a
    RG5dR                     @   s  d Z ddlmZ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;G d!d" d"e0Z<G d#d$ d$ee0eZ=d%S )&z!Sparse rational function fields.     )AnyDict)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)   N/var/www/html/django/DPS/env/lib/python3.9/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>.       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 ]}||  q8t||\}}|jdu rt	dd |D g }t
||d\|_}	t|j|j|j}
g }tdt|dD ]"}||
t|||d   q|r|
|d fS |
|fS d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   r1   zsfield.<locals>.<listcomp>)optr      )r   r3   mapr   r   extendas_numer_denomr   r&   sumr   r"   r#   r'   rangelenappendtuple)exprsr%   optionssingler6   Znumdensexprrepscoeffs_r(   Zfracsir)   r)   r*   sfield1   s&    

 rH   c                   @   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 rt	
| }||_t||_||_tdtfd|i|_||_||_||_||_||j|_||j|_| |_t|j|jD ].\}	}
t|	tr|	j}t||st|||
 q|t|< |S )Nr   PolyRingFracElementr+   )sympy.polys.ringsrJ   r%   ngensr&   r'   __name___field_cachegetobject__new___hash_tuplehash_hashringtyperK   dtypezeroone_gensr#   zip
isinstancer   r-   hasattrsetattr)clsr%   r&   r'   rJ   rV   rM   rS   objsymbol	generatorr-   r)   r)   r*   rR   k   s8    






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)   rX   r.   genselfr)   r*   r0      r1   z#FracField._gens.<locals>.<listcomp>)r?   rV   r#   rg   r)   rg   r*   r[      s    zFracField._gensc                 C   s   | j | j| jfS N)r%   r&   r'   rg   r)   r)   r*   __getnewargs__   s    zFracField.__getnewargs__c                 C   s   | j S ri   )rU   rg   r)   r)   r*   __hash__   s    zFracField.__hash__c                 C   s2   t || jr| j| S td| j|f d S )Nzexpected a %s, got %s instead)r]   rX   rV   indexto_poly
ValueError)rh   rf   r)   r)   r*   rl      s    zFracField.indexc                 C   s2   t |to0| j| j| j| jf|j|j|j|jfkS ri   )r]   r"   r%   rM   r&   r'   rh   otherr)   r)   r*   __eq__   s
    
