o
    Hۂi.                  	   @  s   U 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
mZ d dlmZ d dlmZ d dlmZm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d ZeeeeeeeedZded< dS )!    )annotations)Callable)SAddExprBasicMulPowRational)	fuzzy_not)Boolean)askQTc                   s   t | ts| S | js fdd| jD }| j| } t| dr)|  }|dur)|S | jj}t	
|d}|du r9| S ||  }|du sF| |krH| S t |tsO|S t| S )a  
    Simplify an expression using assumptions.

    Explanation
    ===========

    Unlike :func:`~.simplify` which performs structural simplification
    without any assumption, this function transforms the expression into
    the form which is only valid under certain assumptions. Note that
    ``simplify()`` is generally not done in refining process.

    Refining boolean expression involves reducing it to ``S.true`` or
    ``S.false``. Unlike :func:`~.ask`, the expression will not be reduced
    if the truth value cannot be determined.

    Examples
    ========

    >>> from sympy import refine, sqrt, Q
    >>> from sympy.abc import x
    >>> refine(sqrt(x**2), Q.real(x))
    Abs(x)
    >>> refine(sqrt(x**2), Q.positive(x))
    x

    >>> refine(Q.real(x), Q.positive(x))
    True
    >>> refine(Q.positive(x), Q.real(x))
    Q.positive(x)

    See Also
    ========

    sympy.simplify.simplify.simplify : Structural simplification without assumptions.
    sympy.assumptions.ask.ask : Query for boolean expressions using assumptions.
    c                   s   g | ]}t | qS  )refine).0argassumptionsr   [/home/ubuntu/maya3_transcribe/venv/lib/python3.10/site-packages/sympy/assumptions/refine.py
<listcomp>4   s    zrefine.<locals>.<listcomp>_eval_refineN)
isinstancer   is_Atomargsfunchasattrr   	__class____name__handlers_dictgetr   r   )exprr   r   ref_exprnamehandlernew_exprr   r   r   r      s&   
%





r   c                   s   ddl m} | jd }tt| rttt| r|S tt| r*| S t|t	r_ fdd|jD }g }g }|D ]}t||rO|
|jd  q?|
| q?t	| |t	|  S dS )aF  
    Handler for the absolute value.

    Examples
    ========

    >>> from sympy import Q, Abs
    >>> from sympy.assumptions.refine import refine_abs
    >>> from sympy.abc import x
    >>> refine_abs(Abs(x), Q.real(x))
    >>> refine_abs(Abs(x), Q.positive(x))
    x
    >>> refine_abs(Abs(x), Q.negative(x))
    -x

    r   Absc                   s   g | ]	}t t| qS r   )r   abs)r   ar   r   r   r   b   s    zrefine_abs.<locals>.<listcomp>N)$sympy.functions.elementary.complexesr'   r   r   r   realr   negativer   r   append)r!   r   r'   r   rnon_absin_absir   r   r   
refine_absG   s$   


r2   c                 C  s  ddl m} ddlm} t| j|r0tt| jj	d |r0tt
| j|r0| jj	d | j S tt| j|ra| jjrett
| j|rOt| j| j S tt| j|re|| jt| j| j  S t| jtr~t| jtr~t| jj| jj| j  S | jtju rc| jjre| }| j \}}t|}t }t }t|}	|D ]}
tt
|
|r||
 qtt|
|r||
 q||8 }t|d r||8 }|tj d }n||8 }|d }||kst||	k r|| | jt|  } d| j }tt
||r| r|| j9 }|jrZ| \}}|jrZ|jtju rZtt|j|rZ|d d }tt
||rA| j|j S tt||rR| j|jd  S | j|j|  S || krg| S dS dS dS dS )as  
    Handler for instances of Pow.

    Examples
    ========

    >>> from sympy import Q
    >>> from sympy.assumptions.refine import refine_Pow
    >>> from sympy.abc import x,y,z
    >>> refine_Pow((-1)**x, Q.real(x))
    >>> refine_Pow((-1)**x, Q.even(x))
    1
    >>> refine_Pow((-1)**x, Q.odd(x))
    -1

    For powers of -1, even parts of the exponent can be simplified:

    >>> refine_Pow((-1)**(x+y), Q.even(x))
    (-1)**y
    >>> refine_Pow((-1)**(x+y+z), Q.odd(x) & Q.odd(z))
    (-1)**y
    >>> refine_Pow((-1)**(x+y+2), Q.odd(x))
    (-1)**(y + 1)
    >>> refine_Pow((-1)**(x+3), True)
    (-1)**(x + 1)

    r   r&   )sign      N)r*   r'   sympy.functionsr3   r   baser   r   r+   r   evenexp	is_numberr(   oddr
   r	   r   NegativeOneis_Addas_coeff_addsetlenaddOner   could_extract_minus_signas_two_termsis_Powinteger)r!   r   r'   r3   oldcoeffterms
even_terms	odd_termsinitial_number_of_termst	new_coeffe2r1   pr   r   r   
refine_Powm   sv   







3rQ   c                 C  s"  ddl m} | j\}}tt|t|@ |r||| S tt|t|@ |r4||| tj	 S tt|t|@ |rJ||| tj	 S tt
|t|@ |rZtj	S tt|t
|@ |rltj	d S tt|t
|@ |rtj	 d S tt
|t
|@ |rtjS | S )a  
    Handler for the atan2 function.

