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    *ήc4                 
   @   s  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
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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,m-Z- d dNl Z.d dOl/m0Z0m1Z1 G dPdQ dQe.j2Z2e1dR\
Z3Z4Z5Z6Z7Z8Z9Z:Z;Z<e1dSdTdU\Z=Z>Z?dVdW Z@dXdY ZAdZd[ ZBd\d] ZCd^d_ ZDd`da ZEdbdc ZFddde ZGdfdg ZHe"dhdi ZIe$djdk ZJdldm ZKdndo ZLdpdq ZMdrds ZNdtdu ZOdvdw ZPdxdy ZQdzd{ ZRd|d} ZSd~d ZTdd ZUdd ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd Zddd Zedd Zfdd Zgdd Zhdd Zidd Zjdd Zkdd Zldd Zmdd Zndd Zodd Zpdd Zqdd Zrdd Zsdd Ztdd ZuddÄ Zvddń ZwddǄ ZxddɄ Zydd˄ Zzdd̈́ Z{ddτ Z|ddф Z}ddӄ Z~ddՄ Zddׄ Zddل Zddۄ Zdd݄ Zdd߄ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d Zdd Zdd Zdd Zdd	 Zd
d Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zd d! Zd"d# Zd$d% Zd&d' Zd(d) Zd*d+ Zd,d- Zd.d/ Zd0d1 Zd2d3 Zd4d5 Zd6d7 Zd8d9 Zd:d; Zd<d= Ze"d>d? Zd@dA ZdBdC ZdDdE ZdFdG ZdHdI ZdJdK ZdLdM ZdNdO ZdPdQ ZdRdS ZdTdU ZdVdW ZdXdY ZdZd[ Zd\d] ZÐd^d_ ZĐd`da ZŐdbdc ZƐddde Zǐdfdg ZȐdhdi Zɐdjdk Zʐdldm Zːdndo Z̐dpdq Z͐drds Zΐdtdu Zϐdvdw ZАdxdy Zѐdzd{ ZҐd|d} ZӐd~d ZԐdd ZՐdd Z֐dd Zאdd Zؐdd Zِdd Zڐdd Zېdd Zܐdd Zݐdd Zސdd Zߐdd Zdd Zdd Zdd Zdd Zdd Zdd ZdNS (      )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)Pow)EqNe)S)SymbolWildsymbols)FallingFactorialRisingFactorialbinomial	factorial
factorial2subfactorial)	bernoullibellcatalaneulerlucas	fibonacci
tribonacci)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)divisor_sigmaprimenu
primeomegareduced_totienttotientudivisor_sigma)
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dS )
lowergammaN__name__
__module____qualname__ r   r   F/tmp/pip-target-vg8gfxp4/lib/python/sympy/printing/tests/test_latex.pyr   ^       r   zx y z t w a b c s pk m nTintegerc                  C   sL   G dd dt } t| tdksJ G dd dt } t| tdks$J d S )Nc                   @      e Zd Zdd ZdS )test_printmethod.<locals>.Rc                 S   s   d| | jd  S )Nzfoo(%s)r   )_printargsselfprinterr   r   r   _latexh   s   "test_printmethod.<locals>.R._latexNr   r   r   r   r   r   r   r   Rg       r   zfoo(x)c                   @   r   )r   c                 S      dS )Nfoor   r   r   r   r   r   m      r   Nr   r   r   r   r   r   l   r   r   )r1   r   x)r   r   r   r   test_printmethodf   s   r  c                  C   s  t dt dks
J t td dksJ t tdt  dks J t td t d td  dks2J t dt t dks>J t dt t d	d
dksLJ t dtd  t dd
dks\J t ddt  dd
dksjJ t ttjd  dkswJ t ttjtd ddddksJ t ttjtd ddddksJ t tdddddksJ t tdddddksJ t ttjdtjdddksJ t tdtddddksJ t tdtddddksJ t tdddddksJ t tdddddksJ t tdddddksJ t td dddd!ksJ t tdddddd"ks$J t tddddd#ks2J t tdtjddd$ksAJ t tddtjddd%ksQJ t tddddtddd&ksbJ t tdd ddd'kspJ t td(ddddttddd)ksJ t td(dddt dttddd*ksJ t ttddtdd+ddd,ksJ t dt d-ksJ t dt d.d/d0ksJ t td d d1ksJ t td d d.d/d2ksJ t dtd  d3ksJ t dtt  d d4ksJ t td d5ks	J t td d.d/d6ksJ t tt dt  d7ks%J t tt dt  d.d/d8ks6J t tt dt  dd9d:ksGJ t tt t d;ksTJ t tt t dd9d;kscJ t dt	d t d d<kstJ t dt	d t d dd9d=ksJ t t
ttd>ksJ td?} td@}t | d dAksJ t | d ddBdCksJ t t|| | ddDksJ t t|| | dddBdEksJ t dttt d dFksJ t dttt d d.d/dGksJ t t	tdHks J t ttdd dIksJ t ttdd ddJdKksJ t t	td dLks+J t t	td.dMdHks8J t ttdd d.dMdNksHJ t t	td d.dMdLksWJ t ttdd( dOkseJ t ttdd( d.dPdQksuJ t td tdd( dRksJ t td tdd( d.dPdSksJ t tt	ddTksJ t tt	dddUgdVksJ t tt	ddWdXdYksJ t tt	dddUgdWdXdZksJ t tdtdd  g d[d\dXd]ksJ td}t |jg d^d_ksJ t |jg d^d`dadbksJ t |dcd ddksJ t |dcd d`dadeks.J t |d+d dfks<J t dgt dhksGJ t dgt d	d
diksTJ t dgt djd
dkksaJ t dtt dlksnJ t ttd  dlks{J t tttdd dmksJ t tttdd d.dPdnksJ t t doksJ t tt@ dpksJ t tt@ t@ dqksJ t ttB drksJ t ttB tB dsksJ t tt@ tB dtksJ t tttduksJ t tt ?  dvksJ t tttttdwksJ t tttttdxksJ t tt@  dyks'J t t tdzid{d|ks5J t tt@ tdztd}id{d~ksFJ t tt@ t@ tdztd}tdid{dks[J t ttB tdztd}id{dkslJ t ttB tB tdztd}tdid{dksJ t tt@ tB tdztd}tdid{dksJ t ttttdztd}id{dksJ t ttddd dddksJ t ttddddddksJ t ttdd d dddksJ tdd.d}t t| t| dksJ d S )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}Fevaluatez!\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)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  rJ   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   zr   rB   r&   r!   r   r   rr   r   r   cyclotomic_fieldextfield_elementprimes_aboverH   r}   r   r   r   r8   r9   )x_starr  kr+  r   r   r   test_latex_basicr   s6  $ "" 




 

"
" 
   

 
 










"


""$$r7  c                   C   sT   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 d S )NTz\text{True}Fz\text{False}z\text{None})r   r   r   r   r   r   r   test_latex_builtins  s
   r8  c                   C   s@  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$J t ttttdks0J t ttdd	d
ks<J t ttdddksHJ t ttddd dksVJ t ttddd dksdJ t ttddd dksrJ t ttttd dksJ t ttdd	d dksJ t ttddd d dksJ d S )Nr  r
  z&{\left\langle x - 4 \right\rangle}^{5}z&{\left\langle x + 3 \right\rangle}^{4}r   z"{\left\langle x \right\rangle}^{4}z({\left\langle - a + x \right\rangle}^{n}r)  z'{\left\langle x - 4 \right\rangle}^{-2}r  z'{\left\langle x - 4 \right\rangle}^{-1}r  z.{\left({\langle x - 4 \rangle}^{5}\right)}^{3}z.{\left({\langle x + 3 \rangle}^{4}\right)}^{3}z*{\left({\langle x \rangle}^{4}\right)}^{3}z0{\left({\langle - a + x \rangle}^{n}\right)}^{3}z/{\left({\langle x - 4 \rangle}^{-2}\right)}^{3}z/{\left({\langle x - 4 \rangle}^{-1}\right)}^{9})r   rh   r   anr   r   r   r   test_latex_SingularityFunction  sH   r<  c                   C   sL   t tddddksJ t tddddddksJ t t dks$J d S )	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   r   test_latex_cycle)  s
   rA  c                  C   s$  t tddddksJ t tddddddksJ t t dks$J t tddtd d	ks3J t tdd
ks=J t tdddddksJJ t tdddddddksZJ t t dddkseJ t   tj} dt_t tdddddks}J | t_W d    d S 1 sw   Y  d S )Nr  r  r  r=  r
  r>  r?  r@  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_cyclicr   r   r   test_latex_permutation0  s4   "rE  c                   C   s   t t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ddks.J t tdd	d
dddks<J t tdd	d
dddksJJ t tddd
dddksXJ d S )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   r   test_latex_FloatG  s"   rI  c                  C   s  t d} tt| j| j| j d | j dksJ tt| j| jdks&J ttt| j| j dks5J ttt| j | jdksDJ ttd| j | j dksTJ ttd| j | j | j dksgJ ttdt | j | j d	ksyJ tttd| j | j  d
ksJ ttd| j | j | j dksJ ttd| j | j dksJ tttd| j | j  dksJ tt	| j| j| j d | j dksJ tt	| j| jdksJ tt	t| j | jdksJ ttt	| j| j dksJ tt
| jdksJ tt
| jd| j  dksJ ttt
| j dks,J tt
t| j dks:J tt| jdksFJ tt| jd| j  dksWJ ttt| j dkseJ ttt| j dkssJ d S )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   r6  r   r   r   r   r.  r   )rJ  r   r   r   test_latex_vector_expressionsV  st     


