+
    ‹°³jQ.  ã                  ó  € ^ RI Ht ^ RIHt ^ RIHtHt ^ RI	H
t
Ht ^ RIHt ^ RIHt ^ RIHt ^ RIHt ^ R	IHtHtHt ^ R
IHt ]'       d   ^ RIHt  ! R R]4      t ! R R]]4      t ! R R]]4      t  ! R R]4      t!R# )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   € ] tR t^t$ RtR]R&   ]! R4      R 4       t]! R4      R 4       t]! R4      R	 4       t	]! R
4      R 4       t
]! R]4      ]! R4      R 4       4       t]! R]4      ]! R4      R 4       4       tR t]! R]4      ]! R4      R 4       4       t]! R4      R 4       tR%R lt];P                  ]P$                  P                  ,          un        ]tR t];P                  ]P                  ,          un        R t];P                  ]P                  ,          un        R tR tR tR tR tR t];P                  ]P                  ,          un        R&R  lt R! t!R" t"]";P                  ]#P                  ,          un        R# t$R$t%R# )'ÚBasisDependentz¾
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$   € V P                  W4      # ©N©Ú	_add_func©ÚselfÚothers   &&Ú\/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/vector/basisdependent.pyÚ__add__ÚBasisDependent.__add__   s   € à�~‰~˜dÓ*Ð*ó    r    c                	ó$   € V P                  W4      # r   r   r   s   &&r   r   ÚBasisDependent.__radd__   s   € à�~‰~˜eÓ*Ð*r"   Ú__rsub__c                	ó&   € V P                  W) 4      # r   r   r   s   &&r   Ú__sub__ÚBasisDependent.__sub__#   s   € à�~‰~˜d FÓ+Ð+r"   r'   c                	ó&   € V P                  W) 4      # r   r   r   s   &&r   r%   ÚBasisDependent.__rsub__'   s   € à�~‰~˜e UÓ+Ð+r"   r   Ú__rmul__c                	ó$   € V P                  W4      # r   ©Ú	_mul_funcr   s   &&r   Ú__mul__ÚBasisDependent.__mul__+   s   € ð �~‰~˜dÓ*Ð*r"   r/   c                	ó$   € V P                  W4      # r   r-   r   s   &&r   r+   ÚBasisDependent.__rmul__0   s   € ð �~‰~˜eÓ*Ð*r"   c                	óB   € V P                  \        P                  V 4      # r   )r.   r   ÚNegativeOne©r   s   &r   Ú__neg__ÚBasisDependent.__neg__5   s   € Ø�~‰~œaŸm™m¨TÓ2Ð2r"   Ú__rtruediv__c                	ó$   € V P                  V4      # r   )Ú_div_helperr   s   &&r   Ú__truediv__ÚBasisDependent.__truediv__8   s   € ð ×Ñ Ó&Ð&r"   r;   c                	ó   € \        R 4      # )zInvalid divisor for division)Ú	TypeErrorr   s   &&r   r8   ÚBasisDependent.__rtruediv__=   s   € äÐ7Ó8Ð8r"   Nc                óÀ   € RVRVRVRVRVRV/pV P                   p	V P                  P                  4        F%  w  r«W›P                  ! V3/ VB V
,          ,          p	K'  	  V	# )ze
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nrA   rB   rC   rD   rE   rF   ÚoptionsÚvecÚkÚvs   &&&&&&&&    r   rI   ÚBasisDependent.evalfA   sg   € ð ˜$  t¨V°D¸(À6Ø�t˜Y wð0ˆà�i‰iˆØ—O‘O×)Ñ)Ö+‰DˆAØ—7’7˜1Ñ( Ñ(¨1Õ,Õ,ŠCñ ,àˆ
r"   c           	     óª   € V P                   P                  4        UUu. uF  w  r#\        V3/ VB V,          NK  	  pppV P                  ! V!  # u uppi )zn
Implements the SymPy simplify routine for this quantity.

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

)rG   rH   Úsimpr   )r   ÚkwargsrM   rN   Úsimp_componentss   &,   r   r   ÚBasisDependent.simplifyT   sY   € ð $(§?¡?×#8Ñ#8Ô#:ô<Ù#:™4˜1ô   Ñ, VÑ,¨q×0Ð0Ù#:ð 	ñ <à�~Š~˜Ñ/Ð/ùó<ó   žAc           	     óª   € V P                   P                  4        UUu. uF  w  r#\        V3/ VB V,          NK  	  pppV P                  ! V!  # u uppi )zo
Implements the SymPy trigsimp routine, for this quantity.

