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          d dl mZmZmZ d dlmZ d dlmZ d dlm	Z	m
Z
mZ d dlmZ d dlmZ d dlmZmZ d dlmZ d d	lmZmZmZmZmZ d d
lmZ d dlmZ d dlm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z& d dl'm(Z( d dl)m*Z* d dl+m,Z,m-Z- d dl.m/Z/ d dl0m1Z1m2Z2m3Z3 d dl4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z: d dl;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJ d dlKmLZLmMZMmNZNmOZOmPZPmQZQ d dlRmSZSmTZTmUZU d dlVmWZWmXZX d dlYmZZZm[Z[m\Z\ d dl]m^Z^m_Z_m`Z`maZa d dlbmcZc d dldmeZemfZfmgZgmhZhmiZimjZj d dlkmlZl d dlmmnZnmoZo d dlpmqZqmrZrmsZsmtZt d dlumvZvmwZwmxZxmyZymzZzm{Z{ d dl|m}Z}m~Z~ d d lmZmZ d d!lmZmZmZmZ d d"lmZmZmZmZmZmZmZmZmZ d d#lmZ d d$lmZmZ d d%lmZmZ d d&lmZmZmZmZmZ d d'lmZ d d(lmZmZmZmZmZmZmZmZmZmZ d d)lmZ d d*lmZmZmZmZmZmZmZ d d+lmZ d d,lmZ d d-lmZ d d.lmZ d d/lmZ d d0lmZmZmZmZmZmZmZmZ d d1lmZmZ d d2lmZ d d3lmZmZmZmZmZmZmZ d d4lmZ d d5lmZ d d6lmZ d d7lmZ d d8lmZmZ d d9lmZ d d:lmZ d d;lmZ d d<lmZ d d=lmZmZmZmZ d d>lmZ d d?lmZ d d@lmZmZmZ d dAlmZmZmZ d dBlmZ d dClmZmZmZm Z mZmZmZ d dDlmZ d dElmZ d dFlm	Z	m
Z
mZmZ d dGlmZmZmZmZmZ d dHlmZmZ d dIlmZmZmZ d dJlmZ d dKlmZmZmZm Z m!Z!m"Z"m#Z# d dLl$m%Z%m&Z&m'Z'm(Z( d dMl)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0 d dNl Z1d dOl2m3Z3m4Z4  G dP dQe1jj                        Z5 e3dR      \
  Z6Z7Z8Z9Z:Z;Z<Z=Z>Z? e3dSdTU      \  Z@ZAZBdV ZCdW ZDdX ZEdY ZFdZ ZGd[ ZHd\ ZId] ZJd^ ZKe%d_        ZLe'd`        ZMda ZNdb ZOdc ZPdd ZQde ZRdf ZSdg ZTdh ZUdi ZVdj ZWdk ZXdl ZYdm ZZdn Z[do Z\dp Z]dq Z^dr Z_ds Z`dt Zadu Zbdv Zcdw Zddx Zedy Zfdz Zgd{ Zhd| Zid} Zjd~ Zkd Zld Zmd Znd Zod Zpd Zqd Zrd Zsd Ztd Zud Zvd Zwd Zxd Zyd Zzd Z{d Z|d Z}d Z~d Zd 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 Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd Zd ZdÄ ZdĄ Zdń ZdƄ ZdǄ ZdȄ ZdɄ Ze%dʄ        Zd˄ Zd̄ Zd̈́ Zd΄ Zdτ ZdЄ Zdф Zd҄ Zdӄ ZdԄ ZdՄ Zdք Zdׄ Zd؄ Zdل Zdڄ Zdۄ Zd܄ Zd݄ Zdބ Zd߄ 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 ZyN)    )MatAddMatMulArray)
Quaternion)AccumBounds)CyclePermutationAppliedPermutation)Product)Sum)TupleDict)UnevaluatedExpr)
DerivativeFunctionLambdaSubsdiff)Mod)Mul)AlgebraicNumberFloatIIntegerRationaloopievaluate)Pow)EqNe)S)SymbolWildsymbols)FallingFactorialRisingFactorialbinomial	factorial
factorial2subfactorial)	bernoullibellcatalaneulergenocchilucas	fibonacci
tribonaccidivisor_sigmaudivisor_sigmamobiusprimenu
primeomegatotientreduced_totient)Absarg	conjugateim
polar_liftre)LambertWexplog)asinhcoth)ceilingfloorfrac)MaxMinrootsqrt)	Piecewise)acscasincoscotsintan)beta)
DiracDelta	Heaviside)
elliptic_e
elliptic_f
elliptic_kelliptic_pi)ChiCiEiShiSiexpint)gamma
uppergamma)hypermeijerg)mathieucmathieucprimemathieusmathieusprime)	assoc_laguerreassoc_legendre
chebyshevt
chebyshevu
gegenbauerhermitejacobilaguerrelegendre)SingularityFunction)YnmZnm)KroneckerDelta
LeviCivita)dirichlet_etalerchphipolylog	stieltjeszeta)Integral)
CosineTransformFourierTransformInverseCosineTransformInverseFourierTransformInverseLaplaceTransformInverseMellinTransformInverseSineTransformLaplaceTransformMellinTransformSineTransform)Implies)AndOrXor
EquivalentfalseNottrue)Matrix)KroneckerProduct)MatrixSymbol)PermutationMatrix)MatrixSlice)TransferFunctionSeriesParallelFeedbackTransferFunctionMatrix
MIMOSeriesMIMOParallelMIMOFeedback)
CommutatorOperator)Tr)metergibibytegram	microgramsecondmillimicro)ZZ)field)Poly)ring)RootSumrootof)fps)fourier_series)Limit)Order)SeqAdd
SeqFormulaSeqMulSeqPer)ConditionSet)Contains)ComplexRegionImageSetRange)OrdinalOrdinalOmega
OmegaPower)PowerSet)	FiniteSetIntervalUnionIntersection
ComplementSymmetricDifference
ProductSet)SetExpr)Normal)
CovarianceExpectationProbabilityVariance)ImmutableDenseNDimArrayImmutableSparseNDimArrayMutableSparseNDimArrayMutableDenseNDimArraytensorproduct)ArraySymbolArrayElement)IdxIndexedIndexedBase)PartialDerivative)
CoordSys3DCrossCurlDot
DivergenceGradient	Laplacian)XFAILraises_both_exp_powwarns_deprecated_sympy)latex	translategreek_letters_settex_greek_dictionarymultiline_latexlatex_escapeLatexPrinterN)mutauc                       e Zd Zy)
lowergammaN__name__
__module____qualname__     R/var/www/html/venv/lib/python3.12/site-packages/sympy/printing/tests/test_latex.pyr   r   a   s    r   r   zx y z t w a b c s pk m nTintegerc                       G d dt               } t         | t                    dk(  sJ  G d dt               } t         | t                    dk(  sJ y )Nc                       e Zd Zd Zy)test_printmethod.<locals>.Rc                 D    d|j                  | j                  d         z  S )Nzfoo(%s)r   )_printargsselfprinters     r   _latexz"test_printmethod.<locals>.R._latexk   s    w~~diil;;;r   Nr   r   r   r   r   r   r   Rr   j   s    	<r   r  zfoo(x)c                       e Zd Zd Zy)r   c                      y)Nfoor   r   s     r   r   z"test_printmethod.<locals>.R._latexp   s    r   Nr   r   r   r   r  ztest_printmethod.<locals>.Ro   s    	r   r  )r<   r   x)r  s    r   test_printmethodr  i   sJ    <C < 1;)###C  1;&   r   c                  n   t        dt        z         dk(  sJ t        t        dz        dk(  sJ t        t        dt        z   z        dk(  sJ t        t        dz  t        z   dz   t        dz  z         dk(  sJ t        dt        z  t        z        dk(  sJ t        dt        z  t        z  d	
      dk(  sJ t        dt        dz  z  t        z  d
      dk(  sJ t        ddt        z  z  d
      dk(  sJ t        t        t        j                  dz  z        dk(  sJ t        t        t        j                  t        dz  dd            dk(  sJ t        t        t        j                  t        dz  dd            dk(  sJ t        t        ddd            dk(  sJ t        t        ddd            dk(  sJ t        t        t        j                  dt        j                  d            dk(  sJ t        t        dt        dd            dk(  sJ t        t        dt        dd            dk(  sJ t        t        t        t        d      t        j                  t        z  dz               dk(  sJ t        t        t        t        d      t        dd      t        z  dz               dk(  sJ t        t        t        t        d      dt        z  dz               dk(  sJ t        t        d dd            d!k(  sJ t        t        dd d            d"k(  sJ t        t        ddd            d#k(  sJ t        t        d$dd            d%k(  sJ t        t        dddd            d&k(  sJ t        t        ddd            d'k(  sJ t        t        dt        j                  d            d(k(  sJ t        t        ddt        j                  d            d)k(  sJ t        t        ddddt        d            d*k(  sJ t        t        dd$d            d+k(  sJ t        t        d,dddd t        t        d            d-k(  sJ t        t        d,dddt        z   d t        t        d            d.k(  sJ t        t        t        dd      t        dd/      d            d0k(  sJ t        dt        z        d1k(  sJ t        dt        z  d23      d4k(  sJ t        t        d       dz        d5k(  sJ t        t        d       dz  d23      d6k(  sJ t        dt        dz  z        d7k(  sJ t        dt        t        z   z  dz        d8k(  sJ t        t        dz        d9k(  sJ t        t        dz  d23      d:k(  sJ t        t        t        z   dt        z  z        d;k(  sJ t        t        t        z   dt        z  z  d23      d<k(  sJ t        t        t        z   dt        z  z  d =      d>k(  sJ t        t        t        z   t        z        d?k(  sJ t        t        t        z   t        z  d=      d?k(  sJ t        dt        d      z  t        z  dz        d@k(  sJ t        dt        d      z  t        z  dz  d=      dAk(  sJ t        t        t        t                    dBk(  sJ t        dC      } t        dD      }t        | dz        dEk(  sJ t        | dz  dF      dGk(  sJ t        t         ||       | d            dHk(  sJ t        t         ||       | d      dF      dIk(  sJ t        dt        t        t              z  dz        dJk(  sJ t        dt        t        t              z  dz  d23      dKk(  sJ t        t        t                    dLk(  sJ t        t        t        dd      z        dMk(  sJ t        t        t        dd      z  dN      dOk(  sJ t        t        t              dz        dPk(  sJ t        t        t              d2Q      dLk(  sJ t        t        t        dd      z  d2Q      dRk(  sJ t        t        t              dz  d2Q      dPk(  sJ t        t        t        dd,      z        dSk(  sJ t        t        t        dd,      z  d2T      dUk(  sJ t        t        dz   t        dd,      z        dVk(  sJ t        t        dz   t        dd,      z  d2T      dWk(  sJ t        t!        t        d                  dXk(  sJ t        t!        t        d      ddYg            dZk(  sJ t        t!        t        d      d[\            d]k(  sJ t        t!        t        d      ddYgd[\            d^k(  sJ t        t!        dt        d      dz  z  g d_d`\            dak(  sJ t#        j$                  d      }t        |j&                  j)                  g db            dck(  sJ t        |j&                  j)                  g db      dde      dfk(  sJ t        |j+                  dg      d          dhk(  sJ t        |j+                  dg      d    dde      dik(  sJ t        |j+                  d/      d          djk(  sJ t        dkt        z        dlk(  sJ t        dkt        z  d	
      dmk(  sJ t        dkt        z  dn
      dok(  sJ t        dt-        t              z        dpk(  sJ t        t-        t              d$z        dpk(  sJ t        t-        t              t        dd      z        dqk(  sJ t        t-        t              t        dd      z  d2T      drk(  sJ t        t               dsk(  sJ t        t        t        z        dtk(  sJ t        t        t        z  t        z        duk(  sJ t        t        t        z        dvk(  sJ t        t        t        z  t        z        dwk(  sJ t        t        t        z  t        z        dxk(  sJ t        t/        t        t                    dyk(  sJ t        t        t         z	         dzk(  sJ t        t/        t1        t        t              t                    d{k(  sJ t        t/        t        t1        t        t                          d|k(  sJ t        t        t        z         d}k(  sJ t        t         t        d~i      dk(  sJ t        t        t        z  t        d~t        di      dk(  sJ t        t        t        z  t        z  t        d~t        dt        di      dk(  sJ t        t        t        z  t        d~t        di      dk(  sJ t        t        t        z  t        z  t        d~t        dt        di      dk(  sJ t        t        t        z  t        z  t        d~t        dt        di      dk(  sJ t        t/        t        t              t        d~t        di      dk(  sJ t        t        t        dd      d$d            dk(  sJ t        t        t        dd      dd            dk(  sJ t        t        t3        d      dz  d$d            dk(  sJ t        dd2      }t        t5        |       t7        |      z        dk(  sJ y )N   x + 1   zx^{2}z	x^{x + 1}   zx^{3} + x^{2} + x + 1z2 x ydot
mul_symbolz2 \cdot x \cdot yz\,z3\,x^{2}\,y      ?z1.5 \cdot 3^{x}   z\sqrt[32]{x}Fr   z!\frac{1}{2} x^{2} \left(-5\right)z\frac{1}{2} x^{2} \cdot 5z\left(-5\right) \left(-5\right)z5 \left(-5\right)z'\frac{1}{2} \left(-5\right) \frac{1}{2}z5 i 5z5 i \left(-5\right)z"x^{2} \left(\frac{x}{2} + 1\right)z$x^{3} \left(\frac{2 x}{3} + 1\right)   zx^{11} \left(2 x + 1\right)r   z	0 \cdot 1z	1 \cdot 0z	1 \cdot 1z\left(-1\right) 1z1 \cdot 1 \cdot 1z	1 \cdot 2z1 \cdot \frac{1}{2}z1 \cdot 1 \cdot \frac{1}{2}z1 \cdot 1 \cdot 2 \cdot 3 xz1 \left(-1\right)   z%4 \cdot 3 \cdot 2 \cdot 1 \cdot 0 y xz*4 \cdot 3 \cdot 2 \left(z + 1\right) 0 y x   z\frac{2}{3} \cdot \frac{5}{7}\frac{1}{x}T)fold_short_fracz1 / xz- \frac{3}{2}z- 3 / 2z\frac{1}{x^{2}}z\frac{1}{2 \left(x + y\right)}z\frac{x}{2}zx / 2z\frac{x + y}{2 x}z\left(x + y\right) / 2 x)long_frac_ratioz \frac{1}{2 x} \left(x + y\right)z\frac{x + y}{x}z\frac{2 \sqrt{2} x}{3}z\frac{2 x}{3} \sqrt{2}z{\binom{x}{y}}x^*fz\left(x^{*}\right)^{2})parenthesize_superz{x^{*}}^{2}z=\frac{d^{2}}{d \left(x^{*}\right)^{2}} f{\left(x^{*} \right)}z2\frac{d^{2}}{d {x^{*}}^{2}} f{\left(x^{*} \right)}z\frac{2 \int x\, dx}{3}z\left(2 \int x\, dx\right) / 3z\sqrt{x}z\sqrt[3]{x})root_notationzx^{\frac{1}{3}}zx^{\frac{3}{2}}itexz\root{3}{x}zx^{\frac{3}{4}})fold_frac_powerszx^{3/4}z \left(x + 1\right)^{\frac{3}{4}}z\left(x + 1\right)^{3/4}z\sqrt{2}z-7 + 3 \sqrt{2}alpha)alias\alphaz3 \alpha - 7)r  r  r   rU   z\beta^{2} + 3 \beta - 7)r  r
  r  r  z%\zeta^{3} + 2 \zeta^{2} + 3 \zeta + 4oldorderz%4 + 3 \zeta + 2 \zeta^{2} + \zeta^{3}   z(\left(19, \zeta^{2} + 5 \zeta + 1\right)z(\left(19, 1 + 5 \zeta + \zeta^{2}\right)z\left(7\right)g0)VC Dz1.5 \cdot 10^{20} xz1.5 \cdot 10^{20} \cdot xtimesz1.5 \times 10^{20} \times xz\frac{1}{\sin{\left(x \right)}}z#\sin^{\frac{3}{2}}{\left(x \right)}z\sin^{3/2}{\left(x \right)}z\neg xz
x \wedge yzx \wedge y \wedge zzx \vee yzx \vee y \vee zzz \vee \left(x \wedge y\right)zx \Rightarrow yzx \not\Rightarrow \neg yz#\left(x \vee y\right) \Rightarrow zz#z \Rightarrow \left(x \vee y\right)z\neg \left(x \wedge y\right)x_isymbol_namesz\neg x_iy_izx_i \wedge y_iz_izx_i \wedge y_i \wedge z_izx_i \vee y_izx_i \vee y_i \vee z_iz$z_i \vee \left(x_i \wedge y_i\right)zx_i \Rightarrow y_iz\frac{1}{\frac{1}{3}}z\frac{1}{(\frac{1}{3})^{2}}d   z\frac{1}{\frac{1}{100}}ppositiveze^{- p} \log{\left(p \right)})r   r  yr#   Halfr   r   r    r   zrM   r)   r$   r   r   r}   r   r   cyclotomic_fieldextfield_elementprimes_aboverS   r   r   r   rC   rD   )x_starr  kr0  s       r   test_latex_basicr<  u   s   Q<8###A;("""QU,,,AA1$%)AAAA1Q<8###1Q5)-AAAA1a4e,>>>QTe,0BBBBAFFAI/111QVVQT267;____QVVQT1u56:VVVVRe,-1SSSSQU+,0DDDDQVVR%89=ggggQ1u-.(:::Q2./3IIIISAYq1-.2WWWWSAYAq 01 456:aaaaSBZ1q)*.LLLLQE*+|;;;QE*+|;;;QE*+|;;;RU+,0DDDDQ1u-.2FFFFQE*+|;;;Q/04JJJJQ166E23&' ' 'Q1aU34&' ' 'QU+,0DDDDQ1aAq59:01 1 1Q1ac1aU;<56 6 6Xa^Xa^eDE() ) ) 1:'''1d+x777!A$q>----!A$q$/:===1a4=....AE1!BBBB1:'''1d+x777!a%!A##7777!a%!A#5#$ $ $!a%!A#2+, , ,!a%1111!a%A.2DDDD!DG)A+q!%>>>>!DG)A+q!4!" " "!Q $5555E]FA8888u5GGGAfIva015uuuuAfIva0UK  PE  E  E  E8Aq>!!#$(BBBB8Aq>!!#T:)* * * a>[(((HQN"#~555HQN"%8<NNNNa! 2222at$333HQN"..@@@a!$'+====HQN"#'9999HQN"T:jHHH!a%(1a.()+, , ,!a%(1a.(4@#$ $ $a)*k999a1b'237IIIIa89YFFFa1b'AB  QqT!VjGH"# # # 	AA$$\2301 1 1$$\2%@01 1 1#A&'34 4 4#A&e467 7 7"1%&*;;;;?4444e,0LLLLg.&' ' ' 3q6?@@@@Q BBBBQ!Q'(./ / /Q!Q'$?&' ' ' !9	!!!Q<=(((Q5555Q<;&&&Q1111!a%1!BBBBA#555517 ;;;;Aa!$%)OOOOBqG$%)OOOO1q5?====!1e*-<<<Qa5%9:  Q!UAua)GH$% % %Qa5%9:oMMMQ!UAua)GH ! ! !!a%1Aua5+IJ/0 0 0Aa5-AB  Xa^R%89=UUUUXa^R%89=[[[[WQZ^R%89=WWWW 	sT"AaRQ $DDDDr   c                      t        d      dk(  sJ t        d      dk(  sJ t        d       dk(  sJ t        t              dk(  sJ t        t              dk(  sJ y )NTz\text{True}Fz\text{False}z\text{None})r   r   r   r   r   r   test_latex_builtinsr>    s\    ;.(((<?***;.(((;.(((<?***r   c                  6   t        t        t        dd            dk(  sJ t        t        t        dd            dk(  sJ t        t        t        dd            dk(  sJ t        t        t        t        t                    dk(  sJ t        t        t        dd	            d
k(  sJ t        t        t        dd            dk(  sJ t        t        t        dd      dz        dk(  sJ t        t        t        dd      dz        dk(  sJ t        t        t        dd      dz        dk(  sJ t        t        t        t        t              dz        dk(  sJ t        t        t        dd	      dz        dk(  sJ t        t        t        dd      dz  dz        dk(  sJ y )Nr  r  z&{\left\langle x - 4 \right\rangle}^{5}z&{\left\langle x + 3 \right\rangle}^{4}r   z"{\left\langle x \right\rangle}^{4}z({\left\langle - a + x \right\rangle}^{n}r.  z'{\left\langle x - 4 \right\rangle}^{-2}r  z'{\left\langle x - 4 \right\rangle}^{-1}r  z.{\left({\langle x - 4 \rangle}^{5}\right)}^{3}z.{\left({\langle x + 3 \rangle}^{4}\right)}^{3}z*{\left({\langle x \rangle}^{4}\right)}^{3}z0{\left({\langle - a + x \rangle}^{n}\right)}^{3}z/{\left({\langle x - 4 \rangle}^{-2}\right)}^{3}z/{\left({\langle x - 4 \rangle}^{-1}\right)}^{9})r   rs   r  anr   r   r   test_latex_SingularityFunctionrC    s   $Q1-.12 2 2$QA./12 2 2$Q1-.-. . .$Q1-.34 4 4$Q2./23 3 3$Q2./23 3 3 $Q1-q019: : :$QA.129: : :$Q1-q0156 6 6$Q1-q01;< < <$Q2.12:; ; ;%aB/2Q67:; ; ;r   c                      t        t        ddd            dk(  sJ t         t        dd      ddd            dk(  sJ t        t                     dk(  sJ y )	Nr  r
  r  \left( 1\; 2\; 4\right)r     *\left( 1\; 2\right)\left( 4\; 5\; 6\right)\left( \right))r   r   r   r   r   test_latex_cyclerI  /  s^    q!Q $>>>>q!Q1%&56 6 6>....r   c                     t        t        ddd            dk(  sJ t         t        dd      ddd            dk(  sJ t        t                     dk(  sJ t        t        dd      t        d      z        d	k(  sJ t        t        d            d
k(  sJ t        t        dd      d      dk(  sJ t         t        dd      dd      d      dk(  sJ t        t               d      dk(  sJ t               5  t        j                  } dt        _        t         t        dd      dd            dk(  sJ | t        _        d d d        y # 1 sw Y   y xY w)Nr  r
  r  rE  r  rF  rG  rH  z"\left( 2\; 4\right)\left( 5\right)z\left( 5\right)r   F)perm_cyclicz,\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}r  z<\begin{pmatrix} 0 & 1 & 2 & 3 \\ 1 & 0 & 3 & 2 \end{pmatrix})r   r	   r   print_cyclic)old_print_cyclics    r   test_latex_permutationrN  6  s|   Q1%&*DDDD"Q"1a+,56 6 6#4444Q";q>12-. . .Q $6666Q"678 8 8"Q"1a(e<GH H HE2   
 	! 4&33#( &[A&q!,-KL 	L L#3 4 4 4s   8AE		Ec                     t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d      d      dk(  sJ t        t        d      d	d
d      dk(  sJ t        t        d      d	d
d      dk(  sJ t        t        d      d	d
d      dk(  sJ t        t        d      dd
d      dk(  sJ y )Ng}Ô%ITz1.0 \cdot 10^{100}g0.++z1.0 \cdot 10^{-100}r(  r  z1.0 \times 10^{-100}z10000.0Fr.  r
  )	full_precminmaxz1.0 \cdot 10^{4}r  r  z0.099999Tz9.99990000000000 \cdot 10^{-2})r   r   r   r   r   test_latex_FloatrS  M  s    w $9999x!%;;;;xW5     y!UB  y!UB  y!UB  z"dC)* * *r   c                  v	   t        d      } t        t        | j                  | j                  | j
                  z  dz  | j                  z               dk(  sJ t        t        | j                  | j                              dk(  sJ t        t
        t        | j                  | j                        z        dk(  sJ t        t        t
        | j                  z  | j                              dk(  sJ t        t        d| j
                  z  | j                  z              dk(  sJ t        t        d| j
                  z  | j                  z  | j                  z               dk(  sJ t        t        dt
        z  | j
                  z  | j                  z              d	k(  sJ t        t
        t        d| j
                  z  | j                  z        z        d
k(  sJ t        t        d| j
                  z  | j                  z  | j                  z               dk(  sJ t        t        d| j
