ó
    ±“,jN'  ã                   óÞ   • S SK r S SKrS SKJr   " S S5      r " S S\5      r " S S\5      r " S	 S
\5      r " S S\5      rS r	 " S S\
5      r " S S\5      r " S S\5      rSS jrg)é    N)Údefaultdictc                   ó2   • \ rS rSrS rS rS rS rS rSr	g)	Ú
Expressioné   c                 ó   • g ©N© ©Úselfs    Ú£C:\Users\johnn\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\einx/_src/util/solver.pyÚ__init__ÚExpression.__init__   s   € Øó    c                 ó   • [        X/5      $ r   ©ÚSum©r   Úothers     r   Ú__add__ÚExpression.__add__
   s   € Ü�D�=Ó!Ð!r   c                 ó   • [        X/5      $ r   r   r   s     r   Ú__radd__ÚExpression.__radd__   s   € Ü�E�=Ó!Ð!r   c                 ó   • [        X/5      $ r   ©ÚProductr   s     r   Ú__mul__ÚExpression.__mul__   s   € Ü˜�}Ó%Ð%r   c                 ó   • [        X/5      $ r   r   r   s     r   Ú__rmul__ÚExpression.__rmul__   s   € Ü˜�}Ó%Ð%r   r	   N)
Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__r   r   r   r   r    Ú__static_attributes__r	   r   r   r   r      s   † òò"ò"ò&õ&r   r   c                   ó8   • \ rS rSrS rS rS rS rS rS r	Sr
g	)
ÚVariableé   c                 óF   • [         R                  U 5        Xl        X l        g r   )r   r   ÚidÚname)r   r+   r,   s      r   r   ÚVariable.__init__   s   € Ü×Ñ˜DÔ!ØŒØ�	r   c              #   ó   #   • U v •  g 7fr   r	   r
   s    r   Ú__iter__ÚVariable.__iter__   ó
   é € Ø‹
ùó   ‚c                 ób   • [        U[        5      =(       a    U R                  UR                  :H  $ r   )Ú
isinstancer(   r+   r   s     r   Ú__eq__ÚVariable.__eq__    s!   € Ü˜%¤Ó*×B¨t¯w©w¸%¿(¹(Ñ/BÐBr   c                 ó,   • [        U R                  5      $ r   )Úhashr+   r
   s    r   Ú__hash__ÚVariable.__hash__#   s   € Ü�D—G‘G‹}Ðr   c                 ó   • U R                    $ r   )r,   r
   s    r   Ú__str__ÚVariable.__str__&   s   € Ø—)‘)�Ðr   c                 óB   • [         R                  " U R                  SSS9$ )NT)ÚintegerÚnonnegative)ÚsympyÚSymbolr+   r
   s    r   rA   ÚVariable.sympy)   s   € Ü�|Š|˜DŸG™G¨T¸tÑDÐDr   )r+   r,   N©r"   r#   r$   r%   r   r/   r5   r9   r<   rA   r&   r	   r   r   r(   r(      s"   † òò
òCòòõEr   r(   c                   ó8   • \ rS rSrS rS rS rS rS rS r	Sr
g	)
ÚConstanté-   c                 ó:   • [         R                  U 5        Xl        g r   )r   r   Úvalue)r   rI   s     r   r   ÚConstant.__init__.   s   € Ü×Ñ˜DÔ!Ø�
r   c              #   ó   #   • U v •  g 7fr   r	   r
