U
    L?hR                     @   sn   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
mZmZ ddlmZ eG dd	 d	eeZd
S )z0Implementation of :class:`FractionField` class.     )Field)CompositeDomain)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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Z d1d2 Z!d3d4 Z"d5d6 Z#d7S )8FractionFieldz3A class for representing rational function fields. Tc                 G   s^   |st dt|d }t|| _| j||| _| j||| _| | _| _| | _| _	d S )Nzgenerators not specified   )
r   lenZngensdtypezeroonedomaindomsymbolsgens)selfr   r   Zlev r   W/var/www/html/venv/lib/python3.8/site-packages/sympy/polys/domains/old_fractionfield.py__init__   s    
zFractionField.__init__c                 C   s   | j |f| j S )z-Make a new fraction field with given domain. )	__class__r   )r   r   r   r   r   
set_domain"   s    zFractionField.set_domainc                 C   s   |  || jt| jd S )Nr   )r   r   r   r   )r   elementr   r   r   new&   s    zFractionField.newc                 C   s$   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)hashr   __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   s0   t |  f| j t |  f| j  S )z!Convert ``a`` to a SymPy object. )r   numerZto_sympy_dictr   denomr   ar   r   r   to_sympy4   s    zFractionField.to_sympyc           	      C   s   |  \}}t|| jd\}}t|| jd\}}| D ]\}}| j|||< q8| D ]\}}| j|||< qZ| ||f S )z)Convert SymPy's expression to ``dtype``. )r   )Zas_numer_denomr   r   itemsr   
from_sympycancel)	r   r-   pqnum_Zdenkvr   r   r   r0   9   s    zFractionField.from_sympyc                 C   s   | | j ||S z.Convert a Python ``int`` object to ``dtype``. r   convertK1r-   K0r   r   r   from_ZZH   s    zFractionField.from_ZZc                 C   s   | | j ||S r8   r9   r;   r   r   r   from_ZZ_pythonL   s    zFractionField.from_ZZ_pythonc                 C   s   | | j ||S )z3Convert a Python ``Fraction`` object to ``dtype``. r9   r;   r   r   r   from_QQ_pythonP   s    zFractionField.from_QQ_pythonc                 C   s   | | j ||S )z,Convert a GMPY ``mpz`` object to ``dtype``. r9   r;   r   r   r   from_ZZ_gmpyT   s    zFractionField.from_ZZ_gmpyc                 C   s   | | j ||S )z,Convert a GMPY ``mpq`` object to ``dtype``. r9   r;   r   r   r   from_QQ_gmpyX   s    zFractionField.from_QQ_gmpyc                 C   s   | | j ||S )z.Convert a mpmath ``mpf`` object to ``dtype``. r9   r;   r   r   r   from_RealField\   s    zFractionField.from_RealFieldc                    s   j  j kr:j jkr$| S |j S nJt|  j j \}}j jkrr fdd|D }tt||S dS )z'Convert a ``DMF`` object to ``dtype``. c                    s   g | ]}j | j qS r   r9   .0cr=   r<   r   r   
<listcomp>k   s     z;FractionField.from_GlobalPolynomialRing.<locals>.<listcomp>N)r   r   to_listr:   r   to_dictdictzip)r<   r-   r=   ZmonomsZcoeffsr   rG   r   from_GlobalPolynomialRing`   s    z'FractionField.from_GlobalPolynomialRingc                    s   j  j krJj jkr|S | j | j fS nt j j rt| 	  j j \}}t| 	  j j \}}j jkrȇ 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)
        DMF([1, 2], [1, 1], QQ)

        c                    s   g | ]}j | j qS r   r9   rD   rG   r   r   rH      s     z4FractionField.from_FractionField.<locals>.<listcomp>c                    s   g | ]}j | j qS r   r9   rD   rG   r   r   rH      s     N)r   r   r*   r:   rI   r+   setissubsetr   rJ   rK   rL   )r<   r-   r=   ZnmonomsZncoeffsZdmonomsZdcoeffsr   rG   r   from_FractionFieldo   s*    
  
  z FractionField.from_FractionFieldc                 C   s   ddl m} || jf| j S )z)Returns a ring associated with ``self``. r   )PolynomialRing)Zsympy.polys.domainsrQ   r   r   )r   rQ   r   r   r   get_ring   s    zFractionField.get_ringc                 G   s   t ddS )z(Returns a polynomial ring, i.e. `K[X]`. nested domains not allowedNNotImplementedErrorr   r   r   r   r   	poly_ring   s    zFractionField.poly_ringc                 G   s   t ddS )z'Returns a fraction field, i.e. `K(X)`. rS   NrT   rV   r   r   r   
frac_field   s    zFractionField.frac_fieldc                 C   s   | j |  S )z#Returns True if ``a`` is positive. )r   is_positiver*   LCr,   r   r   r   rY      s    zFractionField.is_positivec                 C   s   | j |  S )z#Returns True if ``a`` is negative. )r   is_negativer*   rZ   r,   r   r   r   r[      s    zFractionField.is_negativec                 C   s   | j |  S )z'Returns True if ``a`` is non-positive. )r   is_nonpositiver*   rZ   r,   r   r   r   r\      s    zFractionField.is_nonpositivec                 C   s   | j |  S )z'Returns True if ``a`` is non-negative. )r   is_nonnegativer*   rZ   r,   r   r   r   r]      s    zFractionField.is_nonnegativec                 C   s   |  S )zReturns numerator of ``a``. )r*   r,   r   r   r   r*      s    zFractionField.numerc                 C   s   |  S )zReturns denominator of ``a``. )r+   r,   r   r   r   r+      s    zFractionField.denomc                 C   s   |  | j|S )zReturns factorial of ``a``. )r   r   	factorialr,   r   r   r   r^      s    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.   r0   r>   r?   r@   rA   rB   rC   rM   rP   rR   rW   rX   rY   r[   r\   r]   r*   r+   r^   r   r   r   r   r
      s>   &r
   N)ra   Zsympy.polys.domains.fieldr   Z#sympy.polys.domains.compositedomainr   Zsympy.polys.polyclassesr   Zsympy.polys.polyerrorsr   Zsympy.polys.polyutilsr   r   r   Zsympy.utilitiesr	   r
   r   r   r   r   <module>   s   