                  z  | j                  z              dk(  sJ t        t
        t        d| j
                  z  | j                  z        z        dk(  sJ t        t        | j                  | j                  | j
                  z  dz  | j                  z               dk(  sJ t        t        | j                  | j                              dk(  sJ t        t        t
        | j                  z  | j                              dk(  sJ t        t
        t        | j                  | j                        z        dk(  sJ t        t        | j
                              dk(  sJ t        t        | j
                  d| j                  z  z               dk(  sJ t        t
        t        | j
                        z        dk(  sJ t        t        t
        | j
                  z              dk(  sJ t        t        | j
                              dk(  sJ t        t        | j
                  d| j                  z  z               dk(  sJ t        t
        t        | j
                        z        dk(  sJ t        t        t
        | j
                  z              dk(  sJ y )NAr  zs\mathbf{\hat{i}_{A}} \times \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}} + \mathbf{\hat{k}_{A}}\right)z0\mathbf{\hat{i}_{A}} \times \mathbf{\hat{j}_{A}}z?x \left(\mathbf{\hat{i}_{A}} \times \mathbf{\hat{j}_{A}}\right)zM- \mathbf{\hat{j}_{A}} \times \left(\left(x\right)\mathbf{\hat{i}_{A}}\right)zM\nabla\times \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)zd\nabla\times \left(\mathbf{\hat{i}_{A}} + \left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)zO\nabla\times \left(\left(3 \mathbf{{x}_{A}} x\right)\mathbf{\hat{j}_{A}}\right)z\x \left(\nabla\times \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)\right)zc\nabla\cdot \left(\mathbf{\hat{i}_{A}} + \left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)zL\nabla\cdot \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)z[x \left(\nabla\cdot \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}}\right)\right)zr\mathbf{\hat{i}_{A}} \cdot \left(\left(3 \mathbf{{x}_{A}}\right)\mathbf{\hat{j}_{A}} + \mathbf{\hat{k}_{A}}\right)z/\mathbf{\hat{i}_{A}} \cdot \mathbf{\hat{j}_{A}}zJ\mathbf{\hat{j}_{A}} \cdot \left(\left(x\right)\mathbf{\hat{i}_{A}}\right)z>x \left(\mathbf{\hat{i}_{A}} \cdot \mathbf{\hat{j}_{A}}\right)z\nabla \mathbf{{x}_{A}}z9\nabla \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)z&x \left(\nabla \mathbf{{x}_{A}}\right)z&\nabla \left(\mathbf{{x}_{A}} x\right)z\Delta \mathbf{{x}_{A}}z9\Delta \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)z&x \left(\Delta \mathbf{{x}_{A}}\right)z&\Delta \left(\mathbf{{x}_{A}} x\right))r   r   r   ijr  r;  r   r   r   r   r3  r   )rU  s    r   test_latex_vector_expressionsrX  \  s9   3AqssACCGAIaccM*+~  qssACC!;< < <5acc?"#JK K Kquacc"#XY Y Y aeACCi!XY Y YaeACCim$%op p pac!##gacck"#Z[ [ [4!##acc	?"#gh h h AaccE!##IaccM*+no o oAaccE!##I&'WX X X:aeACCi(()fg g g QSS!##acc'!)ACC-()}~ ~ ~QSS!##:; ; ;QqssUACC!UV V V3qssACC=!IJ J J !###====!##!##+&'DE E E8ACC=!%NNNN!ACC%!%NNNN133 $>>>>133133;'(DE E E9QSS>!"&OOOO1QSS5!"&OOOOr   c                  &   t        d      \  } }}t        d      \  }}}}t        |      dk(  sJ t        |      dk(  sJ t        |      dk(  sJ t        |      dk(  sJ t        D ch c]  }|j                          }}t	        |t        t        j                               z
        dk(  sJ t        | |z         dk(  sJ t        | |z        dk(  sJ t        t        d            d	k(  sJ t        t        d
            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d      t        d      z        dk(  sJ y c c}w ) NzGamma, lambda, rhoztau, Tau, TAU, taU\tau
\mathrm{T}r   z\Gamma + \lambdaz\Gamma \lambdaq1zq_{1}q21zq_{21}epsilon0z\epsilon_{0}omega1
\omega_{1}91	alpha_newz\alpha_{new}zC^origzC^{orig}zx^alphaz
x^{\alpha}z
beta^alphaz\beta^{\alpha}ze^Alphaze^{\mathrm{A}}zomega_alpha^betaz\omega^{\beta}_{\alpha}omegarU   z\omega^{\beta})	r&   r   r   
capitalizelensetr   keysr$   )	Gammalmbdarhor   TauTAUtaUlcapitalized_letterss	            r   test_latex_symbolsrp    s    45E5# !56Cc3:   :&&&:   :   3DEa1<<>EE"S)=)B)B)D%EEF!KKK#6666#4444(***9,,,
#$777!"m333%'''$%888!"k111	"#}444%&*;;;;	"#'8888*+,0JJJJF6N237HHHH Fs   (Hc                      t        d      \  } }}t        || z  |k(        dk(  sJ t        ||z  | z  dk(        dk(  sJ t        |dz  |dz  z        dk(  sJ y )Nzrho, mass, volumez$\rho \mathrm{volume} = \mathrm{mass}r  z/\rho \mathrm{volume} {\mathrm{mass}}^{(-1)} = 1r  z/{\mathrm{mass}}^{3} \cdot {\mathrm{volume}}^{3}r&   r   )rj  massvolumes      r   test_latex_symbols_failingru    s     34Cv!HI I I$$)*:; ; ;q619$%:; ; ;r   c                  D   t        t        t                    dk(  sJ t        t        d      t        d      z         dk(  sJ t        d      } t         | t                    dk(  sJ t        |       dk(  sJ t        d      }t         |t        t                    dk(  sJ t        |      dk(  sJ t        d	      }t         |t        t        t
                    d
k(  sJ t        |      d	k(  sJ t        d      }t        |      dk(  sJ t         |t                    dk(  sJ t        d      }t         |t        t        t
                    dk(  sJ t        t        t        t                    dk(  sJ t        t        t        d            dk(  sJ t        t        t        t              dz        dk(  sJ t         |t                    dk(  sJ t        |      dk(  sJ t        d      }t         |t        t        t
                    dk(  sJ t         |t                    dk(  sJ t        |      dk(  sJ t        d      }t        |      dk(  sJ t         |t                    dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d             d!k(  sJ t        t        d"            d#k(  sJ t        t        d$            d!k(  sJ t        t        d%            d#k(  sJ t        t        d&            d'k(  sJ t        t        d(            d)k(  sJ t         t        d      t        d*                  d+k(  sJ t         t        d       t        d*                  d,k(  sJ t         t        d"      t        d*                  d-k(  sJ t         t        d$      t        d*                  d,k(  sJ t         t        d&      t        d*                  d.k(  sJ t         t        d(      t        d*                  d/k(  sJ t         t        d             dz        d0k(  sJ t         t        d              dz        d1k(  sJ t         t        d"             dz        d2k(  sJ t         t        d$             dz        d1k(  sJ t         t        d%             dz        d2k(  sJ t         t        d      t        d*            dz        d3k(  sJ t         t        d       t        d*            dz        d4k(  sJ t         t        d"      t        d*            dz        d5k(  sJ t         t        d$      t        d*            dz        d4k(  sJ t         t        d%      t        d*            dz        d5k(  sJ t        t        d6            d6k(  sJ t        t        d7            dk(  sJ t        t        d8            d9k(  sJ t        t        d            dk(  sJ t        t        d:            d9k(  sJ t         t        d6                   d;k(  sJ t         t        d7                   d<k(  sJ t         t        d8                   d=k(  sJ t         t        d                   d<k(  sJ t         t        d:                   d=k(  sJ t         t        d6             dz        d>k(  sJ t         t        d7             dz        d?k(  sJ t         t        d8             dz        d@k(  sJ t         t        d             dz        d?k(  sJ t         t        d:             dz        d@k(  sJ t         t        d6      t        d*            dz        dAk(  sJ t         t        d7      t        d*            dz        dBk(  sJ t         t        d8      t        d*            dz        dCk(  sJ t         t        d      t        d*            dz        dBk(  sJ t         t        d:      t        d*            dz        dCk(  sJ t         t        d6             dDz        dEk(  sJ t         t        d7             dDz        dFk(  sJ t         t        d8             dDz        dGk(  sJ t         t        d             dDz        dFk(  sJ t         t        d:             dDz        dGk(  sJ t         t        d6      t        d*            dDz        dHk(  sJ t         t        d7      t        d*            dDz        dIk(  sJ t         t        d8      t        d*            dDz        dJk(  sJ t         t        d      t        d*            dDz        dIk(  sJ t         t        d:      t        d*            dDz        dJk(  sJ t         t        d6             t        z        dKk(  sJ t         t        d7             t        z        dLk(  sJ t         t        d8             t        z        dMk(  sJ t         t        d             t        z        dLk(  sJ t         t        d:             t        z        dMk(  sJ t         t        d6      t        d*            t        z        dNk(  sJ t         t        d7      t        d*            t        z        dOk(  sJ t         t        d8      t        d*            t        z        dPk(  sJ t         t        d      t        d*            t        z        dOk(  sJ t         t        d:      t        d*            t        z        dPk(  sJ t        d      }t         t        d6             |z        dQk(  sJ t         t        d7             |z        dRk(  sJ t         t        d8             |z        dSk(  sJ t         t        d             |z        dRk(  sJ t         t        d:             |z        dSk(  sJ t         t        d6      t        d*            |z        dTk(  sJ t         t        d7      t        d*            |z        dUk(  sJ t         t        d8      t        d*            |z        dVk(  sJ t         t        d      t        d*            |z        dUk(  sJ t         t        d:      t        d*            |z        dVk(  sJ t         t        dW      t                    dXk(  sJ t         t        dW      t              |z        dYk(  sJ t         t        dZ      t                    dXk(  sJ t         t        dZ      t              |z        dYk(  sJ t         t        d[      t                    d\k(  sJ t        d]      }t        |      d^k(  sJ t         |t                    d_k(  sJ t        t        t                    d`k(  sJ t        t        t              dab      dck(  sJ t        t        dt        dz  z        dab      ddk(  sJ t        t        t        dz        dab      dek(  sJ t        t        t              dz        dfk(  sJ t        t        t              dz  dgh      dik(  sJ t        t        t              dz  djh      dkk(  sJ t        t        t        dz        djdal      dmk(  sJ t        t        t              dgh      dnk(  sJ t        t        t              dgh      dok(  sJ t        t        t                    dpk(  sJ t        t        t                     dqk(  sJ t        t        t              dz        drk(  sJ t        t        t                    dsk(  sJ t        t        t                     dtk(  sJ t        t        t              dz        duk(  sJ t        t!        t                    dvk(  sJ t        t!        t                     dwk(  sJ t        t!        t              dz        dxk(  sJ t        t#        dt                    dyk(  sJ t        t#        dt              dz        dzk(  sJ t        t%        d{t                    d|k(  sJ t        t'        d{t                    d}k(  sJ t        t)        t                    d~k(  sJ t        t+        t                    dk(  sJ t        t-        t                    dk(  sJ t        t)        t              dz        dk(  sJ t        t+        t              dz        dk(  sJ t        t-        t              dz        dk(  sJ t        t/        t        dt        d{z              dk(  sJ t        t/        t        t              dz        dk(  sJ t        t1        t        dt        d{z              dk(  sJ t        t1        t        t              dz        dk(  sJ t        t3        t                    dk(  sJ t        t3        t              dz        dk(  sJ t        t5        t                    dk(  sJ t        t5        t        t        z               dk(  sJ t        t7        t                    dk(  sJ t        t9        t                    dk(  sJ t        t9        t              dz        dk(  sJ t        t9        t        dz              dk(  sJ t        t;        t                    dk(  sJ t=        d      }t        t;        |            dk(  sJ t        t?        t                    dk(  sJ t        t?        t        t                    dk(  sJ t        t?        t        t        df            dk(  sJ t        t?        t        t        t@        f            dk(  sJ t        t?        t        t        z
  t        t        f            dk(  sJ t        t?        t        t        t                    dk(  sJ t        t?        t        t        t                    dk(  sJ t        t?        t        t        t@        ft        t@        f            dk(  sJ t        tC        t        t                    dk(  sJ t        tC        t        t              dz        dk(  sJ t        tE        t        t                    dk(  sJ t        tE        t        t              dz        dk(  sJ t        tG        t                    dk(  sJ t        tI        t                    dk(  sJ t        t5        t                    dk(  sJ t        t7        t                    dk(  sJ t        tK        t        t                    dk(  sJ t        tM        t                    dk(  sJ t        tO        t                    dk(  sJ t        tO        t              dz        dk(  sJ t        tO        t        t                    dk(  sJ t        tO        t        t              dz        dk(  sJ t        tQ        t                    dk(  sJ t        tQ        t              dz        dk(  sJ t        tS        t        t                    dk(  sJ t        tS        t        t              dz        dk(  sJ t        tU        t        t        tV                    dk(  sJ t        tU        t        t        tV              dz        dk(  sJ t        tY        t                    dk(  sJ t        tY        t              dz        dk(  sJ t        tY        t        t                    dk(  sJ t        tY        t        t              dz        dk(  sJ t        t[        t
                    dk(  sJ t        t[        t
              dz        dk(  sJ t        t]        t        t                    dk(  sJ t        t]        t        t              dz        dk(  sJ t        t_        t        t                    dk(  sJ t        t_        t        t              dz        dk(  sJ t        t_        t
                    dk(  sJ t        t_        t
              dz        dk(  sJ t        ta        t        t        t
                    dk(  sJ t        ta        t        t        t
              dz        dk(  sJ t        ta        t        t                    dk(  sJ t        ta        t        t              dz        dk(  sJ t        tc        t                    dk(  sJ t        tc        t              dz        dk(  sJ t        te        t        t                    dk(  sJ t        te        t        t              dz        dk(  sJ t        tg        t              dz        dk(  sJ t        ti        t              dz        dk(  sJ t        tk        t              dz        dk(  sJ t        tm        t              dz        dk(  sJ t        tm        t                    dk(  sJ t        to        tV        t        tp        t                    dk(  sJ t        to        tV        t        tp        t              dz        dk(  sJ t        ts        tV        t        t                    dk(  sJ t        ts        tV        t        t              dz        dk(  sJ t        tu        tV        t                    dk(  sJ t        tu        tV        t              dz        dk(  sJ t        tw        tV        t                    dk(  sJ t        tw        tV        t              dz        dk(  sJ t        ty        tV        t                    dk(  sJ t        ty        tV        t              dz        dk(  sJ t        t{        tV        t        t                    dk(  sJ t        t{        tV        t        t              dz        dk(  sJ t        t}        tV        t                    dk(  sJ t        t}        tV        t              dz        dk(  sJ t        t        tV        t        t                    dk(  sJ t        t        tV        t        t              dz        dk(  sJ t        t        tV        t                    dk(  sJ t        t        tV        t              dz        dk(  sJ t        dda֫      }	t        dda֫      }
t        t        tV        t        |	|
            dk(  sJ t        t        tV        t        |	|
      d{z        dk(  sJ t        t        tV        t        |	|
            dk(  sJ t        t        tV        t        |	|
      d{z        dk(  sJ t        t        d            dk(  sJ t        t        d      d{z        dk(  sJ t        t        tV                    dk(  sJ t        t        tV              dz        dk(  sJ t        t        tV                    dk(  sJ t        t        tV              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t        t                    dk(  sJ t        t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t        t                    dk(  sJ t        t        t        t              dz        dk(  sJ t        t        tV                    dk(  sJ t        t        tV              dz        dk(  sJ t        t        tV                    dk(  sJ t        t        tV              dz        dk(  sJ t        t        tV                    dk(  sJ t        t        tV        d            dk(  sJ t        t        tV        t                    dk(  sJ t        t        tV              t        tV              z        dk(  sJ t        t        t        tV              d            dk(  sJ t        t        tV              t        z        dk(  sJ t        t        tV        t              t        z        dk(  sJ t        t        t        d            dk(  sJ t        t        t        dz   d            dk(  sJ t        t        dt        dz               dk(  sJ t        t        dt        z  d            dk(  sJ t        t        ddt        z              dk(  sJ t        t        t        d      dz         dk(  sJ t        dt        t        d      z        dk(  sJ t        t        ddt        z        tV        z        dk(  sJ t        d      }t         |t                    dk(  sJ t        |      d k(  sJ y (  Nze^{x}r  r
