Ed U d Z ddlmZ ddlmZmZmZ ddlZddlm Z m
Z
m Z m Z m
Z
mZmZmZ ddlmZ ddlmZ ddlmZmZmZ dd lmZ dd
lm Z dd l m Z dd l m Z dd
l!m"Z"m#Z#m$Z$ ddl%m&Z& ddl'm(Z( ddl)m*Z*m+Z+ ddl,m-Z-m.Z. ddl'm/Z/m0Z0 ddl1m2Z2m3Z4 ddl5m6Z6m7Z7 ddl8Z8erddl9m:Z: g dZ;i dddddd d d d d d!d"d#d$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8i d9d:d;d<d=d>d?d@dAdBdCdDdEdFdGdHdIdJdKd,dLdMdNdDdOdPdQdRdSdTdUdVdWdXdYdZd[Zde?d< e@e ZA e8jB d e8jB d fZCddZD G d de* ZEddZF e+eE d ZGd ZHddZIdS )zC
A Printer which converts an expression into its LaTeX equivalent.
) annotations)AnyCallable
TYPE_CHECKINGN)AddFloatModMulNumberSSymbolExpr)greeks)Tuple)Function AppliedUndef
Derivative)AssocOp)Pow)default_sort_key) SympifyError)true BooleanTrue BooleanFalse) NDimArray)precedence_traditional)Printerprint_function)split_super_subrequires_partial)
precedence
PRECEDENCE) prec_to_dpsto_str) has_varietysift)BasisDependent)arcsinarccosarctansincostansinhcoshtanhsqrtlnlogseccsccotcothreimfracrootargAlphaz
\mathrm{A}Betaz
\mathrm{B}Gamma\GammaDeltaz\DeltaEpsilonz
\mathrm{E}Zetaz
\mathrm{Z}Etaz
\mathrm{H}Thetaz\ThetaIotaz
\mathrm{I}Kappaz
\mathrm{K}Lambdaz\LambdaMuz
\mathrm{M}Nuz
\mathrm{N}Xiz\XiomicronoOmicronz
\mathrm{O}Piz\PiRhoz
\mathrm{P}Sigmaz\SigmaTauz
\mathrm{T}Upsilonz\UpsilonPhiz\PhiChiz
\mathrm{X}Psiz\PsiOmegaz\Omegalamdaz\lambdaLamdakhiz\chiKhi
varepsilonz \varepsilonvarkappaz \varkappavarphiz\varphivarpiz\varpivarrhoz\varrhoz \varsigmaz \vartheta)varsigmavartheta>
wpellethmhobethhbaralephgimeldalethhslashmathringc d| z dz S )Nz
\mathring{} ss 4lib/python3.11/site-packages/sympy/printing/latex.pyrt Z s -/$. ddddotc d| z dz S )Nz\ddddot{ro rp rq s rs rt rt [ s A
d* ru dddotc d| z dz S )Nz\dddot{ro rp rq s rs rt rt \ z!|D( ru ddotc d| z dz S )Nz\ddot{ro rp rq s rs rt rt ] s ik$& ru dotc d| z dz S )Nz\dot{ro rp rq s rs rt rt ^ XaZ_ ru checkc d| z dz S )Nz\check{ro rp rq s rs rt rt _ rz ru brevec d| z dz S )Nz\breve{ro rp rq s rs rt rt ` rz ru acutec d| z dz S )Nz\acute{ro rp rq s rs rt rt a rz ru gravec d| z dz S )Nz\grave{ro rp rq s rs rt rt b rz ru tildec d| z dz S )Nz\tilde{ro rp rq s rs rt rt c rz ru hatc d| z dz S )Nz\hat{ro rp rq s rs rt rt d r ru barc d| z dz S )Nz\bar{ro rp rq s rs rt rt e r ru vecc d| z dz S )Nz\vec{ro rp rq s rs rt rt f r ru primec d| z dz S N{z}'rp rq s rs rt rt g s s1uTz ru prmc d| z dz S r rp rq s rs rt rt h s SU4Z ru boldc d| z dz S Nz \boldsymbol{ro rp rq s rs rt rt j s oa', ru bmc d| z dz S r rp rq s rs rt rt k s OA%d* ru c d| z dz S )Nz \mathcal{ro rp rq s rs rt rt l \!^D( ru c d| z dz S )Nz \mathscr{ro rp rq s rs rt rt m r ru c d| z dz S )Nz
\mathfrak{ro rp rq s rs rt rt n s mAod* ru c d| z dz S )Nz\left\|{z }\right\|rp rq s rs rt rt p s k!mL0 ru c d| z dz S )Nz
\left\langle{z}\right\ranglerp rq s rs rt rt q s %a'(99 ru c d| z dz S Nz\left|{z}\right|rp rq s rs rt rt r Z\+- ru c d| z dz S r rp rq s rs rt rt s r ru )calscrfraknormavgabsmagz dict[str, Callable[[str], str]]
modifier_dictz [0-9][} ]*$z[0-9]rr strreturnc | dd } dD ]}| |d|z } | dd } | dd } | S )z
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.
\z\textbackslashz&%$#_{}~z\textasciitilde^z\textasciicircum)replace)rr cs rs latex_escaper ~ sm
$)**A
# #
IIa " " #)**A #*++A Hru c e Zd ZU dZi dddddddddd d
dd dd dd
ddddddddddi dddddddddddddd Zd ed < d\d Zd]d"Zd]d#Zd^d]d$Z d% Z
d]d&Z d_d(Z d_d)Z
d^d_d*Zd_d+Zd_d,Zd_d-Zd`d/Zd0 Zdad3ZeZeZd4 Zd\d5Zd6 Zd7 Zd8 Zd9 Z d: Z d; Z d< Z d= Z d> Z!d? Z"dbdAZ#dB Z$dC Z%dcdEZ&dddGZ'dH Z(dI Z)dJ Z*dedLZ+dM Z,dN Z-dO Z.dP Z/dQ Z0dR Z1dS Z2dfdUZ3d\dgdWZ4dX Z5dY Z6e7dZ Z8d[ Z9d\ Z:d] Z;d\d]d^Zd\d_Z?d\d`Z@d\daZAd\dbZBd\dcZCd\ddZDde ZEdf ZFdg ZGdh ZHdi ZId\djZJd\dkZKd\dlZLd\dmZMd\dnZNd\doZOd\dpZPd\dqZQd\drZRd\dsZSd\dtZTdhdvZUd\dwZVd\dxZWd\dyZXd\d]dzZYeYZZd\d{Z[d\d|Z\d\d}Z]d\d~Z^d\dZ_d\dZ`d\dZad\dZbd\dZcd\dZddidZed]dZfd\dZgd\dZhd\dZid\dZjd\dZkd\dZld\dZmd\dZnd\dZod\dZpdjd]dZqdjd]dZrd\dZsd\dZtd\dZud\dZvd\dZwd\dZxd\dZyd\dZzd\dZ{d\dZ|d\dZ}d\dZ~d\dZd\dZd\dZd\dZd\dZd\dZd\dZd\dZd\dZd\dZdkdZd\dZd\dZd\dZd\dZd Zd ZdldmdZeZdldndZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd\dZdÄ ZdĄ Zdń ZdƄ ZdDŽ ZdȄ ZdɄ Zdʄ Zd˄ Zdod̈́ZdpdЄZdф Zd҄ Zdӄ ZdԄ ZdՄ Zdք Zdׄ Zd Zdل Zd\dڄZdۄ Zd܄ Zd݄ Zdބ Zd߄ Zd Zd Zd\dZd\dZd\dZd\dZd\dZd Zd Zd ZeZd ZŐd\dZƐd\dZǐd\dZȐd\dZɐd\dZʐd\dZd ZeZeZeZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zݐd Zސd Zߐd Zd Zd Zd Zd Zd Zd Zd Zd
Zd Zd Zd
Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd\dZd\dZdqdZd Zd Zd Zd Zd Zd Zd Zd! Zd" Z d# Zd$ Zd% Zd& Zd\d'Zd( Zd) Zd* Zd+ Z d, Z
d- Z d. Z d/ Z
d0 Zd1 Zd2 Zd3 Zd4 Zd5 ZeZd6 Zd7 Zd8 Zd9 Zd: Zd; Zd< Zd= Z d> Z d? Z d@ Z dA Z dB Z!dC Z"dD Z#dE Z$dF Z%dG Z&dH Z'dI Z(dJ Z)dK Z*dL Z+dM Z,d\dNZ-d\dOZ.d\dPZ/d\dQZ0d\dRZ1d\dSZ2dT Z3dU Z4dV Z5dW Z6dX Z7dY Z8dZ Z9 fd[Z: xZ;S (r LatexPrinter_latex full_precFfold_frac_powersfold_func_bracketsfold_short_fracNinv_trig_style abbreviateditex ln_notationlong_frac_ratio mat_delim[mat_strmodeplain
mul_symbolorder symbol_names
root_notationTmat_symbol_styleimaginary_unitiperiodd) gothic_re_imdecimal_separator perm_cyclicparenthesize_superminmax
diff_operatorzdict[str, Any]_default_settingsc 6 t j | | d| j v r"g d}| j d |vrt d | j d | j d dk r
d| j d< ddd d
d } || j d | j d
< n%# t $ r | j d | j d
< Y nw xY w || j d pd | j d< nW# t $ rJ | j d dv r|d | j d< n| j d | j d< Y nw xY wddd| _ dddddddd}| j d }| || | j d < d d d d d }| j d! }| || | j d"< d S )#Nr )inliner equationz equation*zB'mode' must be one of 'inline', 'plain', 'equation' or 'equation*'r r T z \,.\, \cdot \times )Nldotr} timesr mul_symbol_latexr} mul_symbol_latex_numbers) r r z\,z\:\;z\quad)])(r r z
\mathrm{i}z\text{i}jz
\mathrm{j}z\text{j})Nr ritir rjtjr imaginary_unit_latexr z
\mathrm{d}z\text{d})Nr rdtdr diff_operator_latex)r __init__ _settings
ValueErrorKeyErrorstrip _delim_dictget)selfsettings valid_modesmul_symbol_tableimaginary_unit_table imag_unitdiff_operator_tabler s rs r zLatexPrinter.__init__ sW x((( T^ # >( ( (K~f%[8
> "= > > > >+ , 5v&(2 504DN, -
- !=>
N- . . - - -|,
N- . . . -
1 !=!FG
N5 6 6 1 1 1|,2244BC
1 %U+ 9:: N<0 9:
1 "%3//
N#34 1E1I1I)U^1_1_-.
7
0C0G0G
Wd0e0e,---s% 1B
B/.B/3 C AD%$D%r r c , d | S )Nz\left({}\right)formatr rr s rs _add_parenszLatexPrinter._add_parens s !((+++ru c , d | S )Nz\left( {}\right)r r s rs _add_parens_lspacez LatexPrinter._add_parens_lspace s "))!,,,ru c t | }|r*|r(| | | S ||k s|s.||k r(| | | S | | S N)r r _print)r itemlevelis_negstrictprec_vals rs parenthesizezLatexPrinter.parenthesize s )$// 7f 7##DKK$5$566 6 u %v %8u3D %##DKK$5$566 6;;t$$ $ru c | d|v r7| j d r| | S d | S |S )z
Protect superscripts in s
If the parenthesize_super option is set, protect with parentheses, else
wrap in braces.
r r z{{{}}})r r r r s rs r z LatexPrinter.parenthesize_super sK !8 *~ 23
*''*** q)))ru c t j | | }| j d dk r|S | j d dk rd|z S | j d rd|z S | j d }d|d|d |dS )
Nr r r z$%s$r z$$%s$$z\begin{ro z\end{)r doprintr )r exprtexenv_strs rs r zLatexPrinter.doprint s odD)) >& !W , EJ
^F
#x
/ ES=
^F
# E s? "nV,GG.5ggsssGGGD Dru boolc \ |j r|j p |j o|t j uo|j du S )z
Returns True if the expression needs to be wrapped in brackets when
printed, False otherwise. For example: a + b => True; a => False;
10 => False; -10 => True.
F)
is_Integeris_nonnegativeis_Atomr NegativeOne is_Rationalr r s rs _needs_bracketsz LatexPrinter._needs_brackets sH _<)< J I$am*C +H.2.>%.GK Kru c | | sdS |j r| | sdS |j r| | sdS |j s|j rdS dS )a
Returns True if the expression needs to be wrapped in brackets when
passed as an argument to a function, False otherwise. This is a more
liberal version of _needs_brackets, in that many expressions which need
to be wrapped in brackets when added/subtracted/raised to a power do
not need them when passed to a function. Such an example is a*b.
FT)r is_Mul
_mul_is_cleanis_Pow
_pow_is_cleanis_Add is_Functionr s rs _needs_function_bracketsz%LatexPrinter._needs_function_brackets s ##D))
5 {
4#5#5d#;#;
t
T%7%7%=%=
t
0
t uru c Z ddl m} ddlm} ddlm} j r|s rdS n)t t d k rdS j
rdS j rdS t fdt fD rdS |s t fd|||fD rdS d S )
a
Returns True if the expression needs to be wrapped in brackets when
printed as part of a Mul, False otherwise. This is True for Add,
but also for some container objects that would not need brackets
when appearing last in a Mul, e.g. an Integral. ``last=True``
specifies that this expr is the last to appear in a Mul.
``first=True`` specifies that this expr is the first to appear in
a Mul.
r )Product)Sum)IntegralTr
c 3 B K | ]} | V d S r has.0xr s rs z3LatexPrinter._needs_mul_brackets..L - ++qtxx{{++++++ru c 3 B K | ]} | V d S r r* r, s rs r/ z3LatexPrinter._needs_mul_brackets..O s- BBADHHQKKBBBBBBru F)sympy.concrete.productsr& sympy.concrete.summationsr' sympy.integrals.integralsr( r could_extract_minus_signr r"
is_Relational is_Piecewiseanyr )r r firstlastr& r' r( s ` rs _needs_mul_bracketsz LatexPrinter._needs_mul_brackets5 s 433333111111666666 ;
T : : < <
t
#D
)
)Ju,=
= 4
4 4 ++++SF+++ + + 4 BBBB(GS)ABBBBB 4uru c r j rdS t fdt fD rdS j rdS dS )z
Returns True if the expression needs to be wrapped in brackets when
printed as part of an Add, False otherwise. This is False for most
things.