   s    r   r/   ÚConstant.__iter__2   r1   r2   c                 ób   • [        U[        5      =(       a    U R                  UR                  :H  $ r   )r4   rF   rI   r   s     r   r5   ÚConstant.__eq__5   s!   € Ü˜%¤Ó*×H¨t¯z©z¸U¿[¹[Ñ/HÐHr   c                 ó,   • [        U R                  5      $ r   )r8   rI   r
   s    r   r9   ÚConstant.__hash__8   s   € Ü�D—J‘JÓÐr   c                 ó,   • [        U R                  5      $ r   )ÚstrrI   r
   s    r   r<   ÚConstant.__str__;   s   € Ü�4—:‘:‹Ðr   c                 ó   • U R                   $ r   ©rI   r
   s    r   rA   ÚConstant.sympy>   s   € Ø�z‰zÐr   rU   NrD   r	   r   r   rF   rF   -   s!   † òòòIò òõr   rF   c                   óH   • \ rS rSr\S 5       rS rS rS rS r	S r
S rS	rg
)r   éB   c                 óØ   • [        U 5      S:X  a  [        S5      $ [        U 5      S:X  a  U S   $ [        S U  5       5      (       a  [        [        S U  5       5      5      $ [	        U 5      $ )Nr   é   c              3   óB   #   • U  H  n[        U[        5      v •  M     g 7fr   ©r4   rF   ©Ú.0Úcs     r   Ú	<genexpr>ÚSum.maybe.<locals>.<genexpr>I   ó   é € Ð;²(¨Q”˜Aœx×(Ð(²(ùó   ‚c              3   ó8   #   • U  H  oR                   v •  M     g 7fr   rU   r]   s     r   r`   ra   J   s   é € Ð:²¨A§¦²ùó   ‚)ÚlenrF   ÚallÚsumr   ©Úchildrens    r   ÚmaybeÚ	Sum.maybeC   s_   € äˆx‹=˜AÓÜ˜A“;ÐÜ�‹]˜aÓØ˜A‘;ÐÜÑ;±(Ó;×;Ñ;ÜœCÑ:±Ó:Ó:Ó;Ð;ä�x“=Ð r   c                 óz   • [         R                  U 5        U Vs/ s H  n[        U5      PM     snU l        g s  snf r   ©r   r   Ú_to_exprrj   ©r   rj   r_   s      r   r   ÚSum.__init__N   ó-   € Ü×Ñ˜DÔ!Ù.6Ó7ªh¨œ !ž©hÑ7ˆ�ùÒ7ó   š8c              #   óR   #   • U v •  U R                    H  nU S h  v•N   M     g  N	7fr   ri   ©r   Úchilds     r   r/   ÚSum.__iter__R   ó$   é € ØŠ
Ø—]”]ˆEØ×Òò #Ùùó   ‚'›%œ
'c                 ób   • [        U[        5      =(       a    U R                  UR                  :H  $ r   )r4   r   rj   r   s     r   r5   Ú
Sum.__eq__W   s!   € Ü˜%¤Ó%×I¨$¯-©-¸5¿>¹>Ñ*IÐIr   c                 ó>   • [        [        U R                  5      5      $ r   ©r8   Útuplerj   r
   s    r   r9   ÚSum.__hash__Z   ó   € Ü”E˜$Ÿ-™-Ó(Ó)Ð)r   c                 óF   • SR                  S U R                   5       5      $ )Nz + c              3   ó8   #   • U  H  n[        U5      v •  M     g 7fr   ©rR   r]   s     r   r`   ÚSum.__str__.<locals>.<genexpr>^   ó   é € Ð8ª- Qœ#˜aŸ&˜&ª-ùre   ©Újoinrj   r
   s    r   r<   ÚSum.__str__]   ó   € Ø�z‰zÑ8¨$¯-ª-Ó8Ó8Ð8r   c                 ó:   • [        S U R                   5       5      $ )Nc              3   ó@   #   • U  H  oR                  5       v •  M     g 7fr   )rA   r]   s     r   r`   ÚSum.sympy.<locals>.<genexpr>a   s   é € Ð4¢m —7‘7—9�9¢mùs   ‚)rh   rj   r
