ó
    Š*£hÇ  ã                   óz   • S r SSKJr  SSKJr  SSKJr  SSKJr  SSK	J
r
  SSKJr  S	S
KJr  \" S5      4S jrS rg)z:

Routines for computing eigenvectors with DomainMatrix.

é    )ÚDummyé   )ÚFiniteExtension)Údup_factor_list)Úroots)ÚPoly)ÚCRootOfé   )ÚDomainMatrixÚlambdac                 ó˜  • U R                  5       nU R                  u  p4U R                  n[        X%5      u  pg/ n/ n	U GHÚ  u  p«[	        U
5      S:X  aŒ  UnU
S   * U
S   -  n[        U5       VVs/ s H0  n[        U5       Vs/ s H  oþU:X  a  UOUR                  PM     snPM2     nnn[        UX44U5      nU U-
  R                  SS9nUR                  XÍUU45        M¡  [        R                  " X¡US9n[        U5      nU" U5      nU R                  R                  5        VVs/ s H4  nU Vs/ s H#  n[        R                  " U/XS9R                  PM%     snPM6     nnnU VVs/ s H  nU Vs/ s H  nU" U5      PM     snPM     nnn[        UX44U5      n[        U5       VVs/ s H0  n[        U5       Vs/ s H  oþU:X  a  UOUR                  PM     snPM2     nnn[        UX44U5      nUU-
  R                  SS9nU	R                  UUUU45        GMÝ     X‰4$ s  snf s  snnf s  snf s  snnf s  snf s  snnf s  snf s  snnf )Nr   r
   r   T)Údivide_last)Údomain)ÚcharpolyÚshaper   r   ÚlenÚrangeÚzeror   Ú	nullspaceÚappendr   Ú	from_listr   ÚrepÚto_ddm)ÚAÚlr   ÚrowsÚcolsr   Ú_ÚfactorsÚrational_eigenvectsÚalgebraic_eigenvectsÚbaseÚexpÚfieldÚeigenvalÚiÚjÚEE_itemsÚEEÚbasisÚminpolyÚrowÚitemÚAA_itemsÚAAs                           ÚW/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/polys/matrices/eigen.pyÚdom_eigenvectsr1      sW  € Ø�z‰z‹|€HØ—‘�J€DØ�X‰X€FÜ  Ó2�J€AàÐØÐÜ‰	ˆÜˆt‹9˜‹>ØˆEØ˜Q™�x $ q¡'Ñ)ˆHô ˜tœô&â$�Aô >CÀ4¼[ÓIº[¸ !›V‘¨¯©Ò3¹[ÔIÙ$ð ñ &ô ˜h¨¨°eÓ<ˆBà˜‘V×&Ñ&°4Ð&Ð8ˆEØ×&Ñ&¨¸¸eÐ'DÖEä—n’n T°VÑ<ˆGÜ# GÓ,ˆEÙ˜Q“xˆHð Ÿ5™5Ÿ<™<œ>ô+â)�Cñ KNÓNÊ#À$”—’  ¨Ñ9×=Ô=É#ÔNÙ)ð ñ +ñ BJÔJÂ¸#±Ó5²¨™˜tž±Ô5ÁˆHÑJÜ˜h¨¨°eÓ<ˆBô ˜tœô&â$�Aô >CÀ4¼[ÓIº[¸ !›V‘¨¯©Ò3¹[ÔIÙ$ð ñ &ô ˜h¨¨°eÓ<ˆBà˜"‘W×'Ñ'°DÐ'Ð9ˆEØ ×'Ñ'¨°¸¸eÐ(D×Eñ9 ð< Ð4Ð4ùò1 Jùó&ùò Oùó+ùò 6ùÓJùò Jùó&s`   Á/H%ÂH ÂH%Ä$
H0Ä.*H+ÅH0Å'
H;Å1H6ÆH;Æ)IÆ<IÇIÈ H%È+H0È6H;ÉIc                 ó˜  • / nU  H}  u  pVpxUR                   R                  5       nUR                  U5      nU V	V
s/ s H*  n	U" U	 V
s/ s H  o¥R                  U
5      PM     sn
5      PM,     nn	n
UR                  XgU45        M     U GH  u  p\pxUR                   R                  5       nUR                  S   nU V	V
s/ s H#  o™ V
s/ s H  o¥R                  U
5      PM     sn
PM%     nn	n
UR                  5       nUR                  5       n[        XÍ40 UD6n[        U5      U:w  a%  [        U5       Vs/ s H  n[        XÍU5      PM     nnU HO  nU V	V
s/ s H*  n	U" U	 V
s/ s H  oªR                  XÖ5      PM     sn
5      PM,     nn	n
UR                  XgU45        MQ     GM     U$ s  sn
f s  sn
n	f s  sn
f s  sn
n	f s  snf s  sn
f s  sn
n	f )Nr   )r   r   Úto_sympyr   ÚgensÚdegreeÚas_exprr   r   r   r	   Úsubs)r    r!   ÚMatrixÚkwargsÚresultr$   Ú
eigenvalueÚmultiplicityÚ
eigenvectsÚvectÚxÚnew_eigenvectsr+   r   r5   Ú	eigenvalsÚidxs                    r0   Údom_eigenvects_to_sympyrC   :   sº  € ð €Fã7JÑ3ˆ˜<Ø—^‘^×*Ñ*Ó,ˆ
Ø—^‘^ JÓ/ˆ
ñ #ô$â"�ñ ©tÓ4ªt¨!—N‘N 1Ö%©tÑ4Ö5Ù"ð 	ñ $ð 	�‰�z°Ð@ÖAñ 8Kô 5IÑ0ˆ˜Ø—^‘^×*Ñ*Ó,ˆ
Ø�L‰L˜‰OˆáDNÔOÂJ¸D°$Ó7²$¨Q—~‘~ aÖ(±$Ô7ÁJˆ
ÑOà—‘Ó!ˆØ—/‘/Ó#ˆÜ˜'Ñ/¨Ñ/ˆ	Üˆy‹>˜VÓ#Ü=BÀ6¼]ÓKº]°cœ ¨SÖ1¹]ˆIÐKã#ˆJñ 'ô(â&�Dñ ±tÓ<²t°!Ÿ™˜qÖ-±tÑ<Ö=Ù&ð ñ (ð �M‰M˜:°^ÐDÖEô	 $ñ 5Ið$ €Mùò- 5ùó$ùò 8ùÓOùò Lùò =ùó(sM   »F+ÁF&Á!F+Â=	F6ÃF1Ã F6Ä2F<ÅG
Å GÅ:G
Æ&F+Æ1F6ÇG
N)Ú__doc__Úsympy.core.symbolr   Úagca.extensionsr   Úfactortoolsr   Ú	polyrootsr   Ú	polytoolsr   Úrootoftoolsr	   Údomainmatrixr   r1   rC   © ó    r0   Ú<module>rN      s5   ðñõ
 $å -Ý )Ý Ý Ý !å &ñ ˜h›ô &5óR rM   