a
    RG5dY                     @   s   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mZmZ d	d
 Zdd Zdd Zdd Zdd Zdd ZdS )    )defaultdictAdd)Mul)S)construct_domain)PolyNonlinearError   )SDM	sdm_irrefsdm_particular_from_rrefsdm_nullspace_from_rrefc                 C   sH  t |}t| |\}}t|||}|j}|js4|jrH|  d  }t	|\}}}	|rj|d |krjdS t
||d |}
t||j|||	\}}tt}|
 D ] \}}|||  || qt||D ]>\}}|| }| D ]$\}}|||  |||  qqdd | D }tj}t|t| D ]}|||< q4|S )a  Solve a linear system of equations.

    Examples
    ========

    Solve a linear system with a unique solution:

    >>> from sympy import symbols, Eq
    >>> from sympy.polys.matrices.linsolve import _linsolve
    >>> x, y = symbols('x, y')
    >>> eqs = [Eq(x + y, 1), Eq(x - y, 2)]
    >>> _linsolve(eqs, [x, y])
    {x: 3/2, y: -1/2}

    In the case of underdetermined systems the solution will be expressed in
    terms of the unknown symbols that are unconstrained:

    >>> _linsolve([Eq(x + y, 0)], [x, y])
    {x: -y, y: y}

    r   Nr	   c                 S   s   i | ]\}}|t | qS  r   ).0stermsr   r   Y/var/www/html/django/DPS/env/lib/python3.9/site-packages/sympy/polys/matrices/linsolve.py
<dictcomp>j       z_linsolve.<locals>.<dictcomp>)len_linear_eq_to_dictsympy_dict_to_dmdomainis_RealFieldis_ComplexFieldto_ddmrrefto_sdmr   r   r   oner   listitemsappendto_sympyzipr   Zeroset)eqssymsnsymseqsdictrhsAaugKArrefpivotsnzcolsPV	nonpivotssolivZnpiZVisymzeror   r   r   r   	_linsolve.   s.     r9   c                    s   t |jdd | D  }t|ddd\}}tt|| t| }t|}tt|t|g }t| |D ]@\}	}
 fdd|	 D }|
r |
  ||< |rh|| qht	t
|||d f|}|S )z?Convert a system of dict equations to a sparse augmented matrixc                 s   s   | ]}|  V  qd S N)values)r   er   r   r   	<genexpr>w   r   z#sympy_dict_to_dm.<locals>.<genexpr>T)field	extensionc                    s   i | ]\}}|  | qS r   r   )r   r   cZelem_mapZ	sym2indexr   r   r      r   z$sympy_dict_to_dm.<locals>.<dictcomp>r	   )r&   unionr   dictr$   r   ranger!   r"   r
   	enumerate)Z
eqs_coeffseqs_rhsr(   elemsr-   Zelems_KZneqsr)   r*   eqr+   eqdictZsdm_augr   rA   r   r   u   s    r   c                    s   dd   fdd| D S )zUse expand to cancel nonlinear terms.

    This approach matches previous behaviour of linsolve but should be
    deprecated.
    c                 S   s   | j r| j| j } |  S r:   )is_Equalitylhsr+   expand)rH   r   r   r   	expand_eq   s    z)_expand_eqs_deprecated.<locals>.expand_eqc                    s   g | ]} |qS r   r   )r   rH   rM   r   r   
<listcomp>   r   z*_expand_eqs_deprecated.<locals>.<listcomp>r   )r'   r   rN   r   _expand_eqs_deprecated   s    rP   c                 C   s6   zt | |W S  ty0   t| } t | | Y S 0 dS )1Convert a system Expr/Eq equations into dict formN)_linear_eq_to_dict_innerr   rP   )r'   r(   r   r   r   r      s
    r   c                 C   sF   t |}g g  }}| D ]&}t||\}}|| || q||fS )rQ   )r&   _lin_eq2dictr"   )r'   r(   r*   rF   rH   r+   rI   r   r   r   rR      s    

rR   c                    sX  | |v rt j| t jifS | jrtt}g }| jD ]<}t||\}}|| |	 D ]\}}|| | qTq0t
|  dd |	 D }	 |	fS | jr"d }	}
g }| jD ]8}t||\}}|s|| q|	du r|}	|}
qtqt|  |	du  r i fS  fdd|		 D }	 |
 |	fS n2| jr<t| j| j |S | j| sP| i fS tdS )z?Efficiently convert a linear equation to a dict of coefficientsc                 S   s   i | ]\}}|t | qS r   r   )r   r7   coeffsr   r   r   r      r   z _lin_eq2dict.<locals>.<dictcomp>Nc                    s   i | ]\}}| | qS r   r   )r   r7   r@   coeffr   r   r      r   )r   r%   Oneis_Addr   r    argsrS   r"   r!   r   is_Mulr   r   rJ   rK   r+   has_free)asymsetZ
terms_listZ
coeff_listaicitimijZcijr   Zterms_coeffr   rU   r   rS      sD    



rS   N)collectionsr   sympy.core.addr   sympy.core.mulr   sympy.core.singletonr   sympy.polys.constructorr   Zsympy.polys.solversr   sdmr
   r   r   r   r9   r   rP   r   rR   rS   r   r   r   r   <module>   s   G