Tc 3 B K | ]} | V d S r r* r, s rs r/ z3LatexPrinter._needs_add_brackets..\ r0 ru F)r6 r8 r r" r s `rs _needs_add_bracketsz LatexPrinter._needs_add_bracketsT sU 4 ++++SF+++ + + 4 ; 4uru c . |j D ] }|j r dS
dS )NFT)argsr# )r r r< s rs r zLatexPrinter._mul_is_cleanb s. 9 C
uu
tru c 8 | |j S r )r baser s rs r! zLatexPrinter._pow_is_cleanh s '' 2222ru r c | d|d|dS |S )N\left( \right)^{ro rp r r exps rs _do_exponentzLatexPrinter._do_exponentk s' .2ddCCC8 8Kru c |j j }|j r> fd|j D }d}| |d | S d | S )Nc : g | ]} | S rp r )r- rM r s rs
z-LatexPrinter._print_Basic..t s# 444Q$++a..444ru z"\operatorname{{{}}}\left({}\right), z \text{{{}}})_deal_with_super_sub __class____name__r@ r join)r r namelsrr s ` rs _print_BasiczLatexPrinter._print_Basicq sw (( )@AA 9 /4444$)444B5A88D$))B--00 0!((.. .ru e!bool | BooleanTrue | BooleanFalsec d|z S N \text{%s}rp r rU s rs _print_boolzLatexPrinter._print_boolz
a ru c d|z S rX rp rZ s rs _print_NoneTypez LatexPrinter._print_NoneType r\ ru c | || }d}t | D ]b\ }}|dk rn"| r |dz
}| }n|dz
}| | }| | rd|z }||z
}c|S )N)r r r - + \left(%s\right))_as_ordered_terms enumerater5 r r> )r r r termsr r termterm_texs rs
_print_AddzLatexPrinter._print_Add s &&t5&99 '' GAtAv
..00
u uu {{4((H''--
9-8 8OCC
ru c L ddl m} |j dk rdS || }|j }|j }|j d |dz
k r
||dz
ggz }d}|D ](}|t | dd z
})| d d
}| d d }|S )
Nr Permutation\left( \right) r ,r r \left( r \right)) sympy.combinatorics.permutationsrk size cyclic_form
array_formr r )r r rk expr_permsizrg r s rs _print_CyclezLatexPrinter._print_Cycle s @@@@@@ 9> %$${4 $ i ?2 #' ) 0!cAgYK/I 3 3A AsE22 2HH##C44##C44ru c ddl m} ddlm} |j }| |d| dddd n j d
d }|r | S |j dk rd S fd
|j D } fdt t | D }d | }d | }d ||f } d| z S )Nr rj )sympy_deprecation_warningzw
Setting Permutation.print_cyclic is deprecated. Instead use
init_printing(perm_cyclic=z).
z1.6z#deprecated-permutation-print_cyclic )deprecated_since_versionactive_deprecations_target
stacklevelr Trl c : g | ]} | S rp rK r- r< r s rs rL z3LatexPrinter._print_Permutation.. s% ===cS!!===ru c : g | ]} | S rp rK r s rs rL z3LatexPrinter._print_Permutation.. s% ???cS!!???ru & \\ z \begin{pmatrix} %s \end{pmatrix})
rr rk sympy.utilities.exceptionsrz print_cyclicr r rx rs ru rangelenrQ )
r r rk rz r lowerupperrow1row2mats
` rs _print_Permutationz LatexPrinter._print_Permutation sF @@@@@@HHHHHH!. B % %+6 */+P
.,,]DAAK +$$T** * 9> %$$====T_===????U3u::->->???zz% zz% llD$<((2S88ru c t |j \ }}d| | d| | dS )Nz\sigma_{z}(r )r@ r )r r permvars rs _print_AppliedPermutationz&LatexPrinter._print_AppliedPermutation s> I cc%)[[%6%6%6%6 C8H8H8H8HIIru c 0 t |j }| j d rdnd}d| j v r
| j d nd }d| j v r
| j d nd }t |j |||| }| j d }d|v r_| d \ }} | d d
k r
| d d } | j d d
k r| dd }||d| dS |dk rdS |dk rdS | j d d
k r| dd }|S )Nr FTr r ) strip_zeros min_fixed max_fixedr rU r +rn r comma.z{,}z10^{ro z+infz\inftyz-infz- \infty)r# _precr mlib_to_str_mpf_splitr )
r r dpsr lowhighstr_real separatormantrG s
rs _print_FloatzLatexPrinter._print_Float sZ $*%% 4>$','>HdnU##D(- (?It~e$$T tz3ES\`aaa N#=> (? "..--KT31v}
!""g~ 12g=
/||C..%)T999ccc: :
9
;~ 12g=
7#++C66Oru c |j }|j }| |t d d| |t d S )Nr
r _expr1_expr2r
r" r r vec1vec2s rs _print_CrosszLatexPrinter._print_Cross sU {{"&"3"3D*U:K"L"L"L"L"&"3"3D*U:K"L"L"LN Nru c X |j }d| |t d z S )Nz\nabla\times %sr
_exprr
r" r r r s rs _print_CurlzLatexPrinter._print_Curl s) j!D$5$5c:e;L$M$MMMru c X |j }d| |t d z S )Nz\nabla\cdot %sr
r r s rs _print_Divergencez LatexPrinter._print_Divergence s) j 4#4#4S*U:K#L#LLLru c |j }|j }| |t d d| |t d S )Nr
r r r s rs
_print_DotzLatexPrinter._print_Dot sU {{!%!2!24E9J!K!K!K!K!%!2!24E9J!K!K!KM Mru c X |j }d| |t d z S )Nz \nabla %sr
r r r funcs rs _print_Gradientz LatexPrinter._print_Gradient ) zd / /j6G H HHHru c X |j }d| |t d z S )Nz \Delta %sr
r r s rs _print_Laplacianz LatexPrinter._print_Laplacian r ru r c ddl m ddlm ddlm} j d j d d# fd }d# fd
t |t rG|j }|d t j u s!t d |d d D r | S d
}|
r| }d}|j r|dz
}d}nd} ||d \ }}|t j u r)t d dd
|j vr| || z
}n || } || }
t! |
} j d } j d r:| dk r4d|
vr0 |d
r
|d| d|
z
}nn|| d |
z
}nb| St! | | | z k r* |d r|d |
d d| d z
}n|j rt j }
t j }|j D ]n} |d
sJt! ||
|z | | z k s|j |j cxu rd
u r n n||z }i|
|z }
o |d r%|d ||
d!|
d d || d z
}n=|d ||
d!|
d || z
}n|d |
d | z
}n |d | d!|
d z
}|r|d"z
}|S )$Nr )Quantity)Prefix)fractionr r r r c > | j s"t | S j dvr| }nt | j }t |fdd \ }}t |fdd \ }} ||z |z S )N)oldnonec | t | f p)t | t ot | j S r )
isinstancer rB )r. r r s rs rt z:LatexPrinter._print_Mul..convert.. s@ z!hPVEW7X7X 8= )!S 1 1 < )!&( ; ; ru T)binaryc $ t | S r )r )r. r s rs rt z:LatexPrinter._print_Mul..convert.. s
1f8M8M ru )r r r r as_ordered_factorslistr@ r& ) r r@ unitsnonunitsprefixesr r convert_argsr s rs convertz(LatexPrinter._print_Mul..convert s ;
A4;;t,,---:_4 + 2244DD ??D #'t .= .= .= .= .=EI#K #K #Kx #'u.M.M.M.MVZ"["["[%#|Hx$7%$?@@@ru c dx}}t | D ]\ }} | }t |f s ||dk |t | dz
k rd|z }t
d | r3t
d t | r|z
}n|r|
z
}n|r|
z
}||z
}|}|S )Nr r rn )r9 r: rb ) rd r r r; r _between_two_numbers_psearchmatchr ) r@ _tex
last_term_texr rf rg r r numbersepr r s rs r z-LatexPrinter._print_Mul..convert_args s #% %D=$T??
)
)4 ;;t,,!$6(:;; &//Q!V673t99q=6H 0 K K A#5#@.q188 GG *.q177D BB* ) * ) &I%D (
Kru c 3 @ K | ]}t |t V d S r )r r )r- r< s rs r/ z*LatexPrinter._print_Mul..; s, &S&S3z#v'>'>&S&S&S&S&S&Sru rn F- r Tr )exactrm )evaluater r r )r: rD z
\right) / z / z \frac{1}{ro rq \frac{}{r r r )sympy.physics.unitsr sympy.physics.units.prefixesr sympy.simplifyr r r r
r@ r Oner8 r5 r" r r r r; r is_commutative)r r r r r@ include_parensr numerdenomsnumersdenomldenomratioabr. r r r r r s ` @@@@@rs
_print_MulzLatexPrinter._print_Mul s 000000777777++++++ (:; (BC A A A A A A A A A : dC *9DAw!%
*3&S&S$qrr(&S&S&S#S#S
*#|D))) ( ( * * 5DC{
&s
!%C xD111 u AE> + ;c!R% 8 8 8 I + ;
774== CC WU^^F WU^^F ((FN#45E~ /0 !
;Vq[ !
;v%!
; ++E+>> 9CfffffEECC88CC
; ''%,6
; ++E+== MC!66999fff 6 6CC\ MAA "Z # # 33AE3BB # #GGAaCLL$6$6$8$8 9 9E&L H#!"!1Q5E# # # #IN# # # # # FAA FAA///== J &wqzzzz666999ggajjjj J J &wqzzzz66699ggajjj J J C&&&))VVLLCC666666:: 3JC
ru c |j r9| | S | | S r )
is_aliasedr as_polyas_exprr s rs _print_AlgebraicNumberz#LatexPrinter._print_AlgebraicNumber{ sL ? /;;t||~~ 5 5 7 788 8;;t||~~.. .ru c | |j }|j rd| dS | |j }d| d| dS )NrD rq rM )r pis_inertalphar )r r r r s rs _print_PrimeIdealz LatexPrinter._print_PrimeIdeal sh KK = ('Q''' ' DJ . . 0 011,,,e,,,,ru r c |j j r|j j }|j j }t | dk rh|dk rb| j d rU| |j }|dk rd|z }n | j d rd||fz }nd||fz }|j j rd|z S |S | j d r|dk r| |j t d
}|j j r| | }|j j
r!| |j |d | S |d
|d |dS |j j r|j j r|j dk r|j d
|j dS |j j r`|j j }|j j }||z t | k r2|j dk r d|d|dS d|d|dt |j dS | | S |j j
r4| |j | |j S d}| || S )Nrn r r z \sqrt{%s}r z
\root{%d}{%s}z
\sqrt[%d]{%s}z \frac{1}{%s}r r /rG ^{ro rm z\frac{1}{\frac{r }}z\frac{1}{(\frac{z})^{z%s^{%s})rG r r qr r r rB is_negativer
r" is_Symbolr r# r r _helper_print_standard_power)r r r r rB r base_pbase_qs rs
_print_PowzLatexPrinter._print_Pow s 8 % -XZAXZA1vv{ "
-qAv "
-$. *I "
-{{49--6 7&-CC^F+ 7*aY6CC*aY6C8' *S00 J 23
-Q
-((Ju4EFF9& 9 22488D9( H ;;tyAA6F;GGG(,aaa33%
-$)*B
-9> >)-DHHH==9( g"&)+F"&)+F #f++5 g 8r> g gAG#P Pg IOPVPVPVX[\`\dXeXeXeXe#f ft,,, 9 E;;tydkk$(.C.C;DD D00s;;;ru templatec | |j }| |j t d }|j j r| | }nct |j t rI| d r4t j d| r | d r
|dd }|||fz S )Nr rD z\\left\(\\d?d?dotrq i)
r rG r
rB r" r r r r
startswithr8 r endswith)r r r rG rB s rs r z)LatexPrinter._helper_print_standard_power s kk$(## Ju,=>> 9 **400DDJ// ** -t44
j))
2;D4+%%ru c B | |j d S Nr r r@ r s rs _print_UnevaluatedExprz#LatexPrinter._print_UnevaluatedExpr s {{49Q<(((ru c t |j dk r*dt fd|j d D z }n4 fddt dfd|j D z }t |j t r!|d |j z z
}n | |j z
}|S )
Nrn z\sum_{%s=%s}^{%s} c : g | ]} | S rp rK r- r r s rs rL z+LatexPrinter._print_Sum.. # >>>!t{{1~~>>>ru r c j dt fd| d | d | d fD z S )N%s \leq %s \leq %sc : g | ]} | S rp rK r- rr r s rs rL zALatexPrinter._print_Sum.._format_ineq.. # FFFa4;;q>>FFFru rn r r tuplelr s rs _format_ineqz-LatexPrinter._print_Sum.._format_ineq E ,FFFFAaD!A$!3EFFFGGH Hru z\sum_{\substack{%s}} \\c & g | ]
} | S rp rp r- r r s rs rL z+LatexPrinter._print_Sum.. ! !G!G!Ga,,q//!G!G!Gru rb r limitsr r rQ r functionr r r r r r s ` @rs
_print_SumzLatexPrinter._print_Sum s t{ q I'>>>>t{1~>>>??@CC
H
H
H
H
H +!G!G!G!G4;!G!G!GHHIC dmS ) ) . % DM(B(BB BCC 4;;t}-- -C
ru c t |j dk r*dt fd|j d D z }n4 fddt dfd|j D z }t |j t r!|d |j z z
}n | |j z
}|S )
Nrn z\prod_{%s=%s}^{%s} c : g | ]} | S rp rK r
s rs rL z/LatexPrinter._print_Product.. r ru r c j dt fd| d | d | d fD z S )Nr c : g | ]} | S rp rK r s rs rL zELatexPrinter._print_Product.._format_ineq.. r ru rn r r r r s rs r z1LatexPrinter._print_Product.._format_ineq r ru z\prod_{\substack{%s}} r c & g | ]
} | S rp rp r s rs rL z/LatexPrinter._print_Product.. r ru rb r r! s ` @rs _print_ProductzLatexPrinter._print_Product s t{ q I(>>>>t{1~>>>??@CC
H
H
H
H
H ,!G!G!G!G4;!G!G!GHHIC dmS ) ) . % DM(B(BB BCC 4;;t}-- -C
ru 'BasisDependent'c ddl m} g }||j k r |j j S t || r'| }nd|fg}|D ]\ }}t |j }| d |D ]\ }} | dk r |
d|j z )| dk r |
d|j z Md | | z d
z }
|
d|
z |j z d | } | d d k r | d
d } n
| dd } | S )Nr )Vectorc 6 | d S r )__str__)r. s rs rt z4LatexPrinter._print_BasisDependent.. s !A$,,.. ru keyrn ra rm r` rD rq r - )
sympy.vectorr+ zero _latex_formr separateitemsr
componentssortappendr rQ ) r r r+ o1r6 systemvect
inneritemskvarg_stroutstrs rs _print_BasisDependentz"LatexPrinter._print_BasisDependent s '''''' 49 )9( ( dF # # MMOO))++EEYKE !