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

)rG   rH   Útsimpr   )r   ÚoptsrM   rN   Útrig_componentss   &,   r   r   ÚBasisDependent.trigsimpb   sY   € ð $(§?¡?×#8Ñ#8Ô#:ô<Ù#:™4˜1ô ! Ñ+ dÑ+¨a×/Ð/Ù#:ð 	ñ <à�~Š~˜Ñ/Ð/ùó<rU   c                	ó&   € V P                   ! R/ VB # ©N© )r   )r   rR   s   &,r   Ú_eval_simplifyÚBasisDependent._eval_simplifyp   s   € Ø�}Š}Ñ&˜vÑ&Ð&r"   c                	ó&   € V P                   ! R/ VB # r\   )r   )r   rX   s   &,r   Ú_eval_trigsimpÚBasisDependent._eval_trigsimps   s   € Ø�}Š}Ñ$˜tÑ$Ð$r"   c                	ó$   € V P                  V4      # r   r
   )r   Úwrts   &&r   Ú_eval_derivativeÚBasisDependent._eval_derivativev   s   € Ø�y‰y˜‹~Ðr"   c           	     	ó°   € V P                   P                  4        UUu. uF  w  r4\        V.VO5/ VB V,          NK  	  pppV P                  ! V!  # u uppi r   )rG   rH   r   r   )r   ÚsymbolsÚassumptionsrM   rN   Úintegral_componentss   &*,   r   Ú_eval_IntegralÚBasisDependent._eval_Integraly   s`   € à+/¯?©?×+@Ñ+@Ô+BôDÙ+B¡4 1ô  (¨ÐC¨GÒC°{ÑCÀa×GÐGÙ+Bð 	ñ Dà�~Š~Ð2Ñ3Ð3ùóDó   ž!Ac                ó&   € V \         P                  3# )zb
Returns the expression as a tuple wrt the following
transformation -

expression -> a/b -> a, b

©r   ÚOner5   s   &r   Úas_numer_denomÚBasisDependent.as_numer_denom~   s   € ð ”Q—U‘Uˆ{Ðr"   c           	     ó°   € V P                   P                  4        UUu. uF  w  r4\        V.VO5/ VB V,          NK  	  pppV P                  ! V!  # u uppi )z�
Implements the SymPy factor routine, on the scalar parts
of a basis-dependent expression.

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

)rG   rH   Úfctrr   )r   ÚargsrR   rM   rN   Úfctr_componentss   &*,   r   r   ÚBasisDependent.factorˆ   s^   € ð $(§?¡?×#8Ñ#8Ô#:ô<Ù#:™4˜1ô   Ð3 DÒ3¨FÑ3°a×7Ð7Ù#:ð 	ñ <à�~Š~˜Ñ/Ð/ùó<rm   c                ó&   € \         P                  V 3# )z1Efficiently extract the coefficient of a product.ro   )r   Úrationals   &&r   Úas_coeff_MulÚBasisDependent.as_coeff_Mul—   s   € ä—‘�tˆ}Ðr"   c                ó–   a € ^ \         ;QJ d"    . V 3R lS P                   4       F  NK  	  53# ! V 3R lS P                   4       4      3# )z3Efficiently extract the coefficient of a summation.c              3  óV   <"  € T F  qSP                   V,          ,          x € K   	  R # 5ir   )rG   )Ú.0Úxr   s   & €r   Ú	<genexpr>Ú.BasisDependent.as_coeff_add.<locals>.<genexpr>�   s    øé € ÐH¹°1˜DŸO™O¨AÕ.×.Ò.»ùs   ƒ&))ÚtuplerG   )r   Údepss   f*r   Úas_coeff_addÚBasisDependent.as_coeff_add›   s5   ø€ à—%”%ÔH¸¿ºÓH—%ÐHÐH�%ÔH¸¿ºÓHÓHÐHÐHr"   c           	     ó  € V F$  p\        V\        4      '       g   K  \        R4      h	  V P                  P	                  4        UUu. uF  w  rE\        V.VO5/ VB V,          NK  	  pppV P                  ! V!  # u uppi )za
Implements the SymPy diff routine, for vectors.

