a
    RG5dF                     @   s6  d dl mZ d dlmZ d dlmZ d dlmZm	Z	 d dl
mZ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mZmZmZ d d
lmZ d dlmZ d dlmZm Z  d dl!m"Z" G dd deZ#G dd de#Z$e"e$edd Z%G dd de#Z&e"e&edd Z%G dd deZ'e"e'edd Z%dS )    )Tuple)Basic)Expr)AddS)get_integer_partPrecisionExhausted)Function)fuzzy_or)Integer)GtLtGeLe
Relationalis_eq)Symbol)_sympify)imre)dispatchc                   @   sN   e Zd ZU dZee ed< edd Zedd Z	dd Z
d	d
 Zdd ZdS )RoundFunctionz+Abstract base class for rounding functions.argsc           
   	   C   s  |  |}|d ur|S |js&|jdu r*|S |js<tj| jrjt|}|tjs^| |tj S | |ddS tj	 } }}t
|}|D ]@}|js|jrt|jr||7 }q|tr||7 }q||7 }q|s|s|S |r`|r|jr|jstj| js|jr`|jr`z:t|| ji dd\}	}|t|	t|tj  7 }tj	}W n ttfy^   Y n0 ||7 }|sr|S |jstj| jr|| t|ddtj  S t|ttfr|| S || |dd S d S )NFevaluateT)return_ints)_eval_number
is_integer	is_finiteis_imaginaryr   ImaginaryUnitis_realr   hasZeror   	make_argsr   r   _dirr   r   NotImplementedError
isinstancefloorceiling)
clsargviZipartZnpartZsparttermstr r1   _/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/functions/elementary/integers.pyeval   sb    









zRoundFunction.evalc                 C   s
   t  d S N)r&   r*   r+   r1   r1   r2   r   Q   s    zRoundFunction._eval_numberc                 C   s   | j d jS Nr   )r   r   selfr1   r1   r2   _eval_is_finiteU   s    zRoundFunction._eval_is_finitec                 C   s   | j d jS r6   r   r!   r7   r1   r1   r2   _eval_is_realX   s    zRoundFunction._eval_is_realc                 C   s   | j d jS r6   r:   r7   r1   r1   r2   _eval_is_integer[   s    zRoundFunction._eval_is_integerN)__name__
__module____qualname____doc__tTupler   __annotations__classmethodr3   r   r9   r;   r<   r1   r1   r1   r2   r      s   

5
r   c                   @   st   e Zd ZdZdZedd ZdddZdd	d
Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd ZdS )r(   a  
    Floor is a univariate function which returns the largest integer
    value not greater than its argument. This implementation
    generalizes floor to complex numbers by taking the floor of the
    real and imaginary parts separately.

    Examples
    ========

    >>> from sympy import floor, E, I, S, Float, Rational
    >>> floor(17)
    17
    >>> floor(Rational(23, 10))
    2
    >>> floor(2*E)
    5
    >>> floor(-Float(0.567))
    -1
    >>> floor(-I/2)
    -I
    >>> floor(S(5)/2 + 5*I/2)
    2 + 2*I

    See Also
    ========

    sympy.functions.elementary.integers.ceiling

    References
    ==========

    .. [1] "Concrete mathematics" by Graham, pp. 87
    .. [2] http://mathworld.wolfram.com/FloorFunction.html

    c                 C   sB   |j r| S tdd || fD r*|S |jr>|td S d S )Nc                 s   s&   | ]}t tfD ]}t||V  qqd S r4   r(   r)   r'   .0r-   jr1   r1   r2   	<genexpr>   s   z%floor._eval_number.<locals>.<genexpr>r   )	is_Numberr(   anyis_NumberSymbolapproximation_intervalr   r5   r1   r1   r2   r      s    zfloor._eval_numberNr   c           	      C   s   | j d }||d}| |d}|tju rR|j|dt|jrBdndd}t|}|jr||kr|dkr|j	|dd}|j	|dd}||krt
d|  n|j	||d}|jr|d S |S |S |j|||d	S 
Nr   -+dirrD   cdir   z,Two sided limit of %s around 0does not exist)logxrT   )r   subsr   NaNlimitr   is_negativer(   r   rR   
ValueErroras_leading_term	r8   xrV   rT   r+   arg0r0   Zndirlndirr1   r1   r2   _eval_as_leading_term   s&    