zFracField.__eq__c                 C   s
   | |k S ri   r)   ro   r)   r)   r*   __ne__   s    zFracField.__ne__Nc                 C   s   |  ||S ri   rd   rh   numerdenomr)   r)   r*   raw_new   s    zFracField.raw_newc                 C   s*   |d u r| j j}||\}}| ||S ri   )rV   rZ   cancelrv   rs   r)   r)   r*   new   s    zFracField.newc                 C   s   | j |S ri   )r&   convert)rh   elementr)   r)   r*   
domain_new   s    zFracField.domain_newc                 C   s   z|  | j|W S  ty   | j}|js||jr|| j}| }||}||	|}||
|}| || Y S  Y n0 d S ri   )rx   rV   
ground_newr   r&   is_Fieldhas_assoc_Field	get_fieldry   rt   ru   rv   )rh   rz   r&   rV   ground_fieldrt   ru   r)   r)   r*   r|      s    
zFracField.ground_newc                 C   sv  t |trp| |jkr|S t | jtr<| jj|jkr<| |S t | jtrd| jj |jkrd| |S t	dnt |t
r | \}}t | jtr|j| jjkr| j|}n8t | jtr|j| jj kr| j|}n|| j}| j|}| ||S t |tr<t|dkr<tt| jj|\}}| ||S t |trRt	dn t |trh| |S | |S d S )N
conversionr7   parsing)r]   rK   r+   r&   r   r|   r   rV   to_fieldNotImplementedErrorr   clear_denomsto_ringset_ringrv   r?   r=   r3   r8   ring_newrx   strr   	from_expr)rh   rz   ru   rt   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 ri   )is_Powr]   r   as_base_expre   r)   r)   r*   	<genexpr>   s   z*FracField._rebuild_expr.<locals>.<genexpr>c                    s@   | }|d ur|S | jr2tttt | jS | jrNtttt | jS | j	sbt
| ttfr|  \}}D ]<\}\}}||krrt||dkrr |t||    S qr|jr|tjur |t| S n$ d|  d urd d|   S z| W S  ty:   js4jr4 |  Y S  Y n0 d S )Nr      )rP   is_Addr   r   r3   r8   argsis_Mulr   r   r]   r   r   r   r   int
is_Integerr   Onery   r   r}   r~   r   )rC   rc   berf   bgeg_rebuildr&   mappingpowersr)   r*   r      s,    
z)FracField._rebuild_expr.<locals>._rebuild)r&   r?   keys)rh   rC   r   r)   r   r*   _rebuild_expr   s    zFracField._rebuild_exprc                 C   s\   t tt| j| j}z| t||}W n" tyL   td| |f Y n0 | 	|S d S )NzGexpected an expression convertible to a rational function in %s, got %s)
dictr3   r\   r%   r#   r   r   r   rn   r   )rh   rC   r   fracr)   r)   r*   r     s    zFracField.from_exprc                 C   s   t | S ri   r   rg   r)   r)   r*   	to_domain  s    zFracField.to_domainc                 C   s   ddl m} || j| j| jS )Nr   rI   )rL   rJ   r%   r&   r'   )rh   rJ   r)   r)   r*   r     s    zFracField.to_ring)N)N)rN   
__module____qualname____doc__r   rR   r[   rj   rk   rl   rq   rr   rv   rx   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%dLdEdFZ&dMdGdHZ'dNdIdJZ(dS )OrK   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+   rV   rZ   ZeroDivisionErrorrt   ru   rs   r)   r)   r*   __init__!  s    zFracElement.__init__c                 C   s   |  ||S ri   )	__class__frt   ru   r)   r)   r*   rv   *  s    zFracElement.raw_newc                 C   s   | j || S ri   )rv   rw   r   r)   r)   r*   rx   ,  s    zFracElement.newc                 C   s   | j dkrtd| jS )Nr   zf.denom should be 1)ru   rn   rt   r   r)   r)   r*   rm   /  s    
zFracElement.to_polyc                 C   s
   | j  S ri   )r+   r   rg   r)   r)   r*   parent4  s    zFracElement.parentc                 C   s   | j | j| jfS ri   )r+   rt   ru   rg   r)   r)   r*   rj   7  s    zFracElement.__getnewargs__c                 C   s,   | j }|d u r(t| j| j| jf | _ }|S ri   )rU   rT   r+   rt   ru   )rh   rU   r)   r)   r*   rk   <  s    zFracElement.__hash__c                 C   s   |  | j | j S ri   )rv   rt   copyru   rg   r)   r)   r*   r   B  s    zFracElement.copyc                 C   s<   | j |kr| S |j}| j|}| j|}|||S d S ri   )r+   rV   rt   r   ru   rx   )rh   	new_fieldnew_ringrt   ru   r)   r)   r*   	set_fieldE  s    
zFracElement.set_fieldc                 G   s   | j j| | jj|  S ri   )rt   as_exprru   )rh   r%   r)   r)   r*   r   N  s    zFracElement.as_exprc                 C   sL   t |tr.| j|jkr.| j|jko,| j|jkS | j|koF| j| jjjkS d S ri   )r]   rK   r+   rt   ru   rV   rZ   r   gr)   r)   r*   rq   Q  s    zFracElement.__eq__c                 C   s
   | |k S ri   r)   r   r)   r)   r*   rr   W  s    zFracElement.__ne__c                 C   s
   t | jS ri   )boolrt   r   r)   r)   r*   __bool__Z  s    zFracElement.__bool__c                 C   s   | j  | j fS ri   )ru   sort_keyrt   rg   r)   r)   r*   r   ]  s    zFracElement.sort_keyc                 C   s(   t || jjr ||  | S tS d S ri   )r]   r+   rX   r   NotImplemented)f1f2opr)   r)   r*   _cmp`  s    zFracElement._cmpc                 C   s   |  |tS ri   )r   r   r   r   r)   r)   r*   __lt__f  s    zFracElement.__lt__c                 C   s   |  |tS ri   )r   r   r   r)   r)   r*   __le__h  s    zFracElement.__le__c                 C   s   |  |tS ri   )r   r	   r   r)   r)   r*   __gt__j  s    zFracElement.__gt__c                 C   s   |  |tS ri   )r   r
   r   r)   r)   r*   __ge__l  s    zFracElement.__ge__c                 C   s   |  | j| jS z"Negate all coefficients in ``f``. rv   rt   ru   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 nd tyz   |jst|jrt| }z||}W n tyX   Y n0 d||||f Y S Y dS 0 d|d fS d S )N)r   NNr   )	r+   r&   ry   r   r}   r~   r   rt   ru   )rh   rz   r&   r   r)   r)   r*   _extract_groundw  s    zFracElement._extract_groundc                 C   s(  | j }|s| S | s|S t||jrn| j|jkrD| | j|j | jS | | j|j | j|j  | j|j S nt||jjr| | j| j|  | jS t|trt|jt	r|jj |j krn*t|j jt	r|j jj |kr|
| S tS n6t|trt|jtr|jj|jkrn
|
| S | 
|S )z(Add rational functions ``f`` and ``g``. )r+   r]   rX   ru   rx   rt   rV   rK   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 |sdtS | | j| | j|  | j| S d S Nr   	r]   r+   rV   rX   rx   rt   ru   r   r   r   cr   g_numerg_denomr)   r)   r*   r     s    zFracElement.__radd__c                 C   s  | j }|s| S | s| S t||jrp| j|jkrF| | j|j | jS | | j|j | j|j  | j|j S nt||jjr| | j| j|  | jS t|trt|jt	r|jj |j krn*t|j jt	r|j jj |kr|
| S tS n6t|tr t|jtr|jj|jkrn
|
| S | |\}}}|dkrT| | j| j|  | jS |s^tS | | j| | j|  | j| S dS )z-Subtract rational functions ``f`` and ``g``. r   N)r+   r]   rX   ru   rx   rt   rV   rK   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r`| | j | j|  | jS |shtS | | j | | j|  | j| S d 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rt|j	t
r|j	j |j krqt|j j	t
r|j j	j |kr|| S tS n0t|trt|j	tr|j	j|jkrn
|| S | |S )z-Multiply rational functions ``f`` and ``g``. )r+   rY   r]   rX   rx   rt   ru   rV   rK   r&   r   __rmul__r   r   r   r   r)   r)   r*   __mul__  s$    



