ó
~9­\c        	   @   s)	  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 d  d lD mE ZE mF ZF mG ZG mH ZH mI ZI mJ ZJ d  d lK mL ZL mM ZN mO ZO d  d lP mQ ZQ d  d lR mS ZS d  d lT 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| d  d l} m~ Z~ m Z m€ Z€ m Z m‚ Z‚ d  d lƒ m„ Z„ d  d	 l… m† Z† m‡ Z‡ d  d
 lˆ m‰ Z‰ mŠ Z‹ d  d lŒ m Z d  d lŽ m Z d  d l m‘ Z‘ d  d l’ m“ Z“ m” Z” m• Z• m– Z– m— Z— d  d l˜ m™ Z™ d  d lš m› Z› mœ Zœ m Z mž Zž d  d lŸ m  Z  m¡ Z¡ d  d l¢ m£ Z£ m¤ Z¤ m¥ Z¥ m¦ Z¦ m§ Z§ m¨ Z¨ m© Z© d  d l  Zª d eª j« f d „  ƒ  YZ« e2 d ƒ \	 Z¬ Z­ Z® Z¯ Z° Z± Z² Z³ Z´ e
 d ƒ Zµ e) d ƒ Z¶ e) d ƒ Z· e¸ d „ ZŠ e¸ d „ Z¹ d „  Zº d „  Z» d „  Z¼ d „  Z½ d  „  Z¾ d! „  Z¿ d" „  ZÀ d# „  ZÁ d$ „  ZÂ d% „  ZÃ d& „  ZÄ d' „  ZÅ d( „  ZÆ d) „  ZÇ d* „  ZÈ d+ „  ZÉ d, „  ZÊ d- „  ZË d. „  ZÌ d/ „  ZÍ d0 „  ZÎ d1 „  ZÏ d2 „  ZÐ d3 „  ZÑ d4 „  ZÒ d5 „  ZÓ d6 „  ZÔ d7 „  ZÕ d8 „  ZÖ d9 „  Z× d: „  ZØ d; „  ZÙ d< „  ZÚ d= „  ZÛ d> „  ZÜ d? „  ZÝ d@ „  ZÞ dA „  Zß dB „  Zà dC „  Zá dD „  Zâ dE „  Zã dF „  Zä dG „  Zå dH „  Zæ dI „  Zç dJ „  Zè dK „  Zé dL „  Zê dM „  Zë dN „  Zì dO „  Zí dP „  Zî dQ „  Zï dR „  Zð dS „  Zñ dT „  Zò dU „  Zó dV „  Zô dW „  Zõ dX „  Zö dY „  Z÷ dZ „  Zø d[ „  Zù d\ „  Zú d] „  Zû d^ „  Zü d_ „  Zý d` „  Zþ da „  Zÿ db „  Z dc „  Zdd „  Zde „  Zdf „  Zdg „  Zdh „  Zdi „  Zdj „  Zdk „  Z	dl „  Z
dm „  Zdn „  Zdo „  Zdp „  Zdq „  Zdr „  Zds „  Zdt „  Zdu „  Zdv „  Zdw „  Zdx „  Zdy „  Zdz „  Zd{ „  Zd| „  Zd} „  Zd~ „  Zd „  Zd€ „  Zd „  Zd‚ „  Z dƒ „  Z!d„ „  Z"d… „  Z#d† „  Z$d‡ „  Z%dˆ „  Z&d‰ „  Z'dŠ „  Z(d‹ „  Z)dŒ „  Z*d „  Z+dŽ „  Z,d „  Z-d „  Z.d‘ „  Z/d’ „  Z0d“ „  Z1d” „  Z2d• „  Z3d– „  Z4d— „  Z5d˜ „  Z6d S(™   iÿÿÿÿ(C   t   Addt   Andt   Basict
   Derivativet   Dictt   Eqt
   Equivalentt   FFt	   FiniteSett   Functiont   Get   Gtt   It   Impliest   Integralt   SingularityFunctiont   Lambdat   Let   Limitt   Ltt   Matrixt   Mult   Nandt   Net   Nort   Nott   Ot   Ort   Powt   Productt   QQt   RRt   Rationalt   Rayt   rootoft   RootSumt   St   Segmentt   Subst   Sumt   Symbolt   Tuplet   Tracet   Xort   ZZt	   conjugatet   groebnert   oot   pit   symbolst   ilext   grlext   Ranget   Containst   SeqPert
   SeqFormulat   SeqAddt   SeqMult   fourier_seriest   fpst   ITEt
   Complementt   Intervalt   Intersectiont   Uniont
   EulerGammat   GoldenRatio(   t
   Assignmentt   AddAugmentedAssignmentt   SubAugmentedAssignmentt   MulAugmentedAssignmentt   DivAugmentedAssignmentt   ModAugmentedAssignment(   t   ranget   u_decodet   PY3(   t   UnevaluatedExpr(   t   Tr((   t   Abst   Chit   Cit   Eit   KroneckerDeltat	   Piecewiset   Shit   Sit   atan2t   betat   binomialt   catalant   ceilingt   cost   eulert   expt   expintt	   factorialt
   factorial2t   floort   gammat   hypert   logt   meijergt   sint   sqrtt   subfactorialt   tant
   uppergammat   lerchphit
   elliptic_kt
   elliptic_ft
   elliptic_et   elliptic_pit
   DiracDeltat   bellt	   bernoullit	   fibonaccit
   tribonaccit   lucas(   t   Adjointt   Inverset   MatrixSymbolt	   Transposet   KroneckerProduct(   t	   mechanics(   t   joulet   degree(   t   pprintt   pretty(   t   center_accent(   t   ImageSet(   t   SetExpr(   t   ImmutableDenseNDimArrayt   ImmutableSparseNDimArrayt   MutableDenseNDimArrayt   MutableSparseNDimArrayt   tensorproduct(   t   TensorProduct(   t   TensorIndexTypet   tensor_indicest
   tensorheadt   TensorElement(   t   raisest   XFAIL(   t
   CoordSys3Dt   Gradientt   Curlt
   Divergencet   Dott   Crosst	   LaplacianNt
   lowergammac           B   s   e  Z RS(    (   t   __name__t
   __module__(    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR–   /   s   s   a,b,c,d,x,y,z,k,nt   ft   thetat   phic         C   s   t  |  d | d t d t ƒS(   s   ASCII pretty-printingt   ordert   use_unicodet	   wrap_line(   t   xprettyt   False(   t   exprRœ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR   ã   s    c         C   s   t  |  d | d t d t ƒS(   s   Unicode pretty-printingRœ   R   Rž   (   RŸ   t   TrueR    (   R¡   Rœ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   uprettyè   s    c           C   sô   t  d ƒ d k s t ‚ t  d ƒ d k s0 t ‚ t  d ƒ d k sH t ‚ t  d ƒ d k s` t ‚ t  d ƒ d k sx t ‚ t  d ƒ d k s t ‚ t  d ƒ d k s¨ t ‚ t  d ƒ d k sÀ t ‚ t  d ƒ d k sØ t ‚ t  d ƒ d k sð t ‚ d  S(   Nt   xxxs   xxx'xxxs   xxx"xxxs   xxx"xxx'xxxs   xxx
xxx(   R   t   AssertionError(    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ascii_strí   s    c           C   sô   t  d ƒ d k s t ‚ t  d ƒ d k s0 t ‚ t  d ƒ d k sH t ‚ t  d ƒ d k s` t ‚ t  d ƒ d k sx t ‚ t  d ƒ d k s t ‚ t  d ƒ d k s¨ t ‚ t  d ƒ d k sÀ t ‚ t  d ƒ d k sØ t ‚ t  d ƒ d k sð t ‚ d  S(   Nu   xxxu   xxx'xxxu   xxx"xxxu   xxx"xxx'xxxu   xxx
xxx(   R   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_unicode_strú   s    c           C   sv   t  t ƒ d k s t ‚ t  t d ƒ ƒ d k s6 t ‚ t  t d ƒ ƒ d k sT t ‚ t  t d ƒ ƒ d k sr t ‚ d  S(   Nu   âˆžs	   alpha^+_1u   Î±âºâ‚RW   u   Î²t   lambdau   Î»(   R£   R/   R¥   R(   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_upretty_greek  s    c           C   s|   t  t d ƒ ƒ d k s t ‚ t  t d ƒ ƒ d k s< t ‚ t  t d ƒ ƒ d k sZ t ‚ t  t d ƒ ƒ d k sx t ‚ d  S(   Nt   beta12u   Î²â‚â‚‚t   Y00u   Yâ‚€â‚€t   Y_00s   F^+-u   Fâºâ»(   R£   R(   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_upretty_multiindex  s    c           C   s  t  t d ƒ ƒ d k s t ‚ t  t d ƒ ƒ d k s< t ‚ t  t d ƒ ƒ d k sZ t ‚ t  t d ƒ ƒ d k sx t ‚ t  t d	 ƒ ƒ d
 k s– t ‚ t  t d ƒ ƒ d k s´ t ‚ t  t d ƒ ƒ d k sÒ t ‚ t  t d ƒ ƒ d k sð t ‚ t  t d ƒ ƒ d k st ‚ d  S(   Nt   beta_1_2u	   Î²â‚ â‚‚s   beta^1^2u   Î²Â¹ Â²s   beta_1^2u   Î²Â²â‚t
   beta_10_20u   Î²â‚â‚€ â‚‚â‚€s   beta_ax_gamma^iu   Î²â±â‚â‚“ áµ§s	   F^1^2_3_4u   FÂ¹ Â²â‚ƒ â‚„s	   F_1_2^3^4u   FÂ³ â´â‚ â‚‚t	   F_1_2_3_4u   Fâ‚ â‚‚ â‚ƒ â‚„s	   F^1^2^3^4u   FÂ¹ Â² Â³ â´(   R£   R(   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_upretty_sub_super  s    c           C   sŠ  t  t d ƒ ƒ d k s t ‚ t  t d ƒ ƒ d k s< t ‚ t  t d ƒ ƒ d k sZ t ‚ t  t d ƒ ƒ d k sx t ‚ t  t d	 ƒ ƒ d
 k s– t ‚ t  t d ƒ ƒ d k s´ t ‚ t  t d ƒ ƒ d k sÒ t ‚ t  t d ƒ ƒ d k sð t ‚ t  t d ƒ ƒ d k st ‚ t  t d ƒ ƒ d k s,t ‚ t  t d ƒ ƒ d k sJt ‚ t  t d ƒ ƒ d k sht ‚ t  t d ƒ ƒ d k s†t ‚ d  S(   Nt   F_betau   Fáµ¦t   F_gammau   Fáµ§t   F_rhou   Fáµ¨t   F_phiu   Fáµ©t   F_chiu   Fáµªt   F_au   Fâ‚t   F_eu   Fâ‚‘t   F_iu   Fáµ¢t   F_ou   Fâ‚’t   F_uu   Fáµ¤t   F_ru   Fáµ£t   F_vu   Fáµ¥t   F_xu   Fâ‚“(   R£   R(   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_upretty_subs_missing_in_24!  s    c           C   sý   t  rù t t d ƒ ƒ d k s$ t ‚ t t d ƒ ƒ d k sB t ‚ t t d ƒ ƒ d k s` t ‚ t t d ƒ ƒ d k s~ t ‚ t t d	 ƒ ƒ d
 k sœ t ‚ t t d ƒ ƒ d k sº t ‚ t t d ƒ ƒ d k sØ t ‚ t t d ƒ ƒ d k sù t ‚ n  d  S(   Nt   F_hu   Fâ‚•t   F_ku   Fâ‚–t   F_lu   Fâ‚—t   F_mu   Fâ‚˜t   F_nu   Fâ‚™t   F_pu   Fâ‚št   F_su   Fâ‚›t   F_tu   Fâ‚œ(   RK   R£   R(   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_missing_in_2X_issue_90472  s    c           C   s¦  t  t d ƒ ƒ d k s t ‚ t  t d ƒ ƒ d k s< t ‚ t  t d ƒ ƒ d k sZ t ‚ t  t d ƒ ƒ d k sx t ‚ t  t d	 ƒ ƒ d
 k s– t ‚ t  t d ƒ ƒ d k s´ t ‚ t  t d ƒ ƒ d k sÒ t ‚ t  t d ƒ ƒ d k sð t ‚ t  t d ƒ ƒ d k st ‚ t  t d ƒ ƒ d k s,t ‚ t  t d ƒ ƒ d k sJt ‚ t  t d ƒ ƒ d k sht ‚ t  t d ƒ ƒ d k s†t ‚ t  t d ƒ ƒ d k s¤t ‚ t  t d ƒ ƒ d k sÂt ‚ t  t d ƒ ƒ d k sàt ‚ t  t d  ƒ ƒ d! k sþt ‚ t  t d" ƒ ƒ d# k st ‚ t  t d$ ƒ ƒ d% k s:t ‚ t  t d& ƒ ƒ d' k sXt ‚ t  t d( ƒ ƒ d) k svt ‚ t  t d* ƒ ƒ d+ k s”t ‚ t  t d, ƒ ƒ d- k s²t ‚ t  t d. ƒ ƒ d- k sÐt ‚ t  t d/ ƒ ƒ d0 k sît ‚ t  t d1 ƒ ƒ d2 k st ‚ t  t d3 ƒ ƒ d4 k s*t ‚ t  t d5 ƒ ƒ d6 k sHt ‚ t  t d7 ƒ ƒ d8 k sft ‚ t  t d9 ƒ ƒ d: k s„t ‚ t  t d; ƒ ƒ d< k s¢t ‚ d  S(=   Nt	   Fmathringu   FÌŠt   Fddddotu   Fâƒœt   Fdddotu   Fâƒ›t   Fddotu   FÌˆt   Fdotu   FÌ‡t   Fchecku   FÌŒt   Fbreveu   FÌ†t   Facuteu   FÌt   Fgraveu   FÌ€t   Ftildeu   FÌƒt   Fhatu   FÌ‚t   Fbaru   FÌ…t   Fvecu   Fâƒ—t   Fprimeu   Fâ€²t   Fprmt   Fboldu   Fboldt   Fbmu   Fbmt   Fcalu   Fcalt   Fscru   Fscrt   Ffraku   Ffrakt   Fnormu   â€–Fâ€–t   Favgu   âŸ¨FâŸ©t   Fabsu   |F|t   Fmagt   xvecdotu   xâƒ—Ì‡t   xDotVecu   xÌ‡âƒ—t   xHATNormu	   â€–xÌ‚â€–t   xMathring_yCheckPRM__zbreveAbsu   xÌŠ_yÌŒâ€²__|zÌ†|t    alphadothat_nVECDOT__tTildePrimeu   Î±Ì‡Ì‚_nâƒ—Ì‡__tÌƒâ€²t   x_dotu   x_dott   x__dotu   x__dot(   R£   R(   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_upretty_modifiers>  s>    c          C   s˜   d d l  m }  t |  d d ƒ ƒ d k s1 t ‚ t |  d ƒ ƒ d k sO t ‚ t |  d d ƒ d d	 ƒ ƒ d
