§
    PŠtjQ.  ã                  ó  — d dl mZ d dlmZ d dlmZ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mZmZ d d
lmZ erd dlmZ  G d„ de¦  «        Z G d„ dee¦  «        Z G d„ dee¦  «        Z  G d„ de¦  «        Z!dS )é    )Úannotations)ÚTYPE_CHECKING)ÚsimplifyÚtrigsimp)Úcall_highest_priorityÚ
_sympifyit)Ú	StdFactKB©Údiff©ÚIntegral)Úfactor)ÚSÚAddÚMul)ÚExpr)Ú
BaseVectorc                  ó  — e Zd ZU dZded<    ed¦  «        d„ ¦   «         Z ed¦  «        d„ ¦   «         Z ed¦  «        d	„ ¦   «         Z ed
¦  «        d„ ¦   «         Z	 e
de¦  «         ed¦  «        d„ ¦   «         ¦   «         Z e
de¦  «         ed¦  «        d„ ¦   «         ¦   «         Zd„ Z e
de¦  «         ed¦  «        d„ ¦   «         ¦   «         Z ed¦  «        d„ ¦   «         Zd'd„Zexj        ej        j        z  c_        eZd„ Zexj        ej        z  c_        d„ Zexj        ej        z  c_        d„ Zd„ Zd„ Zd „ Zd!„ Zd"„ Zexj        ej        z  c_        d(d#„Zd$„ Z d%„ Z!e!xj        e"j        z  c_        d&„ Z#dS ))ÚBasisDependentzÒ
    Super class containing functionality common to vectors and
    dyadics.
    Named so because the representation of these quantities in
    sympy.vector is dependent on the basis they are expressed in.
    ÚBasisDependentZeroÚzeroÚ__radd__c                ó.   — |                       | |¦  «        S ©N©Ú	_add_func©ÚselfÚothers     úY/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/vector/basisdependent.pyÚ__add__zBasisDependent.__add__   s   € à�~Š~˜d EÑ*Ô*Ð*ó    r!   c                ó.   — |                       || ¦  «        S r   r   r   s     r    r   zBasisDependent.__radd__   s   € à�~Š~˜e TÑ*Ô*Ð*r"   Ú__rsub__c                ó0   — |                       | | ¦  «        S r   r   r   s     r    Ú__sub__zBasisDependent.__sub__#   s   € à�~Š~˜d U FÑ+Ô+Ð+r"   r&   c                ó0   — |                       ||  ¦  «        S r   r   r   s     r    r$   zBasisDependent.__rsub__'   s   € à�~Š~˜e d UÑ+Ô+Ð+r"   r   Ú__rmul__c                ó.   — |                       | |¦  «        S r   ©Ú	_mul_funcr   s     r    Ú__mul__zBasisDependent.__mul__+   s   € ð �~Š~˜d EÑ*Ô*Ð*r"   r,   c                ó.   — |                       || ¦  «        S r   r*   r   s     r    r(   zBasisDependent.__rmul__0   s   € ð �~Š~˜e TÑ*Ô*Ð*r"   c                óB   — |                       t          j        | ¦  «        S r   )r+   r   ÚNegativeOne©r   s    r    Ú__neg__zBasisDependent.__neg__5   s   € Ø�~Š~�aœm¨TÑ2Ô2Ð2r"   Ú__rtruediv__c                ó,   — |                       |¦  «        S r   )Ú_div_helperr   s     r    Ú__truediv__zBasisDependent.__truediv__8   s   € ð ×Ò Ñ&Ô&Ð&r"   r5   c                ó    — t          d¦  «        S )NzInvalid divisor for division)Ú	TypeErrorr   s     r    r2   zBasisDependent.__rtruediv__=   s   € åÐ7Ñ8Ô8Ð8r"   é   Néd   Fc                óŒ   — ||||||dœ}| j         }	| j                             ¦   «         D ]\  }
}|	 |j        |fi |¤Ž|
z  z  }	Œ|	S )z…
        Implements the SymPy evalf routine for this quantity.

