U
    ;qLeJ                     @   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 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	 } }}t
|}|D ]@}|js|jrt|jr||7 }q|tr||7 }q||7 }q|s|s|S |rb|r|jr|jstj| js|jrb|jrbz:t|| ji dd\}	}|t|	t|tj  7 }tj	}W n ttfk
r`   Y nX ||7 }|st|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   z/home/p21-0144/sympy/latex2sympy2solve-back-end/sympyEq/lib/python3.8/site-packages/sympy/functions/elementary/integers.pyeval   sh    






   

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] 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 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   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}|j	r|d S |S |S |j|||dS 	Nr   AccumBounds-+dircdir   logxrV   )!sympy.calculus.accumulationboundsrP   r   subsr   NaNr'   limitr   is_negativer(   r   rT   as_leading_term	r8   xrY   rV   rP   r+   arg0r0   ndirr1   r1   r2   _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 |S |S d S )
Nr   rQ   rR   rS   rO   OrderrW   rD   rU   )r   r[   r   r\   r]   r   r^   r(   is_infiniterZ   rP   sympy.series.orderrf   _eval_nseriesrT   r8   ra   nrY   rV   r+   rb   r0   rP   rf   sorc   r1   r1   r2   ri      s     

 zfloor._eval_nseriesc                 C   s   | j d jS r6   )r   r^   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krz| jrzt jS t	| |ddS Nr   rW   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k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k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k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   rd   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] 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 r4   rE   rF   r1   r1   r2   rI   '  s    
 z'ceiling._eval_number.<locals>.<genexpr>rW   )rJ   r)   rK   rL   rM   r   r5   r1   r1   r2   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}|j	r|S |d S |S |j|||dS rN   )rZ   rP   r   r[   r   r\   r'   r]   r   r^   r)   r   rT   r_   r`   r1   r1   r2   rd   -  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 |d S |S d S )	Nr   rQ   rR   rS   rO   re   rW   rU   )r   r[   r   r\   r]   r   r^   r)   rg   rZ   rP   rh   rf   ri   rT   rj   r1   r1   r2   ri   =  s     

 zceiling._eval_nseriesc                 K   s   t |  S r4   r(   rr   r1   r1   r2   _eval_rewrite_as_floorP  s    zceiling._eval_rewrite_as_floorc                 K   s   |t |  S r4   ru   rr   r1   r1   r2   rw   S  s    zceiling._eval_rewrite_as_fracc                 C   s   | j d jS r6   )r   is_positiver7   r1   r1   r2   _eval_is_positiveV  s    zceiling._eval_is_positivec                 C   s   | j d jS r6   )r   is_nonpositiver7   r1   r1   r2   _eval_is_nonpositiveY  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 rx   )r   r   r!   r   ry   r(   r   r{   r   rz   r   r|   r1   r1   r2   r   \  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   ry   r(   r   r   r   rz   r   r|   r1   r1   r2   r   j  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 rx   )
r   r   r!   r   ry   r(   rz   r   r   r   r|   r1   r1   r2   r   x  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   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   rd   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$d d!Zd%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] https://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   rO   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 rx   )	r   r{   r   r   r#   ry   r\   ComplexInfinityr(   )r+   rP   r*   r1   r2   _eval  s    


zfrac.eval.<locals>._eval)rZ   rP   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 k	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 k	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 k	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 k	r0|S t| |ddS r   )r   r   r   r   r   r   r   r   r1   r1   r2   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   ry   r'   r   r   rz   r   r   r   r1   r1   r2   r   7  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   rO   rU   rX   rW   )rZ   rP   r   r[   r   r   rT   r^   r   Oner_   r   r{   r   r`   r1   r1   r2   rd   @  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   re   rO   rW   rX   rU   )rh   rf   r   r[   rg   rZ   rP   ri   r   rT   r^   r   r   r#   )r8   ra   rk   rY   rV   rf   r+   rb   r0   rP   rm   r   rc   r1   r1   r2   ri   R  s    
2zfrac._eval_nseries)Nr   )r   )r=   r>   r?   r@   rC   r3   r   rt   r9   r;   r   r<   r   rn   r   r   r~   r   r   rd   ri   r1   r1   r1   r2   rv     s$   0
#	
rv   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   r1   r1   r2   r   f  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 
 
 M