o
    ohR                     @  s  U d Z ddlm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( ddl)m*Z* ddl+m,Z, ddl-m.Z. ddl/m0Z0 ddl1m2Z2 ddl3m4Z4 ddl5m6Z6 e2e&fddZ7e2e&fddZ8e2e&fddZ9e2d d! Z:i Z;d"e<d#< G d$d% d%e0Z=G d&d' d'ee0eZ>d(S ))z!Sparse rational function fields.     )annotations)Any)reduce)addmulltlegtge)Expr)Mod)Exp1)S)Symbol)CantSympifysympify)ExpBase)DomainElementFractionField)PolynomialRing)construct_domain)lex)CoercionFailed)build_options)_parallel_dict_from_expr)PolyElement)DefaultPrinting)public)is_sequence)pollutec                 C  s   t | ||}|f|j S )zFConstruct new rational function field returning (field, x1, ..., xn). 	FracFieldgenssymbolsdomainorder_field r)   f/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/sympy/polys/fields.pyfield   s   r+   c                 C  s   t | ||}||jfS )zHConstruct new rational function field returning (field, (x1, ..., xn)). r!   r$   r)   r)   r*   xfield$   s   
r,   c                 C  s(   t | ||}tdd |jD |j |S )zSConstruct new rational function field and inject generators into global namespace. c                 S  s   g | ]}|j qS r)   )name).0symr)   r)   r*   
<listcomp>.   s    zvfield.<locals>.<listcomp>)r"   r    r%   r#   r$   r)   r)   r*   vfield*   s   r1   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)r.   repr)   r)   r*   r0   Y   s    zsfield.<locals>.<listcomp>)optr      )r   r2   mapr   r   extendas_numer_denomr   r&   sumr   r"   r#   r'   rangelenappendtuple)exprsr%   optionssingler5   numdensexprrepscoeffs_r(   fracsir)   r)   r*   sfield1   s&   

 rI   zdict[Any, Any]_field_cachec                   @  s   e Zd ZdZ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dZd#ddZdd Zdd Zdd ZeZdd Zdd Zdd  Zd!d" ZdS )$r"   z2Multivariate distributed rational function field. c                 C  s  ddl m} ||||}|j}|j}|j}|j}| j||||f}t|}|d u rt	
| }||_t||_||_tdtfd|i|_||_||_||_||_||j|_||j|_| |_t|j|jD ]\}	}
t|	tr|	j}t||st|||
 qi|t|< |S )Nr   PolyRingFracElementr+   )sympy.polys.ringsrL   r%   ngensr&   r'   __name__rJ   getobject__new___hash_tuplehash_hashringtyperM   dtypezeroone_gensr#   zip
isinstancer   r-   hasattrsetattr)clsr%   r&   r'   rL   rW   rO   rT   objsymbol	generatorr-   r)   r)   r*   rS   k   s:   





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)   rY   r.   genselfr)   r*   r0      s    z#FracField._gens.<locals>.<listcomp>)r>   rW   r#   rh   r)   rh   r*   r\      s   zFracField._gensc                 C     | j | j| jfS N)r%   r&   r'   rh   r)   r)   r*   __getnewargs__      zFracField.__getnewargs__c                 C  s   | j S rk   )rV   rh   r)   r)   r*   __hash__   s   zFracField.__hash__c                 C  s.   t || jr| j| S td| j|f )Nzexpected a %s, got %s instead)r^   rY   rW   indexto_poly
ValueError)ri   rg   r)   r)   r*   ro      s   zFracField.indexc                 C  s2   t |to| j| j| j| jf|j|j|j|jfkS rk   )r^   r"   r%   rO   r&   r'   ri   otherr)   r)   r*   __eq__   s
   
zFracField.__eq__c                 C  
   | |k S rk   r)   rr   r)   r)   r*   __ne__      
zFracField.__ne__Nc                 C     |  ||S rk   re   ri   numerdenomr)   r)   r*   raw_new      zFracField.raw_newc                 C  s*   |d u r| j j}||\}}| ||S rk   )rW   r[   cancelr|   ry   r)   r)   r*   new   s   zFracField.newc                 C  s   | j |S rk   )r&   convert)ri   elementr)   r)   r*   
domain_new   r}   zFracField.domain_newc                 C  s   z
|  | j|W S  ty?   | j}|js>|jr>| j}| }||}||	|}||
|}| || Y S  w rk   )r   rW   
ground_newr   r&   is_Fieldhas_assoc_Field	get_fieldr   rz   r{   r|   )ri   r   r&   rW   ground_fieldrz   r{   r)   r)   r*   r      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
conversionr6   parsing)r^   rM   r+   r&   r   r   r   rW   to_fieldNotImplementedErrorr   clear_denomsto_ringset_ringr|   r>   r<   r2   r7   ring_newr   strr   	from_expr)ri   r   r{   rz   r)   r)   r*   	field_new   s:   








