wg 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(m)Z) ddl*m+Z+m,Z, ddl%m-Z-m.Z. ddl/m0Z0m1Z2 ddl3m4Z4m5Z5 ddl6Z6er ddl7m8Z8 ddl9m:Z: g dZ;i dddddd d d d d d!d"d#d$d%d&d'd(d)d*d+d,d-d.d/d0d1d2d3d4d5d6d7d8i d9d:d;d<d=d>d?d@dAdBdCdDdEdFdGdHdIdJdKd,dLdMdNdDdOdPdQdRdSdTdUdVdWdXdYdZd[Zde?d< e@e ZA e6j d e6j d fZCddZD G d de( ZEddZF e)eE d ZGd ZHddZIy)zC
A Printer which converts an expression into its LaTeX equivalent.
) annotations)AnyCallable
TYPE_CHECKINGN)AddFloatModMulNumberSSymbolExpr)greeks)Tuple)Function AppliedUndef
Derivative)AssocOp)Pow)default_sort_key) SympifyError)true BooleanTrue BooleanFalse)precedence_traditional)Printerprint_function)split_super_subrequires_partial)
precedence
PRECEDENCE) prec_to_dpsto_str) has_varietysift) NDimArray)BasisDependent)arcsinarccosarctansincostansinhcoshtanhsqrtlnlogseccsccotcothreimfracrootargAlphaz
\mathrm{A}Betaz
\mathrm{B}Gamma\GammaDeltaz\DeltaEpsilonz
\mathrm{E}Zetaz
\mathrm{Z}Etaz
\mathrm{H}Thetaz\ThetaIotaz
\mathrm{I}Kappaz
\mathrm{K}Lambdaz\LambdaMuz
\mathrm{M}Nuz
\mathrm{N}Xiz\XiomicronoOmicronz
\mathrm{O}Piz\PiRhoz
\mathrm{P}Sigmaz\SigmaTauz
\mathrm{T}Upsilonz\UpsilonPhiz\PhiChiz
\mathrm{X}Psiz\PsiOmegaz\Omegalamdaz\lambdaLamdakhiz\chiKhi
varepsilonz \varepsilonvarkappaz \varkappavarphiz\varphivarpiz\varpivarrhoz\varrhoz \varsigmaz \vartheta)varsigmavartheta>
wpellethmhobethhbaralephgimeldalethhslashmathringc d| z dz S )Nz
\mathring{} ss Y/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/sympy/printing/latex.pyrt [ s -/$. 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$& ru dotc d| z dz S )Nz\dot{ro rp rq s rs rt rt _ XaZ_ ru checkc d| z dz S )Nz\check{ro rp rq s rs rt rt ` rz ru brevec d| z dz S )Nz\breve{ro rp rq s rs rt rt a rz ru acutec d| z dz S )Nz\acute{ro rp rq s rs rt rt b rz ru gravec d| z dz S )Nz\grave{ro rp rq s rs rt rt c rz ru tildec d| z dz S )Nz\tilde{ro rp rq s rs rt rt d rz ru hatc d| z dz S )Nz\hat{ro rp rq s rs rt rt e r ru barc d| z dz S )Nz\bar{ro rp rq s rs rt rt f r ru vecc d| z dz S )Nz\vec{ro rp rq s rs rt rt g r ru primec d| z dz S N{z}'rp rq s rs rt rt h s s1uTz ru prmc d| z dz S r rp rq s rs rt rt i s SU4Z ru boldc d| z dz S Nz \boldsymbol{ro rp rq s rs rt rt k s oa', ru bmc d| z dz S r rp rq s rs rt rt l s OA%d* ru c d| z dz S )Nz \mathcal{ro rp rq s rs rt rt m \!^D( ru c d| z dz S )Nz \mathscr{ro rp rq s rs rt rt n r ru c d| z dz S )Nz
\mathfrak{ro rp rq s rs rt rt o s mAod* ru c d| z dz S )Nz\left\|{z }\right\|rp rq s rs rt rt q s k!mL0 ru c d| z dz S )Nz
\left\langle{z}\right\ranglerp rq s rs rt rt r s %a'(99 ru c d| z dz S Nz\left|{z}\right|rp rq s rs rt rt s Z\+- ru c d| z dz S r rp rq s rs rt rt t r ru )calscrfraknormavgabsmagz dict[str, Callable[[str], str]]
modifier_dictz [0-9][} ]*$z(\d|\\frac{\d+}{\d+})c | j dd } dD ] }| j |d|z } | j dd } | j 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 s_
$)*A
#
IIa "# #)*A #*+A Hru c
" e Zd ZU dZi dddddddddd d
dd dd dd
ddddddddddi dddddddddddddd d Zd ed < dNd ZdOd!ZdOd"ZdPdOd#Z d$ Z
dOd%Z dQd&Z dQd'Z
dPdQd(ZdQd)ZdQd*ZdQd+ZdRd,Zd- ZdSd.ZeZeZd/ ZdNd0Zd1 Zd2 Zd3 Zd4 Z d5 Z d6 Z d7 Z d8 Z d9 Z!d: Z"dTd;Z#d< Z$d= Z%dUd>Z&dVd?Z'd@ Z(dA Z)dB Z*dWdCZ+dD Z,dE Z-dF Z.dG Z/dH Z0dI Z1dJ Z2dXdKZ3dNdYdLZ4dM Z5dN Z6e7dO Z8dP Z9dQ Z:dR Z;dNdOdSZdNdTZ?dNdUZ@dNdVZAdNdWZBdNdXZCdNdYZDdZ ZEd[ ZFd\ ZGd] ZHd^ ZIdNd_ZJdNd`ZKdNdaZLdNdbZMdNdcZNdNddZOdNdeZPdNdfZQdNdgZRdNdhZSdNdiZTdZdjZUdNdkZVdNdlZWdNdmZXdNdOdnZYeYZZdNdoZ[dNdpZ\dNdqZ]dNdrZ^dNdsZ_dNdtZ`dNduZadNdvZbdNdwZcdNdxZdd[dyZedOdzZfdNd{ZgdNd|ZhdNd}ZidNd~ZjdNdZkdNdZldNdZmdNdZndNdZodNdZpd\dOdZqd\dOdZrdNdZsdNdZtdNdZudNdZvdNdZwdNdZxdNdZydNdZzdNdZ{dNdZ|dNdZ}dNdZ~dNdZdNdZdNdZdNdZdNdZdNdZdNdZdNdZdNdZdNdZd]dZdNdZdNdZdNdZdNdZd Zd Zd^d_dZeZd^d`dZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdNdZd Zd Zd Zd Zd Zd Zd Zd Zd ZdadZdbdZd Zd Zd Zd Zd ZdÄ ZdĄ Zdń ZdƄ ZdNdDŽZdȄ ZdɄ Zdʄ Zd˄ Zd̄ Zd̈́ Zd΄ ZdNdτZdNdЄZdNdфZdNd҄ZdNdӄZdԄ ZdՄ Zdք ZeZdׄ ZŐdNdZƐdNdلZǐdNdڄZȐdNdۄZɐdNd܄ZʐdNd݄ZːdNdބZ̐dNd߄Zd ZeZeZeZd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdNdZdNdZdcdZd Zd
Zd Zd Zd
Zd Zd Z d Zd Zd Zd Zd Zd ZdNdZd Zd Z d Z
d Z d Z d Z
d Zd Zd Zd Zd! Zd" Zd# Zd$ ZeZd% Zd& Zd' Zd( Zd) Zd* Z d+ Z d, Z d- Z d. Z d/ Z!d0 Z"d1 Z#d2 Z$d3 Z%d4 Z&d5 Z'd6 Z(d7 Z)d8 Z*d9 Z+d: Z,d; Z-d< Z.d= Z/dNd>Z0dNd?Z1dNd@Z2dNdAZ3dNdBZ4dNdCZ5dD Z6dE Z7dF Z8dG Z9dH Z:dI Z;dJ Z<dK Z=dL Z> fdMZ? xZ@S (d 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_unitiperiodddagger) gothic_re_imdecimal_separator perm_cyclicparenthesize_superminmax
diff_operator
adjoint_stylezdict[str, Any]_default_settingsc t j | | d| j v r g d}| j d |vr t d | j d !| j d dk( rd| j d< ddd d
d } || j d | j d
< || j d xs d | j d< ddd| _ dddddddd}| j d }|j || | j d < d d d d d }| j d! }|j || | j d"< y # t $ r | j d | j d
< Y w xY w# t $ rQ | j d j dv r|d | j d< n | j d | j d< Y w xY w)#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__ s x( T^^ #(K~~f%[8 "= > > >>+ , 4v&(204DNN, -
- !=>
NN- .
1 !=!FG
NN5 6 "%3/
NN#34 1E1I1I)U^1_-.
7
0C0G0G
Wd0e,-I -|,
NN- . - 1|,224BC %U+ 9: NN<0 9:
1s% = D8 #E# 8%E E #AF=<F=c $ dj | S )Nz\left({}\right)formatr rr s rs _add_parenszLatexPrinter._add_parens s !((++ru c $ dj | S )Nz\left( {}\right)r r s rs _add_parens_lspacez LatexPrinter._add_parens_lspace s "))!,,ru c t | }|r"|r | j | j | S ||k s|s%||k r | j | j | S | j | S N)r r _print)r itemlevelis_negstrictprec_vals rs parenthesizezLatexPrinter.parenthesize se )$/ f##DKK$56 6 u v8u3D##DKK$56 6;;t$ $ru c p d|v r1| j d r| j | S dj | S |S )z
Protect superscripts in s
If the parenthesize_super option is set, protect with parentheses, else
wrap in braces.
r r z{{{}}})r r r r s rs r z LatexPrinter.parenthesize_super s= !8~~ 23''** q))ru c t j | | }| j d dk( r|S | j d dk( rd|z S | j d rd|z S | j d }d|d|d |dS )
Nr r r z$%s$r z$$%s$$z\begin{ro z\end{)r doprintr )r exprtexenv_strs rs r zLatexPrinter.doprint st oodD) >>& !W ,J
^^F
#x
/S=
^^F
# s? "nnV,G.5sGD Dru c |j xr |j xs0 |j xr" |t j uxr |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 sT __<)<)< J I$amm*C +H.2.>.>%.GK Kru c | j | sy|j r| j | sy|j r| j | sy|j
s |j ryy)a
Returns True if the expression needs to be wrapped in brackets when
passed as an argument to a function, False otherwise. This is a more
liberal version of _needs_brackets, in that many expressions which need
to be wrapped in brackets when added/subtracted/raised to a power do
not need them when passed to a function. Such an example is a*b.
