+
    ibC                     N   R t ^ RIHt ^ RI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 ^ R	IHt ^ R
IHt . ROt ! R R]4      t ! R R]4      t ! R R]4      t ! R R]4      t ! R R]4      t ! R R]4      t ! R R]4      t ! R R]4      tR tR t R# )zPauli operators and states)Add)MulI)Pow)S)exp)OperatorKetBraComplexSpace)Matrix)KroneckerDeltaSigmaXSigmaYSigmaZ
SigmaMinus	SigmaPlus	SigmaZKet	SigmaZBrac                   `   a  ] tR t^t o Rt]R 4       t]R 4       t]R 4       t	R t
R tRtV tR# )	SigmaOpBasez Pauli sigma operator, base classc                (    V P                   ^ ,          #     )argsselfs   &{/Users/tonyclaw/.openclaw/workspace/skills/math-calculator/venv/lib/python3.14/site-packages/sympy/physics/quantum/pauli.pynameSigmaOpBase.name   s    yy|    c                >    \        V P                  ^ ,          4      RJ# )r   F)boolr   r   s   &r   use_nameSigmaOpBase.use_name   s    DIIaL!..r"   c                    R# )F)F r   s   &r   default_argsSigmaOpBase.default_args   s    r"   c                6    \         P                  ! V .VO5/ VB # N)r	   __new__clsr   hintss   &*,r   r-   SigmaOpBase.__new__#   s    4d4e44r"   c                "    \         P                  # r,   r   Zeror   otherr0   s   &&,r   _eval_commutator_BosonOp$SigmaOpBase._eval_commutator_BosonOp&       vvr"   r(   N)__name__
__module____qualname____firstlineno____doc__propertyr    r%   classmethodr)   r-   r7   __static_attributes____classdictcell____classdict__s   @r   r   r      sQ     *  / /  5 r"   r   c                   f   a  ] tR t^*t o RtR tR tR tR tR t	R t
R tR	 tR
 tR tR tRtV tR# )r   ab  Pauli sigma x operator

Parameters
==========

name : str
    An optional string that labels the operator. Pauli operators with
    different names commute.

Examples
========

>>> from sympy.physics.quantum import represent
>>> from sympy.physics.quantum.pauli import SigmaX
>>> sx = SigmaX()
>>> sx
SigmaX()
>>> represent(sx)
Matrix([
[0, 1],
[1, 0]])
c                6    \         P                  ! V .VO5/ VB # r,   r   r-   r.   s   &*,r   r-   SigmaX.__new__B   s    ""37777r"   c                    V P                   VP                   8w  d   \        P                  # ^\        ,          \	        V P                   4      ,          #    r    r   r4   r   r   r5   s   &&,r   _eval_commutator_SigmaYSigmaX._eval_commutator_SigmaYE   3    99

"66Mq56$)),,,r"   c                    V P                   VP                   8w  d   \        P                  # R\        ,          \	        V P                   4      ,          # rK   r    r   r4   r   r   r5   s   &&,r   _eval_commutator_SigmaZSigmaX._eval_commutator_SigmaZK   3    99

"66M7VDII...r"   c                "    \         P                  # r,   r3   r5   s   &&,r   r7   SigmaX._eval_commutator_BosonOpQ   r9   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   _eval_anticommutator_SigmaY"SigmaX._eval_anticommutator_SigmaYT   r9   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   _eval_anticommutator_SigmaZ"SigmaX._eval_anticommutator_SigmaZW   r9   r"   c                    V # r,   r(   r   s   &r   _eval_adjointSigmaX._eval_adjointZ       r"   c                b    V P                   '       d   R \        V P                  4      ,          # R# )z{\sigma_x^{(%s)}}z
{\sigma_x}r%   strr    r   printerr   s   &&*r   _print_contents_latexSigmaX._print_contents_latex]   !    ==='#dii.88 r"   c                    R # )zSigmaX()r(   rf   s   &&*r   _print_contentsSigmaX._print_contentsc       r"   c                    VP                   '       dI   VP                  '       d5   \        V P                  4      P	                  \        V4      ^,          4      # R# R# rK   N)
is_Integeris_positiver   r    __pow__intr   es   &&r   _eval_powerSigmaX._eval_powerf   <    <<<AMMM$))$,,SVaZ88 *<r"   c                    VP                  R R4      pVR8X  d   \        ^ ^.^^ ..4      # \        RV,           R,           4      hformatsympyRepresentation in format  not implemented.getr   NotImplementedErrorr   optionsr|   s   &, r   _represent_default_basisSigmaX._represent_default_basisj   U    Xw/WAq6Aq6*++%&A&,'-/B'C D Dr"   r(   N)r:   r;   r<   r=   r>   r-   rM   rT   r7   rZ   r]   r`   rh   rl   rw   r   rA   rB   rC   s   @r   r   r   *   sH     .8-/!9D Dr"   c                   `   a  ] tR t^st o RtR tR tR tR tR t	R t
R tR	 tR
 tR tRtV tR# )r   ad  Pauli sigma y operator