?
?LFD do 3 3 5 566J OO 8 8O 9 9 9"
?
?16 ?IIeam 34444"W ?IIeam 34444 '$++a.. 8: EGIIego
=>>>>
? ''"++ !9 ABBZFFABBZF
ru c | |j }d|z dz dd t | j |j z z }|S )Nr ro _{%s}ro )r rB rQ mapindices)r r tex_baser s rs _print_IndexedzLatexPrinter._print_Indexed sU ;;ty))(l3 w T\ * **, *, , ,
ru c 6 | |j S r )r labelr s rs _print_IndexedBasez LatexPrinter._print_IndexedBase s {{4:&&&ru c Z | |j }|j | |j }|j | |j }n | t j }d || }d || S |S )Nz%{lower}\mathrel{{..}}\nobreak {upper})r r z{{{label}}}_{{{interval}}})rJ interval)r rJ r r r Zeror )r r rJ r r rM s rs
_print_IdxzLatexPrinter._print_Idx s DJ'' : 4KK
++Ez
, DJ// AF++@GG !5 H 2 2H/66 ( 7 4 4
4 ru c t |j rd}n
| j d }d}d}t |j D ]u\ }}||z
}|dk r ||d| | z
}.||d| | | d| | dz
}v|dk r
d |d
|d}n d |d| | d |d}t d |j D r.|d| |j t d
dd S |d| |j t d
dd S )Nz\partialr r r rn r r ro r r }}{c 3 > K | ]}| V d S r r5 r- r s rs r/ z1LatexPrinter._print_Derivative..9 s. ??q))++??????ru r
Tr
r F) r r r reversedvariable_countr r r8 r@ r
r" )r r diff_symbolr dimr. nums rs _print_Derivativez LatexPrinter._print_Derivative# s DI & & @%KK .)>?K t 233 : :FAs 3JCax
:;;; A?? (,(?(? A(O(O(O(O(, C(8(8(8(8: : !8 O O&1kk3337CC O ,7;; C8H8H8H8H###NC ??TY??? ? ? @ "ssD$5$5di29= !2 !? !? !? @ @ru c |j \ }}} | } fd|D } fd|D }d d t || D }d|d|dS )Nc 3 B K | ]} | V d S r rK r- rU r s rs r/ z+LatexPrinter._print_Subs..G - 11T[[^^111111ru c 3 B K | ]} | V d S r rK r^ s rs r/ z+LatexPrinter._print_Subs..H r_ ru z\\ c 3 > K | ]}|d dz |d z V dS )r =rn Nrp )r- rU s rs r/ z+LatexPrinter._print_Subs..I sL !B !B"#AaD3J1 !B !B !B !B !B !Bru z\left. z \right|_{\substack{ z }})r@ r rQ zip) r subsr r new
latex_expr latex_old latex_new
latex_subss ` rs _print_SubszLatexPrinter._print_SubsD s c3[[&&
1111S111 1111S111 [[ !B !B'*9i'@'@!B !B !B B B
9C9CE Eru c
dg }} j d t |j dk rTt d |j D r6ddt |j dz
z z dz } fd |j D }n
t |j D ]}|d
}|d z
}t | dk r j d d
k r j d s|dz
}t | dk r>|d |d d |d dz
}t | dk r!|d |d z z
}| d
d | |d |j t d t d |j D d d | S ) Nr r c 3 < K | ]}t | d k V dS )rn N)r )r- lims rs r/ z/LatexPrinter._print_Integral..S s, (N(N3SQ (N(N(N(N(N(Nru z\ir rn ntc P g | ]"}d |d #S )\, r rK )r- symbolrX r s rs rL z0LatexPrinter._print_Integral..W sE 2 2 2!6 &1[$++fQi2H2H2HI 2 2 2ru r z\intr r r z\limitsr1 _{}^{r ro ^{%s}rq r r
c 3 > K | ]}| V d S r rS rT s rs r/ z/LatexPrinter._print_Integral..n s/ >o>o`aq?Y?Y?[?[>o>o>o>o>o>oru TrU )
r r r allrV r insertr
r r" r8 r@ rQ )r r r symbolsrn rr rX s ` @rs _print_Integralz LatexPrinter._print_IntegralN sA 2Wn%:; t{ q SS(N(N$+(N(N(N%N%N S #s4; / /! 344t;C2 2 2 2 2%)[2 2 2GG ,,
S
S Qws88a< ?~f-9 *$(N6$:*z)3xx1} Dt{{3q6/B/B/B/B/3{{3q6/B/B/B/B D D3xx1} ?w$++c!f*=*= >>qq T[[=P=P=P"QRRRR SS$"3"3DM4>u4E;>>o>oeien>o>o>o;o;o;? #4 #A #A #A WWW - - - / /ru c |j \ }}}}d| | z }t | dk s|t j t j fv r |d| | z z
}n1|| | d| | dz
}t
|t r|d| | dS |d| | S ) Nz
\lim_{%s \to z+-z%s}r ro rD rq r )r@ r r r InfinityNegativeInfinityr r )r r rU zz0dirr s rs _print_LimitzLatexPrinter._print_Limitr s
1b# Q / s88t Craj!2D%E E C 6DKKOO+ +CC BS1A1A1A1AB BC a ! ! 4+.33 A? ? "ssDKKNNN3 3ru r c | | }| d }| d }|t v rd|z }nt | dk s!| d s |dk s|dk r|}n|dk r;|dk r5d|dt || d |t || d }nC|dk rd|d| d ||d }n$|dk rd|d| d ||d }nd
|z }|S ) ak
Logic to decide how to render a function to latex
- if it is a recognized latex name, use the appropriate latex command
- if it is a single letter, excluding sub- and superscripts, just use that letter
- if it is a longer name, then put \operatorname{} around it and be
mindful of undercores in the name
r _z\%srn r r \operatorname{Nro z\operatorname{%s})rN findaccepted_latex_functionsr r r )r r superscriptidx subscriptidxrR s rs _hprint_Functionz LatexPrinter._hprint_Function s ((.. 3 yy~~ + + 3D=DD
YY!^ 3tt 4 4 3 8I 3^_`M` 3DD !
3lQ&6
3
3:#l>:::;;;\.99::;;= !#
3
3 . ))) ))+ !
3
3 , ''' '') ,d2 ru r c < |j j }t d|z r2t |t s t d|z || S fd|j D } j d }d} j d o3t | dk o |j d }g d}||v r?|d k rn8|d
k r |d d k rd
nd|dd z }n|dk r|dd }d}|d}|r|t v rd|z } nPd|z } nJ|3 | }
|
}
|
d|d} n | } |r|t v r| dz
} n | dz
} n| dz
} |r
|| d|z z
} | d
| z S )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
_print_c T g | ]$}t | %S rp )r r r s rs rL z0LatexPrinter._print_Function.. s- ???cC C(())???ru r Fr rn r ) asinacosatanacscasecacotasinhacoshatanhacschasechacothr fullrm hararcNpowerTz\%s^{-1}z\operatorname{%s}^{-1}r ro z {%s}%s{\left(%s \right)}ru ro )r rP hasattrr r getattrr@ r r r$ r r r rQ ) r r rG r r@ r inv_trig_power_casecan_fold_bracketsinv_trig_tablerR func_texs ` rs _print_Functionz LatexPrinter._print_Function sM y! 4T) * * = ) t\22= )274T!1224== =????TY???D "^,< =N"' $/C D !@D Q!@11$)A,???
N ~%
2!]2
2#v- 2$(HO >DD$qrr(JDD#w. 2 8D*.' 2,1)"
333 <&-DD4t;DD
3 0066 228<<%-XXsss3,,T22
.33 " H$DDEMDD--"
's
'3&#((4..( (ru c F | t | S r )r r r s rs _print_UndefinedFunctionz%LatexPrinter._print_UndefinedFunction s $$SYY///ru c t d| |j d| |j dS )Nr z}_{\circ}\left({z}\right))r r r r s rs _print_ElementwiseApplyFunctionz,LatexPrinter._print_ElementwiseApplyFunction s< KK
& & & & KK " " " "
ru c ^ ddl m} ddlm}m} ddlm} ddlm} ddl m
} |d|d|d |d
|d|d iS ) Nr )KroneckerDelta)gamma
lowergamma)beta)
DiracDelta)rU z\deltar@ \gammaz\operatorname{B}z\operatorname{Chi}) (sympy.functions.special.tensor_functionsr 'sympy.functions.special.gamma_functionsr r &sympy.functions.special.beta_functionsr 'sympy.functions.special.delta_functionsr 'sympy.functions.special.error_functionsrU )r r r r r r rU s rs _special_function_classesz&LatexPrinter._special_function_classes s KKKKKKMMMMMMMM??????FFFFFF?????? I)I* , ,ru c | j D ]1}t || r |j |j k r| j | c S 2| t | S r )r
issubclassrP r r )r r clss rs _print_FunctionClassz!LatexPrinter._print_FunctionClass se 1 ; ;C$$$
; #,)F
;5c::::$$SYY///ru c |j \ }}t | dk r | |d }n"| t | }d|d| | d}|S )Nrn r rp z \mapsto \right))r@ r r r )r r ry r s rs
_print_LambdazLatexPrinter._print_Lambda st
w<<1 2kk'!*--GGkk%..11G18$++d:K:K:K:KL
ru c dS )Nz\left( x \mapsto x \right)rp r s rs _print_IdentityFunctionz$LatexPrinter._print_IdentityFunction s ,,ru c t |j t } fd|D }dt |j dd | d}||d|dS |S ) Nr. c @ g | ]}d | z S )r rK )r- rr r s rs rL z:LatexPrinter._hprint_variadic_function.. s* BBB654;;v...BBBru r rD rM rq r ro )sortedr@ r r r r rQ )r r rG r@ texargsr s ` rs _hprint_variadic_functionz&LatexPrinter._hprint_variadic_function s di%5666BBBBTBBB'*49~~';';'='='='='+yy'9'9'9'9; !$ccc* *Jru c ` d| |j d z }||d|dS |S )Nz \left\lfloor{%s}\right\rfloorr r ro r r r rG r s rs _print_floorzLatexPrinter._print_floor$ s> .TYq\1J1JJ !$ccc* *Jru c ` d| |j d z }||d|dS |S )Nz\left\lceil{%s}\right\rceilr r ro r r s rs _print_ceilingzLatexPrinter._print_ceiling, s> ,t{{49Q "T[[1 %>%>> !$ccc* *Jru c & | j d r0d| |j d t d z }n?d | |j d t d }| || S )Nr z\Re{%s}r Atomz\operatorname{{re}}{{{}}}r r
r@ r" r rH r s rs _print_rezLatexPrinter._print_reG >. ) k t 0 01 z&?Q R RRCC.55d6G6G RS V`agVh6i6ijjC c***ru c & | j d r0d| |j d t d z }n?d | |j d t d }| || S )Nr z\Im{%s}r r z\operatorname{{im}}{{{}}}r r s rs _print_imzLatexPrinter._print_imO r ru c ddl m}m} t |j d | r!| |j d d S t |j d | r!| |j d d S |j d j r#d| |j d z S d| |j d z S )Nr )
EquivalentImpliesz\not\Leftrightarrowz\not\Rightarrowz\neg \left(%s\right)z\neg %s) sympy.logic.boolalgr r r r@ _print_Equivalent_print_Implies
is_Booleanr )r rU r r s rs
_print_NotzLatexPrinter._print_NotW s ======== afQi , , M))!&)5KLL L afQi ) ) F&&qvay2DEE E
F1I 7*T[[-C-CC C AF1I 6 66 6ru c F |d }|j r |j sd| | z }nd| | z }|dd D ]N}|j r'|j s |d|d| | dz
}0|d|d| | z
}O|S )Nr rb r rn r z \left(rq )r is_Notr )r r@ charr< r s rs _print_LogOpzLatexPrinter._print_LogOpb s 1g > +#* +$t{{3'7'77CC$++c***C8 < TYq\!:!:: !$ccc* *Jru c p d}d| |j d z }|
|d|d|S ||S )Nz\operatorname{polar\_lift}r r r ro r )r r rG r r< s rs _print_polar_liftz LatexPrinter._print_polar_lift sQ ,#dkk$)A,&?&?? )#'44cc2 2 "dCC( (ru c t d| |j d z }| || S )Nze^{%s}r )r r@ rH r s rs _print_ExpBasezLatexPrinter._print_ExpBase s6 $++dil333 c***ru c dS )NrU rp rF s rs _print_Exp1zLatexPrinter._print_Exp1 s sru c f d| |j d z }|d|d|S d|z S )Nrb r zK^{ro zK%sr r s rs _print_elliptic_kz LatexPrinter._print_elliptic_k sF 4;;ty|#<#<< "%##ss+ +C< ru c d| |j d d| |j d d}|d|d|S d|z S ) NrD r \middle| rn rq zF^{ro zF%sr r s rs _print_elliptic_fz LatexPrinter._print_elliptic_f si
[[1
&
&
&
& DIaL(A(A(A(AC "%##ss+ +C< ru c " t |j dk rFd| |j d d| |j d d}n#d| |j d z }|d|d |S d
|z S ) Nr rD r r rn rq rb zE^{ro zE%sr r@ r r s rs _print_elliptic_ez LatexPrinter._print_elliptic_e s ty>>Q A ATYq\****DKK ! ,E,E,E,EGCC %t{{49Q<'@'@@C "%##ss+ +C< ru c t |j dk rgd| |j d d| |j d d| |j d d}nEd| |j d d| |j d d}|d |d
|S d |z S ) Nr1 rD r ; rn r r rq z\Pi^{ro z\Pi%sr r s rs _print_elliptic_piz LatexPrinter._print_elliptic_pi s ty>>Q G GTYq\****DKK ! ,E,E,E,ETYq\****,CC G TYq\****DKK ! ,E,E,E,EGC " "$'CC- -c> !ru c d| |j d d| |j d d}|d|d|S d|z S ) NrD r rM rn rq z\operatorname{B}^{ro z\operatorname{B}%sr r s rs _print_betazLatexPrinter._print_beta sm (, DIaL(A(A(A(A(, DIaL(A(A(A(AC / /14cc: :(3. .ru Bc
fd|j D }d|d d|d d}| d|d|d d|d
d |d |
S d|d|d d|d
d
|S )Nc : g | ]} | S rp rK r s rs rL z/LatexPrinter._print_betainc.. s% 777cS!!777ru rD r rM rn rq r z}_{(r r1 z)}^{ro z)})r@ )r r rG operatorlargsr s ` rs _print_betainczLatexPrinter._print_betainc s 7777TY777(-a%(((; [ [=EXXuQxxxQVWXQYQYQY[^[^[^`c`cd d [ 9A%(((ERSHHHVYVYZ Zru c 2 | ||d S )NI)r )r rF s rs _print_betainc_regularizedz'LatexPrinter._print_betainc_regularized s ""4s";;;ru c d| |j d d| |j d d}|d|d|S d|z S ) NrD r rM rn rq z\Gamma^{ro z\Gamma%sr r s rs _print_uppergammaz LatexPrinter._print_uppergamma m (, DIaL(A(A(A(A(, DIaL(A(A(A(AC % %'*ssCC0 0 $ $ru c d| |j d d| |j d d}|d|d|S d|z S ) NrD r rM rn rq z\gamma^{ro \gamma%sr r s rs _print_lowergammaz LatexPrinter._print_lowergamma r ru c d| |j d z }|"| |j d|d|S | |j |S Nrb r r ro )r r@ r r s rs _hprint_one_arg_funcz!LatexPrinter._hprint_one_arg_func sk 4;;ty|#<#<< ;#';;ty#9#9#9#9333D D "kk$) 4 4 4cc: :ru c f d| |j d z }|d|d|S d|z S )Nrb r z\operatorname{Chi}^{ro z\operatorname{Chi}%sr r s rs
