U
    	-e                 
   @   s$  d dl mZmZmZ d dlmZ d dlmZ d dlm	Z	m
Z
mZ d dlmZ d dlmZ d dlmZmZ d dlmZ d d	lmZmZmZmZmZ d d
lmZ d dlmZ d dlm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z& d dl'm(Z( d dl)m*Z* d dl+m,Z,m-Z- d dl.m/Z/ d dl0m1Z1m2Z2m3Z3 d dl4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z: d dl;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZC d dlDmEZEmFZFmGZGmHZHmIZImJZJ d dlKmLZLmMZMmNZN d dlOmPZPmQZQ d dlRmSZSmTZTmUZU d dlVmWZWmXZXmYZYmZZZ d dl[m\Z\ d dl]m^Z^m_Z_m`Z`maZambZbmcZc d dldmeZe d dlfmgZgmhZh d dlimjZjmkZkmlZlmmZm d dlnmoZompZpmqZqmrZrmsZsmtZt d dlumvZvmwZw d d lxmyZymzZz d d!l{m|Z|m}Z}m~Z~mZ d d"lmZmZmZmZmZmZmZmZmZ d d#lmZ d d$lmZmZ d d%lmZmZ d d&lmZmZmZmZmZ d d'lmZ d d(lmZmZmZmZmZmZmZmZmZmZ d d)lmZ d d*lmZmZmZmZmZmZmZ d d+lmZ d d,lmZ d d-lmZ d d.lmZ d d/lmZ d d0lmZmZmZmZmZmZmZmZ d d1lmZmZmZmZmZmZ d d2lmZmZ d d3lmZ d d4lmZmZmZmZmZmZmZ d d5lmZ d d6lmZ d d7lmZ d d8lmZ d d9lmZmZ d d:lmZ d d;lmZ d d<lmZ d d=lmZ d d>lmZmZmZmZ d d?lmZ d d@lmZ d dAlmZmZmZ d dBlmZmZmZ d dClmZ d dDlmZmZmZm Z mZmZmZ d dElmZ d dFlmZ d dGlm	Z	m
Z
mZmZ d dHlmZmZmZmZmZ d dIlmZmZ d dJlmZmZmZ d dKlmZ d dLlmZmZmZm Z m!Z!m"Z"m#Z# d dMl$m%Z%m&Z&m'Z'm(Z( d dNl)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0 d dOl Z1d dPl2m3Z3m4Z4 G dQdR dRe1j5Z5e3dS\
Z6Z7Z8Z9Z:Z;Z<Z=Z>Z?e3dTdUdV\Z@ZAZBdWdX ZCdYdZ ZDd[d\ ZEd]d^ ZFd_d` ZGdadb ZHdcdd ZIdedf ZJdgdh ZKe%didj ZLe'dkdl ZMdmdn ZNdodp ZOdqdr ZPdsdt ZQdudv ZRdwdx ZSdydz ZTd{d| ZUd}d~ ZVdd ZWdd ZXdd ZYdd ZZdd Z[dd Z\dd Z]dd Z^dd Z_dd Z`dd Zadd Zbdd Zcdd Zddd Zedd Zfdd Zgdd Zhdd Zidd Zjdd Zkdd Zldd Zmdd Zndd Zodd Zpdd Zqdd Zrdd Zsdd Ztdd Zudd Zvdd Zwdd ZxddĄ ZyddƄ ZzddȄ Z{ddʄ Z|dd̄ Z}dd΄ Z~ddЄ Zdd҄ ZddԄ Zddք Zdd؄ Zddڄ Zdd܄ Zddބ Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zdd Zdd Zdd Zdd Zd	d
 Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd Zdd  Zd!d" Zd#d$ Zd%d& Zd'd( Zd)d* Zd+d, Zd-d. Zd/d0 Zd1d2 Zd3d4 Zd5d6 Zd7d8 Zd9d: Zd;d< Zd=d> Ze%d?d@ ZdAdB ZdCdD ZdEdF ZdGdH ZdIdJ ZdKdL ZdMdN ZdOdP ZdQdR ZdSdT ZdUdV ZdWdX ZÐdYdZ ZĐd[d\ ZŐd]d^ ZƐd_d` Zǐdadb ZȐdcdd Zɐdedf Zʐdgdh Zːdidj Z̐dkdl Z͐dmdn Zΐdodp Zϐdqdr ZАdsdt Zѐdudv ZҐdwdx ZӐdydz 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 Zdd Zdd Zdd Zdd ZdOS (      )MatAddMatMulArray)
Quaternion)AccumBounds)CyclePermutationAppliedPermutation)Product)Sum)TupleDict)UnevaluatedExpr)
DerivativeFunctionLambdaSubsdiff)Mod)Mul)AlgebraicNumberFloatIIntegerRationaloopievaluate)Pow)EqNe)S)SymbolWildsymbols)FallingFactorialRisingFactorialbinomial	factorial
factorial2subfactorial)	bernoullibellcatalaneulergenocchilucas	fibonacci
tribonacci)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                   @   s   e Zd ZdS )
lowergammaN__name__
__module____qualname__ r   r   `/var/www/html/Darija-Ai-Train/env/lib/python3.8/site-packages/sympy/printing/tests/test_latex.pyr   _   s   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$tG dd dt } t| tdksHtd S )Nc                   @   s   e Zd Zdd ZdS )test_printmethod.<locals>.Rc                 S   s   d| | jd  S )Nzfoo(%s)r   )Z_printargsselfprinterr   r   r   _latexi   s    "test_printmethod.<locals>.R._latexNr   r   r   r   r   r   r   r   Rh   s   r   zfoo(x)c                   @   s   e Zd Zdd ZdS )r   c                 S   s   dS )Nfoor   r   r   r   r   r   n   s    r   Nr   r   r   r   r   r   m   s   r   )r4   r   xAssertionError)r   r   r   r   test_printmethodg   s    r   c                  C   s  t dt dkstt td dks(tt tdt  dks@tt td t d td  dksdtt dt t dks|tt dt t d	d
dkstt dtd  t dd
dkstt ddt  dd
dkstt ttjd  dkstt ttjtd ddddkstt ttjtd ddddks6tt tdddddksRtt tdddddksntt ttjdtjdddkstt tdtddddkstt tdtddddkstt tdddddkstt tdddddkstt tdddddks tt td dddd!ks<tt tdddddd"ksZtt tddddd#ksvtt tdtjddd$kstt tddtjddd%kstt tddddtddd&kstt tdd ddd'kstt td(ddddttddd)kstt td(dddt dttddd*ksBtt tt	ddt	dd+ddd,ksjtt dt d-kstt dt d.d/d0kstt td d d1kstt td d d.d/d2kstt dtd  d3kstt dtt  d d4kstt td d5ks$tt td d.d/d6ks>tt tt dt  d7ks\tt tt dt  d.d/d8ks~tt tt dt  dd9d:kstt tt t d;kstt tt t dd9d;kstt dt
d t d d<kstt dt
d t d dd9d=ks tt tttd>ks8ttd?} td@}t | d dAks^tt | d ddBdCksxtt t|| | ddDkstt t|| | dddBdEkstt dttt d dFkstt dttt d d.d/dGkstt t
tdHkstt tt	dd dIks.tt tt	dd ddJdKksNtt t
td dLkshtt t
td.dMdHkstt tt	dd d.dMdNkstt t
td d.dMdLkstt tt	dd( dOkstt tt	dd( d.dPdQkstt td t	dd( dRkstt td t	dd( d.dPdSks@tt tt
ddTksZtt tt
dddUgdVksztt tt
ddWdXdYkstt tt
dddUgdWdXdZkstt tdtdd  dddUgd[dXd\ksttd}t |jdddd(gd]kstt |jdddd(gd^d_d`ks<tt |dad dbksXtt |dad d^d_dcksxtt |d+d ddkstt det dfkstt det d	d
dgkstt det dhd
dikstt dtt djkstt ttd  djk	stt ttt	dd dkk	s2tt ttt	dd d.dPdlk	sVtt t dmk	sjtt tt@ dnk	stt tt@ t@ dok	stt ttB dpk	stt ttB tB dqk	stt tt@ tB drk	stt tttdsk	stt tt ?  dtk
stt tttttduk
s4tt tttttdvk
sRtt tt@  dwk
sjtt t tdxidydzk
stt tt@ tdxtd{idyd|k
stt tt@ t@ tdxtd{td}idyd~k
stt ttB tdxtd{idydk
stt ttB tB tdxtd{td}idydkstt tt@ tB tdxtd{td}idydksHtt ttttdxtd{idydksltt tt	ddd dddkstt tt	ddddddkstt ttdd d dddksttdd.d}t t| t| dks td S )N   x + 1   zx^{2}z	x^{x + 1}   zx^{3} + x^{2} + x + 1z2 x ydotZ
mul_symbolz2 \cdot x \cdot yz\,z3\,x^{2}\,y      ?z1.5 \cdot 3^{x}   z\sqrt[32]{x}Fr   z!\frac{1}{2} x^{2} \left(-5\right)z\frac{1}{2} x^{2} \cdot 5z\left(-5\right) \left(-5\right)z5 \left(-5\right)z'\frac{1}{2} \left(-5\right) \frac{1}{2}z5 i 5z5 i \left(-5\right)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)Z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)Z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})Z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})Zroot_notationzx^{\frac{1}{3}}zx^{\frac{3}{2}}itexz\root{3}{x}zx^{\frac{3}{4}})Zfold_frac_powerszx^{3/4}z \left(x + 1\right)^{\frac{3}{4}}z\left(x + 1\right)^{3/4}z\sqrt{2}iz-7 + 3 \sqrt{2}alpha)alias\alphaz3 \alpha - 7rM   z\beta^{2} + 3 \beta - 7z%\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Zsymbol_namesz\neg x_iZy_izx_i \wedge y_iZ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   r   yr"   Halfr   r   zr   rE   r(   r#   r   r   ru   r   r   Zcyclotomic_fieldextZfield_elementZprimes_aboverK   r   r   r   r   r;   r<   )x_starr  kr  r   r   r   test_latex_basics   s6   $ $$"




 

"
" 
   

 
"










"