 k sy t ‚ t |  ƒ  ƒ d k s” t ‚ d  S(   Niÿÿÿÿ(   t   Cyclei   i   s   (1 2)s   (2)i   i   i   s
   (1 3)(4 5)s   ()(   t    sympy.combinatorics.permutationsRé   R   R¥   (   Ré   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Cycled  s
    !*c    	      C   s[  t  t d ƒ d ƒ d k s# t ‚ t  t d ƒ d ƒ d k sF t ‚ t }  d } t d ƒ } t  |  ƒ | k sv t ‚ t |  ƒ | k sŽ t ‚ t d }  d	 } t d	 ƒ } t  |  ƒ | k sÂ t ‚ t |  ƒ | k sÚ t ‚ d t }  d
 } t d ƒ } t  |  ƒ | k st ‚ t |  ƒ | k s&t ‚ t d }  d } d } t  |  ƒ | k sTt ‚ t |  ƒ | k slt ‚ t t d ƒ d d t	 ƒ}  d } d } t  |  ƒ | k s«t ‚ t |  ƒ | k sÃt ‚ t
 t d }  d } t d ƒ } t  |  ƒ | k sût ‚ t |  ƒ | k st ‚ t t d d ƒ }  d } t d ƒ } t |  d t	 d t	 d t	 ƒ| k sbt ‚ t |  d t d t	 d t	 ƒ| k sŒt ‚ t t d d ƒ }  d } t d ƒ } t  |  ƒ | k sÉt ‚ t |  ƒ | k sát ‚ d t }  d } t d ƒ } t  |  ƒ | k st ‚ t |  ƒ | k s-t ‚ t d d d t	 ƒ}  d } t d ƒ } t  |  ƒ | k slt ‚ t |  ƒ | k s„t ‚ t d t d }  d } d } d } t d ƒ } t d ƒ } t d ƒ } t  |  ƒ | | | g k sít ‚ t |  ƒ | | | g k st ‚ d t }  d  } d! } t d  ƒ } t d! ƒ } t  |  ƒ | | g k sZt ‚ t |  ƒ | | g k sxt ‚ d d t }  d" } d# } t d$ ƒ } t d% ƒ } t  |  ƒ | | g k sÈt ‚ t |  ƒ | | g k sæt ‚ t t
 }  d& } t d' ƒ } t  |  ƒ | k st ‚ t |  ƒ | k s2t ‚ t t
 }  d( } t d) ƒ } t  |  ƒ | k sgt ‚ t |  ƒ | k st ‚ t d t
 }  d* } d+ } t d, ƒ } t d- ƒ } t  |  ƒ | | g k sÏt ‚ t |  ƒ | | g k sít ‚ d t t
 }  d. } d/ } d0 } t d1 ƒ } t d2 ƒ } t d3 ƒ } t  |  ƒ | | | g k sRt ‚ t |  ƒ | | | g k sst ‚ d t t d4 }  d5 } d6 } t d7 ƒ } t d8 ƒ } t  |  ƒ | | g k sÇt ‚ t |  ƒ | | g k såt ‚ t d ƒ d d t }  d9 } t d: ƒ } t  |  ƒ | k s(t ‚ t |  ƒ | k s@t ‚ t d ƒ d d t }  d; } t d< ƒ } t  |  ƒ | k s‚t ‚ t |  ƒ | k sšt ‚ t d ƒ d d t d }  d= } t d> ƒ } t  |  ƒ | k sát ‚ t |  ƒ | k sùt ‚ t d ƒ d d t d }  d? } t d@ ƒ } t  |  ƒ | k s?t ‚ t |  ƒ | k sWt ‚ d  S(A   Ni   i   s   -1/2i   i   s   -13 
----
 22 R/   s   âˆžs    2
x s   1
-
xs   1
â”€
xg      ð¿s    -1.0
x    t   evaluates    -1.0
2    iþÿÿÿs   y 
--
 2
x s   y 
â”€â”€
 2
x i   s	    1/3
x   R   Rž   t   root_notationiûÿÿÿs    1  
----
 5/2
x   s    1  
â”€â”€â”€â”€
 5/2
x   s       x
(-2) s    1
3 s            2
1 + x + x s    2        
x  + x + 1s    2        
x  + 1 + xs   1 - xs   -x + 1s   1 - 2*xs   -2*x + 1s	   1 - 2â‹…xs
   -2â‹…x + 1s   x
-
ys   x
â”€
ys   -x 
---
 y s   -x 
â”€â”€â”€
 y s   2 + x
-----
  y  s   x + 2
-----
  y  s   2 + x
â”€â”€â”€â”€â”€
  y  s   x + 2
â”€â”€â”€â”€â”€
  y  s	   y*(1 + x)s	   (1 + x)*ys	   y*(x + 1)s   yâ‹…(1 + x)s   (1 + x)â‹…ys   yâ‹…(x + 1)i
   s   -5*x  
------
10 + xs   -5*x  
------
x + 10s"   -5â‹…x  
â”€â”€â”€â”€â”€â”€
10 + xs"   -5â‹…x  
â”€â”€â”€â”€â”€â”€
x + 10s
   -3*x - 1/2s   -3â‹…x - 1/2s	   1/2 - 3*xs   1/2 - 3â‹…xs     3*x   1
- --- - -
   2    2s'     3â‹…x   1
- â”€â”€â”€ - â”€
   2    2s   1   3*x
- - ---
2    2 s!   1   3â‹…x
â”€ - â”€â”€â”€
2    2 (   R   R    R¥   R/   t   uR£   t   xR   R$   R    t   yRŸ   R¢   (	   R¡   t	   ascii_strt	   ucode_strt   ascii_str_1t   ascii_str_2t   ascii_str_3t   ucode_str_1t   ucode_str_2t   ucode_str_3(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_basicl  s>   #	
	
	
			
					!!
				
							!!						c          C   s'  t  t }  d } t d ƒ } t |  ƒ | k s5 t ‚ t |  ƒ | k sM t ‚ t  t t }  d } t d ƒ } t |  ƒ | k s† t ‚ t |  ƒ | k sž t ‚ t  d t }  d } t d ƒ } t |  ƒ | k sÖ t ‚ t |  ƒ | k sî t ‚ t  d t }  d } t d	 ƒ } t |  ƒ | k s't ‚ t |  ƒ | k s?t ‚ t  t t }  d
 } t d ƒ } t |  ƒ | k sxt ‚ t |  ƒ | k st ‚ t t d }  d } t d ƒ } t |  ƒ | k sÉt ‚ t |  ƒ | k sát ‚ t t t }  d } t d ƒ } t |  ƒ | k st ‚ t |  ƒ | k s2t ‚ d t d }  d } t d ƒ } t |  ƒ | k sjt ‚ t |  ƒ | k s‚t ‚ d t d }  d } t d ƒ } t |  ƒ | k sºt ‚ t |  ƒ | k sÒt ‚ t	 d d ƒ }  d } t d ƒ } t |  ƒ | k st ‚ t |  ƒ | k s#t ‚ d  S(   Ns   -x 
---
 y s   -x 
â”€â”€â”€
 y s   -x*z 
-----
  y  s   -xâ‹…z 
â”€â”€â”€â”€â”€
  y  i   s    2
x 
--
y s    2
x 
â”€â”€
y s     2 
-x  
----
 y  s     2 
-x  
â”€â”€â”€â”€
 y  s   -x 
---
y*zs   -x 
â”€â”€â”€
yâ‹…zs   -a 
---
  2
 y s   -a 
â”€â”€â”€
  2
 y s    -a 
 ---
  b 
y   s    -a 
 â”€â”€â”€
  b 
y   iÿÿÿÿs   -1 
---
  2
 y s   -1 
â”€â”€â”€
  2
 y iöÿÿÿs   -10 
----
  2 
 b  s   -10 
â”€â”€â”€â”€
  2 
 b  i8ÿÿÿi%   s   -200 
-----
  37 s   -200 
â”€â”€â”€â”€â”€
  37 (
   Rï   Rð   Rî   R   R¥   R£   t   zt   at   bR    (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_negative_fractions  sx    										c           C   s˜   t  t d t d t d ƒ d t d t d ƒ d k sG t ‚ t t d t d t d ƒ d t d t d ƒ t d ƒ k s” t ‚ d  S(   Ni   i   sO            2           /         ___    \
- (5 - y)  + (x - 5)*\-x - 2*\/ 2  + 5/sO            2                          
- (5 - y)  + (x - 5)â‹…(-x - 2â‹…âˆš2 + 5)(   R   Rï   Rg   Rð   R¥   R£   Rî   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_5524ª  s
    88c          C   sZ  t  t d t d d d ƒd k s* t ‚ t  t d t d d d ƒd k sT t ‚ t  d t d d ƒd k sv t ‚ t  d t d d ƒd	 k s˜ t ‚ t  d d t d d ƒd
 k s¾ t ‚ t  d d t d d ƒd k sä t ‚ d t d t d t d t d }  t  |  d d  ƒd k s(t ‚ t  |  d d ƒd k sFt ‚ t  |  d d ƒd k sdt ‚ t t d d t d d t t d ƒ } d } t d ƒ } t  | d d  ƒ| k sÀt ‚ t | d d  ƒ| k sÞt ‚ t  | d d ƒ| k süt ‚ t | d d ƒ| k st ‚ t  | d d ƒ| k s8t ‚ t | d d ƒ| k sVt ‚ d  S(   Ni   i   Rœ   t   lexs    2        
x  + x + 1s   rev-lexs            2
1 + x + x s   -x + 1s   1 - xs   -2*x + 1s   1 - 2*xi   i   s'      4    2    3    2
2*x  - x  + y  + y s'    2    3    2      4
y  + y  - x  + 2*x i   i   ix   sS        3     5        
    x     x     / 6\
x - -- + --- + O\x /
    6    120        se        3     5        
    x     x     âŽ› 6âŽž
x - â”€â”€ + â”€â”€â”€ + OâŽx âŽ 
    6    120        (   R   Rï   R¥   Rð   t   NoneR   Rî   R£   (   R™   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ordering·  s2    ""&&&,	c           C   sJ   t  t ƒ t t ƒ k o# d k n s. t ‚ t t ƒ d k sF t ‚ d  S(   NRA   u   Î³(   R   RA   t   strR¥   R£   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_EulerGammañ  s    .c           C   sJ   t  t ƒ t t ƒ k o# d k n s. t ‚ t t ƒ d k sF t ‚ d  S(   NRB   u   Ï†(   R   RB   R  R¥   R£   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_GoldenRatioõ  s    .c          C   s  t  t t ƒ }  d } t d ƒ } t |  ƒ | k s9 t ‚ t |  ƒ | k sQ t ‚ t t t ƒ }  d } t d ƒ } t |  ƒ | k sŠ t ‚ t |  ƒ | k s¢ t ‚ t t t ƒ }  d } t d ƒ } t |  ƒ | k sÛ t ‚ t |  ƒ | k só t ‚ t	 t t ƒ }  d } t d ƒ } t |  ƒ | k s,t ‚ t |  ƒ | k sDt ‚ t
 t t ƒ }  d } t d ƒ } t |  ƒ | k s}t ‚ t |  ƒ | k s•t ‚ t t t d t d	 ƒ }  d
 } d } t d ƒ } t d ƒ } t |  ƒ | | g k sòt ‚ t |  ƒ | | g k st ‚ d  S(   Ns   x = ys   x < ys   x > ys   x <= ys   x â‰¤ ys   x >= ys   x â‰¥ yi   i   s#     x       2
----- != y 
1 + y      s#     x       2
----- != y 
y + 1      s,     x      2
â”€â”€â”€â”€â”€ â‰  y 
1 + y     s,     x      2
â”€â”€â”€â”€â”€ â‰  y 
y + 1     (   R   Rï   Rð   Rî   R   R¥   R£   R   R   R   R
   R   (   R¡   Rñ   Rò   Ró   Rô   Rö   R÷   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_relationalù  sN    							c          C   sU   t  t t ƒ }  d } t d ƒ } t |  ƒ | k s9 t ‚ t |  ƒ | k sQ t ‚ d  S(   Ns   x := y(   RC   Rï   Rð   Rî   R   R¥   R£   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_AssignmentR  s    	c          C   s™  t  t t ƒ }  d } t d ƒ } t |  ƒ | k s9 t ‚ t |  ƒ | k sQ t ‚ t t t ƒ }  d } t d ƒ } t |  ƒ | k sŠ t ‚ t |  ƒ | k s¢ t ‚ t t t ƒ }  d } t d ƒ } t |  ƒ | k sÛ t ‚ t |  ƒ | k só t ‚ t	 t t ƒ }  d } t d ƒ } t |  ƒ | k s,t ‚ t |  ƒ | k sDt ‚ t
