o
    8Va$                     @   s  d dl mZ d dlmZ d dlmZmZmZmZm	Z	m
Z
 d dlmZ d dlmZ d dlmZmZmZmZ d dlmZ dd	 Zd
d Zdd ZG dd dZe Ze
dZeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zejdd ej dd ej!dd ej"d d ej#d!d ej$d"d ej%d#d ej&d$d ej'd%d ej(d&d i
Z)eee	ed'd Zd(S ))    )defaultdict)Q)AddMulPowNumberNumberSymbolSymbol)ImaginaryUnit)Abs)
EquivalentAndOrImplies)MatMulc                       t  fdd|jD  S )a  
    Apply all arguments of the expression to the fact structure.

    Parameters
    ==========

    symbol : Symbol
        A placeholder symbol.

    fact : Boolean
        Resulting ``Boolean`` expression.

    expr : Expr

    Examples
    ========

    >>> from sympy import Q
    >>> from sympy.assumptions.sathandlers import allargs
    >>> from sympy.abc import x, y
    >>> allargs(x, Q.negative(x) | Q.positive(x), x*y)
    (Q.negative(x) | Q.positive(x)) & (Q.negative(y) | Q.positive(y))

    c                       g | ]}  |qS  Zsubs.0argfactsymbolr   ?/usr/lib/python3/dist-packages/sympy/assumptions/sathandlers.py
<listcomp>(       zallargs.<locals>.<listcomp>)r   argsr   r   exprr   r   r   allargs      r!   c                    r   )a  
    Apply any argument of the expression to the fact structure.

    Parameters
    ==========

    symbol : Symbol
        A placeholder symbol.

    fact : Boolean
        Resulting ``Boolean`` expression.

    expr : Expr

    Examples
    ========

    >>> from sympy import Q
    >>> from sympy.assumptions.sathandlers import anyarg
    >>> from sympy.abc import x, y
    >>> anyarg(x, Q.negative(x) & Q.positive(x), x*y)
    (Q.negative(x) & Q.positive(x)) | (Q.negative(y) & Q.positive(y))

    c                    r   r   r   r   r   r   r   r   D   r   zanyarg.<locals>.<listcomp>)r   r   r   r   r   r   anyarg+   r"   r#   c                    s8    fdd|j D tfddttD  }|S )a  
    Apply exactly one argument of the expression to the fact structure.

    Parameters
    ==========

    symbol : Symbol
        A placeholder symbol.

    fact : Boolean
        Resulting ``Boolean`` expression.

    expr : Expr

    Examples
    ========

    >>> from sympy import Q
    >>> from sympy.assumptions.sathandlers import exactlyonearg
    >>> from sympy.abc import x, y
    >>> exactlyonearg(x, Q.positive(x), x*y)
    (Q.positive(x) & ~Q.positive(y)) | (Q.positive(y) & ~Q.positive(x))

    c                    r   r   r   r   r   r   r   r   `   r   z!exactlyonearg.<locals>.<listcomp>c              	      sB   g | ]}t  | gd d  d|  |d d  D R  qS )c                 S   s   g | ]}| qS r   r   )r   Zlitr   r   r   r   a   s    z,exactlyonearg.<locals>.<listcomp>.<listcomp>N   )r   )r   i)	pred_argsr   r   r   a   s
    )r   r   rangelen)r   r   r    resr   )r   r&   r   r   exactlyoneargG   s
   
r*   c                   @   s8   e Zd ZdZdd Zdd Zdd Zdd	 Zd
d ZdS )ClassFactRegistrya  
    Register handlers against classes.

    Explanation
    ===========

    ``register`` method registers the handler function for a class. Here,
    handler function should return a single fact. ``multiregister`` method
    registers the handler function for multiple classes. Here, handler function
    should return a container of multiple facts.

    ``registry(expr)`` returns a set of facts for *expr*.

    Examples
    ========

    Here, we register the facts for ``Abs``.

    >>> from sympy import Abs, Q
    >>> from sympy.logic.boolalg import Equivalent
    >>> from sympy.assumptions.sathandlers import ClassFactRegistry
    >>> reg = ClassFactRegistry()
    >>> @reg.register(Abs)
    ... def f1(expr):
    ...     return Q.nonnegative(expr)
    >>> @reg.register(Abs)
    ... def f2(expr):
    ...     arg = expr.args[0]
    ...     return Equivalent(~Q.zero(arg), ~Q.zero(expr))

    Calling the registry with expression returns the defined facts for the
    expression.

    >>> from sympy.abc import x
    >>> reg(Abs(x))
    {Q.nonnegative(Abs(x)), Equivalent(~Q.zero(x), ~Q.zero(Abs(x)))}

    Multiple facts can be registered at once by ``multiregister`` method.

