a Ÿ¬d9„d?d9„d@d9„dAd9„dBd9„dCd9„dDd9„dEd9„dFd9„dGd9„dHd9„dId9„dJd9„dKd9„dLd9„dMd9„dNd9„dOd9„dPd9„dQœZ3e4eƒZ5e/ 6dR¡e/ 6dS¡fZ7dTdU„Z8GdVdW„dWe"ƒZ9dXdY„Z:e#e9ƒdZd[„ƒZ;d\d]„Z ZwpZgimelÚethZdalethZhbarZellZbethZhslashZalephZmhocCsd|dS)Nz \mathring{Ú}©©ÚsrWrWúd/Users/vegardjervell/Documents/master/model/venv/lib/python3.9/site-packages/sympy/printing/latex.pyÚVór[cCsd|dS)Nz\ddddot{rVrWrXrWrWrZr[Wr\cCsd|dS)Nz\dddot{rVrWrXrWrWrZr[Xr\cCsd|dS)Nz\ddot{rVrWrXrWrWrZr[Yr\cCsd|dS)Nz\dot{rVrWrXrWrWrZr[Zr\cCsd|dS)Nz\check{rVrWrXrWrWrZr[[r\cCsd|dS)Nz\breve{rVrWrXrWrWrZr[\r\cCsd|dS)Nz\acute{rVrWrXrWrWrZr[]r\cCsd|dS)Nz\grave{rVrWrXrWrWrZr[^r\cCsd|dS)Nz\tilde{rVrWrXrWrWrZr[_r\cCsd|dS)Nz\hat{rVrWrXrWrWrZr[`r\cCsd|dS)Nz\bar{rVrWrXrWrWrZr[ar\cCsd|dS)Nz\vec{rVrWrXrWrWrZr[br\cCsd|dS©NÚ{z}'rWrXrWrWrZr[cr\cCsd|dSr]rWrXrWrWrZr[dr\cCsd|dS©Nz\boldsymbol{rVrWrXrWrWrZr[fr\cCsd|dSr_rWrXrWrWrZr[gr\cCsd|dS)Nz \mathcal{rVrWrXrWrWrZr[hr\cCsd|dS)Nz \mathscr{rVrWrXrWrWrZr[ir\cCsd|dS)Nz \mathfrak{rVrWrXrWrWrZr[jr\cCsd|dS)Nz\left\|{z }\right\|rWrXrWrWrZr[lr\cCsd|dS)Nz \left\langle{z}\right\ranglerWrXrWrWrZr[mr\cCsd|dS©Nz\left|{z}\right|rWrXrWrWrZr[nr\cCsd|dSr`rWrXrWrWrZr[or\)ZmathringZddddotZdddotZddotÚdotÚcheckZbreveÚacuteZgraveÚtildeZhatÚbarÚvecÚprimeZprmÚboldÚbmÚcalZscrZfrakZnormÚavgÚabsZmagz[0-9][} ]*$z[0-9]cCsB| dd¡}dD]}| |d|¡}q| dd¡}| dd¡}|S)zÉ Escape a string such that latex interprets it as plaintext. We cannot use verbatim easily with mathjax, so escaping is easier. Rules from https://tex.stackexchange.com/a/34586/41112. ú\z\textbackslashz&%$#_{}ú~z\textasciitildeú^z\textasciicircum)Úreplace)rYÚcrWrWrZÚlatex_escapezsrrcsreZdZdZdddddddddddddiddddd ddddd œZdYdd„Zd d„Zdd„ZdZdd„Zdd„Z dd„Z dd„Zdd„Zd[dd„Z dd„Zdd „Zd!d"„Zd#d$„Zd%d&„Zd'd(„ZeZeZd)d*„Zd\d+d,„Zd-d.„Zd/d0„Zd1d2„Zd3d4„Zd5d6„Zd7d8„Zd9d:„Zd;d<„Zd=d>„Z d?d@„Z!dAdB„Z"dCdD„Z#dEdF„Z$dGdH„Z%dIdJ„Z&dKdL„Z'dMdN„Z(dOdP„Z)dQdR„Z*dSdT„Z+dUdV„Z,dWdX„Z-dYdZ„Z.d[d\„Z/d]d^„Z0d_d`„Z1d]dadb„Z2dcdd„Z3dedf„Z4e5dgdh„ƒZ6didj„Z7dkdl„Z8dmdn„Z9d^dodp„Z:e:Z;Z<d_dqdr„Z=d`dsdt„Z>dadudv„Z?dbdwdx„Z@e@ZAdcdydz„ZBddd{d|„ZCd}d~„ZDdd€„ZEdd‚„ZFdƒd„„ZGd…d†„ZHded‡dˆ„ZIdfd‰dŠ„ZJdgd‹dŒ„ZKdhddŽ„ZLdidd„ZMdjd‘d’„ZNdkd“d”„ZOdld•d–„ZPdmd—d˜„ZQdnd™dš„ZRdod›dœ„ZSdpdždŸ„ZTdqd d¡„ZUdrd¢d£„ZVdsd¤d¥„ZWdtd¦d§„ZXeXZYdud¨d©„ZZdvdªd«„Z[dwd¬d„Z\dxd®d¯„Z]dyd°d±„Z^dzd²d³„Z_d{d´dµ„Z`d|d¶d·„Zad}d¸d¹„Zbd~dºd»„Zcd¼d½„Zdd¾d¿„ZeddÀdÁ„Zfd€dÂdÃ„ZgddÄdÅ„Zhd‚dÆdÇ„ZidƒdÈdÉ„Zjd„dÊdË„Zkd…dÌdÍ„Zld†dÎdÏ„Zmd‡dÐdÑ„ZndˆdÒdÓ„Zod‰dÕdÖ„ZpdŠd×dØ„Zqd‹dÙdÚ„ZrdŒdÛdÜ„ZsddÝdÞ„ZtdŽdßdà„Zuddádâ„Zvddãdä„Zwd‘dådæ„Zxd’dçdè„Zyd“dédê„Zzd”dëdì„Z{d•dídî„Z|d–dïdð„Z}d—dñdò„Z~d˜dódô„Zd™dõdö„Z€dšd÷dø„Zd›dùdú„Z‚dœdûdü„Zƒddýdþ„Z„dždÿd„Z…dŸdd„Z†d dd„Z‡d¡dd„Zˆd¢dd„Z‰d£d d „ZŠd¤dd„Z‹d¥d d„ZŒdd„Zdd„ZŽd¦dd„ZeZd§dd„Z‘dd„Z’dd„Z“dd„Z”dd„Z•dd „Z–d!d"„Z—d#d$„Z˜d%d&„Z™d'd(„Zšd)d*„Z›d¨d+d,„Zœd-d.„Zd/d0„Zžd1d2„ZŸd3d4„Z d5d6„Z¡d7d8„Z¢d9d:„Z£d;d<„Z¤d=d>„Z¥d?d@„Z¦ifdAdB„Z§dCdD„Z¨dEdF„Z©dGdH„ZªdIdJ„Z«dKdL„Z¬dMdN„ZdOdP„Z®dQdR„Z¯dSdT„Z°d©dUdV„Z±dWdX„Z²dYdZ„Z³d[d\„Z´d]d^„Zµd_d`„Z¶dadb„Z·dcdd„Z¸dªdedf„Z¹d«dgdh„Zºd¬didj„Z»ddkdl„Z¼d®dmdn„Z½dodp„Z¾dqdr„Z¿dsdt„ZÀeÀZÁdudv„ZÂd¯dwdx„ZÃd°dydz„ZÄd±d{d|„ZÅd²d}d~„ZÆd³dd€„ZÇd´dd‚„ZÈdƒd„„ZÉeÉZÊeÉZËeÉZÌd…d†„ZÍd‡dˆ„ZÎd‰dŠ„ZÏd‹dŒ„ZÐddŽ„ZÑdd„ZÒd‘d’„ZÓd“d”„ZÔd•d–„ZÕd—d˜„ZÖd™dš„Z×d›dœ„ZØddž„ZÙdŸd „ZÚd¡d¢„ZÛd£d¤„ZÜd¥d¦„ZÝd§d¨„ZÞd©dª„Zßd«d¬„Zàdd®„Zád¯d°„Zâd±d²„Zãd³d´„Zädµd¶„Zåd·d¸„Zæd¹dº„Zçd»d¼„Zèd½d¾„Zéd¿dÀ„ZêdÁdÂ„ZëdÃdÄ„ZìdÅdÆ„ZídÇdÈ„ZîdÉdÊ„ZïdËdÌ„ZðdÍdÎ„ZñdµdÏdÐ„Zòd¶dÑdÒ„Zód·dÓdÔ„ZôdÕdÖ„Zõd×dØ„ZödÙdÚ„Z÷dÛdÜ„ZødÝdÞ„Zùdßdà„Zúdádâ„Zûdãdä„Züdådæ„Zýdçdè„Zþdédê„Zÿdëdì„Zdídî„Zd¸dïdð„Zdñdò„Zdódô„Zdõdö„Zd÷dø„Zdùdú„Zdûdü„Zdýdþ„Z dÿd„Z dd„Zdd„Zdd„Z dd„Zd d „Zdd„ZeZd d„Zdd„Zdd„Zdd„Zdd„Zdd„Zdd„Zdd„Zdd„Zdd „Zd!d"„Zd#d$„Zd%d&„Zd'd(„Zd)d*„Z d+d,„Z!d-d.„Z"d/d0„Z#d1d2„Z$d3d4„Z%d5d6„Z&d7d8„Z'd9d:„Z(d;d<„Z)d¹d=d>„Z*dºd?d@„Z+d»dAdB„Z,d¼dCdD„Z-d½dEdF„Z.d¾dGdH„Z/dIdJ„Z0dKdL„Z1dMdN„Z2dOdP„Z3dQdR„Z4dSdT„Z5dUdV„Z6‡fdWdX„Z7‡Z8S(¿ÚLatexPrinterZ_latexFNÚabbreviatedú[ÚplainTÚiÚperiod)Ú full_precÚfold_frac_powersÚfold_func_bracketsÚfold_short_fracÚinv_trig_styleÚitexÚln_notationÚlong_frac_ratioÚ mat_delimÚmat_strÚmodeÚ mul_symbolÚorderÚsymbol_namesÚ root_notationÚmat_symbol_styleÚimaginary_unitÚgothic_re_imÚdecimal_separatorÚperm_cyclicÚparenthesize_superÚminÚmaxcCsjt ||¡d|jvr4gd¢}|jd|vr4tdƒ‚|jddurZ|jddkrZd|jd<ddd d dœ}z||jd|jd <Wn"ty¢|jd|jd <Yn0z||jdp´d|jd<WnFty|jd ¡dvrò|d|jd<n|jd|jd<Yn0dddœ|_ddddddddœ}z||jd|jd<Wn$tyd|jd|jd<Yn0dS)Nrƒ)ÚinlinervZequationz equation*zB'mode' must be one of 'inline', 'plain', 'equation' or 'equation*'r|rTú z \,.\, z \cdot ú \times )NZldotraÚtimesr„Úmul_symbol_latexraÚmul_symbol_latex_numbers)Úr‘rmz\,z\:ú\;z\quadú)ú])ú(rurwz \mathrm{i}z\text{i}Újz \mathrm{j}z\text{j})NrwÚriZtir›ZrjZtjr‰Zimaginary_unit_latex)rÚ__init__Ú _settingsÚ ValueErrorÚKeyErrorÚstripÚ_delim_dict)ÚselfÚsettingsZvalid_modesZmul_symbol_tableZimaginary_unit_tablerWrWrZr¦s\ ÿ üÿÿÿÿÿ ÿù ÿÿzLatexPrinter.__init__cCs d |¡S)Nz\left({}\right)©Úformat©r£rYrWrWrZÚ_add_parensÞszLatexPrinter._add_parenscCs d |¡S)Nz\left( {}\right)r¥r§rWrWrZÚ_add_parens_lspaceâszLatexPrinter._add_parens_lspacecCsRt|ƒ}|r |r | | |¡¡S||ks4|sD||krD| | |¡¡S| |¡SdS©N)rr¨Ú_print)r£ÚitemÚlevelÚis_negÚstrictZprec_valrWrWrZÚparenthesizeåszLatexPrinter.parenthesizecCs*d|vr&|jdr| |¡Sd |¡S|S)z” Protect superscripts in s If the parenthesize_super option is set, protect with parentheses, else wrap in braces. rorz{{{}}})ržr¨r¦r§rWrWrZrïs zLatexPrinter.parenthesize_supercCsbt ||¡}|jddkr|S|jddkr4d|S|jdrFd|S|jd}d|||fSdS)Nrƒrvrz$%s$r~z$$%s$$z\begin{%s}%s\end{%s})rÚdoprintrž)r£ÚexprÚtexZenv_strrWrWrZr±ýs zLatexPrinter.doprintcCs(|jr|jp$|jo$|tjuo$|jduS)zÁ Returns True if the expression needs to be wrapped in brackets when printed, False otherwise. For example: a + b => True; a => False; 10 => False; -10 => True. F)Z is_IntegerZis_nonnegativeÚis_Atomr ÚNegativeOneÚis_Rational©r£r²rWrWrZÚ_needs_brackets sþzLatexPrinter._needs_bracketscCsN| |¡sdS|jr"| |¡s"dS|jr6| |¡s6dS|jsB|jrFdSdSdS)aˆ Returns True if the expression needs to be wrapped in brackets when passed as an argument to a function, False otherwise. This is a more liberal version of _needs_brackets, in that many expressions which need to be wrapped in brackets when added/subtracted/raised to a power do not need them when passed to a function. Such an example is a*b. FTN)r¸Úis_MulÚ _mul_is_cleanZis_PowÚ _pow_is_cleanÚis_AddÚis_Functionr·rWrWrZÚ_needs_function_bracketss z%LatexPrinter._needs_function_bracketscs¨ddlm}ddlm}ddlm}ˆjr<|sZˆ ¡rZdSntˆƒt dkrPdSˆj rZdSˆjrddSt‡fdd„t fDƒƒr€dS|s¤t‡fd d„|||fDƒƒr¤dSd S)aÇ Returns True if the expression needs to be wrapped in brackets when printed as part of a Mul, False otherwise. This is True for Add, but also for some container objects that would not need brackets when appearing last in a Mul, e.g. an Integral. ``last=True`` specifies that this expr is the last to appear in a Mul. ``first=True`` specifies that this expr is the first to appear in a Mul. r)ÚProduct)ÚSum)ÚIntegralTrc3s|]}ˆ |¡VqdSrª©Zhas©Ú.0Úx©r²rWrZÚ Br\z3LatexPrinter._needs_mul_brackets..c3s|]}ˆ |¡VqdSrªrÂrÃrÆrWrZrÇEr\F)Zsympy.concrete.productsr¿Zsympy.concrete.summationsrÀZsympy.integrals.integralsrÁr¹Úcould_extract_minus_signrrÚ is_RelationalZis_PiecewiseÚanyr)r£r²ÚfirstÚlastr¿rÀrÁrWrÆrZÚ_needs_mul_brackets+s& ÿz LatexPrinter._needs_mul_bracketscs4ˆjr dSt‡fdd„tfDƒƒr&dSˆjr0dSdS)z± Returns True if the expression needs to be wrapped in brackets when printed as part of an Add, False otherwise. This is False for most things. Tc3s|]}ˆ |¡VqdSrªrÂrÃrÆrWrZrÇRr\z3LatexPrinter._needs_add_brackets..F)rÉrÊrr¼r·rWrÆrZÚ_needs_add_bracketsJsz LatexPrinter._needs_add_bracketscCs|jD]}|jrdSqdS)NFT)Úargsr½)r£r²r+rWrWrZrºXs zLatexPrinter._mul_is_cleancCs| |j¡Srª)r¸Úbaser·rWrWrZr»^szLatexPrinter._pow_is_cleancCs|durd||fS|SdS)Nú\left(%s\right)^{%s}rW©r£r²ÚexprWrWrZÚ_do_exponentaszLatexPrinter._do_exponentcsLˆ |jj¡}|jr>‡fdd„|jDƒ}d}| |d |¡¡Sd |¡SdS)Ncsg|]}ˆ |¡‘qSrW©r«)rÄr6©r£rWrZÚ jr\z-LatexPrinter._print_Basic..z"\operatorname{{{}}}\left({}\right)ú, z\text{{{}}})Ú_deal_with_super_subÚ __class__Ú__name__rÏr¦Újoin)r£r²ÚnameZlsrYrWrÖrZÚ_print_BasicgszLatexPrinter._print_BasiccCsd|S©Nú \text{%s}rW©r£ÚerWrWrZÚ_print_boolpszLatexPrinter._print_boolcCsd|SrßrWrárWrWrZÚ_print_NoneTypevszLatexPrinter._print_NoneTypecCsv|j||d}d}t|ƒD]V\}}|dkr,n | ¡rD|d7}|}n|d7}| |¡}| |¡rhd|}||7}q|S)N)r…r–rú - ú + ú\left(%s\right))Z_as_ordered_termsÚ enumeraterÈr«rÎ)r£r²r…Útermsr³rwÚtermÚterm_texrWrWrZÚ _print_Addys zLatexPrinter._print_AddcCsŽddlm}|jdkrdS||ƒ}|j}|j}|jd|dkrP||dgg}d}|D]}|t|ƒ dd¡7}qX| d d ¡}| dd¡}|S) Nr©ÚPermutationú\left( \right)éÿÿÿÿér–ú,r—ruz\left( r™ú\right))Ú sympy.combinatorics.permutationsrîÚsizeZcyclic_formÚ array_formÚstrrp)r£r²rîZ expr_permZsizrërwrWrWrZÚ_print_CycleŒs zLatexPrinter._print_Cyclec sÂddlm}ddlm}|j}|dur@|d|›ddddd nˆj d d¡}|r\ˆ |¡S|jdkrjdS‡fd d„|j Dƒ}‡fdd„t t|ƒƒDƒ}d |¡}d |¡}d ||f¡} d| S)Nrrí)Úsympy_deprecation_warningzw Setting Permutation.print_cyclic is deprecated. Instead use init_printing(perm_cyclic=z). z1.6z#deprecated-permutation-print_cyclicé)Zdeprecated_since_versionZactive_deprecations_targetÚ stacklevelrŒTrïcsg|]}ˆ |¡‘qSrWrÕ©rÄr+rÖrWrZr×´r\z3LatexPrinter._print_Permutation..csg|]}ˆ |¡‘qSrWrÕrürÖrWrZr×µr\ú & z \\ z \begin{pmatrix} %s \end{pmatrix}) rôrîZsympy.utilities.exceptionsrùZprint_cyclicržÚgetrørõröÚrangeÚlenrÜ) r£r²rîrùrŒÚlowerÚupperZrow1Zrow2ÚmatrWrÖrZÚ_print_Permutationœs.