zfloor._eval_as_leading_termc                 C   s   | j d }||d}| |d}|tju rR|j|dt|jrBdndd}t|}|jrddl	m
} ddlm}	 |||||}
|dkr|	d|dfn|dd}|
| S ||kr|j||dkr|ndd	}|jr|d S |S |S d S )
Nr   rO   rP   rQ   AccumBoundsOrderrU   rD   rS   )r   rW   r   rX   rY   r   rZ   r(   is_infinite!sympy.calculus.accumulationboundsrc   sympy.series.orderre   _eval_nseriesrR   r8   r^   nrV   rT   r+   r_   r0   rc   re   sor`   r1   r1   r2   ri      s     

 zfloor._eval_nseriesc                 C   s   | j d jS r6   )r   rZ   r7   r1   r1   r2   _eval_is_negative   s    zfloor._eval_is_negativec                 C   s   | j d jS r6   )r   is_nonnegativer7   r1   r1   r2   _eval_is_nonnegative   s    zfloor._eval_is_nonnegativec                 K   s   t |  S r4   r)   r8   r+   kwargsr1   r1   r2   _eval_rewrite_as_ceiling   s    zfloor._eval_rewrite_as_ceilingc                 K   s   |t | S r4   fracrr   r1   r1   r2   _eval_rewrite_as_frac   s    zfloor._eval_rewrite_as_fracc                 C   s   t |}| jd jrJ|jr,| jd |d k S |jrJ|jrJ| jd t|k S | jd |krd|jrdt jS |t ju rz| jrzt jS t	| |ddS Nr   rU   Fr   )
r   r   r!   r   	is_numberr)   trueInfinityr   r   r8   otherr1   r1   r2   __le__   s    zfloor.__le__c                 C   s   t |}| jd jrF|jr(| jd |kS |jrF|jrF| jd t|kS | jd |kr`|jr`t jS |t ju rv| jrvt j	S t
| |ddS Nr   Fr   )r   r   r!   r   ry   r)   falseNegativeInfinityr   rz   r   r|   r1   r1   r2   __ge__   s    zfloor.__ge__c                 C   s   t |}| jd jrJ|jr,| jd |d kS |jrJ|jrJ| jd t|kS | jd |krd|jrdt jS |t ju rz| jrzt j	S t
| |ddS rx   )r   r   r!   r   ry   r)   r   r   r   rz   r   r|   r1   r1   r2   __gt__   s    zfloor.__gt__c                 C   s   t |}| jd jrF|jr(| jd |k S |jrF|jrF| jd t|k S | jd |kr`|jr`t jS |t ju rv| jrvt j	S t
| |ddS r   )r   r   r!   r   ry   r)   r   r{   r   rz   r   r|   r1   r1   r2   __lt__   s    zfloor.__lt__)Nr   )r   )r=   r>   r?   r@   r%   rC   r   ra   ri   rn   rp   rt   rw   r~   r   r   r   r1   r1   r1   r2   r(   _   s   #
	

r(   c                 C   s    t | t|pt | t|S r4   )r   rewriter)   rv   lhsrhsr1   r1   r2   _eval_is_eq   s    r   c                   @   st   e Zd ZdZdZedd ZdddZdd	d
Zdd Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd ZdS )r)   a  
    Ceiling is a univariate function which returns the smallest integer
    value not less than its argument. This implementation
    generalizes ceiling to complex numbers by taking the ceiling of the
    real and imaginary parts separately.

    Examples
    ========

    >>> from sympy import ceiling, E, I, S, Float, Rational
    >>> ceiling(17)
    17
    >>> ceiling(Rational(23, 10))
    3
    >>> ceiling(2*E)
    6
    >>> ceiling(-Float(0.567))
    0
    >>> ceiling(I/2)
    I
    >>> ceiling(S(5)/2 + 5*I/2)
    3 + 3*I

