
~9\c           @   sM
  d  d l  m Z m Z m Z m Z m Z m Z m Z m Z m	 Z	 m
 Z
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m  Z  m! Z! m" Z" m# Z# m$ Z$ m% Z% m& Z& m' Z' m( Z( m) Z) m* Z* m+ Z+ m, Z, m- Z- m. Z. m/ Z/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 m4 Z4 m5 Z5 m6 Z6 m7 Z7 m8 Z8 m9 Z9 m: Z: m; Z; m< Z< m= Z= m> Z> m? Z? m@ Z@ mA ZA mB ZB mC ZC mD ZD mE ZE mF ZF mG ZG mH ZH mI ZI mJ ZJ mK ZK mL ZL mM ZM mN ZN mO ZO mP ZP mQ ZQ mR ZR mS ZS mT ZT mU ZU mV ZV mW ZW mX ZX mY ZY mZ ZZ m[ Z[ m\ Z\ m] Z] m^ Z^ m_ Z_ m` Z` ma Za mb Zb mc Zc md Zd me Ze mf Zf mg Zg mh Zh mi Zi mj Zj mk Zk ml Zl mm Zm mn Zn mo Zo mp Zp mq Zq mr Zr ms Zs mt Zt mu Zu mv Zv mw Zw mx Zx my Zy mz Zz m{ Z{ m| Z| m} Z} m~ Z~ m Z m Z m Z m Z m Z m Z m Z m Z m Z d  d l m Z d  d l m Z m Z d  d l m Z m Z m Z m Z d  d l m Z m Z m Z m Z d  d l m Z d  d l m Z m Z d  d l m Z m Z m Z 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 m Z m Z d  d l m Z 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 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  Z d e j f d     YZ eb d  \ Z Z Z Z Z Z Z eb d d e \ Z Z Z d   Z d   Z d   Z d   Z d   Z d   Z d    Z d!   Z d"   Z e d#    Z d$   Z d%   Z d&   Z d'   Z d(   Z d)   Z d*   Z d+   Z d,   Z d-   Z d.   Z d/   Z d0   Z d1   Z d2   Z d3   Z d4   Z d5   Z d6   Z d7   Z d8   Z d9   Z d:   Z d;   Z d<   Z d=   Z d>   Z d?   Z d@   Z dA   Z dB   Z dC   Z dD   ZdE   ZdF   ZdG   ZdH   ZdI   ZdJ   ZdK   ZdL   Z	dM   Z
dN   ZdO   ZdP   ZdQ   ZdR   ZdS   ZdT   ZdU   ZdV   ZdW   ZdX   ZdY   ZdZ   Zd[   Zd\   Zd]   Zd^   Zd_   Zd`   Zda   Zdb   Zdc   Z dd   Z!de   Z"df   Z#dg   Z$dh   Z%di   Z&dj   Z'dk   Z(dl   Z)dm   Z*dn   Z+do   Z,dp   Z-dq   Z.dr   Z/ds   Z0dt   Z1du   Z2dv   Z3dw   Z4dx   Z5dy   Z6dz   Z7d{   Z8d|   Z9d}   Z:d~   Z;d   Z<d   Z=e d    Z>d   Z?d   Z@d   ZAd   ZBd   ZCd   ZDd   ZEd   ZFd   ZGd   ZHd   ZId   ZJd   ZKd   ZLd   ZMd   ZNd   ZOd   ZPd   ZQd   ZRd   ZSd   ZTd   ZUd   ZVd   ZWd   ZXd   ZYd   ZZd   Z[d   Z\d   Z]d   Z^d S(   i(   t   Addt   Abst   Chit   Cit   CosineTransformt   Dictt   Eit   Eqt   FallingFactorialt	   FiniteSett   Floatt   FourierTransformt   Functiont   Indexedt   IndexedBaset   Integralt   Intervalt   InverseCosineTransformt   InverseFourierTransformt   InverseLaplaceTransformt   InverseMellinTransformt   InverseSineTransformt   Lambdat   LaplaceTransformt   Limitt   Matrixt   Maxt   MellinTransformt   Mint   Mult   Ordert	   Piecewiset   Polyt   ringt   fieldt   ZZt   Powt   Productt   Ranget   Rationalt   RisingFactorialt   rootoft   RootSumt   St   Shit   Sit   SineTransformt   Subst   Sumt   Symbolt   ImageSett   Tuplet   Uniont   Ynmt   Znmt   argt   asint   acsct   Modt   assoc_laguerret   assoc_legendret   betat   binomialt   catalant   ceilingt
   Complementt
   chebyshevtt
   chebyshevut	   conjugatet   cott   cotht   difft   dirichlet_etat   eulert   expt   expintt	   factorialt
   factorial2t   floort   gammat
   gegenbauert   hermitet   hypert   imt   jacobit   laguerret   legendret   lerchphit   logt   meijergt   oot
   polar_liftt   polylogt   ret   roott   sint   sqrtt   symbolst
   uppergammat   zetat   subfactorialt   totientt
   elliptic_kt
   elliptic_ft
   elliptic_et   elliptic_pit   cost   tant   Wildt   truet   falset
   Equivalentt   Nott   Containst   divisor_sigmat   SymmetricDifferencet   SeqPert
   SeqFormulat   SeqAddt   SeqMult   fourier_seriest   pit   ConditionSett   ComplexRegiont   fpst   AccumBoundst   reduced_totientt   primenut
   primeomegat   SingularityFunctiont   UnevaluatedExprt
   Quaterniont   It   KroneckerProductt   Intersection(   t   udivisor_sigma(   t   mut   tau(   t   latext	   translatet   greek_letters_sett   tex_greek_dictionary(   t   ImmutableDenseNDimArrayt   ImmutableSparseNDimArrayt   MutableSparseNDimArrayt   MutableDenseNDimArray(   t   tensorproduct(   t   XFAILt   raises(   t
   DiracDeltat	   Heavisidet   KroneckerDeltat
   LeviCivita(   t	   bernoullit   bellt   lucast	   fibonaccit
   tribonacci(   t   Implies(   t   Andt   Ort   Xor(   t
   Commutatort   Operator(   t   degreet   radiant   kgt   metert   gibibytet	   microgramt   second(   t   Tr(   t   range(   t   Cyclet   Permutation(   t   MatrixSymbolt   ln(   t
   CoordSys3Dt   Crosst   Curlt   Dott
   Divergencet   Gradientt	   Laplacian(   t   SetExprNt
   lowergammac           B   s   e  Z RS(    (   t   __name__t
   __module__(    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR   2   s   s   x y z t a b cs   k m nt   integerc          C   sl   d t  f d     Y}  t |  t   d k s4 t  d t  f d     Y}  t |  t   d k sh t  d  S(   Nt   Rc           B   s   e  Z d    Z RS(   c         S   s   d | j  |  j d  S(   Ns   foo(%s)i    (   t   _printt   args(   t   selft   printer(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   _latex<   s    (   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR   ;   s   s   foo(x)c           B   s   e  Z d    Z RS(   c         S   s   d S(   Nt   foo(    (   R   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR   A   s    (   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR   @   s   R   (   R   R   t   xt   AssertionError(   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_printmethod:   s    c          C   s4	  t  d t  d k s t  t  t d  d k s8 t  t  t d t  d k sX t  t  t d t d t d  d k s t  t  d t t  d k s t  t  d t t d	 d
 d k s t  t  d t d t d	 d d k s t  t  d d t d	 d d k st  t  d t  d k s6t  t  d t d t d k sXt  t  t d  d  d k s{t  t  t d  d d t d k st  t  d t d  d k st  t  d t t d  d k st  t  t d  d k st  t  t d d t d k s&t  t  t t d t  d k sJt  t  t t d t d t d k stt  t  t t d t d d d k st  t  t t t  d k st  t  t t t d d d k st  t  d t d  t d  d k st  t  d t d  t d d d d  k s>t  t  d t t t  d  d! k sgt  t  d t t t  d d t d" k st  t  t t   d# k st  t  t t d d   d$ k st  t  t t d d  d% t	 d& k st  t  t t  d  d' k s&t  t  t t  d( t d# k sJt  t  t t d d  d( t d) k sut  t  t t  d d( t d' k st  t  t t d d*   d+ k st  t  t t d d*  d, t d- k st  t  t d t d d*   d. k st  t  t d t d d*  d, t d/ k sEt  t  d0 t  d1 k sat  t  d0 t d	 d
 d2 k st  t  d0 t d	 d3 d4 k st  t  d t
 t   d5 k st  t  t
 t  d6  d5 k st  t  t
 t  t d d   d7 k st  t  t
 t  t d d  d, t d8 k sEt  t  t  d9 k s^t  t  t t @ d: k szt  t  t t @t @ d; k st  t  t t B d< k st  t  t t Bt B d= k st  t  t t @t B d> k st  t  t t t   d? k st  t  t t ? d@ k s5t  t  t t t t  t   dA k s_t  t  t t t t t    dB k st  t  t dC i dD t 6dE k st  t  t t @dC i dD t 6dF t 6dG k st  t  t t @t @dC i dD t 6dF t 6dH t 6dI k st  t  t t BdC i dD t 6dF t 6dJ k sJt  t  t t Bt BdC i dD t 6dF t 6dH t 6dK k st  t  t t @t BdC i dD t 6dF t 6dH t 6dL k st  t  t t t  dC i dD t 6dF t 6dM k st  t dN dO t }  t  t |   t |    dP k s0	t  d  S(Q   Ni   s   x + 1i   s   x^{2}s	   x^{x + 1}i   s   x^{3} + x^{2} + x + 1s   2 x yt
   mul_symbolt   dots   2 \cdot x \cdot ys   \,s   3\,x^{2}\,yg      ?s   1.5 \cdot 3^{x}s   \frac{1}{x}t   fold_short_fracs   1 / xs   - \frac{3}{2}s   - 3 / 2s   \frac{1}{x^{2}}s   \frac{1}{2 \left(x + y\right)}s   \frac{x}{2}s   x / 2s   \frac{x + y}{2 x}s   \left(x + y\right) / 2 xt   long_frac_ratioi    s    \frac{1}{2 x} \left(x + y\right)s   \frac{x + y}{x}s   \frac{2 \sqrt{2} x}{3}s   \frac{2 x}{3} \sqrt{2}s   \frac{2 \int x\, dx}{3}s   \left(2 \int x\, dx\right) / 3s   \sqrt{x}s   \sqrt[3]{x}t   root_notations   x^{\frac{1}{3}}s   x^{\frac{3}{2}}t   itexs   \root{3}{x}i   s   x^{\frac{3}{4}}t   fold_frac_powerss   x^{3/4}s    \left(x + 1\right)^{\frac{3}{4}}s   \left(x + 1\right)^{3/4}g0)VC Ds   1.5 \cdot 10^{20} xs   1.5 \cdot 10^{20} \cdot xt   timess   1.5 \times 10^{20} \times xs   \frac{1}{\sin{\left(x \right)}}is#   \sin^{\frac{3}{2}}{\left(x \right)}s   \sin^{3/2}{\left(x \right)}s   \neg xs
   x \wedge ys   x \wedge y \wedge zs   x \vee ys   x \vee y \vee zs   z \vee \left(x \wedge y\right)s   x \Rightarrow ys   x \not\Rightarrow \neg ys#   \left(x \vee y\right) \Rightarrow zs#   z \Rightarrow \left(x \vee y\right)t   symbol_namest   x_is   \neg x_it   y_is   x_i \wedge y_it   z_is   x_i \wedge y_i \wedge z_is   x_i \vee y_is   x_i \vee y_i \vee z_is$   z_i \vee \left(x_i \wedge y_i\right)s   x_i \Rightarrow y_it   pt   positives   e^{- p} \log{\left(p \right)}(   R   R   R   t   yt   TrueR+   R`   R   R'   t   FalseR_   t   zR   R   R1   RJ   RX   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_basicF   s     , &*&"#) $"$ &*!) %+"$+(%+ """"   !**&!,0,,&c           C   s|   t  t  d k s t  t  t  d k s0 t  t  d   d k sH t  t  t  d k s` t  t  t  d k sx t  d  S(   Ns   \text{True}s   \text{False}s   \text{None}(   R   R   R   R   t   NoneRm   Rn   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_builtins   s
    c           C   s   t  t t d d   d k s$ t  t  t t d d   d k sH t  t  t t d d   d k sl t  t  t t t t   d k s t  t  t t d d	   d
 k s t  t  t t d d   d k s t  d  S(   Ni   i   s&   {\left\langle x - 4 \right\rangle}^{5}is&   {\left\langle x + 3 \right\rangle}^{4}i    s"   {\left\langle x \right\rangle}^{4}s(   {\left\langle - a + x \right\rangle}^{n}is'   {\left\langle x - 4 \right\rangle}^{-2}is'   {\left\langle x - 4 \right\rangle}^{-1}(   R   R   R   R   t   at   n(    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_SingularityFunction   s    c           C   sp   t  t d d d   d k s$ t  t  t d d  d d d   d k sQ t  t  t    d k sl t  d  S(	   Ni   i   i   s   \left( 1\; 2\; 4\right)i   i   s*   \left( 1\; 2\right)\left( 4\; 5\; 6\right)s   \left( \right)(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_cycle   s    $c           C   s   t  t d d d   d k s$ t  t  t d d  d d d   d k sQ t  t  t    d k sl t  t  t d d  t d   d	 k s t  t  t d   d
 k s t  d  S(   Ni   i   i   s   \left( 1\; 2\; 4\right)i   i   s*   \left( 1\; 2\right)\left( 4\; 5\; 6\right)s   \left( \right)s"   \left( 2\; 4\right)\left( 5\right)s   \left( 5\right)(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_permutation   s    $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  d t  d	 k s| t  t  d