þù zLatexPrinter._print_PermutationcCs"|j\}}d| |¡| |¡fS)Nz\sigma_{%s}(%s))rÏr«)r£r²ÚpermÚvarrWrWrZÚ_print_AppliedPermutation½s z&LatexPrinter._print_AppliedPermutationc Csút|jƒ}|jdrdnd}d|jvr0|jdnd}d|jvrH|jdnd}t|j||||d}|jd}d|vrÀ| d¡\}} | d d kr˜| dd…} |jdd kr²| dd¡}d||| fS|dkrÌdS|dkrØdS|jdd krò| dd¡}|SdS)NryFTrŽr)Zstrip_zerosZ min_fixedZ max_fixedr•rârú+rñr‹ÚcommaÚ.z{,}z%s%s10^{%s}z+infz\inftyz-infz- \infty)rZ_precržÚmlib_to_strZ_mpf_Úsplitrp) r£r²Zdpsr¡ÚlowÚhighZstr_realÚ separatorZmantrÓrWrWrZÚ_print_FloatÁs( zLatexPrinter._print_FloatcCs0|j}|j}d| |td¡| |td¡fS)Nz%s \times %sr©Z_expr1Z_expr2r°r©r£r²Zvec1Zvec2rWrWrZÚ_print_Crossßs ÿzLatexPrinter._print_CrosscCs|j}d| |td¡S)Nz\nabla\times %sr©Z_exprr°r©r£r²rfrWrWrZÚ_print_CurlåszLatexPrinter._print_CurlcCs|j}d| |td¡S)Nz\nabla\cdot %srrrrWrWrZÚ_print_DivergenceészLatexPrinter._print_DivergencecCs0|j}|j}d| |td¡| |td¡fS)Nz%s \cdot %srrrrWrWrZÚ _print_Dotís ÿzLatexPrinter._print_DotcCs|j}d| |td¡S)Nz \nabla %srr©r£r²ÚfuncrWrWrZÚ_print_GradientószLatexPrinter._print_GradientcCs|j}d| |td¡S)Nz\triangle %srrrrWrWrZÚ_print_Laplacian÷szLatexPrinter._print_Laplaciancs¼ddlm‰ddlm}ˆjd‰ˆjd‰‡‡‡fdd„}‡‡‡fdd „‰t|tƒrŒ|j}|dtj us„t d d„|dd…DƒƒrŒˆ|ƒSd }| ¡r¶|}d}|jrº|d7}d}nd}||dd\}}|tj urøt ddd d|jvrø|||ƒ7}n²||ƒ} ||ƒ} t| ¡ƒ}ˆjd}ˆjdrt|dkrtd| vrtˆj|d dr`|d| | f7}n|d| | f7}n6|duršt| ¡ƒ||kršˆj|ddr¸|d| ˆ| f7}nà|jr†tj } tj }|jD]f}ˆj|d ds$t|| |ƒ ¡ƒ||ks$|j|jur d ur.nn ||9}n| |9} qÒˆj|ddrh|d|| ƒ| ˆ||ƒf7}n|d|| ƒ| ˆ||ƒf7}n|d| ˆ| f7}n|d | | f7}|r¸|d!7}|S)"Nr©ÚQuantity)Úfractionr”r•csR|jstˆ |¡ƒSˆjdvr(| ¡}n t|jƒ}t|‡fdd„d}ˆ|ƒSdS)N)ÚoldÚnonecs t|ˆƒpt|tƒot|jˆƒSrª)Ú isinstancerrÐ©rÅrrWrZr[s z:LatexPrinter._print_Mul..convert..©Úkey)r¹r÷r«r…Úas_ordered_factorsÚlistrÏÚsorted)r²rÏ)rÚconvert_argsr£rWrZÚconverts z(LatexPrinter._print_Mul..convertcs’d}}t|ƒD]|\}}ˆ |¡}ˆj||dk|t|ƒdkdrJd|}td |¡rttd t|ƒ¡rt|ˆ7}n|r€|ˆ7}||7}|}q|S)Nr–rrñ)rËrÌrç)rèr«rÍrÚ_between_two_numbers_pÚsearchÚmatchr÷)rÏZ_texZ last_term_texrwrêrë)Ú numbersepr£rrWrZr)s ÿÿ z-LatexPrinter._print_Mul..convert_argscss|]}t|tƒVqdSrª)r"rrürWrWrZrÇ-r\z*LatexPrinter._print_Mul..rñFú- ršTr–)Úexactrð)Úevaluater€r|éro)rÌz\left(%s\right) / %sz%s / %sz\frac{1}{%s}%s\left(%s\right)z\frac{%s}{%s}%s\left(%s\right)z\frac{%s}{%s}%s%sz\frac{1}{%s}%s%sú \frac{%s}{%s}r˜)Zsympy.physics.unitsrZsympy.simplifyrržr"rrÏr ÚOnerÊrÈr¼rrrrÍr¹Úis_commutative)r£r²rr*rÏZinclude_parensr³ÚnumerÚdenomZsnumerZsdenomZldenomZratioÚaÚbrÅrW)rr)r.r£rrZÚ _print_Mulûs~ ( ÿ ÿÿ ÿþ þ ÿÿzLatexPrinter._print_MulcCs*|jr| | ¡ ¡¡S| | ¡¡SdSrª)Z is_aliasedr«Zas_polyZas_exprr·rWrWrZÚ_print_AlgebraicNumbermsz#LatexPrinter._print_AlgebraicNumbercCsø|jjrt|jjƒdkr|jjdkr|jdr| |j¡}|jj}|dkrTd|}n$|jdrld||f}nd||f}|jjrˆd|S|Snd|jd r|jjr|jjdkr| |jt d ¡}|jj|jj}}|jjrê| |¡}|jj r|j|jd||fdSd |||fS|jjrÂ|jjrÂ|jjrÂ|jdkrTd|j|jfS|jjr¸|jj|jjt|jjƒkr¸|jdkrœd|jj|jjfSd|jj|jjt|jƒfS| |¡S|jj rä|j|j| |j¡dSd}| ||¡SdS)Nrñr‡r2z \sqrt{%s}r~z \root{%d}{%s}z \sqrt[%d]{%s}z\frac{1}{%s}rzrz%s/%s©rÓz %s^{%s/%s}ú%s^{%s}rðz\frac{1}{\frac{%s}{%s}}z\frac{1}{(\frac{%s}{%s})^{%s}})rÓr¶rlÚpÚqržr«rÐZis_negativer°rÚ is_Symbolrr½r5r:Ú_helper_print_standard_power)r£r²rÐZexpqr³r>r?rWrWrZÚ _print_PowssR$ÿ ÿ þ ÿ ÿ zLatexPrinter._print_PowcCsv| |j¡}| |jtd¡}|jjr2| |¡}n8t|jtƒrj| d¡rjt d|¡rj| d¡rj|dd…}|||fS)Nrú\left(z\\left\(\\d?d?dotróéiùÿÿÿ) r«rÓr°rÐrr@rr"rÚ startswithr(r-Úendswith)r£r²ÚtemplaterÓrÐrWrWrZrA¥sÿ þýz)LatexPrinter._helper_print_standard_powercCs| |jd¡S©Nr©r«rÏr·rWrWrZÚ_print_UnevaluatedExpr´sz#LatexPrinter._print_UnevaluatedExprcs’t|jƒdkr0dt‡fdd„|jdDƒƒ}n,‡fdd„‰dt d ‡fd d„|jDƒ¡}t|jtƒr~|dˆ |j¡7}n|ˆ |j¡7}|S)Nrñz\sum_{%s=%s}^{%s} csg|]}ˆ |¡‘qSrWrÕ©rÄrwrÖrWrZr×ºr\z+LatexPrinter._print_Sum..rcs,dt‡fdd„|d|d|dfDƒƒS)Nú%s \leq %s \leq %scsg|]}ˆ |¡‘qSrWrÕ©rÄrYrÖrWrZr×¾r\zALatexPrinter._print_Sum.._format_ineq..rñrr2©Útuple©ÚlrÖrWrZÚ_format_ineq¼s&ÿz-LatexPrinter._print_Sum.._format_ineqz\sum_{\substack{%s}} ú\\csg|]}ˆ|ƒ‘qSrWrW©rÄrQ©rRrWrZr×Ár\rç© rÚlimitsrOr÷rÜr"Úfunctionrr«©r£r²r³rW©rRr£rZÚ _print_Sum·sÿÿzLatexPrinter._print_Sumcs’t|jƒdkr0dt‡fdd„|jdDƒƒ}n,‡fdd„‰dt d ‡fd d„|jDƒ¡}t|jtƒr~|dˆ |j¡7}n|ˆ |j¡7}|S)Nrñz\prod_{%s=%s}^{%s} csg|]}ˆ |¡‘qSrWrÕrKrÖrWrZr×Ír\z/LatexPrinter._print_Product..rcs,dt‡fdd„|d|d|dfDƒƒS)NrLcsg|]}ˆ |¡‘qSrWrÕrMrÖrWrZr×Ñr\zELatexPrinter._print_Product.._format_ineq..rñrr2rNrPrÖrWrZrRÏs&ÿz1LatexPrinter._print_Product.._format_ineqz\prod_{\substack{%s}} rScsg|]}ˆ|ƒ‘qSrWrWrTrUrWrZr×Ôr\rçrVrYrWrZrZÚ_print_ProductÊsÿÿzLatexPrinter._print_ProductcCsddlm}g}||jkr"|jjSt||ƒr:| ¡ ¡}n d|fg}|D]Ž\}}t|j ¡ƒ}|j dd„d|D]b\}} | dkr”| d|j¡qr| dkr®| d |j¡qrd | | ¡d} | d| |j¡qrqHd |¡}|dd krü|dd…}n|dd…}|S)Nr)ÚVectorcSs|d ¡SrH)Ú__str__r#rWrWrZr[êr\z4LatexPrinter._print_BasisDependent..r$rñrærðråršr˜r–ú-é) Zsympy.vectorr]ZzeroZ_latex_formr"ZseparateÚitemsr'Ú componentsÚsortÚappendr«rÜ)r£r²r]Zo1raÚsystemZvectZ inneritemsÚkÚvZarg_strZoutstrrWrWrZÚ_print_BasisDependentÝs, z"LatexPrinter._print_BasisDependentcCs4| |j¡}d|ddd t|j|jƒ¡}|S)Nr^rVú_{%s}rò)r«rÐrÜÚmapÚindices)r£r²Ztex_baser³rWrWrZÚ_print_Indexedûs ÿzLatexPrinter._print_IndexedcCs| |j¡Srª)r«Úlabelr·rWrWrZÚ_print_IndexedBaseszLatexPrinter._print_IndexedBasecCsf| |j¡}|jdurb| |j¡}|jdur:| |j¡}n| tj¡}dj||d}dj||dS|S)Nz${lower}\mathrel{{..}}\nobreak{upper})rrz{{{label}}}_{{{interval}}})rmÚinterval)r«rmrrr ÚZeror¦)r£r²rmrrrorWrWrZÚ _print_Idxs ÿÿzLatexPrinter._print_Idxc Csút|jƒrd}nd}d}d}t|jƒD]T\}}||7}|dkrV|d|| |¡f7}q&|d|| | |¡¡| |¡f7}q&|dkr’d||f}nd || |¡|f}td d„|jDƒƒrÚd||j|jt dd d dfSd||j|jt ddd dfS)Nz\partialÚdr–rrñú%s %sz %s %s^{%s}r3z\frac{%s^{%s}}{%s}css|]}| ¡VqdSrª©rÈrKrWrWrZrÇ)r\z1LatexPrinter._print_Derivative..rT©r®r¯F) rr²ÚreversedZvariable_countr«rrÊrÏr°r)r£r²Zdiff_symbolr³ÚdimrÅÚnumrWrWrZÚ_print_Derivatives6 þ ý ýzLatexPrinter._print_Derivativec s`|j\}}}ˆ |¡}‡fdd„|Dƒ}‡fdd„|Dƒ}d dd„t||ƒDƒ¡}d||fS)Nc3s|]}ˆ |¡VqdSrªrÕ©rÄrârÖrWrZrÇ7r\z+LatexPrinter._print_Subs..c3s|]}ˆ |¡VqdSrªrÕrzrÖrWrZrÇ8r\z\\ css"|]}|dd|dVqdS)rú=rñNrWrzrWrWrZrÇ9sz#\left. %s \right|_{\substack{ %s }})rÏr«rÜÚzip) r£Úsubsr²r ÚnewZ latex_exprZ latex_oldZ latex_newZ latex_subsrWrÖrZÚ_print_Subs4s ÿÿzLatexPrinter._print_SubscsHdg}}t|jƒdkr\tdd„|jDƒƒr\ddt|jƒdd}‡fd d „|jDƒ}n´t|jƒD]¨}|d}|d7}t|ƒdkrøˆjd dkr¦ˆjds¦|d7}t|ƒdkrÖ|dˆ |d¡ˆ |d¡f7}t|ƒdkrø|dˆ |d¡7}| ddˆ |¡¡qfd|ˆj|jt dt dd„|jDƒƒddd |¡fS)Nr–écss|]}t|ƒdkVqdS)rñN)r)rÄÚlimrWrWrZrÇBr\z/LatexPrinter._print_Integral..z\irwrñÚntcsg|]}dˆ |d¡‘qS)ú\, d%srrÕ©rÄÚsymbolrÖrWrZr×Fsÿz0LatexPrinter._print_Integral..rz\intrƒrr~z\limitsr`z _{%s}^{%s}r2ú^{%s}rƒz%s %s%srcss|]}| ¡VqdSrªrtrKrWrWrZrÇ]r\Tru) rrWÚallrvržr«Úinsertr°rXrrÊrÏrÜ)r£r²r³Úsymbolsrr…rWrÖrZÚ_print_Integral>s8 " ÿÿÿýüzLatexPrinter._print_IntegralcCsš|j\}}}}d| |¡}t|ƒdks8|tjtjfvrL|d| |¡7}n|d| |¡| |¡f7}t|tƒr„d|| |¡fSd|| |¡fSdS)Nz \lim_{%s \to z+-z%s}z%s^%s}ú%s\left(%s\right)rs)rÏr«r÷r ÚInfinityÚNegativeInfinityr"r)r£r²râÚzZz0Údirr³rWrWrZÚ_print_Limitas zLatexPrinter._print_LimitcCsD| |¡}|tvrd|}n$t|ƒdks2| d¡r8|}nd|}|S)aJ Logic to decide how to render a function to latex - if it is a recognized latex name, use the appropriate latex command - if it is a single letter, just use that letter - if it is a longer name, then put \operatorname{} around it and be mindful of undercores in the name z\%srñrmz\operatorname{%s})rÙÚaccepted_latex_functionsrrE)r£rrÝrWrWrZÚ_hprint_Functionos zLatexPrinter._hprint_Functioncsš|jj}tˆd|ƒr4t|tƒs4tˆd|ƒ||ƒS‡fdd„|jDƒ}ˆjd}d}ˆjdo|t|ƒdko|ˆ |jd¡}gd ¢}||vræ|d kr˜nN|dkrÂ|dd kr°dnd|dd…}n$|dkræ|dd…}d}|duræd}|r |t vrd|} nd|} n6|dur6ˆ |¡} ˆ | ¡} d| |f} n ˆ |¡} |rd|t vrZ| d7} n| d7} n| d7} |rˆ|durˆ| d|7} | d |¡SdS)a# Render functions to LaTeX, handling functions that LaTeX knows about e.g., sin, cos, ... by using the proper LaTeX command (\sin, \cos, ...). For single-letter function names, render them as regular LaTeX math symbols. For multi-letter function names that LaTeX does not know about, (e.g., Li, sech) use \operatorname{} so that the function name is rendered in Roman font and LaTeX handles spacing properly. expr is the expression involving the function exp is an exponent Z_print_csg|]}tˆ |¡ƒ‘qSrW)r÷r«rürÖrWrZr×‘r\z0LatexPrinter._print_Function..r}Fr{rñr)ÚasinÚacosÚatanZacscZasecZacotÚasinhÚacoshÚatanhZacschZasechZacothrtÚfullrðÚhÚarZarcNÚpowerTz\%s^{-1}z\operatorname{%s}^{-1}r=z {%s}ú%sú{\left(%s \right)}r†rò)rrÛÚhasattrr"r ÚgetattrrÏržrr¾r‘r’rrÜ)r£r²rÓrrÏr}Zinv_trig_power_caseZcan_fold_bracketsZinv_trig_tablerÝZfunc_texrWrÖrZÚ_print_Function€sRÿ ÿþ" zLatexPrinter._print_FunctioncCs| t|ƒ¡Srª)r’r÷r·rWrWrZÚ_print_UndefinedFunctionÌsz%LatexPrinter._print_UndefinedFunctioncCsd| |j¡| |j¡fS)Nz{%s}_{\circ}\left({%s}\right))r«rXr²r·rWrWrZÚ_print_ElementwiseApplyFunctionÏs þz,LatexPrinter._print_ElementwiseApplyFunctioncCs\ddlm}ddlm}m}ddlm}ddlm}ddl m }|d|d|d |d |d|diS)Nr)ÚKroneckerDelta)ÚgammaÚ lowergamma)Úbeta)Ú DiracDelta)rQz\deltar.z\gammaz\operatorname{B}z\operatorname{Chi})Z(sympy.functions.special.tensor_functionsr¤Z'sympy.functions.special.gamma_functionsr¥r¦Z&sympy.functions.special.beta_functionsr§Z'sympy.functions.special.delta_functionsr¨Z'sympy.functions.special.error_functionsrQ)r£r¤r¥r¦r§r¨rQrWrWrZÚ_special_function_classesÕsûz&LatexPrinter._special_function_classescCs>|jD](}t||ƒr|j|jkr|j|Sq| t|ƒ¡Srª)r©Ú issubclassrÛr’r÷)r£r²ÚclsrWrWrZÚ_print_FunctionClassãs z!LatexPrinter._print_FunctionClasscCsJ|j\}}t|ƒdkr&| |d¡}n| t|ƒ¡}d|| |¡f}|S)Nrñrz\left( %s \mapsto %s \right))rÏrr«rO)r£r²r‰r³rWrWrZÚ _print_Lambdaés zLatexPrinter._print_LambdacCsdS)Nz\left( x \mapsto x \right)rWr·rWrWrZÚ_print_IdentityFunctionõsz$LatexPrinter._print_IdentityFunctioncsXt|jtd}‡fdd„|Dƒ}dt|jƒ ¡d |¡f}|durPd||fS|SdS)Nr$csg|]}dˆ |¡‘qS)rrÕr„rÖrWrZr×úr\z:LatexPrinter._hprint_variadic_function..z\%s\left(%s\right)rØr=)r(rÏrr÷rrrÜ)r£r²rÓrÏZtexargsr³rWrÖrZÚ_hprint_variadic_functionøsÿz&LatexPrinter._hprint_variadic_functioncCs0d| |jd¡}|dur(d||fS|SdS)Nz\left\lfloor{%s}\right\rfloorrr=rI©r£r²rÓr³rWrWrZÚ_print_floorszLatexPrinter._print_floorcCs0d| |jd¡}|dur(d||fS|SdS)Nz\left\lceil{%s}\right\rceilrr=rIr°rWrWrZÚ_print_ceilingszLatexPrinter._print_ceilingcCsP|jds d| |jd¡}nd| |jd¡}|durHd||fS|SdS)Nrz\log{\left(%s \right)}rz\ln{\left(%s \right)}r=)ržr«rÏr°rWrWrZÚ _print_logs zLatexPrinter._print_logcCs0d| |jd¡}|dur(d||fS|SdS)Nz\left|{%s}\right|rr=rIr°rWrWrZÚ _print_AbsszLatexPrinter._print_AbscCsN|jdr&d| |jdtd¡}nd | |jdtd¡¡}| ||¡S)NrŠz\Re{%s}rÚAtomz\operatorname{{re}}{{{}}}©ržr°rÏrr¦rÔr°rWrWrZÚ _print_re(s zLatexPrinter._print_recCsN|jdr&d| |jdtd¡}nd | |jdtd¡¡}| ||¡S)NrŠz\Im{%s}rrµz\operatorname{{im}}{{{}}}r¶r°rWrWrZÚ _print_im0s zLatexPrinter._print_imcCsŒddlm}m}t|jd|ƒr2| |jdd¡St|jd|ƒrT| |jdd¡S|jdjrtd| |jd¡Sd| |jd¡SdS)Nr)Ú EquivalentÚImpliesz\not\Leftrightarrowz\not\Rightarrowz\neg \left(%s\right)z\neg %s) Úsympy.logic.boolalgr¹rºr"rÏÚ_print_EquivalentÚ_print_ImpliesÚ is_Booleanr«)r£râr¹rºrWrWrZÚ _print_Not8szLatexPrinter._print_NotcCs‚|d}|jr$|js$d| |¡}nd| |¡}|dd…D]>}|jrf|jsf|d|| |¡f7}q>|d|| |¡f7}q>|S)Nrrçrrñz %s \left(%s\right)z %s %s)r¾Zis_Notr«)r£rÏÚcharr+r³rWrWrZÚ_print_LogOpCszLatexPrinter._print_LogOpcCst|jtd}| |d¡S)Nr$z\wedge©r(rÏrrÁ©r£rârÏrWrWrZÚ _print_AndRszLatexPrinter._print_AndcCst|jtd}| |d¡S)Nr$z\veerÂrÃrWrWrZÚ _print_OrVszLatexPrinter._print_OrcCst|jtd}| |d¡S)Nr$z\veebarrÂrÃrWrWrZÚ _print_XorZszLatexPrinter._print_XorcCs| |j|pd¡S)Nz\Rightarrow)rÁrÏ)r£râÚaltcharrWrWrZr½^szLatexPrinter._print_ImpliescCst|jtd}| ||pd¡S)Nr$z\LeftrightarrowrÂ)r£rârÇrÏrWrWrZr¼aszLatexPrinter._print_EquivalentcCs0d| |jd¡}|dur(d||fS|SdS)Nz \overline{%s}rr=rIr°rWrWrZÚ_print_conjugateeszLatexPrinter._print_conjugatecCs>d}d| |jd¡}|dur.d|||fSd||fSdS)Nz\operatorname{polar\_lift}ržrú %s^{%s}%sú%s%srI)r£r²rÓrr+rWrWrZÚ_print_polar_liftms zLatexPrinter._print_polar_liftcCs d| |jd¡}| ||¡S)Nze^{%s}r)r«rÏrÔr°rWrWrZÚ_print_ExpBasevszLatexPrinter._print_ExpBasecCsdS)NrârWrÒrWrWrZÚ_print_Exp1|szLatexPrinter._print_Exp1cCs4d| |jd¡}|dur(d||fSd|SdS)NrçrzK^{%s}%szK%srIr°rWrWrZÚ_print_elliptic_kszLatexPrinter._print_elliptic_kcCsDd| |jd¡| |jd¡f}|dur8d||fSd|SdS)Nú\left(%s\middle| %s\right)rrñzF^{%s}%szF%srIr°rWrWrZÚ_print_elliptic_f†sÿzLatexPrinter._print_elliptic_fcCsht|jƒdkr4d| |jd¡| |jd¡f}nd| |jd¡}|dur\d||fSd|SdS)Nr2rÏrrñrçzE^{%s}%szE%s©rrÏr«r°rWrWrZÚ_print_elliptic_eŽsÿzLatexPrinter._print_elliptic_ecCs†t|jƒdkrBd| |jd¡| |jd¡| |jd¡f}n$d| |jd¡| |jd¡f}|durzd||fSd|SdS) Nr`z\left(%s; %s\middle| %s\right)rrñr2rÏz \Pi^{%s}%sz\Pi%srÑr°rWrWrZÚ_print_elliptic_pi™sÿÿÿzLatexPrinter._print_elliptic_picCsDd| |jd¡| |jd¡f}|dur8d||fSd|SdS)Nú\left(%s, %s\right)rrñz\operatorname{B}^{%s}%sz\operatorname{B}%srIr°rWrWrZÚ_print_beta¦sÿzLatexPrinter._print_betar-csf‡fdd„|jDƒ}d|d|df}|durJd||d|d||fSd ||d|d|fSdS) Ncsg|]}ˆ |¡‘qSrWrÕrürÖrWrZr×°r\z/LatexPrinter._print_betainc..rÔrrñz#\operatorname{%s}_{(%s, %s)}^{%s}%sr2r`z\operatorname{%s}_{(%s, %s)}%s)rÏ)r£r²rÓÚoperatorÚlargsr³rWrÖrZÚ_print_betainc¯s zLatexPrinter._print_betainccCs|j||ddS)Nr2)rÖ)rØrÒrWrWrZÚ_print_betainc_regularized¸sz'LatexPrinter._print_betainc_regularizedcCsDd| |jd¡| |jd¡f}|dur8d||fSd|SdS)NrÔrrñz \Gamma^{%s}%sz\Gamma%srIr°rWrWrZÚ_print_uppergamma»sÿzLatexPrinter._print_uppergammacCsDd| |jd¡| |jd¡f}|dur8d||fSd|SdS)NrÔrrñz \gamma^{%s}%sú\gamma%srIr°rWrWrZÚ_print_lowergammaÄsÿzLatexPrinter._print_lowergammacCsJd| |jd¡}|dur2d| |j¡||fSd| |j¡|fSdS©NrçrrÉrÊ)r«rÏrr°rWrWrZÚ_hprint_one_arg_funcÍsz!LatexPrinter._hprint_one_arg_funccCs4d| |jd¡}|dur(d||fSd|SdS)Nrçrz\operatorname{Chi}^{%s}%sz\operatorname{Chi}%srIr°rWrWrZÚ _print_Chi×szLatexPrinter._print_ChicCsJd| |jd¡}| |jd¡}|dur:d|||fSd||fSdS)Nrçrñrz\operatorname{E}_{%s}^{%s}%sz\operatorname{E}_{%s}%srI)r£r²rÓr³ÚnurWrWrZÚ _print_expintßs zLatexPrinter._print_expintcCs4d| |jd¡}|dur(d||fSd|SdS)NrçrzS^{%s}%szS%srIr°rWrWrZÚ_print_fresnelsèszLatexPrinter._print_fresnelscCs4d| |jd¡}|dur(d||fSd|SdS)NrçrzC^{%s}%szC%srIr°rWrWrZÚ_print_fresnelcðszLatexPrinter._print_fresnelccCs6d| |jdtd¡}|dur.d||fS|SdS)Nz!%srÚFuncrÑ©r°rÏrr°rWrWrZÚ_print_subfactorialøsz LatexPrinter._print_subfactorialcCs6d| |jdtd¡}|dur.d||fS|SdS)Nz%s!rrär=rår°rWrWrZÚ_print_factorialszLatexPrinter._print_factorialcCs6d| |jdtd¡}|dur.d||fS|SdS)Nz%s!!rrär=rår°rWrWrZÚ_print_factorial2szLatexPrinter._print_factorial2cCs@d| |jd¡| |jd¡f}|dur8d||fS|SdS)Nz{\binom{%s}{%s}}rrñr=rIr°rWrWrZÚ_print_binomialsÿzLatexPrinter._print_binomialcCs<|j\}}d| |td¡}d|| |¡f}| ||¡S)Nrräz{%s}^{\left(%s\right)}©rÏr°rr«rÔ)r£r²rÓÚnrfrÐr³rWrWrZÚ_print_RisingFactorials z#LatexPrinter._print_RisingFactorialcCs<|j\}}d| |td¡}d| |¡|f}| ||¡S)Nrräz{\left(%s\right)}_{%s}rê)r£r²rÓrërfÚsubr³rWrWrZÚ_print_FallingFactorial!s z$LatexPrinter._print_FallingFactorialcCsfd|}d}|dur4| d¡dkr0d||f}nd}d|| |j¡| |j¡f}|rb| ||¡}|S)NrFrorðr=Tú%s_{%s}\left(%s\right))Úfindr«r…ÚargumentrÔ)r£r²rÓÚsymr³Zneed_exprWrWrZÚ_hprint_BesselBase)s ÿzLatexPrinter._hprint_BesselBasecCsF|sdSd}|dd…D]}|d| |¡7}q|| |d¡7}|S)Nr–rðz%s, rÕ)r£rfrYrwrWrWrZÚ_hprint_vec:szLatexPrinter._hprint_veccCs| ||d¡S)NÚJ©rórÒrWrWrZÚ_print_besseljCszLatexPrinter._print_besseljcCs| ||d¡S)Nr2rörÒrWrWrZÚ_print_besseliFszLatexPrinter._print_besselicCs| ||d¡S)Nr3rörÒrWrWrZÚ_print_besselkIszLatexPrinter._print_besselkcCs| ||d¡S)NÚYrörÒrWrWrZÚ_print_besselyLszLatexPrinter._print_besselycCs| ||d¡S)NÚyrörÒrWrWrZÚ _print_ynOszLatexPrinter._print_yncCs| ||d¡S)Nr›rörÒrWrWrZÚ _print_jnRszLatexPrinter._print_jncCs| ||d¡S)NzH^{(1)}rörÒrWrWrZÚ_print_hankel1UszLatexPrinter._print_hankel1cCs| ||d¡S)NzH^{(2)}rörÒrWrWrZÚ_print_hankel2XszLatexPrinter._print_hankel2cCs| ||d¡S)Nzh^{(1)}rörÒrWrWrZÚ _print_hn1[szLatexPrinter._print_hn1cCs| ||d¡S)Nzh^{(2)}rörÒrWrWrZÚ _print_hn2^szLatexPrinter._print_hn2r–cCs:d| |jd¡}|dur*d|||fSd||fSdSrÝrI©r£r²rÓÚnotationr³rWrWrZÚ_hprint_airyaszLatexPrinter._hprint_airycCs:d| |jd¡}|dur*d|||fSd||fSdS)Nrçrz{%s^\prime}^{%s}%sz%s^\prime%srIrrWrWrZÚ_hprint_airy_primeiszLatexPrinter._hprint_airy_primecCs| ||d¡S©NZAi©rrÒrWrWrZÚ _print_airyaiqszLatexPrinter._print_airyaicCs| ||d¡S©NZBirrÒrWrWrZÚ _print_airybitszLatexPrinter._print_airybicCs| ||d¡Sr©rrÒrWrWrZÚ_print_airyaiprimewszLatexPrinter._print_airyaiprimecCs| ||d¡Sr rrÒrWrWrZÚ_print_airybiprimezszLatexPrinter._print_airybiprimecCsZd| t|jƒ¡| t|jƒ¡| |j¡| |j¡| |j¡f}|durVd||f}|S)NzN{{}_{%s}F_{%s}\left(\begin{matrix} %s \\ %s \end{matrix}\middle| {%s} \right)}ú {%s}^{%s})r«rÚapÚbqrôrñr°rWrWrZÚ_print_hyper}s þþzLatexPrinter._print_hypercCsŠd| t|jƒ¡| t|jƒ¡| t|jƒ¡| t|jƒ¡| |j¡| |j¡| |j¡| |j¡| |j ¡f }|dur†d||f}|S)Nz^{G_{%s, %s}^{%s, %s}\left(\begin{matrix} %s & %s \\%s & %s \end{matrix} \middle| {%s} \right)}r) r«rrrriÚanrôZaotherZbotherrñr°rWrWrZÚ_print_meijergˆs üþzLatexPrinter._print_meijergcCs0d| |jd¡}|dur(d||fSd|S)Nrçrz\eta^{%s}%sz\eta%srIr°rWrWrZÚ_print_dirichlet_eta•sz!LatexPrinter._print_dirichlet_etacCsVt|jƒdkr&dtt|j|jƒƒ}nd| |jd¡}|durNd||fSd|S)Nr2rÔrçrz\zeta^{%s}%sz\zeta%s©rrÏrOrjr«r°rWrWrZÚ_print_zeta›szLatexPrinter._print_zetacCsVt|jƒdkr&dtt|j|jƒƒ}nd| |jd¡}|durNd||fSd|S)Nr2z_{%s}\left(%s\right)rirz \gamma%s^{%s}rÛrr°rWrWrZÚ_print_stieltjes¤szLatexPrinter._print_stieltjescCs2dtt|j|jƒƒ}|dur&d|Sd||fS)Nz\left(%s, %s, %s\right)z\Phi%sz\Phi^{%s}%s)rOrjr«rÏr°rWrWrZÚ_print_lerchphiszLatexPrinter._print_lerchphicCs<t|j|jƒ\}}d|}|dur.d||fSd|||fS)Nrçz\operatorname{Li}_{%s}%sz\operatorname{Li}_{%s}^{%s}%s©rjr«rÏ)r£r²rÓrYrŽr³rWrWrZÚ_print_polylog³s zLatexPrinter._print_polylogcCsBt|j|jƒ\}}}}d||||f}|dur>d|d|}|S)Nz*P_{%s}^{\left(%s,%s\right)}\left(%s\right)rCú\right)^{%s}r)r£r²rÓrër8r9rÅr³rWrWrZÚ _print_jacobiºs zLatexPrinter._print_jacobicCs>t|j|jƒ\}}}d|||f}|dur:d|d|}|S)Nz'C_{%s}^{\left(%s\right)}\left(%s\right)rCrr©r£r²rÓrër8rÅr³rWrWrZÚ_print_gegenbauerÁs zLatexPrinter._print_gegenbauercCs:t|j|jƒ\}}d||f}|dur6d|d|}|S)NzT_{%s}\left(%s\right)rCrr©r£r²rÓrërÅr³rWrWrZÚ_print_chebyshevtÈs zLatexPrinter._print_chebyshevtcCs:t|j|jƒ\}}d||f}|dur6d|d|}|S)NzU_{%s}\left(%s\right)rCrrr rWrWrZÚ_print_chebyshevuÏs zLatexPrinter._print_chebyshevucCs:t|j|jƒ\}}d||f}|dur6d|d|}|S)NzP_{%s}\left(%s\right)rCrrr rWrWrZÚ_print_legendreÖs zLatexPrinter._print_legendrecCs>t|j|jƒ\}}}d|||f}|dur:d|d|}|S)Nz'P_{%s}^{\left(%s\right)}\left(%s\right)rCrrrrWrWrZÚ_print_assoc_legendreÝs z"LatexPrinter._print_assoc_legendrecCs:t|j|jƒ\}}d||f}|dur6d|d|}|S)NzH_{%s}\left(%s\right)rCrrr rWrWrZÚ_print_hermiteäs zLatexPrinter._print_hermitecCs:t|j|jƒ\}}d||f}|dur6d|d|}|S)NzL_{%s}\left(%s\right)rCrrr rWrWrZÚ_print_laguerreës zLatexPrinter._print_laguerrecCs>t|j|jƒ\}}}d|||f}|dur:d|d|}|S)Nz'L_{%s}^{\left(%s\right)}\left(%s\right)rCrrrrWrWrZÚ_print_assoc_laguerreòs z"LatexPrinter._print_assoc_laguerrecCsBt|j|jƒ\}}}}d||||f}|dur>d|d|}|S)NzY_{%s}^{%s}\left(%s,%s\right)rCrr©r£r²rÓrëÚmÚthetaÚphir³rWrWrZÚ _print_Ynmùs zLatexPrinter._print_YnmcCsBt|j|jƒ\}}}}d||||f}|dur>d|d|}|S)NzZ_{%s}^{%s}\left(%s,%s\right)rCrrr(rWrWrZÚ _print_Znms zLatexPrinter._print_Znmc CsBt|j|ƒ\}}}|rdnd}|s&dnd|}d||||||fS)Nz ^{\prime}r–r†z%s%s\left(%s, %s, %s\right)%s)rjr«) r£Ú characterrÏrgrÓr8r?rŽÚsuprWrWrZZ__print_mathieu_functionssz&LatexPrinter.__print_mathieu_functionscCs|jd|j|dS)NÚCr<©Ú&_LatexPrinter__print_mathieu_functionsrÏrÒrWrWrZÚ_print_mathieuc szLatexPrinter._print_mathieuccCs|jd|j|dS)Nr r<r1rÒrWrWrZÚ_print_mathieusszLatexPrinter._print_mathieuscCs|jd|jd|dS)Nr0T©rgrÓr1rÒrWrWrZÚ_print_mathieucprimesz!LatexPrinter._print_mathieucprimecCs|jd|jd|dS)Nr Tr5r1rÒrWrWrZÚ_print_mathieusprimesz!LatexPrinter._print_mathieusprimecCsb|jdkrRd}|j}|jdkr(d}|}|jdrBd|||jfSd|||jfS| |j¡SdS)Nrñr–rr/r|z %s%d / %dz%s\frac{%d}{%d})r?r>ržr«)r£r²Úsignr>rWrWrZÚ_print_Rationals zLatexPrinter._print_RationalcCsº| |j¡}|jr&tdd„|jDƒƒs4t|jƒdkr²|d7}t|jƒdkr\|| |j¡7}n|jrv|| |jd¡7}|d7}t|jƒdkrž|| |j¡7}n|| |jd¡7}d|S)Ncss|]}|tjkVqdSrª)r rp)rÄr>rWrWrZrÇ(r\z,LatexPrinter._print_Order..rñú; rz\rightarrow zO\left(%s\right))r«r²ZpointrÊrÚ variables©r£r²rYrWrWrZÚ_print_Order&sÿzLatexPrinter._print_OrdercCs,||jdvr|jd|S|j|j|dS)Nr†©Ústyle)ržrÙrÝ)r£r²r?rWrWrZÚ _print_Symbol6szLatexPrinter._print_SymbolcCsŽd|vr|gg}}}n2t|ƒ\}}}t|ƒ}dd„|Dƒ}dd„|Dƒ}|dkr^d |¡}|rt|dd |¡7}|rŠ|d d |¡7}|S) Nr^cSsg|]}t|ƒ‘qSrW©Ú translate©rÄr/rWrWrZr×Er\z5LatexPrinter._deal_with_super_sub..cSsg|]}t|ƒ‘qSrWrA©rÄrírWrWrZr×Fr\rhú \mathbf{{{}}}r†r‘ri)rrBr¦rÜ)r£Ústringr?rÝÚsupersr}rWrWrZrÙ>s z!LatexPrinter._deal_with_super_subcCsR|jdrd}d}nd}d}d||ddd d œ}d| |j¡||j| |j¡fS)Nr~z\gtz\ltú>ú=z<=z!=z%s %s %s)ržr«ÚlhsZrel_opÚrhs)r£r²ÚgtÚltÚcharmaprWrWrZÚ_print_RelationalTs ú ÿzLatexPrinter._print_RelationalcsŠ‡fdd„|jdd…Dƒ}|jdjtkrJ| dˆ |jdj¡¡n.| dˆ |jdj¡ˆ |jdj¡f¡d}|d |¡S)Ncs(g|] \}}dˆ |¡ˆ |¡f‘qS)ú%s & \text{for}\: %srÕ)rÄrârqrÖrWrZr×isÿz1LatexPrinter._print_Piecewise..rðz%s & \text{otherwise}rPz\begin{cases} %s \end{cases}z \\)rÏZcondrrdr«r²rÜ)r£r²Zecpairsr³rWrÖrZÚ_print_Piecewisehs ÿÿÿÿzLatexPrinter._print_Piecewisec sîg}t|jƒD].}| d ‡fdd„||dd…fDƒ¡¡qˆjd}|dur|ˆjddkrdd}n|jdkd urxd }nd}d}| d |¡}|dkr®| ddd|jd¡}ˆjdràˆjd}ˆj|}d||d|}|d |¡S)Nrýcsg|]}ˆ |¡‘qSrWrÕrKrÖrWrZr×yr\z2LatexPrinter._print_MatrixBase..r‚rƒrÚsmallmatrixé TÚmatrixÚarrayú \begin{%MATSTR%}%s\end{%MATSTR%}ú%MATSTR%rr^rqz}%srú\leftú\rightrS)rÿÚrowsrdrÜržÚcolsrpr¢)r£r²ÚlinesÚliner‚Úout_strÚ left_delimÚright_delimrWrÖrZÚ_print_MatrixBaseus., ÿÿzLatexPrinter._print_MatrixBasecCs2|j|jtdddd| |j¡| |j¡fS)NrµT©r¯z _{%s, %s})r°Úparentrr«rwr›r·rWrWrZÚ_print_MatrixElementsÿz!LatexPrinter._print_MatrixElementcsN‡fdd„}ˆj|jtdddd||j|jjƒd||j|jjƒdS) NcsZt|ƒ}|ddkr|d=|ddkr.d|d<|d|krBd|d<d ‡fdd„|Dƒ¡S)Nr2rñrú:c3s$|]}|durˆ |¡ndVqdS)Nr–rÕ)rÄÚxirÖrWrZrÇr\zFLatexPrinter._print_MatrixSlice..latexslice..)r'rÜ)rÅrwrÖrWrZÚ latexslice•sz3LatexPrinter._print_MatrixSlice..latexslicerµTrbú\left[rØú\right])r°rcrZrowslicerZZcolslicer[)r£r²rgrWrÖrZÚ_print_MatrixSlice”s ÿÿþþzLatexPrinter._print_MatrixSlicecCs| |j¡Srª)r«Úblocksr·rWrWrZÚ_print_BlockMatrix¢szLatexPrinter._print_BlockMatrixcCs^|j}ddlm}t||ƒs0|jr0d| |¡S| |t|ƒd¡}d|vrRd|Sd|SdS)Nr©ÚMatrixSymbolz\left(%s\right)^{T}Troz%s^{T}©r+Úsympy.matricesrnr"Z is_MatrixExprr«r°r©r£r²rrnrYrWrWrZÚ_print_Transpose¥szLatexPrinter._print_TransposecCs|j}d| |¡S)Nz!\operatorname{tr}\left(%s \right))r+r«©r£r²rrWrWrZÚ_print_Trace±szLatexPrinter._print_TracecCs^|j}ddlm}t||ƒs0|jr0d| |¡S| |t|ƒd¡}d|vrRd|Sd|SdS)Nrrmz\left(%s\right)^{\dagger}Troz%s^{\dagger}rorqrWrWrZÚ_print_AdjointµszLatexPrinter._print_Adjointcs¶ddlm}‡‡fdd„}ˆj}t|dtƒrL|d ¡t|dd…ƒ}nt|ƒ}tˆ|ƒr¢ˆ ¡r¢|ddkr€|dd…}n|d|d<dd t ||ƒ¡Sd t ||ƒ¡SdS) Nr)ÚMatMulcsˆ |tˆƒd¡S©NF©r°rr#©r²r£rWrZr[Äsÿz,LatexPrinter._print_MatMul..rñrðr/r‘) Z!sympy.matrices.expressions.matmulrvrÏr"rr&r'rÈrÜrj)r£r²rvÚparensrÏrWryrZÚ _print_MatMulÁszLatexPrinter._print_MatMulcCsz|durBd|j|jdtddd|j|jdtddd|fSd|j|jdtddd|j|jdtdddfS)Nz\left(%s \bmod %s\right)^{%s}rrTrbrñz%s \bmod %srårÒrWrWrZÚ _print_ModÖs(ÿÿüÿþþýzLatexPrinter._print_Modcs.|j}td‰|j‰d t‡‡fdd„|ƒ¡S)Nrz \circ csˆ|ˆddS©NTrbrW©r+©rzÚprecrWrZr[ër\z5LatexPrinter._print_HadamardProduct..©rÏrr°rÜrj©r£r²rÏrWrrZÚ_print_HadamardProductåsÿz#LatexPrinter._print_HadamardProductcCs(t|jƒtdkrd}nd}| ||¡S)Nrz%s^{\circ \left({%s}\right)}z%s^{\circ {%s}})rrÓrrA)r£r²rGrWrWrZÚ_print_HadamardPowerísz!LatexPrinter._print_HadamardPowercs.|j}td‰|j‰d t‡‡fdd„|ƒ¡S)Nrú \otimes csˆ|ˆddSr}rWr~rrWrZr[úr\z6LatexPrinter._print_KroneckerProduct..rr‚rWrrZÚ_print_KroneckerProductôsÿz$LatexPrinter._print_KroneckerProductcCsv|j|j}}ddlm}t||ƒs)r@ržr·rWrWrZÚ_print_MatrixSymbol s ÿz LatexPrinter._print_MatrixSymbolcCs|jddkrdSdS)NrˆrvÚ0z \mathbf{0}©rž)r£r0rWrWrZÚ_print_ZeroMatrix sÿÿÿzLatexPrinter._print_ZeroMatrixcCs|jddkrdSdS)NrˆrvÚ1z \mathbf{1}rŠ)r£r7rWrWrZÚ_print_OneMatrixsÿÿÿzLatexPrinter._print_OneMatrixcCs|jddkrdSdS)Nrˆrvz \mathbb{I}z \mathbf{I}rŠ)r£r2rWrWrZÚ_print_IdentitysÿÿÿzLatexPrinter._print_IdentitycCs| |jd¡}d|S)NrzP_{%s}rI)r£r8Zperm_strrWrWrZÚ_print_PermutationMatrixsz%LatexPrinter._print_PermutationMatrixc Cs| ¡dkr| |d¡S|jd}|durd|jddkr@d}n$| ¡dksZ|jddkr`d }nd }d}| d|¡}|jd r¦|jd }|j|}d||d|}| ¡dkrº|dSggdd„t| ¡ƒDƒ}dd„|jDƒ}tj|ŽD]ä}|d | ||¡¡d} t| ¡dddƒD]®} t || dƒ|j| krHqð| rl|| d || d¡¡nR|| |d || d¡¡t || dƒdkr¾d|| dd|| d<| } g|| d<q$qð|dd}| ¡ddkrü||}|S)NrrWr‚rƒrrRrðrSrTrUrVrWrrXrYr–cSsg|]}g‘qSrWrWrKrWrWrZr×6r\z1LatexPrinter._print_NDimArray..cSsg|]}tt|ƒƒ‘qSrW)r'rÿrKrWrWrZr×7r\TrñrýrSrhrir2)Úrankr«ržÚshaperpr¢rÿÚ itertoolsÚproductrdrrÜ)r£r²r‚Z block_strr_r`Z level_strZshape_rangesZouter_iZevenZback_outer_ir^rWrWrZÚ_print_NDimArrays` ÿÿÿÿ ÿÿzLatexPrinter._print_NDimArrayc CsÆ| |¡}d}d}|D]š}|j}||vs,|r<||kr<|d7}||krl|durT|d7}|jrd|d7}n|d7}|| |jd¡7}||vr¨|d7}|| ||¡7}d}nd}|}q|durÂ|d7}|S) NròrVz{}^{z{}_{rr{TF)r«Úis_uprÏ) r£rÝrkÚ index_mapr^Zlast_valenceZprev_mapÚindexZnew_valencerWrWrZÚ_printer_tensor_indicesQs2 ÿ z$LatexPrinter._printer_tensor_indicescCs$|jdjd}| ¡}| ||¡SrH)rÏÚget_indicesr˜)r£r²rÝrkrWrWrZÚ _print_TensormszLatexPrinter._print_TensorcCs0|jjdjd}|j ¡}|j}| |||¡SrH)r²rÏr™r–r˜)r£r²rÝrkr–rWrWrZÚ_print_TensorElementrs z!LatexPrinter._print_TensorElementcs*ˆ ¡\}}|d ‡‡fdd„|Dƒ¡S)Nr–csg|]}ˆ |tˆƒ¡‘qSrW)r°rrüryrWrZr×|r\z/LatexPrinter._print_TensMul..)Z!