  z	e + e^{2}r  zf{\left(x \right)}gzg{\left(x,y \right)}hzh{\left(x,y,z \right)}Liz\operatorname{Li}z"\operatorname{Li}{\left(x \right)}rU   z\beta{\left(x,y,z \right)}z!\operatorname{B}\left(x, y\right)Fr   z!\operatorname{B}\left(x, x\right)z%\operatorname{B}^{2}\left(x, y\right)z\beta{\left(x \right)}\betarb   z\gamma{\left(x,y,z \right)}z\gamma{\left(x \right)}\gammaa_1za_{1}za_{1}{\left(x \right)}abz\operatorname{ab}ab1z\operatorname{ab}_{1}ab12z\operatorname{ab}_{12}ab_1ab_12ab_cz\operatorname{ab}_{c}ab_cdz\operatorname{ab}_{cd}r  z"\operatorname{ab}{\left(x \right)}z&\operatorname{ab}_{1}{\left(x \right)}z'\operatorname{ab}_{12}{\left(x \right)}z&\operatorname{ab}_{c}{\left(x \right)}z'\operatorname{ab}_{cd}{\left(x \right)}z%\operatorname{ab}^{2}{\left( \right)}z)\operatorname{ab}_{1}^{2}{\left( \right)}z*\operatorname{ab}_{12}^{2}{\left( \right)}z&\operatorname{ab}^{2}{\left(x \right)}z*\operatorname{ab}_{1}^{2}{\left(x \right)}z+\operatorname{ab}_{12}^{2}{\left(x \right)}rA  a1a12za_{12}a_12za{\left( \right)}za_{1}{\left( \right)}za_{12}{\left( \right)}za^{2}{\left( \right)}za_{1}^{2}{\left( \right)}za_{12}^{2}{\left( \right)}za^{2}{\left(x \right)}za_{1}^{2}{\left(x \right)}za_{12}^{2}{\left(x \right)}    za^{32}{\left( \right)}za_{1}^{32}{\left( \right)}za_{12}^{32}{\left( \right)}za^{32}{\left(x \right)}za_{1}^{32}{\left(x \right)}za_{12}^{32}{\left(x \right)}za^{a}{\left( \right)}za_{1}^{a}{\left( \right)}za_{12}^{a}{\left( \right)}za^{a}{\left(x \right)}za_{1}^{a}{\left(x \right)}za_{12}^{a}{\left(x \right)}za^{ab}{\left( \right)}za_{1}^{ab}{\left( \right)}za_{12}^{ab}{\left( \right)}za^{ab}{\left(x \right)}za_{1}^{ab}{\left(x \right)}za_{12}^{ab}{\left(x \right)}za^12za^{12}{\left(x \right)}z)\left(a^{12}\right)^{ab}{\left(x \right)}a__12a_1__1_2za^{1}_{1 2}{\left(x \right)}r_  r`  z\omega_{1}{\left(x \right)}z\sin{\left(x \right)}T)fold_func_bracketsz\sin {x}z\sin {2 x^{2}}z\sin {x^{2}}z(\operatorname{asin}^{2}{\left(x \right)}full)inv_trig_stylez\arcsin^{2}{\left(x \right)}powerz\sin^{-1}{\left(x \right)}^{2})r  r  z\sin^{-1} {x^{2}}z&\operatorname{arccsc}{\left(x \right)}z&\operatorname{arsinh}{\left(x \right)}zk!z\left(- k\right)!zk!^{2}z!kz!\left(- k\right)z\left(!k\right)^{2}zk!!z\left(- k\right)!!zk!!^{2}z{\binom{2}{k}}z{\binom{2}{k}}^{2}r  z{\left(3\right)}_{k}z{3}^{\left(k\right)}z\left\lfloor{x}\right\rfloorz\left\lceil{x}\right\rceilz#\operatorname{frac}{\left(x\right)}z \left\lfloor{x}\right\rfloor^{2}z\left\lceil{x}\right\rceil^{2}z'\operatorname{frac}{\left(x\right)}^{2}z\min\left(2, x, x^{3}\right)z\min\left(x, y\right)^{2}z\max\left(2, x, x^{3}\right)z\max\left(x, y\right)^{2}\left|{x}\right|z\left|{x}\right|^{2}!\operatorname{re}{\left(x\right)}zE\operatorname{re}{\left(x\right)} + \operatorname{re}{\left(y\right)}!\operatorname{im}{\left(x\right)}z\overline{x}z\overline{x}^{2}z\Gamma\left(x\right)wz\Gamma\left(w\right)zO\left(x\right)r   z$O\left(x; x\rightarrow \infty\right)z#O\left(x - y; x\rightarrow y\right)zGO\left(x; \left( x, \  y\right)\rightarrow \left( 0, \  0\right)\right)zQO\left(x; \left( x, \  y\right)\rightarrow \left( \infty, \  \infty\right)\right)z\gamma\left(x, y\right)z\gamma^{2}\left(x, y\right)z\Gamma\left(x, y\right)z\Gamma^{2}\left(x, y\right)z\cot{\left(x \right)}z\coth{\left(x \right)}zx^{\frac{1}{y}}z\arg{\left(x \right)}z\zeta\left(x\right)z\zeta^{2}\left(x\right)z\zeta\left(x, y\right)z\zeta^{2}\left(x, y\right)z\eta\left(x\right)z\eta^{2}\left(x\right)z#\operatorname{Li}_{x}\left(y\right)z'\operatorname{Li}_{x}^{2}\left(y\right)z\Phi\left(x, y, n\right)z\Phi^{2}\left(x, y, n\right)z
\gamma_{x}z\gamma_{x}^{2}z\gamma_{x}\left(y\right)z\gamma_{x}\left(y\right)^{2}zK\left(z\right)zK^{2}\left(z\right)zF\left(x\middle| y\right)zF^{2}\left(x\middle| y\right)zE\left(x\middle| y\right)zE^{2}\left(x\middle| y\right)zE\left(z\right)zE^{2}\left(z\right)z\Pi\left(x; y\middle| z\right)z"\Pi^{2}\left(x; y\middle| z\right)z\Pi\left(x\middle| y\right)z\Pi^{2}\left(x\middle| y\right)z"\operatorname{Ei}{\left(x \right)}z&\operatorname{Ei}^{2}{\left(x \right)}z"\operatorname{E}_{x}\left(y\right)z&\operatorname{E}_{x}^{2}\left(y\right)z'\operatorname{Shi}^{2}{\left(x \right)}z&\operatorname{Si}^{2}{\left(x \right)}z&\operatorname{Ci}^{2}{\left(x \right)}z$\operatorname{Chi}^{2}\left(x\right)z \operatorname{Chi}\left(x\right)z&P_{n}^{\left(a,b\right)}\left(x\right)z7\left(P_{n}^{\left(a,b\right)}\left(x\right)\right)^{2}z$C_{n}^{\left(a\right)}\left(x\right)z5\left(C_{n}^{\left(a\right)}\left(x\right)\right)^{2}T_{n}\left(x\right)z$\left(T_{n}\left(x\right)\right)^{2}zU_{n}\left(x\right)z$\left(U_{n}\left(x\right)\right)^{2}zP_{n}\left(x\right)z$\left(P_{n}\left(x\right)\right)^{2}z$P_{n}^{\left(a\right)}\left(x\right)z5\left(P_{n}^{\left(a\right)}\left(x\right)\right)^{2}zL_{n}\left(x\right)z$\left(L_{n}\left(x\right)\right)^{2}z$L_{n}^{\left(a\right)}\left(x\right)z5\left(L_{n}^{\left(a\right)}\left(x\right)\right)^{2}zH_{n}\left(x\right)z$\left(H_{n}\left(x\right)\right)^{2}thetarealphiz!Y_{n}^{m}\left(\theta,\phi\right)z2\left(Y_{n}^{m}\left(\theta,\phi\right)\right)^{3}z!Z_{n}^{m}\left(\theta,\phi\right)z2\left(Z_{n}^{m}\left(\theta,\phi\right)\right)^{3}z+\operatorname{polar\_lift}{\left(0 \right)}z/\operatorname{polar\_lift}^{3}{\left(0 \right)}z\phi\left(n\right)z#\left(\phi\left(n\right)\right)^{2}z\lambda\left(n\right)z&\left(\lambda\left(n\right)\right)^{2}z\sigma\left(x\right)z\sigma^{2}\left(x\right)z\sigma_y\left(x\right)z\sigma^{2}_y\left(x\right)z\sigma^*\left(x\right)z\sigma^*^{2}\left(x\right)z\sigma^*_y\left(x\right)z\sigma^*^{2}_y\left(x\right)z\nu\left(n\right)z"\left(\nu\left(n\right)\right)^{2}z\Omega\left(n\right)z%\left(\Omega\left(n\right)\right)^{2}zW\left(n\right)r  zW_{-1}\left(n\right)zW_{k}\left(n\right)zW^{2}\left(n\right)zW^{k}\left(n\right)zW^{p}_{k}\left(n\right)r  z	x \bmod 7z\left(x + 1\right) \bmod 7z7 \bmod \left(x + 1\right)z2 x \bmod 7z7 \bmod 2 xz\left(x \bmod 7\right) + 1z2 \left(x \bmod 7\right)z\left(7 \bmod 2 x\right)^{n}fjlkdz%\operatorname{fjlkd}{\left(x \right)}z\operatorname{fjlkd})Or   rC   r  r   r3  r5  rU   r$   rA  rS   rP   rO   rE   r*   r;  r,   r+   r)   r'   r(   rH   rG   rI   rK   rJ   r<   rA   r?   r>   rb   r%   r   r   r   rc   rR   rF   rL   r=   r|   rx   rz   ry   rB  r{   rZ   rY   rX   r[   r^   ra   r_   r`   r]   r\   rp   brn   rl   rm   rr   rk   rq   rj   ro   rt   mru   r@   r:   r;   r5   r6   r8   r9   rB   r    r0  r   )r  rw  rx  ry  mybetar|  r}  r_  r  r  r  r  s               r   test_latex_functionsr    s   Q=H$$$Q#a&!\111A1;////8tA1a>44448tA1a 99998t	$B9,,,,A<@@@@fF1a!%BBBBa DDDDa%()-QQQQaQ#KKKK8888=H$$$A1a >>>>1;44448y   
5/C:!!!Q=5555%!X---
 $ $8888%!%====&!"&????&!"&>>>>'"#'@@@@&!"&>>>>'"#'@@@@$s,-1VVVV%-.2[[[[!&!&+./3]]]]!&!&+./3\\\\!&!&+./3\\\\"'"6#;/04^^^^ $!1$%)QQQQ%"A%&*VVVV!&!#Q&'+XXXX!&!#Q&'+WWWW"'"$a'(,YYYY$s,a/04]]]]%-q015bbbb!&!&+.126dddd!&!&+.126cccc"'"6#;/2367 7 7
 #4'''$ H,,,%!Y...%!X---&!"i/// #!%9999$!"&>>>>%"#'@@@@%"#'????!&!#$(AAAA #!#$(@@@@$!1$%)EEEE%"A%&*GGGG%"A%&*FFFF!&!#Q&'+HHHH#vc{+Q./3LLLL$s,a/04QQQQ%-q015SSSS%-q015RRRR!&!&+.126TTTT#"$%)BBBB$!2%&*GGGG%"B&'+IIII%"B&'+HHHH!&!#R'(,JJJJ#vc{+R/04NNNN$s,b015SSSS%-r126UUUU%-r126TTTT!&!&+.237VVVV#!#$(@@@@$!1$%)EEEE%"A%&*GGGG%"A%&*FFFF!&!#Q&'+HHHH#vc{+Q./3LLLL$s,a/04QQQQ%-q015SSSS%-q015RRRR!&!&+.126TTTT	B#"$%)BBBB$!2%&*GGGG%"B&'+IIII%"B&'+HHHH!&!#R'(,JJJJ#vc{+R/04NNNN$s,b015SSSS%-r126UUUU%-r126TTTT!&!&+.237VVVV!&!!$%)CCCC!&!!$*+/[[[["'"1%&*DDDD"'"1%+,0\\\\%*%a()-LLLL hF=M)))====Q=4444QD1[@@@Qq!tV6  QTt4   a! KKKKa!F3'( ( (a!G4)* * *adG$(*   a012 2 2q&112 2 2 1%'''A2#77771q!Y...a!U***qb!"&::::a!#$(>>>>A6)))QB $9999A!"j000!Q $5555!Q"#'<<<<!!Q'(,CCCCA&'+BBBBq?==== ====a>CCCCq1!DDDDQ#DDDDa! JJJJQ1a4!%DDDDQA">>>>Q1a4!%DDDDQA">>>>Q=////Q6666A<????AEPQ Q QA<????1/1111q!%88881a4!%8888q?5555S	Aq?5555q?0000q!!3333q1a&!"&8888q1b'"#'NNNNq1uq!f%&./ / /q!Q RS S Sq!Q RS S Sq1b'Ar7+,\] ] ]Aq!"&@@@@Aq!1$%)GGGGAq!"&@@@@Aq!1$%)GGGGQ=4444a>6666A<????A<????a 2222Q=4444a>3333a! ::::a 9999aQ#@@@@q!"&;;;;q!1$%)BBBBA#IIII1qGH H H!Q"#'BBBB!Q"A%&*IIII1-///1q!%66661a!%@@@@1a!#$(GGGGA#5555A!"&<<<<Aq!"&BBBBAq!1$%)IIIIAq!"&BBBBAq!1$%)IIIIA#5555A!"&<<<<Q1%&*KKKKQ1%q()-. . .Q"#'EEEEQ"A%&*LLLLA<@@@@A?GGGG1"GGGG1q!%NNNNQIIIIA?GGGGA?GGGGQFFFFQ=????1a#$12 2 21a#Q&'BC C CAq!$%/0 0 0Aq!$a'(@A A AAq!"&<<<<Aq!1$%/0 0 0Aq!"&<<<<Aq!1$%/0 0 0!Q $::::!Q"#'NNNN1a()/0 0 01a(!+,@A A A!Q $::::!Q"#'NNNN1a()/0 0 01a(!+,@A A AA#9999A!"&MMMM7&E
T
"CQ5#&'+OOOOQ5#&)*=> > >Q5#&'+OOOOQ5#&)*=> > > A67 7 7A!":; ; ;  5555q!%KKKK#$(@@@@#q()12 2 2 q!"&====q!1$%)DDDDq!$%)BBBBq!$a'(,IIII"#'@@@@"A%&*GGGG1%&*EEEE1%q()-LLLL 4444q!%JJJJA#::::A!#$01 1 1 !!3333!R!%<<<<!Q $::::!x{*+/EEEEXa[!$%)????!a $::::!Q"#'AAAAQ|+++QUA#@@@@QA#@@@@QUA>111QA>111QQ#@@@@SAY#>>>>QA!"&EEEE WEq?FFFF<2222r   c                  v     G d dt               } t        |       dk(  sJ t         | t                    dk(  sJ y )Nc                       e Zd Zy)6test_function_subclass_different_name.<locals>.mygammaNr   r   r   r   mygammar  "  s    r   r  z\operatorname{mygamma}z'\operatorname{mygamma}{\left(x \right)})rb   r   r  )r  s    r   %test_function_subclass_different_namer  !  s9    % >6666 JJJJr   c                     ddl m} m} t        t	        t        t        t        |       t        d      dt        dddt        z        |            dk(  sJ t        t	        t               t        d      dt               |            d	k(  sJ t        t        | dfd
|            dk(  sJ t        t        t               t        d      |            dk(  sJ y )Nr   r  r5  r  )r   r  r
  r  zt{G_{4, 5}^{2, 3}\left(\begin{matrix} \pi, \pi, x & 1 \\0, 1 & 1, 2, \frac{3}{\pi} \end{matrix} \middle| {z} \right)})r   zS{G_{1, 1}^{1, 0}\left(\begin{matrix}  & 1 \\0 &  \end{matrix} \middle| {z} \right)})r  zL{{}_{2}F_{1}\left(\begin{matrix} 2, x \\ 3 \end{matrix}\middle| {z} \right)}zH{{}_{0}F_{1}\left(\begin{matrix}  \\ 1 \end{matrix}\middle| {z} \right)})	sympy.abcr  r5  r   re   r   r   rd   r  s     r   test_hyper_printingr  (  s    r2q)58q!QrT!2A7 8	<< < < %(D%'1=>^_ _ _1vtQ'(	22 2 2 uwa!,-	22 2 2r   c                  |   ddl m} m}m}m}m}m}m}m}m	}m
}	 ddlm}
 t         | t        |
dz        t        z        dk(  sJ t         |t        |
            dk(  sJ t         |t        |
            dk(  sJ t         |t        |
            dk(  sJ t         |t        |
dz        dz        d	k(  sJ t         |t        |
            d
k(  sJ t         |t        |
            dk(  sJ t         |t        |
            dk(  sJ t         |t        |
            dk(  sJ t         |	t        |
            dk(  sJ y )Nr   )
besseljbesselybesselibesselkhankel1hankel2jnynhn1hn2r5  r
  zJ^{k}_{n}\left(z^{2}\right)zY_{n}\left(z\right)zI_{n}\left(z\right)zK_{n}\left(z\right)z.\left(H^{(1)}_{n}\left(z^{2}\right)\right)^{2}zH^{(2)}_{n}\left(z\right)zj_{n}\left(z\right)zy_{n}\left(z\right)zh^{(1)}_{n}\left(z\right)zh^{(2)}_{n}\left(z\right))sympy.functions.special.besselr  r  r  r  r  r  r  r  r  r  r  r5  r   rB  r;  )r  r  r  r  r  r  r  r  r  r  r5  s              r   test_latex_besselr  9  s5   B B B AqD!1$%)GGGGA#9999A#9999A#9999AqD!1$%9: : :A#????Aq?4444Aq?4444Q;;;;Q;;;;r   c                      ddl m} m} ddlm} t         | |            dk(  sJ t         ||            dk(  sJ t         | |      dz        dk(  sJ t         ||      dz        dk(  sJ y )	Nr   )fresnelsfresnelcr  zS\left(z\right)zC\left(z\right)r
  zS^{2}\left(z\right)zC^{2}\left(z\right))'sympy.functions.special.error_functionsr  r  r  r5  r   )r  r  r5  s      r   test_latex_fresnelr  K  sp    L!!3333!!3333!a $::::!a $::::r   c                  2    t        dt        z        dk(  sJ y )Nr  z\left(-1\right)^{x}r   r  r   r   r   test_latex_bracketsr  T  s    "q>3333r   c                  F   t        ddd      } t        t        ddd            }t        | t        |       z        }t        |d   t        |d         z        }|dk(  sJ |dk(  sJ d	}t        t	        d
t        d                  dk(  sJ t        t	        dt        d                  dk(  sJ t        t	        dt        dt        d                        d|z   dz   k(  sJ t        t	        dt        dt        d      dz                     d|z   dz   k(  sJ t        t	        dt        dt        d      t        d      f                  d|z   dz   k(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ y )NPsi_0TF)complexr  Psir   z\Psi_{0} \overline{\Psi_{0}}z \overline{{\Psi}_{0}} {\Psi}_{0}z\mathrel{..}\nobreak x1rV  z{x_{1}}_{i}x2z{x_{2}}_{i}x3Nz{x_{3}}_{{i}_{0zN - 1}}r  zN}}x4rA  r  z{x_{4}}_{{i}_{azb}}rb   r{  za ba_bza_{b})r$   r   r   r>   r   r   )
Psi_symbolPsi_indexedsymbol_latexindexed_latexintervals        r   test_latex_indexedr  X  s   E:JfUDuEFKi
&;;<L+a.9[^+DDEM::::???? )Hvc{+,>>>s3x()^;;;s3s456:LX:UV_:____s3sA678<Nx<WX]<]]]]s3VC[(ABCDHZ[cHcdiHiiiiW%&)333U#$...U#$000r   c                  
   t        t        t        dz  t        d            dk(  sJ t        t        t        t              t        dz  z   t        d            dk(  sJ t        t        t        t        t              t        dz  z   t        d      d            dk(  sJ t        t        t        t        t        t              t        dz  z   t        d      d      d            dk(  sJ t        t        t        t        t        z        t        d            d	k(  sJ t        t        t        t        t        z        t        dz  z   t        d            d
k(  sJ t        t        t        t        t        t        z        t        dz  z   t        d      t        d            dk(  sJ t        t        t        t        t        t        t        z        t        dz  z   t        d      t        d      t        d            dk(  sJ t        d      } t        t        t         | t        t              t        d      t        d            dt         | t        t                    z   k(  sJ t        t        t        t         | t        t              t        d      t        d      t        d            dt         | t        t                    z   k(  sJ t        t        t        t        dz  t        d       t        d            dk(  sJ t        t        t        t        t        t        t        d      t        d       t        d      t        d            dk(  sJ t        t        t        t        t         t        z        t        dt        f      t        d            dk(  sJ t        t        t        t        d      dz        dk(  sJ t        t         | t              t              dz        dk(  sJ t        t         | t              t        t        f            dk(  sJ t        d      }t        d      }t        t         | ||      |            dk(  sJ t        d      }t        t         | t              t        |f            dk(  sJ t        d      }t        t         | t              t        t        ||      f            dk(  sJ t        t         | t              t              d      d k(  sJ y )!Nr  Fr   z\frac{d}{d x} x^{3}r
  z8\frac{d}{d x} \left(x^{2} + \sin{\left(x \right)}\right)z@\frac{d^{2}}{d x^{2}} \left(x^{2} + \sin{\left(x \right)}\right)z@\frac{d^{3}}{d x^{3}} \left(x^{2} + \sin{\left(x \right)}\right)z3\frac{\partial}{\partial x} \sin{\left(x y \right)}zH\frac{\partial}{\partial x} \left(x^{2} + \sin{\left(x y \right)}\right)zP\frac{\partial^{2}}{\partial x^{2}} \left(x^{2} + \sin{\left(x y \right)}\right)zP\frac{\partial^{3}}{\partial x^{3}} \left(x^{2} + \sin{\left(x y \right)}\right)r  z*\frac{\partial^{2}}{\partial y\partial x} z.\frac{\partial^{3}}{\partial y\partial x^{2}} z0\frac{d}{d x} \left(- \frac{d}{d x} y^{2}\right)z<\frac{d^{2}}{d x^{2}} \left(- \frac{d^{2}}{d x^{2}} y\right)r   z5\frac{d}{d y} \int\limits_{0}^{\infty} e^{- x y}\, dxz \left(\frac{d}{d x} x\right)^{2}z1\left(\frac{d}{d x} f{\left(x \right)}\right)^{2}z(\frac{d^{n}}{d x^{n}} f{\left(x \right)}r  r  z<\frac{\partial}{\partial x_{1}} f{\left(x_{1},x_{2} \right)}n1z0\frac{d^{n_{1}}}{d x^{n_{1}}} f{\left(x \right)}n2z`\frac{d^{\max\left(n_{1}, n_{2}\right)}}{d x^{\max\left(n_{1}, n_{2}\right)}} f{\left(x \right)}rddiff_operatorz2\frac{\mathrm{d}}{\mathrm{d} x} f{\left(x \right)})r   r   r  rS   r3  r   r}   rC   r   rB  r$   rJ   )r  r  r  r  r  s        r   test_latex_derivativesr  m  sY   adA./  c!fq!tmQ78CD D Dd3q6AqD=!e<uMNKL L L d4AAq5AER]bcdKL L L c!a%j!e45>? ? ?c!a%j1a4'U;<ST T Td3qs8ad?A>ERS[\ \ \d4AaC1a4UCQQVWYZejkl[\ \ \ 	Ad1Q7A6EJK5a1gFG G G d4!QU;QOQR]bcd9E!Aq'NJK K K tAqDE221eDEI||||dDa5!9!UKKAW\]^_inopGH H H hsA2a4y1a*5q5IJ@A A A aU+Q./+, , , adA!"<= = = adQF#$34 4 4 
B	BaBi$%)hhhh	BadQG$%)\\\\	BadQB,-.kl l l adAd37llllr   c                  d    t        t        t        t        z  t        t        fd            dk(  sJ y )Nr  r
  z+\left. x y \right|_{\substack{ x=1\\ y=2 }})r   r   r  r3  r   r   r   test_latex_subsr    s'    acAq66*+/]]]]r   c                  x   t        t        t        t              t                    dk(  sJ t        t        t        dz  t        ddf            dk(  sJ t        t        t        dz  t        ddf            dk(  sJ t        t        t        t        dz  z  t        ddft                    d	k(  sJ t        t        t        t        dz  z  t        ddft              d
      dk(  sJ t        t        t        t        dz  z  t        ddft              d
d      dk(  sJ t        t        t        t        df            dk(  sJ t        t        t        t        z  t        t                    dk(  sJ t        t        t        t        z  t
        z  t        t        t
                    dk(  sJ t        t        t        t        z  t
        z  t        z  t        t        t
        t                    dk(  sJ t        t        t        t        t        t        t        t        t                    dk(  sJ t        t        t        t        t        t
        ddf            dk(  sJ t        t        t        t        dz  t               t                    dk(  sJ t        t        t        t        t        t               t               t                    dk(  sJ t        t        t
        t
              dz        dk(  sJ t        t        t        t
        z   t
                    dk(  sJ t        t        t        t
        dz  z   t
                    dk(  sJ t        t        t        t        z  t
                    dk(  sJ t        t        t        t              d      dk(  sJ t        t        t        t        ddf      d      dk(  sJ y ) Nz\int \log{\left(x \right)}\, dxr
  r   r  z\int\limits_{0}^{1} x^{2}\, dx
      z \int\limits_{10}^{20} x^{2}\, dxz)\int\int\limits_{0}^{1} x^{2} y\, dx\, dy	equation*modezI\begin{equation*}\int\int\limits_{0}^{1} x^{2} y\, dx\, dy\end{equation*}Tr  r  z&$$\int\int_{0}^{1} x^{2} y\, dx\, dy$$z\int\limits^{0} x\, dxz\iint x y\, dx\, dyz\iiint x y z\, dx\, dy\, dzz#\iiiint t x y z\, dx\, dy\, dz\, dtz8\int\int\int\int\int\int x\, dx\, dx\, dx\, dx\, dx\, dxz,\int\limits_{0}^{1}\int\int x\, dx\, dy\, dzz(\int \left(- \int y^{2}\, dx\right)\, dxz=\int \left(- \int \left(- \int y\, dx\right)\, dx\right)\, dxz\left(\int z\, dz\right)^{2}z\int \left(x + z\right)\, dzz&\int \left(x + \frac{z}{2}\right)\, dzz\int x^{y}\, dzr  r  z\int x\, \mathrm{d}xz#\int\limits_{0}^{1} x\, \mathrm{d}x)r   r}   rD   r  r3  r5  tr   r   r   test_latex_integralsr    s6   #a&!$%)KKKK!Q$Aq	*+)* * *!Q$B,-+, , ,!AqD&1a)Q/045 5 5!AqD&1a)Q/kBTU U U!AqD&1a)Q/kM45 5 5!aV$%)BBBB!A#q!$%)????!A#a%Aq)*.LLLL!A#a%'1aA././ / /!Q1aA./CD D D!QAq!9-.78 8 8 8AqD++A./34 4 48Xa]N155a89HI I I !Q"#'FFFF!a%#$(GGGG!AaC%#$12 2 2!Q$"#'9999 !Qt48OOOO!aAY't<@ffffr   c            	         t         t        fD ]l  } t         | t        t        z  t        dz  g            dk(  sJ t         | t        dd                  dk(  sJ t         | t        dd                  dk(  rlJ  t        } t         | t        t        z  t        dz  g       dk(  sJ t         | t        dd             dk(  sJ t         | t        dd             dk(  sJ y )Nr