   s    r   rA   Ú	Sum.sympy`   s   € ÜÑ4 d§m¢mÓ4Ó4Ð4r   ri   N©r"   r#   r$   r%   Ústaticmethodrk   r   r/   r5   r9   r<   rA   r&   r	   r   r   r   r   B   s3   † Øñ!ó ð!ò8òò
Jò*ò9õ5r   r   c                   óH   • \ rS rSr\S 5       rS rS rS rS r	S r
S rS	rg
)r   éd   c                 óî   • [        U 5      S:X  a  [        S5      $ [        U 5      S:X  a  U S   $ [        S U  5       5      (       a&  [        [        R                  " S U  5       5      5      $ [        U 5      $ )Nr   rZ   c              3   óB   #   • U  H  n[        U[        5      v •  M     g 7fr   r\   r]   s     r   r`   Ú Product.maybe.<locals>.<genexpr>k   rb   rc   c              3   ó8   #   • U  H  oR                   v •  M     g 7fr   rU   r]   s     r   r`   r”   l   s   é € Ð%@²x°!§g¦g²xùre   )rf   rF   rg   ÚmathÚprodr   ri   s    r   rk   ÚProduct.maybee   sd   € äˆx‹=˜AÓÜ˜A“;ÐÜ�‹]˜aÓØ˜A‘;ÐÜÑ;±(Ó;×;Ñ;ÜœDŸIšIÑ%@±xÓ%@Ó@ÓAÐAä˜8Ó$Ð$r   c                 óz   • [         R                  U 5        U Vs/ s H  n[        U5      PM     snU l        g s  snf r   rn   rp   s      r   r   ÚProduct.__init__p   rr   rs   c              #   óR   #   • U v •  U R                    H  nU S h  v•N   M     g  N	7fr   ri   ru   s     r   r/   ÚProduct.__iter__t   rx   ry   c                 ób   • [        U[        5      =(       a    U R                  UR                  :H  $ r   )r4   r   rj   r   s     r   r5   ÚProduct.__eq__y   s!   € Ü˜%¤Ó)×M¨d¯m©m¸u¿~¹~Ñ.MÐMr   c                 ó>   • [        [        U R                  5      5      $ r   r}   r
   s    r   r9   ÚProduct.__hash__|   r€   r   c                 óF   • SR                  S U R                   5       5      $ )Nz * c              3   ó8   #   • U  H  n[        U5      v •  M     g 7fr   rƒ   r]   s     r   r`   Ú"Product.__str__.<locals>.<genexpr>€   r…   re   r†   r
   s    r   r<   ÚProduct.__str__   r‰   r   c                 óˆ   • [         R                  " U R                   Vs/ s H  oR                  5       PM     sn5      $ s  snf r   )r–   r—   rj   rA   )r   r_   s     r   rA   ÚProduct.sympy‚   s+   € Ü�yŠy¨T¯]ª]Ó;ª]¨Ÿ'™'ž)©]Ñ;Ó<Ð<ùÒ;s   Ÿ?ri   NrŽ   r	   r   r   r   r   d   s3   † Øñ%ó ð%ò8òò
Nò*ò9õ=r   r   c                 óž   • [        U [        5      (       a  [        U 5      $ [        U [        5      (       d  [	        S[        U 5       35      eU $ )NzExpected Expression, got )r4   ÚintrF   r   Ú	TypeErrorÚtype)Úxs    r   ro   ro   †   sB   € Ü�!”S×ÑÜ˜‹{Ðä˜!œZ×(Ñ(ÜÐ7¼¸Q»°yÐAÓBÐBØˆr   c                   ó(   ^ • \ rS rSrU 4S jrSrU =r$ )ÚSolveExceptioné�   c                 ó$   >• [         TU ]  U5        g r   )Úsuperr   ©r   ÚmessageÚ	__class__s     €r   r   ÚSolveException.__init__�   s   ø€ Ü‰Ñ˜Õ!r   r	   ©r"   r#   r$   r%   r   r&   Ú__classcell__©r³   s   @r   r­   r­   �   s   ø† ÷"ó "r   r­   c                   ó,   ^ • \ rS rSrSU 4S jjrSrU =r$ )ÚSolveExceptionNoSolutioné”   c           