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

zInvalid arg for differentiation)Ú
isinstancer   r>   rG   rH   Údfr   )r   ru   rR   r   rM   rN   Údiff_componentss   &*,    r   r   ÚBasisDependent.diffŸ   sƒ   € ó ˆAÜ˜!œ^×,Ô,ÜÐ AÓBÐBñ ð $(§?¡?×#8Ñ#8Ô#:ô<Ù#:™4˜1ô ˜aÐ1 $Ò1¨&Ñ1°A×5Ð5Ù#:ð 	ñ <à�~Š~˜Ñ/Ð/ùó<s   Á!A<c                ó²   € V P                    Uu. uF-  pV P                   V,          P                  ! R/ VB V,          NK/  	  ppV P                  ! V!  # u upi )z(Calls .doit() on each term in the Dyadicr]   )rG   Údoitr   )r   Úhintsr   Údoit_componentss   &,  r   rŒ   ÚBasisDependent.doit°   s[   € ð %)§O¢Oó5Ù$3˜qð  Ÿ?™?¨1Õ-×2Ò2Ñ;°UÑ;¸a×?Ð?Ù$3ð 	ð 5à�~Š~˜Ñ/Ð/ùò5s   �3Ar]   )é   Néd   FFNF)F)&Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__Ú__doc__Ú__annotations__r   r    r   r'   r%   r   ÚNotImplementedr/   r+   r6   r;   r8   rI   r   rJ   r   rQ   r   rW   r^   ra   re   rk   rq   r   rt   rz   r„   r   rˆ   rŒ   Ú__static_attributes__r]   r"   r   r   r      s¾  ‡ ñð Óá˜:Ó&ñ+ó 'ð+ñ ˜9Ó%ñ+ó &ð+ñ ˜:Ó&ñ,ó 'ð,ñ ˜9Ó%ñ,ó &ð,ñ �˜Ó(Ù˜:Ó&ñ+ó 'ó )ð+ñ �˜Ó(Ù˜9Ó%ñ+ó &ó )ð+ò3ñ �˜Ó(Ù˜>Ó*ñ'ó +ó )ð'ñ ˜=Ó)ñ9ó *ð9ôð 
‡M‚M�T—Z‘Z×'Ñ'Õ'…Mà€Aò
0ð ×Ò˜Ÿ™Õ$Õò
0ð ×Ò˜Ÿ™Õ%Õò'ò%òò4ò
ò0ð ‡N‚N�d—l‘lÕ"…NôòIò0ð 	‡L‚L�B—J‘JÕ…Lö0r"   r   c                  ó,   a € ] tR t^·tRtV 3R ltRtV ;t# )ÚBasisDependentAddzh
Denotes sum of basis dependent quantities such that they cannot
be expressed as base or Mul instances.
c                	óì  <€ / pV Fì  p\        W@P                  4      '       g~   \        V\        4      '       d   V P                  ! VP                  !  pML\        V\
        4      '       d   V P                  ! VP                  !  pM\        \        V4      R ,           4      hW@P                  8X  d   K­  VP                   F/  pVP                  V^ 4      VP                  V,          ,           W5&   K1  	  Kî  	  \        VP                  4       4      pV F  pW5,          ^ 8X  g   K  W5 K  	  \        V4      ^ 8X  d   V P                  # V Uu. uF  qUW5,          ,          NK  	  pp\        S
V `@  ! V .VO5/ VB p\        V\        4      '       d   V P                  ! VP                  !  # RR/p	\#        V	4      Vn        W8n        \        VP                  4       4      ^ ,          P(                  Vn        V# u upi )z  cannot be interpreted correctlyÚcommutativeT)r‡   Ú
_expr_typer   r.   ru   r   r   r>   Ústrr   rG   ÚgetÚlistÚkeysÚlenÚsuperÚ__new__r	   Ú_assumptionsÚ_componentsÚ_sys)Úclsru   rK   rG   Úargr   ÚtempÚnewargsÚobjri   Ú	__class__s   &*,       €r   r¥   ÚBasisDependentAdd.__new__½   s˜  ø€ Øˆ
ó ˆCÜ˜c§>¡>×2Ò2Ü˜c¤3×'Ò'ØŸ-š-¨#¯(©(Ñ4‘CÜ ¤S×)Ò)ØŸ-š-¨#¯(©(Ñ4‘Cä#¤C¨£HØ$Fõ%Gó Hð Hð —h‘hŒÙà—^”^�Ø *§¡¨q°!Ó 4°s·~±~ÀaÕ7HÕ H�
“ó $ñ ô  �J—O‘OÓ%Ó&ˆÛˆAØ�} Ö!Ø’Mñ ô
