Add builtin PartitionsP[]

Extend combinatorica examples to page 64 or so.

Author: rocky

CHANGES.rst

@@ -13,6 +13,7 @@ New builtins
 * ``CreateTemporary``
 * ``FileNames``
 * ``NIntegrate``
+* ``PartitionsP``
 
 Enhancements
 ++++++++++++

mathics/builtin/combinatorial.py

@@ -7,6 +7,7 @@
 
 import sympy
 from sympy.functions.combinatorial.numbers import stirling
+from sympy.utilities.iterables import partitions
 from mathics.version import __version__  # noqa used in loading to check consistency.
 
 from mathics.builtin.base import Builtin
@@ -105,6 +106,24 @@ def apply(self, n, evaluation):
         return Integer(sympy.fibonacci(n.get_int_value()))
 
 
+class PartitionsP(Builtin):
+    """
+    <dl>
+      <dt>'PartitionsP[$n$]'
+      <dd>return the number $p$($n$) of unrestricted partitions of the integer $n$.
+    </dl>
+
+    >> Table[PartitionsP[k], {k, 0, 12}]
+     = {1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77}
+    """
+
+    attributes = ("Listable", "NumericFunction", "Orderless")
+
+    def apply(self, n, evaluation):
+        "PartitionsP[n_Integer]"
+        return Integer(len(list(partitions(n.get_int_value()))))
+
+
 class _NoBoolVector(Exception):
     pass
 

test/test_combinatorica.py

@@ -472,7 +472,33 @@ def test_combinations_1_5():
             "{Range[5]} ",
             "KSubsets[l, k] == Length(l)",
         ),
-        # Start here in section 2.1 ...
+    ):
+        check_evaluation(str_expr, str_expected, message)
+
+def test_2_1_to_2_3():
+
+    for str_expr, str_expected, message in (
+        (
+            # 2.1.1 - 2.1.3 are broken
+            "PartitionsP[10]",
+            "NumberOfPartitions[10]",
+            "Counting Partitions 2.1.4, Page 57",
+        ),
+        (
+            "NumberOfCompositions[6,3]",
+            "28",
+            "Random Compositions 2.2.1, Page 60",
+        ),
+        (
+            "TableauQ[{{1,2,5}, {3,4,5}, {6}}]",
+            "True",
+            "Young Tableau 2.3, Page 63",
+        ),
+        (
+            "TableauQ[{{1,2,5,9,10}, {5,4,7,13}, {4,8,12},{11}}]",
+            "False",
+            "Young Tableau 2.3, Page 63",
+        ),
     ):
         check_evaluation(str_expr, str_expected, message)