      óê   >• Uc  / nUSSR                  U Vs/ s H  n[        U5      PM     sn5       3-   n[        TU ]  U5        X l        [        S U 5       5      (       d  [        S5      eg s  snf )Nz
Contradicting variables: z, c              3   óB   #   • U  H  n[        U[        5      v •  M     g 7fr   )r4   r(   )r^   Úvs     r   r`   Ú4SolveExceptionNoSolution.__init__.<locals>.<genexpr>›   s   é € ÐLÒ4K¨q”:˜a¤×*Ð*Ò4Kùrc   z;Expected all contradicting variables to be of type Variable)r‡   rR   r°   r   Úcontradicting_variablesrg   r©   )r   r²   r¿   r½   r³   s       €r   r   Ú!SolveExceptionNoSolution.__init__•   s€   ø€ Ø"Ñ*Ø&(Ð#ØÐ9¸$¿)¹)ÑUlÓDmÒUlÐPQÄSÈÆVÑUlÑDmÓ:nÐ9oÐpÑpˆÜ‰Ñ˜Ô!Ø'>Ô$ÜÑLÑ4KÓL×LÑLÜÐYÓZÐZð Mùò Ens   ˜A0)r¿   )Ú Nrµ   r·   s   @r   r¹   r¹   ”   s   ø† ÷[õ [r   r¹   c                   ó,   ^ • \ rS rSrSU 4S jjrSrU =r$ )ÚSolveExceptionTooManySolutionséŸ   c                 ó0   >• [         TU ]  U5        Xl        g r   )r°   r   r²   r±   s     €r   r   Ú'SolveExceptionTooManySolutions.__init__    s   ø€ Ü‰Ñ˜Ô!Ø�r   )r²   r   rµ   r·   s   @r   rÃ   rÃ   Ÿ   s   ø† ÷õ r   rÃ   c                 óä  ^^ ^!^"• U  VVs/ s H  u  p#[        U5      [        U5      4PM     n nnU  VVs/ s H  u  p#X#:w  d  M  X#4PM     n nn[        [        U 5      5      n U  VVVs0 s H9  oD  H0  oU  H'  n[        U[        5      (       d  M  UR
                  U_M)     M2     M;     snnnm"[        [        5      m[        5       nU  GH  u  p#[        U[        5      (       a?  [        U[        5      (       a*  TUR
                     R                  UR                  5        MZ  [        U[        5      (       a?  [        U[        5      (       a*  TUR
                     R                  UR                  5        M®  [        U[        5      (       d  MÅ  [        U[        5      (       d  MÜ  UR                  UR                  :w  d  Mø  [        SUR                   SUR                   3/ 5      e   TR                  5        VV	s1 s H  u  p‰[        U	5      S:w  d  M  T"U   iM     nnn	[        U5      S:”  a  [        SU5      eTR                  5        V
Vs0 s H  u  p¦X¦R                  5       _M     snn
mT" Vs0 s H  ofU1_M     nnU  H�  u  p#[        U[        5      (       d  M  [        U[        5      (       d  M3  UR
                  U;   a  UR
                  U;   d   eX²R
                     nX³R