""$r%  c                   C   sT   t ddkstt ddks tt d dks0tt tdks@tt tdksPtd S )NTz\text{True}Fz\text{False}z\text{None})r   r   r   r   r   r   r   r   test_latex_builtins  s
    r&  c                   C   sF  t ttdddkstt ttdddks0tt ttdddksHtt ttttdks`tt ttdd	d
ksxtt ttdddkstt ttddd dkstt ttddd dkstt ttddd dkstt ttttd dkstt ttdd	d dks tt ttddd d dksBt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   rk   r   r   anr   r   r   r   test_latex_SingularityFunction  sH    

r*  c                   C   sL   t tddddkstt tddddddks6tt t dksHt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   r   test_latex_cycle*  s
    r/  c               	   C   s  t tddddkstt tddddddks6tt t dksHtt tddtd d	ksftt tdd
ksztt tdddddkstt tdddddddkstt t dddkstt 4 tj} dt_t tdddddkst| t_W 5 Q R X d S )Nr   r  r	  r+  r  r,  r-  r.  z"\left( 2\; 4\right)\left( 5\right)z\left( 5\right)r   F)Z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   r   Zprint_cyclic)Zold_print_cyclicr   r   r   test_latex_permutation1  s2    r0  c                   C   s   t tddkstt tddks(tt tddddks@tt tdd	d
dddks\tt tdd	d
dddksxtt tdd	d
dddkstt tddd
dddkst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  )Z	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   r   test_latex_FloatH  s"    r3  c                  C   s  t d} tt| j| j| j d | j dks2ttt| j| jdksLtttt| j| j dksjtttt| j | jdkstttd| j | j dkstttd| j | j | j dkstttdt | j | j d	ksttttd| j | j  d
ksttt	d| j | j | j dks@ttt	d| j | j dksbtttt	d| j | j  dksttt
| j| j| j d | j dksttt
| j| jdksttt
t| j | jdkstttt
| j| j dksttt| jdks(ttt| jd| j  dksJtttt| j dksftttt| j dksttt| jdksttt| jd| j  dkstttt| j dkstttt| j dkst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   r$  r   r   r   r   r   r  r   )r4  r   r   r   test_latex_vector_expressionsW  st     



 





r7  c                  C   s  t d\} }}t d\}}}}t|dks.tt|dks>tt|dksNtt|dks^tdd tD }t|tt  dkstt| | dkstt| | d	kstttd
dkstttddkstttddkstttddkstttddkstttddks.tttddksDtttddksZtttddksptttddkstttddkstttdtd  d!kstd S )"NzGamma, lambda, rhoztau, Tau, TAU, taU\tau
\mathrm{T}c                 S   s   h | ]}|  qS r   )
capitalize).0lr   r   r   	<setcomp>  s     z%test_latex_symbols.<locals>.<setcomp>r   z\Gamma + \lambdaz\Gamma \lambdaq1zq_{1}Zq21zq_{21}Zepsilon0z\epsilon_{0}omega1
\omega_{1}Z91Z	alpha_newz\alpha_{new}zC^origzC^{orig}zx^alphaz
x^{\alpha}z
beta^alphaz\beta^{\alpha}ze^Alphaze^{\mathrm{A}}zomega_alpha^betaz\omega^{\beta}_{\alpha}omegarM   z\omega^{\beta})	r%   r   r   r   lensetr   keysr#   )GammaZlmbdarhor   TauZTAUZtaUZcapitalized_lettersr   r   r   test_latex_symbols  s,    rH  c                  C   sb   t d\} }}t||  |kdks&tt|| |  dkdksBtt|d |d  dks^td S )Nzrho, mass, volumez$\rho \mathrm{volume} = \mathrm{mass}r   z/\rho \mathrm{volume} {\mathrm{mass}}^{(-1)} = 1r  z/{\mathrm{mass}}^{3} \cdot {\mathrm{volume}}^{3}r%   r   r   )rF  Zmassvolumer   r   r   test_latex_symbols_failing  s    
rK  c                  C   s  t ttdkstt tdtd dks0ttd} t | tdksLtt | dks\ttd}t |ttdksztt |dksttd	}t |tttd
kstt |d	ksttd}t |dkstt |tdksttd}t |tttdkstt tttdks tt ttdddks:tt tttd dksVtt |tdksltt |dks~ttd}t |tttdkstt |tdkstt |dksttd}t |dkstt |tdkstt tddkstt tddks$tt td d!ks:tt td"d#ksPtt td$d!ksftt td%d#ks|tt td&d'kstt td(d)kstt tdtd*d+kstt td td*d,kstt td"td*d-kstt td$td*d,ks tt td&td*d.ks>tt td(td*d/ks\tt td d d0ksxtt td  d d1kstt td" d d2kstt td$ d d1kstt td% d d2kstt tdtd*d d3ks
tt td td*d d4ks,tt td"td*d d5ksNtt td$td*d d4ksptt td%td*d d5kstt td6d6kstt td7dkstt td8d9kstt tddkstt td:d9ks tt td6 d;kstt td7 d<ks0tt td8 d=ksHtt td d<ks`tt td: d=ksxtt td6 d d>kstt td7 d d?kstt td8 d d@kstt td d d?kstt td: d d@kstt td6td*d dAks&tt td7td*d dBksHtt td8td*d dCksjtt tdtd*d dBkstt td:td*d dCkstt td6 dD dEkstt td7 dD dFkstt td8 dD dGkstt td dD dFkstt td: dD dGks:tt td6td*dD dHks\tt td7td*dD dIks~tt td8td*dD dJkstt tdtd*dD dIkstt td:td*dD dJkstt td6 t	 dKks tt td7 t	 dLkstt td8 t	 dMks8tt td t	 dLksTtt td: t	 dMksptt td6td*t	 dNkstt td7td*t	 dOkstt td8td*t	 dPkstt tdtd*t	 dOkstt td:td*t	 dPk	sttd}t td6 | dQk	s>tt td7 | dRk	sZtt td8 | dSk	svtt td | dRk	stt td: | dSk	stt td6td*| dTk	stt td7td*| dUk	stt td8td*| dVk
stt tdtd*| dUk
s6tt td:td*| dVk
sXtt tdWtdXk
srtt tdWt| dYk
stt tdZtdXk
stt tdZt| dYk
stt td[td\k
sttd]}t |d^k
stt |td_kstt t
td`ks(tt t
tdadbdcksBtt t
dtd  dadbddksdtt t
td dadbdekstt ttd dfkstt ttd dgdhdikstt ttd djdhdkkstt ttd djdadldmkstt ttdgdhdnkstt ttdgdhdoks,tt ttdpksBtt tt dqksZtt ttd drksttt ttdskstt tt dtkstt ttd dukstt ttdvkstt tt dwkstt ttd dxkstt tdtdykstt tdtd dzks8tt td{td|ksPtt td{td}kshtt ttd~ks~tt ttdkstt ttdkstt ttd dkstt ttd dkstt ttd dkstt ttdtd{ dkstt tttd dks2tt ttdtd{ dksPtt tttd dksltt ttdkstt ttd dkstt ttdkstt ttt dkstt ttdkstt ttdkstt ttd dkstt ttd dks,tt ttdksBttd}t t|dks`tt t tdksvtt t ttdkstt t ttdfdkstt t ttt!fdkstt t tt ttfdkstt t tttdks tt t tttdkstt t ttt!ftt!fdks<tt t"ttdksTtt t"ttd dksptt t#ttdkstt t#ttd dkstt t$tdkstt t%tdkstt ttdkstt ttdkstt t&ttdkstt t'tdks*tt t(tdks@tt t(td dksZtt t(ttdksrtt t(ttd dkstt t)tdkstt t)td dkstt t*ttdkstt t*ttd dkstt t+ttt,dkstt t+ttt,d dks*tt t-tdks@tt t-td dksZtt t-ttdksrtt t-ttd dkstt t.tdkstt t.td dkstt t/ttdkstt t/ttd dkstt t0ttdks
tt t0ttd dks&tt t0tdks<tt t0td dksVtt t1tttdksptt t1tttd dkstt t1ttdkstt t1ttd dkstt t2tdkstt t2td dkstt t3ttdks
tt t3ttd dks&tt t4td dks@tt t5td dksZtt t6td dksttt t7td dkstt t7tdkstt t8t,t	t9tdkstt t8t,t	t9td dkstt t:t,t	tdkstt t:t,t	td dkstt t;t,tdks0tt t;t,td dksLtt t<t,tdksdtt t<t,td dkstt t=t,tdkstt t=t,td dkstt t>t,t	tdkstt t>t,t	td dkstt t?t,tdkstt t?t,td dks tt t@t,t	tdks:tt t@t,t	td dksXtt tAt,tdksptt tAt,td dksttddad֍}	tddad֍}
t tBt,tC|	|
dkstt tBt,tC|	|
d{ dkstt tDt,tC|	|
dkstt tDt,tC|	|
d{ dkstt tEddks2tt tEdd{ dksLtt tFt,dksbtt tFt,d dks|tt tGt,dkstt tGt,d dkstt tHtdkstt tHtd dkstt tHttdkstt tHttd dkstt tItdks&tt tItd dks@tt tIttdksXtt tIttd dksttt tJt,dkstt tJt,d dkstt tKt,dkstt tKt,d dkstt tLt,dkstt tLt,ddkstt tLt,tdkstt tLt,tLt, dks8tt tMtLt,ddksTtt tLt,t dksntt tLt,ttN dkstt tOtddkstt tOtd ddkstt tOdtd dkstt tOdt ddkstt tOddt dkstt tOtdd dks.tt dtOtd dksJtt tOddt t, dksjttd}t |tdkstt |d kst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)}rM   z\beta{\left(x,y,z \right)}z!\operatorname{B}\left(x, y\right)Fr   z!\operatorname{B}\left(x, x\right)z%\operatorname{B}^{2}\left(x, y\right)z\beta{\left(x \right)}\betarZ   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}Zab1z\operatorname{ab}_{1}Zab12z\operatorname{ab}_{12}Zab_1Zab_12Zab_cz\operatorname{ab}_{c}Z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(  Za1Za12za_{12}Z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)}Za__12Za_1__1_2za^{1}_{1 2}{\left(x \right)}r?  r@  z\omega_{1}{\left(x \right)}z\sin{\left(x \right)}T)fold_func_bracketsz\sin {x}z\sin {2 x^{2}}z\sin {x^{2}}z(\operatorname{asin}^{2}{\left(x \right)}full)inv_trig_stylez\arcsin^{2}{\left(x \right)}powerz\sin^{-1}{\left(x \right)}^{2})rV  rT  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})Pr   r;   r   r   r   r  r!  rM   r#   r(  rK   rH   rG   r=   r)   r$  r+   r*   r(   r&   r'   r@   r?   rA   rC   rB   r4   r9   r7   r6   rZ   r$   r   r   r   r[   rJ   r>   rD   r5   rt   rp   rr   rq   r)  rs   rR   rQ   rP   rS   rV   rY   rW   rX   rU   rT   rh   brf   rd   re   rj   rc   ri   rb   rg   rl   mrm   r8   r   r   r   r   r   r   r:   r   r  r   )r  rL  rM  rN  ZmybetarQ  rR  r?  r[  r]  r`  ra  r   r   r   test_latex_functions  s   """"
""""""""""""""""""""






