 t t ƒ }  d } t d ƒ } t |  ƒ | k s}t ‚ t |  ƒ | k s•t ‚ d  S(   Ns   x += ys   x -= ys   x *= ys   x /= ys   x %= y(   RD   Rï   Rð   Rî   R   R¥   R£   RE   RF   RG   RH   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_AugmentedAssignment_  s<    					c          C   sö   t  t d t d ƒ }  t d |  d t ƒ} t | ƒ t d ƒ k sJ t ‚ t |  d d t ƒ} t | ƒ t d ƒ k s} t ‚ t |  d d t ƒ} t | ƒ t d ƒ k s° t ‚ t  t d ƒ } t |  | d t ƒ} t | ƒ t d ƒ k sò t ‚ d  S(	   Ni   i   Rì   s9     âŽ›        xâŽž
2â‹…âŽœx + 1 = â”€âŽŸ
  âŽ        2âŽ i   s=       âŽ›        xâŽž
6 + âŽœx + 1 = â”€âŽŸ
    âŽ        2âŽ sA              2
âŽ›        xâŽž 
âŽœx + 1 = â”€âŽŸ 
âŽ        2âŽ  sK   âŽ›        xâŽž        
âŽœx + 1 = â”€âŽŸâ‹…(x = 2)
âŽ        2âŽ         (	   R   Rï   R   R    R£   Rî   R¥   R    R   (   t   et   qt   e2(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_7117œ  s    c          C   s  t  t d }  d } t d ƒ } t |  ƒ | k s8 t ‚ t |  ƒ | k sP t ‚ t  t d d ƒ t t d d ƒ }  d } t d ƒ } t |  ƒ | k sž t ‚ t |  ƒ | k s¶ t ‚ t t ƒ d t t ƒ d }  d	 } t d
 ƒ } t |  ƒ | k sþ t ‚ t |  ƒ | k st ‚ d  S(   Niþÿÿÿs   y 
--
 2
x s   y 
â”€â”€
 2
x i   i   iûÿÿÿs    3/2
y   
----
 5/2
x   s     3/2
y   
â”€â”€â”€â”€
 5/2
x   s'      3   
sin (x)
-------
   2   
tan (x)s5      3   
sin (x)
â”€â”€â”€â”€â”€â”€â”€
   2   
tan (x)(	   Rð   Rï   Rî   R   R¥   R£   R    Rf   Ri   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_rational»  s$    	$		c    	      C   s®  d t  t t  ƒ }  d } d } t d ƒ } t d ƒ } t |  ƒ | | g k sV t ‚ t |  ƒ | | g k st t ‚ t t  ƒ }  d } t d ƒ } t |  ƒ | k sª t ‚ t |  ƒ | k sÂ t ‚ t t  t  d d ƒ }  d	 } d
 } t d ƒ } t d ƒ } t |  ƒ | | g k st ‚ t |  ƒ | | g k s:t ‚ t d t t t  ƒ ƒ }  d } t d ƒ } t |  ƒ | k s~t ‚ t |  ƒ | k s–t ‚ t d d t	 ƒ} t
 | ƒ }  d } t d ƒ } t |  ƒ | k sÞt ‚ t |  ƒ | k söt ‚ t
 d | ƒ }  d } t d ƒ } t |  ƒ | k s0t ‚ t |  ƒ | k sHt ‚ t
 t
 t
 | ƒ ƒ ƒ }  d } t d ƒ } t |  ƒ | k sŠt ‚ t |  ƒ | k s¢t ‚ t
 | d ƒ }  d } d } t d ƒ } t d ƒ } t |  ƒ | | g k sôt ‚ t |  ƒ | | g k st ‚ t | ƒ }  d } t d ƒ } t |  ƒ | k sHt ‚ t |  ƒ | k s`t ‚ t d | ƒ }  d } t d ƒ } t |  ƒ | k sšt ‚ t |  ƒ | k s²t ‚ t d d t	 ƒ} t | ƒ }  d } t d ƒ } t |  ƒ | k sút ‚ t |  ƒ | k st ‚ t d | ƒ }  d } t d ƒ } t |  ƒ | k sLt ‚ t |  ƒ | k sdt ‚ t t t | ƒ ƒ ƒ }  d } t d ƒ } t |  ƒ | k s¦t ‚ t |  ƒ | k s¾t ‚ t | d ƒ }  d } d } t d ƒ } t d ƒ } t |  ƒ | | g k st ‚ t |  ƒ | | g k s.t ‚ d t | t ƒ }  d  } t d! ƒ } t |  ƒ | k skt ‚ t |  ƒ | k sƒt ‚ d t d | t ƒ }  d" } t d# ƒ } t |  ƒ | k sÄt ‚ t |  ƒ | k sÜt ‚ d t | d t ƒ }  d$ } t d% ƒ } t |  ƒ | k st ‚ t |  ƒ | k s5t ‚ t | ƒ }  d& } t d& ƒ } t |  ƒ | k skt ‚ t |  ƒ | k sƒt ‚ t | ƒ }  d& } t d& ƒ } t |  ƒ | k s¹t ‚ t |  ƒ | k sÑt ‚ t | ƒ }  d' } t d' ƒ } t |  ƒ | k st ‚ t |  ƒ | k st ‚ t | ƒ }  d' } t d' ƒ } t |  ƒ | k sUt ‚ t |  ƒ | k smt ‚ t | ƒ }  d( } t d( ƒ } t |  ƒ | k s£t ‚ t |  ƒ | k s»t ‚ t | ƒ }  d) } t d) ƒ } t |  ƒ | k sñt ‚ t |  ƒ | k s	t ‚ t | ƒ }  d* } t d* ƒ } t |  ƒ | k s?t ‚ t |  ƒ | k sWt ‚ t t  ƒ }  d+ } t d+ ƒ } t |  ƒ | k st ‚ t |  ƒ | k s¥t ‚ t d, ƒ } t | t  d ƒ ƒ }  d- } d. } t d- ƒ } t d. ƒ } t |  ƒ | | g k s		t ‚ t |  ƒ | | g k s'	t ‚ | t  ƒ }  d/ } t d/ ƒ } t |  ƒ | k s]	t ‚ t |  ƒ | k su	t ‚ | t  t ƒ }  d0 } t d0 ƒ } t |  ƒ | k s®	t ‚ t |  ƒ | k sÆ	t ‚ | t  t d t ƒ }  d1 } d2 } t d3 ƒ } t d4 ƒ } t |  ƒ | | g k s
t ‚ t |  ƒ | | g k s=
t ‚ | t  t  t  t  t  t  ƒ }  d5 } t d6 ƒ } t |  ƒ | k s‡
t ‚ t |  ƒ | k sŸ
t ‚ t t  ƒ d }  d7 } t d7 ƒ } t |  ƒ | k sÙ
t ‚ t |  ƒ | k sñ
t ‚ t t t t ƒ }  d8 } t d9 ƒ } t |  ƒ | k s/t ‚ t |  ƒ | k sGt ‚ t t t t t ƒ ƒ }  d: } t d; ƒ } t |  ƒ | k s‹t ‚ t |  ƒ | k s£t ‚ t | d t | t  ƒ ƒ ƒ ƒ }  d< } d= } t d> ƒ } t d? ƒ } t |  ƒ | | g k st ‚ t |  ƒ | | g k s%t ‚ | t  t d t ƒ }  d1 } d2 } t d3 ƒ } t d4 ƒ } t |  ƒ | | g k s~t ‚ t |  ƒ | | g k sœt ‚ t d t t t  ƒ ƒ }  d@ } t dA ƒ } t |  ƒ | k sàt ‚ t |  ƒ | k søt ‚ t d t t t  ƒ ƒ }  dB } t dC ƒ } t |  ƒ | k s<t ‚ t |  ƒ | k sTt ‚ t | ƒ }  dD } t dD ƒ } t |  ƒ | k sŠt ‚ t |  ƒ | k s¢t ‚ t d d d d d | ƒ }  dE } t dF ƒ } t |  ƒ | k sìt ‚ t |  ƒ | k st ‚ t | t  ƒ }  dG } t dG ƒ } t |  ƒ | k s=t ‚ t |  ƒ | k sUt ‚ t | t  d ƒ }  dH } t dI ƒ } t |  ƒ | k s’t ‚ t |  ƒ | k sªt ‚ dJ S(K   s>   Tests for Abs, conjugate, exp, function braces, and factorial.i   s          x
2*x + e s    x      
e  + 2*xs          x
2â‹…x + â„¯ s    x     
â„¯ + 2â‹…xs   |x|s   â”‚xâ”‚i   s#   |  x   |
|------|
|     2|
|1 + x |s#   |  x   |
|------|
| 2    |
|x  + 1|s?   â”‚  x   â”‚
â”‚â”€â”€â”€â”€â”€â”€â”‚
â”‚     2â”‚
â”‚1 + x â”‚s?   â”‚  x   â”‚
â”‚â”€â”€â”€â”€â”€â”€â”‚
â”‚ 2    â”‚
â”‚x  + 1â”‚s   |   1   |
|-------|
|y - |x||s;   â”‚   1   â”‚
â”‚â”€â”€â”€â”€â”€â”€â”€â”‚
â”‚y - â”‚xâ”‚â”‚t   nt   integers   n!s   (2*n)!s   (2â‹…n)!s   ((n!)!)!s   (1 + n)!s   (n + 1)!s   !ns   !(2*n)s   !(2â‹…n)s   n!!s   (2*n)!!s	   (2â‹…n)!!s   ((n!!)!!)!!s	   (1 + n)!!s	   (n + 1)!!s     /n\
2*| |
  \k/s     âŽ›nâŽž
2â‹…âŽœ âŽŸ
  âŽkâŽ s     /2*n\
2*|   |
  \ k /s'     âŽ›2â‹…nâŽž
2â‹…âŽœ   âŽŸ
  âŽ k âŽ s     / 2\
  |n |
2*|  |
  \k /s-     âŽ› 2âŽž
  âŽœn âŽŸ
2â‹…âŽœ  âŽŸ
  âŽk âŽ s   C 
 ns   B 
 ns   F 
 ns   L 
 ns   T 
 ns   _
xR™   s   ________
f(1 + x)s   ________
f(x + 1)s   f(x)s   f(x, y)s#    /  x     \
f|-----, y|
 \1 + y   /s#    /  x     \
f|-----, y|
 \y + 1   /s9    âŽ›  x     âŽž
fâŽœâ”€â”€â”€â”€â”€, yâŽŸ
 âŽ1 + y   âŽ s9    âŽ›  x     âŽž
fâŽœâ”€â”€â”€â”€â”€, yâŽŸ
 âŽy + 1   âŽ sk    / / / / / x\\\\\
 | | | | \x /||||
 | | | \x    /|||
 | | \x       /||
 | \x          /|
f\x             /s»    âŽ› âŽ› âŽ› âŽ› âŽ› xâŽžâŽžâŽžâŽžâŽž
 âŽœ âŽœ âŽœ âŽœ âŽx âŽ âŽŸâŽŸâŽŸâŽŸ
 âŽœ âŽœ âŽœ âŽx    âŽ âŽŸâŽŸâŽŸ
 âŽœ âŽœ âŽx       âŽ âŽŸâŽŸ
 âŽœ âŽx          âŽ âŽŸ
fâŽx             âŽ s      2   
sin (x)s   _     _
a - I*bs   _     _
a - â…ˆâ‹…bs    _     _
 a - I*b
e       s     _     _
 a - â…ˆâ‹…b
â„¯       s#   ___________
 /    ____\
f\1 + f(x)/s#   ___________
 /____    \
f\f(x) + 1/s+   ___________
 âŽ›    ____âŽž
fâŽ1 + f(x)âŽ s+   ___________
 âŽ›____    âŽž
fâŽf(x) + 1âŽ s;        /     1      \
floor|------------|
     \y - floor(x)/s;   âŽ¢   1   âŽ¥
âŽ¢â”€â”€â”€â”€â”€â”€â”€âŽ¥
âŽ£y - âŒŠxâŒ‹âŽ¦sG          /      1       \
ceiling|--------------|
       \y - ceiling(x)/s;   âŽ¡   1   âŽ¤
âŽ¢â”€â”€â”€â”€â”€â”€â”€âŽ¥
âŽ¢y - âŒˆxâŒ‰âŽ¥s   E 
 nsW   E         
     1    
 ---------
       1  
 1 + -----
         1
     1 + -
         nsu   E         
     1    
 â”€â”€â”€â”€â”€â”€â”€â”€â”€
       1  
 1 + â”€â”€â”€â”€â”€
         1
     1 + â”€
         ns   E (x)
 n   s     /x\
E |-|
 n\2/s     âŽ›xâŽž
E âŽœâ”€âŽŸ
 nâŽ2âŽ N(   Rï   R]   Rî   R   R¥   R£   RN   Rð   R(   R¢   R_   Rh   R`   RX   t   kRY   Rq   Rr   Rs   Ru   Rt   R-   R	   Rf   Rû   Rü   R   Ra   RZ   R\   (	   R¡   Ró   Rô   Rö   R÷   Rñ   Rò   R  R™   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_functions÷  s"   																																			 					"							 				c          C   sÝ  t  d ƒ }  d } d } t |  ƒ | k s0 t ‚ t |  ƒ | k sH t ‚ d t d d ƒ }  d } t d ƒ } t |  ƒ | k s… t ‚ t |  ƒ | k s t ‚ d t d d ƒ }  d	 } t d
 ƒ } t |  ƒ | k sÚ t ‚ t |  ƒ | k sò t ‚ t  t d d ƒ }  d } t d ƒ } t |  ƒ | k s0t ‚ t |  ƒ | k sHt ‚ d t  d ƒ t d d ƒ }  d } t d ƒ } t |  ƒ | k st ‚ t |  ƒ | k s§t ‚ d d t }  d } t d ƒ } t |  ƒ | k sßt ‚ t |  ƒ | k s÷t ‚ t  d t ƒ }  d } t d ƒ } t |  ƒ | k s1t ‚ t |  ƒ | k sIt ‚ d d t d d t t d d ƒ d t t d d ƒ t  d t d ƒ }  d } t d ƒ } t |  ƒ | k sÁt ‚ t |  ƒ | k sÙt ‚ d  S(   Ni   s     ___
\/ 2 u   âˆš2i   i   s   3 ___
\/ 2 s   3 ___
â•²â•± 2 iè  s   1000___
  \/ 2 s   1000___
  â•²â•± 2 s#      ________
  /  2     
\/  x  + 1 s)      ________
  â•±  2     
â•²â•±  x  + 1 i   s,      ___________
3 /       ___ 
\/  1 + \/ 5  s   3 ________
â•²â•± 1 + âˆš5 s   x ___
\/ 2 s   x ___
â•²â•± 2 s     ________
\/ 2 + pi s     _______
â•²â•± 2 + Ï€ i   sß        ____________              
    /      2        1000___    
   /      x  + 1      \/ x  + 1
4 /   2 + ------  + -----------
\/        x + 2        ________
                      /  2     
                    \/  x  + 3 s       ____________              
    â•±      2        1000___    
   â•±      x  + 1      â•²â•± x  + 1
4 â•±   2 + â”€â”€â”€â”€â”€â”€  + â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€
