o
    GZh8                     @   s   d 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 ddlmZ ddlmZ dd	lmZ dd
lmZ dddZeG dd deee	Ze ZdS )z,Implementation of :class:`RealField` class.     )
SYMPY_INTSMPQ)Float)Field)SimpleDomain)CharacteristicZero)CoercionFailed)public)	MPContext)to_rationalTc                 C   s  t | j\}}t|}t|}|r||kr||fS d\}}}}||}	}
	 |	|
 }|||  }||kr4n|||||  |f\}}}}|
|	||
  }	}
q%|| | }t||}t|||  |||  }t||}|rm|sq||fS t|| t|| kr|j|jfS |j|jfS )N)r      r   r   )_mpmath_to_rationalZ_mpf_intr   abs	numeratordenominator)sZ	max_denomlimitpqp0q0p1q1ndaq2knumberbound1bound2 r"   L/var/www/auris/lib/python3.10/site-packages/sympy/polys/domains/realfield.pyr      s0   


r   c                   @   s.  e Zd ZdZdZd ZZdZdZdZ	dZ
dZdZedd Zedd	 Zed
d Zedd Zd?d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$ Zd%d& Zd'd( Zd)d* Zd+d, Z d-d. Z!d@d/d0Z"d1d2 Z#d3d4 Z$d5d6 Z%d7d8 Z&dAd9d:Z'd;d< Z(d=d> Z)dS )B	RealFieldz(Real numbers up to the given precision. RRTF5   c                 C   s   | j | jkS N)	precision_default_precisionselfr"   r"   r#   has_default_precisionG      zRealField.has_default_precisionc                 C      | j jS r'   )_contextprecr*   r"   r"   r#   r(   K      zRealField.precisionc                 C   r.   r'   )r/   dpsr*   r"   r"   r#   r2   O   r1   zRealField.dpsc                 C      | j S r'   )
_tolerancer*   r"   r"   r#   	toleranceS      zRealField.toleranceNc                 C   s   t  }|d u r|d u r| j|_n|d u r||_n|d u r ||_ntd|| _|j| _| d| _	| d| _
td|j d d| _| j
| j | _d S )NzCannot set both prec and dpsr   r         c   )r
   r)   r0   r2   	TypeErrorr/   Zmpf_dtypedtypezeroonemax
_max_denomr4   )r+   r0   r2   Ztolcontextr"   r"   r#   __init__W   s   
zRealField.__init__c                 C   r3   r'   )r;   r*   r"   r"   r#   tpq   s   zRealField.tpc                 C   s   t |tr	t|}| |S r'   )
isinstancer   r   r;   )r+   argr"   r"   r#   r<   y   s   

zRealField.dtypec                 C   s   t |to
| j|jkS r'   )rD   r$   r(   )r+   otherr"   r"   r#   __eq__      zRealField.__eq__c                 C   s   t | jj| j| jfS r'   )hash	__class____name__r;   r(   r*   r"   r"   r#   __hash__   rH   zRealField.__hash__c                 C   s   t || jS )z%Convert ``element`` to SymPy number. )r   r2   )r+   elementr"   r"   r#   to_sympy   r-   zRealField.to_sympyc                 C   s*   |j | jd}|jr| |S td| )z%Convert SymPy's number to ``dtype``. )r   zexpected real number, got %s)evalfr2   Z	is_Numberr<   r   )r+   exprr   r"   r"   r#   
from_sympy   s   
zRealField.from_sympyc                 C   
   |  |S r'   r<   r+   rM   baser"   r"   r#   from_ZZ      
zRealField.from_ZZc                 C   rR   r'   rS   rT   r"   r"   r#   from_ZZ_python   rW   zRealField.from_ZZ_pythonc                 C   s   |  t|S r'   )r<   r   rT   r"   r"   r#   from_ZZ_gmpy   s   zRealField.from_ZZ_gmpyc                 C      |  |jt|j S r'   r<   r   r   r   rT   r"   r"   r#   from_QQ   rH   zRealField.from_QQc                 C   rZ   r'   r[   rT   r"   r"   r#   from_QQ_python   rH   zRealField.from_QQ_pythonc                 C   s   |  t|jt|j S r'   )r<   r   r   r   rT   r"   r"   r#   from_QQ_gmpy   s   zRealField.from_QQ_gmpyc                 C   s   |  ||| jS r'   )rQ   rN   rO   r2   rT   r"   r"   r#   from_AlgebraicField   s   zRealField.from_AlgebraicFieldc                 C   rR   r'   rS   rT   r"   r"   r#   from_RealField   rW   zRealField.from_RealFieldc                 C   s   |j s	| |jS d S r'   )imagr<   realrT   r"   r"   r#   from_ComplexField   s   zRealField.from_ComplexFieldc                 C   s   t || j|dS )z*Convert a real number to rational number. )r   )r   r@   )r+   rM   r   r"   r"   r#   r         zRealField.to_rationalc                 C   s   | S )z)Returns a ring associated with ``self``. r"   r*   r"   r"   r#   get_ring   s   zRealField.get_ringc                 C   s   ddl m} |S )z2Returns an exact domain associated with ``self``. r   )QQ)Zsympy.polys.domainsrf   )r+   rf   r"   r"   r#   	get_exact   s   zRealField.get_exactc                 C   r3   )z Returns GCD of ``a`` and ``b``. )r>   r+   r   br"   r"   r#   gcd   r6   zRealField.gcdc                 C   s   || S )z Returns LCM of ``a`` and ``b``. r"   rh   r"   r"   r#   lcm   r1   zRealField.lcmc                 C   s   | j |||S )z+Check if ``a`` and ``b`` are almost equal. )r/   almosteq)r+   r   ri   r5   r"   r"   r#   rl      rd   zRealField.almosteqc                 C   s   |dkS )z8Returns ``True`` if ``a >= 0`` and ``False`` otherwise. r   r"   r+   r   r"   r"   r#   	is_square   r1   zRealField.is_squarec                 C   s   |dkr|d S dS )zNon-negative square root for ``a >= 0`` and ``None`` otherwise.

        Explanation
        ===========
        The square root may be slightly inaccurate due to floating point
        rounding error.
        r   g      ?Nr"   rm   r"   r"   r#   exsqrt   s   zRealField.exsqrt)NNNTr'   )*rK   
__module____qualname____doc__repZis_RealFieldZis_RRZis_ExactZis_NumericalZis_PIDZhas_assoc_RingZhas_assoc_Fieldr)   propertyr,   r(   r2   r5   rB   rC   r<   rG   rL   rN   rQ   rV   rX   rY   r\   r]   r^   r_   r`   rc   r   re   rg   rj   rk   rl   rn   ro   r"   r"   r"   r#   r$   6   sV    





	

r$   Nrp   )rs   Zsympy.external.gmpyr   r   Zsympy.core.numbersr   Zsympy.polys.domains.fieldr   Z sympy.polys.domains.simpledomainr   Z&sympy.polys.domains.characteristiczeror   Zsympy.polys.polyerrorsr   Zsympy.utilitiesr	   Zmpmathr
   Zmpmath.libmpr   r   r$   r%   r"   r"   r"   r#   <module>   s    
& 
&