Ë
    7^(h©  ã                   óJ   — d dl mZ d dlmZ d dlmZ ddlmZ  G d„ de«      Zy)	é    )ÚS)Ú_sympify)ÚPolyé   )Ú
MatrixExprc                   ó>   ‡ — e Zd ZdZˆ fd„Zed„ «       Zd„ Zd„ Zˆ xZ	S )ÚCompanionMatrixaÎ  A symbolic companion matrix of a polynomial.

    Examples
    ========

    >>> from sympy import Poly, Symbol, symbols
    >>> from sympy.matrices.expressions import CompanionMatrix
    >>> x = Symbol('x')
    >>> c0, c1, c2, c3, c4 = symbols('c0:5')
    >>> p = Poly(c0 + c1*x + c2*x**2 + c3*x**3 + c4*x**4 + x**5, x)
    >>> CompanionMatrix(p)
    CompanionMatrix(Poly(x**5 + c4*x**4 + c3*x**3 + c2*x**2 + c1*x + c0,
    x, domain='ZZ[c0,c1,c2,c3,c4]'))
    c                 ó€  •— t        |«      }t        |t        «      st        dj	                  |«      «      ‚|j
                  st        dj	                  |«      «      ‚|j                  st        dj	                  |«      «      ‚|j                  «       dk\  st        dj	                  |«      «      ‚t        ‰| �%  | |«      S )Nz{} must be a Poly instance.z{} must be a monic polynomial.z#{} must be a univariate polynomial.r   z${} must have degree not less than 1.)
r   Ú
isinstancer   Ú
ValueErrorÚformatÚis_monicÚis_univariateÚdegreeÚsuperÚ__new__)ÚclsÚpolyÚ	__class__s     €úb/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/matrices/expressions/companion.pyr   zCompanionMatrix.__new__   s¯   ø€ Ü˜‹~ˆÜ˜$¤Ô%ÜÐ:×AÑAÀ$ÓGÓHÐHØ�}Š}ÜÐ=×DÑDÀTÓJÓKÐKØ×!Ò!ÜØ5×<Ñ<¸TÓBóDð Dà�{‰{‹} Ò!ÜØ6×=Ñ=¸dÓCóEð Eô ‰w‰˜s DÓ)Ð)ó    c                 óH   — | j                   d   }|j                  «       }||fS )Nr   )Úargsr   )Úselfr   Úsizes      r   ÚshapezCompanionMatrix.shape'   s$   € à�y‰y˜‰|ˆØ�{‰{‹}ˆØ�TˆzÐr   c                 ó¾   — || j                   dz
  k(  r$| j                  d   j                  «       d|z
      S ||dz   k(  rt        j                  S t        j
                  S )Nr   r   éÿÿÿÿ)Úcolsr   Ú
all_coeffsr   ÚOneÚZero)r   ÚiÚjs      r   Ú_entryzCompanionMatrix._entry.   sR   € Ø�—	‘	˜A‘ÒØ—I‘I˜a‘L×+Ñ+Ó-¨b°1©fÑ5Ð5Ð5Ø�!�a‘%ŠZÜ—5‘5ˆLÜ�v‰vˆr   c                 óJ   — ddl m} |j                  | j                  d   «      S )Nr   )ÚImmutableDenseMatrix)Úsympy.matrices.immutabler'   Ú	companionr   )r   r'   s     r   Úas_explicitzCompanionMatrix.as_explicit6   s   € ÝAØ#×-Ñ-¨d¯i©i¸©lÓ;Ð;r   )
Ú__name__Ú
__module__Ú__qualname__Ú__doc__r   Úpropertyr   r%   r*   Ú__classcell__)r   s   @r   r	   r	      s+   ø„ ñô*ð  ñó ðòö<r   r	   N)	Úsympy.core.singletonr   Úsympy.core.sympifyr   Úsympy.polys.polytoolsr   Úmatexprr   r	   © r   r   ú<module>r6      s   ðÝ "Ý 'Ý &å ô0<�jõ 0<r   