        evalf's documentation
        =====================

        )ÚsubsÚmaxnÚchopÚstrictÚquadÚverbose)r   Ú
componentsÚitemsÚevalf)r   Únr;   r<   r=   r>   r?   r@   ÚoptionsÚvecÚkÚvs               r    rC   zBasisDependent.evalfA   sp   € ð  t°DÀ6Ø wð0ð 0ˆàŒiˆØ”O×)Ò)Ñ+Ô+ð 	-ð 	-‰DˆAˆqØ�7�1”7˜1Ð(Ð( Ð(Ð(¨1Ñ,Ñ,ˆCˆCØˆ
r"   c                ób   ‡— ˆfd„| j                              ¦   «         D ¦   «         } | j        |Ž S )zŽ
        Implements the SymPy simplify routine for this quantity.

        simplify's documentation
        ========================

        c                ó6   •— g | ]\  }}t          |fi ‰¤Ž|z  ‘ŒS © )Úsimp)Ú.0rG   rH   Úkwargss      €r    ú
<listcomp>z+BasisDependent.simplify.<locals>.<listcomp>\   sB   ø€ ð <ð <ð <Ù˜1˜aõ   Ð,Ð, VÐ,Ð,¨qÑ0ð <ð <ð <r"   ©rA   rB   r   )r   rN   Úsimp_componentss    ` r    r   zBasisDependent.simplifyT   óH   ø€ ð<ð <ð <ð <Ø#'¤?×#8Ò#8Ñ#:Ô#:ð<ñ <ô <ˆàˆtŒ~˜Ð/Ð/r"   c                ób   ‡— ˆfd„| j                              ¦   «         D ¦   «         } | j        |Ž S )z�
        Implements the SymPy trigsimp routine, for this quantity.

        trigsimp's documentation
        ========================

        c                ó6   •— g | ]\  }}t          |fi ‰¤Ž|z  ‘ŒS rK   )Útsimp)rM   rG   rH   Úoptss      €r    rO   z+BasisDependent.trigsimp.<locals>.<listcomp>j   sB   ø€ ð <ð <ð <Ù˜1˜aõ ! Ð+Ð+ dÐ+Ð+¨aÑ/ð <ð <ð <r"   rP   )r   rV   Útrig_componentss    ` r    r   zBasisDependent.trigsimpb   rR   r"   c                ó   —  | j         di |¤ŽS ©NrK   )r   )r   rN   s     r    Ú_eval_simplifyzBasisDependent._eval_simplifyp   s   € ØˆtŒ}Ð&Ð&˜vÐ&Ð&Ð&r"   c                ó   —  | j         di |¤ŽS rY   )r   )r   rV   s     r    Ú_eval_trigsimpzBasisDependent._eval_trigsimps   s   € ØˆtŒ}Ð$Ð$˜tÐ$Ð$Ð$r"   c                ó,   — |                       |¦  «        S r   r
   )r   Úwrts     r    Ú_eval_derivativezBasisDependent._eval_derivativev   s   € Ø�yŠy˜‰~Œ~Ðr"   c                óf   ‡‡— ˆˆfd„| j                              ¦   «         D ¦   «         } | j        |Ž S )Nc                ó<   •— g | ]\  }}t          |g‰¢R i ‰¤Ž|z  ‘ŒS rK   r   )rM   rG   rH   ÚassumptionsÚsymbolss      €€r    rO   z1BasisDependent._eval_Integral.<locals>.<listcomp>z   sP   ø€ ð Dð Dð DÙ#' 1 aõ  (¨ÐC¨GÐCÐCÐC°{ÐCÐCÀaÑGð Dð Dð Dr"   rP   )r   rc   rb   Úintegral_componentss    `` r    Ú_eval_IntegralzBasisDependent._eval_Integraly   sX   øø€ ðDð Dð Dð Dð DØ+/¬?×+@Ò+@Ñ+BÔ+BðDñ Dô DÐàˆtŒ~Ð2Ð3Ð3r"   c                ó   — | t           j        fS )z‚
        Returns the expression as a tuple wrt the following
        transformation -

        expression -> a/b -> a, b

        ©r   ÚOner0   s    r    Úas_numer_denomzBasisDependent.as_numer_denom~   s   € ð •Q”Uˆ{Ðr"   c                óf   ‡‡— ˆˆfd„| j                              ¦   «         D ¦   «         } | j        |Ž S )zµ
        Implements the SymPy factor routine, on the scalar parts
        of a basis-dependent expression.

