ó
    Š*£hZ+ ã                  ó  • S r SSKJr  SSKJr  SSKJr  SSKJr  SSK	J
r
  SSKJr  SSKJrJr  SS	KJrJrJr  SS
KJr  SSKJrJr  SSKJrJrJr   " S S\5      r " S S\5      r " S S\5      r \" \5      SS j5       r!SS jr"\r#g)z
A MathML printer.
é    )Úannotations)ÚAny)ÚMul)ÚS)Údefault_sort_key)Úsympify)Úsplit_super_subÚrequires_partial)Úprecedence_traditionalÚ
PRECEDENCEÚPRECEDENCE_TRADITIONAL)Úgreek_unicode)ÚPrinterÚprint_function)Úprec_to_dpsÚrepr_dpsÚto_strc                  ó^   • \ rS rSr% SrSSSSSSSSSSSS	0 S
SS.rS\S'   SS jrS rS r	Sr
g)ÚMathMLPrinterBaseé   zVContains common code required for MathMLContentPrinter and
MathMLPresentationPrinter.
Nzutf-8FÚabbreviatedÚ[ÚplainTú&#xB7;)ÚorderÚencodingÚfold_frac_powersÚfold_func_bracketsÚfold_short_fracÚinv_trig_styleÚln_notationÚlong_frac_ratioÚ	mat_delimÚmat_symbol_styleÚ
mul_symbolÚroot_notationÚsymbol_namesÚmul_symbol_mathml_numbersÚdisable_split_super_subzdict[str, Any]Ú_default_settingsc                ó¤   ^ ^• [         R                  " T U5        SSKJnJn  U" 5       T l         " S SU5      mUU 4S jnUT R
                  l        g )Nr   )ÚDocumentÚTextc                  ó   • \ rS rSrSS jrSrg)Ú+MathMLPrinterBase.__init__.<locals>.RawTexté6   c                ó~   • U R                   (       a,  UR                  SR                  X R                   U5      5        g g )Nz{}{}{})ÚdataÚwriteÚformat)ÚselfÚwriterÚindentÚ	addindentÚnewls        ÚR/home/mande/repo/quber/.venv/lib/python3.13/site-packages/sympy/printing/mathml.pyÚwritexmlÚ4MathMLPrinterBase.__init__.<locals>.RawText.writexml7   s)   € Ø—9—9Ø—L‘L §¡°¿¹ÀDÓ!IÕJð ó    © N)Ú r?   r?   )Ú__name__Ú
__module__Ú__qualname__Ú__firstlineno__r;   Ú__static_attributes__r>   r=   r:   ÚRawTextr/   6   s   † ÷Kr=   rE   c                óD   >• T" 5       nXl         TR                  Ul        U$ ©N)r2   ÚdomÚownerDocument)r2   ÚrrE   r5   s     €€r:   ÚcreateRawTextNodeÚ5MathMLPrinterBase.__init__.<locals>.createRawTextNode;   s   ø€ Ù“	ˆAØŒFØ"Ÿh™hˆAŒOØˆHr=   )r   Ú__init__Úxml.dom.minidomr,   r-   rH   ÚcreateTextNode)r5   Úsettingsr,   r-   rK   rE   s   `    @r:   rM   ÚMathMLPrinterBase.__init__,   s@   ù€ Ü×Ò˜˜xÔ(ß2á“:ˆŒô	K�dô 	Kö
	ð #4ˆ�‰Õr=   c                ó–   • [         R                  " X5      nUR                  5       nUR                  SS5      nUR	                  5       nU$ )z"
Prints the expression as MathML.
ÚasciiÚxmlcharrefreplace)r   Ú_printÚtoxmlÚencodeÚdecode)r5   ÚexprÚmathMLÚunistrÚxmlbstrÚress         r:   ÚdoprintÚMathMLPrinterBase.doprintC   s?   € ô —’ Ó+ˆØ—‘“ˆØ—-‘- Ð)<Ó=ˆØ�n‰nÓˆØˆ
r=   c                óJ   • U R                   S   (       a  U/ / 4$ [        U5      $ )Nr)   )Ú	_settingsr	   )r5   Únames     r:   Ú_split_super_subÚ"MathMLPrinterBase._split_super_subM   s&   € Ø�>‰>Ð3×4Ø˜"˜b�>Ð!ä" 4Ó(Ð(r=   )rH   rG   )r@   rA   rB   rC   Ú__doc__r*   Ú__annotations__rM   r^   rc   rD   r>   r=   r:   r   r      sT   ‡ ñð
 ØØ!Ø#ØØ'ØØØØ#ØØØØ%-Ø#(ñ)Ð�~ó ô$4ò.õ)r=   r   c                  ó  • \ rS rSrSrSrS rS rS)S jrS r	S	 r
S
 rS rS rS rS rS rS rS rS rS rS rS rS rS rS rS r\r\rS rS rS rS r S r!S r"S  r#S! r$S" r%S# r&\#r'\#r(\#r)S$ r*S% r+S& r,S' r-S(r.g)*ÚMathMLContentPrinteréT   zuPrints an expression to the Content MathML markup language.

References: https://www.w3.org/TR/MathML2/chapter4.html
Ú_mathml_contentc                óþ  • 0 SS_SS_SS_SS_S	S_S
S_SS_SS_SS_SS_SS_SS_SS_SS_SS_SS_SS_0 S S	_S!S"_S#S#_S$S$_S%S%_S&S&_S'S'_S(S(_S)S)_S*S*_S+S+_S,S,_S-S-_S.S._S/S0_S1S2_S3S4_E0 S5S6_S7S8_S9S:_S;S8_S<S=_S>S?_S@SA_SBSC_SDSE_SFSG_SHSI_SJSK_SLSM_SNSO_SPSQ_SRSS_STSU_ESVSWSX.EnUR                   R                   H  nUR                  nXB;   d  M  X$   s  $    UR                   R                  nUR                  5       $ )Yú)Returns the MathML tag for an expression.ÚAddÚplusr   ÚtimesÚ
DerivativeÚdiffÚNumberÚcnÚintÚPowÚpowerÚMaxÚmaxÚMinÚminÚAbsÚabsÚAndÚandÚOrÚorÚXorÚxorÚNotÚnotÚImpliesÚimpliesÚSymbolÚciÚMatrixSymbolÚRandomSymbolÚIntegralÚSumÚsumÚsinÚcosÚtanÚcotÚcscÚsecÚsinhÚcoshÚtanhÚcothÚcschÚsechÚasinÚarcsinÚasinhÚarcsinhÚacosÚarccosÚacoshÚarccoshÚatanÚarctanÚatanhÚarctanhÚatan2ÚacotÚarccotÚacothÚarccothÚasecÚarcsecÚasechÚarcsechÚacscÚarccscÚacschÚarccschÚlogÚlnÚEqualityÚeqÚ
UnequalityÚneqÚGreaterThanÚgeqÚLessThanÚleqÚStrictGreaterThanÚgtÚStrictLessThanÚltÚunionÚ	intersect)ÚUnionÚIntersection©Ú	__class__Ú__mro__r@   Úlower)r5   ÚeÚ	translateÚclsÚns        r:   Ú
mathml_tagÚMathMLContentPrinter.mathml_tag[   sê  € ð6
Ø�6ð6
à�7ð6
ð ˜&ð6
ð �dð	6
ð
 �4ð6
ð �7ð6
ð �5ð6
ð �5ð6
ð �5ð6
ð �5ð6
ð �$ð6
ð �5ð6
ð �5ð6
ð �yð6
ð �dð6
ð  ˜Dð!6
ð" ˜Dñ#6
ð$ ˜ð%6
ð& �5ð'6
ð( �5ð)6
ð* �5ð+6
ð, �5ð-6
ð. �5ð/6
ð0 �5ð16
ð2 �5ð36
ð4 �Fð56
ð6 �Fð76
ð8 �Fð96
ð: �Fð;6
ð< �Fð=6
ð> �Fð?6
ð@ �HðA6
ðB �YðC6
ðD �HòE6
ðF �YðG6
ðH �HðI6
ðJ �YðK6
ðL �XðM6
ðN �HðO6
ðP �YðQ6
ðR �HðS6
ðT �YðU6
ðV �HðW6
ðX �YðY6
ðZ �4ð[6
ð\ ˜ð]6
ð^ ˜%ð_6
ð` ˜5ða6
ðb ˜ðc6
ðd   ðe6
ðf ˜dñg6
ðh Ø'òk6
ˆ	ðp —;‘;×&Ô&ˆCØ—‘ˆAØ�~Ø ‘|Ò#ñ 'ð
 �K‰K× Ñ ˆØ�w‰w‹yÐr=   c                ót  • UR                  5       (       ah  U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U R	                  U* 5      5        U$ SSKJn  U" U5      u  pEU[        R                  La‡  U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U R                  U5      5        UR                  U R                  U5      5        U$ UR                  5       u  pgU[        R                  L a#  [        U5      S:X  a  U R                  US   5      $ U R                  S:w  a$  [        R                  " U5      R                  5       nU R                  R                  S5      nUR                  U R                  R                  S5      5        US:w  a   UR                  U R                  U5      5        U H#  nUR                  U R                  U5      5        M%     U$ )	NÚapplyÚminusr   ©ÚfractionÚdivideé   Úoldro   )Úcould_extract_minus_signrH   ÚcreateElementÚappendChildÚ
_print_MulÚsympy.simplifyrÓ   r   ÚOnerU   Úas_coeff_mulÚlenr   r   Ú
_from_argsÚas_ordered_factors)	r5   rY   ÚxrÓ   ÚnumerÚdenomÚcoeffÚtermsÚterms	            r:   rÚ   ÚMathMLContentPrinter._print_Mul�   s   € à×(Ñ(×*Ñ*Ø—‘×&Ñ& wÓ/ˆAØ�M‰M˜$Ÿ(™(×0Ñ0°Ó9Ô:Ø�M‰M˜$Ÿ/™/¨4¨%Ó0Ô1ØˆHå+Ù “~‰ˆàœŸ™ÒØ—‘×&Ñ& wÓ/ˆAØ�M‰M˜$Ÿ(™(×0Ñ0°Ó:Ô;Ø�M‰M˜$Ÿ+™+ eÓ,Ô-Ø�M‰M˜$Ÿ+™+ eÓ,Ô-ØˆHà×(Ñ(Ó*‰ˆØ”A—E‘EŠ>œc %›j¨A›oð —;‘;˜u Q™xÓ(Ð(à�:‰:˜ÓÜ—N’N 5Ó)×<Ñ<Ó>ˆEà�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨WÓ5Ô6Ø�A‹:Ø�M‰M˜$Ÿ+™+ eÓ,Ô-ÛˆDØ�M‰M˜$Ÿ+™+ dÓ+Ö,ñ àˆr=   Nc                ób  • U R                  XS9nU R                  US   5      n/ nUSS   Hú  nUR                  5       (       a–  U R                  R	                  S5      nUR                  U R                  R	                  S5      5        UR                  U5        UR                  U R                  U* 5      5        UnXcS   :X  a  UR                  U5        M¬  M®  UR                  U5        U R                  U5      nXcS   :X  d  MÚ  UR                  U R                  U5      5        Mü     [        U5      S:X  a  U$ U R                  R	                  S5      nUR                  U R                  R	                  S5      5        U(       a)  UR                  UR                  S5      5        U(       a  M)  U$ )N©r   r   rÕ   rÐ   rÑ   éÿÿÿÿrn   )	Ú_as_ordered_termsrU   r×   rH   rØ   rÙ   ÚappendrÞ   Úpop)r5   rY   r   ÚargsÚlastProcessedÚ	plusNodesÚargrá   s           r:   Ú
_print_AddÚMathMLContentPrinter._print_AddÀ   sc  € Ø×%Ñ% dÐ%Ð8ˆØŸ™ D¨¡GÓ,ˆØˆ	Ø˜˜“8ˆCØ×+Ñ+×-Ñ-à—H‘H×*Ñ*¨7Ó3�Ø—‘˜dŸh™h×4Ñ4°WÓ=Ô>Ø—‘˜mÔ,Ø—‘˜dŸk™k¨3¨$Ó/Ô0à !�Ø˜r™(“?Ø×$Ñ$ ]Ö3ñ #ð × Ñ  Ô/Ø $§¡¨CÓ 0�Ø˜r™(•?Ø×$Ñ$ T§[¡[°Ó%5Ö6ñ ô  ˆy‹>˜QÓØ Ð Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨VÓ4Ô5ÞØ�M‰M˜)Ÿ-™-¨Ó*Ô+÷ ˆiàˆr=   c                ób  • UR                   S   R                  S:w  a  [        S5      eU R                  R	                  S5      n[        UR                   5       HÒ  u  nu  pEU[        UR                   5      S-
  :X  aB  US:X  a<  U R                  R	                  S5      nUR                  U R                  U5      5        O[U R                  R	                  S5      nUR                  U R                  U5      5        UR                  U R                  U5      5        UR                  U5        MÔ     U$ )Nrê   Tz¼All Piecewise expressions must contain an (expr, True) statement to be used as a default condition. Without one, the generated expression may not evaluate to anything under some condition.Ú	piecewiserÕ   Ú	otherwiseÚpiece)	rî   ÚcondÚ
ValueErrorrH   rØ   Ú	enumeraterÞ   rÙ   rU   )r5   rY   ÚrootÚirÉ   Úcr÷   s          r:   Ú_print_PiecewiseÚ%MathMLContentPrinter._print_PiecewiseÜ   sõ   € Ø�9‰9�R‰=×Ñ Ó%ô ð /ó 0ð 0ð
 �x‰x×%Ñ% kÓ2ˆÜ" 4§9¡9Ö-‰IˆA‰v�Ø”C˜Ÿ	™	“N QÑ&Ó&¨1°«9ØŸ™×.Ñ.¨{Ó;�Ø×!Ñ! $§+¡+¨a£.Õ1àŸ™×.Ñ.¨wÓ7�Ø×!Ñ! $§+¡+¨a£.Ô1Ø×!Ñ! $§+¡+¨a£.Ô1Ø×Ñ˜UÖ#ñ .ð ˆr=   c           	     óL  • U R                   R                  S5      n[        UR                  5       Ho  nU R                   R                  S5      n[        UR                  5       H'  nUR                  U R                  XU4   5      5        M)     UR                  U5        Mq     U$ )NÚmatrixÚ	matrixrow)rH   rØ   ÚrangeÚrowsÚcolsrÙ   rU   )r5   Úmrá   rü   Úx_rÚjs         r:   Ú_print_MatrixBaseÚ&MathMLContentPrinter._print_MatrixBaseñ   s|   € Ø�H‰H×"Ñ" 8Ó,ˆÜ�q—v‘v–ˆAØ—(‘(×(Ñ(¨Ó5ˆCÜ˜1Ÿ6™6–]�Ø—‘ §¡¨A°¨d©GÓ 4Ö5ñ #à�M‰M˜#Öñ	 ð
 ˆr=   c                ó  • UR                   S:X  aZ  U R                  R                  S5      nUR                  U R                  R	                  [        UR                  5      5      5        U$ U R                  R                  S5      nUR                  U R                  R                  S5      5        U R                  R                  S5      nUR                  U R                  R	                  [        UR                  5      5      5        U R                  R                  S5      nUR                  U R                  R	                  [        UR                   5      5      5        UR                  U5        UR                  U5        U$ )NrÕ   rs   rÐ   rÔ   )ÚqrH   rØ   rÙ   rO   ÚstrÚp)r5   rÉ   rá   ÚxnumÚxdenoms        r:   Ú_print_RationalÚ$MathMLContentPrinter._print_Rationalú   s  € Ø�3‰3�!‹8à—‘×&Ñ& tÓ,ˆAØ�M‰M˜$Ÿ(™(×1Ñ1´#°a·c±c³(Ó;Ô<ØˆHØ�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨XÓ6Ô7à�x‰x×%Ñ% dÓ+ˆØ×Ñ˜Ÿ™×0Ñ0´°Q·S±S³Ó:Ô;à—‘×'Ñ'¨Ó-ˆØ×Ñ˜4Ÿ8™8×2Ñ2´3°q·s±s³8Ó<Ô=Ø	�‰�dÔØ	�‰�fÔØˆr=   c                ól  • U R                   R                  S5      nUR                  U R                   R                  U R                  U5      5      5        U R                   R                  S5      nU R                   R                  S5      nUR                  U R	                  UR
                  S   5      5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U5        UR                  U R	                  UR
                  S   5      5        U$ )NrÐ   ÚbvarÚlowlimitrÕ   é   r   )rH   rØ   rÙ   rÍ   rU   rî   )r5   rÉ   rá   Úx_1Úx_2s        r:   Ú_print_LimitÚ!MathMLContentPrinter._print_Limit  sÖ   € Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨T¯_©_¸QÓ-?Ó@ÔAà�h‰h×$Ñ$ VÓ,ˆØ�h‰h×$Ñ$ ZÓ0ˆØ�‰˜Ÿ™ A§F¡F¨1¡IÓ.Ô/Ø�‰˜Ÿ™ A§F¡F¨1¡IÓ.Ô/à	�‰�cÔØ	�‰�cÔØ	�‰�d—k‘k !§&¡&¨¡)Ó,Ô-Øˆr=   c                ó8   • U R                   R                  S5      $ )NÚ
imaginaryi©rH   rØ   ©r5   rÉ   s     r:   Ú_print_ImaginaryUnitÚ)MathMLContentPrinter._print_ImaginaryUnit  ó   € Ø�x‰x×%Ñ% lÓ3Ð3r=   c                ó8   • U R                   R                  S5      $ )NÚ
eulergammar  r  s     r:   Ú_print_EulerGammaÚ&MathMLContentPrinter._print_EulerGamma  r!  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )zoWe use unicode #x3c6 for Greek letter phi as defined here
https://www.w3.org/2003/entities/2007doc/isogrk1.htmlrs   u   Ï†©rH   rØ   rÙ   rO   ©r5   rÉ   rá   s      r:   Ú_print_GoldenRatioÚ'MathMLContentPrinter._print_GoldenRatio   s9   € ð �H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-Ð.JÓKÔLØˆr=   c                ó8   • U R                   R                  S5      $ )NÚexponentialer  r  s     r:   Ú_print_Exp1Ú MathMLContentPrinter._print_Exp1'  s   € Ø�x‰x×%Ñ% nÓ5Ð5r=   c                ó8   • U R                   R                  S5      $ )NÚpir  r  s     r:   Ú	_print_PiÚMathMLContentPrinter._print_Pi*  s   € Ø�x‰x×%Ñ% dÓ+Ð+r=   c                ó8   • U R                   R                  S5      $ )NÚinfinityr  r  s     r:   Ú_print_InfinityÚ$MathMLContentPrinter._print_Infinity-  ó   € Ø�x‰x×%Ñ% jÓ1Ð1r=   c                ó8   • U R                   R                  S5      $ )NÚ
notanumberr  r  s     r:   Ú