FT)r is_Mul
_mul_is_cleanis_Pow
_pow_is_cleanis_Add is_Functionr s rs _needs_function_bracketsz%LatexPrinter._needs_function_brackets sZ ##D) {{4#5#5d#;T%7%7%= 0 0 ru c 0 ddl m} ddlm} ddlm} j r|s4j r$yt t d k ryj ryj ryt fdt fD ry|st fd|||fD ryy )
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 @ K | ] }j | y wr has.0xr s rs z3LatexPrinter._needs_mul_brackets..N +qtxx{+ c 3 @ K | ] }j | y wr r) r+ s rs r. z3LatexPrinter._needs_mul_brackets..Q s BADHHQKBr0 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_brackets7 s 416 ;;T : : <
#D
)Ju,=
=
+SF+ +B(GS)ABBru c n j ryt fdt fD ryj ryy)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 @ K | ] }j | y wr r) r+ s rs r. z3LatexPrinter._needs_add_brackets..^ r/ r0 F)r6 r8 r r! r s `rs _needs_add_bracketsz LatexPrinter._needs_add_bracketsV s1 +SF+ + ;;ru c B |j D ] }|j s y y)NFT)argsr" r r r< s rs r zLatexPrinter._mul_is_cleand s$ 99 C ru c : | j |j S r )r baser s rs r zLatexPrinter._pow_is_cleanj s '' 222ru c | d|d|dS |S )N\left( \right)^{ro rp r r exps rs _do_exponentzLatexPrinter._do_exponentm s ?.2C8 8Kru c & | j |j j }|j rK|j D cg c] }| j | }}d}|j |dj
| S dj | S c c}w )Nz"\operatorname{{{}}}\left({}\right), z \text{{{}}})_deal_with_super_sub __class____name__r@ r r join)r r namerM lsrr s rs _print_BasiczLatexPrinter._print_Basics sv (( )@)@A 99*.))4Q$++a.4B45A88D$))B-0 0!((. . 5s Bc d|z S N \text{%s}rp r es rs _print_boolzLatexPrinter._print_bool|
a ru c d|z S rT rp rV s rs _print_NoneTypez LatexPrinter._print_NoneType rY ru c | j || }d}t | D ]U \ }}|dk( rn |j r |dz
}| }n|dz
}| j | }| j | rd|z }||z
}W |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&9 ' GAtAv..0u uu {{4(H''--8 8OC
ru c F ddl m} |j dk( ry || }|j }|j }|j d |dz
k( r
||dz
ggz }d}|D ] }|t | j
dd z
}" |j
d d
}|j
d d }|S )
Nr Permutation\left( \right) r ,r r \left( r \right)) sympy.combinatorics.permutationsrh size cyclic_form
array_formstrr )r r rh expr_permsizrd r s rs _print_CyclezLatexPrinter._print_Cycle s @ 99>$4 $$ ii ??2 #' )!cAgYK/I 3A AsE2 2H 3##C4##C4ru c ddl m} ddlm} |j }| |d| dddd n | j
j
d
d }|r| j | S |j dk( ry |j D cg c] }| j | }}t t | D cg c] }| j | }}d
j | }d
j | } dj || f }
d|
z S c c}w c c}w )Nr rg )sympy_deprecation_warningzw
Setting Permutation.print_cyclic is deprecated. Instead use
init_printing(perm_cyclic=z).
z1.6z#deprecated-permutation-print_cyclic )deprecated_since_versionactive_deprecations_target
stacklevelr Tri & \\ z \begin{pmatrix} %s \end{pmatrix})ro rh sympy.utilities.exceptionsrx print_cyclicr r rv rp rr r rangelenrO ) r r rh rx r r< lowerupperrow1row2mats rs _print_Permutationz LatexPrinter._print_Permutation s @H!.. " %++6- 8 */+P
..,,]DAK $$T* * 99>$-1__=cS!==-23u:->?cS!??zz% zz% llD$<(2S88
>?s 9C=)Dc n |j \ }}d| j | d| j | dS )Nz\sigma_{z}(r r@ r )r r permvars rs _print_AppliedPermutationz&LatexPrinter._print_AppliedPermutation s, II c%)[[%6 C8HIIru c * 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 rO|j d \ }} | d d
k( r| d d } | j d d
k( r|j
dd }||d| dS |dk( ry|dk( ry| j d d
k( r|j
dd }|S )Nr FTr r ) strip_zeros min_fixed max_fixedr rW r +rk r comma.z{,}z10^{ro z+infz\inftyz-infz- \infty)r" _precr mlib_to_str_mpf_splitr )
r r dpsr lowhighstr_real separatormantrH s
rs _print_FloatzLatexPrinter._print_Float s $**% 4$','>dnnU#D(- (?t~~e$T tzz3ES\`a NN#=> (?"..-KT31v}!"g~~ 12g=||C.%)9c: :
~~ 12g=#++C6Oru c |j }|j }| j |t d d| j |t d S )Nr
r _expr1_expr2r
r! r r vec1vec2s rs _print_CrosszLatexPrinter._print_Cross sJ {{{{"&"3"3D*U:K"L"&"3"3D*U:K"LN Nru c R |j }d| j |t d z S )Nz\nabla\times %sr
_exprr
r! r r r s rs _print_CurlzLatexPrinter._print_Curl s( jj!D$5$5c:e;L$MMMru c R |j }d| j |t d z S )Nz\nabla\cdot %sr
r r s rs _print_Divergencez LatexPrinter._print_Divergence s( jj 4#4#4S*U:K#LLLru c |j }|j }| j |t d d| j |t d S )Nr
r r r s rs
_print_DotzLatexPrinter._print_Dot sJ {{{{!%!2!24E9J!K!%!2!24E9J!KM Mru c R |j }d| j |t d z S )Nz \nabla %sr
r r r funcs rs _print_Gradientz LatexPrinter._print_Gradient ( zzd / /j6G HHHru c R |j }d| j |t d z S )Nz \Delta %sr
r r s rs _print_Laplacianz LatexPrinter._print_Laplacian r ru c ddl m} j d j d d fd }d fd t |t r>|j
}|d t j u st d |dd D r | S d }|j r| }d
}|j r
|d z
}d }nd
} ||d \ }}|t j u r't ddd |j
vr
| || z
}n || } || }
t |
j } j d } j d r5| dk r0d|
vr, j |d r
|d| d|
z
}n_|| d|
z
}nS| Dt | j | | z kD r$ j |d r|d|
dd| dz
}n |j rt j }
t j }|j
D ]h } j |d sHt ||
|z j | | z kD s |j |j cxu rd u r n n||z }d|
|z }
j j |d r |d ||
d |
dd || d z
}n7|d ||
d |
d || z
}n|d|
d| z
}n |d | d |
dz
}|r|d z
}|S ) Nr )fractionr r c | j st j | S j dvr| j }nt | j }t |d d \ }}t |d d \ }} ||z |z S )N)oldnonec t | d xs t | d xs( t | t xr t | j d S )N
_scale_factoris_physical_constant)hasattr
isinstancer rC r- s rs rt z:LatexPrinter._print_Mul..convert.. sD ?8S8yW^_`bxWy 8H )!S 1 G &qvv/E F ru T)binaryc t | d S )Nr )r r s rs rt z:LatexPrinter._print_Mul..convert.. s
?8S ru )r rs r r as_ordered_factorslistr@ r% )r r@ unitsnonunitsprefixes convert_argsr s rs convertz(LatexPrinter._print_Mul..convert s ;;4;;t,--::_4 224D ?D #'t .HPT#Vx #'u.S\`"a%#Hx$7%$?@@ru c v dx}}t | D ] \ }}j | }t |d sut |d sij ||dk( |t | dz
k( rd|z }t
d j
| r t
d j | r|z
}n|r
|z
}n|r|z
}||z
}|} |S )Nr r r r rk )r9 r: r_ )ra r r r; r _between_two_numbers_psearchmatch) r@ _tex
last_term_texr rc rd numbersepr r s rs r z-LatexPrinter._print_Mul..convert_args s #% %D=$T?
)4 ;;t, o6'$H^:_//Q!V673t9q=6H 0 K#5#@.q188 G.q177A ) )I%D (
#
)$ Kru c 3 < K | ] }t |t y wr )r r )r, r< s rs r. z*LatexPrinter._print_Mul..: s &S3z#v'>&S rk F- r Tr )exactrj )evaluater r r )r: rE z
\right) / z / z \frac{1}{ro rn \frac{}{r returnrs )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 s ` @@@rs
_print_MulzLatexPrinter._print_Mul s + (:; (BC A 8 dC 99DAw!%% 3&S$qr(&S#S#D)) ( ( *5DC{{s
!%C D1 u AEE>c!R% 8 I
74= C U^F U^F (FNN#45E~~ /0Vq[v%++E+>ffEEC88C" '%,6++E+=!9f 6 6C\\AA "ZZ # 33AE3B #GAaCL$6$6$8 9E&L H!"!1!1Q5E5E!N!N FA FA
# ///= &qz69gaj J J &qz69gaj J J &)VLLC66:: 3JC
ru c |j r-| j |j j S | j |j S r )
is_aliasedr as_polyas_exprr s rs _print_AlgebraicNumberz#LatexPrinter._print_AlgebraicNumberz s< ??;;t||~ 5 5 78 8;;t||~. .ru c | j |j }|j rd| dS | j |j j }d| d| dS )NrE rn rK )r pis_inertalphar )r r r r s rs _print_PrimeIdealz LatexPrinter._print_PrimeIdeal sZ KK == QCw' ' DJJ . . 012eWG,,ru c t |j j rB|j j }|j j }t | dk( ru|dk7 rp| j
d ra| j
|j }|dk( rd|z }n | j
d rd||fz }nd||fz }|j j rd|z S |S | j
d r|dk7 r| j |j t d
}|j j r| j | }|j j r"| j
|j |d | S |d
|d |dS |j j r|j j r|j dk( r |j d
|j dS |j j rt|j j }|j j }||z t | k( r7|j dk( r d|d|dS d|d|dt |j dS | j | S |j j r6| j
|j | j
|j S d}| j! || S )Nrk r r z \sqrt{%s}r z
\root{%d}{%s}z
\sqrt[%d]{%s}z \frac{1}{%s}r r /rH ^{ro rj z\frac{1}{\frac{r }}z\frac{1}{(\frac{z})^{z%s^{%s})rH r r qr r r rC is_negativer
r! is_Symbolr r" r r _helper_print_standard_power)r r r r rC r base_pbase_qs rs
_print_PowzLatexPrinter._print_Pow s. 88 XXZZAXXZZA1v{qAv$.. *I{{499-6&-C^^F+*aY6C*aY6C88''*S00 J 23Q((Ju4EF99&& 2248D99(( ;;tyyA6F;GG(,a33%%$))*B*B99>)-DHH==99(("&))++F"&))++F #f+5 88r>AG#P P * IOPVX[\`\d\dXe#f ft,, 99 ;;tyydkk$((.C;D D00s;;ru c | j |j }| j |j t d }|j j
r| j
| }ns|j j rd|z }nWt |j t r=|j d r,t j d| r|j d r|dd }|||fz S )Nr z{%s}rE z\\left\(\\d?d?dotrn i)r rH r
rC r! r r is_Floatr r
startswithr8 r endswith)r r templaterH rC s rs r z)LatexPrinter._helper_print_standard_power s kk$((# Ju,=> 99 **40D
YY
T>DJ/ *-t4
j)2;D4+%%ru c > | j |j d S Nr r r@ r s rs _print_UnevaluatedExprz#LatexPrinter._print_UnevaluatedExpr s {{499Q<((ru c
t |j dk( r9dt |j d D cg c] } j | c} z }n< fd}dt j d|j D cg c]
} || c} z }t
|j t r#|d j |j z z
}|S | j |j z
}|S c c}w c c}w )Nrk z\sum_{%s=%s}^{%s} r c | dt | d | d | d fD cg c] }j | c} z S c c}w Nz%s \leq %s \leq %srk r r tupler lrr r s rs _format_ineqz-LatexPrinter._print_Sum.._format_ineq C ,AaD!A$!3EFa4;;q>FGH HF 9
z\sum_{\substack{%s}} \\r_ r limitsr r rs rO r functionr r r r r r r s ` rs
_print_SumzLatexPrinter._print_Sum s t{{ q 't{{1~>!t{{1~>?@C
H +4;;!Ga,q/!GHIC dmmS ) % DMM(BB BC
4;;t}}- -C
? "H C,
7C1 c
t |j dk( r9dt |j d D cg c] } j | c} z }n< fd}dt j d|j D cg c]
} || c} z }t
|j t r#|d j |j z z
}|S | j |j z
}|S c c}w c c}w )Nrk z\prod_{%s=%s}^{%s} r c | dt | d | d | d fD cg c] }j | c} z S c c}w r r
r s rs r z1LatexPrinter._print_Product.._format_ineq r r z\prod_{\substack{%s}} r r_ r r s ` rs _print_ProductzLatexPrinter._print_Product s t{{ q (t{{1~>!t{{1~>?@C
H ,4;;!Ga,q/!GHIC dmmS ) % DMM(BB BC
4;;t}}- -C
? "Hr c ddl m} g }||j k( r|j j S t || r |j j
}nd|fg}|D ] \ }}t |j j
}|j d |D ] \ }} | dk( r |j d|j z *| dk( r |j d|j z Nd | j | z d
z }
|j d|
z |j z d j | } | d d k7 r| d
d } | S | dd } | S )Nr )Vectorc ( | d j S r )__str__r s rs rt z4LatexPrinter._print_BasisDependent.. s !A$,,. ru keyrk r^ rj r] rE rn r - )
sympy.vectorr zero _latex_formr separateitemsr
componentssortappendr rO ) r r r o1r* systemvect
inneritemskvarg_stroutstrs rs _print_BasisDependentz"LatexPrinter._print_BasisDependent sB ' 499 99(( ( dF #MMO))+EYKE !
?LFD doo 3 3 56J OO 8O 9"
?16IIeamm 34"WIIeamm 34 '$++a. 8: EGIIego
=>
?