        factor's documentation
        ========================

        c                ó<   •— g | ]\  }}t          |g‰¢R i ‰¤Ž|z  ‘ŒS rK   )Úfctr©rM   rG   rH   ÚargsrN   s      €€r    rO   z)BasisDependent.factor.<locals>.<listcomp>‘   sJ   ø€ ð <ð <ð <Ù˜1˜aõ   Ð3 DÐ3Ð3Ð3¨FÐ3Ð3°aÑ7ð <ð <ð <r"   rP   )r   rn   rN   Úfctr_componentss    `` r    r   zBasisDependent.factorˆ   sN   øø€ ð<ð <ð <ð <ð <Ø#'¤?×#8Ò#8Ñ#:Ô#:ð<ñ <ô <ˆàˆtŒ~˜Ð/Ð/r"   c                ó   — t           j        | fS )z1Efficiently extract the coefficient of a product.rg   )r   Úrationals     r    Úas_coeff_MulzBasisDependent.as_coeff_Mul—   s   € å”�tˆ}Ðr"   c                óH   ‡ — dt          ˆ fd„‰ j        D ¦   «         ¦  «        fS )z3Efficiently extract the coefficient of a summation.r   c              3  ó8   •K  — | ]}|‰j         |         z  V — Œd S r   )rA   )rM   Úxr   s     €r    ú	<genexpr>z.BasisDependent.as_coeff_add.<locals>.<genexpr>�   s/   øè è € ÐHÐH°1˜˜DœO¨AÔ.Ñ.ÐHÐHÐHÐHÐHÐHr"   )ÚtuplerA   )r   Údepss   ` r    Úas_coeff_addzBasisDependent.as_coeff_add›   s-   ø€ à•%ÐHÐHÐHÐH¸¼ÐHÑHÔHÑHÔHÐHÐHr"   c                ó¸   ‡‡— ‰D ]&}t          |t          ¦  «        rt          d¦  «        ‚Œ'ˆˆfd„| j                             ¦   «         D ¦   «         } | j        |Ž S )z�
        Implements the SymPy diff routine, for vectors.

        diff's documentation
        ========================

        zInvalid arg for differentiationc                ó<   •— g | ]\  }}t          |g‰¢R i ‰¤Ž|z  ‘ŒS rK   )Údfrm   s      €€r    rO   z'BasisDependent.diff.<locals>.<listcomp>ª   sJ   ø€ ð <ð <ð <Ù˜1˜aõ ˜aÐ1 $Ð1Ð1Ð1¨&Ð1Ð1°AÑ5ð <ð <ð <r"   )Ú
isinstancer   r7   rA   rB   r   )r   rn   rN   ru   Údiff_componentss    ``  r    r   zBasisDependent.diffŸ   s‰   øø€ ð ð 	Cð 	CˆAÝ˜!�^Ñ,Ô,ð CÝÐ AÑBÔBÐBðCð<ð <ð <ð <ð <Ø#'¤?×#8Ò#8Ñ#:Ô#:ð<ñ <ô <ˆàˆtŒ~˜Ð/Ð/r"   c                óB   ‡ ‡— ˆˆ fd„‰ j         D ¦   «         } ‰ j        |Ž S )z(Calls .doit() on each term in the Dyadicc                óF   •— g | ]} ‰j         |         j        d i ‰¤Ž|z  ‘ŒS )rK   )rA   Údoit)rM   ru   Úhintsr   s     €€r    rO   z'BasisDependent.doit.