_print_NaNÚMathMLContentPrinter._print_NaN0  r!  r=   c                ó8   • U R                   R                  S5      $ )NÚemptysetr  r  s     r:   Ú_print_EmptySetÚ$MathMLContentPrinter._print_EmptySet3  r7  r=   c                ó8   • U R                   R                  S5      $ )NÚtruer  r  s     r:   Ú_print_BooleanTrueÚ'MathMLContentPrinter._print_BooleanTrue6  s   € Ø�x‰x×%Ñ% fÓ-Ð-r=   c                ó8   • U R                   R                  S5      $ )NÚfalser  r  s     r:   Ú_print_BooleanFalseÚ(MathMLContentPrinter._print_BooleanFalse9  s   € Ø�x‰x×%Ñ% gÓ.Ð.r=   c                óä   • U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U R                   R                  S5      5        U$ )NrÐ   rÑ   r4  )rH   rØ   rÙ   r(  s      r:   Ú_print_NegativeInfinityÚ,MathMLContentPrinter._print_NegativeInfinity<  sQ   € Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨WÓ5Ô6Ø	�‰�d—h‘h×,Ñ,¨ZÓ8Ô9Øˆr=   c                ór   ^ ^^• UUU 4S jm[        TR                  5      nUR                  5         T" U5      $ )Nc                ó2  >• TR                   R                  S5      nUR                  TR                   R                  TR                  T5      5      5        TR                   R                  S5      nUR                  TR	                  U S   S   5      5        UR                  U5        [        U S   5      S:X  a¤  TR                   R                  S5      nUR                  TR	                  U S   S   5      5        UR                  U5        TR                   R                  S5      nUR                  TR	                  U S   S   5      5        UR                  U5        [        U S   5      S:X  aR  TR                   R                  S5      nUR                  TR	                  U S   S   5      5        UR                  U5        [        U 5      S:X  a,  UR                  TR	                  TR                  5      5        U$ UR                  T" U SS  5      5        U$ )	NrÐ   r  r   é   r  rÕ   Úuplimitr  )rH   rØ   rÙ   rÍ   rU   rÞ   Úfunction)Úlimitsrá   Ú	bvar_elemÚlow_elemÚup_elemrÉ   Ú
lime_recurr5   s        €€€r:   rT  Ú8MathMLContentPrinter._print_Integral.<locals>.lime_recurC  s¡  ø€ Ø—‘×&Ñ& wÓ/ˆAØ�M‰M˜$Ÿ(™(×0Ñ0°·±ÀÓ1CÓDÔEØŸ™×.Ñ.¨vÓ6ˆIØ×!Ñ! $§+¡+¨f°Q©i¸©lÓ";Ô<Ø�M‰M˜)Ô$ä�6˜!‘9‹~ Ó"ØŸ8™8×1Ñ1°*Ó=�Ø×$Ñ$ T§[¡[°¸±¸1±Ó%>Ô?Ø—‘˜hÔ'ØŸ(™(×0Ñ0°Ó;�Ø×#Ñ# D§K¡K°°q±	¸!±Ó$=Ô>Ø—‘˜gÔ&Ü�6˜!‘9‹~ Ó"ØŸ(™(×0Ñ0°Ó;�Ø×#Ñ# D§K¡K°°q±	¸!±Ó$=Ô>Ø—‘˜gÔ&Ü�6‹{˜aÓØ—‘˜dŸk™k¨!¯*©*Ó5Ô6ð ˆHð —‘™j¨°°¨Ó4Ô5ØˆHr=   )ÚlistrP  Úreverse)r5   rÉ   rP  rT  s   `` @r:   Ú_print_IntegralÚ$MathMLContentPrinter._print_IntegralB  s,   ú€ ÷	ô0 �a—h‘h“ˆØ�‰ÔÙ˜&Ó!Ð!r=   c                ó$   • U R                  U5      $ rG   )rX  r  s     r:   Ú
_print_SumÚMathMLContentPrinter._print_Sum_  s   € ð ×#Ñ# AÓ&Ð&r=   c                óf  ^ • T R                   R                  T R                  U5      5      nU 4S jnS nT R                  UR                  5      u  pVnU" U5      nU Vs/ s H
  o„" U5      PM     nnU V	s/ s H
  o”" U	5      PM     nn	T R                   R                  S5      n
U
R                  T R                   R                  U5      5        U(       dŠ  U(       d,  UR                  T R                   R                  U5      5        U$ T R                   R                  S5      nUR                  U
5        UR                  U" U5      5        UR                  U5         U$ U(       dV  T R                   R                  S5      nUR                  U
5        UR                  U" U5      5        UR                  U5        U$ T R                   R                  S5      nUR                  U
5        UR                  U" U5      5        UR                  U" U5      5        UR                  U5        U$ s  snf s  sn	f )Nc                ó|  >• [        U 5      S:”  aã  TR                  R                  S5      n[        U 5       H·  u  p#US:”  aV  TR                  R                  S5      nUR	                  TR                  R                  S5      5        UR	                  U5        TR                  R                  S5      nUR	                  TR                  R                  U5      5        UR	                  U5        M¹     U$ TR                  R                  S5      nUR	                  TR                  R                  U S   5      5        U$ )NrÕ   zmml:mrowr   zmml:moÚ úmml:mi©rÞ   rH   rØ   rú   rÙ   rO   ©ÚitemsÚmrowrü   ÚitemÚmoÚmir5   s         €r:   ÚjoinÚ0MathMLContentPrinter._print_Symbol.<locals>.joing  só   ø€ Ü�5‹z˜A‹~Ø—x‘x×-Ñ-¨jÓ9�Ü(¨Ö/‘G�AØ˜1“uØ!ŸX™X×3Ñ3°HÓ=˜ØŸ™ t§x¡x×'>Ñ'>¸sÓ'CÔDØ×(Ñ(¨Ô,ØŸ™×/Ñ/°Ó9�BØ—N‘N 4§8¡8×#:Ñ#:¸4Ó#@ÔAØ×$Ñ$ RÖ(ñ  0ð �à—X‘X×+Ñ+¨HÓ5�Ø—‘˜tŸx™x×6Ñ6°u¸Q±xÓ@ÔAØ�	r=   c                óF   • U [         ;   a  [         R                  " U 5      $ U $ rG   ©r   Úget©Úss    r:   rÊ   Ú5MathMLContentPrinter._print_Symbol.<locals>.translatey  ó    € Ø”MÓ!Ü$×(Ò(¨Ó+Ð+à�r=   r`  zmml:msubzmml:msupzmml:msubsup)rH   rØ   rÍ   rc   rb   rÙ   rO   )r5   Úsymrˆ   rh  rÊ   rb   ÚsupersÚsubsÚsupÚsubÚmnameÚmsubÚmsupÚmsubsups   `             r:   Ú_print_SymbolÚ"MathMLContentPrinter._print_Symbold  sÍ  ø€ Ø�X‰X×#Ñ# D§O¡O°CÓ$8Ó9ˆõ	ò$	ð "×2Ñ2°3·8±8Ó<Ñˆ�dÙ˜‹ˆÙ,2Ó3ªF S�)˜C–.©FˆÐ3Ù*.Ó/ª$ 3�	˜#–©$ˆÐ/à—‘×&Ñ& xÓ0ˆØ×Ñ˜$Ÿ(™(×1Ñ1°$Ó7Ô8ÞÞØ—‘˜tŸx™x×6Ñ6°tÓ<Ô=ð$ ˆ	ð! —x‘x×-Ñ-¨jÓ9�Ø× Ñ  Ô'Ø× Ñ ¡ d£Ô,Ø—‘˜tÕ$ð ˆ	ö Ø—x‘x×-Ñ-¨jÓ9�Ø× Ñ  Ô'Ø× Ñ ¡ f£Ô.Ø—‘˜tÔ$ð ˆ	ð Ÿ(™(×0Ñ0°Ó?�Ø×#Ñ# EÔ*Ø×#Ñ#¡D¨£JÔ/Ø×#Ñ#¡D¨£LÔ1Ø—‘˜wÔ'Øˆ	ùò3 4ùÚ/s   ÁH)Á6H.c                óF  • U R                   S   (       Gaa  UR                  R                  (       GaE  UR                  R                  S:X  Ga*  U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  R                  S:w  aŸ  U R                  R                  S5      nU R                  R                  S5      nUR                  U R                  R                  [        UR                  R                  5      5      5        UR                  U5        UR                  U5        UR                  U R                  UR                  5      5        U$ U R                  R                  S5      nU R                  R                  U R                  U5      5      nUR                  U5        UR                  U R                  UR                  5      5        UR                  U R                  UR                  5      5        U$ )Nr&   rÕ   rÐ   rû   r  Údegreers   )ra   ÚexpÚis_Rationalr  rH   rØ   rÙ   r  rO   r  rU   ÚbaserÍ   )r5   rÉ   rá   ÚxmldegÚxmlcnr  s         r:   Ú
_print_PowÚMathMLContentPrinter._print_PowŸ  sl  € ð �N‰N˜?×+Ð+°·±×0A×0AÐ0AØ—E‘E—G‘G˜q”LØ—‘×&Ñ& wÓ/ˆAØ�M‰M˜$Ÿ(™(×0Ñ0°Ó8Ô9Ø�u‰u�w‰w˜!‹|ØŸ™×/Ñ/°Ó9�ØŸ™×.Ñ.¨tÓ4�Ø×!Ñ! $§(¡(×"9Ñ"9¼#¸a¿e¹e¿g¹g»,Ó"GÔHØ×"Ñ" 5Ô)Ø—‘˜fÔ%Ø�M‰M˜$Ÿ+™+ a§f¡fÓ-Ô.ØˆHà�H‰H×"Ñ" 7Ó+ˆØ�h‰h×$Ñ$ T§_¡_°QÓ%7Ó8ˆØ	�‰�cÔØ	�‰�d—k‘k !§&¡&Ó)Ô*Ø	�‰�d—k‘k !§%¡%Ó(Ô)Øˆr=   c                óÀ   • U R                   R                  U R                  U5      5      nUR                  U R                   R	                  [        U5      5      5        U$ rG   ©rH   rØ   rÍ   rÙ   rO   r  r(  s      r:   Ú_print_NumberÚ"MathMLContentPrinter._print_Number¶  óC   € Ø�H‰H×"Ñ" 4§?¡?°1Ó#5Ó6ˆØ	�‰�d—h‘h×-Ñ-¬c°!«fÓ5Ô6Øˆr=   c                ó   • U R                   R                  U R                  U5      5      n[        UR                  [        UR                  5      5      nUR                  U R                   R                  U5      5        U$ rG   )	rH   rØ   rÍ   Úmlib_to_strÚ_mpf_r   Ú_precrÙ   rO   )r5   rÉ   rá   Úrepr_es       r:   Ú_print_FloatÚ!MathMLContentPrinter._print_Float»  sX   € Ø�H‰H×"Ñ" 4§?¡?°1Ó#5Ó6ˆÜ˜QŸW™W¤h¨q¯w©wÓ&7Ó8ˆØ	�‰�d—h‘h×-Ñ-¨fÓ5Ô6Øˆr=   c                óÌ  • U R                   R                  S5      nU R                  U5      n[        UR                  5      (       a  SnUR                  U R                   R                  U5      5        U R                   R                  S5      n[        UR                  5       H‚  u  pVUR                  U R                  U5      5        US:”  d  M-  U R                   R                  S5      nUR                  U R                  [        U5      5      5        UR                  U5        M„     UR                  U5        UR                  U R                  UR                  5      5        U$ )NrÐ   Úpartialdiffr  rÕ   r}  )
rH   rØ   rÍ   r
   rY   rÙ   ÚreversedÚvariable_countrU   r   )r5   rÉ   rá   Údiff_symbolr  rq  ro   r}  s           r:   Ú_print_DerivativeÚ&MathMLContentPrinter._print_DerivativeÁ  s  € Ø�H‰H×"Ñ" 7Ó+ˆØ—o‘o aÓ(ˆÜ˜AŸF™F×#Ñ#Ø'ˆKØ	�‰�d—h‘h×,Ñ,¨[Ó9Ô:Ø�h‰h×$Ñ$ VÓ,ˆä" 1×#3Ñ#3Ö4‰JˆCØ�O‰O˜DŸK™K¨Ó,Ô-Ø�q�yØŸ™×/Ñ/°Ó9�Ø×"Ñ" 4§;¡;¬w°u«~Ó#>Ô?Ø—‘ Ö'ñ 5ð 	
�‰�cÔØ	�‰�d—k‘k !§&¡&Ó)Ô*Øˆr=   c                ó  • U R                   R                  S5      nUR                  U R                   R                  U R                  U5      5      5        UR                   H#  nUR                  U R                  U5      5        M%     U$ ©NrÐ   )rH   rØ   rÙ   rÍ   rî   rU   ©r5   rÉ   rá   rñ   s       r:   Ú_print_FunctionÚ$MathMLContentPrinter._print_FunctionÔ  sb   € Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨T¯_©_¸QÓ-?Ó@ÔAØ—6”6ˆCØ�M‰M˜$Ÿ+™+ cÓ*Ö+ñ àˆr=   c                óÀ   • U R                   R                  U R                  U5      5      nUR                   H#  nUR	                  U R                  U5      5        M%     U$ rG   )rH   rØ   rÍ   rî   rÙ   rU   rš  s       r:   Ú_print_BasicÚ!MathMLContentPrinter._print_BasicÛ  sG   € Ø�H‰H×"Ñ" 4§?¡?°1Ó#5Ó6ˆØ—6”6ˆCØ�M‰M˜$Ÿ+™+ cÓ*Ö+ñ àˆr=   c                ó  • U R                   R                  S5      nU R                   R                  U R                  U5      5      nUR                  U5        UR                   H#  nUR                  U R                  U5      5        M%     U$ r™  )rH   rØ   rÍ   rÙ   rî   rU   )r5   rÉ   rá   r  rñ   s        r:   Ú_print_AssocOpÚ#MathMLContentPrinter._print_AssocOpá  sg   € Ø�H‰H×"Ñ" 7Ó+ˆØ�h‰h×$Ñ$ T§_¡_°QÓ%7Ó8ˆØ	�‰�cÔØ—6”6ˆCØ�M‰M˜$Ÿ+™+ cÓ*Ö+ñ àˆr=   c                óV  • U R                   R                  S5      nUR                  U R                   R                  U R                  U5      5      5        UR                  U R	                  UR
                  5      5        UR                  U R	                  UR                  5      5        U$ r™  )rH   rØ   rÙ   rÍ   rU   ÚlhsÚrhsr(  s      r:   Ú_print_RelationalÚ&MathMLContentPrinter._print_Relationalé  sq   € Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨T¯_©_¸QÓ-?Ó@ÔAØ	�‰�d—k‘k !§%¡%Ó(Ô)Ø	�‰�d—k‘k !§%¡%Ó(Ô)Øˆr=   c                óŽ   • U R                   R                  S5      nU H#  nUR                  U R                  U5      5        M%     U$ )z_MathML reference for the <list> element:
https://www.w3.org/TR/MathML2/chapter4.html#contm.listrV  )rH   rØ   rÙ   rU   )r5   ÚseqÚdom_elementre  s       r:   Ú_print_listÚ MathMLContentPrinter._print_listð  s?   € ð —h‘h×,Ñ,¨VÓ4ˆÛˆDØ×#Ñ# D§K¡K°Ó$5Ö6ñ àÐr=   c                óÀ   • U R                   R                  U R                  U5      5      nUR                  U R                   R	                  [        U5      5      5        U$ rG   r†  ©r5   r  rª  s      r:   Ú
_print_intÚMathMLContentPrinter._print_intø  óF   € Ø—h‘h×,Ñ,¨T¯_©_¸QÓ-?Ó@ˆØ×Ñ §¡× 7Ñ 7¼¸A»Ó ?Ô@ØÐr=   c                ó¢   • U R                   R                  S5      nUR                   H#  nUR                  U R	                  U5      5        M%     U$ )NÚset)rH   rØ   rî   rÙ   rU   rš  s       r:   Ú_print_FiniteSetÚ%MathMLContentPrinter._print_FiniteSet  s>   € Ø�H‰H×"Ñ" 5Ó)ˆØ—6”6ˆCØ�M‰M˜$Ÿ+™+ cÓ*Ö+ñ àˆr=   c                óö   • U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                   H#  nUR                  U R	                  U5      5        M%     U$ )NrÐ   Úsetdiff©rH   rØ   rÙ   rî   rU   rš  s       r:   Ú_print_ComplementÚ&MathMLContentPrinter._print_Complement  sY   € Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,¨YÓ7Ô8Ø—6”6ˆCØ�M‰M˜$Ÿ+™+ cÓ*Ö+ñ àˆr=   c                óö   • U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                   H#  nUR                  U R	                  U5      5        M%     U$ )NrÐ   Úcartesianproductr¸  rš  s       r:   Ú_print_ProductSetÚ&MathMLContentPrinter._print_ProductSet  sZ   € Ø�H‰H×"Ñ" 7Ó+ˆØ	�‰�d—h‘h×,Ñ,Ð-?Ó@ÔAØ—6”6ˆCØ�M‰M˜$Ÿ+™+ cÓ*Ö+ñ àˆr=   c                ól  • U R                   R                  U R                  U5      5      nUR                   HO  nU R                   R                  S5      nUR	                  U R                  U5      5        UR	                  U5        MQ     UR	                  U R                  UR                  5      5        U$ )Nr  )rH   rØ   rÍ   Ú	signaturerÙ   rU   rY   )r5   rÉ   rá   rñ   r  s        r:   Ú_print_LambdaÚ"MathMLContentPrinter._print_Lambda  s„   € ð �H‰H×"Ñ" 4§?¡?°1Ó#5Ó6ˆØ—;”;ˆCØ—(‘(×(Ñ(¨Ó0ˆCØ�O‰O˜DŸK™K¨Ó,Ô-Ø�M‰M˜#Öñ ð 	
�‰�d—k‘k !§&¡&Ó)Ô*Øˆr=   r>   rG   )/r@   rA   rB   rC   re   ÚprintmethodrÍ   rÚ   rò   rþ   r	  r  r  r  r$  r)  r-  r1  r5  r:  r>  rB  rF  rI  rX  r[  rz  Ú_print_MatrixSymbolÚ_print_RandomSymbolrƒ  r‡  r�  r–  r›  rž  r¡  r¦  r«  r¯  Ú_print_ImpliesÚ
_print_NotÚ
_print_Xorr´  r¹  r½  rÁ  rD   r>   r=   r:   rh   rh   T   sà   † ñð $€Kò@òD!ôFò8ò*òò$ò4ò4òò6ò,ò2ò4ò2ò.ò/òò"ò:'ò
6ðp (ÐØ'Ðòò.ò
òò&òòòòòð
 $€NØ€JØ€Jòòòõ	r=   rh   c                  ó‚  • \ rS rSrSrSrS rS rS rS r	S r
S	 rS
 rS rS rS rS�S jrS rSŽS jrS rSŽS jrS rS rS rS rS rS rS rS rS rS rS rS r S  r!S! r"S" r#S# r$S$ r%S% r&S�S& jr'S' r(\'r)S( r*S) r+S* r,S+ r-S, r.S- r/S. r0S/ r1S0 r2S1 r3S2 r4S3 r5S4 r6S5 r7S6 r8SŽS7 jr9\9r:S8 r;SŽS9 jr<SŽS: jr=S; r>S< r?S= r@S> rAS? rBS@ rCSA rDSB rESC rF\FrGSD rHSE rISF rJSG rKSH rLSI rMSJ rNSK rOSL rP\PrQ\PrRSM rSSN rTSO rU\U=rVrWSP rXSQ rYSR rZSS r[ST r\SU r]SV r^SW r_SX r`SY raSZ rbS[ rcS\ rdS] reS^ rfS_ rgS` rhSa riSb rjSc rkSd rl\lrmSe rnSf roSg rpSh rqSi rrSj rsSk rtSl ruSm rvSn rwSo rxSp rySq rzSr r{Ss r|St r}Su r~Sv rSw r€Sx r�Sy r‚Sz rƒS{ r„S| r…S} r†S~ r‡S rˆS€ r‰S� rŠS‚ r‹Sƒ rŒS„ r�S… rŽS† r�S‡ r�Sˆ r‘S‰ r’SŠ r“S‹ r”SŒr•g)�ÚMathMLPresentationPrinteri#  zzPrints an expression to the Presentation MathML markup language.