? ''"+ !9 ABZF
ABZF
ru c | j |j }d|z dz ddj t | j |j z z }|S )Nr ro _{%s}rl )r rC rO mapindices)r r tex_baser s rs _print_IndexedzLatexPrinter._print_Indexed sP ;;tyy)(l3 w T\\ **, , ,
ru c 8 | j |j S r )r labelr s rs _print_IndexedBasez LatexPrinter._print_IndexedBase s {{4::&&ru c d | j |j }|j | j |j }|j | j |j }n | j t j
}dj
|| }dj
|| S |S )Nz%{lower}\mathrel{{..}}\nobreak {upper})r r z{{{label}}}_{{{interval}}})r> interval)r r> r r r Zeror )r r r> r r rA s rs
_print_IdxzLatexPrinter._print_Idx s DJJ' :: !KK
+Ezz% DJJ/ AFF+@GG !5 H 2H/66 ( 7 4
4 ru c t |j rd}n| j d }d}d}t |j D ]d \ }}||z
}|dk( r||d| j | z
}*||d| j
| j | d| j | dz
}f |dk( r
d |d
|d}nd |d| j | d |d}t d |j D r+|d| j |j t d
dd S |d| j |j t d
dd S )Nz\partialr r r rk r r ro r r }}{c 3 < K | ] }|j y wr r5 r, r s rs r. z1LatexPrinter._print_Derivative..: s ?q))+?r 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$ sQ DII &%K ..)>?K t 2 23 :FAs 3JCax; A?? (,(?(? A(O(, C(8: : : !8&137C ,7 C8H#NC ?TYY? ? "D$5$5dii29= !2 !? @ @ru c |j \ }}} j | } fd|D } fd|D }dj d t || D }d|d|dS )Nc 3 @ K | ] }j | y wr r r, rW r s rs r. z+LatexPrinter._print_Subs..H 1T[[^1r0 c 3 @ K | ] }j | y wr rR rS s rs r. z+LatexPrinter._print_Subs..I rT r0 z\\ c 3 8 K | ] }|d dz |d z yw)r =rk Nrp )r, rW s rs r. z+LatexPrinter._print_Subs..J s( !B"#AaD3J1 !B z\left. z \right|_{\substack{ z }})r@ r rO zip) r subsr r new
latex_expr latex_old latex_new
latex_subss ` rs _print_SubszLatexPrinter._print_SubsE sk c3[[&
1S1 1S1 [[ !B'*9i'@!B B
9C9CE Eru c
dg }}| j d }t |j dk rnt d |j D rRddt |j dz
z z dz }|j D cg c] }d || j |d
}}nt |j D ] }|d
}|d z
}t | dkD r| j d d
k7 r| j d s|dz
}t | dk( r0|d| j |d d| j |d dz
}t | dk( r|d| j |d z z
}|j
d
d || j | |d| j |j t d t d |j D d dj | S c c}w )Nr r c 3 8 K | ] }t | d k( yw)rk N)r )r, lims rs r. z/LatexPrinter._print_Integral..T s (N3SQ (NrX z\ir rk ntz\, r z\intr r r z\limitsr% _{}^{r ro ^{%s}r r
c 3 < K | ] }|j y wr rG rH s rs r. z/LatexPrinter._print_Integral..o s >o`aq?Y?Y?[>or TrI )
r r r allr rJ insertr
r r! r8 r@ rO )r r r symbolsrL symbolrd s rs _print_Integralz LatexPrinter._print_IntegralO s 2Wnn%:; t{{ q S(N$++(N%N #s4;; /! 344t;C%)[[2! &1$++fQi2HI 2G 2 ,
S Qws8a<~~f-9$(NN6$:z)3x1}t{{3q6/B/3{{3q6/B D D3x1}w$++c!f*= >>q T[[=P"QR
S" !$"3"3DMM4>u4E;>>oeienen>o;o;? #4 #A WWW - / /+2s 7 Gc |j \ }}}}d| j | z }t | dk( s"|t j t j
fv r|d| j | z z
}n)|| j | d| j | dz
}t
|t r|d| j | dS |d| j | S ) Nz
\lim_{%s \to z+-z%s}r ro rE rn r )r@ r rs r InfinityNegativeInfinityr r )r r rW zz0dirr s rs _print_LimitzLatexPrinter._print_Limits s
1b# Q / s8t rajj!2D2D%E E 6DKKO+ +C BS1AB BC a !+. A? ? "DKKN3 3ru c | j | }|j d }|j d }|t v rd|z }|S t | dk( s|j d s
|dk( s|dk( r|}|S |dkD r)|dkD r$d|dt || d |t || d }|S |dkD rd|d| d ||d }|S |dkD rd|d| d ||d }|S d
|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\%srk r r \operatorname{Nro z\operatorname{%s})rL findaccepted_latex_functionsr r r )r r superscriptidx subscriptidxrP s rs _hprint_Functionz LatexPrinter._hprint_Function s& ((. 3 yy~ + +D=D$ # Y!^tt 4 8I^_`M`D !lQ&6:#l>:;\.9:;= !# .) )+
! ,' ')
,d2 ru c 0 |j j }t | d|z r&t |t s t | d|z || S |j D cg c] }t | j | }}| j d }d}| j d xr/ t | dk( xr | j |j d }g d} || v r.|dk( rn(|d k( r|d
d k( rd nd
|dd z }n|dk( r |dd }d}|d}|r|t v rd|z }
nDd|z }
n>|+| j | } | j | } | d|d}
n| j | }
|r|t v r|
dz
}
n |
dz
}
n|
dz
}
|r
||
d|z z
}
|
dj | z S c c}w )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_r Fr rk r ) asinacosatanacscasecacotasinhacoshatanhacschasechacothr fullrj hararcNpowerTz\%s^{-1}z\operatorname{%s}^{-1}r ro z {%s}%s{\left(%s \right)}rh rl )r rN r r r getattrr@ rs r r r r# rz r} r rO ) r r rH r r< r@ r inv_trig_power_casecan_fold_bracketsinv_trig_tablerP func_texs rs _print_Functionz LatexPrinter._print_Function s yy!! 4T) * t\2274T!124= =59YY?cC C()?D? "^^,< =N"' $/C D !@D Q!@11$))A,??
N ~%!]2#v-$(HOD$qr(JD#w. 8D*.' ,1)"33&-D4t;D 006 228<%-s3,,T2 33 H$DEMD--"s3&#((4.( (s @s !Fc 6 | j t | S r )r} rs r s rs _print_UndefinedFunctionz%LatexPrinter._print_UndefinedFunction s $$SY//ru c x d| j |j d| j |j dS )Nr z}_{\circ}\left({z}\right))r r r r s rs _print_ElementwiseApplyFunctionz,LatexPrinter._print_ElementwiseApplyFunction s, KK
& KK "
ru c ^ ddl m} ddlm}m} ddlm} ddlm} ddl m
} |d|d|d |d
|d|d iS ) Nr )KroneckerDelta)gamma
lowergamma)beta)
DiracDelta)rU z\deltar@ \gammaz\operatorname{B}z\operatorname{Chi}) (sympy.functions.special.tensor_functionsr 'sympy.functions.special.gamma_functionsr r &sympy.functions.special.beta_functionsr 'sympy.functions.special.delta_functionsr 'sympy.functions.special.error_functionsrU )r r r r r r rU s rs _special_function_classesz&LatexPrinter._special_function_classes s; KM?F? I)I* , ,ru c | j D ]9 }t || s|j |j k( s*| j | c S | j t | S r )r
issubclassrN r} rs )r r clss rs _print_FunctionClassz!LatexPrinter._print_FunctionClass sX 11 ;C$$ #,,)F55c:: ; $$SY//ru c |j \ }}t | dk( r| j |d }n| j t | }d|d| j | d}|S )Nrk r rm z \mapsto \right))r@ r r r )r r rl r s rs
_print_LambdazLatexPrinter._print_Lambda
sX
w<1 kk'!*-Gkk%.1G18$++d:KL
ru c y)Nz\left( x \mapsto x \right)rp r s rs _print_IdentityFunctionz$LatexPrinter._print_IdentityFunction s ,ru c t |j t }|D cg c] }d| j | z }}dt |j
j
ddj | d}||d|dS |S c c}w ) Nr" r r rE rK rn r ro )sortedr@ r r rs r r rO )r r rH r@ rm texargsr s rs _hprint_variadic_functionz&LatexPrinter._hprint_variadic_function sv dii%56=AB654;;v..BB'*499~';';'='+yy'9; ?!$c* *J
Cs Bc \ d| j |j d z }||d|dS |S )Nz \left\lfloor{%s}\right\rfloorr r ro r r r rH r s rs _print_floorzLatexPrinter._print_floor% s2 .TYYq\1JJ ?!$c* *Jru c \ d| j |j d z }||d|dS |S )Nz\left\lceil{%s}\right\rceilr r ro r r s rs _print_ceilingzLatexPrinter._print_ceiling- s2 ,t{{499Q> ?!$c* *Jru c | j d r*d| j |j d t d z }n5dj | j |j d t d }| j || S )Nr z\Re{%s}r Atomz\operatorname{{re}}{{{}}}r r
r@ r! r rI r s rs _print_rezLatexPrinter._print_reH r >>. ) t 0 01 z&?Q RRC.55d6G6G RS V`agVh6ijC c**ru c | j d r*d| j |j d t d z }n5dj | j |j d t d }| j || S )Nr z\Im{%s}r r z\operatorname{{im}}{{{}}}r r s rs _print_imzLatexPrinter._print_imP r ru c ddl m}m} t |j d | r | j |j d d S t |j d | r | j
|j d d S |j d j r!d| j |j d z S d| j |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 rW r r s rs
_print_NotzLatexPrinter._print_NotX s = affQi ,))!&&)5KL L affQi )&&qvvay2DE E
FF1I *T[[-CC C AFF1I 66 6ru c B |d }|j r!|j sd| j | z }nd| j | z }|dd D ]P }|j r(|j s |d|d| j | dz
}7|d|d| j | z
}R |S )Nr r_ r rk r z \left(rn )r is_Notr )r r@ charr< r s rs _print_LogOpzLatexPrinter._print_LogOpc s 1g >>#**$t{{3'77C$++c**C8 Q TYYq\*DKK ! ,EGC %t{{499Q<'@@C ?"%s+ +C< ru c t |j dk( rad| j |j d d| j |j d d| j |j d d}nAd| j |j d d| j |j d d}|d |d
|S d |z S ) Nr% rE r ; rk r r rn z\Pi^{ro z\Pi%sr r s rs _print_elliptic_piz LatexPrinter._print_elliptic_pi s tyy>Q TYYq\*DKK ! ,ETYYq\*,C TYYq\*DKK ! ,EGC ?$'- -c> !ru c |j d }t |j dk( r|j d n|j d }d| d| d}|d|d|S d|z S ) Nr rk rE rK rn z\operatorname{B}^{ro z\operatorname{B}%s)r@ r )r r rH r- yr s rs _print_betazLatexPrinter._print_beta sd IIaL Na /DIIaLTYYq\s"QCw' ?14c: :(3. .ru c
|j D cg c] }| j | }}d|d d|d d}|d|d|d d|d d
|d |
S d|d|d d|d d |S c c}w )
NrE r rK rk rn rx z}_{(r r% z)}^{ro z)}r )r r rH operatorr< largsr s rs _print_betainczLatexPrinter._print_betainc s} -1YY7cS!77(-a%(; ?=EuQxQVWXQY[^`cd d 9A%(ERSHVYZ Z
8s A%c * | j ||d S )NI)r )r rG s rs _print_betainc_regularizedz'LatexPrinter._print_betainc_regularized s ""4s";;ru c d| j |j d d| j |j d d}|d|d|S d|z S ) NrE r rK rk rn z\Gamma^{ro z\Gamma%sr r s rs _print_uppergammaz LatexPrinter._print_uppergamma O (, DIIaL(A(, DIIaL(AC ?'*C0 0 $ $ru c d| j |j d d| j |j d d}|d|d|S d|z S ) NrE r rK rk rn z\gamma^{ro \gamma%sr r s rs _print_lowergammaz LatexPrinter._print_lowergamma r ru c d| j |j d z }|#| j |j d|d|S | j |j |S Nr_ r r ro )r r@ r r s rs _hprint_one_arg_funcz!LatexPrinter._hprint_one_arg_func sT 4;;tyy|#<< ?#';;tyy#93D D "kk$)) 4c: :ru c b d| j |j d z }|d|d|S d|z S )Nr_ r z\operatorname{Chi}^{ro z\operatorname{Chi}%sr r s rs
_print_ChizLatexPrinter._print_Chi s8 4;;tyy|#<< ?36< <*S0 0ru c d| j |j d z }| j |j d }| d|d|d|S d|d|S )Nr_ rk r z\operatorname{E}_{rg ro r )r r rH r nus rs
_print_expintzLatexPrinter._print_expint sW 4;;tyy|#<<
[[1
& ?68#sC C 24S9 9ru c b d| j |j d z }|d|d|S d|z S )Nr_ r zS^{ro zS%sr r s rs _print_fresnelsz LatexPrinter._print_fresnels
