o
    jg$                     @   s  d dl mZ d dlmZ d dlmZmZmZmZm	Z	m
Z
 d dlmZ d dlmZ d dlmZmZmZmZ d dlmZ dd	 Zd
d Zdd ZG dd dZe Ze
dZeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zejdd ej dd ej!dd ej"d d ej#d!d ej$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  subs.0argfactsymbolr   U/var/www/html/zoom/venv/lib/python3.10/site-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   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, Equivalent, Q
    >>> 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.   )r0   )funcclsr2   r   r   _   s   z%ClassFactRegistry.register.<locals>._r   )r2   r7   r8   r   r6   r   register   s   zClassFactRegistry.registerc                    r4   )Nc                    s"    D ]}j |  | hO  < q| S r.   )r1   )r5   r7   classesr2   r   r   r8      s   z*ClassFactRegistry.multiregister.<locals>._r   )r2   r;   r8   r   r:   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.   )r0   
issubclassr1   )r2   keyret1kret2r   r   r   __getitem__   s   





zClassFactRegistry.__getitem__c                    sJ   t  }| t  \}}| fdd|D  |D ]	}||  q|S )Nc                 3   s    | ]}| V  qd S r.   r   )r   hr!   r   r   	<genexpr>   s    z-ClassFactRegistry.__call__.<locals>.<genexpr>)settypeupdate)r2   r!   ret	handlers1	handlers2rC   r   rD   r   __call__   s   zClassFactRegistry.__call__N)	__name__
__module____qualname____doc__r3   r9   r<   rB   rL   r   r   r   r   r-   h   s    /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   r8      s   
r8   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"   rQ   r   positivenegativerealrationalrV   r,   rD   r   r   r   r8      s   c                 C   :   t ttt| }tttt| }t|t|t| S r.   r"   rQ   r   rY   r,   
irrationalr   r!   allargs_realonearg_irrationalr   r   r   r8         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   rS   r$   rQ   r"   rW   rY   rZ   rV   r,   commutativerD   r   r   r   r8      s   c                 C   s$   t ttt| }t|t|  S r.   )r"   rQ   r   primer   )r!   allargs_primer   r   r   r8      s   c                 C   sD   t tttttB | }tttt| }t|t|t| S r.   )r"   rQ   r   	imaginaryrY   r,   r   )r!   allargs_imag_or_realonearg_imaginaryr   r   r   r8      s   c                 C   r[   r.   r\   r^   r   r   r   r8     ra   c                 C   s:   t ttt| }tttt| }t|t|t| S r.   )r"   rQ   r   rV   r$   rT   r   r   )r!   allargs_integeranyarg_evenr   r   r   r8     s   c                 C   s:   t ttt| }t ttt| }t|tt| |S r.   )r"   rQ   r   square
invertibler   r   )r!   allargs_squareallargs_invertibler   r   r   r8     ra   c              	   C   s   | j | j}}t|t|@ t|@ t| ? t|t|@ t|@ t| ? t|t|@ t|@ t| ? tt	| t	|t
|@ gS r.   )baseexpr   rY   rT   rR   rU   nonpositiver   rS   rW   )r!   rn   ro   r   r   r   r8      s   &&&c                 C      | j S r.   )is_positiveor   r   r   <lambda>.      ru   c                 C   rq   r.   )is_zerors   r   r   r   ru   /  rv   c                 C   rq   r.   )is_negativers   r   r   r   ru   0  rv   c                 C   rq   r.   )is_rationalrs   r   r   r   ru   1  rv   c                 C   rq   r.   )is_irrationalrs   r   r   r   ru   2  rv   c                 C   rq   r.   )is_evenrs   r   r   r   ru   3  rv   c                 C   rq   r.   )is_oddrs   r   r   r   ru   4  rv   c                 C   rq   r.   )is_imaginaryrs   r   r   r   ru   5  rv   c                 C   rq   r.   )is_primers   r   r   r   ru   6  rv   c                 C   rq   r.   )is_compositers   r   r   r   ru   7  rv   c                 C   sB   g }t  D ]\}}|| }|| }|d ur|t|| q|S r.   )_old_assump_gettersitemsappendr   )r!   rI   pgetterpredpropr   r   r   r8   :  s   N)*collectionsr   sympy.assumptions.askr   
sympy.corer   r   r   r   r   r	   sympy.core.numbersr
   $sympy.functions.elementary.complexesr   sympy.logic.boolalgr   r   r   r   sympy.matrices.expressionsr   r"   r$   r,   r-   class_fact_registryrQ   r<   r8   r9   rW   rS   rX   rZ   r]   rT   rU   re   rc   	compositer   r   r   r   r   <module>   s\     !X

	



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