Merge pull request #1536 from mathics/add-GudermannianRules

Add GudermannianRules

CHANGES.rst

@@ -7,6 +7,8 @@ CHANGES
 New builtins
 ++++++++++++
 
+* ``Guidermannian``
+
 Tensor functions:
 
 * ``RotationTransform``

mathics/autoload/rules/GudermannianRules.m

@@ -0,0 +1,16 @@
+Begin["System`"]
+Gudermannian[Undefined]=Undefined;
+Gudermannian[0]=0;
+Gudermannian[2*Pi*I]=0;
+Gudermannian[6/4*Pi*I]=DirectedInfinity[-I];
+Gudermannian[Infinity]=Pi/2;
+Gudermannian[-Infinity]=-Pi/2;
+Gudermannian[ComplexInfinity]=Indeterminate;
+Gudermannian[z_]=2 ArcTan[Tanh[z / 2]];
+(*
+Gudermannian[z_] := Piecewise[{{1/2*[Pi - 4*ArcCot[E^z]], Re[z]>0||(Re[z]==0&&Im[z]>=0 )}}, 1/2 (-Pi + 4 ArcTan[E^z])];
+D[Gudermannian[f_],x_?NotListQ] := Sech[f] D[f,x];
+Derivative[1][InverseGudermannian] := Sec[#] &;
+Derivative[1][Gudermannian] := Sech[#] &;
+*)
+End[]

test/test_gudermannian.py

@@ -0,0 +1,17 @@
+# -*- coding: utf-8 -*-
+"""
+Unit tests from autoload/GudermannianRules.m
+"""
+
+from .helper import check_evaluation
+
+
+def test_gudermannian():
+    for str_expr, str_expected, message in (
+        (
+            "Gudermannian[4.2]",
+            "1.54081",
+            "https://reference.wolfram.com/language/ref/Gudermannian.html",
+        ),
+    ):
+        check_evaluation(str_expr, str_expected, message)