References: https://www.w3.org/TR/MathML2/chapter3.html
Ú_mathml_presentationc                óü  ^ • 0 SS_SS_SS_SS_SS	_S
S_SS_SS_SS_SS_SS_SS_SS_SS_SS_SS_SS_0 SS_S S_S!S"_S#S$_S%S&_S'S(_S)S*_S+S,_S-S._S/S0_S1S2_S3S4_S5S6_S7S8_S9S8_S:S;_S<S=_ES>S?S@SASBSCSDSESFS@SASGSHSISJ.EnU 4SK jnUR                   R                   H  nUR                  nXR;   d  M  X%   s  $    UR                   R                  SL:X  a  U" 5       $ UR                   R                  nUR                  5       $ )Mrl   rr   ÚmnÚLimitz&#x2192;rp   ú&dd;rt   r‡   rg  r‹   z&int;rŒ   z&#x2211;rŽ   r�   r�   r‘   rš   r›   rœ   r�   rž   rŸ   r    r¡   r¢   r£   r¤   r¥   r§   r¨   r¦   rµ   Ú=r·   z&#x2260;r¹   z&#x2265;r»   z&#x2264;r½   Ú>r¿   Ú<Úlerchphiú&#x3A6;Úzetaz&#x3B6;Údirichlet_etaz&#x3B7;Ú
elliptic_kz&#x39A;Ú
lowergammaú&#x3B3;Ú
uppergammaz&#x393;ÚgammaÚtotientz&#x3D5;Úreduced_totientz&#x3BB;z&#x3BD;z&#x3A9;r   ÚCÚWz&#x398;ÚTrueÚFalseÚNonez	S&#x2032;z	C&#x2032;Úlambda)ÚprimenuÚ
primeomegaÚfresnelsÚfresnelcÚLambertWÚ	HeavisideÚBooleanTrueÚBooleanFalseÚNoneTypeÚmathieusÚmathieucÚmathieusprimeÚmathieucprimeÚLambdac                 ó2  >• T R                   S   b  T R                   S   S:X  a  gT R                   S   S:X  a  gT R                   S   S:X  a  gT R                   S   S:X  a  g	[        T R                   S   [        5      (       d  [        eT R                   S   $ )
Nr%   râ  ú&InvisibleTimes;ro   ú&#xD7;Údotr   Úldotz&#x2024;)ra   Ú
isinstancer  Ú	TypeError)r5   s   €r:   Úmul_symbol_selectionÚBMathMLPresentationPrinter.mathml_tag.<locals>.mul_symbol_selection_  sŒ   ø€ Ø—‘˜|Ñ,Ñ4Ø—N‘N <Ñ0°FÓ:Ø)Ø—‘ Ñ-°Ó8ØØ—‘ Ñ-°Ó6ØØ—‘ Ñ-°Ó7Ø!Ü §¡¨|Ñ <¼c×BÑBÜ�à—~‘~ lÑ3Ð3r=   r   rÅ   )r5   rÉ   rÊ   rù  rË   rÌ   s   `     r:   rÍ   Ú$MathMLPresentationPrinter.mathml_tag*  sA  ø€ ð1
Ø�dð1
à�Zð1
ð ˜&ð1
ð �4ð	1
ð
 �dð1
ð ˜ð1
ð �:ð1
ð �5ð1
ð �5ð1
ð �5ð1
ð �5ð1
ð �Hð1
ð �Yð1
ð �Hð1
ð �Yð1
ð  �Hð!1
ð" �Yñ#1
ð$ �Hð%1
ð& �Xð'1
ð( ˜ð)1
ð* ˜*ð+1
ð, ˜:ð-1
ð. ˜
ð/1
ð0   ð11
ð2 ˜cð31
ð4 ˜	ð51
ð6 �Ið71
ð8 ˜Yð91
ð: ˜)ð;1
ð< ˜)ð=1
ð> ˜)ð?1
ð@ �YðA1
ðB �yðC1
ðD ˜yñE1
ðF !Ø#ØØØØ"Ø!Ø#ØØØØ(Ø(Øòa1
ˆ	õf	4ð —;‘;×&Ô&ˆCØ—‘ˆAØ�~Ø ‘|Ò#ñ 'ð
 �;‰;×Ñ 5Ó(Ù'Ó)Ð)Ø�K‰K× Ñ ˆØ�w‰w‹yÐr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú(r'  ©r5   rf  s     r:   Ú_l_parenÚ"MathMLPresentationPrinter._l_parenw  ó6   € Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Øˆ	r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú)r'  rþ  s     r:   Ú_r_parenÚ"MathMLPresentationPrinter._r_paren|  r  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú{r'  rþ  s     r:   Ú_l_braceÚ"MathMLPresentationPrinter._l_brace�  r  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú}r'  rþ  s     r:   Ú_r_braceÚ"MathMLPresentationPrinter._r_brace†  r  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú,r'  rþ  s     r:   Ú_commaÚ MathMLPresentationPrinter._comma‹  r  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú|r'  rþ  s     r:   Ú_barÚMathMLPresentationPrinter._bar�  r  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  Ú;r'  rþ  s     r:   Ú
_semicolonÚ$MathMLPresentationPrinter._semicolon•  r  r=   c                ól  • U R                   R                  S5      nUR                  U R                  5       5        [	        U5       HK  u  p4U(       a  UR                  U R                  5       5        UR                  U R                  U5      5        MM     UR                  U R                  5       5        U$ ©Nrd  )rH   rØ   rÙ   rÿ  rú   r  rU   r  ©r5   rî   rd  rü   rñ   s        r:   Ú_paren_comma_separatedÚ0MathMLPresentationPrinter._paren_comma_separatedš  sƒ   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ü –o‰FˆAÞØ× Ñ  §¡£Ô/Ø×Ñ˜TŸ[™[¨Ó-Ö.ñ &ð 	×Ñ˜Ÿ™›Ô)Øˆr=   c                ól  • U R                   R                  S5      nUR                  U R                  5       5        [	        U5       HK  u  p4U(       a  UR                  U R                  5       5        UR                  U R                  U5      5        MM     UR                  U R                  5       5        U$ r  )rH   rØ   rÙ   rÿ  rú   r  rU   r  r  s        r:   Ú_paren_bar_separatedÚ.MathMLPresentationPrinter._paren_bar_separated¤  sƒ   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ü –o‰FˆAÞØ× Ñ  §¡£Ô-Ø×Ñ˜TŸ[™[¨Ó-Ö.ñ &ð 	×Ñ˜Ÿ™›Ô)Øˆr=   c                óR  • [        U5      nXB:  d  U(       d€  XB::  a{  U R                  R                  S5      nUR                  U R	                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        U$ U R                  U5      $ r  )r   rH   rØ   rÙ   rÿ  rU   r  )r5   re  ÚlevelÚstrictÚprec_valrd  s         r:   ÚparenthesizeÚ&MathMLPresentationPrinter.parenthesize®  s€   € Ü)¨$Ó/ˆØÓ¦v°8Ó3DØ—8‘8×)Ñ)¨&Ó1ˆDØ×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TŸ[™[¨Ó.Ô/Ø×Ñ˜TŸ]™]›_Ô-ØˆKØ�{‰{˜4Ó Ð r=   c                óH  ^ • U 4S jnT R                   R                  S5      nUR                  5       (       ab  T R                   R                  S5      nUR                  T R                   R	                  S5      5        UR                  U5        U" U* U5      nU$ U" X5      nU$ )Nc                ó"  >• SSK Jn  U" U 5      u  p4U[        R                  La°  TR                  R                  S5      nTR                  S   (       a*  [        [        U 5      5      S:  a  UR                  SS5        TR                  U5      nTR                  U5      nUR                  U5        UR                  U5        UR                  U5        U$ U R                  5       u  p‰U[        R                  L a4  [        U	5      S:X  a%  UR                  TR                  U	S   5      5        U$ TR                  S	:w  a$  [        R                  " U	5      R!                  5       n	US:w  a‡  TR                  U5      n
TR                  R                  S
5      nUR                  TR                  R#                  TR%                  U 5      5      5        UR                  U
5        UR                  U5        U	 Hš  nUR                  TR'                  U[(        S   5      5        XÉS   :X  a  M5  TR                  R                  S
5      nUR                  TR                  R#                  TR%                  U 5      5      5        UR                  U5        Mœ     U$ )Nr   rÒ   Úmfracr   é   ÚbevelledrA  rÕ   rÖ   rf  r   rê   )rÛ   rÓ   r   rÜ   rH   rØ   ra   rÞ   r  ÚsetAttributerU   rÙ   rÝ   r   r   rß   rà   rO   rÍ   r&  r   )rY   rd  rÓ   râ   rã   Úfracr  Úxdenrä   rå   rá   Úyræ   r5   s                €r:   ÚmultiplyÚ6MathMLPresentationPrinter._print_Mul.<locals>.multiplyº  sú  ø€ Ý/Ù# D›>‰LˆEØœAŸE™EÒ!Ø—x‘x×-Ñ-¨gÓ6�Ø—>‘>Ð"3×4¼¼SÀ»Y»È!Ó9KØ×%Ñ% j°&Ô9Ø—{‘{ 5Ó)�Ø—{‘{ 5Ó)�Ø× Ñ  Ô&Ø× Ñ  Ô&Ø× Ñ  Ô&Ø�à×,Ñ,Ó.‰LˆEØœŸ™Š~¤# e£*°£/Ø× Ñ  §¡¨U°1©XÓ!6Ô7Ø�Ø�z‰z˜UÓ"ÜŸš uÓ-×@Ñ@ÓB�à˜‹zØ—K‘K Ó&�Ø—H‘H×*Ñ*¨4Ó0�Ø—‘˜dŸh™h×5Ñ5°d·o±oÀdÓ6KÓLÔMØ× Ñ  Ô#Ø× Ñ  Ô#Û�Ø× Ñ  ×!2Ñ!2°4¼ÀEÑ9JÓ!KÔLØ R™yÕ(ØŸ™×.Ñ.¨tÓ4�AØ—M‘M $§(¡(×"9Ñ"9¸$¿/¹/È$Ó:OÓ"PÔQØ×$Ñ$ QÖ'ñ ð ˆKr=   rd  rf  Ú-)rH   rØ   r×   rÙ   rO   )r5   rY   r1  rd  rá   s   `    r:   rÚ   Ú$MathMLPresentationPrinter._print_Mul¸  s‘   ø€ õ!	ðD �x‰x×%Ñ% fÓ-ˆØ×(Ñ(×*Ñ*Ø—‘×&Ñ& tÓ,ˆAØ�M‰M˜$Ÿ(™(×1Ñ1°#Ó6Ô7Ø×Ñ˜QÔÙ˜T˜E 4Ó(ˆDð ˆñ ˜DÓ'ˆDàˆr=   Nc                ó‚  • U R                   R                  S5      nU R                  XS9nUR                  U R	                  US   5      5        USS   Hè  nUR                  5       (       aX  U R                   R                  S5      nUR                  U R                   R                  S5      5        U R	                  U* 5      nOVU R                   R                  S5      nUR                  U R                   R                  S5      5        U R	                  U5      nUR                  U5        UR                  U5        Mê     U$ )Nrd  ré   r   rÕ   rf  r3  Ú+)rH   rØ   rë   rÙ   rU   r×   rO   )r5   rY   r   rd  rî   rñ   rá   r0  s           r:   rò   Ú$MathMLPresentationPrinter._print_Addç  s  € Ø�x‰x×%Ñ% fÓ-ˆØ×%Ñ% dÐ%Ð8ˆØ×Ñ˜Ÿ™ T¨!¡WÓ-Ô.Ø˜˜“8ˆCØ×+Ñ+×-Ñ-à—H‘H×*Ñ*¨4Ó0�Ø—‘˜dŸh™h×5Ñ5°cÓ:Ô;Ø—K‘K  Ó%‘ð —H‘H×*Ñ*¨4Ó0�Ø—‘˜dŸh™h×5Ñ5°cÓ:Ô;Ø—K‘K Ó$�Ø×Ñ˜QÔØ×Ñ˜QÖñ ð ˆr=   c           	     ó8  • U R                   R                  S5      n[        UR                  5       H›  nU R                   R                  S5      n[        UR                  5       HS  nU R                   R                  S5      nUR                  U R                  XU4   5      5        UR                  U5        MU     UR                  U5        M�     U R                  S   nUS:X  a  U$ U R                   R                  S5      nU R                   R                  S5      n	US:X  aU  UR                  U R                   R                  S5      5        U	R                  U R                   R                  S5      5        OTUR                  U R                   R                  S	5      5        U	R                  U R                   R                  S
5      5        U R                   R                  S5      n
U
R                  U5        U
R                  U5        U
R                  U	5        U
$ )NÚmtableÚmtrÚmtdr#   r?   rf  r   Ú]rý  r  rd  )	rH   rØ   r  r  r  rÙ   rU   ra   rO   )r5   r  Útablerü   rá   r  r0  r#   ÚleftÚrightrd  s              r:   r	  Ú+MathMLPresentationPrinter._print_MatrixBaseû  sœ  € Ø—‘×&Ñ& xÓ0ˆÜ�q—v‘v–ˆAØ—‘×&Ñ& uÓ-ˆAÜ˜1Ÿ6™6–]�Ø—H‘H×*Ñ*¨5Ó1�Ø—‘˜dŸk™k¨!¨q¨D©'Ó2Ô3Ø—‘˜aÖ ñ #ð ×Ñ˜aÖ ñ ð —N‘N ;Ñ/ˆ	Ø˜‹?ØˆLØ�x‰x×%Ñ% dÓ+ˆØ—‘×&Ñ& tÓ,ˆØ˜ÓØ×Ñ˜TŸX™X×4Ñ4°SÓ9Ô:Ø×Ñ˜dŸh™h×5Ñ5°cÓ:Õ;à×Ñ˜TŸX™X×4Ñ4°SÓ9Ô:Ø×Ñ˜dŸh™h×5Ñ5°cÓ:Ô;Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜ÔØ×Ñ˜ÔØˆr=   c                ó¦  • UR                   S:  a  UR                   * nOUR                   nU R                  R                  S5      nU(       d  U R                  S   (       a  UR	                  SS5        UR                  U R                  U5      5        UR                  U R                  UR                  5      5        UR                   S:  a„  U R                  R                  S5      nU R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U5        UR                  U5        U$ U$ )	Nr   r*  r   r,  rA  rd  rf  r3  )	r  rH   rØ   ra   r-  rÙ   rU   r  rO   )r5   rÉ   Úfoldedr  rá   rd  rf  s          r:   Ú_get_printed_RationalÚ/MathMLPresentationPrinter._get_printed_Rational  só   € Ø�3‰3�‹7Ø—‘�‰Aà—‘ˆAØ�H‰H×"Ñ" 7Ó+ˆÞ�T—^‘^Ð$5×6Ø�N‰N˜: vÔ.Ø	�‰�d—k‘k !“nÔ%Ø	�‰�d—k‘k !§#¡#Ó&Ô'Ø�3‰3�‹7Ø—8‘8×)Ñ)¨&Ó1ˆDØ—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°3Ó7Ô8Ø×Ñ˜RÔ Ø×Ñ˜QÔØˆKàˆHr=   c                ó”   • UR                   S:X  a  U R                  UR                  5      $ U R                  XR                  S   5      $ )NrÕ   r   )r  rU   r  rC  ra   r  s     r:   r  Ú)MathMLPresentationPrinter._print_Rational)  s;   € Ø�3‰3�!‹8à—;‘;˜qŸs™sÓ#Ð#à×)Ñ)¨!¯^©^Ð<MÑ-NÓOÐOr=   c                óx  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nU R	                  UR
                  S   5      nU R                   R                  S5      nUR                  U R                   R                  U R                  U5      5      5        U R	                  UR
                  S   5      nUR                  U5        UR                  U5        UR                  U5        UR                  U5        UR                  U5        UR                  U5        UR                  U R	                  UR