_print_ChizLatexPrinter._print_Chi sG 4;;ty|#<#<< 1 13633< <*S0 0ru c d| |j d z }| |j d }| d|d|d|S d|d|S )Nrb rn r z\operatorname{E}_{rt ro r )r r rG r nus rs
_print_expintzLatexPrinter._print_expint sq 4;;ty|#<#<<
[[1
&
& : :68bb###ssC C : 24SS9 9ru c f d| |j d z }|d|d|S d|z S )Nrb r zS^{ro zS%sr r s rs _print_fresnelsz LatexPrinter._print_fresnels F 4;;ty|#<#<< "%##ss+ +C< ru c f d| |j d z }|d|d|S d|z S )Nrb r zC^{ro zC%sr r s rs _print_fresnelcz LatexPrinter._print_fresnelc r ru c z d| |j d t d z }| d|d|dS |S )Nz!%sr FuncrD rE ro r
r@ r" r s rs _print_subfactorialz LatexPrinter._print_subfactorial sL t((1 z&7IJJJ .1cc3337 7Jru c x d| |j d t d z }||d|dS |S )Nz%s!r r r ro r! r s rs _print_factorialz LatexPrinter._print_factorial sG t((1 z&7IJJJ !$ccc* *Jru c x d| |j d t d z }||d|dS |S )Nz%s!!r r r ro r! r s rs _print_factorial2z LatexPrinter._print_factorial2' sG ))$)A,
68JKKK !$ccc* *Jru c d| |j d d| |j d d}||d|dS |S )Nz{\binom{r r rn r r ro r r s rs _print_binomialz LatexPrinter._print_binomial/ sd %)[[1 %>%>%>%>%)[[1 %>%>%>%>@ !$ccc* *Jru c |j \ }}d| |t d z }d|d| | d}| || S )Nr r r }^{\left(\right)}r@ r
r" r rH )r r rG nr> rB r s rs _print_RisingFactorialz#LatexPrinter._print_RisingFactorial8 s` y1t((Jv,>???+/44Q @ c***ru c |j \ }}d| |t d z }d| | d|d}| || S )Nr r z{\left(z
\right)}_{ro r, )r r rG r- r> subr s rs _print_FallingFactorialz$LatexPrinter._print_FallingFactorial@ s` y1d'':f+=>>>+/;;q>>>>333? c***ru symc d|z }d}|$| d dk r |d|d}nd}|d| |j d | |j d
}|r| || }|S ) Nr Fr rm r ro Trs }\left(rq )r r r argumentrH )r r rG r2 r need_exps rs _hprint_BesselBasez LatexPrinter._hprint_BesselBaseH s sm xx}}"
$'CC- +.33 DJ0G0G0G0G+/;;t}+E+E+E+EG .##C--C
ru c |sdS d}|d d D ] }|d| | z z
} || |d z
}|S )Nr rm z%s, rK )r r rr r s rs _hprint_veczLatexPrinter._hprint_vecY se 2 SbS ) )A
$++a..( (AA T[[R
!
!!ru c 0 | ||d S )NJr7 rF s rs _print_besseljzLatexPrinter._print_besseljb &&tS#666ru c 0 | ||d S )Nr
r< rF s rs _print_besselizLatexPrinter._print_besselie r> ru c 0 | ||d S )NKr< rF s rs _print_besselkzLatexPrinter._print_besselkh r> ru c 0 | ||d S )NYr< rF s rs _print_besselyzLatexPrinter._print_besselyk r> ru c 0 | ||d S )Nyr< rF s rs _print_ynzLatexPrinter._print_ynn r> ru c 0 | ||d S )Nr r< rF s rs _print_jnzLatexPrinter._print_jnq r> ru c 0 | ||d S )NzH^{(1)}r< rF s rs _print_hankel1zLatexPrinter._print_hankel1t &&tS)<<>Q A(5T[$)1L1L+M+MMCC$t{{49Q<'@'@@C 0 0&)cc33/ /C ru c t |j dk r+dt t | j |j z }n#d| |j d z }| d|d|dS d|z S ) Nr z_{%s}\left(%s\right)rD r r r ro r rz r s rs _print_stieltjesz LatexPrinter._print_stieltjes s ty>>Q 7)E#dk492M2M,N,NNCCT[[1 6 66C 1 1'*ssCCC0 0S ru c t dt t | j |j z }|d|z S d|d|S )Nz\left(%s, %s, %s\right)z\Phi%sz\Phi^{ro )r rE r r@ r s rs _print_lerchphiz LatexPrinter._print_lerchphi sJ (5T[$)1L1L+M+MM # s? " #!$cc**ru c p t | j |j \ }}d|z }|d|d|S d|d|d|S )Nrb z\operatorname{Li}_{ro rt rE r r@ )r r rG rr r~ r s rs _print_polylogzLatexPrinter._print_polylog s] 4; **1 1$ : :23!!SS9 9 :3411ccc33??ru c | t | j |j \ }}}}d|d|d|d|d }| d|z d|z z }|S )NP_{r* ro \right)}\left(rq rD \right)^{%s}r )r r rG r- r r r. r s rs
_print_jacobizLatexPrinter._print_jacobi s] di00
1a?@qq!!!QQQJ <c/Os$;;C
ru c t t | j |j \ }}}d|d|d|d}| d|z d|z z }|S )NzC_{r* r rq rD r r r r rG r- r r. r s rs _print_gegenbauerz LatexPrinter._print_gegenbauer U dk49--1aa<=AAqqq!!!D <c/Os$;;C
ru c l t | j |j \ }}d|d|d}| d|z d|z z }|S )NzT_{r4 rq rD r r r r rG r- r. r s rs _print_chebyshevtz LatexPrinter._print_chebyshevt M 4; **11*+!!QQQ/ <c/Os$;;C
ru c l t | j |j \ }}d|d|d}| d|z d|z z }|S )NzU_{r4 rq rD r r r s rs _print_chebyshevuz LatexPrinter._print_chebyshevu r ru c l t | j |j \ }}d|d|d}| d|z d|z z }|S )Nr r4 rq rD r r r s rs _print_legendrez LatexPrinter._print_legendre r ru c t t | j |j \ }}}d|d|d|d}| d|z d|z z }|S )Nr r* r rq rD r r r s rs _print_assoc_legendrez"LatexPrinter._print_assoc_legendre r ru c l t | j |j \ }}d|d|d}| d|z d|z z }|S )NzH_{r4 rq rD r r r s rs _print_hermitezLatexPrinter._print_hermite r ru c l t | j |j \ }}d|d|d}| d|z d|z z }|S )NL_{r4 rq rD r r r s rs _print_laguerrez LatexPrinter._print_laguerre
r ru c t t | j |j \ }}}d|d|d|d}| d|z d|z z }|S )Nr r* r rq rD r r r s rs _print_assoc_laguerrez"LatexPrinter._print_assoc_laguerre r ru c | t | j |j \ }}}}d|d|d|d|d }| d|z d|z z }|S )NzY_{rt r4 ro rq rD r r r r rG r- mthetaphir s rs
_print_YnmzLatexPrinter._print_Ynm ^ t{DI661eSS23!!QQQsssC <c/Os$;;C
ru c | t | j |j \ }}}}d|d|d|d|d }| d|z d|z z }|S )NzZ_{rt r4 ro rq rD r r r s rs
_print_ZnmzLatexPrinter._print_Znm r ru c
v t | j | \ }}}|rdnd}|sdnd|z }||d|d|d|d|
S )Nz ^{\prime}r ru rD rM rq )rE r ) r characterr@ r rG r r r~ sups rs __print_mathieu_functionsz&LatexPrinter.__print_mathieu_functions& s` dk4((1a #+ll.bb3 3<9ccc111aaaCCPPru c < | d|j | S )NCr &_LatexPrinter__print_mathieu_functionsr@ rF s rs _print_mathieucz LatexPrinter._print_mathieuc, --c49#-FFFru c < | d|j | S )Nr r r rF s rs _print_mathieusz LatexPrinter._print_mathieus/ r ru c > | d|j d| S )Nr Tr rG r rF s rs _print_mathieucprimez!LatexPrinter._print_mathieucprime2 ! --c49Dc-RRRru c > | d|j d| S )Nr Tr r rF s rs _print_mathieusprimez!LatexPrinter._print_mathieusprime5 r ru c |j dk r@d}|j }|j dk rd}| }| j d r
d|||j fz S d|||j fz S | |j S )Nrn r r r r z %s%d / %dz%s\frac{%d}{%d})r r r r )r r signr s rs _print_Rationalz LatexPrinter._print_Rational8 s 6Q;
'DAvz
B~ /0
8#tQ&777%q$&(99 9;;tv&& &ru c @ | |j }|j r t d |j D st |j dk r|dz
}t |j dk r || |j z
}n*|j r#|| |j d z
}|dz
}t |j dk r || |j z
}n#|| |j d z
}d|z S )Nc 3 6 K | ]}|t j k V d S r )r rN )r- r s rs r/ z,LatexPrinter._print_Order..G s( > >aa16k > > > > > >ru rn r r \rightarrow zO\left(%s\right))r r pointr8 r variables)r r rr s rs _print_OrderzLatexPrinter._print_OrderE s KK " " : 0# > >4: > > >>> 0 t~ " 0
IA4>""Q&
4T[[ 000
4T[[ !2333
A4:"
0T[[,,,T[[A ///"Q&&ru r
c | j d | }||S | |j | S )Nr style)r r rN rR )r r r rR s rs
_print_SymbolzLatexPrinter._print_SymbolU sD N>266t<< K((%(@@@ru stringc : d|v r|g g }}}n:t | \ }}}t | }d |D }d |D }|dk rd | }|r|dd | z z
}|r|dd | z z
}|S ) Nr c , g | ]}t | S rp translater- r s rs rL z5LatexPrinter._deal_with_super_sub..e 777inn777ru c , g | ]}t | S rp r r- r0 s rs rL z5LatexPrinter._deal_with_super_sub..f 333sIcNN333ru r
\mathbf{{{}}}ru r rD )r r r rQ )r r r rR supersrd s rs rN z!LatexPrinter._deal_with_super_sub^ s &= 4!'R$&DD!0!8!8 D&$ T??D77777F33d333D F? 1#**400D / Gchhv . .. .D - Gchhtnn, ,D ru c | j d rd}d}nd}d}d||ddd d
}| |j d ||j d | |j S ) Nr z\gtz\lt>=z<=z!=r )r r lhsrel_oprhs)r r gtltcharmaps rs _print_Relationalz LatexPrinter._print_Relationalt s >& ! BBBBB
"[[ 2 2 2 2 $T[ 1 1 14;;tx3H3H3HJ Jru c fd|j d d D }|j d j t k r<| d |j d j z n`| |j d j d |j d j d}|d | z S )Nc p g | ]2\ }} | d | 3S ) & \text{for}\: rK )r- rU r r s rs rL z1LatexPrinter._print_Piecewise.. sL / / /q! /3kk!nnnndkk!nnnM / / /ru rm z%s & \text{otherwise}r z \begin{cases} %s \end{cases}rr )r@ condr r9 r r rQ )r r ecpairsr s ` rs _print_Piecewisez LatexPrinter._print_Piecewise s / / / / #y"~/ / / 9R= % > NN3 ;;ty}'9:: ;
<
<
<
<
NN KK "
(: ; ; ; ; KK "
(: ; ; ; =
>
>
> .V[[))))ru c
g }t |j D ]@}| d fd||d d f D A j d }|& j d dk rd}n|j dk du rd }nd
}d }| d | }|d
k r$| d
dd|j z z dz }|d | z S )Nr c : g | ]} | S rp rK r
s rs rL z7LatexPrinter._print_matrix_contents.. s# $K$K$KT[[^^$K$K$Kru r r r smallmatrix
Tmatrixarray \begin{%MATSTR%}%s\end{%MATSTR%}%MATSTR%r r r z}%sr )r rowsr9 rQ r colsr )r r linesliner out_strs ` rs _print_matrix_contentsz#LatexPrinter._print_matrix_contents s $)$$ N ND LL$K$K$K$KT$']$K$K$KLL M M M M.+ &~f%1
&'IO, & &GG %G5//*g66 g I oodC#di-,?%,GHHGE****ru c | | }| j d r(| j d }| j | }d|z |z dz |z }|S )Nr \left\right)r r r )r r r
left_delim right_delims rs _print_MatrixBasez LatexPrinter._print_MatrixBase sa --d33 >+ & . "n[ 9J *:6K +g5 "-.Gru c | |j t d d d| |j d| |j dz S )Nr Tr rs rM ro )r
parentr" r r r r s rs _print_MatrixElementz!LatexPrinter._print_MatrixElement s` j.@ NNN ![[ 0 0 0 0$++df2E2E2E2EFG Gru c fd} |j t d d dz ||j |j j z dz ||j |j j z dz S )Nc t | } | d dk r| d= | d dk rd | d< | d |k rd | d< d fd| D S )Nr rn r :c 3 J K | ] }| | ndV d S Nr rK )r- xir s rs r/ zFLatexPrinter._print_MatrixSlice..latexslice.. s6 RR"r EDKKOOO2RRRRRRru )r rQ )r. rY r s rs
latexslicez3LatexPrinter._print_MatrixSlice..latexslice s QAtqy
aDtqy
!ts{
!88RRRRPQRRRRR Rru r Tr \left[rM \right])r
r r" rowslicer colslicer )r r r s ` rs _print_MatrixSlicez LatexPrinter._print_MatrixSlice s S S S S S !!$+z&/A$!OOR[[
4=$+*:;;<>BC
4=$+*:;;<>HI Jru c 6 | |j S r )r blocksr s rs _print_BlockMatrixz LatexPrinter._print_BlockMatrix s {{4;'''ru c |j }ddlm}m} t || s/t || s |j rd| | z S | |t | d }d|v rd|z S d|z S )Nr MatrixSymbol BlockMatrixz\left(%s\right)^{T}Tr z%s^{T} r< sympy.matricesr
r r
is_MatrixExprr r
r r r r r
r rr s rs _print_Transposez LatexPrinter._print_Transpose s h<<<<<<<<3 -- $3 ,, $141B $)DKK,<,<< <!!#'=d'C'CTJJAax
$-11 !|#ru c @ |j }d| | z S )Nz!\operatorname{tr}\left(%s \right))r< r r r r s rs _print_TracezLatexPrinter._print_Trace s h3dkk#6F6FFFru c |j }ddlm}m} t || s/t || s |j rd| | z S | |t | d }d|v rd|z S d|z S )Nr r z\left(%s\right)^{\dagger}Tr z %s^{\dagger}r r s rs _print_AdjointzLatexPrinter._print_Adjoint s h<<<<<<<<3 -- +3 ,, +141B +/$++c2B2BB B!!#'=d'C'CTJJAax
+3a77&**ru c J ddl m fd}t j } rI|d dk r |dd }n |d |d< dd t
|| z S d t
|| S )Nr )MatMulc t | t r%t | s | n# | t d S NF)r r
r r
r )r. r r r s rs rt z,LatexPrinter._print_MatMul.. sZ Z3-?-? F
STV\H]H] F4;;q>>> a!7!=!=u E E ru rm rn r r )sympyr r r@ r5 rQ rE )r r parensr@ r s `` @rs
_print_MatMulzLatexPrinter._print_MatMul s F F F F F F DI ( ( * * /Aw"}
