o
    hS                     @  s  d Z ddlmZ ddlmZ ddlmZmZmZm	Z	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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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/m0Z0 ddl1m2Z2 ddl3m4Z4 ddl5m6Z6 ddl7m8Z8 e4e&fddZ9e4e&fddZ:e4e&fddZ;e4d d! Z<G d"d# d#e2Z=G d$d% d%ee2eZ>d&S )'z!Sparse rational function fields.     )annotations)reduce)addmulltlegtge)Expr)Mod)Exp1)S)Symbol)CantSympifysympify)ExpBase)Domain)DomainElementFractionField)PolynomialRing)construct_domain)lexMonomialOrder)CoercionFailed)build_options)_parallel_dict_from_expr)PolyRingPolyElement)DefaultPrinting)public)is_sequence)pollutec                 C  s   t | ||}|f|j S )zFConstruct new rational function field returning (field, x1, ..., xn). 	FracFieldgenssymbolsdomainorder_field r+   X/home/www/facesmatcher.com/frenv_anti/lib/python3.10/site-packages/sympy/polys/fields.pyfield   s   r-   c                 C  s   t | ||}||jfS )zHConstruct new rational function field returning (field, (x1, ..., xn)). r#   r&   r+   r+   r,   xfield$   s   
r.   c                 C  s(   t | ||}tdd |jD |j |S )zSConstruct new rational function field and inject generators into global namespace. c                 S  s   g | ]}|j qS r+   )name).0Zsymr+   r+   r,   
<listcomp>.   s    zvfield.<locals>.<listcomp>)r$   r"   r'   r%   r&   r+   r+   r,   vfield*   s   r2   c              	   O  s   d}t | s| gd} }ttt| } t||}g }| D ]	}||  qt||\}}|jdu rEt	dd |D g }t
||d\|_}	t|j|j|j}
g }tdt|dD ]}||
t|||d   qX|rr|
|d fS |
|fS )	a  Construct a field deriving generators and domain
    from options and input expressions.

    Parameters
    ==========

    exprs   : py:class:`~.Expr` or sequence of :py:class:`~.Expr` (sympifiable)

    symbols : sequence of :py:class:`~.Symbol`/:py:class:`~.Expr`

    options : keyword arguments understood by :py:class:`~.Options`

    Examples
    ========

    >>> from sympy import exp, log, symbols, sfield

    >>> x = symbols("x")
    >>> K, f = sfield((x*log(x) + 4*x**2)*exp(1/x + log(x)/3)/x**2)
    >>> K
    Rational function field in x, exp(1/x), log(x), x**(1/3) over ZZ with lex order
    >>> f
    (4*x**2*(exp(1/x)) + x*(exp(1/x))*(log(x)))/((x**(1/3))**5)
    FTNc                 S  s   g | ]}t | qS r+   )listvalues)r0   repr+   r+   r,   r1   Y   s    zsfield.<locals>.<listcomp>)optr      )r!   r3   mapr   r   extendZas_numer_denomr   r(   sumr   r$   r%   r)   rangelenappendtuple)Zexprsr'   optionssingler6   ZnumdensexprZrepsZcoeffs_r*   Zfracsir+   r+   r,   sfield1   s&   

 rD   c                   @  s   e Zd ZU dZded< ded< ded< ded	< d
ed< ded< efddZdd Zdd Zdd Z	dd Z
dd Zdd Zdd Zd1dd Zd1d!d"Zd#d$ Zd%d& Zd'd( ZeZd)d* Zd+d, Zd-d. Zd/d0 ZdS )2r$   z2Multivariate distributed rational function field. r   ringztuple[FracElement, ...]r%   ztuple[Expr, ...]r'   intngensr   r(   r   r)   c                 C  s   t |||}|j}|j}|j}|j}| j||||f}t| }||_t	||_
||_||_||_||_||_t||jj|_||j|_||j|_| |_t|j|jD ]\}}	t|tro|j}
t||
sot||
|	 qX|S N)r   r'   rG   r(   r)   __name__object__new___hash_tuplehash_hashrE   FracElementzeroraw_newdtypeone_gensr%   zip
isinstancer   r/   hasattrsetattr)clsr'   r(   r)   rE   rG   rL   objsymbol	generatorr/   r+   r+   r,   rK   q   s2   