 rM  c                  C   s  t d\} }}t d\}}}}t|dksJ t|dksJ t|dks'J t|dks/J dd tD }t|tt  dksDJ t| | dksNJ t| | d	ksXJ ttd
dksbJ ttddkslJ ttddksvJ ttddksJ ttddksJ ttddksJ ttddksJ ttddksJ ttddksJ ttddksJ ttddksJ ttdtd  d!ksJ d S )"NzGamma, lambda, rhoztau, Tau, TAU, taU\tau
\mathrm{T}c                 S   s   h | ]}|  qS r   )
capitalize).0lr   r   r   	<setcomp>      z%test_latex_symbols.<locals>.<setcomp>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}omegarJ   z\omega^{\beta})r#   r   r   lensetr   keysr!   )Gammalmbdarhor   TauTAUtaUcapitalized_lettersr   r   r   test_latex_symbols  s,    rg  c                  C   sb   t d\} }}t||  |kdksJ t|| |  dkdks!J t|d |d  dks/J d S )Nzrho, mass, volumez$\rho \mathrm{volume} = \mathrm{mass}r  z/\rho \mathrm{volume} {\mathrm{mass}}^{(-1)} = 1r  z/{\mathrm{mass}}^{3} \cdot {\mathrm{volume}}^{3}r#   r   )rb  massvolumer   r   r   test_latex_symbols_failing  s   
rk  c                  C   sl  t ttdks
J t tdtd dksJ td} t | tdks&J t | dks.J td}t |ttdks=J t |dksEJ td	}t |tttd
ksUJ t |d	ks]J td}t |dksiJ t |tdkssJ td}t |tttdksJ t tttdksJ t tttd dksJ t |tdksJ t |dksJ td}t |tttdksJ t |tdksJ t |dksJ td}t |dksJ t |tdksJ t tddksJ t tddksJ t tddksJ t tdd ksJ t td!dksJ t td"d ks%J t td#d$ks0J t td%d&ks;J t tdtd'd(ksJJ t tdtd'd)ksYJ t tdtd'd*kshJ t td!td'd)kswJ t td#td'd+ksJ t td%td'd,ksJ t td d d-ksJ t td d d.ksJ t td d d/ksJ t td! d d.ksJ t td" d d/ksJ t tdtd'd d0ksJ t tdtd'd d1ksJ t tdtd'd d2ksJ t td!td'd d1ksJ t td"td'd d2ks0J t td3d3ks;J t td4dksFJ t td5d6ksQJ t tddks\J t td7d6ksgJ t td3 d8kssJ t td4 d9ksJ t td5 d:ksJ t td d9ksJ t td7 d:ksJ t td3 d d;ksJ t td4 d d<ksJ t td5 d d=ksJ t td d d<ksJ t td7 d d=ksJ t td3td'd d>ksJ t td4td'd d?ksJ t td5td'd d@ksJ t tdtd'd d?ks-J t td7td'd d@ks>J t td3 dA dBksLJ t td4 dA dCksZJ t td5 dA dDkshJ t td dA dCksvJ t td7 dA dDksJ t td3td'dA dEksJ t td4td'dA dFksJ t td5td'dA dGksJ t tdtd'dA dFksJ t td7td'dA dGksJ t td3 t dHksJ t td4 t dIksJ t td5 t dJksJ t td t dIksJ t td7 t dJksJ t td3td't dKks0J t td4td't dLksAJ t td5td't dMksRJ t tdtd't dLkscJ t td7td't dMkstJ td}t td3 | dNksJ t td4 | dOksJ t td5 | dPksJ t td | dOksJ t td7 | dPksJ t td3td'| dQksJ t td4td'| dRksJ t td5td'| dSksJ t tdtd'| dRksJ t td7td'| dSksJ t tdTtdUks J t tdTt| dVks/J t tdWtdUks<J t tdWt| dVksKJ t tdXtdYksXJ tdZ}t |d[kseJ t |td\kspJ t t	td]ks{J t t	td^d_d`ksJ t t	dtd  d^d_daksJ t t	td d^d_dbksJ t t
td dcksJ t t
td dddedfksJ t t
td dgdedhksJ t t
td dgd^didjksJ t ttdddedkksJ t ttdddedlksJ t ttdmksJ t tt dnksJ t ttd doks!J t ttdpks,J t tt dqks8J t ttd drksEJ t ttdsksPJ t tt dtks\J t ttd duksiJ t tdtdvksuJ t tdtd dwksJ t tdxtdyksJ t tdxtdzksJ t ttd{ksJ t ttd|ksJ t ttd}ksJ t ttd d~ksJ t ttd dksJ t ttd dksJ t ttdtdx dksJ t tttd dks J t ttdtdx dksJ t tttd dksJ t ttdks(J t ttd dks5J t ttdks@J t ttt dksMJ t ttdksXJ t ttdkscJ t ttd dkspJ t ttd dks}J t ttdksJ td}t t|dksJ t ttdksJ t tttdksJ t tttdfdksJ t tttt fdksJ t ttt ttfdksJ t ttttdksJ t ttttdksJ t tttt ftt fdksJ t t!ttdksJ t t!ttd dksJ t t"ttdks+J t t"ttd dks9J t t#tdksDJ t t$tdksOJ t ttdksZJ t ttdkseJ t t%ttdksqJ t t&tdks|J t t'tdksJ t t'td dksJ t t'ttdksJ t t'ttd dksJ t t(tdksJ t t(td dksJ t t)ttdksJ t t)ttd dksJ t t*ttt+dksJ t t*ttt+d dksJ t t,tdk	sJ t t,td dk	sJ t t,ttdk	s J t t,ttd dk	s.J t t-tdk	s9J t t-td dk	sFJ t t.ttdk	sRJ t t.ttd dk	s`J t t/ttdk	slJ t t/ttd dk	szJ t t/tdk	sJ t t/td dk	sJ t t0tttdk	sJ t t0tttd dk	sJ t t0ttdk	sJ t t0ttd dk	sJ t t1tdk	sJ t t1td dk	sJ t t2ttdk	sJ t t2ttd dk	sJ t t3td dk
sJ t t4td dk
sJ t t5td dk
s!J t t6td dk
s.J t t6tdk
s9J t t7t+tt8tdk
sGJ t t7t+tt8td dk
sWJ t t9t+ttdk
sdJ t t9t+ttd dk
ssJ t t:t+tdk
sJ t t:t+td dk
sJ t t;t+tdk
sJ t t;t+td dk
sJ t t<t+tdk
sJ t t<t+td dk
sJ t t=t+ttdk
sJ t t=t+ttd dk
sJ t t>t+tdk
sJ t t>t+td dk
sJ t t?t+ttdksJ t t?t+ttd dksJ t t@t+tdksJ t t@t+td dks-J tdd^dӍ}	tdd^dӍ}
t tAt+tB|	|
dksGJ t tAt+tB|	|
dx dksWJ t tCt+tB|	|
dkseJ t tCt+tB|	|
dx dksuJ t tDddksJ t tDddx dksJ t tEt+dksJ t tEt+d dksJ t tFt+dksJ t tFt+d dksJ t tGtdksJ t tGtd dksJ t tGttdksJ t tGttd dksJ t tHtdksJ t tHtd dksJ t tHttdksJ t tHttd dks!J t tIt+dks,J t tIt+d dks9J t tJt+dksDJ t tJt+d dksQJ t tKt+dks\J t tKt+ddkshJ t tKt+tdkstJ t tKt+tKt+ dksJ t tLtKt+ddksJ t tKt+t dksJ t tKt+ttM dksJ t tNtddksJ t tNtd ddksJ t tNdtd dksJ t tNdt ddksJ t tNddt dksJ t tNtdd dksJ t dtNtd dksJ t tNddt t+ dksJ td}t |tdks+J t |dks4J d S )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)}rJ   z\beta{\left(x,y,z \right)}z!\operatorname{B}\left(x, y\right)z%\operatorname{B}^{2}\left(x, y\right)z\beta{\left(x \right)}\betarW   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)}r:  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)}rX  rY  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$\left(H_{n}\left(x\right)\right)^{2}thetarealphiz!Y_{n}^{m}\left(\theta,\phi\right)z2\left(Y_{n}^{m}\left(\theta,\phi\right)\right)^{3}z!Z_{n}^{m}\left(\theta,\phi\right)z2\left(Z_{n}^{m}\left(\theta,\phi\right)\right)^{3}z+\operatorname{polar\_lift}{\left(0 \right)}z/\operatorname{polar\_lift}^{3}{\left(0 \right)}z\phi\left(n\right)z#\left(\phi\left(n\right)\right)^{2}z\lambda\left(n\right)z&\left(\lambda\left(n\right)\right)^{2}z\sigma\left(x\right)z\sigma^{2}\left(x\right)z\sigma_y\left(x\right)z\sigma^{2}_y\left(x\right)z\sigma^*\left(x\right)z\sigma^*^{2}\left(x\right)z\sigma^*_y\left(x\right)z\sigma^*^{2}_y\left(x\right)z\nu\left(n\right)z"\left(\nu\left(n\right)\right)^{2}z\Omega\left(n\right)z%\left(\Omega\left(n\right)\right)^{2}zW\left(n\right)r  zW_{-1}\left(n\right)zW_{k}\left(n\right)zW^{2}\left(n\right)zW^{k}\left(n\right)zW^{p}_{k}\left(n\right)r  z	x \bmod 7z\left(x + 1\right) \bmod 7z7 \bmod \left(x + 1\right)z2 x \bmod 7z7 \bmod 2 xz\left(x \bmod 7\right) + 1z2 \left(x \bmod 7\right)z\left(7 \bmod 2 x\right)^{n}fjlkdz%\operatorname{fjlkd}{\left(x \right)}z\operatorname{fjlkd})Or   r8   r   r   r.  r0  rJ   r!   r:  rH   rE   rD   r:   r'   r6  r)   r(   r&   r$   r%   r=   r<   r>   r@   r?   r1   r6   r4   r3   rW   r"   r   r   r   rX   rG   r;   rA   r2   rq   rm   ro   rn   r;  rp   rO   rN   rM   rP   rS   rV   rT   rU   rR   rQ   re   brc   ra   rb   rg   r`   rf   r_   rd   ri   mrj   r5   r   r   r   r   r   r   r7   r   r+  r   )r  rl  rm  rn  mybetarq  rr  rX  r  r  r  r  r   r   r   test_latex_functions  s  """"
""""""""""""""""""""