 t  d k s t  d  S(   Ng}Ô%ITs   1.0 \cdot 10^{100}g0.++s   1.0 \cdot 10^{-100}R   R   s   1.0 \times 10^{-100}g      ?s   \inftyg      s   - \infty(   R   R
   R   RZ   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Float   s    c          C   s  t  d  }  t t |  j |  j |  j d |  j   d k sE t  t t |  j |  j   d k sl t  t t t |  j |  j   d k s t  t t t |  j |  j   d k s t  t t d |  j |  j   d k s t  t t d |  j |  j |  j   d k s!t  t t d t |  j |  j   d	 k sQt  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 st  t t t	 d |  j |  j   d k st  t t
 |  j |  j |  j d |  j   d k sIt  t t
 |  j |  j   d k spt  t t
 t |  j |  j   d k st  t t t
 |  j |  j   d k st  t t |  j   d k st  t t |  j d |  j   d k st  t t t |  j   d k s8t  t t t |  j   d k s]t  t t |  j   d k s~t  t t |  j d |  j   d k st  t t t |  j   d k st  t t t |  j   d k st  d  S(   Nt   Ai   sh   \mathbf{\hat{i}_{A}} \times \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}} + \mathbf{\hat{k}_{A}}\right)s0   \mathbf{\hat{i}_{A}} \times \mathbf{\hat{j}_{A}}s?   x \left(\mathbf{\hat{i}_{A}} \times \mathbf{\hat{j}_{A}}\right)sB   - \mathbf{\hat{j}_{A}} \times \left((x)\mathbf{\hat{i}_{A}}\right)sB   \nabla\times \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)sY   \nabla\times \left(\mathbf{\hat{i}_{A}} + (3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)sD   \nabla\times \left((3 \mathbf{{x}_{A}} x)\mathbf{\hat{j}_{A}}\right)sQ   x \left(\nabla\times \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)\right)sX   \nabla\cdot \left(\mathbf{\hat{i}_{A}} + (3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)sA   \nabla\cdot \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)sP   x \left(\nabla\cdot \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}}\right)\right)sg   \mathbf{\hat{i}_{A}} \cdot \left((3 \mathbf{{x}_{A}})\mathbf{\hat{j}_{A}} + \mathbf{\hat{k}_{A}}\right)s/   \mathbf{\hat{i}_{A}} \cdot \mathbf{\hat{j}_{A}}s?   \mathbf{\hat{j}_{A}} \cdot \left((x)\mathbf{\hat{i}_{A}}\right)s>   x \left(\mathbf{\hat{i}_{A}} \cdot \mathbf{\hat{j}_{A}}\right)s   \nabla \mathbf{{x}_{A}}s9   \nabla \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)s&   x \left(\nabla \mathbf{{x}_{A}}\right)s&   \nabla \left(\mathbf{{x}_{A}} x\right)s   \triangle \mathbf{{x}_{A}}s<   \triangle \left(\mathbf{{x}_{A}} + 3 \mathbf{{y}_{A}}\right)s)   x \left(\triangle \mathbf{{x}_{A}}\right)s)   \triangle \left(\mathbf{{x}_{A}} x\right)(   R   R   R   t   it   jR   t   kR   R   R   R   R   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_vector_expressions   sR    *$!!$!*!%%!%c          C   sy  t  d  \ }  } } t  d  \ } } } } t |  d k sE t  t |  d k s] t  t |  d k su t  t |  d k s t  t d   t D  } t | t t j     d k s t  t |  |  d k s t  t |  |  d k st  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 s{t  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 st  t t d   d k st  t t d   d k s/t  t t d   d k sMt  t t d  t d   d  k sut  d  S(!   Ns   Gamma, lambda, rhos   tau, Tau, TAU, taUs   \taut   Tc         s   s   |  ] } | j    Vq d  S(   N(   t
   capitalize(   t   .0t   l(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pys	   <genexpr>  s    i    s   \Gamma + \lambdas   \Gamma \lambdat   q1s   q_{1}t   q21s   q_{21}t   epsilon0s   \epsilon_{0}t   omega1s
   \omega_{1}t   91t	   alpha_news   \alpha_{new}s   C^origs   C^{orig}s   x^alphas
   x^{\alpha}s
   beta^alphas   \beta^{\alpha}s   e^Alphas   e^{A}s   omega_alpha^betas   \omega^{\beta}_{\alpha}t   omegaR=   s   \omega^{\beta}(	   Ra   R   R   t   setR   t   lenR   t   keysR1   (   t   Gammat   lmbdat   rhoR   t   Taut   TAUt   taUt   capitalized_letters(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_symbols   s,    (c          C   s   t  d  \ }  } } t | |  | k  d k s7 t  t | | |  d k  d k s] t  t | d | d  d k s t  d  S(   Ns   rho, mass, volumes$   \rho \mathrm{volume} = \mathrm{mass}i   s/   \rho \mathrm{volume} {\mathrm{mass}}^{(-1)} = 1i   s/   {\mathrm{mass}}^{3} \cdot {\mathrm{volume}}^{3}(   Ra   R   R   (   R   t   masst   volume(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_symbols_failing  s    c          C   s  t  t t   d k s t  t  t d  t d   d k sF t  t d  }  t  |  t   d k sp t  t  |   d k s t  t d  } t  | t t   d k s t  t  |  d k s t  t d	  } t  | t t t   d
 k s t  t  |  d	 k st  t d  } t  |  d k s9t  t  | t   d k sWt  t d  } t  | t t t   d k st  t  t t t   d k st  t  t t t  d  d k st  t  | t   d k st  t  |  d k st  t d  } t  | t t t   d k s3t  t  | t   d k sQt  t  |  d k sit  t d  } t  |  d k st  t  | t   d k st  t d  } t  |  d k st  t  | t   d k st  t  t t   d k st  t  t t  d t	 d  k s/t  t  t d t d  d t	 d! k s[t  t  t t d  d t	 d" k st  t  t
 t  d  d# k st  t  t
 t  d d$ d% d& k st  t  t
 t  d d$ d' d( k st  t  t
 t d  d$ d' d t	 d) k s#t  t  t t  d$ d% d* k sGt  t  t t   d+ k set  t  t t   d, k st  t  t t  d  d- k st  t  t t   d. k st  t  t t   d/ k st  t  t t  d  d0 k st  t  t t   d1 k s#t  t  t t   d2 k sBt  t  t t  d  d3 k sdt  t  t d t   d4 k st  t  t d t  d  d5 k st  t  t d6 t   d7 k st  t  t d6 t   d8 k st  t  t t   d9 k s
t  t  t t   d: k s(t  t  t t  d  d; k sJt  t  t t  d  d< k slt  t  t t d t d6   d= k st  t  t t t  d  d> k st  t  t t d t d6   d? k st  t  t t t  d  d@ k st  t  t t   dA k s$t  t  t t  d  dB k sFt  t  t t   dC k sdt  t  t t t   dD k st  t  t t   dE k st  t  t t   dF k st  t  t t  d  dG k st  t  t t d   dG k st  t  t t   dH k s$t  t dI  } t  t |   dJ k sNt  t  t t   dK k slt  t  t t t   dK k st  t  t t t dL f   dK k st  t  t t t t f   dM k st  t  t t t t t f   dN k s	t  t  t t t t   dO k s*	t  t  t t t t   dO k sN	t  t  t t t t f t t f   dP k s~	t  t  t t t   dQ k s	t  t  t t t  d  dR k s	t  t  t  t t   dS k s	t  t  t  t t  d  dT k s

t  t  t! t   dU k s(
t  t  t" t   dV k sF
t  t  t t   dC k sd
t  t  t t   dE k s
t  t  t# t t   dW k s
t  t  t$ t   dX k s
t  t  t% t   dY k s
t  t  t% t   dY k s
t  t  t% t  d  dZ k st  t  t% t t   d[ k s@t  t  t% t t  d  d\ k set  t  t& t   d] k st  t  t& t  d  d^ k st  t  t' t t   d_ k st  t  t' t t  d  d` k st  t  t( t t t)   da k st  t  t( t t t)  d  db k s7t  t  t* t   dc k sUt  t  t* t  d  dd k swt  t  t+ t t   de k st  t  t+ t t  d  df k st  t  t, t t   dg k st  t  t, t t  d  dh k st  t  t, t   di k s!t  t  t, t  d  dj k sCt  t  t- t t t   dk k sgt  t  t- t t t  d  dl k st  t  t- t t   dm k st  t  t- t t  d  dn k st  t  t. t   do k st  t  t. t  d  dp k st  t  t/ t t   dq k s6t  t  t/ t t  d  dr k s[t  t  t0 t  d  ds k s}t  t  t1 t  d  dt k st  t  t2 t  d  du k st  t  t3 t  d  dv k st  t  t3 t   dw k st  t  t4 t) t5 t6 t   dx k s(t  t  t4 t) t5 t6 t  d  dy k sSt  t  t7 t) t5 t   dz k swt  t  t7 t) t5 t  d  d{ k st  t  t8 t) t   d| k st  t  t8 t) t  d  d} k st  t  t9 t) t   d~ k st  t  t9 t) t  d  d k s+t  t  t: t) t   d k sLt  t  t: t) t  d  d k sqt  t  t; t) t5 t   d k st  t  t; t) t5 t  d  d k st  t  t< t) t   d k st  t  t< t) t  d  d k st  t  t= t) t5 t   d k s't  t  t= t) t5 t  d  d k sOt  t  t> t) t   d k spt  t  t> t) t  d  d k st  t? d d t	 } t? d d t	 }	 t  t@ t) tA | |	   d k st  t  t@ t) tA | |	  d6  d k st  t  tB t) tA | |	   d k s2t  t  tB t) tA | |	  d6  d k s]t  t  tC dL   d k s{t  t  tC dL  d6  d k st  t  tD t)   d k st  t  tD t)  d  d k st  t  tE t)   d k st  t  tE t)  d  d k st  t  tF t   d k s;t  t  tF t  d  d k s]t  t  tF t t   d k s~t  t  tF t t  d  d k st  t  tG t   d k st  t  tG t  d  d k st  t  tG t t   d k st  t  tG t t  d  d k s)t  t  tH t)   d k sGt  t  tH t)  d  d k sit  t  tI t)   d k st  t  tI t)  d  d k st  t  tJ t d   d k st  t  tJ t d d   d k st  t  tJ d t d   d k st  t  tJ t d  d  d k s9t  t  d tJ t d   d k s^t  t d  }
 t  |
 t   d k st  t  |
  d k st  d  S(   Ns   e^{x}i   i   s	   e + e^{2}t   fs   f{\left(x \right)}t   gs   g{\left(x,y \right)}t   hs   h{\left(x,y,z \right)}t   Lis   \operatorname{Li}s"   \operatorname{Li}{\left(x \right)}R=   s   \beta{\left(x,y,z \right)}s!   \operatorname{B}\left(x, y\right)s%   \operatorname{B}^{2}\left(x, y\right)s   \beta{\left(x \right)}s   \betaRO   s   \gamma{\left(x,y,z \right)}s   \gamma{\left(x \right)}s   \gammat   a_1s   \operatorname{a_{1}}s%   \operatorname{a_{1}}{\left(x \right)}R   s
   \omega_{1}s   \omega_{1}{\left(x \right)}s   \sin{\left(x \right)}t   fold_func_bracketss   \sin {x}s   \sin {2 x^{2}}s   \sin {x^{2}}s(   \operatorname{asin}^{2}{\left(x \right)}t   inv_trig_stylet   fulls   \arcsin^{2}{\left(x \right)}t   powers   \sin^{-1}{\left(x \right)}^{2}s   \sin^{-1} {x^{2}}s&   \operatorname{arccsc}{\left(x \right)}s   k!s   \left(- k\right)!s   k!^{2}s   !ks   !\left(- k\right)s   \left(!k\right)^{2}s   k!!s   \left(- k\right)!!s   k!!^{2}s   {\binom{2}{k}}s   {\binom{2}{k}}^{2}i   s   {\left(3\right)}_{k}s   {3}^{\left(k\right)}s   \left\lfloor{x}\right\rfloors   \left\lceil{x}\right\rceils    \left\lfloor{x}\right\rfloor^{2}s   \left\lceil{x}\right\rceil^{2}s   \min\left(2, x, x^{3}\right)s   \min\left(x, y\right)^{2}s   \max\left(2, x, x^{3}\right)s   \max\left(x, y\right)^{2}s   \left|{x}\right|s   \left|{x}\right|^{2}s!   \operatorname{re}{\left(x\right)}sE   \operatorname{re}{\left(x\right)} + \operatorname{re}{\left(y\right)}s!   \operatorname{im}{\left(x\right)}s   \overline{x}s   \overline{x}^{2}s   \Gamma\left(x\right)t   ws   \Gamma\left(w\right)s   O\left(x\right)i    s$   O\left(x; x\rightarrow \infty\right)s#   O\left(x - y; x\rightarrow y\right)sG   O\left(x; \left( x, \  y\right)\rightarrow \left( 0, \  0\right)\right)sQ   O\left(x; \left( x, \  y\right)\rightarrow \left( \infty, \  \infty\right)\right)s   \gamma\left(x, y\right)s   \gamma^{2}\left(x, y\right)s   \Gamma\left(x, y\right)s   \Gamma^{2}\left(x, y\right)s   \cot{\left(x \right)}s   \coth{\left(x \right)}s   x^{\frac{1}{y}}s   \arg{\left(x \right)}s   \zeta\left(x\right)s   \zeta^{2}\left(x\right)s   \zeta\left(x, y\right)s   \zeta^{2}\left(x, y\right)s   \eta\left(x\right)s   \eta^{2}\left(x\right)s#   \operatorname{Li}_{x}\left(y\right)s'   \operatorname{Li}_{x}^{2}\left(y\right)s   \Phi\left(x, y, n\right)s   \Phi^{2}\left(x, y, n\right)s   K\left(z\right)s   K^{2}\left(z\right)s   F\left(x\middle| y\right)s   F^{2}\left(x\middle| y\right)s   E\left(x\middle| y\right)s   E^{2}\left(x\middle| y\right)s   E\left(z\right)s   E^{2}\left(z\right)s   \Pi\left(x; y\middle| z\right)s"   \Pi^{2}\left(x; y\middle| z\right)s   \Pi\left(x\middle| y\right)s   \Pi^{2}\left(x\middle| y\right)s"   \operatorname{Ei}{\left(x \right)}s&   \operatorname{Ei}^{2}{\left(x \right)}s"   \operatorname{E}_{x}\left(y\right)s&   \operatorname{E}_{x}^{2}\left(y\right)s'   \operatorname{Shi}^{2}{\left(x \right)}s&   \operatorname{Si}^{2}{\left(x \right)}s&   \operatorname{Ci}^{2}{\left(x \right)}s$   \operatorname{Chi}^{2}\left(x\right)s    \operatorname{Chi}\left(x\right)s&   P_{n}^{\left(a,b\right)}\left(x\right)s7   \left(P_{n}^{\left(a,b\right)}\left(x\right)\right)^{2}s$   C_{n}^{\left(a\right)}\left(x\right)s5   \left(C_{n}^{\left(a\right)}\left(x\right)\right)^{2}s   T_{n}\left(x\right)s$   \left(T_{n}\left(x\right)\right)^{2}s   U_{n}\left(x\right)s$   \left(U_{n}\left(x\right)\right)^{2}s   P_{n}\left(x\right)s$   \left(P_{n}\left(x\right)\right)^{2}s$   P_{n}^{\left(a\right)}\left(x\right)s5   \left(P_{n}^{\left(a\right)}\left(x\right)\right)^{2}s   L_{n}\left(x\right)s$   \left(L_{n}\left(x\right)\right)^{2}s$   L_{n}^{\left(a\right)}\left(x\right)s5   \left(L_{n}^{\left(a\right)}\left(x\right)\right)^{2}s   H_{n}\left(x\right)s$   \left(H_{n}\left(x\right)\right)^{2}t   thetat   realt   phis!   Y_{n}^{m}\left(\theta,\phi\right)s2   \left(Y_{n}^{m}\left(\theta,\phi\right)\right)^{3}s!   Z_{n}^{m}\left(\theta,\phi\right)s2   \left(Z_{n}^{m}\left(\theta,\phi\right)\right)^{3}s+   \operatorname{polar\_lift}{\left(0 \right)}s/   \operatorname{polar\_lift}^{3}{\left(0 \right)}s   \phi\left(n\right)s#   \left(\phi\left(n\right)\right)^{2}s   \lambda\left(n\right)s&   \left(\lambda\left(n\right)\right)^{2}s   \sigma\left(x\right)s   \sigma^{2}\left(x\right)s   \sigma_y\left(x\right)s   \sigma^{2}_y\left(x\right)s   \sigma^*\left(x\right)s   \sigma^*^{2}\left(x\right)s   \sigma^*_y\left(x\right)s   \sigma^*^{2}_y\left(x\right)s   \nu\left(n\right)s"   \left(\nu\left(n\right)\right)^{2}s   \Omega\left(n\right)s%   \left(\Omega\left(n\right)\right)^{2}i   s	   x\bmod{7}s   \left(x + 1\right)\bmod{7}s   2 x\bmod{7}s   \left(x\bmod{7}\right) + 1s   2 \left(x\bmod{7}\right)t   fjlkds%   \operatorname{fjlkd}{\left(x \right)}s   \operatorname{fjlkd}(K   R   RJ   R   R   R   R   R   R=   R_   R   R8   R9   RL   R   Rd   RM   R>   R   R(   RN   R@   R   R   R   R]   RS   RD   RO   Rl   R   RZ   R   Rb   RE   RF   R^   R7   Rc   RH   R\   RW   R   Rf   Rg   Rh   Ri   R   RK   R,   R-   R   R   RT   R   t   bRP   RB   RC   RV   R<   RU   R;   RQ   R1   R5   t   mR6   R[   Re   R~   Rr   R   R   R   R:   (   R   R  R  R  t   mybetat   a1R   R	  R
  R  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_functions%  s   (!$$!%$$""""!%!!""(%(%"""!''!!%!%!"!%"!"$("!%!%"$!%"!%""""!!!%!%!%''""!%"!%"!%%%%c          C   sP   d t  f d     Y}  t |   d k s. t  t |  t   d k sL t  d  S(   Nt   mygammac           B   s   e  Z RS(    (   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR    s   s   \operatorname{mygamma}s'   \operatorname{mygamma}{\left(x \right)}(   RO   R   R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt%   test_function_subclass_different_name  s    c       
   C   s  d d l  m }  d d l m } m } t t t |  |  |  t d  d t d d d |   |   d k sr t  t t t   t d  d t   |   d	 k s t  t t	 | d f d |   d
 k s t  t t	 t   t d  |   d k s t  d  S(   Ni(   Ry   (   R   R   i   i    i   i   st   {G_{4, 5}^{2, 3}\left(\begin{matrix} \pi, \pi, x & 1 \\0, 1 & 1, 2, \frac{3}{\pi} \end{matrix} \middle| {z} \right)}sS   {G_{1, 1}^{1, 0}\left(\begin{matrix}  & 1 \\0 &  \end{matrix} \middle| {z} \right)}sL   {{}_{2}F_{1}\left(\begin{matrix} x, 2 \\ 3 \end{matrix}\middle| {z} \right)}sH   {{}_{0}F_{1}\left(\begin{matrix}  \\ 1 \end{matrix}\middle| {z} \right)}(   i    i   (   i    (   i   (
   t   sympyRy   t	   sympy.abcR   R   R   RY   R3   R   RR   (   Ry   R   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_hyper_printing  s    'c          C   s  d d l  m }  m } m } m } m } m } m } m } m	 } m
 }	 d d l m }
 t |  t |
 d  t  d k s t  t | t |
   d k s t  t | t |
   d k s t  t | t |
   d k s t  t | t |
 d  d  d	 k st  t | t |
   d
 k s,t  t | t |
   d k sMt  t | t |
   d k snt  t | t |
   d k st  t |	 t |
   d k st  d  S(   Ni(
   t   besseljt   besselyt   besselit   besselkt   hankel1t   hankel2t   jnt   ynt   hn1t   hn2(   R   i   s   J^{k}_{n}\left(z^{2}\right)s   Y_{n}\left(z\right)s   I_{n}\left(z\right)s   K_{n}\left(z\right)s.   \left(H^{(1)}_{n}\left(z^{2}\right)\right)^{2}s   H^{(2)}_{n}\left(z\right)s   j_{n}\left(z\right)s   y_{n}\left(z\right)s   h^{(1)}_{n}\left(z\right)s   h^{(2)}_{n}\left(z\right)(   t   sympy.functions.special.besselR  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   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_bessel0  s    F)!!!!!!!c          C   s   d d l  m }  m } d d l m } t |  |   d k sD t  t | |   d k sb t  t |  |  d  d k s t  t | |  d  d k s t  d  S(	   Ni(   t   fresnelst   fresnelc(   R   s   S\left(z\right)s   C\left(z\right)i   s   S^{2}\left(z\right)s   C^{2}\left(z\right)(   t'   sympy.functions.special.error_functionsR$  R%  R  R   R   R   (   R$  R%  R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_fresnelB  s    "c           C   s    t  d t  d k s t  d  S(   Nis   \left(-1\right)^{x}(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_bracketsK  s    c          C   s  t  d d t d t }  t t  d d t d t  } t |  t |    } t | d t | d   } | d k s| t  | d k s t  t t d 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 st  d  S(   Nt   Psi_0t   complexR  t   Psii    s   \Psi_{0} \overline{\Psi_{0}}s    \overline{{\Psi}_{0}} {\Psi}_{0}t   x1R   s   {x_{1}}_{i}RO   s   \gammas   a bt   a_bs   a_{b}(   R1   R   R   R   R   RD   R   R   (   t
   Psi_symbolt   Psi_indexedt   symbol_latext   indexed_latex(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_indexedO  s    'c          C   s  t  t t d t d t  d k s+ t  t  t t t  t d t d t  d k s` t  t  t t t t  t d t d t d t  d k s t  t  t t t t t  t d t d t d t d t  d k s t  t  t t t t  t d t  d k st  t  t t t t  t d t d t  d	 k sXt  t  t t t t t  t d t d t t d t  d
 k st  t  t t t t t t  t d t d t t d t t d t  d k st  t d  }  t  t t |  t t  t d t t d t  d t  |  t t   k sUt  t  t t t |  t t  t d t t d t t d t  d t  |  t t   k st  t  t t t	 t t  t d t
 f  t d t  d k st  t  t t t d t d  d k s%t  t  t |  t  t  d  d k sPt  t  t |  t  t t f   d k s}t  d  S(   Ni   t   evaluates   \frac{d}{d x} x^{3}i   s8   \frac{d}{d x} \left(x^{2} + \sin{\left(x \right)}\right)s@   \frac{d^{2}}{d x^{2}} \left(x^{2} + \sin{\left(x \right)}\right)s@   \frac{d^{3}}{d x^{3}} \left(x^{2} + \sin{\left(x \right)}\right)s3   \frac{\partial}{\partial x} \sin{\left(x y \right)}sH   \frac{\partial}{\partial x} \left(x^{2} + \sin{\left(x y \right)}\right)sP   \frac{\partial^{2}}{\partial x^{2}} \left(x^{2} + \sin{\left(x y \right)}\right)sP   \frac{\partial^{3}}{\partial x^{3}} \left(x^{2} + \sin{\left(x y \right)}\right)R   s*   \frac{\partial^{2}}{\partial y\partial x} s.   \frac{\partial^{3}}{\partial y\partial x^{2}} i    s5   \frac{d}{d y} \int\limits_{0}^{\infty} e^{- x y}\, dxs    \left(\frac{d}{d x} x\right)^{2}s1   \left(\frac{d}{d x} f{\left(x \right)}\right)^{2}s(   \frac{d^{n}}{d x^{n}} f{\left(x \right)}(   R   RG   R   R   R   R_   R   R   R   RJ   RZ   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_derivatives_  s:    &2>"*9H0"?"5c           C   s2   t  t t t t t f d   d k s. t  d  S(   Ni   i   s+   \left. x y \right|_{\substack{ x=1\\ y=2 }}(   i   i   (   R   R/   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_subs  s    c        	   C   s  t  t t t  t   d k s' t  t  t t d t d d f   d k sU t  t  t t d t d d f   d k s t  t  t t t d t d d f t   d	 k s t  t  t t t d t d d f t  d
 d d k s t  t  t t t d t d d f t  d
 d d t d k s4t  t  t t t d f   d k s[t  t  t t t t t   d k st  t  t t t t t t t   d k st  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 sHt  t  t t t  d  d k smt  t  t t t t   d k st  t  t t t d t   d k st  t  t t t t   d k st  d  S(   Ns   \int \log{\left(x \right)}\, dxi   i    i   s   \int\limits_{0}^{1} x^{2}\, dxi
   i   s    \int\limits_{10}^{20} x^{2}\, dxs)   \int\int\limits_{0}^{1} x^{2} y\, dx\, dyt   modes	   equation*sI   \begin{equation*}\int\int\limits_{0}^{1} x^{2} y\, dx\, dy\end{equation*}R   s&   $$\int\int_{0}^{1} x^{2} y\, dx\, dy$$s   \int\limits^{0} x\, dxs   \iint x y\, dx\, dys   \iiint x y z\, dx\, dy\, dzs#   \iiiint t x y z\, dx\, dy\, dz\, dts8   \int\int\int\int\int\int x\, dx\, dx\, dx\, dx\, dx\, dxs,   \int\limits_{0}^{1}\int\int x\, dx\, dy\, dzs   \left(\int z\, dz\right)^{2}s   \int \left(x + z\right)\, dzs&   \int \left(x + \frac{z}{2}\right)\, dzs   \int x^{y}\, dz(	   R   R   RX   R   R   R   R   R   t   t(    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_integrals  s2    '&,2'(/'!!%%c          C   s  x t  t f D] }  t |  t t t d g   d k s? t  t |  t d d    d k sf t  t |  t d d    d k s t  q Wt }  t |  t t t d g    d k s t  t |  t d d     d k s t  t |  t d d     d k st  d  S(   Ni   s   \left\{x^{2}, x y\right\}i   i   s   \left\{1, 2, 3, 4, 5\right\}i   s4   \left\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\right\}(   t	   frozensetR   R   R   R   R   R   R	   (   t   s(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_sets  s    ,','c          C   s7   t  d d  }  t |   } t |  d k s3 t  d  S(   Ni   i   s%   SetExpr\left(\left[1, 3\right]\right)(   R   R   R   R   (   t   ivt   se(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_SetExpr  s    c           C   s  t  t d d   d k s! t  t  t d d   d k sB t  t  t d d d   d k sf t  t  t d d	 d   d
 k s t  t  t d	 d d   d k s t  t  t d t d   d k s t  t  t t d d   d k s t  t  t d t d   d k st  d  S(   Ni   i3   s   \left\{1, 2, \ldots, 50\right\}i   s   \left\{1, 2, 3\right\}i    i   s   \left\{0, 1, 2\right\}i   s   \left\{0, 1, \ldots, 29\right\}is    \left\{30, 29, \ldots, 2\right\}i   s   \left\{0, 2, \ldots\right\}is   \left\{\ldots, 2, 0\right\}s   \left\{-2, -3, \ldots\right\}(   R   R&   R   RZ   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Range  s    !$$$$$c    
