+
    ‹°³jã ã                  óÄ  a € 0 t $ R t^ RIHt ^ RIHtHtHt ^ RIt^ RI	H
t
HtHtHtHtHtHtHt ^ RIHt ^ RIHt ^ RIHtHtHt ^ RIHt ^ R	IHt ^ R
IHt ^ RI H!t! ^ RI"H#t#H$t$H%t% ^ RI&H't' ^ RI(H)t)H*t* ^ RI+H,t,H-t- ^ RI&H.t.H/t/ ^ RI0H1t1H2t3 ^ RI4H5t5H6t6 ^ RI7t7]'       d   ^ RI8H9t9 ^ RI:H;t; . R˜Ot</ RRbRRbRRbRRbRRbRR bR!R"bR#R$bR%R&bR'R(bR)R*bR+R,bR-R.bR/R0bR1R2bR3R4bR5R6b/ R7R8bR9R:bR;R<bR=R>bR?R@bRARBbRCRDbRERFbRGRHbRIR*bRJRKbRLRBbRMRNbRORPbRQRRbRSRTbRURVbCRWRXRYRZ/Ct=0 R™mt>/ R[R\ bR]R^ bR_R` bRaRb bRcRd bReRf bRgRh bRiRj bRkRl bRmRn bRoRp bRqRr bRsRt bRuRv bRwRx bRyRz bR{R| bR}R~ RR€ R�R‚ RƒR„ R…R† R‡Rˆ R‰RŠ /Ct?R‹]@RŒ&   ]A! ]4      tB]7P†                  ! R�4      ]7P†                  ! RŽ4      3tDR� R� ltE ! R‘ R’])4      tFR“ R” ltG]*! ]F4      R• 4       tHR– tIRšR— ltJR# )›zC
A Printer which converts an expression into its LaTeX equivalent.
)Úannotations)ÚAnyÚCallableÚTYPE_CHECKINGN)ÚAddÚFloatÚModÚMulÚNumberÚSÚSymbolÚExpr)Úgreeks)ÚTuple)ÚFunctionÚAppliedUndefÚ
Derivative)ÚAssocOp)ÚPow)Údefault_sort_key)ÚSympifyError)ÚtrueÚBooleanTrueÚBooleanFalse)Úprecedence_traditional)ÚPrinterÚprint_function)Úsplit_super_subÚrequires_partial)Ú
precedenceÚ
PRECEDENCE)Úprec_to_dpsÚto_str)Úhas_varietyÚsift)Ú	NDimArray)ÚBasisDependentÚAlphaz
\mathrm{A}ÚBetaz
\mathrm{B}ÚGammaú\GammaÚDeltaz\DeltaÚEpsilonz
\mathrm{E}ÚZetaz
\mathrm{Z}ÚEtaz
\mathrm{H}ÚThetaz\ThetaÚIotaz
\mathrm{I}ÚKappaz
\mathrm{K}ÚLambdaz\LambdaÚMuz
\mathrm{M}ÚNuz
\mathrm{N}ÚXiz\XiÚomicronÚoÚOmicronz
\mathrm{O}ÚPiz\PiÚRhoz
\mathrm{P}ÚSigmaz\SigmaÚTauz
\mathrm{T}ÚUpsilonz\UpsilonÚPhiz\PhiÚChiz
\mathrm{X}ÚPsiz\PsiÚOmegaz\OmegaÚlamdaz\lambdaÚLamdaÚkhiz\chiÚKhiÚ
varepsilonz\varepsilonÚvarkappaz	\varkappaÚvarphiz\varphiÚvarpiz\varpiÚvarrhoz\varrhoÚvarsigmaz	\varsigmaÚvarthetaz	\varthetaÚmathringc                ó"   € R V ,           R,           # )z
\mathring{Ú}© ©Úss   &ÚU/home/luca/screen-checking/.venv/lib/python3.14/site-packages/sympy/printing/latex.pyÚ<lambda>rT   [   s   € ˜-¨�/¨$Ö.ó    Úddddotc                ó"   € R V ,           R,           # )z\ddddot{rO   rP   rQ   s   &rS   rT   rT   \   s   € ˜ A� dÖ*rU   Údddotc                ó"   € R V ,           R,           # )z\dddot{rO   rP   rQ   s   &rS   rT   rT   ]   ó   € �z !•| DÖ(rU   Úddotc                ó"   € R V ,           R,           # )z\ddot{rO   rP   rQ   s   &rS   rT   rT   ^   s   € �i •k $Ö&rU   Údotc                ó"   € R V ,           R,           # )z\dot{rO   rP   rQ   s   &rS   rT   rT   _   ó   € �X˜a•Z –_rU   Úcheckc                ó"   € R V ,           R,           # )z\check{rO   rP   rQ   s   &rS   rT   rT   `   rZ   rU   Úbrevec                ó"   € R V ,           R,           # )z\breve{rO   rP   rQ   s   &rS   rT   rT   a   rZ   rU   Úacutec                ó"   € R V ,           R,           # )z\acute{rO   rP   rQ   s   &rS   rT   rT   b   rZ   rU   Úgravec                ó"   € R V ,           R,           # )z\grave{rO   rP   rQ   s   &rS   rT   rT   c   rZ   rU   Útildec                ó"   € R V ,           R,           # )z\tilde{rO   rP   rQ   s   &rS   rT   rT   d   rZ   rU   Úhatc                ó"   € R V ,           R,           # )z\hat{rO   rP   rQ   s   &rS   rT   rT   e   r_   rU   Úbarc                ó"   € R V ,           R,           # )z\bar{rO   rP   rQ   s   &rS   rT   rT   f   r_   rU   Úvecc                ó"   € R V ,           R,           # )z\vec{rO   rP   rQ   s   &rS   rT   rT   g   r_   rU   Úprimec                ó"   € R V ,           R,           # ©Ú{z}'rP   rQ   s   &rS   rT   rT   h   s   € �s˜1•u˜T–zrU   Úprmc                ó"   € R V ,           R,           # rr   rP   rQ   s   &rS   rT   rT   i   s   € �S˜•U˜4–ZrU   Úboldc                ó"   € R V ,           R,           # ©z\boldsymbol{rO   rP   rQ   s   &rS   rT   rT   k   s   € �o aÕ'¨Ö,rU   Úbmc                ó"   € R V ,           R,           # rx   rP   rQ   s   &rS   rT   rT   l   s   € �O AÕ% dÖ*rU   Úcalc                ó"   € R V ,           R,           # )z	\mathcal{rO   rP   rQ   s   &rS   rT   rT   m   ó   € �\ !•^ DÖ(rU   Úscrc                ó"   € R V ,           R,           # )z	\mathscr{rO   rP   rQ   s   &rS   rT   rT   n   r}   rU   Úfrakc                ó"   € R V ,           R,           # )z
\mathfrak{rO   rP   rQ   s   &rS   rT   rT   o   s   € �m A•o dÖ*rU   Únormc                ó"   € R V ,           R,           # )z\left\|{z	}\right\|rP   rQ   s   &rS   rT   rT   q   s   € �k !•m LÖ0rU   Úavgc                ó"   € R V ,           R,           # )z\left\langle{z}\right\ranglerP   rQ   s   &rS   rT   rT   r   s   € Ð% aÕ'Ð(9Ö9rU   Úabsc                ó"   € R V ,           R,           # ©z\left|{z}\right|rP   rQ   s   &rS   rT   rT   s   ó   € �Z •\ +Ö-rU   Úmagc                ó"   € R V ,           R,           # rˆ   rP   rQ   s   &rS   rT   rT   t   r‰   rU   zdict[str, Callable[[str], str]]Úmodifier_dictz[0-9][} ]*$z(\d|\\frac{\d+}{\d+})c               ó    € V ^8„  d   QhRRRR/# ©é   rR   ÚstrÚreturnrP   )Úformats   "rS   Ú__annotate__r“      s   € ÷ ñ �Cð ˜Cñ rU   c                ó¶   € V P                  RR4      p R F  pV P                  VRV,           4      p K  	  V P                  RR4      p V P                  RR4      p V # )z¹
Escape a string such that latex interprets it as plaintext.

We cannot use verbatim easily with mathjax, so escaping is easier.
Rules from https://tex.stackexchange.com/a/34586/41112.
Ú\z\textbackslashz&%$#_{}Ú~z\textasciitildeÚ^z\textasciicircum)Úreplace)rR   Úcs   & rS   Úlatex_escaperš      sZ   € ð 	
�	‰	�$Ð)Ó*€AÛˆØ�I‰I�a˜ �Ó"Šñ à	�	‰	�#Ð)Ó*€AØ	�	‰	�#Ð*Ó+€AØ€HrU   c                  ó°  a € ] tR t^Žt$ Rt/ RRbRRbRRbRRbRR	bR
RbRRbRRbRRbRRbRRbRRbRRbR/ bRRbRRbRRbRRRRRRRRRRR RR!R"R#R$R%R/	CtR&]R'&   ERvR( ltR) R* ltR+ R, lt	ERwR- R. llt
R/ tR0 R1 ltR2 R3 ltR4 R5 ltERwR6 R7 lltR8 R9 ltR: R; ltR< R= ltR> R? ltR@ tRA RB lt]t]tRC tERvRD ltRE tRF tRG tRH tRI tRJ tRK t RL t!RM t"RN t#RO RP lt$RQ t%RR t&RS RT lt'RU RV lt(RW t)RX t*RY t+RZ R[ lt,R\ t-R] t.R^ t/R_ t0R` t1Ra t2Rb t3Rc Rd lt4ERvRe Rf llt5Rg t6Rh t7]8Ri 4       t9Rj t:Rk t;Rl t<ERvRm Rn llt=]=;t>t?ERvRo lt@ERvRp ltAERvRq ltBERvRr ltCERvRs ltDERvRt ltERu tFRv tGRw tHRx tIRy tJERvRz ltKERvR{ ltLERvR| ltMERvR} ltNERvR~ ltOERvR ltPERvR€ ltQERvR� ltRERvR‚ ltSERvRƒ ltTERvR„ ltUERxR… ltVERvR† ltWERvR‡ ltXERvRˆ ltYERvR‰ RŠ lltZ]Zt[ERvR‹ lt\ERvRŒ lt]ERvR� lt^ERvRŽ lt_ERvR� lt`ERvR� ltaERvR‘ ltbERvR’ ltcERvR“ ltdERvR” lteR• R– ltfR— R˜ ltgERvR™ lthERvRš ltiERvR› ltjERvRœ ltkERvR� ltlERvRž ltmERvRŸ ltnERvR  ltoERvR¡ ltpERvR¢ ltqERyR£ R¤ lltrERyR¥ R¦ lltsERvR§ lttERvR¨ ltuERvR© ltvERvRª ltwERvR« ltxERvR¬ ltyERvR­ ltzERvR® lt{ERvR¯ lt|ERvR° lt}ERvR± lt~ERvR² ltERvR³ lt€ERvR´ lt�ERvRµ lt‚ERvR¶ ltƒERvR· lt„ERvR¸ lt…ERvR¹ lt†ERvRº lt‡ERvR» ltˆERvR¼ lt‰ERzR½ ltŠERvR¾ lt‹ERvR¿ ltŒERvRÀ lt�ERvRÁ ltŽRÂ t�RÃ t�ER{RÄ RÅ llt‘]‘t’RÆ RÇ lt“ER{RÈ RÉ llt”RÊ t•RË t–RÌ t—RÍ t˜RÎ t™RÏ tšRÐ t›RÑ tœRÒ t�RÓ tžRÔ tŸRÕ t RÖ t¡ERvR× lt¢RØ t£RÙ t¤RÚ t¥RÛ t¦RÜ t§RÝ t¨RÞ t©Rß tªRà t«Rá Râ lt¬Rã Rä lt­Rå t®Ræ t¯Rç t°Rè t±Ré t²Rê t³Rë t´Rì tµRí t¶ERvRî lt·Rï t¸Rð t¹Rñ tºRò t»Ró t¼Rô t½Rõ t¾ERvRö lt¿ERvR÷ ltÀERvRø ltÁERvRù ltÂERvRú ltÃRû tÄRü tÅRý tÆ]ÆtÇRþ tÈERvRÿ ltÉERvER  ltÊERvER ltËERvER ltÌERvER ltÍERvER ltÎERvER ltÏERvER ltÐER tÑ]ÑtÒ]ÑtÓ]ÑtÔER tÕER	 tÖER
 t×ER tØER tÙER tÚER tÛER tÜER tÝER tÞER tßER tàER táER tâER tãER täER tåER tæER tçER tèER téER têER tëER tìER  tíER! tîER" tïER# tðER$ tñER% tòER& tóER' tôER( tõER) töER* t÷ER+ tøER, tùERvER- ltúERvER. ltûER|ER/ ltüER0 týER1 tþER2 tÿER3 Et ER4 EtER5 EtER6 EtER7 EtER8 EtER9 EtER: EtER; EtER< Et	ERvER= lEt
ER> EtER? EtER@ EtERA EtERB EtERC EtERD EtERE EtERF EtERG EtERH EtERI EtERJ EtERK EtE]EtERL EtERM EtERN EtERO EtERP EtERQ EtERR Et ERS Et!ERT Et"ERU Et#ERV Et$ERW Et%ERX Et&ERY Et'ERZ Et(ER[ Et)ER\ Et*ER] Et+ER^ Et,ER_ Et-ER` Et.ERa Et/ERb Et0ERc Et1ERd Et2ERvERe lEt3ERvERf lEt4ERvERg lEt5ERvERh lEt6ERvERi lEt7ERvERj lEt8ERk Et9ERl Et:ERm Et;ERn Et<ERo Et=ERp Et>ERq Et?ERr Et@ERs EtAV 3ERt lEtBERuEtCV ;EtD# (}  ÚLatexPrinterÚ_latexÚ	full_precFÚfold_frac_powersÚfold_func_bracketsÚfold_short_fracNÚinv_trig_styleÚabbreviatedÚitexÚln_notationÚlong_frac_ratioÚ	mat_delimÚ[Úmat_strÚmodeÚplainÚ
mul_symbolÚorderÚsymbol_namesÚroot_notationTÚmat_symbol_styleÚimaginary_unitÚiÚgothic_re_imÚdecimal_separatorÚperiodÚperm_cyclicÚparenthesize_superÚminÚmaxÚdiff_operatorÚdÚadjoint_styleÚdaggerÚdisable_split_super_subzdict[str, Any]Ú_default_settingsc                	ó0  € \         P                  ! W4       R V P                  9   d(   . R'OpV P                  R ,          V9  d   \        R4      hV P                  R,          f(   V P                  R ,          R8X  d   RV P                  R&   RRRRR	R
RR/p W0P                  R,          ,          V P                  R&    Y0P                  R,          ;'       g    R	,          V P                  R&   RRRR/V n        RRRRRRRRRRRRRR/pV P                  R,          pVP                  WU4      V P                  R&   RR R R R!R"R#R$/pV P                  R%,          pVP                  Ww4      V P                  R&&   R#   \         d$    T P                  R,          T P                  R&    Lçi ; i  \         dd    T P                  R,          P                  4       R(9   d   TR	,          T P                  R&    ELT P                  R,          T P                  R&    EL'i ; i))rª   ÚinlinezB'mode' must be one of 'inline', 'plain', 'equation' or 'equation*'r¡   NTÚ Úldotz \,.\, r]   ú \cdot Útimesú \times r¬   Úmul_symbol_latexÚmul_symbol_latex_numbersÚ(Ú)r¨   Ú]r²   Úriz
\mathrm{i}Útiz\text{i}ÚjÚrjz
\mathrm{j}Útjz\text{j}r±   Úimaginary_unit_latexr»   Úrdz
\mathrm{d}Útdz\text{d}rº   Údiff_operator_latex)rÁ   r«   Úequationz	equation*)Ú rÂ   r•   z\,z\:ú\;z\quad)r   Ú__init__Ú	_settingsÚ
ValueErrorÚKeyErrorÚstripÚ_delim_dictÚget)ÚselfÚsettingsÚvalid_modesÚmul_symbol_tableÚimaginary_unit_tableÚ	imag_unitÚdiff_operator_tablerº   s   &&      rS   rØ   ÚLatexPrinter.__init__®   s(  € Ü×Ò˜Ô(à�T—^‘^Ô#ò(ˆKà�~‰~˜fÕ%¨[Ô8Ü ð "=ó >ð >ð �>‰>Ð+Õ,Ò4Ø—‘˜vÕ&¨(Ô2Ø04ˆD�N‰NÐ,Ñ-ð �$Ø�JØ�:Ø�[ð	
Ðð	-à §¡°Õ!=Õ>ð �N‰NÐ-Ñ.ð

	1à §¡°Õ!=×!FÐ!FÀÕGð �N‰NÐ5Ñ6ð    c¨3Ð/ˆÔð �$Ø�Ø�-Ø�+Ø�Ø�-Ø�+ð 
Ðð —N‘NÐ#3Õ4ˆ	Ø1E×1IÑ1IÈ)Ó1_ˆ�‰Ð-Ñ.ð �$Ø�Ø�-Ø�+ð	
Ðð Ÿ™ Õ7ˆØ0C×0GÑ0GÈÓ0eˆ�‰Ð,Ó-øôI ô 	-à—‘˜|Õ,ð �N‰NÐ-Ó.ð	-ûô ô 	1Ø—‘˜|Õ,×2Ñ2Ó4ØBôCð % UÕ+ð —‘Ð9Ô:ð —N‘N <Õ0ð —‘Ð9Ô:ð	1ús1   Â&E6 Â=F' ÃF' Å6+F$Æ#F$Æ'AHÇ1 HÈHc               ó   € V ^8„  d   QhRR/# ©r�   r‘   r�   rP   )r’   s   "rS   r“   ÚLatexPrinter.__annotate__ë   s   € ÷ ,ñ , ñ ,rU   c                	ó$   € R P                  V4      # )z\left({}\right)©r’   ©rß   rR   s   &&rS   Ú_add_parensÚLatexPrinter._add_parensë   s   € Ø!×(Ñ(¨Ó+Ð+rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   ï   s   € ÷ -ñ - sñ -rU   c                	ó$   € R P                  V4      # )z\left( {}\right)rë   rì   s   &&rS   Ú_add_parens_lspaceÚLatexPrinter._add_parens_lspaceï   s   € Ø"×)Ñ)¨!Ó,Ð,rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   ò   s   € ÷ %ñ %Àsñ %rU   c                	ó  € \        V4      pV'       d)   V'       d!   V P                  V P                  V4      4      # WR8  g   V'       g'   WR8:  d!   V P                  V P                  V4      4      # V P                  V4      # ©N)r   rí   Ú_print)rß   ÚitemÚlevelÚis_negÚstrictÚprec_vals   &&&&& rS   ÚparenthesizeÚLatexPrinter.parenthesizeò   sa   € Ü)¨$Ó/ˆß—fØ×#Ñ# D§K¡K°Ó$5Ó6Ð6àÔ§v°8Ô3DØ×#Ñ# D§K¡K°Ó$5Ó6Ð6à—;‘;˜tÓ$Ð$rU   c                óŠ   € RV9   d<   V P                   R,          '       d   V P                  V4      # RP                  V4      # V# )zt
Protect superscripts in s

