
    Цi                     R    S SK JrJrJr  S SKJr  S SKJr  S SKJ	r	   " S S\5      r
g)    )
AtomicExprSymbolS)_sympify)
prettyForm)
PRECEDENCEc                      ^  \ rS rSrSrSU 4S jjrSrSr\S 5       r	Sr
S rSS jrSS jr\S	   r\S
 5       rS rSrU =r$ )
BaseScalar   zV
A coordinate symbol/base scalar.

Ideally, users should not instantiate this class.

c                 6  > SSK Jn  Uc  SR                  U5      nO![        U[        5      (       a  UR
                  nUc  SR                  U5      nO![        U[        5      (       a  UR
                  n[        U5      n[        U5      n[        TU ]!  XU5      n[        X%5      (       d  [        S5      eU[        SS5      ;  a  [        S5      eX4Ul        UR                  S-   UR                  U   -   =Ul        Ul        S	U-   Ul        XFl        X&l        U$ )
Nr   )
CoordSys3Dzx{}zx_{}zsystem should be a CoordSys3D   zInvalid index specified.. )sympy.vector.coordsysrectr   format
isinstancer   namer   super__new__	TypeErrorrange
ValueError_id_name_variable_names_pretty_form_latex_form_system)clsindexsystem
pretty_str	latex_strr   obj	__class__s          R/var/www/html/ai-image-ml/venv/lib/python3.13/site-packages/sympy/vector/scalar.pyr   BaseScalar.__new__   s    8e,J
F++#Je,I	6**!I&!goc&1&--;<<a#788/%||c1F4J4J54QQQ	CH
?#
    Tc                     U 1$ N selfs    r'   free_symbolsBaseScalar.free_symbols-   s	    vr)   c                 L    X:X  a  [         R                  $ [         R                  $ r+   )r   OneZero)r.   ss     r'   _eval_derivativeBaseScalar._eval_derivative3   s    955Lvvr)   c                     U R                   $ r+   )r   r.   printers     r'   _latexBaseScalar._latex8   s    r)   c                 ,    [        U R                  5      $ r+   )r   r   r8   s     r'   _prettyBaseScalar._pretty;   s    $++,,r)   Atomc                     U R                   $ r+   )r   r-   s    r'   r"   BaseScalar.system@   s    ||r)   c                     U R                   $ r+   )r   r8   s     r'   	_sympystrBaseScalar._sympystrD   s    zzr)   r,   )NNr+   )__name__
__module____qualname____firstlineno____doc__r   is_commutative	is_symbolpropertyr/   	_diff_wrtr5   r:   r=   r   
precedencer"   rC   __static_attributes____classcell__)r&   s   @r'   r
   r
      si    6 NI  I
 - F#J  r)   r
   N)
sympy.corer   r   r   sympy.core.sympifyr    sympy.printing.pretty.stringpictr   sympy.printing.precedencer   r
   r,   r)   r'   <module>rU      s     , , ' 7 0> >r)   