_get_args_for_traditional_printerrÜ)r£r²r8rÏrWryrZÚ_print_TensMulxsÿzLatexPrinter._print_TensMulcCsLg}|j}|D]}| | |t|ƒ¡¡q| ¡d |¡}| dd¡}|S)Nræz+ -r/)rÏrdr°rrcrÜrp)r£r²r8rÏrÅrYrWrWrZÚ_print_TensAdds zLatexPrinter._print_TensAddcCs"d|jrdnd| |jd¡fS)Nz{}%s{%s}roÚ_r)r•r«rÏr·rWrWrZÚ_print_TensorIndex‰sþzLatexPrinter._print_TensorIndexcstt|jƒdkr6dˆ |jd¡ˆ |jtdd¡fSdt|jƒd ‡fdd „|jDƒ¡ˆ |jtdd¡fSdS) Nrñz"\frac{\partial}{\partial {%s}}{%s}rrFz\frac{\partial^{%s}}{%s}{%s}r‘csg|]}dˆ |¡‘qS)z \partial {%s}rÕrKrÖrWrZr×˜r\z9LatexPrinter._print_PartialDerivative..)rr;r«r°r²rrÜr·rWrÖrZÚ_print_PartialDerivativesþýz%LatexPrinter._print_PartialDerivativecCs| |j¡Srª)r«rÝr·rWrWrZÚ_print_ArraySymbolœszLatexPrinter._print_ArraySymbolcs2dˆ |jtdd¡d ‡fdd„|jDƒ¡fS)Nz{{%s}_{%s}}räTrØcsg|]}ˆ |¡›‘qSrWrÕrKrÖrWrZr×¢r\z4LatexPrinter._print_ArrayElement..)r°rÝrrÜrkr·rWrÖrZÚ_print_ArrayElementŸsþz LatexPrinter._print_ArrayElementcCsdS)Nz \mathbb{U}rWr·rWrWrZÚ_print_UniversalSet¤sz LatexPrinter._print_UniversalSetcCs8|durd| |jd¡Sd| |jd¡|fSdS)Nz$\operatorname{frac}{\left(%s\right)}rz)\operatorname{frac}{\left(%s\right)}^{%s}rIrÒrWrWrZÚ_print_frac§s ÿzLatexPrinter._print_fraccszˆjddkrd}nˆjddkr(d}ntdƒ‚t|ƒdkrTˆ ˆ |d¡|¡Sˆ |d ‡fd d„|Dƒ¡¡SdS)Nr‹r ú;rxròúUnknown Decimal Separatorrñrz \ csg|]}ˆ |¡‘qSrWrÕrKrÖrWrZr×»r\z-LatexPrinter._print_tuple..)ržrŸrr©r«rÜ)r£r²ÚseprWrÖrZÚ_print_tuple®sÿzLatexPrinter._print_tuplecs‡fdd„|jDƒ}d |¡S)Ncsg|]}ˆ |¡‘qSrWrÕ©rÄr8rÖrWrZr×¾r\z5LatexPrinter._print_TensorProduct..r…©rÏrÜ©r£r²ÚelementsrWrÖrZÚ_print_TensorProduct½sz!LatexPrinter._print_TensorProductcs‡fdd„|jDƒ}d |¡S)Ncsg|]}ˆ |¡‘qSrWrÕr©rÖrWrZr×Âr\z4LatexPrinter._print_WedgeProduct..z \wedge rªr«rWrÖrZÚ_print_WedgeProductÁsz LatexPrinter._print_WedgeProductcCs | |¡Srª)r¨r·rWrWrZÚ_print_TupleÅszLatexPrinter._print_Tuplecs`ˆjddkr*dd ‡fdd„|Dƒ¡SˆjddkrTdd ‡fd d„|Dƒ¡Std ƒ‚dS)Nr‹r z\left[ %s\right]z; \ csg|]}ˆ |¡‘qSrWrÕrKrÖrWrZr×Ër\z,LatexPrinter._print_list..rxú, \ csg|]}ˆ |¡‘qSrWrÕrKrÖrWrZr×Îr\r¦)ržrÜrŸr·rWrÖrZÚ_print_listÈsÿÿzLatexPrinter._print_listcCsRt| ¡td}g}|D]*}||}| d| |¡| |¡f¡qdd |¡S)Nr$z%s : %sz\left\{ %s\right\}r°)r(Úkeysrrdr«rÜ)r£rrr²rar%ÚvalrWrWrZÚ_print_dictÓs zLatexPrinter._print_dictcCs | |¡Srª)r´r·rWrWrZÚ_print_DictÝszLatexPrinter._print_DictcCsjt|jƒdks|jddkr2d| |jd¡}n$d| |jd¡| |jd¡f}|rfd||f}|S)Nrñrz\delta\left(%s\right)z+\delta^{\left( %s \right)}\left( %s \right)rÑrÑr°rWrWrZÚ_print_DiracDeltaàsÿzLatexPrinter._print_DiracDeltacCsP| |jd|jd¡}| |jd¡}d||f}|durLd|||f}|S)Nrrñr2z${\left\langle %s \right\rangle}^{%s}z-{\left({\langle %s \rangle}^{%s}\right)}^{%s}rI)r£r²rÓÚshiftrœr³rWrWrZÚ_print_SingularityFunctionêsz'LatexPrinter._print_SingularityFunctioncs6d ‡fdd„|jDƒ¡}d|}|r2d||f}|S)NrØc3s|]}ˆ |¡VqdSrªrÕrürÖrWrZrÇór\z0LatexPrinter._print_Heaviside..z\theta\left(%s\right)rÑ)rÜÚpargs)r£r²rÓr¹r³rWrÖrZÚ_print_Heavisideòs zLatexPrinter._print_HeavisidecCsj| |jd¡}| |jd¡}|jdjrF|jdjrFd||f}nd||f}|durfd||f}|S)Nrrñz\delta_{%s %s}z\delta_{%s, %s}rÑ)r«rÏr´)r£r²rÓrwr›r³rWrWrZÚ_print_KroneckerDeltaùsz"LatexPrinter._print_KroneckerDeltacCsTt|j|jƒ}tdd„|jDƒƒr2dd |¡}ndd |¡}|rPd||f}|S)Ncss|]}|jVqdSrª)r´rÃrWrWrZrÇr\z1LatexPrinter._print_LeviCivita..z\varepsilon_{%s}r‘rØrÑ)rjr«rÏr‡rÜ)r£r²rÓrkr³rWrWrZÚ_print_LeviCivitaszLatexPrinter._print_LeviCivitacCsnt|dƒrd| | ¡¡St|dƒrFd| |j¡d| |j¡St|dƒr`d| |j¡S| d¡SdS)NÚ as_booleanz\text{Domain: }Úsetz \in r‰z\text{Domain on })rŸr«r½r‰r¾)r£rrrWrWrZÚ_print_RandomDomains ÿ z LatexPrinter._print_RandomDomaincCst|jtd}| |¡S)Nr$)r(rÏrÚ _print_set©r£rYrarWrWrZÚ_print_FiniteSetszLatexPrinter._print_FiniteSetcCs`t|td}|jddkr.d t|j|ƒ¡}n*|jddkrPd t|j|ƒ¡}ntdƒ‚d|S) Nr$r‹r r:rxrØr¦ú\left\{%s\right\})r(rržrÜrjr«rŸrÁrWrWrZrÀszLatexPrinter._print_setcs‡‡fdd„}tƒ‰ˆjjrLˆjjrLˆjjr<ˆdddˆf}qêˆdddˆf}nžˆjjrnˆˆdˆjˆdf}n|ˆjjr’tˆƒ}t|ƒt|ƒˆf}nXˆjduräˆj dkdkr´t ˆƒ}qêˆjrÜtˆƒ}t|ƒt|ƒˆˆdf}qê|ƒSn|ƒSdd ‡‡fd d„|Dƒ¡dS) Ncs¢ˆjddkrJˆjddkr.ˆ ˆjd¡}q–d ‡fdd„ˆjDƒ¡}nLˆjddkr|d ‡fdd„ˆjdd…Dƒ¡}nd ‡fdd„ˆjDƒ¡}d |›d S)Nrr2rñrØc3s|]}ˆ |¡VqdSrªrÕrürÖrWrZrÇ1r\zKLatexPrinter._print_Range.._print_symbolic_range..c3s|]}ˆ |¡VqdSrªrÕrürÖrWrZrÇ4r\c3s|]}ˆ |¡VqdSrªrÕrürÖrWrZrÇ6r\z\text{Range}\left(ró)rÏr«rÜ)Úcont)rYr£rWrZÚ_print_symbolic_range+s$z8LatexPrinter._print_Range.._print_symbolic_rangerðrrñr€Tz\left\{rØc3s$|]}|ˆurˆ |¡ndVqdS©z\ldotsNrÕ©rÄÚel©Údotsr£rWrZrÇQr\z,LatexPrinter._print_Range..z\right\}) ÚobjectÚstartÚis_infiniteÚstopÚstepZis_positiveÚiterÚnextZis_emptyrõrOÚis_iterablerÜ)r£rYrÅÚprintsetÚitrW)rÊrYr£rZÚ_print_Range*s0 ÿþzLatexPrinter._print_RangecCs”t|jƒdkrd|dur>d|| |jd¡|| |jd¡fSd|| |jd¡| |jd¡fSd|| |jd¡f}|durd||f}|S)Nr2z%s_{%s}^{%s}\left(%s\right)rrñrïz%s_{%s}r=rÑ)r£r²ÚletterrÓr³rWrWrZZ__print_number_polynomialTsþÿz&LatexPrinter.__print_number_polynomialcCs| |d|¡S)Nr-©Ú&_LatexPrinter__print_number_polynomialrÒrWrWrZÚ_print_bernoullibszLatexPrinter._print_bernoullics†t|jƒdkrxdˆ |jd¡ˆ |jd¡f}dd ‡fdd„|jd Dƒ¡}|durld |||f}n||}|Sˆ |d|¡S)Nr`z B_{%s, %s}rrñrçrØc3s|]}ˆ |¡VqdSrªrÕrÇrÖrWrZrÇisÿz+LatexPrinter._print_bell..r2rÉr-)rrÏr«rÜrØ)r£r²rÓZtex1Ztex2r³rWrÖrZÚ_print_bellesÿÿ zLatexPrinter._print_bellcCs| |d|¡S©NÚFr×rÒrWrWrZÚ_print_fibonaccisszLatexPrinter._print_fibonaccicCs,d| |jd¡}|dur(d||f}|S)NzL_{%s}rr=rIr°rWrWrZÚ_print_lucasvszLatexPrinter._print_lucascCs| |d|¡S)Nr9r×rÒrWrWrZÚ_print_tribonacci|szLatexPrinter._print_tribonaccicsøtƒ‰t|jjƒdks&t|jjƒdkrZdˆ |j¡ˆ |jd¡ˆ |j¡ˆ |j¡fS|jtj ur |j}ˆ| |d¡| |d¡| |d¡| |¡f}n6|jtjus¶|jdkrÎ|dd…}| ˆ¡nt|ƒ}dd ‡‡fd d „|Dƒ¡dS)Nrz\left\{%s\right\}_{%s=%s}^{%s}r`r2rñr€rhrØc3s$|]}|ˆurˆ |¡ndVqdSrÆrÕrÇrÉrWrZrÇ“r\z1LatexPrinter._print_SeqFormula..ri)rËrrÌZfree_symbolsrÎr«Úformular;r rÚcoeffrŒÚlengthrdrOrÜ)r£rYrÎrÓrWrÉrZÚ_print_SeqFormulas, üÿÿþzLatexPrinter._print_SeqFormulacCs`|j|jkrd| |j¡S|jr(d}nd}|jr8d}nd}d|| |j¡| |j¡|fSdS)NrÃršrur˜r™z\left%s%s, %s\right%s)rÌÚendr«Z left_openZ right_open)r£rwÚleftÚrightrWrWrZÚ_print_IntervalšsÿzLatexPrinter._print_IntervalcCsd| |j¡| |j¡fS)Nz \left\langle %s, %s\right\rangle)r«rŽr©r£rwrWrWrZÚ_print_AccumulationBounds¬sÿz&LatexPrinter._print_AccumulationBoundscs(t|ƒ‰‡‡fdd„|jDƒ}d |¡S)Ncsg|]}ˆ |ˆ¡‘qSrW©r°rK©r€r£rWrZr×²r\z-LatexPrinter._print_Union..z \cup ©rrÏrÜ©r£ÚuÚargs_strrWrërZÚ_print_Union°szLatexPrinter._print_Unioncs(t|ƒ‰‡‡fdd„|jDƒ}d |¡S)Ncsg|]}ˆ |ˆ¡‘qSrWrêrKrërWrZr×·r\z2LatexPrinter._print_Complement..z \setminus rìrírWrërZÚ_print_ComplementµszLatexPrinter._print_Complementcs(t|ƒ‰‡‡fdd„|jDƒ}d |¡S)Ncsg|]}ˆ |ˆ¡‘qSrWrêrKrërWrZr×¼r\z4LatexPrinter._print_Intersection..z \cap rìrírWrërZÚ_print_Intersectionºsz LatexPrinter._print_Intersectioncs(t|ƒ‰‡‡fdd„|jDƒ}d |¡S)Ncsg|]}ˆ |ˆ¡‘qSrWrêrKrërWrZr×Ár\z;LatexPrinter._print_SymmetricDifference..z \triangle rìrírWrërZÚ_print_SymmetricDifference¿sz'LatexPrinter._print_SymmetricDifferencecs\t|ƒ‰t|jƒdkr@t|jƒs@ˆ |jdˆ¡dt|jƒSd ‡‡fdd„|jDƒ¡S)Nrñrz^{%d}r’c3s|]}ˆ |ˆ¡VqdSrªrê)rÄr¾rërWrZrÇÈsz1LatexPrinter._print_ProductSet..)rrÚsetsrr°rÜ©r£r>rWrërZÚ_print_ProductSetÄs ÿzLatexPrinter._print_ProductSetcCsdS)Nz \emptysetrWrárWrWrZÚ_print_EmptySetËszLatexPrinter._print_EmptySetcCsdS)Nz \mathbb{N}rW©r£rërWrWrZÚ_print_NaturalsÎszLatexPrinter._print_NaturalscCsdS)Nz\mathbb{N}_0rWrørWrWrZÚ_print_Naturals0ÑszLatexPrinter._print_Naturals0cCsdS©Nz \mathbb{Z}rWrèrWrWrZÚ_print_IntegersÔszLatexPrinter._print_IntegerscCsdS©Nz \mathbb{Q}rWrèrWrWrZÚ_print_Rationals×szLatexPrinter._print_RationalscCsdS©Nz \mathbb{R}rWrèrWrWrZÚ_print_RealsÚszLatexPrinter._print_RealscCsdS©Nz \mathbb{C}rWrèrWrWrZÚ_print_ComplexesÝszLatexPrinter._print_ComplexescsP|jj}|jj}‡fdd„t||jƒDƒ}d dd„|Dƒ¡}dˆ |¡|fS)Nc3s&|]\}}ˆ |¡ˆ |¡fVqdSrªrÕ)rÄrÅrürÖrWrZrÇãr\z/LatexPrinter._print_ImageSet..rØcss|]}d|VqdS)ú %s \in %sNrW)rÄZxyrWrWrZrÇär\z!