U
    L?h                     @   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
d	d	d	d	d	dZeG dd de	eeZe ZdS )z3Implementation of :class:`ExpressionDomain` class.     )sympifySympifyError)DomainElement)CharacteristicZero)Field)SimpleDomain)PicklableWithSlots)publicFT)deepmulZ	power_expZ
power_basebasicZmultinomiallogc                   @   s2  e Zd ZdZd ZZG dd deeZeZ	edZ
edZd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$ Zd%d& Zd'd( Zd)d* Zd+d, Z d-d. Z!d/d0 Z"d1d2 Z#d3d4 Z$d5d6 Z%d7d8 Z&d9d: Z'd;d< Z(d=d> Z)d?d@ Z*dAdB Z+dCS )DExpressionDomainz#A class for arbitrary expressions. Tc                   @   s   e Zd 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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9S ):zExpressionDomain.ExpressionzAn arbitrary expression. exc                 C   s$   t || jst|| _n|j| _d S N)
isinstance	__class__r   r   )selfr    r   V/var/www/html/venv/lib/python3.8/site-packages/sympy/polys/domains/expressiondomain.py__init__   s    z$ExpressionDomain.Expression.__init__c                 C   s   dt | j S NzEX(%s))reprr   fr   r   r   __repr__    s    z$ExpressionDomain.Expression.__repr__c                 C   s   dt | j S r   )strr   r   r   r   r   __str__#   s    z#ExpressionDomain.Expression.__str__c                 C   s   t | jj| jfS r   )hashr   __name__r   r   r   r   r   __hash__&   s    z$ExpressionDomain.Expression.__hash__c                 C   s   t S r   )EXr!   r   r   r   parent)   s    z"ExpressionDomain.Expression.parentc                 C   s   | j S r   r   r   r   r   r   as_expr,   s    z#ExpressionDomain.Expression.as_exprc                 C   s   |  | j d S )Nr   r   r   Zas_numer_denomr   r   r   r   numer/   s    z!ExpressionDomain.Expression.numerc                 C   s   |  | j d S N   r&   r   r   r   r   denom2   s    z!ExpressionDomain.Expression.denomc                 C   s   |  | jf tS r   )r   cancelexpandeflags)r   r   r   r   r   simplify5   s    z$ExpressionDomain.Expression.simplifyc                 C   s   |  t| jS r   )r   absr   r   r   r   r   __abs__8   s    z#ExpressionDomain.Expression.__abs__c                 C   s   |  | j S r   )r   r   r   r   r   r   __neg__;   s    z#ExpressionDomain.Expression.__neg__c                 C   s(   z|  |W S  tk
r"   Y d S X d S r   )r   r   r   gr   r   r   _to_ex>   s    z"ExpressionDomain.Expression._to_exc                 C   s   | j  |j  k S r   )r   sort_keyr2   r   r   r   __lt__D   s    z"ExpressionDomain.Expression.__lt__c                 C   sH   |  |}|d krtS |tjkr$| S | tjkr2|S | | j|j S d S r   r4   NotImplementedr#   zeror.   r   r2   r   r   r   __add__G   s    


z#ExpressionDomain.Expression.__add__c                 C   s   |  | |j| j S r   r.   r   r   r2   r   r   r   __radd__S   s    z$ExpressionDomain.Expression.__radd__c                 C   sJ   |  |}|d krtS |tjkr$| S | tjkr4| S | | j|j S d S r   r7   r2   r   r   r   __sub__V   s    


z#ExpressionDomain.Expression.__sub__c                 C   s   |  | |j| j S r   r;   r2   r   r   r   __rsub__b   s    z$ExpressionDomain.Expression.__rsub__c                 C   s^   |  |}|d krtS tj| |fkr*tjS | jjrL|jjrL| | j|j S | | j|j S r   )r4   r8   r#   r9   r   Z	is_Numberr   r.   r2   r   r   r   __mul__e   s    
z#ExpressionDomain.Expression.__mul__c                 C   s   |  | |j| j S r   r;   r2   r   r   r   __rmul__r   s    z$ExpressionDomain.Expression.__rmul__c                 C   s,   |  |}|d k	r$| | j|j S tS d S r   r4   r.   r   r8   )r   nr   r   r   __pow__u   s    
z#ExpressionDomain.Expression.__pow__c                 C   s,   |  |}|d k	r$| | j|j S tS d S r   rA   r2   r   r   r   __truediv__}   s    
z'ExpressionDomain.Expression.__truediv__c                 C   s   |  | |j| j S r   r;   r2   r   r   r   __rtruediv__   s    z(ExpressionDomain.Expression.__rtruediv__c                 C   s   | j | |j kS r   )r   r   r2   r   r   r   __eq__   s    z"ExpressionDomain.Expression.__eq__c                 C   s
   | |k S r   r   r2   r   r   r   __ne__   s    z"ExpressionDomain.Expression.__ne__c                 C   s
   | j j S r   )r   is_zeror   r   r   r   __bool__   s    z$ExpressionDomain.Expression.__bool__c                 C   s&   ddl m} | || j| |jS )Nr   )gcd)sympy.polysrJ   r   r   )r   r3   rJ   r   r   r   rJ      s    zExpressionDomain.Expression.gcdc                 C   s&   ddl m} | || j| |jS )Nr   lcm)rK   rM   r   r   )r   r3   rM   r   r   r   rM      s    zExpressionDomain.Expression.lcmN) r    