 rd  c                  C   s8   G dd dt } t| dks tt| tdks4td S )Nc                   @   s   e Zd ZdS )z6test_function_subclass_different_name.<locals>.mygammaNr   r   r   r   r   mygamma  s   re  z\operatorname{mygamma}z'\operatorname{mygamma}{\left(x \right)})rZ   r   r   r   )re  r   r   r   %test_function_subclass_different_name  s    rf  c               
   C   s   ddl m} m} ttttt| tddtdddt |dksDtttt tddt |d	kshttt| dfd
|dkstttt td|dkstd S )Nr   r   r!  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   r!  r   r]   r   r   r   r\   rg  r   r   r   test_hyper_printing#  s"      ri  c                  C   s0  ddl m} m}m}m}m}m}m}m}m	}m
}	 ddlm}
 t| t|
d t dksZtt|t|
dksptt|t|
dkstt|t|
dkstt|t|
d d d	kstt|t|
d
kstt|t|
dkstt|t|
dkstt|t|
dkstt|	t|
dks,td S )Nr   )
besseljbesselybesselibesselkhankel1hankel2jnynhn1hn2r!  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))Zsympy.functions.special.besselrj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rh  r!  r   r)  r$  r   )rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  r!  r   r   r   test_latex_bessel4  s    0ru  c                  C   sx   ddl m} m} ddlm} t| |dks0tt||dksDtt| |d dks\tt||d dksttd S )	Nr   )fresnelsfresnelcrt  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_functionsrv  rw  rh  r!  r   r   )rv  rw  r!  r   r   r   test_latex_fresnelF  s    ry  c                   C   s   t dt dkstd S )Nr  z\left(-1\right)^{x}r   r   r   r   r   r   r   test_latex_bracketsO  s    r{  c                  C   sd  t dddd} tt dddd}t| t|  }t|d t|d  }|dksTt|dks`td	}ttd
t ddks~tttdtddkstttdtdt dd| d kstttdtdt dd d| d kstttdtdt dt dfd| d kstttddks4tttddksJtttddks`td S )NZPsi_0TF)complexr_  Psir   z\Psi_{0} \overline{\Psi_{0}}z \overline{{\Psi}_{0}} {\Psi}_{0}z\mathrel{..}\nobreak x1r5  z{x_{1}}_{i}x2z{x_{2}}_{i}Zx3Nz{x_{3}}_{{i}_{0zN - 1}}r   zN}}Zx4r(  rb  z{x_{4}}_{{i}_{azb}}rZ   rP  za bZa_bza_{b})r#   r   r   r6   r   r   r   )Z
Psi_symbolZPsi_indexedZsymbol_latexZindexed_latexintervalr   r   r   test_latex_indexedS  s    (,2r  c               	   C   s  t ttd tdddkstt ttttd  tdddksDtt tttttd  tdddddksrtt ttttttd  tdddddddkstt tttt tddd	kstt tttt td  tddd
kstt ttttt td  tddtdddks*tt tttttt td  tddtddtdddksjttd} t tt| tttddtdddt | tt kstt ttt| tttddtddtdddt | tt kstt tttd tdd tdddkstt ttttttddtdd tddtdddksXtt tttt t tdt	ftdddkstt tttddd dkstt t| ttd dkstt t| ttt
fdksttd}td}t t| |||dksttd}t t| tt|fdks@ttd}t t| ttt||fdksntt t| ttddd kst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Zdiff_operatorz2\frac{\mathrm{d}}{\mathrm{d} x} f{\left(x \right)})r   r   r   r   rK   r  r   ru   r;   r   r)  r#   rB   )r  r~  r  r  r  r   r   r   test_latex_derivativesh  sr    $, *
4
 
*
,0
&



 
r  c                   C   s$   t ttt ttfddks td S )Nr   r  z+\left. x y \right|_{\substack{ x=1\\ y=2 }})r   r   r   r  r   r   r   r   r   test_latex_subs  s    r  c                	   C   s  t ttttdkstt ttd tddfdks:tt ttd tddfdksZtt tttd  tddftd	kstt tttd  tddftd
ddkstt tttd  tddftd
dddkstt tttdfdkstt ttt ttdkstt ttt t tttdks2tt ttt t t ttttdks\tt ttttttttdks~tt tttttddfdkstt tttd t tdkstt ttttt t tdkstt tttd dkstt ttt tdks$tt tttd  tdksDtt ttt tdks`tt tttdddks|tt tttddfdddkst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   ru   r<   r   r   r  r!  tr   r   r   r   test_latex_integrals  sT     "$





r  c                  C   s   t tfD ]X} t| tt td gdks,tt| tdddksFtt| tdddkstqt} t| tt td g dkstt| tdd dkstt| tdd dkstd S )Nr  z\left\{x^{2}, x y\right\}r   r,  z\left\{1, 2, 3, 4, 5\right\}   z4\left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right\})	frozensetrC  r   r   r  r   ranger   sr   r   r   test_latex_sets  s     
 r  c                  C   s&   t dd} t| }t|dks"td S )Nr   r  z%SetExpr\left(\left[1, 3\right]\right))r   r   r   r   )Zivser   r   r   test_latex_SetExpr  s    
r  c                  C   s  t tdddkstt tdddks,tt tddddksDtt tdd	dd
ks\tt td	dddksttt tdtddkstt ttdddkstt tdt ddkstt tt tdkstt ttt ddksttd\} }}t t| ||dkstt t| dddks2tt td|ddksLtt tdd|dksfttddd}tdddd}tdddd }t t||d d!kstt tt |dd"kstt t|td#kstt t| | d d$kst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)r5  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(  rb  cr5  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.td}t||ksBtt td d}tdd}d}t||ksntd}t||kstt td t df}tdt df}d	}t||kstd
}t||kstd}tt| ||kstd}tt|||kstd}tt|||ks td}tt| ||ks<td}tt|||ksXtd}tt|||ksttt td tdtf}d}t||kstt	d}t |td  tddf}	d}t|	|kst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}rb  z\left[0, b, 4 b\right])
r   r(  r   r   r   r   r   r   r   r#   )
s1s2	latex_strZs3Zs4Zs5Zs6Zs7rb  Zs8r   r   r   test_latex_sequences  sJ    
r  c                  C   s&   d} t tttt tf| ks"t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   r   test_latex_FourierSeries@  s    r  c                  C   s$   d} t ttdt | ks td S )Nz;\sum_{k=1}^{\infty} - \frac{\left(-1\right)^{- k} x^{k}}{k}r   )r   r   r<   r   r   r  r   r   r   test_latex_FormalPowerSeriesF  s    r  c                  C   s   t ddd} ttdddks"tttd| dks8tttd| dddksRtttd| dddksltttd| ddd	kstttd| ddd
kst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   r   test_latex_intervalsK  s    r  c                  C   sZ   t ddd} ttdddks"tttd| dks8ttt| d | d d	ksVt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   r   test_latex_AccumuBoundsU  s    r  c                   C   s   t tjdkstd S )N	\emptyset)r   r"   EmptySetr   r   r   r   r   test_latex_emptyset]  s    r  c                   C   s   t tjdkstd S )Nz
\mathbb{U})r   r"   UniversalSetr   r   r   r   r   test_latex_universalseta  s    r  c                  C   s2   t d} t d}t|| }t| dks.td S )Nr4  Bz- (A B - B A))r   r   r   doitr   )r4  r  Zcommr   r   r   test_latex_commutatore  s    
r  c                   C   sP   t ttddtdddks"tt ttddtddtdddksLt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   r   test_latex_unionl  s     r  c                   C   s&   t ttddtttdks"td S )Nr   r   z(\left[0, 1\right] \cap \left[x, y\right])r   r   r   r   r  r   r   r   r   r   test_latex_intersections  s    r  c                   C   s*   t ttddtdddddks&td S )Nr  r  r	  r
  Fr   z-\left[2, 5\right] \triangle \left[4, 7\right])r   r   r   r   r   r   r   r   test_latex_symmetric_differencex  s
    r  c                   C   s   t ttjtjdkstd S )Nz\mathbb{R} \setminus \mathbb{N})r   r   r"   RealsNaturalsr   r   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<tt| d dt|  ksXtt| | |  dt| t|t|f kstd S )	Nr   r   r  r  r  z%s^{2}z%s^{10}z%s \times %s \times %s)r   r   r   r   flatten)lineZbiglinefsetr   r   r   test_latex_productset  s    

  r  c                  C   s$   t ddd} tt| dks td S )Nr   r  r  z.\mathcal{P}\left(\left\{1, 2, 3\right\}\right))r   r   r   r   )r  r   r   r   test_latex_powerset  s    r  c                  C   sr   t  } t| dksttdd}t|dks0ttt|tdddksLttttddtdddksntd S )N\omegar  r  z3 \omega^{2}r   z3 \omega^{2} + \omegaz\omega^{2} + 2 \omega)r   r   r   r   r   )r[  wpr   r   r   test_latex_ordinals  s    
r  c                  C   s`  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sttt||	dddksttt||dddksttt||dddks ttt||dddks<ttt||ddd	ksXttt|
|ddd
kstttt||dddksttt||dddksttt||dddksttt||dddksttt||	dddks ttt|
|dddksttt||dddks8ttt||dddksTttt||dddkspttt||	dddksttt|
|dddksttt||dddksttt||dddksttt||	 dksttt||	dksttt|
|dks,ttt||dksDttt||dks\t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(  rb  r  dr4  r  CDZU1ZU2ZI1ZI2ZC1ZC2ZD1ZD2ZP1ZP2r   r   r   test_set_operators_parenthesis  s    