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 rk   )is_Powr^   r   as_base_exprf   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      )rQ   is_Addr   r   r2   r7   argsis_Mulr   r   r^   r   r   r   r   int
is_Integerr   Oner   r   r   r   r   )rC   rd   berg   bgeg_rebuildr&   mappingpowersr)   r*   r      s2   
z)FracField._rebuild_expr.<locals>._rebuild)r&   r>   keys)ri   rC   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)
dictr2   r]   r%   r#   r   r   r   rq   r   )ri   rC   r   fracr)   r)   r*   r     s   
zFracField.from_exprc                 C  s   t | S rk   r   rh   r)   r)   r*   	to_domain  s   zFracField.to_domainc                 C  s   ddl m} || j| j| jS )Nr   rK   )rN   rL   r%   r&   r'   )ri   rL   r)   r)   r*   r     s   zFracField.to_ringrk   )rP   
__module____qualname____doc__r   rS   r\   rl   rn   ro   rt   rv   r|   r   r   r   r   __call__r   r   r   r   r)   r)   r)   r*   r"   h   s&    &

%#
r"   c                   @  s<  e Zd ZdZdKddZd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 )LrM   z=Element of multivariate distributed rational function field. Nc                 C  s0   |d u r
| j jj}n|std|| _|| _d S )Nzzero denominator)r+   rW   r[   ZeroDivisionErrorrz   r{   ry   r)   r)   r*   __init__!  s   
zFracElement.__init__c                 C  rx   rk   )	__class__frz   r{   r)   r)   r*   r|   *  r}   zFracElement.raw_newc                 C  s   | j || S rk   )r|   r~   r   r)   r)   r*   r   ,  rm   zFracElement.newc                 C  s   | j dkr	td| jS )Nr   zf.denom should be 1)r{   rq   rz   r   r)   r)   r*   rp   /  s   
zFracElement.to_polyc                 C  s
   | j  S rk   )r+   r   rh   r)   r)   r*   parent4  rw   zFracElement.parentc                 C  rj   rk   )r+   rz   r{   rh   r)   r)   r*   rl   7  rm   zFracElement.__getnewargs__c                 C  s,   | j }|d u rt| j| j| jf | _ }|S rk   )rV   rU   r+   rz   r{   )ri   rV   r)   r)   r*   rn   <  s   zFracElement.__hash__c                 C  s   |  | j | j S rk   )r|   rz   copyr{   rh   r)   r)   r*   r   B     zFracElement.copyc                 C  s8   | j |kr| S |j}| j|}| j|}|||S rk   )r+   rW   rz   r   r{   r   )ri   	new_fieldnew_ringrz   r{   r)   r)   r*   	set_fieldE  s   
zFracElement.set_fieldc                 G  s   | j j| | jj|  S rk   )rz   as_exprr{   )ri   r%   r)   r)   r*   r   N  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 rk   )r^   rM   r+   rz   r{   rW   r[   r   gr)   r)   r*   rt   Q  s   zFracElement.__eq__c                 C  ru   rk   r)   r   r)   r)   r*   rv   W  rw   zFracElement.__ne__c                 C  s
   t | jS rk   )boolrz   r   r)   r)   r*   __bool__Z  rw   zFracElement.__bool__c                 C  s   | j  | j fS rk   )r{   sort_keyrz   rh   r)   r)   r*   r   ]  s   zFracElement.sort_keyc                 C  s$   t || jjr||  | S tS rk   )r^   r+   rY   r   NotImplemented)f1f2opr)   r)   r*   _cmp`  s   zFracElement._cmpc                 C     |  |tS rk   )r   r   r   r   r)   r)   r*   __lt__f  r}   zFracElement.__lt__c                 C  r   rk   )r   r   r   r)   r)   r*   __le__h  r}   zFracElement.__le__c                 C  r   rk   )r   r	   r   r)   r)   r*   __gt__j  r}   zFracElement.__gt__c                 C  r   rk   )r   r
   r   r)   r)   r*   __ge__l  r}   zFracElement.__ge__c                 C  s   |  | j| jS z"Negate all coefficients in ``f``. r|   rz   r{   r   r)   r)   r*   __pos__o  s   zFracElement.__pos__c                 C  s   |  | j | jS r   r   r   r)   r)   r*   __neg__s  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&   r   r   r   r   r   rz   r{   )ri   r   r&   r   r)   r)   r*   _extract_groundw  s    
zFracElement._extract_groundc                 C  s  | j }|s| S | s|S t||jr6| j|jkr"| | j|j | jS | | j|j | j|j  | j|j S t||jjrJ| | j| j|  | jS t|trrt|jt	r]|jj |j kr]n-t|j jt	rp|j jj |krp|
| S tS t|trt|jtr|jj|jkrn|
| S | 
|S )z(Add rational functions ``f`` and ``g``. )r+   r^   rY   r{   r   rz   rW   rM   r&   r   __radd__r   r   r   r   r   r+   r)   r)   r*   __add__  s,   (