      C   s  t  t d d t f  }  t d  } d } t |   | k sC t  d } t |  | k sa t  t  t d d  } t d d  } d } t |  | k s t  d } t |  | k s t  t  t d t d f  } t d t d f  } d } t |  | k st  d	 } t |  | k s+t  d
 } t t |  |   | k sRt  d } t t | |   | k syt  d } t t | |   | k st  d } t t |  |   | k st  d } t t | |   | k st  d } t t | |   | k st  t  t d t d t f  } d } t |  | k sOt  t	 d  } t  | t d t d d f  }	 d } t |	  | k st  d  S(   Ni   i    i   s   \left[0, 1, 4, 9, \ldots\right]s   \left[1, 2, 1, 2, \ldots\right]s   \left[0, 1, 4\right]s   \left[1, 2, 1\right]s   \left[\ldots, 9, 4, 1, 0\right]s   \left[\ldots, 2, 1, 2, 1\right]s    \left[1, 3, 5, 11, \ldots\right]s   \left[1, 3, 5\right]s    \left[\ldots, 11, 5, 3, 1\right]s    \left[0, 2, 4, 18, \ldots\right]s   \left[0, 2, 4\right]s    \left[\ldots, 18, 4, 2, 0\right]s   \left\{a^{2}\right\}_{a=0}^{x}R  s   \left[0, b, 4 b\right](   i   i   (   i    i   (   i   i   (   i    i   (   i   i   (
   Ru   R   RZ   Rt   R   R   Rv   Rw   R   R1   (
   t   s1t   s2t	   latex_strt   s3t   s4t   s5t   s6t   s7R  t   s8(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_sequences  sJ    !!!!!! c          C   s5   d }  t  t t t t t f   |  k s1 t  d  S(   Ns`   2 \sin{\left(x \right)} - \sin{\left(2 x \right)} + \frac{2 \sin{\left(3 x \right)}}{3} + \ldots(   R   Rx   R   Ry   R   (   RB  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_FourierSeries  s    c          C   s2   d }  t  t t d t    |  k s. t  d  S(   Ns;   \sum_{k=1}^{\infty} - \frac{\left(-1\right)^{- k} x^{k}}{k}i   (   R   R|   RX   R   R   (   RB  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_FormalPowerSeries  s    c          C   s   t  d d t }  t t d d   d k s3 t  t t d |    d k sT t  t t d |  t t   d k s{ t  t t d |  t t   d k s t  t t d |  t t   d k s t  t t d |  t t   d k s t  d  S(	   NR   R  i    s   \left\{0\right\}s   \left[0, a\right]s   \left(0, a\right]s   \left[0, a\right)s   \left(0, a\right)(   R1   R   R   R   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_intervals  s    !!'''c          C   s   t  d d t }  t t d d   d k s3 t  t t d |    d k sT t  t t |  d |  d   d k s} t  d  S(	   NR   R  i    i   s   \left\langle 0, 1\right\rangles   \left\langle 0, a\right\ranglei   s&   \left\langle a + 1, a + 2\right\rangle(   R1   R   R   R}   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_AccumuBounds$  s
    !!c           C   s   t  t j  d k s t  d  S(   Ns	   \emptyset(   R   R+   t   EmptySetR   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_emptyset,  s    c          C   sI   t  d  }  t  d  } t | |   } t | j    d k sE t  d  S(   NR   t   Bs   - (A B - B A)(   R   R   R   t   doitR   (   R   RP  t   comm(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_commutator0  s    c           C   sv   t  t t d d  t d d    d k s3 t  t  t t d d  t d d  t d d    d k sr t  d  S(   Ni    i   i   i   s(   \left[0, 1\right] \cup \left[2, 3\right]i   s*   \left\{1, 2\right\} \cup \left[3, 4\right](   R   R4   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_union7  s    $0c           C   s7   t  t t d d  t t t    d k s3 t  d  S(   Ni    i   s(   \left[0, 1\right] \cap \left[x, y\right](   R   R   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_intersection>  s    $c           C   s=   t  t t d d  t d d  d t  d k s9 t  d  S(   Ni   i   i   i   R3  s-   \left[2, 5\right] \triangle \left[4, 7\right](   R   Rs   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_symmetric_differenceC  s    !	c           C   s+   t  t t j t j   d k s' t  d  S(   Ns   \mathbb{R} \setminus \mathbb{N}(   R   RA   R+   t   Realst   NaturalsR   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_ComplementI  s    c           C   s   t  t j  d k s t  d  S(   Ns
   \mathbb{C}(   R   R+   t	   ComplexesR   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_ComplexesN  s    c          C   s   t  d d  }  t  d d  } t d d d  } t |  d  d t |   k sV t  t |  d  d t |   k s| t  t |  | |  d t |   t |  t |  f k s t  d  S(	   Ni    i   i
   i   i   s   %s^{2}s   %s^{10}s   %s \times %s \times %s(   R   R	   R   R   (   t   linet   biglinet   fset(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_productsetR  s    &&c           C   s   t  t j  d k s t  d  S(   Ns
   \mathbb{N}(   R   R+   RX  R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Naturals\  s    c           C   s   t  t j  d k s t  d  S(   Ns   \mathbb{N}_0(   R   R+   t	   Naturals0R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Naturals0`  s    c           C   s   t  t j  d k s t  d  S(   Ns
   \mathbb{Z}(   R   R+   t   IntegersR   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Integersd  s    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 s t  d  S(	   NR   i   s+   \left\{x^{2}\; |\; x \in \mathbb{N}\right\}R   i   i   i   sR   \left\{x + y\; |\; x \in \left\{1, 2, 3\right\}, y \in \left\{3, 4\right\}\right\}(   R1   R   R2   R   R+   RX  R   (   R   R   t   imgset(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_ImageSeth  s    "4	c          C   sx   t  d  }  t t |  t |  d d  t j   d k s@ t  t t |  t |  d d  t j   d k st t  d  S(   NR   i   i   s8   \left\{x \mid x \in \mathbb{R} \wedge x^{2} = 1 \right\}s    \left\{x \mid x^{2} = 1 \right\}(   R1   R   Rz   R   R+   RW  R   t   UniversalSet(   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_ConditionSetr  s
    %%c           C   sv   t  t t d d  t d d    d k s4 t  t  t t d d  t d d t  d	 t  d
 k sr t  d  S(   Ni   i   i   i   sQ   \left\{x + y i\; |\; x, y \in \left[3, 5\right] \times \left[4, 6\right] \right\}i    i   i   t   polars   \left\{r \left(i \sin{\left(\theta \right)} + \cos{\left(\theta \right)}\right)\; |\; r, \theta \in \left[0, 1\right] \times \left[0, 2 \pi\right) \right\}(   R   R{   R   R   Ry   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_ComplexRegionz  s    %/c          C   s4   t  d  }  t t |  t j   d k s0 t  d  S(   NR   s   x \in \mathbb{N}(   R1   R   Rq   R+   RX  R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Contains  s    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 sl t  t  t t d t t d d f   d k s t  t  t t d t t d d f  d  d k s t  d  S(	   Ni   iii   s<   \sum_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}s   \sum_{x=-2}^{2} x^{2}s&   \sum_{x=-2}^{2} \left(x^{2} + y\right)s7   \left(\sum_{x=-2}^{2} \left(x^{2} + y\right)\right)^{2}(   R   R0   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_sum  s    /#'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 sl t  t  t t d t t d d f   d k s t  t  t t t d d f  d  d k s t  d  S(	   Ni   iii   s=   \prod_{\substack{-2 \leq x \leq 2\\-5 \leq y \leq 5}} x y^{2}s   \prod_{x=-2}^{2} x^{2}s'   \prod_{x=-2}^{2} \left(x^{2} + y\right)s#   \left(\prod_{x=-2}^{2} x\right)^{2}(   R   R%   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_product  s    /#c          C   s   t  t t t t   d k s$ t  t d  }  t  t |  t  t d   d k sZ t  t  t |  t  t d d   d k s t  t  t |  t  t d  d  d k s t  t  t |  t  t d d	 d
  d k s t  d  S(   Ns   \lim_{x \to \infty} xR   i    s#   \lim_{x \to 0^+} f{\left(x \right)}t   -s#   \lim_{x \to 0^-} f{\left(x \right)}i   s4   \left(\lim_{x \to 0^+} f{\left(x \right)}\right)^{2}t   dirs   +-s!   \lim_{x \to 0} f{\left(x \right)}(   R   R   R   RZ   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_limits  s    $*!c           C   s  t  t t   d k s t  t  t t   d k s< t  t  t t  d t d k s` t  t  t t  t t   d k s t  t  t t  t t  d t d k s t  t  t t t  t   d k s t  t  t t t  t  d t d k s
t  d  S(   Ns   \log{\left(x \right)}t   ln_notations   \ln{\left(x \right)}s-   \log{\left(x \right)} + \log{\left(y \right)}s+   \ln{\left(x \right)} + \ln{\left(y \right)}s   \log{\left(x \right)}^{x}s   \ln{\left(x \right)}^{x}(   R   RX   R   R   R   R   R   t   pow(    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_log  s    $'c          C   s`   t  d  }  |  t } t |  d k s. t  t  d  }  |  t } t |  d k s\ t  d  S(   Ns   \betas	   \beta + xs	   x + \betaR=   (   s	   \beta + xs	   x + \beta(   s	   \beta + xs	   x + \beta(   R1   R   R   R   (   R=   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_3568  s    

c           C   s   t  d t t d d   d k s) t  t  d t t d d  d d d k sX t  t  d t t d d  d d d t d	 k s t  t  d t t g  d
 k s t  d  S(   Ni   i   s   8 \sqrt{2} \tau^{\frac{7}{2}}R6  s	   equation*s<   \begin{equation*}8 \sqrt{2} \mu^{\frac{7}{2}}\end{equation*}t   equationR   s    $$8 \sqrt{2} \mu^{\frac{7}{2}}$$s   \left[ \frac{2}{x}, \  y\right](   R   R   R'   R   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt
   test_latex  s    ) &c          C   sp   i d t  d  6d t d 6d t 6d t d 6}  t |   d k sH t  t |   } t |  d k sl t  d  S(   Ni   i   i   i   s;   \left\{ 1 : 1, \  x : 3, \  x^{2} : 2, \  x^{3} : 4\right\}(   R'   R   R   R   R   (   t   dt   D(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_dict  s    0		c          C   s=   t  d  t  d  t  d  g }  t |   d k s9 t  d  S(   NR   R   t   alphas)   \left[ \omega_{1}, \  a, \  \alpha\right](   R1   R   R   (   t   ll(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_list  s    !c           C   s   t  t d d   d k s" t  t  t d d   d k sC t  t  t d d   d k sd t  t  t d d   d k s t  t  t d d  t  d k s t  t  t d d  t t d d  t  d	 k s t  d  S(