r  c                   C   s   t tjdkstd S )N
\mathbb{C})r   r"   	Complexesr   r   r   r   r   test_latex_Complexes  s    r  c                   C   s   t tjdkstd S )N
\mathbb{N})r   r"   r  r   r   r   r   r   test_latex_Naturals  s    r  c                   C   s   t tjdkstd S )N\mathbb{N}_0)r   r"   	Naturals0r   r   r   r   r   test_latex_Naturals0  s    r  c                   C   s   t tjdkstd S )N
\mathbb{Z})r   r"   Integersr   r   r   r   r   test_latex_Integers  s    r  c                  C   s   t d} ttt| | d tjdks*tt d}tt| |f| | dddhddh}t|dksfttt| |ff| | tdddhddh}t|d	kstd S )
Nr   r  z2\left\{x^{2}\; \middle|\; x \in \mathbb{N}\right\}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   r  Zimgsetr   r   r   test_latex_ImageSet"  s    $*r  c                  C   sT   t d} tt| t| d dtjdks,ttt| t| d dtjdksPtd S )Nr   r  r   z@\left\{x\; \middle|\; x \in \mathbb{R} \wedge x^{2} = 1 \right\}z(\left\{x\; \middle|\; x^{2} = 1 \right\})r#   r   r   r    r"   r  r   r  r   r   r   r   test_latex_ConditionSet1  s    r  c                   C   sT   t ttddtdd dks$tt ttddtddt  d	d
dksPt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)Z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   r   test_latex_ComplexRegion9  s    "r  c                  C   s$   t d} tt| tjdks td S )Nr   zx \in \mathbb{N})r#   r   r   r"   r  r   r  r   r   r   test_latex_ContainsA  s    r  c                   C   s   t tttd  tddftddfdks,tt ttd tddfdksLtt ttd t tddfdksptt ttd t tddfd dkst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   r   test_latex_sumF  s    "r  c                   C   s   t tttd  tddftddfdks,tt ttd tddfdksLtt ttd t tddfdksptt tttddfd dkst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   r   test_latex_productQ  s    "r  c                  C   s   t ttttdksttd} t t| ttddks<tt t| ttdddksZtt t| ttdd dksztt t| ttdd	d
dkst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   r   test_latex_limits]  s    r  c                   C   s   t ttdkstt ttdddks,tt tttt dksHtt tttt dddkshtt ttttdkstt ttttdddkstd S )	Nz\log{\left(x \right)}T)Z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   r<   r   r   r  powr   r   r   r   test_latex_logn  s    r  c                  C   sD   t d} | t }t|dks tt d} | t }t|dks@td S )NrO  )z	\beta + xz	x + \betarM   )r#   r   r   r   )rM   r  r   r   r   test_issue_3568z  s    r  c                   C   s   t dt tdd dkstt dt tdd dddks@tt dt tdd ddd	d
ksdtt dt tgdks|t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   r   
test_latex  s    r  c                  C   sL   t ddtd dtdtd di} t| dks0tt| }t|dksHt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   r   test_latex_dict  s     r  c                  C   s*   t dt dt dg} t| dks&td S )Nr?  r(  r  z)\left[ \omega_{1}, \  a, \  \alpha\right]r#   r   r   )llr   r   r   test_latex_list  s    r  c                   C   sp   t tjdkstt tjdks$tt tjdks6tt tjdksHtt tjdksZtt tjdksltd S )NGrP  e\phi\piz\text{TribonacciConstant})	r   r"   ZCatalanr   Z
EulerGammaZExp1ZGoldenRatioPiZTribonacciConstantr   r   r   r   test_latex_NumberSymbols  s    r  c                   C   s   t tdd dkstt tdddks.tt tdddksDtt tdd dks\tt tdd t dksxtt tdd t tddt  d	kstd S )
Nr   r  z- \frac{1}{2}r  r  z\frac{1}{2}z- \frac{x}{2}r  z- \frac{x}{2} - \frac{2 y}{3})r   r   r   r   r  r   r   r   r   test_latex_rational  s     r  c                   C   s0   t dt dkstt dtt  dks,td S )Nr   r  z\frac{1}{x + y})r   r   r   r  r   r   r   r   test_latex_inverse  s    r  c                   C   sv   t ttdkstt ttd dks,tt ttddksBtt ttddksXtt ttdd dksrtd S )Nz\delta\left(x\right)r  z%\left(\delta\left(x\right)\right)^{2}r   r  z)\delta^{\left( 5 \right)}\left( x \right)z:\left(\delta^{\left( 5 \right)}\left( x \right)\right)^{2})r   rN   r   r   r   r   r   r   test_latex_DiracDelta  s    r  c                   C   s0   t ttdkstt ttd dks,td S )Nz\theta\left(x\right)r  z%\left(\theta\left(x\right)\right)^{2})r   rO   r   r   r   r   r   r   test_latex_Heaviside  s    r  c                   C   sn   t tttdkstt tttd dks0tt ttd tdksJtt ttttddddksjtd S )	Nz\delta_{x y}r   z\delta_{x, y + 1}z\delta_{y, x + 1}r  Fr   z\left(\delta_{x y}\right)^{2})r   rn   r   r  r   r   r   r   r   r   test_latex_KroneckerDelta  s    r  c                   C   s   t ttttdkstt ttttd dks4tt ttttd dksPtt tttd tdksltt ttd ttdkstd S )Nz\varepsilon_{x y z}r  z$\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   ro   r   r  r!  r   r   r   r   r   test_latex_LeviCivita  s    r  c                      s~   t t  t dkstt dddks,tt dddks@tt dddksTtt ddd	ksht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   r   
ValueErrorr   r   r  r   	test_mode  s"      r  c                   C   s   t ttttdkstt ttttdks0tt ttttd dksLtt ttttd dkshtt ttttdkstt ttttdkstt ttttd dkstt ttttd d	kst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  r!  r   r`   r_   ra   r   r   r   r   test_latex_mathieu  s    r  c                  C   s  t ttdk ftd df} t| dks*tt| dddks>tt ttdk fdtdkf} t| dkshttd	d
d\}}t |d t||f|| df} d}t| |kstt||  d| kstt| | d| ksttt ttdk ftd tdk fdkst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Z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})rF   r   r   r   r%   r    )r  r4  r  r  r   r   r   test_latex_Piecewise  s     
  r  c                  C   s   t dt tgttd gg} t| dks,tt| dddks@tt| dddksTtt| d	dd
kshtt| d d	ddks~tt ddtd}t|dkstd S )Nr   z;\left[\begin{matrix}x + 1 & y\\y & x - 1\end{matrix}\right]r  r  zG$\left[\begin{smallmatrix}x + 1 & y\\y & x - 1\end{smallmatrix}\right]$array)mat_strz=\left[\begin{array}{cc}x + 1 & y\\y & x - 1\end{array}\right]Zbmatrixz=\left[\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}\right])Z	mat_delimr  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   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sht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   rK   rI   r   r   r   )r  r   r  expectedr   r   r    test_latex_matrix_with_functions  s    "r  c                  C   s,  t d\} }}}ttttfD ]}|| }t|dks:t|d|  |g||gg}|d|  ||g}t||}t||}t|dkstt|dkstt|dkstt|dkst|| |d| gg}	|| g|gd| gg}
||
 g}t|	dkstt|
d	kstt|d
kst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   r   tolist)r   r  r!  r[  	ArrayTyper  ZM1r  ZM3ZMrowZMcolumnZMcol2r   r   r   test_latex_NDimArray'  sF     