7 4;;tyy|#<< ?"%s+ +C< ru c b d| j |j d z }|d|d|S d|z S )Nr_ r zC^{ro zC%sr r s rs _print_fresnelcz LatexPrinter._print_fresnelc r ru c n d| j |j d t d z }| d|d|dS |S )Nz!%sr FuncrE rF ro r
r@ r! r s rs _print_subfactorialz LatexPrinter._print_subfactorial s; t((1 z&7IJJ ?.137 7Jru c l d| j |j d t d z }||d|dS |S )Nz%s!r r r ro r r s rs _print_factorialz LatexPrinter._print_factorial" s; t((1 z&7IJJ ?!$c* *Jru c l d| j |j d t d z }||d|dS |S )Nz%s!!r r r ro r r s rs _print_factorial2z LatexPrinter._print_factorial2* s; ))$))A,
68JKK ?!$c* *Jru c d| j |j d d| j |j d d}||d|dS |S )Nz{\binom{r r rk r r ro r r s rs _print_binomialz LatexPrinter._print_binomial2 sI %)[[1 %>%)[[1 %>@ ?!$c* *Jru c |j \ }}d| j |t d z }d|d| j | d}| j || S )Nr r r }^{\left(\right)}r@ r
r! r rI )r r rH nr2 rC r s rs _print_RisingFactorialz#LatexPrinter._print_RisingFactorial; sP yy1t((Jv,>??+/Q @ c**ru c |j \ }}d| j |t d z }d| j | d|d}| j || S )Nr r z{\left(z
\right)}_{ro r )r r rH r r2 subr s rs _print_FallingFactorialz$LatexPrinter._print_FallingFactorialC sP yy1d'':f+=>>+/;;q>3? c**ru c d|z }d}| |j d dk( r |d|d}nd}|d| j |j d | j |j d
}|r| j || }|S ) Nr Fr rj r ro Trf }\left(rn )ry r r argumentrI )r r rH symr need_exps rs _hprint_BesselBasez LatexPrinter._hprint_BesselBaseK sz sm ?xx}"$'- +. DJJ0G+/;;t}}+EG ##C-C
ru c |syd}|d d D ] }|d| j | z z
} || j |d z
}|S )Nr rj z%s, rR )r r rr r s rs _hprint_veczLatexPrinter._hprint_vec\ sU Sb )A
$++a.( (A ) T[[R
!!ru c ( | j ||d S )NJr' rG s rs _print_besseljzLatexPrinter._print_besselje &&tS#66ru c ( | j ||d S )Nr r, rG s rs _print_besselizLatexPrinter._print_besselih r. ru c ( | j ||d S )NKr, rG s rs _print_besselkzLatexPrinter._print_besselkk r. ru c ( | j ||d S )NYr, rG s rs _print_besselyzLatexPrinter._print_besselyn r. ru c ( | j ||d S )Nr r, rG s rs _print_ynzLatexPrinter._print_ynq r. ru c ( | j ||d S )Nr r, rG s rs _print_jnzLatexPrinter._print_jnt r. ru c ( | j ||d S )NzH^{(1)}r, rG s rs _print_hankel1zLatexPrinter._print_hankel1w &&tS)<Q (5T[[$))1L+MMC$t{{499Q<'@@C ?&)3/ /C ru c t |j dk( r-dt t | j |j z }n!d| j |j d z }| d|d|dS d|z S ) Nr z_{%s}\left(%s\right)r8 r r r ro r ri r s rs _print_stieltjesz LatexPrinter._print_stieltjes sf tyy>Q )E#dkk4992M,NNCT[[1 66C ?'*C0 0S ru c x dt t | j |j z }|d|z S d|d|S )Nz\left(%s, %s, %s\right)z\Phi%sz\Phi^{ro )r r9 r r@ r s rs _print_lerchphiz LatexPrinter._print_lerchphi s? (5T[[$))1L+MM ; s? " !$c**ru c | t | j |j \ }}d|z }|d|d|S d|d|d|S )Nr_ z\operatorname{Li}_{ro rg r9 r r@ )r r rH rr rr r s rs _print_polylogzLatexPrinter._print_polylog sF 4;; *1 1$ ;23S9 9 34c3??ru c t | j |j \ }}}}d|d|d|d|d }| d|z d|z z }|S )NP_{r rl \right)}\left(rn rE \right)^{%s}rp )r r rH r r r r- r s rs
_print_jacobizLatexPrinter._print_jacobi sI dii0
1a?@!QJ ?c/Os$;;C
ru c t | j |j \ }}}d|d|d|d}| d|z d|z z }|S )NzC_{r rt rn rE ru rp r r rH r r r- r s rs _print_gegenbauerz LatexPrinter._print_gegenbauer E dkk499-1a<=q!D ?c/Os$;;C
ru c x t | j |j \ }}d|d|d}| d|z d|z z }|S )NzT_{r# rn rE ru rp r r rH r r- r s rs _print_chebyshevtz LatexPrinter._print_chebyshevt A 4;; *1*+Q/ ?c/Os$;;C
ru c x t | j |j \ }}d|d|d}| d|z d|z z }|S )NzU_{r# rn rE ru rp r| s rs _print_chebyshevuz LatexPrinter._print_chebyshevu r~ ru c x t | j |j \ }}d|d|d}| d|z d|z z }|S )Nrs r# rn rE ru rp r| s rs _print_legendrez LatexPrinter._print_legendre r~ ru c t | j |j \ }}}d|d|d|d}| d|z d|z z }|S )Nrs r rt rn rE ru rp rx s rs _print_assoc_legendrez"LatexPrinter._print_assoc_legendre rz ru c x t | j |j \ }}d|d|d}| d|z d|z z }|S )NzH_{r# rn rE ru rp r| s rs _print_hermitezLatexPrinter._print_hermite r~ ru c x t | j |j \ }}d|d|d}| d|z d|z z }|S )NL_{r# rn rE ru rp r| s rs _print_laguerrez LatexPrinter._print_laguerre
r~ ru c t | j |j \ }}}d|d|d|d}| d|z d|z z }|S )Nr r rt rn rE ru rp rx s rs _print_assoc_laguerrez"LatexPrinter._print_assoc_laguerre rz ru c t | j |j \ }}}}d|d|d|d|d }| d|z d|z z }|S )NzY_{rg r# rl rn rE ru rp r r rH r mthetaphir s rs
_print_YnmzLatexPrinter._print_Ynm J t{{DII61eS23QsC ?c/Os$;;C
ru c t | j |j \ }}}}d|d|d|d|d }| d|z d|z z }|S )NzZ_{rg r# rl rn rE ru rp r s rs
_print_ZnmzLatexPrinter._print_Znm" r ru c
x t | j | \ }}}|rdnd}|sdnd|z }||d|d|d|d|
S )Nz ^{\prime}r rh rE rK rn )r9 r ) r characterr@ r rH r r rr sups rs __print_mathieu_functionsz&LatexPrinter.__print_mathieu_functions) sA dkk4(1a #lb3 3 | j d|j | S )NCr &_LatexPrinter__print_mathieu_functionsr@ rG s rs _print_mathieucz LatexPrinter._print_mathieuc/ --c499#-FFru c > | j d|j | S )Nr r r rG s rs _print_mathieusz LatexPrinter._print_mathieus2 r ru c @ | j d|j d| S )Nr Tr rH r rG s rs _print_mathieucprimez!LatexPrinter._print_mathieucprime5 --c499Dc-RRru c @ | j d|j d| S )Nr Tr r rG s rs _print_mathieusprimez!LatexPrinter._print_mathieusprime8 r ru c |j dk7 rUd}|j }|j dk rd}| }| j d rd|||j fz S d|||j fz S | j |j S )Nrk 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_Rational; s~ 66Q;DAvvzB~~ /0#tQ&777%q$&&(99 9;;tvv& &ru c V | j |j }|j r t d |j D st |j
dkD r|dz
}t |j
dkD r || j |j
z
}n-|j
r!|| j |j
d z
}|dz
}t |j dkD r#|| j |j z
}d|z S || j |j d z
}d|z S )Nc 3 B K | ] }|t j k7 y wr )r rB )r, r s rs r. z,LatexPrinter._print_Order..J s >aa166k >s rk r r \rightarrow zO\left(%s\right))r r pointr8 r variables)r r rr s rs _print_OrderzLatexPrinter._print_OrderH s KK " ::# >4:: >> t~~ "
IA4>>"Q&T[[ 00 T[[ !233
A4::"T[[,, #Q&& T[[A //"Q&&ru c | j d j | }||S | j |j | S )Nr style)r r rL rP )r r r rP s rs
_print_SymbolzLatexPrinter._print_SymbolX s@ NN>266t< K((%(@@ru c T d|v r|g g }}}nJt | \ }}}t | }|D cg c]
}t | }}|D cg c]
}t | }}|dk( rdj | }|r|ddj | z z
}|r|ddj | z z
}|S c c}w c c}w )Nr r
\mathbf{{{}}}rh r r8 )r translater rO )r stringr rP supersrZ r r s rs rL z!LatexPrinter._deal_with_super_suba s &=!'R$&D!0!8 D&$ T?D067in7F7.23sIcN3D3 F?#**40D Gchhv .. .D Gchhtn, ,D 83s B B%c | j d rd}d}nd}d}d||ddd d
}| j |j d ||j d | j |j S ) Nr z\gtz\lt>=z<=z!=r )r r lhsrel_oprhs)r r gtltcharmaps rs _print_Relationalz LatexPrinter._print_Relationalw sv >>& !BBBB
"[[ 2 $T[[ 14;;txx3HJ Jru c < |j d d D cg c]* \ }}| j | d| j | , }}}|j d j t k( r;|j d| j |j d j
z nb|j | j |j d j
d| j |j d j d}|dj
| z S c c}}w )Nrj z & \text{for}\: z%s & \text{otherwise}z \begin{cases} %s \end{cases}ra )r@ r condr r- r rO )r r rW r ecpairsr s rs _print_Piecewisez LatexPrinter._print_Piecewise s #yy"~/q! /3kk!ndkk!nM / / 99R= % NN3 ;;tyy}'9'9: ;
<
NN KK "
(:(: ; KK "
(:(: ; =
> .V[[)))/s /Dc g }t |j D ]F }|j dj ||d d f D cg c] }| j | c} H | j
d }|+| j
d dk( rd}n|j dk du rd}nd }d
}|j d | }|d k( r%|j d d
d|j z z dz }|dj | z S c c}w )Nr} r r r smallmatrix
Tmatrixarray \begin{%MATSTR%}%s\end{%MATSTR%}%MATSTR%r r r }%sr )r rowsr- rO r r colsr )r r linesliner r out_strs rs _print_matrix_contentsz#LatexPrinter._print_matrix_contents s $))$ ND LLT$']$KT[[^$KL M N ..+ ?~~f%1'IIO, &G %G5//*g6 g oodC#dii-,?%,GHGE***! %Ls C/c | j | }| 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 s` --d3 >>+ & 4J **:6K +g5 "-.Gru c | j |j t d d }| j |j d| j |j
}d| d| dS )Nr Tr rl r }_{ro )r
parentr! r r r )r r matrix_part
index_parts rs _print_MatrixElementz!LatexPrinter._print_MatrixElement sd '' Z5GPT'U DFF+,Adkk$&&.A-BC
K=j\44ru c
fd} j |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< dj fd| D S )Nr rk r :c 3 H K | ] }|j | nd y wNr rR )r, xir s rs r. zFLatexPrinter._print_MatrixSlice..latexslice.. s" R"r~DKKO2 ERs ")r rO )r- rM r s rs
latexslicez3LatexPrinter._print_MatrixSlice..latexslice s\ QAtqyaDtqy!ts{!88RPQRR Rru r Tr \left[rK \right])r
r r! rowslicer colslicer )r r r s ` rs _print_MatrixSlicez LatexPrinter._print_MatrixSlice s S !!$++z&/A$!OR[[4==$++*:*:;<>BC4==$++*:*:;<>HI Jru c 8 | j |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| j
| z S | j |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 st hh<3 -3 ,1B1B)DKK,<< <!!#'=d'CTJAax-11 !|#ru c B |j }d| j | z S )Nz!\operatorname{tr}\left(%s \right))r< r r r r s rs _print_TracezLatexPrinter._print_Trace s hh3dkk#6FFFru c N dddd}|j | j d d }|j }ddlm}m} t
|| s0t
|| s$|j rd| j | d |d
S | j |t | d }d |v r d|d |d
S |d
|d
S )Nz\daggerz\astz
\mathsf{H})r star hermitianr r r rE rF ro Tr r ) r r r< r r r r r r r
r )r r style_to_latexr r r r rr s rs _print_AdjointzLatexPrinter._print_Adjoint s # &
'**4>>/+JJW
hh<3 -3 ,1B1B.2kk#.>
N N!!#'=d'CTJAax23]CC%&
66ru c ddl m fd}t j }j r5|d dk( r|dd }n |d |d< ddj t
|| z S dj t
|| S )Nr )MatMulc t | t r t | sj | S j | t d S NF)r r
r r
r )r- r r r s rs rt z,LatexPrinter._print_MatMul.. s@ Z3-?