#ABBx 7(Q#((3vt#4#4555 588C - -.. .ru c |j }|j rKddlm} t || r d| |j z S d| | z S d| | z S )Nr )r r )r< r &sympy.matrices.expressions.blockmatrixr r r r r )r r r r s rs _print_Determinantz LatexPrinter._print_Determinant s h ; J J J J J J#{++
V+d.I.I#*.U.UUU'$++c*:*:: :#d&A&A#&F&FFFru c |dd| |j d t d d d| |j d t d d d|d S | |j d t d d d| |j d t d d S )
NrD r r
Tr z \bmod rn rE ro r! rF s rs
_print_ModzLatexPrinter._print_Mod s ""49Q<E1B*. # 0 0 0 0""49Q<E1B*. # 0 0 0 0
"&!2!249Q<3=e3D:> "3 "@ "@ "@ "@ "&!2!249Q<3=e3D:> "3 "@ "@ "@A Aru c |j }t d | j d t fd| S )Nr z \circ c | d S NTr rp r< r precs rs rt z5LatexPrinter._print_HadamardProduct.. FF3T : : : ru r@ r" r
rQ rE r r r@ r r& s @@rs _print_HadamardProductz#LatexPrinter._print_HadamardProduct sP y% " :::::D A AC C Cru c ~ t |j t d k rd}nd}| || S )Nr
z %s^{\circ \left({%s}\right)}z%s^{\circ {%s}})r rG r" r )r r r s rs _print_HadamardPowerz!LatexPrinter._print_HadamardPower s@ !$( + +j.? ? *6HH)H00x@@@ru c |j }t d | j d t fd| S )Nr \otimes c | d S r$ rp r% s rs rt z6LatexPrinter._print_KroneckerProduct..& r' ru r( r) s @@rs _print_KroneckerProductz$LatexPrinter._print_KroneckerProduct sR y% " :::::D A AC C Cru c V |j |j }}ddlm} t || s6|j r/d| | d| | dS | | }d|v r d|d| | dS |d| | dS )Nr )r
rD rE ro r r )rB rG r
r
r r r )r r rB rG r
base_strs rs
_print_MatPowzLatexPrinter._print_MatPow( s Itxc//////$ -- @$2D @ @/3{{4/@/@/@/@.2kk#.>.>.>.>@
@ {{4((Hh
@
@2:((DKK.>.>.>??ru c F | || j d S )Nr r )r r r s rs _print_MatrixSymbolz LatexPrinter._print_MatrixSymbol5 s+ !!$dn / ! ! ! !ru c , | j d dk rdndS )Nr r 0z
\mathbf{0}r )r Zs rs _print_ZeroMatrixz LatexPrinter._print_ZeroMatrix9 ( n #*+ >ss0= >ru c , | j d dk rdndS )Nr r 1z
\mathbf{1}r8 )r Os rs _print_OneMatrixz LatexPrinter._print_OneMatrix= r; ru c , | j d dk rdndS )Nr r z
\mathbb{I}z
\mathbf{I}r8 )r r
s rs _print_Identityz LatexPrinter._print_IdentityA s( $ ! #*!+ >}}0= >ru c L | |j d }d|z S )Nr zP_{%s}r )r Pperm_strs rs _print_PermutationMatrixz%LatexPrinter._print_PermutationMatrixE s$ ;;qvay))(""ru r c
| dk r| |d S | j d }|B| j d dk rd}n.| dk s|j d dk rd }nd
}d }| d | }|d
k r| d
d }| j d r(| j d }| j | }d|z |z dz |z }| dk r|dz S d t
| dz D }d |j D }t j | D ]C}|d | || d} t
| dz
dd D ]}
t ||
dz |j |
k r n| r8||
d ||
dz ns||
|d ||
dz z t ||
dz dk r d||
d z dz ||
d< | } g ||
dz < E|d d } | dz dk r|| z } | S ) Nr rp r r r r rm r r r r r r z{}%sr r r r c g | ]}g S rp rp rT s rs rL z1LatexPrinter._print_NDimArray..d s %I%I%IQb%I%I%Iru rn c F g | ] }t t | S rp )r r rT s rs rL z1LatexPrinter._print_NDimArray..e s$ ;;;1U1XX;;;ru Tr r r r r ) rankr r shaper r r itertoolsproductr9 r rQ ) r r r block_strr r level_str shape_rangesouter_ieven back_outer_ir s rs _print_NDimArrayz LatexPrinter._print_NDimArrayI s! 99;;! );;tBx(( (.+ &~f%1
&'IIKK1$ &$*R.B*> & &GG %G7 %%j':: g 6 ((f55I >+ & 0 "n[ 9J *:6K :- 9!"$/0I 99;;! " r> !%I%I% a2H2H%I%I%I ;;
;;; (,7 / /G bM T']!;!; < < <D %diikk!mR < <
/
/ y a 011DJ|4LL E E l+22 Il1n$=>>@ @ @ @ l+22!UZZ ,q.0I%J%JKM M M9\!^455: E6? %l 3B 778:D7E ,/3 x,. ,q.))A,q/ 99;;?a * ')Gru index_mapdictc ` | | }d }d }|D ]}|j }||v s|r ||k r|dz
}||k r||dz
}|j r|dz
}n|dz
}|| |j d z
}||v r&|dz
}|| || z
}d}nd}|}||dz
}|S ) Nro ro z{}^{z{}_{r rb TF)r is_upr@ ) r rR rF rT r last_valenceprev_mapindex new_valences rs _printer_tensor_indicesz$LatexPrinter._printer_tensor_indices s ++d## ' 'E +K)#
K/
3{*
& #sNG; &v%GGv%G t{{5:a=11 1G !
!34;;y'7888 &LL sNGru c |j d j d }| }| ||i S r )r@ get_indicesr\ )r r rR rF s rs
_print_TensorzLatexPrinter._print_Tensor s> y| #""$$++D'2>>>ru c |j j d j d }|j }|j }| ||| S r )r r@ r^ rT r\ )r r rR rF rT s rs _print_TensorElementz!LatexPrinter._print_TensorElement sJ y~a %a()''))N ++D'9EEEru c ~ \ }}|d fd|D z S )Nr c V g | ]%} |t &S rp )r
r! )r- r< r r s rs rL z/LatexPrinter._print_TensMul.. s1 F F F#T
sJt$4$4
5
5 F F Fru )!_get_args_for_traditional_printerrQ )r r r r@ s `` rs _print_TensMulzLatexPrinter._print_TensMul sP ;;==
dbgg F F F F F F F F
ru c g }|j }|D ]8}| | |t | 9| d | }| dd }|S )Nra z+ -r )r@ r9 r
r! r8 rQ r )r r r r@ r. rr s rs _print_TensAddzLatexPrinter._print_TensAdd s~ y = =A
HHT&&q*T*:*:;; < < < < JJqMM
IIeT " "ru c b d|j rdndd| |j d dS )Nz{}r r r r ro )rW r r@ r s rs _print_TensorIndexz LatexPrinter._print_TensorIndex s= : &CC3 & & KK ! % % % %
ru c
t |j dk rLd |j d d |j t
d d dS dt |j dd fd
|j D d |j t
d d dS ) Nrn z\frac{\partial}{\partial {r rQ r
Fro z\frac{\partial^{r c @ g | ]}d | z S )z
\partial {%s}rK r
s rs rL z9LatexPrinter._print_PartialDerivative.. s) TTT*T[[^^;TTTru r )r r r r
r r" rQ r s ` rs _print_PartialDerivativez%LatexPrinter._print_PartialDerivative s t~ ! #
DN1 -....!!$)Z->FFFF
DN####TTTTT^TTTUUUU!!$)Z->FFFF
ru c 6 | |j S r )r rR r s rs _print_ArraySymbolz LatexPrinter._print_ArraySymbol s {{49%%%ru c d |j t d d dd fd|j D dS )Nz{{r T}_{rM c < g | ]} | S rp rK r
s rs rL z4LatexPrinter._print_ArrayElement.. s& AAAq$++a..*AAAru r )r
rR r" rQ rF r s ` rs _print_ArrayElementz LatexPrinter._print_ArrayElement s_ diF);T B B B B IIAAAADLAAA B B B BD Dru c dS )Nz
\mathbb{U}rp r s rs _print_UniversalSetz LatexPrinter._print_UniversalSet }ru c |#d| |j d z S d| |j d d|dS )Nz$\operatorname{frac}{\left(%s\right)}r z\operatorname{frac}{\left(z
\right)}^{ro r rF s rs _print_fraczLatexPrinter._print_frac sZ 4:T[[ST =V=VV V 4 KK ! ----sss4
4ru c h j d dk rd}n# j d dk rd}nt d t | dk r1 |d |z S |d z fd
|D S ) Nr r ;r ro Unknown Decimal Separatorrn r z \ c : g | ]} | S rp rK r
s rs rL z-LatexPrinter._print_tuple.. s# %C%C%Cdkk!nn%C%C%Cru )r r r r r rQ )r r seps ` rs _print_tuplezLatexPrinter._print_tuple s >- .' 9 :CC
^ /
0H
< :CC 899 9 t99> F**4;;tAw+?+?#+EFF F**w $$%C%C%C%Cd%C%C%CDDF F
Fru c T fd|j D }d | S )Nc : g | ]} | S rp rK r- r r s rs rL z5LatexPrinter._print_TensorProduct.. # 666qDKKNN666ru r. r@ rQ r r elementss ` rs _print_TensorProductz!LatexPrinter._print_TensorProduct s2 6666DI666 ***ru c T fd|j D }d | S )Nc : g | ]} | S rp rK r s rs rL z4LatexPrinter._print_WedgeProduct.. r ru \wedge r r s ` rs _print_WedgeProductz LatexPrinter._print_WedgeProduct s2 6666DI666 )))ru c , | | S r )r} r s rs _print_TuplezLatexPrinter._print_Tuple s &&&ru c j d dk r$dd fd|D z S j d dk r$dd fd|D z S t d )
Nr r z\left[ %s\right]z; \ c : g | ]} | S rp rK r
s rs rL z,LatexPrinter._print_list.. # < < . r ru rz )r rQ r r s ` rs _print_listzLatexPrinter._print_list s >- .' 9 :&
< < <
>
^ /
0H
< :&
< < <
> 899 9ru c t | t }g }|D ]J}|| }| | | d| | Kdd | z S )Nr. z : z\left\{ %s\right\}r )r keysr r9 r rQ )r r r r6 r/ vals rs _print_dictzLatexPrinter._print_dict s affhh$4555 K KCC&C LLdkk#&6&6&6&6 C8H8H8HI J J J J$x}}U';';;;ru c , | | S r )r r s rs _print_DictzLatexPrinter._print_Dict s %%%ru c @ t |j dk s|j d dk r$d| |j d z }nEd| |j d d| |j d d}|r d|d|d }|S )
Nrn r z\delta\left(%s\right)z\delta^{\left( z \right)}\left( r rD rE ro r r s rs _print_DiracDeltaz LatexPrinter._print_DiracDelta s ty>>Q F$)A,!"3 F*T[[1 -F-FFCC F DIaL))))4;;ty|+D+D+D+DFC 7 7-0SS###6C
ru c | |j d |j d z
}| |j d }d|d|d}| d|d|d |d}|S )
Nr rn r z{\left\langle z \right\rangle}^{ro z{\left({\langle z \rangle}^{z }\right)}^{r )r r rG shiftr r s rs _print_SingularityFunctionz'LatexPrinter._print_SingularityFunction s~ DIaL49Q< 788 DIaL))9>F Y YFKeeUUUTWTWTWXC
ru c t d fd|j D }d|z }|r d|d|d}|S )NrM c 3 B K | ]} | V d S r rK r s rs r/ z0LatexPrinter._print_Heaviside..! s/ AAs$++c**AAAAAAru z\theta\left(%s\right)rD rE ro )rQ pargs)r r rG r r s ` rs _print_Heavisidez LatexPrinter._print_Heaviside sY AAAAdjAAAAA&. 7 7-0SS###6C
ru c
| |j d }| |j d }|j d j r |j d j r
d|d|d}n d|d|d}| d|d|d}|S ) Nr rn z\delta_{r ro rM rD rE )r r@ r )r r rG r r r s rs _print_KroneckerDeltaz"LatexPrinter._print_KroneckerDelta' s KK ! % % KK ! % % 9Q< .DIaL$8 . .'(qq!!!,CC()111-C 7 7-0SS###6C
ru c t | j |j }t d |j D rdd | z }ndd | z }|r d|d|d}|S )Nc 3 $ K | ] }|j V d S r )r )r- r. s rs r/ z1LatexPrinter._print_LeviCivita..4 s$ ,,Qqy,,,,,,ru z\varepsilon_{%s}r rM rD rE ro )rE r r@ rw rQ )r r rG rF r s rs _print_LeviCivitaz LatexPrinter._print_LeviCivita2 s dk49-- ,,$),,, , , ;%(9(99CC% '(:(::C 7 7-0SS###6C
ru c t |d r*d| | z S t |d r;d| |j z dz | |j z S t |d r d| |j z S | d S )N
as_booleanz\text{Domain: }set \in ry z\text{Domain on })r r r ry r )r r s rs _print_RandomDomainz LatexPrinter._print_RandomDomain< s 1l # # %% ALLNN(C(CC C
Q
%&QY)?)??(JKK&&'
(
Q
"
" %'$++ai*@*@@ @;;t$$ $ru c b t |j t }| | S )Nr. )r r@ r
_print_setr rr r6 s rs _print_FiniteSetz LatexPrinter._print_FiniteSetG s) qv#3444u%%%ru c > t |t }| j d dk r)d t | j | }nI| j d dk r)d t | j | }nt
d d|z S ) Nr. r r r r rM rz \left\{%s\right\})r r r rQ rE r r r s rs r zLatexPrinter._print_setK s q ./// >- .' 9 :IIc$+u 5 566EE
^ /
0H
< :IIc$+u 5 566EE 899 9#e++ru c fd}t j j r(j j r j j rdddf}ndddf}n؉j j rd j z
d f}nj j r/t
}t | t | f}nwj fj dk dk rt }nQj r6t
}t | t | d f}n | S | S dd fd |D z d
z S ) Nc j d dk rYj d dk r! j d } nd fdj D } nfj d dk r/d fdj d d D } n&d fdj D } d| d S )
Nr r rn rM c 3 B K | ]} | V d S r rK r s rs r/ zKLatexPrinter._print_Range.._print_symbolic_range.._ / $H$H#T[[%5%5$H$H$H$H$H$Hru c 3 B K | ]} | V d S r rK r s rs r/ zKLatexPrinter._print_Range.._print_symbolic_range..b s/ $L$L#T[[%5%5$L$L$L$L$L$Lru c 3 B K | ]} | V d S r rK r s rs r/ zKLatexPrinter._print_Range.._print_symbolic_range..d r ru z\text{Range}\left(rq )r@ r rQ )contrr r s rs _print_symbolic_rangez8LatexPrinter._print_Range.._print_symbolic_rangeY s vayA~
I6!9> I ;;qvay11DD 99$H$H$H$H$H$H$HHHDD6!9> I 99$L$L$L$L$L$L$LLLDD 99$H$H$H$H$H$H$HHHD:D::: ;ru rm r rn rl T\left\{rM c 3 N K | ] }|ur | nd V dS z\ldotsNrK r- eldotsr s rs r/ z,LatexPrinter._print_Range.. ; __PRbnK4;;r???)______ru \right\})
objectstart is_infinitestopstep is_positiveiternextis_emptyrs r is_iterablerQ )r rr r printsetitr s `` @rs _print_RangezLatexPrinter._print_RangeX s
<
<
<
<
<
< xx 7 +16#5 +v!