If the parenthesize_super option is set, protect with parentheses, else
wrap in braces.
r—   r·   z{{{}}})rÙ   rí   r’   rì   s   &&rS   r·   ÚLatexPrinter.parenthesize_superü   s@   € ð �!Œ8Ø�~‰~Ð2×3Ô3Ø×'Ñ'¨Ó*Ð*à—‘ qÓ)Ð)ØˆrU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   
  s   € ÷ Eñ E˜sñ ErU   c                	ó,  € \         P                  ! W4      pV P                  R ,          R8X  d   V# V P                  R ,          R8X  d
   RV,          # V P                  R,          '       d
   RV,          # V P                  R ,          pRV: RV: RV: R2# )	rª   r«   rÁ   z$%s$r¤   z$$%s$$z\begin{rO   z\end{)r   ÚdoprintrÙ   )rß   ÚexprÚtexÚenv_strs   &&  rS   r  ÚLatexPrinter.doprint
  su   € Ü�oŠo˜dÓ)ˆà�>‰>˜&Õ! WÔ,ØˆJØ�^‰^˜FÕ# xÔ/Ø˜S•=Ð Ø�^‰^˜F×#Ô#Ø˜s•?Ð"à—n‘n VÕ,‰GÛ.5³s»GÐDÐDrU   c               ó   € V ^8„  d   QhRR/# ©r�   r‘   ÚboolrP   )r’   s   "rS   r“   ré     s   € ÷ Kñ K tñ KrU   c                óÔ   € VP                   ;'       d    VP                  ;'       g=    VP                  ;'       d)    V\        P                  J;'       d    VP
                  RJ '       * # )z¡
Returns True if the expression needs to be wrapped in brackets when
printed, False otherwise. For example: a + b => True; a => False;
10 => False; -10 => True.
F)Ú
is_IntegerÚis_nonnegativeÚis_Atomr   ÚNegativeOneÚis_Rational©rß   r  s   &&rS   Ú_needs_bracketsÚLatexPrinter._needs_brackets  si   € ð —_‘_×<Ð<¨×)<Ñ)<÷ Jð JØŸ™÷ Ið I¨$´a·m±mÐ*C÷ +Hð +HØ.2×.>Ñ.>À%Ð.GôKð 	KrU   c               ó   € V ^8„  d   QhRR/# r  rP   )r’   s   "rS   r“   ré   !  s   € ÷ ñ °ñ rU   c                ó0  € V P                  V4      '       g   R# VP                  '       d   V P                  V4      '       g   R# VP                  '       d   V P	                  V4      '       g   R# VP
                  '       g   VP                  '       d   R# R# )aX  
Returns True if the expression needs to be wrapped in brackets when
passed as an argument to a function, False otherwise. This is a more
liberal version of _needs_brackets, in that many expressions which need
to be wrapped in brackets when added/subtracted/raised to a power do
not need them when passed to a function. Such an example is a*b.
FT)r  Úis_MulÚ_mul_is_cleanÚis_PowÚ_pow_is_cleanÚis_AddÚis_Functionr  s   &&rS   Ú_needs_function_bracketsÚ%LatexPrinter._needs_function_brackets!  sl   € ð ×#Ñ# D×)Ò)Ùð �{�{ˆ{ 4×#5Ñ#5°d×#;Ò#;Ùà——� T×%7Ñ%7¸×%=Ò%=Ùà——� × 0× 0Ð 0ÙárU   c               ó   € V ^8„  d   QhRR/# r  rP   )r’   s   "rS   r“   ré   8  s   € ÷ ñ ÀDñ rU   c                óP  a€ ^ RI Hp ^ RIHp ^ RIHp SP                  '       d"   V'       g   SP                  4       '       d   R# M1\        S4      \        R,          8  d   R# SP                  '       d   R# SP                  '       d   R# \        ;QJ d$    V3R l\        3 4       F  '       g   K   RM	  RM! V3R l\        3 4       4      '       d   R# V'       gG   \        ;QJ d!    V3R lWdV3 4       F  '       g   K   RM	  RM! V3R lWdV3 4       4      '       d   R# R# )	a‡  
Returns True if the expression needs to be wrapped in brackets when
printed as part of a Mul, False otherwise. This is True for Add,
but also for some container objects that would not need brackets
when appearing last in a Mul, e.g. an Integral. ``last=True``
specifies that this expr is the last to appear in a Mul.
``first=True`` specifies that this expr is the first to appear in
a Mul.
)ÚProduct)ÚSum)ÚIntegralTr	   c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   ©Úhas©Ú.0Úxr  s   & €rS   Ú	<genexpr>Ú3LatexPrinter._needs_mul_brackets.<locals>.<genexpr>O  ó   øé € Ð+¡F˜qˆt�x‰x˜�{ˆ{£Fùó   ƒ!Fc              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r#  r%  s   & €rS   r(  r)  R  s   øé € ÐBÑ)A A�D—H‘H˜Q—K�KÓ)Aùr+  )Úsympy.concrete.productsr  Úsympy.concrete.summationsr   Úsympy.integrals.integralsr!  r  Úcould_extract_minus_signr   r    Úis_RelationalÚis_PiecewiseÚanyr   )rß   r  ÚfirstÚlastr  r   r!  s   &f&&   rS   Ú_needs_mul_bracketsÚ LatexPrinter._needs_mul_brackets8  s»   ø€ õ 	4Ý1Ý6à�;�;ˆ;ß˜T×:Ñ:×<Ò<ÙøÜ# DÓ)¬J°uÕ,=Ô=ÙØ××ÐÙØ××ÐÙß‹3Ô+¤S¡FÓ+�3�3Š3Ô+¤S¡FÓ+×+Ò+Ùßß“ÔB¨(¸SÑ)AÓB——’ÔB¨(¸SÑ)AÓB×BÒBÙárU   c               ó   € V ^8„  d   QhRR/# r  rP   )r’   s   "rS   r“   ré   W  s   € ÷ ñ ¨4ñ rU   c                óð   a€ SP                   '       d   R# \        ;QJ d$    V3R l\        3 4       F  '       g   K   RM	  RM! V3R l\        3 4       4      '       d   R# SP                  '       d   R# R# )z‘
Returns True if the expression needs to be wrapped in brackets when
printed as part of an Add, False otherwise.  This is False for most
things.
Tc              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r#  r%  s   & €rS   r(  Ú3LatexPrinter._needs_add_brackets.<locals>.<genexpr>_  r*  r+  F)r1  r3  r   r  r  s   &frS   Ú_needs_add_bracketsÚ LatexPrinter._needs_add_bracketsW  sK   ø€ ð ××ÐÙß‹3Ô+¤S¡FÓ+�3�3Š3Ô+¤S¡FÓ+×+Ò+ÙØ�;�;ˆ;ÙÙrU   c               ó   € V ^8„  d   QhRR/# r  rP   )r’   s   "rS   r“   ré   e  s   € ÷ ñ  Tñ rU   c                	óV   € VP                    F  pVP                  '       g   K   R # 	  R# )FT)Úargsr  ©rß   r  Úargs   && rS   r  ÚLatexPrinter._mul_is_cleane  s!   € Ø—9”9ˆCØ��ŠÚñ ñ rU   c               ó   € V ^8„  d   QhRR/# r  rP   )r’   s   "rS   r“   ré   k  s   € ÷ 3ñ 3 Tñ 3rU   c                	óB   € V P                  VP                  4      '       * # rõ   )r  Úbaser  s   &&rS   r  ÚLatexPrinter._pow_is_cleank  s   € Ø×'Ñ'¨¯	©	Ó2Ô2Ð2rU   c               ó   € V ^8„  d   QhRR/# )r�   r  r�   rP   )r’   s   "rS   r“   ré   n  s   € ÷ ñ  ñ rU   c                	ó$   € Ve   RV: RV: R2# V# )Nú\left(ú	\right)^{rO   rP   ©rß   r  Úexps   &&&rS   Ú_do_exponentÚLatexPrinter._do_exponentn  s   € Ø‹?Û.2³CÐ8Ð8àˆKrU   c                	ó4  € V P                  VP                  P                  4      pVP                  '       dM   VP                   Uu. uF  q0P	                  V4      NK  	  ppR pVP                  VRP                  V4      4      # RP                  V4      # u upi )z"\operatorname{{{}}}\left({}\right)ú, z\text{{{}}})Ú_deal_with_super_subÚ	__class__Ú__name__r@  rö   r’   Újoin)rß   r  Únamer7   ÚlsrR   s   &&    rS   Ú_print_BasicÚLatexPrinter._print_Basict  sw   € Ø×(Ñ(¨¯©×)@Ñ)@ÓAˆØ�9�9ˆ9Ø*.¯)ª)Ó4©) Q—+‘+˜a–.©)ˆBÐ4Ø5ˆAØ—8‘8˜D $§)¡)¨B£-Ó0Ð0à!×(Ñ(¨Ó.Ð.ùò	 5s   ÁBc               ó   € V ^8„  d   QhRR/# )r�   Úez!bool | BooleanTrue | BooleanFalserP   )r’   s   "rS   r“   ré   }  s   € ÷  ñ  Ð>ñ  rU   c                	ó   € R V,          # ©ú	\text{%s}rP   ©rß   r[  s   &&rS   Ú_print_boolÚLatexPrinter._print_bool}  ó   € Ø˜aÕÐrU   c                	ó   € R V,          # r]  rP   r_  s   &&rS   Ú_print_NoneTypeÚLatexPrinter._print_NoneTypeƒ  rb  rU   c                	ó0  € V P                  WR 7      pRp\        V4       Fr  w  rVV^ 8X  d   M,VP                  4       '       d   VR,          pV) pM	VR,          pV P                  V4      pV P	                  V4      '       d
   RV,          pWG,          pKt  	  V# ))r­   rÖ   ú - ú + ú\left(%s\right))Ú_as_ordered_termsÚ	enumerater0  rö   r<  )rß   r  r­   Útermsr  r²   ÚtermÚterm_texs   &&&     rS   Ú
_print_AddÚLatexPrinter._print_Add†  s”   € Ø×&Ñ& tÐ&Ó9ˆàˆÜ  Ö'‰GˆAØ�AŒvØØ×.Ñ.×0Ò0Ø�u•�Ø�u‘à�u•�Ø—{‘{ 4Ó(ˆHØ×'Ñ'¨×-Ò-Ø-°Õ8�Ø�OŠCñ (ð ˆ
rU   c                	óz  € ^ RI Hp VP                  ^ 8X  d   R# V! V4      pVP                  pVP                  pVP                  R
,          V^,
          8X  d   W4^,
          ..,           pRpV F%  pV\        V4      P                  RR4      ,          pK'  	  VP                  RR4      pVP                  RR	4      pV# )é    ©ÚPermutationú\left( \right)rÖ   Ú,r×   r¨   ú\left( rË   ú\right)éÿÿÿÿ)Ú sympy.combinatorics.permutationsrt  ÚsizeÚcyclic_formÚ
array_formr�   r˜   )rß   r  rt  Ú	expr_permÚsizrn  r²   s   &&     rS   Ú_print_CycleÚLatexPrinter._print_Cycle™  s§   € Ý@Ø�9‰9˜Œ>Ù$Ù˜4Ó ˆØ×$Ñ$ˆ	Ø�i‰iˆØ�?‰?˜2Õ #¨¥'Ô)Ø!¨A¥g Y KÕ/ˆIØˆÛˆAØœ˜A›Ÿ™ s¨EÓ2Õ2ŠHñ à×#Ñ# C¨Ó4ˆØ×#Ñ# C¨Ó4ˆØˆrU   c                	ó.  € ^ RI Hp ^ RIHp VP                  pVe   V! RV R2RR^R7       MV P
                  P                  RR	4      pV'       d   V P                  V4      # VP                  ^ 8X  d   R
# VP                   Uu. uF  qPP                  V4      NK  	  pp\        \        V4      4       Uu. uF  qPP                  V4      NK  	  ppRP                  V4      pRP                  V4      p	RP                  W‰34      p
RV
,          # u upi u upi )rr  rs  )Úsympy_deprecation_warningzw
                Setting Permutation.print_cyclic is deprecated. Instead use
                init_printing(perm_cyclic=z).
                z1.6z#deprecated-permutation-print_cyclic)Údeprecated_since_versionÚactive_deprecations_targetÚ
stacklevelr¶   Tru  ú & ú \\ z \begin{pmatrix} %s \end{pmatrix})rz  rt  Úsympy.utilities.exceptionsrƒ  Úprint_cyclicrÙ   rÞ   r€  r{  r}  rö   ÚrangeÚlenrU  )rß   r  rt  rƒ  r¶   rB  ÚlowerÚupperÚrow1Úrow2Úmats   &&         rS   Ú_print_PermutationÚLatexPrinter._print_Permutation©  sþ   € Ý@ÝHà!×.Ñ.ˆØÒ"Ù%ð+à+6¨-ð 8ðð */Ø+PØöð Ÿ.™.×,Ñ,¨]¸DÓAˆKçØ×$Ñ$ TÓ*Ð*à�9‰9˜Œ>Ù$à-1¯_ª_Ó=©_ c—‘˜SÖ!©_ˆÐ=Ü-2´3°u³:Ô->Ó?Ñ-> c—‘˜SÖ!Ñ->ˆÐ?à�z‰z˜%Ó ˆØ�z‰z˜%Ó ˆØ�l‰l˜D˜<Ó(ˆØ2°SÕ8Ð8ùò >ùÚ?s   ÂDÂ5Dc                	óp   € VP                   w  r#R V P                  V4      : RV P                  V4      : R2# )z\sigma_{z}(rÊ   ©r@  rö   )rß   r  ÚpermÚvars   &&  rS   Ú_print_AppliedPermutationÚ&LatexPrinter._print_AppliedPermutationÊ  s,   € Ø—I‘I‰	ˆˆcØ%)§[¡[°Ö%6¸¿¹ÀCÖ8HÐIÐIrU   c                	ó   € \        VP                  4      pV P                  R ,          '       d   RMRpRV P                  9   d   V P                  R,          MRpRV P                  9   d   V P                  R,          MRp\        VP                  W#WER7      pV P                  R,          pRV9   db   VP                  R4      w  r‰V	^ ,          R	8X  d
   V	R
,          p	V P                  R,          R8X  d   VP                  RR4      pV: V: RV	: R2# VR8X  d   R# VR8X  d   R# V P                  R,          R8X  d   VP                  RR4      pV# )rž   FTr¸   Nr¹   )Ústrip_zerosÚ	min_fixedÚ	max_fixedrÈ   r[  Ú+ºé   NNr´   ÚcommaÚ.z{,}z10^{rO   z+infz\inftyz-infz- \infty)r!   Ú_precrÙ   Úmlib_to_strÚ_mpf_Úsplitr˜   )
rß   r  ÚdpsrÜ   ÚlowÚhighÚstr_realÚ	separatorÚmantrM  s
   &&        rS   Ú_print_FloatÚLatexPrinter._print_FloatÎ  s  € ä˜$Ÿ*™*Ó%ˆØŸ™¨×4Ô4‘¸$ˆØ',°·±Ô'>ˆd�n‰n˜UÖ#ÀDˆØ(-°·±Ô(?ˆt�~‰~˜eÖ$ÀTˆÜ˜tŸz™z¨3ÈSÔaˆð —N‘NÐ#=Õ>ˆ	à�(Œ?Ø"Ÿ.™.¨Ó-‰KˆTà�1�v˜Œ}Ø˜"•g�Ø�~‰~Ð1Õ2°gÔ=Ø—|‘| C¨Ó.�â%)«9³cÐ:Ð:Ø˜ÔÙØ˜ÔÙà�~‰~Ð1Õ2°gÔ=Ø#×+Ñ+¨C°Ó6�ØˆOrU   c                	ó°   € VP                   pVP                  pV P                  V\        R ,          4      : RV P                  V\        R ,          4      : 2# )r	   rÆ   ©Ú_expr1Ú_expr2rü   r    ©rß   r  Úvec1Úvec2s   &&  rS   Ú_print_CrossÚLatexPrinter._print_Crossì  sJ   € Ø�{‰{ˆØ�{‰{ˆØ"&×"3Ñ"3°D¼*ÀUÕ:KÖ"LØ"&×"3Ñ"3°D¼*ÀUÕ:KÕ"LðNð 	NrU   c                	ób   € VP                   pR V P                  V\        R,          4      ,          # )z\nabla\times %sr	   ©Ú_exprrü   r    ©rß   r  rn   s   && rS   Ú_print_CurlÚLatexPrinter._print_Curlò  s(   € Ø�j‰jˆØ! D×$5Ñ$5°c¼:ÀeÕ;LÓ$MÕMÐMrU   c                	ób   € VP                   pR V P                  V\        R,          4      ,          # )z\nabla\cdot %sr	   r¹  r»  s   && rS   Ú_print_DivergenceÚLatexPrinter._print_Divergenceö  s(   € Ø�j‰jˆØ  4×#4Ñ#4°S¼*ÀUÕ:KÓ#LÕLÐLrU   c                	ó°   € VP                   pVP                  pV P                  V\        R ,          4      : RV P                  V\        R ,          4      : 2# )r	   rÄ   r°  r³  s   &&  rS   Ú
_print_DotÚLatexPrinter._print_Dotú  sJ   € Ø�{‰{ˆØ�{‰{ˆØ!%×!2Ñ!2°4¼ÀEÕ9JÖ!KØ!%×!2Ñ!2°4¼ÀEÕ9JÕ!KðMð 	MrU   c                	ób   € VP                   pR V P                  V\        R,          4      ,          # )z	\nabla %sr	   r¹  ©rß   r  Úfuncs   && rS   Ú_print_GradientÚLatexPrinter._print_Gradient   ó(   € Ø�z‰zˆØ˜d×/Ñ/°´jÀÕ6GÓHÕHÐHrU   c                	ób   € VP                   pR V P                  V\        R,          4      ,          # )z	\Delta %sr	   r¹  rÅ  s   && rS   Ú_print_LaplacianÚLatexPrinter._print_Laplacian  rÉ  rU   c               ó   € V ^8„  d   QhRR/# )r�   r  r   rP   )r’   s   "rS   r“   ré     s   € ÷ qñ q˜tñ qrU   c                	óx  a aaa€ ^ RI Hp S P                  R,          oS P                  R,          oR VV 3R llpR VV V3R llo\        V\        4      '       dx   VP
                  pV^ ,          \        P                  J gI   \        ;QJ d#    R VR	,           4       F  '       g   K   R
M	  RM! R VR	,           4       4      '       d	   S! V4      # RpVP                  4       '       d$   V) pRpVP                  '       d   VR,          pR
pMRpV! VR
R7      w  rxV\        P                  J d.   \        ^RRR7      VP
                  9  d   Wc! V4      ,          pEMLV! V4      p	V! V4      p
\        V
P                  4       4      pS P                  R,          pS P                  R,          '       dL   V^8:  dE   RV
9  d>   S P                  VRR7      '       d   VRV	: RV
: 2,          pEM½Wi: RV
: 2,          pEM¬VEe–   \        V	P                  4       4      WË,          8”  Edq   S P                  VR
R7      '       d   VRV
: RS: RV	: R2,          pEMQVP                  '       Ed   \        P                  p\        P                  pVP
                   F‚  pS P                  VRR7      '       gU   \        V! Wß,          4      P                  4       4      WË,          8”  g%   VP                   VP                   u;J d   RJ d   M M
Wï,          pKz  Wß,          pK„  	  S P                  VR
R7      '       d(   VRV! V4      : RV
: RS: RV! V4      : R2	,          pMLVRV! V4      : RV
: RS: V! V4      : 2,          pM'VRV
: RS: V	: 2,          pMVRV	: RV
: R2,          pV'       d
   VR,          pV# )rr  )ÚfractionrÇ   rÈ   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   Ú-LatexPrinter._print_Mul.<locals>.__annotate__  s   € ÷ 	Añ 	A˜Sñ 	ArU   c                ó8  <€ V P                   '       g   \        SP                  V 4      4      # SP                  R9  d   V P	                  4       pM\        V P                  4      p\        VR RR7      w  r#\        VR RR7      w  rBS! W4,           V,           4      # )Úoldc                ó®   € \        V R 4      ;'       gC    \        V R4      ;'       g/    \        V \        4      ;'       d    \        V P                  R4      # )Ú_scale_factorÚis_physical_constant)ÚhasattrÚ
isinstancer   rF  ©r'  s   &rS   rT   Ú:LatexPrinter._print_Mul.<locals>.convert.<locals>.<lambda>  sW   € ¼ÀÀ?Ó8S÷ 8HÐ8yÔW^Ð_`ÐbxÓWy÷ 8Hð 8HÜ)¨!¬SÓ1÷  Gð  GÜ& q§v¡vÐ/EÓFð8HrU   T)Úbinaryc                ó   € \        V R 4      # )rÕ  )r×  rÙ  s   &rS   rT   rÚ    s   € ¼ÀÀ?Ô8SrU   )rÓ  Únone)r  r�   rö   r­   Úas_ordered_factorsÚlistr@  r$   )r  r@  ÚunitsÚnonunitsÚprefixesÚconvert_argsrß   s   &    €€rS   ÚconvertÚ(LatexPrinter._print_Mul.<locals>.convert  sˆ   ø€ Ø—;—;�;Ü˜4Ÿ;™; tÓ,Ó-Ð-à—:‘: _Ô4Ø×2Ñ2Ó4‘Dä §	¡	›?�Dô #' tñ .HàPTô#V‘�ô #' uÑ.SÐ\`Ô"a‘�Ù# HÕ$7¸%Õ$?Ó@Ð@rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   rÑ    s   € ÷ 	ñ 	 #ñ 	rU   c           	     ó  <€ R ;r\        V 4       Fí  w  r4SP                  V4      p\        VR4      '       g«   \        VR4      '       g™   SP                  WC^ 8H  V\	        V 4      ^,
          8H  R7      '       d
   RV,          p\
        ^ ,          P                  V4      '       d-   \
        ^,          P                  V4      '       d   VS,          pM#V'       d
   VS,          pMV'       d
   VS,          pW,          pTpKï  	  V# )rÖ   rÕ  rÖ  )r4  r5  ri  )rk  rö   r×  r6  rŒ  Ú_between_two_numbers_pÚsearchÚmatch)	r@  Ú_texÚlast_term_texr²   rm  rn  Ú	numberseprß   r«  s	   &     €€€rS   rã  Ú-LatexPrinter._print_Mul.<locals>.convert_args  sâ   ø€ Ø#%Ð%ˆDä$ Tž?‘�ØŸ;™; tÓ,�Ü  o×6Ò6¼'À$ÐH^×:_Ò:_Ø×/Ñ/°À!¹VØ67¼3¸t»9Àq½=Ñ6Hð 0÷ Kò Kà#5¸Õ#@˜ä.¨qÕ1×8Ñ8¸×GÒGÜ.¨qÕ1×7Ñ7¸×AÒAà 	Õ)™ßØ 	Õ)˜øßØ˜IÕ%�DàÕ �Ø (’ñ# +ð$ ˆKrU   c              3  óB   "  € T F  p\        V\        4      x € K  	  R # 5irõ   )rØ  r
   )r&  rB  s   & rS   r(  Ú*LatexPrinter._print_Mul.<locals>.<genexpr>;  s   é € Ð&SÉ(À3¤z°#´v×'>Ð'>Ë(ùs   ‚rŸ  TFú- rÉ   rÖ   )Úexact)Úevaluater¦   r¡   r—   )r5  rJ  z
\right) / z / z	\frac{1}{rO   rx  ú\frac{ú}{rÊ   ry  )Úsympy.simplifyrÏ  rÙ   rØ  r	   r@  r   ÚOner3  r0  r  r   rŒ  r¦  r6  r  Úis_commutative)rß   r  rÏ  rä  r@  Úinclude_parensr  ÚnumerÚdenomÚsnumerÚsdenomÚldenomÚratioÚaÚbr'  rã  rí  r«  s   f&              @@@rS   Ú
_print_MulÚLatexPrinter._print_Mul  sð  û€ Ý+ØŸ™Ð(:Õ;ˆ	ØŸ™Ð(BÕCˆ	÷	Añ 	A÷ 	ò 	ô8 �dœC× Ò Ø—9‘9ˆDØ�A�wœ!Ÿ%™%Ó§3£3Ñ&SÈ$ÈrÎ(Ó&S§3§3¢3Ñ&SÈ$ÈrÎ(Ó&S×#SÒ#SÙ# DÓ)Ð)àˆØ×(Ñ(×*Ò*Ø�5ˆDØˆCØ�{�{ˆ{Ø�s•
�Ø!%�øàˆCá ¨DÔ1‰ˆà”A—E‘E‹>œc ! R°%Ô8ÀÇ	Á	ÔIð �7˜4“=Õ ŠCñ ˜U“^ˆFÙ˜U“^ˆFÜ˜Ÿ™›Ó(ˆFØ—N‘NÐ#4Õ5ˆEØ�~‰~Ð/×0Ô0°V¸q´[Ø˜vÔ%à×+Ñ+¨E¸Ð+×>Ò>Ù³fºfÐEÕE’Càª²Ð8Õ8’CØÓ"Ü˜Ÿ™›Ó'¨%­,Õ6à×+Ñ+¨E¸Ð+×=Ò=ÙÛ!£9«fð6õ 6’Cà—\—\‘\äŸ™�AÜŸ™�AØ"ŸZœZ˜Ø×3Ñ3°A¸EÐ3×BÒBÜ #¡G¨A­C£L×$6Ñ$6Ó$8Ó 9¸E½LÔ HØ!"×!1Ñ!1°Q×5EÑ5EÕ!NÈÖ!NØ�FšAà�FšAñ (ð ×/Ñ/°¸Ð/×=Ò=ÙÙ& qžz«6³9¹gÀa¾jð Jõ J™ñ Ù& qžz«6²9¹gÀa½jð Jõ J™ñ ³&º)ÂVÐLÕL‘Cá«6³6Ð:Õ:�çØ�3�JˆCØˆ
rU   c                	ó¾   € VP                   '       d.   V P                  VP                  4       P                  4       4      # V P                  VP                  4       4      # rõ   )Ú
is_aliasedrö   Úas_polyÚas_exprr  s   &&rS   Ú_print_AlgebraicNumberÚ#LatexPrinter._print_AlgebraicNumber{  s>   € Ø�?�?ˆ?Ø—;‘;˜tŸ|™|›~×5Ñ5Ó7Ó8Ð8à—;‘;˜tŸ|™|›~Ó.Ð.rU   c                	óÌ   € V P                  VP                  4      pVP                  '       d   R V R2# V P                  VP                  P	                  4       4      pR V RV R2# )rJ  rx  rQ  )rö   ÚpÚis_inertÚalphar  )rß   r  r  r  s   &&  rS   Ú_print_PrimeIdealÚLatexPrinter._print_PrimeIdeal�  s\   € Ø�K‰K˜Ÿ™ÓˆØ�=�=ˆ=Ø˜Q˜C˜wÐ'Ð'Ø—‘˜DŸJ™J×.Ñ.Ó0Ó1ˆØ˜˜˜2˜e˜W GÐ,Ð,rU   c               ó   € V ^8„  d   QhRR/# )r�   r  r   rP   )r’   s   "rS   r“   ré   ˆ  s   € ÷ +<ñ +<˜sñ +<rU   c                	ól  € VP                   P                  '       Ed´   VP                   P                  pVP                   P                  p\	        V4      ^8X  d¢   V^8w  d›   V P
                  R,          '       d‚   V P                  VP                  4      pV^8X  d   RV,          pM.V P
                  R,          '       d   RW43,          pM
RW43,          pVP                   P                  '       d
   RV,          # V# V P
                  R,          '       dª   V^8w  d£   V P                  VP                  \        R,          4      pVP                  P                  '       d   V P                  V4      pVP                  P                  '       d%   V P                  VP                  V: R	V: 2R
7      # V: RV: R	V: R2# VP                   P                  '       dù   VP                  P                  '       dÝ   VP                  ^8X  d   VP                  : RVP                   : R2# VP                  P                  '       d�   VP                  P                  pVP                  P                  pWg,          \	        V4      8X  d?   VP                   R8X  d   RV: RV: R2# RV: RV: R\	        VP                   4      : R2# V P                  V4      # VP                  P                  '       d7   V P                  VP                  V P                  VP                   4      R
7      # RpV P!                  W4      # )r   r¯   z	\sqrt{%s}r¤   z\root{%d}{%s}z\sqrt[%d]{%s}z\frac{1}{%s}rŸ   r   Ú/©rM  ú^{rO   z\frac{1}{\frac{rõ  ú}}z\frac{1}{(\frac{z})^{z%s^{%s}ry  )rM  r  r  Úqr†   rÙ   rö   rF  Úis_negativerü   r    Ú	is_Symbolr·   r  rø  r  Ú_helper_print_standard_power)rß   r  r  r  rF  r  Úbase_pÚbase_qs   &&      rS   Ú
_print_PowÚLatexPrinter._print_Powˆ  sG  € à�8‰8××ÑØ—X‘X—Z‘ZˆAØ—X‘X—Z‘ZˆAÜ�1‹v˜Œ{˜q Aœv¨$¯.©.¸×*IÔ*IØ—{‘{ 4§9¡9Ó-�Ø˜”6Ø&¨Õ-‘CØ—^‘^ F×+Ô+Ø*¨a¨YÕ6‘Cà*¨a¨YÕ6�CØ—8‘8×'×'Ð'Ø*¨SÕ0Ð0à�JØ—‘Ð 2×3Ô3¸¸Q¼Ø×(Ñ(¨¯©´J¸uÕ4EÓF�à—9‘9×&×&Ð&Ø×2Ñ2°4Ó8�DØ—9‘9×(×(Ð(ØŸ;™; t§y¡yÃÂAÐ6F˜;ÓGÐGÛ(,«a³Ð3Ð3Ø—‘×%×%Ð%¨$¯)©)×*B×*BÐ*Bà—9‘9 ”>Ø)-¯¬°D·H´HÐ=Ð=à—9‘9×(×(Ð(Ø"&§)¡)§+¡+�FØ"&§)¡)§+¡+�FØ•¬#¨f«+Ô5ØŸ8™8 r�>ÛAGËÐ#PÐPð *ó IOÓPVÔX[Ð\`×\dÑ\dÖXeÐ#fÐfà—‘ tÓ,Ð,Ø�9‰9× × Ð Ø—;‘;˜tŸy™y¨d¯k©k¸$¿(¹(Ó.C�;ÓDÐDØˆØ×0Ñ0°Ó;Ð;rU   c               ó    € V ^8„  d   QhRRRR/# )r�   Útemplater�   r‘   rP   )r’   s   "rS   r“   ré   µ  s   € ÷ &ñ &¸3ð &À3ñ &rU   c                	ó"  € V P                  VP                  4      pV P                  VP                  \        R ,          4      pVP                  P
                  '       d   V P                  V4      pM–VP                  P                  '       d   RV,          pMp\        VP                  \        4      '       dQ   VP                  R4      '       d:   \        P                  ! RV4      '       d   VP                  R4      '       d   V^R pW$V3,          # )r   z{%s}rJ  z\\left\(\\d?d?dotrx  iùÿÿÿ)rö   rM  rü   rF  r    r  r·   Úis_FloatrØ  r   Ú
startswithÚrerê  Úendswith)rß   r  r  rM  rF  s   &&&  rS   r  Ú)LatexPrinter._helper_print_standard_powerµ  sÃ   € Ø�k‰k˜$Ÿ(™(Ó#ˆð × Ñ  §¡¬J°uÕ,=Ó>ˆØ�9‰9××ÐØ×*Ñ*¨4Ó0‰DØ�Y‰Y××ÐØ˜T•>‰DÜ˜Ÿ™¤J×/Ò/Ø—‘ 	×*Ò*Ü—’Ð-¨t×4Ò4Ø—‘˜j×)Ò)à˜˜2�;ˆDØ ˜+Õ%Ð%rU   c                	óF   € V P                  VP                  ^ ,          4      # ©rr  ©rö   r@  r  s   &&rS   Ú_print_UnevaluatedExprÚ#LatexPrinter._print_UnevaluatedExprÆ  s   € Ø�{‰{˜4Ÿ9™9 Q�<Ó(Ð(rU   c           
     	ó4  a € \        VP                  4      ^8X  dD   R\        VP                  ^ ,           Uu. uF  pS P                  V4      NK  	  up4      ,          pMBV 3R lpR\        P                  RVP                   Uu. uF
  qT! V4      NK  	  up4      ,          p\        VP                  \        4      '       d,   VRS P                  VP                  4      ,          ,          pV# VS P                  VP                  4      ,          pV# u upi u upi )r   z\sum_{%s=%s}^{%s} c           	     ó    <€ R \        V ^,          V ^ ,          V ^,          3 Uu. uF  pSP                  V4      NK  	  up4      ,          # u upi ©z%s \leq %s \leq %s©Útuplerö   ©ÚlrR   rß   s   & €rS   Ú_format_ineqÚ-LatexPrinter._print_Sum.<locals>._format_ineqÎ  óI   ø€ Ø,Ü°A°aµD¸!¸A½$ÀÀ!ÅÑ3EÓFÑ3E¨a˜4Ÿ;™; qž>Ñ3EÑFÓGõHð HùÚFó   ¤A
z\sum_{\substack{%s}} ú\\ri  ©	rŒ  Úlimitsr/  rö   r�   rU  rØ  Úfunctionr   ©rß   r  r²   r  r2  r1  s   f&    rS   Ú
_print_SumÚLatexPrinter._print_SumÉ  sÞ   ø€ Üˆt�{‰{Ó˜qÔ Ø'Ü¨t¯{©{¸1®~Ó>©~¨!�t—{‘{ 1–~©~Ñ>Ó?õ@‰CõHð +Ü—‘˜¸4¿;º;Ó!G¹;°a ,¨q¦/¹;Ñ!GÓHõIˆCô �d—m‘m¤S×)Ò)ØÐ%¨¯©°D·M±MÓ(BÕBÕBˆCð ˆ
ð �4—;‘;˜tŸ}™}Ó-Õ-ˆCàˆ
ùò ?ùò "Hó   ·D
ÂDc           
     	ó4  a € \        VP                  4      ^8X  dD   R\        VP                  ^ ,           Uu. uF  pS P                  V4      NK  	  up4      ,          pMBV 3R lpR\        P                  RVP                   Uu. uF
  qT! V4      NK  	  up4      ,          p\        VP                  \        4      '       d,   VRS P                  VP                  4      ,          ,          pV# VS P                  VP                  4      ,          pV# u upi u upi )r   z\prod_{%s=%s}^{%s} c           	     ó    <€ R \        V ^,          V ^ ,          V ^,          3 Uu. uF  pSP                  V4      NK  	  up4      ,          # u upi r-  r.  r0  s   & €rS   r2  Ú1LatexPrinter._print_Product.<locals>._format_ineqá  r4  r5  z\prod_{\substack{%s}} r6  ri  r7  r:  s   f&    rS   Ú_print_ProductÚLatexPrinter._print_ProductÜ  sÞ   ø€ Üˆt�{‰{Ó˜qÔ Ø(Ü¨t¯{©{¸1®~Ó>©~¨!�t—{‘{ 1–~©~Ñ>Ó?õ@‰CõHð ,Ü—‘˜¸4¿;º;Ó!G¹;°a ,¨q¦/¹;Ñ!GÓHõIˆCô �d—m‘m¤S×)Ò)ØÐ%¨¯©°D·M±MÓ(BÕBÕBˆCð ˆ
ð �4—;‘;˜tŸ}™}Ó-Õ-ˆCàˆ
ùò ?ùò "Hr=  c               ó   € V ^8„  d   QhRR/# )r�   r  z'BasisDependent'rP   )r’   s   "rS   r“   ré   ï  s   € ÷ ñ Ð*:ñ rU   c                	ó  € ^ RI Hp . pWP                  8X  d   VP                  P                  # \	        W4      '       d    VP                  4       P                  4       pM^ V3.pV Fä  w  rV\        VP                  P                  4       4      pVP                  R R7       V F£  w  r‰V	^8X  d%   VP                  RVP                  ,           4       K0  V	R8X  d%   VP                  RVP                  ,           4       K[  RV P                  V	4      ,           R,           p
VP                  RV
,           VP                  ,           4       K¥  	  Kæ  	  RP                  V4      pV^,          R	8w  d   VR
,          pV# VR,          pV# )rr  )ÚVectorc                ó0   € V ^ ,          P                  4       # r'  )Ú__str__rÙ  s   &rS   rT   Ú4LatexPrinter._print_BasisDependent.<locals>.<lambda>ü  s   € ¨!¨A­$¯,©,¬.rU   ©Úkeyrh  rg  rJ  rx  rÖ   Ú-:é   NNrŸ  ry  )Úsympy.vectorrE  ÚzeroÚ_latex_formrØ  ÚseparateÚitemsrß  Ú
componentsÚsortÚappendrö   rU  )rß   r  rE  Úo1rQ  ÚsystemÚvectÚ
inneritemsÚkÚvÚarg_strÚoutstrs   &&          rS   Ú_print_BasisDependentÚ"LatexPrinter._print_BasisDependentï  s/  € Ý'àˆØ—9‘9ÔØ—9‘9×(Ñ(Ð(Ü�d×#Ò#Ø—M‘M“O×)Ñ)Ó+‰Eà˜�Y�KˆEã!‰LˆFÜ˜dŸo™o×3Ñ3Ó5Ó6ˆJØ�O‰OÑ 8ˆOÔ9Û"‘�Ø˜”6Ø—I‘I˜e a§m¡mÕ3Ö4Ø˜"”WØ—I‘I˜e a§m¡mÕ3Ö4à'¨$¯+©+°a«.Õ8¸:ÕE�GØ—I‘I˜e g�o°·±Õ=Ö>ó #ñ "ð —'‘'˜"“+ˆØ�!�9˜ÔØ˜B•ZˆFð ˆð ˜B•ZˆFØˆrU   c                	óÒ   € V P                  VP                  4      pR V,           R,           RRP                  \        V P                   VP                  4      4      ,          ,           pV# )rs   rO   ú_{%s}rv  )rö   rF  rU  ÚmapÚindices)rß   r  Útex_baser  s   &&  rS   Ú_print_IndexedÚLatexPrinter._print_Indexed  sP   € Ø—;‘;˜tŸy™yÓ)ˆØ�(�l˜3Õ˜w¨¯©Ü�—‘˜TŸ\™\Ó*ó*,õ  ,õ ,ˆàˆ
rU   c                	ó8   € V P                  VP                  4      # rõ   )rö   Úlabelr  s   &&rS   Ú_print_IndexedBaseÚLatexPrinter._print_IndexedBase  s   € Ø�{‰{˜4Ÿ:™:Ó&Ð&rU   c                	óh  € V P                  VP                  4      pVP                  e‰   V P                  VP                  4      pVP                  e   V P                  VP                  4      pMV P                  \        P
                  4      pRP                  WCR7      pRP                  W%R7      # V# )Nz%{lower}\mathrel{{..}}\nobreak {upper})r�  rŽ  z{{{label}}}_{{{interval}}})rg  Úinterval)rö   rg  rŽ  r�  r   ÚZeror’   )rß   r  rg  rŽ  r�  rk  s   &&    rS   Ú
_print_IdxÚLatexPrinter._print_Idx  s™   € Ø—‘˜DŸJ™JÓ'ˆØ�:‰:Ò!Ø—K‘K §
¡
Ó+ˆEØ�z‰zÒ%ØŸ™ D§J¡JÓ/‘àŸ™¤A§F¡FÓ+�Ø@×GÑGØ!ð Hó 2ˆHà/×6Ñ6Øð 7ó 4ð 4ð ˆrU   c           	     	óJ  € \        VP                  4      '       d   R pMV P                  R,          pRp^ p\        VP                  4       Fu  w  rVWF,          pV^8X  d!   W2: RV P                  V4      : 2,          pK4  W2: RV P                  V P                  V4      4      : RV P                  V4      : R2,          pKw  	  V^8X  d   RV: RV: R2pMRV: RV P                  V4      : RV: R2p\        ;QJ d&    R	 VP                   4       F  '       g   K   R
M	  RM! R	 VP                   4       4      '       d2   V: RV P                  VP                  \        R,          R
R
R7      : 2# V: RV P                  VP                  \        R,          RR
R7      : 2# )z\partialrÔ   rÖ   rÂ   r  rO   rô  rõ  ú}}{c              3  ó@   "  € T F  qP                  4       x € K  	  R # 5irõ   ©r0  ©r&  r²   s   & rS   r(  Ú1LatexPrinter._print_Derivative.<locals>.<genexpr>;  s   é € Ð?±Y°×)Ñ)×+Ð+³Yùó   ‚TFr	   ©rù   rú   )r   r  rÙ   ÚreversedÚvariable_countrö   r·   r3  r@  rü   r    )rß   r  Údiff_symbolr  Údimr'  Únums   &&     rS   Ú_print_DerivativeÚLatexPrinter._print_Derivative%  sb  € Ü˜DŸI™I×&Ò&Ø%‰KàŸ.™.Ð)>Õ?ˆKàˆØˆÜ˜t×2Ñ2Ö3‰FˆAØ�JˆCØ�aŒxØ¢;°·±¸AµÐ?Õ?’àªØ(,×(?Ñ(?ÀÇÁÈAÃÖ(OØ(,¯©°CÖ(8ð:õ :’ñ 4ð �!�8Û&1³3Ð7‰Cð ó ,7¸¿¹ÀCÖ8HË#ÐNˆCç‹3Ñ?°T·Y²YÓ?�3�3Š3Ñ?°T·Y²YÓ?×?Ò?Û" D×$5Ñ$5°d·i±iÜ2<¸UÕ2CØ9=Ø9=ð %6õ %?ð @ð @ó
  × 1Ñ 1°$·)±)Ü2<¸UÕ2CØ9>Ø9=ð !2õ !?ð @ð 	@rU   c                	óÌ   a € VP                   w  r#pS P                  V4      pV 3R  lV 4       pV 3R lV 4       pRP                  R \        Wg4       4       4      pRV: RV: R2# )c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   ©rö   ©r&  r[  rß   s   & €rS   r(  Ú+LatexPrinter._print_Subs.<locals>.<genexpr>I  ó   øé € Ð1©S¨�T—[‘[ —^�^«Sùr+  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  r�  s   & €rS   r(  r‚  J  rƒ  r+  z\\ c              3  ó\   "  € T F"  q^ ,          R,           V^,          ,           x € K$  	  R# 5i)rr  Ú=NrP   )r&  r[  s   & rS   r(  r‚  K  s'   é € ð !BÙ'@ !ˆa�D�3�J˜˜1�×ÒÓ'@ùs   ‚*,z\left. z \right|_{\substack{ z }})r@  rö   rU  Úzip)	rß   Úsubsr  rÓ  ÚnewÚ
latex_exprÚ	latex_oldÚ	latex_newÚ
latex_subss	   f&       rS   Ú_print_SubsÚLatexPrinter._print_SubsF  sg   ø€ ØŸ™‰ˆ�3Ø—[‘[ Ó&ˆ
Ü1©SÓ1ˆ	Ü1©SÓ1ˆ	Ø—[‘[ñ !BÜ'*¨9Ô'@ó!Bó B‰
ã9CÛ9CðEð 	ErU   c           
     	ó<  € R . r2V P                   R,          p\        VP                  4      ^8:  dº   \        ;QJ d&    R VP                   4       F  '       d   K   RM	  RM! R VP                   4       4      '       dl   RR\        VP                  4      ^,
          ,          ,           R,           pVP                   Uu. uF"  pRV: V P	                  V^ ,          4      : 2NK$  	  ppEM&\        VP                  4       EF  pV^ ,          pVR	,          p\        V4      ^8”  d¿   V P                   R
,          R8w  d#   V P                   R,          '       g
   VR,          p\        V4      ^8X  d?   VRV P	                  V^,          4      : RV P	                  V^,          4      : R2,          p\        V4      ^8X  d'   VRV P	                  V^,          4      ,          ,          pVP                  ^ RV: V P	                  V4      : 24       EK  	  V: RT P                  VP                  \        R,          \        ;QJ d&    R VP                   4       F  '       g   K   RM	  RM! R VP                   4       4      RR7      : R P                  V4      : 2# u upi )rÖ   rÔ   c              3  ó>   "  € T F  p\        V4      ^8H  x € K  	  R# 5i)r   N)rŒ  )r&  Úlims   & rS   r(  Ú/LatexPrinter._print_Integral.<locals>.<genexpr>U  s   é € Ð(NÁ+¸3¬¨S«°Q®Ã+ùs   ‚FTz\ir²   Úntz\, z\intrª   rÁ   r¤   z\limitsú_{ú}^{rO   ú^{%s}rÂ   r	   c              3  ó@   "  € T F  qP                  4       x € K  	  R # 5irõ   rr  rs  s   & rS   r(  r“  p  s   é € Ð>oÑenÐ`a×?YÑ?Y×?[Ð?[Óenùru  rv  )rÙ   rŒ  r8  Úallrö   rw  Úinsertrü   r9  r    r3  r@  rU  )rß   r  r  Úsymbolsry  Úsymbolr’  s   &&     rS   Ú_print_IntegralÚLatexPrinter._print_IntegralP  sû  € Ø˜2ˆWØ—n‘nÐ%:Õ;ˆô ˆt�{‰{Ó˜qÔ §S£SÑ(NÀ$Ç+Â+Ó(N§S§S¢SÑ(NÀ$Ç+Â+Ó(N×%NÒ%Nð ˜#œs 4§;¡;Ó/°!Õ3Õ4Õ4°tÕ;ˆCà%)§[¢[ó2Ù%0™6ò &1°$·+±+¸fÀQ½iÕ2HÓIÙ%0ð ð 2‰Gô   §¡×,�Ø˜Q��Ø�w•�ä�s“8˜a”<Ø—~‘~ fÕ-°Ô9Ø$(§N¡N°6×$:Ô$:Ø˜zÕ)˜ä˜3“x 1”}Ù¨t¯{©{¸3¸q½6Ö/BØ/3¯{©{¸3¸q½6Ö/Bð Dõ D˜ä˜3“x 1”}Ø˜w¨$¯+©+°c¸!µfÓ*=Õ>Õ>˜à—‘™q²¸T¿[¹[ÈÕ=PÐ"Q×Rñ -ó" ! $×"3Ñ"3°D·M±MÜ4>¸uÕ4Eß;>»3Ñ>oÐei×enÒenÓ>o¿3¿3º3Ñ>oÐei×enÒenÓ>oÓ;oØ;?ð #4õ #Að  ŸW™W WÕ-ð	/ð 	/ùò+2s   Â>(Jc                	óä  € VP                   w  r#rER V P                  V4      ,          p\        V4      R8X  g&   V\        P                  \        P
                  39   d!   VRV P                  V4      ,          ,          pM.W`P                  V4      : RV P                  V4      : R2,          p\        V\        4      '       d   V: RV P                  V4      : R2# V: RV P                  V4      : 2# )z\lim_{%s \to z+-z%s}r—   rO   rJ  rx  rÂ   )r@  rö   r�   r   ÚInfinityÚNegativeInfinityrØ  r   )rß   r  r[  ÚzÚz0Údirr  s   &&     rS   Ú_print_LimitÚLatexPrinter._print_Limitt  s«   € ØŸ	™	‰ˆˆbà §¡¨Q£Õ/ˆÜˆs‹8�tÔ˜r¤a§j¡j´!×2DÑ2DÐ%EÔEØ�6˜DŸK™K¨›OÕ+Õ+‰Cà§¡¨B¦°·±¸SÖ1AÐBÕBˆCä�aœ×!Ò!Û+.°·±¸A¶Ð?Ð?ã" D§K¡K°¥NÐ3Ð3rU   c               ó    € V ^8„  d   QhRRRR/# )r�   rÆ  r�   r‘   rP   )r’   s   "rS   r“   ré   ‚  s   € ÷ ñ  Sð ¨Sñ rU   c                óà  € V P                  V4      pVP                  R4      pVP                  R4      pV\        9   d   RV,          pV# \        V4      ^8X  g&   VP	                  R4      '       g   V^8X  g   V^8X  d   TpV# V^ 8”  d,   V^ 8”  d%   RVR\        W24       : RV\        W24      R : 2pV# V^ 8”  d   RVRV : RWR : 2pV# V^ 8”  d   RVRV : RWR : 2pV# RV,          pV# )	a;  
Logic to decide how to render a function to latex
  - if it is a recognized latex name, use the appropriate latex command
  - if it is a single letter, excluding sub- and superscripts, just use that letter
  - if it is a longer name, then put \operatorname{} around it and be
    mindful of undercores in the name
r—   Ú_z\%sr•   ú\operatorname{NrO   z\operatorname{%s})rR  ÚfindÚaccepted_latex_functionsrŒ  r"  r¸   )rß   rÆ  ÚsuperscriptidxÚsubscriptidxrV  s   &&   rS   Ú_hprint_FunctionÚLatexPrinter._hprint_Function‚  s!  € ð ×(Ñ(¨Ó.ˆØŸ™ 3›ˆØ—y‘y “~ˆØÔ+Ô+Ø˜D•=ˆDð$ ˆô# �‹Y˜!Œ^˜tŸ™¨t×4Ò4¸ÈÔ8IÈ^Ð_`ÔM`ØˆDð  ˆð  Ô! l°QÕ&6àÐ:œ#˜lÓ:Ó;Øœ˜\Ó9Ð:Ò;ð=�ð ˆð   !Õ#à˜˜.Ó)Ø˜Ò)ð+�ð ˆð  Õ!à˜˜,Ó'Ø˜Ò'ð)�ð
 ˆð ,¨dÕ2�ØˆrU   c               ó    € V ^8„  d   QhRRRR/# )r�   r  r   r‘   r�   rP   )r’   s   "rS   r“   ré   ¢  s   € ÷ J)ñ J) Hð J)¸3ñ J)rU   c                óF  € VP                   P                  p\        V RV,           4      '       d0   \        V\        4      '       g   \        V RV,           4      ! W4      # VP                   Uu. uF  p\        V P                  V4      4      NK  	  ppV P                  R,          pRpV P                  R,          ;'       d>    \        V4      ^8H  ;'       d(    V P                  VP                  ^ ,          4      '       * p. ROp	W99   dI   VR8X  d   M@VR8X  d"   VR,          R8X  d   RMR	VR
,          ,           pMVR8X  d   VR
,          pRpVe   RpV'       d    V\        9   d   RV,          p
MLRV,          p
MBVe.   V P                  V4      pV P                  V4      pV: RV: R2p
MV P                  V4      p
V'       d    V\        9   d   V
R,          p
MV
R,          p
M	V
R,          p
V'       d   Ve   V
RV,          ,          p
V
RP                  V4      ,          # u upi )aÛ  
Render functions to LaTeX, handling functions that LaTeX knows about
e.g., sin, cos, ... by using the proper LaTeX command (\sin, \cos, ...).
For single-letter function names, render them as regular LaTeX math
symbols. For multi-letter function names that LaTeX does not know
about, (e.g., Li, sech) use \operatorname{} so that the function name
is rendered in Roman font and LaTeX handles spacing properly.