   Ni   i   s   - \frac{1}{2}iis   \frac{1}{2}s   - \frac{x}{2}i   s   - \frac{x}{2} - \frac{2 y}{3}(   R   R'   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_rational  s    "!!"&(c           C   s@   t  d t  d k s t  t  d t t  d k s< t  d  S(   Ni   s   \frac{1}{x}s   \frac{1}{x + y}(   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_inverse  s    c           C   s   t  t t   d k s t  t  t t  d  d k s@ t  t  t t d   d k sa t  t  t t d   d k s t  t  t t d  d  d k s t  d  S(   Ns   \delta\left(x\right)i   s%   \left(\delta\left(x\right)\right)^{2}i    i   s)   \delta^{\left( 5 \right)}\left( x \right)s:   \left(\delta^{\left( 5 \right)}\left( x \right)\right)^{2}(   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_DiracDelta  s    "!c           C   sD   t  t t   d k s t  t  t t  d  d k s@ t  d  S(   Ns   \theta\left(x\right)i   s%   \left(\theta\left(x\right)\right)^{2}(   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Heaviside  s    c           C   s   t  t t t   d k s! t  t  t t t d   d k sF t  t  t t d t   d k sk t  t  t t t t  d d t  d k s t  d  S(   Ns   \delta_{x y}i   s   \delta_{x, y + 1}s   \delta_{y, x + 1}i   R3  s   \left(\delta_{x y}\right)^{2}(   R   R   R   R   R   R$   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_KroneckerDelta  s
    !%%!c           C   s   t  t t t t   d k s$ t  t  t t t t  d  d k sL t  t  t t t t d   d k st t  t  t t t d t   d k s t  t  t t d t t   d k s t  d  S(   Ns   \varepsilon_{x y z}i   s$   \left(\varepsilon_{x y z}\right)^{2}i   s   \varepsilon_{x, y, z + 1}s   \varepsilon_{x, y + 1, z}s   \varepsilon_{x + 1, y, z}(   R   R   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_LeviCivita  s    $((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 s| t  t   d d d	 k s t  t t   f d
    d  S(   Ns   x + yR6  t   plaint   inlines   $x + y$s	   equation*s%   \begin{equation*}x + y\end{equation*}Ru  s#   \begin{equation}x + y\end{equation}c              s   t    d d S(   NR6  R   (   R   (    (   t   expr(    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   <lambda>  t    (   R   R   R   R   R   t
   ValueError(    (    (   R  s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt	   test_mode  s    
c          C   s}  t  t t d k  f t d t f  }  t |   d k s= t  t |  d t d k s[ t  t  t t d k  f d t d k f  }  t |   d k s t  t d d	 t \ } } t  | d t | |  f | | t f  }  d
 } t |   | k s t  t | |   d | k st  t |  |  d | k s<t  t t  t t d k  f t d t d k  f   d k syt  d  S(   Ni   i   sK   \begin{cases} x & \text{for}\: x < 1 \\x^{2} & \text{otherwise} \end{cases}R   sM   \begin{cases} x & \text{for}\: x \lt 1 \\x^{2} & \text{otherwise} \end{cases}i    sG   \begin{cases} x & \text{for}\: x < 0 \\0 & \text{otherwise} \end{cases}s   A Bt   commutativesM   \begin{cases} A^{2} & \text{for}\: A = B \\A B & \text{otherwise} \end{cases}s   A \left(%s\right)s   \left(%s\right) AsM   \begin{cases} x & \text{for}\: x < 1 \\x^{2} & \text{for}\: x < 2 \end{cases}(   R   R   R   R   R   Ra   R   R   (   R   R   RP  R:  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Piecewise  s    %',  .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 sz t  t |  d d	 d
 k s t  t |  d d  d d	 d k s t  t  d d t d   } t |  d k s t  d  S(   Ni   s;   \left[\begin{matrix}x + 1 & y\\y & x - 1\end{matrix}\right]R6  R  sG   $\left[\begin{smallmatrix}x + 1 & y\\y & x - 1\end{smallmatrix}\right]$t   mat_strt   arrays=   \left[\begin{array}{cc}x + 1 & y\\y & x - 1\end{array}\right]t   bmatrixs=   \left[\begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}\right]t	   mat_delims0   \begin{bmatrix}x + 1 & y\\y & x - 1\end{bmatrix}i   s\   \left[\begin{array}{ccccccccccc}0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10\end{array}\right](   R   R   R   R   R   R   R   (   t   Mt   M2(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Matrix1  s    &		c          C   s   t  d  }  t  d d t } t t | |    t | |    g t | |   j |    t | |   j |    g g  } d } t |  | k s t  d  S(   NR7  t   theta1t   clss  \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](   Ra   R   R   R_   Rj   RG   R   R   (   R7  R  R  t   expected(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt    test_latex_matrix_with_functionsD  s    $<c          C   s  t  d  \ }  } } } xt t t t f D]~} | |   } t |  d k sU t  | d |  | g | | g g  } | d |  | | g  } t | |  } t | |  } t |  d k s t  t |  d k s t  t |  d k s t  t |  d k st  | |  | d | g g  }	 | |  g | g d | g g  }
 | |
 j   g  } t |	  d k syt  t |
  d	 k st  t |  d
 k s+ t  q+ Wd  S(   Ns   x y z wR   i   s=   \left[\begin{matrix}\frac{1}{x} & y\\z & w\end{matrix}\right]s:   \left[\begin{matrix}\frac{1}{x} & y & z\end{matrix}\right]s  \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]s]  \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]sG   \left[\left[\begin{matrix}x & y & \frac{1}{z}\end{matrix}\right]\right]s8   \left[\begin{matrix}x\\y\\\frac{1}{z}\end{matrix}\right]s_   \left[\begin{matrix}\left[\begin{matrix}x\\y\\\frac{1}{z}\end{matrix}\right]\end{matrix}\right](	   Ra   R   R   R   R   R   R   R   t   tolist(   R   R   R   R	  t	   ArrayTypeR  t   M1R  t   M3t   Mrowt   Mcolumnt   Mcol2(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_NDimArrayV  s4    	"				"			c           C   s   t  d d t d d d k s& t  t  d d t d d d k sL t  t  d d t d d d k sr t  t  d t d d d	 k s t  t  d t d d d
 k s t  t  d t d d d k s t  d  S(   Ni   R   R   s   4 \times 4^{x}R   s   4 \cdot 4^{x}t   ldots   4 \,.\, 4^{x}s
   4 \times xs	   4 \cdot xs	   4 \,.\, x(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_mul_symbol  s    &&&""c          C   sL   d d t  d  }  t |   d k s, t  t d |   d k sH t  d  S(   Ni   i   s!   4 \cdot 4^{\log{\left(2 \right)}}i   s+   \frac{1}{4 \cdot 4^{\log{\left(2 \right)}}}(   RX   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_issue_4381  s    c           C   s\  t  t d   d k s t  t  t d   d k s< t  t  t d   d k sZ t  t  t d   d k sx t  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 s t  t  t d   d k st  t  t d   d k s,t  t  t d   d k sJt  t  t d   d k sht  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 st  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 sXt  d  S(%   Nt	   beta_13_2s   \beta_{13 2}t   beta_132_20s   \beta_{132 20}t   beta_13s
   \beta_{13}t   x_a_bs   x_{a b}t   x_1_2_3s	   x_{1 2 3}t   x_a_b1s   x_{a b1}t   x_a_1s   x_{a 1}t   x_1_as   x_{1 a}s   x_1^aas
   x^{aa}_{1}t   x_1__aas   x_11^as
   x^{a}_{11}t   x_11__at	   x_a_a_a_as   x_{a a a a}s	   x_a_a^a^as   x^{a a}_{a a}t   x_a_a__a__at   alpha_11s   \alpha_{11}t   alpha_11_11s   \alpha_{11 11}t   alpha_alphas   \alpha_{\alpha}s   alpha^alephs   \alpha^{\aleph}t   alpha__aleph(   R   R1   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_issue_4576  s(    c          C   sl   t  d  }  d t t |   d  j d d  k s; t  d t d |  d  j d d  k sh t  d  S(   NR   s   e^{-x}i   t    R  s   3^{-x}i   (   R1   R   RJ   t   replaceR   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_pow_fraction  s    /c          C   s   t  d d t \ }  } } t |  | | d  d k s? t  t | d |  |  d k sc t  t |  | d |  d k s t  d  S(   Ns   A,B,CR  is
   A B C^{-1}s
   C^{-1} A Bs
   A C^{-1} B(   Ra   R   R   R   (   R   RP  t   C(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_noncommutative  s    $$c          C   s   t  d t  d t t d d t  t d }  t |  d d d k sL t  t |  d d d k sj t  t |  d d	 d
 k s t  d  S(   Ni   i   i   t   ordert   lexs#   x^{3} + x^{2} y + 3 x y^{3} + y^{4}s   rev-lexs#   y^{4} + 3 x y^{3} + x^{2} y + x^{3}t   nones#   x^{3} + y^{4} + y x^{2} + 3 x y^{3}(   R   R   R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_order  s
    .c           C   sT   t  t t t d   d k s% t  t  t t t f t d   d k sP t  d  S(   Ni   s   \left( x \mapsto x + 1 \right)s2   \left( \left( x, \  y\right) \mapsto x + 1 \right)(   R   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Lambda  s    c          C   s  t  d t  \ }  } } t  d |   \ } } } } t | |  d k sO t  t | d  d k sk t  t | d  d k s t  t | d d | | d | d | | d  d	 k s t  t | d d | | d | d | | d |  d
 k st  t | d d | | d | d | | d | d  d k sSt  t | d d | | d | d | | d | d  d k st  t | d | d | d | | d  d k st  t | d | d | d | | d  d k st  d  S(   Ns   u,vs   x,y,zt   0i   s   x - 1s   x + 1i   i   s2   \left({u}^{2} + 3 u v + 1\right) {x}^{2} y + u + 1sA   \left({u}^{2} + 3 u v + 1\right) {x}^{2} y + \left(u + 1\right) xsE   \left({u}^{2} + 3 u v + 1\right) {x}^{2} y + \left(u + 1\right) x + 1sF   -\left({u}^{2} - 3 u v + 1\right) {x}^{2} y - \left(u + 1\right) x - 1s+   -\left({v}^{2} + v + 1\right) x + 3 u v + 1s+   -\left({v}^{2} + v + 1\right) x - 3 u v + 1(   R!   R#   R   R   (   t   Ruvt   ut   vt   RxyzR   R   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_PolyElement  s"    159:**c          C   sp  t  d t  \ }  } } t  d |   \ } } } } } t | |  d k sR t  t | d  d k sn t  t | d  d k s t  t | d  d k s t  t | |  d	 k s t  t | | |  d
 k s t  t | | |  d k st  t | | | |  d k s&t  t | d |  d k sFt  t | d |  d k sft  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 | d | d  d k s(t  t | d | | d | d | | | | d  d k slt  d  S(   Ns   u,vs   x,y,z,tR  i   s   x - 1s   x + 1i   s   \frac{x}{3}s   \frac{x}{z}s   \frac{x y}{z}s   \frac{x}{z t}s   \frac{x y}{z t}s   \frac{x - 1}{y}s   \frac{x + 1}{y}s   \frac{-x - 1}{y}s   \frac{x + 1}{y z}s   \frac{-y}{x + 1}s   \frac{y z}{x + 1}s;   \frac{\left(u + 1\right) x y + 1}{\left(v - 1\right) z - 1}sC   \frac{\left(u + 1\right) x y + 1}{\left(v - 1\right) z - u v t - 1}(   R"   R#   R   R   (   t   FuvR  R  t   FxyztR   R   R   R7  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_FracElement  s(      $  !$!