Parameters
==========

name : str
    An optional string that labels the operator. Pauli operators with
    different names commute.

Examples
========

>>> from sympy.physics.quantum import represent
>>> from sympy.physics.quantum.pauli import SigmaY
>>> sy = SigmaY()
>>> sy
SigmaY()
>>> represent(sy)
Matrix([
[0, -I],
[I,  0]])
c                2    \         P                  ! V .VO5!  # r,   rG   r.   s   &*,r   r-   SigmaY.__new__       ""3...r"   c                    V P                   VP                   8w  d   \        P                  # ^\        ,          \	        V P                   4      ,          # rJ   r    r   r4   r   r   r5   s   &&,r   rT   SigmaY._eval_commutator_SigmaZ   rO   r"   c                    V P                   VP                   8w  d   \        P                  # R\        ,          \	        V P                   4      ,          # rQ   rL   r5   s   &&,r   _eval_commutator_SigmaXSigmaY._eval_commutator_SigmaX   rV   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   _eval_anticommutator_SigmaX"SigmaY._eval_anticommutator_SigmaX   r9   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   r]   "SigmaY._eval_anticommutator_SigmaZ   r9   r"   c                    V # r,   r(   r   s   &r   r`   SigmaY._eval_adjoint   rb   r"   c                b    V P                   '       d   R \        V P                  4      ,          # R# )z{\sigma_y^{(%s)}}z
{\sigma_y}rd   rf   s   &&*r   rh   SigmaY._print_contents_latex   rj   r"   c                    R # )zSigmaY()r(   rf   s   &&*r   rl   SigmaY._print_contents   rn   r"   c                    VP                   '       dI   VP                  '       d5   \        V P                  4      P	                  \        V4      ^,          4      # R# R# rp   )rq   rr   r   r    rs   rt   ru   s   &&r   rw   SigmaY._eval_power   ry   r"   c                    VP                  R R4      pVR8X  d   \        ^ \        ) .\        ^ ..4      # \        RV,           R,           4      hr{   )r   r   r   r   r   s   &, r   r   SigmaY._represent_default_basis   sW    Xw/WAr7QF+,,%&A&,'-/B'C D Dr"   r(   N)r:   r;   r<   r=   r>   r-   rT   r   r   r]   r`   rh   rl   rw   r   rA   rB   rC   s   @r   r   r   s   C     ./-/!9D Dr"   c                   `   a  ] tR t^t o RtR tR tR tR tR t	R t
R tR	 tR
 tR tRtV tR# )r   ai  Pauli sigma z operator

Parameters
==========

name : str
    An optional string that labels the operator. Pauli operators with
    different names commute.