<locals>.<listcomp>²   sH   ø€ ð 5ð 5ð 5Ø ð 3˜4œ?¨1Ô-Ô2Ð;Ð;°UÐ;Ð;¸aÑ?ð 5ð 5ð 5r"   )rA   r   )r   r‚   Údoit_componentss   `` r    r�   zBasisDependent.doit°   sB   øø€ ð5ð 5ð 5ð 5ð 5Ø$(¤Oð5ñ 5ô 5ˆàˆtŒ~˜Ð/Ð/r"   )r8   Nr9   FFNF)F)$Ú__name__Ú
__module__Ú__qualname__Ú__doc__Ú__annotations__r   r!   r   r&   r$   r   ÚNotImplementedr,   r(   r1   r5   r2   rC   r   rD   r   rL   r   rU   rZ   r\   r_   re   ri   r   rl   rr   ry   r   r|   r�   rK   r"   r    r   r      sü  € € € € € € ðð ð ÐÐÑàÐ˜:Ñ&Ô&ð+ð +ñ 'Ô&ð+ð Ð˜9Ñ%Ô%ð+ð +ñ &Ô%ð+ð Ð˜:Ñ&Ô&ð,ð ,ñ 'Ô&ð,ð Ð˜9Ñ%Ô%ð,ð ,ñ &Ô%ð,ð €Z�˜Ñ(Ô(ØÐ˜:Ñ&Ô&ð+ð +ñ 'Ô&ñ )Ô(ð+ð €Z�˜Ñ(Ô(ØÐ˜9Ñ%Ô%ð+ð +ñ &Ô%ñ )Ô(ð+ð3ð 3ð 3ð €Z�˜Ñ(Ô(ØÐ˜>Ñ*Ô*ð'ð 'ñ +Ô*ñ )Ô(ð'ð Ð˜=Ñ)Ô)ð9ð 9ñ *Ô)ð9ðð ð ð ð 
€M„M�T”ZÔ'Ñ'€M„Mà€Að
0ð 
0ð 
0ð ÐÔ˜œÑ$ÐÔð
0ð 
0ð 
0ð ÐÔ˜œÑ%ÐÔð'ð 'ð 'ð%ð %ð %ðð ð ð4ð 4ð 4ð
ð ð ð0ð 0ð 0ð €N„N�d”lÑ"€N„Nðð ð ð ðIð Ið Ið0ð 0ð 0ð 	€L„L�B”JÑ€L„Lð0ð 0ð 0ð 0ð 0r"   r   c                  ó"   ‡ — e Zd ZdZˆ fd„Zˆ xZS )ÚBasisDependentAddzt
    Denotes sum of basis dependent quantities such that they cannot
    be expressed as base or Mul instances.
    c                ój  •‡	— i Š	|D ]½}t          || j        ¦  «        sit          |t          ¦  «        r | j        |j        Ž }nDt          |t
          ¦  «        r | j        |j        Ž }nt          t          |¦  «        dz   ¦  «        ‚|| j	        k    rŒŒ|j
        D ])}‰	                     |d¦  «        |j
        |         z   ‰	|<   Œ*Œ¾t          ‰	                     ¦   «         ¦  «        }|D ]}‰	|         dk    r‰	|= Œt          ‰	¦  «        dk    r| j	        S ˆ	fd„‰	D ¦   «         } t          ¦   «         j        | g|¢R i |¤Ž}t          |t          ¦  «        r | j        |j        Ž S ddi}t#          |¦  «        |_        ‰	|_        t          ‰	                     ¦   «         ¦  «        d         j        |_        |S )Nz  cannot be interpreted correctlyr   c                ó&   •— g | ]}|‰|         z  ‘ŒS rK   rK   )rM   ru   rA   s     €r    rO   z-BasisDependentAdd.__new__.<locals>.<listcomp>Û   s"   ø€ Ð9Ð9Ð9¨�1�z !”}Ñ$Ð9Ð9Ð9r"   ÚcommutativeT)r}   Ú
