Merge pull request #922 from GarkGarcia/discrete-limit

Implement the DiscreteLimit builtin

Author: GarkGarcia

CHANGES.rst

@@ -12,6 +12,7 @@ Major package dependencies ave been up dated to more recent releases. These incl
 
 New features:
 
+- ``DiscreteLimit`` #922
 - ``IterationLimit``
 - support for ``MATHICS_MAX_RECURSION_DEPTH``
 - ``RemoveDiacritics[]``, ``Transliterate[]`` #617

mathics/builtin/calculus.py

@@ -962,6 +962,62 @@ def apply(self, expr, x, x0, evaluation, options={}):
             return from_sympy(result)
 
 
+class DiscreteLimit(Builtin):
+    """
+    <dl>
+    <dt>'DiscreteLimit[$f$, $k$->Infinity]'
+        <dd>gives the limit of the sequence $f$ as $k$ tends to infinity.
+    </dl>
+
+    >> DiscreteLimit[n/(n + 1), n -> Infinity]
+     = 1
+
+    >> DiscreteLimit[f[n], n -> Infinity]
+     = f[Infinity]
+    """
+
+    # TODO: Make this work
+    """
+    >> DiscreteLimit[(n/(n + 2)) E^(-m/(m + 1)), {m -> Infinity, n -> Infinity}]
+     = 1 / E
+    """
+
+    attributes = ('Listable',)
+
+    options = {
+        'Trials': '5',
+    }
+
+    messages = {
+        'dltrials': "The value of Trials should be a positive integer",
+    }
+
+    def apply(self, f, n, n0, evaluation, options={}):
+        'DiscreteLimit[f_, n_->n0_, OptionsPattern[DiscreteLimit]]'
+
+        f = f.to_sympy(convert_all_global_functions=True)
+        n = n.to_sympy()
+        n0 = n0.to_sympy()
+
+        if n0 != sympy.oo:
+            return
+
+        if f is None or n is None:
+            return
+
+        trials = options['System`Trials'].get_int_value()
+
+        if trials is None or trials <= 0:
+            evaluation.message('DiscreteLimit', 'dltrials')
+            trials = 5
+
+        try:
+            return from_sympy(sympy.limit_seq(f, n, trials))
+        except:
+            pass
+            
+
+
 class FindRoot(Builtin):
     r"""
     <dl>