expr is the expression involving the function
exp is an exponent
Ú_print_r¢   Fr    r£   ÚfullÚhÚarÚarcrŸ  ÚpowerTz\%s^{-1}z\operatorname{%s}^{-1}r  rO   z {%s}ú%sú{\left(%s \right)}r—  rv  )ÚasinÚacosÚatanÚacscÚasecÚacotÚasinhÚacoshÚatanhÚacschÚasechÚacothry  )rÆ  rT  r×  rØ  r   Úgetattrr@  r�   rö   rÙ   rŒ  r  r¬  r¯  r·   rU  )rß   r  rM  rÆ  rB  r@  r¢   Úinv_trig_power_caseÚcan_fold_bracketsÚinv_trig_tablerV  Úfunc_texs   &&&         rS   Ú_print_FunctionÚLatexPrinter._print_Function¢  sî  € ð �y‰y×!Ñ!ˆÜ�4˜ TÕ)×*Ò*Ü˜t¤\×2Ò2Ü˜4 ¨TÕ!1Ô2°4Ó=Ð=à59·Y²YÓ?±Y¨c”C˜Ÿ™ CÓ(Ö)±YˆDÐ?ð "Ÿ^™^Ð,<Õ=ˆNà"'Ðà $§¡Ð/CÕ D÷ !@ð !@Ü�D“	˜Q‘÷!@ð !@à×1Ñ1°$·)±)¸Aµ,Ó?Ô?ð òˆNð Ô%Ø! ]Ô2ØØ# vÔ-Ø$(¨¥H°¤O™D¸À$ÀrÅ(ÕJ‘DØ# wÔ.Ø �8�DØ*.Ð'ð ’Ø,1Ð)ç"ØÔ3Ô3Ø&¨Õ-‘Dà4°tÕ;‘DØ’Ø×0Ñ0°Ó6�Ø×2Ñ2°8Ó<�Û%-«sÐ3‘à×,Ñ,¨TÓ2�ç ØÔ3Ô3ð ˜HÕ$‘Dà˜E•M‘DàÐ-Õ-�ç" s¢Ø˜ 3�Õ&�à˜#Ÿ(™( 4›.Õ(Ð(ùòs @s   Á-#Hc                	ó6   € V P                  \        V4      4      # rõ   )r¯  r�   r  s   &&rS   Ú_print_UndefinedFunctionÚ%LatexPrinter._print_UndefinedFunctionî  s   € Ø×$Ñ$¤S¨£YÓ/Ð/rU   c                	ó|   € R V P                  VP                  4      : RV P                  VP                  4      : R2# )rs   z}_{\circ}\left({z}\right))rö   r9  r  r  s   &&rS   Ú_print_ElementwiseApplyFunctionÚ,LatexPrinter._print_ElementwiseApplyFunctionñ  s,   � à�K‰K˜Ÿ™Ö&Ø�K‰K˜Ÿ	™	Ö"ð
ð 	
rU   c                	ó^   € ^ RI Hp ^ RIHpHp ^ RIHp ^ RIHp ^ RI	H
p VRVRVRVR	VRVR
/# )rr  )ÚKroneckerDelta)ÚgammaÚ
lowergamma)Úbeta)Ú
DiracDelta)r?   z\deltar*   ú\gammaz\operatorname{B}z\operatorname{Chi})Ú(sympy.functions.special.tensor_functionsrÕ  Ú'sympy.functions.special.gamma_functionsrÖ  r×  Ú&sympy.functions.special.beta_functionsrØ  Ú'sympy.functions.special.delta_functionsrÙ  Ú'sympy.functions.special.error_functionsr?   )rß   rÕ  rÖ  r×  rØ  rÙ  r?   s   &      rS   Ú_special_function_classesÚ&LatexPrinter._special_function_classes÷  s;   € åKßMÝ?ÝFÝ?Ø 	Ø˜	Ø˜IØÐ)Ø˜IØÐ*ð,ð 	,rU   c                	óâ   € V P                    FF  p\        W4      '       g   K  VP                  VP                  8X  g   K3  V P                   V,          u # 	  V P                  \	        V4      4      # rõ   )rà  Ú
issubclassrT  r¯  r�   )rß   r  Úclss   && rS   Ú_print_FunctionClassÚ!LatexPrinter._print_FunctionClass  sT   € Ø×1Ô1ˆCÜ˜$×$Ô$¨¯©¸#¿,¹,Ö)FØ×5Ñ5°cÕ:Ò:ñ 2ð ×$Ñ$¤S¨£YÓ/Ð/rU   c                	óÜ   € VP                   w  r!\        V4      ^8X  d   V P                  V^ ,          4      pMV P                  \        V4      4      pRV: RV P                  V4      : R2pV# )r   rw  z	 \mapsto ú \right))r@  rŒ  rö   r/  )rß   r  r›  r  s   &&  rS   Ú_print_LambdaÚLatexPrinter._print_Lambda  sV   € ØŸ	™	‰ˆäˆw‹<˜1ÔØ—k‘k '¨!¥*Ó-‰Gà—k‘k¤%¨£.Ó1ˆGøã18¸$¿+¹+ÀdÖ:KÐLˆàˆ
rU   c                	ó   € R # )z\left( x \mapsto x \right)rP   r  s   &&rS   Ú_print_IdentityFunctionÚ$LatexPrinter._print_IdentityFunction  s   € Ù,rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré     s   € ÷ ñ ¸3ñ rU   c                	ó&  € \        VP                  \        R 7      pV Uu. uF  pRV P                  V4      ,          NK  	  ppR\	        VP
                  4      P                  4       : RRP                  V4      : R2pVe   V: RV: R2# V# u upi )rI  r¹  r•   rJ  rQ  rx  r  rO   )Úsortedr@  r   rö   r�   rÆ  r�  rU  )rß   r  rM  r@  rœ  Útexargsr  s   &&&    rS   Ú_hprint_variadic_functionÚ&LatexPrinter._hprint_variadic_function  s|   € Ü�d—i‘iÔ%5Ô6ˆÙ=AÓB¹T°6�5˜4Ÿ;™; vÓ.×.Ð.¹TˆÐBˆÜ'*¨4¯9©9£~×';Ñ';Ö'=Ø'+§y¡y°Ö'9ð;ˆàŠ?Û!$£cÐ*Ð*àˆJùò Cs    !Bc                	ót   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: R2# V# )z\left\lfloor{%s}\right\rfloorr  rO   r(  ©rß   r  rM  r  s   &&& rS   Ú_print_floorÚLatexPrinter._print_floor&  s2   € Ø.°·±¸T¿Y¹YÀq½\Ó1JÕJˆàŠ?Û!$£cÐ*Ð*àˆJrU   c                	ót   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: R2# V# )z\left\lceil{%s}\right\rceilr  rO   r(  rõ  s   &&& rS   Ú_print_ceilingÚLatexPrinter._print_ceiling.  s2   € Ø,¨t¯{©{¸4¿9¹9ÀQ½<Ó/HÕHˆàŠ?Û!$£cÐ*Ð*àˆJrU   c                	óú   € V P                   R ,          '       g+   RV P                  VP                  ^ ,          4      ,          pM)RV P                  VP                  ^ ,          4      ,          pVe   V: RV: R2# V# )r¥   z\log{\left(%s \right)}z\ln{\left(%s \right)}r  rO   )rÙ   rö   r@  rõ  s   &&& rS   Ú
_print_logÚLatexPrinter._print_log6  s\   € Ø�~‰~˜m×,Ô,Ø+¨d¯k©k¸$¿)¹)ÀA½,Ó.GÕG‰Cà*¨T¯[©[¸¿¹À1½Ó-FÕFˆCàŠ?Û!$£cÐ*Ð*àˆJrU   c                	ót   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: R2# V# )ú\left|{%s}\right|r  rO   r(  rõ  s   &&& rS   Ú
_print_AbsÚLatexPrinter._print_AbsA  s2   € Ø" T§[¡[°·±¸1µÓ%>Õ>ˆàŠ?Û!$£cÐ*Ð*àˆJrU   c                	ó<  € V P                   R ,          '       d7   RV P                  VP                  ^ ,          \        R,          4      ,          pM=RP	                  V P                  VP                  ^ ,          \        R,          4      4      pV P                  W24      # )r³   z\Re{%s}ÚAtomz\operatorname{{re}}{{{}}}©rÙ   rü   r@  r    r’   rN  rõ  s   &&& rS   Ú	_print_reÚLatexPrinter._print_reI  ós   € Ø�>‰>˜.×)Ô)Ø˜t×0Ñ0°·±¸1µ¼zÈ&Õ?QÓRÕR‰Cà.×5Ñ5°d×6GÑ6GÈÏ	É	ÐRSÍÔV`ÐagÕVhÓ6iÓjˆCà× Ñ  Ó*Ð*rU   c                	ó<  € V P                   R ,          '       d7   RV P                  VP                  ^ ,          \        R,          4      ,          pM=RP	                  V P                  VP                  ^ ,          \        R,          4      4      pV P                  W24      # )r³   z\Im{%s}r  z\operatorname{{im}}{{{}}}r  rõ  s   &&& rS   Ú	_print_imÚLatexPrinter._print_imQ  r  rU   c                	ó  € ^ RI HpHp \        VP                  ^ ,          V4      '       d$   V P                  VP                  ^ ,          R4      # \        VP                  ^ ,          V4      '       d$   V P                  VP                  ^ ,          R4      # VP                  ^ ,          P                  '       d*   RV P                  VP                  ^ ,          4      ,          # RV P                  VP                  ^ ,          4      ,          # )rr  )Ú
EquivalentÚImpliesz\not\Leftrightarrowz\not\Rightarrowz\neg \left(%s\right)z\neg %s)	Úsympy.logic.boolalgr  r  rØ  r@  Ú_print_EquivalentÚ_print_ImpliesÚ
is_Booleanrö   )rß   r[  r  r  s   &&  rS   Ú
_print_NotÚLatexPrinter._print_NotY  s³   € ß=Ü�a—f‘f˜Q•i ×,Ò,Ø×)Ñ)¨!¯&©&°­)Ð5KÓLÐLÜ�a—f‘f˜Q•i ×)Ò)Ø×&Ñ& q§v¡v¨a¥yÐ2DÓEÐEØ�F‰F�1�I× × Ð Ø*¨T¯[©[¸¿¹À½Ó-CÕCÐCà §¡¨A¯F©F°1­IÓ 6Õ6Ð6rU   c                	ó°  € V^ ,          pVP                   '       d,   VP                  '       g   RV P                  V4      ,          pMRV P                  V4      ,          pVR,           Fj  pVP                   '       d6   VP                  '       g$   VRV: RV P                  V4      : R2,          pKJ  VRV: RV P                  V4      : 2,          pKl  	  V# )rr  ri  r¹  rŸ  rÂ   z \left(rx  )r  Úis_Notrö   )rß   r@  ÚcharrB  r  s   &&&  rS   Ú_print_LogOpÚLatexPrinter._print_LogOpd  sš   € Ø�1�gˆØ�>�>ˆ> #§*§* *Ø$ t§{¡{°3Ó'7Õ7‰Cà˜$Ÿ+™+ cÓ*Õ*ˆCà˜—8�8ˆCØ�~�~ˆ~ c§j§j jÙ³°t·{±{À3Ö7GÐHÕH’á£D¨$¯+©+°cÕ*:Ð;Õ;’ñ	 ð ˆ
rU   c                	ó\   € \        VP                  \        R 7      pV P                  VR4      # )rI  z\wedge©rð  r@  r   r  ©rß   r[  r@  s   && rS   Ú
_print_AndÚLatexPrinter._print_Ands  s&   € Ü�a—f‘fÔ"2Ô3ˆØ× Ñ   yÓ1Ð1rU   c                	ó\   € \        VP                  \        R 7      pV P                  VR4      # )rI  z\veer  r  s   && rS   Ú	_print_OrÚLatexPrinter._print_Orw  s&   € Ü�a—f‘fÔ"2Ô3ˆØ× Ñ   wÓ/Ð/rU   c                	ó\   € \        VP                  \        R 7      pV P                  VR4      # )rI  z\veebarr  r  s   && rS   Ú
_print_XorÚLatexPrinter._print_Xor{  s&   € Ü�a—f‘fÔ"2Ô3ˆØ× Ñ   zÓ2Ð2rU   c                	óN   € T P                  VP                  T;'       g    R 4      # )z\Rightarrow)r  r@  )rß   r[  Úaltchars   &&&rS   r  ÚLatexPrinter._print_Implies  s!   € Ø× Ñ  §¡¨×)BÐ)B°NÓCÐCrU   c                	ón   € \        VP                  \        R 7      pT P                  Y2;'       g    R4      # )rI  z\Leftrightarrowr  )rß   r[  r%  r@  s   &&& rS   r  ÚLatexPrinter._print_Equivalent‚  s-   € Ü�a—f‘fÔ"2Ô3ˆØ× Ñ  ×'DÐ'DÐ2DÓEÐErU   c                	ót   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: R2# V# )z\overline{%s}r  rO   r(  rõ  s   &&& rS   Ú_print_conjugateÚLatexPrinter._print_conjugate†  s2   € Ø §¡¨T¯Y©Y°q­\Ó!:Õ:ˆàŠ?Û!$£cÐ*Ð*àˆJrU   c                	óŠ   € R pRV P                  VP                  ^ ,          4      ,          pVe   V: RV: RV: 2# V: V: 2# )z\operatorname{polar\_lift}rº  r  rO   r(  )rß   r  rM  rÆ  rB  s   &&&  rS   Ú_print_polar_liftÚLatexPrinter._print_polar_liftŽ  s?   € Ø,ˆØ# d§k¡k°$·)±)¸Aµ,Ó&?Õ?ˆàŠ?Û#'«ªcÐ2Ð2â"¢CÐ(Ð(rU   c                	óv   € R V P                  VP                  ^ ,          4      ,          pV P                  W24      # )ze^{%s})rö   r@  rN  rõ  s   &&& rS   Ú_print_ExpBaseÚLatexPrinter._print_ExpBase—  s0   € ð ˜$Ÿ+™+ d§i¡i°¥lÓ3Õ3ˆØ× Ñ  Ó*Ð*rU   c                	ó   € R # )r[  rP   rL  s   &&&rS   Ú_print_Exp1ÚLatexPrinter._print_Exp1�  s   € ÙrU   c                	ó‚   € R V P                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )ri  zK^{rO   zK%sr(  rõ  s   &&& rS   Ú_print_elliptic_kÚLatexPrinter._print_elliptic_k   s7   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆØ‹?Û"%¢sÐ+Ð+à˜C•<ÐrU   c                	óÆ   € R V P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2pVe   RV: RV: 2# RV,          # )rJ  ú	\middle| rx  zF^{rO   zF%sr(  rõ  s   &&& rS   Ú_print_elliptic_fÚLatexPrinter._print_elliptic_f§  sK   � à�[‰[˜Ÿ™ 1�Ö&¨¯©°D·I±I¸aµLÖ(AðCˆà‹?Û"%¢sÐ+Ð+à˜C•<ÐrU   c                	óN  € \        VP                  4      ^8X  dM   RV P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2pM)RV P                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )r�   rJ  r9  rx  ri  zE^{rO   zE%s©rŒ  r@  rö   rõ  s   &&& rS   Ú_print_elliptic_eÚLatexPrinter._print_elliptic_e¯  sx   € Üˆt�y‰y‹>˜QÕà—‘˜TŸY™Y q�\Ö*¨D¯K©K¸¿	¹	À!½Ö,EðG‰Cð % t§{¡{°4·9±9¸Qµ<Ó'@Õ@ˆCØ‹?Û"%¢sÐ+Ð+à˜C•<ÐrU   c           	     	óÚ  € \        VP                  4      ^8X  dq   RV P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : RV P                  VP                  ^,          4      : R2pMKRV P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2pVe   RV: RV: 2# RV,          # )rL  rJ  ú; r9  rx  z\Pi^{rO   z\Pi%sr=  rõ  s   &&& rS   Ú_print_elliptic_piÚLatexPrinter._print_elliptic_piº  s¤   € Üˆt�y‰y‹>˜QÕà—‘˜TŸY™Y q�\Ö*¨D¯K©K¸¿	¹	À!½Ö,EØ—‘˜TŸY™Y q�\Ö*ð,‰Cð ð —‘˜TŸY™Y q�\Ö*¨D¯K©K¸¿	¹	À!½Ö,EðGˆCà‹?Û$'ªÐ-Ð-à˜c•>Ð!rU   c                	óè   € VP                   ^ ,          p\        VP                   4      ^8X  d   VP                   ^ ,          MVP                   ^,          pRV RV R2pVe   RV: RV: 2# RV,          # )rr  rJ  rQ  rx  z\operatorname{B}^{rO   z\operatorname{B}%s)r@  rŒ  )rß   r  rM  r'  Úyr  s   &&&   rS   Ú_print_betaÚLatexPrinter._print_betaÇ  sd   € Ø�I‰I�a�Lˆä §	¡	›N¨aÔ/ˆD�I‰I�aŽL°T·Y±Y¸qµ\ˆØ˜�s˜"˜Q˜C˜wÐ'ˆà‹?Û14²cÐ:Ð:à(¨3Õ.Ð.rU   c           
     	ó   € VP                    Uu. uF  q@P                  V4      NK  	  ppR V^ ,          : RV^,          : R2pVe%   RV: RV^,          : RV^,          : RV: RV: 2
# RV: RV^,          : RV^,          : RV: 2# u upi )rJ  rQ  rx  rª  z}_{(z)}^{rO   z)}r•  )rß   r  rM  ÚoperatorrB  Úlargsr  s   &&&&   rS   Ú_print_betaincÚLatexPrinter._print_betaincÒ  s‹   € Ø-1¯YªYÓ7©Y c—‘˜SÖ!©YˆÐ7ˆØ(-¨a¯¨°%¸·(°(Ð;ˆà‹?Û=EÀuÈQÇxÀxÐQVÐWX×QYÐQYÓ[^Ò`cÐdÐdð ó 9AÀ%ÈÇ(À(ÈEÐRSÏHÈHÒVYÐZÐZùò 8s   �Bc                	ó(   € V P                  WR R7      # )ÚI)rI  )rK  rL  s   &&&rS   Ú_print_betainc_regularizedÚ'LatexPrinter._print_betainc_regularizedÛ  s   € Ø×"Ñ" 4°sÐ"Ó;Ð;rU   c                	óÆ   € R V P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2pVe   RV: RV: 2# RV,          # )rJ  rQ  rx  z\Gamma^{rO   z\Gamma%sr(  rõ  s   &&& rS   Ú_print_uppergammaÚLatexPrinter._print_uppergammaÞ  óO   � Ø(,¯©°D·I±I¸aµLÖ(AØ(,¯©°D·I±I¸aµLÖ(AðCˆð ‹?Û'*ªCÐ0Ð0à Õ$Ð$rU   c                	óÆ   € R V P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2pVe   RV: RV: 2# RV,          # )rJ  rQ  rx  z\gamma^{rO   ú\gamma%sr(  rõ  s   &&& rS   Ú_print_lowergammaÚLatexPrinter._print_lowergammaç  rT  rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   ð  s   € ÷ ;ñ ;°cñ ;rU   c                	óê   € R V P                  VP                  ^ ,          4      ,          pVe'   V P                  VP                  4      : RV: RV: 2# V P                  VP                  4      : V: 2# ©ri  r  rO   )rö   r@  rÆ  rõ  s   &&& rS   Ú_hprint_one_arg_funcÚ!LatexPrinter._hprint_one_arg_funcð  sT   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆàŠ?Ø#'§;¡;¨t¯y©yÖ#9»3ÂÐDÐDà"Ÿk™k¨$¯)©)Õ4²cÐ:Ð:rU   c                	ó‚   € R V P                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )ri  z\operatorname{Chi}^{rO   z\operatorname{Chi}%sr(  rõ  s   &&& rS   Ú
_print_ChiÚLatexPrinter._print_Chiú  s8   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆà‹?Û36ºÐ<Ð<à*¨SÕ0Ð0rU   c                	óÐ   € R V P                  VP                  ^,          4      ,          pV P                  VP                  ^ ,          4      pVe   RV: RV: RV: 2# RV: RV: 2# )ri  z\operatorname{E}_{r–  rO   r(  )rß   r  rM  r  Únus   &&&  rS   Ú_print_expintÚLatexPrinter._print_expint  sW   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆØ�[‰[˜Ÿ™ 1�Ó&ˆà‹?Û68»#ºsÐCÐCð ó 24²SÐ9Ð9rU   c                	ó‚   € R V P                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )ri  zS^{rO   zS%sr(  rõ  s   &&& rS   Ú_print_fresnelsÚLatexPrinter._print_fresnels  ó7   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆà‹?Û"%¢sÐ+Ð+à˜C•<ÐrU   c                	ó‚   € R V P                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )ri  zC^{rO   zC%sr(  rõ  s   &&& rS   Ú_print_fresnelcÚLatexPrinter._print_fresnelc  rh  rU   c                	óŽ   € R V P                  VP                  ^ ,          \        R,          4      ,          pVe   RV: RV: R2# V# )z!%sÚFuncrJ  rK  rO   ©rü   r@  r    rõ  s   &&& rS   Ú_print_subfactorialÚ LatexPrinter._print_subfactorial  s;   € Ø�t×(Ñ(¨¯©°1­´zÀ&Õ7IÓJÕJˆà‹?Û.1³3Ð7Ð7àˆJrU   c                	óŒ   € R V P                  VP                  ^ ,          \        R,          4      ,          pVe   V: RV: R2# V# )z%s!rm  r  rO   rn  rõ  s   &&& rS   Ú_print_factorialÚLatexPrinter._print_factorial#  s;   € Ø�t×(Ñ(¨¯©°1­´zÀ&Õ7IÓJÕJˆàŠ?Û!$£cÐ*Ð*àˆJrU   c                	óŒ   € R V P                  VP                  ^ ,          \        R,          4      ,          pVe   V: RV: R2# V# )z%s!!rm  r  rO   rn  rõ  s   &&& rS   Ú_print_factorial2ÚLatexPrinter._print_factorial2+  s;   € Ø˜×)Ñ)¨$¯)©)°A­,¼
À6Õ8JÓKÕKˆàŠ?Û!$£cÐ*Ð*àˆJrU   c                	ó¸   € R V P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2pVe   V: RV: R2# V# )z{\binom{rõ  r  r  rO   r(  rõ  s   &&& rS   Ú_print_binomialÚLatexPrinter._print_binomial3  sI   � Ø%)§[¡[°·±¸1µÖ%>Ø%)§[¡[°·±¸1µÖ%>ð@ˆð Š?Û!$£cÐ*Ð*àˆJrU   c                	ó¼   € VP                   w  r4R V P                  V\        R,          4      ,          pRV: RV P                  V4      : R2pV P	                  Wb4      # )r¹  rm  rs   ú	}^{\left(ú\right)}©r@  rü   r    rö   rN  )rß   r  rM  ÚnrY  rF  r  s   &&&    rS   Ú_print_RisingFactorialÚ#LatexPrinter._print_RisingFactorial<  sL   € Ø�y‰y‰ˆØ�t×(Ñ(¨¬J°vÕ,>Ó?Õ?‰ã+/°·±¸Q¶Ð@ˆà× Ñ  Ó*Ð*rU   c                	ó¼   € VP                   w  r4R V P                  V\        R,          4      ,          pRV P                  V4      : RV: R2pV P	                  Wb4      # )r¹  rm  z{\left(z
\right)}_{rO   r}  )rß   r  rM  r~  rY  Úsubr  s   &&&    rS   Ú_print_FallingFactorialÚ$LatexPrinter._print_FallingFactorialD  sL   € Ø�y‰y‰ˆØ�d×'Ñ'¨¬:°fÕ+=Ó>Õ>‰à+/¯;©;°q®>»3Ð?ˆà× Ñ  Ó*Ð*rU   c               ó    € V ^8„  d   QhRRRR/# )r�   Úsymr�   r‘   rP   )r’   s   "rS   r“   ré   L  s   € ÷ ñ °ð ¸ñ rU   c                	ó  € R V,          pRpVe$   VP                  R4      R	8X  d   V: RV: R2pMRpV: RV P                  VP                  4      : RV P                  VP                  4      : R2pV'       d   V P	                  WB4      pV# )
r¹  Fr—   r  rO   Tr•  ú}\left(rx  ry  )r«  rö   r­   ÚargumentrN  )rß   r  rM  r†  r  Úneed_exps   &&&&  rS   Ú_hprint_BesselBaseÚLatexPrinter._hprint_BesselBaseL  sx   € Ø�s�mˆàˆØŠ?Ø�x‰x˜‹} Ô"Û$'«Ð-‘à�ã+.°·±¸D¿J¹JÖ0GØ+/¯;©;°t·}±}Ö+EðGˆ÷ Ø×#Ñ# CÓ-ˆCØˆ
rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   ]  s   € ÷ ñ  #ñ rU   c                	ó°   € V'       g   R # R pVRR  F"  pVRV P                  V4      ,          ,          pK$  	  W P                  VR,          4      ,          pV# )rÖ   Nz%s, ry  r€  )rß   rn   rR   r²   s   &&  rS   Ú_hprint_vecÚLatexPrinter._hprint_vec]  sN   € ßÙØˆØ�S�b“ˆAØ�˜$Ÿ+™+ a›.Õ(Õ(ŠAñ à	�[‰[˜˜R�Ó!Õ!ˆØˆrU   c                	ó&   € V P                  WR 4      # )ÚJ©r‹  rL  s   &&&rS   Ú_print_besseljÚLatexPrinter._print_besseljf  ó   € Ø×&Ñ& t°#Ó6Ð6rU   c                	ó&   € V P                  WR 4      # )rN  r“  rL  s   &&&rS   Ú_print_besseliÚLatexPrinter._print_besselii  r–  rU   c                	ó&   € V P                  WR 4      # )ÚKr“  rL  s   &&&rS   Ú_print_besselkÚLatexPrinter._print_besselkl  r–  rU   c                	ó&   € V P                  WR 4      # )ÚYr“  rL  s   &&&rS   Ú_print_besselyÚLatexPrinter._print_besselyo  r–  rU   c                	ó&   € V P                  WR 4      # )rE  r“  rL  s   &&&rS   Ú	_print_ynÚLatexPrinter._print_ynr  r–  rU   c                	ó&   € V P                  WR 4      # )rÎ   r“  rL  s   &&&rS   Ú	_print_jnÚLatexPrinter._print_jnu  r–  rU   c                	ó&   € V P                  WR 4      # )zH^{(1)}r“  rL  s   &&&rS   Ú_print_hankel1ÚLatexPrinter._print_hankel1x  ó   € Ø×&Ñ& t°)Ó<Ð<rU   c                	ó&   € V P                  WR 4      # )zH^{(2)}r“  rL  s   &&&rS   Ú_print_hankel2ÚLatexPrinter._print_hankel2{  r«  rU   c                	ó&   € V P                  WR 4      # )zh^{(1)}r“  rL  s   &&&rS   Ú
_print_hn1ÚLatexPrinter._print_hn1~  r«  rU   c                	ó&   € V P                  WR 4      # )zh^{(2)}r“  rL  s   &&&rS   Ú
_print_hn2ÚLatexPrinter._print_hn2�  r«  rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   „  s   € ÷ -ñ -¸3ñ -rU   c                	ó†   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: RV: 2# V: V: 2# r[  r(  ©rß   r  rM  Únotationr  s   &&&& rS   Ú_hprint_airyÚLatexPrinter._hprint_airy„  s:   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆàŠ?Û#+«S²#Ð6Ð6â&ªÐ,Ð,rU   c               ó   € V ^8„  d   QhRR/# rè   rP   )r’   s   "rS   r“   ré   Œ  s   € ÷ 4ñ 4Àñ 4rU   c                	óŠ   € R V P                  VP                  ^ ,          4      ,          pVe   RV: RV: RV: 2# V: RV: 2# )ri  rs   z
^\prime}^{rO   z^\primer(  r·  s   &&&& rS   Ú_hprint_airy_primeÚLatexPrinter._hprint_airy_primeŒ  s:   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆà‹?Û,4³cº3Ð?Ð?ã%-ªsÐ3Ð3rU   c                	ó&   € V P                  WR 4      # ©ÚAi©r¹  rL  s   &&&rS   Ú_print_airyaiÚLatexPrinter._print_airyai”  ó   € Ø× Ñ  ¨DÓ1Ð1rU   c                	ó&   € V P                  WR 4      # ©ÚBirÂ  rL  s   &&&rS   Ú_print_airybiÚLatexPrinter._print_airybi—  rÅ  rU   c                	ó&   € V P                  WR 4      # rÀ  ©r½  rL  s   &&&rS   Ú_print_airyaiprimeÚLatexPrinter._print_airyaiprimeš  ó   € Ø×&Ñ& t°$Ó7Ð7rU   c                	ó&   € V P                  WR 4      # rÇ  rÌ  rL  s   &&&rS   Ú_print_airybiprimeÚLatexPrinter._print_airybiprime�  rÏ  rU   c                	óp  € R V P                  \        VP                  4      4      : RV P                  \        VP                  4      4      : RV P	                  VP                  4      : RV P	                  VP                  4      : RV P                  VP