                     nU H  nXËU'   UR                  U5        M     M‘     [        UR                  5        Vs0 s H  n[        U5      U_M     snR                  5       5      nU VVs0 s H  nU  H  ofU_M     M     nnn0 m [        5       nU Hâ  n[        U4S jU 5       5      (       av  U Vs1 s H  nUT;   d  M  TU   iM     nn[        U5      S:”  d   e[        U5      S:”  a  UR!                  U"4S jU 5       5        [        [#        [%        U5      5      5      nO9[	        S[        U5       3S	U Vs1 s H  nT"U   R&                  iM     sn 35      nU H  nUT ;  d   eUT U'   M     Mä     [        U5      S:”  a  [        S
U5      eU U!4S jm!/ n[        5       nU  HÛ  u  nnT!" U5      nT!" U5      n[        U[        5      (       a—  [        U[        5      (       a‚  UR                  UR                  :w  af  UU4 VVVs/ s H@  nU  H6  n[        U[        5      (       d  M  UUR
                       H  nT"U   PM
     M8     MB     nnnnUR!                  U5        MÀ  MÂ  X#:w  d  MÉ  UR)                  X#45        MÝ     Un [        U5      S:”  a  [        S[        U5      5      eU(       a'  [+        S5        U  H  u  p#[+        SU SU 35        M     0 n[        U 5      S:”  GaB  U  VVs/ s H8  u  p#[,        R.                  " UR-                  5       UR-                  5       5      PM:     nnn[1        S U 5       5      (       a  0 nOá[,        R2                  " USSS9nU/ :X  a  0 nOÂ[        U[4        5      (       a¢  [        U5      S:X  a“  Uu  m"n[        U5      S:X  a  [        S5      e[        U5      S:”  a  [7        S5      e[#        [%        U5      5      n[9        T"USS9 V
Vs0 s H-  u  p¦UR:                  (       d  M  [=        U
5      [?        U5      _M/     nn
nO[A        S5      e0 nT R                  5        Hn  u  p¦[        U[        5      (       a  UR                  UU
'   M+  [        U[        5      (       a&  UR
                  U;   a  UUR
                     UU
'   Md  Mf  [A        5       e   U$ s  snnf s  snnf s  snnnf s  sn	nf s  snn
f s  snf s  snf s  snnf s  snf s  snf s  snnnf s  snnf s  snn
f )Nz#Found contradictory input equation z != rZ   r   z5Found contradictory definitions for the same variablec              3   ó,   >#   • U  H	  oT;   v •  M     g 7fr   r	   )r^   ÚnÚ	constantss     €r   r`   Úsolve.<locals>.<genexpr>Í   s   øé € Ð3¢{ !�IŽ~¢{ùs   ƒc              3   ó.   >#   • U  H