zFracElement.__add__c                 C  s   t || jjjr| | j| j|  | jS | |\}}}|dkr.| | j| j|  | jS |s2tS | | j| | j|  | j| S Nr   	r^   r+   rW   rY   r   rz   r{   r   r   r   cr   g_numerg_denomr)   r)   r*   r     s   "zFracElement.__radd__c                 C  sr  | j }|s| S | s| S t||jr7| j|jkr#| | j|j | jS | | j|j | j|j  | j|j S t||jjrK| | j| j|  | jS t|trst|jt	r^|jj |j kr^n-t|j jt	rq|j jj |krq|
| 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+   r^   rY   r{   r   rz   rW   rM   r&   r   __rsub__r   r   r   r   r   r   r+   r   r   r   r)   r)   r*   __sub__  s6   (



"zFracElement.__sub__c                 C  s   t || jjjr| | j | j|  | jS | |\}}}|dkr0| | j | j|  | jS |s4tS | | j | | j|  | j| S r   r   r   r)   r)   r*   r     s   $zFracElement.__rsub__c                 C  s   | j }| r|s
|jS t||jr| | j|j | j|j S t||jjr/| | j| | jS t|trWt|j	t
rB|j	j |j krBn-t|j j	t
rU|j j	j |krU|| S tS t|trot|j	trj|j	j|jkrjn|| S | |S )z-Multiply rational functions ``f`` and ``g``. )r+   rZ   r^   rY   r   rz   r{   rW   rM   r&   r   __rmul__r   r   r   r   r)   r)   r*   __mul__  s$   




zFracElement.__mul__c                 C  sp   t || jjjr| | j| | jS | |\}}}|dkr(| | j| | jS |s,tS | | j| | j| S r   r   r   r)   r)   r*   r     s   zFracElement.__rmul__c                 C  s$  | j }|stt||jr| | j|j | j|j S t||jjr,| | j| j| S t|trTt|j	t
r?|j	j |j kr?n-t|j j	t
rR|j j	j |krR|| S tS t|trlt|j	trg|j	j|jkrgn|| S | |\}}}|dkr| | j| j| S |stS | | j| | j| S )z0Computes quotient of fractions ``f`` and ``g``. r   )r+   r   r^   rY   r   rz   r{   rW   rM   r&   r   __rtruediv__r   r   r   r   r   r)   r)   r*   __truediv__  s.   



zFracElement.__truediv__c                 C  sx   | st t|| jjjr| | j| | jS | |\}}}|dkr,| | j| | jS |s0t	S | | j| | j| S r   )
r   r^   r+   rW   rY   r   r{   rz   r   r   r   r)   r)   r*   r   2  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   )r|   rz   r{   r   )r   nr)   r)   r*   __pow__A  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)

        r6   )rp   r   rz   diffr{   )r   xr)   r)   r*   r   J  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+   rO   evaluater2   r]   r#   rq   )r   r3   r)   r)   r*   r   [  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)   rp   r.   Xar)   r)   r*   r0   c      z(FracElement.evaluate.<locals>.<listcomp>)	r^   r2   rz   r   r{   rp   rW   r   r   )r   r   r   rz   r{   r+   r)   r)   r*   r   a  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*   r0   n  r   z$FracElement.subs.<locals>.<listcomp>)r^   r2   rz   subsr{   rp   r   )r   r   r   rz   r{   r)   r)   r*   r   l  s   zFracElement.subsc                 C  s   t rk   )r   )r   r   r   r)   r)   r*   composev  s   zFracElement.composerk   ))rP   r   r   r   r   r|   r   rp   r   rl   rV   rn   r   r   r   rt   rv   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*   rM     sN    
		&!	


rM   N)?r   
__future__r   typingr   	functoolsr   operatorr   r   r   r   r	   r
   sympy.core.exprr   sympy.core.modr   sympy.core.numbersr   sympy.core.singletonr   sympy.core.symbolr   sympy.core.sympifyr   r   &sympy.functions.elementary.exponentialr   !sympy.polys.domains.domainelementr   !sympy.polys.domains.fractionfieldr   "sympy.polys.domains.polynomialringr   sympy.polys.constructorr   sympy.polys.orderingsr   sympy.polys.polyerrorsr   sympy.polys.polyoptionsr   sympy.polys.polyutilsr   rN   r   sympy.printing.defaultsr   sympy.utilitiesr   sympy.utilities.iterablesr   sympy.utilities.magicr    r+   r,   r1   rI   rJ   __annotations__r"   rM   r)   r)   r)   r*   <module>   sJ     
4 7