Examples
========

>>> from sympy.physics.quantum import represent
>>> from sympy.physics.quantum.pauli import SigmaZ
>>> sz = SigmaZ()
>>> sz ** 3
SigmaZ()
>>> represent(sz)
Matrix([
[1,  0],
[0, -1]])
c                2    \         P                  ! V .VO5!  # r,   rG   r.   s   &*,r   r-   SigmaZ.__new__   r   r"   c                    V P                   VP                   8w  d   \        P                  # ^\        ,          \	        V P                   4      ,          # rJ   rS   r5   s   &&,r   r   SigmaZ._eval_commutator_SigmaX   rO   r"   c                    V P                   VP                   8w  d   \        P                  # R\        ,          \	        V P                   4      ,          # rQ   r   r5   s   &&,r   rM   SigmaZ._eval_commutator_SigmaY   rV   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   r   "SigmaZ._eval_anticommutator_SigmaX   r9   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   rZ   "SigmaZ._eval_anticommutator_SigmaY   r9   r"   c                    V # r,   r(   r   s   &r   r`   SigmaZ._eval_adjoint   rb   r"   c                b    V P                   '       d   R \        V P                  4      ,          # R# )z{\sigma_z^{(%s)}}z
{\sigma_z}rd   rf   s   &&*r   rh   SigmaZ._print_contents_latex   rj   r"   c                    R # )zSigmaZ()r(   rf   s   &&*r   rl   SigmaZ._print_contents   rn   r"   c                    VP                   '       dI   VP                  '       d5   \        V P                  4      P	                  \        V4      ^,          4      # R# R# rp   )rq   rr   r   r    rs   rt   ru   s   &&r   rw   SigmaZ._eval_power   ry   r"   c                    VP                  R R4      pVR8X  d   \        ^^ .^ R..4      # \        RV,           R,           4      h)r|   r}   r~   r   r   r   s   &, r   r   SigmaZ._represent_default_basis   sU    Xw/WAq6Ar7+,,%&A&,'-/B'C D Dr"   r(   N)r:   r;   r<   r=   r>   r-   r   rM   r   rZ   r`   rh   rl   rw   r   rA   rB   rC   s   @r   r   r      r   r"   c                   x   a  ] tR t^t o RtR tR tR tR tR t	R t
R tR	 tR
 tR tR tR tR tR tRtV tR# )r   a  Pauli sigma minus operator

Parameters
==========

name : str
    An optional string that labels the operator. Pauli operators with
    different names commute.

Examples
========

>>> from sympy.physics.quantum import represent, Dagger
>>> from sympy.physics.quantum.pauli import SigmaMinus
>>> sm = SigmaMinus()
>>> sm
SigmaMinus()
>>> Dagger(sm)
SigmaPlus()
>>> represent(sm)
Matrix([
[0, 0],
[1, 0]])
c                2    \         P                  ! V .VO5!  # r,   rG   r.   s   &*,r   r-   SigmaMinus.__new__  r   r"   c                    V P                   VP                   8w  d   \        P                  # \        V P                   4      ) # r,   r    r   r4   r   r5   s   &&,r   r   "SigmaMinus._eval_commutator_SigmaX  s-    99

"66M499%%%r"   c                    V P                   VP                   8w  d   \        P                  # \        \	        V P                   4      ,          # r,   rL   r5   s   &&,r   rM   "SigmaMinus._eval_commutator_SigmaY"  /    99

"66Mvdii(((r"   c                    ^V ,          # rJ   r(   r5   s   &&,r   rT   "SigmaMinus._eval_commutator_SigmaZ(  s    4xr"   c                ,    \        V P                  4      # r,   r   r    r5   s   &&,r   _eval_commutator_SigmaMinus&SigmaMinus._eval_commutator_SigmaMinus+      dii  r"   c                "    \         P                  # r,   r3   r5   s   &&,r   r]   &SigmaMinus._eval_anticommutator_SigmaZ.  r9   r"   c                "    \         P                  # r,   r   Oner5   s   &&,r   r   &SigmaMinus._eval_anticommutator_SigmaX1      uur"   c                8    \         \        P                  ,          # r,   )r   r   NegativeOner5   s   &&,r   rZ   &SigmaMinus._eval_anticommutator_SigmaY4  s    1==  r"   c                "    \         P                  # r,   r   r5   s   &&,r   _eval_anticommutator_SigmaPlus)SigmaMinus._eval_anticommutator_SigmaPlus7  r   r"   c                ,    \        V P                  4      # r,   )r   r    r   s   &r   r`   SigmaMinus._eval_adjoint:  s    ##r"   c                r    VP                   '       d%   VP                  '       d   \        P                  # R # R # r,   rq   rr   r   r4   ru   s   &&r   rw   SigmaMinus._eval_power=  #    <<<AMMM66M *<r"   c                b    V P                   '       d   R \        V P                  4      ,          # R# )z{\sigma_-^{(%s)}}z
{\sigma_-}rd   rf   s   &&*r   rh    SigmaMinus._print_contents_latexA  rj   r"   c                    R # )zSigmaMinus()r(   rf   s   &&*r   rl   SigmaMinus._print_contentsG  s    r"   c                    VP                  R R4      pVR8X  d   \        ^ ^ .^^ ..4      # \        RV,           R,           4      hr{   r   r   s   &, r   r   #SigmaMinus._represent_default_basisJ  r   r"   r(   N)r:   r;   r<   r=   r>   r-   r   rM   rT   r   r]   r   rZ   r   r`   rw   rh   rl   r   rA   rB   rC   s   @r   r   r      sW     2/&)!!$!D Dr"   c                   ~   a  ] tR tRt o RtR tR tR tR tR t	R t
R	 tR
 tR tR tR tR tR tR tR tRtV tR# )r   iS  a  Pauli sigma plus operator