                  4      : R2pVe   RV: RV: R2pV# )	z{{}_{z}F_{ú}\left(\begin{matrix} rˆ  z \end{matrix}\middle| {ú
} \right)}rs   r–  rO   )rö   rŒ  ÚapÚbqr�  r‰  rõ  s   &&& rS   Ú_print_hyperÚLatexPrinter._print_hyper   s{   � ð �[‰[œ˜TŸW™W›Ö&¨¯©´C¸¿¹³LÖ(AØ×Ñ˜tŸw™wÖ'¨×)9Ñ)9¸$¿'¹'Ö)BØ�k‰k˜$Ÿ-™-Ö(ð	*ˆð ‹?Û"%£sÐ+ˆCØˆ
rU   c                	ó|  € R V P                  \        VP                  4      4      : RV P                  \        VP                  4      4      : RV P                  \        VP                  4      4      : RV P                  \        VP
                  4      4      : RV P                  VP
                  4      : RV P                  VP                  4      : RV P                  VP                  4      : RV P                  VP                  4      : RV P                  VP                  4      : R2pVe   RV: RV: R	2pV# )
z{G_{rQ  r–  rÔ  r‡  ú \\z \end{matrix} \middle| {rÕ  rs   rO   )
rö   rŒ  rÖ  r×  ry   Úanr�  ÚaotherÚbotherr‰  rõ  s   &&& rS   Ú_print_meijergÚLatexPrinter._print_meijerg«  sÅ   � ð �[‰[œ˜TŸW™W›Ö&¨¯©´C¸¿¹³LÖ(AØ�k‰kœ#˜dŸg™g›,Ö'¨¯©´S¸¿¹³\Ö)BØ×Ñ˜tŸw™wÖ'¨×)9Ñ)9¸$¿+¹+Ö)FØ×Ñ˜tŸw™wÖ'¨×)9Ñ)9¸$¿+¹+Ö)FØ�k‰k˜$Ÿ-™-Ö(ð*ˆð ‹?Û"%£sÐ+ˆCØˆ
rU   c                	ó‚   € R V P                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )ri  z\eta^{rO   z\eta%sr(  rõ  s   &&& rS   Ú_print_dirichlet_etaÚ!LatexPrinter._print_dirichlet_eta¸  s7   € Ø  4§;¡;¨t¯y©y¸­|Ó#<Õ<ˆØ‹?Û%(ª#Ð.Ð.Ø˜3�ÐrU   c                	ó  € \        VP                  4      ^8X  d2   R\        \        V P                  VP                  4      4      ,          pM)RV P	                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )r�   z\left(%s, %s\right)ri  z\zeta^{rO   z\zeta%s©rŒ  r@  r/  ra  rö   rõ  s   &&& rS   Ú_print_zetaÚLatexPrinter._print_zeta¾  sf   € Üˆt�y‰y‹>˜QÔØ(¬5´°T·[±[À$Ç)Á)Ó1LÓ+MÕM‰Cà$ t§{¡{°4·9±9¸Qµ<Ó'@Õ@ˆCØ‹?Û&)ª3Ð/Ð/Ø˜CÕÐrU   c                	ó  € \        VP                  4      ^8X  d2   R\        \        V P                  VP                  4      4      ,          pM)RV P	                  VP                  ^ ,          4      ,          pVe   RV: RV: R2# RV,          # )r�   z_{%s}\left(%s\right)r`  rÚ  r  rO   rV  rå  rõ  s   &&& rS   Ú_print_stieltjesÚLatexPrinter._print_stieltjesÇ  sf   € Üˆt�y‰y‹>˜QÔØ)¬E´#°d·k±kÀ4Ç9Á9Ó2MÓ,NÕN‰Cà˜TŸ[™[¨¯©°1­Ó6Õ6ˆCØ‹?Û'*«CÐ0Ð0Ø˜SÕ Ð rU   c                	ó�   € R \        \        V P                  VP                  4      4      ,          pVf
   RV,          # RV: RV: 2# )z\left(%s, %s, %s\right)z\Phi%sz\Phi^{rO   )r/  ra  rö   r@  rõ  s   &&& rS   Ú_print_lerchphiÚLatexPrinter._print_lerchphiÐ  s?   € Ø(¬5´°T·[±[À$Ç)Á)Ó1LÓ+MÕMˆØŠ;Ø˜s•?Ð"ð ã!$¢cÐ*Ð*rU   c                	ó�   € \        V P                  VP                  4      w  r4R V,          pVf   RV: RV: 2# RV: RV: RV: 2# )ri  z\operatorname{Li}_{rO   r–  ©ra  rö   r@  )rß   r  rM  rR   r¢  r  s   &&&   rS   Ú_print_polylogÚLatexPrinter._print_polylogÖ  sD   € Ü�4—;‘; §	¡	Ó*‰ˆØ  1Õ$ˆØ‹;Û23²SÐ9Ð9ð ã34³cº3Ð?Ð?rU   c           	     	ó¨   € \        V P                  VP                  4      w  r4rVR V: RV: RV: RV: R2	pVe   RV,           RV,          ,           pV# )úP_{r{  rv  ú\right)}\left(rx  rJ  ú\right)^{%s}rï  )rß   r  rM  r~  r   r  r'  r  s   &&&     rS   Ú_print_jacobiÚLatexPrinter._print_jacobiÝ  sG   € Ü˜Ÿ™ d§i¡iÓ0‰
ˆˆa�Û?@Ã!ÃQËÐJˆØŠ?Ø˜c•/ O°sÕ$;Õ;ˆCØˆ
rU   c                	ó    € \        V P                  VP                  4      w  r4pR V: RV: RV: R2pVe   RV,           RV,          ,           pV# )zC_{r{  rô  rx  rJ  rõ  rï  ©rß   r  rM  r~  r   r'  r  s   &&&    rS   Ú_print_gegenbauerÚLatexPrinter._print_gegenbauerä  óC   € Ü�d—k‘k 4§9¡9Ó-‰ˆ‰aÛ<=»qÃ!ÐDˆØŠ?Ø˜c•/ O°sÕ$;Õ;ˆCØˆ
rU   c                	ó–   € \        V P                  VP                  4      w  r4R V: RV: R2pVe   RV,           RV,          ,           pV# )zT_{rˆ  rx  rJ  rõ  rï  ©rß   r  rM  r~  r'  r  s   &&&   rS   Ú_print_chebyshevtÚLatexPrinter._print_chebyshevtë  óA   € Ü�4—;‘; §	¡	Ó*‰ˆˆ1Û*+«QÐ/ˆØŠ?Ø˜c•/ O°sÕ$;Õ;ˆCØˆ
rU   c                	ó–   € \        V P                  VP                  4      w  r4R V: RV: R2pVe   RV,           RV,          ,           pV# )zU_{rˆ  rx  rJ  rõ  rï  rþ  s   &&&   rS   Ú_print_chebyshevuÚLatexPrinter._print_chebyshevuò  r  rU   c                	ó–   € \        V P                  VP                  4      w  r4R V: RV: R2pVe   RV,           RV,          ,           pV# )ró  rˆ  rx  rJ  rõ  rï  rþ  s   &&&   rS   Ú_print_legendreÚLatexPrinter._print_legendreù  r  rU   c                	ó    € \        V P                  VP                  4      w  r4pR V: RV: RV: R2pVe   RV,           RV,          ,           pV# )ró  r{  rô  rx  rJ  rõ  rï  rù  s   &&&    rS   Ú_print_assoc_legendreÚ"LatexPrinter._print_assoc_legendre   rü  rU   c                	ó–   € \        V P                  VP                  4      w  r4R V: RV: R2pVe   RV,           RV,          ,           pV# )zH_{rˆ  rx  rJ  rõ  rï  rþ  s   &&&   rS   Ú_print_hermiteÚLatexPrinter._print_hermite  r  rU   c                	ó–   € \        V P                  VP                  4      w  r4R V: RV: R2pVe   RV,           RV,          ,           pV# )úL_{rˆ  rx  rJ  rõ  rï  rþ  s   &&&   rS   Ú_print_laguerreÚLatexPrinter._print_laguerre  r  rU   c                	ó    € \        V P                  VP                  4      w  r4pR V: RV: RV: R2pVe   RV,           RV,          ,           pV# )r  r{  rô  rx  rJ  rõ  rï  rù  s   &&&    rS   Ú_print_assoc_laguerreÚ"LatexPrinter._print_assoc_laguerre  rü  rU   c           	     	ó¨   € \        V P                  VP                  4      w  r4rVR V: RV: RV: RV: R2	pVe   RV,           RV,          ,           pV# )zY_{r–  rˆ  rv  rx  rJ  rõ  rï  ©rß   r  rM  r~  ÚmÚthetaÚphir  s   &&&     rS   Ú
_print_YnmÚLatexPrinter._print_Ynm  óH   € Ü˜tŸ{™{¨D¯I©IÓ6Ñˆˆe�SÛ23³Q»»sÐCˆØŠ?Ø˜c•/ O°sÕ$;Õ;ˆCØˆ
rU   c           	     	ó¨   € \        V P                  VP                  4      w  r4rVR V: RV: RV: RV: R2	pVe   RV,           RV,          ,           pV# )zZ_{r–  rˆ  rv  rx  rJ  rõ  rï  r  s   &&&     rS   Ú
_print_ZnmÚLatexPrinter._print_Znm#  r  rU   c           
     	ó¢   € \        V P                  V4      w  rVpV'       d   R MRpV'       g   RMRV,          pV: V: RV: RV: RV: RV: 2
# )z	^{\prime}rÖ   r—  rJ  rQ  rx  )ra  rö   )	rß   Ú	characterr@  rp   rM  r   r  r¢  Úsups	   &&&&&    rS   Ú__print_mathieu_functionsÚ&LatexPrinter.__print_mathieu_functions*  s?   € Ü�d—k‘k 4Ó(‰ˆˆaß#‰l¨ˆß‰b ¨3¥ˆÚ3<»cÃ1ÃaËÊCÐPÐPrU   c                	ó>   € V P                  R VP                  VR7      # )ÚCr  ©Ú&_LatexPrinter__print_mathieu_functionsr@  rL  s   &&&rS   Ú_print_mathieucÚLatexPrinter._print_mathieuc0  ó   € Ø×-Ñ-¨c°4·9±9À#Ð-ÓFÐFrU   c                	ó>   € V P                  R VP                  VR7      # )r   r  r'  rL  s   &&&rS   Ú_print_mathieusÚLatexPrinter._print_mathieus3  r+  rU   c                	ó@   € V P                  R VP                  RVR7      # )r&  T©rp   rM  r'  rL  s   &&&rS   Ú_print_mathieucprimeÚ!LatexPrinter._print_mathieucprime6  ó    € Ø×-Ñ-¨c°4·9±9ÀDÈcÐ-ÓRÐRrU   c                	ó@   € V P                  R VP                  RVR7      # )r   Tr0  r'  rL  s   &&&rS   Ú_print_mathieusprimeÚ!LatexPrinter._print_mathieusprime9  r3  rU   c                	ó(  € VP                   ^8w  dh   RpVP                  pVP                  ^ 8  d   RpV) pV P                  R,          '       d   RW#VP                   3,          # RW#VP                   3,          # V P                  VP                  4      # )r   rÖ   rñ  r¡   z	%s%d / %dz%s\frac{%d}{%d})r  r  rÙ   rö   )rß   r  Úsignr  s   &&  rS   Ú_print_RationalÚLatexPrinter._print_Rational<  s}   € Ø�6‰6�QŒ;ØˆDØ—‘ˆAØ�v‰v˜ŒzØ�Ø�B�Ø�~‰~Ð/×0Ô0Ø# t°·±Ð&7Õ7Ð7Ø%¨°$·&±&Ð(9Õ9Ð9à—;‘;˜tŸv™vÓ&Ð&rU   c                	ó&  € V P                  VP                  4      pVP                  '       dO   \        ;QJ d&    R  VP                   4       F  '       g   K   RM	  RM! R  VP                   4       4      '       g   \	        VP
                  4      ^8”  dõ   VR,          p\	        VP
                  4      ^8”  d#   W P                  VP
                  4      ,          pM:VP
                  '       d)   W P                  VP
                  ^ ,          4      ,          pVR,          p\	        VP                  4      ^8”  d+   W P                  VP                  4      ,          pRV,          # W P                  VP                  ^ ,          4      ,          pRV,          # )c              3  óF   "  € T F  q\         P                  8g  x € K  	  R # 5irõ   )r   rl  )r&  r  s   & rS   r(  Ú,LatexPrinter._print_Order.<locals>.<genexpr>K  s   é € Ð>±:¨a¤1§6¡6žk³:ùs   ‚!TFrA  ú\rightarrow zO\left(%s\right))rö   r  Úpointr3  rŒ  Ú	variables)rß   r  rR   s   && rS   Ú_print_OrderÚLatexPrinter._print_OrderI  s
  € Ø�K‰K˜Ÿ	™	Ó"ˆØ�:�:ˆ:Ÿ#›#Ñ>°4·:²:Ó>Ÿ#Ÿ#š#Ñ>°4·:²:Ó>×>Ò>Üˆt�~‰~Ó Ô"Ø��IˆAÜ�4—>‘>Ó" QÔ&Ø—[‘[ §¡Ó0Õ0‘Ø——�Ø—[‘[ §¡°Õ!2Ó3Õ3�Ø�Õ ˆAÜ�4—:‘:‹ Ô"Ø—[‘[ §¡Ó,Õ,�ð # QÕ&Ð&ð —[‘[ §¡¨A¥Ó/Õ/�Ø" QÕ&Ð&rU   c               ó   € V ^8„  d   QhRR/# )r�   r  r   rP   )r’   s   "rS   r“   ré   Y  s   € ÷ Añ A &ñ ArU   c                	óŒ   € V P                   R ,          P                  V4      pVe   V# V P                  VP                  VR7      # )r®   ©Ústyle)rÙ   rÞ   rR  rV  )rß   r  rF  rV  s   &&& rS   Ú_print_SymbolÚLatexPrinter._print_SymbolY  s@   € Ø—N‘N >Õ2×6Ñ6°tÓ<ˆØÒØˆKà×(Ñ(¨¯©¸%Ð(Ó@Ð@rU   c               ó    € V ^8„  d   QhRRRR/# )r�   rV  r�   r‘   z tuple[str, list[str], list[str]]rP   )r’   s   "rS   r“   ré   b  s   € ÷ 
$ñ 
$ Sð 
$Ð-Mñ 
$rU   c                	óV  € Ve   RV9   d   V. . 3# V P                   R,          '       d'   VP                  RR4      P                  RR4      . . r2pM\        V4      w  rp\        V4      pV Uu. uF  p\        V4      NK  	  ppV Uu. uF  p\        V4      NK  	  ppWV3# u upi u upi )Nrs   r¾   r©  z\_r—   z\^)rÙ   r˜   r   Ú	translate)rß   rV  Úsupersrˆ  r"  r‚  s   &&    rS   Ú_split_super_subÚLatexPrinter._split_super_subb  s«   € ØŠ<˜3 $œ;Ø˜"˜b�>Ð!Ø�^‰^Ð5×6Ô6Ø"&§,¡,¨s°EÓ":×"BÑ"BÀ3ÈÓ"NÐPRÐTV˜$ˆD˜$ä!0°Ó!6ÑˆD˜$Ü˜‹ˆÙ,2Ó3©F S”)˜C–.©FˆÐ3Ù*.Ó/©$ 3”	˜#–©$ˆÐ/Ø˜dÐ#Ð#ùò 4ùÚ/s   Á-B!ÂB&c               ó    € V ^8„  d   QhRRRR/# )r�   Ústringr�   r‘   rP   )r’   s   "rS   r“   ré   n  s   € ÷ ñ ¨3ð À#ñ rU   c                	óú   € V P                  V4      w  r4pVR 8X  d   RP                  V4      pV'       d    VRRP                  V4      ,          ,          pV'       d    VRRP                  V4      ,          ,          pV# )rv   ú\mathbf{{{}}}r—  rÂ   r`  )rM  r’   rU  )rß   rP  rF  rV  rL  rˆ  s   &&&   rS   rR  Ú!LatexPrinter._deal_with_super_subn  sl   € Ø!×2Ñ2°6Ó:Ñˆ�dð �FŒ?Ø#×*Ñ*¨4Ó0ˆD÷ Ø�G˜cŸh™h vÓ.Õ.Õ.ˆDßØ�G˜cŸh™h t›nÕ,Õ,ˆDàˆrU   c                	ó   € V P                   R ,          '       d   RpRpMRpRpRRRVRVRRR	R
RR/pV P                  VP                  4      : RWAP                  ,          : RV P                  VP                  4      : 2# )r¤   z\gtz\ltÚ>Ú<z==r†  z>=z\geqz<=z\leqz!=z\neqrÂ   )rÙ   rö   ÚlhsÚrel_opÚrhs)rß   r  ÚgtÚltÚcharmaps   &&   rS   Ú_print_RelationalÚLatexPrinter._print_Relational}  s†   € Ø�>‰>˜&×!Ô!ØˆBØ‰BàˆBØˆBð �#Ø�Ø�Ø�'Ø�'Ø�'ð
ˆð "Ÿ[™[¨¯©Ö2Ø$§[¡[×1Ð1°4·;±;¸t¿x¹xÕ3HðJð 	JrU   c           	     	óz  € VP                   R R  UUu. uF,  w  r#V P                  V4      : RV P                  V4      : 2NK.  	  pppVP                   R,          P                  \        8X  dD   VP	                  RV P                  VP                   R,          P
                  4      ,          4       MlVP	                  V P                  VP                   R,          P
                  4      : RV P                  VP                   R,          P                  4      : 24       RpVRP                  V4      ,          # u uppi )Nz & \text{for}\: z%s & \text{otherwise}z\begin{cases} %s \end{cases}rÛ  ry  )r@  rö   Úcondr   rT  r  rU  )rß   r  r[  r™   Úecpairsr  s   &&    rS   Ú_print_PiecewiseÚLatexPrinter._print_Piecewise‘  sî   € à#Ÿy™y¨¨"™~ô/Ù-‘t�qð /3¯k©k¸!®n¸d¿k¹kÈ!½nÓMÙ-ð 	ñ /à�9‰9�R�=×Ñ¤Ô%Ø�N‰NÐ3ØŸ;™; t§y¡y°¥}×'9Ñ'9Ó:õ;õ <ð �N‰NØ ŸK™K¨¯	©	°"­×(:Ñ(:Ö;Ø ŸK™K¨¯	©	°"­×(:Ñ(:Õ;ð=ô >ð .ˆØ�V—[‘[ Ó)Õ)Ð)ùó/s   “2D7c                	ó0  € . p\        VP                  4       FI  pTP                  R P                  WR3,           Uu. uF  q@P	                  V4      NK  	  up4      4       KK  	  V P
                  R,          pVf4   V P
                  R,          R8X  d   RpMVP                  ^
8*  RJ d   RpMRpR	pVP                  R
V4      pVR8X  d2   VP                  RRRVP                  ,          ,           R,           4      pVRP                  V4      ,          # u upi )r‡  :NNNr©   rª   rÁ   ÚsmallmatrixTÚmatrixÚarrayú \begin{%MATSTR%}%s\end{%MATSTR%}ú%MATSTR%r¹  rs   r™   ú}%sr6  )r‹  ÚrowsrT  rU  rö   rÙ   Úcolsr˜   )rß   r  ÚlinesÚliner²   r©   Úout_strs   &&     rS   Ú_print_matrix_contentsÚ#LatexPrinter._print_matrix_contentsž  sè   € Øˆä˜$Ÿ)™)Ö$ˆDØ�L‰L˜Ÿ™¸TÈÀ'¾]Ó$K¹]¸§[¡[°¦^¹]Ñ$KÓLÖMñ %ð —.‘. Õ+ˆØŠ?Ø�~‰~˜fÕ%¨Ô1Ø'‘à—I‘I ‘O¨Ó,Ø&‘Gà%�Gà5ˆØ—/‘/ *¨gÓ6ˆØ�gÔØ—o‘o d¨C°#°d·i±iµ-Õ,?À%Õ,GÓHˆGØ˜Ÿ™ EÓ*Õ*Ð*ùò! %Ls   ½Dc                	óâ   € V P                  V4      pV P                  R ,          '       dE   V P                  R ,          pV P                  V,          pRV,           V,           R,           V,           pV# )r§   ú\leftú\right)rp  rÙ   rÝ   )rß   r  ro  Ú
left_delimÚright_delims   &&   rS   Ú_print_MatrixBaseÚLatexPrinter._print_MatrixBase´  sc   € Ø×-Ñ-¨dÓ3ˆØ�>‰>˜+×&Ô&ØŸ™¨Õ4ˆJØ×*Ñ*¨:Õ6ˆKØ Õ+¨gÕ5Øõ Ø"-õ.ˆGàˆrU   c                	óØ   € V P                  VP                  \        R ,          RR7      pV P                  VP                  4       RV P                  VP
                  4       2pRV RV R2# )r  T©rú   rv  rs   ú}_{rO   )rü   Úparentr    rö   r²   rÎ   )rß   r  Úmatrix_partÚ
index_parts   &&  rS   Ú_print_MatrixElementÚ!LatexPrinter._print_MatrixElement½  sd   € Ø×'Ñ'¨¯©´ZÀÕ5GÐPTÐ'ÓUˆØŸ™ D§F¡FÓ+Ð,¨A¨d¯k©k¸$¿&¹&Ó.AÐ-BÐCˆ
Ø�K�=  j \°Ð4Ð4rU   c                	ó<  a € V 3R  lpS P                  VP                  \        R,          RR7      R,           V! VP                  VP                  P                  4      ,           R,           V! VP
                  VP                  P                  4      ,           R,           # )c                ó¾   <€ \        V 4      p V ^,          ^8X  d   V ^ V ^ ,          ^ 8X  d   RV ^ &   V ^,          V8X  d   RV ^&   RP                  V3R lV  4       4      # )r�   NÚ:c              3  óP   <"  € T F  qe   SP                  V4      MRx € K  	  R # 5i©NrÖ   r€  )r&  Úxirß   s   & €rS   r(  ÚFLatexPrinter._print_MatrixSlice.<locals>.latexslice.<locals>.<genexpr>Ë  s"   øé € ÐRÑPQÈ"ª~˜DŸK™K¨œOÀ2ÔEÓPQùs   ƒ#&)rß  rU  )r'  rz  rß   s   &&€rS   Ú
latexsliceÚ3LatexPrinter._print_MatrixSlice.<locals>.latexsliceÃ  s\   ø€ Ü�Q“ˆAØ��t�qŒyØ�a�DØ��t�qŒyØ��!‘Ø��t�sŒ{Ø��!‘Ø—8‘8ÔRÑPQÓRÓRÐRrU   r  Trz  ú\left[rQ  ú\right])rü   r|  r    Úrowslicerk  Úcolslicerl  )rß   r  rˆ  s   f& rS   Ú_print_MatrixSliceÚLatexPrinter._print_MatrixSliceÂ  s�   ø€ õ	Sð ×!Ñ! $§+¡+¬z¸&Õ/AÈ$Ð!ÓOÐR[Õ[Ù˜4Ÿ=™=¨$¯+©+×*:Ñ*:Ó;õ<Ø>BõCá˜4Ÿ=™=¨$¯+©+×*:Ñ*:Ó;õ<à>HõIð 	JrU   c                	ó8   € V P                  VP                  4      # rõ   )rö   Úblocksr  s   &&rS   Ú_print_BlockMatrixÚLatexPrinter._print_BlockMatrixÐ  s   € Ø�{‰{˜4Ÿ;™;Ó'Ð'rU   c                	ó,  € VP                   p^ RIHpHp \	        W#4      '       g<   \	        W$4      '       g+   VP
                  '       d   RV P                  V4      ,          # V P                  V\        V4      R4      pRV9   d
   RV,          # RV,          # )rr  ©ÚMatrixSymbolÚBlockMatrixz\left(%s\right)^{T}Tr—   z%s^{T})	rB  Úsympy.matricesr–  r—  rØ  Úis_MatrixExprrö   rü   r   )rß   r  r‘  r–  r—  rR   s   &&    rS   Ú_print_TransposeÚLatexPrinter._print_TransposeÓ  sy   € Ø�h‰hˆß<Ü˜3×-Ò-Ü˜3×,Ò,°×1B×1BÐ1BØ)¨D¯K©K¸Ó,<Õ<Ð<à×!Ñ! #Ô'=¸dÓ'CÀTÓJˆAØ�aŒxØ-°Õ1Ð1à !•|Ð#rU   c                	óJ   € VP                   pR V P                  V4      ,          # )z!\operatorname{tr}\left(%s \right))rB  rö   ©rß   r  r‘  s   && rS   Ú_print_TraceÚLatexPrinter._print_Traceà  s   € Ø�h‰hˆØ3°d·k±kÀ#Ó6FÕFÐFrU   c                	óŒ  € R RRRRR/pVP                  V P                  R,          R4      pVP                  p^ RIHpHp \        WE4      '       g>   \        WF4      '       g-   VP                  '       d   RV P                  V4      : R	V: R
2# V P                  V\        V4      R4      pRV9   d   RV: R	V: R
2# V: RV: R
2# )r½   z\daggerÚstarz\astÚ	hermitianz
\mathsf{H}r¼   r•  rJ  rK  rO   Tr—   r  )rÞ   rÙ   rB  r˜  r–  r—  rØ  r™  rö   rü   r   )rß   r  Ústyle_to_latexr¼   r‘  r–  r—  rR   s   &&      rS   Ú_print_AdjointÚLatexPrinter._print_Adjointä  s­   € à˜Ø˜Ø˜ð
ˆð
 '×*Ñ*¨4¯>©>¸/Õ+JÈJÓWˆØ�h‰hˆß<Ü˜3×-Ò-Ü˜3×,Ò,°×1B×1BÑ1BØ.2¯k©k¸#Ö.>ÃÐNÐNà×!Ñ! #Ô'=¸dÓ'CÀTÓJˆAØ�a�xÛ23³]ÐCÐCã%&«Ð6Ð6rU   c                	ó:  a aa€ ^ RI Ho VVV 3R lp\        SP                  4      pSP	                  4       '       dG   V^ ,          R8X  d   VR,          pMV^ ,          ) V^ &   RRP                  \        W#4      4      ,           # RP                  \        W#4      4      # )rr  )ÚMatMulc                ó®   <€ \        V \        4      '       d$   \        V S4      '       g   SP                  V 4      # SP                  V \	        S4      R 4      # ©F)rØ  r	   rö   rü   r   )r'  r§  r  rß   s   &€€€rS   rT   Ú,LatexPrinter._print_MatMul.<locals>.<lambda>û  sK   ø€ ¬Z¸¼3×-?Ò-?Ì
ÐSTÐV\×H]ÒH]˜4Ÿ;™; q›>ð FØ×Ñ˜aÔ!7¸Ó!=¸uÓEðFrU   rŸ  rñ  rÂ   ry  )Úsympyr§  rß  r@  r0  rU  ra  )rß   r  Úparensr@  r§  s   ff  @rS   Ú_print_MatMulÚLatexPrinter._print_MatMul÷  s|   ú€ Ý öFˆô �D—I‘I‹ˆØ×(Ñ(×*Ò*Ø�A�w˜"Œ}Ø˜B•x‘à �7˜(��Q‘Ø˜#Ÿ(™(¤3 vÓ#4Ó5Õ5Ð5à—8‘8œC Ó-Ó.Ð.rU   c                	ó~   € \        V4      pVP                  w  r4V P                  W24       R V P                  WB4       2# )rÄ   )r   r@  rü   )rß   r  rø   ÚleftÚrights   &&   rS   Ú_print_DotProductÚLatexPrinter._print_DotProduct  s@   € Ü& tÓ,ˆØ—i‘i‰ˆØ×$Ñ$ TÓ1Ð2°'¸$×:KÑ:KÈEÓ:YÐ9ZÐ[Ð[rU   c                	ó  € VP                   pVP                  '       dR   ^ RIHp \	        W#4      '       d#   RV P                  VP                  4      ,          # RV P                  V4      ,          # RV P                  V4      ,          # )rr  )r—  rÿ  )rB  r™  Ú&sympy.matrices.expressions.blockmatrixr—  rØ  rp  r‘  rö   )rß   r  r‘  r—  s   &&  rS   Ú_print_DeterminantÚLatexPrinter._print_Determinant  si   € Ø�h‰hˆØ××ÐÝJÜ˜#×+Ò+Ø+¨d×.IÑ.IÈ#Ï*É*Ó.UÕUÐUØ'¨$¯+©+°cÓ*:Õ:Ð:Ø# d×&AÑ&AÀ#Ó&FÕFÐFrU   c           	     	óª  € Vel   RV P                  VP                  ^ ,          \        R,          RR7      : RV P                  VP                  ^,          \        R,          RR7      : RV: R2# V P                  VP                  ^ ,          \        R,          RR7      : RV P                  VP                  ^,          \        R,          RR7      : 2# )NrJ  r	   Trz  z \bmod rK  rO   rn  rL  s   &&&rS   Ú