  z\left\{x^{2}, x y\right\}r  rF  z\left\{1, 2, 3, 4, 5\right\}   z4\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right\})	frozensetrf  r   r  r3  ranger   ss    r   test_latex_setsr    s     DQ!QT{^$(DDDDQuQ{^$(GGGGQuQ|_%CD 	D DD 	AQqS!Q$K!%AAAAE!QK!%DDDDE!RL!"?@ @ @r   c                  R    t        dd      } t        |       }t        |      dk(  sJ y )Nr  r  z%SetExpr\left(\left[1, 3\right]\right))r   r   r   )ivses     r   test_latex_SetExprr    s)    	!QB	B9@@@@r   c                     t        t        dd            dk(  sJ t        t        dd            dk(  sJ t        t        ddd            dk(  sJ t        t        dd	d            d
k(  sJ t        t        d	dd            dk(  sJ t        t        dt        d            dk(  sJ t        t        t        dd            dk(  sJ t        t        dt         d            dk(  sJ t        t        t         t                    dk(  sJ t        t        t        t         d            dk(  sJ t        d      \  } }}t        t        | ||            dk(  sJ t        t        | dd            dk(  sJ t        t        d|d            dk(  sJ t        t        dd|            dk(  sJ t	        dd      }t	        ddd      }t	        ddd       }t        t        ||dz               d!k(  sJ t        t        t         |d            d"k(  sJ t        t        |t                    d#k(  sJ t        t        | | dz               d$k(  sJ y )%Nr  3   z\left\{1, 2, \ldots, 50\right\}r  z\left\{1, 2, 3\right\}r   r  z\left\{0, 1, 2\right\}   z\left\{0, 1, \ldots, 29\right\}r  z \left\{30, 29, \ldots, 2\right\}r
  z\left\{0, 2, \ldots\right\}r.  z\left\{\ldots, 2, 0\right\}z\left\{-2, -3, \ldots\right\}z'\left\{\ldots, -1, 0, 1, \ldots\right\}z'\left\{\ldots, 1, 0, -1, \ldots\right\}za:cz \text{Range}\left(a, b, c\right)r  z\text{Range}\left(a, 10\right)z\text{Range}\left(b\right)z!\text{Range}\left(0, 10, c\right)rV  Tr   rB  )negativer   r0  )r2  r   z\left\{i, i + 1, i + 2\right\}z#\left\{\ldots, n - 4, n - 2\right\}z\left\{p, p + 1, \ldots\right\}z!\text{Range}\left(a, a + 3\right))r   r   r   r&   r$   )rA  r  crV  rB  r0  s         r   test_latex_Ranger    s<   q""DDDDq!!::::q!Q $====q"a!%GGGGr1b!"&IIIIq"a!%CCCCr2r"#'EEEErB3#$(HHHHsB $NNNNrB3#$(RRRRenGAq!q!Q $GGGGq"a!%FFFFq!Q $AAAAq"a!%IIIIsD!AsT40AsT40Aq!a%!%FFFFsAq!"&LLLLq""DDDD q!a%!%IIIIr   c                     t        t        dz  dt        f      } t        d      }d}t	        |       |k(  sJ d}t	        |      |k(  sJ t        t        dz  d      }t        dd      }d}t	        |      |k(  sJ d}t	        |      |k(  sJ t        t        dz  t         df      }t        dt         df      }d	}t	        |      |k(  sJ d
}t	        |      |k(  sJ d}t	        t        | |            |k(  sJ d}t	        t        ||            |k(  sJ d}t	        t        ||            |k(  sJ d}t	        t        | |            |k(  sJ d}t	        t        ||            |k(  sJ d}t	        t        ||            |k(  sJ t        t        dz  t        dt        f      }d}t	        |      |k(  sJ t        d      }t        |t        dz  z  t        ddf      }	d}t	        |	      |k(  sJ y )Nr
  r   r  z\left[0, 1, 4, 9, \ldots\right]z\left[1, 2, 1, 2, \ldots\right])r   r
  z\left[0, 1, 4\right]z\left[1, 2, 1\right]z\left[\ldots, 9, 4, 1, 0\right]z\left[\ldots, 2, 1, 2, 1\right]z \left[1, 3, 5, 11, \ldots\right]z\left[1, 3, 5\right]z \left[\ldots, 11, 5, 3, 1\right]z \left[0, 2, 4, 18, \ldots\right]z\left[0, 2, 4\right]z \left[\ldots, 18, 4, 2, 0\right]z\left\{a^{2}\right\}_{a=0}^{x}r  z\left[0, b, 4 b\right])	r   rA  r   r   r   r   r   r  r$   )
s1s2	latex_strs3s4s5s6s7r  s8s
             r   test_latex_sequencesr    s
   	AqD1b'	"B	B2I9	!!!2I9	!!!	AqD&	!B		B'I9	!!!'I9	!!!	AqDB3(	#B	"a	!B2I9	!!!2I9	!!!3IB I---'IB I---3IB I---3IB I---'IB I---3IB I--- 
AqD1a)	$B1I9	!!!sA	AadFQ1I	&B)I9	!!!r   c                  d    d} t        t        t        t        t         t        f            | k(  sJ y )Nz`2 \sin{\left(x \right)} - \sin{\left(2 x \right)} + \frac{2 \sin{\left(3 x \right)}}{3} + \ldots)r   r   r  r   r  s    r   test_latex_FourierSeriesr  E  s,    k AsB<01Y>>>r   c                  Z    d} t        t        t        dt        z                     | k(  sJ y )Nz;\sum_{k=1}^{\infty} - \frac{\left(-1\right)^{- k} x^{k}}{k}r  )r   r   rD   r  r  s    r   test_latex_FormalPowerSeriesr  K  s&    NISQZ!Y...r   c                  f   t        dd      } t        t        dd            dk(  sJ t        t        d|             dk(  sJ t        t        d| dd            dk(  sJ t        t        d| dd            dk(  sJ t        t        d| dd            d	k(  sJ t        t        d| dd            d
k(  sJ y )NrA  Tr  r   z\left\{0\right\}z\left[0, a\right]Fz\left(0, a\right]z\left[0, a\right)z\left(0, a\right))r$   r   r   rA  s    r   test_latex_intervalsr  P  s    sA!Q $7777!Q $8888!Qu-.2FFFF!Qe,-1EEEE!Qt,-1EEEE!Qd+,0DDDDr   c                      t        dd      } t        t        dd            dk(  sJ t        t        d|             dk(  sJ t        t        | dz   | dz               d	k(  sJ y )
NrA  Tr  r   r  z\left\langle 0, 1\right\ranglez\left\langle 0, a\right\rangler
  z&\left\langle a + 1, a + 2\right\rangle)r$   r   r   r   s    r   test_latex_AccumuBoundsr  Z  sm    sAQ"#'HHHHQ"#'HHHHQUAE*+12 2 2r   c                  @    t        t        j                        dk(  sJ y )N	\emptyset)r   r#   EmptySetr   r   r   test_latex_emptysetr  b  s    ,,,r   c                  @    t        t        j                        dk(  sJ y )Nz
\mathbb{U})r   r#   UniversalSetr   r   r   test_latex_universalsetr
  f  s     M111r   c                      t        d      } t        d      }t        ||       }t        |j                               dk(  sJ y )NrU  Bz- (A B - B A))r   r   r   doit)rU  r  comms      r   test_latex_commutatorr  j  s:    AAaD!1111r   c            
          t        t        t        dd      t        dd                  dk(  sJ t        t        t        dd      t        dd      t        dd                  dk(  sJ y )Nr   r  r
  r  z(\left[0, 1\right] \cup \left[2, 3\right]r  z*\left\{1, 2\right\} \cup \left[3, 4\right])r   r   r   r   r   r   test_latex_unionr  q  sd    x1~x1~6734 4 4x1~x1~x1~FG56 6 6r   c            	      p    t        t        t        dd      t        t        t                          dk(  sJ y )Nr   r  z(\left[0, 1\right] \cap \left[x, y\right])r   r   r   r  r3  r   r   r   test_latex_intersectionr  x  s/    hq!nhq!n=>34 4 4r   c            	      d    t        t        t        dd      t        dd      d            dk(  sJ y )Nr
  r  r  r  Fr   z-\left[2, 5\right] \triangle \left[4, 7\right])r   r   r   r   r   r   test_latex_symmetric_differencer  }  s7    $Xa^Xa^.35 689 9 9r   c                  p    t        t        t        j                  t        j                              dk(  sJ y )Nz\mathbb{R} \setminus \mathbb{N})r   r   r#   RealsNaturalsr   r   r   test_latex_Complementr    s+    AGGQZZ01*+ + +r   c                  X   t        dd      } t        dd      }t        ddd      }t        | dz        dt        |       z  k(  sJ t        | dz        dt        |       z  k(  sJ t        | |z  |z  j                               t        |       dt        |      dt        |      k(  sJ y )	Nr   r  r  r
  r  z%s^{2}z%s^{10}z \times )r   r   r   flatten)linebiglinefsets      r   test_latex_productsetr    s    Aq>Dq"oGQ1Dq>Yt4444r?j5;6666$.4'0023dU7^U4[82 2 2 2r   c                  P    t        ddd      } t        t        |             dk(  sJ y )Nr  r
  r  z.\mathcal{P}\left(\left\{1, 2, 3\right\}\right))r   r   r   )r  s    r   test_latex_powersetr!    s(    Q1D$ $UUUUr   c            	         t               } t        |       dk(  sJ t        dd      }t        |      dk(  sJ t        t        |t        dd                  dk(  sJ t        t        t        dd      t        dd                  dk(  sJ y )N\omegar
  r  z3 \omega^{2}r  z3 \omega^{2} + \omegaz\omega^{2} + 2 \omega)r   r   r   r   )r  wps     r   test_latex_ordinalsr%    s    A8y   	Aq	B9'''Z1-./3KKKKAq):a+;<=AYYYYr   c                     t        d      \  } }}}t        |       }t        |      }t        |      }t        |      }t        ||d      }t        ||d      }	t        ||d      }
t        ||d      }t	        ||d      }t	        ||d      }t        ||d      }t        ||d      }t        ||      }t        ||      }t        t        ||	d            dk(  sJ t        t        ||	d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||d            d	k(  sJ t        t        |
|d            d
k(  sJ t        t        ||d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||d            dk(  sJ t        t	        ||d            dk(  sJ t        t	        ||	d            dk(  sJ t        t	        |
|d            dk(  sJ t        t	        ||d            dk(  sJ t        t	        ||d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||	d            dk(  sJ t        t        |
|d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||d            dk(  sJ t        t        ||      j                               dk(  sJ t        t        ||	            dk(  sJ t        t        |
|            dk(  sJ t        t        ||            dk(  sJ t        t        ||            dk(  sJ y )Nza:dFr   zI\left\{a\right\} \cap \left(\left\{c\right\} \cup \left\{d\right\}\right)zl\left(\left\{a\right\} \cup \left\{b\right\}\right) \cap \left(\left\{c\right\} \cup \left\{d\right\}\right)zv\left(\left\{a\right\} \setminus \left\{b\right\}\right) \cap \left(\left\{c\right\} \setminus \left\{d\right\}\right)zv\left(\left\{a\right\} \triangle \left\{b\right\}\right) \cap \left(\left\{c\right\} \triangle \left\{d\right\}\right)zp\left(\left\{a\right\} \times \left\{b\right\}\right) \cap \left(\left\{c\right\} \times \left\{d\right\}\right)zI\left\{a\right\} \cup \left(\left\{c\right\} \cap \left\{d\right\}\right)zl\left(\left\{a\right\} \cap \left\{b\right\}\right) \cup \left(\left\{c\right\} \cap \left\{d\right\}\right)zv\left(\left\{a\right\} \setminus \left\{b\right\}\right) \cup \left(\left\{c\right\} \setminus \left\{d\right\}\right)zv\left(\left\{a\right\} \triangle \left\{b\right\}\right) \cup \left(\left\{c\right\} \triangle \left\{d\right\}\right)zp\left(\left\{a\right\} \times \left\{b\right\}\right) \cup \left(\left\{c\right\} \times \left\{d\right\}\right)zS\left\{a\right\} \setminus \left(\left\{c\right\} \setminus \left\{d\right\}\right)zq\left(\left\{a\right\} \cup \left\{b\right\}\right) \setminus \left(\left\{c\right\} \cup \left\{d\right\}\right)zq\left(\left\{a\right\} \cap \left\{b\right\}\right) \setminus \left(\left\{c\right\} \cap \left\{d\right\}\right)z{\left(\left\{a\right\} \triangle \left\{b\right\}\right) \setminus \left(\left\{c\right\} \triangle \left\{d\right\}\right)zu\left(\left\{a\right\} \times \left\{b\right\}\right) \setminus \left(\left\{c\right\} \times \left\{d\right\}\right)zS\left\{a\right\} \triangle \left(\left\{c\right\} \triangle \left\{d\right\}\right)zq\left(\left\{a\right\} \cup \left\{b\right\}\right) \triangle \left(\left\{c\right\} \cup \left\{d\right\}\right)zq\left(\left\{a\right\} \cap \left\{b\right\}\right) \triangle \left(\left\{c\right\} \cap \left\{d\right\}\right)z{\left(\left\{a\right\} \setminus \left\{b\right\}\right) \triangle \left(\left\{c\right\} \setminus \left\{d\right\}\right)zu\left(\left\{a\right\} \times \left\{b\right\}\right) \triangle \left(\left\{c\right\} \times \left\{d\right\}\right)z@\left\{a\right\} \times \left\{c\right\} \times \left\{d\right\}zn\left(\left\{a\right\} \cup \left\{b\right\}\right) \times \left(\left\{c\right\} \cup \left\{d\right\}\right)zn\left(\left\{a\right\} \cap \left\{b\right\}\right) \times \left(\left\{c\right\} \cap \left\{d\right\}\right)zx\left(\left\{a\right\} \setminus \left\{b\right\}\right) \times \left(\left\{c\right\} \setminus \left\{d\right\}\right)zx\left(\left\{a\right\} \triangle \left\{b\right\}\right) \times \left(\left\{c\right\} \triangle \left\{d\right\}\right))	r&   r   r   r   r   r   r   r   r  )rA  r  r  drU  r  CDU1U2I1I2C1C2D1D2P1P2s                     r   test_set_operators_parenthesisr4    s   JAq!Q!A!A!A!A	q!e	$B	q!e	$B	aU	+B	aU	+B	Aq5	)B	Aq5	)B	QE	2B	QE	2B	Aq	B	Aq	Bae45	?? ? ? b"u56	DD D D b"u56	-- - - b"u56	-- - - b"u56	## # #
 q"u-.	?? ? ? r2./	DD D D r2./	-- - - r2./	-- - - r2./	## # #
 ArE23	-- - - BU34	## # # BU34	## # # BU34	DD D D BU34	## # #
 $QU;<	-- - - $Re<=	## # # $Re<=	## # # $Re<=	DD D D $Re<=	## # # Ar"**,-	   B#$	## # # B#$	## # # B#$	-- - - B#$	-- - -r   c                  @    t        t        j                        dk(  sJ y )N
\mathbb{C})r   r#   	Complexesr   r   r   test_latex_Complexesr8    s    ...r   c                  @    t        t        j                        dk(  sJ y )N
\mathbb{N})r   r#   r  r   r   r   test_latex_Naturalsr;        ---r   c                  @    t        t        j                        dk(  sJ y )N\mathbb{N}_0)r   r#   	Naturals0r   r   r   test_latex_Naturals0r@    s    000r   c                  @    t        t        j                        dk(  sJ y )N
\mathbb{Z})r   r#   Integersr   r   r   test_latex_IntegersrD  #  r<  r   c            	      n   t        d      } t        t        t        | | dz        t        j
                              dk(  sJ t        d      }t        t        | |f| |z         h dddh      }t        |      dk(  sJ t        t        | |ff| |z         t        h dddh            }t        |      d	k(  sJ y )
Nr  r
  z2\left\{x^{2}\; \middle|\; x \in \mathbb{N}\right\}r3  >   r  r
  r  r  r  zY\left\{x + y\; \middle|\; x \in \left\{1, 2, 3\right\}, y \in \left\{3, 4\right\}\right\}zm\left\{x + y\; \middle|\; \left( x, \  y\right) \in \left\{1, 2, 3\right\} \times \left\{3, 4\right\}\right\})r$   r   r   r   r#   r  r   )r  r3  imgsets      r   test_latex_ImageSetrG  '  s    sA&AqD/1::67=> > > 	sAfaVQU+YA?F=de e e fq!fYA.
9q!f0MNF=xy y yr   c            	          t        d      } t        t        | t        | dz  d      t        j
                              dk(  sJ t        t        | t        | dz  d      t        j                              dk(  sJ y )Nr  r
  r  z@\left\{x\; \middle|\; x \in \mathbb{R} \wedge x^{2} = 1 \right\}z(\left\{x\; \middle|\; x^{2} = 1 \right\})r$   r   r   r!   r#   r  r	  r  s    r   test_latex_ConditionSetrJ  6  sp    sAaAqD!agg67KL L LaAqD!ann=>34 4 4r   c            
          t        t        t        dd      t        dd      z              dk(  sJ t        t        t        dd      t        ddt        z        z  d	
            dk(  sJ y )Nr  r  r  rF  zX\left\{x + y i\; \middle|\; x, y \in \left[3, 5\right] \times \left[4, 6\right] \right\}r   r  r
  T)polarz\left\{r \left(i \sin{\left(\theta \right)} + \cos{\left(\theta \right)}\right)\; \middle|\; r, \theta \in \left[0, 1\right] \times \left[0, 2 \pi\right) \right\})r   r   r   r   r   r   r   test_latex_ComplexRegionrM  >  sr    x1~hq!n<=>cd d dx1~hq!B$.??tLM	nn n nr   c                  j    t        d      } t        t        | t        j                              dk(  sJ y )Nr  zx \in \mathbb{N})r$   r   r   r#   r  rI  s    r   test_latex_ContainsrO  F  s*    sA!QZZ()-@@@@r   c            	         t        t        t        t        dz  z  t        ddft        ddf            dk(  sJ t        t        t        dz  t        ddf            dk(  sJ t        t        t        dz  t        z   t        ddf            dk(  sJ t        t        t        dz  t        z   t        ddf      dz        dk(  sJ y )	Nr
  r.  r  r  z<\sum_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}z\sum_{x=-2}^{2} x^{2}z&\sum_{x=-2}^{2} \left(x^{2} + y\right)z7\left(\sum_{x=-2}^{2} \left(x^{2} + y\right)\right)^{2})r   r   r  r3  r   r   r   test_latex_sumrQ  K  s    Qq!tVaQZ!R45GH H HQTAr1:&' ! ! !QTAX2qz*+12 2 2QTAX2qz*A-.BC C Cr   c            	      p   t        t        t        t        dz  z  t        ddft        ddf            dk(  sJ t        t        t        dz  t        ddf            dk(  sJ t        t        t        dz  t        z   t        ddf            dk(  sJ t        t        t        t        ddf      dz        dk(  sJ y )	Nr
  r.  r  r  z=\prod_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}z\prod_{x=-2}^{2} x^{2}z'\prod_{x=-2}^{2} \left(x^{2} + y\right)z#\left(\prod_{x=-2}^{2} x\right)^{2})r   r   r  r3  r   r   r   test_latex_productrS  V  s    1a4!RaQZ89HI I IA2qz*+!" " "AAr1:./23 3 3 QAJ'*+./ / /r   c                     t        t        t        t        t                    dk(  sJ t	        d      } t        t         | t              t        d            dk(  sJ t        t         | t              t        dd            dk(  sJ t        t         | t              t        d      dz        dk(  sJ t        t         | t              t        dd	
            dk(  sJ y )Nz\lim_{x \to \infty} xr  r   z#\lim_{x \to 0^+} f{\left(x \right)}-z#\lim_{x \to 0^-} f{\left(x \right)}r
  z4\left(\lim_{x \to 0^+} f{\left(x \right)}\right)^{2}z+-)dirz!\lim_{x \to 0} f{\left(x \right)})r   r   r  r   r   )r  s    r   test_latex_limitsrW  b  s    q!R!%==== 	AqtQ"#'MMMMqtQ3'(./ / / qtQ"A%&?@ @ @ qtQt,-,- - -r   c                     t        t        t                    dk(  sJ t        t        t              d      dk(  sJ t        t        t              t        t              z         dk(  sJ t        t        t              t        t              z   d      dk(  sJ t        t	        t        t              t                    dk(  sJ t        t	        t        t              t              d      dk(  sJ y )	Nz\log{\left(x \right)}T)ln_notationz\ln{\left(x \right)}z-\log{\left(x \right)} + \log{\left(y \right)}z+\ln{\left(x \right)} + \ln{\left(y \right)}z\log{\left(x \right)}^{x}z\ln{\left(x \right)}^{x})r   rD   r  r3  powr   r   r   test_latex_logr[  s  s    Q=4444QT*.EEEEQ#a&!89 9 9Q#a&d367 7 7SVQ $@@@@SVQT2#$ $ $r   c                      t        d      } | t        z   }t        |      dv sJ t        d      } | t        z   }t        |      dv sJ y )Nrz  )z	\beta + xz	x + \betarU   )r$   r  r   )rU   r3  s     r   test_issue_3568r]    sM    (DqA83333'?DqA83333r   c                      t        dt        z  t        dd      z        dk(  sJ t        dt        z  t        dd      z  d      dk(  sJ t        dt        z  t        dd      z  dd	      d
k(  sJ t        dt        z  t
        g      dk(  sJ y )Nr
  r  z8 \sqrt{2} \tau^{\frac{7}{2}}r  r  z<\begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}equationTr  z $$8 \sqrt{2} \mu^{\frac{7}{2}}$$z\left[ \frac{2}{x}, \  y\right])r   r   r   r   r  r3  r   r   r   
test_latexr`    s    !C%(1a.()-MMMM!B$!Q'k:GH H H!B$!Q'jtD+, , ,!A#q?@@@@r   c                      t        d      dt        dz  dt        dt        dz  di} t        |       dk(  sJ t        |       }t        |      dk(  sJ y )Nr  r
  r  r  z;\left\{ 1 : 1, \  x : 3, \  x^{2} : 2, \  x^{3} : 4\right\})r   r  r   r   )r'  r)  s     r   test_latex_dictrb    se    	!aAq!Q1a0A8FG G GQA8FG G Gr   c                  d    t        d      t        d      t        d      g} t        |       dk(  sJ y )Nr_  rA  r!  z)\left[ \omega_{1}, \  a, \  \alpha\right]r$   r   )lls    r   test_latex_listrf    s.    