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








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


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






 r  c                  C   s8   G dd dt } t| dksJ t| tdksJ d S )Nc                   @   r   )z6test_function_subclass_different_name.<locals>.mygammaNr   r   r   r   r   mygamma  r   r  z\operatorname{mygamma}z'\operatorname{mygamma}{\left(x \right)})rW   r   r   )r  r   r   r   %test_function_subclass_different_name  s   r  c               
   C   s   ddl m} m} ttttt| tddtdddt |dks"J ttt tddt |d	ks4J tt| dfd
|dksBJ ttt td|dksQJ d S )Nr   r   r0  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} x, 2 \\ 3 \end{matrix}\middle| {z} \right)}zH{{}_{0}F_{1}\left(\begin{matrix}  \\ 1 \end{matrix}\middle| {z} \right)})	sympy.abcr   r0  r   rZ   r   r   rY   r  r   r   r   test_hyper_printing!  s   r  c                  C   s,  ddl m} m}m}m}m}m}m}m}m	}m
}	 ddlm}
 t| t|
d t dks-J t|t|
dks8J t|t|
dksCJ t|t|
dksNJ t|t|
d d d	ks]J t|t|
d
kshJ t|t|
dkssJ t|t|
dks~J t|t|
dksJ t|	t|
dksJ d S )Nr   )
besseljbesselybesselibesselkhankel1hankel2jnynhn1hn2r0  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  r0  r   r;  r6  )r  r  r  r  r  r  r  r  r  r  r0  r   r   r   test_latex_bessel2  s   0r  c                  C   sx   ddl m} m} ddlm} t| |dksJ t||dks"J t| |d dks.J t||d dks:J d S )	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  r0  r   )r  r  r0  r   r   r   test_latex_fresnelD  s   r  c                   C   s   t dt dks
J d S )Nr  z\left(-1\right)^{x}r   r   r   r   r   r   test_latex_bracketsM     r  c                  C   s\  t dddd} tt dddd}t| t|  }t|d t|d  }|dks*J |dks0J d	}ttd
t ddks?J ttdtddksLJ ttdtdt dd| d ks`J ttdtdt dd d| d ksvJ ttdtdt dt dfd| d ksJ ttddksJ ttddksJ ttddksJ d S )NPsi_0TF)complexr  Psir   z\Psi_{0} \overline{\Psi_{0}}z \overline{{\Psi}_{0}} {\Psi}_{0}z\mathrel{..}\nobreak x1rK  z{x_{1}}_{i}x2z{x_{2}}_{i}x3Nz{x_{3}}_{{i}_{0zN - 1}}r  zN}}x4r:  r  z{x_{4}}_{{i}_{azb}}rW   rp  za ba_bza_{b})r!   r   r   r3   r   r   )
Psi_symbolPsi_indexedsymbol_latexindexed_latexintervalr   r   r   test_latex_indexedQ  s   (,0r  c               	   C   s  t ttd tdddksJ t ttttd  tdddks"J t tttttd  tdddddks9J t ttttttd  tdddddddksTJ t tttt tddd	kseJ t tttt td  tddd
kszJ t ttttt td  tddtdddksJ t tttttt td  tddtddtdddksJ td} t tt| tttddtdddt | tt ksJ t ttt| tttddtddtdddt | tt ksJ t tttd tdd tdddks
J t ttttttddtdd tddtdddks(J t tttt t tdtftdddksAJ t tttddd dksQJ t t| ttd dksaJ t t| ttt	fdksqJ t
d}t
d}t t| |||dksJ t
d}t t| tt|fdksJ t
d}t t| ttt||fdksJ t t| ttddd ksJ d S )!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   rH   r.  r   rr   r8   r   r;  r!   r?   )r  r  r  r  r  r   r   r   test_latex_derivativesf  sr   $, *4 *,0
&



 
$r  c                   C   s$   t ttt ttfddksJ d S )Nr  r  z+\left. x y \right|_{\substack{ x=1\\ y=2 }})r   r   r   r.  r   r   r   r   test_latex_subs  s   $r  c                	   C   s  t ttttdksJ t ttd tddfdksJ t ttd tddfdks-J t tttd  tddftd	ks@J t tttd  tddftd
ddksUJ t tttd  tddftd
dddkskJ t tttdfdksxJ t ttt ttdksJ t ttt t tttdksJ t ttt t t ttttdksJ t ttttttttdksJ t tttttddfdksJ t tttd t tdksJ t ttttt t tdksJ t tttd dksJ t ttt tdks
J t tttd  tdksJ t ttt tdks(J t tttdddks6J t tttddfdddksGJ d S ) 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   rr   r9   r   r.  r0  tr   r   r   r   test_latex_integrals  sT    ""
&r  c                  C   s   t tfD ],} t| tt td gdksJ t| tdddks#J t| tdddks0J qt} t| tt td g dksCJ t| tdd dksPJ t| tdd dks]J d S )Nr  z\left\{x^{2}, x y\right\}r  r>  z\left\{1, 2, 3, 4, 5\right\}   z4\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right\})	frozensetr^  r   r   r.  ranger   sr   r   r   test_latex_sets  s    
 r  c                  C   s&   t dd} t| }t|dksJ d S )Nr  r  z%SetExpr\left(\left[1, 3\right]\right))r   r   r   )ivser   r   r   test_latex_SetExpr  s   
r  c                  C   s  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sFJ t ttdddksRJ t tdt ddks_J t tt tdkskJ t ttt ddksxJ td\} }}t t| ||dksJ t t| dddksJ t td|ddksJ t tdd|dksJ tddd}tdddd}tdddd }t t||d d!ksJ t tt |dd"ksJ t t|td#ksJ t t| | d d$ksJ d S )%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)rK  Tr   r;  )negativer   r+  )r-  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!   )r:  r  crK  r;  r+  r   r   r   test_latex_Range  s,   r  c            
      C   s  t td dtf} td}d}t| |ksJ d}t||ks!J t td d}tdd}d}t||ks7J d}t||ksAJ t td t df}tdt df}d	}t||ks]J d
}t||ksgJ d}tt| ||kstJ d}tt|||ksJ d}tt|||ksJ d}tt| ||ksJ d}tt|||ksJ d}tt|||ksJ t td tdtf}d}t||ksJ td}t |td  tddf}	d}t|	|ksJ d S )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   r:  r   r   r   r   r   r   r!   )
s1s2	latex_strs3s4s5s6s7r  s8r   r   r   test_latex_sequences  sJ   
r  c                  C   s&   d} t tttt tf| ksJ d S )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  r   r   r   test_latex_FourierSeries>  s   "r  c                  C   s$   d} t ttdt | ksJ d S )Nz;\sum_{k=1}^{\infty} - \frac{\left(-1\right)^{- k} x^{k}}{k}r  )r   r   r9   r   r  r   r   r   test_latex_FormalPowerSeriesD  s    r  c                  C   s   t d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s6J ttd| ddd	ksCJ ttd| ddd
ksPJ d S )Nr:  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   r:  r   r   r   test_latex_intervalsI  s   r  c                  C   sZ   t ddd} ttdddksJ ttd| dksJ tt| d | d d	ks+J d S )
Nr:  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  r   r   r   test_latex_AccumuBoundsS  s   r  c                   C      t tjdks	J d S )N	\emptyset)r   r    EmptySetr   r   r   r   test_latex_emptyset[     r  c                   C   r  )Nz
\mathbb{U})r   r    UniversalSetr   r   r   r   test_latex_universalset_  r  r  c                  C   s2   t d} t d}t|| }t| dksJ d S )NrJ  Bz- (A B - B A))r   r   r   doit)rJ  r  commr   r   r   test_latex_commutatorc  s   
r  c                   C   sP   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 d S )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   r   test_latex_unionj  s    r  c                   C   s&   t ttddtttdksJ d S )Nr   r  z(\left[0, 1\right] \cap \left[x, y\right])r   r   r   r   r.  r   r   r   r   test_latex_intersectionq     r  c                   C   s*   t ttddtdddddksJ d S )Nr  r
  r  r  Fr  z-\left[2, 5\right] \triangle \left[4, 7\right])r   r   r   r   r   r   r   test_latex_symmetric_differencev  s
   r  c                   C   s   t ttjtjdksJ d S )Nz\mathbb{R} \setminus \mathbb{N})r   r   r    RealsNaturalsr   r   r   r   test_latex_Complement|  s   r  c                  C   s   t dd} t dd}tddd}t| d dt|  ksJ t| d dt|  ks,J t| | |  dt| t|t|f ksEJ d S )	Nr   r  r  r  r  z%s^{2}z%s^{10}z%s \times %s \times %s)r   r   r   flatten)linebiglinefsetr   r   r   test_latex_productset  s   

r  c                  C   s$   t ddd} tt| dksJ d S )Nr  r  r  z.\mathcal{P}\left(\left\{1, 2, 3\right\}\right))r   r   r   )r  r   r   r   test_latex_powerset     r  c                  C   sr   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s7J d S )N\omegar  r  z3 \omega^{2}r  z3 \omega^{2} + \omegaz\omega^{2} + 2 \omega)r   r   r   r   )r  wpr   r   r   test_latex_ordinals  s   
&r  c                  C   sL  t d\} }}}t| }t|}t|}t|}t||dd}t||dd}	t||dd}
t||dd}t||dd}t||dd}t||dd}t||dd}t||}t||}tt||	dddksgJ tt||	dddkstJ tt||dddksJ tt||dddksJ tt||dddksJ tt||ddd	ksJ tt|
|ddd
ksJ tt||dddksJ tt||dddksJ tt||dddksJ tt||dddksJ tt||	dddksJ 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dks<J tt|
|dddksJJ tt||dddksXJ tt||dddksfJ tt|| dkstJ tt||	dksJ tt|
|dksJ tt||dksJ tt||dksJ d S )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  )r:  r  r  drJ  r  CDU1U2I1I2C1C2D1D2P1P2r   r   r   test_set_operators_parenthesis  s   