$)5c           C   s|   t  t t d d t t   d k s- t  t  t t t t   d k sR t  t  t d t t   d k sx t  d  S(   Ni   sE   \operatorname{Poly}{\left( x^{2} + 2 x, x, domain=\mathbb{Z} \right)}sU   \operatorname{Poly}{\left( \frac{1}{y} x, x, domain=\mathbb{Z}\left(y\right) \right)}g       @sJ   \operatorname{Poly}{\left( 2.0 x + 1.0 y, x, y, domain=\mathbb{R} \right)}(   R   R    R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Poly  s    c           C   s   t  t t d t d t d g t   d k s3 t  t  t t d t t d d g t   d k sg t  t  t t t d t d t t t t t d t t t d t t t t t t f   d k s t  d  S(   Ni   i   i   s{   \operatorname{Poly}{\left( a x^{5} + x^{4} + b x^{3} + 2 x^{2} + c x + 3, x, domain=\mathbb{Z}\left[a, b, c\right] \right)}s   \operatorname{Poly}{\left( a x^{4} + x^{3} + \left(b + c\right) x^{2} + 2 x + 3, x, domain=\mathbb{Z}\left[a, b, c\right] \right)}s   \operatorname{Poly}{\left( a x^{3} + x^{2}y -  b xy^{2} - xy -  a x -  c y^{3} + y + b, x, y, domain=\mathbb{Z}\left[a, b, c\right] \right)}(   R   R    R   R  t   cR   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_Poly_order  s    $%Qc           C   s1   t  t t d t d d   d k s- t  d  S(   Ni   i   i    s6   \operatorname{CRootOf} {\left(x^{5} + x + 3, 0\right)}(   R   R)   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_ComplexRootOf  s    c           C   s1   t  t t d t d t   d k s- t  d  S(   Ni   i   sc   \operatorname{RootSum} {\left(x^{5} + x + 3, \left( x \mapsto \sin{\left(x \right)} \right)\right)}(   R   R*   R   R_   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_RootSum  s    c           C   s   t  t d    d  S(   Nc           S   s   t  t t d d S(   Nt   methodt   garbage(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR  #  R  (   R   t	   TypeError(    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_settings"  s    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  d  d k s t  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  d  d k s t  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  d  d k st  d  S(   Ns   C_{n}i   s	   C_{n}^{2}s   B_{n}s	   B_{n}^{2}s   F_{n}s	   F_{n}^{2}s   L_{n}s	   L_{n}^{2}s   T_{n}s	   T_{n}^{2}(	   R   R?   R   R   R   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_numbers&  s    """""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 sd t  d  S(   Ns   E_{n}s   E_{n}\left(x\right)i   s   E_{n}^{2}\left(x\right)(   R   RI   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_euler4  s    !c           C   s@   t  t d   d k s t  t  t d   d k s< t  d  S(   Nt   lamdas   \lambdat   Lamdas   \Lambda(   R   R1   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt
   test_lamda:  s    c          C   s   t  d  }  t  d  } t |   d k s0 t  t |  d i d |  6d k sU t  t |  | d i d |  6d k s~ t  t |  d d i d |  6d k s t  t |  | d i d |  6d | 6d	 k s t  d  S(
   NR   R   R   R   s   x_i + yi   s   x_i^{2}t   y_js	   x_i + y_j(   R1   R   R   (   R   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_custom_symbol_names?  s    %))c          C   s   d d l  m }  d d l m } |  d d d  } |  d d d  } |   } | j | d |  d k sp t  | j | d |  d k s t  | j | d |  d k s t  | j | d |  d k s t  d  S(   Ni(   R   (   t   LatexPrinterR  i   RP  i   s	   - 2 B + Cs   C -2 Bs   2 B + Cs   C + 2 Bs   B - 2 Cs	   - 2 C + Bs   B + 2 Cs   2 C + B(   s	   - 2 B + Cs   C -2 B(   s   2 B + Cs   C + 2 B(   s   B - 2 Cs	   - 2 C + B(   s   B + 2 Cs   2 C + B(   R  R   t   sympy.printing.latexR  R   R   (   R   R  R  RP  R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_matAddI  s    	###c          C   s  d d l  m }  d d l m } |  d d d  } |  d d d  } t d  } |   } | j d |  d	 k sx t  | j d | |  d
 k s t  | j d |  d k s t  | j d |  d k s t  | j t d  |  d k s t  | j t d  |  d k s$t  | j d t d  | |  d k sQt  | j d | | d |  d k s|t  d  S(   Ni(   R   (   R  R   i   RP  R   i   s   2 As   2 x Ais   - 2 Ag      ?s   1.5 As
   \sqrt{2} As   - \sqrt{2} As   2 \sqrt{2} x As   - 2 A \left(A + 2 B\right)s   - 2 A \left(2 B + A\right)(   s   - 2 A \left(A + 2 B\right)s   - 2 A \left(2 B + A\right)(   R  R   R  R  R1   t   _print_MatMulR   R`   (   R   R  R   RP  R   t   lp(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_matMulU  s    	#%&-c          C   s   d d l  m }  t |  d d d  d  d  d d d  f  d	 k sM t  t |  d d d  d d  d d  f  d
 k s t  d  S(   Ni(   R   t   Xi
   i   i   i	   i   s   X\left[:5, 1:9:2\right]s   X\left[5, :5:2\right](   t   sympy.matrices.expressionsR   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_MatrixSliceg  s
    .(c    
      C   s  d d l  m }  m } m } m } m } d d l m } |  d d d  } t | | d k   d k sn t	  | d d	  } t | | d
 k   d k s t	  | d d  } | d d  }	 t | t
 | |	   j  d k s t	  t | t t  t d d    d k st	  d  S(   Ni(   t   Normalt   Diet   Exponentialt   pspacet   where(   t   RandomDomainR,  i    i   s.   \text{Domain: }0 < x_{1} \wedge x_{1} < \inftyt   d1i   i   s'   \text{Domain: }d_{1} = 5 \vee d_{1} = 6R   R  sK   \text{Domain: }0 \leq a \wedge 0 \leq b \wedge a < \infty \wedge b < \inftyi   s=   \text{Domain: }\left\{x\right\}\text{ in }\left\{1, 2\right\}(   t   sympy.statsR  R  R  R  R  t   sympy.stats.rvR  R   R   R3   t   domainR	   R   (
   R  R  R  R  R  R  R  Rx  R   RP  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_RandomDomaino  s    ($$!c          C   s   d d l  m }  |  j t t  } |  t t f } t | j t t t   t t t t  k si t  t | j t t   t t t  k s t  d  S(   Ni(   t   QQ(   t   sympy.polys.domainsR  t
   frac_fieldR   R   R   t   convertR   (   R  t   FR   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_PrettyPoly  s
    7c          C   s  t  d  }  t  d  } t d  } t  d  } t  d  } t t | |   |  |   d k sf t  t t | |  | |  | |   d k s t  t t | |   |  |   d k s t  t t | |  | |  | | f   d	 k s t  t t | |   |  |   d
 k st  t t	 | |  | |    d k sGt  t t
 | |   |  |   d k sqt  t t | |  | |    d k st  t t | |   |  |   d k st  t t | |  | |    d k st  d  S(   NR   R   R   R   R  s<   \mathcal{M}_{x}\left[f{\left(x \right)}\right]\left(k\right)sA   \mathcal{M}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)s<   \mathcal{L}_{x}\left[f{\left(x \right)}\right]\left(k\right)sA   \mathcal{L}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)s<   \mathcal{F}_{x}\left[f{\left(x \right)}\right]\left(k\right)sA   \mathcal{F}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)s>   \mathcal{COS}_{x}\left[f{\left(x \right)}\right]\left(k\right)sC   \mathcal{COS}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)s>   \mathcal{SIN}_{x}\left[f{\left(x \right)}\right]\left(k\right)sC   \mathcal{SIN}^{-1}_{k}\left[f{\left(k \right)}\right]\left(x\right)(   R1   R   R   R   R   R   R   R   R   R   R   R   R.   R   (   R   R   R   R   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_integral_transforms  s2    !$c          C   sb   d d l  m }  t |  j t t   d k s4 t  t |  j t t d d  d k s^ t  d  S(   Ni(   R  s   \mathbb{Q}\left[x, y\right]R  t   ilexs#   S_<^{-1}\mathbb{Q}\left[x, y\right](   R  R  R   t   old_poly_ringR   R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_PolynomialRingBase  s    $c          C   s%  d d l  m }  m } m } m } m } m } |  d  } |  d  } |  d  } | | | d  }	 | | | d  }
 | |  } | d  } t |  d	 k s t  t |	  d
 k s t  t |  d k s t  t |
 |	  d k s t  t |  d k s
t  |   } t |  d k s+t  | i d |	 6t	 j
 |
 6 } t |  d k s`t  | i d |	 6t	 j
 |
 6i d |
 |	 6 } t |  d k st  |  d  } |  d  } |  d  } | | | d  } | | | d  } | | | g  } | |  } t |  d k s!t  d  S(   Ni(   t   Objectt   IdentityMorphismt   NamedMorphismt   Categoryt   Diagramt   DiagramGridt   A1t   A2t   A3t   f1t   f2t   K1s   A_{1}s   f_{1}:A_{1}\rightarrow A_{2}s   id:A_{1}\rightarrow A_{1}s'   f_{2}\circ f_{1}:A_{1}\rightarrow A_{3}s   \mathbf{K_{1}}s	   \emptysett   uniques'  \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\}s  \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\}R   RP  R  R   R  s-   \begin{array}{cc}
A & B \\
 & C 
\end{array}
(   t   sympy.categoriesR  R  R  R  R  R  R   R   R+   RN  (   R  R  R  R  R  R  R  R  R  R  R  t   id_A1R  Rw  R   RP  R  R   R  t   grid(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_categories  s6    .	+
c          C   ss  d d l  m }  d d l m } |  j t t  } | j d  } | j t t g d t d g  } t	 |  d k s{ t
  t	 |  d k s t
  | j t d t  } t	 |  d k s t
  | | } t	 |  d	 k s t
  t	 | j d t d
 d g d t g   d k st
  | |  j t  j d  |  j t  j d  d d g  } t	 |  d k sot
  d  S(   Ni(   R  (   t   homomorphismi   i   s!   {\mathbb{Q}\left[x, y\right]}^{2}sP   \left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangles&   \left\langle {x^{2}},{y} \right\ranglesz   \frac{{\mathbb{Q}\left[x, y\right]}^{2}}{\left\langle {\left[ {x},{y} \right]},{\left[ {1},{x^{2}} \right]} \right\rangle}i   s  \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\ranglei    s}   {\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  t   sympy.polys.agcaR  R  R   R   t   free_modulet	   submoduleR   R   t   ideal(   R  R  R   R  R  R   t   QR  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Modules  s&    "	
	)$	c          C   se   d d l  m }  |  j t  t d d g } t |  d k sF t  t | j  d k sa t  d  S(   Ni(   R  i   i   sG   \frac{\mathbb{Q}\left[x\right]}{\left\langle {x^{2} + 1} \right\rangle}s.   {1} + {\left\langle {x^{2} + 1} \right\rangle}(   R  R  R  R   R   R   t   one(   R  R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_QuotientRing  s
    	c          C   sD   t  d d t \ }  } t |  |  } t |  d k s@ t  d  S(   Ns   A BR  s!   \operatorname{tr}\left(A B\right)(   Ra   R   R   R   R   (   R   RP  R7  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Tr  s    c          C   s8  d d l  m }  m } m } m } |  d d d  } |  d d d  } t | |   d k sd t  t | | |   d k s t  t | |  | |   d k s t  t | | |   d	 k s t  t | |  | |   d
 k s t  t | | d   d k st  t | |  d  d k s<t  t | | |    d k s`t  t | | |    d k st  t | | |    d k st  t | | |    d k st  t | | |  |   d k st  t | |   d k st  t | | |   d k s4t  d  S(   Ni(   R   t   Adjointt   Inverset	   TransposeR  i   t   Ys   X^{\dagger}s   \left(X + Y\right)^{\dagger}s   X^{\dagger} + Y^{\dagger}s   \left(X Y\right)^{\dagger}s   Y^{\dagger} X^{\dagger}s   \left(X^{2}\right)^{\dagger}s   \left(X^{\dagger}\right)^{2}s   \left(X^{-1}\right)^{\dagger}s   \left(X^{\dagger}\right)^{-1}s   \left(X^{T}\right)^{\dagger}s   \left(X^{\dagger}\right)^{T}s    \left(X^{\dagger} + Y\right)^{T}s   X^{T}s   \left(X + Y\right)^{T}(   t   sympy.matricesR   R  R  R  R   R   (   R   R  R  R  R  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Adjoint  s"    ""("(""$$$$(c          C   s   d d l  m }  m } |  d d d  } |  d d d  } t | | | |   d k s_ t  t | | |  |  d k s t  d  S(   Ni(   R   t   HadamardProductR  i   R  s   X \circ Y^{2}s   \left(X \circ Y\right) Y(   R  R   R  R   R   (   R   R  R  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Hadamard2  s
    %c          C   s5   d d l  m }  t |  d d   d k s1 t  d  S(   Ni(   t
   ZeroMatrixi   s
   \mathbb{0}(   R  R  R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_ZeroMatrix:  s    c          C   s2   d d l  m }  t |  d   d k s. t  d  S(   Ni(   t   Identityi   s
