U
    L?hM                     @   s.  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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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$dS )    )Tuple)Basic)Expr)AddS)get_integer_partPrecisionExhausted)Function)fuzzy_or)Integer
int_valued)GtLtGeLe
Relationalis_eq)_sympify)imre)dispatchc                   @   sN   e Zd ZU dZee ed< edd Zedd Z	dd Z
d	d
 Zdd ZdS )RoundFunctionz+Abstract base class for rounding functions.argsc           
   	   C   s  |  |}|d k	r|S |js&|jdkr*|S |js<tj| jrjt|}|tjs^| |tj S | |ddS tj	 } }}dd }t
|D ]`}|jr|t| }d k	r||tj 7 }q|| }d k	r||7 }q|jr||7 }q||7 }q|s|s|S |r|r2|jr"|js2tj| js2|jr|jrz:t|| ji dd\}	}|t|	t|tj  7 }tj	}W n ttfk
r   Y nX ||7 }|s|S |jstj| jr|| t|ddtj  S t|ttfr|| S || |dd S d S )NFevaluatec                 S   s   t | rt| S | jr| S d S N)r   int
is_integer)x r   U/var/www/html/venv/lib/python3.8/site-packages/sympy/functions/elementary/integers.py<lambda>,   s   z$RoundFunction.eval.<locals>.<lambda>T)Zreturn_ints)_eval_numberr   	is_finiteis_imaginaryr   ImaginaryUnitis_realr   hasZeror   	make_args	is_numberr   _dirr   r   NotImplementedError
isinstancefloorceiling)
clsargviZipartZnpartZspartZintoftrr   r   r    eval   sl    




   

zRoundFunction.evalc                 C   s
   t  d S r   )r,   r0   r1   r   r   r    r"   R   s    zRoundFunction._eval_numberc                 C   s   | j d jS Nr   )r   r#   selfr   r   r    _eval_is_finiteV   s    zRoundFunction._eval_is_finitec                 C   s   | j d jS r8   r   r&   r9   r   r   r    _eval_is_realY   s    zRoundFunction._eval_is_realc                 C   s   | j d jS r8   r<   r9   r   r   r    _eval_is_integer\   s    zRoundFunction._eval_is_integerN)__name__
__module____qualname____doc__tTupler   __annotations__classmethodr6   r"   r;   r=   r>   r   r   r   r    r      s   

7
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] https://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 r   r.   r/   r-   .0r3   jr   r   r    	<genexpr>   s    
 z%floor._eval_number.<locals>.<genexpr>r   )	is_Numberr.   anyis_NumberSymbolapproximation_intervalr   r7   r   r   r    r"      s    zfloor._eval_numberNr   c           	      C   s   ddl m} | jd }||d}| |d}|tjksBt||rh|j|dt|j	rXdndd}t
|}|jr||kr|j||dkr|ndd}|j	r|d S |jr|S td| n|S |j|||d	S 
Nr   AccumBounds-+dir   cdirNot sure of sign of %slogxrY   )!sympy.calculus.accumulationboundsrR   r   subsr   NaNr-   limitr   is_negativer.   r#   rV   is_positiver,   as_leading_term	r:   r   r\   rY   rR   r1   arg0r5   ndirr   r   r    _eval_as_leading_term   s"    
zfloor._eval_as_leading_termc                 C   s   | j d }||d}| |d}|tjk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 |jr|S td
| n|S d S )Nr   rS   rT   rU   rQ   OrderrW   rF   rX   rZ   )r   r^   r   r_   r`   r   ra   r.   is_infiniter]   rR   sympy.series.orderri   _eval_nseriesrV   rb   r,   r:   r   nr\   rY   r1   re   r5   rR   ri   sorf   r   r   r    rl      s(    

