o
    eJ                     @   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r5t|}|tjs/| |tj S | |ddS tj	 } }}t
|}|D ] }|jsP|jrUt|jrU||7 }qC|tr_||7 }qC||7 }qC|sj|sj|S |r|r|jrz|jstj| js|jr|jrzt|| ji dd\}	}|t|	t|tj  7 }tj	}W n ttfy   Y nw ||7 }|s|S |jstj| jr|| t|ddtj  S t|ttfr|| S || |dd S )NFevaluateT)Z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npartsparttermstr r1   SD:\Projects\ConvertPro\env\Lib\site-packages\sympy/functions/elementary/integers.pyeval   sd   









zRoundFunction.evalc                 C   s   t  N)r%   r)   r*   r1   r1   r2   r   Q   s   zRoundFunction._eval_numberc                 C      | j d jS Nr   )r   r   selfr1   r1   r2   _eval_is_finiteU      zRoundFunction._eval_is_finitec                 C   r6   r7   r   r    r8   r1   r1   r2   _eval_is_realX   r;   zRoundFunction._eval_is_realc                 C   r6   r7   r<   r8   r1   r1   r2   _eval_is_integer[   r;   zRoundFunction._eval_is_integerN)__name__
__module____qualname____doc__tTupler   __annotations__classmethodr3   r   r:   r=   r>   r1   r1   r1   r2   r      s   
 
5
r   c                   @   t   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   B   |j r| S tdd || fD r|S |jr|td S d S )Nc                 s   (    | ]}t tfD ]}t||V  qqd S r4   r'   r(   r&   .0r,   jr1   r1   r2   	<genexpr>       z%floor._eval_number.<locals>.<genexpr>r   )	is_Numberr'   anyis_NumberSymbolapproximation_intervalr   r5   r1   r1   r2   r         zfloor._eval_numberNr   c           	      C   s   ddl m} | jd }||d}| |d}|tju s!t||r4|j|dt|j	r,dndd}t
|}|jrM||krK|j||d}|j	rI|d S |S |S |j|||dS 	Nr   AccumBounds-+dircdir   logxr]   )!sympy.calculus.accumulationboundsrW   r   subsr   NaNr&   limitr   is_negativer'   r   r[   as_leading_term	r9   xr`   r]   rW   r*   arg0r0   ndirr1   r1   r2   _eval_as_leading_term      
zfloor._eval_as_leading_termc                 C   s   | j d }||d}| |d}|tju r)|j|dt|jr!dndd}t|}|jrTddl	m
} ddlm}	 |||||}
|dkrK|	d|dfn|dd}|
| S ||krn|j||dkra|ndd	}|jrl|d S |S |S )
Nr   rX   rY   rZ   rV   Orderr^   rG   r\   )r   rb   r   rc   rd   r   re   r'   is_infinitera   rW   sympy.series.orderrn   _eval_nseriesr[   r9   rh   nr`   r]   r*   ri   r0   rW   rn   sorj   r1   r1   r2   rq          

 zfloor._eval_nseriesc                 C   r6   r7   )r   re   r8   r1   r1   r2   _eval_is_negative   r;   zfloor._eval_is_negativec                 C   r6   r7   )r   Zis_nonnegativer8   r1   r1   r2   _eval_is_nonnegative   r;   zfloor._eval_is_nonnegativec                 K      t |  S r4   r(   r9   r*   kwargsr1   r1   r2   _eval_rewrite_as_ceiling   r;   zfloor._eval_rewrite_as_ceilingc                 K      |t | S r4   fracr{   r1   r1   r2   _eval_rewrite_as_frac   r;   zfloor._eval_rewrite_as_fracc                 C   s   t |}| jd jr%|jr| jd |d k S |jr%|jr%| jd t|k S | jd |kr2|jr2t jS |t ju r=| jr=t jS t	| |ddS Nr   r^   Fr   )
r   r   r    r   	is_numberr(   trueInfinityr   r   r9   otherr1   r1   r2   __le__      zfloor.__le__c                 C   s   t |}| jd jr#|jr| jd |kS |jr#|jr#| jd t|kS | jd |kr0|jr0t jS |t ju r;| jr;t j	S t
| |ddS Nr   Fr   )r   r   r    r   r   r(   falseNegativeInfinityr   r   r   r   r1   r1   r2   __ge__      zfloor.__ge__c                 C   s   t |}| jd jr%|jr| jd |d kS |jr%|jr%| jd t|kS | jd |kr2|jr2t jS |t ju r=| jr=t j	S t
| |ddS r   )r   r   r    r   r   r(   r   r   r   r   r   r   r1   r1   r2   __gt__   r   zfloor.__gt__c                 C   s   t |}| jd jr#|jr| jd |k S |jr#|jr#| jd t|k S | jd |kr0|jr0t jS |t ju r;| jr;t j	S t
| |ddS r   )r   r   r    r   r   r(   r   r   r   r   r   r   r1   r1   r2   __lt__   r   zfloor.__lt__r7   r   )r?   r@   rA   rB   r$   rE   r   rk   rq   rw   rx   r}   r   r   r   r   r   r1   r1   r1   r2   r'   _       #