zFracField.__new__c                   s   t  fdd jjD S )z(Return a list of polynomial generators. c                   s   g | ]}  |qS r+   rR   r0   genselfr+   r,   r1      s    z#FracField._gens.<locals>.<listcomp>)r>   rE   r%   r`   r+   r`   r,   rT      s   zFracField._gensc                 C     | j | j| jfS rH   )r'   r(   r)   r`   r+   r+   r,   __getnewargs__      zFracField.__getnewargs__c                 C  s   | j S rH   )rN   r`   r+   r+   r,   __hash__   s   zFracField.__hash__c                 C  s,   |  |r| j| S td| j|f )Nzexpected a %s, got %s instead)
is_elementrE   indexto_poly
ValueErrorrR   )ra   r_   r+   r+   r,   rg      s   
zFracField.indexc                 C  s2   t |to| j| j| j| jf|j|j|j|jfkS rH   )rV   r$   r'   rG   r(   r)   ra   otherr+   r+   r,   __eq__   s
   
zFracField.__eq__c                 C  
   | |k S rH   r+   rj   r+   r+   r,   __ne__      
zFracField.__ne__c                 C  s   t |to	|j| kS )zBTrue if ``element`` is an element of this field. False otherwise. )rV   rO   r-   ra   elementr+   r+   r,   rf      s   zFracField.is_elementNc                 C  s   |  ||S rH   r]   ra   numerdenomr+   r+   r,   rQ         zFracField.raw_newc                 C  s*   |d u r| j j}||\}}| ||S rH   )rE   rS   cancelrQ   rr   r+   r+   r,   new   s   zFracField.newc                 C  s   | j |S rH   )r(   convertrp   r+   r+   r,   
domain_new   ru   zFracField.domain_newc                 C  s   z
|  | j|W S  ty?   | j}|js>|jr>| j}| }||}||	|}||
|}| || Y S  w rH   )rw   rE   
ground_newr   r(   is_Fieldhas_assoc_Field	get_fieldrx   rs   rt   rQ   )ra   rq   r(   rE   ground_fieldrs   rt   r+   r+   r,   rz      s   
zFracField.ground_newc                 C  sb  t |tr6| |jkr|S t | jtr| jj|jkr| |S t | jtr2| jj |jkr2| |S t	dt |t
r}| \}}t | jtrU|j| jjkrU| j|}nt | jtrk|j| jj krk| j|}n|| j}| j|}| ||S t |trt|dkrtt| jj|\}}| ||S t |trt	dt |tr| |S | |S )N
conversionr7   Zparsing)rV   rO   r-   r(   r   rz   r   rE   to_fieldNotImplementedErrorr   Zclear_denomsto_ringset_ringrQ   r>   r<   r3   r8   Zring_newrw   strr
   	from_expr)ra   rq   rt   rs   r+   r+   r,   	field_new   sB   