r  c                   C   r  )N
\mathbb{C})r   r    	Complexesr   r   r   r   test_latex_Complexes  r  r  c                   C   r  )N
\mathbb{N})r   r    r  r   r   r   r   test_latex_Naturals  r  r  c                   C   r  )N\mathbb{N}_0)r   r    	Naturals0r   r   r   r   test_latex_Naturals0  r  r  c                   C   r  )N
\mathbb{Z})r   r    Integersr   r   r   r   test_latex_Integers  r  r  c                  C   s   t d} ttt| | d tjdksJ t d}tt| |f| | h dddh}t|dks2J tt| |ff| | th dddh}t|d	ksNJ d S )
Nr   r  z2\left\{x^{2}\; \middle|\; x \in \mathbb{N}\right\}r.  >   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   r.  imgsetr   r   r   test_latex_ImageSet   s   "(r  c                  C   sT   t d} tt| t| d dtjdksJ tt| t| d dtjdks(J d S )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   r   r   r   test_latex_ConditionSet/  s   r  c                   C   sT   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 d S )Nr  r
  r  r>  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   r   test_latex_ComplexRegion7  s   "r!  c                  C   s$   t d} tt| tjdksJ d S )Nr   zx \in \mathbb{N})r!   r   r   r    r  r  r   r   r   test_latex_Contains?     r"  c                   C   s   t tttd  tddftddfdksJ t ttd tddfdks&J t ttd t tddfdks8J t ttd t tddfd dksLJ d S )	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   r.  r   r   r   r   test_latex_sumD  s   "r$  c                   C   s   t tttd  tddftddfdksJ t ttd tddfdks&J t ttd t tddfdks8J t tttddfd dksHJ d S )	Nr  r)  r  r
  z=\prod_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}z\prod_{x=-2}^{2} x^{2}z'\prod_{x=-2}^{2} \left(x^{2} + y\right)z#\left(\prod_{x=-2}^{2} x\right)^{2})r   r
   r   r.  r   r   r   r   test_latex_productO  s   "r%  c                  C   s   t ttttdksJ td} t t| ttddksJ t t| ttdddks-J t t| ttdd dks=J t t| ttdd	d
dksMJ d S )Nz\lim_{x \to \infty} xr  r   z#\lim_{x \to 0^+} f{\left(x \right)}-z#\lim_{x \to 0^-} f{\left(x \right)}r  z4\left(\lim_{x \to 0^+} f{\left(x \right)}\right)^{2}z+-)dirz!\lim_{x \to 0} f{\left(x \right)})r   r   r   r   r   )r  r   r   r   test_latex_limits[  s   r(  c                   C   s   t ttdks
J t ttdddksJ t tttt dks$J t tttt dddks4J t ttttdksAJ t ttttdddksPJ d S )	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   r9   r   r.  powr   r   r   r   test_latex_logl  s   r+  c                  C   sD   t d} | t }t|dv sJ t d} | t }t|dv s J d S )Nro  )z	\beta + xz	x + \betarJ   )r!   r   r   )rJ   r.  r   r   r   test_issue_3568x  s   r,  c                   C   s   t dt tdd dksJ t dt tdd dddks J t dt tdd ddd	d
ks2J t dt tgdks>J d S )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   r.  r   r   r   r   
test_latex  s   r.  c                  C   sL   t ddtd dtdtd di} t| dksJ t| }t|dks$J d S )Nr  r  r  r  z;\left\{ 1 : 1, \  x : 3, \  x^{2} : 2, \  x^{3} : 4\right\})r   r   r   r   )r  r  r   r   r   test_latex_dict  s    r/  c                  C   s*   t dt dt dg} t| dksJ d S )NrX  r:  r  z)\left[ \omega_{1}, \  a, \  \alpha\right]r!   r   )llr   r   r   test_latex_list     r2  c                   C   p   t tjdks	J t tjdksJ t tjdksJ t tjdks$J t tjdks-J t tjdks6J d S )NGrp  e\phi\piz\text{TribonacciConstant})r   r    Catalan
EulerGammaExp1GoldenRatioPiTribonacciConstantr   r   r   r   test_latex_NumberSymbols     r?  c                   C   s   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 dks<J t tdd t tddt  d	ksQJ d S )
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   r.  r   r   r   r   test_latex_rational  s    rA  c                   C   s0   t dt dks
J t dtt  dksJ d S )Nr  r  z\frac{1}{x + y}r   r   r.  r   r   r   r   test_latex_inverse  s   rC  c                   C   sv   t tt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 t ttdd dks9J d S )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   rK   r   r   r   r   r   test_latex_DiracDelta  s   rD  c                   C   s0   t ttdks
J t ttd dksJ d S )Nz\theta\left(x\right)r  z%\left(\theta\left(x\right)\right)^{2})r   rL   r   r   r   r   r   test_latex_Heaviside  s   rE  c                   C   sn   t tttdksJ t tttd dksJ t ttd tdks%J t ttttddddks5J d S )	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   rk   r   r.  r   r   r   r   r   test_latex_KroneckerDelta  s   rF  c                   C   s   t ttttdksJ t ttttd dksJ t ttttd dks(J t tttd tdks6J t ttd ttdksDJ d S )Nz\varepsilon_{x y z}r  z$\left(\varepsilon_{x y z}\right)^{2}r  z\varepsilon_{x, y, z + 1}z\varepsilon_{x, y + 1, z}z\varepsilon_{x + 1, y, z})r   rl   r   r.  r0  r   r   r   r   test_latex_LeviCivita  s    rG  c                      s~   t t  t dksJ t dddksJ t dddks J t dddks*J t ddd	ks4J tt fd
d d S )Nzx + yplainr  inlinez$x + y$r  z%\begin{equation*}x + y\end{equation*}r-  z#\begin{equation}x + y\end{equation}c                      s   t  ddS )Nr   r  r   r   exprr   r   <lambda>      ztest_mode.<locals>.<lambda>)r   r.  r   r   
ValueErrorr   r   rK  r   	test_mode  s   rP  c                   C   s   t ttttdksJ t ttttdksJ t ttttd dks&J t ttttd dks4J t ttttdks@J t ttttdksLJ t ttttd dksZJ t ttttd d	kshJ d S )
NzC\left(x, y, z\right)zS\left(x, y, z\right)r  zC\left(x, y, z\right)^{2}zS\left(x, y, z\right)^{2}zC^{\prime}\left(x, y, z\right)zS^{\prime}\left(x, y, z\right)z"C^{\prime}\left(x, y, z\right)^{2}z"S^{\prime}\left(x, y, z\right)^{2})r   r[   r   r.  r0  r]   r\   r^   r   r   r   r   test_latex_mathieu  s    rQ  c                  C   s
  t ttdk ftd df} t| dksJ t| dddksJ t ttdk fdtdkf} t| dks4J td	d
d\}}t |d t||f|| df} d}t| |ksVJ t||  d| ksbJ t| | d| ksnJ tt ttdk ftd tdk fdksJ d S )Nr  r  TzK\begin{cases} x & \text{for}\: x < 1 \\x^{2} & \text{otherwise} \end{cases}r  zM\begin{cases} x & \text{for}\: x \lt 1 \\x^{2} & \text{otherwise} \end{cases}r   zG\begin{cases} x & \text{for}\: x < 0 \\0 & \text{otherwise} \end{cases}A BFcommutativezM\begin{cases} A^{2} & \text{for}\: A = B \\A B & \text{otherwise} \end{cases}zA \left(%s\right)z\left(%s\right) AzM\begin{cases} x & \text{for}\: x < 1 \\x^{2} & \text{for}\: x < 2 \end{cases})rC   r   r   r#   r   )r+  rJ  r  r  r   r   r   test_latex_Piecewise  s    
  rU  c                  C   s   t dt tgttd gg} t| dksJ t| dddks J t| dddks*J t| d	dd
ks4J t| d d	ddks?J t ddtd}t|dksOJ d S )Nr  z;\left[\begin{matrix}x + 1 & y\\y & x - 1\end{matrix}\right]rI  r  zG$\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_delimrW  z0\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}   z\\left[\begin{array}{ccccccccccc}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right])r   r   r.  r   r  )MM2r   r   r   test_latex_Matrix  s(   


r]  c                  C   sl   t d} t dtd}tt|| t|| gt|| | t|| | gg}d}t||ks4J d S )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   rH   rF   r   r   )r  r^  r[  expectedr   r   r    test_latex_matrix_with_functions  s   "rb  c                  C   s&  t d\} }}}ttttfD ]}|| }t|dksJ |d|  |g||gg}|d|  ||g}t||}t||}t|dksCJ t|dksKJ t|dksSJ t|dks[J || |d| gg}	|| g|gd| gg}
||
 g}t|	dksJ t|
d	ksJ t|d
ksJ qd S )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   r.  r0  r  	ArrayTyper[  M1r\  M3MrowMcolumnMcol2r   r   r   test_latex_NDimArray%  sF   