r  c                   C   s   t ddt  dddkstt ddt  dddks8tt ddt  dddksTtt dt ddd	ksltt dt ddd
kstt dt dddkstd S )Nr	  r  r  z4 \times 4^{x}r  z4 \cdot 4^{x}Zldotz4 \,.\, 4^{x}z
4 \times xz	4 \cdot xz	4 \,.\, xrz  r   r   r   r   test_latex_mul_symbolU  s    r  c                  C   s8   ddt d  } t| dks ttd|  dks4td S )Nr	  r  z!4 \cdot 4^{\log{\left(2 \right)}}r   z+\frac{1}{4 \cdot 4^{\log{\left(2 \right)}}})r<   r   r   )r  r   r   r   test_latex_issue_4381_  s    r	  c                   C   s  t tddkstt tddks(tt tddks<tt tddksPtt td	d
ksdtt tddksxtt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddks2tt tddksHtt tddks^tt td d!ksttt td"d#kstt td$d#kstd S )%NZ	beta_13_2z\beta_{13 2}Zbeta_132_20z\beta_{132 20}Zbeta_13z
\beta_{13}Zx_a_bzx_{a b}Zx_1_2_3z	x_{1 2 3}Zx_a_b1zx_{a b1}Zx_a_1zx_{a 1}Zx_1_azx_{1 a}zx_1^aaz
x^{aa}_{1}Zx_1__aazx_11^az
x^{a}_{11}Zx_11__aZ	x_a_a_a_azx_{a a a a}z	x_a_a^a^azx^{a a}_{a a}Zx_a_a__a__aZalpha_11z\alpha_{11}Zalpha_11_11z\alpha_{11 11}Zalpha_alphaz\alpha_{\alpha}zalpha^alephz\alpha^{\aleph}Zalpha__alephr   r#   r   r   r   r   r   test_latex_issue_4576e  s(    r  c                  C   sP   t d} dtt|  d ddks*tdtd|   d ddksLtd S )Nr   ze^{-x}r    z3^{-x}r  )r#   r   r;   replacer   r  r   r   r   test_latex_pow_fraction|  s    "r  c                  C   sj   t ddd\} }}t| | |d  dks.tt|d |  | dksJtt| |d  | dksftd S )NzA,B,CFr  r  z
A B C^{-1}z
C^{-1} A Bz
A C^{-1} BrI  r4  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@tt| dddksTtt| d	dd
ksht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   r   r  r   r   r   test_latex_order  s    , r  c                   C   sR   t tttd dkstt tttftd dks8tt tttdksNt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   r   test_latex_Lambda  s    r  c                  C   s  t dt\} }}t d| \}}}}t|| dks6tt|d dksJtt|d dks^tt|d d| |  d |d  | | d d	kstt|d d| |  d |d  | |d |  d
kstt|d d| |  d |d  | |d |  d dkstt|d  d| |  d |d  | |d |  d dksXtt|d | d  | d| |  d dkstt|d | d  | d| |  d dkst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   r   )ZRuvuvZRxyzr   r  r!  r   r   r   test_latex_PolyElement  s.    .26
8
(
(r  c                  C   s  t dt\} }}t d| \}}}}}t|| dks8tt|d dksLtt|d dks`tt|d dksttt|| d	kstt|| | d
kstt|||  dkstt|| ||  dkstt|d | dkstt|d | dkstt| d | dks"tt|d ||  dks@tt| |d  dks\tt|| |d  dksztt|d | | d |d | d  dkstt|d | | d |d | || |  d  dkst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   r   )ZFuvr  r  ZFxyztr   r  r!  r  r   r   r   test_latex_FracElement  s,    &
2r  c                   C   s\   t ttd dt  tdks"tt ttt tdks<tt tdt t dksXt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   r   test_latex_Poly  s    r  c                   C   s   t ttdtdtdgtdks"tt ttdtt ddgtdksFt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st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(  rb  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"td S )Nr  r  r   z6\operatorname{CRootOf} {\left(x^{5} + x + 3, 0\right)})r   r   r   r   r   r   r   r   test_latex_ComplexRootOf  s    r  c                   C   s&   t ttd t d tdks"td S )Nr  r  zc\operatorname{RootSum} {\left(x^{5} + x + 3, \left( x \mapsto \sin{\left(x \right)} \right)\right)})r   r   r   rK   r   r   r   r   r   test_latex_RootSum  s    r   c                   C   s   t tdd  d S )Nc                   S   s   t tt ddS )Ngarbage)method)r   r   r  r   r   r   r   r    r  ztest_settings.<locals>.<lambda>)r   	TypeErrorr   r   r   r   test_settings  s    r$  c                   C   s  t ttdkstt ttd dks,tt ttdks@tt tttdksVtt ttd dksntt tttd dkstt ttdkstt tttd	kstt ttd d
kstt tttd dkstt ttdkstt tttdkstt ttttt	fdks.tt ttd dksHtt tttd dksdtt ttttt	fd dkstt t
tdkstt t
ttdkstt t
td dkstt t
ttd dkstt ttdks tt ttd dkstt ttdks0tt tttdksHtt ttd dksbtt tttd dks~t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G_{n}zG_{n}\left(x\right)z	G_{n}^{2}zG_{n}^{2}\left(x\right)zB_{n, m}\left(x, y\right)zB_{n, m}^{2}\left(x, y\right)zF_{n}zF_{n}\left(x\right)z	F_{n}^{2}zF_{n}^{2}\left(x\right)zL_{n}z	L_{n}^{2}zT_{n}r\  z	T_{n}^{2}zT_{n}^{2}\left(x\right))r   r.   r)  r   r,   r   r0   r-   rc  r  r2   r1   r3   r   r   r   r   test_latex_numbers  s4    "r%  c                   C   sH   t ttdkstt tttdks*tt tttd dksDt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   r   test_latex_euler  s    r&  c                   C   s,   t tddkstt tddks(td S )NZlamda\lambdaZLamda\Lambdar
  r   r   r   r   
test_lamda  s    r)  c                  C   s   t d} t d}t| dks tt| | diddks8tt| | | diddksTtt| d | diddksptt| | | d|didd	kstd S )
Nr   r  r  r  zx_i + yr  zx_i^{2}Zy_jz	x_i + y_jr  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ksDtt| d|  d	ks\tt|d|   d
ksttt|d|   dkstt|| | |j ||j   dkstttt||t||dkstttt||t||dkst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   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s4ttd| |  dksLttd|  d	ks`ttd
|  dksttttd|  dkstttd |  dksttdtd | |  dksttd|  | d|   dkstd S )Nr4  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   r   rE   )r4  r  r   r   r   r   test_matMul8  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sZtt|||d ||d f dkstt|||d d||d df dkstt|d ||d f dkstt|d ||d f dkstt||d d |f dkstt|||||f dks2tt|||||||f dksXtt||d ||d |f dks~tt|d ||d ||f dkstt|d d |d d |f dksttt|ddd
ksttt|d | d fd | d fd
ks
ttt|d| d fd| d fd
ks0ttt|d| dfd| dfdksVtt|ddddddf dks|tt|ddddddf dkstt|ddd d kstt|d ddd!df d"kstt|d ddddf d#kstt|dd ddf d$ks&tt|ddddf d%ksHtt|ddddddf d&ksntt|| dd dd f d'kstd S )(Nr)  Tr   z	x y z w tXYr  Z)NNNzX\left[:, :\right]r   zX\left[x:x + 1, y:y + 1\right]r  z"X\left[x:x + 1:2, y:y + 1:2\right]zX\left[:x, y:\right]zX\left[x:, :y\right]zX\left[x:y, z:w\right]zX\left[x:y:t, w:t:x\right]zX\left[x::y, t::w\right]zX\left[:x:y, :t:w\right]zX\left[::x, ::y\right])r   NNr   zX\left[::2, ::2\right]r  r	  r  r,  zX\left[1:2:3, 4:5:6\right]   zX\left[1:3:5, 4:6:8\right]zX\left[1:10:2, :\right]	   zY\left[:5, 1:9:2\right]zY\left[:5, 1::2\right]zY\left[5:6, :5:2\right]zX\left[:1, :1\right]zX\left[:1:2, :1:2\right]z%\left(Y + Z\right)\left[2:, 2:\right])r#   r%   r   r   r   r   )	r)  r   r  r!  r[  r  r/  r0  r1  r   r   r   test_latex_MatrixSliceG  s:    (,  ""&&&&&&&&&$$ "&r4  c            
      C   s   ddl m} m}m}m}m} ddlm} | ddd}t||dkdksLt	|dd}t||d	kd
ksnt	|dd}|dd}	t|t
||	jdkst	t|tttdddkst	d S )Nr   )r   DieExponentialpspacewhere)RandomDomainr~  r   z.\text{Domain: }0 < x_{1} \wedge x_{1} < \inftyZd1r,  r	  z'\text{Domain: }d_{1} = 5 \vee d_{1} = 6r(  rb  zK\text{Domain: }0 \leq a \wedge 0 \leq b \wedge a < \infty \wedge b < \inftyr  z7\text{Domain: }\left\{x\right\} \in \left\{1, 2\right\})Zsympy.statsr   r5  r6  r7  r8  Zsympy.stats.rvr9  r   r   r   domainr   r   )
r   r5  r6  r7  r8  r9  r/  r  r4  r  r   r   r   test_latex_RandomDomainh  s     


r;  c                  C   st   ddl m}  | tt}| ttf }t|ttt  tttt  ksNtt|tt ttt ksptd S )Nr   QQ)sympy.polys.domainsr=  Z
frac_fieldr   r  r   convertr   )r=  Fr   r   r   r   test_PrettyPoly{  s
    *rA  c                  C   sT  t d} t d}td}t d}t d}tt|| | |dksDttt|||| ||dksdttt|| | |dksttt|||| ||fd	ksttt|| | |d
ksttt	|||| dksttt
|| | |dksttt|||| dksttt|| | |dks2ttt|||| dksPtd S )Nr   r$  r  r(  rb  z<\mathcal{M}_{x}\left[f{\left(x \right)}\right]\left(k\right)zA\mathcal{M}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z<\mathcal{L}_{x}\left[f{\left(x \right)}\right]\left(k\right)zA\mathcal{L}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z<\mathcal{F}_{x}\left[f{\left(x \right)}\right]\left(k\right)zA\mathcal{F}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z>\mathcal{COS}_{x}\left[f{\left(x \right)}\right]\left(k\right)zC\mathcal{COS}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)z>\mathcal{SIN}_{x}\left[f{\left(x \right)}\right]\left(k\right)zC\mathcal{SIN}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right))r#   r   r   r~   r   r{   r}   rz   rw   ry   rv   rx   r   r|   )r   r$  r  r(  rb  r   r   r   test_integral_transforms  sF    

rB  c                  C   sD   ddl m}  t| ttdks$tt| jttdddks@td S )Nr   r<  z\mathbb{Q}\left[x, y\right]Zilexr  z#S_<^{-1}\mathbb{Q}\left[x, y\right])r>  r=  r   old_poly_ringr   r  r   r<  r   r   r   test_PolynomialRingBase  s
    rD  c                  C   st  ddl m} m}m}m}m}m} | d}| d}| d}|||d}	|||d}
||}|d}t|d	ksptt|	d
kstt|dkstt|
|	 dkstt|dkst| }t|dkst||	d|
t	j
i}t|dkst||	d|
t	j
i|
|	 di}t|dkst| d}| d}| d}|||d}|||d}|||g}||}t|dkspt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\}r4  r  r  r  rL  z-\begin{array}{cc}
A & B \\
 & C 
\end{array}
)Zsympy.categoriesrE  rF  rG  rH  rI  rJ  r   r   r"   r  )rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  Zid_A1rP  r  r4  r  r  r  rL  gridr   r   r   test_categories  s6     
rS  c                  C   s  ddl m}  ddlm} | tt}|d}|ttgdtd g}t	|dksVt
t	|dksft
|td t}t	|dkst
|| }t	|d	kst
t	|dtd
 d gdtgdkst
|| td| tdddg}t	|dkst
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=  Zsympy.polys.agcarT  rC  r   r  Zfree_module	submoduler   r   Zideal)r=  rT  r   r@  r  r   QrM  r   r   r   test_Modules  s2    
 rW  c                  C   sJ   ddl m}  | ttd d g }t|dks4tt|jdksFt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=  rC  r   r   r   one)r=  r   r   r   r   test_QuotientRing  s    rY  c                  C   s0   t ddd\} }t| | }t|dks,td S )Nr  Fr  z!\operatorname{tr}\left(A B\right))r%   r   r   r   )r4  r  r  r   r   r   test_Tr  s    rZ  c                  C   s   ddl m} m}m}m}m} td}t| |dks8tt| ||dksPtt	ddd}t| |dksptt| || d	kstt| ||dd|f||ddffd
kst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_  rc  r/  r   r   r   test_Determinant  s     rb  c            
      C   s   ddl m} m}m} tddd}tddd}t| |dks@tt| || dksXtt| || | dksttt| || d	kstt| || | d
kstt| |d dkstt| |d dkstt| ||dkstt|| |dks
tt| ||dks$tt|| |dks>tt|| || dks\ttd}t| |dksztt| || dkstddl m}m	}m
} t| ||dd|f||ddffdksttddd}	t| |	dkstd S )Nr   )Adjointr\  	Transposer/  r  r0  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})ra  rc  r\  rd  r   r   r   r   r]  r^  r_  )
rc  r\  rd  r/  r0  rc  r]  r^  r_  Mxr   r   r   test_Adjoint&  s8    

