o
    GZh                     @   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$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9S ):zExpressionDomain.ExpressionzAn arbitrary expression. exc                 C   s&   t || jst|| _d S |j| _d S N)
isinstance	__class__r   r   )selfr    r   S/var/www/auris/lib/python3.10/site-packages/sympy/polys/domains/expressiondomain.py__init__   s   z$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   t S r   )EXr#   r   r   r   parent)      z"ExpressionDomain.Expression.parentc                 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   denom2   r-   z!ExpressionDomain.Expression.denomc                 C   s   |  | jdi tS )Nr   )r   cancelexpandeflags)r   r   r   r   r   simplify5   s   z$ExpressionDomain.Expression.simplifyc                 C   s   |  t| jS r   )r   absr   r   r   r   r   __abs__8   s   z#ExpressionDomain.Expression.__abs__c                 C   s   |  | j S r   )r   r   r   r   r   r   __neg__;   r   z#ExpressionDomain.Expression.__neg__c                 C   s"   z|  |W S  ty   Y d S w r   )r   r   r   gr   r   r   _to_ex>   s
   z"ExpressionDomain.Expression._to_exc                 C   s   | j  |j  k S r   )r   sort_keyr8   r   r   r   __lt__D   r-   z"ExpressionDomain.Expression.__lt__c                 C   sD   |  |}|d u rtS |tjkr| S | tjkr|S | | j|j S r   r:   NotImplementedr&   zeror4   r   r8   r   r   r   __add__G   s   


z#ExpressionDomain.Expression.__add__c                 C   s   |  | |j| j S r   r4   r   r   r8   r   r   r   __radd__S      z$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   r=   r8   r   r   r   __sub__V   s   


z#ExpressionDomain.Expression.__sub__c                 C   s   |  | |j| j S r   rA   r8   r   r   r   __rsub__b   rC   z$ExpressionDomain.Expression.__rsub__c                 C   s^   |  |}|d u rtS tj| |fv rtjS | jjr&|jjr&| | j|j S | | j|j S r   )r:   r>   r&   r?   r   Z	is_Numberr   r4   r8   r   r   r   __mul__e   s   
z#ExpressionDomain.Expression.__mul__c                 C   s   |  | |j| j S r   rA   r8   r   r   r   __rmul__r   rC   z$ExpressionDomain.Expression.__rmul__c                 C   s(   |  |}|d ur| | j|j S tS r   r:   r4   r   r>   )r   nr   r   r   __pow__u      
z#ExpressionDomain.Expression.__pow__c                 C   s(   |  |}|d ur| | j|j S tS r   rH   r8   r   r   r   __truediv__}   rK   z'ExpressionDomain.Expression.__truediv__c                 C   s   |  | |j| j S r   rA   r8   r   r   r   __rtruediv__   rC   z(ExpressionDomain.Expression.__rtruediv__c                 C   s   | j | |j kS r   )r   r   r8   r   r   r   __eq__   r%   z"ExpressionDomain.Expression.__eq__c                 C   s
   | |k S r   r   r8   r   r   r   __ne__      
z"ExpressionDomain.Expression.__ne__c                 C   s
   | j j S r   )r   is_zeror   r   r   r   __bool__   rP   z$ExpressionDomain.Expression.__bool__c                 C   &   ddl m} | || j| |jS )Nr   )gcd)sympy.polysrT   r   r   )r   r9   rT   r   r   r   rT         zExpressionDomain.Expression.gcdc                 C   rS   )Nr   lcm)rU   rX   r   r   )r   r9   rX   r   r   r   rX      rV   zExpressionDomain.Expression.lcmN) r"   
__module____qualname____doc__	__slots__r   r   r    r$   r'   r)   r,   r0   r4   r6   r7   r:   r<   r@   rB   rD   rE   rF   rG   rJ   rL   rM   rN   rO   rR   rT   rX   r   r   r   r   
Expression   s<    r]   r   r/   r&   Fc                 C   s   d S r   r   r#   r   r   r   r      r(   zExpressionDomain.__init__c                 C   s   t |trdS tS )NT)r   r   r>   )r   otherr   r   r   rN      s   
zExpressionDomain.__eq__c                 C   s   t dS )Nr&   )r!   r#   r   r   r   r$         zExpressionDomain.__hash__c                 C      |  S )z!Convert ``a`` to a SymPy object. )r)   r   ar   r   r   to_sympy      zExpressionDomain.to_sympyc                 C   s