_print_ModÚLatexPrinter._print_Mod  sÄ   € Ø‹?à×"Ñ" 4§9¡9¨Q¥<´¸EÕ1BØ*.ð #ö 0à×"Ñ" 4§9¡9¨Q¥<´¸EÕ1BØ*.ð #ö 0ãðð ð "&×!2Ñ!2°4·9±9¸Qµ<Ü3=¸eÕ3DØ:>ð "3ö "@ð "&×!2Ñ!2°4·9±9¸Qµ<Ü3=¸eÕ3DØ:>ð "3õ "@ðAð 	ArU   c                	óˆ   aa€ VP                   p\        R ,          oV P                  oRP                  VV3R lV 4       4      # )r   z \circ c              3  ó:   <"  € T F  pS! VSR R7      x € K  	  R# 5i©Trz  NrP   ©r&  rB  r¬  Úprecs   & €€rS   r(  Ú6LatexPrinter._print_HadamardProduct.<locals>.<genexpr>,  ó   øé € Ð<±t°‰V�C˜ d×+Ñ+³tùó   ƒ©r@  r    rü   rU  ©rß   r  r@  r¬  r¿  s   && @@rS   Ú_print_HadamardProductÚ#LatexPrinter._print_HadamardProduct&  s:   ù€ Ø�y‰yˆÜ˜%Õ ˆØ×"Ñ"ˆà�‰Ý<±tÓ<ó>ð 	>rU   c                	óx   € \        VP                  4      \        R ,          8  d   RpMRpV P                  W4      # )r	   z%s^{\circ \left({%s}\right)}z%s^{\circ {%s}})r   rM  r    r  )rß   r  r  s   && rS   Ú_print_HadamardPowerÚ!LatexPrinter._print_HadamardPower.  s3   € Ü! $§(¡(Ó+¬j¸Õ.?Ô?Ø6‰Hà)ˆHØ×0Ñ0°Ó@Ð@rU   c                	óˆ   aa€ VP                   p\        R ,          oV P                  oRP                  VV3R lV 4       4      # )r   ú	 \otimes c              3  ó:   <"  € T F  pS! VSR R7      x € K  	  R# 5ir½  rP   r¾  s   & €€rS   r(  Ú7LatexPrinter._print_KroneckerProduct.<locals>.<genexpr>;  rÁ  rÂ  rÃ  rÄ  s   && @@rS   Ú_print_KroneckerProductÚ$LatexPrinter._print_KroneckerProduct5  s<   ù€ Ø�y‰yˆÜ˜%Õ ˆØ×"Ñ"ˆà× Ñ Ý<±tÓ<ó>ð 	>rU   c                	ój  € VP                   VP                  r2^ RIHp \	        W$4      '       g<   VP
                  '       d*   RV P                  V4      : RV P                  V4      : R2# V P                  V4      pRV9   d   RV: RV P                  V4      : R2# V: RV P                  V4      : R2# )rr  )r–  rJ  rK  rO   r—   r  )rF  rM  r˜  r–  rØ  r™  rö   )rß   r  rF  rM  r–  Úbase_strs   &&    rS   Ú_print_MatPowÚLatexPrinter._print_MatPow=  s�   € Ø—I‘I˜tŸx™xˆcÝ/Ü˜$×-Ò-°$×2D×2DÑ2DØ/3¯{©{¸4Ö/@Ø.2¯k©k¸#Ö.>ð@ð @ð —{‘{ 4Ó(ˆHØ�h�Û2:¸D¿K¹KÈÖ<LÐMÐMã$,¨d¯k©k¸#Ö.>Ð?Ð?rU   c                	óH   € V P                  WP                  R ,          R7      # )r°   rE  )rG  rÙ   r  s   &&rS   Ú_print_MatrixSymbolÚ LatexPrinter._print_MatrixSymbolJ  s&   € Ø×!Ñ! $¯n©nØõ/ Ð!ó !ð 	!rU   c                	ó:   € V P                   R ,          R8X  d   R# R# )r°   r«   Ú0z
\mathbf{0}©rÙ   )rß   ÚZs   &&rS   Ú_print_ZeroMatrixÚLatexPrinter._print_ZeroMatrixN  ó(   € Ø—n‘nØõ Ø#*ô+ˆsð 	>Ø0=ð	>rU   c                	ó:   € V P                   R ,          R8X  d   R# R# )r°   r«   Ú1z
\mathbf{1}rÙ  )rß   ÚOs   &&rS   Ú_print_OneMatrixÚLatexPrinter._print_OneMatrixR  rÝ  rU   c                	ó:   € V P                   R ,          R8X  d   R# R# )r°   r«   z
\mathbb{I}z
\mathbf{I}rÙ  )rß   rN  s   &&rS   Ú_print_IdentityÚLatexPrinter._print_IdentityV  s(   € Ø $§¡Øõ! Ø#*ô!+ˆ}ð 	>Ø0=ð	>rU   c                	óX   € V P                  VP                  ^ ,          4      pRV,          # )rr  zP_{%s}r(  )rß   ÚPÚperm_strs   && rS   Ú_print_PermutationMatrixÚ%LatexPrinter._print_PermutationMatrixZ  s#   € Ø—;‘;˜qŸv™v a�yÓ)ˆØ˜(Õ"Ð"rU   c               ó   € V ^8„  d   QhRR/# )r�   r  r%   rP   )r’   s   "rS   r“   ré   ^  s   € ÷ 5ñ 5 Yñ 5rU   c           
     	óÞ  € VP                  4       ^ 8X  d   V P                  VR,          4      # V P                  R,          pVfN   V P                  R,          R8X  d   RpM2VP                  4       ^ 8X  g   VP                  R,          ^
8:  d   RpMRpRpVP	                  RV4      pVR8X  d9   VP	                  R	R
RVP                  ^ ,          ,          ,           R,           4      pV P                  R,          '       dE   V P                  R,          pV P
                  V,          pRV,           V,           R,           V,           pVP                  4       ^ 8X  d
   VR,          # \        VP                  4       ^,           4       Uu. uF  p. NK  	  ppVP                   Uu. uF  p\        \        V4      4      NK  	  pp\        P                  ! V!   EFZ  p	VR,          P                  V P                  W,          4      4       Rp
\        VP                  4       ^,
          RR4       EF   p\        W{^,           ,          4      VP                  V,          8  d    KŠ  V
'       d5   W{,          P                  RP                  W{^,           ,          4      4       M}W{,          P                  VRP                  W{^,           ,          4      ,          4       \        W{^,           ,          4      ^8X  d'   RW{,          R,          ,           R,           W{,          R&   V
'       * p
. W{^,           &   EK  	  EK]  	  V^ ,          ^ ,          pVP                  4       ^,          ^8X  d	   W<,          pV# u upi u upi )rr  r©   rª   rÁ   re  rf  rg  rh  ri  r¹  rs   r™   rj  r§   rs  rt  rÖ   Tr‡  r6  rŠ  r‹  rP   ry  )Úrankrö   rÙ   Úshaper˜   rÝ   r‹  rß  Ú	itertoolsÚproductrT  rŒ  rU  )rß   r  r©   Ú	block_strru  rv  r²   Ú	level_strÚshape_rangesÚouter_iÚevenÚback_outer_iro  s   &&           rS   Ú_print_NDimArrayÚLatexPrinter._print_NDimArray^  s²  € à�9‰9‹;˜!ÔØ—;‘;˜t B�xÓ(Ð(à—.‘. Õ+ˆØŠ?Ø�~‰~˜fÕ%¨Ô1Ø'‘à—I‘I“K 1Ô$¨$¯*©*°R­.¸BÔ*>Ø&‘Gà%�GØ7ˆ	Ø×%Ñ% j°'Ó:ˆ	Ø�gÔØ!×)Ñ)¨$°°c¸$¿*¹*ÀQ½-Õ6GÕ0GÈ%Õ0OÓPˆIà�>‰>˜+×&Ô&Ø"Ÿn™n¨[Õ9ˆJØ×*Ñ*¨:Õ6ˆKØ  :Õ-°	Õ9Ø!õ"Ø$/õ0ˆIð �9‰9‹;˜!ÔØ˜r•>Ð!ä27¸¿	¹	»Àa½Ô2HÓ%IÑ2H¨Q£bÑ2Hˆ	Ð%IØ04·
²
Ó;±
¨1œœU 1›Xž±
ˆÐ;Ü ×(Ò(¨,Õ7ˆGØ�b�M× Ñ  §¡¨T­]Ó!;Ô<ØˆDÜ % d§i¡i£k°!¥m°R¸× <�Ü�y¨a¥Õ0Ó1°D·J±J¸|Õ4LÔLÚßØÕ+×2Ñ2ØŸ™ I¸1­nÕ$=Ó>õ@ð Õ+×2Ñ2Ø! U§Z¡Z°	Àq½.Õ0IÓ%JÕKôMä˜9°!¥^Õ4Ó5¸Ô:Ø6?Ø%Õ3°BÕ7õ78Ø:Dõ7E˜	Õ/°Ñ3à”x�Ø,.�	 q�.Ô)ô !=ñ 8ð$ ˜A•,˜q•/ˆà�9‰9‹;˜�?˜aÔØÕ)ˆGàˆùò3 &JùÚ;s   ÆM%ÆM*c               ó   € V ^8„  d   QhRR/# )r�   Ú	index_mapÚdictrP   )r’   s   "rS   r“   ré   •  s   € ÷ ñ Àñ rU   c                	óÔ  € V P                  V4      pR pR pV F¿  pVP                  pWs9   g	   V'       d   WX8X  d
   VR,          pWX8w  d3   Ve
   VR,          pVP                  '       d   VR,          pM	VR,          pW@P                  VP                  ^ ,          4      ,          pWs9   d*   VR,          pW@P                  W7,          4      ,          pRpMRpTpKÁ  	  Ve
   VR,          pV# )Nrv  rO   z{}^{z{}_{r†  TF)rö   Úis_upr@  )	rß   rV  rb  rú  ro  Úlast_valenceÚprev_mapÚindexÚnew_valences	   &&&&     rS   Ú_printer_tensor_indicesÚ$LatexPrinter._printer_tensor_indices•  s×   € Ø—+‘+˜dÓ#ˆØˆØˆÛˆEØŸ+™+ˆKØÔ#¯Ø Ô/Ø˜3•�ØÔ*ØÒ+Ø˜s•N�GØ—;—;�;Ø˜vÕ%‘Gà˜vÕ%�GØ—{‘{ 5§:¡:¨a¥=Ó1Õ1ˆGØÔ!Ø˜3•�ØŸ;™; yÕ'7Ó8Õ8�Ø‘à �Ø&ŠLñ' ð( Ò#Ø�s�NˆGØˆrU   c                	óŽ   € VP                   ^ ,          P                   ^ ,          pVP                  4       pV P                  W#/ 4      # r'  )r@  Úget_indicesr  )rß   r  rV  rb  s   &&  rS   Ú_print_TensorÚLatexPrinter._print_Tensor±  s;   € Ø�y‰y˜�|× Ñ  Õ#ˆØ×"Ñ"Ó$ˆØ×+Ñ+¨D¸2Ó>Ð>rU   c                	óÎ   € VP                   P                  ^ ,          P                  ^ ,          pVP                   P                  4       pVP                  pV P	                  W#V4      # r'  )r  r@  r  rú  r  )rß   r  rV  rb  rú  s   &&   rS   Ú_print_TensorElementÚ!LatexPrinter._print_TensorElement¶  sM   € Ø�y‰y�~‰~˜aÕ ×%Ñ% aÕ(ˆØ—)‘)×'Ñ'Ó)ˆØ—N‘Nˆ	Ø×+Ñ+¨D¸9ÓEÐErU   c                	ó°   € VP                  4       w  r#TR P                  V Uu. uF  q@P                  V\        V4      4      NK  	  up4      ,           # u upi )rÖ   )Ú!_get_args_for_traditional_printerrU  rü   r   )rß   r  r8  r@  rB  s   &&   rS   Ú_print_TensMulÚLatexPrinter._print_TensMul¼  sO   € à×;Ñ;Ó=‰
ˆØ�b—g‘gÙAEÓFÁ¸#×Ñ˜s¤J¨tÓ$4Ö5ÁÑFó
õ 
ð 	
ùÚFs   £#A
c           	     	óî   € . pVP                   pV F-  pVP                  V P                  V\        V4      4      4       K/  	  VP	                  4        R P                  V4      pVP                  RR4      pV# )rh  z+ -rñ  )r@  rT  rü   r   rS  rU  r˜   )rß   r  r   r@  r'  rR   s   &&    rS   Ú_print_TensAddÚLatexPrinter._print_TensAddÃ  sc   € ØˆØ�y‰yˆÛˆAØ�H‰H�T×&Ñ& q¬*°TÓ*:Ó;Ö<ñ à	�‰ŒØ�J‰J�q‹MˆØ�I‰I�e˜TÓ"ˆØˆrU   c                	ó€   € R VP                   '       d   RMR: RV P                  VP                  ^ ,          4      : R2# )z{}r—   r©  rs   rO   )rý  rö   r@  r  s   &&rS   Ú_print_TensorIndexÚLatexPrinter._print_TensorIndexÍ  s0   � à—:—:�:‰C 3Ò&Ø�K‰K˜Ÿ	™	 !�Ö%ð
ð 	
rU   c                	óð  € \        VP                  4      ^8X  dR   RV P                  VP                  ^ ,          4      : RV P                  VP                  \
        R,          R4      : R2# R\        VP                  4      : RRP                  VP                   Uu. uF  pRV P                  V4      ,          NK  	  up4      : R	V P                  VP                  \
        R,          R4      : R2# u upi )
r   z\frac{\partial}{\partial {rp  r	   FrO   z\frac{\partial^{rÂ   z\partial {%s}rõ  )rŒ  r@  rö   rü   r  r    rU  ©rß   r  r²   s   && rS   Ú_print_PartialDerivativeÚ%LatexPrinter._print_PartialDerivativeÓ  s¸   € Üˆt�~‰~Ó !Õ#à—‘˜DŸN™N¨1Õ-Ö.Ø×!Ñ! $§)¡)¬Z¸Õ->ÀÖFðð ð $ô �D—N‘NÖ#Ø—‘ÀTÇ^Â^ÓTÁ^ÀÐ*¨T¯[©[¸«^×;Ð;Á^ÑTÖUØ×!Ñ! $§)¡)¬Z¸Õ->ÀÖFðð ùâTs   Â!C3c                	ó8   € V P                  VP                  4      # rõ   )rö   rV  r  s   &&rS   Ú_print_ArraySymbolÚLatexPrinter._print_ArraySymbolà  s   € Ø�{‰{˜4Ÿ9™9Ó%Ð%rU   c                	óÞ   € R V P                  VP                  \        R,          R4      : RRP                  VP                   Uu. uF  q P                  V4       NK  	  up4      : R2# u upi )z{{rm  Tr{  rQ  r  )rü   rV  r    rU  rb  rö   r  s   && rS   Ú_print_ArrayElementÚ LatexPrinter._print_ArrayElementã  sW   � à×Ñ˜dŸi™i¬°FÕ);¸TÖBØ�I‰I°D·L²LÓA±L¨qŸ+™+ a›.Ð)Ò*±LÑAÖBðDð 	DùâAs   ÁA*c                	ó   € R # )z
\mathbb{U}rP   r  s   &&rS   Ú_print_UniversalSetÚ LatexPrinter._print_UniversalSetè  ó   € ÙrU   c                	ó²   € Vf*   RV P                  VP                  ^ ,          4      ,          # RV P                  VP                  ^ ,          4      : RV: R2# )Nz$\operatorname{frac}{\left(%s\right)}z\operatorname{frac}{\left(z
\right)}^{rO   r(  rL  s   &&&rS   Ú_print_fracÚLatexPrinter._print_fracë  sK   € ØŠ;Ø:¸T¿[¹[ÈÏÉÐSTÍÓ=VÕVÐVð ð —K‘K §	¡	¨!¥Ö-«sð4ð 4rU   c           
     	ó”  € V P                   R ,          R8X  d   RpM&V P                   R ,          R8X  d   RpM\        R4      h\        V4      ^8X  d/   V P                  V P	                  V^ ,          4      V,           4      # T P                  VR,           P                  V Uu. uF  q0P	                  V4      NK  	  up4      4      # u upi )r´   r¡  Ú;rµ   rv  úUnknown Decimal Separatorz \  )rÙ   rÚ   rŒ  rñ   rö   rU  )rß   r  Úsepr²   s   &&  rS   Ú_print_tupleÚLatexPrinter._print_tupleò  s©   € Ø�>‰>Ð-Õ.°'Ô9Ø‰CØ�^‰^Ð/Õ0°HÔ<Ø‰CäÐ8Ó9Ð9äˆt‹9˜Œ>à×*Ñ*¨4¯;©;°t¸AµwÓ+?À#Õ+EÓFÐFà×*Ñ*Ø�w•×$Ñ$¹dÓ%C¹d¸§k¡k°!¦n¹dÑ%CÓDóFð FùÚ%Cs   Â!Cc                	ó€   € VP                    Uu. uF  q P                  V4      NK  	  ppR P                  V4      # u upi )rË  ©r@  rö   rU  ©rß   r  r   Úelementss   &&  rS   Ú_print_TensorProductÚ!LatexPrinter._print_TensorProduct  s6   € Ø,0¯IªIÓ6©I q—K‘K –N©IˆÐ6Ø× Ñ  Ó*Ð*ùò 7ó   �;c                	ó€   € VP                    Uu. uF  q P                  V4      NK  	  ppR P                  V4      # u upi )ú \wedge r-  r.  s   &&  rS   Ú_print_WedgeProductÚ LatexPrinter._print_WedgeProduct  s6   € Ø,0¯IªIÓ6©I q—K‘K –N©IˆÐ6Ø×Ñ Ó)Ð)ùò 7r2  c                	ó$   € V P                  V4      # rõ   )r*  r  s   &&rS   Ú_print_TupleÚLatexPrinter._print_Tuple	  s   € Ø× Ñ  Ó&Ð&rU   c           	     	ód  € V P                   R ,          R8X  d7   RRP                  V Uu. uF  q P                  V4      NK  	  up4      ,          # V P                   R ,          R8X  d7   RRP                  V Uu. uF  q P                  V4      NK  	  up4      ,          # \        R4      hu upi u upi )r´   r¡  z\left[ %s\right]z; \  rµ   ú, \  r(  )rÙ   rU  rö   rÚ   r  s   && rS   Ú_print_listÚLatexPrinter._print_list  sš   € Ø�>‰>Ð-Õ.°'Ô9Ø&Ø—‘±tÓ<±t°!Ÿ{™{¨1ž~±tÑ<Ó=õ>ð >à�^‰^Ð/Õ0°HÔ<Ø&Ø—‘±tÓ<±t°!Ÿ{™{¨1ž~±tÑ<Ó=õ>ð >ô Ð8Ó9Ð9ùò =ùò =s   ©B(
Á7B-
c                	ó  € \        VP                  4       \        R 7      p. pV FA  pW,          pVP                  V P	                  V4      : RV P	                  V4      : 24       KC  	  RRP                  V4      ,          # )rI  z : z\left\{ %s\right\}r;  )rð  Úkeysr   rT  rö   rU  )rß   r»   r?  rQ  rJ  Úvals   &&    rS   Ú_print_dictÚLatexPrinter._print_dict  sd   € Ü�a—f‘f“hÔ$4Ô5ˆØˆãˆCØ•&ˆCØ�L‰L d§k¡k°#Ö&6¸¿¹ÀCÕ8HÐIÖJñ ð % x§}¡}°UÓ';Õ;Ð;rU   c                	ó$   € V P                  V4      # rõ   )rA  r  s   &&rS   Ú_print_DictÚLatexPrinter._print_Dict!  s   € Ø×Ñ Ó%Ð%rU   c                	óz  € \        VP                  4      ^8X  g   VP                  ^,          ^ 8X  d+   RV P                  VP                  ^ ,          4      ,          pMKRV P                  VP                  ^,          4      : RV P                  VP                  ^ ,          4      : R2pV'       d   RV: RV: R2pV# )r   z\delta\left(%s\right)z\delta^{\left( z \right)}\left( rè  rJ  rK  rO   r=  rõ  s   &&& rS   Ú_print_DiracDeltaÚLatexPrinter._print_DiracDelta$  s†   € Üˆt�y‰y‹>˜QÔ $§)¡)¨A¥,°!Ô"3Ø*¨T¯[©[¸¿¹À1½Ó-FÕF‰Cð #4ð —‘˜DŸI™I a�LÖ)¨4¯;©;°t·y±yÀµ|Ö+DðFˆCçˆ3Û-0³#Ð6ˆCØˆ
rU   c                	óú   € V P                  VP                  ^ ,          VP                  ^,          ,
          4      pV P                  VP                  ^,          4      pRV: RV: R2pVe   RV: RV: RV: R2pV# )rr  z{\left\langle z \right\rangle}^{rO   z{\left({\langle z \rangle}^{z}\right)}^{r(  )rß   r  rM  Úshiftr¸  r  s   &&&   rS   Ú_print_SingularityFunctionÚ'LatexPrinter._print_SingularityFunction.  s\   € Ø—‘˜DŸI™I a�L¨4¯9©9°Q­<Õ7Ó8ˆØ—‘˜DŸI™I a�LÓ)‰Û9>ÃÐFˆØ‹?ÛFKËUÓTWÐXˆCØˆ
rU   c                	óŠ   a € R P                  V 3R lVP                   4       4      pRV,          pV'       d   RV: RV: R2pV# )rQ  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  ©r&  rB  rß   s   & €rS   r(  Ú0LatexPrinter._print_Heaviside.<locals>.<genexpr>7  s   øé € ÐA±j¨s˜$Ÿ+™+ c×*Ð*³jùr+  z\theta\left(%s\right)rJ  rK  rO   )rU  Úpargs)rß   r  rM  rQ  r  s   f&&  rS   Ú_print_HeavisideÚLatexPrinter._print_Heaviside6  s9   ø€ Ø—	‘	ÔA°d·j²jÓAÓAˆØ&¨Õ.ˆßˆ3Û-0³#Ð6ˆCØˆ
rU   c                	óf  € V P                  VP                  ^ ,          4      pV P                  VP                  ^,          4      pVP                  ^ ,          P                  '       d0   VP                  ^,          P                  '       d   RV: RV: R2pMRV: RV: R2pVe   RV: RV: R2pV# )rr  z\delta_{rÂ   rO   rQ  rJ  rK  )rö   r@  r  )rß   r  rM  r²   rÎ   r  s   &&&   rS   Ú_print_KroneckerDeltaÚ"LatexPrinter._print_KroneckerDelta=  s~   € Ø�K‰K˜Ÿ	™	 !�Ó%ˆØ�K‰K˜Ÿ	™	 !�Ó%ˆØ�9‰9�Q�<××Ð D§I¡I¨a¥L×$8×$8Ñ$8Û'(«!Ð,‰Cøã()«1Ð-ˆCØ‹?Û-0³#Ð6ˆCØˆ
rU   c                	ój  € \        V P                  VP                  4      p\        ;QJ d&    R  VP                   4       F  '       d   K   RM	  RM! R  VP                   4       4      '       d   RRP	                  V4      ,          pMRRP	                  V4      ,          pV'       d   RV: RV: R2pV# )	c              3  ó8   "  € T F  qP                   x € K  	  R # 5irõ   )r  )r&  r'  s   & rS   r(  Ú1LatexPrinter._print_LeviCivita.<locals>.<genexpr>J  s   é € Ð,¡)˜Q�yŽy£)ùs   ‚FTz\varepsilon_{%s}rÂ   rQ  rJ  rK  rO   )ra  rö   r@  r™  rU  )rß   r  rM  rb  r  s   &&&  rS   Ú_print_LeviCivitaÚLatexPrinter._print_LeviCivitaH  sy   € Ü�d—k‘k 4§9¡9Ó-ˆß‹3Ñ, $§)¢)Ó,�3�3Š3Ñ, $§)¢)Ó,×,Ò,Ø%¨¯©°Ó(9Õ9‰Cà%¨¯	©	°'Ó(:Õ:ˆCßˆ3Û-0³#Ð6ˆCØˆ
rU   c                	ó²  € \        VR 4      '       d'   RV P                  VP                  4       4      ,           # \        VR4      '       dJ   RV P                  VP                  4      ,           R,           V P                  VP                  4      ,           # \        VR4      '       d#   RV P                  VP                  4      ,           # V P                  R4      # )Ú
as_booleanz\text{Domain: }Úsetú \in r›  z\text{Domain on }N)r×  rö   r]  r›  r^  )rß   r»   s   &&rS   Ú_print_RandomDomainÚ LatexPrinter._print_RandomDomainR  sž   € Ü�1�l×#Ò#Ø%¨¯©°A·L±L³NÓ(CÕCÐCÜ�Q˜×ÒØ&¨¯©°Q·Y±YÓ)?Õ?À(ÕJØ—K‘K §¡Ó&õ'ð (ä�Q˜	×"Ò"Ø'¨$¯+©+°a·i±iÓ*@Õ@Ð@à—;‘;˜tÓ$Ð$rU   c                	óZ   € \        VP                  \        R 7      pV P                  V4      # )rI  )rð  r@  r   Ú
_print_set©rß   rR   rQ  s   && rS   Ú_print_FiniteSetÚLatexPrinter._print_FiniteSet]  s"   € Ü�q—v‘vÔ#3Ô4ˆØ�‰˜uÓ%Ð%rU   c                	óR  € \        V\        R 7      pV P                  R,          R8X  d/   RP                  \	        V P
                  V4      4      pRV,          # V P                  R,          R8X  d/   RP                  \	        V P
                  V4      4      pRV,          # \        R4      h)rI  r´   r¡  rA  rµ   rQ  r(  ú\left\{%s\right\})rð  r   rÙ   rU  ra  rö   rÚ   rd  s   && rS   rc  ÚLatexPrinter._print_seta  s�   € Ü�qÔ.Ô/ˆØ�>‰>Ð-Õ.°'Ô9Ø—I‘Iœc $§+¡+¨uÓ5Ó6ˆEð
 $ eÕ+Ð+ð	 �^‰^Ð/Õ0°HÔ<Ø—I‘Iœc $§+¡+¨uÓ5Ó6ˆEð $ eÕ+Ð+ô Ð8Ó9Ð9rU   c                	ó:  a aa€ VV 3R  lp\        4       oSP                  P                  '       dJ   SP                  P                  '       d.   SP                  P
                  '       d
   SR^ ^S3pEMS^^ RS3pMùSP                  P                  '       d&   SSR,          SP                  ,
          SR,          3pM¸SP                  P                  '       d$   \        S4      p\        V4      \        V4      S3pMySP                  ee   SP                  ^8  R8X  d   \        S4      pMKSP                  '       d,   \        S4      p\        V4      \        V4      SSR,          3pMV! 4       # V! 4       # RRP                  VV 3R lV 4       4      ,           R,           # )c                 óÖ  <€ SP                   ^ ,          ^ 8X  db   SP                   ^,          ^8X  d$   SP                  SP                   ^,          4      p M�RP                  V3R lSP                    4       4      p MjSP                   ^,          ^8X  d.   RP                  V3R lSP                   R,           4       4      p M%RP                  V3R lSP                    4       4      p RV  R2# )rr  rQ  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  rO  s   & €rS   r(  ÚKLatexPrinter._print_Range.<locals>._print_symbolic_range.<locals>.<genexpr>u  ó   øé € Ð$HÁ¸# T§[¡[°×%5Ð%5Ãùr+  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  rO  s   & €rS   r(  rm  x  s   øé € Ð$LÁ¸# T§[¡[°×%5Ð%5Ãùr+  :Nr�   Nc              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  rO  s   & €rS   r(  rm  z  rn  r+  z\text{Range}\left(rx  r-  )ÚcontrR   rß   s    €€rS   Ú_print_symbolic_rangeÚ8LatexPrinter._print_Range.<locals>._print_symbolic_rangeo  s¡   ø€ à�v‰v�a�y˜AŒ~Ø—6‘6˜!•9 ”>ØŸ;™; q§v¡v¨a¥yÓ1‘DàŸ9™9Ô$HÀÇÂÓ$HÓH‘Dà—6‘6˜!•9 ”>ØŸ9™9Ô$LÀÇÁÈÆÓ$LÓL‘DàŸ9™9Ô$HÀÇÂÓ$HÓH�Dà+¨D¨6°Ð:Ð;rU   Tú\left\{rQ  c              3  óT   <"  € T F  qSJd   SP                  V4      MR x € K  	  R# 5i©z\ldotsNr€  ©r&  ÚelÚdotsrß   s   & €€rS   r(  Ú,LatexPrinter._print_Range.<locals>.<genexpr>•  ó%   øé € Ð_ÑV^ÐPR¸«n˜4Ÿ;™; rœ?À)ÔKÓV^ùó   ƒ%(ú\right\}ry  )ÚobjectÚstartÚis_infiniteÚstopÚstepÚis_positiveÚiterÚnextÚis_emptyr{  r/  Úis_iterablerU  )rß   rR   rr  ÚprintsetÚitry  s   ff   @rS   Ú_print_RangeÚLatexPrinter._print_Rangen  sC  ú€ ö	<ô ‹xˆà�7‰7××Ð 1§6¡6×#5×#5Ð#5Ø�v‰v×!×!Ð!Ø  Q¨¨4Ð/’à  A r¨4Ð/‘Ø�W‰W× × Ð Ø˜Q˜r�U Q§V¡V�^¨Q¨r­UÐ2‰HØ�V‰V××ÐÜ�a“ˆBÜ˜B“x¤ b£¨4Ð/‰HØ�Z‰ZÒ#Ø—‘˜‘
˜tÔ#Ü  ›8‘Ø——�Ü˜!“W�Ü ›8¤T¨"£X¨t°Q°rµUÐ:‘á,Ó.Ð.á(Ó*Ð*ØØ—
‘
Õ_ÑV^Ó_Ó_õ`àõð 	rU   c           
