o
    ÎeÔ$  ã                   @   sÞ  d dl mZ d dlmZ d dlmZmZmZmZm	Z	m
Z
 d dlmZ d dlmZ d dlmZmZmZmZ d dlmZ dd	„ Zd
d„ Zdd„ ZG dd„ dƒZeƒ Ze
dƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZe e¡dd„ ƒZejdd„ ej dd„ ej!dd„ ej"d d„ ej#d!d„ ej$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„ ƒZd(S ))é    )Údefaultdict)ÚQ)ÚAddÚMulÚPowÚNumberÚNumberSymbolÚSymbol)ÚImaginaryUnit)ÚAbs)Ú
EquivalentÚAndÚOrÚImplies)ÚMatMulc                    ó   t ‡ ‡fdd„|jD ƒŽ S )aú  
    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                    ó   g | ]}ˆ   ˆ|¡‘qS © ©Úsubs©Ú.0Úarg©ÚfactÚsymbolr   úMD:\Projects\ConvertPro\env\Lib\site-packages\sympy/assumptions/sathandlers.pyÚ
<listcomp>(   ó    zallargs.<locals>.<listcomp>)r   Úargs©r   r   Úexprr   r   r   Úallargs   ó   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   Úanyarg+   r#   r$   c                    s8   ‡ ‡fdd„|j D ƒ‰t‡fdd„ttˆƒƒD ƒŽ }|S )aÿ  
    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 ˆ | gd d„ ˆ d|… ˆ |d d…  D ƒ¢R Ž ‘qS )c                 S   s   g | ]}| ‘qS r   r   )r   Zlitr   r   r   r   a   s    z,exactlyonearg.<locals>.<listcomp>.<listcomp>Né   )r   )r   Úi)Ú	pred_argsr   r   r   a   s
    ÿÿ)r   r   ÚrangeÚlen)r   r   r!   Úresr   )r   r'   r   r   ÚexactlyoneargG   s
   
ÿ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 )Ú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ƒ| _t tƒ| _d S ©N)r   Ú	frozensetÚsinglefactsÚ
multifacts)Úselfr   r   r   Ú__init__˜   s   
zClassFactRegistry.__init__c                    ó   ‡ ‡fdd„}|S )Nc                    s   ˆj ˆ   | hO  < | S r-   )r/   )Úfunc©Úclsr1   r   r   Ú_   s   z%ClassFactRegistry.register.<locals>._r   )r1   r6   r7   r   r5   r   Úregisterœ   s   zClassFactRegistry.registerc                    r3   )Nc                    s"   ˆ D ]}ˆj |  | hO  < q| S r-   )r0   )r4   r6   ©Úclassesr1   r   r   r7   £   s   z*ClassFactRegistry.multiregister.<locals>._r   )r1   r:   r7   r   r9   r   Úmultiregister¢   s   zClassFactRegistry.multiregisterc                 C   sd   | j | }| j D ]}t||ƒr|| j | O }q| j| }| jD ]}t||ƒr-|| j| O }q||fS r-   )r/   Ú
issubclassr0   )r1   ÚkeyZret1ÚkZret2r   r   r   Ú__getitem__©   s   