rh  c            
      C   s`  ddl m} m}m} tddd}tddd}t| |dks@tt| || dksXtt| ||ddksrtt|| |dd	kstt| ||dd
kstt|| |ddksttd}t| |dkstt| || dkstddl m}m	}m
} t| ||dd|f||ddffdks:ttddd}	t| |	dks\td S )Nr   )rd  MatPowHadamardPowerr/  r  r0  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}re  zi\left[\begin{matrix}1 & X\\\left[\begin{matrix}1 & 2\\3 & 4\end{matrix}\right] & 0\end{matrix}\right]^{T}rf  z\left(M^{x}\right)^{T})ra  rd  ri  rj  r   r   r   r   r]  r^  r_  )
rd  ri  rj  r/  r0  rc  r]  r^  r_  rg  r   r   r   test_TransposeC  s,    
rk  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sVt	t| ||| dkspt	t||dd	kst	t||d
dkst	t||||ddkst	t||||ddkst	t|||d
d
dkst	t|||d
d
dkst	t||t
d dks*t	d S )Nr   )HadamardProductrj  )r   r   ri  r/  r  r0  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)})ra  rl  rj  sympy.matrices.expressionsr   r   ri  r   r   r   r)  )rl  rj  r   r   ri  r/  r0  r   r   r   test_Hadamard[  s.    
rn  c                  C   s   ddl m}  tddd}tddd}t| |ddks:tt| || ddksTtt| || ddksntt| || dd	kstt| || dd
ksttddd}t| |ddkstd S )Nr   )ri  r/  r  r0  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}rf  z\left(M^{x}\right)^{2})rm  ri  r   r   r   )ri  r/  r0  rg  r   r   r   test_MatPows  s    ro  c                  C   sT   t ddd} | j|  t}t|dks,t| ttdt }t|dksPt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,  Z	applyfuncrK   r   r   r   r   )r/  r  r   r   r   test_ElementwiseApplyFunction  s
    rp  c                  C   sD   ddl m}  t| dddddks&tt| dddddks@td S )	Nr   r_  r   r  Zmat_symbol_styler  boldz
\mathbf{0})"sympy.matrices.expressions.specialr_  r   r   rq  r   r   r   test_ZeroMatrix  s    ru  c                  C   sD   ddl m}  t| dddddks&tt| ddddd	ks@td S )
Nr   r^  r  r	  r  rr  1rs  z
\mathbf{1})rt  r^  r   r   rv  r   r   r   test_OneMatrix  s    rx  c                  C   s@   ddl m}  t| ddddks$tt| ddddks<td S )	Nr   Identityr   r  rr  z
\mathbb{I}rs  z
\mathbf{I})rt  rz  r   r   ry  r   r   r   test_Identity  s    r{  c                  C   s<   ddl m} m} t| ddks$tt|tdks8td S )Nr   DFTIDFTr  z\text{DFT}_{13}z\text{IDFT}_{x})Z"sympy.matrices.expressions.fourierr}  r~  r   r   r   r|  r   r   r   test_latex_DFT_IDFT  s    r  c                  C   sl   t d} t|  }t|dks tt|  }t|dks8tt|  }t|dksPtt|  }t|dkshtd S )Nza:fz.a \wedge b \wedge c \wedge d \wedge e \wedge fz$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   r   )Zsymsr  r   r   r   test_boolean_args_order  s    r  c                  C   s   t d} t| dkstd S )Nr  r5  )rE   r   r   )r5  r   r   r   test_imaginary  s    r  c                   C   sd   t tdkstt tdks tt tdks0tt tdks@tt tdksPtt tdks`td S )Nz\sinz\cosz\tanz\logz\operatorname{Ei}\zeta)r   rK   r   rI   rL   r<   rV   rt   r   r   r   r   test_builtins_without_args  s    r  c                  C   s   t d} t| dkstt| tdks,tt d} t| dksDtt d} t| dks\tt| tdksptt d	}t|d
kstt d}t|tdkstt|dkst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   r   test_latex_greek_functions  s    r  c                  C   s   d} t | dkstd} t | dks(td} t | dks<td} t | dksPtd	} t | d
ksdtd} t | dksxtd} t | dkstd S )Nr  r  r  r  r  r  omicronor  r  r   r  ZLamdaHatDOTz\dot{\hat{\Lambda}})r   r   r  r   r   r   test_translate  s    r  c                  C   s2   ddl m}  | D ]}tt|d| kstqd S )Nr   )other_symbols\)sympy.printing.latexr  r   r%   r   )r  r  r   r   r   test_other_symbols  s    r  c                   C   s  t tddkstt tddks(tt tddks<tt tddksPtt td	d
ksdtt tddksxtt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddks2tt tdd ksHtt td!d"ks^tt td#d$ksttt td%d$kstt td&dkstt td'dkstt td(d(kstt td)d)kstt td*d*kstt td+d+kstt td,d,ks$tt td-d-ks:tt td.d.ksPtt td/d0ksftt td1d1ks|tt td2d2kstt td3d3kstt td4d4kstt td5d5kstt td6d6kstt td7d7ks tt td8d8kstt td9d9ks,tt td:d:ksBtt td;d;ksXtt td<d=ksntt td>d?kstt td@dAkstt tdBdCkstt tdDdEkstt tdFdGkstd S )HNZ	xMathringz\mathring{x}ZxCheckz	\check{x}ZxBrevez	\breve{x}ZxAcutez	\acute{x}ZxGravez	\grave{x}ZxTildez	\tilde{x}ZxPrimez{x}'ZxddDDotz
\ddddot{x}ZxDdDotz	\dddot{x}ZxDDotz\ddot{x}ZxBoldz\boldsymbol{x}ZxnOrMz\left\|{x}\right\|ZxAVGz\left\langle{x}\right\rangleZxHatz\hat{x}ZxDotz\dot{x}ZxBarz\bar{x}ZxVecz\vec{x}ZxAbsrX  ZxMagZxPrMZxBMZMathringZCheckZBreveZAcuteZGraveZTildePrimeZDDotz\dot{D}ZBoldZNORmZAVGZHatr   ZBarZVecr4   ZMagZPrMZBMZhbarz\hbarZxvecdotz\dot{\vec{x}}ZxDotVecz\vec{\dot{x}}ZxHATNormz\left\|{\hat{x}}\right\|Z xMathringBm_yCheckPRM__zbreveAbszC\boldsymbol{\mathring{x}}^{\left|{\breve{z}}\right|}_{{\check{y}}'}Z alphadothat_nVECDOT__tTildePrimez1\hat{\dot{\alpha}}^{{\tilde{t}}'}_{\dot{\vec{n}}})r   r%   r   r   r   r   r   test_modifiers  sd    


r  c                   C   s  t tddkstt tddks(tt tddks<tt tddksPtt td	d
ksdtt tddksxtt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddkstt tddks2tt tdd ksHtt td!d"ks^tt td#d$ksttt td%d&kstt td'd(kstt td)d*kstt td+d,kstt td-d.kstt td/d0kstt td1d2kstt td3d4ks$tt td5d6ks:tt td7d8ksPtt td9d:ksftt td;d<ks|tt td=d>kstt td?d@kstt tdAdBkstt tdCdDkstt tdEdFkstt tdGdHks tt tdIdJkstt tdKdLks,tt tdMdNksBtt tdOdPksXtt tdQdRksntt tdSdTkstt tdUdVkstt tdWdXkstt tdYdZkstt td[d\kstt td]d^kstt td_d`kstt tdadbkstt tdcddks4tt tdedfksJtt tdgdhks`tt tdidjksvtt tdkdlkstt tdmdnkstd S )oNr  r  rM   rO  rZ   rP  delta\deltaepsilonz\epsilonrt   r  etaz\etar]  z\thetaiotaz\iotakappaz\kappalambdar'  r   z\munuz\nuxiz\xir  r  r   r  rF  z\rhosigmaz\sigmar   r8  upsilonz\upsilonr`  r  r  r  psiz\psirA  r  r  r  r  r  rE  \GammaDeltaz\DeltaEpsilonz
\mathrm{E}Zetaz
\mathrm{Z}r  r  Thetaz\ThetaIotaz
\mathrm{I}Kappaz
\mathrm{K}r   r(  Muz
\mathrm{M}Nuz
\mathrm{N}Xiz\XiOmicronz
\mathrm{O}r  r  Rhoz
\mathrm{P}Sigmaz\SigmarG  r9  Upsilonz\UpsilonPhiz\PhirT   z
\mathrm{X}r}  z\PsiOmegaz\OmegaZ
varepsilonz\varepsilonZvarkappaz	\varkappaZvarphiz\varphiZvarpiz\varpiZvarrhoz\varrhoZvarsigmaz	\varsigmaZvarthetaz	\varthetar
  r   r   r   r   test_greek_symbols'	  sn    r  c                   C   sp   t tjdkstt tjdks$tt tjdks6tt tjdksHtt tjdksZtt tjdksltd S )Nz
\mathbb{Q}r  r  r  z
\mathbb{R}r  )	r   r"   Z	Rationalsr   r  r  r  r  r  r   r   r   r   test_fancyset_symbolsc	  s    r  c                   C   s   t tdkstd S )Nz\mathcal{COS})r   rv   r   r   r   r   r   *test_builtin_without_args_mismatched_namesl	  s    r  c                   C   sd   t tdkstt tdks tt tdks0tt tdks@tt tdksPtt tdks`td S )Nz\operatorname{Chi}z\operatorname{B}r  r  rP  )r   rT   r   rM   rZ   rn   rN   r   r   r   r   r   test_builtin_no_argsq	  s    r  c                  C   s    t d} t| tdkstd S )Nr  z\Pi{\left(x \right)})r   r   r   r   r  r   r   r   test_issue_6853z	  s    r  c                  C   s   t dtd dd} t| dks"tt dtd dd} t| dksDtt tjtd dd} t| dkshtt ttd dd} t| d	kstt t td dd} t| d
kstt dtd } t| dkstt dtd } t| dkst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   r  )r  r   r   r   test_Mul	  s    r  c                  C   sX   t dddd} t| dksttttdd dks8ttd}t|d d	ksTt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   r#   )r  r  r   r   r   test_Pow	  s
    r  c                   C   s4   t tttdkstt ttttdks0td S )Nzx \Leftrightarrow yzx \not\Leftrightarrow y)r   r   r   r  r   r   r   r   r   r   test_issue_7180	  s    r  c                   C   s   t tjt dkstd S )Nz\left(\frac{1}{2}\right)^{n})r   r"   r   r)  r   r   r   r   r   test_issue_8409	  s    r  c                  C   s,   ddl m}  | ddd}t|dks(td S )Nr   
parse_exprz-B*AFr   zA \left(- B\right)Zsympy.parsing.sympy_parserr  r   r   )r  r  r   r   r   test_issue_8470	  s    r  c                  C   sx   t ddd} t ddd}t| | || dks6tt| | |d| dksVtt| | | |  dkstt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   r   test_issue_15439	  s
     r  c                   C   s   t tddkstd S )Nz\frac{a_1}{b_1}r
  r   r   r   r   test_issue_2934	  s    r  c                  C   s4   d} t | }t|| ksttt|dks0td S )Nz	C_{x_{0}}z\cos{\left(C_{x_{0}} \right)})r#   r   r   rI   )ZlatexSymbolWithBracer  r   r   r   test_issue_10489	  s    r  c                  C   s,   t d\} }t| d |d  dks(td S )Nz
m__1, l__1r  z/\left(l^{1}\right)^{2} + \left(m^{1}\right)^{2}rI  )Zm__1Zl__1r   r   r   test_issue_12886	  s    r  c                  C   s,   ddl m}  | ddd}t|dks(td S )Nr   r  z5/1Fr   z\frac{5}{1}r  )r  r  r   r   r   test_issue_13559	  s    r  c                  C   s*   t tdtt dd } t| dks&td S )Nr  Fr   zc - \left(a + b\right))r  r   r(  rb  r   r   r  r   r   r   test_issue_13651	  s    r  c                  C   sz   t d} td|  }t|td|    kr4dks:n tt|d dksNtt|d dksbtt| | dksvt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   )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s8ttd| d  dksPt|d || | }t|d	kstttd
\}}}t d||}t d||}t|| ||f dkstd S )Nr4  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  r%   )	r4  r  r  r@  r5  r6  r$  r  r  r   r   r   test_MatrixElement_printing	  s    r  c                  C   s|   t ddd} t ddd}t ddd}t|  dks6tt| | |  | dksRtt|  | | | |  | dksxtd S )Nr4  r  r  r  z- AzA - A B - Bz- A B - A B C - B)r   r   r   r  r   r   r   test_MatrixSymbol_printing	  s    r  c                  C   s2   t ddd} t ddd}tt| |dks.td S )Nr4  r  r  r  A \otimes B)r   r   r   r   )r4  r  r   r   r   test_KroneckerProduct_printing	  s    r  c            	      C   s  t ttd  t td td  t} t tt tt t}t ttd  tt t  t tt t}tt| |dksvttt| ||dksttt| | dkstt	dt
 gddt
  gg}t|t
}t	ddt
d  gg}t|t
}t|||  d  kr$ttt|||ks*n tt	ddgddt
 gg}t|t
}t|| | d	  krttt|||ksn t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  r!  r  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    $(
r  c                  C   sx   t td td t} t| dks$tt td dt t}t|dksHtt ttd dt  d t}t|dkstt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   r   test_TransferFunction_printing
  s    r  c                  C   sT  t ttd  t td td  t} t tt tt t}tt| |dksNttt| | dksft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rJtt|||  krJtt|t||  krJttt|||ksPn t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  r!  r  r   r   r   r   r  r   r  r   )r  r  r  r  r  r  r  r  r   r   r   test_Parallel_printing
  s*    $  