F3K	9B9DDDDr   c                  l   t        t        j                        dk(  sJ t        t        j                        dk(  sJ t        t        j                        dk(  sJ t        t        j
                        dk(  sJ t        t        j                        dk(  sJ t        t        j                        dk(  sJ y )NGr{  e\phi\piz\text{TribonacciConstant})r   r#   Catalan
EulerGammaExp1GoldenRatioPiTribonacciConstantr   r   r   test_latex_NumberSymbolsrr    s    s""")+++=C7***;&   %%&*FFFFr   c                     t        t        dd             dk(  sJ t        t        dd            dk(  sJ t        t        dd            dk(  sJ t        t        dd             dk(  sJ t        t        dd       t        z        dk(  sJ t        t        dd       t        z  t        dd      t        z  z         d	k(  sJ y )
Nr  r
  z- \frac{1}{2}r  r.  z\frac{1}{2}z- \frac{x}{2}r  z- \frac{x}{2} - \frac{2 y}{3})r   r   r  r3  r   r   r   test_latex_rationalrt    s    (1a.!%5555"a!%5555!R!%5555(2q/!"n444(1a."#'7777(1a."Xb!_Q%667() ) )r   c                  n    t        dt        z        dk(  sJ t        dt        t        z   z        dk(  sJ y )Nr  r  z\frac{1}{x + y}r   r  r3  r   r   r   test_latex_inverserw    s4    1:'''AE1111r   c                  8   t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t        d            dk(  sJ t        t        t        d            dk(  sJ t        t        t        d      dz        dk(  sJ y )Nz\delta\left(x\right)r
  z%\left(\delta\left(x\right)\right)^{2}r   r  z)\delta^{\left( 5 \right)}\left( x \right)z:\left(\delta^{\left( 5 \right)}\left( x \right)\right)^{2})r   rV   r  r   r   r   test_latex_DiracDeltary    s    A#::::A!"&NNNNAq!"&====Aq!"45 5 5Aq!1$%EF F Fr   c                  ~    t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ y )Nz\theta\left(x\right)r
  z%\left(\theta\left(x\right)\right)^{2})r   rW   r  r   r   r   test_latex_Heavisider{    s6    1"99991q!%MMMMr   c                  8   t        t        t        t                    dk(  sJ t        t        t        t        dz               dk(  sJ t        t        t        dz   t                    dk(  sJ t        t	        t        t        t              dd            dk(  sJ y )	Nz\delta_{x y}r  z\delta_{x, y + 1}z\delta_{y, x + 1}r
  Fr   z\left(\delta_{x y}\right)^{2})r   rv   r  r3  r    r   r   r   test_latex_KroneckerDeltar}    s    1%&/9991q5)*.BBBBAq)*.BBBB^Aq)1u=>() ) )r   c                     t        t        t        t        t                    dk(  sJ t        t        t        t        t              dz        dk(  sJ t        t        t        t        t        dz               dk(  sJ t        t        t        t        dz   t                    dk(  sJ t        t        t        dz   t        t                    dk(  sJ y )Nz\varepsilon_{x y z}r
  z$\left(\varepsilon_{x y z}\right)^{2}r  z\varepsilon_{x, y, z + 1}z\varepsilon_{x, y + 1, z}z\varepsilon_{x + 1, y, z})r   rw   r  r3  r5  r   r   r   test_latex_LeviCivitar    s    Aq!$%)????Aq!$a'(/0 0 0Aq!a%()-IIIIAq1ua()-IIIIAE1a()-IIIIr   c                       t         t        z    t               dk(  sJ t         d      dk(  sJ t         d      dk(  sJ t         d      dk(  sJ t         d      d	k(  sJ t        t         fd
       y )Nzx + yplainr  inlinez$x + y$r  z%\begin{equation*}x + y\end{equation*}r_  z#\begin{equation}x + y\end{equation}c                      t         d      S )Nr  r  r   exprs   r   <lambda>ztest_mode.<locals>.<lambda>  s    uT6 r   )r  r3  r   r   
ValueErrorr  s   @r   	test_moder    s    q5D;("""G$000H%333; #KL L L:"HI I I
:67r   c                     t        t        t        t        t                    dk(  sJ t        t        t        t        t                    dk(  sJ t        t        t        t        t              dz        dk(  sJ t        t        t        t        t              dz        dk(  sJ t        t        t        t        t                    dk(  sJ t        t        t        t        t                    dk(  sJ t        t        t        t        t              dz        dk(  sJ t        t        t        t        t              dz        d	k(  sJ y )
NzC\left(x, y, z\right)zS\left(x, y, z\right)r
  zC\left(x, y, z\right)^{2}zS\left(x, y, z\right)^{2}zC^{\prime}\left(x, y, z\right)zS^{\prime}\left(x, y, z\right)z"C^{\prime}\left(x, y, z\right)^{2}z"S^{\prime}\left(x, y, z\right)^{2})r   rf   r  r3  r5  rh   rg   ri   r   r   r   test_latex_mathieur    s    !Q"#'????!Q"#'????!Q"A%&*FFFF!Q"A%&*FFFFq!Q'(,MMMMq!Q'(,MMMMq!Q'*+/TTTTq!Q'*+/TTTTr   c                  :   t        t        t        dk  ft        dz  df      } t        |       dk(  sJ t        | d      dk(  sJ t        t        t        dk  fdt        dk\  f      } t        |       dk(  sJ t        d	d
      \  }}t        |dz  t	        ||      f||z  df      } d}t        |       |k(  sJ t        || z        d|z  k(  sJ t        | |z        d|z  k(  sJ t        t        t        t        dk  ft        dz  t        dk  f            dk(  sJ y )Nr  r
  TzK\begin{cases} x & \text{for}\: x < 1 \\x^{2} & \text{otherwise} \end{cases}r  zM\begin{cases} x & \text{for}\: x \lt 1 \\x^{2} & \text{otherwise} \end{cases}r   zG\begin{cases} x & \text{for}\: x < 0 \\0 & \text{otherwise} \end{cases}A BFcommutativezM\begin{cases} A^{2} & \text{for}\: A = B \\A B & \text{otherwise} \end{cases}zA \left(%s\right)z\left(%s\right) AzM\begin{cases} x & \text{for}\: x < 1 \\x^{2} & \text{for}\: x < 2 \end{cases})rN   r  r   r&   r!   )r0  rU  r  r  s       r   test_latex_Piecewiser    sK   1a!e*q!tTl+A8 8 8 8 8	)) ) ) 	1a!e*q!q&k*A8 8 8 8 85e,DAq1a4Aq"QqS$K0AXA8q==1:-11111:-1111Aq1u:1a!e}56	GG G Gr   c                  P   t        dt        z   t        gt        t        dz
  gg      } t        |       dk(  sJ t        | d      dk(  sJ t        | d      dk(  sJ t        | d	      d
k(  sJ t        | d d	      dk(  sJ t        ddt	        d            }t        |      dk(  sJ y )Nr  z;\left[\begin{matrix}x + 1 & y\\y & x - 1\end{matrix}\right]r  r  zG$\left[\begin{smallmatrix}x + 1 & y\\y & x - 1\end{smallmatrix}\right]$array)mat_strz=\left[\begin{array}{cc}x + 1 & y\\y & x - 1\end{array}\right]bmatrixz=\left[\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}\right])	mat_delimr  z0\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}r  \\left[\begin{array}{ccccccccccc}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right])r   r  r3  r   r  )MM2s     r   test_latex_Matrixr    s    Q
QAJ'(A8FG G G"	.. . . G$HI I II&HI I IdI6;< < < 
2uRy	!B9	HH H Hr   c            	      6   t        d      } t        dt              }t        t         ||             t	         ||             gt	         ||       j                  |             t         ||       j                  |             gg      }d}t        |      |k(  sJ y )Nr  theta1clsa  \left[\begin{matrix}\sin{\left(\theta_{1}{\left(t \right)} \right)} & \cos{\left(\theta_{1}{\left(t \right)} \right)}\\\cos{\left(\frac{d}{d t} \theta_{1}{\left(t \right)} \right)} & \sin{\left(\frac{d}{d t} \theta_{1}{\left(t \right)} \right)}\end{matrix}\right])r&   r   r   rS   rQ   r   r   )r  r  r  expecteds       r    test_latex_matrix_with_functionsr    s    AX8,FVAYVAY0VAY^^A&'VAY^^A->)?@B 	CA)H 8xr   c                  F   t        d      \  } }}}t        t        t        t        fD ]  } ||       }t        |      dk(  sJ  |d| z  |g||gg      } |d| z  ||g      }t        ||      }t        ||      }t        |      dk(  sJ t        |      dk(  sJ t        |      dk(  sJ t        |      dk(  sJ  || |d|z  gg      }	 || g|gd|z  gg      }
 ||
j                         g      }t        |	      dk(  sJ t        |
      d	k(  sJ t        |      d
k(  rJ  y )Nzx y z wr  r  z=\left[\begin{matrix}\frac{1}{x} & y\\z & w\end{matrix}\right]z:\left[\begin{matrix}\frac{1}{x} & y & z\end{matrix}\right]a  \left[\begin{matrix}\left[\begin{matrix}\frac{1}{x^{2}} & \frac{y}{x}\\\frac{z}{x} & \frac{w}{x}\end{matrix}\right] & \left[\begin{matrix}\frac{y}{x} & y^{2}\\y z & w y\end{matrix}\right] & \left[\begin{matrix}\frac{z}{x} & y z\\z^{2} & w z\end{matrix}\right]\end{matrix}\right]a]  \left[\begin{matrix}\left[\begin{matrix}\frac{1}{x^{2}} & \frac{y}{x}\\\frac{z}{x} & \frac{w}{x}\end{matrix}\right] & \left[\begin{matrix}\frac{y}{x} & y^{2}\\y z & w y\end{matrix}\right]\\\left[\begin{matrix}\frac{z}{x} & y z\\z^{2} & w z\end{matrix}\right] & \left[\begin{matrix}\frac{w}{x} & w y\\w z & w^{2}\end{matrix}\right]\end{matrix}\right]zG\left[\left[\begin{matrix}x & y & \frac{1}{z}\end{matrix}\right]\right]z8\left[\begin{matrix}x\\y\\\frac{1}{z}\end{matrix}\right]z_\left[\begin{matrix}\left[\begin{matrix}x\\y\\\frac{1}{z}\end{matrix}\right]\end{matrix}\right])r&   r   r   r   r   r   r   tolist)r  r3  r5  r  	ArrayTyper  M1r  M3MrowMcolumnMcol2s               r   test_latex_NDimArrayr  ,  s   #JAq!Q-/G+-CE (o	 aLQx4AqzAq6*+Aq!}%2q!1a QxLM 	M MRyIJ 	J JRy## 	# # Ry'' 	' ' 1a1+'aS1#!u-.7>>+,-T{VW 	W WW~GH 	H HU|no 	o oO(or   c                  B   t        ddt        z  z  d      dk(  sJ t        ddt        z  z  d      dk(  sJ t        ddt        z  z  d      dk(  sJ t        dt        z  d      d	k(  sJ t        dt        z  d      d
k(  sJ t        dt        z  d      dk(  sJ y )Nr  r(  r  z4 \times 4^{x}r  z4 \cdot 4^{x}ldotz4 \,.\, 4^{x}z
4 \times xz	4 \cdot xz	4 \,.\, xr  r   r   r   test_latex_mul_symbolr  Z  s    1a4G,0AAAA1a4E*.>>>>1a4F+/????1)]:::1'<7771(L888r   c                  l    ddt        d      z  z  } t        |       dk(  sJ t        d| z        dk(  sJ y )Nr  r
  z!4 \cdot 4^{\log{\left(2 \right)}}r  z+\frac{1}{4 \cdot 4^{\log{\left(2 \right)}}})rD   r   )r3  s    r   test_latex_issue_4381r  d  s=    	!SV)A8;;;;1:GGGGr   c                     t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d	            d
k(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d             d!k(  sJ t        t        d"            d#k(  sJ t        t        d$            d#k(  sJ y )%N	beta_13_2z\beta_{13 2}beta_132_20z\beta_{132 20}beta_13z
\beta_{13}x_a_bzx_{a b}x_1_2_3z	x_{1 2 3}x_a_b1zx_{a b1}x_a_1zx_{a 1}x_1_azx_{1 a}zx_1^aaz
x^{aa}_{1}x_1__aazx_11^az
x^{a}_{11}x_11__a	x_a_a_a_azx_{a a a a}z	x_a_a^a^azx^{a a}_{a a}x_a_a__a__aalpha_11z\alpha_{11}alpha_11_11z\alpha_{11 11}alpha_alphaz\alpha_{\alpha}zalpha^alephz\alpha^{\aleph}alpha__alephr   r$   r   r   r   test_latex_issue_4576r  j  s   $%888&'+<<<<	"#}444!Z///	"#|333!"k111!Z///!Z///!"m333	"#}444!"m333	"#}444$%777$%)9999&'+;;;;
#$666&'+<<<<&'+====&'+===='(,>>>>r   c                      t        d      } dt        t        |        dz        j                  dd      v sJ dt        d|  z  dz        j                  dd      v sJ y )Nr  ze^{-x}r
    z3^{-x}r  )r$   r   rC   replacerI  s    r   test_latex_pow_fractionr    s`    sAc1"gai(00b9999 a!eAg..sB7777r   c                      t        dd      \  } }}t        | |z  |dz  z        dk(  sJ t        |dz  | z  |z        dk(  sJ t        | |dz  z  |z        dk(  sJ y )NzA,B,CFr  r  z
A B C^{-1}z
C^{-1} A Bz
A C^{-1} Brr  rU  r  r(  s      r   test_noncommutativer    sq    g51GAq!1QU},,,Bq},,,1b5},,,r   c                      t         dz  t         dz  t        z  z   t        dz  z   dt         z  t        dz  z  z   } t        | d      dk(  sJ t        | d      dk(  sJ t        | d	      d
k(  sJ y )Nr  r
  r  lexr%  z#x^{3} + x^{2} y + 3 x y^{3} + y^{4}zrev-lexz#y^{4} + 3 x y^{3} + x^{2} y + x^{3}nonez#x^{3} + y^{4} + y x^{2} + 3 x y^{3})r  r3  r   r  s    r   test_latex_orderr    s    a4!Q$q&=1a4!A#ad(*DU#'MMMMI"HI I IV$(NNNNr   c                      t        t        t        t        dz               dk(  sJ t        t        t        t        ft        dz               dk(  sJ t        t        t        t                    dk(  sJ y )Nr  z\left( x \mapsto x + 1 \right)z2\left( \left( x, \  y\right) \mapsto x + 1 \right)z\left( x \mapsto x \right))r   r   r  r3  r   r   r   test_latex_Lambdar    s^    1q5!"&GGGGAA&'+````1"????r   c                     t        dt              \  } }}t        d|       \  }}}}t        ||z
        dk(  sJ t        |dz
        dk(  sJ t        |dz         dk(  sJ t        |dz  d|z  |z  z   dz   |dz  z  |z  |z   dz         d	k(  sJ t        |dz  d|z  |z  z   dz   |dz  z  |z  |dz   |z  z         d
k(  sJ t        |dz  d|z  |z  z   dz   |dz  z  |z  |dz   |z  z   dz         dk(  sJ t        |dz   d|z  |z  z   dz
  |dz  z  |z  |dz   |z  z
  dz
        dk(  sJ t        |dz  |z   dz    |z  d|z  |z  z   dz         dk(  sJ t        |dz  |z   dz    |z  d|z  |z  z
  dz         dk(  sJ y )Nu,vzx,y,z0r  x - 1r	  r
  r  z2\left({u}^{2} + 3 u v + 1\right) {x}^{2} y + u + 1zA\left({u}^{2} + 3 u v + 1\right) {x}^{2} y + \left(u + 1\right) xzE\left({u}^{2} + 3 u v + 1\right) {x}^{2} y + \left(u + 1\right) x + 1zF-\left({u}^{2} - 3 u v + 1\right) {x}^{2} y - \left(u + 1\right) x - 1z+-\left({v}^{2} + v + 1\right) x + 3 u v + 1z+-\left({v}^{2} + v + 1\right) x - 3 u v + 1)r   r   r   )RuvuvRxyzr  r3  r5  s          r   test_latex_PolyElementr    s#   UBICA#&MD!QQ<4Q<8###Q<8###!Q$1Q,"AqD(*Q.23=> > >!Q$1Q,"AqD(*a!eQY67LM M M!Q$1Q,"AqD(*a!eQY6:;PQ Q Q1a4%!A#a%-!#QT)!+q1uai7!;<QR R R 1a4!8a<"QqSU*Q./67 7 71a4!8a<"QqSU*Q./67 7 7r   c                  b   t        dt              \  } }}t        d|       \  }}}}}t        ||z
        dk(  sJ t        |dz
        dk(  sJ t        |dz         dk(  sJ t        |dz        dk(  sJ t        ||z        d	k(  sJ t        ||z  |z        d
k(  sJ t        |||z  z        dk(  sJ t        ||z  ||z  z        dk(  sJ t        |dz
  |z        dk(  sJ t        |dz   |z        dk(  sJ t        | dz
  |z        dk(  sJ t        |dz   ||z  z        dk(  sJ t        | |dz   z        dk(  sJ t        ||z  |dz   z        dk(  sJ t        |dz   |z  |z  dz   |dz
  |z  dz
  z        dk(  sJ t        |dz   |z  |z  dz   |dz
  |z  ||z  |z  z
  dz
  z        dk(  sJ y )Nr  zx,y,z,tr  r  r  r	  r  z\frac{x}{3}z\frac{x}{z}z\frac{x y}{z}z\frac{x}{z t}z\frac{x y}{z t}z\frac{x - 1}{y}z\frac{x + 1}{y}z\frac{-x - 1}{y}z\frac{x + 1}{y z}z\frac{-y}{x + 1}z\frac{y z}{x + 1}z;\frac{\left(u + 1\right) x y + 1}{\left(v - 1\right) z - 1}zC\frac{\left(u + 1\right) x y + 1}{\left(v - 1\right) z - u v t - 1})r   r   r   )Fuvr  r  Fxyztr  r3  r5  r  s           r   test_latex_FracElementr    s-   eR ICAi-E1aAQ<4Q<8###Q<8###1:'''1:'''1Q<++++AaC>----1ac1111!a%1111!a%11111"q&! 3333!a%!A##7777!QU 33331a!e!55551q5!)A+/QUAIM23FG G G1q5!)A+/QUAI!A$5$9:;NO O Or   c                     t        t        t        dz  dt        z  z   t                    dk(  sJ t        t        t        t        z  t                    dk(  sJ t        t        dt        z  t        z               dk(  sJ y )Nr
  zE\operatorname{Poly}{\left( x^{2} + 2 x, x, domain=\mathbb{Z} \right)}zU\operatorname{Poly}{\left( \frac{1}{y} x, x, domain=\mathbb{Z}\left(y\right) \right)}g       @zJ\operatorname{Poly}{\left( 2.0 x + 1.0 y, x, y, domain=\mathbb{R} \right)})r   r   r  r3  r   r   r   test_latex_Polyr    s    adQUlA&'PQ Q Qac1`a a ac!eai!UV V Vr   c            
         t        t        t        dt        dt        dgt
                    dk(  sJ t        t        t        dt        t        z   ddgt
                    dk(  sJ t        t        t        t
        dz  z  t
        dz  t        z  z   t
        t        z  z
  t        t        dz  z  z
  t        t
        z  t        dz  z  z
  t        z   t        t
        z  z
  t        z   t
        t        f            dk(  sJ y )Nr  r
  r  z{\operatorname{Poly}{\left( a x^{5} + x^{4} + b x^{3} + 2 x^{2} + c x + 3, x, domain=\mathbb{Z}\left[a, b, c\right] \right)}z\operatorname{Poly}{\left( a x^{4} + x^{3} + \left(b + c\right) x^{2} + 2 x + 3, x, domain=\mathbb{Z}\left[a, b, c\right] \right)}z\operatorname{Poly}{\left( a x^{3} + x^{2}y -  b xy^{2} - xy -  a x -  c y^{3} + y + b, x, y, domain=\mathbb{Z}\left[a, b, c\right] \right)})r   r   rA  r  r  r  r3  r   r   r   test_latex_Poly_orderr    s    q!Q1a(!,-	EE E E q!QqS!Q'+,	NN N N a1fq!tAvo!+a1f4qs1a4x?!CacIAM!f 	XX X Xr   c                  Z    t        t        t        dz  t        z   dz   d            dk(  sJ y )Nr  r  r   z6\operatorname{CRootOf} {\left(x^{5} + x + 3, 0\right)})r   r   r  r   r   r   test_latex_ComplexRootOfr    s2    1q1a()AB B Br   c                  b    t        t        t        dz  t        z   dz   t                    dk(  sJ y )Nr  r  zc\operatorname{RootSum} {\left(x^{5} + x + 3, \left( x \mapsto \sin{\left(x \right)} \right)\right)})r   r   r  rS   r   r   r   test_latex_RootSumr    s2    AAs+,no o or   c                  &    t        t        d        y )Nc                  2    t        t        t        z  d      S )Ngarbage)methodrv  r   r   r   r  ztest_settings.<locals>.<lambda>  s    eAaC	: r   )r   	TypeErrorr   r   r   test_settingsr    s    
9:;r   c                  T   t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t        t                    d	k(  sJ t        t        t              dz        d
k(  sJ t        t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t        t                    dk(  sJ t        t        t        t        t        t        f            dk(  sJ t        t        t              dz        dk(  sJ t        t        t        t              dz        dk(  sJ t        t        t        t        t        t        f      dz        dk(  sJ t        t        t                    dk(  sJ t        t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ t        t        t        t              dz        dk(  sJ t        t        t                    dk(  sJ t        t        t              dz        dk(  sJ y )NzC_{n}r
  z	C_{n}^{2}zB_{n}zB_{n}\left(x\right)z	B_{n}^{2}zB_{n}^{2}\left(x\right)zG_{n}zG_{n}\left(x\right)z	G_{n}^{2}zG_{n}^{2}\left(x\right)zB_{n, m}\left(x, y\right)zB_{n, m}^{2}\left(x, y\right)zF_{n}zF_{n}\left(x\right)z	F_{n}^{2}zF_{n}^{2}\left(x\right)zL_{n}z	L_{n}^{2}zT_{n}r  z	T_{n}^{2}zT_{n}^{2}\left(x\right)z\mu\left(n\right)z\mu^{2}\left(n\right))r   r/   rB  r-   r  r1   r.   r  r3  r3   r2   r4   r7   r   r   r   test_latex_numbersr    s   (((Q<///1(***1a!%;;;;1q!\1111a!#$(BBBB!)))!Q $::::!a L000!Q"#'AAAAa>X%%%a 6666aQF#$(DDDDa!,,,aQ#====aQF#Q&'+KKKK1(***1a!%;;;;1q!\1111a!#$(BBBBq?h&&&q1---A8+++Aq!"&<<<<A!"l222Aq!1$%)CCCC3333A"::::r   c                      t        t        t                    dk(  sJ t        t        t        t                    dk(  sJ t        t        t        t              dz        dk(  sJ y )NzE_{n}zE_{n}\left(x\right)r
  zE_{n}^{2}\left(x\right))r   r0   rB  r  r   r   r   test_latex_eulerr    sP    q?h&&&q!!7777q!a $>>>>r   c                  h    t        t        d            dk(  sJ t        t        d            dk(  sJ y )Nlamda\lambdaLamda\Lambdar  r   r   r   
test_lamdar    s0    !Z///!Z///r   c                     t        d      } t        d      }t        |       dk(  sJ t        | | di      dk(  sJ t        | |z   | di      dk(  sJ t        | dz  | di      dk(  sJ t        | |z   | d|di      d	k(  sJ y )
Nr  r3  r)  r*  zx_i + yr
  zx_i^{2}y_jz	x_i + y_jrd  r  r3  s     r   test_custom_symbol_namesr  $  s    sAsA8t!U,666QaZ0J>>>AQJ/:===Qa5%9:lJJJr   c            	      0   t        ddd      } t        ddd      }t        d      }t        ddd      }t        | d|z  z
        dv sJ t        | d|z  z         d	v sJ t        |d| z  z
        d
v sJ t        |d| z  z         dv sJ t        ||z  | |j                  z   ||j                  z   z  z
        dk(  sJ t        t	        t	        ||      t	        ||                  dk(  sJ t        t        t        ||      t        ||                  dk(  sJ y )Nr(  r  r  rB  rx  r  r
  )z	- 2 B + CzC -2 B)z2 B + CzC + 2 B)zB - 2 Cz	- 2 C + B)zB + 2 Cz2 C + Bz5n h - \left(- h + h^{T}\right) \left(h + h^{T}\right)z'\left(h + h\right) + \left(h + h\right)z!\left(h h\right) \left(h h\right))r   r&   r   Tr   r   )r(  r  rB  rx  s       r   test_matAddr  .  s#   S!QAS!QAAS!QAQqS>6666QqS>5555QqS>7777QqS>5555Q1"qss(q133w//04ooooq!fQl348eeeeq!fQl348____r   c                     t        ddd      } t        ddd      }t        d      }t        d| z        dk(  sJ t        d|z  | z        dk(  sJ t        d| z        d	k(  sJ t        d
| z        dk(  sJ t        t        d      | z        dk(  sJ t        t        d       | z        dk(  sJ t        dt        d      z  |z  | z        dk(  sJ t        d| z  | d|z  z   z        dv sJ y )NrU  r  r  r  r
  z2 Az2 x Ar.  z- 2 Ar  z1.5 Az
\sqrt{2} Az- \sqrt{2} Az2 \sqrt{2} x A)z- 2 A \left(A + 2 B\right)z- 2 A \left(2 B + A\right))r   r$   r   rM   )rU  r  r  s      r   test_matMulr  ?  s   S!QAS!QAsA1:1Q<8###A;("""Q<8###a},,,$q'!///471Q#4444Aq1Q3w  %G G G Gr   c            	         t        dd      } t        d      \  }}}}}t        d| |       }t        ddd      }t        ddd      }t        t	        |d	d	            d
k(  sJ t        |||dz   ||dz   f         dk(  sJ t        |||dz   d||dz   df         dk(  sJ t        |d ||d f         dk(  sJ t        |d ||d f         dk(  sJ t        ||d d |f         dk(  sJ t        |||||f         dk(  sJ t        |||||||f         dk(  sJ t        ||d ||d |f         dk(  sJ t        |d ||d ||f         dk(  sJ t        |d d |d d |f         dk(  sJ t        t	        |dd            d
k(  sJ t        t	        |d | d fd | d f            d
k(  sJ t        t	        |d| d fd| d f            d
k(  sJ t        t	        |d| dfd| df            dk(  sJ t        |ddddddf         dk(  sJ t        |ddddddf         dk(  sJ t        |ddd         d k(  sJ t        |d ddd!df         d"k(  sJ t        |d ddddf         d#k(  sJ t        |dd ddf         d$k(  sJ t        |ddddf         d%k(  sJ t        |ddddddf         d&k(  sJ t        ||z   dd dd f         d'k(  sJ y )(NrB  Tr   z	x y z w tXYr  Z)NNNzX\left[:, :\right]r  zX\left[x:x + 1, y:y + 1\right]r