     	óò  € \        VP                  4      ^8X  d¥   VeS   V: RV P                  VP                  ^ ,          4      : RV: RV P                  VP                  ^,          4      : R2# V: RV P                  VP                  ^ ,          4      : RV P                  VP                  ^,          4      : R2# V: RV P                  VP                  ^ ,          4      : R2pVe   V: RV: R2pV# )r�   r•  r–  rˆ  rx  rO   r  r=  )rß   r  ÚletterrM  r  s   &&&& rS   Ú__print_number_polynomialÚ&LatexPrinter.__print_number_polynomial˜  s·   € Üˆt�y‰y‹>˜QÔØŠÛ9?Ø ŸK™K¨¯	©	°!­Ö5³sØ ŸK™K¨¯	©	°!­Ö5ð7ð 7ó 17ØŸ™ D§I¡I¨a¥LÖ1°4·;±;¸t¿y¹yÈ½|Ö3LðNð Nó # D§K¡K°·	±	¸!µÖ$=Ð>ˆØŠ?Û #£SÐ)ˆCØˆ
rU   c                	ó(   € V P                  VR V4      # )ÚB©Ú&_LatexPrinter__print_number_polynomialrL  s   &&&rS   Ú_print_bernoulliÚLatexPrinter._print_bernoulli¦  ó   € Ø×-Ñ-¨d°C¸Ó=Ð=rU   c                	ó(   € V P                  VR V4      # )ÚGr’  rL  s   &&&rS   Ú_print_genocchiÚLatexPrinter._print_genocchi©  r–  rU   c                	ó”  a € \        VP                  4      ^8X  dœ   RS P                  VP                  ^ ,          4      : RS P                  VP                  ^,          4      : R2pRRP                  V 3R lVP                  ^,           4       4      ,          pVe   V: RV: RV: 2pV# W4,           pV# S P	                  VRV4      # )rL  zB_{rQ  rO   ri  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  )r&  rx  rß   s   & €rS   r(  Ú+LatexPrinter._print_bell.<locals>.<genexpr>°  s#   øé € ð 3CÙ5A¨rð 48·;±;¸r·?°?Û5Aùr+  r  r‘  )rŒ  r@  rö   rU  r“  )rß   r  rM  Útex1Útex2r  s   f&&   rS   Ú_print_bellÚLatexPrinter._print_bell¬  s«   ø€ Üˆt�y‰y‹>˜QÕØ$(§K¡K°·	±	¸!µÖ$=Ø $§¡¨D¯I©I°a­LÖ 9ð;ˆDà%¨¯
©
ô 3CØ59·Y±Y¸q¶\ó3Có )Cõ CˆDàŠÛ&*«C²Ð6�ð ˆJð •k�ØˆJØ×-Ñ-¨d°C¸Ó=Ð=rU   c                	ó(   € V P                  VR V4      # ©ÚFr’  rL  s   &&&rS   Ú_print_fibonacciÚLatexPrinter._print_fibonacci¹  r–  rU   c                	ót   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: R2pV# )zL_{%s}r  rO   r(  rõ  s   &&& rS   Ú_print_lucasÚLatexPrinter._print_lucas¼  ó1   € Ø˜$Ÿ+™+ d§i¡i°¥lÓ3Õ3ˆØŠ?Û #£SÐ)ˆCØˆ
rU   c                	ó(   € V P                  VR V4      # )ÚTr’  rL  s   &&&rS   Ú_print_tribonacciÚLatexPrinter._print_tribonacciÂ  r–  rU   c                	ó²   € Vf*   RV P                  VP                  ^ ,          4      ,          # RV: RV P                  VP                  ^ ,          4      : R2# )Nz\mu\left(%s\right)z\mu^{rˆ  rx  r(  rL  s   &&&rS   Ú_print_mobiusÚLatexPrinter._print_mobiusÅ  sD   € ØŠ;Ø(¨4¯;©;°t·y±yÀµ|Ó+DÕDÐDð ã-0°$·+±+¸d¿i¹iÈ½lÖ2KÐLÐLrU   c           
     	óª  a a€ \        4       o\        VP                  P                  4      ^ 8”  g%   \        VP                  P                  4      ^ 8”  d   RS P                  VP                  4      : RS P                  VP                  ^ ,          4      : RS P                  VP                  4      : RS P                  VP                  4      : R2	# VP                  \        P                  J df   VP                  pSVP                  V^,
          4      VP                  V^,
          4      VP                  V^,
          4      VP                  V4      3pMUVP                  \        P                  J g   VP                  ^8”  d   VR,          pVP                  S4       M\        V4      pRRP                  VV 3R	 lV 4       4      ,           R
,           # )rr  rt  z
\right\}_{r†  r–  rO   :Né   NrŠ  rQ  c              3  óT   <"  € T F  qSJd   SP                  V4      MR x € K  	  R# 5irv  r€  rw  s   & €€rS   r(  Ú1LatexPrinter._print_SeqFormula.<locals>.<genexpr>Þ  r{  r|  r‹  )r~  rŒ  r  Úfree_symbolsr�  rö   Úformular@  r   r¡  Úcoeffr   ÚlengthrT  r/  rU  )rß   rR   r�  rˆ  ry  s   f&  @rS   Ú_print_SeqFormulaÚLatexPrinter._print_SeqFormulaÊ  sF  ù€ Ü‹xˆÜˆq�w‰w×#Ñ#Ó$ qÔ(¬C°·±×0CÑ0CÓ,DÀqÔ,Høà—‘˜AŸI™IÖ&Ø—‘˜AŸK™K¨�NÖ+Ø—‘˜AŸG™GÖ$Ø—‘˜AŸF™FÖ#ð	ð ð �7‰7”a×(Ñ(Ó(Ø—6‘6ˆDØ˜aŸg™g d¨Q¥hÓ/°·±¸À½Ó1BØŸ™  q¥Ó)¨1¯7©7°4«=ð:‰Hà�V‰V”q—z‘zÓ! Q§X¡X°¤\Ø˜•uˆHØ�O‰O˜DÕ!ä˜Q“xˆHàØ—
‘
Õ_ÑV^Ó_Ó_õ`àõð 	rU   c                	ó^  € VP                   VP                  8X  d#   R V P                  VP                   4      ,          # VP                  '       d   RpMRpVP                  '       d   RpMRpRV: V P                  VP                   4      : RV P                  VP                  4      : RV: 2# )rh  rÉ   r¨   rÊ   rË   rs  rQ  rt  )r  Úendrö   Ú	left_openÚ
right_open)rß   r²   r°  r±  s   &&  rS   Ú_print_IntervalÚLatexPrinter._print_Intervalå  s„   € Ø�7‰7�a—e‘eÔØ'¨$¯+©+°a·g±gÓ*>Õ>Ð>ð �{�{ˆ{Ø‘à�à�|�|ˆ|Ø‘à�øò ˜$Ÿ+™+ a§g¡gÖ.°·±¸A¿E¹EÖ0BÂEðKð KrU   c                	ó|   € R V P                  VP                  4      : RV P                  VP                  4      : R2# )z\left\langle rQ  z\right\rangle)rö   r¸   r¹   ©rß   r²   s   &&rS   Ú_print_AccumulationBoundsÚ&LatexPrinter._print_AccumulationBounds÷  s+   � à—‘˜QŸU™UÖ# T§[¡[°·±Ö%7ð9ð 	9rU   c                	ó–   € \        V4      pVP                   Uu. uF  q0P                  W24      NK  	  ppR P                  V4      # u upi )z \cup ©r   r@  rü   rU  ©rß   Úur¿  r²   Úargs_strs   &&   rS   Ú_print_UnionÚLatexPrinter._print_Unionû  óB   € Ü% aÓ(ˆØ89¿ºÓ?¹°1×%Ñ% aÖ.¹ˆÐ?Ø�~‰~˜hÓ'Ð'ùò @ó   šAc                	ó–   € \        V4      pVP                   Uu. uF  q0P                  W24      NK  	  ppR P                  V4      # u upi )z \setminus rÇ  rÈ  s   &&   rS   Ú_print_ComplementÚLatexPrinter._print_Complement 	  óD   € Ü% aÓ(ˆØ89¿ºÓ?¹°1×%Ñ% aÖ.¹ˆÐ?Ø×"Ñ" 8Ó,Ð,ùò @rÎ  c                	ó–   € \        V4      pVP                   Uu. uF  q0P                  W24      NK  	  ppR P                  V4      # u upi )z \cap rÇ  rÈ  s   &&   rS   Ú_print_IntersectionÚ LatexPrinter._print_Intersection	  rÍ  rÎ  c                	ó–   € \        V4      pVP                   Uu. uF  q0P                  W24      NK  	  ppR P                  V4      # u upi )z \triangle rÇ  rÈ  s   &&   rS   Ú_print_SymmetricDifferenceÚ'LatexPrinter._print_SymmetricDifference
	  rÒ  rÎ  c                	óZ  a a€ \        V4      o\        VP                  4      ^8¼  d`   \        VP                  4      '       gE   S P	                  VP                  ^ ,          S4      R\        VP                  4      ,          ,           # RP                  VV 3R lVP                   4       4      # )r   z^{%d}rÆ   c              3  óH   <"  € T F  pSP                  VS4      x € K  	  R # 5irõ   )rü   )r&  r^  r¿  rß   s   & €€rS   r(  Ú1LatexPrinter._print_ProductSet.<locals>.<genexpr>	  s$   øé € ð  <Ù4:¨SˆD×Ñ˜c 4×(Ð(³Fùs   ƒ")r   rŒ  Úsetsr#   rü   rU  )rß   r  r¿  s   f&@rS   Ú_print_ProductSetÚLatexPrinter._print_ProductSet	  s|   ù€ Ü% aÓ(ˆÜˆq�v‰v‹;˜!Ô¤K°·±×$7Ò$7Ø×$Ñ$ Q§V¡V¨A¥Y°Ó5¸Ä#ÀaÇfÁfÃ+Õ8MÕMÐMØ×Ñõ  <Ø45·F²Fó <ó <ð 	<rU   c                	ó   € R # )z	\emptysetrP   r_  s   &&rS   Ú_print_EmptySetÚLatexPrinter._print_EmptySet	  s   € ÙrU   c                	ó   € R # )z
\mathbb{N}rP   ©rß   r~  s   &&rS   Ú_print_NaturalsÚLatexPrinter._print_Naturals	  r"  rU   c                	ó   € R # )z\mathbb{N}_0rP   rã  s   &&rS   Ú_print_Naturals0ÚLatexPrinter._print_Naturals0	  s   € ÙrU   c                	ó   € R # ©z
\mathbb{Z}rP   rÃ  s   &&rS   Ú_print_IntegersÚLatexPrinter._print_Integers	  r"  rU   c                	ó   € R # ©z
\mathbb{Q}rP   rÃ  s   &&rS   Ú_print_RationalsÚLatexPrinter._print_Rationals"	  r"  rU   c                	ó   € R # ©z
\mathbb{R}rP   rÃ  s   &&rS   Ú_print_RealsÚLatexPrinter._print_Reals%	  r"  rU   c                	ó   € R # ©z
\mathbb{C}rP   rÃ  s   &&rS   Ú_print_ComplexesÚLatexPrinter._print_Complexes(	  r"  rU   c                	óþ   a € VP                   P                  pVP                   P                  pV 3R  l\        W1P                  4       4       pRP                  R V 4       4      pRS P                  V4      : RV: R2# )c              3  ól   <"  € T F)  w  rSP                  V4      SP                  V4      3x € K+  	  R # 5irõ   r€  )r&  r'  rE  rß   s   &  €rS   r(  Ú/LatexPrinter._print_ImageSet.<locals>.<genexpr>.	  s*   øé € ÐRÑ<Q±D°A�—‘˜A“ §¡¨A£Õ/Ó<Qùs   ƒ14rQ  c              3  ó4   "  € T F  pR V,          x € K  	  R# 5i)ú	%s \in %sNrP   )r&  Úxys   & rS   r(  rû  /	  s   é € Ð;±s°˜<¨"×,Ò,³sùs   ‚rt  ú\; \middle|\; r}  )rB   r  Ú	signaturer‡  Ú	base_setsrU  rö   )rß   rR   r  ÚsigÚxysÚxinyss   f&    rS   Ú_print_ImageSetÚLatexPrinter._print_ImageSet+	  sZ   ø€ Ø�w‰w�|‰|ˆØ�g‰g×ÑˆÜR¼CÀÇ[Á[Ô<QÓRˆØ—
‘
Ñ;±sÓ;Ó;‰Ø7;·{±{À4Ö7HË%ÐPÐPrU   c           
     	óž  € R P                  \        VP                  4       Uu. uF  q P                  V4      NK  	  up4      pVP                  \
        P                  J d%   RV: RV P                  VP                  4      : R2# RV: RV: RV P                  VP                  4      : RV P                  VP                  4      : R2	# u upi )rQ  rt  rÿ  ú	 \right\}r_  r4  )rU  r   r†  rö   Úbase_setr   ÚUniversalSetÚ	condition©rß   rR   r—  Ú
vars_prints   &&  rS   Ú_print_ConditionSetÚ LatexPrinter._print_ConditionSet2	  s—   € Ø—Y‘Y¼EÀ!Ç%Á%¼LÓI¹L°S§¡¨CÖ 0¹LÑIÓJˆ
Ø�:‰:œŸ™Ô'ã˜TŸ[™[¨¯©Ö5ð7ð 7ð (ó
 ÛØ�K‰K˜Ÿ
™
Ö#Ø�K‰K˜Ÿ™Ö$ð	&ð 	&ùò  Js   £C
c                	óh   € V P                  VP                  ^ ,          4      pRP                  V4      # )rr  z\mathcal{{P}}\left({}\right)©rö   r@  r’   )rß   r  Ú	arg_prints   && rS   Ú_print_PowerSetÚLatexPrinter._print_PowerSet>	  s)   € Ø—K‘K §	¡	¨!¥Ó-ˆ	Ø.×5Ñ5°iÓ@Ð@rU   c                	ó   € R P                  VP                   Uu. uF  q P                  V4      NK  	  up4      pRV P                  VP                  4      : RV: RV P                  VP                  4      : R2# u upi )rQ  rt  rÿ  r_  r  )rU  r@  rö   r  rÜ  r  s   &&  rS   Ú_print_ComplexRegionÚ!LatexPrinter._print_ComplexRegionB	  s]   € Ø—Y‘Y¸A¿KºKÓH¹K°S§¡¨CÖ 0¹KÑHÓI‰
à�K‰K˜Ÿ™ÖÛØ�K‰K˜Ÿ™Öð!ð 	!ùò  Is   šA;c                	óª   a € R \         ;QJ d'    . V 3R lVP                   4       F  NK  	  5,          # ! V 3R lVP                   4       4      ,          # )rý  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  )r&  r   rß   s   & €rS   r(  Ú/LatexPrinter._print_Contains.<locals>.<genexpr>J	  s   øé € Ð#C¹F°q D§K¡K°§N N»Fùr+  )r/  r@  r_  s   f&rS   Ú_print_ContainsÚLatexPrinter._print_ContainsI	  s5   ø€ ØŸeœeÔ#C¸A¿FºFÓ#CŸeÕCÐC˜eÔ#C¸A¿FºFÓ#CÓCÕCÐCrU   c                	ó$  € VP                   P                  \        P                  J dD   VP                  P                  \        P                  J d   V P                  VP                  4      # V P                  VP                  4       4      R ,           # )z	 + \ldots)	rÜ  r·  r   rl  Úbnrö   Úa0ro  Útruncaterì   s   &&rS   Ú_print_FourierSeriesÚ!LatexPrinter._print_FourierSeriesL	  sV   € Ø�4‰4�<‰<œ1Ÿ6™6Ó! a§d¡d§l¡l´a·f±fÓ&<Ø—;‘;˜qŸt™tÓ$Ð$Ø�‰˜qŸz™z›|Ó,¨|Õ;Ð;rU   c                	ó8   € V P                  VP                  4      # rõ   )ro  Úinfiniterì   s   &&rS   Ú_print_FormalPowerSeriesÚ%LatexPrinter._print_FormalPowerSeriesQ	  s   € Ø�‰˜qŸz™zÓ*Ð*rU   c                	ó(   € R VP                   ,          # )z\mathbb{F}_{%s})Úmodr  s   &&rS   Ú_print_FiniteFieldÚLatexPrinter._print_FiniteFieldT	  s   € Ø! D§H¡HÕ,Ð,rU   c                	ó   € R # rê  rP   r  s   &&rS   Ú_print_IntegerRingÚLatexPrinter._print_IntegerRingW	  r"  rU   c                	ó   € R # rî  rP   r  s   &&rS   Ú_print_RationalFieldÚ!LatexPrinter._print_RationalFieldZ	  r"  rU   c                	ó   € R # rò  rP   r  s   &&rS   Ú_print_RealFieldÚLatexPrinter._print_RealField]	  r"  rU   c                	ó   € R # rö  rP   r  s   &&rS   Ú_print_ComplexFieldÚ LatexPrinter._print_ComplexField`	  r"  rU   c                	óª   € V P                  VP                  4      pR P                  \        V P                   VP                  4      4      pV: RV: R2# )rQ  rŠ  r‹  ©rö   ÚdomainrU  ra  r›  ©rß   r  r9  r›  s   &&  rS   Ú_print_PolynomialRingÚ"LatexPrinter._print_PolynomialRingc	  ó<   € Ø—‘˜TŸ[™[Ó)ˆØ—)‘)œC §¡¨T¯\©\Ó:Ó;ˆÛ'-«wÐ7Ð7rU   c                	óª   € V P                  VP                  4      pR P                  \        V P                   VP                  4      4      pV: RV: R2# )rQ  rJ  rx  r8  r:  s   &&  rS   Ú_print_FractionFieldÚ!LatexPrinter._print_FractionFieldh	  r=  rU   c                	óÜ   € V P                  VP                  4      pR P                  \        V P                   VP                  4      4      pRpVP
                  '       g   RpV: V: RV: R2# )rQ  rÖ   zS_<^{-1}rŠ  r‹  )rö   r9  rU  ra  r›  Úis_Poly)rß   r  r9  r›  Úinvs   &&   rS   Ú_print_PolynomialRingBaseÚ&LatexPrinter._print_PolynomialRingBasem	  sQ   € Ø—‘˜TŸ[™[Ó)ˆØ—)‘)œC §¡¨T¯\©\Ó:Ó;ˆØˆØ�|�|ˆ|ØˆCÚ),«f³gÐ>Ð>rU   c           	     	óP  € VP                   P                  p. pVP                  4        EF›  w  rER p\        V4       Fq  w  rxV^ 8”  g   K  V^8X  d+   W`P	                  VP
                  V,          4      ,          pK?  W`P	                  \        VP
                  V,          V4      4      ,          pKs  	  VP                  '       d4   V'       d   RV P	                  V4      ,          p	M~V P	                  V4      p	MlV'       dT   V\        P                  J d   VP                  RV.4       Kþ  V\        P                  J d   VP                  RV.4       EK(  V P	                  V4      p	V'       g   T	p
MV	R,           V,           p
V
P                  R4      '       d   VP                  RV
R,          .4       EKˆ  VP                  RV
.4       EKž  	  V^ ,          R9   d,   VP                  ^ 4      pVR8X  d   RV^ ,          ,           V^ &   RP                  V4      p\        \!        V P                  VP
                  4      4      pRV P	                  VP#                  4       4      ,          pRP                  V.V,           V.,           4      pV\$        9   d   RV: R	V: R
2pV# RV: RV: R
2pV# )rÖ   ri  rž  rK  rÂ   rŸ  z	domain=%srQ  r•   ú {\left(z	 \right)}rª  z	}{\left( )rK  rž  )rS  rT  rl  rk  rö   ÚgensÚpowr  r   r÷  Úextendr  r"  ÚpoprU  rß  ra  Ú
get_domainr¬  )rß   Úpolyrä  rl  Úmonomr¸  Ús_monomr²   rM  Ús_coeffÚs_termÚmodifierr  rH  r9  r@  r  s   &&               rS   Ú_print_PolyÚLatexPrinter._print_Polyu	  s  € Ø�n‰n×%Ñ%ˆØˆØ ŸJ™JŸL‰LˆEØˆGÜ# EÖ*‘�Ø˜–7Ø˜a”xØ§;¡;¨t¯y©y¸­|Ó#<Õ<šà§;¡;¬s°4·9±9¸Qµ<ÀÓ/EÓ#FÕFšñ +ð �|�|ˆ|ßØ0°4·;±;¸uÓ3EÕE‘Gà"Ÿk™k¨%Ó0‘GçØ¤§¡“~ØŸ™ c¨7 ^Ô4Ù à¤§¡Ó-ØŸ™ c¨7 ^Ô4Ú àŸ+™+ eÓ,�çØ ‘à  3�¨Õ0�à× Ñ  ×%Ò%Ø—‘˜c 6¨"¥:Ð.×/à—‘˜c 6˜]×+ñE )ðH ��8�zÔ!Ø—y‘y “|ˆHà˜3ŒØ  q¥�>��a‘à�x‰x˜‹ˆÜ”C˜Ÿ™ T§Y¡YÓ/Ó0ˆØ˜tŸ{™{¨4¯?©?Ó+<Ó=Õ=ˆà�y‰y˜$˜ $�¨&¨Õ1Ó2ˆØÔ*Õ*Û/2³DÐ9ˆCð ˆ
ð +ó >AÃ$ÐGˆCàˆ
rU   c                	óÐ   € VP                   P                  pVR 8X  d   RpV P                  VP                  4      pVP                  pV\
        9   d   RW#V3,          # RW#V3,          # )ÚComplexRootOfÚCRootOfz\%s {\left(%s, %d\right)}z'\operatorname{%s} {\left(%s, %d\right)})rS  rT  rö   r  r   r¬  )rß   Úrooträ  r  r   s   &&   rS   Ú_print_ComplexRootOfÚ!LatexPrinter._print_ComplexRootOf®	  sm   € Ø�n‰n×%Ñ%ˆØ�/Ô!ØˆCØ�{‰{˜4Ÿ9™9Ó%ˆØ—
‘
ˆØÔ*Ô*Ø/°3¸eÐ2DÕDÐDà=ÀØAFðAHõ Hð HrU   c                	ót  € VP                   P                  pV P                  VP                  4      .pVP                  \
        P                  Jd+   VP                  V P                  VP                  4      4       V\        9   d   R V: RRP                  V4      : R2# RV: RRP                  V4      : R2# )r•   rG  rQ  r|  rª  z	} {\left()
rS  rT  rö   r  Úfunr   ÚIdentityFunctionrT  r¬  rU  )rß   r  rä  r@  s   &&  rS   Ú_print_RootSumÚLatexPrinter._print_RootSumº	  s�   € Ø�n‰n×%Ñ%ˆØ—‘˜DŸI™IÓ&Ð'ˆà�8‰8œ1×-Ñ-Ó-Ø�K‰K˜Ÿ™ D§H¡HÓ-Ô.àÔ*Õ*Û/2°D·I±I¸d¶OÐDÐDð +ó >AØ=A¿Y¹YÀt¾_ðNð NrU   c                	ó   € R # )ú\omegarP   r  s   &&rS   Ú_print_OrdinalOmegaÚ LatexPrinter._print_OrdinalOmegaÇ	  s   € ÙrU   c                	ó²   € VP                   w  r#V^8w  d*   V^8w  d   RP                  W24      # RP                  V4      # V^8w  d   RP                  V4      # R# )r   z{} \omega^{{{}}}z	{} \omegaz\omega^{{{}}}ra  )r@  r’   )rß   r  rM  Úmuls   &&  rS   Ú_print_OmegaPowerÚLatexPrinter._print_OmegaPowerÊ	  sX   € Ø—9‘9‰ˆØ�!Œ8Ø�aŒxØ*×1Ñ1°#Ó;Ð;à#×*Ñ*¨3Ó/Ð/à�aŒxØ'×.Ñ.¨sÓ3Ð3á rU   c                	ó~   € R P                  VP                   Uu. uF  q P                  V4      NK  	  up4      # u upi ©rh  )rU  r@  rö   rA  s   && rS   Ú_print_OrdinalÚLatexPrinter._print_Ordinal×	  s.   € Ø�z‰z°t·y²yÓA±y°Ÿ;™; sÖ+±yÑAÓBÐBùÒAs   š:c                	óX   € V P                   R ,          pVP                  V \        RV4      # )rÇ   z	{%s}^{%d})rÙ   r�   r    )rß   rM  r¬   s   && rS   Ú_print_PolyElementÚLatexPrinter._print_PolyElementÚ	  s&   € Ø—^‘^Ð$6Õ7ˆ
Ø�x‰x˜œj¨+°zÓBÐBrU   c                	óÜ   € VP                   ^8X  d   V P                  VP                  4      # V P                  VP                  4      pV P                  VP                   4      pRV: RV: R2# )r   rô  rõ  rO   )rû  rö   rú  )rß   Úfracrú  rû  s   &&  rS   Ú_print_FracElementÚLatexPrinter._print_FracElementÞ	  sO   € Ø�:‰:˜Œ?Ø—;‘;˜tŸz™zÓ*Ð*à—K‘K §
¡
Ó+ˆEØ—K‘K §
¡
Ó+‰EÛ',«eÐ4Ð4rU   c                	ó  € \        VP                  4      ^8X  d   VP                  ^ ,          R3MVP                  w  r4RV P                  V4      ,          pVe   V: RV: R2pVe   V: RV P                  V4      : R2pV# )r   NzE_{%s}r  rO   rJ  rx  r=  )rß   r  rM  r  r'  r  s   &&&   rS   Ú_print_eulerÚLatexPrinter._print_euleræ	  sh   € Ü'*¨4¯9©9£~¸Ô':�—	‘	˜!•˜dÑ#ÀÇ	Á	‰ˆØ˜$Ÿ+™+ a›.Õ(ˆØŠ?Û #£SÐ)ˆCØŠ=Û*-¨t¯{©{¸1®~Ð>ˆCØˆ
rU   c                	ót   € R V P                  VP                  ^ ,          4      ,          pVe   V: RV: R2pV# )zC_{%s}r  rO   r(  rõ  s   &&& rS   Ú_print_catalanÚLatexPrinter._print_catalanï	  rª  rU   c           
     	óþ   € R P                  Y#'       d   RMRV P                  VP                  ^,          4      V P                  VP                  ^ ,          4      V P                  VP                  ^,          4      4      # )z5\mathcal{{{}}}{}_{{{}}}\left[{}\right]\left({}\right)z^{-1}rÖ   ©r’   rö   r@  )rß   r  rR   Úinverses   &&&&rS   Ú_print_UnifiedTransformÚ$LatexPrinter._print_UnifiedTransformõ	  sÏ   € ØG×NÑNÈqÖ]dÑRYÐjlÐnr×nyÑnyÐz~÷  {Dñ  {Dð  EFõ  {Gó  oHð  JN÷  JUñ  JUð  VZ÷  V_ñ  V_ð  `aõ  Vbó  Jcð  ei÷  epñ  epð  qu÷  qzñ  qzð  {|õ  q}ó  e~ó  ð  	rU   c                	ó&   € V P                  VR 4      # )ÚM©r|  r  s   &&rS   Ú_print_MellinTransformÚ#LatexPrinter._print_MellinTransformø	  ó   € Ø×+Ñ+¨D°#Ó6Ð6rU   c                	ó(   € V P                  VR R4      # )r  Tr€  r  s   &&rS   Ú_print_InverseMellinTransformÚ*LatexPrinter._print_InverseMellinTransformû	  ó   € Ø×+Ñ+¨D°#°tÓ<Ð<rU   c                	ó&   € V P                  VR 4      # )ÚLr€  r  s   &&rS   Ú_print_LaplaceTransformÚ$LatexPrinter._print_LaplaceTransformþ	  rƒ  rU   c                	ó(   € V P                  VR R4      # )r‰  Tr€  r  s   &&rS   Ú_print_InverseLaplaceTransformÚ+LatexPrinter._print_InverseLaplaceTransform
  r‡  rU   c                	ó&   € V P                  VR 4      # r£  r€  r  s   &&rS   Ú_print_FourierTransformÚ$LatexPrinter._print_FourierTransform
  rƒ  rU   c                	ó(   € V P                  VR R4      # )r¤  Tr€  r  s   &&rS   Ú_print_InverseFourierTransformÚ+LatexPrinter._print_InverseFourierTransform
  r‡  rU   c                	ó&   € V P                  VR 4      # )ÚSINr€  r  s   &&rS   Ú_print_SineTransformÚ!LatexPrinter._print_SineTransform