r  c                  C   s   t ttt t} t t t tt t}t ttd dt  d t}tt| g|ggdks^ttt| |g||  ggdkstd S )Nr  r  zP\left[\begin{matrix}\frac{p}{p + x}\\\frac{p - s}{p + s}\end{matrix}\right]_\tauz\left[\begin{matrix}\frac{p}{p + x} & \frac{p - s}{p + s}\\\frac{p}{y^{2} + 2 y + 3} & \frac{\left(-1\right) p}{p + x}\end{matrix}\right]_\tau)r   r  r   r  r  r   r   r   r  r   r   r   $test_TransferFunctionMatrix_printing1
  s    r  c                  C   s   t ttt t} t t t tt t}tt| |dks<ttt| | t ddtdks^ttt| |ddksvttt| | dddkst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   r   test_Feedback_printing;
  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sttt|| |ddkst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  r  Ztf4Ztfm_1Ztfm_2r   r   r   test_MIMOFeedback_printingJ
  s    r  c                  C   sf   t tttt} t| dkstt ttttt } t| dks@tt ttttt } t| dksbtd S )Nzx + y i + z j + t kzx + y i + z j + t x kz$x + y i + z j + \left(t + x\right) k)r   r   r  r!  r  r   r   )qr   r   r   test_Quaternion_latex_printingb
  s    r  c                  C   s>   ddl m}  tddd}tddd}t| ||dks:td S )Nr   )TensorProductr4  r  r  r  )Zsympy.tensor.functionsr  r   r   r   )r  r4  r  r   r   r   test_TensorProduct_printingk
  s    r  c                  C   s:   ddl m}  ddlm} || j| j}t|dks6td S )Nr   R2)WedgeProductz*\operatorname{d}x \wedge \operatorname{d}y)sympy.diffgeom.rnr  sympy.diffgeomr  ZdxZdyr   r   )r  r  r  r   r   r   test_WedgeProduct_printingr
  s    r  c                  C   s   t dddd} t| dkstt dt dddddd}t|dksFtt dddd}t|d	ksdtt dddd}t|d
kstd S )Nr   r  Fr   z1^{-1}z
1^{1^{-1}}r  r  z\frac{1}{9}z1^{-2})r   r   r   )Zexpr_1Zexpr_2Zexpr_3Zexpr_4r   r   r   test_issue_9216y
  s    r  c                  C   sn  ddl m} m}m}m} | d}|d|\}}}}|d|}	|d|g\}
}}}|d||g}|d||||g}t|d	kstt| d
kst|
|}t|dkst|
|	}t|dkst|
| }t|dkstd|
| }t|dkst|||| |	 }t|dkst||| | |	}t|dks@t||| ||	 }t|dksdt||| }t|dkst|||}t|dkst|| | }t|dkstdt |
| }t|dkst||| }t|dkst||| |
| || }t|dks,t|
|d||  }t|dksRtddl m} |||||||d|di}t|dkst|||||||di}t|dkst|||| |||d|di}t|d kst|||| || |d|di}t|d!kst||||| | |d| di}t|d"ksLt||||| | |di}t|d#ksztt	|
||
|}t|d$kstt	|
| |
| }t|d%kstt	|||| | |
t
|
t }t|d&kstt	|| |
|  |
| |
t }t|d'ks6tt	d|
|  |
| |
t }t|d(ksjtd S ))Nr   )TensorIndexTypetensor_indices
TensorHeadtensor_headsLzi j k lZi_0zA B C DHKz{}^{i}z{}_{i}zA{}^{i}zA{}^{i_{0}}zA{}_{i}r'  z	-3A{}^{i}zK{}^{ij}{}_{ki_{0}}zK{}^{i}{}_{jk}{}^{i_{0}}zK{}^{i}{}_{j}{}^{k}{}_{i_{0}}zH{}^{i}{}_{j}zH{}^{ij}zH{}_{ij}r   z\left(x + 1\right)A{}^{i}zH{}^{L_{0}}{}_{L_{0}}z#H{}^{i}{}_{L_{0}}A{}^{L_{0}}B{}^{k}r  z3B{}^{i} + A{}^{i})TensorElementr  zK{}^{i=3,j,k=2,l}zK{}^{i=3,jkl}zK{}^{i=3}{}_{j}{}^{k=2,l}zK{}^{i=3}{}_{j}{}^{k=2}{}_{l}zK{}^{i=3,j}{}_{k=2,l}zK{}^{i=3,j}{}_{kl}z4\frac{\partial}{\partial {A{}^{L_{0}}}}{A{}^{L_{0}}}z,\frac{\partial}{\partial {A{}_{j}}}{A{}_{i}}zK\frac{\partial^{2}}{\partial {A{}^{m}} \partial {A{}_{n}}}{K{}^{ij}{}_{kl}}zZ\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(A{}_{i} + B{}_{i}\right)}zQ\frac{\partial^{2}}{\partial {A{}_{j}} \partial {A{}_{n}}}{\left(3A{}_{i}\right)})Zsympy.tensor.tensorr  r  r  r  r   r   r   r  r   rc  r)  )r  r  r  r  r  r5  r6  r$  r<  Zi0r4  r  r  r  r  r  r  r  r   r   r   test_latex_printer_tensor
  sx    


 "$("r  c                     s  t d\} }}}}|  d|  d|  d|  d|   d}t dd|ksTtd	}t ddd|ksptd
}t ddd|kstd}t dddd|kstd}	t d|	kstt ddd|	kstd}
t ddd|
kst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}Z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  Z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}ZIEEEeqnarrayc                      s   t  ddS )Nr   r  )r   r   r  r  r   r   r    r  z&test_multiline_latex.<locals>.<lambda>)r%   r   r   r   r  )r(  rb  r  r  r  r  Z	expected2Z	expected3Zexpected3dotsZexpected3alignZ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sTt	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    rK   rI   r"   r  r   r   )r(  r   Zsolr   r   r   test_issue_15353  s     " r  c                  C   s   t d} t ddd}td| |}tt|dks4ttt|dksHttt|dkd	ks`ttd
| |}tt||dkstd S )Nr   r  Tr  r/  z\operatorname{E}\left[X\right]z \operatorname{Var}\left(X\right)r   z"\operatorname{P}\left(X > 0\right)r0  z#\operatorname{Cov}\left(X, Y\right))r%   r   r   r   r   r   r   r   )r   r  r/  r0  r   r   r   test_latex_symbolic_probability!  s    r  c                  C   sH   ddl m}  tddd}t| |dks,tt| |d dksDtd S )Nr   tracer4  r   \operatorname{tr}\left(A \right)z$\operatorname{tr}\left(A^{2} \right)Z sympy.matrices.expressions.tracer  r   r   r   )r  r4  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sXtt|td dksptt|tdkst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  r  r  r   r   r  <  s    z3test_print_basic.<locals>.UnimplementedExpr.__new__N)r   r   r   r  r   r  r   r   UnimplementedExpr;  s   r  c                    s    |   S r  )r  r  r  r   r   unimplemented_expr@  s    z,test_print_basic.<locals>.unimplemented_exprc                    s    | }d|j _|S )NzUnimplementedExpr_x^1)	__class__r   )r  resultr  r   r   unimplemented_expr_sup_subD  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))Zsympy.core.basicr   sympy.core.exprr  r   r   r   )r  r  r	  r   )r   r  r   test_print_basic4  s    
r  c                  C   s  ddl m}  tddd}t| |dddks0tt| |ddd	ksHttdd
d
}tdd
d
}tdd
d
}t| dddkstt|||  | dddkstt| | || |  | dddksttdd
d
}t|dddksttdd
d
}t|dddkstd S )Nr   r  r4  r  rs  rr  z)\operatorname{tr}\left(\mathbf{A} \right)r  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  r4  r  r  r  r   r   r   test_MatrixSymbol_boldP  s,     r  c                  C   s.   t ddd} td}tt| |dks*td S )Nr   r   r  r   z#\sigma_{\left( 0\; 1\; 2\right)}(x))r   r#   r   r	   r   )r  r   r   r   r   test_AppliedPermutationi  s
    r  c                  C   sH   t ddd} tt| dks tt dddd} tt| dksDt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   r   r  r   r   r   test_PermutationMatrixp  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stt|||t tfdtd|dtftd|dtffdkst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   rF   rI   rK   r!   r   r   )r  r  r   r$  r)  for   r   r   test_issue_21758x  s(     L
 r  c                   C   s   t dt dkstt dt dddks,tt dt dddksDtt dt dddks\tt td	dd
ksptt tdddkstd S )Nr   z1 + ir5  imaginary_unitr6  z1 + jr   z1 + footiz\text{i}Ztjz\text{j})r   r   r   r   r   r   r   test_imaginary_unit  s    r  c                   C   sd   t ttdddkstt ttdddks0tt ttdddksHtt ttdddks`td S )NT)Zgothic_re_imz\Im{\left(x\right)}FrZ  z\Re{\left(x\right)}rY  )r   r7   r   r   r9   r   r   r   r   test_text_re_im  s    r  c                  C   s   ddl m} m}m}m}m} ddlm} tddd\}}| dd}t	|d	ksRt
|d
|}	t	|	dkslt
|d|	||g}
t	|
dkst
||
d}t	|dkst
td}||j|j}t	||dkst
d S )Nr   )ManifoldPatchCoordSystemBaseScalarFieldDifferentialr  zx yTr^  r  r  z\text{M}Pz\text{P}_{\text{M}}rectz!\text{rect}^{\text{P}}_{\text{M}}z
\mathbf{x}rL  zC\operatorname{d}\left(g{\left(\mathbf{x},\mathbf{y} \right)}\right))r  r  r  r  r  r  r  r  r%   r   r   r   r   r  )r  r  r  r  r  r  r   r  rc  r  r!  rb  rL  Zs_fieldr   r   r   test_latex_diffgeom  s     



