a
    kº”h©  ã                   @   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œZeG dd„ de	eeƒƒZeƒ ZdS )z3Implementation of :class:`ExpressionDomain` class. é    )ÚsympifyÚSympifyError)ÚDomainElement)ÚCharacteristicZero)ÚField)ÚSimpleDomain)ÚPicklableWithSlots)ÚpublicFT)ÚdeepÚmulZ	power_expZ
power_baseÚbasicZmultinomialÚlogc                   @   s2  e Zd ZdZd ZZG dd„ deeƒZeZ	edƒZ
edƒ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 )DÚExpressionDomainz#A class for arbitrary expressions. Tc                   @   sì   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$„ Zd%d&„ Zd'd(„ Zd)d*„ Zd+d,„ Zd-d.„ Zd/d0„ Zd1d2„ Zd3d4„ Zd5d6„ Zd7d8„ Zd9S ):zExpressionDomain.ExpressionzAn arbitrary expression. ©Úexc                 C   s$   t || jƒst|ƒ| _n|j| _d S ©N)Ú
isinstanceÚ	__class__r   r   )Úselfr   © r   úR/var/www/auris/lib/python3.9/site-packages/sympy/polys/domains/expressiondomain.pyÚ__init__   s    z$ExpressionDomain.Expression.__init__c                 C   s   dt | jƒ S ©NzEX(%s))Úreprr   ©Úfr   r   r   Ú__repr__    s    z$ExpressionDomain.Expression.__repr__c                 C   s   dt | jƒ S r   )Ústrr   r   r   r   r   Ú__str__#   s    z#ExpressionDomain.Expression.__str__c                 C   s   t | jj| jfƒS r   )Úhashr   Ú__name__r   ©r   r   r   r   Ú__hash__&   s    z$ExpressionDomain.Expression.__hash__c                 C   s   t S r   )ÚEXr!   r   r   r   Úparent)   s    z"ExpressionDomain.Expression.parentc                 C   s   | j S r   r   r   r   r   r   Úas_expr,   s    z#ExpressionDomain.Expression.as_exprc                 C   s   |   | j ¡ d ¡S )Nr   ©r   r   Zas_numer_denomr   r   r   r   Únumer/   s    z!ExpressionDomain.Expression.numerc                 C   s   |   | j ¡ d ¡S ©Né   r&   r   r   r   r   Údenom2   s    z!ExpressionDomain.Expression.denomc                 C   s   |   | ¡ jf i t¤Ž¡S r   )r   ÚcancelÚexpandÚeflags)r   r   r   r   r   Úsimplify5   s    z$ExpressionDomain.Expression.simplifyc                 C   s   |   t| jƒ¡S r   )r   Úabsr   r   r   r   r   Ú__abs__8   s    z#ExpressionDomain.Expression.__abs__c                 C   s   |   | j ¡S r   )r   r   r   r   r   r   Ú__neg__;   s    z#ExpressionDomain.Expression.__neg__c                 C   s&   z|   |¡W S  ty    Y d S 0 d S r   )r   r   ©r   Úgr   r   r   Ú_to_ex>   s    z"ExpressionDomain.Expression._to_exc                 C   s   | j  ¡ |j  ¡ k S r   )r   Úsort_keyr2   r   r   r   Ú__lt__D   s    z"ExpressionDomain.Expression.__lt__c                 C   sH   |   |¡}|d u rtS |tjkr$| S | tjkr2|S |  | j|j ¡S d S r   ©r4   ÚNotImplementedr#   Úzeror.   r   r2   r   r   r   Ú__add__G   s    


z#ExpressionDomain.Expression.__add__c                 C   s   |   |  |¡j| j ¡S r   ©r.   r   r   r2   r   r   r   Ú__radd__S   s    z$ExpressionDomain.Expression.__radd__c                 C   sJ   |   |¡}|d u rtS |tjkr$| S | tjkr4| S |  | j|j ¡S d S r   r7   r2   r   r   r   Ú__sub__V   s    


z#ExpressionDomain.Expression.__sub__c                 C   s   |   |  |¡j| j ¡S r   r;   r2   r   r   r   Ú__rsub__b   s    z$ExpressionDomain.Expression.__rsub__c                 C   s^   |   |¡}|d u rtS tj| |fv 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   Ú__mul__e   s    
z#ExpressionDomain.Expression.__mul__c                 C   s   |   |  |¡j| j ¡S r   r;   r2   r   r   r   Ú__rmul__r   s    z$ExpressionDomain.Expression.__rmul__c                 C   s,   |   |¡}|d ur$|  | j|j ¡S tS d S r   ©r4   r.   r   r8   )r   Únr   r   r   Ú__pow__u   s    
z#ExpressionDomain.Expression.__pow__c                 C   s,   |   |¡}|d ur$|  | j|j ¡S tS d S r   rA   r2   r   r   r   Ú__truediv__}   s    
z'ExpressionDomain.Expression.__truediv__c                 C   s   |   |  |¡j| j ¡S r   r;   r2   r   r   r   Ú__rtruediv__…   s    z(ExpressionDomain.Expression.__rtruediv__c                 C   s   | j |  |¡j kS r   )r   r   r2   r   r   r   Ú__eq__ˆ   s    z"ExpressionDomain.Expression.__eq__c                 C   s
   | |k S r   r   r2   r   r   r   Ú__ne__‹   s    z"ExpressionDomain.Expression.__ne__c                 C   s