    >>> reg2 = ClassFactRegistry()
    >>> @reg2.multiregister(Abs)
    ... def _(expr):
    ...     arg = expr.args[0]
    ...     return [Q.even(arg) >> Q.even(expr), Q.odd(arg) >> Q.odd(expr)]
    >>> reg2(Abs(x))
    {Implies(Q.even(x), Q.even(Abs(x))), Implies(Q.odd(x), Q.odd(Abs(x)))}

    c                 C   s   t t| _t t| _d S N)r   	frozensetsinglefacts
multifacts)selfr   r   r   __init__   s   
zClassFactRegistry.__init__c                        fdd}|S )Nc                    s   j    | hO  < | S r,   )r.   )funcclsr0   r   r   _   s   z%ClassFactRegistry.register.<locals>._r   )r0   r5   r6   r   r4   r   register   s   zClassFactRegistry.registerc                    r2   )Nc                    s"    D ]}j |  | hO  < q| S r,   )r/   )r3   r5   classesr0   r   r   r6      s   z*ClassFactRegistry.multiregister.<locals>._r   )r0   r9   r6   r   r8   r   multiregister   s   zClassFactRegistry.multiregisterc                 C   sd   | j | }| j D ]}t||r|| j | O }q| j| }| jD ]}t||r-|| j| O }q||fS r,   )r.   
issubclassr/   )r0   keyZret1kZret2r   r   r   __getitem__   s   





zClassFactRegistry.__getitem__c                 C   sH   t  }| |j \}}|D ]	}||| q|D ]	}||| q|S r,   )setr3   addupdate)r0   r    retZ	handlers1Z	handlers2hr   r   r   __call__   s   zClassFactRegistry.__call__N)	__name__
__module____qualname____doc__r1   r7   r:   r>   rD   r   r   r   r   r+   h   s    0r+   xc                 C   sd   | j d }t| tt| t|  t|t| ? t|t| ? t|t| ? gS )Nr   )r   r   nonnegativer   zeroevenoddinteger)r    r   r   r   r   r6      s   
r6   c              
   C   s   t ttt| t| ? t ttt| t| ? t ttt| t| ? t ttt| t| ? t ttt| t| ? tttt | t|  ? gS r,   )	r!   rI   r   positivenegativerealrationalrN   r*   r    r   r   r   r6      s   c                 C   :   t ttt| }tttt| }t|t|t| S r,   r!   rI   r   rQ   r*   
irrationalr   r    Zallargs_realZonearg_irrationalr   r   r   r6         c                 C   s   t t| tttt| tttt| t| ? tttt| t| ? tttt| t| ? ttt	t| t	| ? t
ttt | t	|  ? tttt| t| ? gS r,   )r   r   rK   r#   rI   r!   rO   rQ   rR   rN   r*   ZcommutativerS   r   r   r   r6      s   c                 C   s$   t ttt| }t|t|  S r,   )r!   rI   r   primer   )r    Zallargs_primer   r   r   r6      s   c                 C   sD   t tttttB | }tttt| }t|t|t| S r,   )r!   rI   r   	imaginaryrQ   r*   r   )r    Zallargs_imag_or_realZonearg_imaginaryr   r   r   r6      s   c                 C   rT   r,   rU   rW   r   r   r   r6     rX   c                 C   s:   t ttt| }tttt| }t|t|t| S r,   )r!   rI   r   rN   r#   rL   r   r   )r    Zallargs_integerZanyarg_evenr   r   r   r6     s   c                 C   s:   t ttt| }t ttt| }t|tt| |S r,   )r!   rI   r   ZsquareZ
invertibler   r   )r    Zallargs_squareZallargs_invertibler   r   r   r6     rX   c              	   C   s   | j | j}}t|t|@ t|@ t| ? t|t|@ t|@ t| ? t|t|@ t|@ t| ? tt	| t	|t
|@ gS r,   )baseexpr   rQ   rL   rJ   rM   nonpositiver   rK   rO   )r    r[   r\   r   r   r   r6   "  s   &&&c                 C      | j S r,   )Zis_positiveor   r   r   <lambda>0      ra   c                 C   r^   r,   )Zis_zeror_   r   r   r   ra   1  rb   c                 C   r^   r,   )Zis_negativer_   r   r   r   ra   2  rb   c                 C   r^   r,   )Zis_rationalr_   r   r   r   ra   3  rb   c                 C   r^   r,   )Zis_irrationalr_   r   r   r   ra   4  rb   c                 C   r^   r,   )Zis_evenr_   r   r   r   ra   5  rb   c                 C   r^   r,   )Zis_oddr_   r   r   r   ra   6  rb   c                 C   r^   r,   )Zis_imaginaryr_   r   r   r   ra   7  rb   c                 C   r^   r,   )Zis_primer_   r   r   r   ra   8  rb   c                 C   r^   r,   )Zis_compositer_   r   r   r   ra   9  rb   c                 C   sB   g }t  D ]\}}|| }|| }|d ur|t|| q|S r,   )_old_assump_gettersitemsappendr   )r    rB   pgetterZpredZpropr   r   r   r6   <  s   N)*collectionsr   Zsympy.assumptions.askr   Z
sympy.corer   r   r   r   r   r	   Zsympy.core.numbersr
   Z$sympy.functions.elementary.complexesr   Zsympy.logic.boolalgr   r   r   r   Zsympy.matrices.expressionsr   r!   r#   r*   r+   Zclass_fact_registryrI   r:   r6   r7   rO   rK   rP   rR   rV   rL   rM   rZ   rY   Z	compositerc   r   r   r   r   <module>   s\     !Z

	


