Parameters
==========

name : str
    An optional string that labels the operator. Pauli operators with
    different names commute.

Examples
========

>>> from sympy.physics.quantum import represent, Dagger
>>> from sympy.physics.quantum.pauli import SigmaPlus
>>> sp = SigmaPlus()
>>> sp
SigmaPlus()
>>> Dagger(sp)
SigmaMinus()
>>> represent(sp)
Matrix([
[0, 1],
[0, 0]])
c                2    \         P                  ! V .VO5!  # r,   rG   r.   s   &*,r   r-   SigmaPlus.__new__m  r   r"   c                    V P                   VP                   8w  d   \        P                  # \        V P                   4      # r,   r   r5   s   &&,r   r   !SigmaPlus._eval_commutator_SigmaXp  s*    99

"66M$))$$r"   c                    V P                   VP                   8w  d   \        P                  # \        \	        V P                   4      ,          # r,   rL   r5   s   &&,r   rM   !SigmaPlus._eval_commutator_SigmaYv  r   r"   c                j    V P                   VP                   8w  d   \        P                  # RV ,          # rQ   )r    r   r4   r5   s   &&,r   rT   !SigmaPlus._eval_commutator_SigmaZ|  s%    99

"66M9r"   c                ,    \        V P                  4      # r,   r   r5   s   &&,r   r   %SigmaPlus._eval_commutator_SigmaMinus  r   r"   c                "    \         P                  # r,   r3   r5   s   &&,r   r]   %SigmaPlus._eval_anticommutator_SigmaZ  r9   r"   c                "    \         P                  # r,   r   r5   s   &&,r   r   %SigmaPlus._eval_anticommutator_SigmaX  r   r"   c                    \         # r,   r   r5   s   &&,r   rZ   %SigmaPlus._eval_anticommutator_SigmaY  s    r"   c                "    \         P                  # r,   r   r5   s   &&,r   _eval_anticommutator_SigmaMinus)SigmaPlus._eval_anticommutator_SigmaMinus  r   r"   c                ,    \        V P                  4      # r,   )r   r    r   s   &r   r`   SigmaPlus._eval_adjoint  s    $))$$r"   c                    W,          # r,   r(   )r   r6   s   &&r   	_eval_mulSigmaPlus._eval_mul  s
    |r"   c                r    VP                   '       d%   VP                  '       d   \        P                  # R # R # r,   r   ru   s   &&r   rw   SigmaPlus._eval_power  r   r"   c                b    V P                   '       d   R \        V P                  4      ,          # R# )z{\sigma_+^{(%s)}}z
{\sigma_+}rd   rf   s   &&*r   rh   SigmaPlus._print_contents_latex  rj   r"   c                    R # )zSigmaPlus()r(   rf   s   &&*r   rl   SigmaPlus._print_contents  s    r"   c                    VP                  R R4      pVR8X  d   \        ^ ^.^ ^ ..4      # \        RV,           R,           4      hr{   r   r   s   &, r   r   "SigmaPlus._represent_default_basis  r   r"   r(   N)r:   r;   r<   r=   r>   r-   r   rM   rT   r   r]   r   rZ   r   r`   r   rw   rh   rl   r   rA   rB   rC   s   @r   r   r   S  s\     2/%)!%!D Dr"   c                      a  ] tR tRt o RtR t]R 4       t]R 4       t	]R 4       t
R tR tR	 tR
 tR tR tR tRtV tR# )r   i  znKet for a two-level system quantum system.