0 Q4/ Ar4/
W
+QrUQV^QrU2HH
V
+aBBxxb4/HH
Z +
t#
/ 88
/!WW 88T"XXtQrU:,,...((** *
_____V^_____` ru c
t |j dk r|J|d| |j d d|d| |j d dS |d| |j d d| |j d dS |d| |j d d}||d |d}|S )
Nr rs r rt r4 rn rq ro r r )r r letterrG r s rs __print_number_polynomialz&LatexPrinter.__print_number_polynomial s ty>>Q N
79? KK ! 5 5 5 5sss KK ! 5 5 5 57 7 17 DIaL11114;;ty|3L3L3L3LN
N #FFDKK ! $=$=$=$=> * #SSS)C
ru c 0 | |d| S Nr &_LatexPrinter__print_number_polynomialrF s rs _print_bernoulliz LatexPrinter._print_bernoulli --dC===ru c r t |j dk rd |j d d |j d d}dd fd|j d D z }| |d
|d|}n||z }|S |d | S ) Nr1 zB_{r rM rn ro rb c 3 B K | ]} | V d S r rK )r- r r s rs r/ z+LatexPrinter._print_bell.. sI 3C 3C/1 48;;r?? 3C 3C 3C 3C 3C 3Cru r r r )r r@ r rQ r )r r rG tex1tex2r s ` rs _print_bellzLatexPrinter._print_bell s ty>>Q $(KK ! $=$=$=$= $ DIaL 9 9 9 9;D%
3C 3C 3C 3C59Yq\3C 3C 3C )C )C CD
"&*ddCCC6TkJ--dC===ru c 0 | |d| S NFr rF s rs _print_fibonacciz LatexPrinter._print_fibonacci r ru c ` d| |j d z }||d|d}|S )NzL_{%s}r r ro r r s rs _print_lucaszLatexPrinter._print_lucas = $++dil333 * #SSS)C
ru c 0 | |d| S )NTr rF s rs _print_tribonacciz LatexPrinter._print_tribonacci r ru c
X t t |j j dk s t |j j dk rud |j d |j d d |j d |j d S |j t j u rd|j }|
|dz
|
|dz
|
|d z
|
| f}nM|j t j u s |j d
k r |d d
}|
nt | }d d fd
|D z dz S )Nr r z
\right\}_{rb rt ro r1 r rn rl r rM c 3 N K | ] }|ur | nd V dS r rK r s rs r/ z1LatexPrinter._print_SeqFormula.. r ru r )r r r free_symbolsr r formular r r} coeffr| lengthr9 r rQ )r rr r r r s ` @rs _print_SeqFormulaz LatexPrinter._print_SeqFormula s xx qw# $ $q ( C0C,D,Dq,H AI&&&& AKN++++ AG$$$$ AF####
7a( ( 6D aggdQh / /1B1Bq))1774==:HH
Vqz
! QX\ !uH OOD ! ! ! ! QxxH
_____V^_____` ru c |j |j k r d| |j z S |j rd}nd}|j rd}nd}d|| |j d| |j d|S ) Nr r r r r r rM r )r endr left_open
right_open)r r leftrights rs _print_Intervalz LatexPrinter._print_Interval s 7ae K'$++ag*>*>> > {
|
D$++ag.... AE0B0B0B0BEEK
Kru c t d| |j d| |j dS )Nz
\left\langle rM z
\right\rangle)r r r r r s rs _print_AccumulationBoundsz&LatexPrinter._print_AccumulationBounds s; QU####T[[%7%7%7%79 9ru c v t | fd|j D }d | S )Nc < g | ]} | S rp r
r- r r& r s rs rL z-LatexPrinter._print_Union.. ) ???1D%%a..???ru z \cup r r@ rQ r uargs_strr& s ` @rs _print_UnionzLatexPrinter._print_Union A %a((????????~~h'''ru c v t | fd|j D }d | S )Nc < g | ]} | S rp r r s rs rL z2LatexPrinter._print_Complement.. r ru z \setminus r r s ` @rs _print_Complementz LatexPrinter._print_Complement C %a((???????? ""8,,,ru c v t | fd|j D }d | S )Nc < g | ]} | S rp r r s rs rL z4LatexPrinter._print_Intersection.. r ru z \cap r r s ` @rs _print_Intersectionz LatexPrinter._print_Intersection r ru c v t | fd|j D }d | S )Nc < g | ]} | S rp r r s rs rL z;LatexPrinter._print_SymmetricDifference.. r ru z \triangle r r s ` @rs _print_SymmetricDifferencez'LatexPrinter._print_SymmetricDifference r ru c < t | t |j dk rMt |j s9 |j d dt |j z z S d fd|j D S )Nrn r z^{%d}r c 3 D K | ]} | V d S r r )r- r r& r s rs r/ z1LatexPrinter._print_ProductSet.. sD < <-0D c4 ( ( < < < < < . s@ RRDAq A A/RRRRRRru rM c 3 K | ] }d |z V
dS ) %s \in %sNrp )r- xys rs r/ z/LatexPrinter._print_ImageSet.. s' ;;<",;;;;;;ru r \; \middle|\; r )rX r signaturerc base_setsrQ r )r rr r sigxysxinyss ` rs _print_ImageSetz LatexPrinter._print_ImageSet s~ w|g RRRRCQ[. s% I I IS C 0 0 I I Iru r r( \right\}r r )rQ r r2 base_setr UniversalSetr conditionr rr
vars_prints ` rs _print_ConditionSetz LatexPrinter._print_ConditionSet s YY I I I IE!%LL I I IJJ
: ' 7 7T[[ 5 5 5 57
7 7
JJ JJ KK
# # # # KK $ $ $ $ & &ru c l | |j d }d | S )Nr z \mathcal{{P}}\left({}\right)r r@ r )r r arg_prints rs _print_PowerSetz LatexPrinter._print_PowerSet! s- KK ! -- .55i@@@ru c d fd|j D }d |j d|d |j dS )NrM c : g | ]} | S rp rK r1 s rs rL z5LatexPrinter._print_ComplexRegion..& s% H H HS C 0 0 H H Hru r r( r r2 )rQ r r r r r6 s ` rs _print_ComplexRegionz!LatexPrinter._print_ComplexRegion% sl YY H H H HAK H H HII
KK JJ KK ! !ru c J dt fd|j D z S )Nr& c 3 B K | ]} | V d S r rK r s rs r/ z/LatexPrinter._print_Contains..- s- #C#CqDKKNN#C#C#C#C#C#Cru )r r@ rZ s ` rs _print_Containsz LatexPrinter._print_Contains, s- e#C#C#C#CAF#C#C#C C CCCru c |j j t j u r2|j j t j u r| |j S | | dz S )Nz + \ldots) rs r r rN bnr a0rh truncater s rs _print_FourierSeriesz!LatexPrinter._print_FourierSeries/ sZ 4<16 ! %adlaf&< %;;qt$$ $qzz||,,|;;ru c 6 | |j S r )rh infiniter s rs _print_FormalPowerSeriesz%LatexPrinter._print_FormalPowerSeries4 s qz***ru c d|j z S )Nz\mathbb{F}_{%s})modr s rs _print_FiniteFieldz LatexPrinter._print_FiniteField7 s !DH,,ru c dS r rp r s rs _print_IntegerRingz LatexPrinter._print_IntegerRing: ru ru c dS r rp r s rs _print_RationalFieldz!LatexPrinter._print_RationalField= ru ru c dS r rp r s rs _print_RealFieldz LatexPrinter._print_RealField@ ru ru c dS r! rp r s rs _print_ComplexFieldz LatexPrinter._print_ComplexFieldC ru ru c | |j }d t | j |j }|d|dS )NrM r r r domainrQ rE ry r r rX ry s rs _print_PolynomialRingz"LatexPrinter._print_PolynomialRingF G T[))))C T\ : :;;'-vvwww77ru c | |j }d t | j |j }|d|dS )NrM rD rq rW rY s rs _print_FractionFieldz!LatexPrinter._print_FractionFieldK r[ ru c | |j }d t | j |j }d}|j sd}||d|dS )NrM r zS_<^{-1}r r )r rX rQ rE ry is_Poly)r r rX ry invs rs _print_PolynomialRingBasez&LatexPrinter._print_PolynomialRingBaseP s_ T[))))C T\ : :;;| C),fffggg>>ru c |j j }g }| D ]t\ }}d}t | D ]f\ }}|dk r[|dk r$|| |j | z
}5|| t
|j | | z
}g|j r1|rd| | z } nz| | } nd|rM|t j u r|
d|g |t j u r|
d|g | | } |s| }
n| dz |z }
|
d r!|
d|
dd g ]|
d|
g v|d dv r)|
d } | dk rd|d z |d< d | } t t! | j |j }
d | | z }d
| g|
z |gz }|t$ v r
d |d |d
}n d|d|d
}|S )Nr r rn rb r r0 r )r0 r z domain=%srM r {\left(z \right)}r z }{\left( )rO rP re rd r genspowr" r r extendr r poprQ r rE
get_domainr )r polyr re monomr s_monomr rG s_coeffs_termmodifierr rd rX r@ r s rs _print_PolyzLatexPrinter._print_PolyX s n% JJLL " , " ,LE5G#E**
G
G37 Gax G 4;;ty|#<#<< 4;;s49Q</E/E#F#FF|
- 1 04;;u3E3E EGG "kk% 0 0GG ! ~ ! c7^444
- ! c7^444 ++e,,
1 3 0 %%
, c6!"": .//// c6]++++ 8z ! * yy||H3
* q>axxC TY//00 t{{4??+<+< = ==yy$$ &122 * * H H/2ssDDD9CC H >ASS$$$GC
ru c |j j }|dk rd}| |j }|j }|t
v rd|||fz S d|||fz S )N
ComplexRootOfCRootOfz\%s {\left(%s, %d\right)}z'\operatorname{%s} {\left(%s, %d\right)})rO rP r r rZ r )r r; r r rZ s rs _print_ComplexRootOfz!LatexPrinter._print_ComplexRootOf sv n% / ! C{{49%%
* * H/3e2DD D=dAFAH H
Hru c R |j j }| |j g}|j t
j ur-| | |j |t v r d|dd | dS d|dd | dS )Nr rc rM r+ r z } {\left()
rO rP r r funr IdentityFunctionr9 r rQ )r r r r@ s rs _print_RootSumzLatexPrinter._print_RootSum s n% DI&&' 81- - / KK DH-- . . . * * N N/2ssDIIdOOOOD D N >ASS=AYYt____N
Nru c dS )N\omegarp r s rs _print_OrdinalOmegaz LatexPrinter._print_OrdinalOmega s yru c |j \ }}|dk r1|dk rd || S d | S |dk rd | S dS )Nrn z{} \omega^{{{}}}z {} \omegaz
\omega^{{{}}}ry )r@ r )r r rG muls rs _print_OmegaPowerz LatexPrinter._print_OmegaPower st 9S !8 !ax
0*11#s;;;#**3///ax
!'..s333 yru c P d fd|j D S )Nra c : g | ]} | S rp rK r s rs rL z/LatexPrinter._print_Ordinal.. s% AAA4;;s++AAAru )rQ r@ r s ` rs _print_OrdinalzLatexPrinter._print_Ordinal s, zzAAAAtyAAABBBru c V | j d }| | t d| S )Nr z {%s}^{%d})r r r" )r ri r s rs _print_PolyElementz LatexPrinter._print_PolyElement s' ^$67
xxj+zBBBru c |j dk r| |j S | |j }| |j }d|d|dS )Nrn r r ro )r r r )r r: r r s rs _print_FracElementz LatexPrinter._print_FracElement s_ :? 5;;tz** *KK
++EKK
++EE',uueee4 4ru c t |j dk r|j d d fn|j \ }}d| | z }||d|d}||d| | d}|S )Nrn r zE_{%s}r ro rD rq r )r r rG r r. r s rs _print_eulerzLatexPrinter._print_euler s '*49~~':I ! d## 1$++a..( * #SSS)C ?*-##t{{1~~~~>C
ru c ` d| |j d z }||d|d}|S )NzC_{%s}r r ro r r s rs _print_catalanzLatexPrinter._print_catalan r ru c
d ||rdnd| |j d | |j d | |j d S )Nz5\mathcal{{{}}}{}_{{{}}}\left[{}\right]\left({}\right)z^{-1}r rn r r r r r@ )r r rr inverses rs _print_UnifiedTransformz$LatexPrinter._print_UnifiedTransform s GNNq]dRlRYRYjlnrnynyz~ {D EF {G oH oH JN JU JU VZ V_ `a Vb Jc Jc ei ep ep qu qz {| q} e~ e~ ru c . | |d S )NMr r s rs _print_MellinTransformz#LatexPrinter._print_MellinTransform ++D#666ru c 0 | |dd S )Nr Tr r s rs _print_InverseMellinTransformz*LatexPrinter._print_InverseMellinTransform ++D#t<<>>ru c . | |d S )NCOSr r s rs _print_CosineTransformz#LatexPrinter._print_CosineTransform r ru c 0 | |dd S )Nr Tr r s rs _print_InverseCosineTransformz*LatexPrinter._print_InverseCosineTransform r ru c |j -| |j | S n# t $ r Y nw xY w| t | S r )ringr to_sympyr reprr r s rs
_print_DMPzLatexPrinter._print_DMP sp v
7{{16??1#5#5666
7 D {{477###s 37
AAc , | | S r )r r s rs
_print_DMFzLatexPrinter._print_DMF
s q!!!ru c P | t |j S r r r
rR )r r s rs
_print_ObjectzLatexPrinter._print_Object
s {{6&+..///ru c | |j d }|d|dnd}t |j dk r
d|d|d}n7| |j d }d ||| }|S )
Nr r ro r rn WrD rq z W{0}_{{{1}}}\left({2}\right))r r@ r r )r r rG arg0resultarg1s rs _print_LambertWz LatexPrinter._print_LambertW
s {{49Q<((#&::### ty>>Q N N.1cc4448FF;;ty|,,D5<.