  ó   € Ø×+Ñ+¨D°%Ó8Ð8rU   c                	ó(   € V P                  VR R4      # )r–  Tr€  r  s   &&rS   Ú_print_InverseSineTransformÚ(LatexPrinter._print_InverseSineTransform
  ó   € Ø×+Ñ+¨D°%¸Ó>Ð>rU   c                	ó&   € V P                  VR 4      # )ÚCOSr€  r  s   &&rS   Ú_print_CosineTransformÚ#LatexPrinter._print_CosineTransform
  r™  rU   c                	ó(   € V P                  VR R4      # )rŸ  Tr€  r  s   &&rS   Ú_print_InverseCosineTransformÚ*LatexPrinter._print_InverseCosineTransform
  r�  rU   c                	óÌ   €  VP                   e+   V P                  VP                   P                  V4      4      #  V P                  \	        V4      4      #   \         d     L'i ; irõ   )Úringrö   Úto_sympyr   Úrepr©rß   r  s   &&rS   Ú
_print_DMPÚLatexPrinter._print_DMP
  s[   € ð	Ø�v‰vÒ!à—{‘{ 1§6¡6§?¡?°1Ó#5Ó6Ð6ð "ð
 �{‰{œ4 ›7Ó#Ð#øô ô 	Ùð	ús   ‚7A ÁA#Á"A#c                	ó$   € V P                  V4      # rõ   )rª  r©  s   &&rS   Ú
_print_DMFÚLatexPrinter._print_DMF
  s   € Ø�‰˜qÓ!Ð!rU   c                	óJ   € V P                  \        VP                  4      4      # rõ   )rö   r   rV  )rß   r~  s   &&rS   Ú_print_ObjectÚLatexPrinter._print_Object"
  s   € Ø�{‰{œ6 &§+¡+Ó.Ó/Ð/rU   c                	ó  € V P                  VP                  ^ ,          4      pVe   RV: R2MRp\        VP                  4      ^8X  d   RV: RV: R2pV# V P                  VP                  ^,          4      pRP                  W%V4      pV# )rr  r  rO   rÖ   ÚWrJ  rx  zW{0}_{{{1}}}\left({2}\right))rö   r@  rŒ  r’   )rß   r  rM  Úarg0ÚresultÚarg1s   &&&   rS   Ú_print_LambertWÚLatexPrinter._print_LambertW%
  sv   € Ø�{‰{˜4Ÿ9™9 Q�<Ó(ˆØ#&£?›#Ñ¸ˆÜˆt�y‰y‹>˜QÕÛ.1³4Ð8ˆFð ˆð —;‘;˜tŸy™y¨�|Ó,ˆDØ5×<Ñ<¸SÈÓMˆFØˆrU   c                	ód   € R P                  V P                  VP                  ^ ,          4      4      # )z!\operatorname{{E}}\left[{}\right]rz  r  s   &&rS   Ú_print_ExpectationÚLatexPrinter._print_Expectation/
  ó%   € Ø3×:Ñ:¸4¿;¹;ÀtÇyÁyÐQRÅ|Ó;TÓUÐUrU   c                	ód   € R P                  V P                  VP                  ^ ,          4      4      # )z#\operatorname{{Var}}\left({}\right)rz  r  s   &&rS   Ú_print_VarianceÚLatexPrinter._print_Variance2
  s%   € Ø5×<Ñ<¸T¿[¹[ÈÏÉÐSTÍÓ=VÓWÐWrU   c                	ól   a € R P                  RP                  V 3R lVP                   4       4      4      # )z#\operatorname{{Cov}}\left({}\right)rQ  c              3  óF   <"  € T F  pSP                  V4      x € K  	  R # 5irõ   r€  rO  s   & €rS   r(  Ú1LatexPrinter._print_Covariance.<locals>.<genexpr>6
  s!   øé € ÐFmÑclÐ\_ÀtÇ{Á{ÐSV×GWÐGWÓclùr+  )r’   rU  r@  r  s   f&rS   Ú_print_CovarianceÚLatexPrinter._print_Covariance5
  s*   ø€ Ø5×<Ñ<¸T¿Y¹YÔFmÐcg×clÒclÓFmÓ=mÓnÐnrU   c                	ód   € R P                  V P                  VP                  ^ ,          4      4      # )z!\operatorname{{P}}\left({}\right)rz  r  s   &&rS   Ú_print_ProbabilityÚLatexPrinter._print_Probability8
  r¼  rU   c                	ó€   € V P                  VP                  4      pV P                  VP                  4      pV: R V: 2# )r>  )rö   r9  Úcodomain)rß   Úmorphismr9  rÉ  s   &&  rS   Ú_print_MorphismÚLatexPrinter._print_Morphism;
  s3   € Ø—‘˜XŸ_™_Ó-ˆØ—;‘;˜x×0Ñ0Ó1ˆÛ&,ªhÐ7Ð7rU   c                	ó‚   € V P                  VP                  4      V P                  VP                  4      r2R V: RV: R2# )rô  rõ  rO   )rö   r{  Úden)rß   r  r{  rÎ  s   &&  rS   Ú_print_TransferFunctionÚ$LatexPrinter._print_TransferFunction@
  s.   € Ø—;‘;˜tŸx™xÓ(¨$¯+©+°d·h±hÓ*?‰SÛ#&«Ð,Ð,rU   c                	ór   a a€ \        SP                  4      pVV 3R  lpRP                  \        W24      4      # )c                ó<   <€ SP                  V \        S4      R 4      # r©  )rü   r   )r'  r  rß   s   &€€rS   rT   Ú,LatexPrinter._print_Series.<locals>.<lambda>F
  s   ø€ ˜4×,Ñ,¨QÔ0FÀtÓ0LØ,1ô3rU   rÂ   )rß  r@  rU  ra  )rß   r  r@  r¬  s   ff  rS   Ú_print_SeriesÚLatexPrinter._print_SeriesD
  s+   ù€ Ü�D—I‘I‹ˆõ3ˆà�x‰xœ˜FÓ)Ó*Ð*rU   c                	ó–   a aa€ ^ RI Ho \        SP                  4      RRR1,          pVVV 3R lpRP	                  \        W24      4      # )rr  )ÚMIMOParallelNc                ó‚   <€ \        V S4      '       d   SP                  V \        S4      R 4      # SP                  V 4      # r©  )rØ  rü   r   rö   )r'  r×  r  rß   s   &€€€rS   rT   Ú0LatexPrinter._print_MIMOSeries.<locals>.<lambda>M
  sH   ø€ Ü7AÀ!À\×7RÒ7Rð  ×,Ñ,¨QÔ0FÀtÓ0LØ-2ó4ð gØX\×XcÑXcÐdeÓXfðgrU   z\cdotry  )Úsympy.physics.control.ltir×  rß  r@  rU  ra  )rß   r  r@  r¬  r×  s   ff  @rS   Ú_print_MIMOSeriesÚLatexPrinter._print_MIMOSeriesJ
  s8   ú€ Ý:Ü�D—I‘I‹™t ˜tÕ$ˆögˆà�}‰}œS Ó.Ó/Ð/rU   c                	ó`   € R P                  \        V P                  VP                  4      4      # ri  ©rU  ra  rö   r@  r  s   &&rS   Ú_print_ParallelÚLatexPrinter._print_ParallelQ
  ó    € Ø�z‰zœ#˜dŸk™k¨4¯9©9Ó5Ó6Ð6rU   c                	ó`   € R P                  \        V P                  VP                  4      4      # ri  rÞ  r  s   &&rS   Ú_print_MIMOParallelÚ LatexPrinter._print_MIMOParallelT
  rá  rU   c           	     	ó   € ^ RI HpHp VP                  V! ^^VP                  4      rT\        WC4      '       d   \        VP                  4      MV.p\        VP                  V4      '       d    \        VP                  P                  4      MVP                  .pTp\        WC4      '       d)   \        VP                  V4      '       d   V! . VOVO5!  p	MÑ\        WC4      '       dL   \        VP                  V4      '       d0   VP                  V8X  d   V! V!  p	MŒWS! . VOVP                  N5!  3p	Mu\        WB4      '       d5   \        VP                  V4      '       d   WE8X  d   V! V!  p	M;V! V.VO5!  p	M0WE8X  d   V! V!  p	M#VP                  V8X  d   V! V!  p	MV! . VOVO5!  p	V P                  V4      p
V P                  V4      pV P                  V	4      pVP                  R8X  d   RMRpRV
: RV: RV: RV: R2	# )	rr  )ÚTransferFunctionÚSeriesrž  rK  rô  rõ  rÂ   rO   ry  )Úsympy.physics.controlræ  rç  Úsys1r—  rØ  rß  r@  Úsys2rö   r8  )rß   r  ræ  rç  r{  ÚtfÚnum_arg_listÚden_arg_listÚ
den_term_1Ú
den_term_2rú  Údenom_1Údenom_2Ú_signs   &&            rS   Ú_print_FeedbackÚLatexPrinter._print_FeedbackW
  s¡  € ßBà—)‘)Ñ-¨a°°D·H±HÓ=ˆRÜ)3°C×)@Ò)@”t˜CŸH™H”~ÀsÀeˆä�t—y‘y &×)Ò)ô ˜DŸI™IŸN™NÔ+Ø04·	±	¨{ð 	àˆ
ä�c×"Ò"¤z°$·)±)¸V×'DÒ'DÙÐ= Ð=°Ó=‰JÜ˜×$Ò$¬°D·I±IÐ?O×)PÒ)PØ�y‰y˜BŒÙ# \Ñ2‘
à Ð!A¨Ð!A°t·y±yÓ!AÐA‘
Ü˜×.Ò.´:¸d¿i¹iÈ×3PÒ3PØŒyÙ# \Ñ2‘
á# CÐ7¨,Ó7‘
àŒyÙ# \Ñ2‘
Ø—‘˜b”Ù# \Ñ2‘
á#ÐA \ÐA°LÓA�
à—‘˜CÓ ˆØ—+‘+˜jÓ)ˆØ—+‘+˜jÓ)ˆØ—y‘y B”‘¨C‰ã).³»ÃÐHÐHrU   c                	óâ   € ^ RI Hp V P                  V! VP                  VP                  4      4      pV P                  VP                  4      pVP
                  R8X  d   RMRpRV: RV: RV: 2# )rr  )Ú
MIMOSeriesrž  rK  z\left(I_{\tau} rÂ   z\right)^{-1} \cdot ry  )rè  rö  rö   rê  ré  r8  )rß   r  rö  Úinv_matré  rò  s   &&    rS   Ú_print_MIMOFeedbackÚ LatexPrinter._print_MIMOFeedback{
  sR   € Ý4Ø—+‘+™j¨¯©°D·I±IÓ>Ó?ˆØ�{‰{˜4Ÿ9™9Ó%ˆØ—y‘y B”‘¨C‰Û?DÃgÊtÐTÐTrU   c                	óJ   € V P                  VP                  4      pR V,          # )z%s_\tau)rö   Ú	_expr_matr�  s   && rS   Ú_print_TransferFunctionMatrixÚ*LatexPrinter._print_TransferFunctionMatrix‚
  s   € Ø�k‰k˜$Ÿ.™.Ó)ˆØ˜CÕÐrU   c                	ób   € R P                  VP                  P                  VP                  4      # )z\text{{{}}}_{{{}}})r’   rS  rT  r~  r  s   &&rS   Ú
_print_DFTÚLatexPrinter._print_DFT†
  s#   € Ø$×+Ñ+¨D¯N©N×,CÑ,CÀTÇVÁVÓLÐLrU   c                	ó~   € V P                  \        VP                  4      4      pV P                  V4      pV: R V: 2# )rƒ  )rö   r   rV  rË  )rß   rÊ  Úpretty_nameÚpretty_morphisms   &&  rS   Ú_print_NamedMorphismÚ!LatexPrinter._print_NamedMorphismŠ
  s4   € Ø—k‘k¤&¨¯©Ó"7Ó8ˆØ×.Ñ.¨xÓ8ˆÛ%¢Ð7Ð7rU   c                	óh   € ^ RI Hp V P                  V! VP                  VP                  R4      4      # )rr  )ÚNamedMorphismÚid)Úsympy.categoriesr  r  r9  rÉ  )rß   rÊ  r  s   && rS   Ú_print_IdentityMorphismÚ$LatexPrinter._print_IdentityMorphism�
  s0   € Ý2Ø×(Ñ(©Ø�O‰O˜X×.Ñ.°ó*6ó 7ð 	7rU   c                	ó  € VP                    Uu. uF'  pV P                  \        VP                  4      4      NK)  	  ppVP	                  4        R P                  V4      R,           pV P                  V4      pWE,           # u upi )z\circ rƒ  )rR  rö   r   rV  ÚreverserU  rË  )rß   rÊ  Ú	componentÚcomponent_names_listÚcomponent_namesr  s   &&    rS   Ú_print_CompositeMorphismÚ%LatexPrinter._print_CompositeMorphism”
  s}   € ð .6×-@Ò-@ó BÙ-@ 	ð !%§¡¬F°9·>±>Ó,BÖ CÙ-@ð 	ð  Bà×$Ñ$Ô&Ø#Ÿ.™.Ð)=Ó>ÀÕDˆà×.Ñ.¨xÓ8ˆØÕ0Ð0ùò Bs   �-A?c                	óh   € R P                  V P                  \        VP                  4      4      4      # ©rR  )r’   rö   r   rV  )rß   rÊ  s   &&rS   Ú_print_CategoryÚLatexPrinter._print_CategoryŸ
  s%   € Ø×&Ñ& t§{¡{´6¸(¿-¹-Ó3HÓ'IÓJÐJrU   c                	ó  € VP                   '       g    V P                  \        P                  4      # V P                  VP                   4      pVP                  '       d*   VR V P                  VP                  4      ,          ,          pV# )z\Longrightarrow %s)Úpremisesrö   r   ÚEmptySetÚconclusions)rß   ÚdiagramÚlatex_results   && rS   Ú_print_DiagramÚLatexPrinter._print_Diagram¢
  sm   € Ø××Ðà—;‘;œqŸz™zÓ*Ð*à—{‘{ 7×#3Ñ#3Ó4ˆØ××ÐØÐ1Ø ŸK™K¨×(;Ñ(;Ó<õ=õ =ˆLð ÐrU   c                	ó¸  € R RVP                   ,          ,          p\        VP                  4       F�  p\        VP                   4       FX  pWV3,          '       d   V\        WV3,          4      ,          pVR,          pWAP                   ^,
          8w  g   KO  VR,          pKZ  	  W1P                  ^,
          8w  d
   VR,          pVR,          pKŸ  	  VR,          pV# )z\begin{array}{%s}
r™   rÂ   ú& r6  Ú
z\end{array}
)Úwidthr‹  ÚheightÚlatex)rß   Úgridr  r²   rÎ   s   &&   rS   Ú_print_DiagramGridÚLatexPrinter._print_DiagramGrid®
  s´   € Ø-°°t·z±zÕ1AÕBˆä�t—{‘{Ö#ˆAÜ˜4Ÿ:™:Ö&�Ø˜1˜—:”:Ø ¤E¨$°!¨t­*Ó$5Õ5�LØ Õ#�ØŸ
™
 Q�Ö&Ø  DÕ(’Lñ 'ð —K‘K !•OÔ#Ø Õ&�Ø˜DÕ ŠLñ $ð 	Ð(Õ(ˆØÐrU   c                	óŠ   € R P                  V P                  VP                  4      V P                  VP                  4      4      # )z{{{}}}^{{{}}})r’   rö   r¦  rí  ©rß   r  s   &&rS   Ú_print_FreeModuleÚLatexPrinter._print_FreeModuleÀ
  s/   € Ø×%Ñ% d§k¡k°!·&±&Ó&9¸4¿;¹;ÀqÇvÁvÓ;NÓOÐOrU   c                	óX   a € R P                  RP                  V 3R lV 4       4      4      # )ú\left[ {} \right]rv  c              3  ób   <"  € T F$  pR SP                  V4      ,           R,           x € K&  	  R# 5i©rs   rO   Nr€  ©r&  r'  rß   s   & €rS   r(  Ú8LatexPrinter._print_FreeModuleElement.<locals>.<genexpr>Å
  s)   øé € ð 43Ù01¨1ˆC�$—+‘+˜a“.Õ  3×&Ò&³ùó   ƒ,/)r’   rU  )rß   r  s   f&rS   Ú_print_FreeModuleElementÚ%LatexPrinter._print_FreeModuleElementÃ
  s.   ø€ à#×*Ñ*¨3¯8©8ô 43Ù01ó43ó ,3ó 4ð 	4rU   c                	ó(  aa€ VP                    UUu. uF;  q" Uu. uF,  q0P                  VP                  P                  V4      4      NK.  	  upNK=  	  pppR  oR oRP	                  VV3R lV 4       4      pRP                  V4      # u upi u uppi )c                ó"   € R V ,           R,           # )rs   rO   rP   ©r7   s   &rS   rT   Ú/LatexPrinter._print_SubModule.<locals>.<lambda>Ê
  s   € ˜$ �( Tž/rU   c                ó"   € R V ,           R,           # )z\left[ z \right]rP   r7  s   &rS   rT   r8  Ë
  s   € ˜:¨�>¨KÖ7rU   rv  c           	   3  ór   <"  € T F,  pS! S! R P                  V3R lV 4       4      4      4      x € K.  	  R# 5i)rv  c              3  ó4   <"  € T F  pS! V4      x € K  	  R # 5irõ   rP   )r&  r'  Úcurlys   & €rS   r(  Ú:LatexPrinter._print_SubModule.<locals>.<genexpr>.<genexpr>Ì
  s   øé € Ð3HÁaÀ±E¸!·H°HÃaùs   ƒN)rU  )r&  Úgr<  Úsquares   & €€rS   r(  Ú0LatexPrinter._print_SubModule.<locals>.<genexpr>Ì
  s/   øé € ÐYÑTXÈq™e¡F¨3¯8©8Ô3HÁaÓ3HÓ+HÓ$I×JÐJÓTXùs   ƒ47ú\left\langle {} \right\rangle)rH  rö   r¦  r§  rU  r’   )rß   r  r>  r'  rH  Ú
gens_latexr<  r?  s   &&    @@rS   Ú_print_SubModuleÚLatexPrinter._print_SubModuleÈ
  sv   ù€ ØFGÇfÂfÔMÁfÀ¸!Ó<¹!°Q—‘˜QŸV™VŸ_™_¨QÓ/Ö0¹!Ô<ÁfˆÑMÙ)ˆÙ7ˆØ—X‘XÕYÑTXÓYÓYˆ
Ø/×6Ñ6°zÓBÐBùò	 =ùÓMs   ’Bš2B	ÁBÂ	Bc           	     	ó¾   € R P                  VP                   Uu. uF"  pRV P                  V4      ,           R,           NK$  	  up4      pRP                  V4      # u upi )rv  rs   rO   rA  )rU  rH  rö   r’   )rß   r  r>  rB  s   &&  rS   Ú_print_SubQuotientModuleÚ%LatexPrinter._print_SubQuotientModuleÏ
  sO   € Ø—X‘XÀ1Ç6Â6ÓJÁ6¸a˜s T§[¡[°£^Õ3°c×9Ð9Á6ÑJÓKˆ
Ø/×6Ñ6°zÓBÐBùò Ks   š(Ac                	óä   a € VP                   P                   Uu. uF  w  q!P                  P                  V4      NK!  	  ppR P	                  V 3R lV 4       4      pRP                  V4      # u upi )rv  c              3  ób   <"  € T F$  pR SP                  V4      ,           R,           x € K&  	  R# 5ir/  r€  r0  s   & €rS   r(  Ú=LatexPrinter._print_ModuleImplementedIdeal.<locals>.<genexpr>Õ
  s&   øé € ÐGÁ$¸Q˜c D§K¡K°£NÕ2°S×8Ò8Ã$ùr2  rA  )Ú_modulerH  r¦  r§  rU  r’   )rß   r  r'  rH  rB  s   f&   rS   Ú_print_ModuleImplementedIdealÚ*LatexPrinter._print_ModuleImplementedIdealÓ
  sV   ø€ Ø./¯i©i¯nªnÓ=©n¡s¨—‘—‘ Ö"©nˆÐ=Ø—X‘XÔGÁ$ÓGÓGˆ
Ø/×6Ñ6°zÓBÐBùò >s   š%A-c           	     	ó2  € VP                    Uu. uF"  pV P                  V\        R ,          RR7      NK$  	  ppV^ ,          .\        VR,          R4       UUu. uF  w  r$VR,           V,           NK  	  upp,           pRP	                  V4      # u upi u uppi )r	   Trz  rŸ  ÚijkrÂ   rh  )r@  rü   r    r‡  rU  )rß   r  r²   rR   rÎ   r   s   &&    rS   Ú_print_QuaternionÚLatexPrinter._print_QuaternionØ
  s�   € ð —i’ió!Ù�ð ×Ñ˜q¤*¨UÕ"3¸DÐÖAÙð 	
ð !àˆq�TˆF¬#¨a°­e°UÔ*;Ô<Ñ*;¡$ !�a˜•e˜A—g�gÑ*;Ò<Õ<ˆØ�z‰z˜!‹}Ðùò!ùã<s   �(BÁBc                	óŠ   € R P                  V P                  VP                  4      V P                  VP                  4      4      # ©z\frac{{{}}}{{{}}})r’   rö   r¦  Ú
base_ideal)rß   ÚRs   &&rS   Ú_print_QuotientRingÚ LatexPrinter._print_QuotientRingà
  s4   € à#×*Ñ*¨4¯;©;°q·v±vÓ+>Ø—‘˜QŸ\™\Ó*ó,ð 	,rU   c                	óÀ   € V P                  VP                  P                  V4      4      pR P                  VV P                  VP                  P                  4      4      # )ú{{{}}} + {{{}}})rö   r¦  r§  r’   rT  )rß   r'  Úx_latexs   && rS   Ú_print_QuotientRingElementÚ'LatexPrinter._print_QuotientRingElementå
  sH   € Ø—+‘+˜aŸf™fŸo™o¨aÓ0Ó1ˆØ!×(Ñ(¨Ø—‘˜QŸV™V×.Ñ.Ó/ó1ð 	1rU   c                	óF  a € VP                    Uu. uF'  q!P                  P                  P                  V4      NK)  	  ppR P	                  RP                  V 3R lV 4       4      4      pRP	                  VS P                  VP                  P                  4      4      # u upi )r-  rv  c              3  ób   <"  € T F$  pR SP                  V4      ,           R,           x € K&  	  R# 5ir/  r€  r0  s   & €rS   r(  Ú<LatexPrinter._print_QuotientModuleElement.<locals>.<genexpr>ì
  s)   øé € ð :6Ù04¨1ˆC�$—+‘+˜a“.Õ  3×&Ò&³ùr2  rY  )ÚdataÚmoduler¦  r§  r’   rU  rö   Úkilled_module)rß   r  r'  r`  Ú
data_latexs   f&   rS   Ú_print_QuotientModuleElementÚ)LatexPrinter._print_QuotientModuleElementê
  s„   ø€ Ø34·6²6Ó:±6¨a—‘—‘×&Ñ& qÖ)±6ˆÐ:Ø)×0Ñ0°·±ô :6Ù04ó:6ó 26ó 7ˆ
à!×(Ñ(¨Ø—‘˜QŸX™X×3Ñ3Ó4ó6ð 	6ùò ;s   �-Bc                	óŠ   € R P                  V P                  VP                  4      V P                  VP                  4      4      # rS  )r’   rö   rF  rb  r)  s   &&rS   Ú_print_QuotientModuleÚ"LatexPrinter._print_QuotientModuleñ
  s4   € à#×*Ñ*¨4¯;©;°q·v±vÓ+>Ø—‘˜QŸ_™_Ó-ó/ð 	/rU   c                	óÆ   € R P                  V P                  VP                  4       4      V P                  VP                  4      V P                  VP                  4      4      # )z{{{}}} : {{{}}} \to {{{}}})r’   rö   Ú_sympy_matrixr9  rÉ  )rß   rµ  s   &&rS   Ú_print_MatrixHomomorphismÚ&LatexPrinter._print_MatrixHomomorphismö
  sF   € Ø,×3Ñ3°D·K±KÀÇÁÓ@QÓ4RØ�K‰K˜Ÿ™Ó! 4§;¡;¨q¯z©zÓ#:ó<ð 	<rU   c                	ó  € V P                  VP                  P                  4      w  r#pR V,          pV'       d    VRRP                  V4      ,          ,          pV'       d    VRRP                  V4      ,          ,          pV# )r^  r—  rÂ   r`  )rM  rV  rU  )rß   ÚmanifoldrV  rL  rˆ  s   &&   rS   Ú_print_ManifoldÚLatexPrinter._print_Manifoldú
  se   € Ø!×2Ñ2°8·=±=×3EÑ3EÓFÑˆ�dà˜dÕ"ˆßØ�G˜cŸh™h vÓ.Õ.Õ.ˆDßØ�G˜cŸh™h t›nÕ,Õ,ˆDàˆrU   c                	ó|   € R V P                  VP                  4      : RV P                  VP                  4      : R2# )ú\text{r{  rO   )rö   rV  rn  )rß   Úpatchs   &&rS   Ú_print_PatchÚLatexPrinter._print_Patch  s'   � Ø$(§K¡K°·
±
Ö$;¸T¿[¹[ÈÏÉÖ=XÐYÐYrU   c                	óÊ   € R V P                  VP                  4      : RV P                  VP                  P                  4      : RV P                  VP                  4      : R2# )rr  z	}^{\text{z}}_{rO   )rö   rV  rs  rn  )rß   Úcoordsyss   &&rS   Ú_print_CoordSystemÚLatexPrinter._print_CoordSystem  sC   � à�K‰K˜Ÿ™Ö&¨¯©°H·N±N×4GÑ4GÖ(HÈ$Ï+É+ÐV^×VgÑVgÖJhð
ð 	
rU   c                	óF   € R V P                  VP                  4      ,          # )z\mathbb{\nabla}_{%s})rö   Ú_wrt)rß   Úcvds   &&rS   Ú_print_CovarDerivativeOpÚ%LatexPrinter._print_CovarDerivativeOp  s   € Ø&¨¯©°S·X±XÓ)>Õ>Ð>rU   c                	ó¶   € VP                   P                  VP                  ,          P                  pR P	                  V P                  \        V4      4      4      # r  ©Ú
_coord_sysr›  Ú_indexrV  r’   rö   r   ©rß   ÚfieldrP  s   && rS   Ú_print_BaseScalarFieldÚ#LatexPrinter._print_BaseScalarField  s@   € Ø×!Ñ!×)Ñ)¨%¯,©,Õ7×<Ñ<ˆØ×&Ñ& t§{¡{´6¸&³>Ó'BÓCÐCrU   c                	ó¶   € VP                   P                  VP                  ,          P                  pR P	                  V P                  \        V4      4      4      # )z\partial_{{{}}}r€  rƒ  s   && rS   Ú_print_BaseVectorFieldÚ#LatexPrinter._print_BaseVectorField  s@   € Ø×!Ñ!×)Ñ)¨%¯,©,Õ7×<Ñ<ˆØ!×(Ñ(¨¯©´V¸F³^Ó)DÓEÐErU   c                	ó6  € VP                   p\        VR 4      '       d[   VP                  P                  VP                  ,          P
                  pRP                  V P                  \        V4      4      4      # V P                  V4      pRP                  V4      # )r�  z\operatorname{{d}}{}z!\operatorname{{d}}\left({}\right))	Ú_form_fieldr×  r�  r›  r‚  rV  r’   rö   r   )rß   Údiffr„  rP  s   &&  rS   Ú_print_DifferentialÚ LatexPrinter._print_Differential  sw   € Ø× Ñ ˆÜ�5˜,×'Ò'Ø×%Ñ%×-Ñ-¨e¯l©lÕ;×@Ñ@ˆFØ*×1Ñ1°$·+±+¼fÀV»nÓ2MÓNÐNà—[‘[ Ó'ˆFØ7×>Ñ>¸vÓFÐFrU   c                	óh   € V P                  VP                  ^ ,          4      pRP                  V4      # )rr  z"\operatorname{{tr}}\left({}\right)r  )rß   r  Úcontentss   && rS   Ú	_print_TrÚLatexPrinter._print_Tr!  s)   € à—;‘;˜qŸv™v a�yÓ)ˆØ4×;Ñ;¸HÓEÐErU   c                	ó²   € Ve,   RV P                  VP                  ^ ,          4      : RV: R2# RV P                  VP                  ^ ,          4      ,          # )Nz\left(\phi\left(ú\right)\right)^{rO   z\phi\left(%s\right)r(  rL  s   &&&rS   Ú_print_totientÚLatexPrinter._print_totient&  sC   € Ø‹?à—‘˜TŸY™Y q�\Ö*«Cð1ð 1à%¨¯©°D·I±I¸aµLÓ(AÕAÐArU   c                	ó²   € Ve,   RV P                  VP                  ^ ,          4      : RV: R2# RV P                  VP                  ^ ,          4      ,          # )Nz\left(\lambda\left(r”  rO   z\lambda\left(%s\right)r(  rL  s   &&&rS   Ú_print_reduced_totientÚ#LatexPrinter._print_reduced_totient,  sC   € Ø‹?à—‘˜TŸY™Y q�\Ö*«Cð1ð 1à(¨4¯;©;°t·y±yÀµ|Ó+DÕDÐDrU   c           	     	óL  € \        VP                  4      ^8X  dL   R\        \        V P                  VP                  ^,          VP                  ^ ,          34      4      ,          pM)RV P	                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )r�   ú_%s\left(%s\right)ri  z\sigma^{rO   z\sigma%srå  rõ  s   &&& rS   Ú_print_divisor_sigmaÚ!LatexPrinter._print_divisor_sigma2  sƒ   € Üˆt�y‰y‹>˜QÔØ'¬%´°D·K±KØ15·±¸1µ¸t¿y¹yÈ½|Ð0Ló1Nó +Oõ O‰Cð % t§{¡{°4·9±9¸Qµ<Ó'@Õ@ˆCØ‹?Û'*ªCÐ0Ð0Ø˜SÕ Ð rU   c           	     	óL  € \        VP                  4      ^8X  dL   R\        \        V P                  VP                  ^,          VP                  ^ ,          34      4      ,          pM)RV P	                  VP                  ^ ,          4      ,          pVe   RV: RV: 2# RV,          # )r�   r›  ri  z
\sigma^*^{rO   z
\sigma^*%srå  rõ  s   &&& rS   Ú_print_udivisor_sigmaÚ"LatexPrinter._print_udivisor_sigma<  sƒ   € Üˆt�y‰y‹>˜QÔØ'¬%´°D·K±KØ15·±¸1µ¸t¿y¹yÈ½|Ð0Ló1Nó +Oõ O‰Cð % t§{¡{°4·9±9¸Qµ<Ó'@Õ@ˆCØ‹?Û),ªcÐ2Ð2Ø˜sÕ"Ð"rU   c                	ó²   € Ve,   RV P                  VP                  ^ ,          4      : RV: R2# RV P                  VP                  ^ ,          4      ,          # )Nz\left(\nu\left(r”  rO   z\nu\left(%s\right)r(  rL  s   &&&rS   Ú_print_primenuÚLatexPrinter._print_primenuF  sC   € Ø‹?à—‘˜TŸY™Y q�\Ö*«Cð1ð 1à$ t§{¡{°4·9±9¸Qµ<Ó'@Õ@Ð@rU   c                	ó²   € Ve,   RV P                  VP                  ^ ,          4      : RV: R2# RV P                  VP                  ^ ,          4      ,          # )Nz\left(\Omega\left(r”  rO   z\Omega\left(%s\right)r(  rL  s   &&&rS   Ú_print_primeomegaÚLatexPrinter._print_primeomegaL  sC   € Ø‹?à—‘˜TŸY™Y q�\Ö*«Cð1ð 1à'¨$¯+©+°d·i±iÀµlÓ*CÕCÐCrU   c                	ó,   € \        VP                  4      # rõ   )r�   rV  rì   s   &&rS   Ú
_print_StrÚLatexPrinter._print_StrR  s   € Ü�1—6‘6‹{ÐrU   c                	ó6   € V P                  \        V4      4      # rõ   )rö   r   r  s   &&rS   Ú_print_floatÚLatexPrinter._print_floatU  s   € Ø�{‰{œ5 ›;Ó'Ð'rU   c                	ó   € \        V4      # rõ   ©r�   r  s   &&rS   Ú
_print_intÚLatexPrinter._print_intX  ó   € Ü�4‹yÐrU   c                	ó   € \        V4      # rõ   r®  r  s   &&rS   Ú
_print_mpzÚLatexPrinter._print_mpz[  r±  rU   c                	ó   € \        V4      # rõ   r®  r  s   &&rS   Ú
_print_mpqÚLatexPrinter._print_mpq^  r±  rU   c                	ó   € \        V4      # rõ   r®  r  s   &&rS   Ú_print_fmpzÚLatexPrinter._print_fmpza  r±  rU   c                	ó   € \        V4      # rõ   r®  r  s   &&rS   Ú_print_fmpqÚLatexPrinter._print_fmpqd  r±  rU   c                	ó\   € R P                  \        \        VP                  4      4      4      # )z"\operatorname{{Q}}_{{\text{{{}}}}})r’   rš   r�   rV  r  s   &&rS   Ú_print_PredicateÚLatexPrinter._print_Predicateg  s    € Ø4×;Ñ;¼LÌÈTÏYÉYËÓ<XÓYÐYrU   c                	óÐ   € VP                   pVP                  pV P                  V4      pR P                  V Uu. uF  qPP                  V4      NK  	  up4      pV: RV: R2# u upi )rQ  rÉ   rÊ   )r9  Ú	argumentsrö   rU  )rß   r  Úpredr@  Ú
pred_latexr   Ú
args_latexs   &&     rS   Ú_print_AppliedPredicateÚ$LatexPrinter._print_AppliedPredicatej  sU   € Ø�}‰}ˆØ�~‰~ˆØ—[‘[ Ó&ˆ
Ø—Y‘Y¹Ó=¹°1§¡¨A¦¹Ñ=Ó>ˆ
Û%£zÐ2Ð2ùò  >s   ¹A#c                	óF   <€ \         SV `  V4      pR \        V4      ,          # )z\mathtt{\text{%s}})ÚsuperÚemptyPrinterrš   )rß   r  rR   rS  s   && €rS   rÊ  ÚLatexPrinter.emptyPrinterq  s!   ø€ ä‰GÑ  Ó&ˆà$¤|°A£Õ6Ð6rU   )rÝ   rõ   )FF)Nr‘  r…  )FN)r«   r©  (E  rT  Ú
__module__Ú__qualname__Ú__firstlineno__Úprintmethodr¿   Ú__annotations__rØ   rí   rñ   rü   r·   r  r  r  r6  r<  r  r  rN  rX  r`  Ú_print_BooleanTrueÚ_print_BooleanFalserd  ro  r€  r’  r˜  r­  r¶  r¼  r¿  rÂ  rÇ  rË  r  r  r  r  r  r)  r;  rA  r]  rd  rh  rm  r|  rŽ  r�  r¥  r¯  rÌ  rÏ  rÒ  Úpropertyrà  rå  ré  rì  rò  Ú
_print_MinÚ
_print_Maxrö  rù  rü  r   r  r	  r  r  r  r  r"  r  r  r*  r-  r0  r3  r6  r:  r>  rB  rF  rK  rO  rR  rW  r\  Ú_print_gammar_  rc  rf  rj  ro  rr  ru  rx  r  rƒ  r‹  r�  r”  r˜  rœ  r   r£  r¦  r©  r­  r°  r³  r¹  r½  rÃ  rÉ  rÍ  rÑ  rØ  rß  râ  ræ  ré  rì  rð  rö  rú  rÿ  r  r  r	  r  r  r  r  r  r(  r)  r-  r1  r5  r9  rA  rG  Ú_print_RandomSymbolrM  rR  r]  rb  rp  rw  r  rŽ  r’  rš  rž  r¤  r­  r²  r¶  r¹  rÅ  rÈ  rÎ  rÒ  rÕ  rÛ  rá  rä  ré  r÷  r  r  r	  r  r  r  r  r  r  r   r$  r*  r0  r5  r8  r<  rA  rD  rG  rK  rR  rU  rZ  r`  re  rc  Ú_print_frozensetrŠ  r“  r”  r™  r   r¥  r¨  r­  r°  rº  Ú_print_SeqPerÚ_print_SeqAddÚ_print_SeqMulrÀ  rÄ  rË  rÐ  rÔ  r×  rÝ  rà  rä  rç  rë  rï  ró  r÷  r  r  r  r  r  r!  r%  r)  r,  r/  r2  r5  r;  r?  rD  rS  rY  r^  rb  rf  rj  rm  rq  rt  rw  r|  r�  r…  rŠ  r�  r�  r“  r—  r›  r   r£  rª  r­  r°  r·  rº  r¾  rÃ  rÆ  rË  rÏ  rÔ  rÛ  rß  rã  ró  rø  rü  rÿ  Ú_print_IDFTr  r
  r  r  r  r&  r*  r3  rC  rF  rL  rP  rV  r[  rd  rg  rk  ro  rt  rx  r}  r…  rˆ  r�  r‘  r•  r˜  rœ  rŸ  r¢  r¥  r¨  r«  r¯  r³  r¶  r¹  r¼  r¿  rÆ  rÊ  Ú__static_attributes__Ú__classcell__)rS  s   @rS   rœ   rœ   Ž   sá  ø‡ Ø€Kð)Ø�Uð)à˜Eð)ð 	˜eð)ð 	˜4ð	)ð
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Check for a modifier ending the string.  If present, convert the
modifier to latex and translate the rest recursively.