rj  c                   C   s   t ddt  dddksJ t ddt  dddksJ t ddt  dddks*J t dt ddd	ks6J t dt ddd
ksBJ t dt dddksNJ d S )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   r   test_latex_mul_symbolS  s   rl  c                  C   s8   ddt d  } t| dksJ td|  dksJ d S )Nr  r  z!4 \cdot 4^{\log{\left(2 \right)}}r  z+\frac{1}{4 \cdot 4^{\log{\left(2 \right)}}})r9   r   )r.  r   r   r   test_latex_issue_4381]  s   rm  c                   C   s  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s2J t tddks<J t tddksFJ t tddksPJ t tddksZJ t tddksdJ t tddksnJ t tddksxJ t tddksJ t tddksJ t tddksJ t tddksJ t tddksJ t td d!ksJ t td"d#ksJ t td$d#ksJ d S )%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   r   test_latex_issue_4576c  s(   r  c                  C   sP   t d} dtt|  d ddv sJ dtd|   d ddv s&J d S )Nr   ze^{-x}r    z3^{-x}r  )r!   r   r8   replacer  r   r   r   test_latex_pow_fractionz  s   "&r  c                  C   sj   t ddd\} }}t| | |d  dksJ t|d |  | dks%J t| |d  | dks3J d S )NzA,B,CFrS  r  z
A B C^{-1}z
C^{-1} A Bz
A C^{-1} Brh  rJ  r  r  r   r   r   test_noncommutative  s    r  c                  C   sl   t d t d t  td  dt  td   } t| dddks J t| dddks*J t| d	dd
ks4J d S )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   r.  r   rK  r   r   r   test_latex_order  s   ,r  c                   C   sR   t tttd dksJ t tttftd dksJ t tttdks'J d S )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   r.  r   r   r   r   test_latex_Lambda  s   r  c                  C   s  t dt\} }}t d| \}}}}t|| dksJ t|d dks%J t|d dks/J t|d d| |  d |d  | | d d	ksKJ t|d d| |  d |d  | |d |  d
ksiJ t|d d| |  d |d  | |d |  d dksJ t|d  d| |  d |d  | |d |  d dksJ t|d | d  | d| |  d dksJ t|d | d  | d| |  d dksJ d S )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   r.  r0  r   r   r   test_latex_PolyElement  s.   .268((r  c                  C   s  t dt\} }}t d| \}}}}}t|| dksJ t|d dks&J t|d dks0J t|d dks:J t|| d	ksDJ t|| | d
ksPJ t|||  dks\J t|| ||  dksjJ t|d | dksvJ t|d | dksJ t| d | dksJ t|d ||  dksJ t| |d  dksJ t|| |d  dksJ t|d | | d |d | d  dksJ t|d | | d |d | || |  d  dksJ d S )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   r.  r0  r  r   r   r   test_latex_FracElement  s,   &2r  c                   C   s\   t ttd dt  tdksJ t ttt tdksJ t tdt t dks,J d S )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   r.  r   r   r   r   test_latex_Poly  s   r  c                   C   s   t ttdtdtdgtdksJ t ttdtt ddgtdks#J t tttd  td t  tt  ttd   tt td   t tt  t ttfdksTJ d S )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   r:  r  r  r   r.  r   r   r   r   test_latex_Poly_order  s   Nr  c                   C   s&   t ttd t d ddksJ d S )Nr
  r  r   z6\operatorname{CRootOf} {\left(x^{5} + x + 3, 0\right)})r   r   r   r   r   r   r   test_latex_ComplexRootOf  r  r  c                   C   s&   t ttd t d tdksJ d S )Nr
  r  zc\operatorname{RootSum} {\left(x^{5} + x + 3, \left( x \mapsto \sin{\left(x \right)} \right)\right)})r   r   r   rH   r   r   r   r   test_latex_RootSum  r  r  c                   C   s   t tdd  d S )Nc                   S   s   t tt ddS )Ngarbage)methodrB  r   r   r   r   rM        ztest_settings.<locals>.<lambda>)r   	TypeErrorr   r   r   r   test_settings  s   r  c                   C   s
  t ttdks
J t ttd dksJ t ttdks J t tttdks+J t ttd dks7J t tttd dksDJ t ttdksNJ t tttdksYJ t tttttfdksgJ t ttd dkssJ t tttd dksJ t tttttfd d	ksJ t ttd
ksJ t tttdksJ t ttd dksJ t tttd dksJ t t	tdksJ t t	td dksJ t t
tdksJ t t
ttdksJ t t
td dksJ t t
ttd dksJ d S )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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))r   r,   r;  r*   r   r+   r  r.  r/   r.   r0   r   r   r   r   test_latex_numbers  s,     r  c                   C   sH   t ttdks
J t tttdksJ t tttd dks"J d S )NzE_{n}zE_{n}\left(x\right)r  zE_{n}^{2}\left(x\right))r   r-   r;  r   r   r   r   r   test_latex_euler  s   r  c                   C   s,   t tddks
J t tddksJ d S )Nlamda\lambdaLamda\Lambdar~  r   r   r   r   
test_lamda  s   r  c                  C   s   t d} t d}t| dksJ t| | diddksJ t| | | diddks*J t| d | diddks8J t| | | d|didd	ksHJ d S )
Nr   r.  r$  r%  zx_i + yr  zx_i^{2}y_jz	x_i + y_jr0  r   r.  r   r   r   test_custom_symbol_names  s   $r  c                  C   s   t ddd} t ddd}td}t ddd}t| d|  dv s"J t| d|  d	v s.J t|d|   d
v s:J t|d|   dv sFJ t|| | |j ||j   dks[J ttt||t||dkslJ ttt||t||dks}J d S )Nr  r
  r  r;  rm  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  r;  rm  r   r   r   test_matAdd!  s   *"&r  c                  C   s   t ddd} t ddd}td}td|  dksJ td| |  dks&J td|  d	ks0J td
|  dks:J ttd|  dksFJ ttd |  dksSJ tdtd | |  dkscJ td|  | d|   dv ssJ d S )NrJ  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   rB   )rJ  r  r   r   r   r   test_matMul2  s    $r  c            	      C   s  t ddd} td\}}}}}td| | }tddd}tddd}tt|d	d	d
ks-J t|||d ||d f dksAJ t|||d d||d df dksWJ t|d ||d f dksgJ t|d ||d f dkswJ t||d d |f dksJ t|||||f dksJ t|||||||f dksJ t||d ||d |f dksJ t|d ||d ||f dksJ t|d d |d d |f dksJ tt|ddd
ksJ tt|d | d fd | d fd
ksJ tt|d| d fd| d fd
ksJ tt|d| dfd| dfdks#J t|ddddddf dks6J t|ddddddf dksIJ t|ddd d ksWJ t|d ddd!df d"ksiJ t|d ddddf d#ks{J t|dd ddf d$ksJ t|ddddf d%ksJ t|ddddddf d&ksJ t|| dd dd f d'ksJ d S )(Nr;  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
  r>  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   )	r;  r   r.  r0  r  r  r  r  r  r   r   r   test_latex_MatrixSliceA  s:   (,    $$$$$&&&&$$ "&*r  c            
      C   s   ddl m} m}m}m}m} ddlm} | ddd}t||dkdks&J |dd}t||d	kd
ks7J |dd}|dd}	t|t	||	j
dksOJ t|tttdddks_J d S )Nr   )r   DieExponentialpspacewhere)RandomDomainr  r  z.\text{Domain: }0 < x_{1} \wedge x_{1} < \inftyd1r>  r  z'\text{Domain: }d_{1} = 5 \vee d_{1} = 6r:  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  rJ  r  r   r   r   test_latex_RandomDomainb  s    


r  c                  C   st   ddl m}  | tt}| ttf }t|ttt  tttt  ks'J t|tt ttt ks8J d S )Nr   QQ)sympy.polys.domainsr  
frac_fieldr   r.  r   convert)r  Fr   r   r   r   test_PrettyPolyu  s
   *&r  c                  C   sN  t d} t d}td}t d}t d}tt|| | |dks"J tt|||| ||dks2J tt|| | |dks@J tt|||| ||fd	ksQJ tt|| | |d
ks_J tt|||| dksmJ tt	|| | |dks{J tt
|||| dksJ tt|| | |dksJ tt|||| dksJ d S )Nr   r6  r  r:  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{   rx   rz   rw   rt   rv   rs   ru   r|   ry   )r   r6  r  r:  r  r   r   r   test_integral_transforms~  sF   r  c                  C   sD   ddl m}  t| ttdksJ t| jttdddks J d S )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   r.  r  r   r   r   test_PolynomialRingBase  s
   r  c                  C   sp  ddl m} m}m}m}m}m} | d}| d}| d}|||d}	|||d}
||}|d}t|d	ks8J t|	d
ks@J t|dksHJ t|
|	 dksRJ t|dksZJ | }t|dkseJ ||	d|
tj	i}t|dksvJ ||	d|
tj	i|
|	 di}t|dksJ | d}| d}| d}|||d}|||d}|||g}||}t|dksJ d S )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\}rJ  r  r  r  rl  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  rJ  r  r  r  rl  gridr   r   r   test_categories  s6    
r  c                  C   s  ddl m}  ddlm} | tt}|d}|ttgdtd g}t	|dks+J t	|dks3J |
td t}t	|dksCJ || }t	|d	ksOJ t	|dtd
 d gdtgdkscJ || td| tdddg}t	|dksJ d S )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.agcar  r  r   r.  free_module	submoduler   ideal)r  r  r   r  r[  r   Qrm  r   r   r   test_Modules  s0   
r  c                  C   sJ   ddl m}  | ttd d g }t|dksJ t|jdks#J d S )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   r   r   r   test_QuotientRing  s   r  c                  C   s0   t ddd\} }t| | }t|dksJ d S )NrR  FrS  z!\operatorname{tr}\left(A B\right))r#   r   r   )rJ  r  r  r   r   r   test_Tr
  s   r  c                  C   s   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s8J t| || d	ksDJ t| ||dd|f||ddffd
ks\J d S )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  r  r   r   r   )r  r  r  r  r  r  r  r   r   r   test_Determinant  s    r  c            
      C   s  ddl m} m}m} tddd}tddd}t| |dks J t| || dks,J t| || | dks:J t| || d	ksFJ t| || | d
ksTJ t| |d dks`J t| |d dkslJ t| ||dksxJ t|| |dksJ t| ||dksJ t|| |dksJ t|| || dksJ td}t| |dksJ t| || dksJ ddl m}m}m	} t| ||dd|f||ddffdksJ tddd}	t| |	dksJ d S )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}r  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  r  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})
r  r  r  r  r   r   r   r  r  r  )
r  r  r  r  r  r  r  r  r  Mxr   r   r   test_Adjoint   s8   r  c            
      C   s\  ddl m} m}m} tddd}tddd}t| |dks J t| || dks,J t| ||ddks9J t|| |dd	ksFJ t| ||dd
ksSJ t|| |ddks`J td}t| |dksnJ t| || dkszJ ddl m}m}m	} t| ||dd|f||ddffdksJ tddd}	t| |	dksJ d S )Nr   )r  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}r  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}r  zi\left[\begin{matrix}1 & X\\\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] & 0\end{matrix}\right]^{T}r  z\left(M^{x}\right)^{T})
r  r  r  r  r   r   r   r  r  r  )
r  r  r  r  r  r  r  r  r  r  r   r   r   test_Transpose=  s,   r  c                  C   s*  ddl m} m} ddlm}m}m} tddd}tddd}t| ||| dks+J t| ||| dks8J t||dd	ksCJ t||d
dksNJ t||||ddks\J t||||ddksjJ t|||d
d
dksxJ t|||d
d
dksJ t||t	d dksJ d S )Nr   )HadamardProductr  )r   r   r  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)})
r  r  r  sympy.matrices.expressionsr   r   r  r   r   r;  )r  r  r   r   r  r  r  r   r   r   test_HadamardU  s.   r  c                  C   s   ddl m}  tddd}tddd}t| |ddksJ t| || ddks*J t| || ddks7J t| || dd	ksDJ t| || dd
ksQJ tddd}t| |ddksbJ d S )Nr   )r  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}r  z\left(M^{x}\right)^{2})r  r  r   r   )r  r  r  r  r   r   r   test_MatPowm  s   r  c                  C   sT   t ddd} | j|  t}t|dksJ | ttdt }t|dks(J d S )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  	applyfuncrH   r   r   r   )r  rL  r   r   r   test_ElementwiseApplyFunction{  s
   r  c                  C   sD   ddl m}  t| dddddksJ t| dddddks J d S )	Nr   r  r  rH  mat_symbol_styler  boldz
\mathbf{0})"sympy.matrices.expressions.specialr  r   r  r   r   r   test_ZeroMatrix     r  c                  C   sD   ddl m}  t| dddddksJ t| ddddd	ks J d S )
Nr   r  r  r  rH  r  1r  z
\mathbf{1})r  r  r   r  r   r   r   test_OneMatrix  r  r  c                  C   s@   ddl m}  t| ddddksJ t| ddddksJ d S )	Nr   Identityr  rH  r  z
\mathbb{I}r  z
\mathbf{I})r  r  r   r  r   r   r   test_Identity  s   r  c                  C   s<   ddl m} m} t| ddksJ t|tdksJ d S )Nr   DFTIDFTr  z\text{DFT}_{13}z\text{IDFT}_{x})"sympy.matrices.expressions.fourierr  r  r   r   r  r   r   r   test_latex_DFT_IDFT  s   r	  c                  C   sl   t d} t|  }t|dksJ t|  }t|dksJ t|  }t|dks(J t|  }t|dks4J d S )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   )symsrL  r   r   r   test_boolean_args_order  s   r  c                  C   s   t d} t| dksJ d S )Nr  rK  )rB   r   )rK  r   r   r   test_imaginary  s   r  c                   C   sd   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s0J d S )Nz\sinz\cosz\tanz\logz\operatorname{Ei}\zeta)r   rH   rF   rI   r9   rS   rq   r   r   r   r   test_builtins_without_args     r  c                  C   s   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s8J t d	}t|d
ksDJ t d}t|tdksRJ t|dksZJ d S )NAlpha
\mathrm{A}z\mathrm{A}{\left(x \right)}Beta
\mathrm{B}Eta
\mathrm{H}z\mathrm{H}{\left(x \right)}r=  \Pichiz\chi{\left(x \right)}\chir   r   r   )r  r+  r  r   r   r   test_latex_greek_functions  s   r  c                  C   s   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s2J d} t | dks<J d} t | dksFJ d S )Nr  r  r  r  r  r  omicronor=  r  r   r8  LamdaHatDOTz\dot{\hat{\Lambda}})r   r  r   r   r   test_translate  s   r  c                  C   s2   ddl m}  | D ]}tt|d| ksJ qd S )Nr   )other_symbols\)sympy.printing.latexr  r   r#   )r  r  r   r   r   test_other_symbols  s   r"  c                   C   s  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s2J t tddks<J t tddksFJ t tddksPJ t tddksZJ t tddksdJ t tddksnJ t tddksxJ t tddksJ t tddksJ t tddksJ t tdd ksJ t td!d"ksJ t td#d$ksJ t td%d$ksJ t td&dksJ t td'dksJ t td(d(ksJ t td)d)ksJ t td*d*ksJ t td+d+ksJ 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s1J t td2d2ks<J t td3d3ksGJ t td4d4ksRJ t td5d5ks]J t td6d6kshJ t td7d7kssJ t td8d8ks~J t td9d9ksJ t td:d:ksJ t td;d;ksJ t td<d=ksJ t td>d?ksJ t td@dAksJ t tdBdCksJ t tdDdEksJ t tdFdGksJ d S )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Vecr1   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   r   test_modifiers  sd   