	
r'   c                 C       t | t|pt | t|S r4   )r   rewriter(   r   lhsrhsr1   r1   r2   _eval_is_eq   s   r   c                   @   rF   )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

    r^   c                 C   rH   )Nc                 s   rI   r4   rJ   rK   r1   r1   r2   rN   '  rO   z'ceiling._eval_number.<locals>.<genexpr>r^   )rP   r(   rQ   rR   rS   r   r5   r1   r1   r2   r   #  rT   zceiling._eval_numberNr   c           	      C   s   ddl m} | jd }||d}| |d}|tju s!t||r4|j|dt|j	r,dndd}t
|}|jrM||krK|j||d}|j	rG|S |d S |S |j|||dS rU   )ra   rW   r   rb   r   rc   r&   rd   r   re   r(   r   r[   rf   rg   r1   r1   r2   rk   -  rl   zceiling._eval_as_leading_termc                 C   s   | j d }||d}| |d}|tju r)|j|dt|jr!dndd}t|}|jrTddl	m
} ddlm}	 |||||}
|dkrK|	d|dfn|dd}|
| S ||krn|j||dkra|ndd}|jrj|S |d S |S )	Nr   rX   rY   rZ   rV   rm   r^   r\   )r   rb   r   rc   rd   r   re   r(   ro   ra   rW   rp   rn   rq   r[   rr   r1   r1   r2   rq   =  rv   zceiling._eval_nseriesc                 K   ry   r4   r'   r{   r1   r1   r2   _eval_rewrite_as_floorP  r;   zceiling._eval_rewrite_as_floorc                 K      |t |  S r4   r   r{   r1   r1   r2   r   S     zceiling._eval_rewrite_as_fracc                 C   r6   r7   )r   is_positiver8   r1   r1   r2   _eval_is_positiveV  r;   zceiling._eval_is_positivec                 C   r6   r7   )r   Zis_nonpositiver8   r1   r1   r2   _eval_is_nonpositiveY  r;   zceiling._eval_is_nonpositivec                 C   s   t |}| jd jr%|jr| jd |d kS |jr%|jr%| jd t|kS | jd |kr2|jr2t jS |t ju r=| jr=t j	S t
| |ddS r   )r   r   r    r   r   r'   r   r   r   r   r   r   r1   r1   r2   r   \  r   zceiling.__lt__c                 C   s   t |}| jd jr#|jr| jd |kS |jr#|jr#| jd t|kS | jd |kr0|jr0t jS |t ju r;| jr;t j	S t
| |ddS r   )r   r   r    r   r   r'   r   r   r   r   r   r   r1   r1   r2   r   j  r   zceiling.__gt__c                 C   s   t |}| jd jr%|jr| jd |d kS |jr%|jr%| jd t|kS | jd |kr2|jr2t jS |t ju r=| jr=t jS t	| |ddS r   )
r   r   r    r   r   r'   r   r   r   r   r   r1   r1   r2   r   x  r   zceiling.__ge__c                 C   s   t |}| jd jr#|jr| jd |kS |jr#|jr#| jd t|kS | jd |kr0|jr0t jS |t ju r;| jr;t j	S t
| |ddS r   )r   r   r    r   r   r'   r   r   r   r   r   r   r1   r1   r2   r     r   zceiling.__le__r7   r   )r?   r@   rA   rB   r$   rE   r   rk   rq   r   r   r   r   r   r   r   r   r1   r1   r1   r2   r(      r   r(   c                 C   r   r4   )r   r   r'   r   r   r1   r1   r2   r     s    c                   @   s   e Zd ZdZedd Zdd Zdd Zdd	 Zd
d Z	dd Z
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd$d d!Zd%d"d#ZdS )&r   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

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 
 M