STV\H]4;;q> a!7!=u E ru rj rk r r )sympyr r r@ r5 rO r9 )r r parensr@ r s `` @rs
_print_MatMulzLatexPrinter._print_MatMul s F DII ( ( *Aw"}ABx 7(Q#((3vt#455 588C -. .ru c |j }|j rDddlm} t || r d| j |j z S d| j | z S d| j | 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 se hh J#{++d.I.I#**.UUU'$++c*:: :#d&A&A#&FFFru c \ |Xd| j |j d t d d d| j |j d t d d d|d S | j |j d t d d d| j |j d t d d S )
NrE r r
Tr z \bmod rk rF ro r rG s rs
_print_ModzLatexPrinter._print_Mod s ?""499Q<E1B*. # 0""499Q<E1B*. # 0
"&!2!2499Q<3=e3D:> "3 "@ "&!2!2499Q<3=e3D:> "3 "@A Aru c ~ |j }t d | j dj fd|D S )Nr z \circ c 3 4 K | ] } |d ywTr Nrp r, r< r precs rs r. z6LatexPrinter._print_HadamardProduct..! <VCd
+
+ < r@ r! r
rO r r r@ r r s @@rs _print_HadamardProductz#LatexPrinter._print_HadamardProduct s: yy% "" >ru c n t |j t d k rd}nd}| j || S )Nr
z %s^{\circ \left({%s}\right)}z%s^{\circ {%s}})r rH r! r )r r r s rs _print_HadamardPowerz!LatexPrinter._print_HadamardPower# s5 !$(( +j.? ?6H)H00x@@ru c ~ |j }t d | j dj fd|D S )Nr \otimes c 3 4 K | ] } |d ywr rp r s rs r. z7LatexPrinter._print_KroneckerProduct..0 r r r r s @@rs _print_KroneckerProductz$LatexPrinter._print_KroneckerProduct* s< yy% "" >ru c D |j |j }}ddlm} t || s3|j
r'd| j
| d| j
| dS | j
| }d|v rd|d| j
| dS |d| j
| dS )Nr )r rE rF ro r r )rC rH r r r r r )r r rC rH r base_strs rs
_print_MatPowzLatexPrinter._print_MatPow2 s IItxxc/$ -$2D2D/3{{4/@.2kk#.>@
@ {{4(Hh2:DKK??ru c B | j || j d S )Nr r )r r r s rs _print_MatrixSymbolz LatexPrinter._print_MatrixSymbol? s( !!$dnn / ! ! !ru c . | j d dk( rdS dS )Nr r 0z
\mathbf{0}r )r Zs rs _print_ZeroMatrixz LatexPrinter._print_ZeroMatrixC ( nn #*+s >0= >ru c . | j d dk( rdS dS )Nr r 1z
\mathbf{1}r# )r Os rs _print_OneMatrixz LatexPrinter._print_OneMatrixG r& ru c . | j d dk( rdS dS )Nr r z
\mathbb{I}z
\mathbf{I}r# )r r s rs _print_Identityz LatexPrinter._print_IdentityK s( $ ! #*!+} >0= >ru c H | j |j d }d|z S )Nr zP_{%s}r )r Pperm_strs rs _print_PermutationMatrixz%LatexPrinter._print_PermutationMatrixO s# ;;qvvay)(""ru c
> |j dk( r| j |d S | j d }|?| j d dk( rd}n*|j dk( s|j d dk rd }nd
}d }|j d | }|d
k( r(|j d
dd|j d z z dz }| j d r,| j d }| j
| }d|z |z dz |z }|j dk( r|dz S t
|j dz D cg c] }g }}|j D cg c] }t t
| }}t j | D ] } |d j | j || d}
t
|j dz
dd D ] } t || dz |j | k r o|
r*|| j dj || dz nT|| j |dj || dz z t || dz dk( rd|| d z dz || d< |
}
g || dz < |d d } |j dz dk( r|| z } | S c c}w c c}w ) Nr rp r r r r rj r r r r r r r r r r r r r rk Tr} r r r r )
rankr r shaper r r r itertoolsproductr- r rO )
r r r block_strr r r level_str shape_rangesouter_ieven back_outer_ir s
rs _print_NDimArrayz LatexPrinter._print_NDimArrayS s 99;! ;;tBx( (..+ ?~~f%1'IIK1$$**R.B*> &G %G7 %%j': g !))$c$**Q-6G0G%0OPI >>+ & "nn[ 9J **:6K :- 9!"$/0I 99;! r> !27 a2H%IQb%I %I04
;1U1X; ; ((,7 /G bM T']!; <D %diik!mR <
/ y a 01DJJ|4LL l+22 Il1n$=>@ l+22!UZZ ,q.0I%JKM9\!^45:6? %l 3B 778:D7E ,/3 x,. ,q.)
/ /$ A,q/ 99;?a ')G3 &J;s * JJc Z | j | }d }d }|D ] }|j }||v s|r
||k( r|dz
}||k7 r ||dz
}|j r|dz
}n|dz
}|| j |j d z
}||v r |dz
}|| j || z
}d}nd}|} ||dz
}|S ) Nrl ro z{}^{z{}_{r rW TF)r is_upr@ ) r rP r: index_mapr last_valenceprev_mapindex new_valences rs _printer_tensor_indicesz$LatexPrinter._printer_tensor_indices s ++d# 'E ++K)# K/3{* +sNG;;v%Gv%G t{{5::a=1 1G !34;;y'788 &L' '( # sNGru c |j d j d }|j }| j ||i S r )r@ get_indicesrD )r r rP r: s rs
_print_TensorzLatexPrinter._print_Tensor s= yy| #""$++D'2>>ru c |j j d j d }|j j }|j }| j ||| S r )r r@ rF r? rD )r r rP r: r? s rs _print_TensorElementz!LatexPrinter._print_TensorElement sO yy~~a %%a())'')NN ++D'9EEru c |j \ }}|dj |D cg c] }| j |t | c} z S c c}w r )!_get_args_for_traditional_printerrO r
r )r r r r@ r< s rs _print_TensMulzLatexPrinter._print_TensMul sO ;;=
dbggAE F#T
sJt$4
5 F
Fs "A
c g }|j }|D ], }|j | j |t | . |j dj | }|j
dd }|S )Nr^ z+ -r )r@ r- r
r r, rO r )r r r r@ r- rr s rs _print_TensAddzLatexPrinter._print_TensAdd sh yy =A
HHT&&q*T*:; < = JJqM
IIeT "ru c h d|j rdndd| j |j d dS )Nz{}r rw r r ro )r> r r@ r s rs _print_TensorIndexz LatexPrinter._print_TensorIndex s. ::C3 & KK ! %
ru c t |j dk( rGd| j |j d d| j |j t
d d dS dt |j dd j
|j D cg c] }d
| j | z c} d | j |j t
d d dS c c}w ) Nrk z\frac{\partial}{\partial {r rE r
Fro z\frac{\partial^{r z
\partial {%s}r )r r r r
r r! rO r r r s rs _print_PartialDerivativez%LatexPrinter._print_PartialDerivative s t~~ ! # DNN1 -.!!$))Z->F
$ DNN#T^^T*T[[^;TU!!$))Z->F
Ts Cc 8 | j |j S r )r rP r s rs _print_ArraySymbolz LatexPrinter._print_ArraySymbol s {{499%%ru c d| j |j t d d ddj |j D cg c] }| j | c} dS c c}w )Nz{{r Tr rK r )r
rP r! rO r: r rR s rs _print_ArrayElementz LatexPrinter._print_ArrayElement sU diiF);T B IIDLLAq$++a.)*A BD DAs A#c y)Nz
\mathbb{U}rp r s rs _print_UniversalSetz LatexPrinter._print_UniversalSet ru c |!d| j |j d z S d| j |j d d|dS )Nz$\operatorname{frac}{\left(%s\right)}r z\operatorname{frac}{\left(z
\right)}^{ro r rG s rs _print_fraczLatexPrinter._print_frac sK ;:T[[ST =VV V KK ! -s4
4ru c
^ | j d dk( rd}n | j d dk( rd}n t d t | dk( r&| j | j |d |z S | j |d z j |D cg c] }| j | c} S c c}w )
Nr r ;r rl Unknown Decimal Separatorrk r z \ )r r r r r rO )r r sepr s rs _print_tuplezLatexPrinter._print_tuple s >>- .' 9C
^^ /
0H
<C 89 9 t9>**4;;tAw+?#+EF F**w $$d%Cdkk!n%CDF
F%Cs B* c ~ |j D cg c] }| j | }}dj | S c c}w )Nr r@ r rO r r r elementss rs _print_TensorProductz!LatexPrinter._print_TensorProduct s7 ,0II6qDKKN66 ** 7 :c ~ |j D cg c] }| j | }}dj | S c c}w )N \wedge rc rd s rs _print_WedgeProductz LatexPrinter._print_WedgeProduct s7 ,0II6qDKKN66 )) 7rg c $ | j | S r )ra r s rs _print_TuplezLatexPrinter._print_Tuple s &&ru c 8 | j d dk( r1ddj |D cg c] }| j | c} z S | j d dk( r1ddj |D cg c] }| j | c} z S t d c c}w c c}w )Nr r z\left[ %s\right]z; \ r , \ r_ )r rO r r rR s rs _print_listzLatexPrinter._print_list s >>- .' 9&
t
>
^^ /
0H
<&
t
> 89 9 = =s B
&B
c t |j t }g }|D ]; }|| }|j | j | d| j | = ddj | z S )Nr" z : z\left\{ %s\right\}rn )r keysr r- r rO )r r rq r* r# vals rs _print_dictzLatexPrinter._print_dict sm affh$45 KCC&C LLdkk#&6 C8HI J K %x}}U';;;ru c $ | j | S r )rs r s rs _print_DictzLatexPrinter._print_Dict s %%ru c 6 t |j dk( s|j d dk( r"d| j |j d z }nAd| j |j d d| j |j d d}|r d|d|d }|S )
Nrk r z\delta\left(%s\right)z\delta^{\left( z \right)}\left( r rE rF ro r r s rs _print_DiracDeltaz LatexPrinter._print_DiracDelta s tyy>Q $))A,!"3*T[[1 -FFC #4 DIIaL)4;;tyy|+DFC -0#6C
ru c | j |j d |j d z
}| j |j d }d|d|d}| d|d|d |d}|S )
Nr rk r z{\left\langle z \right\rangle}^{ro z{\left({\langle z \rangle}^{z }\right)}^{r )r r rH shiftr r s rs _print_SingularityFunctionz'LatexPrinter._print_SingularityFunction# s\ DIIaL499Q< 78 DIIaL)9>F ?FKUTWXC
ru c p dj fd|j D }d|z }|r d|d|d}|S )NrK c 3 @ K | ] }j | y wr rR r, r< r s rs r. z0LatexPrinter._print_Heaviside.., s As$++c*Ar0 z\theta\left(%s\right)rE rF ro )rO pargs)r r rH r~ r s ` rs _print_Heavisidez LatexPrinter._print_Heaviside+ s7 AdjjAA&. -0#6C
ru c | j |j d }| j |j d }|j d j r#|j d j r
d|d|d}n d|d|d}| d|d|d}|S ) Nr rk z\delta_{r ro rK rE rF )r r@ r )r r rH r r r s rs _print_KroneckerDeltaz"LatexPrinter._print_KroneckerDelta2 sx KK ! % KK ! % 99Q< DIIaL$8$8'(!,C()1-C ?-0#6C