  z"X\left[x:x + 1:2, y:y + 1:2\right]zX\left[:x, y:\right]zX\left[x:, :y\right]zX\left[x:y, z:w\right]zX\left[x:y:t, w:t:x\right]zX\left[x::y, t::w\right]zX\left[:x:y, :t:w\right]zX\left[::x, ::y\right])r   NNr   zX\left[::2, ::2\right]r  r  r  rF  zX\left[1:2:3, 4:5:6\right]   zX\left[1:3:5, 4:6:8\right]zX\left[1:10:2, :\right]	   zY\left[:5, 1:9:2\right]zY\left[:5, 1::2\right]zY\left[5:6, :5:2\right]zX\left[:1, :1\right]zX\left[:1:2, :1:2\right]z%\left(Y + Z\right)\left[2:, 2:\right])r$   r&   r   r   r   )	rB  r  r3  r5  r  r  r  r  r   s	            r   test_latex_MatrixSlicer  N  s   sD!A[)NAq!QS!QAS"b!AS"b!AQ 24FGHLaaaa1QU7Aa!eG#$%)JJJJ1QU19aAai'()-RRRR2A2qr666662A2qr6666612rr666661Q3!8!::::1Qq5!Aa%<!%BBBB14a4A:#>>>>4Aa4!A:#>>>>3Q3!8!::::QABF[[[[Qq$$4ABF[[[[QAtq!Tl;<@UUUUQAq	Aq!956:SSSS1Qq5!Aa%<!%BBBB1Qq5!Aa%<!%BBBB1R699992A2q1u9"<<<<2A2qAv:#<<<<1dqd7 ::::1Q3!8!88881Qq5!Aa%<!%@@@@!a%QR!%MMMMr   c            	         ddl m} m}m}m}m} ddlm}  | ddd      }t         ||dkD              dk(  sJ  |dd      }t         ||d	kD              d
k(  sJ  |dd      } |dd      }	t         |t        ||	            j                        dk(  sJ t         |t        t              t        dd                  dk(  sJ y )Nr   )r   DieExponentialpspacewhere)RandomDomainr  r  z.\text{Domain: }0 < x_{1} \wedge x_{1} < \inftyd1rF  r  z'\text{Domain: }d_{1} = 5 \vee d_{1} = 6rA  r  zK\text{Domain: }0 \leq a \wedge 0 \leq b \wedge a < \infty \wedge b < \inftyr
  z7\text{Domain: }\left\{x\right\} \in \left\{1, 2\right\})sympy.statsr   r  r  r  r  sympy.stats.rvr	  r   r   domainr   r  )
r   r  r  r  r  r	  r  r)  rU  r  s
             r   test_latex_RandomDomainr  o  s    CC+tQAq1u"SSSSD!Aq1u"LLLLCACAuQ{""$VW W W ilIaO<=BC C Cr   c                  v   ddl m}  | j                  t        t              }| t        t        f   }t        |j                  t        t        t        z   z              t        t        t        t        z   z        k(  sJ t        |j                  t        t        z               t        t        t        z         k(  sJ y )Nr   QQ)sympy.polys.domainsr  
frac_fieldr  r3  r   convert)r  Fr  s      r   test_PrettyPolyr    s{    &
aA
1a4A1a!e9%&%1q5	*::::1q5!"eAEl222r   c            	         t        d      } t        d      }t        d      }t        d      }t        d      }t        t         ||       | |            dk(  sJ t        t	         ||      || ||            dk(  sJ t        t         ||       | |            dk(  sJ t        t         ||      || ||f            d	k(  sJ t        t         ||       | |            d
k(  sJ t        t         ||      ||             dk(  sJ t        t         ||       | |            dk(  sJ t        t         ||      ||             dk(  sJ t        t         ||       | |            dk(  sJ t        t         ||      ||             dk(  sJ y )Nr  r;  r  rA  r  z<\mathcal{M}_{x}\left[f{\left(x \right)}\right]\left(k\right)zA\mathcal{M}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z<\mathcal{L}_{x}\left[f{\left(x \right)}\right]\left(k\right)zA\mathcal{L}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z<\mathcal{F}_{x}\left[f{\left(x \right)}\right]\left(k\right)zA\mathcal{F}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z>\mathcal{COS}_{x}\left[f{\left(x \right)}\right]\left(k\right)zC\mathcal{COS}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z>\mathcal{SIN}_{x}\left[f{\left(x \right)}\right]\left(k\right)zC\mathcal{SIN}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right))r$   r   r   r   r   r   r   r   r   r~   r   r   r   )r  r;  r  rA  r  s        r   test_integral_transformsr    s   sAsAAsAsA1q!,-GH H H'!aAq9:LM M M !!A$1-.GH H H(1q!aV<=LM M M !!A$1-.GH H H(1q!45LM M M 1q!,-IJ J J'!a34NO O O qtQ*+IJ J J%adAq12NO O Or   c                      ddl m}  t        | j                  t        t
                    dk(  sJ t        | j                  t        t
        d            dk(  sJ y )Nr   r  z\mathbb{Q}\left[x, y\right]ilexr%  z#S_<^{-1}\mathbb{Q}\left[x, y\right])r  r  r   old_poly_ringr  r3  r  s    r   test_PolynomialRingBaser    sR    &!!!Q'(,JJJJ!!!Qf!56./ / /r   c                     ddl m} m}m}m}m}m}  | d      } | d      } | d      } |||d      }	 |||d      }
 ||      } |d      }t        |      d	k(  sJ t        |	      d
k(  sJ t        |      dk(  sJ t        |
|	z        dk(  sJ t        |      dk(  sJ  |       }t        |      dk(  sJ  ||	d|
t        j                  i      }t        |      dk(  sJ  ||	d|
t        j                  i|
|	z  di      }t        |      dk(  sJ  | d      } | d      } | d      } |||d      } |||d      } |||g      } ||      }t        |      dk(  sJ y )Nr   )ObjectIdentityMorphismNamedMorphismCategoryDiagramDiagramGridA1A2A3f1f2K1zA_{1}zf_{1}:A_{1}\rightarrow A_{2}zid:A_{1}\rightarrow A_{1}z'f_{2}\circ f_{1}:A_{1}\rightarrow A_{3}z\mathbf{K_{1}}r  uniquea'  \left\{ f_{2}\circ f_{1}:A_{1}\rightarrow A_{3} : \emptyset, \  id:A_{1}\rightarrow A_{1} : \emptyset, \  id:A_{2}\rightarrow A_{2} : \emptyset, \  id:A_{3}\rightarrow A_{3} : \emptyset, \  f_{1}:A_{1}\rightarrow A_{2} : \left\{unique\right\}, \  f_{2}:A_{2}\rightarrow A_{3} : \emptyset\right\}a  \left\{ f_{2}\circ f_{1}:A_{1}\rightarrow A_{3} : \emptyset, \  id:A_{1}\rightarrow A_{1} : \emptyset, \  id:A_{2}\rightarrow A_{2} : \emptyset, \  id:A_{3}\rightarrow A_{3} : \emptyset, \  f_{1}:A_{1}\rightarrow A_{2} : \left\{unique\right\}, \  f_{2}:A_{2}\rightarrow A_{3} : \emptyset\right\}\Longrightarrow \left\{ f_{2}\circ f_{1}:A_{1}\rightarrow A_{3} : \left\{unique\right\}\right\}rU  r  r(  r  rw  z-\begin{array}{cc}
A & B \\
 & C 
\end{array}
)
sympy.categoriesr  r  r   r!  r"  r#  r   r#   r  )r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  id_A1r)  r'  rU  r  r(  r  rw  grids                       r   test_categoriesr.    s   / / 
B	B	B	r2t	$B	r2t	$BR E	$B9   97777<7777B<EEEE9))))	A8|###Xr1::./A8 ? ? ? ? 	Xr1::.b(0CDA8 = = = = 	sAsAsAaC AaC AAAq>D;    r   c                     ddl m}  ddlm} | j	                  t
        t              }|j                  d      }|j                  t
        t        gdt
        dz  g      }t        |      dk(  sJ t        |      dk(  sJ |j                  t
        dz  t              }t        |      dk(  sJ ||z  }t        |      d	k(  sJ t        |j                  dt
        d
z  dz  gdt        g            dk(  sJ  || j	                  t
              j                  d      | j	                  t
              j                  d      ddg      }t        |      dk(  sJ y )Nr   r  )homomorphismr
  r  z!{\mathbb{Q}\left[x, y\right]}^{2}zP\left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\ranglez&\left\langle {x^{2}},{y} \right\ranglezz\frac{{\mathbb{Q}\left[x, y\right]}^{2}}{\left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle}r  a  \left\langle {{\left[ {1},{\frac{x^{3}}{2}} \right]} + {\left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle}},{{\left[ {2},{y} \right]} + {\left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle}} \right\ranglez}{\left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]} : {{\mathbb{Q}\left[x\right]}^{2}} \to {{\mathbb{Q}\left[x\right]}^{2}})r  r  sympy.polys.agcar0  r  r  r3  free_module	submoduler   ideal)r  r0  r  r  r  r   Qrx  s           r   test_Modulesr6    sf   &-
AA	aA	QFQ1I&A8;;;;8[\ \ \ 	
1aA8@@@@	AA8	DD D D aAa[1a&12	WW W W 	R%%a(44Q7%%a(44Q7!Q	AA 8	QQ Q Qr   c                      ddl m}  | j                  t              t        dz  dz   gz  }t	        |      dk(  sJ t	        |j
                        dk(  sJ y )Nr   r  r
  r  zG\frac{\mathbb{Q}\left[x\right]}{\left\langle {x^{2} + 1} \right\rangle}z.{1} + {\left\langle {x^{2} + 1} \right\rangle})r  r  r  r  r   one)r  r  s     r   test_QuotientRingr9    sW    &
QTAXJ&A8RS S S<LLLLr   c                  `    t        dd      \  } }t        | |z        }t        |      dk(  sJ y )Nr  Fr  z!\operatorname{tr}\left(A B\right))r&   r   r   )rU  r  r  s      r   test_Trr;    s2    5e,DAq
1Q3A8;;;;r   c                  r   ddl m} m}m}m}m} t        d      }t         | |            dk(  sJ t         |  ||                  dk(  sJ t        ddd      }t         | |            dk(  sJ t         | ||z               d	k(  sJ t         |  | |dd      |f| |dd      ff                  d
k(  sJ y )Nr   )DeterminantInverseBlockMatrix	OneMatrix
ZeroMatrixr  )r  r  z5\left|{\begin{matrix}1 & 2\\3 & 4\end{matrix}}\right|zG\left|{\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]^{-1}}\right|r  r
  z\left|{X}\right|zF\left|{\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] + X}\right|zg\left|{\begin{matrix}1 & X\\\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] & 0\end{matrix}}\right|)	sympy.matricesr=  r>  r?  r@  rA  r   r   r   )r=  r>  r?  r@  rA  r  r  s          r   test_DeterminantrD    s    WW AQ $aaaaWQZ()YZ Z ZS!QAQ $8888QU#$XY Y Y[9Q?A*>+,jA.>*?*A B C D}~ ~ ~r   c                  Z   ddl m} m}m} t	        ddd      }t	        ddd      }t         | |            dk(  sJ t         | ||z               dk(  sJ t         | |       | |      z         dk(  sJ t         | ||z              d	k(  sJ t         | |       | |      z        d
k(  sJ t         | |dz              dk(  sJ t         | |      dz        dk(  sJ t         |  ||                  dk(  sJ t         | | |                  dk(  sJ t         |  ||                  dk(  sJ t         | | |                  dk(  sJ t         | | |      |z               dk(  sJ t        d      }t         | |            dk(  sJ t         | ||z               dk(  sJ ddl m}m}m	} t         |  | |dd      |f| |dd      ff                  dk(  sJ t	        ddd      }	t         | |	            dk(  sJ t         | |      d      dk(  sJ t         | ||z         d      dk(  sJ t         | |       | |      z   d      dk(  sJ t         | |       | |      z        d
k(  sJ t         | |dz        d      dk(  sJ t         | |      dz  d      d k(  sJ y )!Nr   )Adjointr>  	Transposer  r
  r  zX^{\dagger}z\left(X + Y\right)^{\dagger}zX^{\dagger} + Y^{\dagger}z\left(X Y\right)^{\dagger}zY^{\dagger} X^{\dagger}z\left(X^{2}\right)^{\dagger}z\left(X^{\dagger}\right)^{2}z\left(X^{-1}\right)^{\dagger}z\left(X^{\dagger}\right)^{-1}z\left(X^{T}\right)^{\dagger}z\left(X^{\dagger}\right)^{T}z \left(X^{\dagger} + Y\right)^{T}rB  z=\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]^{\dagger}zN\left(\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] + X\right)^{\dagger}r?  r@  rA  zo\left[\begin{matrix}1 & X\\\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] & 0\end{matrix}\right]^{\dagger}M^xz\left(M^{x}\right)^{\dagger}star)adjoint_stylezX^{\ast}	hermitianz\left(X + Y\right)^{\mathsf{H}}daggerz\left(X^{2}\right)^{\ast}z\left(X^{\mathsf{H}}\right)^{2})
rC  rF  r>  rG  r   r   r   r?  r@  rA  )
rF  r>  rG  r  r  r  r?  r@  rA  Mxs
             r   test_AdjointrO  -  s   ::S!QAS!QA...Q $CCCCgaj()-IIII1"????GAJ&'+EEEEA#BBBBQ#BBBB$%)IIII$%)IIII1&'+JJJJ71:&'+JJJJ71:>*+/RRRR A ffff1ab b bAAyA&:'(*Q*:&;&= > ? @ 	GG G G 
eQ	"B!@@@@ 62kAAAQ{;?aaaagaj(AEaaaaGAJ&'+EEEEAf59UUUUQk:>````r   c                     ddl m} m}m} t	        ddd      }t	        ddd      }t         | |            dk(  sJ t         | ||z               dk(  sJ t         |  ||d                  dk(  sJ t         | | |      d            d	k(  sJ t         |  ||d                  d
k(  sJ t         | | |      d            dk(  sJ t        d      }t         | |            dk(  sJ t         | ||z               dk(  sJ ddl m}m}m	} t         |  | |dd      |f| |dd      ff                  dk(  sJ t	        ddd      }	t         | |	            dk(  sJ y )Nr   )rG  MatPowHadamardPowerr  r
  r  zX^{T}z\left(X + Y\right)^{T}z\left(X^{\circ {2}}\right)^{T}z\left(X^{T}\right)^{\circ {2}}z\left(X^{2}\right)^{T}z\left(X^{T}\right)^{2}rB  z7\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right]^{T}zH\left(\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] + X\right)^{T}rH  zi\left[\begin{matrix}1 & X\\\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] & 0\end{matrix}\right]^{T}rI  z\left(M^{x}\right)^{T})
rC  rG  rQ  rR  r   r   r   r?  r@  rA  )
rG  rQ  rR  r  r  r  r?  r@  rA  rN  s
             r   test_TransposerS  Q  s   ??S!QAS!QA1(***1q5!"&????=A./04UUUUy|Q/04UUUU6!Q<()-FFFF	!a()-FFFF A1"aaaa1Q3 Z[ [ [AA;1a!(<)*Jq!,<(=(? @ A B@ @ @ 
eQ	"B2#<<<<r   c                  L   ddl m} m} ddlm}m}m} t        ddd      }t        ddd      }t         | |||z              dk(  sJ t         | ||      |z        dk(  sJ t         ||d            d	k(  sJ t         ||d
            dk(  sJ t         | |||      d            dk(  sJ t         | |||      d            dk(  sJ t         | ||d
      d
            dk(  sJ t         | ||d
      d
            dk(  sJ t         ||t        dz               dk(  sJ y )Nr   )HadamardProductrR  )r   r   rQ  r  r
  r  zX \circ Y^{2}z\left(X \circ Y\right) YzX^{\circ {2}}r  zX^{\circ \left({-1}\right)}z\left(X + Y\right)^{\circ {2}}z\left(X Y\right)^{\circ {2}}z-\left(X^{-1}\right)^{\circ \left({-1}\right)}z-\left(X^{\circ \left({-1}\right)}\right)^{-1}r  zX^{\circ \left({n + 1}\right)})
rC  rU  rR  sympy.matrices.expressionsr   r   rQ  r   r   rB  )rU  rR  r   r   rQ  r  r  s          r   test_HadamardrW  i  sb   =AAS!QAS!QAAaC()-====A&q()-HHHHq!$%)9999q"%&*HHHHva|Q/0)* * *va|Q/0'( ( ( va}b1289 9 9a,b1289 9 9 q!A#&')* * *r   c                     ddl m}  t        ddd      }t        ddd      }t         | |d            dk(  sJ t         | ||z  d            dk(  sJ t         | ||z  d            dk(  sJ t         | ||z   d            d	k(  sJ t         | ||z   d            d
k(  sJ t        ddd      }t         | |d            dk(  sJ y )Nr   )rQ  r  r
  r  zX^{2}z\left(X^{2}\right)^{2}z\left(X Y\right)^{2}z\left(X + Y\right)^{2}z\left(2 X\right)^{2}rI  z\left(M^{x}\right)^{2})rV  rQ  r   r   )rQ  r  r  rN  s       r   test_MatPowrY    s    1S!QAS!QA1')))!Q $>>>>!Q $<<<<Aq!"&@@@@Aq!"&>>>>	eQ	"BA#<<<<r   c                      t        ddd      } | j                  | z  j                  t              }t	        |      dk(  sJ | j                  t        t        dt        z              }t	        |      dk(  sJ y )Nr  r
  zN{\left( d \mapsto \sin{\left(d \right)} \right)}_{\circ}\left({X^{T} X}\right)r  z>{\left( x \mapsto \frac{1}{x} \right)}_{\circ}\left({X}\right))r   r  	applyfuncrS   r   r   r  )r  r  s     r   test_ElementwiseApplyFunctionr\    sf    S!QACCES!D;kkkk;;va1~&D;[[[[r   c                  t    ddl m}  t         | dd      d      dk(  sJ t         | dd      d      dk(  sJ y )	Nr   rA  r  r  mat_symbol_styler  boldz
\mathbf{0})"sympy.matrices.expressions.specialrA  r   r^  s    r   test_ZeroMatrixrc    s=    =Aq!G<DDDAq!F;}LLLr   c                  t    ddl m}  t         | dd      d      dk(  sJ t         | dd      d      d	k(  sJ y )
Nr   r@  r  r  r  r_  1ra  z
\mathbf{1})rb  r@  r   re  s    r   test_OneMatrixrg    s;    <1a7;tCCC1a6:mKKKr   c                  p    ddl m}  t         | d      d      dk(  sJ t         | d      d      dk(  sJ y )	Nr   Identityr  r  r_  z
\mathbb{I}ra  z
\mathbf{I})rb  rj  r   ri  s    r   test_Identityrk    s7    ;!w7=HHH!v6-GGGr   c                  t    ddl m} m} t         | d            dk(  sJ t         |t                    dk(  sJ y )Nr   DFTIDFTr  z\text{DFT}_{13}z\text{IDFT}_{x})"sympy.matrices.expressions.fourierrn  ro  r   r  rm  s     r   test_latex_DFT_IDFTrq    s3    <R>////a>////r   c                      t        d      } t        |  }t        |      dk(  sJ t        |  }t        |      dk(  sJ t	        |  }t        |      dk(  sJ t        |  }t        |      dk(  sJ y )Nza:fz.a \wedge b \wedge c \wedge d \wedge e \wedge fz$a \vee b \vee c \vee d \vee e \vee fz[a \Leftrightarrow b \Leftrightarrow c \Leftrightarrow d \Leftrightarrow e \Leftrightarrow fz3a \veebar b \veebar c \veebar d \veebar e \veebar f)r&   r   r   r   r   r   )symsr  s     r   test_boolean_args_orderrt    s    5>D:D;KKKKt9D;AAAAtD;fg g g :D;>? ? ?r   c                  :    t        d      } t        |       dk(  sJ y )Nr  rV  )rM   r   )rV  s    r   test_imaginaryrv    s    RA8tr   c                      t        t              dk(  sJ t        t              dk(  sJ t        t              dk(  sJ t        t              dk(  sJ t        t
              dk(  sJ t        t              dk(  sJ y )Nz\sinz\cosz\tanz\logz\operatorname{Ei}\zeta)r   rS   rQ   rT   rD   r^   r|   r   r   r   test_builtins_without_argsry    so    :   :   :   :   9,,,,;("""r   c                     t        d      } t        |       dk(  sJ t         | t                    dk(  sJ t        d      } t        |       dk(  sJ t        d      } t        |       dk(  sJ t         | t                    dk(  sJ t        d	      }t        |      d
k(  sJ t        d      }t         |t                    dk(  sJ t        |      dk(  sJ y )NAlpha
\mathrm{A}z\mathrm{A}{\left(x \right)}Beta
\mathrm{B}Eta
\mathrm{H}z\mathrm{H}{\left(x \right)}rp  \Pichiz\chi{\left(x \right)}\chir   r   r  )r  r0  r  s      r   test_latex_greek_functionsr    s     	A8}$$$1;8888A8}$$$A8}$$$1;8888 	A8v 	A1;22228wr   c                      d} t        |       dk(  sJ d} t        |       dk(  sJ d} t        |       dk(  sJ d} t        |       dk(  sJ d	} t        |       d
k(  sJ d} t        |       dk(  sJ d} t        |       dk(  sJ y )Nr{  r|  r}  r~  r  r  omicronorp  r  r   rk  LamdaHatDOTz\dot{\hat{\Lambda}})r   r  s    r   test_translater    s    AQ<=(((AQ<=(((AQ<=(((AQ<4AQ<6!!!AQ<6!!!AQ<1111r   c                  V    ddl m}  | D ]  }t        t        |            d|z   k(  rJ  y )Nr   )other_symbols\)sympy.printing.latexr  r   r&   )r  r  s     r   test_other_symbolsr    s/    2 1WQZ HqL0001r   c                   	   t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d	            d
k(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            d k(  sJ t        t        d!            d"k(  sJ t        t        d#            d$k(  sJ t        t        d%            d$k(  sJ t        t        d&            dk(  sJ t        t        d'            dk(  sJ t        t        d(            d(k(  sJ t        t        d)            d)k(  sJ t        t        d*            d*k(  sJ t        t        d+            d+k(  sJ t        t        d,            d,k(  sJ t        t        d-            d-k(  sJ t        t        d.            d.k(  sJ t        t        d/            d0k(  sJ t        t        d1            d1k(  sJ t        t        d2            d2k(  sJ t        t        d3            d3k(  sJ t        t        d4            d4k(  sJ t        t        d5            d5k(  sJ t        t        d6            d6k(  sJ t        t        d7            d7k(  sJ t        t        d8            d8k(  sJ t        t        d9            d9k(  sJ t        t        d:            d:k(  sJ t        t        d;            d;k(  sJ t        t        d<            d=k(  sJ t        t        d>            d?k(  sJ t        t        d@            dAk(  sJ t        t        dB            dCk(  sJ t        t        dD            dEk(  sJ t        t        dF            dGk(  sJ y )HN	xMathringz\mathring{x}xCheckz	\check{x}xBrevez	\breve{x}xAcutez	\acute{x}xGravez	\grave{x}xTildez	\tilde{x}xPrimez{x}'xddDDotz
\ddddot{x}xDdDotz	\dddot{x}xDDotz\ddot{x}xBoldz\boldsymbol{x}xnOrMz\left\|{x}\right\|xAVGz\left\langle{x}\right\ranglexHatz\hat{x}xDotz\dot{x}xBarz\bar{x}xVecz\vec{x}xAbsr  xMagxPrMxBMMathringCheckBreveAcuteGraveTildePrimeDDotz\dot{D}BoldNORmAVGHatr   BarVecr<   MagPrMBMhbarz\hbarxvecdotz\dot{\vec{x}}xDotVecz\vec{\dot{x}}xHATNormz\left\|{\hat{x}}\right\| xMathringBm_yCheckPRM__zbreveAbszC\boldsymbol{\mathring{x}}^{\left|{\breve{z}}\right|}_{{\check{y}}'} alphadothat_nVECDOT__tTildePrimez1\hat{\dot{\alpha}}^{{\tilde{t}}'}_{\dot{\vec{n}}})r   r&   r   r   r   test_modifiersr    sZ    %&/999"#|333"#|333"#|333"#|333"#|333"#w...#$555"#|333!"k111!"&7777!"&;;;;!%DDDD!Z///!Z///!Z///!Z///!%8888!%8888!W,,, $5555$%444!"h...!"h...!"h...!"h...!"h...!"h...!Z///!W,,,!W,,, F*** F*** F*** F*** F*** F*** F*** F***5(((!X---#$(8888#$(8888$%)DDDD;<=NO O O;<=<= = =r   c                  
   t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d	            d
k(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            dk(  sJ t        t        d            d k(  sJ t        t        d!            d"k(  sJ t        t        d#            d$k(  sJ t        t        d%            d&k(  sJ t        t        d'            d(k(  sJ t        t        d)            d*k(  sJ t        t        d+            d,k(  sJ t        t        d-            d.k(  sJ t        t        d/            d0k(  sJ t        t        d1            d2k(  sJ t        t        d3            d4k(  sJ t        t        d5            d6k(  sJ t        t        d7            d8k(  sJ t        t        d9            d:k(  sJ t        t        d;            d<k(  sJ t        t        d=            d>k(  sJ t        t        d?            d@k(  sJ t        t        dA            dBk(  sJ t        t        dC            dDk(  sJ t        t        dE            dFk(  sJ t        t        dG            dHk(  sJ t        t        dI            dJk(  sJ t        t        dK            dLk(  sJ t        t        dM            dNk(  sJ t        t        dO            dPk(  sJ t        t        dQ            dRk(  sJ t        t        dS            dTk(  sJ t        t        dU            dVk(  sJ t        t        dW            dXk(  sJ t        t        dY            dZk(  sJ t        t        d[            d\k(  sJ t        t        d]            d^k(  sJ t        t        d_            d`k(  sJ t        t        da            dbk(  sJ t        t        dc            ddk(  sJ t        t        de            dfk(  sJ t        t        dg            dhk(  sJ t        t        di            djk(  sJ t        t        dk            dlk(  sJ t        t        dm            dnk(  sJ y )oNr!  r#  rU   rz  rb   r{  delta\deltaepsilonz\epsilonr|   rx  etaz\etar  z\thetaiotaz\iotakappaz\kappalambdar  r   z\munuz\nuxiz\xir  r  r   rk  rj  z\rhosigmaz\sigmar   rZ  upsilonz\upsilonr  rj  r  r  psiz\psirc  r#  r{  r|  r}  r~  rh  \GammaDeltaz\DeltaEpsilonz