   |  |S )z)Convert SymPy's expression to ``dtype``. )dtypera   r   r   r   
from_sympy      
zExpressionDomain.from_sympyc                 C      | | |S z.Convert a Python ``int`` object to ``dtype``. rc   ZK1rb   ZK0r   r   r   from_ZZ      zExpressionDomain.from_ZZc                 C   rh   ri   rj   rk   r   r   r   from_ZZ_python   rm   zExpressionDomain.from_ZZ_pythonc                 C   rh   z3Convert a Python ``Fraction`` object to ``dtype``. rj   rk   r   r   r   from_QQ   rm   zExpressionDomain.from_QQc                 C   rh   ro   rj   rk   r   r   r   from_QQ_python   rm   zExpressionDomain.from_QQ_pythonc                 C   rh   )z,Convert a GMPY ``mpz`` object to ``dtype``. rj   rk   r   r   r   from_ZZ_gmpy   rm   zExpressionDomain.from_ZZ_gmpyc                 C   rh   )z,Convert a GMPY ``mpq`` object to ``dtype``. rj   rk   r   r   r   from_QQ_gmpy   rm   zExpressionDomain.from_QQ_gmpyc                 C   rh   z4Convert a ``GaussianRational`` object to ``dtype``. rj   rk   r   r   r   from_GaussianIntegerRing   rm   z)ExpressionDomain.from_GaussianIntegerRingc                 C   rh   rt   rj   rk   r   r   r   from_GaussianRationalField   rm   z+ExpressionDomain.from_GaussianRationalFieldc                 C   rh   )z(Convert an ``ANP`` object to ``dtype``. rj   rk   r   r   r   from_AlgebraicField   rm   z$ExpressionDomain.from_AlgebraicFieldc                 C   rh   )z.Convert a mpmath ``mpf`` object to ``dtype``. rj   rk   r   r   r   from_RealField   rm   zExpressionDomain.from_RealFieldc                 C   rh   )z.Convert a mpmath ``mpc`` object to ``dtype``. rj   rk   r   r   r   from_ComplexField   rm   z"ExpressionDomain.from_ComplexFieldc                 C   rh   )z'Convert a ``DMP`` object to ``dtype``. rj   rk   r   r   r   from_PolynomialRing   rm   z$ExpressionDomain.from_PolynomialRingc                 C   rh   )z'Convert a ``DMF`` object to ``dtype``. rj   rk   r   r   r   from_FractionField   rm   z#ExpressionDomain.from_FractionFieldc                 C   s   |S )z&Convert a ``EX`` object to ``dtype``. r   rk   r   r   r   from_ExpressionDomain      z&ExpressionDomain.from_ExpressionDomainc                 C      | S )z)Returns a ring associated with ``self``. r   r#   r   r   r   get_ring   r}   zExpressionDomain.get_ringc                 C   r~   )z*Returns a field associated with ``self``. r   r#   r   r   r   	get_field   r}   zExpressionDomain.get_fieldc                 C      |j  d jS )z#Returns True if ``a`` is positive. r   )r   as_coeff_mulis_positivera   r   r   r   r         zExpressionDomain.is_positivec                 C   s
   |j  S )z#Returns True if ``a`` is negative. )r   Zcould_extract_minus_signra   r   r   r   is_negative   rg   zExpressionDomain.is_negativec                 C   r   )z'Returns True if ``a`` is non-positive. r   )r   r   is_nonpositivera   r   r   r   r      r   zExpressionDomain.is_nonpositivec                 C   r   )z'Returns True if ``a`` is non-negative. r   )r   r   is_nonnegativera   r   r   r   r     r   zExpressionDomain.is_nonnegativec                 C   r`   )zReturns numerator of ``a``. )r,   ra   r   r   r   r,     rd   zExpressionDomain.numerc                 C   r`   )zReturns denominator of ``a``. )r0   ra   r   r   r   r0     rd   zExpressionDomain.denomc                 C   s   | dS r.   r   r   rb   br   r   r   rT     r_   zExpressionDomain.gcdc                 C   s
   | |S r   rW   r   r   r   r   rX     rP   zExpressionDomain.lcmN),r"   rY   rZ   r[   Zis_SymbolicDomainZis_EXr   r   r]   re   r?   onerepZhas_assoc_RingZhas_assoc_Fieldr   rN   r$   rc   rf   rl   rn   rp   rq   rr   rs   ru   rv   rw   rx   ry   rz   r{   r|   r   r   r   r   r   r   r,   r0   rT   rX   r   r   r   r   r      sP     r   N)r[   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	   r3   r   r&   r   r   r   r   <module>   s       