                  S   5      5        U$ )	Nrd  Úmunderrg  ÚlimrÕ   rf  r  r   )rH   rØ   rÙ   rO   rU   rî   rÍ   )	r5   rÉ   rd  rH  rg  rá   r  Úarrowr  s	            r:   r  Ú&MathMLPresentationPrinter._print_Limit0  sE  € Ø�x‰x×%Ñ% fÓ-ˆØ—‘×'Ñ'¨Ó1ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨uÓ5Ô6à�H‰H×"Ñ" 6Ó*ˆØ�k‰k˜!Ÿ&™& ™)Ó$ˆØ—‘×&Ñ& tÓ,ˆØ×Ñ˜$Ÿ(™(×1Ñ1°$·/±/À!Ó2DÓEÔFØ�k‰k˜!Ÿ&™& ™)Ó$ˆØ	�‰�cÔØ	�‰�eÔØ	�‰�cÔà×Ñ˜2ÔØ×Ñ˜1ÔØ×Ñ˜Ô Ø×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0àˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z&ImaginaryI;r'  r(  s      r:   r  Ú.MathMLPresentationPrinter._print_ImaginaryUnitF  s6   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨nÓ=Ô>Øˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  rÔ  r'  r(  s      r:   r)  Ú,MathMLPresentationPrinter._print_GoldenRatioK  ó6   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨iÓ8Ô9Øˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z&ExponentialE;r'  r(  s      r:   r-  Ú%MathMLPresentationPrinter._print_Exp1P  s7   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-Ð.>Ó?Ô@Øˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z&pi;r'  r(  s      r:   r1  Ú#MathMLPresentationPrinter._print_PiU  s6   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨fÓ5Ô6Øˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  ú&#x221E;r'  r(  s      r:   r5  Ú)MathMLPresentationPrinter._print_InfinityZ  ó6   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨jÓ9Ô:Øˆr=   c                ó,  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        U R	                  U5      nUR                  U5        UR                  U5        U$ )Nrd  rf  r3  )rH   rØ   rÙ   rO   r5  )r5   rÉ   rd  r0  rá   s        r:   rI  Ú1MathMLPresentationPrinter._print_NegativeInfinity_  sv   € Ø�x‰x×%Ñ% fÓ-ˆØ�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨cÓ2Ô3Ø× Ñ  Ó#ˆØ×Ñ˜ÔØ×Ñ˜ÔØˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z&#x210F;r'  r(  s      r:   Ú_print_HBarÚ%MathMLPresentationPrinter._print_HBarh  rX  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  rÙ  r'  r(  s      r:   r$  Ú+MathMLPresentationPrinter._print_EulerGammam  rP  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  ÚTribonacciConstantr'  r(  s      r:   Ú_print_TribonacciConstantÚ3MathMLPresentationPrinter._print_TribonacciConstantr  s7   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-Ð.BÓCÔDØˆr=   c                óê   • U R                   R                  S5      nUR                  U R                  UR                  S   5      5        UR                  U R                   R                  S5      5        U$ )Nrx  r   ú&#x2020;©rH   rØ   rÙ   rU   rî   rO   ©r5   rÉ   rx  s      r:   Ú_print_DaggerÚ'MathMLPresentationPrinter._print_Daggerw  sW   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0Ø×Ñ˜Ÿ™×0Ñ0°Ó<Ô=Øˆr=   c                óœ  • U R                   R                  S5      nUR                  U R                  UR                  S   5      5        U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R                  UR                  S   5      5        U$ )Nrd  r   rf  z&#x2208;rÕ   rf  )r5   rÉ   rd  rf  s       r:   Ú_print_ContainsÚ)MathMLPresentationPrinter._print_Contains}  s–   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨zÓ:Ô;Ø×Ñ˜ÔØ×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0Øˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z&#x210B;r'  r(  s      r:   Ú_print_HilbertSpaceÚ-MathMLPresentationPrinter._print_HilbertSpace†  rX  r=   c                óê   • U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U R	                  UR
                  S   5      5        U$ )Nrx  z	&#x1D49E;r   ©rH   rØ   rÙ   rO   rU   rî   rg  s      r:   Ú_print_ComplexSpaceÚ-MathMLPresentationPrinter._print_ComplexSpace‹  sW   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™×0Ñ0°Ó=Ô>Ø×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0Øˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z&#x2131;r'  r(  s      r:   Ú_print_FockSpaceÚ*MathMLPresentationPrinter._print_FockSpace‘  rX  r=   c                ó6  • SSSS.nU R                   R                  S5      n[        UR                  5      S::  a�  [	        S UR                   5       5      (       an  U R                   R                  S5      nUR                  U R                   R                  U[        UR                  5         5      5        UR                  U5        GO‰[        UR                  5       GHo  nU R                   R                  S5      nUR                  U R                   R                  US	   5      5        [        U5      S	:X  a  UR                  U5        [        U5      S
:X  a`  U R                   R                  S5      nUR                  U5        UR                  U R                  US	   5      5        UR                  U5        [        U5      S:X  d  Mì  U R                   R                  S5      nUR                  U5        UR                  U R                  US	   5      5        UR                  U R                  US
   5      5        UR                  U5        GMr     UR                  U R                  UR                  [        S   SS95        [        UR                  5       H|  nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R                  US   5      5        M~     U$ )Nz&#x222B;z&#x222C;z&#x222D;)rÕ   r  rM  rd  rM  c              3  ó>   #   • U  H  n[        U5      S :H  v •  M     g7f)rÕ   N)rÞ   )Ú.0rI  s     r:   Ú	<genexpr>Ú<MathMLPresentationPrinter._print_Integral.<locals>.<genexpr>›  s   é € Ð(NÂ+¸3¬¨S«°Q®Â+ùs   ‚rf  rÕ   r  rx  ry  r   T©r$  rÏ  r   )rH   rØ   rÞ   rP  ÚallrÙ   rO   r“  rU   r&  rO  r   )	r5   rY   Ú
intsymbolsrd  rf  rI  rx  ry  Úds	            r:   rX  Ú)MathMLPresentationPrinter._print_Integral—  s`  € Ø#¨
°zÑBˆ
à�x‰x×%Ñ% fÓ-ˆÜˆt�{‰{Ó˜qÓ ¤SÑ(NÀ$Ç+Â+Ó(N×%NÑ%Nà—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°:¼cÀ$Ç+Á+Ó>NÑ3OÓPÔQØ×Ñ˜RÖ ô   §¡×,�Ø—X‘X×+Ñ+¨DÓ1�Ø—‘˜tŸx™x×6Ñ6°zÀ!±}ÓEÔFÜ�s“8˜q“=Ø×$Ñ$ RÔ(Ü�s“8˜q“=ØŸ8™8×1Ñ1°&Ó9�DØ×$Ñ$ RÔ(Ø×$Ñ$ T§[¡[°°Q±Ó%8Ô9Ø×$Ñ$ TÔ*Ü�s“8˜q•=Ø"Ÿh™h×4Ñ4°YÓ?�GØ×'Ñ'¨Ô+Ø×'Ñ'¨¯©°C¸±FÓ(;Ô<Ø×'Ñ'¨¯©°C¸±FÓ(;Ô<Ø×$Ñ$ W×-ñ -ð" 	×Ñ˜×*Ñ*¨4¯=©=¼*ÀUÑ:KØ26ð +ð 8ô 	9ô ˜DŸK™KÖ(ˆCØ—‘×&Ñ& tÓ,ˆAØ�M‰M˜$Ÿ(™(×1Ñ1°&Ó9Ô:Ø×Ñ˜QÔØ×Ñ˜TŸ[™[¨¨Q©Ó0Ö1ñ	 )ð
 ˆr=   c                óä  • [        UR                  5      nU R                  R                  S5      nU R	                  US   S   5      nU R	                  US   S   5      nU R                  R                  S5      nUR                  U R                  R                  U R                  U5      5      5        U R                  R                  S5      nU R	                  US   S   5      nU R                  R                  S5      n	U	R                  U R                  R                  S5      5        UR                  U5        UR                  U	5        UR                  U5        UR                  U5        UR                  U5        UR                  U5        U R                  R                  S5      n
U
R                  U5        U
R                  U R                  UR                  [        U5      5      5        U
$ )NÚ
munderoverr   rÕ   r  rf  rd  rÐ  )rV  rP  rH   rØ   rU   rÙ   rO   rÍ   r&  rO  r   )r5   rÉ   rP  ÚsubsuprR  rS  ÚsummandÚlowÚvarÚequalrd  s              r:   r[  Ú$MathMLPresentationPrinter._print_Sum½  s~  € Ü�a—h‘h“ˆØ—‘×'Ñ'¨Ó5ˆØ—;‘;˜v a™y¨™|Ó,ˆØ—+‘+˜f Q™i¨™lÓ+ˆØ—(‘(×(Ñ(¨Ó.ˆØ×Ñ˜DŸH™H×3Ñ3°D·O±OÀAÓ4FÓGÔHà�h‰h×$Ñ$ VÓ,ˆØ�k‰k˜& ™) A™,Ó'ˆØ—‘×&Ñ& tÓ,ˆØ×Ñ˜$Ÿ(™(×1Ñ1°#Ó6Ô7Ø�‰˜ÔØ�‰˜ÔØ�‰˜Ô!à×Ñ˜7Ô#Ø×Ñ˜3ÔØ×Ñ˜7Ô#à�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ô Ø×Ñ˜×*Ñ*¨1¯:©:Ô7MÈaÓ7PÓQÔRØˆr=   c                ó´  ^ • U 4S jnS nT R                  UR                  5      u  pVnU" U5      nU Vs/ s H
  o„" U5      PM     nnU V	s/ s H
  o”" U	5      PM     nn	T R                  R                  S5      n
U
R	                  T R                  R                  U5      5        [        U5      S:X  aV  [        U5      S:X  a  U
nOñT R                  R                  S5      nUR	                  U
5        UR	                  U" U5      5        O­[        U5      S:X  aD  T R                  R                  S5      nUR	                  U
5        UR	                  U" U5      5        OZT R                  R                  S5      nUR	                  U
5        UR	                  U" U5      5        UR	                  U" U5      5        US:X  a  UR                  S	S5        U$ s  snf s  sn	f )
Nc                ó|  >• [        U 5      S:”  aã  TR                  R                  S5      n[        U 5       H·  u  p#US:”  aV  TR                  R                  S5      nUR	                  TR                  R                  S5      5        UR	                  U5        TR                  R                  S5      nUR	                  TR                  R                  U5      5        UR	                  U5        M¹     U$ TR                  R                  S5      nUR	                  TR                  R                  U S   5      5        U$ )NrÕ   rd  r   rf  r_  rg  ra  rb  s         €r:   rh  Ú5MathMLPresentationPrinter._print_Symbol.<locals>.join×  só   ø€ Ü�5‹z˜A‹~Ø—x‘x×-Ñ-¨fÓ5�Ü(¨Ö/‘G�AØ˜1“uØ!ŸX™X×3Ñ3°DÓ9˜ØŸ™ t§x¡x×'>Ñ'>¸sÓ'CÔDØ×(Ñ(¨Ô,ØŸ™×/Ñ/°Ó5�BØ—N‘N 4§8¡8×#:Ñ#:¸4Ó#@ÔAØ×$Ñ$ RÖ(ñ  0ð �à—X‘X×+Ñ+¨DÓ1�Ø—‘˜tŸx™x×6Ñ6°u¸Q±xÓ@ÔAØ�	r=   c                óF   • U [         ;   a  [         R                  " U 5      $ U $ rG   rk  rm  s    r:   rÊ   Ú:MathMLPresentationPrinter._print_Symbol.<locals>.translateé  rp  r=   rg  r   rw  rx  ry  ÚboldÚmathvariant)rc   rb   rH   rØ   rÙ   rO   rÞ   r-  )r5   rq  Ústylerh  rÊ   rb   rr  rs  rt  ru  rv  rá   s   `           r:   rz  Ú'MathMLPresentationPrinter._print_SymbolÖ  s{  ø€ õ	ò$	ð "×2Ñ2°3·8±8Ó<Ñˆ�dÙ˜‹ˆÙ,2Ó3ªF S�)˜C–.©FˆÐ3Ù*.Ó/ª$ 3�	˜#–©$ˆÐ/à—‘×&Ñ& tÓ,ˆØ×Ñ˜$Ÿ(™(×1Ñ1°$Ó7Ô8Üˆv‹;˜!ÓÜ�4‹y˜A‹~Ø‘à—H‘H×*Ñ*¨6Ó2�Ø—‘˜eÔ$Ø—‘™d 4›jÕ)ä�4‹y˜A‹~Ø—H‘H×*Ñ*¨6Ó2�Ø—‘˜eÔ$Ø—‘™d 6›lÕ+à—H‘H×*Ñ*¨9Ó5�Ø—‘˜eÔ$Ø—‘™d 4›jÔ)Ø—‘™d 6›lÔ+à�F‹?Ø�N‰N˜=¨&Ô1Øˆùò3 4ùÚ/s   µGÁGc                ó<   • U R                  UU R                  S   S9$ )Nr$   )r�  )rz  ra   )r5   rq  s     r:   rÄ  Ú-MathMLPresentationPrinter._print_MatrixSymbol  s+   € Ø×!Ñ! #Ø(,¯©Ð7IÑ(Jð "ð Lð 	Lr=   c                óº   • U R                   R                  S5      nUR                  SS5        UR                  U R	                  UR
                  S   5      5        U$ )NÚmencloseÚnotationÚtopr   )rH   rØ   r-  rÙ   rU   rî   )r5   rY   Úencs      r:   Ú_print_conjugateÚ*MathMLPresentationPrinter._print_conjugate  sH   € Ø�h‰h×$Ñ$ ZÓ0ˆØ×Ñ˜ UÔ+Ø�‰˜Ÿ™ D§I¡I¨a¡LÓ1Ô2Øˆ
r=   c                ó8  • U R                   R                  S5      nUR                  U R                  U[        S   5      5        U R                   R                  S5      nUR                  U R                   R                  U5      5        UR                  U5        U$ )Nrd  ÚFuncrf  )rH   rØ   rÙ   r&  r   rO   )r5   ÚoprY   Úrowrf  s        r:   Ú_print_operator_afterÚ/MathMLPresentationPrinter._print_operator_after  st   € Ø�h‰h×$Ñ$ VÓ,ˆØ�‰˜×)Ñ)¨$´
¸6Ñ0BÓCÔDØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨rÓ2Ô3Ø�‰˜ÔØˆ
r=   c                ó@   • U R                  SUR                  S   5      $ )NÚ!r   ©rŸ  rî   ©r5   rY   s     r:   Ú_print_factorialÚ*MathMLPresentationPrinter._print_factorial   s   € Ø×)Ñ)¨#¨t¯y©y¸©|Ó<Ð<r=   c                ó@   • U R                  SUR                  S   5      $ )Nz!!r   r£  r¤  s     r:   Ú_print_factorial2Ú+MathMLPresentationPrinter._print_factorial2#  s   € Ø×)Ñ)¨$°·	±	¸!±Ó=Ð=r=   c                óè  • U R                   R                  S5      nUR                  SS5        UR                  U R	                  UR
                  S   5      5        UR                  U R	                  UR
                  S   5      5        U R                   R                  S5      nUR                  U R                  5       5        UR                  U5        UR                  U R                  5       5        U$ )Nr*  ÚlinethicknessÚ0r   rÕ   rd  )rH   rØ   r-  rÙ   rU   rî   rÿ  r  )r5   rY   r.  Úbracs       r:   Ú_print_binomialÚ)MathMLPresentationPrinter._print_binomial&  s³   € Ø�x‰x×%Ñ% gÓ.ˆØ×Ñ˜/¨3Ô/Ø×Ñ˜Ÿ™ T§Y¡Y¨q¡\Ó2Ô3Ø×Ñ˜Ÿ™ T§Y¡Y¨q¡\Ó2Ô3Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ø×Ñ˜ÔØ×Ñ˜Ÿ™›Ô)Øˆr=   c                ó"
  • UR                   R                  (       Ga°  [        UR                   R                  5      S:X  GaŒ  UR                   R                  S:w  Gaq  U R
                  S   (       Ga\  UR                   R                  S:X  aE  U R                  R                  S5      nUR                  U R                  UR                  5      5        UR                   R                  S:w  ay  U R                  R                  S5      nUR                  U R                  UR                  5      5        UR                  U R                  UR                   R                  5      5        UR                   R                  S:X  aN  U R                  R                  S5      nUR                  U R                  S5      5        UR                  W5        U$ W$ UR                   R                  (       Ga‘  UR                   R                  S:w  Gav  UR                   R                  (       aÔ  U R                  R                  S5      nUR                  U R                  S5      5        U R                  R                  S5      nUR                  U R                  UR                  [        S	   5      5        UR                  U R                  UR                   * U R
                  S
   5      5        UR                  U5        U$ U R                  R                  S5      nUR                  U R                  UR                  [        S	   5      5        UR                  U R                  UR                   U R
                  S