zFracElement.__mul__c                 C   st   t || jjjr$| | j| | jS | |\}}}|dkrP| | j| | jS |sXtS | | j| | j| S d S r   r   r   r)   r)   r*   r     s    zFracElement.__rmul__c                 C   s0  | j }|stnt||jr8| | j|j | j|j S t||jjrZ| | j| j| S t|trt|j	t
r|j	j |j krqt|j j	t
r|j j	j |kr|| S tS n0t|trt|j	tr|j	j|jkrn
|| S | |\}}}|dkr
| | j| j| S |stS | | j| | j| S dS )z0Computes quotient of fractions ``f`` and ``g``. r   N)r+   r   r]   rX   rx   rt   ru   rV   rK   r&   r   __rtruediv__r   r   r   r   r   r)   r)   r*   __truediv__  s.    




zFracElement.__truediv__c                 C   s~   | s
t n$t|| jjjr.| | j| | jS | |\}}}|dkrZ| | j| | jS |sbt	S | | j| | j| S d S r   )
r   r]   r+   rV   rX   rx   ru   rt   r   r   r   r)   r)   r*   r   2  s    zFracElement.__rtruediv__c                 C   sJ   |dkr |  | j| | j| S | s*tn|  | j|  | j|  S dS )z+Raise ``f`` to a non-negative power ``n``. r   N)rv   rt   ru   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)

        r7   )rm   rx   rt   diffru   )r   xr)   r)   r*   r   J  s    zFracElement.diffc                 G   sT   dt |  k r| jjkr8n n| tt| jj|S td| jjt |f d S )Nr   z1expected at least 1 and at most %s values, got %s)r=   r+   rM   evaluater3   r\   r#   rn   )r   r4   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   s   g | ]\}}|  |fqS r)   rm   r.   Xar)   r)   r*   r0   c  r1   z(FracElement.evaluate.<locals>.<listcomp>)	r]   r3   rt   r   ru   rm   rV   r   rx   )r   r   r   rt   ru   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   s   g | ]\}}|  |fqS r)   r   r   r)   r)   r*   r0   n  r1   z$FracElement.subs.<locals>.<listcomp>)r]   r3   rt   subsru   rm   rx   )r   r   r   rt   ru   r)   r)   r*   r   l  s    zFracElement.subsc                 C   s   t d S ri   )r   )r   r   r   r)   r)   r*   composev  s    zFracElement.compose)N)N)N)N))rN   r   r   r   r   rv   rx   rm   r   rj   rU   rk   r   r   r   rq   rr   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*   rK     sL   
		&!	


rK   N)>r   typingr   r   tDict	functoolsr   operatorr   r   r   r   r	   r
   sympy.core.exprr   Zsympy.core.modr   sympy.core.numbersr   Z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   Zsympy.polys.polyoptionsr   sympy.polys.polyutilsr   rL   r   sympy.printing.defaultsr   Zsympy.utilitiesr   sympy.utilities.iterablesr   sympy.utilities.magicr    r+   r,   r2   rH   rO   r"   rK   r)   r)   r)   r*   <module>   sF    
4 7