    See Also
    ========

    sympy.functions.elementary.integers.floor

    References
    ==========

    .. [1] "Concrete mathematics" by Graham, pp. 87
    .. [2] http://mathworld.wolfram.com/CeilingFunction.html

    rU   c                 C   sB   |j r| S tdd || fD r*|S |jr>|td S d S )Nc                 s   s&   | ]}t tfD ]}t||V  qqd S r4   rE   rF   r1   r1   r2   rI   -  s   z'ceiling._eval_number.<locals>.<genexpr>rU   )rJ   r)   rK   rL   rM   r   r5   r1   r1   r2   r   )  s    zceiling._eval_numberNr   c           	      C   s   | j d }||d}| |d}|tju rR|j|dt|jrBdndd}t|}|jr||kr|dkr|j	|dd}|j	|dd}||krt
d|  n|j	||d}|jr|S |d S |S |j|||d	S rN   )r   rW   r   rX   rY   r   rZ   r)   r   rR   r[   r\   r]   r1   r1   r2   ra   3  s&    

zceiling._eval_as_leading_termc                 C   s   | j d }||d}| |d}|tju rR|j|dt|jrBdndd}t|}|jrddl	m
} ddlm}	 |||||}
|dkr|	d|dfn|dd}|
| S ||kr|j||dkr|ndd}|jr|S |d S |S d S )	Nr   rO   rP   rQ   rb   rd   rU   rS   )r   rW   r   rX   rY   r   rZ   r)   rf   rg   rc   rh   re   ri   rR   rj   r1   r1   r2   ri   I  s     

 zceiling._eval_nseriesc                 K   s   t |  S r4   r(   rr   r1   r1   r2   _eval_rewrite_as_floor\  s    zceiling._eval_rewrite_as_floorc                 K   s   |t |  S r4   ru   rr   r1   r1   r2   rw   _  s    zceiling._eval_rewrite_as_fracc                 C   s   | j d jS r6   )r   is_positiver7   r1   r1   r2   _eval_is_positiveb  s    zceiling._eval_is_positivec                 C   s   | j d jS r6   )r   is_nonpositiver7   r1   r1   r2   _eval_is_nonpositivee  s    zceiling._eval_is_nonpositivec                 C   s   t |}| jd jrJ|jr,| jd |d kS |jrJ|jrJ| jd t|kS | jd |krd|jrdt jS |t ju rz| jrzt j	S t
| |ddS rx   )r   r   r!   r   ry   r(   r   r{   r   rz   r   r|   r1   r1   r2   r   h  s    zceiling.__lt__c                 C   s   t |}| jd jrF|jr(| jd |kS |jrF|jrF| jd t|kS | jd |kr`|jr`t jS |t ju rv| jrvt j	S t
| |ddS r   )r   r   r!   r   ry   r(   r   r   r   rz   r   r|   r1   r1   r2   r   v  s    zceiling.__gt__c                 C   s   t |}| jd jrJ|jr,| jd |d kS |jrJ|jrJ| jd t|kS | jd |krd|jrdt jS |t ju rz| jrzt jS t	| |ddS rx   )
r   r   r!   r   ry   r(   rz   r   r   r   r|   r1   r1   r2   r     s    zceiling.__ge__c                 C   s   t |}| jd jrF|jr(| jd |kS |jrF|jrF| jd t|kS | jd |kr`|jr`t jS |t ju rv| jrvt j	S t
| |ddS r   )r   r   r!   r   ry   r(   r   r{   r   rz   r   r|   r1   r1   r2   r~     s    zceiling.__le__)Nr   )r   )r=   r>   r?   r@   r%   rC   r   ra   ri   r   rw   r   r   r   r   r   r~   r1   r1   r1   r2   r)     s   #
	

r)   c                 C   s    t | t|pt | t|S r4   )r   r   r(   rv   r   r1   r1   r2   r     s    c                   @   s   e Zd ZdZedd Zdd Zdd Zdd	 Zd
d Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd ZdS )rv   a  Represents the fractional part of x

    For real numbers it is defined [1]_ as

    .. math::
        x - \left\lfloor{x}\right\rfloor

    Examples
    ========

    >>> from sympy import Symbol, frac, Rational, floor, I
    >>> frac(Rational(4, 3))
    1/3
    >>> frac(-Rational(4, 3))
    2/3

    returns zero for integer arguments

    >>> n = Symbol('n', integer=True)
    >>> frac(n)
    0

    rewrite as floor

    >>> x = Symbol('x')
    >>> frac(x).rewrite(floor)
    x - floor(x)

    for complex arguments

    >>> r = Symbol('r', real=True)
    >>> t = Symbol('t', real=True)
    >>> frac(t + I*r)
    I*frac(r) + frac(t)