\left\{%s\; \middle|\; %s\right\})rTr²Ú signaturer|Z base_setsrÜr«)r£rYr²ÚsigZxysZxinysrWrÖrZÚ_print_ImageSetàs zLatexPrinter._print_ImageSetcs^d ‡fdd„t|jƒDƒ¡}|jtjur>d|ˆ |j¡fSd||ˆ |j¡ˆ |j¡fS)NrØcsg|]}ˆ |¡‘qSrWrÕ©rÄrrÖrWrZr×èr\z4LatexPrinter._print_ConditionSet..z"\left\{%s\; \middle|\; %s \right\}z3\left\{%s\; \middle|\; %s \in %s \wedge %s \right\})rÜrròZbase_setr ZUniversalSetr«Ú condition©r£rYZ vars_printrWrÖrZÚ_print_ConditionSetçsÿ üz LatexPrinter._print_ConditionSetcCs| |jd¡}d |¡S)Nrz\mathcal{{P}}\left({}\right)©r«rÏr¦)r£r²Z arg_printrWrWrZÚ_print_PowerSetószLatexPrinter._print_PowerSetcs8d ‡fdd„|jDƒ¡}dˆ |j¡|ˆ |j¡fS)NrØcsg|]}ˆ |¡‘qSrWrÕrrÖrWrZr×ør\z5LatexPrinter._print_ComplexRegion..z)\left\{%s\; \middle|\; %s \in %s \right\})rÜr;r«r²rôr rWrÖrZÚ_print_ComplexRegion÷s ýz!LatexPrinter._print_ComplexRegioncsdt‡fdd„|jDƒƒS)Nrc3s|]}ˆ |¡VqdSrªrÕr©rÖrWrZrÇÿr\z/LatexPrinter._print_Contains..)rOrÏrárWrÖrZÚ_print_ContainsþszLatexPrinter._print_ContainscCs:|jjtjur(|jjtjur(| |j¡S| | ¡¡dS)Nz + \ldots) rràr rpZbnr«Za0rìÚtruncater§rWrWrZÚ_print_FourierSeries sz!LatexPrinter._print_FourierSeriescCs| |j¡Srª)rìZinfiniter§rWrWrZÚ_print_FormalPowerSeries sz%LatexPrinter._print_FormalPowerSeriescCs d|jS)Nz\mathbb{F}_{%s})Úmodr·rWrWrZÚ_print_FiniteField szLatexPrinter._print_FiniteFieldcCsdSrûrWr·rWrWrZÚ_print_IntegerRing szLatexPrinter._print_IntegerRingcCsdSrýrWr·rWrWrZÚ_print_RationalField sz!LatexPrinter._print_RationalFieldcCsdSrÿrWr·rWrWrZÚ_print_RealField szLatexPrinter._print_RealFieldcCsdSrrWr·rWrWrZÚ_print_ComplexField sz LatexPrinter._print_ComplexFieldcCs,| |j¡}d t|j|jƒ¡}d||fS)NrØz%s\left[%s\right]©r«ÚdomainrÜrjr‰©r£r²rr‰rWrWrZÚ_print_PolynomialRing sz"LatexPrinter._print_PolynomialRingcCs,| |j¡}d t|j|jƒ¡}d||fS)NrØr‹rrrWrWrZÚ_print_FractionField sz!LatexPrinter._print_FractionFieldcCs<| |j¡}d t|j|jƒ¡}d}|js.d}d|||fS)NrØr–zS_<^{-1}z%s%s\left[%s\right])r«rrÜrjr‰Zis_Poly)r£r²rr‰ÚinvrWrWrZÚ_print_PolynomialRingBase" sz&LatexPrinter._print_PolynomialRingBasecCsÄ|jj}g}| ¡D]\}}d}t|ƒD]H\}}|dkr*|dkrX|| |j|¡7}q*|| t|j||ƒ¡7}q*|jrš|rŽd| |¡} qÜ| |¡} nB|rÒ|tj ur¸| d|g¡q|tjurÒ| d|g¡q| |¡} |sæ| } n| d|} | d¡r| d| dd…g¡q| d| g¡q|ddvrX| d¡}|dkrXd|d|d<d |¡}tt|j|jƒƒ} d | | ¡¡}d |g| |g¡}|tvr´d||f}nd||f}|S) Nr–rrñrçrr_r‘)r_rz domain=%srØz\%s {\left(%s \right)}z$\operatorname{%s}{\left( %s \right)})rÚrÛrérèr«ÚgensÚpowr¼r r4ÚextendrµrEÚpoprÜr'rjZ get_domainr‘)r£Úpolyr«réZmonomráZs_monomrwrÓZs_coeffZs_termÚmodifierr²rrrÏr³rWrWrZÚ_print_Poly* sN zLatexPrinter._print_PolycCsN|jj}|dkrd}| |j¡}|j}|tvr.)rÜrÏr·rWrÖrZÚ_print_OrdinalŒ szLatexPrinter._print_OrdinalcCs|jd}| |td|¡S)Nr”z {%s}^{%d})ržr÷r)r£r#r„rWrWrZÚ_print_PolyElement s zLatexPrinter._print_PolyElementcCs>|jdkr| |j¡S| |j¡}| |j¡}d||fSdS)Nrñr3)r7r«r6)r£r)r6r7rWrWrZÚ_print_FracElement“ s zLatexPrinter._print_FracElementcCsft|jƒdkr|jddfn|j\}}d| |¡}|durHd||f}|durbd|| |¡f}|S)NrñrzE_{%s}r=r‹rÑ)r£r²rÓr)rÅr³rWrWrZÚ_print_euler› s&zLatexPrinter._print_eulercCs,d| |jd¡}|dur(d||f}|S)NzC_{%s}rr=rIr°rWrWrZÚ_print_catalan¤ szLatexPrinter._print_catalanc Cs>d ||rdnd| |jd¡| |jd¡| |jd¡¡S)Nz5\mathcal{{{}}}{}_{{{}}}\left[{}\right]\left({}\right)z^{-1}r–rñrr2©r¦r«rÏ)r£r²rYZinverserWrWrZÚ_print_UnifiedTransformª sz$LatexPrinter._print_UnifiedTransformcCs| |d¡S)Nr4©r2r·rWrWrZÚ_print_MellinTransform sz#LatexPrinter._print_MellinTransformcCs| |dd¡S)Nr4Tr3r·rWrWrZÚ_print_InverseMellinTransform° sz*LatexPrinter._print_InverseMellinTransformcCs| |d¡S)NÚLr3r·rWrWrZÚ_print_LaplaceTransform³ sz$LatexPrinter._print_LaplaceTransformcCs| |dd¡S)Nr6Tr3r·rWrWrZÚ_print_InverseLaplaceTransform¶ sz+LatexPrinter._print_InverseLaplaceTransformcCs| |d¡SrÛr3r·rWrWrZÚ_print_FourierTransform¹ sz$LatexPrinter._print_FourierTransformcCs| |dd¡S)NrÜTr3r·rWrWrZÚ_print_InverseFourierTransform¼ sz+LatexPrinter._print_InverseFourierTransformcCs| |d¡S)NÚSINr3r·rWrWrZÚ_print_SineTransform¿ sz!LatexPrinter._print_SineTransformcCs| |dd¡S)Nr;Tr3r·rWrWrZÚ_print_InverseSineTransformÂ sz(LatexPrinter._print_InverseSineTransformcCs| |d¡S)NÚCOSr3r·rWrWrZÚ_print_CosineTransformÅ sz#LatexPrinter._print_CosineTransformcCs| |dd¡S)Nr>Tr3r·rWrWrZÚ_print_InverseCosineTransformÈ sz*LatexPrinter._print_InverseCosineTransformcCsDz"|jdur | |j |¡¡WSWnty4Yn0| t|ƒ¡Srª)Úringr«Zto_sympyrÚreprrõrWrWrZÚ _print_DMPË s zLatexPrinter._print_DMPcCs | |¡Srª)rCrõrWrWrZÚ _print_DMFÔ szLatexPrinter._print_DMFcCs| t|jƒ¡Srª©r«r rÝ)r£rËrWrWrZÚ _print_Object× szLatexPrinter._print_ObjectcCsd| |jd¡}|dur"d|fnd}t|jƒdkrBd||f}n| |jd¡}d |||¡}|S)Nrr†r–rñzW%s\left(%s\right)zW{0}_{{{1}}}\left({2}\right))r«rÏrr¦)r£r²rÓZarg0ÚresultZarg1rWrWrZÚ_print_LambertWÚ szLatexPrinter._print_LambertWcCsd | |jd¡¡S)Nz!\operatorname{{E}}\left[{}\right]rr1r·rWrWrZÚ_print_Expectationä szLatexPrinter._print_ExpectationcCsd | |jd¡¡S)Nz#\operatorname{{Var}}\left({}\right)rr1r·rWrWrZÚ_print_Varianceç szLatexPrinter._print_Variancecs d d ‡fdd„|jDƒ¡¡S)Nz#\operatorname{{Cov}}\left({}\right)rØc3s|]}ˆ |¡VqdSrªrÕrürÖrWrZrÇë r\z1LatexPrinter._print_Covariance..)r¦rÜrÏr·rWrÖrZÚ_print_Covarianceê szLatexPrinter._print_CovariancecCsd | |jd¡¡S)Nz!\operatorname{{P}}\left({}\right)rr1r·rWrWrZÚ_print_Probabilityí szLatexPrinter._print_ProbabilitycCs$| |j¡}| |j¡}d||fS)Nz%s\rightarrow %s)r«rÚcodomain)r£ÚmorphismrrMrWrWrZÚ_print_Morphismð szLatexPrinter._print_MorphismcCs&| |j¡| |j¡}}d||fS)Nr3)r«rxÚden)r£r²rxrPrWrWrZÚ_print_TransferFunctionõ sz$LatexPrinter._print_TransferFunctioncs(tˆjƒ}‡‡fdd„}d t||ƒ¡S)Ncsˆ |tˆƒd¡Srwrxr#ryrWrZr[û sÿz,LatexPrinter._print_Series..r‘)r'rÏrÜrj©r£r²rÏrzrWryrZÚ _print_Seriesù s zLatexPrinter._print_Seriescs@ddlm‰tˆjƒddd…}‡‡‡fdd„}d t||ƒ¡S)Nr)ÚMIMOParallelrðcs&t|ˆƒrˆ |tˆƒd¡Sˆ |¡Srw)r"r°rr«r#©rTr²r£rWrZr[ s ÿÿz0LatexPrinter._print_MIMOSeries..z\cdot)Zsympy.physics.control.ltirTr'rÏrÜrjrRrWrUrZÚ_print_MIMOSeriesÿ szLatexPrinter._print_MIMOSeriescCsd t|j|jƒ¡S©Nræ©rÜrjr«rÏr·rWrWrZÚ_print_Parallel szLatexPrinter._print_ParallelcCsd t|j|jƒ¡SrWrXr·rWrWrZÚ_print_MIMOParallel sz LatexPrinter._print_MIMOParallelcCsddlm}m}|j|dd|jƒ}}t||ƒr:t|jƒn|g}t|j|ƒrXt|jjƒn|jg}|}t||ƒrŽt|j|ƒrŽ|g|¢|¢RŽ} nÀt||ƒrÒt|j|ƒrÒ|j|kr¸||Ž} n||g|¢|j‘RŽf} n|t||ƒrt|j|ƒr||kr||Ž} n||g|¢RŽ} n<||kr&||Ž} n(|j|kr<||Ž} n|g|¢|¢RŽ} | |¡} | |¡}| | ¡}|j dkr|dnd} d| || |fS)Nr)ÚTransferFunctionÚSeriesrñrðrr_z\frac{%s}{%s %s %s})Úsympy.physics.controlr[r\Úsys1rr"r'rÏÚsys2r«r8)r£r²r[r\rxÚtfZnum_arg_listZden_arg_listZ den_term_1Z den_term_2r6Zdenom_1Zdenom_2Ú_signrWrWrZÚ_print_Feedback s8 ÿÿ zLatexPrinter._print_FeedbackcCsLddlm}| ||j|jƒ¡}| |j¡}|jdkr:dnd}d|||fS)Nr)Ú MIMOSeriesrðrr_z)\left(I_{\tau} %s %s\right)^{-1} \cdot %s)r]rcr«r_r^r8)r£r²rcZinv_matr^rarWrWrZÚ_print_MIMOFeedback0 s z LatexPrinter._print_MIMOFeedbackcCs| |j¡}d|S)Nz%s_\tau)r«Z _expr_matrsrWrWrZÚ_print_TransferFunctionMatrix7 sz*LatexPrinter._print_TransferFunctionMatrixcCsd |jj|j¡S)Nz\text{{{}}}_{{{}}})r¦rÚrÛrër·rWrWrZÚ _print_DFT; szLatexPrinter._print_DFTcCs&| t|jƒ¡}| |¡}d||fS)Nz%s:%s)r«r rÝrO)r£rNZpretty_nameÚpretty_morphismrWrWrZÚ_print_NamedMorphism? s z!LatexPrinter._print_NamedMorphismcCs"ddlm}| ||j|jdƒ¡S)Nr)Ú NamedMorphismÚid)Zsympy.categoriesrirhrrM)r£rNrirWrWrZÚ_print_IdentityMorphismD s ÿz$LatexPrinter._print_IdentityMorphismcs<‡fdd„|jDƒ}| ¡d |¡d}ˆ |¡}||S)Ncsg|]}ˆ t|jƒ¡‘qSrWrE)rÄÚ componentrÖrWrZr×L sÿz9LatexPrinter._print_CompositeMorphism..z\circ re)rbÚreverserÜrO)r£rNZcomponent_names_listZcomponent_namesrgrWrÖrZÚ_print_CompositeMorphismI s ÿ z%LatexPrinter._print_CompositeMorphismcCsd | t|jƒ¡¡S©NrE)r¦r«r rÝ)r£rNrWrWrZÚ_print_CategoryT szLatexPrinter._print_CategorycCs<|js| tj¡S| |j¡}|jr8|d| |j¡7}|S)Nz\Longrightarrow %s)Zpremisesr«r ZEmptySetZconclusions)r£ZdiagramÚlatex_resultrWrWrZÚ_print_DiagramW s ÿzLatexPrinter._print_DiagramcCs–dd|j}t|jƒD]p}t|jƒD]B}|||frJ|t|||fƒ7}|d7}||jdkr&|d7}q&||jdkr€|d7}|d7}q|d7}|S) Nz\begin{array}{%s} rqr‘rñú& rSÚ z\end{array} )ÚwidthrÿÚheightÚlatex)r£Zgridrqrwr›rWrWrZÚ_print_DiagramGridc s zLatexPrinter._print_DiagramGridcCsd | |j¡| |j¡¡S)Nz {{{}}}^{{{}}})r¦r«rAr©r£r4rWrWrZÚ_print_FreeModuleu szLatexPrinter._print_FreeModulecsd d ‡fdd„|Dƒ¡¡S)Nz\left[ {} \right]ròc3s |]}dˆ |¡dVqdS©r^rVNrÕrÃrÖrWrZrÇz sz8LatexPrinter._print_FreeModuleElement..)r¦rÜ©r£r)rWrÖrZÚ_print_FreeModuleElementx sÿz%LatexPrinter._print_FreeModuleElementcs d d ‡fdd„|jDƒ¡¡S)Nú\left\langle {} \right\rangleròc3s |]}dˆ |¡dVqdSr{rÕrÃrÖrWrZrÇ~ sz0LatexPrinter._print_SubModule..)r¦rÜrr|rWrÖrZÚ_print_SubModule} sÿzLatexPrinter._print_SubModulecs"d d ‡fdd„|jjDƒ¡¡S)Nr~ròc3s"|]\}dˆ |¡dVqdSr{rÕrÃrÖrWrZrÇ‚ sz=LatexPrinter._print_ModuleImplementedIdeal..)r¦rÜÚ_modulerr|rWrÖrZÚ_print_ModuleImplementedIdeal