_expr_typer   r+   rn   r   r   r7   Ústrr   rA   ÚgetÚlistÚkeysÚlenÚsuperÚ__new__r	   Ú_assumptionsÚ_componentsÚ_sys)Úclsrn   rE   Úargru   ÚtempÚnewargsÚobjrb   rA   Ú	__class__s            @€r    r–   zBasisDependentAdd.__new__½   sò  øø€ Øˆ
ð ð 	Ið 	IˆCÝ˜c 3¤>Ñ2Ô2ð HÝ˜c¥3Ñ'Ô'ð HØ'˜#œ-¨#¬(Ð4�C�CÝ ¥SÑ)Ô)ð HØ'˜#œ-¨#¬(Ð4�C�Cå#¥C¨¡H¤HØ$Fñ%Gñ Hô Hð Hð �c”hŠˆØà”^ð Ið I�Ø *§¢¨q°!Ñ 4Ô 4°s´~ÀaÔ7HÑ H�
˜1‘�ðIõ �J—O’OÑ%Ô%Ñ&Ô&ˆØð 	"ð 	"ˆAØ˜!Œ} Ò!Ð!Ø˜q�Møõ ˆz‰?Œ?˜aÒÐØ”8ˆOð :Ð9Ð9Ð9¨jÐ9Ñ9Ô9ˆØ�e‰gŒgŒo˜cÐ7 GÐ7Ð7Ð7¨wÐ7Ð7ˆÝ�c�3ÑÔð 	,Ø �3”= #¤(Ð+Ð+Ø$ dÐ+ˆÝ$ [Ñ1Ô1ˆÔØ$ˆŒÝ˜ŸšÑ*Ô*Ñ+Ô+¨QÔ/Ô4ˆŒàˆ
r"   )r„   r…   r†   r‡   r–   Ú__classcell__©rŸ   s   @r    r‹   r‹   ·   sB   ø€ € € € € ðð ð
'ð 'ð 'ð 'ð 'ð 'ð 'ð 'ð 'r"   r‹   c                  óD   ‡ — e Zd ZdZd„ Zd„ Zeˆ fd„¦   «         Zd„ Zˆ xZ	S )ÚBasisDependentMulzJ
    Denotes product of base- basis dependent quantity with a scalar.
    c                ó    —  | j         |i |¤Ž}|S r   )Ú_new)rš   rn   rE   rž   s       r    r–   zBasisDependentMul.__new__ì   s   € ØˆcŒh˜Ð( Ð(Ð(ˆØˆ
r"   c                ó&   —  t          | ¦  «        |Ž S r   )Útype)r   rn   s     r    Ú_new_rawargszBasisDependentMul._new_rawargsð   s   € ð �t�D‰zŒz˜4Ð Ð r"   c                óš  •‡ ‡— ddl m}m}m}m} d}t
          j        Šd}g }	|D ]±}
t          |
‰ j        ¦  «        r|dz  }d}Œ|
t
          j	        k    rd}Œ2t          |
‰ j
        ‰ j        f¦  «        r|dz  }|
j        }‰|
j        z  ŠŒet          |
‰ j        ¦  «        r|dz  }|
}Œ‚t          |
||||f¦  «        r|	                     |
¦  «         Œ¬‰|