   5      5        U$ UR                   R                  (       Ga  U R                  R                  S5      nUR                  U R                  S5      5        UR                   S:X  a,  UR                  U R                  UR                  5      5        U$ U R                  R                  S5      nUR                  U R                  UR                  [        S	   5      5        UR                  U R                  UR                   * 5      5        UR                  U5        U$ U R                  R                  S5      nUR                  U R                  UR                  [        S	   5      5        UR                  U R                  UR                   5      5        U$ )NrÕ   r&   r  ÚmsqrtÚmrootrê   r*  rx  ru   r   )r~  r  r|   r  r  ra   rH   rØ   rÙ   rU   r€  Úis_negativer&  r   rC  )r5   rÉ   rá   r.  r—  s        r:   rƒ  Ú$MathMLPresentationPrinter._print_Pow1  sx  € ð �E‰E××Ð¤# a§e¡e§g¡g£,°!Ô"3¸¿¹¿¹À1¼Ø—‘˜×/Ð/Ø�u‰u�w‰w˜!‹|Ø—H‘H×*Ñ*¨7Ó3�Ø—‘˜dŸk™k¨!¯&©&Ó1Ô2Ø�u‰u�w‰w˜!‹|Ø—H‘H×*Ñ*¨7Ó3�Ø—‘˜dŸk™k¨!¯&©&Ó1Ô2Ø—‘˜dŸk™k¨!¯%©%¯'©'Ó2Ô3Ø�u‰u�w‰w˜"‹}Ø—x‘x×-Ñ-¨gÓ6�Ø× Ñ  §¡¨Q£Ô0Ø× Ñ  Ô#Ø�à�à�5‰5××Ð §¡§¡¨A¤Ø�u‰u× × Ø—h‘h×,Ñ,¨WÓ5�Ø—‘ §¡¨A£Ô/Ø—H‘H×*Ñ*¨6Ó2�Ø—‘˜d×/Ñ/°·±¼
À5Ñ8IÓJÔKØ—‘˜d×8Ñ8¸!¿%¹%¸Ø$(§N¡NÐ3EÑ$FóHô Ià—‘ Ô"Ø�
à—H‘H×*Ñ*¨6Ó2�Ø—‘˜d×/Ñ/°·±¼
À5Ñ8IÓJÔKØ—‘˜d×8Ñ8¸¿¹Ø$(§N¡NÐ3EÑ$FóHô Ià�à�5‰5××ÐØ—h‘h×,Ñ,¨WÓ5�Ø—‘ §¡¨A£Ô/Ø—5‘5˜B“;Ø—O‘O D§K¡K°·±Ó$7Ô8ð �
ð	 Ÿ™×.Ñ.¨vÓ6�AØ—M‘M $×"3Ñ"3°A·F±F¼JÀuÑ<MÓ"NÔOØ—M‘M $§+¡+¨q¯u©u¨fÓ"5Ô6Ø—O‘O AÔ&Ø�
à�H‰H×"Ñ" 6Ó*ˆØ	�‰�d×'Ñ'¨¯©´
¸5Ñ0AÓBÔCØ	�‰�d—k‘k !§%¡%Ó(Ô)Øˆr=   c                óÀ   • U R                   R                  U R                  U5      5      nUR                  U R                   R	                  [        U5      5      5        U$ rG   r†  r(  s      r:   r‡  Ú'MathMLPresentationPrinter._print_Numberg  r‰  r=   c                óz  • U R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nUR                  U5        UR                  U R	                  UR
                  5      5        UR                  U R                  5       5        UR                  U R	                  UR                  5      5        UR                  U5        U$ )Nrf  õ   âŸ¨õ   âŸ©rd  )rH   rØ   rÙ   rO   rU   rz   r  rx   )r5   rü   r>  r?  r­  s        r:   Ú_print_AccumulationBoundsÚ3MathMLPresentationPrinter._print_AccumulationBoundsl  sã   € Ø�x‰x×%Ñ% dÓ+ˆØ×Ñ˜Ÿ™×0Ñ0°Ó:Ô;Ø—‘×&Ñ& tÓ,ˆØ×Ñ˜$Ÿ(™(×1Ñ1°(Ó;Ô<Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜Ÿ™ Q§U¡UÓ+Ô,Ø×Ñ˜Ÿ™›Ô'Ø×Ñ˜Ÿ™ Q§U¡UÓ+Ô,Ø×Ñ˜ÔØˆr=   c                ó<  • [        UR                  5      (       a  SnOU R                  U5      nU R                  R	                  S5      nSn[        UR                  5       GH  u  pVXF-  nUS:¼  a’  U R                  R	                  S5      nU R                  R	                  S5      nUR                  U R                  R                  U5      5        UR                  U5        UR                  U R                  U5      5        OEU R                  R	                  S5      nUR                  U R                  R                  U5      5        UR                  U5        U R                  U5      n	UR                  U	5        GM     U R                  R	                  S5      n
US:¼  a’  U R                  R	                  S5      nU R                  R	                  S5      nUR                  U R                  R                  U5      5        UR                  U5        UR                  U R                  U5      5        OEU R                  R	                  S5      nUR                  U R                  R                  U5      5        U
R                  U5        U R                  R	                  S5      nU R                  R	                  S5      nUR                  U
5        UR                  U5        UR                  U5        UR                  U R                  UR                  5      5        U$ )Nz&#x2202;rd  r   r  rx  rf  r*  )
r
   rY   rÍ   rH   rØ   r“  r”  rÙ   rO   rU   )r5   rÉ   r  r  Údimrq  Únumrá   Úxxr0  Úmnumrd  r.  s                r:   r–  Ú+MathMLPresentationPrinter._print_Derivativey  sO  € ä˜AŸF™F×#Ñ#Ø‰Aà—‘ Ó"ˆAð �H‰H×"Ñ" 6Ó*ˆØˆÜ  ×!1Ñ!1×2‰HˆCØ‰JˆCØ�a‹xØ—H‘H×*Ñ*¨6Ó2�Ø—X‘X×+Ñ+¨DÓ1�Ø—‘˜tŸx™x×6Ñ6°qÓ9Ô:Ø—‘˜bÔ!Ø—‘˜dŸk™k¨#Ó.Õ/à—H‘H×*Ñ*¨4Ó0�Ø—‘˜dŸh™h×5Ñ5°aÓ8Ô9Ø�M‰M˜!ÔØ—‘˜CÓ ˆAØ�M‰M˜!×ñ 3ð �x‰x×%Ñ% fÓ-ˆØ�!‹8Ø—‘×&Ñ& vÓ.ˆAØ—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°1Ó5Ô6Ø�M‰M˜"ÔØ�M‰M˜$Ÿ+™+ cÓ*Õ+à—‘×&Ñ& tÓ,ˆAØ�M‰M˜$Ÿ(™(×1Ñ1°!Ó4Ô5à×Ñ˜ÔØ�x‰x×%Ñ% fÓ-ˆØ�x‰x×%Ñ% gÓ.ˆØ×Ñ˜ÔØ×Ñ˜ÔØ×Ñ˜Ôð 	×Ñ˜Ÿ™ Q§V¡VÓ,Ô-àˆr=   c                óþ  • U R                   R                  S5      nU R                  U5      S:X  a?  U R                  S   (       a+  UR	                  U R                   R                  S5      5        O9UR	                  U R                   R                  U R                  U5      5      5        U R                   R                  S5      nUR	                  U5        UR	                  U R                  " UR                  6 5        U$ )Nrg  r³   r!   r´   rd  )rH   rØ   rÍ   ra   rÙ   rO   r  rî   )r5   rÉ   rá   rd  s       r:   r›  Ú)MathMLPresentationPrinter._print_Function©  sµ   € Ø�H‰H×"Ñ" 4Ó(ˆØ�?‰?˜1Ó Ó&¨4¯>©>¸-×+HØ�M‰M˜$Ÿ(™(×1Ñ1°$Ó7Õ8à�M‰M˜$Ÿ(™(×1Ñ1°$·/±/À!Ó2DÓEÔFØ�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜×4Ò4°a·f±fÐ=Ô>Øˆr=   c                óð  • [        UR                  5      n[        UR                  USS9nU R                  S   nU R
                  R                  S5      nSU;   Ga§  UR                  S5      u  pgUS   S:X  a  USS  nU R
                  R                  S	5      nUR                  U R
                  R                  U5      5        UR                  U5        U R
                  R                  S
5      n	U	R                  U R
                  R                  U5      5        UR                  U	5        U R
                  R                  S5      n
U R
                  R                  S	5      nUR                  U R
                  R                  S5      5        U
R                  U5        U R
                  R                  S	5      nUR                  U R
                  R                  U5      5        U
R                  U5        UR                  U
5        U$ US:X  a  U R                  S 5      $ US:X  a  U R                  S 5      $ U R
                  R                  S	5      nUR                  U R
                  R                  U5      5        U$ )NT)Ústrip_zerosr(   rd  rÉ   r   r6  rÕ   rÍ  rf  rx  Ú10z+infz-inf)r   r�  r‹  rŒ  ra   rH   rØ   ÚsplitrÙ   rO   r5  rI  )r5   rY   ÚdpsÚstr_realÚ	separatorrd  Úmantr~  rÍ  rf  rx  s              r:   r�  Ú&MathMLPresentationPrinter._print_Float´  sõ  € ä˜$Ÿ*™*Ó%ˆÜ˜tŸz™z¨3¸DÑAˆð —N‘NÐ#>Ñ?ˆ	Ø�x‰x×%Ñ% fÓ-ˆØ�(Œ?Ø"Ÿ.™.¨Ó-‰KˆTà�1‰v˜‹}Ø˜!˜"�g�à—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°4Ó8Ô9Ø×Ñ˜RÔ Ø—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°9Ó=Ô>Ø×Ñ˜RÔ Ø—8‘8×)Ñ)¨&Ó1ˆDØ—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°4Ó8Ô9Ø×Ñ˜RÔ Ø—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°3Ó7Ô8Ø×Ñ˜RÔ Ø×Ñ˜TÔ"ØˆKØ˜ÓØ×'Ñ'¨Ó-Ð-Ø˜ÓØ×/Ñ/°Ó5Ð5à—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°8Ó<Ô=ØˆIr=   c                óÈ  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        U R                   R                  S5      nUR                  U R                  5       5        UR                  U R	                  UR
                  S   5      5        UR                  U R                  5       5        UR                  U5        U$ )Nrd  rw  rg  ÚLir   rÕ   )rH   rØ   rÙ   rO   rU   rî   rÿ  r  )r5   rY   rd  r  rg  r­  s         r:   Ú_print_polylogÚ(MathMLPresentationPrinter._print_polylogÛ  sþ   € Ø�x‰x×%Ñ% fÓ-ˆØ�H‰H×"Ñ" 6Ó*ˆà�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨tÓ4Ô5Ø	�‰�bÔØ	�‰�d—k‘k $§)¡)¨A¡,Ó/Ô0Ø×Ñ˜ÔØ�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ø×Ñ˜Ÿ™ T§Y¡Y¨q¡\Ó2Ô3Ø×Ñ˜Ÿ™›Ô)Ø×Ñ˜ÔØˆr=   c                óV  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  U R	                  U5      5      5        UR                  U5        UR                  U R
                  " UR                  6 5        U$ ©Nrd  rg  )rH   rØ   rÙ   rO   rÍ   r  rî   )r5   rÉ   rd  rg  s       r:   rž  Ú&MathMLPresentationPrinter._print_Basicë  s~   € Ø�x‰x×%Ñ% fÓ-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨t¯©¸qÓ/AÓBÔCØ×Ñ˜ÔØ×Ñ˜×4Ò4°a·f±fÐ=Ô>Øˆr=   c                ó4   • U R                   " UR                  6 $ rG   )r  rî   r  s     r:   Ú_print_TupleÚ&MathMLPresentationPrinter._print_Tupleó  s   € Ø×*Ò*¨A¯F©FÐ3Ð3r=   c                ój  • U R                   R                  S5      nUR                  (       a+  UR                  U R                   R	                  S5      5        O*UR                  U R                   R	                  S5      5        U R                   R                  S5      nUR
                  (       a+  UR                  U R                   R	                  S5      5        O*UR                  U R                   R	                  S5      5        U R                   R                  S5      nUR                  U5        UR                  U R                  UR                  5      5        UR                  U R                  5       5        UR                  U R                  UR                  5      5        UR                  U5        U$ )Nrf  r  r<  rý  r   rd  )
rH   rØ   Ú
right_openrÙ   rO   Ú	left_openrU   Ústartr  Úend)r5   rü   r?  r>  rd  s        r:   Ú_print_IntervalÚ)MathMLPresentationPrinter._print_Intervalö  s+  € Ø—‘×&Ñ& tÓ,ˆØ�<�<Ø×Ñ˜dŸh™h×5Ñ5°cÓ:Õ;à×Ñ˜dŸh™h×5Ñ5°cÓ:Ô;Ø�x‰x×%Ñ% dÓ+ˆØ�;�;Ø×Ñ˜TŸX™X×4Ñ4°SÓ9Õ:à×Ñ˜TŸX™X×4Ñ4°SÓ9Ô:Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜Ÿ™ Q§W¡WÓ-Ô.Ø×Ñ˜Ÿ™›Ô'Ø×Ñ˜Ÿ™ Q§U¡UÓ+Ô,Ø×Ñ˜ÔØˆr=   c                ó  • U R                   R                  S5      nUR                  U R                  5       5        UR                  U R	                  UR
                  S   5      5        UR                  U R                  5       5        U$ )Nrd  r   )rH   rØ   rÙ   r  rU   rî   )r5   rY   r~  rd  s       r:   Ú
_print_AbsÚ$MathMLPresentationPrinter._print_Abs	  sb   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô%Ø×Ñ˜Ÿ™ T§Y¡Y¨q¡\Ó2Ô3Ø×Ñ˜Ÿ™›Ô%Øˆr=   c                óü  • U R                   R                  S5      nUR                  U R                  5       5        UR                  U R	                  U5      5        UR                  U R                  5       5        U R                   R                  S5      nUR                  U R                   R                  U5      5        U R                   R                  S5      nUR                  U5        UR                  U5        U$ rÒ  )rH   rØ   rÙ   rÿ  rU   r  rO   )r5   rý   rY   r­  rg  rd  s         r:   Ú_print_re_imÚ&MathMLPresentationPrinter._print_re_im  s¹   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ø×Ñ˜Ÿ™ TÓ*Ô+Ø×Ñ˜Ÿ™›Ô)Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨qÓ1Ô2Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜ÔØˆr=   c                ó@   • U R                  SUR                  S   5      $ )Nu   â„œr   ©râ  rî   ©r5   rY   r~  s      r:   Ú	_print_reÚ#MathMLPresentationPrinter._print_re  ó   € Ø× Ñ  ¨4¯9©9°Q©<Ó8Ð8r=   c                ó@   • U R                  SUR                  S   5      $ )Nu   â„‘r   rå  ræ  s      r:   Ú	_print_imÚ#MathMLPresentationPrinter._print_im!  ré  r=   c                ól  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  U R	                  U5      5      5        UR                  U5        UR
                   H#  nUR                  U R                  U5      5        M%     U$ rÒ  )rH   rØ   rÙ   rO   rÍ   rî   rU   )r5   rÉ   rd  rg  rñ   s        r:   r¡  Ú(MathMLPresentationPrinter._print_AssocOp$  s†   € Ø�x‰x×%Ñ% fÓ-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨t¯©¸qÓ/AÓBÔCØ×Ñ˜ÔØ—6”6ˆCØ×Ñ˜TŸ[™[¨Ó-Ö.ñ àˆr=   c                ó´  • U R                   R                  S5      nUR                  U R                  UR                  S   U5      5        UR                  SS   H{  nU R                   R                  S5      nUR                  U R                   R                  U5      5        U R                  XS5      nUR                  U5        UR                  U5        M}     U$ ©Nrd  r   rÕ   rf  )rH   rØ   rÙ   r&  rî   rO   )r5   rY   ÚsymbolÚprecrd  rñ   rá   r0  s           r:   Ú_print_SetOpÚ&MathMLPresentationPrinter._print_SetOp-  s¯   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜×*Ñ*¨4¯9©9°Q©<¸Ó>Ô?Ø—9‘9˜Q˜R“=ˆCØ—‘×&Ñ& tÓ,ˆAØ�M‰M˜$Ÿ(™(×1Ñ1°&Ó9Ô:Ø×!Ñ! #Ó,ˆAØ×Ñ˜QÔØ×Ñ˜QÖñ !ð ˆr=   c                ó:   • [         S   nU R                  USU5      $ )NrÃ   z&#x222A;©r   ró  ©r5   rY   rò  s      r:   Ú_print_UnionÚ&MathMLPresentationPrinter._print_Union8  s!   € Ü% gÑ.ˆØ× Ñ   z°4Ó8Ð8r=   c                ó:   • [         S   nU R                  USU5      $ )NrÄ   z&#x2229;rö  r÷  s      r:   Ú_print_IntersectionÚ-MathMLPresentationPrinter._print_Intersection<  s!   € Ü% nÑ5ˆØ× Ñ   z°4Ó8Ð8r=   c                ó:   • [         S   nU R                  USU5      $ )NÚ
