+
     ‡i©  ã                   óL   € ^ RI Ht ^ RIHt ^ RIHt ^RIHt  ! R R]4      tR# )é    )ÚS)Ú_sympify)ÚPoly)Ú
MatrixExprc                   óR   a a€ ] tR t^t oRtV 3R lt]R 4       tR tR t	Rt
VtV ;t# )ÚCompanionMatrixa¢  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¦  <€ \        V4      p\        V\        4      '       g   \        R P	                  V4      4      hVP
                  '       g   \        RP	                  V4      4      hVP                  '       g   \        RP	                  V4      4      hVP                  4       ^8¼  g   \        RP	                  V4      4      h\        SV `%  W4      # )z{} must be a Poly instance.z{} must be a monic polynomial.z#{} must be a univariate polynomial.z${} must have degree not less than 1.)
r   Ú
isinstancer   Ú
ValueErrorÚformatÚis_monicÚis_univariateÚdegreeÚsuperÚ__new__)ÚclsÚpolyÚ	__class__s   &&€Ú„/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/matrices/expressions/companion.pyr   ÚCompanionMatrix.__new__   sµ   ø€ Ü˜‹~ˆÜ˜$¤×%Ò%ÜÐ:×AÑAÀ$ÓGÓHÐHØ}}ˆ}ÜÐ=×DÑDÀTÓJÓKÐKØ×!×!Ð!ÜØ5×<Ñ<¸TÓBóDð Dà{‰{‹} Ô!ÜØ6×=Ñ=¸dÓCóEð Eô ‰w‰˜sÓ)Ð)ó    c                óN   € V P                   ^ ,          pVP                  4       pW"3# )r   )Úargsr   )Úselfr   Úsizes   &  r   ÚshapeÚCompanionMatrix.shape'   s"   € ày‰y˜|ˆØ{‰{‹}ˆØˆzÐr   c                óê   € W P                   ^,
          8X  d1   V P                  ^ ,          P                  4       RV,
          ,          ) # W^,           8X  d   \        P                  # \        P
                  # )é   éÿÿÿÿ)Úcolsr   Ú
all_coeffsr   ÚOneÚZero)r   ÚiÚjs   &&&r   Ú_entryÚCompanionMatrix._entry.   sN   € Ø—	‘	˜A•ÔØ—I‘I˜a•L×+Ñ+Ó-¨b°1­fÕ5Ð5Ð5Øa•%ŒZÜ—5‘5ˆLÜv‰vˆr   c                óR   € ^ RI Hp VP                  V P                  ^ ,          4      # )r   )ÚImmutableDenseMatrix)Úsympy.matrices.immutabler*   Ú	companionr   )r   r*   s   & r   Úas_explicitÚCompanionMatrix.as_explicit6   s   € ÝAØ#×-Ñ-¨d¯i©i¸­lÓ;Ð;r   © )Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__r   Úpropertyr   r'   r-   Ú__static_attributes__Ú__classdictcell__Ú__classcell__)r   Ú__classdict__s   @@r   r   r      s2   ù‡ € ñõ*ð  ñó ðò÷<ò <r   r   N)	Úsympy.core.singletonr   Úsympy.core.sympifyr   Úsympy.polys.polytoolsr   Úmatexprr   r   r/   r   r   Ú<module>r>      s   ðÝ "Ý 'Ý &å ô0<jö 0<r   