o
    8Va"                     @   s|   d 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mZmZ ddlmZ eG d	d
 d
eeeZdS )z0Implementation of :class:`FractionField` class.     )Field)CompositeDomain)CharacteristicZero)DMF)GeneratorsNeeded)dict_from_basicbasic_from_dict_dict_reorder)publicc                   @   s   e Zd ZdZeZd ZZdZ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  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Z d1d2 Z!d3d4 Z"d5S )6FractionFieldz3A class for representing rational function fields. Tc                 G   sf   |st dt|d }t|| _| jj||| d| _| jj||| d| _| | _| _| | _| _	d S )Nzgenerators not specified   Zring)
r   lenZngensdtypeZzeroZonedomaindomsymbolsgens)selfr   r   Zlev r   G/usr/lib/python3/dist-packages/sympy/polys/domains/old_fractionfield.py__init__   s   
zFractionField.__init__c                 C   s   | j || jt| jd | dS )Nr   r   )r   r   r   r   )r   elementr   r   r   new#   s   zFractionField.newc                 C   s$   t | jd dtt | j d S )N(,))strr   joinmapr   r   r   r   r   __str__&   s   $zFractionField.__str__c                 C   s   t | jj| j| j| jfS )N)hash	__class____name__r   r   r   r    r   r   r   __hash__)   s   zFractionField.__hash__c                 C   s.   t |to| j|jko| j|jko| j|jkS )z0Returns ``True`` if two domains are equivalent. )
isinstancer   r   r   r   )r   otherr   r   r   __eq__,   s   



zFractionField.__eq__c                 C   s4   t |  g| jR  t |  g| jR   S )z!Convert ``a`` to a SymPy object. )r   numerZto_sympy_dictr   denomr   ar   r   r   to_sympy1   s   zFractionField.to_sympyc           	      C   s   |  \}}t|| jd\}}t|| jd\}}| D ]\}}| j|||< q| D ]\}}| j|||< q-| ||f S )z)Convert SymPy's expression to ``dtype``. )r   )Zas_numer_denomr   r   itemsr   
from_sympyZcancel)	r   r,   pqZnum_Zdenkvr   r   r   r/   6   s   zFractionField.from_sympyc                 C      | | j ||S z.Convert a Python ``int`` object to ``dtype``. r   convertK1r,   K0r   r   r   from_ZZE      zFractionField.from_ZZc                 C   r5   r6   r7   r9   r   r   r   from_ZZ_pythonI   r=   zFractionField.from_ZZ_pythonc                 C   r5   )z3Convert a Python ``Fraction`` object to ``dtype``. r7   r9   r   r   r   from_QQ_pythonM   r=   zFractionField.from_QQ_pythonc                 C   r5   )z,Convert a GMPY ``mpz`` object to ``dtype``. r7   r9   r   r   r   from_ZZ_gmpyQ   r=   zFractionField.from_ZZ_gmpyc                 C   r5   )z,Convert a GMPY ``mpq`` object to ``dtype``. r7   r9   r   r   r   from_QQ_gmpyU   r=   zFractionField.from_QQ_gmpyc                 C   r5   )z.Convert a mpmath ``mpf`` object to ``dtype``. r7   r9   r   r   r   from_RealFieldY   r=   zFractionField.from_RealFieldc                    s~   j  j krj jkr|jS |jjS t|  j j \}}j jkr6 fdd|D }tt||S )z'Convert a ``DMF`` object to ``dtype``. c                       g | ]
}j | j qS r   r7   .0cr;   r:   r   r   
<listcomp>h       z;FractionField.from_GlobalPolynomialRing.<locals>.<listcomp>)r   r   repr8   r	   to_dictdictzip)r:   r,   r;   ZmonomsZcoeffsr   rG   r   from_GlobalPolynomialRing]   s   
z'FractionField.from_GlobalPolynomialRingc                    s   j  j kr"j jkr|S | jj| jjfS t j j rqt| 	  j j \}}t| 	  j j \}}j jkra fdd|D } fdd|D }t
t||t
t||fS dS )a  
        Convert a fraction field element to another fraction field.

        Examples
        ========

        >>> from sympy.polys.polyclasses import DMF
        >>> from sympy.polys.domains import ZZ, QQ
        >>> from sympy.abc import x

        >>> f = DMF(([ZZ(1), ZZ(2)], [ZZ(1), ZZ(1)]), ZZ)

        >>> QQx = QQ.old_frac_field(x)
        >>> ZZx = ZZ.old_frac_field(x)

        >>> QQx.from_FractionField(f, ZZx)
        (x + 2)/(x + 1)

        c                    rC   r   r7   rD   rG   r   r   rH      rI   z4FractionField.from_FractionField.<locals>.<listcomp>c                    rC   r   r7   rD   rG   r   r   rH      rI   N)r   r   r)   r8   rJ   r*   setissubsetr	   rK   rL   rM   )r:   r,   r;   ZnmonomsZncoeffsZdmonomsZdcoeffsr   rG   r   from_FractionFieldl   s$    z FractionField.from_FractionFieldc                 C   s    ddl m} || jg| jR  S )z)Returns a ring associated with ``self``. r   )PolynomialRing)Zsympy.polys.domainsrR   r   r   )r   rR   r   r   r   get_ring   s   zFractionField.get_ringc                 G      t d)z(Returns a polynomial ring, i.e. `K[X]`. nested domains not allowedNotImplementedErrorr   r   r   r   r   	poly_ring      zFractionField.poly_ringc                 G   rT   )z'Returns a fraction field, i.e. `K(X)`. rU   rV   rX   r   r   r   
frac_field   rZ   zFractionField.frac_fieldc                 C      | j |  S )z#Returns True if ``a`` is positive. )r   is_positiver)   LCr+   r   r   r   r]         zFractionField.is_positivec                 C   r\   )z#Returns True if ``a`` is negative. )r   is_negativer)   r^   r+   r   r   r   r`      r_   zFractionField.is_negativec                 C   r\   )z'Returns True if ``a`` is non-positive. )r   is_nonpositiver)   r^   r+   r   r   r   ra      r_   zFractionField.is_nonpositivec                 C   r\   )z'Returns True if ``a`` is non-negative. )r   is_nonnegativer)   r^   r+   r   r   r   rb      r_   zFractionField.is_nonnegativec                 C      |  S )zReturns numerator of ``a``. )r)   r+   r   r   r   r)      rZ   zFractionField.numerc                 C   rc   )zReturns denominator of ``a``. )r*   r+   r   r   r   r*      rZ   zFractionField.denomc                 C   s   |  | j|S )zReturns factorial of ``a``. )r   r   	factorialr+   r   r   r   rd      r=   zFractionField.factorialN)#r$   
__module____qualname____doc__r   r   Zis_FractionFieldZis_FracZhas_assoc_RingZhas_assoc_Fieldr   r   r!   r%   r(   r-   r/   r<   r>   r?   r@   rA   rB   rN   rQ   rS   rY   r[   r]   r`   ra   rb   r)   r*   rd   r   r   r   r   r      s>    &r   N)rg   Zsympy.polys.domains.fieldr   Z#sympy.polys.domains.compositedomainr   Z&sympy.polys.domains.characteristiczeror   Zsympy.polys.polyclassesr   Zsympy.polys.polyerrorsr   Zsympy.polys.polyutilsr   r   r	   Zsympy.utilitiesr
   r   r   r   r   r   <module>   s    