z  ŠŒ²|dk    rt!          d¦  «        ‚|dk    rt#          |i |¤ŽS |r‰ j        S t          |‰ j        ¦  «        rˆ ˆfd„|j        D ¦   «         } ‰ j        |Ž S  t)          ¦   «         j        ‰ ‰|j        g|	¢R i |¤Ž}t          |t,          ¦  «        r ‰ j        |j        Ž S |j        |_        ‰|_        ddi}t/          |¦  «        |_        |j        ‰i|_        |j        j        |_        |S )	Nr   )ÚCrossÚDotÚCurlÚGradientFé   TzInvalid multiplicationc                ó<   •— g | ]}‰                      ‰|¦  «        ‘ŒS rK   r*   )rM   ru   rš   Úmeasure_numbers     €€r    rO   z*BasisDependentMul._new.<locals>.<listcomp>  s7   ø€ ð 'ð 'ð 'Øð —}’} ^°QÑ7Ô7ð 'ð 'ð 'r"   rŽ   )Úsympy.vectorrª   r«   r¬   r­   r   rh   r}   Ú
_zero_funcÚZeroÚ
_base_funcr+   Ú_base_instanceÚ_measure_numberr   ÚappendÚ
ValueErrorr   r   rn   r•   r–   r   r	   r—   r˜   r™   )rš   rn   rE   rª   r«   r¬   r­   ÚcountÚzeroflagÚ
extra_argsr›   Úexprr�   rž   rb   r°   rŸ   s   `              @€r    r¥   zBasisDependentMul._newö   sj  øøø€ à;Ð;Ð;Ð;Ð;Ð;Ð;Ð;Ð;Ð;Ð;Ð;ØˆÝœˆØˆØˆ
ð
 ð 	&ð 	&ˆCÝ˜#˜sœ~Ñ.Ô.ð &Ø˜‘
�Ø��Ø�œ’�Ø��Ý˜C #¤.°#´-Ð!@ÑAÔAð 
&Ø˜‘
�ØÔ)�Ø #Ô"5Ñ5��Ý˜C ¤Ñ/Ô/ð &Ø˜‘
�Ø��Ý˜C %¨¨d°HÐ!=Ñ>Ô>ð &Ø×!Ò! #Ñ&Ô&Ð&Ð&à #Ñ%��à�1Š9ˆ9ÝÐ5Ñ6Ô6Ð6Ø�aŠZˆZÝ˜Ð( Ð(Ð(Ð(àð 	Ø”8ˆOõ �d˜CœMÑ*Ô*ð 	+ð'ð 'ð 'ð 'ð 'Ø œIð'ñ 'ô 'ˆGà �3”= 'Ð*Ð*à�e‰gŒgŒo˜c >Ø"Ô1ð)à)ð)ð )ð )ð !(ð)ð )ˆõ �c�3ÑÔð 	,Ø �3”= #¤(Ð+Ð+Ø!Ô0ˆÔØ,ˆÔØ$ dÐ+ˆÝ$ [Ñ1Ô1ˆÔØÔ.°Ð?ˆŒØÔ&Ô+ˆŒàˆ
r"   c                óž   — |                      | j        ¦  «        }d|v sd|v sd|v rd|z   dz   }|dz   |                      | j        ¦  «        z   S )Nú(ú-ú+ú)Ú*)Ú_printr¶   rµ   )r   ÚprinterÚmeasure_strs      r    Ú	_sympystrzBasisDependentMul._sympystr1  sd   € Ø—n’n TÔ%9Ñ:Ô:ˆØ�;ÐÐ #¨Ð"4Ð"4Ø�{Ð"Ð"Ø Ñ+¨cÑ1ˆKØ˜SÑ  7§>¢>°$Ô2EÑ#FÔ#FÑFÐFr"   )
r„   r…   r†   r‡   r–   r¨   Úclassmethodr¥   rÆ   r    r¡   s   @r    r£   r£   ç   sƒ   ø€ € € € € ðð ðð ð ð!ð !ð !ð ð8ð 8ð 8ð 8ñ „[ð8ðtGð Gð Gð Gð Gð Gð Gr"   r£   c                  ó   ‡ — e Zd ZU dZi Zded<   ded<   ˆ fd„Zd„ Z ed¦  «        d	„ ¦   «         Z	e	Z
 ed
¦  «        d„ ¦   «         Z ed¦  «        d„ ¦   «         Z ed¦  «        d„ ¦   «         Z ed¦  «        d„ ¦   «         Zd„ Zd„ Zd„ Zˆ xZS )r   z:
    Class to denote a zero basis dependent instance.
