a
    kh                     @   sR   d Z ddlmZ ddlmZ ddlmZmZ ddlm	Z	 e	G dd deeZ
dS )	z0Implementation of :class:`FractionField` class.     )CompositeDomain)Field)CoercionFailedGeneratorsError)publicc                   @   s.  e Zd ZdZd ZZdZdZdDddZdd Z	dd	 Z
ed
d Ze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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Z d4d5 Z!d6d7 Z"d8d9 Z#d:d; Z$d<d= Z%d>d? Z&d@dA Z'dBdC Z(dS )EFractionFieldz@A class for representing multivariate rational function fields. TNc                 C   sr   ddl m} t||r,|d u r,|d u r,|}n||||}|| _|j| _|j| _|j| _|j| _|j| _| j| _	d S )Nr   )	FracField)
Zsympy.polys.fieldsr   
isinstancefielddtypeZgensZngenssymbolsdomaindom)selfZdomain_or_fieldr   orderr   r
    r   O/var/www/auris/lib/python3.9/site-packages/sympy/polys/domains/fractionfield.py__init__   s    zFractionField.__init__c                 C   s   | j |S N)r
   Z	field_newr   elementr   r   r   new%   s    zFractionField.newc                 C   s   | j |S )z%Check if ``a`` is of type ``dtype``. )r
   Z
is_elementr   r   r   r   of_type(   s    zFractionField.of_typec                 C   s   | j jS r   )r
   zeror   r   r   r   r   ,   s    zFractionField.zeroc                 C   s   | j jS r   )r
   oner   r   r   r   r   0   s    zFractionField.onec                 C   s   | j jS r   )r
   r   r   r   r   r   r   4   s    zFractionField.orderc                 C   s$   t | jd dtt | j d S )N(,))strr   joinmapr   r   r   r   r   __str__8   s    zFractionField.__str__c                 C   s   t | jj| j| j| jfS r   )hash	__class____name__r
   r   r   r   r   r   r   __hash__;   s    zFractionField.__hash__c                 C   s   t |tstS | j|jkS )z0Returns ``True`` if two domains are equivalent. )r	   r   NotImplementedr
   )r   otherr   r   r   __eq__>   s    
zFractionField.__eq__c                 C   s   |  S )z!Convert ``a`` to a SymPy object. )Zas_exprr   ar   r   r   to_sympyD   s    zFractionField.to_sympyc                 C   s   | j |S )z)Convert SymPy's expression to ``dtype``. )r
   Z	from_exprr*   r   r   r   
from_sympyH   s    zFractionField.from_sympyc                 C   s   | | j ||S z.Convert a Python ``int`` object to ``dtype``. r   convertK1r+   K0r   r   r   from_ZZL   s    zFractionField.from_ZZc                 C   s   | | j ||S r.   r/   r1   r   r   r   from_ZZ_pythonP   s    zFractionField.from_ZZ_pythonc                 C   sL   | j }|j}|jr:| ||||| |||| S | |||S dS )3Convert a Python ``Fraction`` object to ``dtype``. N)r   convert_fromZis_ZZnumerdenom)r2   r+   r3   r   convr   r   r   from_QQT   s
    (zFractionField.from_QQc                 C   s   | | j ||S )r6   r/   r1   r   r   r   from_QQ_python]   s    zFractionField.from_QQ_pythonc                 C   s   | | j ||S )z,Convert a GMPY ``mpz`` object to ``dtype``. r/   r1   r   r   r   from_ZZ_gmpya   s    zFractionField.from_ZZ_gmpyc                 C   s   | | j ||S )z,Convert a GMPY ``mpq`` object to ``dtype``. r/   r1   r   r   r   from_QQ_gmpye   s    zFractionField.from_QQ_gmpyc                 C   s   | | j ||S )z4Convert a ``GaussianRational`` object to ``dtype``. r/   r1   r   r   r   from_GaussianRationalFieldi   s    z(FractionField.from_GaussianRationalFieldc                 C   s   | | j ||S )z3Convert a ``GaussianInteger`` object to ``dtype``. r/   r1   r   r   r   from_GaussianIntegerRingm   s    z&FractionField.from_GaussianIntegerRingc                 C   s   | | j ||S z.Convert a mpmath ``mpf`` object to ``dtype``. r/   r1   r   r   r   from_RealFieldq   s    zFractionField.from_RealFieldc                 C   s   | | j ||S rA   r/   r1   r   r   r   from_ComplexFieldu   s    zFractionField.from_ComplexFieldc                 C   s.   | j |kr| j ||}|dur*| |S dS )z*Convert an algebraic number to ``dtype``. N)r   r7   r   r1   r   r   r   from_AlgebraicFieldy   s    
z!FractionField.from_AlgebraicFieldc                 C   sx   |j r| |d|jS z| || jjW S  tt	fyr   z| |W  Y S  tt	fyl   Y Y dS 0 Y n0 dS )z#Convert a polynomial to ``dtype``.    N)
Z	is_groundr7   Zcoeffr   r   Zset_ringr
   Zringr   r   r1   r   r   r   from_PolynomialRing   s    z!FractionField.from_PolynomialRingc              	   C   s,   z| | jW S  ttfy&   Y dS 0 dS )z*Convert a rational function to ``dtype``. N)Z	set_fieldr
   r   r   r1   r   r   r   from_FractionField   s    z FractionField.from_FractionFieldc                 C   s   | j   S )z*Returns a field associated with ``self``. )r
   Zto_ringZ	to_domainr   r   r   r   get_ring   s    zFractionField.get_ringc                 C   s   | j |jjS )z'Returns True if ``LC(a)`` is positive. )r   is_positiver8   LCr*   r   r   r   rI      s    zFractionField.is_positivec                 C   s   | j |jjS )z'Returns True if ``LC(a)`` is negative. )r   is_negativer8   rJ   r*   r   r   r   rK      s    zFractionField.is_negativec                 C   s   | j |jjS )z+Returns True if ``LC(a)`` is non-positive. )r   is_nonpositiver8   rJ   r*   r   r   r   rL      s    zFractionField.is_nonpositivec                 C   s   | j |jjS )z+Returns True if ``LC(a)`` is non-negative. )r   is_nonnegativer8   rJ   r*   r   r   r   rM      s    zFractionField.is_nonnegativec                 C   s   |j S )zReturns numerator of ``a``. )r8   r*   r   r   r   r8      s    zFractionField.numerc                 C   s   |j S )zReturns denominator of ``a``. )r9   r*   r   r   r   r9      s    zFractionField.denomc                 C   s   |  | j|S )zReturns factorial of ``a``. )r   r   	factorialr*   r   r   r   rN      s    zFractionField.factorial)NN))r%   
__module____qualname____doc__Zis_FractionFieldZis_FracZhas_assoc_RingZhas_assoc_Fieldr   r   r   propertyr   r   r   r"   r&   r)   r,   r-   r4   r5   r;   r<   r=   r>   r?   r@   rB   rC   rD   rF   rG   rH   rI   rK   rL   rM   r8   r9   rN   r   r   r   r   r   	   sN   



	r   N)rQ   Z#sympy.polys.domains.compositedomainr   Zsympy.polys.domains.fieldr   Zsympy.polys.polyerrorsr   r   Zsympy.utilitiesr   r   r   r   r   r   <module>   s   