â•²â•±        x + 2        ________
                      â•±  2     
                    â•²â•±  x  + 3 (   Rg   R   R¥   R£   R    Rî   Rï   R0   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_sqrt­  s`    						K
	c          C   sj   t  d ƒ }  t d ƒ } d } t |  d t d t ƒ| k sB t ‚ t |  d t d t ƒ| k sf t ‚ d  S(   Ni   s     ___
â•²â•± 2 u   âˆš2R   t   use_unicode_sqrt_char(   Rg   Rî   RŸ   R¢   R    R¥   (   R¡   t
   ucode_str1t
   ucode_str2(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_sqrt_char_knob*  s    	c          C   s:   t  t d ƒ ƒ }  t d ƒ } t |  ƒ | k s6 t ‚ d  S(   Nt   C1s     ____
â•²â•± Câ‚ (   Rg   R(   Rî   R£   R¥   (   R¡   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt(   test_pretty_sqrt_longsymbol_no_sqrt_char:  s    	c          C   sg   t  d ƒ \ }  } t |  | ƒ } d } t d ƒ } t | ƒ | k sK t ‚ t | ƒ | k sc t ‚ d  S(   Ns   x, ys	   d   
 x,ys
   Î´   
 x,y(   R1   RR   Rî   R   R¥   R£   (   Rï   Rð   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_KroneckerDeltaE  s    	c          C   sâ   t  d ƒ \ }  } } } t  d d t ƒ} t | |  d d ƒ |  | d | f ƒ } t d ƒ } d } t | |  d d ƒ |  | d | f | d | f ƒ } t d	 ƒ } d
 } t | ƒ | k sÆ t ‚ t | ƒ | k sÞ t ‚ d  S(   Ns   n m k lR™   t   clsi   i   sÔ       l           
â”€â”¬â”€â”€â”€â”€â”€â”€â”¬â”€      
 â”‚      â”‚   âŽ› 2âŽž
 â”‚      â”‚   âŽœn âŽŸ
 â”‚      â”‚  fâŽœâ”€â”€âŽŸ
 â”‚      â”‚   âŽ9 âŽ 
 â”‚      â”‚       
       2        
  n = k         s˜       l           
__________      
 |      |   / 2\
 |      |   |n |
 |      |  f|--|
 |      |   \9 /
 |      |       
       2        
  n = k         i   s_      m          l           
â”€â”¬â”€â”€â”€â”€â”€â”€â”¬â”€ â”€â”¬â”€â”€â”€â”€â”€â”€â”¬â”€      
 â”‚      â”‚   â”‚      â”‚   âŽ› 2âŽž
 â”‚      â”‚   â”‚      â”‚   âŽœn âŽŸ
 â”‚      â”‚   â”‚      â”‚  fâŽœâ”€â”€âŽŸ
 â”‚      â”‚   â”‚      â”‚   âŽ9 âŽ 
 â”‚      â”‚   â”‚      â”‚       
  l = 1           2        
             n = k         sû       m          l           
__________ __________      
 |      |   |      |   / 2\
 |      |   |      |   |n |
 |      |   |      |  f|--|
 |      |   |      |   \9 /
 |      |   |      |       
  l = 1           2        
             n = k         (   R1   R	   R   Rî   R   R¥   R£   (   R  t   mR  t   lR™   R¡   t   unicode_strRñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_productV  s    *		6		c          C   sà  t  t t ƒ }  t |  ƒ d k s' t ‚ t |  ƒ d k s? t ‚ t  t t d ƒ }  t |  ƒ d k sj t ‚ t |  ƒ d k s‚ t ‚ t  t t d ƒ }  d } t d ƒ } t |  ƒ | k s¿ t ‚ t |  ƒ | k s× t ‚ t  t t d ƒ d }  d	 } t d
 ƒ } t |  ƒ | k st ‚ t |  ƒ | k s0t ‚ t  t t f t ƒ }  d } d } t |  ƒ | k sit ‚ t |  ƒ | k st ‚ t  t t f t d ƒ }  d } t d ƒ } t |  ƒ | k sÄt ‚ t |  ƒ | k sÜt ‚ d  S(   Ns   x -> xu   x â†¦ xi   s
   x -> x + 1u   x â†¦ x + 1i   s         2
x -> x s        2
x â†¦ x s             2
/      2\ 
\x -> x / s'           2
âŽ›     2âŽž 
âŽx â†¦ x âŽ  s   (x, y) -> xu   (x, y) â†¦ xs              2
(x, y) -> x s             2
(x, y) â†¦ x (   R   Rð   R   R¥   R£   Rï   Rî   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_lambda  s:    			c          C   s  t  d ƒ }  d } t d ƒ } t |  ƒ | k s6 t ‚ t |  ƒ | k sN t ‚ t  d t ƒ }  d } t d ƒ } t |  ƒ | k sˆ t ‚ t |  ƒ | k s  t ‚ t  t d t d ƒ }  d } t d ƒ } t |  ƒ | k sâ t ‚ t |  ƒ | k sú t ‚ t  d t t f ƒ }  d } t d	 ƒ } t |  ƒ | k s9t ‚ t |  ƒ | k sQt ‚ t  d t t t f ƒ }  d
 } t d ƒ } t |  ƒ | k s”t ‚ t |  ƒ | k s¬t ‚ t  t d t d t t f t t f ƒ }  d } t d ƒ } t |  ƒ | k s t ‚ t |  ƒ | k st ‚ d  S(   Ni   s   O(1)s    /1\
O|-|
 \x/s    âŽ›1âŽž
OâŽœâ”€âŽŸ
 âŽxâŽ i   s9    / 2    2                  \
O\x  + y ; (x, y) -> (0, 0)/sA    âŽ› 2    2                 âŽž
OâŽx  + y ; (x, y) â†’ (0, 0)âŽ s   O(1; x -> oo)s   O(1; x â†’ âˆž)s)    /1         \
O|-; x -> oo|
 \x         /s5    âŽ›1       âŽž
OâŽœâ”€; x â†’ âˆžâŽŸ
 âŽx       âŽ s=    / 2    2                    \
O\x  + y ; (x, y) -> (oo, oo)/sE    âŽ› 2    2                 âŽž
OâŽx  + y ; (x, y) â†’ (âˆž, âˆž)âŽ (   R   Rî   R   R¥   R£   Rï   Rð   R/   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_orderÌ  sH    					*	c    	      C   sN  t  t t ƒ t d t ƒ}  d } t d ƒ } t |  ƒ | k sE t ‚ t |  ƒ | k s] t ‚ t  t t ƒ t d t ƒt }  d } d } t d ƒ } t d ƒ } t |  ƒ | | g k s¾ t ‚ t |  ƒ | | g k sÜ t ‚ t  t t t ƒ t t ƒ }  d } d	 } t d
 ƒ } t d ƒ } t |  ƒ | | g k s;t ‚ t |  ƒ | | g k set t |  ƒ ƒ ‚ t  t t ƒ t d t t ƒ }  d } d } t d ƒ } t d ƒ } t |  ƒ | | g k sÇt ‚ t |  ƒ | | g k såt ‚ t  d t t t t ƒ t d }  d } d } t d ƒ } t d ƒ } t |  ƒ | | g k sIt ‚ t |  ƒ | | g k sgt ‚ t  d t t t t ƒ }  d } t d ƒ } t |  ƒ | k s«t ‚ t |  ƒ | k sÃt ‚ t  d t t t d ƒ }  d } t d ƒ } t |  ƒ | k st ‚ t |  ƒ | k st ‚ t  d t t t t t ƒ }  d } t d ƒ } t |  ƒ | k sft ‚ t |  ƒ | k s~t ‚ t	 d ƒ } t
 d ƒ } | | ƒ j | ƒ }  d } t d ƒ } t |  ƒ | k sÕt ‚ t |  ƒ | k sít ‚ t  t t ƒ t t f ƒ }  d  } t d! ƒ } t |  ƒ | k s2t ‚ t |  ƒ | k sJt ‚ d  S("   NRì   s    d         
--(log(x))
dx        s$   d         
â”€â”€(log(x))
dx        s,       d         
x + --(log(x))
    dx        s,   d             
--(log(x)) + x
dx            s0       d         
x + â”€â”€(log(x))
    dx        s0   d             
â”€â”€(log(x)) + x
dx            s8   d                 
--(log(x + y) + x)
dx                s8   d                 
--(x + log(x + y))
dx                s@   âˆ‚                 
â”€â”€(log(x + y) + x)
âˆ‚x                s@   âˆ‚                 
â”€â”€(x + log(x + y))
âˆ‚x                i   sK      2              
  d  /          2\
-----\log(x) + x /
dy dx             sK      2              
  d  / 2         \
-----\x  + log(x)/
dy dx             s]      2              
  d  âŽ›          2âŽž
â”€â”€â”€â”€â”€âŽlog(x) + x âŽ 
dy dx             s]      2              
  d  âŽ› 2         âŽž
â”€â”€â”€â”€â”€âŽx  + log(x)âŽ 
dy dx             sG      2             
  d             2
-----(2*x*y) + x 
dx dy            sG           2        
 2     d         
x  + -----(2*x*y)
     dx dy       s[      2             
  âˆ‚             2
â”€â”€â”€â”€â”€(2â‹…xâ‹…y) + x 
âˆ‚x âˆ‚y            s[           2        
 2     âˆ‚         
x  + â”€â”€â”€â”€â”€(2â‹…xâ‹…y)
     âˆ‚x âˆ‚y       s6     2       
 d        
---(2*x*y)
  2       
dx        sD     2       
 âˆ‚        
â”€â”€â”€(2â‹…xâ‹…y)
  2       
âˆ‚x        i   s;    17        
d          
----(2*x*y)
  17       
dx         sK    17        
âˆ‚          
â”€â”€â”€â”€(2â‹…xâ‹…y)
  17       
âˆ‚x         sE      3         
  d          
------(2*x*y)
     2       
dy dx        s[      3         
  âˆ‚          
â”€â”€â”€â”€â”€â”€(2â‹…xâ‹…y)
     2       
âˆ‚y âˆ‚x        t   alphaRW   s;     d                
------(beta(alpha))
dalpha             s!   d       
â”€â”€(Î²(Î±))
dÎ±      s1     n      
 d       
---(f(x))
  n      
dx       s7     n      
 d       
â”€â”€â”€(f(x))
  n      
dx       (   R   Rd   Rï   R    Rî   R   R¥   R£   Rð   R(   R	   t   diffR™   R  (	   R¡   Rñ   Rò   Ró   Rô   Rö   R÷   R   RW   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_derivatives"	  s”    					* 		"								c          C   s  t  t t ƒ t ƒ }  d } t d ƒ } t |  ƒ | k s? t ‚ t |  ƒ | k sW t ‚ t  t d t ƒ }  d } t d ƒ } t |  ƒ | k s” t ‚ t |  ƒ | k s¬ t ‚ t  t t ƒ d t t ƒ d ƒ }  d } t d ƒ } t |  ƒ | k sú t ‚ t |  ƒ | k st ‚ t  t d t t ƒ }  d } t d	 ƒ } t |  ƒ | k sSt ‚ t |  ƒ | k skt ‚ t  t d t d
 d f ƒ }  d } t d ƒ } t |  ƒ | k s±t ‚ t |  ƒ | k sÉt ‚ t  t d t t	 d
 d ƒ d f ƒ }  d } t d ƒ } t |  ƒ | k st ‚ t |  ƒ | k s0t ‚ t  t d t
 d t t
 ƒ }  d } t d ƒ } t |  ƒ | k sxt ‚ t |  ƒ | k st ‚ t  t t ƒ t t ƒ t d t f t d d t f ƒ }  d } t d ƒ } t |  ƒ | k sòt ‚ t |  ƒ | k s
t ‚ d  S(   Ns@     /         
 |          
 | log(x) dx
 |          
/           s)   âŒ           
âŽ® log(x) dx
âŒ¡          i   s5     /     
 |      
 |  2   
 | x  dx
 |      
/       s'   âŒ       
âŽ®  2   
âŽ® x  dx
âŒ¡      s}     /          
 |           
 |    2      
 | sin (x)   
 | ------- dx
 |    2      
 | tan (x)   
 |           
/            sv   âŒ            