rO  c                   C   s  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s2J t tddks<J t tddksFJ t tddksPJ t tddksZJ t tddksdJ t tddksnJ t tddksxJ t tddksJ t tddksJ t tddksJ t tdd ksJ t td!d"ksJ t td#d$ksJ t td%d&ksJ t td'd(ksJ t td)d*ksJ t td+d,ksJ t td-d.ksJ t td/d0ksJ t td1d2ksJ 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s1J t td=d>ks<J t td?d@ksGJ t tdAdBksRJ t tdCdDks]J t tdEdFkshJ t tdGdHkssJ t tdIdJks~J t tdKdLksJ t tdMdNksJ t tdOdPksJ t tdQdRksJ t tdSdTksJ t tdUdVksJ t tdWdXksJ t tdYdZksJ t td[d\ksJ t td]d^ksJ t td_d`ksJ 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s9J t tdmdnksDJ d S )oNr  r  rJ   ro  rW   rp  delta\deltaepsilonz\epsilonrq   r  etaz\etar  z\thetaiotaz\iotakappaz\kappalambdar  r   z\munuz\nuxiz\xir  r  r   r8  rb  z\rhosigmaz\sigmar   rN  upsilonz\upsilonr  r7  r  r  psiz\psir\  r   r  r  r  r  r`  \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}r=  r  Rhoz
\mathrm{P}Sigmaz\Sigmarc  rO  Upsilonz\UpsilonPhiz\PhirQ   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   r   test_greek_symbols!	  sn   rs  c                   C   r4  )Nz
\mathbb{Q}r  r  r  z
\mathbb{R}r  )r   r    	Rationalsr  r  r  r  r  r   r   r   r   test_fancyset_symbols]	  r@  ru  c                   C   s   t tdksJ d S )Nz\mathcal{COS})r   rs   r   r   r   r   *test_builtin_without_args_mismatched_namesf	  s   rv  c                   C   sd   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s0J d S )Nz\operatorname{Chi}z\operatorname{B}r\  rQ  rp  )r   rQ   rJ   rW   rk   rK   r   r   r   r   r   test_builtin_no_argsk	  r  rw  c                  C   s    t d} t| tdksJ d S )Nr=  z\Pi{\left(x \right)}r  r+  r   r   r   test_issue_6853t	  s   ry  c                  C   s   t dtd dd} t| dksJ t dtd dd} t| dks"J t tjtd dd} t| dks4J t ttd dd} t| d	ksEJ t t td dd} t| d
ksWJ t dtd } t| dksfJ t dtd } t| dksuJ d S )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    r/  r.  )r6  r   r   r   test_Muly	  s   rz  c                  C   sX   t dddd} t| dksJ tttdd dksJ td}t|d d	ks*J d S )
Nr  Fr  z2^{2}r  r  z\frac{1}{\sqrt[3]{x}}zx^2z\left(x^{2}\right)^{2})r   r   r   r   r!   )r6  r  r   r   r   test_Pow	  s
   r{  c                   C   s4   t tttdksJ t ttttdksJ d S )Nzx \Leftrightarrow yzx \not\Leftrightarrow y)r   r   r   r.  r   r   r   r   r   test_issue_7180	  s   r|  c                   C   s   t tjt dksJ d S )Nz\left(\frac{1}{2}\right)^{n})r   r    r/  r;  r   r   r   r   test_issue_8409	  s   r}  c                  C   ,   ddl m}  | ddd}t|dksJ d S )Nr   
parse_exprz-B*AFr  zA \left(- B\right)sympy.parsing.sympy_parserr  r   )r  r6  r   r   r   test_issue_8470	     r  c                  C   sx   t ddd} t ddd}t| | || dksJ t| | |d| dks+J t| | | |  dks:J d S )Nr   r  r.  zx \left(- y\right)r)  zx \left(- 2 y\right)z\left(- x\right) y)r   r   subsr  r   r   r   test_issue_15439	  s
    "r  c                   C   s   t tddks
J d S )Nz\frac{a_1}{b_1}r~  r   r   r   r   test_issue_2934	  r  r  c                  C   s4   d} t | }t|| ksJ tt|dksJ d S )Nz	C_{x_{0}}z\cos{\left(C_{x_{0}} \right)})r!   r   rF   )latexSymbolWithBracer  r   r   r   test_issue_10489	  s   r  c                  C   s,   t d\} }t| d |d  dksJ d S )Nz
m__1, l__1r  z/\left(l^{1}\right)^{2} + \left(m^{1}\right)^{2}rh  )m__1l__1r   r   r   test_issue_12886	  s   r  c                  C   r~  )Nr   r  z5/1Fr  z\frac{5}{1}r  )r  rL  r   r   r   test_issue_13559	  r  r  c                  C   s*   t tdtt dd } t| dksJ d S )Nr  Fr  zc - \left(a + b\right))r  r   r:  r  r   rK  r   r   r   test_issue_13651	  r3  r  c                  C   s|   t d} td|  }t|td|    krdksJ  J t|d dks(J t|d dks2J t| | dks<J d S )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   her   r   r   test_latex_UnevaluatedExpr	  s   (r  c            	      C   s   t ddd} t ddd}t ddd}t| d dksJ td| d  dks(J |d || | }t|d	ks:J td
\}}}t d||}t d||}t|| ||f dks[J d S )NrJ  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  z0\sum_{i_{1}=0}^{k - 1} M_{i, i_{1}} N_{i_{1}, j})r   r   r  r#   )	rJ  r  r  r  rK  rL  r6  r[  r  r   r   r   test_MatrixElement_printing	  s   r  c                  C   s|   t ddd} t ddd}t ddd}t|  dksJ t| | |  | dks)J t|  | | | |  | dks<J d S )NrJ  r  r  r  z- AzA - A B - Bz- A B - A B C - B)r   r   r  r   r   r   test_MatrixSymbol_printing	  s   *r  c                  C   s2   t ddd} t ddd}tt| |dksJ d S )NrJ  r  r  r  A \otimes B)r   r   r   )rJ  r  r   r   r   test_KroneckerProduct_printing	  s   r  c            	      C   s  t ttd  t td td  t} t tt tt t}t ttd  tt t  t tt t}tt| |dks;J tt| ||dksGJ tt| | dksSJ tdt	 gddt	  gg}t
|t	}tddt	d  gg}t
|t	}t|||  d  krttt|||ksJ  J tddgddt	 gg}t
|t	}t|| | d	  krttt|||ksJ  J d S )
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
  r>  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   r.  r0  r  r  r   r   r   r  r   from_Matrixr   r   )	tf1tf2tf3M_1T_1M_2T_2M_3T_3r   r   r   test_Series_printing	  s4   $(r  c                  C   sx   t td td t} t| dksJ t td dt t}t|dks$J t ttd dt  d t}t|dks:J d S )Nr  z\frac{x - 1}{x + 1}r  z\frac{x + 1}{2 - y}r  z\frac{y}{y^{2} + 2 y + 3})r   r   r   r.  r  r  r  r   r   r   test_TransferFunction_printing
  s   r  c                  C   sN  t ttd  t td td  t} t tt tt t}tt| |dks'J tt| | dks3J tddgddt gg}t	
|t}tdt dgddtd  gg}t	
|t}tddttd   gddgg}t	
|t}t|| | d  krtt|||  krtt|t||  krttt|||ksJ  J d S )	Nr  r  z9\frac{x y^{2} - z}{- t^{3} + y^{3}} + \frac{x - y}{x + y}z;\frac{- x + y}{x + y} + \frac{x y^{2} - z}{- t^{3} + y^{3}}r
  r>  r  a=  \left[\begin{matrix}\frac{5}{1} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{5}{s} & \frac{6}{1}\\\frac{6}{1} & \frac{5}{s - 1}\end{matrix}\right]_\tau + \left[\begin{matrix}\frac{6}{1} & \frac{5}{s \left(s - 1\right)}\\\frac{5}{1} & \frac{6}{1}\end{matrix}\right]_\tau)r   r   r.  r0  r  r   r   r   r  r   r  r   )r  r  r  r  r  r  r  r  r   r   r   test_Parallel_printing
  s*   $  r  c                  C   s   t ttt t} t t t tt t}t ttd dt  d t}tt| g|ggdks/J tt| |g||  ggdks@J d S )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   r+  r   r  r.  r   r   r  r   r   r   $test_TransferFunctionMatrix_printing+
  s   r  c                  C   s   t ttt t} t t t tt t}tt| |dksJ tt| | t ddtdks/J tt| |ddks;J tt| | dddksIJ d S )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   r+  r   r  r   r   )r  r  r   r   r   test_Feedback_printing5
  s   r  c                  C   s   t dtt} t ttd d t}t ttd t}t td td d t}t| |g||gg}t||g|| gg}tt||dksCJ tt|| |ddksQJ d S )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_2r   r   r   test_MIMOFeedback_printingD
  s   r  c                  C   sf   t tttt} t| dksJ t ttttt } t| dks J t ttttt } t| dks1J d S )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   r.  r0  r  r   )qr   r   r   test_Quaternion_latex_printing\
  s   r  c                  C   s>   ddl m}  tddd}tddd}t| ||dksJ d S )Nr   )TensorProductrJ  r  r  r  )sympy.tensor.functionsr  r   r   )r  rJ  r  r   r   r   test_TensorProduct_printinge
  s   r  c                  C   s:   ddl m}  ddlm} || j| j}t|dksJ d S )Nr   R2)WedgeProductz*\operatorname{d}x \wedge \operatorname{d}y)sympy.diffgeom.rnr  sympy.diffgeomr  dxdyr   )r  r  r  r   r   r   test_WedgeProduct_printingl
  s   r  c                  C   s   t dddd} t| dksJ t dt dddddd}t|dks#J t dddd}t|d	ks2J t dddd}t|d
ksAJ d S )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_4r   r   r   test_issue_9216s
  s   r  c                  C   s^  ddl m} m}m}m} | d}|d|\}}}}|d|}	|d|g\}
}}}|d||g}|d||||g}t|d	ks@J t| d
ksIJ |
|}t|dksUJ |
|	}t|dksaJ |
| }t|dksnJ d|
| }t|dks|J |||| |	 }t|dksJ ||| | |	}t|dksJ ||| ||	 }t|dksJ ||| }t|dksJ |||}t|dksJ || | }t|dksJ dt |
| }t|dksJ ||| }t|dksJ ||| |
| || }t|dksJ |
|d||  }t|dks!J ddl m} |||||||d|di}t|dks>J |||||||di}t|dksSJ |||| |||d|di}t|d kskJ |||| || |d|di}t|d!ksJ ||||| | |d| di}t|d"ksJ ||||| | |di}t|d#ksJ t|
||
|}t|d$ksJ t|
| |
| }t|d%ksJ t|||| | |
t	|
t
 }t|d&ksJ t|| |
|  |
| |
t
 }t|d'ksJ td|
|  |
| |
t
 }t|d(ks-J d S ))Nr   )TensorIndexTypetensor_indices
TensorHeadtensor_headsLzi j k li_0zA B C DHKz{}^{i}z{}_{i}zA{}^{i}zA{}^{i_{0}}zA{}_{i}r9  z	-3A{}^{i}zK{}^{ij}{}_{ki_{0}}zK{}^{i}{}_{jk}{}^{i_{0}}zK{}^{i}{}_{j}{}^{k}{}_{i_{0}}zH{}^{i}{}_{j}zH{}^{ij}zH{}_{ij}r  z\left(x + 1\right)A{}^{i}zH{}^{L_{0}}{}_{L_{0}}z#H{}^{i}{}_{L_{0}}A{}^{L_{0}}B{}^{k}r  z3B{}^{i} + A{}^{i})TensorElementr  zK{}^{i=3,j,k=2,l}zK{}^{i=3,jkl}zK{}^{i=3}{}_{j}{}^{k=2,l}zK{}^{i=3}{}_{j}{}^{k=2}{}_{l}zK{}^{i=3,j}{}_{k=2,l}zK{}^{i=3,j}{}_{kl}z4\frac{\partial}{\partial {A{}^{L_{0}}}}{A{}^{L_{0}}}z,\frac{\partial}{\partial {A{}_{j}}}{A{}_{i}}zK\frac{\partial^{2}}{\partial {A{}^{m}} \partial {A{}_{n}}}{K{}^{ij}{}_{kl}}zZ\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(A{}_{i} + B{}_{i}\right)}zQ\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(3A{}_{i}\right)})sympy.tensor.tensorr  r  r  r  r   r   r  r   r  r;  )r  r  r  r  r  rK  rL  r6  rR  i0rJ  r  r  r  r  r  rL  r  r   r   r   test_latex_printer_tensor
  sx   


