Redo PartionsP using SymPy...

alphabetize numbertheory functions.

Author: rocky

mathics/builtin/combinatorial.py

@@ -5,7 +5,6 @@
 
 
 import math
-from functools import lru_cache
 from sympy.functions.combinatorial.numbers import stirling
 from mathics.version import __version__  # noqa used in loading to check consistency.
 
@@ -102,62 +101,6 @@ class Fibonacci(_MPMathFunction):
     sympy_name = "fibonacci"
     mpmath_name = "fibonacci"
 
-# Note: memoizing functions is a big win. For a value of n, more than
-# n different values (positive and negative) occur.
-# For this function to be effective across top-level calls,
-# it needs to be at the module level rather than inside the class.
-# Finally, docs say that `maxsize` is best at a power of 2.
-# With 1024 we can handle reasonably values of slightly greater than 1024
-# values without trouble:
-# PartitionsP[1070] = 366665450770488753893927654278831
-@lru_cache(maxsize=1024)
-def number_of_partitions(n: int) -> int:
-    """Algorithm NumberOfPartitions from Page 67 of Skiena: Implementing
-    Discrete Mathematics, using Euler's recurrence"""
-    if n < 0:
-        return 0
-    elif n == 0:
-        return 1
-    sum = 0
-    for m in range(math.ceil((1 + math.sqrt(1.0 + 24 * n)) / 6), 0, -1):
-        mx3 = m * 3
-        j = n - m * (mx3 - 1) / 2
-        k = n - m * (mx3 + 1) / 2
-        # Cut down on memoization by filtering negative numbers here.
-        # In contrast to the multitude of negative numbers, the n==0
-        # case isn't worth saving memoization checking since that is
-        # one single entry.
-        part_j = 0 if j < 0 else number_of_partitions(j)
-        part_k = 0 if k < 0 else number_of_partitions(k)
-        if m % 2:
-            sum += part_j + part_k
-        else:
-            sum += -part_j - part_k
-    return sum
-
-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, -2, 12}]
-     = {0, 0, 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(number_of_partitions(n.get_int_value()))
-
-        # Simpler but inefficient.
-        # from sympy.utilities.iterables import partitions
-        # return Integer(len(list(partitions(n.get_int_value()))))
-
-
 class _NoBoolVector(Exception):
     pass