âŽ®    2      
âŽ® sin (x)   
âŽ® â”€â”€â”€â”€â”€â”€â”€ dx
âŽ®    2      
âŽ® tan (x)   
âŒ¡           sS     /        
 |         
 |  / x\   
 |  \2 /   
 | x     dx
 |         
/          sH   âŒ          
âŽ®  âŽ› xâŽž   
âŽ®  âŽ2 âŽ    
âŽ® x     dx
âŒ¡         i   sO     2      
  /      
 |       
 |   2   
 |  x  dx
 |       
/        
1        s7   2      
âŒ       
âŽ®  2   
âŽ® x  dx
âŒ¡      
1      i
   sO    10      
  /      
 |       
 |   2   
 |  x  dx
 |       
/        
1/2      sC    10      
 âŒ        
 âŽ®   2   
 âŽ®  x  dx
 âŒ¡       
1/2      sk     /  /           
 |  |            
 |  |  2  2      
 |  | x *y  dx dy
 |  |            
/  /             sQ   âŒ  âŒ             
âŽ® âŽ®  2  2      
âŽ® âŽ® x â‹…y  dx dy
âŒ¡ âŒ¡            i    sC   2*pi pi                           
   /   /                           
  |   |                            
  |   |  sin(theta)                
  |   |  ---------- d(theta) d(phi)
  |   |   cos(phi)                 
  |   |                            
 /   /                             
 0   0                             s¬   2â‹…Ï€ Ï€             
 âŒ   âŒ              
 âŽ®  âŽ® sin(Î¸)      
 âŽ®  âŽ® â”€â”€â”€â”€â”€â”€ dÎ¸ dÏ†
 âŽ®  âŽ® cos(Ï†)      
 âŒ¡  âŒ¡             
 0  0             (   R   Rd   Rï   Rî   R   R¥   R£   Rf   Ri   R    Rð   t   thR[   t   phR0   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_integrals
  s`    			$	
		%			8	c          C   sí  t  ƒ  }  d } d } t |  ƒ | k s- t ‚ t |  ƒ | k sE t ‚ t  d d d „  ƒ }  d } d } t |  ƒ | k s~ t ‚ t |  ƒ | k s– t ‚ t  d d d „  ƒ }  d } d } t |  ƒ | k sÏ t ‚ t |  ƒ | k sç t ‚ t  t d d d g t t t g g ƒ }  d } d } t d	 ƒ } t d
 ƒ } t |  ƒ | | g k sSt ‚ t |  ƒ | | g k sqt ‚ t  t t t t g d t t	 t
 t ƒ d g g ƒ }  d } t d ƒ } t |  ƒ | k sÑt ‚ t |  ƒ | k sét ‚ d  S(   Ns   []i   i    c         S   s   d S(   Ni    (    (   t   it   j(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   <lambda>Ð
  t    c         S   s   d S(   Ni    (    (   R&  R'  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR(  Õ
  R)  i   s?   [     2       ]
[1 + x     1  ]
[             ]
[  y     x + y]s?   [ 2           ]
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âŽ¢             âŽ¥
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âŽ¢x  + 1    1  âŽ¥
âŽ¢             âŽ¥
âŽ£  y     x + yâŽ¦s}   [x                 ]
[-     y      theta]
[y                 ]
[                  ]
[    I*k*phi       ]
[0  e           1  ]s}   âŽ¡x           âŽ¤
âŽ¢â”€    y     Î¸âŽ¥
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âŽ¢    â…ˆâ‹…kâ‹…Ï†   âŽ¥
âŽ£0  â„¯       1âŽ¦(   R   R   R¥   R£   Rï   Rð   Rî   R#  R]   R   R  R$  (   R¡   Rñ   R  Ró   Rô   Rö   R÷   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_matrixÉ
  s<    	*		6		c          C   sï  t  d ƒ \ }  } } } xÐt t t t f D]¼} | |  ƒ } t | ƒ d k sU t ‚ t | ƒ d k sm t ‚ | d |  | g | | g g ƒ } | d |  | | g ƒ } t | | ƒ } t | | ƒ } d }	 t	 d ƒ }
 t | ƒ |	 k sð t ‚ t | ƒ |
 k st ‚ d }	 t	 d ƒ }
 t | ƒ |	 k s2t ‚ t | ƒ |
 k sJt ‚ d }	 t	 d	 ƒ }
 t | ƒ |	 k stt ‚ t | ƒ |
 k sŒt ‚ d
 }	 t	 d ƒ }
 t | ƒ |	 k s¶t ‚ t | ƒ |
 k sÎt ‚ | |  | d | g g ƒ } | |  g | g d | g g ƒ } | | j
 ƒ  g ƒ } d }	 t	 d ƒ }
 t | ƒ |	 k sKt ‚ t | ƒ |
 k sct ‚ d }	 t	 d ƒ }
 t | ƒ |	 k st ‚ t | ƒ |
 k s¥t ‚ d }	 t	 d ƒ }
 t | ƒ |	 k sÏt ‚ t | ƒ |
 k s+ t ‚ q+ Wd  S(   Ns   x y z wRï   i   s"   [1   ]
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âŽ¢â”€  y  zâŽ¥
âŽ£x      âŽ¦s  [[1   y]                       ]
[[--  -]              [z      ]]
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[[x    ]  [ -   y  ]  [x      ]]
[[     ]  [ x      ]  [       ]]
[[z   w]  [        ]  [ 2     ]]
[[-   -]  [y*z  w*y]  [z   w*z]]
[[x   x]                       ]s‰  âŽ¡âŽ¡1   yâŽ¤                       âŽ¤
âŽ¢âŽ¢â”€â”€  â”€âŽ¥              âŽ¡z      âŽ¤âŽ¥
âŽ¢âŽ¢ 2  xâŽ¥  âŽ¡ y    2 âŽ¤  âŽ¢â”€   yâ‹…zâŽ¥âŽ¥
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âŽ¢âŽ¢z   wâŽ¥  âŽ¢        âŽ¥  âŽ¢ 2     âŽ¥âŽ¥
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âŽ£âŽ£x   xâŽ¦                       âŽ¦sg  [ [1   y]             ]
[ [--  -]             ]
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[ [x    ]   [ -   y  ]]
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[[z      ]  [ w      ]]
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[[z   w*z]  [w*z  w  ]]s#  âŽ¡ âŽ¡1   yâŽ¤             âŽ¤
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[[x  y  -]]
[[      z]]s=   âŽ¡âŽ¡      1âŽ¤âŽ¤
âŽ¢âŽ¢x  y  â”€âŽ¥âŽ¥
âŽ£âŽ£      zâŽ¦âŽ¦s   [x]
[ ]
[y]
[ ]
[1]
[-]
[z]s9   âŽ¡xâŽ¤
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âŽ¢â”€âŽ¥
âŽ£zâŽ¦s)   [[x]]
[[ ]]
[[y]]
[[ ]]
[[1]]
[[-]]
[[z]]sc   âŽ¡âŽ¡xâŽ¤âŽ¤
âŽ¢âŽ¢ âŽ¥âŽ¥
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âŽ¢âŽ¢â”€âŽ¥âŽ¥
âŽ£âŽ£zâŽ¦âŽ¦(   R1   Rƒ   R„   R…   R†   R   R¥   R£   R‡   Rî   t   tolist(   Rï   Rð   Rú   t   wt	   ArrayTypet   Mt   M1t   M2t   M3Rñ   Rò   t   Mrowt   Mcolumnt   Mcol2(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ndim_arrays  s^    "						"			c          C   sm   t  d d d ƒ }  t  d d d ƒ } t t |  | ƒ ƒ d k sE t ‚ t t |  | |  ƒ ƒ d k si t ‚ d  S(   Nt   Ai   t   Bs   A\u2297Bs   A\u2297B\u2297A(   Rx   R£   Rˆ   R¥   (   R6  R7  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_tensor_TensorProductÅ  s    !c          C   sW   d d l  m }  d d l m } | |  j |  j ƒ } t | ƒ t d ƒ k sS t ‚ d  S(   Niÿÿÿÿ(   t   R2(   t   WedgeProducts   â…† xâˆ§â…† y(	   t   sympy.diffgeom.rnR9  t   sympy.diffgeomR:  t   dxt   dyR£   Rî   R¥   (   R9  R:  t   wp(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt    test_diffgeom_print_WedgeProductÌ  s    c          C   s4  t  d d d ƒ }  t  d d d ƒ } t t |  ƒ ƒ d k sB t ‚ t t |  | ƒ ƒ d k sd t ‚ t t |  ƒ t | ƒ ƒ d k sŒ t ‚ t t |  | ƒ ƒ d k s® t ‚ t t | ƒ t |  ƒ ƒ d k sÖ t ‚ t t |  d ƒ ƒ d	 k sø t ‚ t t |  ƒ d ƒ d
 k st ‚ t t t |  ƒ ƒ ƒ d k s>t ‚ t t t |  ƒ ƒ ƒ d k sbt ‚ t t t |  ƒ ƒ ƒ d k s†t ‚ t t t |  ƒ ƒ ƒ d k sªt ‚ t t |  ƒ ƒ d k sÈt ‚ t t |  | ƒ ƒ d k sêt ‚ t t |  ƒ t | ƒ ƒ d k st ‚ t t |  | ƒ ƒ d k s4t ‚ t t | ƒ t |  ƒ ƒ d k s\t ‚ t t |  d ƒ ƒ d k s~t ‚ t t |  ƒ d ƒ d k s t ‚ t t t |  ƒ ƒ ƒ d k sÄt ‚ t t t |  ƒ ƒ ƒ d k sèt ‚ t t t |  ƒ ƒ ƒ d k st ‚ t t t |  ƒ ƒ ƒ d k s0t ‚ d  S(   Nt   Xi   t   Ys    +
X s          +
(X + Y) s    +    +
X  + Y s        +
(X*Y) s    +  +
Y *X s       +
/ 2\ 
\X / s       2
/ +\ 
\X / s        +
/ -1\ 
\X  / s       -1
/ +\  
\X /  s       +
/ T\ 
\X / s       T
/ +\ 
\X / u    â€ 
X u          â€ 
(X + Y) u    â€     â€ 
X  + Y u        â€ 
(Xâ‹…Y) u    â€   â€ 
Y â‹…X u       â€ 
âŽ› 2âŽž 
âŽX âŽ  u       2
âŽ› â€ âŽž 
âŽX âŽ  u        â€ 
âŽ› -1âŽž 
âŽX  âŽ  u       -1
âŽ› â€ âŽž  
âŽX âŽ   u       â€ 
âŽ› TâŽž 
âŽX âŽ  u       T
âŽ› â€ âŽž 
âŽX âŽ  (   Rx   R   Rv   R¥   Rw   Ry   R£   (   RA  RB  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_AdjointÓ  s<    "("(""$$$$"("(c          C   sð   t  d d g d d g g ƒ }  t  d d g d d g g ƒ } d } t d ƒ } d	 } t d
 ƒ } t t |  ƒ ƒ | k s~ t ‚ t t |  ƒ ƒ | k sœ t ‚ t t |  ƒ t | ƒ ƒ | k sÄ t ‚ t t |  ƒ t | ƒ ƒ | k sì t ‚ d  S(   Ni   i   i   i   i   i   s      /[1  2]\
tr|[    ]|
  \[3  4]/s8     âŽ›âŽ¡1  2âŽ¤âŽž
trâŽœâŽ¢    âŽ¥âŽŸ
  âŽâŽ£3  4âŽ¦âŽ sG     /[1  2]\     /[2  4]\
tr|[    ]| + tr|[    ]|
  \[3  4]/     \[6  8]/sw     âŽ›âŽ¡1  2âŽ¤âŽž     âŽ›âŽ¡2  4âŽ¤âŽž
trâŽœâŽ¢    âŽ¥âŽŸ + trâŽœâŽ¢    âŽ¥âŽŸ
  âŽâŽ£3  4âŽ¦âŽ      âŽâŽ£6  8âŽ¦âŽ (   R   Rî   R   R*   R¥   R£   (   RA  RB  Ró   Rö   Rô   R÷   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Trace_issue_9044ó  s    		(c          C   sÿ   t  d d t ƒ}  t d |  |  ƒ } t | ƒ t | ƒ k oG d k n sR t ‚ | d d d … d d d	 … f } d
 } } t | ƒ | k s– t ‚ t | ƒ | k s® t ‚ | d d d … } d } } t | ƒ | k sã t ‚ t | ƒ | k sû t ‚ d  S(   NR  R  RA  i   i   i   i   i   i   s   X[1:3, 4:6]i
   s   X[1:10:2, :n](   R(   R¢   Rx   R   R£   R¥   (   R  RA  RB  Rñ   Rò   t   Z(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_MatrixExpressions  s    ."