 zfloor._eval_nseriesc                 C   s   | j d jS r8   )r   ra   r9   r   r   r    _eval_is_negative   s    zfloor._eval_is_negativec                 C   s   | j d jS r8   )r   Zis_nonnegativer9   r   r   r    _eval_is_nonnegative   s    zfloor._eval_is_nonnegativec                 K   s   t |  S r   r/   r:   r1   kwargsr   r   r    _eval_rewrite_as_ceiling   s    zfloor._eval_rewrite_as_ceilingc                 K   s   |t | S r   fracrt   r   r   r    _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krz| jrzt jS t	| |ddS Nr   rW   Fr   )
r   r   r&   r   r*   r/   trueInfinityr#   r   r:   otherr   r   r    __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krv| jrvt j	S t
| |ddS Nr   Fr   )r   r   r&   r   r*   r/   falseNegativeInfinityr#   r{   r   r}   r   r   r    __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krz| jrzt j	S t
| |ddS rz   )r   r   r&   r   r*   r/   r   r   r#   r{   r   r}   r   r   r    __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krv| jrvt j	S t
| |ddS r   )r   r   r&   r   r*   r/   r   r|   r#   r{   r   r}   r   r   r    __lt__   s    zfloor.__lt__)Nr   )r   )r?   r@   rA   rB   r+   rE   r"   rg   rl   rq   rr   rv   ry   r   r   r   r   r   r   r   r    r.   `   s   #
	

r.   c                 C   s    t | t|pt | t|S r   )r   rewriter/   rx   lhsrhsr   r   r    _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] https://mathworld.wolfram.com/CeilingFunction.html

    rW   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 r   rG   rH   r   r   r    rK   2  s    
 z'ceiling._eval_number.<locals>.<genexpr>rW   )rL   r/   rM   rN   rO   r   r7   r   r   r    r"   .  s    zceiling._eval_numberNr   c           	      C   s   ddl m} | jd }||d}| |d}|tjksBt||rh|j|dt|j	rXdndd}t
|}|jr||kr|j||dkr|ndd}|j	r|S |jr|d S td| n|S |j|||d	S rP   )r]   rR   r   r^   r   r_   r-   r`   r   ra   r/   r#   rV   rb   r,   rc   rd   r   r   r    rg   8  s"    
zceiling._eval_as_leading_termc                 C   s   | j d }||d}| |d}|tjk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 |jr|d S td	| n|S d S )
Nr   rS   rT   rU   rQ   rh   rW   rX   rZ   )r   r^   r   r_   r`   r   ra   r/   rj   r]   rR   rk   ri   rl   rV   rb   r,   rm   r   r   r    rl   M  s(    

 zceiling._eval_nseriesc                 K   s   t |  S r   r.   rt   r   r   r    _eval_rewrite_as_floore  s    zceiling._eval_rewrite_as_floorc                 K   s   |t |  S r   rw   rt   r   r   r    ry   h  s    zceiling._eval_rewrite_as_fracc                 C   s   | j d jS r8   )r   rb   r9   r   r   r    _eval_is_positivek  s    zceiling._eval_is_positivec                 C   s   | j d jS r8   )r   Zis_nonpositiver9   r   r   r    _eval_is_nonpositiven  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krz| jrzt j	S t
| |ddS rz   )r   r   r&   r   r*   r.   r   r|   r#   r{   r   r}   r   r   r    r   q  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krv| jrvt j	S t
| |ddS r   )r   r   r&   r   r*   r.   r   r   r#   r{   r   r}   r   r   r    r     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krz| jrzt jS t	| |ddS rz   )
r   r   r&   r   r*   r.   r{   r   r#   r   r}   r   r   r    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krv| jrvt j	S t
| |ddS r   )r   r   r&   r   r*   r.   r   r|   r#   r{   r   r}   r   r   r    r     s    zceiling.__le__)Nr   )r   )r?   r@   rA   rB   r+   rE   r"   rg   rl   r   ry   r   r   r   r   r   r   r   r   r   r    r/     s   #
	

r/   c                 C   s    t | t|pt | t|S r   )r   r   r.   rx   r   r   r   r    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$d d!Zd%d"d#ZdS )&rx   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] https://mathworld.wolfram.com/FractionalPart.html

    c                    s   ddl m   fdd}tjtj }}t|D ]F}|jsHtj| jrpt	|}|
tjsf||7 }qx||7 }q2||7 }q2||}||}|tj|  S )Nr   rQ   c                    sd   | t jt jfkr ddS | jr&t jS | jrX| t jkr<t jS | t jkrLt jS | t|  S | ddS rz   )	r   r|   r   r   r(   r*   r_   ComplexInfinityr.   )r1   rR   r0   r   r    _eval  s    