 "$("r  c                     s  t d\} }}}}|  d|  d|  d|  d|   d}t dd|ks*J d	}t ddd|ks8J d
}t ddd|ksFJ d}t dddd|ksUJ d}	t d|	ksaJ t ddd|	ksmJ d}
t ddd|
ks{J tt fdd d S )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)r  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                      s   t  ddS )Nr   r  )r   r   rL  r  r   r   rM    s    z&test_multiline_latex.<locals>.<lambda>)r#   r   r   rO  )r:  r  r  r  r6  ra  	expected2	expected3expected3dotsexpected3alignexpected2ieeer   r  r   test_multiline_latex
  s    &r  c                  C   sX   t d\} }tt|| tt| | dtt| | d@ tjd }t|dks*J d S )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   rH   rF   r    r  r   )r:  r   solr   r   r   test_issue_15353  s   2r  c                  C   s   t d} t ddd}td| |}tt|dksJ tt|dks$J tt|dkd	ks0J td
| |}tt||dksAJ d S )Nr   rY  Tr,  r  z\operatorname{E}\left[X\right]z \operatorname{Var}\left(X\right)r   z"\operatorname{P}\left(X > 0\right)r  z#\operatorname{Cov}\left(X, Y\right))r#   r   r   r   r   r   r   )r   rY  r  r  r   r   r   test_latex_symbolic_probability  s   r  c                  C   sH   ddl m}  tddd}t| |dksJ t| |d dks"J d S )Nr   tracerJ  r   \operatorname{tr}\left(A \right)z$\operatorname{tr}\left(A^{2} \right) sympy.matrices.expressions.tracer  r   r   )r  rJ  r   r   r   
test_trace&  s   r  c                     s   ddl m  ddlm}  G  fddd| fdd}fdd	}t|td
ks,J t|td dks8J t|tdksBJ d S )Nr   Basic)Exprc                       s   e Zd Z fddZdS )z+test_print_basic.<locals>.UnimplementedExprc                    s     | |S N)__new__)r`  r6  r  r   r   r  6     z3test_print_basic.<locals>.UnimplementedExpr.__new__N)r   r   r   r  r   r  r   r   UnimplementedExpr5  s    r  c                    s    |   S r  )r  rK  r  r   r   unimplemented_expr:  r  z,test_print_basic.<locals>.unimplemented_exprc                    s    | }d|j _|S )NzUnimplementedExpr_x^1)	__class__r   )rL  resultr  r   r   unimplemented_expr_sup_sub>  s   z4test_print_basic.<locals>.unimplemented_expr_sup_subz.\operatorname{UnimplementedExpr}\left(x\right)r  z2\operatorname{UnimplementedExpr}\left(x^{2}\right)z6\operatorname{UnimplementedExpr^{1}_{x}}\left(x\right))sympy.core.basicr  sympy.core.exprr  r   r   )r  r  r  r   )r  r  r   test_print_basic.  s   
r  c                  C   s  ddl m}  tddd}t| |dddksJ t| |ddd	ks$J tdd
d
}tdd
d
}tdd
d
}t| dddksAJ t|||  | dddksQJ t| | || |  | dddksfJ tdd
d
}t|dddksvJ tdd
d
}t|dddksJ d S )Nr   r  rJ  r  r  r  z)\operatorname{tr}\left(\mathbf{A} \right)rH  r  r  r  r  z- \mathbf{A}z/\mathbf{A} - \mathbf{A} \mathbf{B} - \mathbf{B}zG- \mathbf{A} \mathbf{B} - \mathbf{A} \mathbf{B} \mathbf{C} - \mathbf{B}A_kz\mathbf{A}_{k}z\nabla_kz\mathbf{\nabla}_{k}r  )r  rJ  r  r  r  r   r   r   test_MatrixSymbol_boldJ  s,    r  c                  C   s.   t ddd} td}tt| |dksJ d S )Nr   r  r  r   z#\sigma_{\left( 0\; 1\; 2\right)}(x))r   r!   r   r	   )r+  r   r   r   r   test_AppliedPermutationc  s
   r  c                  C   sH   t ddd} tt| dksJ t dddd} tt| dks"J d S )Nr   r  r  zP_{\left( 0\; 1\; 2\right)}r  z*P_{\left( 0\; 3\right)\left( 1\; 2\right)})r   r   r   rx  r   r   r   test_PermutationMatrixj  s   
r  c                  C   s  ddl m}  ddlm} td}td\}}|||t tfdtd|dtftt	dt t
|t  | dt|t  |d   |t k|tk @ t|d@ fd	t||  t |dtff}t| |d
kshJ t|||t tfdtd|dtftd|dtffdksJ d S )Nr   )piecewise_fold)FourierSeriesr   zk nr  r)  r  )r   Tz\begin{cases} 2 \sin{\left(x \right)} - \sin{\left(2 x \right)} + \frac{2 \sin{\left(3 x \right)}}{3} + \ldots & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}r  )$sympy.functions.elementary.piecewiser  sympy.series.fourierr  r!   r#   r   r   r   rC   rF   rH   r   r   )r  r  r   r6  r;  for   r   r   test_issue_21758s  s(    L
 r  c                   C   s   t dt dks
J t dt dddksJ t dt dddks"J t dt dddks.J t td	dd
ks8J t tdddksBJ d S )Nr  z1 + irK  imaginary_unitrL  z1 + jr   z1 + footiz\text{i}tjz\text{j})r   r   r   r   r   r   test_imaginary_unit  s   r  c                   C   sd   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$J t ttdddks0J d S )NT)gothic_re_imz\Im{\left(x\right)}Fr  z\Re{\left(x\right)}r  )r   r4   r   r6   r   r   r   r   test_text_re_im  s   r  c                  C   s   ddl m} m}m}m}m} ddlm} tddd\}}| dd}t	|d	ks)J |d
|}	t	|	dks6J |d|	||g}
t	|
dksFJ ||
d}t	|dksSJ t
d}||j|j}t	||dkshJ d S )Nr   )ManifoldPatchCoordSystemBaseScalarFieldDifferentialr  zx yTr  r[  r  z\text{M}Pz\text{P}_{\text{M}}rectz!\text{rect}^{\text{P}}_{\text{M}}z
\mathbf{x}rl  zC\operatorname{d}\left(g{\left(\mathbf{x},\mathbf{y} \right)}\right))r  r  r  r  r   r  r  r  r#   r   r   r   r.  )r  r  r  r   r  r  r   r.  r  r+  r  r  rl  s_fieldr   r   r   test_latex_diffgeom  s    