c          C   s  d d l  m }  m } d d l m } t d d t ƒ} | d | d ƒ } | d | d ƒ } |  d d	 d d
 d	 g ƒ } |  d d	 d d	 d g ƒ } t | | | ƒ ƒ d k s³ t ‚ t | | | ƒ ƒ d k sÔ t ‚ t	 | | | ƒ ƒ d k sõ t ‚ t	 | | | ƒ ƒ d k st ‚ d  S(   Niÿÿÿÿ(   R   Rx   (   t
   DotProductR  R  R6  i   R7  i   i   i   u   A*Bu   [1  2  3]*[1  3  4]u   Aâ‹…Bu   [1  2  3]â‹…[1  3  4](
   t   sympy.matricesR   Rx   t%   sympy.matrices.expressions.dotproductRG  R1   R¢   R   R¥   R£   (   R   Rx   RG  R  R6  R7  t   Ct   D(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_dotproduct)  s    !!!c       	   C   sÃ  t  t t d k  f t d t f ƒ }  d } t d ƒ } t |  ƒ | k sO t ‚ t |  ƒ | k sg t ‚ t  t t d k  f t d t f ƒ }  d } t d ƒ } t |  ƒ | k s· t ‚ t |  ƒ | k sÏ t ‚ t t  t t d k f t t f ƒ t  t t t d k  f t d t d k f d t f ƒ d }  d } t d	 ƒ } t |  ƒ | k sXt ‚ t |  ƒ | k spt ‚ t t  t t d k f t t f ƒ t  t t t d k  f t d t d k f d t f ƒ d }  d
 } t d ƒ } t |  ƒ | k sùt ‚ t |  ƒ | k st ‚ t t  t t d k f t t f ƒ }  d } t d ƒ } t |  ƒ | k s`t ‚ t |  ƒ | k sxt ‚ t  t t d k f t t f ƒ t  t t t d k  f t d t d k f d t f ƒ }  d } t d ƒ } t |  ƒ | k sùt ‚ t |  ƒ | k st ‚ t  t t d k f t t f ƒ t  t t t d k  f t d t d k f d t f ƒ }  d } t d ƒ } t |  ƒ | k s“t ‚ t |  ƒ | k s«t ‚ t  d t d t ƒ d k  f d t t ƒ d k  f t t	 d d f d d f d t ƒ t f ƒ }  d } t d ƒ } t |  ƒ | k s5t ‚ t |  ƒ | k sMt ‚ t
 t  t t d k f t t f ƒ d d t ƒ}  d } t d ƒ } t |  ƒ | k s§t ‚ t |  ƒ | k s¿t ‚ d  S(   Ni   i   sJ   /x   for x < 1
|             
< 2           
|x   otherwise
\             sT   âŽ§x   for x < 1
âŽª             
âŽ¨ 2           
âŽªx   otherwise
âŽ©             sY    //x   for x < 1\
 ||             |
-|< 2           |
 ||x   otherwise|
 \\             /sw    âŽ›âŽ§x   for x < 1âŽž
 âŽœâŽª             âŽŸ
-âŽœâŽ¨ 2           âŽŸ
 âŽœâŽªx   otherwiseâŽŸ
 âŽâŽ©             âŽ i    s‚                        //x            \    
                      ||-   for x < 2|    
                      ||y            |    
    //x  for x > 0\   ||             |    
x + |<            | + |< 2           | + 1
    \\y  otherwise/   ||y   for x > 2|    
                      ||             |    
                      ||1   otherwise|    
                      \\             /    sÌ                        âŽ›âŽ§x            âŽž    
                      âŽœâŽªâ”€   for x < 2âŽŸ    
                      âŽœâŽªy            âŽŸ    
    âŽ›âŽ§x  for x > 0âŽž   âŽœâŽª             âŽŸ    
x + âŽœâŽ¨            âŽŸ + âŽœâŽ¨ 2           âŽŸ + 1
    âŽâŽ©y  otherwiseâŽ    âŽœâŽªy   for x > 2âŽŸ    
                      âŽœâŽª             âŽŸ    
                      âŽœâŽª1   otherwiseâŽŸ    
                      âŽâŽ©             âŽ     s‚                        //x            \    
                      ||-   for x < 2|    
                      ||y            |    
    //x  for x > 0\   ||             |    
x - |<            | + |< 2           | + 1
    \\y  otherwise/   ||y   for x > 2|    
                      ||             |    
                      ||1   otherwise|    
                      \\             /    sÌ                        âŽ›âŽ§x            âŽž    
                      âŽœâŽªâ”€   for x < 2âŽŸ    
                      âŽœâŽªy            âŽŸ    
    âŽ›âŽ§x  for x > 0âŽž   âŽœâŽª             âŽŸ    
x - âŽœâŽ¨            âŽŸ + âŽœâŽ¨ 2           âŽŸ + 1
    âŽâŽ©y  otherwiseâŽ    âŽœâŽªy   for x > 2âŽŸ    
                      âŽœâŽª             âŽŸ    
                      âŽœâŽª1   otherwiseâŽŸ    
                      âŽâŽ©             âŽ     s5     //x  for x > 0\
x*|<            |
  \\y  otherwise/sI     âŽ›âŽ§x  for x > 0âŽž
xâ‹…âŽœâŽ¨            âŽŸ
  âŽâŽ©y  otherwiseâŽ s(                  //x            \
                ||-   for x < 2|
                ||y            |
//x  for x > 0\ ||             |
|<            |*|< 2           |
\\y  otherwise/ ||y   for x > 2|
                ||             |
                ||1   otherwise|
                \\             /st                  âŽ›âŽ§x            âŽž
                âŽœâŽªâ”€   for x < 2âŽŸ
                âŽœâŽªy            âŽŸ
âŽ›âŽ§x  for x > 0âŽž âŽœâŽª             âŽŸ
âŽœâŽ¨            âŽŸâ‹…âŽœâŽ¨ 2           âŽŸ
âŽâŽ©y  otherwiseâŽ  âŽœâŽªy   for x > 2âŽŸ
                âŽœâŽª             âŽŸ
                âŽœâŽª1   otherwiseâŽŸ
                âŽâŽ©             âŽ s1                   //x            \
                 ||-   for x < 2|
                 ||y            |
 //x  for x > 0\ ||             |
-|<            |*|< 2           |
 \\y  otherwise/ ||y   for x > 2|
                 ||             |
                 ||1   otherwise|
                 \\             /s}                   âŽ›âŽ§x            âŽž
                 âŽœâŽªâ”€   for x < 2âŽŸ
                 âŽœâŽªy            âŽŸ
 âŽ›âŽ§x  for x > 0âŽž âŽœâŽª             âŽŸ
-âŽœâŽ¨            âŽŸâ‹…âŽœâŽ¨ 2           âŽŸ
 âŽâŽ©y  otherwiseâŽ  âŽœâŽªy   for x > 2âŽŸ
                 âŽœâŽª             âŽŸ
                 âŽœâŽª1   otherwiseâŽŸ
                 âŽâŽ©             âŽ sp  /                                |1|    
|            0               for |-| < 1
|                                |y|    
|                                       
<            1               for |y| < 1
|                                       
|   __0, 2 /2, 1       | 1\             
|y*/__     |           | -|   otherwise 
\  \_|2, 2 \      1, 0 | y/             s¼  âŽ§                                â”‚1â”‚    
âŽª            0               for â”‚â”€â”‚ < 1
âŽª                                â”‚yâ”‚    
âŽª                                       
âŽ¨            1               for â”‚yâ”‚ < 1
âŽª                                       
âŽª  â•­â”€â•®0, 2 âŽ›2, 1       â”‚ 1âŽž             
âŽªyâ‹…â”‚â•¶â”     âŽœ           â”‚ â”€âŽŸ   otherwise 
âŽ©  â•°â”€â•¯2, 2 âŽ      1, 0 â”‚ yâŽ              Rì   sC                  2
//x  for x > 0\ 
|<            | 
\\y  otherwise/ sU                  2
âŽ›âŽ§x  for x > 0âŽž 
âŽœâŽ¨            âŽŸ 
âŽâŽ©y  otherwiseâŽ  (   i   i   (    (    (   i   i    (   RS   Rï   R¢   Rî   R   R¥   R£   Rð   RN   Re   R   R    (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_piecewise8  sr    %	&	_
	_
	%	>
	?
	:&
	0	c          C   sL   t  t t t ƒ }  t |  ƒ d k s* t ‚ t |  ƒ t d ƒ k sH t ‚ d  S(   Ns)   /y    for x  
<            
\z  otherwises/   âŽ§y    for x  
âŽ¨            
âŽ©z  otherwise(   R<   Rï   Rð   Rú   R   R¥   R£   Rî   (   R¡   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ITE  s
    	c          C   sµ  d }  d } t  d ƒ } t |  ƒ | k s0 t ‚ t |  ƒ | k sH t ‚ g  }  d } t  d ƒ } t |  ƒ | k sx t ‚ t |  ƒ | k s t ‚ i  }  i  } d } t  d ƒ } t |  ƒ | k sÆ t ‚ t | ƒ | k sÞ t ‚ t |  ƒ | k sö t ‚ t | ƒ | k st ‚ d t f }  d } t  d ƒ } t |  ƒ | k sEt ‚ t |  ƒ | k s]t ‚ t d d t t t t t ƒ d t t	 ƒ d g }  d } t  d	 ƒ } t |  ƒ | k s¼t ‚ t |  ƒ | k sÔt ‚ t d d t t t t t ƒ d t t	 ƒ d f }  d
 } t  d ƒ } t |  ƒ | k s3t ‚ t |  ƒ | k sKt ‚ t
 t d d t t t t t ƒ d t t	 ƒ d ƒ }  d
 } t  d ƒ } t |  ƒ | k s­t ‚ t |  ƒ | k sÅt ‚ i t t ƒ t 6}  t i t t ƒ t 6ƒ } d } t  d ƒ } t |  ƒ | k st ‚ t | ƒ | k s3t ‚ t |  ƒ | k sKt ‚ t | ƒ | k sct ‚ i d t d t 6t t ƒ d t 6}  t i d t d t 6t t ƒ d t 6ƒ } d } t  d ƒ } t |  ƒ | k sßt ‚ t | ƒ | k s÷t ‚ t |  ƒ | k st ‚ t | ƒ | k s't ‚ t d g }  d } t  d ƒ } t |  ƒ | k s^t ‚ t |  ƒ | k svt ‚ t d f }  d } t  d ƒ } t |  ƒ | k s­t ‚ t |  ƒ | k sÅt ‚ t
 t d ƒ }  d } t  d ƒ } t |  ƒ | k sÿt ‚ t |  ƒ | k st ‚ i d t d 6}  t i d t d 6ƒ } d } t  d ƒ } t |  ƒ | k sit ‚ t | ƒ | k st ‚ t |  ƒ | k s™t ‚ t | ƒ | k s±t ‚ d  S(   Ns   ()s   []s   {}i   s    1  
(-,)
 x  s   âŽ›1 âŽž
âŽœâ”€,âŽŸ
âŽx âŽ i   s†                    2        
  2  1        sin (theta) 
[x , -, x, y, -----------]
     x            2       
               cos (phi)  s˜   âŽ¡                2   âŽ¤
âŽ¢ 2  1        sin (Î¸)âŽ¥
âŽ¢x , â”€, x, y, â”€â”€â”€â”€â”€â”€â”€âŽ¥
âŽ¢    x           2   âŽ¥
âŽ£             cos (Ï†)âŽ¦s†                    2        
  2  1        sin (theta) 
(x , -, x, y, -----------)
     x            2       
               cos (phi)  s˜   âŽ›                2   âŽž
âŽœ 2  1        sin (Î¸)âŽŸ
âŽœx , â”€, x, y, â”€â”€â”€â”€â”€â”€â”€âŽŸ
