o
    8Va                  	   @   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 e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)CharacteristicZero)Field)SimpleDomain)PicklableWithSlots)publicFT)ZdeepmulZ	power_expZ
power_baseZbasicZmultinomiallogc                   @   s  e Zd ZdZd ZZG dd d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;S )<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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5S )6zExpressionDomain.ExpressionzAn arbitrary expression. exc                 C   s&   t || jst|| _d S |j| _d S N)
isinstance	__class__r   r   )selfr    r   F/usr/lib/python3/dist-packages/sympy/polys/domains/expressiondomain.py__init__   s   z$ExpressionDomain.Expression.__init__c                 C      dt | j S NzEX(%s))reprr   fr   r   r   __repr__      z$ExpressionDomain.Expression.__repr__c                 C   r   r   )strr   r   r   r   r   __str__"   r   z#ExpressionDomain.Expression.__str__c                 C   s   t | jj| jfS r   )hashr   __name__r   r   r   r   r   __hash__%      z$ExpressionDomain.Expression.__hash__c                 C   s   | j S r   r   r   r   r   r   as_expr(   s   z#ExpressionDomain.Expression.as_exprc                 C      |  | j d S )Nr   r   r   Zas_numer_denomr   r   r   r   numer+      z!ExpressionDomain.Expression.numerc                 C   r$   N   r%   r   r   r   r   denom.   r'   z!ExpressionDomain.Expression.denomc                 C   s   |  | jdi tS )Nr   )r   Zcancelexpandeflags)r   r   r   r   r   simplify1   s   z$ExpressionDomain.Expression.simplifyc                 C   s   |  t| jS r   )r   absr   r   r   r   r   __abs__4   s   z#ExpressionDomain.Expression.__abs__c                 C   s   |  | j S r   )r   r   r   r   r   r   __neg__7   r   z#ExpressionDomain.Expression.__neg__c                 C   s"   z|  |W S  ty   Y d S w r   )r   r   r   gr   r   r   _to_ex:   s
   z"ExpressionDomain.Expression._to_exc                 C   sD   |  |}|d u rtS |tjkr| S | tjkr|S | | j|j S r   r3   NotImplementedEXzeror-   r   r1   r   r   r   __add__@   s   


z#ExpressionDomain.Expression.__add__c                 C   s   |  | |j| j S r   r-   r   r   r1   r   r   r   __radd__L      z$ExpressionDomain.Expression.__radd__c                 C   sF   |  |}|d u rtS |tjkr| S | tjkr| S | | j|j S r   r4   r1   r   r   r   __sub__O   s   