Complementz&#x2216;rö  r÷  s      r:   r¹  Ú+MathMLPresentationPrinter._print_Complement@  ó!   € Ü% lÑ3ˆØ× Ñ   z°4Ó8Ð8r=   c                ó:   • [         S   nU R                  USU5      $ )NÚSymmetricDifferenceú&#x2206;rö  r÷  s      r:   Ú_print_SymmetricDifferenceÚ4MathMLPresentationPrinter._print_SymmetricDifferenceD  s"   € Ü%Ð&;Ñ<ˆØ× Ñ   z°4Ó8Ð8r=   c                ó:   • [         S   nU R                  USU5      $ )NÚ
ProductSetz&#x00d7;rö  r÷  s      r:   r½  Ú+MathMLPresentationPrinter._print_ProductSetH  r   r=   c                ó8   • U R                  UR                  5      $ rG   )Ú
_print_setrî   )r5   rn  s     r:   r´  Ú*MathMLPresentationPrinter._print_FiniteSetL  s   € Ø�‰˜qŸv™vÓ&Ð&r=   c                óˆ  • [        U[        S9nU R                  R                  S5      nUR	                  U R                  5       5        [        U5       HK  u  pEU(       a  UR	                  U R                  5       5        UR	                  U R                  U5      5        MM     UR	                  U R                  5       5        U$ )N©Úkeyrd  )
Úsortedr   rH   rØ   rÙ   r  rú   r  rU   r  )r5   rn  rc  r­  rü   re  s         r:   r
  Ú$MathMLPresentationPrinter._print_setO  s‘   € Ü�qÔ.Ñ/ˆØ�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ü  Ö'‰GˆAÞØ× Ñ  §¡£Ô/Ø×Ñ˜TŸ[™[¨Ó.Ö/ñ (ð 	×Ñ˜Ÿ™›Ô)Øˆr=   c                ó2  • U R                   R                  S5      nUS   R                  (       a¢  US   R                  (       dŽ  U R                   R                  S5      nUR	                  U R                  5       5        UR	                  U R                  US   5      5        UR	                  U R                  5       5        UR	                  U5        O#UR	                  U R                  US   5      5        USS   GH  nU R                   R                  S5      nUR	                  U R                   R                  U5      5        UR                  (       a‹  UR                  (       dz  U R                   R                  S5      nUR	                  U R                  5       5        UR	                  U R                  U5      5        UR	                  U R                  5       5        OU R                  U5      nUR	                  U5        UR	                  U5        GM     U$ rð  )	rH   rØ   Ú
is_BooleanÚis_NotrÙ   rÿ  rU   r  rO   )r5   rî   rñ  rd  r­  rñ   rá   r0  s           r:   Ú_print_LogOpÚ&MathMLPresentationPrinter._print_LogOp\  sw  € Ø�x‰x×%Ñ% fÓ-ˆØ�‰7×× d¨1¡g§n§nØ—8‘8×)Ñ)¨&Ó1ˆDØ×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TŸ[™[¨¨a©Ó1Ô2Ø×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TÕ"à×Ñ˜TŸ[™[¨¨a©Ó1Ô2Ø˜˜”8ˆCØ—‘×&Ñ& tÓ,ˆAØ�M‰M˜$Ÿ(™(×1Ñ1°&Ó9Ô:Ø�~�~ c§j§jØ—H‘H×*Ñ*¨6Ó2�Ø—‘˜dŸm™m›oÔ.Ø—‘˜dŸk™k¨#Ó.Ô/Ø—‘˜dŸm™m›oÕ.à—K‘K Ó$�Ø×Ñ˜QÔØ×Ñ˜Q×ñ ð ˆr=   c                óx  • SSK Jn  XR                  :X  a  U R                  UR                  5      $ [	        X5      (       a  UR                  5       R                  5       nOSU4/nU R                  R                  S5      nU GH³  u  pV[        UR                  R                  5       5      nUR                  S S9  [        U5       GHj  u  nu  pšU
S:X  a  U(       aV  U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U5        UR                  U R                  U	5      5        MŽ  U
S	:X  ay  U R                  R                  S5      nUR                  U R                  R                  S
5      5        UR                  U5        UR                  U R                  U	5      5        GM  U(       aV  U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U5        U R                  R                  S5      nUR                  U R                  5       5        UR                  U R                  U
5      5        UR                  U R!                  5       5        UR                  U5        U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U5        UR                  U R                  U	5      5        GMm     GM¶     U$ )Nr   )ÚVectorrd  c                ó(   • U S   R                  5       $ )Nr   )Ú__str__)rá   s    r:   Ú<lambda>ÚAMathMLPresentationPrinter._print_BasisDependent.<locals>.<lambda>‚  s   € ¨1¨Q©4¯<©<¬>r=   r  rÕ   rf  r6  rê   r3  ró  )Úsympy.vectorr  ÚzerorU   r÷  Úseparaterc  rH   rØ   rV  Ú
componentsÚsortrú   rÙ   rO   rÿ  r  )r5   rY   r  rc  rd  ÚsystemÚvectÚ
inneritemsrü   ÚkÚvrf  Úmbracs                r:   Ú_print_BasisDependentÚ/MathMLPresentationPrinter._print_BasisDependentt  sY  € Ý'à—9‘9Óà—;‘;˜tŸy™yÓ)Ð)Ü�d×#Ñ#Ø—M‘M“O×)Ñ)Ó+‰Eà˜�Y�KˆEà�x‰x×%Ñ% fÓ-ˆÜ!‰LˆFÜ˜dŸo™o×3Ñ3Ó5Ó6ˆJØ�O‰OÑ"9ˆOÑ:Ü& z×2‘	�‘6�AØ˜“6ÞØ!ŸX™X×3Ñ3°DÓ9˜ØŸ™ t§x¡x×'>Ñ'>¸sÓ'CÔDØ×(Ñ(¨Ô,Ø×$Ñ$ T§[¡[°£^Ö4Ø˜"“WØŸ™×/Ñ/°Ó5�BØ—N‘N 4§8¡8×#:Ñ#:¸3Ó#?Ô@Ø×$Ñ$ RÔ(Ø×$Ñ$ T§[¡[°£^×4æØ!ŸX™X×3Ñ3°DÓ9˜ØŸ™ t§x¡x×'>Ñ'>¸sÓ'CÔDØ×(Ñ(¨Ô,Ø ŸH™H×2Ñ2°6Ó:�EØ×%Ñ% d§m¡m£oÔ6Ø×%Ñ% d§k¡k°!£nÔ5Ø×%Ñ% d§m¡m£oÔ6Ø×$Ñ$ UÔ+ØŸ™×/Ñ/°Ó5�BØ—N‘N 4§8¡8×#:Ñ#:Ð;MÓ#NÔOØ×$Ñ$ RÔ(Ø×$Ñ$ T§[¡[°£^×4ô3 3ñ "ð: ˆr=   c                óV   • [        UR                  [        S9nU R                  US5      $ )Nr  z&#x2227;©r  rî   r   r  ©r5   rY   rî   s      r:   Ú
_print_AndÚ$MathMLPresentationPrinter._print_And   ó&   € Ü�d—i‘iÔ%5Ñ6ˆØ× Ñ   zÓ2Ð2r=   c                óV   • [        UR                  [        S9nU R                  US5      $ )Nr  z&#x2228;r*  r+  s      r:   Ú	_print_OrÚ#MathMLPresentationPrinter._print_Or¤  r.  r=   c                óV   • [        UR                  [        S9nU R                  US5      $ )Nr  z&#x22BB;r*  r+  s      r:   rÈ  Ú$MathMLPresentationPrinter._print_Xor¨  r.  r=   c                ó:   • U R                  UR                  S5      $ )Nz&#x21D2;)r  rî   r¤  s     r:   rÆ  Ú(MathMLPresentationPrinter._print_Implies¬  s   € Ø× Ñ  §¡¨JÓ7Ð7r=   c                óV   • [        UR                  [        S9nU R                  US5      $ )Nr  z&#x21D4;r*  r+  s      r:   Ú_print_EquivalentÚ+MathMLPresentationPrinter._print_Equivalent¯  r.  r=   c                ó�  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  S   R
                  (       a‡  U R                   R                  S5      nUR                  U R                  5       5        UR                  U R                  UR                  S   5      5        UR                  U R                  5       5        OU R                  UR                  S   5      nUR                  U5        U$ )Nrd  rf  z&#xAC;r   )	rH   rØ   rÙ   rO   rî   r  rÿ  rU   r  )r5   rÉ   rd  rf  rá   s        r:   rÇ  Ú$MathMLPresentationPrinter._print_Not³  sâ   € Ø�x‰x×%Ñ% fÓ-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨xÓ8Ô9Ø×Ñ˜ÔØ�F‰F�1‰I× × Ø—‘×&Ñ& vÓ.ˆAØ�M‰M˜$Ÿ-™-›/Ô*Ø�M‰M˜$Ÿ+™+ a§f¡f¨Q¡iÓ0Ô1Ø�M‰M˜$Ÿ-™-›/Õ*à—‘˜AŸF™F 1™IÓ&ˆAØ×Ñ˜ÔØˆr=   c                ó®   • U R                   R                  S5      nUR                  U R                   R                  U R	                  U5      5      5        U$ ©Nrg  ©rH   rØ   rÙ   rO   rÍ   ©r5   rÉ   rg  s      r:   Ú_print_boolÚ%MathMLPresentationPrinter._print_boolÂ  ó?   € Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨t¯©¸qÓ/AÓBÔCØˆ	r=   c                ó®   • U R                   R                  S5      nUR                  U R                   R                  U R	                  U5      5      5        U$ r<  r=  r>  s      r:   Ú_print_NoneTypeÚ)MathMLPresentationPrinter._print_NoneTypeÊ  rA  r=   c                óN  • SnUR                   R                  (       aF  UR                  R                  (       a+  UR                  R                  (       a  USSSU4nO¹USSSU4nO±UR                   R                  (       a  X!S   UR                  -
  US   4nO~UR                  R                  (       a#  [        U5      n[        U5      [        U5      U4nO@[        U5      S:”  a&  [        U5      n[        U5      [        U5      X!S   4nO[        U5      nU R                  R                  S5      nUR                  U R                  5       5        [        U5       H¨  u  pgU(       a  UR                  U R                  5       5        Xr:X  aX  U R                  R                  S5      nUR                  U R                  R                  U5      5        UR                  U5        Mˆ  UR                  U R!                  U5      5        Mª     UR                  U R#                  5       5        U$ )Nu   â€¦rê   r   rÕ   é   rd  rg  )rÚ  Úis_infiniteÚstopÚstepÚis_positiveÚiterÚnextrÞ   ÚtuplerH   rØ   rÙ   r  rú   r  rO   rU   r  )	r5   rn  ÚdotsÚprintsetÚitr­  rü   Úelrg  s	            r:   Ú_print_RangeÚ&MathMLPresentationPrinter._print_RangeÏ  s–  € ØˆØ�7‰7×× 1§6¡6×#5×#5Ø�v‰v×!×!Ø  Q¨¨4Ð/‘à  A r¨4Ð/‘Ø�W‰W× × Ø˜r™U Q§V¡V™^¨Q¨r©UÐ2‰HØ�V‰V××Ü�a“ˆBÜ˜B“x¤ b£¨4Ð/‰HÜ�‹V�a‹ZÜ�a“ˆBÜ˜B“x¤ b£¨4°2±Ð6‰Hä˜Q“xˆHØ�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™›Ô)Ü˜xÖ(‰EˆAÞØ× Ñ  §¡£Ô/Ø‹zØ—X‘X×+Ñ+¨DÓ1�Ø—‘˜tŸx™x×6Ñ6°tÓ<Ô=Ø× Ñ  Ö$à× Ñ  §¡¨R£Ö1ñ )ð 	×Ñ˜Ÿ™›Ô)Øˆr=   c                ó–  • [        UR                  [        S9nU R                  R	                  S5      nU R                  R	                  S5      nUR                  U R                  R                  [        UR                  5      R                  5       5      5        UR                  U5        UR                  U R                  " U6 5        U$ )Nr  rd  rf  )r  rî   r   rH   rØ   rÙ   rO   r  ÚfuncrÈ   r  )r5   rY   rî   rd  rf  s        r:   Ú_hprint_variadic_functionÚ3MathMLPresentationPrinter._hprint_variadic_functionî  s“   € Ü�d—i‘iÔ%5Ñ6ˆØ�x‰x×%Ñ% fÓ-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.´°D·I±I³×/EÑ/EÓ/GÓHÔIØ×Ñ˜ÔØ×Ñ˜×4Ò4°dÐ;Ô<Øˆr=   c                óÖ   • U R                   R                  S5      nUR                  U R                  S 5      5        UR                  U R	                  UR
                  S   5      5        U$ )Nrx  r   )rH   rØ   rÙ   r-  rU   rî   )r5   rY   rx  s      r:   Ú
_print_expÚ$MathMLPresentationPrinter._print_expù  sS   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜×)Ñ)¨$Ó/Ô0Ø×Ñ˜Ÿ™ T§Y¡Y¨q¡\Ó2Ô3Øˆr=   c                ó®  • U R                   R                  S5      nUR                  U R                  UR                  5      5        U R                   R                  S5      nUR                  U R                   R                  U R                  U5      5      5        UR                  U5        UR                  U R                  UR                  5      5        U$ )Nrd  rf  )rH   rØ   rÙ   rU   r¤  rO   rÍ   r¥  )r5   rÉ   rd  rá   s       r:   r¦  Ú+MathMLPresentationPrinter._print_Relationalÿ  s—   € Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜Ÿ™ Q§U¡UÓ+Ô,Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨d¯o©o¸aÓ.@ÓAÔBØ×Ñ˜ÔØ×Ñ˜Ÿ™ Q§U¡UÓ+Ô,Øˆr=   c                óÀ   • U R                   R                  U R                  U5      5      nUR                  U R                   R	                  [        U5      5      5        U$ rG   r†  r®  s      r:   r¯  Ú$MathMLPresentationPrinter._print_int  r±  r=   c                ó&  • U R                   R                  S5      nUR                  u  p4U R                   R                  S5      nUR                  SS5        UR	                  U R                   R                  UR                  U   5      5        UR	                  U5        U R                   R                  S5      nUR                  SS5        UR	                  U R                   R                  UR                  5      5        UR	                  U5        U$ )Nrw  rg  r�  rŽ  )rH   rØ   Ú_idr-  rÙ   rO   Ú_variable_namesÚ_name)r5   rÉ   rw  Úindexr!  rg  s         r:   Ú_print_BaseScalarÚ+MathMLPresentationPrinter._print_BaseScalar  sË   € Ø�x‰x×%Ñ% fÓ-ˆØŸ™‰ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰˜ vÔ.Ø
�‰�t—x‘x×.Ñ.¨v×/EÑ/EÀeÑ/LÓMÔNØ×Ñ˜ÔØ�X‰X×#Ñ# DÓ)ˆØ
�‰˜ vÔ.Ø
�‰�t—x‘x×.Ñ.¨v¯|©|Ó<Ô=Ø×Ñ˜ÔØˆr=   c                ó*  • U R                   R                  S5      nUR                  u  p4U R                   R                  S5      nU R                   R                  S5      nUR                  SS5        UR	                  U R                   R                  UR                  U   5      5        UR	                  U5        U R                   R                  S5      nUR	                  U R                   R                  S5      5        UR	                  U5        UR	                  U5        U R                   R                  S5      nUR                  SS5        UR	                  U R                   R                  UR                  5      5        UR	                  U5        U$ )Nrw  Úmoverrg  r�  rŽ  rf  Ú^)rH   rØ   r`  r-  rÙ   rO   Ú_vector_namesrb  )r5   rÉ   rw  rc  r!  rg  rg  rf  s           r:   Ú_print_BaseVectorÚ+MathMLPresentationPrinter._print_BaseVector  s*  € Ø�x‰x×%Ñ% fÓ-ˆØŸ™‰ˆØ—‘×&Ñ& wÓ/ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰˜ vÔ.Ø
