o
    jg                     @   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dBd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$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Z d4d5 Z!d6d7 Z"d8d9 Z#d:d; Z$d<d= Z%d>d? Z&d@dA Z'dS )C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)
sympy.polys.fieldsr   
isinstancefielddtypegensngenssymbolsdomaindom)selfdomain_or_fieldr   orderr   r    r   Y/var/www/html/zoom/venv/lib/python3.10/site-packages/sympy/polys/domains/fractionfield.py__init__   s   zFractionField.__init__c                 C      | j |S N)r   	field_new)r   elementr   r   r   new%   s   zFractionField.newc                 C      | j jS r   )r   zeror   r   r   r   r   (      zFractionField.zeroc                 C   r   r   )r   oner   r   r   r   r!   ,   r    zFractionField.onec                 C   r   r   )r   r   r   r   r   r   r   0   r    zFractionField.orderc                 C   s$   t | jd dtt | j d S )N(,))strr   joinmapr   r   r   r   r   __str__4   s   $zFractionField.__str__c                 C   s   t | jj| jj| j| jfS r   )hash	__class____name__r   r   r   r   r   r   r   r   __hash__7   s   zFractionField.__hash__c                 C   s.   t |to| jj| j| jf|jj|j|jfkS )z0Returns ``True`` if two domains are equivalent. )r
   r   r   r   r   r   )r   otherr   r   r   __eq__:   s
   
zFractionField.__eq__c                 C   s   |  S )z!Convert ``a`` to a SymPy object. )as_exprr   ar   r   r   to_sympy@   r    zFractionField.to_sympyc                 C   r   )z)Convert SymPy's expression to ``dtype``. )r   	from_exprr0   r   r   r   
from_sympyD   s   zFractionField.from_sympyc                 C      | | j ||S z.Convert a Python ``int`` object to ``dtype``. r   convertK1r1   K0r   r   r   from_ZZH      zFractionField.from_ZZc                 C   r5   r6   r7   r9   r   r   r   from_ZZ_pythonL   r=   zFractionField.from_ZZ_pythonc                 C   sH   | j }|j}|jr| ||||| |||| S | |||S z3Convert a Python ``Fraction`` object to ``dtype``. )r   convert_fromis_ZZnumerdenom)r:   r1   r;   r   convr   r   r   from_QQP   s
   (zFractionField.from_QQc                 C   r5   r?   r7   r9   r   r   r   from_QQ_pythonY   r=   zFractionField.from_QQ_pythonc                 C   r5   )z,Convert a GMPY ``mpz`` object to ``dtype``. r7   r9   r   r   r   from_ZZ_gmpy]   r=   zFractionField.from_ZZ_gmpyc                 C   r5   )z,Convert a GMPY ``mpq`` object to ``dtype``. r7   r9   r   r   r   from_QQ_gmpya   r=   zFractionField.from_QQ_gmpyc                 C   r5   )z4Convert a ``GaussianRational`` object to ``dtype``. r7   r9   r   r   r   from_GaussianRationalFielde   r=   z(FractionField.from_GaussianRationalFieldc                 C   r5   )z3Convert a ``GaussianInteger`` object to ``dtype``. r7   r9   r   r   r   from_GaussianIntegerRingi   r=   z&FractionField.from_GaussianIntegerRingc                 C   r5   z.Convert a mpmath ``mpf`` object to ``dtype``. r7   r9   r   r   r   from_RealFieldm   r=   zFractionField.from_RealFieldc                 C   r5   rK   r7   r9   r   r   r   from_ComplexFieldq   r=   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   r@   r   r9   r   r   r   from_AlgebraicFieldu   s
   

z!FractionField.from_AlgebraicFieldc                 C   sp   |j r| |d|jS z| || jjW S  tt	fy7   z| |W  Y S  tt	fy6   Y Y dS w w )z#Convert a polynomial to ``dtype``.    N)
	is_groundr@   coeffr   r   set_ringr   ringr   r   r9   r   r   r   from_PolynomialRing|   s   z!FractionField.from_PolynomialRingc              	   C   s(   z| | jW S  ttfy   Y dS w )z*Convert a rational function to ``dtype``. N)	set_fieldr   r   r   r9   r   r   r   from_FractionField   s
   z FractionField.from_FractionFieldc                 C   s   | j   S )z*Returns a field associated with ``self``. )r   to_ring	to_domainr   r   r   r   get_ring   s   zFractionField.get_ringc                 C      | j |jjS )z'Returns True if ``LC(a)`` is positive. )r   is_positiverB   LCr0   r   r   r   r[         zFractionField.is_positivec                 C   rZ   )z'Returns True if ``LC(a)`` is negative. )r   is_negativerB   r\   r0   r   r   r   r^      r]   zFractionField.is_negativec                 C   rZ   )z+Returns True if ``LC(a)`` is non-positive. )r   is_nonpositiverB   r\   r0   r   r   r   r_      r]   zFractionField.is_nonpositivec                 C   rZ   )z+Returns True if ``LC(a)`` is non-negative. )r   is_nonnegativerB   r\   r0   r   r   r   r`      r]   zFractionField.is_nonnegativec                 C      |j S )zReturns numerator of ``a``. )rB   r0   r   r   r   rB         zFractionField.numerc                 C   ra   )zReturns denominator of ``a``. )rC   r0   r   r   r   rC      rb   zFractionField.denomc                 C   s   |  | j|S )zReturns factorial of ``a``. )r   r   	factorialr0   r   r   r   rc      r=   zFractionField.factorial)NN)(r+   
__module____qualname____doc__is_FractionFieldis_Frachas_assoc_Ringhas_assoc_Fieldr   r   propertyr   r!   r   r(   r,   r.   r2   r4   r<   r>   rE   rF   rG   rH   rI   rJ   rL   rM   rN   rT   rV   rY   r[   r^   r_   r`   rB   rC   rc   r   r   r   r   r   	   sN    



	r   N)rf   #sympy.polys.domains.compositedomainr   sympy.polys.domains.fieldr   sympy.polys.polyerrorsr   r   sympy.utilitiesr   r   r   r   r   r   <module>   s    