    Examples
    ========

    >>> from sympy import Q, atan2
    >>> from sympy.assumptions.refine import refine_atan2
    >>> from sympy.abc import x, y
    >>> refine_atan2(atan2(y,x), Q.real(y) & Q.positive(x))
    atan(y/x)
    >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.negative(x))
    atan(y/x) - pi
    >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.negative(x))
    atan(y/x) + pi
    >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.negative(x))
    pi
    >>> refine_atan2(atan2(y,x), Q.positive(y) & Q.zero(x))
    pi/2
    >>> refine_atan2(atan2(y,x), Q.negative(y) & Q.zero(x))
    -pi/2
    >>> refine_atan2(atan2(y,x), Q.zero(y) & Q.zero(x))
    nan
    r   )atanr4   )(sympy.functions.elementary.trigonometricrR   r   r   r   r+   positiver,   r   PizeroNaN)r!   r   rR   yxr   r   r   refine_atan2   s"   

rZ   c                 C  s>   | j d }tt||r|S tt||rtjS t| |S )a  
    Handler for real part.

    Examples
    ========

    >>> from sympy.assumptions.refine import refine_re
    >>> from sympy import Q, re
    >>> from sympy.abc import x
    >>> refine_re(re(x), Q.real(x))
    x
    >>> refine_re(re(x), Q.imaginary(x))
    0
    r   )r   r   r   r+   	imaginaryr   Zero_refine_reimr!   r   r   r   r   r   	refine_re   s   

r_   c                 C  sF   | j d }tt||rtjS tt||rtj | S t| |S )a  
    Handler for imaginary part.

    Explanation
    ===========

    >>> from sympy.assumptions.refine import refine_im
    >>> from sympy import Q, im
    >>> from sympy.abc import x
    >>> refine_im(im(x), Q.real(x))
    0
    >>> refine_im(im(x), Q.imaginary(x))
    -I*x
    r   )	r   r   r   r+   r   r\   r[   ImaginaryUnitr]   r^   r   r   r   	refine_im  s   

ra   c                 C  s:   | j d }tt||rtjS tt||rtjS dS )a"  
    Handler for complex argument

    Explanation
    ===========

    >>> from sympy.assumptions.refine import refine_arg
    >>> from sympy import Q, arg
    >>> from sympy.abc import x
    >>> refine_arg(arg(x), Q.positive(x))
    0
    >>> refine_arg(arg(x), Q.negative(x))
    pi
    r   N)r   r   r   rT   r   r\   r,   rU   )r!   r   rgr   r   r   
refine_arg+  s   
rc   c                 C  s.   | j dd}|| krt||}||kr|S d S )NT)complex)expandr   )r!   r   expandedrefinedr   r   r   r]   B  s   
r]   c                 C  s   | j d }tt||rtjS tt|r-tt||r"tjS tt	||r-tj
S tt|rQ| \}}tt||rEtjS tt	||rQtj S | S )a*  
    Handler for sign.

    Examples
    ========

    >>> from sympy.assumptions.refine import refine_sign
    >>> from sympy import Symbol, Q, sign, im
    >>> x = Symbol('x', real = True)
    >>> expr = sign(x)
    >>> refine_sign(expr, Q.positive(x) & Q.nonzero(x))
    1
    >>> refine_sign(expr, Q.negative(x) & Q.nonzero(x))
    -1
    >>> refine_sign(expr, Q.zero(x))
    0
    >>> y = Symbol('y', imaginary = True)
    >>> expr = sign(y)
    >>> refine_sign(expr, Q.positive(im(y)))
    I
    >>> refine_sign(expr, Q.negative(im(y)))
    -I
    r   )r   r   r   rV   r   r\   r+   rT   rB   r,   r<   r[   as_real_imagr`   )r!   r   r   arg_rearg_imr   r   r   refine_signM  s   
rk   c                 C  sH   ddl m} | j\}}}tt||r"||  r| S ||||S dS )aU  
    Handler for symmetric part.

    Examples
    ========

    >>> from sympy.assumptions.refine import refine_matrixelement
    >>> from sympy import MatrixSymbol, Q
    >>> X = MatrixSymbol('X', 3, 3)
    >>> refine_matrixelement(X[0, 1], Q.symmetric(X))
    X[0, 1]
    >>> refine_matrixelement(X[1, 0], Q.symmetric(X))
    X[0, 1]
    r   )MatrixElementN)"sympy.matrices.expressions.matexprrl   r   r   r   	symmetricrC   )r!   r   rl   matrixr1   jr   r   r   refine_matrixelementv  s   rq   )r'   r	   atan2reimr   r3   rl   z*dict[str, Callable[[Expr, Boolean], Expr]]r   N)T)
__future__r   typingr   
sympy.corer   r   r   r   r   r	   r
   sympy.core.logicr   sympy.logic.boolalgr   sympy.assumptionsr   r   r   r2   rQ   rZ   r_   ra   rc   r]   rk   rq   r   __annotations__r   r   r   r   <module>   s2    $
<&d-)