   \mathbb{I}(   R  R  R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Identity?  s    c          C   s   t  d  }  t |    } t |  d k s0 t  t |    } t |  d k sT t  t |    } t |  d k sx t  t |    } t |  d k s t  d  S(   Ns   a:fs.   a \wedge b \wedge c \wedge d \wedge e \wedge fs$   a \vee b \vee c \vee d \vee e \vee fs[   a \Leftrightarrow b \Leftrightarrow c \Leftrightarrow d \Leftrightarrow e \Leftrightarrow fs3   a \veebar b \veebar c \veebar d \veebar e \veebar f(   Ra   R   R   R   R   Ro   R   (   t   symsR  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_boolean_args_orderD  s    		c          C   s(   t  d  }  t |   d k s$ t  d  S(   NiR   (   R`   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_imaginaryV  s    c           C   s   t  t  d k s t  t  t  d k s0 t  t  t  d k sH t  t  t  d k s` t  t  t  d k sx t  t  t  d k s t  d  S(   Ns   \sins   \coss   \tans   \logs   \operatorname{Ei}s   \zeta(   R   R_   R   Rj   Rk   RX   R   Rc   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_builtins_without_args[  s    c          C   s  t  d  }  t |   d k s$ t  t |  t   d k sB t  t  d  }  t |   d k sf t  t  d  }  t |   d k s t  t |  t   d k s t  t  d	  } t |  d
 k s t  t  d  } t | t   d k s t  t |  d k st  d  S(   Nt   AlphaR   s   A{\left(x \right)}t   BetaRP  t   Etat   Hs   H{\left(x \right)}t   Pis   \Pit   chis   \chi{\left(x \right)}s   \chi(   R   R   R   R   (   R:  R   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_greek_functionsd  s    c          C   s   d }  t  |   d k s t  d }  t  |   d k s< t  d }  t  |   d k sZ t  d }  t  |   d k sx t  d	 }  t  |   d
 k s t  d }  t  |   d k s t  d }  t  |   d k s t  d  S(   NR  R   R   RP  R!  R"  t   omicront   oR#  s   \PiRy   s   \pit   LamdaHatDOTs   \dot{\hat{\Lambda}}(   R   R   (   R:  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_translate{  s    c          C   sG   d d l  m }  x0 |  D]( } t t |   d | k s t  q Wd  S(   Ni(   t   other_symbolss   \(   R  R*  R   Ra   R   (   R*  R:  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_other_symbols  s    c           C   sh  t  t d   d k s t  t  t d   d k s< t  t  t d   d k sZ t  t  t d   d k sx t  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 s t  t  t d   d k st  t  t d   d k s,t  t  t d   d k sJt  t  t d   d k sht  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 st  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 sXt  t  t d'   d k svt  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 st  t  t d,   d, k st  t  t d-   d- k s*t  t  t d.   d. k sHt  t  t d/   d0 k sft  t  t d1   d1 k st  t  t d2   d2 k st  t  t d3   d3 k st  t  t d4   d4 k st  t  t d5   d5 k st  t  t d6   d6 k st  t  t d7   d7 k s8t  t  t d8   d8 k sVt  t  t d9   d9 k stt  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 st  t  t d@   dA k s
t  t  t dB   dC k s(t  t  t dD   dE k sFt  t  t dF   dG k sdt  d  S(H   Nt	   xMathrings   \mathring{x}t   xChecks	   \check{x}t   xBreves	   \breve{x}t   xAcutes	   \acute{x}t   xGraves	   \grave{x}t   xTildes	   \tilde{x}t   xPrimes   {x}'t   xddDDots
   \ddddot{x}t   xDdDots	   \dddot{x}t   xDDots   \ddot{x}t   xBolds   \boldsymbol{x}t   xnOrMs   \left\|{x}\right\|t   xAVGs   \left\langle{x}\right\ranglet   xHats   \hat{x}t   xDots   \dot{x}t   xBars   \bar{x}t   xVecs   \vec{x}t   xAbss   \left|{x}\right|t   xMagt   xPrMt   xBMt   Mathringt   Checkt   Brevet   Acutet   Gravet   Tildet   Primet   DDots   \dot{D}t   Boldt   NORmt   AVGt   HatR   t   Bart   VecR   t   Magt   PrMt   BMt   hbars   \hbart   xvecdots   \dot{\vec{x}}t   xDotVecs   \vec{\dot{x}}t   xHATNorms   \left\|{\hat{x}}\right\|t    xMathringBm_yCheckPRM__zbreveAbssC   \boldsymbol{\mathring{x}}^{\left|{\breve{z}}\right|}_{{\check{y}}'}t    alphadothat_nVECDOT__tTildePrimes1   \hat{\dot{\alpha}}^{{\tilde{t}}'}_{\dot{\vec{n}}}(   R   Ra   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_modifiers  s`    c           C   sv  t  t d   d k s t  t  t d   d k s< t  t  t d   d k sZ t  t  t d   d k sx t  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 s t  t  t d   d k st  t  t d   d k s,t  t  t d   d k sJt  t  t d   d k sht  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 st  t  t d!   d" k st  t  t d#   d$ k st  t  t d%   d& k s:t  t  t d'   d( k sXt  t  t d)   d* k svt  t  t d+   d, k st  t  t d-   d. k st  t  t d/   d0 k st  t  t d1   d2 k st  t  t d3   d4 k st  t  t d5   d6 k s*t  t  t d7   d8 k sHt  t  t d9   d: k sft  t  t d;   d< k st  t  t d=   d> k st  t  t d?   d@ k st  t  t dA   dB k st  t  t dC   dD k st  t  t dE   dF k st  t  t dG   dH k s8t  t  t dI   dJ k sVt  t  t dK   dL k stt  t  t dM   dN k st  t  t dO   dP k st  t  t dQ   dR k st  t  t dS   dT k st  t  t dU   dV k s
t  t  t dW   dX k s(t  t  t dY   dZ k sFt  t  t d[   d\ k sdt  t  t d]   d^ k st  t  t d_   d` k st  t  t da   db k st  t  t dc   dd k st  t  t de   df k st  t  t dg   dh k st  t  t di   dj k s6t  t  t dk   dl k sTt  t  t dm   dn k srt  d  S(o   NRz  s   \alphaR=   s   \betaRO   s   \gammat   deltas   \deltat   epsilons   \epsilonRc   s   \zetat   etas   \etaR
  s   \thetat   iotas   \iotat   kappas   \kappat   lambdas   \lambdaR   s   \mut   nus   \nut   xis   \xiR&  R'  Ry   s   \piR   s   \rhot   sigmas   \sigmaR   s   \taut   upsilons   \upsilonR  s   \phiR$  s   \chit   psis   \psiR   s   \omegaR  R   R   RP  R   s   \Gammat   Deltas   \Deltat   Epsilont   Et   Zetat   ZR!  R"  t   Thetas   \Thetat   IotaR   t   Kappat   KR   s   \Lambdat   MuR  t   Nut   Nt   Xis   \Xit   Omicront   OR#  s   \Pit   Rhot   Pt   Sigmas   \SigmaR   R   t   Upsilons   \Upsilont   Phis   \PhiR   R  R+  s   \Psit   Omegas   \Omegat
   varepsilons   \varepsilont   varkappas	   \varkappat   varphis   \varphit   varpis   \varpit   varrhos   \varrhot   varsigmas	   \varsigmat   varthetas	   \vartheta(   R   R1   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_greek_symbols  sn    c           C   s   t  t  d k s t  d  S(   Ns   \mathcal{COS}(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt*   test_builtin_without_args_mismatched_names  s    c           C   s   t  t  d k s t  t  t  d k s0 t  t  t  d k sH t  t  t  d k s` t  t  t  d k sx t  t  t  d k s t  d  S(   Ns   \operatorname{Chi}s   \operatorname{B}s   \Gammas   \deltas   \gamma(   R   R   R   R=   RO   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_builtin_no_args  s    c          C   s.   t  d  }  t |  t   d k s* t  d  S(   NR#  s   \Pi{\left(x \right)}(   R   R   R   R   (   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_6853  s    c          C   sW  t  d t d d t }  t |   d k s1 t  t  d t d d t }  t |   d k sb t  t  t j d t d d t }  t |   d k s t  t  t t d d t }  t |   d k s t  t  t t d d t }  t |   d	 k s t  t  d t d  }  t |   d
 k s(t  t  d t d  }  t |   d k sSt  d  S(   Nii   R3  s   - 2 \left(x + 1\right)i   s   2 \left(x + 1\right)s   \frac{x + 1}{2}s   y \left(x + 1\right)s   - y \left(x + 1\right)s	   - 2 x - 2s   2 x + 2(   R   R   R   R   R   R+   t   OneR   (   t   e(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Mul  s     c          C   s~   t  d d d t }  t |   d k s- t  t t t d d   d k sR t  t d  } t | d  d k sz t  d  S(	   Ni   R3  s   2^{2}ii   s   \frac{1}{\sqrt[3]{x}}s   x^2s   \left(x^{2}\right)^{2}(   R$   R   R   R   R   R'   R1   (   R  t   x2(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Pow*  s
    %c           C   sL   t  t t t   d k s! t  t  t t t t    d k sH t  d  S(   Ns   x \Leftrightarrow ys   x \not\Leftrightarrow y(   R   Ro   R   R   R   Rp   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_71802  s    !c           C   s#   t  t j t  d k s t  d  S(   Ns   \left(\frac{1}{2}\right)^{n}(   R   R+   t   HalfR   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_84097  s    c          C   s>   d d l  m }  |  d d t } t |  d k s: t  d  S(   Ni(   t
   parse_exprs   -B*AR3  s   A \left(- B\right)(   t   sympy.parsing.sympy_parserR  R   R   R   (   R  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_8470;  s    c          C   s   t  t d d t  }  t d |  d t } t |  d k sD t  t d |  d t } t |  d k sq t  t |  d d t } t |  d k s t  d  S(   Ni   i   R3  s   2 \left(x + 1 = 2 x\right)i   s   6 + \left(x + 1 = 2 x\right)s   \left(x + 1 = 2 x\right)^{2}(   R   R   R   R   R   R   R    R$   (   R  t   q(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_7117A  s    c          C   s   t  d d d  }  t  d d d  } t |  | j | |   d k sM t  t |  | j | d |   d k sy t  t |  | j |  |    d k s t  d  S(   NR   i   R   s   x \left(- y\right)is   x \left(- 2 y\right)s   - x y(   R   R   t   subsR   (   R   R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_15439L  s
    ),c           C   s"   t  t d   d k s t  d  S(   Ns   \frac{a_1}{b_1}(   R   R1   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_2934T  s    c          C   sL   d }  t  |   } t |  |  k s* t  t t |   d k sH t  d  S(   Ns	   C_{x_{0}}s   \cos{\left(C_{x_{0}} \right)}(   R1   R   R   Rj   (   t   latexSymbolWithBraceR:  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_10489X  s    c          C   s:   t  d  \ }  } t |  d | d  d k s6 t  d  S(   Ns
   m__1, l__1i   s/   \left(l^{1}\right)^{2} + \left(m^{1}\right)^{2}(   Ra   R   R   (   t   m__1t   l__1(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_12886_  s    c          C   s>   d d l  m }  |  d d t } t |  d k s: t  d  S(   Ni(   R  s   5/1R3  s   \frac{5}{1}(   R  R  R   R   R   (   R  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_13559e  s    c          C   s9   t  t d t t d t }  t |   d k s5 t  d  S(   NiR3  s   c - \left(a + b\right)(   R  R   R   R  R   R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_13651k  s    c          C   s   t  d  }  t d |   } t |  t d |   k oC d k n sN t  t | d  d k sj t  t | d  d k s t  t |  |  d k s t  d  S(   NR   i   s   \frac{1}{x}i   s   \left(\frac{1}{x}\right)^{2}s   1 + \frac{1}{x}s   x \frac{1}{x}(   Ra   R   R   R   (   R   t   he(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_UnevaluatedExprp  s    2c    	      C   s  t  d d d  }  t  d d d  } t  d d d  } t |  d  d k sR t  t d |  d  d k sr t  | d j | |  |  } t |  d	 k s t  t d