âŽœ    x           2   âŽŸ
âŽ             cos (Ï†)âŽ s   {x: sin(x)}s8    1  1        2    
{-: -, x: sin (x)}
 x  y             sH   âŽ§1  1        2   âŽ«
âŽ¨â”€: â”€, x: sin (x)âŽ¬
âŽ©x  y            âŽ­s	     2 
[x ]s   âŽ¡ 2âŽ¤
âŽ£x âŽ¦s     2  
(x ,)s   âŽ› 2 âŽž
âŽx ,âŽ s     2    
{x : 1}s#   âŽ§ 2   âŽ«
âŽ¨x : 1âŽ¬
âŽ©     âŽ­(    (   Rî   R   R¥   R£   Rï   Rð   Rf   R#  R[   R$  R)   R   (   R¡   Rñ   Rò   t   expr_2(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_seq%  s´    				5	5	8		&,					c          C   s"  t  ƒ  }  t  t  ƒ  ƒ } | |  g } t | ƒ d k s< t ‚ t | ƒ d k sT t ‚ | |  h } t | ƒ d k sx t ‚ t | ƒ d k s t ‚ i |  | 6| |  6} t i |  | 6| |  6ƒ } t | ƒ d k sÖ t ‚ t | ƒ d k sî t ‚ t | ƒ d k st ‚ t | ƒ d k st ‚ d  S(   Ns   [Basic(Basic()), Basic()]u   [Basic(Basic()), Basic()]s   {Basic(), Basic(Basic())}u   {Basic(), Basic(Basic())}s2   {Basic(): Basic(Basic()), Basic(Basic()): Basic()}u2   {Basic(): Basic(Basic()), Basic(Basic()): Basic()}(   R   R   R¥   R£   R   (   t   b1t   b2R¡   t   expr2(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_any_object_in_sequenceù  s"    	c          C   sì   t  t ƒ  ƒ d k s t ‚ t t ƒ  ƒ d k s6 t ‚ t  t ƒ  ƒ d k sQ t ‚ t t ƒ  ƒ d k sl t ‚ d t t h }  t |  ƒ } t  |  ƒ d k s  t ‚ t |  ƒ d k s¸ t ‚ t  | ƒ d k sÐ t ‚ t | ƒ d	 k sè t ‚ d  S(
   Ns   set()u   set()s   frozenset()u   frozenset()i   s    1    
{-, x}
 x    u"   âŽ§1   âŽ«
âŽ¨â”€, xâŽ¬
âŽ©x   âŽ­s5              1     
frozenset({-, x})
           x     uO            âŽ›âŽ§1   âŽ«âŽž
frozensetâŽœâŽ¨â”€, xâŽ¬âŽŸ
         âŽâŽ©x   âŽ­âŽ (   R   t   setR¥   R£   t	   frozensetRï   (   t   s1t   s2(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_print_builtin_set  s    				c          C   sT  t  }  t |  t t t d g Œ  ƒ d k s2 t ‚ t |  t d d ƒ Œ  ƒ d k sY t ‚ t |  t d d ƒ Œ  ƒ d k s€ t ‚ t t t t t d g ƒ ƒ d k s¬ t ‚ t t t d d ƒ ƒ ƒ d k sÓ t ‚ t t t d d ƒ ƒ ƒ d k sú t ‚ t t t t t d g ƒ ƒ d k s&t ‚ t t t d d ƒ ƒ ƒ d	 k sMt ‚ t t t d d ƒ ƒ ƒ d
 k stt ‚ t t d d d ƒ ƒ d k s˜t ‚ d } d } t t d d d ƒ ƒ | k sÈt ‚ t	 t d d d ƒ ƒ | k sìt ‚ d } t
 d ƒ } t t d d d ƒ ƒ | k s"t ‚ t	 t d d d ƒ ƒ | k sFt ‚ d } d } t t d t d ƒ ƒ | k svt ‚ t	 t d t d ƒ ƒ | k sšt ‚ d } t
 d ƒ } t t t d d ƒ ƒ | k sÐt ‚ t	 t t d d ƒ ƒ | k sôt ‚ d } t
 d ƒ } t t d t d ƒ ƒ | k s+t ‚ t	 t d t d ƒ ƒ | k sPt ‚ d  S(   Ni   s     2      
{x , x*y}i   i   s   {1, 2, 3, 4, 5}i   s'   {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}s)               2       
frozenset({x , x*y})s   frozenset({1, 2, 3, 4, 5})s2   frozenset({1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12})i    i   s	   {0, 1, 2}s   {0, 1, ..., 29}u   {0, 1, â€¦, 29}i   s   {30, 29, ..., 2}s   {30, 29, â€¦, 2}iÿÿÿÿs   {0, 2, ...}u   {0, 2, â€¦}s   {..., 2, 0}s   {â€¦, 2, 0}iþÿÿÿs   {-2, -3, ...}s   {-2, -3, â€¦}(   R   R   Rï   Rð   R¥   RI   RU  RV  R4   R£   Rî   R/   (   t   sRñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_sets4  sH    ''''$$$$$$$$$%c          C   sa   t  d d ƒ }  t |  ƒ } d } t d ƒ } t | ƒ | k sE t ‚ t | ƒ | k s] t ‚ d  S(   Ni   i   s   SetExpr([1, 3])(   R>   R‚   Rî   R   R¥   R£   (   t   ivt   seRñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_SetExprl  s    c          C   sÛ   t  t t t f t t ƒ d d d h d d h ƒ }  d } t d ƒ } t |  ƒ | k s^ t ‚ t |  ƒ | k sv t ‚ t  t t t d ƒ t j	 ƒ }  d } t d ƒ } t |  ƒ | k s¿ t ‚ t |  ƒ | k s× t ‚ d  S(	   Ni   i   i   i   s&   {x + y | x in {1, 2, 3} , y in {3, 4}}s(   {x + y | x âˆŠ {1, 2, 3} , y âˆŠ {3, 4}}s)     2                 
{x  | x in Naturals}s6   âŽ§ 2        âŽ«
âŽ¨x  | x âˆŠ â„•âŽ¬
âŽ©          âŽ­(
   R   R   Rï   Rð   Rî   R   R¥   R£   R$   t   Naturals(   t   imgsetRñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ImageSetu  s    4	c          C   s  d d l  m }  d } d } t |  t t t t ƒ d ƒ t j ƒ ƒ | k sR t ‚ t	 |  t t t t ƒ d ƒ t j ƒ ƒ | k sˆ t ‚ t |  t t
 t t j d t ƒt d ƒ ƒ ƒ d k sÄ t ‚ t	 |  t t
 t t j d t ƒt d ƒ ƒ ƒ d	 k s t ‚ t |  t t t d k t d k  ƒ t d d
 d ƒ ƒ ƒ d k sEt ‚ t	 |  t t t d k t d k  ƒ t d d
 d ƒ ƒ ƒ d k sŠt ‚ t |  t t t d k t d k  ƒ t d d
 ƒ ƒ ƒ d k sÌt ‚ t	 |  t t t d k t d k  ƒ t d d
 ƒ ƒ ƒ d k st ‚ d  S(   Niÿÿÿÿ(   t   ConditionSets#   {x | x in (-oo, oo) and sin(x) = 0}u   {x | x âˆŠ â„ âˆ§ sin(x) = 0}i    Rì   i   s   {1}u   {1}i   i   s
   EmptySet()u   âˆ…s   {2}u   {2}(   t   sympyRb  R   Rï   R   Rf   R$   t   RealsR¥   R£   R5   R    R   R   R   (   Rb  Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ConditionSetˆ  s    66<<EEBc          C   s’   d d l  m }  d } t |  t d d ƒ t d d ƒ ƒ ƒ | k sJ t ‚ d } t |  t d	 d
 ƒ t d	 d t ƒ d t ƒƒ | k sŽ t ‚ d  S(   Niÿÿÿÿ(   t   ComplexRegionu)   {x + yâ‹…â…ˆ | x, y âˆŠ [3, 5] Ã— [4, 6]}i   i   i   i   uA   {râ‹…(â…ˆâ‹…sin(Î¸) + cos(Î¸)) | r, Î¸ âˆŠ [0, 1] Ã— [0, 2â‹…Ï€)}i    i   i   t   polar(   Rc  Rf  R£   R>   R¥   R0   R¢   (   Rf  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ComplexRegion™  s
    4c          C   sq   t  d d ƒ t  d d ƒ }  } d } d } t t |  | ƒ ƒ | k sL t ‚ t t |  | ƒ ƒ | k sm t ‚ d  S(   Ni   i   i   i   u   [2, 3] âˆª [4, 7]s   [2, 3] U [4, 7](   R>   R£   R@   R¥   R   (   Rû   Rü   Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Union_issue_10414¡  s
    !c          C   s‰   t  d ƒ \ }  } } } t |  | ƒ t | | ƒ } } d } d } t t | | ƒ ƒ | k sd t ‚ t t | | ƒ ƒ | k s… t ‚ d  S(   Ns
   x, y, z, wu   [x, y] âˆ© [z, w]s   [x, y] n [z, w](   R1   R>   R£   R?   R¥   R   (   Rï   Rð   Rú   R,  Rû   Rü   Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt$   test_pretty_Intersection_issue_10414¨  s    !c          C   sk   d }  t  d d ƒ t  d d ƒ t  d d ƒ } } } t t | | | t d d ƒ ƒ ƒ |  k sg t ‚ d  S(   Nu)   ([4, 7] Ã— {1, 2}) âˆª ([2, 3] Ã— [4, 7])i   i   i   i   i   i	   (   R>   R£   R@   R   R¥   (   Rò   Rû   Rü   t   c(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_ProductSet_paranthesis°  s    /c          C   sg   d }  d } t  d d ƒ t  d d ƒ } } t | | ƒ |  k sG t ‚ t | | ƒ | k sc t ‚ d  S(   Ns   [2, 3] x [4, 7]u   [2, 3] Ã— [4, 7]i   i   i   i   (   R>   R   R¥   R£   (   Rñ   Rò   Rû   Rü   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt%   test_ProductSet_prod_char_issue_10413¶  s
    c    
         sg  t  t d d t f ƒ }  t d! ƒ } d } d } t |  ƒ | k sI t ‚ t |  ƒ | k sa t ‚ d } d } t | ƒ | k s… t ‚ t | ƒ | k s t ‚ t  t d d" ƒ } t d# d$ ƒ } d } d	 } t | ƒ | k sã t ‚ t | ƒ | k sû t ‚ d
 } d } t | ƒ | k st ‚ t | ƒ | k s7t ‚ t  t d t d f ƒ } t d% t d f ƒ } d } d } t | ƒ | k s‹t ‚ t | ƒ | k s£t ‚ d } d } t | ƒ | k sÇt ‚ t | ƒ | k sßt ‚ d } d } t t |  | ƒ ƒ | k st ‚ t t |  | ƒ ƒ | k s-t ‚ d } d } t t | | ƒ ƒ | k sZt ‚ t t | | ƒ ƒ | k s{t ‚ d } d } t t | | ƒ ƒ | k s¨t ‚ t t | | ƒ ƒ | k sÉt ‚ d } d } t t |  | ƒ ƒ | k söt ‚ t t |  | ƒ ƒ | k st ‚ d } d } t t | | ƒ ƒ | k sDt ‚ t t | | ƒ ƒ | k set ‚ d } d } t t | | ƒ ƒ | k s’t ‚ t t | | ƒ ƒ | k s³t ‚ t  t d t d t	 f ƒ ‰  t
 t ‡  f d †  ƒ t
 t ‡  f d †  ƒ t d ƒ } t  | t d t d d f ƒ }	 d } d  } t |	 ƒ | k sKt ‚ t |	 ƒ | k sct ‚ d  S(&   Ni   i    i   s   [0, 1, 4, 9, ...]u   [0, 1, 4, 9, â€¦]s   [1, 2, 1, 2, ...]u   [1, 2, 1, 2, â€¦]s	   [0, 1, 4]u	   [0, 1, 4]s	   [1, 2, 1]u	   [1, 2, 1]s   [..., 9, 4, 1, 0]u   [â€¦, 9, 4, 1, 0]s   [..., 2, 1, 2, 1]u   [â€¦, 2, 1, 2, 1]s   [1, 3, 5, 11, ...]u   [1, 3, 5, 11, â€¦]s	   [1, 3, 5]u	   [1, 3, 5]s   [..., 11, 5, 3, 1]u   [â€¦, 11, 5, 3, 1]s   [0, 2, 4, 18, ...]u   [0, 2, 4, 18, â€¦]s	   [0, 2, 4]u	   [0, 2, 4]s   [..., 18, 4, 2, 0]u   [â€¦, 18, 4, 2, 0]c              s
   t  ˆ  ƒ S(   N(   R   (    (   t   s7(    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR(    R)  c              s
   t  ˆ  ƒ S(   N(   R£   (    (   Rn  (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR(    R)  Rü   u   [0, b, 4*b]u   [0, b, 4â‹…b](   i   i   (   i    i   (   i   i   (   i    i   (   i   i   (   R7   Rû   R/   R6   R   R¥   R£   R8   R9   Rï   R   t   NotImplementedErrorR(   (
   RW  RX  Rñ   Rò   t   s3t   s4t   s5t   s6Rü   t   s8(    (   Rn  sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_sequences¾  s~    !!!!!!!!!!!! c          C   s_   t  t t t t f ƒ }  d } t d ƒ } t |  ƒ | k sC t ‚ t |  ƒ | k s[ t ‚ d  S(   Nst                         2*sin(3*x)      
2*sin(x) - sin(2*x) + ---------- + ...