ru c t | j |j }t d |j D rddj | z }nddj | z }|r d|d|d}|S )Nc 3 4 K | ] }|j y wr )r )r, r- s rs r. z1LatexPrinter._print_LeviCivita..? s ,Qqyy,s z\varepsilon_{%s}r rK rE rF ro )r9 r r@ rj rO )r r rH r: r s rs _print_LeviCivitaz LatexPrinter._print_LeviCivita= s` dkk499- ,$)), ,%(99C% '(::C -0#6C
ru c f t |d r"d| j |j z S t |d r=d| j |j z dz | j |j z S t |d r d| j |j z S | j d S )N
as_booleanz\text{Domain: }set \in rl z\text{Domain on })r r r rl r )r r s rs _print_RandomDomainz LatexPrinter._print_RandomDomainG s 1l #% ALLN(CC C
Q
&QYY)??(JKK&'
(
Q
"'$++aii*@@ @;;t$ $ru c Z t |j t }| j | S )Nr" )r r@ r
_print_setr rr r* s rs _print_FiniteSetz LatexPrinter._print_FiniteSetR s" qvv#34u%%ru c * t |t }| j d dk( r*dj t | j
| }d|z S | j d dk( r*dj t | j
| }d|z S t
d ) Nr" r r r r rK r_ \left\{%s\right\})r r r rO r9 r r r s rs r zLatexPrinter._print_setV s q ./ >>- .' 9IIc$++u 56E
$e++ ^^ /
0H
<IIc$++u 56E $e++ 89 9ru c fd}t j j r<j j r&j j
rdddf}nۉdddf}nӉj j rd j z
d f}nj j r#t
}t | t | f}nkj Xj dk dk( r t }nAj r't
}t | t | d f}n | S | S ddj fd |D z d
z S ) Nc j d dk( rVj d dk( r j j d } ndj fdj D } n^j d dk( r(dj fdj d d D } n$dj fdj D } d| d S )
Nr r rk rK c 3 @ K | ] }j | y wr rR r} s rs r. zKLatexPrinter._print_Range.._print_symbolic_range..j $H#T[[%5$Hr0 c 3 @ K | ] }j | y wr rR r} s rs r. zKLatexPrinter._print_Range.._print_symbolic_range..m s $L#T[[%5$Lr0 c 3 @ K | ] }j | y wr rR r} s rs r. zKLatexPrinter._print_Range.._print_symbolic_range..o r r0 z\text{Range}\left(rn rc )contrr r s rs _print_symbolic_rangez8LatexPrinter._print_Range.._print_symbolic_ranged s vvayA~66!9> ;;qvvay1D 99$H$HHD66!9> 99$L$LLD 99$H$HHD+D6: ;ru rj r rk rb T\left\{rK c 3 L K | ] }|urj | nd ywz\ldotsNrR r, eldotsr s rs r. z,LatexPrinter._print_Range.. % _PRbn4;;r?)K_ !$\right\})
objectstart is_infinitestopstep is_positiveiternextis_emptyrp r is_iterablerO )r rr r printsetitr s `` @rs _print_RangezLatexPrinter._print_Rangec s2
< x 77 166#5#5vv!! Q4/ Ar4/
WW
QrUQVV^QrU2H
VV
aBBxb4/H
ZZ
#
t# 8 !W 8T"XtQrU:,..(* *
_V^__` ru c
t |j dk( r|F|d| j |j d d|d| j |j d dS |d| j |j d d| j |j d dS |d| j |j d d}||d |d}|S )
Nr rf r rg r# rk rn ro r r )r r letterrH r s rs __print_number_polynomialz&LatexPrinter.__print_number_polynomial s tyy>Q 9? KK ! 5s KK ! 57 7 17 DIIaL14;;tyy|3LN
N #DKK ! $=> ? #S)C
ru c ( | j |d| S NB&_LatexPrinter__print_number_polynomialrG s rs _print_bernoulliz LatexPrinter._print_bernoulli --dC==ru c ( | j |d| S )NGr rG s rs _print_genocchiz LatexPrinter._print_genocchi r ru c Z t |j dk( rd j |j d d j |j d d}ddj fd|j d D z }| |d
|d|}|S ||z }|S j |d | S ) Nr% zB_{r rK rk ro r_ c 3 @ K | ] }j | y wr rR )r, r r s rs r. z+LatexPrinter._print_bell.. s# 3C/1 48;;r? 3Cr0 r r r )r r@ r rO r )r r rH tex1tex2r s ` rs _print_bellzLatexPrinter._print_bell s tyy>Q $(KK ! $= $ DIIaL 9;D%
3C59YYq\3C )C CD&*C6 J TkJ--dC==ru c ( | j |d| S NFr rG s rs _print_fibonacciz LatexPrinter._print_fibonacci r ru c \ d| j |j d z }||d|d}|S )NzL_{%s}r r ro r r s rs _print_lucaszLatexPrinter._print_lucas 1 $++diil33 ? #S)C
ru c ( | j |d| S )NTr rG s rs _print_tribonacciz LatexPrinter._print_tribonacci r ru c |!d| j |j d z S d|d| j |j d dS )Nz\mu\left(%s\right)r z\mu^{r# rn r rG s rs
_print_mobiuszLatexPrinter._print_mobius sD ;(4;;tyy|+DD D -0$++diil2KLLru c
T t t |j j dkD s"t |j j dkD rvd j |j d j |j d d j |j d j |j d S |j t j u rY|j }|j |dz
|j |dz
|j |d z
|j | f}nM|j t j u s|j d
kD r|d d
}|j n t | }d d j fd
|D z dz S )Nr r z
\right\}_{rW rg ro r% r rk rb r rK c 3 L K | ] }|urj | nd ywr rR r s rs r. z1LatexPrinter._print_SeqFormula.. r r r )r r r free_symbolsr r formular r rq coeffrp lengthr- r rO )r rr r r r s ` @rs _print_SeqFormulaz LatexPrinter._print_SeqFormula sH x qww## $q (C0C0C,Dq,H AII& AKKN+ AGG$ AFF#
77a(( (66D aggdQh /1Bq)1774=:H
VVqzz
!QXX\!uH OOD ! QxH
_V^__` ru c 2 |j |j k( r d| j |j z S |j rd}nd}|j rd}nd}d|| j |j d| j |j d|S ) Nr r r r r r rK r )r endr left_open
right_open)r r leftrights rs _print_Intervalz LatexPrinter._print_Interval s 77aee '$++agg*>> > {{|| $++agg. AEE0BEK
Kru c x d| j |j d| j |j dS )Nz
\left\langle rK z
\right\rangle)r r r r r s rs _print_AccumulationBoundsz&LatexPrinter._print_AccumulationBounds s+ QUU#T[[%79 9ru c t | }|j D cg c] }| j || }}dj | S c c}w )Nz \cup r r@ r
rO r ur r args_strs rs _print_UnionzLatexPrinter._print_Union E %a(89?1D%%a.??~~h'' @ Ac t | }|j D cg c] }| j || }}dj | S c c}w )Nz \setminus r r s rs _print_Complementz LatexPrinter._print_Complement G %a(89?1D%%a.?? ""8,, @r c t | }|j D cg c] }| j || }}dj | S c c}w )Nz \cap r r s rs _print_Intersectionz LatexPrinter._print_Intersection r r c t | }|j D cg c] }| j || }}dj | S c c}w )Nz \triangle r r s rs _print_SymmetricDifferencez'LatexPrinter._print_SymmetricDifference r r c 0 t | t |j dk\ rMt |j s8 j |j d dt |j z z S dj fd|j D S )Nrk r z^{%d}r c 3 B K | ] }j | y wr )r
)r, r r r s rs r. z1LatexPrinter._print_ProductSet.. s# <-0D c4 ( .# s* RDAq A A/Rs /2rK c 3 & K | ] }d |z yw) %s \in %sNrp )r, xys rs r. z/LatexPrinter._print_ImageSet..$ s ;<",;s r \; \middle|\; r )rX r signaturerY base_setsrO r )r rr r sigxysxinyss ` rs _print_ImageSetz LatexPrinter._print_ImageSet s\ ww||gg RCQ[[.? s #CqDKKN#Cr0 )r r@ rV s ` rs _print_Containsz LatexPrinter._print_Contains> s e#CAFF#C CCCru c |j j t j u rA|j j t j u r| j |j S | j |j dz S )Nz + \ldots) rb r r rB bnr a0re truncater s rs _print_FourierSeriesz!LatexPrinter._print_FourierSeriesA sV 44<<166 !addllaff&<;;qtt$ $qzz|,|;;ru c 8 | j |j S r )re infiniter s rs _print_FormalPowerSeriesz%LatexPrinter._print_FormalPowerSeriesF s qzz**ru c d|j z S )Nz\mathbb{F}_{%s})modr s rs _print_FiniteFieldz LatexPrinter._print_FiniteFieldI s !DHH,,ru c yr rp r s rs _print_IntegerRingz LatexPrinter._print_IntegerRingL rZ ru c yr rp r s rs _print_RationalFieldz!LatexPrinter._print_RationalFieldO rZ ru c yr rp r s rs _print_RealFieldz LatexPrinter._print_RealFieldR rZ ru c yr rp r s rs _print_ComplexFieldz LatexPrinter._print_ComplexFieldU rZ ru c | j |j }dj t | j |j }|d|dS )NrK r r r domainrO r9 rl r r r5 rl s rs _print_PolynomialRingz"LatexPrinter._print_PolynomialRingX < T[[)))C T\\ :;'-w77ru c | j |j }dj t | j |j }|d|dS )NrK rE rn r4 r6 s rs _print_FractionFieldz!LatexPrinter._print_FractionField] r8 ru c | j |j }dj t | j |j }d}|j
sd}||d|dS )NrK r zS_<^{-1}r r )r r5 rO r9 rl is_Poly)r r r5 rl invs rs _print_PolynomialRingBasez&LatexPrinter._print_PolynomialRingBaseb sO T[[)))C T\\ :;|| C),fg>>ru c p |j j }g }|j D ]P \ }}d}t | D ]] \ }}|dkD s |dk( r"|| j |j
| z
}3|| j t
|j
| | z
}_ |j r)|rd| j | z } nq| j | } n_|rL|t j u r|j d|g |t j u r|j d|g | j | } |s| }
n| dz |z }
|
j d r|j d|
dd g >|j d|
g S |d dv r!|j d } | dk( r d|d z |d< dj | } t t! | j |j
}
d | j |j# z }d
j | g|
z |gz }|t$ v r d |d |d
}|S d|d|d
}|S )Nr r rk r_ r r$ r )r$ r z domain=%srK r {\left(z \right)}rx z }{\left( )rM rN rb ra r genspowr! r r extendr r poprO r r9
get_domainrz )r polyr rb monomr s_monomr rH s_coeffs_termmodifierr rA r5 r@ r s rs _print_PolyzLatexPrinter._print_Polyj s nn%% JJL " ,LE5G#E*
G37ax 4;;tyy|#<< 4;;s499Q</E#FF
G || 04;;u3E EG "kk% 0G ~ c7^4
- c7^4 ++e, 3 0 % c6!": ./ c6]+E" ,H 8z ! yy|H3 q>axxC TYY/0 t{{4??+< ==yy$$ &12 * */2D9C
+ >A$GC
ru c |j j }|dk( rd}| j |j }|j }|t
