
    MZda                     j    d dl mZ d dlmZ d dlmZ d dlmZ d dlm	Z	 ddl
mZmZmZ  G d d	e      Zy
)    )
_sympifyit)global_parameters)
fuzzy_bool)S)_sympify   )Set	FiniteSetSetKindc                   z     e Zd ZdZd fd	Zed        Zd Z ede	      d        Z
d Zd Zd	 Zed
        Z xZS )PowerSetaE  A symbolic object representing a power set.

    Parameters
    ==========

    arg : Set
        The set to take power of.

    evaluate : bool
        The flag to control evaluation.

        If the evaluation is disabled for finite sets, it can take
        advantage of using subset test as a membership test.

    Notes
    =====

    Power set `\mathcal{P}(S)` is defined as a set containing all the
    subsets of `S`.

    If the set `S` is a finite set, its power set would have
    `2^{\left| S \right|}` elements, where `\left| S \right|` denotes
    the cardinality of `S`.

    Examples
    ========

    >>> from sympy import PowerSet, S, FiniteSet

    A power set of a finite set:

    >>> PowerSet(FiniteSet(1, 2, 3))
    PowerSet({1, 2, 3})

    A power set of an empty set:

    >>> PowerSet(S.EmptySet)
    PowerSet(EmptySet)
    >>> PowerSet(PowerSet(S.EmptySet))
    PowerSet(PowerSet(EmptySet))

    A power set of an infinite set:

    >>> PowerSet(S.Reals)
    PowerSet(Reals)

    Evaluating the power set of a finite set to its explicit form:

    >>> PowerSet(FiniteSet(1, 2, 3)).rewrite(FiniteSet)
    FiniteSet(EmptySet, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3})

    References
    ==========

    .. [1] https://en.wikipedia.org/wiki/Power_set

    .. [2] https://en.wikipedia.org/wiki/Axiom_of_power_set
    c                     |t         j                  }t        |      }t        |t              st        dj                  |            t        | !  | |      S )Nz{} must be a set.)	r   evaluater   
isinstancer	   
ValueErrorformatsuper__new__)clsargr   	__class__s      5/usr/lib/python3/dist-packages/sympy/sets/powerset.pyr   zPowerSet.__new__E   sO    &//Hsm#s#077<==wsC((    c                      | j                   d   S )Nr   )argsselfs    r   r   zPowerSet.argP   s    yy|r   c                 T    | j                   }|j                  r|j                         S y N)r   is_FiniteSetpowerset)r   r   kwargsr   s       r   _eval_rewrite_as_FiniteSetz#PowerSet._eval_rewrite_as_FiniteSetT   s#    hh<<>!r   otherc                 l    t        |t              sy t        | j                  j	                  |            S r   )r   r	   r   r   is_supersetr   r$   s     r   	_containszPowerSet._containsZ   s)    %%$((..u566r   c                 n    t        |t              r%| j                  j                  |j                        S y r   )r   r   r   	is_subsetr'   s     r   _eval_is_subsetzPowerSet._eval_is_subseta   s*    eX&88%%eii00 'r   c                 2    dt        | j                        z  S )N   )lenr   r   s    r   __len__zPowerSet.__len__e   s    CM!!r   c              #      K   t         j                  g}t         j                   | j                  D ]A  }g }t        |      }|D ]  }||z   }| |j	                  |        |j                  |       C y wr   )r   EmptySetr   r
   appendextend)r   foundxtempynews         r   __iter__zPowerSet.__iter__h   ss     jj 	AD!A !!e	C ! LL	s   A5A7c                 @    t        | j                  j                        S r   )r   r   kindr   s    r   r;   zPowerSet.kindu   s    txx}}%%r   r   )__name__
__module____qualname____doc__r   propertyr   r#   r   NotImplementedr(   r+   r/   r9   r;   __classcell__)r   s   @r   r   r   
   se    9t	)   (7 )71" & &r   r   N)sympy.core.decoratorsr   sympy.core.parametersr   sympy.core.logicr   sympy.core.singletonr   sympy.core.sympifyr   setsr	   r
   r   r    r   r   <module>rJ      s(    , 3 ' " ' ) )m&s m&r   