sÿz*LatexPrinter._print_ModuleImplementedIdealcsD‡fdd„|jDƒ}|dgdd„t|dd…dƒDƒ}d |¡S)Ncs g|]}ˆj|tddd‘qS)rTrb)r°rrKrÖrWrZr×ˆ sÿz2LatexPrinter._print_Quaternion..rcSsg|]\}}|d|‘qS)r‘rW)rÄrwr›rWrWrZr×Š r\rñZijkræ)rÏr|rÜ)r£r²rYr8rWrÖrZÚ_print_Quaternion… s ÿ&zLatexPrinter._print_QuaternioncCsd | |j¡| |j¡¡S©Nz\frac{{{}}}{{{}}})r¦r«rAÚ base_ideal)r£ÚRrWrWrZÚ_print_QuotientRing s ÿz LatexPrinter._print_QuotientRingcCsd | |j¡| |jj¡¡S©Nz{{{}}} + {{{}}})r¦r«ÚdatarAr„)r£rÅrWrWrZÚ_print_QuotientRingElement’ sÿz'LatexPrinter._print_QuotientRingElementcCsd | |j¡| |jj¡¡Sr‡)r¦r«rˆÚmoduleÚ killed_moduler|rWrWrZÚ_print_QuotientModuleElement– sÿz)LatexPrinter._print_QuotientModuleElementcCsd | |j¡| |j¡¡Srƒ)r¦r«rÐr‹ryrWrWrZÚ_print_QuotientModuleš s ÿz"LatexPrinter._print_QuotientModulecCs(d | | ¡¡| |j¡| |j¡¡S)Nz{{{}}} : {{{}}} \to {{{}}})r¦r«Z _sympy_matrixrrM)r£ršrWrWrZÚ_print_MatrixHomomorphismŸ sÿz&LatexPrinter._print_MatrixHomomorphismcCsŒ|jj}d|vr"|gg}}}n2t|ƒ\}}}t|ƒ}dd„|Dƒ}dd„|Dƒ}d|}|rr|dd |¡7}|rˆ|dd |¡7}|S) Nr^cSsg|]}t|ƒ‘qSrWrArCrWrWrZr×« r\z0LatexPrinter._print_Manifold..cSsg|]}t|ƒ‘qSrWrArDrWrWrZr×¬ r\ràr†r‘ri)rÝrrBrÜ)r£ÚmanifoldrFrÝrGr}rWrWrZÚ_print_Manifold£ szLatexPrinter._print_ManifoldcCsd| |j¡| |j¡fS)Nz\text{%s}_{%s})r«rÝr)r£ÚpatchrWrWrZÚ_print_Patch¶ szLatexPrinter._print_PatchcCs(d| |j¡| |jj¡| |j¡fS)Nz\text{%s}^{\text{%s}}_{%s})r«rÝr‘r)r£ZcoordsysrWrWrZÚ_print_CoordSystem¹ s ÿzLatexPrinter._print_CoordSystemcCsd| |j¡S)Nz\mathbb{\nabla}_{%s})r«Z_wrt)r£ZcvdrWrWrZÚ_print_CovarDerivativeOp¾ sz%LatexPrinter._print_CovarDerivativeOpcCs$|jj|jj}d | t|ƒ¡¡Sro©Ú _coord_sysr‰Ú_indexrÝr¦r«r ©r£ÚfieldrFrWrWrZÚ_print_BaseScalarFieldÁ sz#LatexPrinter._print_BaseScalarFieldcCs$|jj|jj}d | t|ƒ¡¡S)Nz\partial_{{{}}}r•r˜rWrWrZÚ_print_BaseVectorFieldÅ sz#LatexPrinter._print_BaseVectorFieldcCsL|j}t|dƒr4|jj|jj}d | t|ƒ¡¡S| |¡}d |¡SdS)Nr–z\operatorname{{d}}{}z!\operatorname{{d}}\left({}\right)) Z_form_fieldrŸr–r‰r—rÝr¦r«r )r£Údiffr™rFrWrWrZÚ_print_DifferentialÉ s z LatexPrinter._print_DifferentialcCs| |jd¡}d |¡S)Nrz"\operatorname{{tr}}\left({}\right)r)r£r>ÚcontentsrWrWrZÚ _print_TrÒ szLatexPrinter._print_TrcCs4|dur d| |jd¡|fSd| |jd¡S)Nz%\left(\phi\left(%s\right)\right)^{%s}rz\phi\left(%s\right)rIrÒrWrWrZÚ_print_totient× s ÿzLatexPrinter._print_totientcCs4|dur d| |jd¡|fSd| |jd¡S)Nz(\left(\lambda\left(%s\right)\right)^{%s}rz\lambda\left(%s\right)rIrÒrWrWrZÚ_print_reduced_totientÝ s ÿz#LatexPrinter._print_reduced_totientcCsdt|jƒdkr4dtt|j|jd|jdfƒƒ}nd| |jd¡}|dur\d||fSd|S)Nr2ú_%s\left(%s\right)rñrrçz \sigma^{%s}%sz\sigma%srr°rWrWrZÚ_print_divisor_sigmaã s ÿ z!LatexPrinter._print_divisor_sigmacCsdt|jƒdkr4dtt|j|jd|jdfƒƒ}nd| |jd¡}|dur\d||fSd|S)Nr2r¢rñrrçz\sigma^*^{%s}%sz \sigma^*%srr°rWrWrZÚ_print_udivisor_sigmaí s ÿ z"LatexPrinter._print_udivisor_sigmacCs4|dur d| |jd¡|fSd| |jd¡S)Nz$\left(\nu\left(%s\right)\right)^{%s}rz\nu\left(%s\right)rIrÒrWrWrZÚ_print_primenu÷ s ÿzLatexPrinter._print_primenucCs4|dur d| |jd¡|fSd| |jd¡S)Nz'\left(\Omega\left(%s\right)\right)^{%s}rz\Omega\left(%s\right)rIrÒrWrWrZÚ_print_primeomegaý s ÿzLatexPrinter._print_primeomegacCs t|jƒSrª)r÷rÝr§rWrWrZÚ _print_StrszLatexPrinter._print_StrcCs| t|ƒ¡Srª)r«rr·rWrWrZÚ_print_floatszLatexPrinter._print_floatcCst|ƒSrª©r÷r·rWrWrZÚ _print_int szLatexPrinter._print_intcCst|ƒSrªr©r·rWrWrZÚ _print_mpzszLatexPrinter._print_mpzcCst|ƒSrªr©r·rWrWrZÚ _print_mpqszLatexPrinter._print_mpqcCsd tt|jƒƒ¡S)Nz"\operatorname{{Q}}_{{\text{{{}}}}})r¦rrr÷rÝr·rWrWrZÚ_print_PredicateszLatexPrinter._print_Predicatecs:|j}|j}ˆ |¡}d ‡fdd„|Dƒ¡}d||fS)NrØcsg|]}ˆ |¡‘qSrWrÕr©rÖrWrZr×r\z8LatexPrinter._print_AppliedPredicate..z%s(%s))rXÚ argumentsr«rÜ)r£r²ÚpredrÏZ pred_latexZ args_latexrWrÖrZÚ_print_AppliedPredicates z$LatexPrinter._print_AppliedPredicatecstƒ |¡}dt|ƒS)Nz\mathtt{\text{%s}})ÚsuperÚemptyPrinterrrr<©rÚrWrZr²szLatexPrinter.emptyPrinter)N)FF)FF)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)Nr-)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)Nr–)Nr–)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)FN)N)N)N)N)rv)rv)N)N)N)N)N)N)N)N)N)N)N)N)N)N)N)F)N)N)N)N)N)N)N(9rÛÚ __module__Ú__qualname__ZprintmethodZ_default_settingsrr¨r©r°rr±r¸r¾rÍrÎrºr»rÔrÞrãZ_print_BooleanTrueZ_print_BooleanFalserärìrørrrrrrrrrr:r;rBrArJr[r\rhrlrnrqryrrŠrr’r¡r¢r£Úpropertyr©r¬rr®r¯Z _print_MinZ _print_Maxr±r²r³r´Z_print_Determinantr·r¸r¿rÁrÄrÅrÆr½r¼rÈrËrÌrÍrÎrÐrÒrÓrÕrØrÙrÚrÜrÞZ_print_gammarßrárârãrærçrèrérìrîrórôr÷rørùrûrýrþrÿrrrrrr rr rrrrrrrrrrr!r"r#r$r%r&r'r,r-r2r3r4r6r7r9r=r@Z_print_RandomSymbolrÙrOrQrardrjrlrrrtrur{r|rƒr„r†r‡rˆr‹rrŽrr”r˜ršr›rœrrŸr r¡r¢r£r¤r¨rr®r¯r±r´rµr¶r¸rºr»r¼r¿rÂrÀZ_print_frozensetrÕrØrÙrÚrÝrÞrßrãZ _print_SeqPerZ _print_SeqAddZ _print_SeqMulrçrérðrñròrórör÷rùrúrürþrrrr rr rrrrrrrrrrrr%r&r'r)r+r,r-r.r/r0r2r4r5r7r8r9r:r<r=r?r@rCrDrFrHrIrJrKrLrOrQrSrVrYrZrbrdrerfZ_print_IDFTrhrkrnrprrrxrzr}rrr‚r†r‰rŒrrŽrr’r“r”ršr›rrŸr r¡r£r¤r¥r¦r§r¨rªr«r¬rr°r²Ú __classcell__rWrWr³rZrs‰s–é8 !r2! #L 4 *9 $ rscCsšt |¡}|r|S| ¡tvr*d| ¡S|tvr:d|Stt ¡tddD]D}| ¡ |¡rLt|ƒt|ƒkrLt|t |dt|ƒ…ƒƒSqL|SdS)aŽ Check for a modifier ending the string. If present, convert the modifier to latex and translate the rest recursively. Given a description of a Greek letter or other special character, return the appropriate latex. Let everything else pass as given. >>> from sympy.printing.latex import translate >>> translate('alphahatdotprime') "{\\dot{\\hat{\\alpha}}}'" rmT)r%rmN)Útex_greek_dictionaryrþrÚgreek_letters_setÚ other_symbolsr(Ú modifier_dictr²rrFrB)rYr³r%rWrWrZrB#s $rBcKst|ƒ |¡S)aŸ#Convert the given expression to LaTeX string representation. Parameters ========== full_prec: boolean, optional If set to True, a floating point number is printed with full precision. fold_frac_powers : boolean, optional Emit ``^{p/q}`` instead of ``^{\frac{p}{q}}`` for fractional powers. fold_func_brackets : boolean, optional Fold function brackets where applicable. fold_short_frac : boolean, optional Emit ``p / q`` instead of ``\frac{p}{q}`` when the denominator is simple enough (at most two terms and no powers). The default value is ``True`` for inline mode, ``False`` otherwise. inv_trig_style : string, optional How inverse trig functions should be displayed. Can be one of ``abbreviated``, ``full``, or ``power``. Defaults to ``abbreviated``. itex : boolean, optional Specifies if itex-specific syntax is used, including emitting ``$$...$$``. ln_notation : boolean, optional If set to ``True``, ``\ln`` is used instead of default ``\log``. long_frac_ratio : float or None, optional The allowed ratio of the width of the numerator to the width of the denominator before the printer breaks off long fractions. If ``None`` (the default value), long fractions are not broken up. mat_delim : string, optional The delimiter to wrap around matrices. Can be one of ``[``, ``(``, or the empty string. Defaults to ``[``. mat_str : string, optional Which matrix environment string to emit. ``smallmatrix``, ``matrix``, ``array``, etc. Defaults to ``smallmatrix`` for inline mode, ``matrix`` for matrices of no more than 10 columns, and ``array`` otherwise. mode: string, optional Specifies how the generated code will be delimited. ``mode`` can be one of ``plain``, ``inline``, ``equation`` or ``equation*``. If ``mode`` is set to ``plain``, then the resulting code will not be delimited at all (this is the default). If ``mode`` is set to ``inline`` then inline LaTeX ``$...$`` will be used. If ``mode`` is set to ``equation`` or ``equation*``, the resulting code will be enclosed in the ``equation`` or ``equation*`` environment (remember to import ``amsmath`` for ``equation*``), unless the ``itex`` option is set. In the latter case, the ``$$...