r"  c                   C   s   t dt dkstt dt dks(tt dt t dks@tt dt t t dks\tt dt t dksttt td	kstd S )
Nr  z
5 \text{m}r  z3 \text{gibibyte}r	  z\frac{4 \mu\text{g}}{\text{s}}z\frac{4 \mu \text{g}}{\text{s}}z5 \text{m} \text{m}z\text{m})	r   r   r   r   r   r   r   r   r   r   r   r   r   test_unit_printing  s    r#  c                  C   s$   t d} tt| | ddks td S )Nr  r  z,\frac{d^{2}}{d \left(x^{*}\right)^{2}} x^{*})r#   r   r   r   )r#  r   r   r   test_issue_17092  s    r$  c            
      C   s  t d\} }}}t ddd\}}}t dtd\}}}	tddd	gd
ddksNtttddd	d
ddksjttdd
ddks~ttdd
ddksttddd	gdddkstttddd	dddksttddddksttddddksttddd	gdkstttddd	dks"ttddks4ttddksFtttddd
ddksbttdd
ddksxtt d} t d}t d}t| d d|d   d	 | d
ddksttd d
dd!kstttd d
dd!ksttd"d
dd#kstttd"d
dd#ksttd$d
dd%ks4tttd&d' d
dd(ksRtttd)d
dd(ksltt d} td*|  d d
dd+kstttddd	dddkstttd,d-  ttd.d-  ttd/d-  d S )0Nzx y z tr   Tr   zf g hr  r   ffffff@      @commaZdecimal_separatorz#\left[ 1; \  2{,}3; \  4{,}5\right]z\left\{1; 2{,}3; 4{,}5\right\})r   r%  gffffff@z#\left( 1; \  2{,}3; \  4{,}6\right))r   z\left( 1;\right)Z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  r!  r  z#2^{y^{3{,}4}} + 5{,}3 x + z + 4{,}5g/$?z0{,}987g333333?z0{,}3g|)v>z5{,}8 \cdot 10^{-7}g@gHz>z5{,}7 \cdot 10^{-7}g<sAC >g333333?z1{,}2 x + 3{,}4c                   S   s   t dddgddS )Nr   r%  r&  Z&non_existing_decimal_separator_in_listr(  r  r   r   r   r   r    r  z.test_latex_decimal_separator.<locals>.<lambda>c                   S   s   t tdddddS )Nr   r%  r&  Z%non_existing_decimal_separator_in_setr(  )r   r   r   r   r   r   r    r  c                   S   s   t dddS )N)r   r%  r&  Z'non_existing_decimal_separator_in_tupler(  r  r   r   r   r   r    r  )	r%   r   r   r   r   r   r"   r   r  )
r   r  r!  r  r$  rc  r)  r  rL  rM  r   r   r   test_latex_decimal_separator  sD    .r)  c                  C   s$   ddl m}  t| ddks td S )Nr   Strr   )sympy.core.symbolr+  strr   r*  r   r   r   test_Str  s    r.  c                   C   s.   t ddddddddd	d
ddg
ks*td S )Nz
~^\&%$#_{}r  z\textasciitildez\textasciicircumz\textbackslashz\&z\%z\$z\#z\_z\{z\})r   joinr   r   r   r   r   test_latex_escape  s    
r0  c                  C   s8   G dd d} t |  dks tt |  fdks4td S )Nc                   @   s   e Zd Zdd ZdS )z#test_emptyPrinter.<locals>.MyObjectc                 S   s   dS )Nz<MyObject with {...}>r   )r   r   r   r   __repr__  s    z,test_emptyPrinter.<locals>.MyObject.__repr__N)r   r   r   r1  r   r   r   r   MyObject  s   r2  z'\mathtt{\text{<MyObject with \{...\}>}}z6\left( \mathtt{\text{<MyObject with \{...\}>}},\right))r   r   )r2  r   r   r   test_emptyPrinter  s    r3  c                  C   s   dd l } | tjd jdks"tttdks2tz:tj	dd | tjd jdksZtttdksjtW 5 tjd= X | tjd jdkstttdkstd S )Nr   r  r5  r6  r  )
inspect	signaturer   
parametersdefaultr   r   r   Z_global_settingsZset_global_settings)r4  r   r   r   test_global_settings  s    
r8  c                  C   s$   dd l } | | ttks td S )Nr   )pickleloadsdumpsr   r   )r9  r   r   r   test_pickleable  s    r<  c                  C   st   t tdddkstt tddddt  dfdks:ttddd} td	dd}t t| | tdgd
ksptd S )Nr4  )r  r  r	  r  r   r   z{{A}_{2, \frac{1}{1 - x}, 0}}r  r  r  z{{\left(M N\right)}_{x, 0}})r   r   r   r   r   r   )r  r  r   r   r   %test_printing_latex_array_expressions"  s
    $r=  c                  C   s<   t td} t| dkstt td} t| dks8td S )Nr  zL\left[\begin{matrix}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\end{matrix}\right]r  zQ\left[\begin{array}{}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right])r   r  r   r   )Zarrr   r   r   
test_Array)  s    r>  c                	   C   s,   t d ttt dkstW 5 Q R X d S )NFza a)r   r   r(  r   r   r   r   r   test_latex_with_unevaluated1  s    
r?  (  Zsympyr   r   r   Zsympy.algebras.quaternionr   Z!sympy.calculus.accumulationboundsr   Z sympy.combinatorics.permutationsr   r   r	   Zsympy.concrete.productsr
   Zsympy.concrete.summationsr   Zsympy.core.containersr   r   r
  r   Zsympy.core.functionr   r   r   r   r   Zsympy.core.modr   Zsympy.core.mulr   Zsympy.core.numbersr   r   r   r   r   r   r   Zsympy.core.parametersr   Zsympy.core.powerr   Zsympy.core.relationalr    r!   Zsympy.core.singletonr"   r,  r#   r$   r%   Z(sympy.functions.combinatorial.factorialsr&   r'   r(   r)   r*   r+   Z%sympy.functions.combinatorial.numbersr,   r-   r.   r/   r0   r1   r2   r3   Z$sympy.functions.elementary.complexesr4   r5   r6   r7   r8   r9   Z&sympy.functions.elementary.exponentialr:   r;   r<   Z%sympy.functions.elementary.hyperbolicr=   r>   Z#sympy.functions.elementary.integersr?   r@   rA   Z(sympy.functions.elementary.miscellaneousrB   rC   rD   rE   r  rF   Z(sympy.functions.elementary.trigonometricrG   rH   rI   rJ   rK   rL   Z&sympy.functions.special.beta_functionsrM   Z'sympy.functions.special.delta_functionsrN   rO   Z*sympy.functions.special.elliptic_integralsrP   rQ   rR   rS   rx  rT   rU   rV   rW   rX   rY   Z'sympy.functions.special.gamma_functionsrZ   r[   Zsympy.functions.special.hyperr\   r]   Z)sympy.functions.special.mathieu_functionsr^   r_   r`   ra   Z#sympy.functions.special.polynomialsrb   rc   rd   re   rf   rg   rh   ri   rj   Z-sympy.functions.special.singularity_functionsrk   Z+sympy.functions.special.spherical_harmonicsrl   rm   Z(sympy.functions.special.tensor_functionsrn   ro   Z&sympy.functions.special.zeta_functionsrp   rq   rr   rs   rt   Zsympy.integrals.integralsru   Zsympy.integrals.transformsrv   rw   rx   ry   rz   r{   r|   r}   r~   r   Zsympy.logicr   Zsympy.logic.boolalgr   r   r   r   r   r   r   Zsympy.matrices.denser   Z$sympy.matrices.expressions.kroneckerr   Z"sympy.matrices.expressions.matexprr   Z&sympy.matrices.expressions.permutationr   Z sympy.matrices.expressions.slicer   Zsympy.physics.control.ltir   r   r   r   r   r   r   r   Zsympy.ntheory.factor_r   r   r   r   r   r   Zsympy.physics.quantumr   r   Zsympy.physics.quantum.tracer   Zsympy.physics.unitsr   r   r   r   r   r   r   Zsympy.polys.domains.integerringr   Zsympy.polys.fieldsr   Zsympy.polys.polytoolsr   Zsympy.polys.ringsr   Zsympy.polys.rootoftoolsr   r   Zsympy.series.formalr   r  r   Zsympy.series.limitsr   Zsympy.series.orderr   Zsympy.series.sequencesr   r   r   r   Zsympy.sets.conditionsetr   Zsympy.sets.containsr   Zsympy.sets.fancysetsr   r   r   Zsympy.sets.ordinalsr   r   r   Zsympy.sets.powersetr   Zsympy.sets.setsr   r   r   r   r   r   r   Zsympy.sets.setexprr   Zsympy.stats.crv_typesr   Z sympy.stats.symbolic_probabilityr   r   r   r   Zsympy.tensor.arrayr   r   r   r   r   Z0sympy.tensor.array.expressions.array_expressionsr   r   Zsympy.tensor.indexedr   r   r   Zsympy.tensor.toperatorsr   Zsympy.vectorr   r   r   r   r   r   r   Zsympy.testing.pytestr   r   r   r   r  r   r   r   r   r   r   r   symrh  r   r   r   r   r  r!  r  r[  r(  rb  r  r  r  r$  rc  r)  r   r%  r&  r*  r/  r0  r3  r7  rH  rK  rd  rf  ri  ru  ry  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  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$  r%  r&  r)  r+  r-  r.  r4  r;  rA  rB  rD  rS  rW  rY  rZ  rb  rh  rk  rn  ro  rp  ru  rx  r{  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  r#  r$  r)  r.  r0  r3  r8  r<  r=  r>  r?  r   r   r   r   <module>   s   $ (   ,0$( $4*2"B*B
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