z#ExpressionDomain.Expression.__sub__c                 C   s   |  | |j| j S r   r9   r1   r   r   r   __rsub__[   r;   z$ExpressionDomain.Expression.__rsub__c                 C   s^   |  |}|d u rtS tj| |fv rtjS | jjr&|jjr&| | j|j S | | j|j S r   )r3   r5   r6   r7   r   Z	is_Numberr   r-   r1   r   r   r   __mul__^   s   
z#ExpressionDomain.Expression.__mul__c                 C   s   |  | |j| j S r   r9   r1   r   r   r   __rmul__k   r;   z$ExpressionDomain.Expression.__rmul__c                 C   s(   |  |}|d ur| | j|j S tS r   r3   r-   r   r5   )r   nr   r   r   __pow__n      
z#ExpressionDomain.Expression.__pow__c                 C   s(   |  |}|d ur| | j|j S tS r   r@   r1   r   r   r   __truediv__v   rC   z'ExpressionDomain.Expression.__truediv__c                 C   s   |  | |j| j S r   r9   r1   r   r   r   __rtruediv__~   r;   z(ExpressionDomain.Expression.__rtruediv__c                 C   s   | j | |j kS r   )r   r   r1   r   r   r   __eq__   r"   z"ExpressionDomain.Expression.__eq__c                 C   s
   | |k S r   r   r1   r   r   r   __ne__      
z"ExpressionDomain.Expression.__ne__c                 C   s
   | j j S r   )r   Zis_zeror   r   r   r   __bool__   rH   z$ExpressionDomain.Expression.__bool__c                 C   &   ddl m} | || j| |jS )Nr   )gcd)sympy.polysrK   r   r   )r   r2   rK   r   r   r   rK         zExpressionDomain.Expression.gcdc                 C   rJ   )Nr   lcm)rL   rO   r   r   )r   r2   rO   r   r   r   rO      rM   zExpressionDomain.Expression.lcmN)r   
__module____qualname____doc__	__slots__r   r   r   r!   r#   r&   r*   r-   r/   r0   r3   r8   r:   r<   r=   r>   r?   rB   rD   rE   rF   rG   rI   rK   rO   r   r   r   r   
Expression   s8    rT   r   r)   r6   Fc                 C   s   d S r   r   r    r   r   r   r      s   zExpressionDomain.__init__c                 C      |  S )z!Convert ``a`` to a SymPy object. )r#   r   ar   r   r   to_sympy      zExpressionDomain.to_sympyc                 C   s
   |  |S )z)Convert SymPy's expression to ``dtype``. )dtyperV   r   r   r   
from_sympy      
zExpressionDomain.from_sympyc                 C      | | |S z.Convert a Python ``int`` object to ``dtype``. rX   ZK1rW   ZK0r   r   r   from_ZZ      zExpressionDomain.from_ZZc                 C   r]   r^   r_   r`   r   r   r   from_ZZ_python   rb   zExpressionDomain.from_ZZ_pythonc                 C   r]   z3Convert a Python ``Fraction`` object to ``dtype``. r_   r`   r   r   r   from_QQ   rb   zExpressionDomain.from_QQc                 C   r]   rd   r_   r`   r   r   r   from_QQ_python   rb   zExpressionDomain.from_QQ_pythonc                 C   r]   )z,Convert a GMPY ``mpz`` object to ``dtype``. r_   r`   r   r   r   from_ZZ_gmpy   rb   zExpressionDomain.from_ZZ_gmpyc                 C   r]   )z,Convert a GMPY ``mpq`` object to ``dtype``. r_   r`   r   r   r   from_QQ_gmpy   rb   zExpressionDomain.from_QQ_gmpyc                 C   r]   z4Convert a ``GaussianRational`` object to ``dtype``. r_   r`   r   r   r   from_GaussianIntegerRing   rb   z)ExpressionDomain.from_GaussianIntegerRingc                 C   r]   ri   r_   r`   r   r   r   from_GaussianRationalField   rb   z+ExpressionDomain.from_GaussianRationalFieldc                 C   r]   )z.Convert a mpmath ``mpf`` object to ``dtype``. r_   r`   r   r   r   from_RealField   rb   zExpressionDomain.from_RealFieldc                 C   r]   )z'Convert a ``DMP`` object to ``dtype``. r_   r`   r   r   r   from_PolynomialRing   rb   z$ExpressionDomain.from_PolynomialRingc                 C   r]   )z'Convert a ``DMF`` object to ``dtype``. r_   r`   r   r   r   from_FractionField   rb   z#ExpressionDomain.from_FractionFieldc                 C   s   |S )z&Convert a ``EX`` object to ``dtype``. r   r`   r   r   r   from_ExpressionDomain      z&ExpressionDomain.from_ExpressionDomainc                 C      | S )z)Returns a ring associated with ``self``. r   r    r   r   r   get_ring   rp   zExpressionDomain.get_ringc                 C   rq   )z*Returns a field associated with ``self``. r   r    r   r   r   	get_field   rp   zExpressionDomain.get_fieldc                 C      |j  d jS )z#Returns True if ``a`` is positive. r   )r   as_coeff_mulis_positiverV   r   r   r   rv         zExpressionDomain.is_positivec                 C   s
   |j  S )z#Returns True if ``a`` is negative. )r   Zcould_extract_minus_signrV   r   r   r   is_negative   r\   zExpressionDomain.is_negativec                 C   rt   )z'Returns True if ``a`` is non-positive. r   )r   ru   is_nonpositiverV   r   r   r   ry      rw   zExpressionDomain.is_nonpositivec                 C   rt   )z'Returns True if ``a`` is non-negative. r   )r   ru   is_nonnegativerV   r   r   r   rz      rw   zExpressionDomain.is_nonnegativec                 C   rU   )zReturns numerator of ``a``. )r&   rV   r   r   r   r&      rY   zExpressionDomain.numerc                 C   rU   )zReturns denominator of ``a``. )r*   rV   r   r   r   r*      rY   zExpressionDomain.denomc                 C   s   | dS r(   r   r   rW   br   r   r   rK      s   zExpressionDomain.gcdc                 C   s
   | |S r   rN   r{   r   r   r   rO      rH   zExpressionDomain.lcmN)'r   rP   rQ   rR   Zis_SymbolicDomainZis_EXr   rT   rZ   r7   ZoneZrepZhas_assoc_RingZhas_assoc_Fieldr   rX   r[   ra   rc   re   rf   rg   rh   rj   rk   rl   rm   rn   ro   rr   rs   rv   rx   ry   rz   r&   r*   rK   rO   r   r   r   r   r      sF    ~r   N)rR   Z
sympy.corer   r   Z&sympy.polys.domains.characteristiczeror   Zsympy.polys.domains.fieldr   Z sympy.polys.domains.simpledomainr   Zsympy.polys.polyutilsr   Zsympy.utilitiesr   dictr,   r   r6   r   r   r   r   <module>   s    
 
p