v rd|||fz S d|||fz S )N
ComplexRootOfCRootOfz\%s {\left(%s, %d\right)}z'\operatorname{%s} {\left(%s, %d\right)})rM rN r r rB rz )r r; r r rB s rs _print_ComplexRootOfz!LatexPrinter._print_ComplexRootOf sq nn%% / !C{{499%
* */3e2DD D=dAFAH H
Hru c b |j j }| j |j g}|j t
j ur*|j | j |j |t v rd|ddj | dS d|ddj | dS )Nr r@ rK r rx z } {\left()
rM rN r r funr IdentityFunctionr- rz rO )r r r r@ s rs _print_RootSumzLatexPrinter._print_RootSum s nn%% DII&' 881-- - KK DHH- . * */2DIIdOD D + >A=AYYt_N
Nru c y)N\omegarp r s rs _print_OrdinalOmegaz LatexPrinter._print_OrdinalOmega s ru c |j \ }}|dk7 r(|dk7 rdj || S dj | S |dk7 rdj | S y)Nrk z{} \omega^{{{}}}z {} \omegaz
\omega^{{{}}}rV )r@ r )r r rH muls rs _print_OmegaPowerz LatexPrinter._print_OmegaPower s\ 99S !8ax*11#s;;#**3//ax'..s33 ru c | dj |j D cg c] }| j | c} S c c}w Nr^ )rO r@ r rA s rs _print_OrdinalzLatexPrinter._print_Ordinal s, zztyyA4;;s+ABBAs 9c P | j d }|j | t d| S )Nr z {%s}^{%d})r rs r! )r rF r s rs _print_PolyElementz LatexPrinter._print_PolyElement s& ^^$67
xxj+zBBru c |j dk( r| j |j S | j |j }| j |j }d|d|dS )Nrk r r ro )r r r )r r: r r s rs _print_FracElementz LatexPrinter._print_FracElement sO ::?;;tzz* *KK
+EKK
+E',e4 4ru c t |j dk( r|j d d fn |j \ }}d| j | z }||d|d}||d| j | d}|S )Nrk r zE_{%s}r ro rE rn r )r r rH r r- r s rs _print_eulerzLatexPrinter._print_euler sj '*499~': ! d# 1$++a.( ? #S)C =*-t{{1~>C
ru c \ d| j |j d z }||d|d}|S )NzC_{%s}r r ro r r s rs _print_catalanzLatexPrinter._print_catalan r ru c
dj ||rdnd| j |j d | j |j d | j |j d S )Nz5\mathcal{{{}}}{}_{{{}}}\left[{}\right]\left({}\right)z^{-1}r rk r r r r r@ )r r rr inverses rs _print_UnifiedTransformz$LatexPrinter._print_UnifiedTransform s GNNq]dRYjlnrnynyz~ {D {D EF {G oH JN JU JU VZ V_ V_ `a Vb Jc ei ep ep qu qz qz {| q} e~ ru c & | j |d S )NMri r s rs _print_MellinTransformz#LatexPrinter._print_MellinTransform ++D#66ru c ( | j |dd S )Nrk Trl r s rs _print_InverseMellinTransformz*LatexPrinter._print_InverseMellinTransform ++D#t<>ru c & | j |d S )NCOSrl r s rs _print_CosineTransformz#LatexPrinter._print_CosineTransform
r~ ru c ( | j |dd S )Nr Trl r s rs _print_InverseCosineTransformz*LatexPrinter._print_InverseCosineTransform
r ru c |j *| j |j j | S | j t | S # t $ r Y %w xY wr )ringr to_sympyr reprr r s rs
_print_DMPzLatexPrinter._print_DMP
s[ vv!{{166??1#566 "
{{47## s 5A A A c $ | j | S r )r r s rs
_print_DMFzLatexPrinter._print_DMF
s q!!ru c J | j t |j S r )r r
rP )r r s rs
_print_ObjectzLatexPrinter._print_Object
s {{6&++.//ru c | j |j d }|d|dnd}t |j dk( r d|d|d}|S | j |j d }d j ||| }|S )
Nr r ro r rk WrE rn z W{0}_{{{1}}}\left({2}\right))r r@ r r )r r rH arg0resultarg1s rs _print_LambertWz LatexPrinter._print_LambertW
sx {{499Q<(#&?# tyy>Q .148F
;;tyy|,D5<.+
s Fm\_t{{SVGWFmr0 )r rO r@ r s ` rs _print_Covariancez LatexPrinter._print_Covariance*
s* 5<.;
s 4,,Q0Ft0L,1 3 ru r )r r@ rO r9 )r r r@ r s `` rs
_print_SerieszLatexPrinter._print_Series9
s- DII3xxFD)**ru c ddl m t j d d d } fd}dj t || S )Nr ) MIMOParallelrj c v t | r j | t d S j | S r )r r
r r )r- r r r s rs rt z0LatexPrinter._print_MIMOSeries..B
s@ 7A!\7R ,,Q0Ft0L-2 4 X\XcXcdeXf ru z\cdot)sympy.physics.control.ltir r r@ rO r9 )r r r@ r r s `` @rs _print_MIMOSeriesz LatexPrinter._print_MIMOSeries?
s: :DIItt$g}}S .//ru c ` dj t | j |j S r\ rO r9 r r@ r s rs _print_Parallelz LatexPrinter._print_ParallelF
zz#dkk499566ru c ` dj t | j |j S r\ r r s rs _print_MIMOParallelz LatexPrinter._print_MIMOParallelI
r ru c ddl m}m} |j |dd|j }}t || rt
|j n|g}t |j | r t
|j j n |j g}|}t || r!t |j | r |g || } nt || rBt |j | r,|j |k( r || } nx| |g ||j f} nat || r+t |j | r||k( r || } n4 ||g| } n*||k( r || } n |j |k( r || } n
|g || } | j | }
| j | } | j | } |j dk( rdnd}
d|
d| d |
d | d
S ) Nr )TransferFunctionSeriesrk rj r r$ r r r ro ) sympy.physics.controlr r sys1r r r r@ sys2r r )r r r r rN tf num_arg_list den_arg_list
den_term_1
den_term_2r denom_1denom_2_signs rs _print_Feedbackz LatexPrinter._print_FeedbackL
s B)) -aDHH =R)3C)@tCHH~se tyy& ) DIINN+04 {
c6 "z$))V'D = = =J
V
$DII?O)PyyB #\ 2
!A !Atyy!A A
-
.:dii3Pby #\ 2
#C 7, 7
by #\ 2
b #\ 2
# A\ AL A
C ++j)++j)yyBC).HHru c ddl m} | j ||j |j }| j |j }|j
dk( rdnd}d|d|d|S ) Nr )
MIMOSeriesrj r r$ 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_MIMOFeedbackp
sR 4++jDII >?{{499%yyBC?DgtTTru c B | j |j }d|z S )Nz%s_\tau)r _expr_matr s rs _print_TransferFunctionMatrixz*LatexPrinter._print_TransferFunctionMatrixw
s kk$..)C ru c b dj |j j |j S )Nz\text{{{}}}_{{{}}})r rM rN r r s rs
_print_DFTzLatexPrinter._print_DFT{
s# $++DNN,C,CTVVLLru c z | j t |j }| j | }|d|S )Nr )r r
rP r )r r pretty_namepretty_morphisms rs _print_NamedMorphismz!LatexPrinter._print_NamedMorphism
s4 kk& "78 ..x8%77ru c h ddl m} | j ||j |j d S )Nr )
NamedMorphismid)sympy.categoriesr r r5 r )r r r s rs _print_IdentityMorphismz$LatexPrinter._print_IdentityMorphism
s0 2(( OOX . .*6 7 7ru c |j D cg c]& }| j t |j ( }}|j dj | dz }| j
| }||z S c c}w )Nz\circ r )r+ r r
rP reverserO r )r r componentcomponent_names_listcomponent_namesr s rs _print_CompositeMorphismz%LatexPrinter._print_CompositeMorphism
s~ .6-@-@ B ) !% F9>>,B C B B $$&#..)=>D ..x8 00
Bs +A6c h dj | j t |j S Nr )r r r
rP )r r s rs _print_Categoryz LatexPrinter._print_Category
s% &&t{{6(--3H'IJJru c |j s | j t j S | j |j }|j r!|d| j |j z z
}|S )Nz\Longrightarrow %s)premisesr r EmptySet conclusions)r diagram latex_results rs _print_DiagramzLatexPrinter._print_Diagram
sg ;;qzz* *{{7#3#34 1 KK(;(; < =
=L ru c B dd|j z z }t |j D ]o }t |j D ]9 }|||f r|t |||f z
}|dz
}||j dz
k7 s5|dz
}; ||j dz
k7 r|dz
}|dz
}q |dz
}|S ) Nz\begin{array}{%s}
r r rk & r
z \end{array}
)widthr heightlatex)r gridr r r s rs _print_DiagramGridz LatexPrinter._print_DiagramGrid
s -tzz1AB t{{#
!A4::&
)1: E$q!t*$55L #
Q& D(L
) DKK!O# & D L
! (( ru c dj | j |j | j |j S )Nz
{{{}}}^{{{}}})r r r r2 r rk s rs _print_FreeModulez LatexPrinter._print_FreeModule
s/ %%dkk!&&&94;;qvv;NOOru c V dj dj fd|D S )N\left[ {} \right]rl c 3 L K | ] }d j | z dz ywr ro NrR r, r- r s rs r. z8LatexPrinter._print_FreeModuleElement..
s( 43+,C$++a. 3 &43r )r rO )r r s ` rs _print_FreeModuleElementz%LatexPrinter._print_FreeModuleElement
s. #**388 430143 ,3 4 4ru c " |j D cg c]: }|D cg c], }| j |j j | . c}< }}}d d dj fd|D }dj | S c c}w c c}}w )Nc d| z dz S )Nr ro rp rM s rs rt z/LatexPrinter._print_SubModule..
s $(T/ ru c d| z dz S )Nz\left[ z \right]rp r s rs rt z/LatexPrinter._print_SubModule..
s :>K7 ru rl c 3 j K | ]* } d j fd|D , yw)rl c 3 . K | ] } | y wr rp )r, r- curlys rs r. z:LatexPrinter._print_SubModule...
s 3HE!H3Hs N)rO )r, gr squares rs r. z0LatexPrinter._print_SubModule..
s* YqeF3883Ha3H+H$I J Ys 03 \left\langle {} \right\rangle)rA r r r rO r )r r r r- rA
gens_latexr r s @@rs _print_SubModulez LatexPrinter._print_SubModule
ss FGffM!.
s# GQcDKKN 2S 8 Gr r )_modulerA r r rO r )r r r- rA r s ` rs _print_ModuleImplementedIdealz*LatexPrinter._print_ModuleImplementedIdeal
sW ./iinn=s"==XX G$ GG
/66zBB >s $A+c |j D cg c] }| j |t d d }}|d gt |dd d D cg c]
\ }}|dz |z c}}z }dj | S c c}w c c}}w ) Nr
Tr r rk ijkr r^ )r@ r
r! rY rO )r r r rr r r s rs _print_Quaternionz LatexPrinter._print_Quaternion
s ii
!
q*U"3D
A
!