    zdict['BaseVector', Expr]rA   r�   Ú_latex_formc                ó”   •— t          ¦   «                              | ¦  «        }t          j        | f                     ¦   «         |_        |S r   )r•   r–   r   r³   Ú__hash__Ú_hash)rš   rž   rŸ   s     €r    r–   zBasisDependentZero.__new__@  s8   ø€ Ý‰gŒg�oŠo˜cÑ"Ô"ˆõ ”V˜S�M×*Ò*Ñ,Ô,ˆŒ	Øˆ
r"   c                ó   — | j         S r   )rÌ   r0   s    r    rË   zBasisDependentZero.__hash__G  s
   € ØŒzÐr"   Ú__req__c                ó,   — t          || j        ¦  «        S r   )r}   r²   r   s     r    Ú__eq__zBasisDependentZero.__eq__J  s   € å˜% ¤Ñ1Ô1Ð1r"   r   c                óN   — t          || j        ¦  «        r|S t          d¦  «        ‚©Nz#Invalid argument types for addition©r}   r�   r7   r   s     r    r!   zBasisDependentZero.__add__P  ó+   € å�e˜Tœ_Ñ-Ô-ð 	CØˆLåÐAÑBÔBÐBr"   r!   c                óN   — t          || j        ¦  «        r|S t          d¦  «        ‚rÒ   rÓ   r   s     r    r   zBasisDependentZero.__radd__W  rÔ   r"   r$   c                óP   — t          || j        ¦  «        r| S t          d¦  «        ‚©Nz&Invalid argument types for subtractionrÓ   r   s     r    r&   zBasisDependentZero.__sub__^  s-   € å�e˜Tœ_Ñ-Ô-ð 	FØ�6ˆMåÐDÑEÔEÐEr"   r&   c                óN   — t          || j        ¦  «        r|S t          d¦  «        ‚r×   rÓ   r   s     r    r$   zBasisDependentZero.__rsub__e  s+   € å�e˜Tœ_Ñ-Ô-ð 	FØˆLåÐDÑEÔEÐEr"   c                ó   — | S r   rK   r0   s    r    r1   zBasisDependentZero.__neg__l  s   € Øˆr"   c                ó   — | S )z@
        Returns the normalized version of this vector.
        rK   r0   s    r    Ú	normalizezBasisDependentZero.normalizeo  s	   € ð ˆr"   c                ó   — dS )NÚ0rK   )r   rÄ   s     r    rÆ   zBasisDependentZero._sympystru  s   € Øˆsr"   )r„   r…   r†   r‡   rA   rˆ   r–   rË   r   rÐ   rÎ   r!   r   r&   r$   r1   rÛ   rÆ   r    r¡   s   @r    r   r   9  ss  ø€ € € € € € ðð ð ,.€JÐ-Ð-Ð-Ñ-ØÐÐÑðð ð ð ð ðð ð ð Ð˜9Ñ%Ô%ð2ð 2ñ &Ô%ð2ð €GàÐ˜:Ñ&Ô&ðCð Cñ 'Ô&ðCð Ð˜9Ñ%Ô%ðCð Cñ &Ô%ðCð Ð˜:Ñ&Ô&ðFð Fñ 'Ô&ðFð Ð˜9Ñ%Ô%ðFð Fñ &Ô%ðFðð ð ðð ð ðð ð ð ð ð ð r"   r   N)"Ú
__future__r   Útypingr   Úsympy.simplifyr   rL   r   rU   Úsympy.core.decoratorsr   r   Úsympy.core.assumptionsr	   Úsympy.core.functionr   r|   Úsympy.integrals.integralsr   Úsympy.polys.polytoolsr   rl   Ú
sympy.corer   r   r   Úsympy.core.exprr   Úsympy.vector.vectorr   r   r‹   r£   r   rK   r"   r    ú<module>ré      s¼  ðØ "Ð "Ð "Ð "Ð "Ð "Ø  Ð  Ð  Ð  Ð  Ð  à >Ð >Ð >Ð >Ð >Ð >Ð >Ð >Ø CÐ CÐ CÐ CÐ CÐ CÐ CÐ CØ ,Ð ,Ð ,Ð ,Ð ,Ð ,Ø *Ð *Ð *Ð *Ð *Ð *Ø .Ð .Ð .Ð .Ð .Ð .Ø 0Ð 0Ð 0Ð 0Ð 0Ð 0Ø "Ð "Ð "Ð "Ð "Ð "Ð "Ð "Ð "Ð "Ø  Ð  Ð  Ð  Ð  Ð  àð /Ø.Ð.Ð.Ð.Ð.Ð.ðc0ð c0ð c0ð c0ð c0�Tñ c0ô c0ð c0ðL-ð -ð -ð -ð -˜¨ñ -ô -ð -ð`OGð OGð OGð OGð OG˜¨ñ OGô OGð OGðd=ð =ð =ð =ð =˜ñ =ô =ð =ð =ð =r"   