r  c                   C   s   t dt dks
J t dt dksJ t dt t dks J t dt t t dks.J t dt t dks:J t td	ksBJ d S )
Nr
  z
5 \text{m}r  z3 \text{gibibyte}r  z\frac{4 \mu\text{g}}{\text{s}}z\frac{4 \mu \text{g}}{\text{s}}z5 \text{m} \text{m}z\text{m})r   r   r   r   r   r   r   r   r   r   r   r   test_unit_printing  s   r  c                  C   s$   t d} tt| | ddksJ d S )Nr  r  z,\frac{d^{2}}{d \left(x^{*}\right)^{2}} x^{*})r!   r   r   )r5  r   r   r   test_issue_17092  r#  r  c            
      C   s  t d\} }}}t ddd\}}}t dtd\}}}	tg ddd	d
ks&J ttddddd	dks4J tddd	dks>J tddd	dksHJ tg ddd	dksTJ ttddddd	dksbJ tddd	dkslJ tddd	dksvJ tg ddksJ ttddddksJ tddksJ tddksJ ttdddd	dksJ tddd	dksJ t d} t d}t d}t| d d|d   d | dd	d ksJ td!dd	d"ksJ ttd!dd	d"ksJ td#dd	d$ksJ ttd#dd	d$ksJ 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 d} td+|  d dd	d,ks<J ttddddd	dksKJ ttd-d.  ttd/d.  ttd0d.  d S )1Nz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   r.  r0  r  z#2^{y^{3{,}4}} + 5{,}3 x + z + 4{,}5g/$?z0{,}987g333333?z0{,}3g|)v>z5{,}8 \cdot 10^{-7}g@gHz>z5{,}7 \cdot 10^{-7}g<sAC >g333333?z1{,}2 x + 3{,}4c                   S   s   t g dddS )Nr  &non_existing_decimal_separator_in_listr  rJ  r   r   r   r   rM    r  z.test_latex_decimal_separator.<locals>.<lambda>c                   S   s   t tdddddS )Nr  r	  r
  %non_existing_decimal_separator_in_setr  )r   r   r   r   r   r   rM    rT  c                   S   s   t dddS )Nr  'non_existing_decimal_separator_in_tupler  rJ  r   r   r   r   rM    rN  )r#   r   r   r   r   r    r   rO  )
r   r.  r0  r  r6  r  r;  r  rl  rm  r   r   r   test_latex_decimal_separator  sD   ,r  c                  C   s$   ddl m}  t| ddksJ d S )Nr   Strr   )sympy.core.symbolr  strr  r   r   r   test_Str  r  r  c                   C   s   t ddg dksJ d S )Nz
~^\&%$#_{}r  )
z\textasciitildez\textasciicircumz\textbackslashz\&z\%z\$z\#z\_z\{z\})r   joinr   r   r   r   test_latex_escape  s   r  c                  C   s8   G dd d} t |  dksJ t |  fdksJ d S )Nc                   @   r   )z#test_emptyPrinter.<locals>.MyObjectc                 S   r   )Nz<MyObject with {...}>r   )r   r   r   r   __repr__  r   z,test_emptyPrinter.<locals>.MyObject.__repr__N)r   r   r   r  r   r   r   r   MyObject  r   r  z'\mathtt{\text{<MyObject with \{...\}>}}z6\left( \mathtt{\text{<MyObject with \{...\}>}},\right)rJ  )r  r   r   r   test_emptyPrinter  s   r  c                  C   s   dd l } | tjd jdksJ ttdksJ z!tjdd | tjd jdks-J ttdks5J W tjd= ntjd= w | tjd jdksMJ ttdksUJ d S )Nr   r  rK  rL  r  )	inspect	signaturer   
parametersdefaultr   r   set_global_settings_global_settings)r  r   r   r   test_global_settings  s   r#  c                  C   s$   dd l } | | ttu sJ d S )Nr   )pickleloadsdumpsr   )r$  r   r   r   test_pickleable  s   r'  c                  C   st   t tdddksJ t tddddt  dfdksJ tddd} td	dd}t t| | tdgd
ks8J d S )NrJ  )r  r  r  r  r  r   z{{A}_{2, \frac{1}{1 - x}, 0}}r[  r  r  z{{\left(M N\right)}_{x, 0}})r   r   r   r   r   )r[  r  r   r   r   %test_printing_latex_array_expressions  s
   $"r(  c                  C   s<   t td} t| dksJ t td} t| dksJ d S )Nr  zL\left[\begin{matrix}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\end{matrix}\right]rZ  zQ\left[\begin{array}{}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right])r   r  r   )arrr   r   r   
test_Array$  s   r*  (  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.powerr   sympy.core.relationalr   r   sympy.core.singletonr    r  r!   r"   r#   (sympy.functions.combinatorial.factorialsr$   r%   r&   r'   r(   r)   %sympy.functions.combinatorial.numbersr*   r+   r,   r-   r.   r/   r0   $sympy.functions.elementary.complexesr1   r2   r3   r4   r5   r6   &sympy.functions.elementary.exponentialr7   r8   r9   %sympy.functions.elementary.hyperbolicr:   r;   #sympy.functions.elementary.integersr<   r=   r>   (sympy.functions.elementary.miscellaneousr?   r@   rA   rB   r  rC   (sympy.functions.elementary.trigonometricrD   rE   rF   rG   rH   rI   &sympy.functions.special.beta_functionsrJ   'sympy.functions.special.delta_functionsrK   rL   *sympy.functions.special.elliptic_integralsrM   rN   rO   rP   r  rQ   rR   rS   rT   rU   rV   'sympy.functions.special.gamma_functionsrW   rX   sympy.functions.special.hyperrY   rZ   )sympy.functions.special.mathieu_functionsr[   r\   r]   r^   #sympy.functions.special.polynomialsr_   r`   ra   rb   rc   rd   re   rf   rg   -sympy.functions.special.singularity_functionsrh   +sympy.functions.special.spherical_harmonicsri   rj   (sympy.functions.special.tensor_functionsrk   rl   &sympy.functions.special.zeta_functionsrm   rn   ro   rp   rq   sympy.integrals.integralsrr   sympy.integrals.transformsrs   rt   ru   rv   rw   rx   ry   rz   r{   r|   sympy.logicr}   sympy.logic.boolalgr~   r   r   r   r   r   r   sympy.matrices.denser   $sympy.matrices.expressions.kroneckerr   "sympy.matrices.expressions.matexprr   &sympy.matrices.expressions.permutationr    sympy.matrices.expressions.slicer   sympy.physics.control.ltir   r   r   r   r   r   r   r   sympy.ntheory.factor_r   r   r   r   r   r   sympy.physics.quantumr   r   sympy.physics.quantum.tracer   sympy.physics.unitsr   r   r   r   r   r   r   sympy.polys.domains.integerringr   sympy.polys.fieldsr   sympy.polys.polytoolsr   sympy.polys.ringsr   sympy.polys.rootoftoolsr   r   sympy.series.formalr   r  r   sympy.series.limitsr   sympy.series.orderr   sympy.series.sequencesr   r   r   r   sympy.sets.conditionsetr   sympy.sets.containsr   sympy.sets.fancysetsr   r   r   sympy.sets.ordinalsr   r   r   sympy.sets.powersetr   sympy.sets.setsr   r   r   r   r   r   r   sympy.sets.setexprr   sympy.stats.crv_typesr    sympy.stats.symbolic_probabilityr   r   r   r   sympy.tensor.arrayr   r   r   r   r   0sympy.tensor.array.expressions.array_expressionsr   r   sympy.tensor.indexedr   r   r   sympy.tensor.toperatorsr   sympy.vectorr   r   r   r   r   r   r   sympy.testing.pytestr   r   r   r   r!  r   r   r   r   r   r   r   symr  r   r   r   r   r.  r0  r  r  r:  r  r  r  r+  r6  r  r;  r  r7  r8  r<  rA  rE  rI  rM  rg  rk  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r!  r"  r$  r%  r(  r+  r,  r.  r/  r2  r?  rA  rC  rD  rE  rF  rG  rP  rQ  rU  r]  rb  rj  rl  rm  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  r  r	  r  r  r  r  r  r"  rO  rs  ru  rv  rw  ry  rz  r{  r|  r}  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r#  r'  r(  r*  r   r   r   r   <module>   s   $ $   ,0$( $(*2"B*B
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!	!:!		8<				
	[4			2