\mathrm{E}Zetaz
\mathrm{Z}r  r  Thetaz\ThetaIotaz
\mathrm{I}Kappaz
\mathrm{K}r   r  Muz
\mathrm{M}Nuz
\mathrm{N}Xiz\XiOmicronz
\mathrm{O}rp  r  Rhoz
\mathrm{P}Sigmaz\Sigmark  r[  Upsilonz\UpsilonPhiz\Phir\   z
\mathrm{X}r  z\PsiOmegaz\Omega
varepsilonz\varepsilonvarkappaz	\varkappavarphiz\varphivarpiz\varpivarrhoz\varrhovarsigmaz	\varsigmavarthetaz	\varthetar  r   r   r   test_greek_symbolsr  5	  s   !y000 x///!y000!y000	"#{222 x///w...!y000 x///!y000!"z111v---v---v---	"#t+++v---w...!y000w...	"#{222w...w...w...!y000!}444 }444!y000!y000	"#}444 }444}444!y000 }444!}444!"z111}444}444v---	"#}444v---}444!y000}444	"#{222w...}444w...!y000%&.888
#$444!"j000!Y...!"j000
#$444
#$444r   c                  l   t        t        j                        dk(  sJ t        t        j                        dk(  sJ t        t        j                        dk(  sJ t        t        j
                        dk(  sJ t        t        j                        dk(  sJ t        t        j                        dk(  sJ y )Nz
\mathbb{Q}r:  r>  rB  z
\mathbb{R}r6  )r   r#   	Rationalsr  r?  rC  r  r7  r   r   r   test_fancyset_symbolsr  q	  s    ...---000--->]***...r   c                  ,    t        t              dk(  sJ y )Nz\mathcal{COS})r   r~   r   r   r   *test_builtin_without_args_mismatched_namesr  z	  s    !%5555r   c                      t        t              dk(  sJ t        t              dk(  sJ t        t              dk(  sJ t        t              dk(  sJ t        t
              dk(  sJ t        t              dk(  sJ y )Nz\operatorname{Chi}z\operatorname{B}r  r  r{  )r   r\   rU   rb   rv   rV   r   r   r   r   test_builtin_no_argsr  	  ss    :....;----<9$$$ I---	)))	)))r   c                  N    t        d      } t         | t                    dk(  sJ y )Nrp  z\Pi{\left(x \right)}r  r0  s    r   test_issue_6853r  	  s"    A1;1111r   c                  0   t        dt        dz   d      } t        |       dk(  sJ t        dt        dz   d      } t        |       dk(  sJ t        t        j                  t        dz   d      } t        |       dk(  sJ t        t
        t        dz   d      } t        |       d	k(  sJ t        t
         t        dz   d      } t        |       d
k(  sJ t        dt        dz         } t        |       dk(  sJ t        dt        dz         } t        |       dk(  sJ y )Nr.  r  Fr   z- 2 \left(x + 1\right)r
  z2 \left(x + 1\right)z\frac{x + 1}{2}zy \left(x + 1\right)z- y \left(x + 1\right)z	- 2 x - 2z2 x + 2)r   r  r   r#   r4  r3  )ri  s    r   test_Mulr  	  s   BA&A80000Aq1uu%A8....AFFAEE*A8))))Aq1uu%A8....QBA&A80000BAA8|###Aq1uA8z!!!r   c                      t        ddd      } t        |       dk(  sJ t        t        t        dd      z        dk(  sJ t	        d      }t        |dz        d	k(  sJ t        t        d
      t        z        dk(  sJ y )Nr
  Fr   z2^{2}r  r  z\frac{1}{\sqrt[3]{x}}zx^2z\left(x^{2}\right)^{2}z
1.453e4500z{1.453 \cdot 10^{4500}}^{x})r    r   r  r   r$   r#   )ri  r  s     r   test_Powr  	  s~    Aq5!A8xXb!_%&*BBBB	BQ<4444<!#$(FFFFr   c                      t        t        t        t                    dk(  sJ t        t	        t        t        t                          dk(  sJ y )Nzx \Leftrightarrow yzx \not\Leftrightarrow y)r   r   r  r3  r   r   r   r   test_issue_7180r  	  s=    Aq!"&<<<<Z1%&'+EEEEr   c                  N    t        t        j                  t        z        dk(  sJ y )Nz\left(\frac{1}{2}\right)^{n})r   r#   r4  rB  r   r   r   test_issue_8409r  	  s    >>>>r   c                  D    ddl m}   | dd      }t        |      dk(  sJ y )Nr   
parse_exprz-B*AFr   zA \left(- B\right)sympy.parsing.sympy_parserr  r   )r  ri  s     r   test_issue_8470r  	  s$    56E*A8,,,,r   c                     t        ddd      } t        ddd      }t        | |z  j                  ||             dk(  sJ t        | |z  j                  |d|z              dk(  sJ t        | |z  j                  | |              dk(  sJ y )Nr  r
  r3  zx \left(- y\right)r.  zx \left(- 2 y\right)z\left(- x\right) y)r   r   subsr  s     r   test_issue_15439r  	  s    S!QAS!QA!a%a!$%)>>>>!a%aA&'+BBBB!a%a!$%)>>>>r   c                  6    t        t        d            dk(  sJ y )Nz\frac{a_1}{b_1}r  r   r   r   test_issue_2934r  	  s    *+,0BBBBr   c                  p    d} t        |       }t        |      | k(  sJ t        t        |            dk(  sJ y )Nz	C_{x_{0}}z\cos{\left(C_{x_{0}} \right)})r$   r   rQ   )latexSymbolWithBracer  s     r   test_issue_10489r  	  s=    '#$A8++++Q=<<<<r   c                  R    t        d      \  } }t        | dz  |dz  z         dk(  sJ y )Nz
m__1, l__1r
  z/\left(l^{1}\right)^{2} + \left(m^{1}\right)^{2}rr  )m__1l__1s     r   test_issue_12886r  	  s7    &JD$q47"#:; ; ;r   c                  D    ddl m}   | dd      }t        |      dk(  sJ y )Nr   r  z5/1Fr   z\frac{5}{1}r  )r  r  s     r   test_issue_13559r  	  s#    5ee,D;.(((r   c                  d    t         t        dt        t        z   d      z   } t	        |       dk(  sJ y )Nr  Fr   zc - \left(a + b\right))r  r   rA  r  r   r  s    r   test_issue_13651r
  	  s,    s2q1uu--D;3333r   c                      t        d      } t        d| z        }t        |      t        d| z        cxk(  rdk(  sJ  J t        |dz        dk(  sJ t        |dz         dk(  sJ t        | |z        dk(  sJ y )Nr  r  r  r
  z\left(\frac{1}{x}\right)^{2}z1 + \frac{1}{x}zx \frac{1}{x})r&   r   r   )r  hes     r   test_latex_UnevaluatedExprr  	  s    A	1	B9ac
4n44444Q<::::a=....2;****r   c                     t        ddd      } t        ddd      }t        ddd      }t        | d         dk(  sJ t        d| d   z        dk(  sJ |d   j                  || |z
        }t        |      d	k(  sJ t        d
      \  }}}t        d||      }t        d||      }t        ||z  ||f         dk(  sJ t        ddd      }	t        |	d         dk(  sJ y )NrU  r  r  r  r(  )r   r   z	{A}_{0,0}z3 {A}_{0,0}z{\left(A - B\right)}_{0,0}zi j kr  r  z2\sum_{i_{1}=0}^{k - 1} {M}_{i,i_{1}} {N}_{i_{1},j}X_az{X_{a}}_{0,0})r   r   r  r&   )
rU  r  r(  r  rV  rW  r;  r  r  r  s
             r   test_MatrixElement_printingr  	  s   S!QAS!QAS!QA4>\)))QtW///	$QAA84444gGAq!S!QAS!QA!A#q!t=> > > ua
#CT////r   c                      t        ddd      } t        ddd      }t        ddd      }t        |        dk(  sJ t        | | |z  z
  |z
        dk(  sJ t        |  |z  | |z  |z  z
  |z
        dk(  sJ y )NrU  r  r  r(  z- AzA - A B - Bz- A B - A B C - B)r   r   r  s      r   test_MatrixSymbol_printingr  	  s    S!QAS!QAS!QA!9QqS1///!A!A!"&::::r   c                  l    t        ddd      } t        ddd      }t        t        | |            dk(  sJ y )NrU  r  r  r
  A \otimes B)r   r   r   )rU  r  s     r   test_KroneckerProduct_printingr  
  s9    S!QAS!QA!!Q'(N:::r   c            	         t        t        t        dz  z  t        z
  t        dz  t        dz  z
  t              } t        t        t        z
  t        t        z   t              }t        t        t        dz  z  t        t
        z  t        z  z
  t
        z   t        t        z
  t              }t        t        | |            dk(  sJ t        t        | ||            dk(  sJ t        t        | |             dk(  sJ t        dt        z  gddt        z  z  gg      }t        j                  |t              }t        ddt        dz  z  gg      }t        j                  |t              }t        |||z   z        dcxk(  r#t        t        t        ||      |            k(  sJ  J t        ddgddt        z  gg      }t        j                  |t              }t        ||z  |z         d	cxk(  r#t        t        t        ||      |            k(  sJ  J y )
Nr
  r  zQ\left(\frac{x y^{2} - z}{- t^{3} + y^{3}}\right) \left(\frac{x - y}{x + y}\right)z\left(\frac{x y^{2} - z}{- t^{3} + y^{3}}\right) \left(\frac{x - y}{x + y}\right) \left(\frac{t x^{2} - t^{w} x + w}{t - y}\right)zS\left(\frac{- x + y}{x + y}\right) \left(\frac{x y^{2} - z}{- t^{3} + y^{3}}\right)r  rF  z\left[\begin{matrix}\frac{5}{s}\\\frac{5}{2 s}\end{matrix}\right]_\tau\cdot\left(\left[\begin{matrix}\frac{5}{1} & \frac{6 s^{3}}{1}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{5}{1} & \frac{6 s^{3}}{1}\end{matrix}\right]_\tau\right)z\left[\begin{matrix}\frac{5}{s}\\\frac{5}{2 s}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{5}{1} & \frac{6 s^{3}}{1}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{5}{1} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s}\end{matrix}\right]_\tau)r   r  r3  r5  r  r  r   r   r   r  r   from_Matrixr   r   )	tf1tf2tf3M_1T_1M_2T_2M_3T_3s	            r   test_Series_printingr!  
  s   
1QT6A:q!tad{A
6C
1q5!a%
+C
1QT6AqDF?Q.Aq
9CS!"\] ] ]S#&' 	NN N Nc"#^_ _ _ 1Q3%!QqS'#
$C
 
,
,S!
4C
1a1f+
C
 
,
,S!
4CcCi!	K> ZS# 6<=> > > > >
 1a&1ac(#
$C
 
,
,S!
4CS3 $3 e6;LTWY\I]_b<c6de e e e er   c                  2   t        t        dz
  t        dz   t              } t        |       dk(  sJ t        t        dz   dt        z
  t              }t        |      dk(  sJ t        t        t        dz  dt        z  z   dz   t              }t        |      dk(  sJ y )Nr  z\frac{x - 1}{x + 1}r
  z\frac{x + 1}{2 - y}r  z\frac{y}{y^{2} + 2 y + 3})r   r  r   r3  r  r  r  s      r   test_TransferFunction_printingr$  '
  s    
1q5!a%
+C:////
1q5!a%
+C:////
1adQqSj1na
0C:5555r   c            
      p   t        t        t        dz  z  t        z
  t        dz  t        dz  z
  t              } t        t        t        z
  t        t        z   t              }t        t        | |            dk(  sJ t        t        | |             dk(  sJ t        ddgddt        z  gg      }t        j                  |t              }t        dt        z  dgddt        dz
  z  gg      }t        j                  |t              }t        ddt        t        dz
  z  z  gddgg      }t        j                  |t              }t        ||z   |z         dcxk(  r`t        t        |||            cxk(  rFt        t        |t        ||                  cxk(  r#t        t        t        ||      |            k(  sJ  J y )	Nr
  r  z9\frac{x y^{2} - z}{- t^{3} + y^{3}} + \frac{x - y}{x + y}z;\frac{- x + y}{x + y} + \frac{x y^{2} - z}{- t^{3} + y^{3}}r  rF  r  a=  \left[\begin{matrix}\frac{5}{1} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{5}{s} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s - 1}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{6}{1} & \frac{5}{s \left(s - 1\right)}\\\frac{5}{1} & \frac{6}{1}\end{matrix}\right]_\tau)r   r  r3  r5  r  r   r   r   r  r   r  r   )r  r  r  r  r  r  r  r   s           r   test_Parallel_printingr&  0
  s   
1QT6A:q!tad{A
6C
1q5!a%
+C#s#$DE E E3$$%FG G G 1a&1ac(#
$C
 
,
,S!
4C
1Q3(Q1q5	N+
,C
 
,
,S!
4C
1aAEm$q!f-
.C
 
,
,S!
4CsS! &o ^ c345^ :?|CQ]^acfQg?h9i^ nss  AM  NQ  SV  AW  Y\  t]  n^^ ^ ^ ^ ^r   c                  `   t        t        t        t        z   t              } t        t         t        z   t        t        z   t              }t        t        t        dz  dt        z  z   dz   t              }t        t        | g|gg            dk(  sJ t        t        | |g||  gg            dk(  sJ y )Nr
  r  zP\left[\begin{matrix}\frac{p}{p + x}\\\frac{p - s}{p + s}\end{matrix}\right]_\tauz\left[\begin{matrix}\frac{p}{p + x} & \frac{p - s}{p + s}\\\frac{p}{y^{2} + 2 y + 3} & \frac{\left(-1\right) p}{p + x}\end{matrix}\right]_\tau)r   r0  r  r  r3  r   r   r#  s      r   $test_TransferFunctionMatrix_printingr(  D
  s    
1a!eQ
'C
A261q5!
,C
1adQqSj1na
0C'#78[\ \ \'#scC4[(ABC 	ZZ Z Zr   c            
         t        t        t        t        z   t              } t        t         t        z   t        t        z   t              }t	        t        | |            dk(  sJ t	        t        | |z  t        ddt                          dk(  sJ t	        t        | |d            dk(  sJ t	        t        | |z  d            dk(  sJ y )Nzc\frac{\frac{p}{p + x}}{\frac{1}{1} + \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}r  z\frac{\left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}{\frac{1}{1} + \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}zc\frac{\frac{p}{p + x}}{\frac{1}{1} - \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)})signz\frac{\left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)}{\frac{1}{1} - \left(\frac{p}{p + x}\right) \left(\frac{p - s}{p + s}\right)})r   r0  r  r  r   r   )r  r  s     r   test_Feedback_printingr+  N
  s    
1a!eQ
'C
A261q5!
,C#s#$no o o#c'#3Aq!#<=> 	]] ] ] #sA&'no o o#c'*+ 	]] ] ]r   c                     t        dt        t              } t        t        t        dz  dz
  t              }t        t        t        dz
  t              }t        t        dz  t        dz  dz
  t              }t        | |g||gg      }t        ||g|| gg      }t        t	        ||            dk(  sJ t        t	        ||z  |d            dk(  sJ y )Nr  r
  a  \left(I_{\tau} + \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{s^{2}}{s^{2} - 1} & \frac{s}{s - 1}\\\frac{s}{s^{2} - 1} & \frac{1}{s}\end{matrix}\right]_\tau\right)^{-1} \cdot \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\taua  \left(I_{\tau} - \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{s^{2}}{s^{2} - 1} & \frac{s}{s - 1}\\\frac{s}{s^{2} - 1} & \frac{1}{s}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\right)^{-1} \cdot \left[\begin{matrix}\frac{1}{s} & \frac{s}{s^{2} - 1}\\\frac{s}{s - 1} & \frac{s^{2}}{s^{2} - 1}\end{matrix}\right]_\tau\cdot\left[\begin{matrix}\frac{s^{2}}{s^{2} - 1} & \frac{s}{s - 1}\\\frac{s}{s^{2} - 1} & \frac{1}{s}\end{matrix}\right]_\tau)r   r  r   r   r   )r  r  r  tf4tfm_1tfm_2s         r   test_MIMOFeedback_printingr0  ]
  s    
1a
#C
1adQh
*C
1a!eQ
'C
1a4A1
-C"S#Jc
#;<E"S#Jc
#;<E eU+,	pp p p eEk5!45	22 2 2r   c                  4   t        t        t        t        t              } t        |       dk(  sJ t        t        t        t        t        t        z        } t        |       dk(  sJ t        t        t        t        t        t        z         } t        |       dk(  sJ y )Nzx + y i + z j + t kzx + y i + z j + t x kz$x + y i + z j + \left(t + x\right) k)r   r  r3  r5  r  r   )qs    r   test_Quaternion_latex_printingr3  u
  ss    1aAA8----1aAaC A8////1aAE"A8>>>>r   c                  r    ddl m}  t        ddd      }t        ddd      }t         | ||            dk(  sJ y )Nr   )TensorProductrU  r  r  r  )sympy.tensor.functionsr5  r   r   )r5  rU  r  s      r   test_TensorProduct_printingr7  ~
  s;    4S!QAS!QAq!$%777r   c                  v    ddl m}  ddlm}  || j                  | j
                        }t        |      dk(  sJ y )Nr   R2)WedgeProductz*\operatorname{d}x \wedge \operatorname{d}y)sympy.diffgeom.rnr:  sympy.diffgeomr;  dxdyr   )r:  r;  r$  s      r   test_WedgeProduct_printingr@  
  s/    $+	beeRUU	#B9EEEEr   c                     t        ddd      } t        |       dk(  sJ t        dt        ddd      d      }t        |      dk(  sJ t        ddd      }t        |      d	k(  sJ t        ddd      }t        |      d
k(  sJ y )Nr  r  Fr   z1^{-1}z
1^{1^{-1}}r  r.  z\frac{1}{9}z1^{-2})r    r   )expr_1expr_2expr_3expr_4s       r   test_issue_9216rF  
  s    B'F=I%%%C2.?F=M)))B'F=N***B'F=I%%%r   c                      ddl m} m}m}m}  | d      } |d|      \  }}}} |d|      }	 |d|g      \  }
}}} |d||g      } |d||||g      }t        |      d	k(  sJ t        |       d
k(  sJ  |
|      }t        |      dk(  sJ  |
|	      }t        |      dk(  sJ  |
|       }t        |      dk(  sJ d |
|      z  }t        |      dk(  sJ  |||| |	       }t        |      dk(  sJ  ||| | |	      }t        |      dk(  sJ  ||| ||	       }t        |      dk(  sJ  |||       }t        |      dk(  sJ  |||      }t        |      dk(  sJ  || |       }t        |      dk(  sJ dt        z    |
|      z  }t        |      dk(  sJ  |||       }t        |      dk(  sJ  |||        |
|      z   ||      z  }t        |      dk(  sJ  |
|      d ||      z  z   }t        |      dk(  sJ ddl m}  | |||||      |d|di      }t        |      dk(  sJ  | |||||      |di      }t        |      dk(  sJ  | ||| ||      |d|di      }t        |      d k(  sJ  | ||| ||       |d|di      }t        |      d!k(  sJ  | |||| |       |d| di      }t        |      d"k(  sJ  | |||| |       |di      }t        |      d#k(  sJ t         |
|       |
|            }t        |      d$k(  sJ t         |
|        |
|             }t        |      d%k(  sJ t         |||| |        |
t               |
t                     }t        |      d&k(  sJ t         ||        |
|       z    |
|        |
t                     }t        |      d'k(  sJ t        d |
|       z   |
|        |
t                     }t        |      d(k(  sJ y ))Nr   )TensorIndexTypetensor_indices
TensorHeadtensor_headsLzi j k li_0zA B C DHKz{}^{i}z{}_{i}zA{}^{i}zA{}^{i_{0}}zA{}_{i}r@  z	-3A{}^{i}zK{}^{ij}{}_{ki_{0}}zK{}^{i}{}_{jk}{}^{i_{0}}zK{}^{i}{}_{j}{}^{k}{}_{i_{0}}zH{}^{i}{}_{j}zH{}^{ij}zH{}_{ij}r  z\left(x + 1\right)A{}^{i}zH{}^{L_{0}}{}_{L_{0}}z#H{}^{i}{}_{L_{0}}A{}^{L_{0}}B{}^{k}r  z3B{}^{i} + A{}^{i})TensorElementr
  zK{}^{i=3,j,k=2,l}zK{}^{i=3,jkl}zK{}^{i=3}{}_{j}{}^{k=2,l}zK{}^{i=3}{}_{j}{}^{k=2}{}_{l}zK{}^{i=3,j}{}_{k=2,l}zK{}^{i=3,j}{}_{kl}z4\frac{\partial}{\partial {A{}^{L_{0}}}}{A{}^{L_{0}}}z,\frac{\partial}{\partial {A{}_{j}}}{A{}_{i}}zK\frac{\partial^{2}}{\partial {A{}^{m}} \partial {A{}_{n}}}{K{}^{ij}{}_{kl}}zZ\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(A{}_{i} + B{}_{i}\right)}zQ\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(3A{}_{i}\right)})sympy.tensor.tensorrH  rI  rJ  rK  r   r  rP  r   r  rB  )rH  rI  rJ  rK  rL  rV  rW  r;  rn  i0rU  r  r(  r)  rN  rO  r  rP  s                     r   test_latex_printer_tensorrS  
  s   ]]A	1-JAq!Q	q	!Bi!-JAq!Q3AA3Aq!%A8y   !9	!!!Q4D;*$$$R5D;.(((aR5D;*$$$ad7D;,&&&QA2sD;0000QQBD;5555QAsD;::::Q8D;****Q7D;+%%%aR!9D;+%%%aC1:D;6666Q8D;2222Q8AaD=1D;@@@@Q4!AaD&=D;//// 21aAAq!5D;....1aAA/D;****1qb!Q!Q16D;66661qb!aR1aA,7D;::::1a!aR1a!Q-8D;22221a!aR1a&1D;////QqT1Q4(D;QQQQQrUAqbE*D;IIIIQq!aR!_adAqbE:D;hhhhQrUQrU]AqbE1aR59D;wwwwQq!uWaeQrU3D;nnnnr   c                     t        d      \  } }}}}|  d|z  z   d|z  z
  d|z  z   d|z  z
  d}t        d      |k(  sJ d	}t        dd      |k(  sJ d
}t        dd      |k(  sJ d}t        ddd      |k(  sJ d}	t        d      |	k(  sJ t        dd      |	k(  sJ d}
t        dd      |
k(  sJ t        t        fd       y )Nza b c d e fr
  r  r  r  z\begin{eqnarray}
f & = &- a \nonumber\\
& & + 2 b \nonumber\\
& & - 3 c \nonumber\\
& & + 4 d \nonumber\\
& & - 5 e 
\end{eqnarray}eqnarrayenvironmentzc\begin{eqnarray}
f & = &- a + 2 b \nonumber\\
& & - 3 c + 4 d \nonumber\\
& & - 5 e 
\end{eqnarray}zS\begin{eqnarray}
f & = &- a + 2 b - 3 c \nonumber\\
& & + 4 d - 5 e 
\end{eqnarray}zX\begin{eqnarray}
f & = &- a + 2 b - 3 c \dots\nonumber\\
& & + 4 d - 5 e 
\end{eqnarray}T)rW  use_dotszB\begin{align*}
f = &- a + 2 b - 3 c \\
& + 4 d - 5 e 
\end{align*}zalign*zp\begin{IEEEeqnarray}{rCl}
f & = &- a + 2 b \nonumber\\
& & - 3 c + 4 d \nonumber\\
& & - 5 e 
\end{IEEEeqnarray}IEEEeqnarrayc                       t         d      S )Nr  rV  )r   )r  r  s   r   r  z&test_multiline_latex.<locals>.<lambda>'  s    q$EJ r   )r&   r   r   r  )rA  r  r  r'  ri  r  	expected2	expected3expected3dotsexpected3alignexpected2ieeer  r  s              @@r   test_multiline_latexr`  
  s2   }-Aq!Q12!8QqS=!A#qs"DH 1d
;xGGGI 1dA:>)KKKI
 1dA:>)KKKM
 1dA:MQ^^^^N
 1dA&.8881dA8<NNNM 1dA>BmSSS
:JKr   c            
          t        d      \  } }t        t        ||       t        t	        | |z        d      t        t        | |z        d      z  t        j                  dz        }t        |      dk(  sJ y )Nza xr   r
  z\left\{\left( x, \  a\right)\; \middle|\; \left( x, \  a\right) \in \mathbb{C}^{2} \wedge \sin{\left(a x \right)} = 0 \wedge \cos{\left(a x \right)} = 0 \right\})	r&   r   r   r!   rS   rQ   r#   r7  r   )rA  r  sols      r   test_issue_15353rc  )  sk    5>DAq
aRAaC!_r#ac(A6QHC:	00 0 0r   c                  8   t        d      } t        dd      }t        d| |      }t        t        |            dk(  sJ t        t	        |            dk(  sJ t        t        |dkD              d	k(  sJ t        d
| |      }t        t        ||            dk(  sJ y )Nr   r  Tr1  r  z\operatorname{E}\left[X\right]z \operatorname{Var}\left(X\right)r   z"\operatorname{P}\left(X > 0\right)r  z#\operatorname{Cov}\left(X, Y\right))r&   r   r   r   r   r   r   )r   r  r  r  s       r   test_latex_symbolic_probabilityre  4  s    	BGd+EsBAQ $EEEE!!DDDDQU#$(MMMMsBAAq!"&LLLLr   c                      ddl m}  t        ddd      }t         | |            dk(  sJ t         | |dz              dk(  sJ y )Nr   tracerU  r
   \operatorname{tr}\left(A \right)z$\operatorname{tr}\left(A^{2} \right) sympy.matrices.expressions.tracerh  r   r   )rh  rU  s     r   
test_tracerl  ?  sF    6S!QAq?AAAAq!t!HHHHr   c                      ddl m ddlm}   G fdd|       fd}fd}t	         |t
                    dk(  sJ t	         |t
        d	z              d
k(  sJ t	         |t
                    dk(  sJ y )Nr   Basic)Exprc                       e Zd Z fdZy)+test_print_basic.<locals>.UnimplementedExprc                 (    j                  | |      S N)__new__)r  ri  ro  s     r   ru  z3test_print_basic.<locals>.UnimplementedExpr.__new__O  s    ==a((r   N)r   r   r   ru  rn  s   r   UnimplementedExprrr  N  s    	)r   rv  c                 0     |       j                         S rt  )r  )r  rv  s    r   unimplemented_exprz,test_print_basic.<locals>.unimplemented_exprS  s     &++--r   c                 :     |       }d|j                   _        |S )NzUnimplementedExpr_x^1)	__class__r   )r  resultrv  s     r   unimplemented_expr_sup_subz4test_print_basic.<locals>.unimplemented_expr_sup_subW  s     "4($;!r   z.\operatorname{UnimplementedExpr}\left(x\right)r
  z2\operatorname{UnimplementedExpr}\left(x^{2}\right)z6\operatorname{UnimplementedExpr^{1}_{x}}\left(x\right))sympy.core.basicro  sympy.core.exprrp  r   r  )rp  rx  r|  ro  rv  s      @@r   test_print_basicr  G  s    &$)D )
.
