a
    ͶDf$                     @   s  d dl mZ d dlmZ d dlmZmZmZmZm	Z	m
Z
 d dlmZ d dlmZ d dlmZmZmZmZ d dlmZ dd	 Zd
d Zdd ZG dd dZe Ze
dZeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zeedd Zejdd ej dd ej!dd ej"d d ej#d!d ej$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                    s   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                    s   g | ]}  |qS  subs.0argfactsymbolr   j/nfs/NAS7/SABIOD/METHODE/ermites/ermites_venv/lib/python3.9/site-packages/sympy/assumptions/sathandlers.py
<listcomp>(       zallargs.<locals>.<listcomp>)r   argsr   r   exprr   r   r   allargs   s    r    c                    s   t  fdd|jD  S )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                    s   g | ]}  |qS r   r   r   r   r   r   r   D   r   zanyarg.<locals>.<listcomp>)r   r   r   r   r   r   anyarg+   s    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                    s   g | ]}  |qS 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   r   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                    s    fdd}|S )Nc                    s   j    | hO  < | S r*   )r,   )funcclsr.   r   r   _   s    z%ClassFactRegistry.register.<locals>._r   )r.   r2   r3   r   r1   r   register   s    zClassFactRegistry.registerc                    s    fdd}|S )Nc                    s"    D ]}j |  | hO  < q| S r*   )r-   )r0   r2   classesr.   r   r   r3      s    z*ClassFactRegistry.multiregister.<locals>._r   )r.   r6   r3   r   r5   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-   )r.   keyZret1kZret2r   r   r   __getitem__   s    





zClassFactRegistry.__getitem__c                 C   sJ   t  }| t| \}}|D ]}||| q|D ]}||| q2|S r*   )settypeaddupdate)r.   r   retZ	handlers1Z	handlers2hr   r   r   __call__   s    zClassFactRegistry.__call__N)	__name__
__module____qualname____doc__r/   r4   r7   r;   rB   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   r3      s    
r3   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    rG   r   positivenegativerealrationalrL   r(   r   r   r   r   r3      s    c                 C   s:   t ttt| }tttt| }t|t|t| S r*   r    rG   r   rO   r(   
irrationalr   r   Zallargs_realZonearg_irrationalr   r   r   r3      s    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   rI   r!   rG   r    rM   rO   rP   rL   r(   ZcommutativerQ   r   r   r   r3      s    c                 C   s$   t ttt| }t|t|  S r*   )r    rG   r   primer   )r   Zallargs_primer   r   r   r3      s    c                 C   sD   t tttttB | }tttt| }t|t|t| S r*   )r    rG   r   	imaginaryrO   r(   r   )r   Zallargs_imag_or_realZonearg_imaginaryr   r   r   r3      s    c                 C   s:   t ttt| }tttt| }t|t|t| S r*   rR   rT   r   r   r   r3     s    c                 C   s:   t ttt| }tttt| }t|t|t| S r*   )r    rG   r   rL   r!   rJ   r   r   )r   Zallargs_integerZanyarg_evenr   r   r   r3     s    c                 C   s:   t ttt| }t ttt| }t|tt| |S r*   )r    rG   r   ZsquareZ
invertibler   r   )r   Zallargs_squareZallargs_invertibler   r   r   r3     s    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   rO   rJ   rH   rK   nonpositiver   rI   rM   )r   rW   rX   r   r   r   r3   !  s    &&&c                 C   s   | j S r*   )Zis_positiveor   r   r   <lambda>/  r   r\   c                 C   s   | j S r*   )is_zerorZ   r   r   r   r\   0  r   c                 C   s   | j S r*   )Zis_negativerZ   r   r   r   r\   1  r   c                 C   s   | j S r*   )Zis_rationalrZ   r   r   r   r\   2  r   c                 C   s   | j S r*   )Zis_irrationalrZ   r   r   r   r\   3  r   c                 C   s   | j S r*   )Zis_evenrZ   r   r   r   r\   4  r   c                 C   s   | j S r*   )Zis_oddrZ   r   r   r   r\   5  r   c                 C   s   | j S r*   )Zis_imaginaryrZ   r   r   r   r\   6  r   c                 C   s   | j S r*   )Zis_primerZ   r   r   r   r\   7  r   c                 C   s   | j S r*   )Zis_compositerZ   r   r   r   r\   8  r   c                 C   sB   g }t  D ]0\}}|| }|| }|d ur|t|| q|S r*   )_old_assump_gettersitemsappendr   )r   r@   pgetterpredpropr   r   r   r3   ;  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_registryrG   r7   r3   r4   rM   rI   rN   rP   rS   rJ   rK   rV   rU   Z	compositer^   r   r   r   r   <module>   sZ    !Y

	


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