class_docstr: This class represents an integer partition.
  
  Explanation
  ===========
  
  In number theory and combinatorics, a partition of a positive integer,
  ``n``, also called an integer partition, is a way of writing ``n`` as a
  list of positive integers that sum to n. Two partitions that differ only
  in the order of summands are considered to be the same partition; if order
  matters then the partitions are referred to as compositions. For example,
  4 has five partitions: [4], [3, 1], [2, 2], [2, 1, 1], and [1, 1, 1, 1];
  the compositions [1, 2, 1] and [1, 1, 2] are the same as partition
  [2, 1, 1].
  
  See Also
  ========
  
  sympy.utilities.iterables.partitions,
  sympy.utilities.iterables.multiset_partitions
  
  References
  ==========
  
  .. [1] https://en.wikipedia.org/wiki/Partition_%28number_theory%29
docstr: Return the partition as a dictionary whose keys are the
  partition integers and the values are the multiplicity of that
  integer.
  
  Examples
  ========
  
  >>> from sympy.combinatorics.partitions import IntegerPartition
  >>> IntegerPartition([1]*3 + [2] + [3]*4).as_dict()
  {1: 3, 2: 1, 3: 4}
code: def as_dict(self):
      """Return the partition as a dictionary whose keys are the
      partition integers and the values are the multiplicity of that
      integer.
  
      Examples
      ========
  
      >>> from sympy.combinatorics.partitions import IntegerPartition
      >>> IntegerPartition([1]*3 + [2] + [3]*4).as_dict()
      {1: 3, 2: 1, 3: 4}
      """
      if self._dict is None:
          groups = group(self.partition, multiple=False)
          self._keys = [g[0] for g in groups]
          self._dict = dict(groups)
      return self._dict
  
imports: from sympy.core import Basic, Dict, sympify, Tuple
  from sympy.core.numbers import Integer
  from sympy.core.sorting import default_sort_key
  from sympy.core.sympify import _sympify
  from sympy.functions.combinatorial.numbers import bell
  from sympy.matrices import zeros
  from sympy.sets.sets import FiniteSet, Union
  from sympy.utilities.iterables import flatten, group
  from sympy.utilities.misc import as_int
  from collections import defaultdict
label_desc: Use image node_id 4 for calling the IntegerPartition obj's underlying member method code with example usage: obj.as_dict() and returns: self