__module____qualname____doc__	__slots__r   r   r   r"   r$   r%   r'   r*   r.   r0   r1   r4   r6   r:   r<   r=   r>   r?   r@   rC   rD   rE   rF   rG   rI   rJ   rM   r   r   r   r   
Expression   s:   rR   r   r)   r#   Fc                 C   s   d S r   r   r!   r   r   r   r      s    zExpressionDomain.__init__c                 C   s   t |trdS tS d S )NT)r   r   r8   )r   otherr   r   r   rF      s    
zExpressionDomain.__eq__c                 C   s   t dS )Nr#   )r   r!   r   r   r   r"      s    zExpressionDomain.__hash__c                 C   s   |  S )z!Convert ``a`` to a SymPy object. )r%   r   ar   r   r   to_sympy   s    zExpressionDomain.to_sympyc                 C   s
   |  |S )z)Convert SymPy's expression to ``dtype``. )dtyperT   r   r   r   
from_sympy   s    zExpressionDomain.from_sympyc                 C   s   | | |S z.Convert a Python ``int`` object to ``dtype``. rV   ZK1rU   ZK0r   r   r   from_ZZ   s    zExpressionDomain.from_ZZc                 C   s   | | |S rY   rZ   r[   r   r   r   from_ZZ_python   s    zExpressionDomain.from_ZZ_pythonc                 C   s   | | |S z3Convert a Python ``Fraction`` object to ``dtype``. rZ   r[   r   r   r   from_QQ   s    zExpressionDomain.from_QQc                 C   s   | | |S r^   rZ   r[   r   r   r   from_QQ_python   s    zExpressionDomain.from_QQ_pythonc                 C   s   | | |S )z,Convert a GMPY ``mpz`` object to ``dtype``. rZ   r[   r   r   r   from_ZZ_gmpy   s    zExpressionDomain.from_ZZ_gmpyc                 C   s   | | |S )z,Convert a GMPY ``mpq`` object to ``dtype``. rZ   r[   r   r   r   from_QQ_gmpy   s    zExpressionDomain.from_QQ_gmpyc                 C   s   | | |S z4Convert a ``GaussianRational`` object to ``dtype``. rZ   r[   r   r   r   from_GaussianIntegerRing   s    z)ExpressionDomain.from_GaussianIntegerRingc                 C   s   | | |S rc   rZ   r[   r   r   r   from_GaussianRationalField   s    z+ExpressionDomain.from_GaussianRationalFieldc                 C   s   | | |S )z(Convert an ``ANP`` object to ``dtype``. rZ   r[   r   r   r   from_AlgebraicField   s    z$ExpressionDomain.from_AlgebraicFieldc                 C   s   | | |S )z.Convert a mpmath ``mpf`` object to ``dtype``. rZ   r[   r   r   r   from_RealField   s    zExpressionDomain.from_RealFieldc                 C   s   | | |S )z.Convert a mpmath ``mpc`` object to ``dtype``. rZ   r[   r   r   r   from_ComplexField   s    z"ExpressionDomain.from_ComplexFieldc                 C   s   | | |S )z'Convert a ``DMP`` object to ``dtype``. rZ   r[   r   r   r   from_PolynomialRing   s    z$ExpressionDomain.from_PolynomialRingc                 C   s   | | |S )z'Convert a ``DMF`` object to ``dtype``. rZ   r[   r   r   r   from_FractionField   s    z#ExpressionDomain.from_FractionFieldc                 C   s   |S )z&Convert a ``EX`` object to ``dtype``. r   r[   r   r   r   from_ExpressionDomain   s    z&ExpressionDomain.from_ExpressionDomainc                 C   s   | S )z)Returns a ring associated with ``self``. r   r!   r   r   r   get_ring   s    zExpressionDomain.get_ringc                 C   s   | S )z*Returns a field associated with ``self``. r   r!   r   r   r   	get_field   s    zExpressionDomain.get_fieldc                 C   s   |j  d jS )z#Returns True if ``a`` is positive. r   )r   as_coeff_mulis_positiverT   r   r   r   ro      s    zExpressionDomain.is_positivec                 C   s
   |j  S )z#Returns True if ``a`` is negative. )r   Zcould_extract_minus_signrT   r   r   r   is_negative   s    zExpressionDomain.is_negativec                 C   s   |j  d jS )z'Returns True if ``a`` is non-positive. r   )r   rn   is_nonpositiverT   r   r   r   rq      s    zExpressionDomain.is_nonpositivec                 C   s   |j  d jS )z'Returns True if ``a`` is non-negative. r   )r   rn   is_nonnegativerT   r   r   r   rr     s    zExpressionDomain.is_nonnegativec                 C   s   |  S )zReturns numerator of ``a``. )r'   rT   r   r   r   r'     s    zExpressionDomain.numerc                 C   s   |  S )zReturns denominator of ``a``. )r*   rT   r   r   r   r*     s    zExpressionDomain.denomc                 C   s   | dS r(   r   r   rU   br   r   r   rJ     s    zExpressionDomain.gcdc                 C   s
   | |S r   rL   rs   r   r   r   rM     s    zExpressionDomain.lcmN),r    rN   rO   rP   Zis_SymbolicDomainZis_EXr   r   rR   rW   r9   onerepZhas_assoc_RingZhas_assoc_Fieldr   rF   r"   rV   rX   r\   r]   r_   r`   ra   rb   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   ro   rp   rq   rr   r'   r*   rJ   rM   r   r   r   r   r      sN    r   N)rP   Z
sympy.corer   r   Z!sympy.polys.domains.domainelementr   Z&sympy.polys.domains.characteristiczeror   Zsympy.polys.domains.fieldr   Z sympy.polys.domains.simpledomainr   Zsympy.polys.polyutilsr   Zsympy.utilitiesr	   r-   r   r#   r   r   r   r   <module>   s"       