s1 FmFm\_t{{SVGWGWFmFmFmFmFmFmru )r rQ r@ r s ` rs _print_Covariancez LatexPrinter._print_Covariance
s< 5<.)
s' 4,,Q0Ft0L0L,1 3 3 ru r )r r@ rQ rE )r r r@ r s `` rs
_print_SerieszLatexPrinter._print_Series'
sH DI3 3 3 3 3xxFD))***ru c ddl m t j d d d } fd}d t || S )Nr ) MIMOParallelrm c t | r$ | t d n | S r )r r
r r )r. r r r s rs rt z0LatexPrinter._print_MIMOSeries..0
sT 7A!\7R7R g4,,Q0Ft0L0L-2 4 4 4X\XcXcdeXfXf ru z\cdot)sympy.physics.control.ltir r r@ rQ rE )r r r@ r r s `` @rs _print_MIMOSeriesz LatexPrinter._print_MIMOSeries-
sq ::::::DIttt$g g g g g g}}S . .///ru c \ d t | j |j S Nra rQ rE r r@ r s rs _print_Parallelz LatexPrinter._print_Parallel4
" zz#dk4955666ru c \ d t | j |j S r r r s rs _print_MIMOParallelz LatexPrinter._print_MIMOParallel7
r ru c p ddl m}m} |j |dd|j }}t || rt
|j n|g}t |j | rt
|j j n|j g}|}t || r t |j | r |g ||R } nt || r8t |j | r#|j |k r || } nt| |g ||j R f} nbt || r+t |j | r||k r || } n1 ||g|R } n'||k r || } n|j |k r || } n
|g ||R } | | }
| | } | | } |j
dk rdnd}
d|
d| d |
d | d
S ) Nr )TransferFunctionSeriesrn rm r r0 r r r ro ) sympy.physics.controlr r sys1r r r r@ sys2r r )r r r r rZ tf num_arg_list den_arg_list
den_term_1
den_term_2r denom_1denom_2_signs rs _print_Feedbackz LatexPrinter._print_Feedback:
sO BBBBBBBB) - -aDH = =R)3C)@)@KtCH~~~se ty& ) );tDIN+++04 {
c6 " " Bz$)V'D'D B = = ===JJ
V
$
$ BDI?O)P)P ByB
B #V\ 2
!A !Aty!A!A!A A
-
.
. B:di3P3P Bby
8 #V\ 2
#VC 7, 7 7 7
by
B #V\ 2
b
B #V\ 2
#V A\ AL A A A
C ++j))++j))yB/C).HHru c ddl m} | ||j |j }| |j }|j dk rdnd}d|d|d|S ) Nr )
MIMOSeriesrm r r0 z\left(I_{\tau} r z\right)^{-1} \cdot )r r r r r r )r r r inv_matr r s rs _print_MIMOFeedbackz LatexPrinter._print_MIMOFeedback^
su 444444++jjDI > >??{{49%%yB/C?DuugggttTTru c @ | |j }d|z S )Nz%s_\tau)r _expr_matr s rs _print_TransferFunctionMatrixz*LatexPrinter._print_TransferFunctionMatrixe
s kk$.))C ru c L d |j j |j S )Nz\text{{{}}}_{{{}}})r rO rP r- r s rs
_print_DFTzLatexPrinter._print_DFTi
s $++DN,CTVLLLru c | t |j }| | }|d|S )Nr )r r
rR r )r r pretty_namepretty_morphisms rs _print_NamedMorphismz!LatexPrinter._print_NamedMorphismm
sA kk& "7"788 ..x88%++77ru c b ddl m} | ||j |j d S )Nr )
NamedMorphismid)sympy.categoriesr r rX r )r r r s rs _print_IdentityMorphismz$LatexPrinter._print_IdentityMorphismr
sF 222222(( OX .*6 *6 7 7 7ru c fd|j D }| d | dz } | }||z S )Nc ^ g | ])} t |j *S rp r )r- componentr s rs rL z9LatexPrinter._print_CompositeMorphism..z
sE B B B ) !% F9>,B,B C C B B Bru z\circ r )r7 reverserQ r )r r component_names_listcomponent_namesr s ` rs _print_CompositeMorphismz%LatexPrinter._print_CompositeMorphismw
s} B B B B-5-@ B B B $$&&&#..)=>>D ..x88 00ru c v d | t |j S Nr )r r r
rR )r r s rs _print_Categoryz LatexPrinter._print_Category
s, &&t{{6(-3H3H'I'IJJJru c |j s | t j S | |j }|j r |d| |j z z
}|S )Nz\Longrightarrow %s)premisesr r EmptySet conclusions)r diagram latex_results rs _print_DiagramzLatexPrinter._print_Diagram
sl +;;qz** *{{7#344 = 1 KK(; < < =
=L ru c . dd|j z z }t |j D ]m}t |j D ]>}|||f r|t |||f z
}|dz
}||j dz
k r|dz
}?||j dz
k r|dz
}|dz
}n|dz
}|S ) Nz\begin{array}{%s}
r r rn & r
z \end{array}
)widthr heightlatex)r gridr r r s rs _print_DiagramGridz LatexPrinter._print_DiagramGrid
s -tz1AB t{##
!
!A4:&&
)
)1: 6 E$q!t*$5$55L #
Q& ) D(LDK!O#
' & D LL(( ru c d | |j | |j S )Nz
{{{}}}^{{{}}})r r r rI r r s rs _print_FreeModulez LatexPrinter._print_FreeModule
s4 %%dkk!&&9&94;;qv;N;NOOOru c l d d fd|D S )Nz\left[ {} \right]ro c 3 N K | ] }d | z dz V dS r ro NrK r- r. r s rs r/ z8LatexPrinter._print_FreeModuleElement..
sH 43 43+,C$++a.. 3 &43 43 43 43 43 43ru )r rQ r r s ` rs _print_FreeModuleElementz%LatexPrinter._print_FreeModuleElement
sQ #**388 43 43 43 430143 43 43 ,3 ,3 4 4 4ru c v d d fd|j D S )N \left\langle {} \right\ranglero c 3 N K | ] }d | z dz V dS r rK r s rs r/ z0LatexPrinter._print_SubModule..
sP @8 @8+,C$++a.. 3 &@8 @8 @8 @8 @8 @8ru )r rQ rd r s ` rs _print_SubModulez LatexPrinter._print_SubModule
sZ /66sxx @8 @8 @8 @801@8 @8 @8 88 88 9 9 9ru c d d fd|j j D S )Nr ro c 3 R K | ]!\ }d | z dz V "dS r rK r s rs r/ z=LatexPrinter._print_ModuleImplementedIdeal..
sZ @B @B+.AC$++a.. 3 &@B @B @B @B @B @Bru )r rQ _modulerd r s ` rs _print_ModuleImplementedIdealz*LatexPrinter._print_ModuleImplementedIdeal
sh /66sxx @B @B @B @B23).@B @B @B 8B 8B C C Cru c fd|j D }|d gd t |dd d D z }d | S )Nc V g | ]%} |t d d &S )r
Tr )r
r" r
s rs rL z2LatexPrinter._print_Quaternion..
sC
!
!
!
q*U"3D
A
A
!
!
!ru r c $ g | ]
\ }}|d z |z S )r rp )r- r r s rs rL z2LatexPrinter._print_Quaternion..
s$ <<<$!QaeAg<<+>Q\**, , ,ru c d | |j | |j j S Nz{{{}}} + {{{}}})r r datar r- )r r. s rs _print_QuotientRingElementz'LatexPrinter._print_QuotientRingElement
s> !((QV)<)<QV .//1 1 1ru c d | |j | |j j S r1 )r r r2 module
killed_moduler s rs _print_QuotientModuleElementz)LatexPrinter._print_QuotientModuleElement
s> !((QV)<)<QX 3446 6 6ru c d | |j | |j S r, )r r rB r6 r s rs _print_QuotientModulez"LatexPrinter._print_QuotientModule
s; #**4;;qv+>+>Q_--/ / /ru c d | | | |j | |j S )Nz{{{}}} : {{{}}} \to {{{}}})r r
_sympy_matrixrX r )r r s rs _print_MatrixHomomorphismz&LatexPrinter._print_MatrixHomomorphism
sS ,33DKK@Q@Q4R4R KK ! !4;;qz#:#:< < .
r ru c , g | ]}t | S rp r r s rs rL z0LatexPrinter._print_Manifold..