�‰�t—x‘x×.Ñ.¨v×/CÑ/CÀEÑ/JÓKÔLØ×Ñ˜"ÔØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø×Ñ˜"ÔØ×Ñ˜ÔØ�X‰X×#Ñ# DÓ)ˆØ
�‰˜ vÔ.Ø
�‰�t—x‘x×.Ñ.¨v¯|©|Ó<Ô=Ø×Ñ˜ÔØˆr=   c                ó¸  • U R                   R                  S5      nU R                   R                  S5      nUR                  SS5        UR                  U R                   R	                  S5      5        UR                  U5        U R                   R                  S5      nUR                  U R                   R	                  S5      5        UR                  U5        U$ )Nrg  rg  r�  rŽ  r¬  rf  rh  ©rH   rØ   r-  rÙ   rO   )r5   rÉ   rg  rg  rf  s        r:   Ú_print_VectorZeroÚ+MathMLPresentationPrinter._print_VectorZero,  s£   € Ø—‘×&Ñ& wÓ/ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰˜ vÔ.Ø
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø×Ñ˜"ÔØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø×Ñ˜"ÔØˆr=   c                ó¸  • U R                   R                  S5      nUR                  nUR                  nUR	                  U R                  U[        S   5      5        U R                   R                  S5      nUR	                  U R                   R                  S5      5        UR	                  U5        UR	                  U R                  U[        S   5      5        U$ )Nrd  r   rf  rô  ©rH   rØ   Ú_expr1Ú_expr2rÙ   r&  r   rO   ©r5   rY   rd  Úvec1Úvec2rf  s         r:   Ú_print_CrossÚ&MathMLPresentationPrinter._print_Cross7  óª   € Ø�x‰x×%Ñ% fÓ-ˆØ�{‰{ˆØ�{‰{ˆØ×Ñ˜×*Ñ*¨4´¸EÑ1BÓCÔDØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨xÓ8Ô9Ø×Ñ˜ÔØ×Ñ˜×*Ñ*¨4´¸EÑ1BÓCÔDØˆr=   c                óø  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  [        S   5      5        U$ )Nrd  rf  ú&#x2207;rô  r   ©rH   rØ   rÙ   rO   r&  Ú_exprr   ©r5   rY   rd  rf  s       r:   Ú_print_CurlÚ%MathMLPresentationPrinter._print_CurlB  ó¹   € Ø�x‰x×%Ñ% fÓ-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨zÓ:Ô;Ø×Ñ˜ÔØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨xÓ8Ô9Ø×Ñ˜ÔØ×Ñ˜×*Ñ*¨4¯:©:´zÀ%Ñ7HÓIÔJØˆr=   c                óø  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  [        S   5      5        U$ )Nrd  rf  r{  r   r   r|  r~  s       r:   Ú_print_DivergenceÚ+MathMLPresentationPrinter._print_DivergenceM  r�  r=   c                ó¸  • U R                   R                  S5      nUR                  nUR                  nUR	                  U R                  U[        S   5      5        U R                   R                  S5      nUR	                  U R                   R                  S5      5        UR	                  U5        UR	                  U R                  U[        S   5      5        U$ )Nrd  r   rf  r   rq  rt  s         r:   Ú
_print_DotÚ$MathMLPresentationPrinter._print_DotX  ry  r=   c                óL  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  [        S   5      5        U$ )Nrd  rf  r{  r   r|  r~  s       r:   Ú_print_GradientÚ)MathMLPresentationPrinter._print_Gradientc  ó|   € Ø�x‰x×%Ñ% fÓ-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨zÓ:Ô;Ø×Ñ˜ÔØ×Ñ˜×*Ñ*¨4¯:©:´zÀ%Ñ7HÓIÔJØˆr=   c                óL  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  [        S   5      5        U$ )Nrd  rf  r  r   r|  r~  s       r:   Ú_print_LaplacianÚ*MathMLPresentationPrinter._print_Laplaciank  r‹  r=   c                ó´   • U R                   R                  S5      nUR                  SS5        UR                  U R                   R	                  S5      5        U$ )Nrg  r�  Únormalz&#x2124;rm  r(  s      r:   Ú_print_IntegersÚ)MathMLPresentationPrinter._print_Integerss  óD   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�} hÔ/Ø	�‰�d—h‘h×-Ñ-¨jÓ9Ô:Øˆr=   c                ó´   • U R                   R                  S5      nUR                  SS5        UR                  U R                   R	                  S5      5        U$ )Nrg  r�  r�  z&#x2102;rm  r(  s      r:   Ú_print_ComplexesÚ*MathMLPresentationPrinter._print_Complexesy  r“  r=   c                ó´   • U R                   R                  S5      nUR                  SS5        UR                  U R                   R	                  S5      5        U$ )Nrg  r�  r�  z&#x211D;rm  r(  s      r:   Ú_print_RealsÚ&MathMLPresentationPrinter._print_Reals  r“  r=   c                ó´   • U R                   R                  S5      nUR                  SS5        UR                  U R                   R	                  S5      5        U$ )Nrg  r�  r�  ú&#x2115;rm  r(  s      r:   Ú_print_NaturalsÚ)MathMLPresentationPrinter._print_Naturals…  r“  r=   c                óh  • U R                   R                  S5      nU R                   R                  S5      nUR                  SS5        UR                  U R                   R	                  S5      5        UR                  U5        UR                  U R                  [        R                  5      5        U$ )Nrw  rg  r�  r�  r›  )rH   rØ   r-  rÙ   rO   rU   r   ÚZero)r5   rÉ   ru  rá   s       r:   Ú_print_Naturals0Ú*MathMLPresentationPrinter._print_Naturals0‹  s}   € Ø�h‰h×$Ñ$ VÓ,ˆØ�H‰H×"Ñ" 4Ó(ˆØ	�‰�} hÔ/Ø	�‰�d—h‘h×-Ñ-¨jÓ9Ô:Ø�‰˜ÔØ�‰˜Ÿ™¤A§F¡FÓ+Ô,Øˆ
r=   c                óÈ  • UR                   S   UR                   S   -
  nUR                   S   nU R                  R                  S5      nUR                  U R                  R	                  S5      5        U R                  R                  S5      nUR                  U R                  R	                  S5      5        U R                  R                  S5      nUR                  U5        UR                  U R                  U5      5        UR                  U5        U R                  R                  S5      nUR                  U5        UR                  U R                  U5      5        U$ )	Nr   rÕ   r  rf  r¸  r¹  rd  rx  )rî   rH   rØ   rÙ   rO   rU   )r5   rY   Úshiftrv   r>  r?  r­  rt  s           r:   Ú_print_SingularityFunctionÚ4MathMLPresentationPrinter._print_SingularityFunction”  s  € Ø—	‘	˜!‘˜tŸy™y¨™|Ñ+ˆØ—	‘	˜!‘ˆØ�x‰x×%Ñ% dÓ+ˆØ×Ñ˜Ÿ™×0Ñ0°Ó:Ô;Ø—‘×&Ñ& tÓ,ˆØ×Ñ˜$Ÿ(™(×1Ñ1°(Ó;Ô<Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜Ÿ™ UÓ+Ô,Ø×Ñ˜ÔØ�h‰h×$Ñ$ VÓ,ˆØ�‰˜ÔØ�‰˜Ÿ™ EÓ*Ô+Øˆ
r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  ÚNaNr'  r(  s      r:   r:  Ú$MathMLPresentationPrinter._print_NaN¤  s6   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨eÓ4Ô5Øˆr=   c                ó&  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  U5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        [        UR
                  5      S:X  a  U$ U R                   R                  S5      nUR                  U5        UR                  U R                  " UR
                  SS  6 5        U$ )Nrw  rg  r   rÕ   rd  )rH   rØ   rÙ   rO   rU   rî   rÞ   r  )r5   rÉ   rb   ru  rg  rd  s         r:   Ú_print_number_functionÚ0MathMLPresentationPrinter._print_number_function©  sÏ   € ð �h‰h×$Ñ$ VÓ,ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨tÓ4Ô5Ø�‰˜ÔØ�‰˜Ÿ™ A§F¡F¨1¡IÓ.Ô/Üˆq�v‰v‹;˜!ÓØˆJØ�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜×4Ò4°a·f±f¸Q¸R°jÐAÔBØˆr=   c                ó&   • U R                  US5      $ )NÚB©rª  r  s     r:   Ú_print_bernoulliÚ*MathMLPresentationPrinter._print_bernoulli¸  ó   € Ø×*Ñ*¨1¨cÓ2Ð2r=   c                ó&   • U R                  US5      $ )NrÞ  r®  r  s     r:   Ú_print_catalanÚ(MathMLPresentationPrinter._print_catalan½  r±  r=   c                ó&   • U R                  US5      $ )NÚEr®  r  s     r:   Ú_print_eulerÚ&MathMLPresentationPrinter._print_eulerÀ  r±  r=   c                ó&   • U R                  US5      $ )NÚFr®  r  s     r:   Ú_print_fibonacciÚ*MathMLPresentationPrinter._print_fibonacciÃ  r±  r=   c                ó&   • U R                  US5      $ )NÚLr®  r  s     r:   Ú_print_lucasÚ&MathMLPresentationPrinter._print_lucasÆ  r±  r=   c                ó&   • U R                  US5      $ )Nz&#x03B3;r®  r  s     r:   Ú_print_stieltjesÚ*MathMLPresentationPrinter._print_stieltjesÉ  s   € Ø×*Ñ*¨1¨jÓ9Ð9r=   c                ó&   • U R                  US5      $ )NÚTr®  r  s     r:   Ú_print_tribonacciÚ+MathMLPresentationPrinter._print_tribonacciÌ  r±  r=   c                ó”  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        U$ )Nrg  rf  rV  Ú~r'  )r5   rÉ   rá   rf  s       r:   Ú_print_ComplexInfinityÚ0MathMLPresentationPrinter._print_ComplexInfinityÏ  s‘   € Ø�H‰H×"Ñ" 7Ó+ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨zÓ:Ô;Ø	�‰�bÔØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø	�‰�bÔØˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  z&#x2205;r'  r(  s      r:   r>  Ú)MathMLPresentationPrinter._print_EmptySetÙ  rX  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrf  z	&#x1D54C;r'  r(  s      r:   Ú_print_UniversalSetÚ-MathMLPresentationPrinter._print_UniversalSetÞ  ó6   € Ø�H‰H×"Ñ" 4Ó(ˆØ	�‰�d—h‘h×-Ñ-¨kÓ:Ô;Øˆr=   c                ó‚  • SSK Jn  UR                  nU R                  R	                  S5      n[        X25      (       d‹  U R                  R	                  S5      nUR                  U R                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        UR                  U5        O UR                  U R                  U5      5        U R                  R	                  S5      nUR                  U R                  R                  S5      5        UR                  U5        U$ )Nr   ©r‰   rx  rd  rf  re  ©Úsympy.matricesr‰   rñ   rH   rØ   r÷  rÙ   rÿ  rU   r  rO   ©r5   rY   r‰   Úmatrt  r­  rf  s          r:   Ú_print_AdjointÚ(MathMLPresentationPrinter._print_Adjointã  sá   € Ý/Ø�h‰hˆØ�h‰h×$Ñ$ VÓ,ˆÜ˜#×,Ñ,Ø—8‘8×)Ñ)¨&Ó1ˆDØ×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TŸ[™[¨Ó-Ô.Ø×Ñ˜TŸ]™]›_Ô-Ø�O‰O˜DÕ!à�O‰O˜DŸK™K¨Ó,Ô-Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨zÓ:Ô;Ø�‰˜ÔØˆ
r=   c                ó‚  • SSK Jn  UR                  nU R                  R	                  S5      n[        X25      (       d‹  U R                  R	                  S5      nUR                  U R                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        UR                  U5        O UR                  U R                  U5      5        U R                  R	                  S5      nUR                  U R                  R                  S5      5        UR                  U5        U$ )Nr   rÓ  rx  rd  rf  rÅ  rÔ  rÖ  s          r:   Ú_print_TransposeÚ*MathMLPresentationPrinter._print_Transposeô  sá   € Ý/Ø�h‰hˆØ�h‰h×$Ñ$ VÓ,ˆÜ˜#×,Ñ,Ø—8‘8×)Ñ)¨&Ó1ˆDØ×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TŸ[™[¨Ó-Ô.Ø×Ñ˜TŸ]™]›_Ô-Ø�O‰O˜DÕ!à�O‰O˜DŸK™K¨Ó,Ô-Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø�‰˜ÔØˆ
r=   c                ó  • SSK Jn  UR                  nU R                  R	                  S5      n[        X25      (       d‹  U R                  R	                  S5      nUR                  U R                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        UR                  U5        O UR                  U R                  U5      5        UR                  U R                  S5      5        U$ )Nr   rÓ  rx  rd  rê   )
rÕ  r‰   rñ   rH   rØ   r÷  rÙ   rÿ  rU   r  )r5   rY   r‰   r×  rt  r­  s         r:   Ú_print_InverseÚ(MathMLPresentationPrinter._print_Inverse  sº   € Ý/Ø�h‰hˆØ�h‰h×$Ñ$ VÓ,ˆÜ˜#×,Ñ,Ø—8‘8×)Ñ)¨&Ó1ˆDØ×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TŸ[™[¨Ó-Ô.Ø×Ñ˜TŸ]™]›_Ô-Ø�O‰O˜DÕ!à�O‰O˜DŸK™K¨Ó,Ô-Ø�‰˜Ÿ™ B›Ô(Øˆ
r=   c           	     óˆ  • SSK Jn  U R                  R                  S5      nUR                  n[        US   [        5      (       a#  US   R                  5       [        USS  5      -   nO[        U5      n[        X5      (       aƒ  UR                  5       (       an  US   S:X  a  USS  nO	US   * US'   U R                  R                  S5      nUR                  U R                  R                  S5      5        UR                  U5        US S  H„  nUR                  U R                  U[        U5      S5      5        U R                  R                  S5      nUR                  U R                  R                  S	5      5        UR                  U5        M†     UR                  U R                  US   [        U5      S5      5        U$ )
Nr   )ÚMatMulrd  rÕ   rê   rf  r3  Fró  )Ú!sympy.matrices.expressions.matmulrá  rH   rØ   rî   r÷  r   rà   rV  r×   rÙ   rO   r&  r   )r5   rY   rá  rá   rî   rf  rñ   s          r:   Ú_print_MatMulÚ'MathMLPresentationPrinter._print_MatMul  sy  € Ý<à�H‰H×"Ñ" 6Ó*ˆØ�y‰yˆÜ�d˜1‘gœs×#Ñ#Ø˜‘7×-Ñ-Ó/´$°t¸A¸B°x³.Ñ@‰Dä˜“:ˆDä�d×#Ñ#¨×(EÑ(E×(GÑ(GØ�A‰w˜"‹}Ø˜A˜B�x‘à ™7˜(��Q‘Ø—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°3Ó7Ô8Ø�M‰M˜"Ôà˜˜“9ˆCØ�M‰M˜$×+Ñ+¨CÔ1GÈÓ1MØ,1ó3ô 4à—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2Ð3EÓFÔGØ�M‰M˜"Öñ ð 	