Parameters
==========

n : Number
    The state number (0 or 1).

c                R    VR9  d   \        R4      h\        P                  ! W4      # r   zn must be 0 or 1)r      )
ValueErrorr
   r-   r/   ns   &&r   r-   SigmaZKet.__new__  $    F?/00{{3""r"   c                (    V P                   ^ ,          # r   labelr   s   &r   r  SigmaZKet.n      zz!}r"   c                    \         # r,   )r   r   s   &r   
dual_classSigmaZKet.dual_class      r"   c                    \        ^4      # rJ   r   )r/   r  s   &&r   _eval_hilbert_spaceSigmaZKet._eval_hilbert_space  s    Ar"   c                B    \        V P                  VP                  4      # r,   )r   r  )r   brar0   s   &&,r   _eval_innerproduct_SigmaZBra&SigmaZKet._eval_innerproduct_SigmaZBra  s    dffcee,,r"   c                V    V P                   ^ 8X  d   V # \        P                  V ,          # r   )r  r   r   r   opr   s   &&,r   _apply_from_right_to_SigmaZ%SigmaZKet._apply_from_right_to_SigmaZ  s!    66Q;K==4''r"   c                P    V P                   ^ 8X  d   \        ^4      # \        ^ 4      # r   )r  r   r  s   &&,r   _apply_from_right_to_SigmaX%SigmaZKet._apply_from_right_to_SigmaX  s    #vv{y|<	!<r"   c                ~    V P                   ^ 8X  d   \        \        ^4      ,          # \        ) \        ^ 4      ,          # r   )r  r   r   r  s   &&,r   _apply_from_right_to_SigmaY%SigmaZKet._apply_from_right_to_SigmaY  s+    #'66Q;q9Q<GaR9Q<4GGr"   c                Z    V P                   ^ 8X  d   \        ^4      # \        P                  # r   )r  r   r   r4   r  s   &&,r   _apply_from_right_to_SigmaMinus)SigmaZKet._apply_from_right_to_SigmaMinus  s     66Q;Q<66Mr"   c                Z    V P                   ^ 8X  d   \        P                  # \        ^ 4      # r   )r  r   r4   r   r  s   &&,r   _apply_from_right_to_SigmaPlus(SigmaZKet._apply_from_right_to_SigmaPlus  s     66Q;66MQ<r"   c                    VP                  R R4      pVR8X  d0   V P                  ^ 8X  d   \        ^.^ ..4      # \        ^ .^..4      # \        RV,           R,           4      hr{   )r   r  r   r   r   s   &, r   r   "SigmaZKet._represent_default_basis  sl    Xw/W)-16A3*%L&1#s:LL%&A&,'-/B'C D Dr"   r(   N)r:   r;   r<   r=   r>   r-   r?   r  r@   r  r  r  r  r!  r$  r'  r*  r   rA   rB   rC   s   @r   r   r     sv     #
      -(=H D Dr"   c                   J   a  ] tR tRt o RtR t]R 4       t]R 4       t	Rt
V tR# )r   i  zgBra for a two-level quantum system.

Parameters
==========

n : Number
    The state number (0 or 1).