r ru rY ru r rD )rR r r rQ )r manifoldr rR r rd s rs _print_Manifoldz LatexPrinter._print_Manifold
s # &= 4!'R$&DD!0!8!8 D&$ T??D77777F33d333Dd" / Gchhv . .. .D - Gchhtnn, ,D ru c t d| |j d| |j dS )N\text{rp ro )r rR r@ )r patchs rs _print_PatchzLatexPrinter._print_Patch
s7 $(KK
$;$;$;$;T[[ =X=X=X=XYYru c d| |j d| |j j d| |j dS )NrC z }^{\text{z}}_{ro )r rR rD r@ )r coordsyss rs _print_CoordSystemz LatexPrinter._print_CoordSystem
sV KK
& & & & HN4G(H(H(H(H$++V^VgJhJhJhJh
ru c < d| |j z S )Nz\mathbb{\nabla}_{%s})r _wrt)r cvds rs _print_CovarDerivativeOpz%LatexPrinter._print_CovarDerivativeOp
s &SX)>)>>>ru c |j j |j j }d | t
| S r
_coord_sysry _indexrR r r r
r fieldr s rs _print_BaseScalarFieldz#LatexPrinter._print_BaseScalarField
s= !)%,7< &&t{{6&>>'B'BCCCru c |j j |j j }d | t
| S )Nz\partial_{{{}}}rN rQ s rs _print_BaseVectorFieldz#LatexPrinter._print_BaseVectorField
s= !)%,7<!((VF^^)D)DEEEru c & |j }t |d rQ|j j |j j }d | t | S | | }d | S )NrO z\operatorname{{d}}{}z!\operatorname{{d}}\left({}\right)) _form_fieldr rO ry rP rR r r r
)r diffrR r s rs _print_Differentialz LatexPrinter._print_Differential
s} 5, ' ' G%-el;@F*11$++fVnn2M2MNN N[[''F7>>vFF Fru c l | |j d }d | S )Nr z"\operatorname{{tr}}\left({}\right)r: )r r contentss rs _print_TrzLatexPrinter._print_Tr s- ;;qvay))4;;HEEEru c |'d| |j d d|dS d| |j d z S )Nz\left(\phi\left(r \right)\right)^{ro z\phi\left(%s\right)r rF s rs _print_totientzLatexPrinter._print_totient sW 1 1TYq\****CCC1
1% DIaL(A(AAAru c |'d| |j d d|dS d| |j d z S )Nz\left(\lambda\left(r r^ ro z\lambda\left(%s\right)r rF s rs _print_reduced_totientz#LatexPrinter._print_reduced_totient sW 1 1TYq\****CCC1
1(4;;ty|+D+DDDru c t |j dk r>dt t | j |j d |j d f z }n#d| |j d z }|d|d|S d|z S ) Nr _%s\left(%s\right)rn r rb z\sigma^{ro z\sigma%srz r s rs _print_divisor_sigmaz!LatexPrinter._print_divisor_sigma s ty>>Q A'%DK151 ty|0L1N 1N +O +O OCC %t{{49Q<'@'@@C 1 1'*ssCC0 0S ru c t |j dk r>dt t | j |j d |j d f z }n#d| |j d z }|d|d|S d|z S ) Nr rc rn r rb z
\sigma^*^{ro z
\sigma^*%srz r s rs _print_udivisor_sigmaz"LatexPrinter._print_udivisor_sigma s ty>>Q A'%DK151 ty|0L1N 1N +O +O OCC %t{{49Q<'@'@@C 3 3),cc2 2 s""ru c |'d| |j d d|dS d| |j d z S )Nz\left(\nu\left(r r^ ro z\nu\left(%s\right)r rF s rs _print_primenuzLatexPrinter._print_primenu% sW 1 1TYq\****CCC1
1$t{{49Q<'@'@@@ru c |'d| |j d d|dS d| |j d z S )Nz\left(\Omega\left(r r^ ro z\Omega\left(%s\right)r rF s rs _print_primeomegaz LatexPrinter._print_primeomega+ sW 1 1TYq\****CCC1
1'$++dil*C*CCCru c * t |j S r )r rR r s rs
_print_StrzLatexPrinter._print_Str1 s 16{{ru c F | t | S r )r r r s rs _print_floatzLatexPrinter._print_float4 s {{5;;'''ru c t | S r r r s rs
_print_intzLatexPrinter._print_int7 4yyru c t | S r rp r s rs
_print_mpzzLatexPrinter._print_mpz: rr ru c t | S r rp r s rs
_print_mpqzLatexPrinter._print_mpq= rr ru c j d t t |j S )Nz"\operatorname{{Q}}_{{\text{{{}}}}})r r r rR r s rs _print_Predicatez LatexPrinter._print_Predicate@ s& 4;;LTY .G s# = = =1 A = = =ru r r )r argumentsr rQ )r r predr@
pred_latex
args_latexs ` rs _print_AppliedPredicatez$LatexPrinter._print_AppliedPredicateC s[ }~[[&&
YY = = = = = = =>>
%::zzz22ru c j t | }dt | z S )Nz\mathtt{\text{%s}})super emptyPrinterr )r r rr rO s rs r zLatexPrinter.emptyPrinterJ s+ GG & &$|A66ru r r )FF)r r )r r )rU rV )r r )r r )r r r r )r r) )r r r r )r r r r r )r2 r r r r )FN)r )r r
)r r r r )r r )rT rU )F(< rP
__module__ __qualname__ printmethodr __annotations__r r r r
r r r r$ r; r> r r! rH rT r[ _print_BooleanTrue_print_BooleanFalser^ rh rx r r r r r r r r r r r r r r r
r" r( rB rH rK rO r[ rj rz r r r r r propertyr r r r r
_print_Min
_print_Maxr r r r r r r r r r r r r r r r r r r r r r r r r
r r _print_gammar r r r r" r$ r& r( r. r1 r7 r9 r= r@ rC rF rI rK rM rP rR rT rX rZ r_ rd rg rj rp rv rx r{ r} r r r r r r r r r r r r r r r r r r r r r _print_RandomSymbolrN r r r r r r r r r r r r r! r* r, r0 r3 r5 r: r? rA rE rS r\ r_ ra re rg ri rl rn rr rt rw r} r r r r r r r r r r r r r r _print_frozensetr r r r r r r r
_print_SeqPer
_print_SeqAdd
_print_SeqMulr r r r r r r r r r r r r r" r. r8 r< r? rB rG rJ rM rO rQ rS rU rZ r] ra ro rs rw rz r} r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r r _print_IDFTr r r r r r r r r! r% r* r/ r3 r7 r9 r< rA rE rH rL rS rU rY r\ r_ ra rd rf rh rj rl rn rq rt rv rx r r
__classcell__)rO s @rs r r sg K)U)E) e) 4 )
- )
) u) 4) S) 4) ) d) ) ) ) G!)" ##)$ % " 1) ) ) 6;f ;f ;f ;fz, , , ,- - - -% % % % % E E E EK K K K . > 3 3 3 3 / / / %% & 9 9 9BJ J J <N N N N N NM M MM M M I I II I It t t tl/ / / - - -+< +< +< + > >> > >> > ># # #4 4 4 4l 8? ? ?
F F F
& & &D D D
4 4 4 4
F
F
F + + +* * *' ' ': : :< < <& & & % % %& & &, , , "( ( ( T > > > > > > > > > > > > > > > > . &M%M%MK K K$9 9 9( ( (
- - -
( ( (
- - -
< < < Q Q Q
&
&
&A A A! ! !D D D< < <
+ + +- - - 8 8 8
8 8 8
? ? ?7 7 7r
H
H
H N N N ! ! !C C CC C C5 5 5 7 7 7= = =7 7 7= = =7 7 7= = =9 9 9? ? ?9 9 9? ? ?$ $ $" " "0 0 0 V V VX X Xo o oV V V8 8 8
- - -+ + + 0 0 07 7 77 7 7"I "I "IHU U U M M M K8 8 8
7 7 7
1 1 1K K K
$P P P4 4 4
9 9 9C C C , , ,
1 1 16 6 6/ / /
< < < &Z Z Z
? ? ?D D DF F FG G GF F F
B B B B E E E E ! ! ! !# # # #A A A A D D D D ( ( ( Z Z Z3 3 37 7 7 7 7 7 7 7 7ru r c
& t | }|r|S | t v rd| z S | t v rd| z S t t t d D ]}| | rZt | t | k r:t
| t | dt | c S | S )a
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}}}'"
r T)r/ r N) tex_greek_dictionaryr r greek_letters_set
other_symbolsr r r r r r )rr r r/ s rs r r Q s
"
"1
%
%C
' ' aggii
m ax -,,..CFFF D DCwwyy!!#&&
D3q66CHH+<
D$S))AjCyjM*B*BCCCCCru c F t | | S )a % Convert the given expression to LaTeX string representation.
Parameters
==========
full_prec: boolean, optional
If set to True, a floating point number is printed with full precision.
fold_frac_powers : boolean, optional
Emit ``^{p/q}`` instead of ``^{\frac{p}{q}}`` for fractional powers.
fold_func_brackets : boolean, optional
Fold function brackets where applicable.
fold_short_frac : boolean, optional
Emit ``p / q`` instead of ``\frac{p}{q}`` when the denominator is
simple enough (at most two terms and no powers). The default value is
``True`` for inline mode, ``False`` otherwise.
inv_trig_style : string, optional
How inverse trig functions should be displayed. Can be one of
``'abbreviated'``, ``'full'``, or ``'power'``. Defaults to
``'abbreviated'``.
itex : boolean, optional
Specifies if itex-specific syntax is used, including emitting
``$$...$$``.
ln_notation : boolean, optional
If set to ``True``, ``\ln`` is used instead of default ``\log``.
long_frac_ratio : float or None, optional
The allowed ratio of the width of the numerator to the width of the
denominator before the printer breaks off long fractions. If ``None``
(the default value), long fractions are not broken up.
mat_delim : string, optional
The delimiter to wrap around matrices. Can be one of ``'['``, ``'('``,
or the empty string ``''``. Defaults to ``'['``.
mat_str : string, optional
Which matrix environment string to emit. ``'smallmatrix'``,
``'matrix'``, ``'array'``, etc. Defaults to ``'smallmatrix'`` for
inline mode, ``'matrix'`` for matrices of no more than 10 columns, and
``'array'`` otherwise.
mode: string, optional
Specifies how the generated code will be delimited. ``mode`` can be one
of ``'plain'``, ``'inline'``, ``'equation'`` or ``'equation*'``. If
``mode`` is set to ``'plain'``, then the resulting code will not be
delimited at all (this is the default). If ``mode`` is set to
``'inline'`` then inline LaTeX ``$...$`` will be used. If ``mode`` is
set to ``'equation'`` or ``'equation*'``, the resulting code will be
enclosed in the ``equation`` or ``equation*`` environment (remember to
import ``amsmath`` for ``equation*``), unless the ``itex`` option is
set. In the latter case, the ``$$...$$`` syntax is used.
mul_symbol : string or None, optional
The symbol to use for multiplication. Can be one of ``None``,
``'ldot'``, ``'dot'``, or ``'times'``.
order: string, optional
Any of the supported monomial orderings (currently ``'lex'``,
``'grlex'``, or ``'grevlex'``), ``'old'``, and ``'none'``. This
parameter does nothing for `~.Mul` objects. Setting order to ``'old'``
uses the compatibility ordering for ``~.Add`` defined in Printer. For
very large expressions, set the ``order`` keyword to ``'none'`` if
speed is a concern.
symbol_names : dictionary of strings mapped to symbols, optional
Dictionary of symbols and the custom strings they should be emitted as.
root_notation : boolean, optional
If set to ``False``, exponents of the form 1/n are printed in fractonal
form. Default is ``True``, to print exponent in root form.
mat_symbol_style : string, optional
Can be either ``'plain'`` (default) or ``'bold'``. If set to
``'bold'``, a `~.MatrixSymbol` A will be printed as ``\mathbf{A}``,
otherwise as ``A``.
imaginary_unit : string, optional
String to use for the imaginary unit. Defined options are ``'i'``
(default) and ``'j'``. Adding ``r`` or ``t`` in front gives ``\mathrm``
or ``\text``, so ``'ri'`` leads to ``\mathrm{i}`` which gives
`\mathrm{i}`.
gothic_re_im : boolean, optional
If set to ``True``, `\Re` and `\Im` is used for ``re`` and ``im``, respectively.
The default is ``False`` leading to `\operatorname{re}` and `\operatorname{im}`.
decimal_separator : string, optional
Specifies what separator to use to separate the whole and fractional parts of a
floating point number as in `2.5` for the default, ``period`` or `2{,}5`
when ``comma`` is specified. Lists, sets, and tuple are printed with semicolon
separating the elements when ``comma`` is chosen. For example, [1; 2; 3] when
``comma`` is chosen and [1,2,3] for when ``period`` is chosen.
parenthesize_super : boolean, optional
If set to ``False``, superscripted expressions will not be parenthesized when
powered. Default is ``True``, which parenthesizes the expression when powered.
min: Integer or None, optional
Sets the lower bound for the exponent to print floating point numbers in
fixed-point format.
max: Integer or None, optional
Sets the upper bound for the exponent to print floating point numbers in
fixed-point format.
diff_operator: string, optional
String to use for differential operator. Default is ``'d'``, to print in italic
form. ``'rd'``, ``'td'`` are shortcuts for ``\mathrm{d}`` and ``\text{d}``.
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.
)r r r r s rs r r p s! h ! ! ) )$ / //ru c : t t | fi | dS )z`Prints LaTeX representation of the given expression. Takes the same
settings as ``latex()``.N)printr r s rs print_latexr G s(
%
!
!
!
!"""""ru rn align*Fc
t d i |}|dk r d}d}d} d}
d} nD|dk r d}d}d} d }
d} n3|d
k r d }d }d
} d}
d} n"t d | d
} |rd} | }
t |
}d}t | D ]}|
| }d
}d
}d}||k r | rd}nd}d}||k r||dz
k r | | z dz dz }nd
}| d dk rd|z }d}|dk rK|dk rd
}|d | | ||| | | z
}n.|d ||| | | z
}|dz
}||
z
}|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.
eqnarrayz\begin{eqnarray}
z& = &z \nonumberz
\end{eqnarray}T IEEEeqnarrayz\begin{IEEEeqnarray}{rCl}
z
\end{IEEEeqnarray}r z\begin{align*}
z= &r z
\end{align*}FzUnknown environment: {}z\dotsrn r z& & r r r r rm r0 z{:s} {:s}{:s} {:s} {:s}z{:s}{:s} {:s} {:s}rp )r r r as_ordered_termsr r r r )r r terms_per_line environmentuse_dotsr r r
first_termnonumberend_termdoubleetr re n_terms
term_countr rf
term_startterm_endr s rs multiline_latexr N sC F x Aj H+
& &
H4
* H)
%299+FFGGG
D
" "E%jjGJ
7^^ Qx
&
" #
!
J ' 719}
(?U2T9 " " $ $Q '2 - d7DD 6 3s{
077 #"D!))D//8E E
EFF
+22:t $3 3
3Fa
hF Mru )rr r r r )rn r F)J__doc__
__future__r typingr r r rK
sympy.corer r r r
r r r
r sympy.core.alphabetsr sympy.core.containersr sympy.core.functionr r r sympy.core.operationsr sympy.core.powerr sympy.core.sortingr sympy.core.sympifyr r r r r sympy.tensor.arrayr sympy.printing.precedencer sympy.printing.printerr r sympy.printing.conventionsr r r! r" mpmath.libmp.libmpfr# r$ r sympy.utilities.iterablesr% r& r8 sympy.vector.basisdependentr' r r r r r frozensetr compiler r r r r r r rp ru rs r s7 # " " " " " / / / / / / / / / / D D D D D D D D D D D D D D D D D D D D ' ' ' ' ' ' ' ' ' ' ' ' B B B B B B B B B B ) ) ) ) ) ) / / / / / / + + + + + + ? ? ? ? ? ? ? ? ? ? ( ( ( ( ( ( = < < < < < : : : : : : : : H H H H H H H H < < < < < < < < B B B B B B B B 7 7 7 7 7 7 7 7 ;:::::: % ]%
M% Y% Y %
} % M
%
=% Y% M% ]%
j% -% -% & % s % }!%" &#% %$
=%%& Y'%(
=)%* {+%,
7-%.
=/%0
71%2 Y3%4 Z5%6 Z7%8
79%:
=;%< .=%> ?%@
jA%B YC%D
jE% %F I% % % N, , ,
2.. 2
** 2
(
( 2
& & 2
$ $
2
(
( 2
(
( 2
(
( 2
(
( 2
(
( 2
$ $ 2
$ $ 2
$ $ 2
!
! 2
! 2$ , ,% 2&
*
*' 2( ) ( ( ( * * 0 0 9 9 - - - -7 2 2 2
< If%% BJ~ BJx
A+7 A+7 A+7 A+7 A+77 A+7 A+7 A+7HV > S0 S0 S0l# # #~ ~ ~ ~ ~ ~ru