zFracField.field_newc                   s6   | j tdd  D  fdd  |S )Nc                 s  s,    | ]}|j st|tr|| fV  qd S rH   )is_PowrV   r   as_base_expr^   r+   r+   r,   	<genexpr>   s    z*FracField._rebuild_expr.<locals>.<genexpr>c                   s2   | }|d ur|S | jrtttt | jS | jr'tttt | jS | j	s1t
| ttfri|  \}}D ]\}\}}||krWt||dkrW |t||    S q9|jrh|tjurh |t| S n d|  d ur{d d|   S z| W S  ty   jsjr |  Y S  w )Nr      )getZis_Addr   r   r3   r8   argsZis_Mulr   r   rV   r   r   r   r   rF   Z
is_Integerr   ZOnerx   r   r{   r|   r}   )rA   r\   ber_   bgeg_rebuildr(   mappingZpowersr+   r,   r      s2   
z)FracField._rebuild_expr.<locals>._rebuild)r(   r>   keys)ra   rA   r   r+   r   r,   _rebuild_expr   s   zFracField._rebuild_exprc                 C  sT   t tt| j| j}z
| t||}W n ty$   td| |f w | 	|S )NzGexpected an expression convertible to a rational function in %s, got %s)
dictr3   rU   r'   r%   r   r   r   ri   r   )ra   rA   r   fracr+   r+   r,   r     s   
zFracField.from_exprc                 C  s   t | S rH   r   r`   r+   r+   r,   	to_domain  s   zFracField.to_domainc                 C  s   t | j| j| jS rH   )r   r'   r(   r)   r`   r+   r+   r,   r   !  s   zFracField.to_ringrH   )rI   
__module____qualname____doc____annotations__r   rK   rT   rc   re   rg   rl   rn   rf   rQ   rw   ry   rz   r   __call__r   r   r   r   r+   r+   r+   r,   r$   g   s4   
 "

%#
r$   c                   @  s>  e Zd ZdZdKddZdKddZdd Zd	d
 Zdd Zdd Z	dZ
dd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Z d;d< Z!d=d> Z"d?d@ Z#dAdB Z$dCdD Z%dKdEdFZ&dKdGdHZ'dKdIdJZ(dS )LrO   z=Element of multivariate distributed rational function field. Nc                 C  s4   |d u r	|j j}n|std|| _|| _|| _d S )Nzzero denominator)rE   rS   ZeroDivisionErrorr-   rs   rt   )ra   r-   rs   rt   r+   r+   r,   __init__'  s   

zFracElement.__init__c                 C  s   |  | j||S rH   )	__class__r-   frs   rt   r+   r+   r,   rQ   1  rd   zFracElement.raw_newc                 C  s   | j || S rH   )rQ   rv   r   r+   r+   r,   rw   4  rd   zFracElement.newc                 C  s   | j dkr	td| jS )Nr   zf.denom should be 1)rt   ri   rs   r   r+   r+   r,   rh   7  s   
zFracElement.to_polyc                 C  s
   | j  S rH   )r-   r   r`   r+   r+   r,   parent<  ro   zFracElement.parentc                 C  rb   rH   )r-   rs   rt   r`   r+   r+   r,   rc   ?  rd   zFracElement.__getnewargs__c                 C  s,   | j }|d u rt| j| j| jf | _ }|S rH   )rN   rM   r-   rs   rt   )ra   rN   r+   r+   r,   re   D  s   zFracElement.__hash__c                 C  s   |  | j | j S rH   )rQ   rs   copyrt   r`   r+   r+   r,   r   J     zFracElement.copyc                 C  s8   | j |kr| S |j}| j|}| j|}|||S rH   )r-   rE   rs   r   rt   rw   )ra   Z	new_fieldZnew_ringrs   rt   r+   r+   r,   	set_fieldM  s   
zFracElement.set_fieldc                 G  s   | j j| | jj|  S rH   )rs   as_exprrt   )ra   r'   r+   r+   r,   r   V  r   zFracElement.as_exprc                 C  sH   t |tr| j|jkr| j|jko| j|jkS | j|ko#| j| jjjkS rH   )rV   rO   r-   rs   rt   rE   rS   r   gr+   r+   r,   rl   Y  s   zFracElement.__eq__c                 C  rm   rH   r+   r   r+   r+   r,   rn   _  ro   zFracElement.__ne__c                 C  s
   t | jS rH   )boolrs   r   r+   r+   r,   __bool__b  ro   zFracElement.__bool__c                 C  s   | j  | j fS rH   )rt   sort_keyrs   r`   r+   r+   r,   r   e  s   zFracElement.sort_keyc                 C  s"   | j |r||  | S tS rH   )r-   rf   r   NotImplemented)f1f2opr+   r+   r,   _cmph  s   zFracElement._cmpc                 C     |  |tS rH   )r   r   r   r   r+   r+   r,   __lt__n  ru   zFracElement.__lt__c                 C  r   rH   )r   r   r   r+   r+   r,   __le__p  ru   zFracElement.__le__c                 C  r   rH   )r   r   r   r+   r+   r,   __gt__r  ru   zFracElement.__gt__c                 C  r   rH   )r   r	   r   r+   r+   r,   __ge__t  ru   zFracElement.__ge__c                 C  s   |  | j| jS z"Negate all coefficients in ``f``. rQ   rs   rt   r   r+   r+   r,   __pos__w  s   zFracElement.__pos__c                 C  s   |  | j | jS r   r   r   r+   r+   r,   __neg__{  s   zFracElement.__neg__c                 C  s   | j j}z||}W n4 ty?   |js<|jr<| }z||}W n ty.   Y Y dS w d||||f Y S Y dS w d|d fS )N)r   NNr   )	r-   r(   rx   r   r{   r|   r}   rs   rt   )ra   rq   r(   r~   r+   r+   r,   _extract_ground  s    
zFracElement._extract_groundc                 C  s  | j }|s| S | s|S ||r5| j|jkr!| | j|j | jS | | j|j | j|j  | j|j S |j|rH| | j| j|  | jS t|trpt|jt	r[|jj |j kr[qt|j jt	rn|j jj |krn|
| S tS t|trt|jtr|jj|jkrn|
| S | 
|S )z(Add rational functions ``f`` and ``g``. )r-   rf   rt   rw   rs   rE   rV   rO   r(   r   __radd__r   r   r   r   r   r-   r+   r+   r,   __add__  s,   
(