  \ } } } t  d | |  } t  d | |  } t | | | | f  d k st  d  S(   NR   i   i   RP  R  i    s   A_{0, 0}s
   3 A_{0, 0}s   \left(A - B\right)_{0, 0}s   i j kR  Ro  s0   \sum_{i_{1}=0}^{k - 1} M_{i, i_{1}} N_{i_{1}, j}(   i    i    (   i    i    (   i    i    (   R   R   R   R  Ra   (	   R   RP  R  R  R   R   R   R  Ro  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_MatrixElement_printingy  s     c          C   s   t  d d d  }  t  d d d  } t  d d d  } t |   d k sO t  t |  |  | |  d k ss t  t |  | |  | | |  d k s t  d  S(   NR   i   RP  R  s   - As   A - A B - Bs   - A B - A B C - B(   R   R   R   (   R   RP  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_MatrixSymbol_printing  s    $c          C   sI   t  d d d  }  t  d d d  } t t |  |   d k sE t  d  S(   NR   i   RP  i   s   A \otimes B(   R   R   R   R   (   R   RP  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_KroneckerProduct_printing  s    c          C   s   t  t t t t  }  t |   d k s- t  t  t t t t t  }  t |   d k s^ t  t  t t t t t  }  t |   d k s t  d  S(   Ns   x + y i + z j + t ks   x + y i + z j + t x ks$   x + y i + z j + \left(t + x\right) k(   R   R   R   R   R7  R   R   (   R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_Quaternion_latex_printing  s    c          C   sY   d d l  m }  t d d d  } t d d d  } t |  | |   d k sU t  d  S(   Ni(   t   TensorProductR   i   RP  s   A \otimes B(   t   sympy.tensor.functionsR  R   R   R   (   R  R   RP  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_TensorProduct_printing  s    c          C   sQ   d d l  m }  d d l m } | |  j |  j  } t |  d k sM t  d  S(   Ni(   t   R2(   t   WedgeProducts*   \operatorname{d}x \wedge \operatorname{d}y(   t   sympy.diffgeom.rnR  t   sympy.diffgeomR  t   dxt   dyR   R   (   R  R  t   wp(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_WedgeProduct_printing  s    c          C   s   d d  l  j j }  |  j d  } |  j d d  \ } } t d  } t | | | d | j  d k sp t  t | | d | j  d k s t  t | | t	 | j  d	 k s t  d  S(
   NiR   s
   theta, phii   t   Li   s>   L \left(\dot{\phi} + \dot{\theta}\right)^{2}\mathbf{\hat{a}_x}s<   \left(\dot{\phi} + \dot{\theta}\right)^{2}\mathbf{\hat{a}_x}s:   \left(\dot{\phi} \dot{\theta}\right)^{a}\mathbf{\hat{a}_x}(
   t   sympy.physics.mechanicst   physicst	   mechanicst   ReferenceFramet   dynamicsymbolsR1   R   R   R   R   (   t   met   A_framet   thetadt   phidR  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_14041  s    c          C   s   t  d d d t }  t |   d k s- t  t  d t  d d d t d t } t |  d k si t  t  d d d t } t |  d k s t  t  d d d t } t |  d	 k s t  d  S(
   Ni   iR3  s   1^{-1}s
   1^{1^{-1}}i   is   \frac{1}{9}s   1^{-2}(   R$   R   R   R   (   t   expr_1t   expr_2t   expr_3t   expr_4(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_9216  s    $c          C   s  d d l  m }  m } m } |  d  } | d |  \ } } } } | d |  } | d | g d g g  \ }	 }
 } } | d | | g d g d g g  } | d	 | | | | g d g d g d g d g g  } t |  d
 k s t  t |  d k st  |	 |  } t |  d k s(t  |	 |  } t |  d k sLt  |	 |  } t |  d k sqt  d |	 |  } t |  d k st  | | | | |  } t |  d k st  | | | | |  } t |  d k st  | | | | |  } t |  d k s&t  | | |  } t |  d k sNt  | | |  } t |  d k sut  | | |  } t |  d k st  d t |	 |  } t |  d k st  | | |  } t |  d k st  | | |  |	 |  |
 |  } t |  d k s.t  |	 |  d |
 |  } t |  d k s`t  d d l  m } | | | | | |  i d | 6d | 6 } t |  d k st  | | | | | |  i d | 6 } t |  d k st  | | | | | |  i d | 6d | 6 } t |  d  k s6t  | | | | | |  i d | 6d | 6 } t |  d! k s|t  | | | | | |  i d | 6d | 6 } t |  d" k st  | | | | | |  i d | 6 } t |  d# k st  d  S($   Ni(   t   TensorIndexTypet   tensor_indicest
   tensorheadR  s   i j k lt   i_0s   A B C Di   R"  Rl  s   {}^{i}s   {}_{i}s   A{}^{i}s   A{}^{i_{0}}s   A{}_{i}is	   -3A{}^{i}s   K{}^{ij}{}_{ki_{0}}s   K{}^{i}{}_{jk}{}^{i_{0}}s   K{}^{i}{}_{j}{}^{k}{}_{i_{0}}s   H{}^{i}{}_{j}s   H{}^{ij}s   H{}_{ij}s   \left(x + 1\right)A{}^{i}s   H{}^{L_{0}}{}_{L_{0}}s#   H{}^{i}{}_{L_{0}}A{}^{L_{0}}B{}^{k}i   s   3B{}^{i} + A{}^{i}(   t   TensorElementi   s   K{}^{i=3,j,k=2,l}s   K{}^{i=3,jkl}s   K{}^{i=3}{}_{j}{}^{k=2,l}s   K{}^{i=3}{}_{j}{}^{k=2}{}_{l}s   K{}^{i=3,j}{}_{k=2,l}s   K{}^{i=3,j}{}_{kl}(   t   sympy.tensor.tensorR  R  R  R   R   R   R  (   R  R  R  R  R   R   R   R   t   i0R   RP  R  Rx  R"  Rl  R  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_latex_printer_tensor  sd    '$6$,%-./'c    	      C   s   d d l  m }  m } m } m } m } m } t d  \ } } |  | | |  | | | |  | | |   | j  } t	 |  d k s t
  d  S(   Ni(   Rz   R3   R	   R+   R_   Rj   s   a xs   \left\{\left( x, \  a\right) \mid \left( x, \  a\right) \in \mathbb{C} \wedge \left\{\sin{\left(a x \right)}, \cos{\left(a x \right)}\right\} \right\}(   R  Rz   R3   R	   R+   R_   Rj   Ra   RZ  R   R   (	   Rz   R3   R	   R+   R_   Rj   R   R   t   sol(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_issue_15353  s
    .;	c          C   sf   d d l  m }  t d d d  } t |  |   d k s@ t  t |  | d   d k sb t  d  S(   Ni(   t   traceR   i   s    \operatorname{tr}\left(A \right)s$   \operatorname{tr}\left(A^{2} \right)(   R  R  R   R   R   (   R  R   (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt
   test_trace(  s    c             s   d d l  m   m }  d |  f   f d     Y  f d   }  f d   } t | t   d k sn t  t | t d   d	 k s t  t | t   d
 k s t  d  S(   Ni(   t   Basict   Exprt   UnimplementedExprc              s   e  Z   f d    Z RS(   c            s     j  |  |  S(   N(   t   __new__(   R  R  (   R  (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR  7  s    (   R   R   R  (    (   R  (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyR  6  s   c            s     |   j    S(   N(   RQ  (   R  (   R  (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   unimplemented_expr;  s    c            s     |   } d | j  _ | S(   Ns   UnimplementedExpr_x^1(   t	   __class__R   (   R  t   result(   R  (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   unimplemented_expr_sup_sub?  s    s   UnimplementedExpr\left(x\right)i   s#   UnimplementedExpr\left(x^{2}\right)s'   UnimplementedExpr^{1}_{x}\left(x\right)(   R  R  R  R   R   R   (   R  R  R  (    (   R  R  s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_print_basic0  s    c          C   sP  d d l  m }  t d d d  } t |  |  d d d k sF t  t |  |  d d d	 k sj t  t d d
 d
  } t d d
 d
  } t d d
 d
  } t | d d d k s t  t | | | | d d d k s t  t | | | | | | d d d k st  t d d
 d
  } t | d d d k sLt  d  S(   Ni(   R  R   i   t   mat_symbol_stylet   bolds)   \operatorname{tr}\left(\mathbf{A} \right)R  s    \operatorname{tr}\left(A \right)i   RP  R  s   - \mathbf{A}s/   \mathbf{A} - \mathbf{A} \mathbf{B} - \mathbf{B}sG   - \mathbf{A} \mathbf{B} - \mathbf{A} \mathbf{B} \mathbf{C} - \mathbf{B}t   A_ks   \mathbf{A_{k}}(   R  R  R   R   R   (   R  R   RP  R  (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_MatrixSymbol_boldK  s     $c           C   s   t  d t  d k s t  t  d t d d d k s> t  t  d t d d d k s` t  t  d t d d d k s t  t  t d d	 d
 k s t  t  t d d d k s t  d  S(   Ni   s   1 + it   imaginary_unitR   R   s   1 + jR   s   1 + foot   tis   \text{i}t   tjs   \text{j}(   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_imaginary_unitb  s    """c           C   s   t  t t  d t d k s$ t  t  t t  d t d k sH t  t  t t  d t d k sl t  t  t t  d t d k s t  d  S(   Nt   gothic_re_ims   \Im{\left(x\right)}s!   \operatorname{im}{\left(x\right)}s   \Re{\left(x\right)}s!   \operatorname{re}{\left(x\right)}(   R   RS   R   R   R   R   R]   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_text_re_imk  s    $$$c          C   s  d d l  m }  m } m } m } m } d d l m } |  d d  } t |  d k s_ t	  | d |  } t |  d k s t	  | d	 |  } t |  d
 k s t	  | | d  }	 t |	  d k s t	  t
 d  }
 |
 | j | j  } t | |   d k st	  d  S(   Ni(   t   Manifoldt   Patcht   CoordSystemt   BaseScalarFieldt   Differential(   R  R  i   s   \text{M}Rt  s   \text{P}_{\text{M}}t   rects!   \text{rect}^{\text{P}}_{\text{M}}i    s   \mathbf{rect_{0}}R  sC   \operatorname{d}\left(g{\left(\mathbf{x},\mathbf{y} \right)}\right)(   R  R  R  R  R  R  R  R  R   R   R   R   R   (   R  R  R  R  R  R  R  R   R  R  R  t   s_field(    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_DiffGeomMethodsr  s    (c           C   s\   t  d t  d k s t  t  d t  d k s8 t  t  d t t  d k sX t  d  S(   Ni   s
   5 \text{m}i   s   3 \text{gibibyte}i   s   \frac{4 \mu\text{g}}{\text{s}}(   R   R   R   R   R   R   (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   test_unit_ptinting  s    (_  R  R    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Re   Rf   Rg   Rh   Ri   Rj   Rk   Rl   Rm   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R}   R~   R   R   R   R   R   R   R   R   t   sympy.ntheory.factor_R   R  R   R   R  R   R   R   R   t   sympy.tensor.arrayR   R   R   R   R   t   sympy.utilities.pytestR   R   t   sympy.functionsR   R   R   R   t%   sympy.functions.combinatorial.numbersR   R   R   R   R   t   sympy.logicR   t   sympy.logic.boolalgR   R   R   t   sympy.physics.quantumR   R   t   sympy.physics.unitsR   R   R   R   R   R   R   t   sympy.core.traceR   t   sympy.core.compatibilityR   t    sympy.combinatorics.permutationsR   R   R   R   t   sympy.vectorR   R   R   R   R   R   R   t   sympy.sets.setexprR   t   symR   R   R   R   R7  R   R  R  R   R   R  R   R   R   R   R   R   R   R   R   R   R   R  R  R  R#  R'  R(  R2  R4  R5  R8  R;  R>  R?  RI  RJ  RK  RL  RM  RO  RS  RT  RU  RV  RY  R[  R_  R`  Rb  Rd  Rf  Rh  Rj  Rk  Rl  Rm  Rp  Rs  Rt  Rv  Ry  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R%  R)  R+  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  (    (    (    s>   lib/python2.7/site-packages/sympy/printing/tests/test_latex.pyt   <module>   sB     7"""(44!		X				
			1										-						9			
									
				
								
								
										.	
																			
							!		:	!															8	<																											L								