 ˆz‹?˜aÔØ—8‘8ˆOñ /9Ó9©j¨�z•}×$Ð$©jˆÐ9Ü‰gŠo˜cÐ7 GÒ7¨wÑ7ˆÜ�cœ3×ÒØ—=’= #§(¡(Ñ+Ð+Ø$ dÐ+ˆÜ$ [Ó1ˆÔØ$ŒÜ˜Ÿ™Ó*Ó+¨QÕ/×4Ñ4ˆŒàˆ
ùò :s   Å	G1r]   )r’   r“   r”   r•   r–   r¥   r™   Ú__classcell__©r®   s   @r   r›   r›   ·   s   ø† ñ÷
'ó 'r"   r›   c                  óH   a € ] tR t^çtRtR tR t]V 3R l4       tR t	Rt
V ;t# )ÚBasisDependentMulzB
Denotes product of base- basis dependent quantity with a scalar.
c                	ó*   € V P                   ! V/ VB pV# r   )Ú_new)r©   ru   rK   r­   s   &*, r   r¥   ÚBasisDependentMul.__new__ì   s   € Ø�hŠh˜Ð( Ñ(ˆØˆ
r"   c                	ó    € \        V 4      ! V!  # r   )Útype)r   ru   s   &*r   Ú_new_rawargsÚBasisDependentMul._new_rawargsð   s   € ô �DŒz˜4Ñ Ð r"   c                	ó¤  <€ ^ RI HpHpHpHp ^ p\
        P                  pRp	. p
V Fë  p\        W°P                  4      '       d   V^,          pRp	K+  V\
        P                  8X  d   Rp	KD  \        W°P                  V P                  34      '       d*   V^,          pVP                  pW‹P                  ,          pK”  \        W°P                  4      '       d   V^,          pTpK¼  \        W³WEV34      '       d   V
P                  V4       Kã  W‹,          pKí  	  V^8”  d   \!        R4      hV^ 8X  d   \#        V/ VB # V	'       d   V P$                  # \        XV P                  4      '       d;   VP&                   Uu. uF  pV P                  W�4      NK  	  ppV P                  ! V!  # \(        SV `T  ! WVP                  .V
O5/ VB p\        V\,        4      '       d   V P                  ! VP&                  !  # VP                  Vn        W�n        RR/p\/        V4      Vn        VP                  V/Vn        VP                  P4                  Vn        V# u upi )r   )ÚCrossÚDotÚCurlÚGradientFTzInvalid multiplicationr�   )Úsympy.vectorr¼   r½   r¾   r¿   r   rp   r‡   Ú
_zero_funcÚZeroÚ
_base_funcr.   Ú_base_instanceÚ_measure_numberr   ÚappendÚ
ValueErrorr   r   ru   r¤   r¥   r   r	   r¦   r§   r¨   )r©   ru   rK   r¼   r½   r¾   r¿   ÚcountÚmeasure_numberÚzeroflagÚ
extra_argsrª   Úexprr   r¬   r­   ri   r®   s   &*,              €r   rµ   ÚBasisDependentMul._newö   s  ø€ ç;Ó;ØˆÜŸ™ˆØˆØˆ
ó
 ˆCÜ˜#Ÿ~™~×.Ò.Ø˜•
�Ø’ØœŸ™”Ø’Ü˜C§.¡.°#·-±-Ð!@×AÒAØ˜•
�Ø×)Ñ)�Ø×"5Ñ"5Õ5’Ü˜C§¡×/Ò/Ø˜•
�Ø’Ü˜C¨°HÐ!=×>Ò>Ø×!Ñ! #Ö&àÕ%’ñ! ð$ �1Œ9ÜÐ5Ó6Ð6Ø�aŒZÜ˜Ð( Ñ(Ð(çØ—8‘8ˆOô �d˜CŸM™M×*Ò*à ŸIšIó'Ù%�qð —}‘} ^Ö7Ù%ð ð 'à—=’= 'Ñ*Ð*ä‰gŠo˜cØ"×1Ñ1ð)à)ò)ð !(ñ)ˆô �cœ3×ÒØ—=’= #§(¡(Ñ+Ð+Ø!×0Ñ0ˆÔØ,ÔØ$ dÐ+ˆÜ$ [Ó1ˆÔØ×.Ñ.°Ð?ˆŒØ×&Ñ&×+Ñ+ˆŒàˆ
ùò#'s   Å7Ic                	óÔ   € VP                  V P                  4      pR V9   g   RV9   g   RV9   d   R V,           R,           pVR,           VP                  V P                  4      ,           # )Ú(Ú-Ú+Ú)Ú*)Ú_printrÅ   rÄ   )r   ÚprinterÚmeasure_strs   && r   Ú	_sympystrÚBasisDependentMul._sympystr1  s[   € Ø—n‘n T×%9Ñ%9Ó:ˆØ�;Ô #¨Ô"4Ø�{Ô"Ø Õ+¨cÕ1ˆKØ˜SÕ  7§>¡>°$×2EÑ2EÓ#FÕFÐFr"   r]   )r’   r“   r”   r•   r–   r¥   r¹   Úclassmethodrµ   r×   r™   r°   r±   s   @r   r³   r³   ç   s3   ø† ñòò!ð ô8ó ð8÷tGð Gr"   r³   c                  óî   a € ] tR tRt$ Rt/ tR]R&   R]R&   V 3R ltR t]	! R	4      R