  nTU   v •  M     g 7fr   r	   )r^   ÚvidÚ	variabless     €r   r`   rË   Ò   s   øé € Ð.UÊÀ#¨y¸®~Êùs   ƒz__EquivalenceClass-zEquivalent expressions z8Found contradictory constants for same equivalence classc                 óî  >• [        U [        5      (       a  U R                  T;   a  TU R                     $ [        U [        5      (       a  U $ [        U [        5      (       a6  [        R                  U R                   Vs/ s H  nT" U5      PM     sn5      $ [        U [        5      (       a6  [        R                  U R                   Vs/ s H  nT" U5      PM     sn5      $ [        5       es  snf s  snf r   )	r4   r(   r+   rF   r   rk   rj   r   ÚAssertionError)Útr_   Úorigvar_to_solvevarÚreplaces     €€r   rÓ   Úsolve.<locals>.replaceÞ   s´   ø€ Ü�aœ×"Ñ" q§t¡tÐ/BÓ'BØ& q§t¡tÑ,Ð,Ü˜œ8×$Ñ$ØˆHÜ˜œ3×ÑÜ—9‘9°!·*²*Ó=²*¨Q™g ažj±*Ñ=Ó>Ð>Ü˜œ7×#Ñ#Ü—=‘=°a·j²jÓ!A²j°¡'¨!¦*±jÑ!AÓBÐBä Ó"Ð"ùò	 >ùâ!As   Á?C-Ã
C2z5Found contradictory values for same equivalence classz)Solving equations of equivalence classes:z  z = c              3   ó\   #   • U  H"  oR                   =(       a    [        U5      v •  M$     g 7fr   )Ú
is_BooleanÚbool)r^   Úeqs     r   r`   rË     s   é € ÐD²O¨b�}‰}×)¤ b£Ô)²Oùs   ‚*,T)ÚsetÚmanualé   zSympy returned no solutionsz*Sympy returned multiple possible solutionsF)Ústrictz Sympy returned unexpected result)!ro   ÚlistrÙ   r4   r(   r+   r   rF   ÚaddrI   r¹   Úitemsrf   ÚpopÚvaluesÚanyÚupdateÚnextÚiterr,   ÚappendÚprintrA   ÚEqrg   Úsolver~   rÃ   ÚzipÚ	is_numberrR   r¨   rÐ   )#Ú	equationsÚverboseÚt1Út2ÚequationÚtermr½   r¿   Úvariable_idrá   ÚkÚclassesÚset1Úset2Út_idÚsr_   Úvariableid_to_classÚequiv_classrÉ   Úclass_constantsrÍ   Ú
equations2Út1oÚt2oÚtoÚv0ÚvarsÚ	solutionsÚsympy_equationsÚorig_solutionsrÊ   rÒ   rÓ   rÎ   s#                                  @@@@r   ré   ré   ¥   s&  û€ Ù<EÔFºI±&°"”(˜2“,¤¨£Ó-¹I€IÑFÙ(1Ô>ª	™f˜b°R±X“�"“©	€IÑ>Ü”S˜“^Ó$€IÙ)2Õqª˜X»x°tÓQUÈAÔYcÐdeÔgo×Yp“�—‘�q’ÑQU‘¹x‘©Óq€Iô œCÓ €IÜ!›eÐÜ‰ˆÜ�bœ(×#Ñ#¬
°2´x×(@Ñ(@Ø�b—e‘eÑ× Ñ  §¡Ö*Ü˜œH×%Ñ%¬*°R¼×*BÑ*BØ�b—e‘eÑ× Ñ  §¡Ö*Ü˜œH×%Ó%¬*°R¼×*BÓ*BØ�x‰x˜2Ÿ8™8Õ#Ü.Ð1TÐUW×U]ÑU]ÐT^Ð^bÐce×ckÑckÐblÐ/mÐoqÓrÐrñ ð R[×Q`ÑQ`ÔQbÔwÒQbÑ:M¸+ÔfiÐjpÓfqÐuvÑfvÓ5˜y¨Ô5ÑQbÐÑwÜ
Ð"Ó# aÓ'Ü&Ð'^Ð`wÓxÐxØ(1¯©Ô(9Ô:Ò(9¡ �—E‘E“G’Ñ(9Ò:€Iñ  )Ó)šy˜!�1�#Šv™y€GÐ)Û‰ˆÜ�bœ(×#Ó#¬
°2´x×(@Ó(@Ø—5‘5˜GÓ#¨¯©°Ó(8Ð8Ð8ØŸ5™5‘>ˆDØŸ5™5‘>ˆDÛ�Ø $˜‘Ø—‘˜–ó ñ ô  g§n¡nÔ&6Ó7Ò&6 ”B�q“E˜1’HÑ&6Ñ7×>Ñ>Ó@ÓA€GÙ)0Ô<ª A¼!°Q˜aš4¹!™1©ÐÑ<ð ÐÜ!›eÐÛˆÜÔ3¡{Ó3×3Ñ3á5@ÓS²[°ÀAÈÁN›|˜y¨œ|±[ˆOÐSÜ�Ó'¨!Ó+Ð+Ð+Ü�?Ó# aÓ'Ø'×.Ñ.Ô.UÉÓ.UÔUÜœœd ?Ó3Ó4Ó5‰Aô Ð.¬r°+«Ð.?Ð@ÐD[ñ  ~Ió  ^Jò  ~IÐvyÐ^gÐhkÑ^l×^qÔ^qñ  ~Iñ  ^Jð  \Lð  CMó  NˆAÛˆAØÐ/Ó/Ð/Ð/Ø%&Ð Ó"ó ñ ô Ð"Ó# aÓ'Ü&Ð'aÐczÓ{Ð{ö
#ð €JÜ!›eÐÛ‰ˆˆSÙ�S‹\ˆÙ�S‹\ˆÜ�bœ(×#Ñ#¬
°2´x×(@Ñ(@Ø�x‰x˜2Ÿ8™8Ó#Ø25°s±õ  L²¨2ÄbÀÌJÐWYÔ[c×Ld›ð  qDð  EG÷  EJñ  EJõ  qKÐil˜	 #œñ  qK™Áb™±�ò  LØ'×.Ñ.¨tÖ4ñ $ð �XØ×Ñ˜r˜hÖ'ñ ð €IÜ
Ð"Ó# aÓ'Ü&Ð'^Ô`dÐe|Ó`}Ó~Ð~æÜÐ9Ô:Û‰FˆBÜ�B�r�d˜#˜b˜TÐ"Ö#ñ  ð €IÜ
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[˜~ô [ô ^ô õ{r   