!
qTF#aeU*;<$!QaeAg< <zz!}
!Q\\*, ,ru c | j |j j | }dj || j |j j S )N{{{}}} + {{{}}})r r r r r )r r- x_latexs rs _print_QuotientRingElementz'LatexPrinter._print_QuotientRingElement
sH ++affooa 01!((QVV . ./1 1ru c B |j D cg c]' }|j j j | ) }}dj dj fd|D }dj | j
|j j S c c}w )Nr rl c 3 L K | ] }d j | z dz ywr rR r s rs r. z.
s( :6+,C$++a. 3 &:6r r )datamoduler r r rO r
killed_module)r r r- r
data_latexs ` rs _print_QuotientModuleElementz)LatexPrinter._print_QuotientModuleElement
s 3466:a
&&q)::)00 :604:6 26 7
!((QXX 3 346 6 ;s ,B c dj | j |j | j |j S r )r r rC r r s rs _print_QuotientModulez"LatexPrinter._print_QuotientModule
s4 #**4;;qvv+>Q__-/ /ru c dj | j |j | j |j | j |j S )Nz{{{}}} : {{{}}} \to {{{}}})r r
_sympy_matrixr5 r )r r s rs _print_MatrixHomomorphismz&LatexPrinter._print_MatrixHomomorphism
sF ,33DKK@Q4R KK !4;;qzz#:< d| j |j z S )Nz\mathbb{\nabla}_{%s})r _wrt)r cvds rs _print_CovarDerivativeOpz%LatexPrinter._print_CovarDerivativeOp
s &SXX)>>>ru c |j j |j j }dj | j t
| S r
_coord_sysrl _indexrP r r r
r fieldr s rs _print_BaseScalarFieldz#LatexPrinter._print_BaseScalarField
s@ !!))%,,7<< &&t{{6&>'BCCru c |j j |j j }dj | j t
| S )Nz\partial_{{{}}}r1 r4 s rs _print_BaseVectorFieldz#LatexPrinter._print_BaseVectorField s@ !!))%,,7<<!((VF^)DEEru c " |j }t |d rV|j j |j j
}dj
| j t | S | j | }dj
| S )Nr2 z\operatorname{{d}}{}z!\operatorname{{d}}\left({}\right)) _form_fieldr r2 rl r3 rP r r r
)r diffr5 r s rs _print_Differentialz LatexPrinter._print_Differential st 5, '%%--ell;@@F*11$++fVn2MN N[['F7>>vF Fru c ` | j |j d }dj | S )Nr z"\operatorname{{tr}}\left({}\right)r )r r contentss rs _print_TrzLatexPrinter._print_Tr s) ;;qvvay)4;;HEEru c |%d| j |j d d|dS d| j |j d z S )Nz\left(\phi\left(r \right)\right)^{ro z\phi\left(%s\right)r rG s rs _print_totientzLatexPrinter._print_totient# sC ?TYYq\*C1
1% DIIaL(AAAru c |%d| j |j d d|dS d| j |j d z S )Nz\left(\lambda\left(r rA ro z\lambda\left(%s\right)r rG s rs _print_reduced_totientz#LatexPrinter._print_reduced_totient) sC ?TYYq\*C1
1(4;;tyy|+DDDru c t |j dk( r?dt t | j |j d |j d f z }n!d| j |j d z }|d|d|S d|z S ) Nr _%s\left(%s\right)rk r r_ z\sigma^{ro z\sigma%sri r s rs _print_divisor_sigmaz!LatexPrinter._print_divisor_sigma/ s tyy>Q '%DKK151 tyy|0L1N +O OC %t{{499Q<'@@C ?'*C0 0S ru c t |j dk( r?dt t | j |j d |j d f z }n!d| j |j d z }|d|d|S d|z S ) Nr rF rk r r_ z
\sigma^*^{ro z
\sigma^*%sri r s rs _print_udivisor_sigmaz"LatexPrinter._print_udivisor_sigma9 s tyy>Q '%DKK151 tyy|0L1N +O OC %t{{499Q<'@@C ?),c2 2 s""ru c |%d| j |j d d|dS d| j |j d z S )Nz\left(\nu\left(r rA ro z\nu\left(%s\right)r rG s rs _print_primenuzLatexPrinter._print_primenuC sC ?TYYq\*C1
1$t{{499Q<'@@@ru c |%d| j |j d d|dS d| j |j d z S )Nz\left(\Omega\left(r rA ro z\Omega\left(%s\right)r rG s rs _print_primeomegaz LatexPrinter._print_primeomegaI sC ?TYYq\*C1
1'$++diil*CCCru c , t |j S r )rs rP r s rs
_print_StrzLatexPrinter._print_StrO s 166{ru c 6 | j t | S r )r r r s rs _print_floatzLatexPrinter._print_floatR s {{5;''ru c t | S r rs r s rs
_print_intzLatexPrinter._print_intU 4yru c t | S r rS r s rs
_print_mpzzLatexPrinter._print_mpzX rU ru c t | S r rS r s rs
_print_mpqzLatexPrinter._print_mpq[ rU ru c t | S r rS r s rs _print_fmpzzLatexPrinter._print_fmpz^ rU ru c t | S r rS r s rs _print_fmpqzLatexPrinter._print_fmpqa rU ru c \ dj t t |j S )Nz"\operatorname{{Q}}_{{\text{{{}}}}})r r rs rP r s rs _print_Predicatez LatexPrinter._print_Predicated s 4;;LTYY
%z22 >s A c > t | | }dt | z S )Nz\mathtt{\text{%s}})super emptyPrinterr )r r rr rM s rs rh zLatexPrinter.emptyPrintern s! G &$|A66ru r r )FF)r bool)r rs )rW z!bool | BooleanTrue | BooleanFalse)r r )r r )r rs r rs )r z'BasisDependent')r rs r rs )r r r rs r )r% rs r rs r )FN)r )r r
)r rs r rs )r r& )r? dict)F(A rN
__module__ __qualname__ printmethodr __annotations__r r r r
r r r r# r; r> r r rI rR rX _print_BooleanTrue_print_BooleanFalser[ re rv r r r r r r r r r r r r r r r r r r6 r< r? rC rO r` rn ru 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 r! r' r) r- r0 r3 r6 r8 r: r< r? rA rC rG rI rN rS rV rY r_ re rg rj rl rn rq rv ry r} r r r r r r r r r r r r r r r r _print_RandomSymbolrL r r r r r r r r r r r r r r r r r r r% r* r, r0 r< rD rG rI rL rN rP rS rU rW rY r\ ra rf rj rl ro rs ru rw rz r r r r r r _print_frozensetr r r 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 r r r r r$ r' r* r, r. r0 r2 r7 r: r> rL rP rT rW rZ r] r_ ra rc re ri rm rp rt rv rx rz 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 r r r r r! r$ r( r+ r/ r6 r8 r< r? rB rD rG rI rK rM rO rQ rT rW rY r[ r] r_ re rh
__classcell__)rM s @rs r r s K)U)E) e) 4 )
- )
) u) 4) S) 4) ) d) ) ) ) G!)" ##)$ % " !3)~ 8;fz,-% EK . > 3 / %% & 9BJ <N NMM IIqf/ -+A> @!>>>#5n8?
F
&D
4
F +*':<& %&, "( T >> >> >M
. &M%M%MK$9(
-
(
-
< Q
&A!D<
+- 8
8
?7r
H N !CC5 7=7=7=9?9?$"0VXoV8
-+ 077"IHU M K8
7
1K
$P4
CCC
,
1
6/
<&Z
?DFGF
B E !#A D (Z37 7ru r c
t j | }|r|S | j t v rd| j z S | t v rd| z S t t j t d D ]_ }| j j | s#t | t | kD s;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 rq r r r )rr r r# s rs r r u s
"
"1
%C
' 'aggi
m ax -,,.CF DCwwy!!#&3q6CH+<$S))AjCyM*BCC D ru c 6 t | j | 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}``.
adjoint_style: string, optional
String to use for the adjoint symbol. Defined options are ``'dagger'``
(default),``'star'``, and ``'hermitian'``.
Notes
=====
Not using a print statement for printing, results in double backslashes for
latex commands since that's the way Python escapes backslashes in strings.
>>> from sympy import latex, Rational
>>> from sympy.abc import tau
>>> latex((2*tau)**Rational(7,2))
'8 \\sqrt{2} \\tau^{\\frac{7}{2}}'
>>> print(latex((2*tau)**Rational(7,2)))
8 \sqrt{2} \tau^{\frac{7}{2}}
Examples
========
>>> from sympy import latex, pi, sin, asin, Integral, Matrix, Rational, log
>>> from sympy.abc import x, y, mu, r, tau
Basic usage:
>>> print(latex((2*tau)**Rational(7,2)))
8 \sqrt{2} \tau^{\frac{7}{2}}
``mode`` and ``itex`` options:
>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
8 \sqrt{2} \mu^{\frac{7}{2}}
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
$8 \sqrt{2} \tau^{7 / 2}$
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$
>>> print(latex((2*mu)**Rational(7,2), mode='plain'))
8 \sqrt{2} \mu^{\frac{7}{2}}
>>> print(latex((2*tau)**Rational(7,2), mode='inline'))
$8 \sqrt{2} \tau^{7 / 2}$
>>> print(latex((2*mu)**Rational(7,2), mode='equation*'))
\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}
>>> print(latex((2*mu)**Rational(7,2), mode='equation'))
\begin{equation}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation}
>>> print(latex((2*mu)**Rational(7,2), mode='equation', itex=True))
$$8 \sqrt{2} \mu^{\frac{7}{2}}$$
Fraction options:
>>> print(latex((2*tau)**Rational(7,2), fold_frac_powers=True))
8 \sqrt{2} \tau^{7/2}
>>> print(latex((2*tau)**sin(Rational(7,2))))
\left(2 \tau\right)^{\sin{\left(\frac{7}{2} \right)}}
>>> print(latex((2*tau)**sin(Rational(7,2)), fold_func_brackets=True))
\left(2 \tau\right)^{\sin {\frac{7}{2}}}
>>> print(latex(3*x**2/y))
\frac{3 x^{2}}{y}
>>> print(latex(3*x**2/y, fold_short_frac=True))
3 x^{2} / y
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=2))
\frac{\int r\, dr}{2 \pi}
>>> print(latex(Integral(r, r)/2/pi, long_frac_ratio=0))
\frac{1}{2 \pi} \int r\, dr
Multiplication options:
>>> print(latex((2*tau)**sin(Rational(7,2)), mul_symbol="times"))
\left(2 \times \tau\right)^{\sin{\left(\frac{7}{2} \right)}}
Trig options:
>>> print(latex(asin(Rational(7,2))))
\operatorname{asin}{\left(\frac{7}{2} \right)}
>>> print(latex(asin(Rational(7,2)), inv_trig_style="full"))
\arcsin{\left(\frac{7}{2} \right)}
>>> print(latex(asin(Rational(7,2)), inv_trig_style="power"))
\sin^{-1}{\left(\frac{7}{2} \right)}
Matrix options:
>>> print(latex(Matrix(2, 1, [x, y])))
\left[\begin{matrix}x\\y\end{matrix}\right]
>>> print(latex(Matrix(2, 1, [x, y]), mat_str = "array"))
\left[\begin{array}{c}x\\y\end{array}\right]
>>> print(latex(Matrix(2, 1, [x, y]), mat_delim="("))
\left(\begin{matrix}x\\y\end{matrix}\right)
Custom printing of symbols:
>>> print(latex(x**2, symbol_names={x: 'x_i'}))
x_i^{2}
Logarithms:
>>> print(latex(log(10)))
\log{\left(10 \right)}
>>> print(latex(log(10), ln_notation=True))
\ln{\left(10 \right)}
``latex()`` also supports the builtin container types :class:`list`,
:class:`tuple`, and :class:`dict`:
>>> print(latex([2/x, y], mode='inline'))
$\left[ 2 / x, \ y\right]$
Unsupported types are rendered as monospaced plaintext:
>>> print(latex(int))
\mathtt{\text{}}
>>> 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 s n ! ) )$ //ru c . t t | fi | y)z`Prints LaTeX representation of the given expression. Takes the same
settings as ``latex()``.N)printr r s rs print_latexr n s
%
!
!"ru c
t d i |}|dk( r d}d}d} d}
d} n:|dk( r d}d}d} d }
d} n*|d
k( r d }d }d
} d}
d} nt dj | d
} |rd} |j }
t |
}d}t | D ] }|
| }d
}d
}d}||kD r | rd}nd}d}||k( r||dz
k r | | z dz dz }nd
}|j
d dk( rd|z }d}|dk( r>|dk( rd
}|dj |j | |||j | | z
}n&|d j |||j | | 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}align*z\begin{align*}
z= &r z
\end{align*}FzUnknown environment: {}z\dotsrk r z& & r r r r rj r$ 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 rb n_terms
term_countr rc
term_startterm_endr s rs multiline_latexr u s F x Aj +
& &4
* )
%299+FGG
D
"E%jGJ
7^ Qx
& #
!
J '719} (?U2T9 " " $Q '2 -d7DD 6s{ 077 #"D!))D/8E
EF
+22:t $3
3Fa
= > hF Mru )rr rs r rs )rk r F)J__doc__
__future__r typingr r r r4
sympy.corer r r r
r r r
r sympy.core.alphabetsr sympy.core.containersr sympy.core.functionr r r sympy.core.operationsr sympy.core.powerr sympy.core.sortingr sympy.core.sympifyr r r r r sympy.printing.precedencer sympy.printing.printerr r sympy.printing.conventionsr r r r! mpmath.libmp.libmpfr" r# r sympy.utilities.iterablesr$ r% r8 sympy.tensor.arrayr& sympy.vector.basisdependentr' rz r} r r rn frozensetr~ compiler r r r r r r rp ru rs r s # / / D D D ' ' B B ) / + ? ? = : H < B 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 9 - -7 2
. < f% BJJ~ BJJ'(
d+77 d+7NW> V0 V0r#~ru