c                R    VR9  d   \        R4      h\        P                  ! W4      # r  )r  r   r-   r  s   &&r   r-   SigmaZBra.__new__  r
  r"   c                (    V P                   ^ ,          # r   r  r   s   &r   r  SigmaZBra.n  r  r"   c                    \         # r,   )r   r   s   &r   r  SigmaZBra.dual_class  r  r"   r(   N)r:   r;   r<   r=   r>   r-   r?   r  r@   r  rA   rB   rC   s   @r   r   r     s7     #
    r"   c                ^   \        V \        4      '       d   \        V\        4      '       g   \        W4      # V P                  VP                  8w  d2   V P                  VP                  8  d   \        W4      # \        W4      # \        V \        4      '       Ed$   \        V\        4      '       d   \
        P                  # \        V\        4      '       d!   \        \        V P                  4      ,          # \        V\        4      '       d"   \        ) \        V P                  4      ,          # \        V\        4      '       d2   \
        P                  \        V P                  4      ^,          ,           # \        V\        4      '       d2   \
        P                  \        V P                  4      ^,          ,
          # R# \        V \        4      '       Ed;   \        V\        4      '       d"   \        ) \        V P                  4      ,          # \        V\        4      '       d   \
        P                  # \        V\        4      '       d!   \        \	        V P                  4      ,          # \        V\        4      '       d>   \        ) \
        P                  \        V P                  4      ,           ,          ^,          # \        V\        4      '       d=   \        \
        P                  \        V P                  4      ,
          ,          ^,          # R# \        V \        4      '       d   \        V\        4      '       d!   \        \        V P                  4      ,          # \        V\        4      '       d"   \        ) \	        V P                  4      ,          # \        V\        4      '       d   \
        P                  # \        V\        4      '       d   \        V P                  4      ) # \        V\        4      '       d   \        V P                  4      # R# \        V \        4      '       Ed5   \        V\        4      '       d2   \
        P                  \        V P                  4      ,
          ^,          # \        V\        4      '       d>   \        ) \
        P                  \        V P                  4      ,
          ,          ^,          # \        V\        4      '       d   \        VP                  4      # \        V\        4      '       d   \
        P                  # \        V\        4      '       d2   \
        P                  \        V P                  4      ^,          ,
          # R# \        V \        4      '       Ed5   \        V\        4      '       d2   \
        P                  \        V P                  4      ,           ^,          # \        V\        4      '       d=   \        \
        P                  \        V P                  4      ,           ,          ^,          # \        V\        4      '       d   \        V P                  4      ) # \        V\        4      '       d2   \
        P                  \        V P                  4      ,           ^,          # \        V\        4      '       d   \
        P                  # R# W,          # )zG
Internal helper function for simplifying products of Pauli operators.
N)
isinstancer   r   r    r   r   r   r   r   r   r   Halfr   r4   )abs   &&r   _qsimplify_pauli_productr:    s!    q+&&:a+E+E1yvv66AFF?q9q9	Av		a  55La  vaff~%%a  3''a$$FFVAFF^A--.a##FFVAFF^A--. $ 
Av		a  3''a  55La  vaff~%%a$$2/022a##qvv./11 $ 
Av		a  vaff~%%a  3''a  55La$$'''a##QVV$$ $ 
Az	"	"a  EEF166N*A--a  3!%%&.01!33a  aff%%a$$66Ma##66F166N1,,, $ 
Ay	!	!a  EEF166N*A--a  qvv./11a  aff%%%a$$EEF166N*A--a##66M $ ur"   c                   \        V \        4      '       d   V # \        V \        \        \        34      '       d#   \        V 4      pV! R V P                   4       !  # \        V \        4      '       d   V P                  4       w  r#. pV'       d   VP                  ^ 4      p\        V4      '       d   \        V\        4      '       d   \        V^ ,          \        4      '       dd   VP                  V^ ,          P                  8X  dB   VP                  ^ 4      p\        WV4      pVP                  4       w  r\        V	!  pW(,           pK  VP                  V4       K  \        V!  \        V!  ,          # V # )a  
Simplify an expression that includes products of pauli operators.

Parameters
==========

e : expression
    An expression that contains products of Pauli operators that is
    to be simplified.

Examples
========

>>> from sympy.physics.quantum.pauli import SigmaX, SigmaY
>>> from sympy.physics.quantum.pauli import qsimplify_pauli
>>> sx, sy = SigmaX(), SigmaY()
>>> sx * sy
SigmaX()*SigmaY()
>>> qsimplify_pauli(sx * sy)
I*SigmaZ()
c              3   8   "   T F  p\        V4      x  K  	  R # 5ir,   )qsimplify_pauli).0args   & r   	<genexpr>"qsimplify_pauli.<locals>.<genexpr>  s     :6C?3''6s   )r6  r	   r   r   r   typer   r   args_cncpoplenr   r    r:  append)
rv   tcncnc_scurrxyc1nc1s
   &         r   r=  r=  o  s	   , !X!c3_%%G:166:;;!S

66!9Dr77dK00be[11991

*FF1I,T5**,CyFKKAwd##Hr"   N)r   r   r   r   r   r   r   r=  )!r>   sympy.core.addr   sympy.core.mulr   sympy.core.numbersr   sympy.core.powerr   sympy.core.singletonr   &sympy.functions.elementary.exponentialr   sympy.physics.quantumr	   r
   r   r   sympy.matricesr   (sympy.functions.special.tensor_functionsr   __all__r   r   r   r   r   r   r   r   r:  r=  r(   r"   r   <module>rZ     s            " 6 4 4 . ! C( ,FD[ FDRCD[ CDLCD[ CDLQD QDhWD WDt=D =D@ 2fR4r"   