$$`` syntax is used. mul_symbol : string or None, optional The symbol to use for multiplication. Can be one of ``None``, ``ldot``, ``dot``, or ``times``. order: string, optional Any of the supported monomial orderings (currently ``lex``, ``grlex``, or ``grevlex``), ``old``, and ``none``. This parameter does nothing for Mul objects. Setting order to ``old`` uses the compatibility ordering for Add defined in Printer. For very large expressions, set the ``order`` keyword to ``none`` if speed is a concern. symbol_names : dictionary of strings mapped to symbols, optional Dictionary of symbols and the custom strings they should be emitted as. root_notation : boolean, optional If set to ``False``, exponents of the form 1/n are printed in fractonal form. Default is ``True``, to print exponent in root form. mat_symbol_style : string, optional Can be either ``plain`` (default) or ``bold``. If set to ``bold``, a MatrixSymbol A will be printed as ``\mathbf{A}``, otherwise as ``A``. imaginary_unit : string, optional String to use for the imaginary unit. Defined options are "i" (default) and "j". Adding "r" or "t" in front gives ``\mathrm`` or ``\text``, so "ri" leads to ``\mathrm{i}`` which gives `\mathrm{i}`. gothic_re_im : boolean, optional If set to ``True``, `\Re` and `\Im` is used for ``re`` and ``im``, respectively. The default is ``False`` leading to `\operatorname{re}` and `\operatorname{im}`. decimal_separator : string, optional Specifies what separator to use to separate the whole and fractional parts of a floating point number as in `2.5` for the default, ``period`` or `2{,}5` when ``comma`` is specified. Lists, sets, and tuple are printed with semicolon separating the elements when ``comma`` is chosen. For example, [1; 2; 3] when ``comma`` is chosen and [1,2,3] for when ``period`` is chosen. parenthesize_super : boolean, optional If set to ``False``, superscripted expressions will not be parenthesized when powered. Default is ``True``, which parenthesizes the expression when powered. min: Integer or None, optional Sets the lower bound for the exponent to print floating point numbers in fixed-point format. max: Integer or None, optional Sets the upper bound for the exponent to print floating point numbers in fixed-point format. Notes ===== Not using a print statement for printing, results in double backslashes for latex commands since that's the way Python escapes backslashes in strings. >>> from sympy import latex, Rational >>> from sympy.abc import tau >>> latex((2*tau)**Rational(7,2)) '8 \\sqrt{2} \\tau^{\\frac{7}{2}}' >>> print(latex((2*tau)**Rational(7,2))) 8 \sqrt{2} \tau^{\frac{7}{2}} Examples ======== >>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational, log >>> from sympy.abc import x, y, mu, r, tau Basic usage: >>> print(latex((2*tau)**Rational(7,2))) 8 \sqrt{2} \tau^{\frac{7}{2}} ``mode`` and ``itex`` options: >>> print(latex((2*mu)**Rational(7,2), mode='plain')) 8 \sqrt{2} \mu^{\frac{7}{2}} >>> print(latex((2*tau)**Rational(7,2), mode='inline')) $8 \sqrt{2} \tau^{7 / 2}$ >>> print(latex((2*mu)**Rational(7,2), mode='equation*')) \begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*} >>> print(latex((2*mu)**Rational(7,2), mode='equation')) \begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation} >>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True)) $$8 \sqrt{2} \mu^{\frac{7}{2}}$$ >>> print(latex((2*mu)**Rational(7,2), mode='plain')) 8 \sqrt{2} \mu^{\frac{7}{2}} >>> print(latex((2*tau)**Rational(7,2), mode='inline')) $8 \sqrt{2} \tau^{7 / 2}$ >>> print(latex((2*mu)**Rational(7,2), mode='equation*')) \begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*} >>> print(latex((2*mu)**Rational(7,2), mode='equation')) \begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation} >>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True)) $$8 \sqrt{2} \mu^{\frac{7}{2}}$$ Fraction options: >>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True)) 8 \sqrt{2} \tau^{7/2} >>> print(latex((2*tau)**sin(Rational(7,2)))) \left(2 \tau\right)^{\sin{\left(\frac{7}{2} \right)}} >>> print(latex((2*tau)**sin(Rational(7,2)), fold_func_brackets=True)) \left(2 \tau\right)^{\sin {\frac{7}{2}}} >>> print(latex(3*x**2/y)) \frac{3 x^{2}}{y} >>> print(latex(3*x**2/y, fold_short_frac=True)) 3 x^{2} / y >>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=2)) \frac{\int r\, dr}{2 \pi} >>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=0)) \frac{1}{2 \pi} \int r\, dr Multiplication options: >>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times")) \left(2 \times \tau\right)^{\sin{\left(\frac{7}{2} \right)}} Trig options: >>> print(latex(asin(Rational(7,2)))) \operatorname{asin}{\left(\frac{7}{2} \right)} >>> print(latex(asin(Rational(7,2)), inv_trig_style="full")) \arcsin{\left(\frac{7}{2} \right)} >>> print(latex(asin(Rational(7,2)), inv_trig_style="power")) \sin^{-1}{\left(\frac{7}{2} \right)} Matrix options: >>> print(latex(Matrix(2, 1, [x, y]))) \left[\begin{matrix}x\\y\end{matrix}\right] >>> print(latex(Matrix(2, 1, [x, y]), mat_str = "array")) \left[\begin{array}{c}x\\y\end{array}\right] >>> print(latex(Matrix(2, 1, [x, y]), mat_delim="(")) \left(\begin{matrix}x\\y\end{matrix}\right) Custom printing of symbols: >>> print(latex(x**2, symbol_names={x: 'x_i'})) x_i^{2} Logarithms: >>> print(latex(log(10))) \log{\left(10 \right)} >>> print(latex(log(10), ln_notation=True)) \ln{\left(10 \right)} ``latex()`` also supports the builtin container types :class:`list`, :class:`tuple`, and :class:`dict`: >>> print(latex([2/x, y], mode='inline')) $\left[ 2 / x, \ y\right]$ Unsupported types are rendered as monospaced plaintext: >>> print(latex(int)) \mathtt{\text{}} >>> print(latex("plain % text")) \mathtt{\text{plain \% text}} See :ref:`printer_method_example` for an example of how to override this behavior for your own types by implementing ``_latex``. .. versionchanged:: 1.7.0 Unsupported types no longer have their ``str`` representation treated as valid latex. )rsr±©r²r¤rWrWrZrwBsMrwcKstt|fi|¤ŽƒdS)z`Prints LaTeX representation of the given expression. Takes the same settings as ``latex()``.N)Úprintrwr¼rWrWrZÚprint_latexsr¾rñúalign*Fc Ks„tfi|¤Ž}|dkr,d}d}d} d} d}nJ|dkrJd}d}d} d } d}n,|d krhd}d}d } d} d}ntd |¡ƒ‚d }|r‚d}| ¡} t| ƒ}d}t|ƒD]Ø}| |}d }d }d}||krÐ|rÈd}nd}d}||krú||dkrö|| dd}nd }| ¡ddkrd|}d}|dkrT|dkr0d }|d | |¡||| |¡|¡7}n|d ||| |¡|¡7}|d7}qž|| 7}|S)a¦ This function generates a LaTeX equation with a multiline right-hand side in an ``align*``, ``eqnarray`` or ``IEEEeqnarray`` environment. Parameters ========== lhs : Expr Left-hand side of equation rhs : Expr Right-hand side of equation terms_per_line : integer, optional Number of terms per line to print. Default is 1. environment : "string", optional Which LaTeX wnvironment to use for the output. Options are "align*" (default), "eqnarray", and "IEEEeqnarray". use_dots : boolean, optional If ``True``, ``\\dots`` is added to the end of each line. Default is ``False``. Examples ======== >>> from sympy import multiline_latex, symbols, sin, cos, exp, log, I >>> x, y, alpha = symbols('x y alpha') >>> expr = sin(alpha*y) + exp(I*alpha) - cos(log(y)) >>> print(multiline_latex(x, expr)) \begin{align*} x = & e^{i \alpha} \\ & + \sin{\left(\alpha y \right)} \\ & - \cos{\left(\log{\left(y \right)} \right)} \end{align*} Using at most two terms per line: >>> print(multiline_latex(x, expr, 2)) \begin{align*} x = & e^{i \alpha} + \sin{\left(\alpha y \right)} \\ & - \cos{\left(\log{\left(y \right)} \right)} \end{align*} Using ``eqnarray`` and dots: >>> print(multiline_latex(x, expr, terms_per_line=2, environment="eqnarray", use_dots=True)) \begin{eqnarray} x & = & e^{i \alpha} + \sin{\left(\alpha y \right)} \dots\nonumber\\ & & - \cos{\left(\log{\left(y \right)} \right)} \end{eqnarray} Using ``IEEEeqnarray``: >>> print(multiline_latex(x, expr, environment="IEEEeqnarray")) \begin{IEEEeqnarray}{rCl} x & = & e^{i \alpha} \nonumber\\ & & + \sin{\left(\alpha y \right)} \nonumber\\ & & - \cos{\left(\log{\left(y \right)} \right)} \end{IEEEeqnarray} Notes ===== All optional parameters from ``latex`` can also be used. Zeqnarrayz\begin{eqnarray} z& = &z \nonumberz \end{eqnarray}TZIEEEeqnarrayz\begin{IEEEeqnarray}{rCl} z \end{IEEEeqnarray}r¿z\begin{align*} z= &r–z \end{align*}FzUnknown environment: {}z\dotsrñrz& & rsrSrtrrðr_z{:s} {:s}{:s} {:s} {:s}z{:s}{:s} {:s} {:s})rsrŸr¦Zas_ordered_termsrrÿr&r±)rJrKZterms_per_lineÚenvironmentZuse_dotsr¤rQrGZ first_termZnonumberZend_termZdoubleetrÊréZn_termsZ term_countrwrêZ term_startZterm_endr8rWrWrZÚmultiline_latexsnC ÿ ÿ rÁ)rñr¿F)>Ú__doc__ÚtypingrrZtDictr’Z sympy.corerrrrrr r Zsympy.core.alphabetsrZsympy.core.containersrZsympy.core.functionr rZsympy.core.operationsrZsympy.core.powerrZsympy.core.sortingrZsympy.core.sympifyrr»rZsympy.printing.precedencerZsympy.printing.printerrrZsympy.printing.conventionsrrrrZmpmath.libmp.libmpfrrrZsympy.utilities.iterablesrr(r‘r¸rºr»Ú frozensetr¹Úcompiler+rrrsrBrwr¾rÁrWrWrWrZÚsæ$Ü'åþ/ O