€


€zClassFactRegistry.__getitem__c                 C   sJ   t ƒ }| t|ƒ \}}|D ]	}| ||ƒ¡ q|D ]	}| ||ƒ¡ q|S r-   )ÚsetÚtypeÚaddÚupdate)r1   r!   ÚretZ	handlers1Z	handlers2Úhr   r   r   Ú__call__¶   s   zClassFactRegistry.__call__N)	Ú__name__Ú
__module__Ú__qualname__Ú__doc__r2   r8   r;   r?   rF   r   r   r   r   r,   h   s    /r,   Úxc                 C   sd   | j d }t | ¡tt |¡ t | ¡ ƒt |¡t | ¡? t |¡t | ¡? t |¡t | ¡? gS )Nr   )r   r   Únonnegativer   ÚzeroÚevenÚoddÚinteger)r!   r   r   r   r   r7   Ë   s   
ür7   c              
   C   s¤   t tt t¡| ƒt | ¡? t tt t¡| ƒt | ¡? t tt t¡| ƒt | ¡? t tt t¡| ƒt | ¡? t tt t¡| ƒt | ¡? ttt t¡ | ƒt | ¡ ? gS r-   )	r"   rK   r   ÚpositiveÚnegativeÚrealÚrationalrP   r+   ©r!   r   r   r   r7   Ø   s   ûc                 C   ó:   t tt t¡| ƒ}ttt t¡| ƒ}t|t|t | ¡ƒƒS r-   ©r"   rK   r   rS   r+   Ú
irrationalr   ©r!   Zallargs_realZonearg_irrationalr   r   r   r7   â   ó   c                 C   sÀ   t t | ¡ttt t¡| ƒƒttt t¡| ƒt | ¡? ttt t¡| ƒt | ¡? ttt t¡| ƒt | ¡? ttt 	t¡| ƒt 	| ¡? t
tt t¡ | ƒt 	| ¡ ? ttt t¡| ƒt | ¡? gS r-   )r   r   rM   r$   rK   r"   rQ   rS   rT   rP   r+   ZcommutativerU   r   r   r   r7   ë   s   úc                 C   s$   t tt t¡| ƒ}t|t | ¡ ƒS r-   )r"   rK   r   Úprimer   )r!   Zallargs_primer   r   r   r7   ö   s   c                 C   sD   t tt t¡t t¡B | ƒ}ttt t¡| ƒ}t|t|t | ¡ƒƒS r-   )r"   rK   r   Ú	imaginaryrS   r+   r   )r!   Zallargs_imag_or_realZonearg_imaginaryr   r   r   r7   ÿ   s   c                 C   rV   r-   rW   rY   r   r   r   r7     rZ   c                 C   s:   t tt t¡| ƒ}ttt t¡| ƒ}t|t|t | ¡ƒƒS r-   )r"   rK   r   rP   r$   rN   r   r   )r!   Zallargs_integerZanyarg_evenr   r   r   r7     s   c                 C   s:   t tt t¡| ƒ}t tt t¡| ƒ}t|tt | ¡|ƒƒS r-   )r"   rK   r   ZsquareZ
invertibler   r   )r!   Zallargs_squareZallargs_invertibler   r   r   r7     rZ   c              	   C   s¢   | j | j}}t |¡t |¡@ t |¡@ t | ¡? t |¡t |¡@ t |¡@ t | ¡? t |¡t |¡@ t |¡@ t | ¡? tt 	| ¡t 	|¡t 
|¡@ ƒgS r-   )ÚbaseÚexpr   rS   rN   rL   rO   Únonpositiver   rM   rQ   )r!   r]   r^   r   r   r   r7   !  s   &&&üc                 C   ó   | j S r-   )Zis_positive©Úor   r   r   Ú<lambda>/  ó    rc   c                 C   r`   r-   )Úis_zerora   r   r   r   rc   0  rd   c                 C   r`   r-   )Zis_negativera   r   r   r   rc   1  rd   c                 C   r`   r-   )Zis_rationalra   r   r   r   rc   2  rd   c                 C   r`   r-   )Zis_irrationalra   r   r   r   rc   3  rd   c                 C   r`   r-   )Zis_evenra   r   r   r   rc   4  rd   c                 C   r`   r-   )Zis_oddra   r   r   r   rc   5  rd   c                 C   r`   r-   )Zis_imaginaryra   r   r   r   rc   6  rd   c                 C   r`   r-   )Zis_primera   r   r   r   rc   7  rd   c                 C   r`   r-   )Zis_compositera   r   r   r   rc   8  rd   c                 C   sB   g }t  ¡ D ]\}}|| ƒ}|| ƒ}|d ur| t||ƒ¡ q|S r-   )Ú_old_assump_gettersÚitemsÚappendr   )r!   rD   ÚpÚgetterÚpredÚpropr   r   r   r7   ;  s   €N)*Úcollectionsr   Zsympy.assumptions.askr   Z
sympy.corer   r   r   r   r   r	   Zsympy.core.numbersr
   Z$sympy.functions.elementary.complexesr   Zsympy.logic.boolalgr   r   r   r   Zsympy.matrices.expressionsr   r"   r$   r+   r,   Zclass_fact_registryrK   r;   r7   r8   rQ   rM   rR   rT   rX   rN   rO   r\   r[   Z	compositerf   r   r   r   r   Ú<module>   s\     !Y

	








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
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
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ö