024 10:21:26 -0500
Subject: [PATCH] Add rule for ArcTan[ComplexInfinity]

Fixes #510
---
 mathics/builtin/numbers/trig.py   | 1 +
 test/builtin/numbers/test_trig.py | 7 +++++++
 2 files changed, 8 insertions(+)

diff --git a/mathics/builtin/numbers/trig.py b/mathics/builtin/numbers/trig.py
index 8ea925163..21a25f8e1 100644
--- a/mathics/builtin/numbers/trig.py
+++ b/mathics/builtin/numbers/trig.py
@@ -557,6 +557,7 @@ class ArcTan(MPMathFunction):
     rules = {
         "ArcTan[0]": "0",
         "ArcTan[1]": "Pi/4",
+        "ArcTan[DirectedInfinity[]]": "Indeterminate",
         "ArcTan[Undefined]": "Undefined",
         "ArcTan[Undefined, x_]": "Undefined",
         "ArcTan[y_, Undefined]": "Undefined",
diff --git a/test/builtin/numbers/test_trig.py b/test/builtin/numbers/test_trig.py
index dbe01c2d4..22aec0da5 100644
--- a/test/builtin/numbers/test_trig.py
+++ b/test/builtin/numbers/test_trig.py
@@ -8,6 +8,7 @@
 from test.helper import check_evaluation
 
 import pytest
+from sympy.core.numbers import ComplexInfinity
 
 
 def test_ArcCos():
@@ -29,6 +30,12 @@ def test_ArcCos():
 @pytest.mark.parametrize(
     ("str_expr", "msgs", "str_expected", "fail_msg"),
     [
+        (
+            "ArcTan[ComplexInfinity]",
+            None,
+            "Indeterminate",
+            "Rule added for Arctan[ComplexInfinity]",
+        ),
         ("ArcTan[-1, 1]", None, "3 Pi / 4", None),
         ("ArcTan[1, -1]", None, "-Pi / 4", None),
         ("ArcTan[-1, -1]", None, "-3 Pi / 4", None),