zFracElement.__add__c                 C  s   | j j|r| | j| j|  | jS | |\}}}|dkr-| | j| j|  | jS |s1tS | | j| | j|  | j| S Nr   r-   rE   rf   rw   rs   rt   r   r   r   cr   g_numerg_denomr+   r+   r,   r     s   "zFracElement.__radd__c                 C  sn  | j }|s| S | s| S ||r6| j|jkr"| | j|j | jS | | j|j | j|j  | j|j S |j|rI| | j| j|  | jS t|trqt|jt	r\|jj |j kr\qt|j jt	ro|j jj |kro|
| S tS t|trt|jtr|jj|jkrn|
| S | |\}}}|dkr| | j| j|  | jS |stS | | j| | j|  | j| S )z-Subtract rational functions ``f`` and ``g``. r   )r-   rf   rt   rw   rs   rE   rV   rO   r(   r   __rsub__r   r   r   r   r   r   r-   r   r   r   r+   r+   r,   __sub__  s6   
(



"zFracElement.__sub__c                 C  s   | j j|r| | j | j|  | jS | |\}}}|dkr/| | j | j|  | jS |s3tS | | j | | j|  | j| S r   r   r   r+   r+   r,   r     s   $zFracElement.__rsub__c                 C  s   | j }| r|s
|jS ||r| | j|j | j|j S |j|r-| | j| | jS t|trUt|j	t
r@|j	j |j kr@qmt|j j	t
rS|j j	j |krS|| S tS t|trmt|j	trh|j	j|jkrhn|| S | |S )z-Multiply rational functions ``f`` and ``g``. )r-   rP   rf   rw   rs   rt   rE   rV   rO   r(   r   __rmul__r   r   r   r   r+   r+   r,   __mul__  s$   





zFracElement.__mul__c                 C  sn   | j j|r| | j| | jS | |\}}}|dkr'| | j| | jS |s+tS | | j| | j| S r   r   r   r+   r+   r,   r     s   zFracElement.__rmul__c                 C  s   | j }|st||r| | j|j | j|j S |j|r*| | j| j| S t|trRt|j	t
r=|j	j |j kr=qjt|j j	t
rP|j j	j |krP|| S tS t|trjt|j	tre|j	j|jkren|| S | |\}}}|dkr| | j| j| S |stS | | j| | j| S )z0Computes quotient of fractions ``f`` and ``g``. r   )r-   r   rf   rw   rs   rt   rE   rV   rO   r(   r   __rtruediv__r   r   r   r   r   r+   r+   r,   __truediv__  s.   