 #A&'+\\\\#AqD)*=> > >+A./AB B Br   c                     ddl m}  t        ddd      }t         | |      d      dk(  sJ t         | |      d      d	k(  sJ t        dd
d
      }t        dd
d
      }t        dd
d
      }t        | d      dk(  sJ t        |||z  z
  |z
  d      dk(  sJ t        | |z  ||z  |z  z
  |z
  d      dk(  sJ t        dd
d
      }t        |d      dk(  sJ t        dd
d
      }t        |d      dk(  sJ y )Nr   rg  rU  r
  ra  r_  z)\operatorname{tr}\left(\mathbf{A} \right)r  ri  r  r  r(  z- \mathbf{A}z/\mathbf{A} - \mathbf{A} \mathbf{B} - \mathbf{B}zG- \mathbf{A} \mathbf{B} - \mathbf{A} \mathbf{B} \mathbf{C} - \mathbf{B}A_kz\mathbf{A}_{k}z\nabla_kz\mathbf{\nabla}_{k}rj  )rh  rU  r  r(  r  s        r   test_MatrixSymbol_boldr  c  s>   6S!QAqF345 5 5qG4+, , , 	S!QAS!QAS!QA!f-@@@QqS1v6:; ; ;!A!A!F;RS S S ua
#Cv.2CCCC[!Q'AV,0FFFFr   c                  h    t        ddd      } t        d      }t        t        | |            dk(  sJ y )Nr   r  r
  r  z#\sigma_{\left( 0\; 1\; 2\right)}(x))r	   r$   r   r
   )r0  r  s     r   test_AppliedPermutationr  |  s;    Aq!AsA#Aq)*./ / /r   c                      t        ddd      } t        t        |             dk(  sJ  t        dd      dd      } t        t        |             dk(  sJ y )Nr   r  r
  zP_{\left( 0\; 1\; 2\right)}r  z*P_{\left( 0\; 3\right)\left( 1\; 2\right)})r	   r   r   r  s    r   test_PermutationMatrixr    s_    Aq!A"1%&*HHHHAq!QA"1%&56 6 6r   c                  v   ddl m}  ddlm} t	        d      }t        d      \  }} |||t         t        fdt        d|dt        f      t        t        dt        z  t        |t        z        z  |z  dt        |t        z        z  |dz  z  z   |t         kD  |t        k  z  t        |d      z  fd	      t        ||z        z  t        z  |dt        f      f      }t         | |            d
k(  sJ t         |||t         t        fdt        d|dt        f      t        d|dt        f      f            dk(  sJ y )Nr   )piecewise_fold)FourierSeriesr  zk nr  r.  r
  )r   Tz\begin{cases} 2 \sin{\left(x \right)} - \sin{\left(2 x \right)} + \frac{2 \sin{\left(3 x \right)}}{3} + \ldots & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}r  )$sympy.functions.elementary.piecewiser  sympy.series.fourierr  r$   r&   r   r   r   rN   rQ   rS   r"   r   )r  r  r  r;  rB  fos         r   test_issue_21758r    sT   C2sA5>DAq	q1rc2,Jq1a*,Ez2b5QrT?1$qQrT{1a4'77!rc'a"f9MPRSTVWPX9XY	 1X	&&(	)+,a*H6 )7 
8B #$ )C C C C q1rc2,Jq1a*4M1;A1bz1J1L M NQTU U Ur   c                      t        dt        z         dk(  sJ t        dt        z   d      dk(  sJ t        dt        z   d      dk(  sJ t        dt        z   d      dk(  sJ t        t        d	      d
k(  sJ t        t        d      dk(  sJ y )Nr  z1 + irV  imaginary_unitrW  z1 + jr  z1 + footiz\text{i}tjz\text{j})r   r   r   r   r   test_imaginary_unitr    s    Q<8###Qs+x777Qs+x777Qu-;;;4(K7774(K777r   c                      t        t        t              d      dk(  sJ t        t        t              d      dk(  sJ t        t        t              d      dk(  sJ t        t        t              d      dk(  sJ y )NT)gothic_re_imz\Im{\left(x\right)}Fr  z\Re{\left(x\right)}r  )r   r?   r  rA   r   r   r   test_text_re_imr    sj    AT*.DDDDAU+/SSSSAT*.DDDDAU+/SSSSr   c                     ddl m} m}m}m}m} ddlm} t        dd      \  }} | dd      }t        |      d	k(  sJ  |d
|      }	t        |	      dk(  sJ  |d|	||g      }
t        |
      dk(  sJ  ||
d      }t        |      dk(  sJ t        d      } ||j                  |j                        }t         ||            dk(  sJ y )Nr   )ManifoldPatchCoordSystemBaseScalarFieldDifferentialr9  zx yTr  r  r
  z\text{M}Pz\text{P}_{\text{M}}rectz!\text{rect}^{\text{P}}_{\text{M}}z
\mathbf{x}rw  zC\operatorname{d}\left(g{\left(\mathbf{x},\mathbf{y} \right)}\right))r=  r  r  r  r  r  r<  r:  r&   r   r   r  r3  )r  r  r  r  r  r:  r  r3  r  r0  r  r  rw  s_fields                 r   test_latex_diffgeomr    s    ZZ$
%d
#CAaaA8{"""c1A8----vq1a&)D;>>>>a A8}$$$AbddmGg&'NO O Or   c                  J   t        dt        z        dk(  sJ t        dt        z        dk(  sJ t        dt        z  t        z        dk(  sJ t        dt
        z  t        z  t        z        dk(  sJ t        dt        z  t        z        dk(  sJ t        t              d	k(  sJ y )
Nr  z
5 \text{m}r  z3 \text{gibibyte}r  z\frac{4 \mu\text{g}}{\text{s}}z\frac{4 \mu \text{g}}{\text{s}}z5 \text{m} \text{m}z\text{m})r   r   r   r   r   r   r   r   r   r   r   test_unit_printingr    s    5>]***8 44449V#$(IIII5f$%)KKKK5#9999<;&&&r   c                  P    t        d      } t        t        | | d            dk(  sJ y )Nr  r
  z,\frac{d^{2}}{d \left(x^{*}\right)^{2}} x^{*})r$   r   r   )r:  s    r   test_issue_17092r    s(    E]FFF1-.2aaaar   c                  t   t        d      \  } }}}t        dd      \  }}}t        dt              \  }}}	t        g dd	      d
k(  sJ t        t        ddd      d	      dk(  sJ t        dd	      dk(  sJ t        dd	      dk(  sJ t        g dd	      dk(  sJ t        t        ddd      d	      dk(  sJ t        dd	      dk(  sJ t        dd	      dk(  sJ t        g d      dk(  sJ t        t        ddd            dk(  sJ t        d      dk(  sJ t        d      dk(  sJ t        t	        dd      d	      dk(  sJ t        dd	      dk(  sJ t        d      } t        d      }t        d      }t        | dz  d|dz  z  z   dz   |z   d	      d k(  sJ t        d!d	      d"k(  sJ t        t        d!      d	      d"k(  sJ t        d#d	      d$k(  sJ t        t        d#      d	      d$k(  sJ t        d%d	      d&k(  sJ t        t        d'      d(z  d	      d)k(  sJ t        t        d*      d	      d)k(  sJ t        d      } t        d+| z  dz   d	      d,k(  sJ t        t        ddd      d	      dk(  sJ t        t        d-        t        t        d.        t        t        d/        y )0Nzx y z tr   Tr   zf g hr  r  ffffff@      @commadecimal_separatorz#\left[ 1; \  2{,}3; \  4{,}5\right]r  r  r  z\left\{1; 2{,}3; 4{,}5\right\})r  r  gffffff@z#\left( 1; \  2{,}3; \  4{,}6\right))r  z\left( 1;\right)periodz\left[ 1, \  2.3, \  4.5\right]z\left\{1, 2.3, 4.5\right\}z\left( 1, \  2.3, \  4.6\right)z\left( 1,\right)g333333@g333333@z18{,}02gQ2@r  r3  r5  r
  z#2^{y^{3{,}4}} + 5{,}3 x + z + 4{,}5g/$?z0{,}987g333333?z0{,}3g|)v>z5{,}8 \cdot 10^{-7}g@gHz>z5{,}7 \cdot 10^{-7}g<sAC >g333333?z1{,}2 x + 3{,}4c                       t        g dd      S )Nr  &non_existing_decimal_separator_in_listr  r  r   r   r   r  z.test_latex_decimal_separator.<locals>.<lambda>  s    u[Dlm r   c                  2    t        t        ddd      d      S )Nr  r  r  %non_existing_decimal_separator_in_setr  )r   r   r   r   r   r  z.test_latex_decimal_separator.<locals>.<lambda>  s    uYqS%9Mtu r   c                      t        dd      S )Nr  'non_existing_decimal_separator_in_tupler  r  r   r   r   r  z.test_latex_decimal_separator.<locals>.<lambda>  s    u[Dmn r   )r&   r   r   r   r   r#   r   r  )
r  r3  r5  r  r;  r  rB  r  rw  rx  s
             r   test_latex_decimal_separatorr    s   #JAq!Qgt,GAq!g8,GAq! ':>dded1c3'7CGhhihG<@ffgf15HHIH (;?aaca1c3'8DHeefeH=Accdc26IIJI #EEFE1c3'(,IIJI#EEFE;--.-S7;zIJIg6*DEDAAA3AsF"S(1,'JNttut'2j@A@5W5CDCw/8;<;2'2h>?> 9=SSTS3G<@VVWV<G<@VVWVAQsg6:LLML1c3'8DHeefe :mn
:uv
:nor   c                  <    ddl m}  t         | d            dk(  sJ y )Nr   Strr  )sympy.core.symbolr  strr  s    r   test_Strr    s    %s3x=D   r   c                  F    t        d      dj                  g d      k(  sJ y )Nz
~^\&%$#_{}r  )
z\textasciitildez\textasciicircumz\textbackslashz\&z\%z\$z\#z\_z\{z\})r   joinr   r   r   test_latex_escaper    s)    &"'' 3 +   r   c                  n     G d d      } t         |              dk(  sJ t         |        f      dk(  sJ y )Nc                       e Zd Zd Zy)#test_emptyPrinter.<locals>.MyObjectc                      y)Nz<MyObject with {...}>r   )r   s    r   __repr__z,test_emptyPrinter.<locals>.MyObject.__repr__  s    *r   N)r   r   r   r  r   r   r   MyObjectr    s    	+r   r  z'\mathtt{\text{<MyObject with \{...\}>}}z6\left( \mathtt{\text{<MyObject with \{...\}>}},\right)r  )r  s    r   test_emptyPrinterr    s>    + +
  JJJJ (*#\\\\r   c                  (   dd l } | j                  t              j                  d   j                  dk(  sJ t        t
              dk(  sJ 	 t        j                  d       | j                  t              j                  d   j                  dk(  sJ t        t
              dk(  sJ 	 t        j                  d= | j                  t              j                  d   j                  dk(  sJ t        t
              dk(  sJ y # t        j                  d= w xY w)Nr   r  rV  rW  r  )	inspect	signaturer   
parametersdefaultr   r   set_global_settings_global_settings)r  s    r   test_global_settingsr    s     U#../?@HHDPPP8t	<((<  '223CDLLPTTTTQx4 ))*:; U#../?@HHDPPP8t	 ))*:;s   AC> >Dc                  d    dd l } | j                  | j                  t                    t        u sJ y )Nr   )pickleloadsdumpsr   )r  s    r   test_pickleabler  0  s%    <<U+,555r   c            	          t        t        dd            dk(  sJ t        t        ddddt        z
  z  df            dk(  sJ t	        ddd      } t	        d	dd      }t        t        | |z  t        dg            d
k(  sJ y )NrU  )r
  r  r  r
  r  r   z{{A}_{2, \frac{1}{1 - x}, 0}}r  r  r  z{{\left(M N\right)}_{x, 0}})r   r   r   r  r   )r  r  s     r   %test_printing_latex_array_expressionsr  5  s    S),-444cAq!A#w?348XXXXS!QAS!QAacAq6*+/NNNNr   c                      t        t        d            } t        |       dk(  sJ t        t        d            } t        |       dk(  sJ y )Nr  zL\left[\begin{matrix}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\end{matrix}\right]r  r  )r   r  r   )arrs    r   
test_Arrayr  <  sD    
b	
C:hhhh
b	
C:xxxxr   c                  |    t        d      5  t        t        t        z        dk(  sJ 	 d d d        y # 1 sw Y   y xY w)NFza a)r   r   rA  r   r   r   test_latex_with_unevaluatedr  D  s4    	% &QU|v%%%& & &s   2;(  sympyr   r   r   sympy.algebras.quaternionr   !sympy.calculus.accumulationboundsr    sympy.combinatorics.permutationsr   r	   r
   sympy.concrete.productsr   sympy.concrete.summationsr   sympy.core.containersr   r   r~  r   sympy.core.functionr   r   r   r   r   sympy.core.modr   sympy.core.mulr   sympy.core.numbersr   r   r   r   r   r   r   sympy.core.parametersr   sympy.core.powerr    sympy.core.relationalr!   r"   sympy.core.singletonr#   r  r$   r%   r&   (sympy.functions.combinatorial.factorialsr'   r(   r)   r*   r+   r,   %sympy.functions.combinatorial.numbersr-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   $sympy.functions.elementary.complexesr<   r=   r>   r?   r@   rA   &sympy.functions.elementary.exponentialrB   rC   rD   %sympy.functions.elementary.hyperbolicrE   rF   #sympy.functions.elementary.integersrG   rH   rI   (sympy.functions.elementary.miscellaneousrJ   rK   rL   rM   r  rN   (sympy.functions.elementary.trigonometricrO   rP   rQ   rR   rS   rT   &sympy.functions.special.beta_functionsrU   'sympy.functions.special.delta_functionsrV   rW   *sympy.functions.special.elliptic_integralsrX   rY   rZ   r[   r  r\   r]   r^   r_   r`   ra   'sympy.functions.special.gamma_functionsrb   rc   sympy.functions.special.hyperrd   re   )sympy.functions.special.mathieu_functionsrf   rg   rh   ri   #sympy.functions.special.polynomialsrj   rk   rl   rm   rn   ro   rp   rq   rr   -sympy.functions.special.singularity_functionsrs   +sympy.functions.special.spherical_harmonicsrt   ru   (sympy.functions.special.tensor_functionsrv   rw   &sympy.functions.special.zeta_functionsrx   ry   rz   r{   r|   sympy.integrals.integralsr}   sympy.integrals.transformsr~   r   r   r   r   r   r   r   r   r   sympy.logicr   sympy.logic.boolalgr   r   r   r   r   r   r   sympy.matrices.denser   $sympy.matrices.expressions.kroneckerr   "sympy.matrices.expressions.matexprr   &sympy.matrices.expressions.permutationr    sympy.matrices.expressions.slicer   sympy.physics.control.ltir   r   r   r   r   r   r   r   sympy.physics.quantumr   r   sympy.physics.quantum.tracer   sympy.physics.unitsr   r   r   r   r   r   r   sympy.polys.domains.integerringr   sympy.polys.fieldsr   sympy.polys.polytoolsr   sympy.polys.ringsr   sympy.polys.rootoftoolsr   r   sympy.series.formalr   r  r   sympy.series.limitsr   sympy.series.orderr   sympy.series.sequencesr   r   r   r   sympy.sets.conditionsetr   sympy.sets.containsr   sympy.sets.fancysetsr   r   r   sympy.sets.ordinalsr   r   r   sympy.sets.powersetr   sympy.sets.setsr   r   r   r   r   r   r   sympy.sets.setexprr   sympy.stats.crv_typesr    sympy.stats.symbolic_probabilityr   r   r   r   sympy.tensor.arrayr   r   r   r   r   0sympy.tensor.array.expressions.array_expressionsr   r   sympy.tensor.indexedr   r   r   sympy.tensor.toperatorsr   sympy.vectorr   r   r   r   r   r   r   sympy.testing.pytestr   r   r   r   r  r   r   r   r   r   r   r   symr  r   r   r   r  r3  r5  r  r  rA  r  r  r  r0  r;  r  rB  r  r<  r>  rC  rI  rN  rS  rX  rp  ru  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%  r4  r8  r;  r@  rD  rG  rJ  rM  rO  rQ  rS  rW  r[  r]  r`  rb  rf  rr  rt  rw  ry  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.  r6  r9  r;  rD  rO  rS  rW  rY  r\  rc  rg  rk  rq  rt  rv  ry  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$  r&  r(  r+  r0  r3  r7  r@  rF  rS  r`  rc  re  rl  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r   r   <module>r      s   ' ' 0 9 S S + ) - + J J   U U U *   ( " 5 5 H  HM M M M M [ Z G G ? F F K K : U U 7 K h h R R G : h h Z  Z  Z M B Q f f . u  u  u  L L L ' A ; D 8 S  S  S 6 * V V V . $ & " 5 # / % $ G G 0 ( A A A A ( s s s s & & ( (E E E/ / / /
 W V < < < 5 5 V V V V V: : :> > > > >   	 	  ''<= 1aAq!Q1
'4
(1a	!SEl+;8/4.*/PbI4 ; ; j3 j3\K2"<$;41*=m@^%gP@AJ>6"r?/
E2-2264
9+
2V
Zt-n/.1.y4nA
C	/-"	$4AGE
G)2FN
)J	8UG*H( $+o\9H?.
8-O@
7.O6V
XB
o
<;>?0
K`"GNBC&3OB/7tQBM<~"aH=0*0=\MLH0?$
#.2"15=p95x/ 6 6*2
""GF
?-?C=;)4
+0,;;e86^(Z]20?8F&Xov2Lh0MIB8G2/6U 8TO&'b
0pd!	]*6
Oy&r   