   | j j S r   )r   Úis_zeror   r   r   r   Ú__bool__Ž   s    z$ExpressionDomain.Expression.__bool__c                 C   s&   ddl m} |  || j|  |¡jƒ¡S )Nr   )Úgcd)Úsympy.polysrJ   r   r   )r   r3   rJ   r   r   r   rJ   ‘   s    zExpressionDomain.Expression.gcdc                 C   s&   ddl m} |  || j|  |¡jƒ¡S )Nr   ©Úlcm)rK   rM   r   r   )r   r3   rM   r   r   r   rM   •   s    zExpressionDomain.Expression.lcmN) r    Ú
__module__Ú__qualname__Ú__doc__Ú	__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   Ú
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ƒrdS tS d S )NT)r   r   r8   )r   Úotherr   r   r   rF   ¦   s    
zExpressionDomain.__eq__c                 C   s   t dƒ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   Úar   r   r   Úto_sympy¯   s    zExpressionDomain.to_sympyc                 C   s
   |   |¡S )z)Convert SymPy's expression to ``dtype``. )ÚdtyperT   r   r   r   Ú
from_sympy³   s    zExpressionDomain.from_sympyc                 C   s   | |  |¡ƒS ©z.Convert a Python ``int`` object to ``dtype``. ©rV   ©ZK1rU   ZK0r   r   r   Úfrom_ZZ·   s    zExpressionDomain.from_ZZc                 C   s   | |  |¡ƒS rY   rZ   r[   r   r   r   Úfrom_ZZ_python»   s    zExpressionDomain.from_ZZ_pythonc                 C   s   | |  |¡ƒS ©z3Convert a Python ``Fraction`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_QQ¿   s    zExpressionDomain.from_QQc                 C   s   | |  |¡ƒS r^   rZ   r[   r   r   r   Úfrom_QQ_pythonÃ   s    zExpressionDomain.from_QQ_pythonc                 C   s   | |  |¡ƒS )z,Convert a GMPY ``mpz`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_ZZ_gmpyÇ   s    zExpressionDomain.from_ZZ_gmpyc                 C   s   | |  |¡ƒS )z,Convert a GMPY ``mpq`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_QQ_gmpyË   s    zExpressionDomain.from_QQ_gmpyc                 C   s   | |  |¡ƒS ©z4Convert a ``GaussianRational`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_GaussianIntegerRingÏ   s    z)ExpressionDomain.from_GaussianIntegerRingc                 C   s   | |  |¡ƒS rc   rZ   r[   r   r   r   Úfrom_GaussianRationalFieldÓ   s    z+ExpressionDomain.from_GaussianRationalFieldc                 C   s   | |  |¡ƒS )z(Convert an ``ANP`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_AlgebraicField×   s    z$ExpressionDomain.from_AlgebraicFieldc                 C   s   | |  |¡ƒS )z.Convert a mpmath ``mpf`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_RealFieldÛ   s    zExpressionDomain.from_RealFieldc                 C   s   | |  |¡ƒS )z.Convert a mpmath ``mpc`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_ComplexFieldß   s    z"ExpressionDomain.from_ComplexFieldc                 C   s   | |  |¡ƒS )z'Convert a ``DMP`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_PolynomialRingã   s    z$ExpressionDomain.from_PolynomialRingc                 C   s   | |  |¡ƒS )z'Convert a ``DMF`` object to ``dtype``. rZ   r[   r   r   r   Úfrom_FractionFieldç   s    z#ExpressionDomain.from_FractionFieldc                 C   s   |S )z&Convert a ``EX`` object to ``dtype``. r   r[   r   r   r   Úfrom_ExpressionDomainë   s    z&ExpressionDomain.from_ExpressionDomainc                 C   s   | S )z)Returns a ring associated with ``self``. r   r!   r   r   r   Úget_ringï   s    zExpressionDomain.get_ringc                 C   s   | S )z*Returns a field associated with ``self``. r   r!   r   r   r   Ú	get_fieldó   s    zExpressionDomain.get_fieldc                 C   s   |j  ¡ d jS )z#Returns True if ``a`` is positive. r   )r   Úas_coeff_mulÚ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   Úis_negativeû   s    zExpressionDomain.is_negativec                 C   s   |j  ¡ d jS )z'Returns True if ``a`` is non-positive. r   )r   rn   Úis_nonpositiverT   r   r   r   rq   ÿ   s    zExpressionDomain.is_nonpositivec                 C   s   |j  ¡ d jS )z'Returns True if ``a`` is non-negative. r   )r   rn   Ú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ƒS r(   r   ©r   rU   Ú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   ZoneÚ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   Ú<module>   s   ÿ  