 4       t
]
t]	! R4      R 4       t]	! R4      R 4       t]	! R4      R 4       t]	! R4      R 4       tR tR tR tRtV ;t# )r   i9  z2
Class to denote a zero basis dependent instance.
zdict['BaseVector', Expr]rG   rŸ   Ú_latex_formc                	óp   <€ \         SV `  V 4      p\        P                  V 3P	                  4       Vn        V# r   )r¤   r¥   r   rÂ   Ú__hash__Ú_hash)r©   r­   r®   s   & €r   r¥   ÚBasisDependentZero.__new__@  s0   ø€ Ü‰g‰o˜cÓ"ˆô —V‘V˜S�M×*Ñ*Ó,ˆŒ	Øˆ
r"   c                	ó   € V P                   # r   )rÞ   r5   s   &r   rÝ   ÚBasisDependentZero.__hash__G  s   € Ø�z‰zÐr"   Ú__req__c                	ó,   € \        WP                  4      # r   )r‡   rÁ   r   s   &&r   Ú__eq__ÚBasisDependentZero.__eq__J  s   € ä˜%§¡Ó1Ð1r"   r   c                	óR   € \        WP                  4      '       d   V# \        R 4      h©z#Invalid argument types for addition©r‡   rž   r>   r   s   &&r   r    ÚBasisDependentZero.__add__P  ó"   € ä�eŸ_™_×-Ò-ØˆLäÐAÓBÐBr"   r    c                	óR   € \        WP                  4      '       d   V# \        R 4      hrç   rè   r   s   &&r   r   ÚBasisDependentZero.__radd__W  rê   r"   r%   c                	óT   € \        WP                  4      '       d   V) # \        R 4      h©z&Invalid argument types for subtractionrè   r   s   &&r   r'   ÚBasisDependentZero.__sub__^  s$   € ä�eŸ_™_×-Ò-Ø�6ˆMäÐDÓEÐEr"   r'   c                	óR   € \        WP                  4      '       d   V# \        R 4      hrî   rè   r   s   &&r   r%   ÚBasisDependentZero.__rsub__e  s"   € ä�eŸ_™_×-Ò-ØˆLäÐDÓEÐEr"   c                	ó   € V # r   r]   r5   s   &r   r6   ÚBasisDependentZero.__neg__l  s   € Øˆr"   c                ó   € V # )z0
Returns the normalized version of this vector.
r]   r5   s   &r   Ú	normalizeÚBasisDependentZero.normalizeo  s	   € ð ˆr"   c                	ó   € R # )Ú0r]   )r   rÕ   s   &&r   r×   ÚBasisDependentZero._sympystru  s   € Ùr"   r]   )r’   r“   r”   r•   r–   rG   r—   r¥   rÝ   r   rä   râ   r    r   r'   r%   r6   rõ   r×   r™   r°   r±   s   @r   r   r   9  sÃ   ø‡ ñð ,.€JÐ(Ó-ØÓõòñ ˜9Ó%ñ2ó &ð2ð €Gá˜:Ó&ñCó 'ðCñ ˜9Ó%ñCó &ðCñ ˜:Ó&ñFó 'ðFñ ˜9Ó%ñFó &ðFòò÷ð r"   r   N)"Ú
__future__r   Útypingr   Úsympy.simplifyr   rQ   r   rW   Úsympy.core.decoratorsr   r   Úsympy.core.assumptionsr	   Úsympy.core.functionr   rˆ   Úsympy.integrals.integralsr   Úsympy.polys.polytoolsr   rt   Ú
sympy.corer   r   r   Úsympy.core.exprr   Úsympy.vector.vectorr   r   r›   r³   r   r]   r"   r   Ú<module>r     si   ðÝ "Ý  ç >ß CÝ ,Ý *Ý .Ý 0ß "Ñ "Ý  çÝ.ôc0�Tô c0ôL-˜¨ô -ô`OG˜¨ô OGôd=˜ö =r"   