    See Also
    ========

    sympy.functions.elementary.integers.floor
    sympy.functions.elementary.integers.ceiling

    References
    ===========

    .. [1] https://en.wikipedia.org/wiki/Fractional_part
    .. [2] http://mathworld.wolfram.com/FractionalPart.html

    c                    s   ddl m   fdd}t|}tjtj }}|D ]F}|jsLtj| jrtt	|}|
tjsj||7 }q|||7 }q6||7 }q6||}||}|tj|  S )Nr   rb   c                    sd   | t jt jfv r ddS | jr&t jS | jrX| t ju r<t jS | t ju rLt jS | t|  S | ddS rx   )	r   r{   r   r   r#   ry   rX   ComplexInfinityr(   )r+   rc   r*   r1   r2   _eval  s    


zfrac.eval.<locals>._eval)rg   rc   r   r$   r   r#   r   r    r!   r   r"   )r*   r+   r   r.   realimagr/   r-   r1   r   r2   r3     s    



z	frac.evalc                 K   s   |t | S r4   r   rr   r1   r1   r2   r     s    zfrac._eval_rewrite_as_floorc                 K   s   |t |  S r4   rq   rr   r1   r1   r2   rt     s    zfrac._eval_rewrite_as_ceilingc                 C   s   dS )NTr1   r7   r1   r1   r2   r9     s    zfrac._eval_is_finitec                 C   s   | j d jS r6   )r   is_extended_realr7   r1   r1   r2   r;     s    zfrac._eval_is_realc                 C   s   | j d jS r6   )r   r   r7   r1   r1   r2   _eval_is_imaginary  s    zfrac._eval_is_imaginaryc                 C   s   | j d jS r6   )r   r   r7   r1   r1   r2   r<   
  s    zfrac._eval_is_integerc                 C   s   t | jd j| jd jgS r6   )r
   r   is_zeror   r7   r1   r1   r2   _eval_is_zero  s    zfrac._eval_is_zeroc                 C   s   dS )NFr1   r7   r1   r1   r2   rn     s    zfrac._eval_is_negativec                 C   s@   | j r2t|}|jrtjS | |}|d ur2| S t| |ddS NFr   )r   r   is_extended_nonpositiver   rz   _value_one_or_morer   r8   r}   resr1   r1   r2   r     s    
zfrac.__ge__c                 C   s@   | j r2t|}| |}|d ur&| S |jr2tjS t| |ddS r   )r   r   r   is_extended_negativer   rz   r   r   r1   r1   r2   r     s    
zfrac.__gt__c                 C   s>   | j r0t|}|jrtjS | |}|d ur0|S t| |ddS r   )r   r   r   r   r   r   r   r   r1   r1   r2   r~   +  s    
zfrac.__le__c                 C   s>   | j r0t|}|jrtjS | |}|d ur0|S t| |ddS r   )r   r   r   r   r   r   r   r   r1   r1   r2   r   7  s    
zfrac.__lt__c                 C   s>   |j r:|jr(|dk}|r(t|ts(tjS |jr:|jr:tjS d S )NrU   )r   ry   r'   r   r   rz   r   r   r   r1   r1   r2   r   C  s    zfrac._value_one_or_moreN)r=   r>   r?   r@   rC   r3   r   rt   r9   r;   r   r<   r   rn   r   r   r~   r   r   r1   r1   r1   r2   rv     s    0
#rv   c                 C   sD   |  t|ks|  t|kr dS |jr*dS | |}|d ur@dS d S )NTF)r   r(   r)   r   r   )r   r   r   r1   r1   r2   r   M  s    
N)(typingr   rA   sympy.core.basicr   sympy.core.exprr   
sympy.corer   r   Zsympy.core.evalfr   r   sympy.core.functionr	   sympy.core.logicr
   sympy.core.numbersr   sympy.core.relationalr   r   r   r   r   r   sympy.core.symbolr   sympy.core.sympifyr   $sympy.functions.elementary.complexesr   r   sympy.multipledispatchr   r   r(   r   r)   rv   r1   r1   r1   r2   <module>   s2    I 
 
 (