zFracElement.__truediv__c                 C  sv   | st | jj|r| | j| | jS | |\}}}|dkr+| | j| | jS |s/tS | | j| | j| S r   )	r   r-   rE   rf   rw   rt   rs   r   r   r   r+   r+   r,   r   :  s   zFracElement.__rtruediv__c                 C  sD   |dkr|  | j| | j| S | st|  | j|  | j|  S )z+Raise ``f`` to a non-negative power ``n``. r   )rQ   rs   rt   r   )r   nr+   r+   r,   __pow__I  s
   zFracElement.__pow__c                 C  s:   |  }| | j|| j | j| j|  | jd S )a  Computes partial derivative in ``x``.

        Examples
        ========

        >>> from sympy.polys.fields import field
        >>> from sympy.polys.domains import ZZ

        >>> _, x, y, z = field("x,y,z", ZZ)
        >>> ((x**2 + y)/(z + 1)).diff(x)
        2*x/(z + 1)

        r7   )rh   rw   rs   diffrt   )r   xr+   r+   r,   r   R  s   2zFracElement.diffc                 G  sP   dt |  k r| jjkrn n| tt| jj|S td| jjt |f )Nr   z1expected at least 1 and at most %s values, got %s)r<   r-   rG   evaluater3   rU   r%   ri   )r   r4   r+   r+   r,   r   c  s    zFracElement.__call__c                 C  sx   t |tr|d u rdd |D }| j|| j|}}n| }| j||| j||}}|j }|||S )Nc                 S     g | ]
\}}|  |fqS r+   rh   r0   Xar+   r+   r,   r1   k      z(FracElement.evaluate.<locals>.<listcomp>)	rV   r3   rs   r   rt   rh   rE   r   rw   )r   r   r   rs   rt   r-   r+   r+   r,   r   i  s   
zFracElement.evaluatec                 C  sn   t |tr|d u rdd |D }| j|| j|}}n| }| j||| j||}}| ||S )Nc                 S  r   r+   r   r   r+   r+   r,   r1   v  r   z$FracElement.subs.<locals>.<listcomp>)rV   r3   rs   subsrt   rh   rw   )r   r   r   rs   rt   r+   r+   r,   r   t  s   zFracElement.subsc                 C  s   t rH   )r   )r   r   r   r+   r+   r,   compose~  s   zFracElement.composerH   ))rI   r   r   r   r   rQ   rw   rh   r   rc   rN   re   r   r   r   rl   rn   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r+   r+   r+   r,   rO   $  sN    


	&!	


rO   N)?r   
__future__r   	functoolsr   operatorr   r   r   r   r   r	   Zsympy.core.exprr
   Zsympy.core.modr   Zsympy.core.numbersr   Zsympy.core.singletonr   Zsympy.core.symbolr   Zsympy.core.sympifyr   r   Z&sympy.functions.elementary.exponentialr   Zsympy.polys.domains.domainr   Z!sympy.polys.domains.domainelementr   Z!sympy.polys.domains.fractionfieldr   Z"sympy.polys.domains.polynomialringr   Zsympy.polys.constructorr   Zsympy.polys.orderingsr   r   Zsympy.polys.polyerrorsr   Zsympy.polys.polyoptionsr   Zsympy.polys.polyutilsr   Zsympy.polys.ringsr   r   Zsympy.printing.defaultsr   Zsympy.utilitiesr    Zsympy.utilities.iterablesr!   Zsympy.utilities.magicr"   r-   r.   r2   rD   r$   rO   r+   r+   r+   r,   <module>   sH     
5 >