zfrac.eval.<locals>._eval)r]   rR   r   r(   r   r)   r$   r%   r&   r   r'   )r0   r1   r   realimagr4   r3   r   r   r    r6     s    


z	frac.evalc                 K   s   |t | S r   r   rt   r   r   r    r     s    zfrac._eval_rewrite_as_floorc                 K   s   |t |  S r   rs   rt   r   r   r    rv     s    zfrac._eval_rewrite_as_ceilingc                 C   s   dS )NTr   r9   r   r   r    r;   	  s    zfrac._eval_is_finitec                 C   s   | j d jS r8   )r   is_extended_realr9   r   r   r    r=     s    zfrac._eval_is_realc                 C   s   | j d jS r8   )r   r$   r9   r   r   r    _eval_is_imaginary  s    zfrac._eval_is_imaginaryc                 C   s   | j d jS r8   )r   r   r9   r   r   r    r>     s    zfrac._eval_is_integerc                 C   s   t | jd j| jd jgS r8   )r
   r   is_zeror   r9   r   r   r    _eval_is_zero  s    zfrac._eval_is_zeroc                 C   s   dS )NFr   r9   r   r   r    rq     s    zfrac._eval_is_negativec                 C   s@   | j r2t|}|jrtjS | |}|d k	r2| S t| |ddS NFr   )r   r   is_extended_nonpositiver   r{   _value_one_or_morer   r:   r~   resr   r   r    r     s    
zfrac.__ge__c                 C   s@   | j r2t|}| |}|d k	r&| S |jr2tjS t| |ddS r   )r   r   r   is_extended_negativer   r{   r   r   r   r   r    r   '  s    
zfrac.__gt__c                 C   s>   | j r0t|}|jrtjS | |}|d k	r0|S t| |ddS r   )r   r   r   r   r   r   r   r   r   r   r    r   3  s    
zfrac.__le__c                 C   s>   | j r0t|}|jrtjS | |}|d k	r0|S t| |ddS r   )r   r   r   r   r   r   r   r   r   r   r    r   ?  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 )NrW   )r   r*   r-   r   r   r{   r   rb   r   r   r   r    r   K  s    zfrac._value_one_or_moreNr   c           	      C   s   ddl m} | jd }||d}| |d}|jrn|jrh|j||d}|jrTtj	S || j
|||dS |S n|tjtjtjfkr|ddS |j
|||dS )Nr   rQ   rX   r[   rW   )r]   rR   r   r^   r#   r   rV   ra   r   Onerc   r   r|   r   rd   r   r   r    rg   T  s    

zfrac._eval_as_leading_termc                 C   s   ddl m} | jd }||d}| |d}|jrvddlm}	 |dkrV|d|dfn|	dd||| |df }
|
S || j||||d}|jr|j	||d}||j
rtjntj7 }n||7 }|S d S )Nr   rh   rQ   rW   r[   rX   )rk   ri   r   r^   rj   r]   rR   rl   r   rV   ra   r   r   r(   )r:   r   rn   r\   rY   ri   r1   re   r5   rR   rp   r   rf   r   r   r    rl   f  s    
2zfrac._eval_nseries)Nr   )r   )r?   r@   rA   rB   rE   r6   r   rv   r;   r=   r   r>   r   rq   r   r   r   r   r   rg   rl   r   r   r   r    rx     s$   0
"	
rx   c                 C   sD   |  t|ks|  t|kr dS |jr*dS | |}|d k	r@dS d S )NTF)r   r.   r/   r   r   )r   r   r   r   r   r    r   z  s    
N)'typingr   rC   Zsympy.core.basicr   Zsympy.core.exprr   Z
sympy.corer   r   Zsympy.core.evalfr   r   Zsympy.core.functionr	   Zsympy.core.logicr
   Zsympy.core.numbersr   r   Zsympy.core.relationalr   r   r   r   r   r   Zsympy.core.sympifyr   Z$sympy.functions.elementary.complexesr   r   Zsympy.multipledispatchr   r   r.   r   r/   rx   r   r   r   r    <module>   s0    K #
 #
 L