Given a description of a Greek letter or other special character,
return the appropriate latex.

Let everything else pass as given.

>>> from sympy.printing.latex import translate
>>> translate('alphahatdotprime')
"{\\dot{\\hat{\\alpha}}}'"
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"Ñ
" 1Ó
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ŒmÔ	Ø�a�xˆô œ-×,Ñ,Ó.´CÀ×FˆCØ�w‰w‹y×!Ñ! #×&Ô&¬3¨q«6´C¸³HÖ+<Ü$ SÖ)¬)°A°j¼¸C»°y°MÓ*BÓCÒCñ Gð ˆrU   c                ó6   € \        V4      P                  V 4      # )aÊ"  Convert the given expression to LaTeX string representation.

Parameters
==========
full_prec: boolean, optional
    If set to True, a floating point number is printed with full precision.
fold_frac_powers : boolean, optional
    Emit ``^{p/q}`` instead of ``^{\frac{p}{q}}`` for fractional powers.
fold_func_brackets : boolean, optional
    Fold function brackets where applicable.
fold_short_frac : boolean, optional
    Emit ``p / q`` instead of ``\frac{p}{q}`` when the denominator is
    simple enough (at most two terms and no powers). The default value is
    ``True`` for inline mode, ``False`` otherwise.
inv_trig_style : string, optional
    How inverse trig functions should be displayed. Can be one of
    ``'abbreviated'``, ``'full'``, or ``'power'``. Defaults to
    ``'abbreviated'``.
itex : boolean, optional
    Specifies if itex-specific syntax is used, including emitting
    ``$$...$$``.
ln_notation : boolean, optional
    If set to ``True``, ``\ln`` is used instead of default ``\log``.
long_frac_ratio : float or None, optional
    The allowed ratio of the width of the numerator to the width of the
    denominator before the printer breaks off long fractions. If ``None``
    (the default value), long fractions are not broken up.
mat_delim : string, optional
    The delimiter to wrap around matrices. Can be one of ``'['``, ``'('``,
    or the empty string ``''``. Defaults to ``'['``.
mat_str : string, optional
    Which matrix environment string to emit. ``'smallmatrix'``,
    ``'matrix'``, ``'array'``, etc. Defaults to ``'smallmatrix'`` for
    inline mode, ``'matrix'`` for matrices of no more than 10 columns, and
    ``'array'`` otherwise.
mode: string, optional
    Specifies how the generated code will be delimited. ``mode`` can be one
    of ``'plain'``, ``'inline'``, ``'equation'`` or ``'equation*'``.  If
    ``mode`` is set to ``'plain'``, then the resulting code will not be
    delimited at all (this is the default). If ``mode`` is set to
    ``'inline'`` then inline LaTeX ``$...$`` will be used. If ``mode`` is
    set to ``'equation'`` or ``'equation*'``, the resulting code will be
    enclosed in the ``equation`` or ``equation*`` environment (remember to
    import ``amsmath`` for ``equation*``), unless the ``itex`` option is
    set. In the latter case, the ``$$...$$`` syntax is used.
mul_symbol : string or None, optional
    The symbol to use for multiplication. Can be one of ``None``,
    ``'ldot'``, ``'dot'``, or ``'times'``.
order: string, optional
    Any of the supported monomial orderings (currently ``'lex'``,
    ``'grlex'``, or ``'grevlex'``), ``'old'``, and ``'none'``. This
    parameter does nothing for `~.Mul` objects. Setting order to ``'old'``
    uses the compatibility ordering for ``~.Add`` defined in Printer. For
    very large expressions, set the ``order`` keyword to ``'none'`` if
    speed is a concern.
symbol_names : dictionary of strings mapped to symbols, optional
    Dictionary of symbols and the custom strings they should be emitted as.
root_notation : boolean, optional
    If set to ``False``, exponents of the form 1/n are printed in fractonal
    form. Default is ``True``, to print exponent in root form.
mat_symbol_style : string, optional
    Can be either ``'plain'`` (default) or ``'bold'``. If set to
    ``'bold'``, a `~.MatrixSymbol` A will be printed as ``\mathbf{A}``,
    otherwise as ``A``.
imaginary_unit : string, optional
    String to use for the imaginary unit. Defined options are ``'i'``
    (default) and ``'j'``. Adding ``r`` or ``t`` in front gives ``\mathrm``
    or ``\text``, so ``'ri'`` leads to ``\mathrm{i}`` which gives
    `\mathrm{i}`.
gothic_re_im : boolean, optional
    If set to ``True``, `\Re` and `\Im` is used for ``re`` and ``im``, respectively.
    The default is ``False`` leading to `\operatorname{re}` and `\operatorname{im}`.
decimal_separator : string, optional
    Specifies what separator to use to separate the whole and fractional parts of a
    floating point number as in `2.5` for the default, ``period`` or `2{,}5`
    when ``comma`` is specified. Lists, sets, and tuple are printed with semicolon
    separating the elements when ``comma`` is chosen. For example, [1; 2; 3] when
    ``comma`` is chosen and [1,2,3] for when ``period`` is chosen.
parenthesize_super : boolean, optional
    If set to ``False``, superscripted expressions will not be parenthesized when
    powered. Default is ``True``, which parenthesizes the expression when powered.
min: Integer or None, optional
    Sets the lower bound for the exponent to print floating point numbers in
    fixed-point format.
max: Integer or None, optional
    Sets the upper bound for the exponent to print floating point numbers in
    fixed-point format.
diff_operator: string, optional
    String to use for differential operator. Default is ``'d'``, to print in italic
    form. ``'rd'``, ``'td'`` are shortcuts for ``\mathrm{d}`` and ``\text{d}``.
adjoint_style: string, optional
    String to use for the adjoint symbol. Defined options are ``'dagger'``
    (default),``'star'``, and ``'hermitian'``.

Notes
=====

Not using a print statement for printing, results in double backslashes for
latex commands since that's the way Python escapes backslashes in strings.

>>> from sympy import latex, Rational
>>> from sympy.abc import tau
>>> latex((2*tau)**Rational(7,2))
'8 \\sqrt{2} \\tau^{\\frac{7}{2}}'
>>> print(latex((2*tau)**Rational(7,2)))
8 \sqrt{2} \tau^{\frac{7}{2}}

Examples
========

>>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational, log
>>> from sympy.abc import x, y, mu, r, tau

Basic usage:

>>> print(latex((2*tau)**Rational(7,2)))
8 \sqrt{2} \tau^{\frac{7}{2}}

``mode`` and ``itex`` options:

>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
8 \sqrt{2} \mu^{\frac{7}{2}}
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
$8 \sqrt{2} \tau^{7 / 2}$
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$
>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
8 \sqrt{2} \mu^{\frac{7}{2}}
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
$8 \sqrt{2} \tau^{7 / 2}$
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$

Fraction options:

>>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True))
8 \sqrt{2} \tau^{7/2}
>>> print(latex((2*tau)**sin(Rational(7,2))))
\left(2 \tau\right)^{\sin{\left(\frac{7}{2} \right)}}
>>> print(latex((2*tau)**sin(Rational(7,2)), fold_func_brackets=True))
\left(2 \tau\right)^{\sin {\frac{7}{2}}}
>>> print(latex(3*x**2/y))
\frac{3 x^{2}}{y}
>>> print(latex(3*x**2/y, fold_short_frac=True))
3 x^{2} / y
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=2))
\frac{\int r\, dr}{2 \pi}
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=0))
\frac{1}{2 \pi} \int r\, dr

Multiplication options:

>>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times"))
\left(2 \times \tau\right)^{\sin{\left(\frac{7}{2} \right)}}

Trig options:

>>> print(latex(asin(Rational(7,2))))
\operatorname{asin}{\left(\frac{7}{2} \right)}
>>> print(latex(asin(Rational(7,2)), inv_trig_style="full"))
\arcsin{\left(\frac{7}{2} \right)}
>>> print(latex(asin(Rational(7,2)), inv_trig_style="power"))
\sin^{-1}{\left(\frac{7}{2} \right)}

Matrix options:

>>> print(latex(Matrix(2, 1, [x, y])))
\left[\begin{matrix}x\\y\end{matrix}\right]
>>> print(latex(Matrix(2, 1, [x, y]), mat_str = "array"))
\left[\begin{array}{c}x\\y\end{array}\right]
>>> print(latex(Matrix(2, 1, [x, y]), mat_delim="("))
\left(\begin{matrix}x\\y\end{matrix}\right)

Custom printing of symbols:

>>> print(latex(x**2, symbol_names={x: 'x_i'}))
x_i^{2}

Logarithms:

>>> print(latex(log(10)))
\log{\left(10 \right)}
>>> print(latex(log(10), ln_notation=True))
\ln{\left(10 \right)}

``latex()`` also supports the builtin container types :class:`list`,
:class:`tuple`, and :class:`dict`:

>>> print(latex([2/x, y], mode='inline'))
$\left[ 2 / x, \  y\right]$

Unsupported types are rendered as monospaced plaintext:

>>> print(latex(int))
\mathtt{\text{<class 'int'>}}
>>> print(latex("plain % text"))
\mathtt{\text{plain \% text}}

See :ref:`printer_method_example` for an example of how to override
this behavior for your own types by implementing ``_latex``.

.. versionchanged:: 1.7.0
    Unsupported types no longer have their ``str`` representation treated as valid latex.

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          8  d   WÉ,           R,           R,           pMRpVP                  4       ^ ,          R8X  d   RV,          pRpV^ 8X  dE   VR8X  d   RpVRP                  VP                  V 4      VVVP                  V4      V4      ,          pM*VRP                  VVVP                  V4      V4      ,          pV^,          pKû  	  Wz,          pV# )aâ  
This function generates a LaTeX equation with a multiline right-hand side
in an ``align*``, ``eqnarray`` or ``IEEEeqnarray`` environment.

Parameters
==========

lhs : Expr
    Left-hand side of equation

rhs : Expr
    Right-hand side of equation

terms_per_line : integer, optional
    Number of terms per line to print. Default is 1.

environment : "string", optional
    Which LaTeX wnvironment to use for the output. Options are "align*"
    (default), "eqnarray", and "IEEEeqnarray".

use_dots : boolean, optional
    If ``True``, ``\\dots`` is added to the end of each line. Default is ``False``.

Examples
========

>>> from sympy import multiline_latex, symbols, sin, cos, exp, log, I
>>> x, y, alpha = symbols('x y alpha')
>>> expr = sin(alpha*y) + exp(I*alpha) - cos(log(y))
>>> print(multiline_latex(x, expr))
\begin{align*}
x = & e^{i \alpha} \\
& + \sin{\left(\alpha y \right)} \\
& - \cos{\left(\log{\left(y \right)} \right)}
\end{align*}

Using at most two terms per line:
>>> print(multiline_latex(x, expr, 2))
\begin{align*}
x = & e^{i \alpha} + \sin{\left(\alpha y \right)} \\
& - \cos{\left(\log{\left(y \right)} \right)}
\end{align*}

Using ``eqnarray`` and dots:
>>> print(multiline_latex(x, expr, terms_per_line=2, environment="eqnarray", use_dots=True))
\begin{eqnarray}
x & = & e^{i \alpha} + \sin{\left(\alpha y \right)} \dots\nonumber\\
& & - \cos{\left(\log{\left(y \right)} \right)}
\end{eqnarray}

Using ``IEEEeqnarray``:
>>> print(multiline_latex(x, expr, environment="IEEEeqnarray"))
\begin{IEEEeqnarray}{rCl}
x & = & e^{i \alpha} \nonumber\\
& & + \sin{\left(\alpha y \right)} \nonumber\\
& & - \cos{\left(\log{\left(y \right)} \right)}
\end{IEEEeqnarray}

Notes
=====

All optional parameters from ``latex`` can also be used.

Úeqnarrayr!  z& = &z	\nonumberz
\end{eqnarray}TÚIEEEeqnarrayz
\end{IEEEeqnarray}úalign*z= &rÖ   z
\end{align*}FzUnknown environment: {}z\dotsrž  z& & r   r6  rK  z{:s} {:s}{:s} {:s} {:s}z{:s}{:s} {:s} {:s}rP   z\begin{eqnarray}
z\begin{IEEEeqnarray}{rCl}
z\begin{align*}
ry  )rœ   rÚ   r’   Úas_ordered_termsrŒ  r‹  rÞ  r  )rW  rY  Úterms_per_lineÚenvironmentÚuse_dotsrà   r1  rµ  Ú
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term_startÚterm_endr8  s   &&&&&,               rS   Úmultiline_latexrù  x  sÉ  € ôF 	Ñ �xÑ €AØ�jÔ Ø+ˆØˆ
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ØˆØ%ˆØ‰äÐ2×9Ñ9¸+ÓFÓGÐGØ€DßØˆØ× Ñ Ó"€EÜ�%‹j€GØ€JÜ�7Ž^ˆØ�Q�xˆØˆ
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