�‰�d×'Ñ'¨¨R©Ô2HÈÓ2NØ(-ó/ô 	0àˆr=   c                ó,  • SSK Jn  UR                  UR                  pCU R                  R                  S5      n[        X25      (       d‹  U R                  R                  S5      nUR                  U R                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        UR                  U5        O UR                  U R                  U5      5        UR                  U R                  U5      5        U$ )Nr   rÓ  rx  rd  )rÕ  r‰   r€  r~  rH   rØ   r÷  rÙ   rÿ  rU   r  )r5   rY   r‰   r€  r~  rt  r­  s          r:   Ú_print_MatPowÚ'MathMLPresentationPrinter._print_MatPow1  sÁ   € Ý/Ø—I‘I˜tŸx™xˆcØ�h‰h×$Ñ$ VÓ,ˆÜ˜$×-Ñ-Ø—8‘8×)Ñ)¨&Ó1ˆDØ×Ñ˜TŸ]™]›_Ô-Ø×Ñ˜TŸ[™[¨Ó.Ô/Ø×Ñ˜TŸ]™]›_Ô-Ø�O‰O˜DÕ!à�O‰O˜DŸK™K¨Ó-Ô.Ø�‰˜Ÿ™ CÓ(Ô)Øˆ
r=   c           	     óÊ  • U R                   R                  S5      nUR                  nUS S  H„  nUR                  U R	                  U[        U5      S5      5        U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        M†     UR                  U R	                  US   [        U5      S5      5        U$ )Nrd  rê   Frf  z&#x2218;)rH   rØ   rî   rÙ   r&  r   rO   )r5   rY   rá   rî   rñ   rf  s         r:   Ú_print_HadamardProductÚ0MathMLPresentationPrinter._print_HadamardProduct@  s¿   € Ø�H‰H×"Ñ" 6Ó*ˆØ�y‰yˆØ˜˜“9ˆCØ�M‰MØ×!Ñ! #Ô'=¸dÓ'CÀUÓKôMà—‘×'Ñ'¨Ó-ˆBØ�N‰N˜4Ÿ8™8×2Ñ2°:Ó>Ô?Ø�M‰M˜"Öñ ð 	
�‰Ø×Ñ˜d 2™hÔ(>¸tÓ(DÀeÓLô	Nàˆr=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )NrÍ  z&#x1D7D8r'  ©r5   ÚZrá   s      r:   Ú_print_ZeroMatrixÚ+MathMLPresentationPrinter._print_ZeroMatrixM  rX  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )NrÍ  z&#x1D7D9r'  rì  s      r:   Ú_print_OneMatrixÚ*MathMLPresentationPrinter._print_OneMatrixR  rX  r=   c                ó�   • U R                   R                  S5      nUR                  U R                   R                  S5      5        U$ )Nrg  z	&#x1D540;r'  )r5   ÚIrá   s      r:   Ú_print_IdentityÚ)MathMLPresentationPrinter._print_IdentityW  rÑ  r=   c                óî  • U R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nUR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        U$ )Nrf  u   âŒŠu   âŒ‹rd  r   rq  ©r5   rÉ   r>  r?  rd  s        r:   Ú_print_floorÚ&MathMLPresentationPrinter._print_floor\  ó¸   € Ø�x‰x×%Ñ% dÓ+ˆØ×Ñ˜Ÿ™×0Ñ0°Ó:Ô;Ø—‘×&Ñ& tÓ,ˆØ×Ñ˜$Ÿ(™(×1Ñ1°(Ó;Ô<Ø�x‰x×%Ñ% fÓ-ˆØ×Ñ˜ÔØ×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0Ø×Ñ˜ÔØˆr=   c                óî  • U R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nUR                  U R                   R                  S5      5        U R                   R                  S5      nUR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        U$ )Nrf  u   âŒˆu   âŒ‰rd  r   rq  rø  s        r:   Ú_print_ceilingÚ(MathMLPresentationPrinter._print_ceilingg  rû  r=   c                óh  • U R                   R                  S5      nUR                  S   n[        U5      S:X  a  U R	                  US   5      nOU R	                  U5      nUR                  U R                  5       5        UR                  U5        U R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR                  S   5      5        UR                  U R                  5       5        U$ )Nrd  r   rÕ   rf  z&#x21A6;)	rH   rØ   rî   rÞ   rU   rÙ   rÿ  rO   r  )r5   rÉ   rd  Úsymbolsrf  s        r:   rÁ  Ú'MathMLPresentationPrinter._print_Lambdar  sæ   € Ø�x‰x×%Ñ% fÓ-ˆØ—&‘&˜‘)ˆÜˆw‹<˜1ÓØ—k‘k '¨!¡*Ó-‰Gà—k‘k 'Ó*ˆGØ×Ñ˜Ÿ™›Ô)Ø×Ñ˜Ô!Ø�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨zÓ:Ô;Ø×Ñ˜ÔØ×Ñ˜Ÿ™ Q§V¡V¨A¡YÓ/Ô0Ø×Ñ˜Ÿ™›Ô)Øˆr=   c                ó    • U R                   " U6 $ rG   )r  r  s     r:   Ú_print_tupleÚ&MathMLPresentationPrinter._print_tuple‚  s   € Ø×*Ò*¨AÐ.Ð.r=   c                ó8   • U R                  UR                  5      $ rG   )rU   Úlabelr  s     r:   Ú_print_IndexedBaseÚ,MathMLPresentationPrinter._print_IndexedBase…  s   € Ø�{‰{˜1Ÿ7™7Ó#Ð#r=   c                ót  • U R                   R                  S5      nUR                  U R                  UR                  5      5        [        UR                  5      S:X  a/  UR                  U R                  UR                  S   5      5        U$ UR                  U R                  UR                  5      5        U$ )Nrw  rÕ   r   )rH   rØ   rÙ   rU   r€  rÞ   Úindicesr(  s      r:   Ú_print_IndexedÚ(MathMLPresentationPrinter._print_Indexedˆ  s   € Ø�H‰H×"Ñ" 6Ó*ˆØ	�‰�d—k‘k !§&¡&Ó)Ô*Üˆq�y‰y‹>˜QÓØ�M‰M˜$Ÿ+™+ a§i¡i°¡lÓ3Ô4ØˆHØ	�‰�d—k‘k !§)¡)Ó,Ô-Øˆr=   c                ó¾  • U R                   R                  S5      nUR                  U R                  UR                  [
        S   SS95        U R                   R                  S5      n[        UR                  5       HK  u  pEU(       a  UR                  U R                  5       5        UR                  U R                  U5      5        MM     UR                  U5        U$ )Nrw  ÚAtomTr|  rd  )
rH   rØ   rÙ   r&  Úparentr   rú   r
  r  rU   )r5   rÉ   rá   r­  rü   rñ   s         r:   Ú_print_MatrixElementÚ.MathMLPresentationPrinter._print_MatrixElement‘  s§   € Ø�H‰H×"Ñ" 6Ó*ˆØ	�‰�d×'Ñ'¨¯©´*¸VÑ2DÈtÐ'ÐTÔUØ�x‰x×%Ñ% fÓ-ˆÜ §	¡	Ö*‰FˆAÞØ× Ñ  §¡£Ô/Ø×Ñ˜TŸ[™[¨Ó-Ö.ñ +ð 	
�‰�dÔØˆr=   c                ó8  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R                  " UR
                  6 5        U$ )Nrd  rg  z	&#x1d5a5;©rH   rØ   rÙ   rO   r   rî   ©r5   rÉ   rá   rg  s       r:   Ú_print_elliptic_fÚ+MathMLPresentationPrinter._print_elliptic_fœ  óq   € Ø�H‰H×"Ñ" 6Ó*ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨{Ó;Ô<Ø	�‰�bÔØ	�‰�d×/Ò/°·±Ð8Ô9Øˆr=   c                ó8  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R                  " UR
                  6 5        U$ )Nrd  rg  z	&#x1d5a4;r  r  s       r:   Ú_print_elliptic_eÚ+MathMLPresentationPrinter._print_elliptic_e¤  r  r=   c                ó$  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        U R                   R                  S5      nUR                  U R	                  5       5        [        UR                  5      S:X  an  UR                  u  pVUR                  U R                  U5      5        UR                  U R                  5       5        UR                  U R                  U5      5        O­UR                  u  pVnUR                  U R                  U5      5        UR                  U R                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        UR                  U R                  U5      5        UR                  U R                  5       5        UR                  U5        U$ )Nrd  rg  z	&#x1d6f1;r  )rH   rØ   rÙ   rO   rÿ  rÞ   rî   rU   r  r  r  )r5   rÉ   rá   rg  r0  rÌ   r  Úzs           r:   Ú_print_elliptic_piÚ,MathMLPresentationPrinter._print_elliptic_pi¬  s]  € Ø�H‰H×"Ñ" 6Ó*ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨{Ó;Ô<Ø	�‰�bÔØ�H‰H×"Ñ" 6Ó*ˆØ	�‰�d—m‘m“oÔ&Üˆq�v‰v‹;˜!ÓØ—6‘6‰DˆAØ�M‰M˜$Ÿ+™+ a›.Ô)Ø�M‰M˜$Ÿ)™)›+Ô&Ø�M‰M˜$Ÿ+™+ a›.Õ)à—f‘f‰GˆA�!Ø�M‰M˜$Ÿ+™+ a›.Ô)Ø�M‰M˜$Ÿ/™/Ó+Ô,Ø�M‰M˜$Ÿ+™+ a›.Ô)Ø�M‰M˜$Ÿ)™)›+Ô&Ø�M‰M˜$Ÿ+™+ a›.Ô)Ø	�‰�d—m‘m“oÔ&Ø	�‰�aÔØˆr=   c                ó<  • U R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  5      5        U$ )Nrd  rg  ÚEirq  r  s       r:   Ú	_print_EiÚ#MathMLPresentationPrinter._print_EiÃ  so   € Ø�H‰H×"Ñ" 6Ó*ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨tÓ4Ô5Ø	�‰�bÔØ	�‰�d—k‘k !§&¡&Ó)Ô*Øˆr=   c                óô  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  rw  rf  r¶  r   rÕ   rq  ©r5   rÉ   rá   r0  rf  s        r:   Ú_print_expintÚ'MathMLPresentationPrinter._print_expintË  ó²   € Ø�H‰H×"Ñ" 6Ó*ˆØ�H‰H×"Ñ" 6Ó*ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø	�‰�bÔØ	�‰�d—k‘k !§&¡&¨¡)Ó,Ô-Ø	�‰�aÔØ	�‰�d—k‘k !§&¡&¨¨ *Ó-Ô.Øˆr=   c                óN  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U R	                  UR
                  SS 5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  ry  rf  ÚPr   rÕ   rM  rq  r$  s        r:   Ú_print_jacobiÚ'MathMLPresentationPrinter._print_jacobiÖ  óÑ   € Ø�H‰H×"Ñ" 6Ó*ˆØ�H‰H×"Ñ" 9Ó-ˆØ�X‰X×#Ñ# DÓ)ˆØ
�‰�t—x‘x×.Ñ.¨sÓ3Ô4Ø	�‰�bÔØ	�‰�d—k‘k !§&¡&¨¡)Ó,Ô-Ø	�‰�d—k‘k !§&¡&¨¨1 +Ó.Ô/Ø	�‰�aÔØ	�‰�d—k‘k !§&¡&¨¨ *Ó-Ô.Øˆr=   c                óN  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U R	                  UR
                  SS 5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  ry  rf  rÞ  r   rÕ   r  rq  r$  s        r:   Ú_print_gegenbauerÚ+MathMLPresentationPrinter._print_gegenbauerâ  r,  r=   c                óô  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  rw  rf  rÅ  r   rÕ   rq  r$  s        r:   Ú_print_chebyshevtÚ+MathMLPresentationPrinter._print_chebyshevtî  r'  r=   c                óô  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  rw  rf  ÚUr   rÕ   rq  r$  s        r:   Ú_print_chebyshevuÚ+MathMLPresentationPrinter._print_chebyshevuù  r'  r=   c                óô  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  rw  rf  r)  r   rÕ   rq  r$  s        r:   Ú_print_legendreÚ)MathMLPresentationPrinter._print_legendre  r'  r=   c                óN  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U R	                  UR
                  SS 5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  ry  rf  r)  r   rÕ   r  rq  r$  s        r:   Ú_print_assoc_legendreÚ/MathMLPresentationPrinter._print_assoc_legendre  r,  r=   c                óô  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  rw  rf  r¾  r   rÕ   rq  r$  s        r:   Ú_print_laguerreÚ)MathMLPresentationPrinter._print_laguerre  r'  r=   c                óN  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U R	                  UR
                  SS 5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  ry  rf  r¾  r   rÕ   r  rq  r$  s        r:   Ú_print_assoc_laguerreÚ/MathMLPresentationPrinter._print_assoc_laguerre&  r,  r=   c                óô  • U R                   R                  S5      nU R                   R                  S5      nU R                   R                  S5      nUR                  U R                   R                  S5      5        UR                  U5        UR                  U R	                  UR
                  S   5      5        UR                  U5        UR                  U R	                  UR
                  SS  5      5        U$ )Nrd  rw  rf  ÚHr   rÕ   rq  r$  s        r:   Ú_print_hermiteÚ(MathMLPresentationPrinter._print_hermite2  r'  r=   r>   )FrG   )r   )–r@   rA   rB   rC   re   rÃ  rÍ   rÿ  r  r  r  r  r  r  r  r   r&  rÚ   rò   r	  rC  r  r  r  r)  r-  r1  r5  rI  r\  r$  rb  rh  rk  rn  rr  ru  rX  r[  rz  rÄ  rÅ  r™  rŸ  r¥  r¨  r®  rƒ  r‡  rº  r–  r›  r�  rÏ  rž  rÕ  rÜ  rß  Ú_print_Determinantrâ  rç  rë  r¡  ró  rø  rû  r¹  r  r½  r´  r
  Ú_print_frozensetr  r'  r,  r0  rÈ  rÆ  r7  rÇ  r?  rB  rF  rC  rR  rV  Ú
_print_MinÚ
_print_MaxrY  r¦  r¯  rd  rj  rn  rw  r  rƒ  r†  r‰  r�  r‘  r•  r˜  rœ  r   r¤  r:  rª  r¯  Ú_print_bellr³  r·  r»  r¿  rÂ  rÆ  rÊ  r>  rÏ  rØ  rÛ  rÞ  rã  ræ  ré  rî  rñ  rõ  rù  rý  rÁ  r  r  r  r  r  r  r  r!  r%  r*  r.  r1  r5  r8  r;  r>  rA  rE  rD   r>   r=   r:   rÊ  rÊ  #  sõ  † ñð )€KòKòZò
ò
ò
ò
ò
ò
ò
òô!ò-ô^ò(ô4ò(Pòò,ò
ò
ò
ò
ò
òò
ò
ò
òòò
òò$òLô24òlLð (Ðòòò=ò>ò	ò4òlò
ò.ò`	ò%òNò ò4òô&ð $Ðò
ô9ô9òò	ò9ò9ò9ò9ò9ò'ò	ð "Ðòò0)òX3ò3ò3ò8ò3òòð
 %ÐØ%Ðòò
ò>ð 8Ð7€J�òòòò
òò$	ò	ò	ò	ò	òòòòòòòòò ò
ò3ð #€Kò3ò3ò3ò3ò:ò3òòò
ò
ò"ò"òò:òòò
ò
ò
	ò	òò /ò$òò	òòòò.ò	ò
ò
ò	ò	ò	ò
ò	ò
õ	r=   rÊ  c                óv   • US:X  a  [        U5      R                  U 5      $ [        U5      R                  U 5      $ )z‚Returns the MathML representation of expr. If printer is presentation
then prints Presentation MathML else prints content MathML.
Úpresentation)rÊ  r^   rh   )rY   ÚprinterrP   s      r:   ÚmathmlrO  >  s8   € ð
 �.Ó Ü(¨Ó2×:Ñ:¸4Ó@Ð@ä# HÓ-×5Ñ5°dÓ;Ð;r=   c                ó¨   • US:X  a  [        U5      nO[        U5      nUR                  [        U 5      5      nUR	                  5       n[        U5        g)aÊ  
Prints a pretty representation of the MathML code for expr. If printer is
presentation then prints Presentation MathML else prints content MathML.

Examples
========

>>> ##
>>> from sympy import print_mathml
>>> from sympy.abc import x
>>> print_mathml(x+1) #doctest: +NORMALIZE_WHITESPACE
<apply>
    <plus/>
    <ci>x</ci>
    <cn>1</cn>
</apply>
>>> print_mathml(x+1, printer='presentation')
<mrow>
    <mi>x</mi>
    <mo>+</mo>
    <mn>1</mn>
</mrow>

rM  N)rÊ  rh   rU   r   ÚtoprettyxmlÚprint)rY   rN  rP   rn  ÚxmlÚ
pretty_xmls         r:   Úprint_mathmlrU  I  sF   € ð2 �.Ó Ü% hÓ/‰ä  Ó*ˆØ
�(‰(”7˜4“=Ó
!€CØ—‘Ó"€Jä	ˆ*Õr=   N)Úcontent)$re   Ú
__future__r   Útypingr   Úsympy.core.mulr   Úsympy.core.singletonr   Úsympy.core.sortingr   Úsympy.core.sympifyr   Úsympy.printing.conventionsr	   r
   Úsympy.printing.precedencer   r   r   Ú&sympy.printing.pretty.pretty_symbologyr   Úsympy.printing.printerr   r   Úmpmath.libmpr   r   r   r‹  r   rh   rÊ  rO  rU  ÚMathMLPrinterr>   r=   r:   Ú<module>rc     s‹   ðñõ #Ý å Ý "Ý /Ý &ß H÷?ñ ?å @ß :ç EÑ Eô<)˜ô <)ô~JÐ,ô Jô^XÐ 1ô Xñv0 Ð!Ó"ó<ó #ð<ô ðH %�r=   