                          3           sŒ                         2â‹…sin(3â‹…x)    
2â‹…sin(x) - sin(2â‹…x) + â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ + â€¦
                          3         (   R:   Rï   R0   Rî   R   R¥   R£   (   R™   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_FourierSeries  s    	c          C   s\   t  t d t ƒ ƒ }  d } t d ƒ } t |  ƒ | k s@ t ‚ t |  ƒ | k sX t ‚ d  S(   Ni   s¡     oo             
____             
\   `            
 \         -k  k 
  \   -(-1)  *x  
  /   -----------
 /         k     
/___,            
k = 1            sá     âˆž              
 ____            
 â•²               
  â•²        -k  k 
   â•²  -(-1)  â‹…x  
   â•±  â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€
  â•±        k     
 â•±               
 â€¾â€¾â€¾â€¾            
k = 1            (   R;   Rd   Rï   Rî   R   R¥   R£   (   R™   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_FormalPowerSeries/  s    	c          C   s±  t  t t t ƒ }  d } t d ƒ } t |  ƒ | k s< t ‚ t |  ƒ | k sT t ‚ t  t d t d ƒ }  d } t d ƒ } t |  ƒ | k s” t ‚ t |  ƒ | k s¬ t ‚ t  d t t d ƒ }  d } t d	 ƒ } t |  ƒ | k sì t ‚ t |  ƒ | k st ‚ t  t t ƒ t t d ƒ }  d
 } t d ƒ } t |  ƒ | k sJt ‚ t |  ƒ | k sbt ‚ t  t t ƒ t t d d ƒ }  d } t d ƒ } t |  ƒ | k s«t ‚ t |  ƒ | k sÃt ‚ t  t t t ƒ t d ƒ }  d } t d ƒ } t |  ƒ | k s	t ‚ t |  ƒ | k s!t ‚ t  t t d ƒ d }  d } t d ƒ } t |  ƒ | k sat ‚ t |  ƒ | k syt ‚ t  t t  t d t d ƒ t d ƒ }  d } t d ƒ } t |  ƒ | k sÉt ‚ t |  ƒ | k sát ‚ d t  t t  t d t d ƒ t d ƒ }  d } t d ƒ } t |  ƒ | k s5t ‚ t |  ƒ | k sMt ‚ t  t t ƒ t d d d ƒ}  d } t d ƒ } t |  ƒ | k s•t ‚ t |  ƒ | k s­t ‚ d  S(   Ns    lim x
x->oo s   lim x
xâ”€â†’âˆž i   i    s         2
 lim x 
x->0+  s         2
 lim x 
xâ”€â†’0âº  i   s        1
 lim -
x->0+xs        1
 lim â”€
xâ”€â†’0âºxs)        /sin(x)\
 lim |------|
x->0+\  x   /sG        âŽ›sin(x)âŽž
 lim âŽœâ”€â”€â”€â”€â”€â”€âŽŸ
xâ”€â†’0âºâŽ  x   âŽ t   -s)        /sin(x)\
 lim |------|
x->0-\  x   /sG        âŽ›sin(x)âŽž
 lim âŽœâ”€â”€â”€â”€â”€â”€âŽŸ
xâ”€â†’0â»âŽ  x   âŽ s#    lim (x + sin(x))
x->0+            s)    lim (x + sin(x))
xâ”€â†’0âº            s           2
/ lim x\ 
\x->0+ / s+           2
âŽ› lim xâŽž 
âŽxâ”€â†’0âº âŽ  s5        /       /y\\
 lim |x* lim |-||
x->0+\  y->0+\2//s]        âŽ›       âŽ›yâŽžâŽž
 lim âŽœxâ‹… lim âŽœâ”€âŽŸâŽŸ
xâ”€â†’0âºâŽ  yâ”€â†’0âºâŽ2âŽ âŽ s;          /       /y\\
2* lim |x* lim |-||
  x->0+\  y->0+\2//se          âŽ›       âŽ›yâŽžâŽž
2â‹… lim âŽœxâ‹… lim âŽœâ”€âŽŸâŽŸ
  xâ”€â†’0âºâŽ  yâ”€â†’0âºâŽ2âŽ âŽ t   dirs   +-s   lim sin(x)
x->0      s   lim sin(x)
xâ”€â†’0      (	   R   Rï   R/   Rî   R   R¥   R£   Rf   Rð   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_limitsR  sx    							&	*		c          C   se   t  t d d t d d ƒ }  d } t d ƒ } t |  ƒ | k sI t ‚ t |  ƒ | k sa t ‚ d  S(   Ni   i   i   i    s3          / 5              \
CRootOf\x  + 11*x - 2, 0/s=          âŽ› 5              âŽž
CRootOfâŽx  + 11â‹…x - 2, 0âŽ (   R"   Rï   Rî   R   R¥   R£   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ComplexRootOfï  s    	c          C   sØ   t  t d d t d d t ƒ}  d } t d ƒ } t |  ƒ | k sL t ‚ t |  ƒ | k sd t ‚ t  t d d t d t t t	 t ƒ ƒ ƒ }  d } t d ƒ } t |  ƒ | k s¼ t ‚ t |  ƒ | k sÔ t ‚ d  S(	   Ni   i   i   t   autos-          / 5           \
RootSum\x  + 11*x - 2/s7          âŽ› 5           âŽž
RootSumâŽx  + 11â‹…x - 2âŽ s?          / 5                   z\
RootSum\x  + 11*x - 2, z -> e /sK          âŽ› 5                  zâŽž
RootSumâŽx  + 11â‹…x - 2, z â†¦ â„¯ âŽ (
   R#   Rï   R    Rî   R   R¥   R£   R   Rú   R]   (   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_RootSum   s    "	.	c          C   s7  t  g  t t ƒ }  d } t d ƒ } t |  ƒ | k s< t ‚ t |  ƒ | k sT t ‚ t d d t t d t d d t t d g } t  | t t d d ƒ}  d } t d	 ƒ } t |  ƒ | k sÊ t ‚ t |  ƒ | k sâ t ‚ |  j d
 ƒ }  d } t d ƒ } t |  ƒ | k st ‚ t |  ƒ | k s3t ‚ d  S(   Ns-   GroebnerBasis([], x, y, domain=ZZ, order=lex)s.   GroebnerBasis([], x, y, domain=â„¤, order=lex)i   i   i   Rœ   R3   s£                /[ 2                 2              ]                              \
GroebnerBasis\[x  - x - 3*y + 1, y  - 2*x + y - 1], x, y, domain=ZZ, order=grlex/s·                âŽ›âŽ¡ 2                 2              âŽ¤                             âŽž
GroebnerBasisâŽâŽ£x  - x - 3â‹…y + 1, y  - 2â‹…x + y - 1âŽ¦, x, y, domain=â„¤, order=grlexâŽ Rÿ   sµ                /[       2           4      3      2           ]                            \
GroebnerBasis\[2*x - y  - y + 1, y  + 2*y  - 3*y  - 16*y + 7], x, y, domain=ZZ, order=lex/sÍ                âŽ›âŽ¡       2           4      3      2           âŽ¤                           âŽž
GroebnerBasisâŽâŽ£2â‹…x - y  - y + 1, y  + 2â‹…y  - 3â‹…y  - 16â‹…y + 7âŽ¦, x, y, domain=â„¤, order=lexâŽ (   R.   Rï   Rð   Rî   R   R¥   R£   t   fglm(   R¡   Rñ   Rò   t   F(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_GroebnerBasis   s&    	4		c          C   s+  t  t d t ƒ}  t |  ƒ d k s* t ‚ t |  ƒ d k sB t ‚ t t t ƒ }  t |  ƒ d k si t ‚ t |  ƒ d k s t ‚ t t t ƒ }  t |  ƒ d k s¨ t ‚ t |  ƒ d k sÀ t ‚ t	 d ƒ } t | Œ  }  t |  ƒ d	 k sð t ‚ t |  ƒ d
 k st ‚ t | Œ  }  t |  ƒ d k s,t ‚ t |  ƒ d k sDt ‚ t
 t t d t ƒ}  t |  ƒ d k sqt ‚ t |  ƒ d k s‰t ‚ t t t d t ƒ}  t |  ƒ d k s¶t ‚ t |  ƒ d k sÎt ‚ t t t d t ƒ}  t |  ƒ d k sût ‚ t |  ƒ d k st ‚ t t t d t ƒ}  t |  ƒ d k s@t ‚ t |  ƒ d k sXt ‚ t t t d t ƒ}  t |  ƒ d k s…t ‚ t |  ƒ d k st ‚ t t t d t ƒ}  t |  ƒ d k sÊt ‚ t |  ƒ d k sât ‚ t t t d t ƒ}  t |  ƒ d k st ‚ t |  ƒ d k s't ‚ d  S(   NRì   s   Not(x)u   Â¬xs	   And(x, y)u   x âˆ§ ys   Or(x, y)u   x âˆ¨ ys   a:fs   And(a, b, c, d, e, f)u   a âˆ§ b âˆ§ c âˆ§ d âˆ§ e âˆ§ fs   Or(a, b, c, d, e, f)u   a âˆ¨ b âˆ¨ c âˆ¨ d âˆ¨ e âˆ¨ fs	   Xor(x, y)u   x âŠ» ys
   Nand(x, y)u   x âŠ¼ ys	   Nor(x, y)u   x âŠ½ ys   Implies(x, y)u   x â†’ ys   Implies(y, x)u   y â†’ xs   Equivalent(x, y)u   x â‡” y(   R   Rï   R    R   R¥   R£   R   Rð   R   R1   R+   R   R   R   R   (   R¡   t   syms(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_BooleanQ  sJ    c          C   sm  t  d ƒ }  t |  ƒ d k s$ t ‚ t |  ƒ d k s< t ‚ t }  t |  ƒ d k sZ t ‚ t |  ƒ d k sr t ‚ t }  t |  ƒ d k s t ‚ t |  ƒ d k s¨ t ‚ t }  t |  ƒ d k sÆ t ‚ t |  ƒ d	 k sÞ t ‚ t t }  t |  ƒ d
 k s t ‚ t |  ƒ d k st ‚ t t t f }  t |  ƒ d k s@t ‚ t |  ƒ d k sXt ‚ t j	 t ƒ }  t |  ƒ d k st ‚ t |  ƒ d k s—t ‚ t j	 t t ƒ }  t |  ƒ d k sÁt ‚ t |  ƒ d k sÙt ‚ t j
 t t d t ƒ}  t |  ƒ d k s	t ‚ t |  ƒ d k s!t ‚ t j
 t t d t ƒ}  t |  ƒ d k sQt ‚ t |  ƒ d k sit ‚ d  S(   Ni   s   GF(23)u	   â„¤â‚‚â‚ƒR,   u   â„¤R   u   â„šR   u   â„s   QQ[x]u   â„š[x]s   QQ[x, y]u	   â„š[x, y]s   ZZ(x)u   â„¤(x)s   ZZ(x, y)u	   â„¤(x, y)Rœ   s   QQ[x, y, order=grlex]u   â„š[x, y, order=grlex]s   QQ[x, y, order=ilex]u   â„š[x, y, order=ilex](   R   R   R¥   R£   R,   R   R   Rï   Rð   t
   frac_fieldt	   poly_ringR3   R2   (   R¡   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Domain‘  s<    
c           C   s  t  t d ƒ d t d t ƒd k s* t ‚ t  t d ƒ d d d t ƒd k sT t ‚ t  t d ƒ d t d t ƒd k s~ t ‚ t  t d ƒ t d t d t d t ƒd k s² t ‚ t  t d ƒ t d d d t d t ƒd k sæ t ‚ t  t d ƒ t d t d t d t ƒd k st ‚ d  S(   Ns   0.3t	   full_precRž   s   0.300000000000000R|  R   s   0.300000000000000*xs   x*0.300000000000000s   0.3*xs   x*0.3(   s   0.300000000000000*xs   x*0.300000000000000(   s   0.3*xs   x*0.3(   s   0.3*xs   x*0.3(   RŸ   R$   R¢   R    R¥   Rï   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_precÅ  s    ***% % % c          C   sz   d d  l  }  d d l m } | ƒ  } |  j } | |  _ z t t d t d t ƒWd  | |  _ X| j ƒ  d k sv t ‚ d  S(   Niÿÿÿÿ(   t   StringIOR   Rž   s   pi
(	   t   syst   sympy.core.compatibilityRˆ  t   stdoutR~   R0   R    t   getvalueR¥   (   R‰  Rˆ  t   fdt   sso(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pprint×  s    			
c          C   si   d d d „  ƒ  Y}  d t  f d „  ƒ  Y} t |  ƒ t |  ƒ k sG t ‚ t | ƒ t | ƒ k se t ‚ d S(   s;   Test that the printer dispatcher correctly handles classes.RJ  c           B   s   e  Z RS(    (   R—   R˜   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyRJ  æ  s   RK  c           B   s   e  Z RS(    (   R—   R˜   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyRK  é  s   N(    (   t   objectR   R  R¥   (   RJ  RK  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_classä  s    c          C   s   d }  x, t  d ƒ D] } |  | t | t ƒ 7}  q Wt |  ƒ j d ƒ d k sV t ‚ t |  d t ƒj d ƒ d k s} t ‚ d  S(   Ni    i   s   
iÿÿÿÿRž   (   RI   Rf   Rï   RŸ   t   findR¥   R    (   t	   huge_exprR&  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_no_wrap_lineð  s
    !c           C   s   t  t d „  ƒ d  S(   Nc           S   s   t  t d ƒ d d ƒS(   Ni   t   methodt   garbage(   R   R$   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR(  ù  R)  (   R   t	   TypeError(    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_settingsø  s    c    	   	   C   sÐ  d d l  m }  m } m } m } m } m } t | | | d | f ƒ } d } t d ƒ } t	 | ƒ | k st t
 ‚ t | ƒ | k sŒ t
 ‚ t | | | t | f ƒ } d } t d ƒ } t	 | ƒ | k sÒ t
 ‚ t | ƒ | k sê t
 ‚ t | t |  | |  t t f ƒ | d | | f ƒ } d } t d	 ƒ } t	 | ƒ | k sKt
 ‚ t | ƒ | k sct
 ‚ t | t |  | |  t t f ƒ | d t |  |  |  t t f ƒ f ƒ } d
 } t d ƒ } t	 | ƒ | k s×t
 ‚ t | ƒ | k sït
 ‚ t | t |  | |  t t f ƒ | |  | |  d | d |  | d |  t |  |  |  t t f ƒ f ƒ } d } t d ƒ } t	 | ƒ | k s‡t
 ‚ t | ƒ | k sŸt
 ‚ t | t |  | |  t t f ƒ | d |  | |  d | d |  | d |  f ƒ } d } t d ƒ } t	 | ƒ | k s t
 ‚ t | ƒ | k s8t
 ‚ t |  |  d t f ƒ } d } t d ƒ } t	 | ƒ | k szt
 ‚ t | ƒ | k s’t
 ‚ t |  d |  d t f ƒ } t d ƒ } t d ƒ } t	 | ƒ | k sÞt
 ‚ t | ƒ | k söt
 ‚ t |  d |  d t f ƒ } d } t d ƒ } t	 | ƒ | k s<t
 ‚ t | ƒ | k sTt
 ‚ t |  d d |  d t f ƒ } d } t d ƒ } t	 | ƒ | k sžt
 ‚ t | ƒ | k s¶t
 ‚ t |  d t |  d | |  d t f ƒ } d } t d ƒ } t	 | ƒ | k st
 ‚ t | ƒ | k s$t
 ‚ t d |  d |  d t f ƒ } d } t d ƒ } t	 | ƒ | k snt
 ‚ t | ƒ | k s†t
 ‚ t d t | | |  d t f ƒ } d } t d  ƒ } t	 | ƒ | k sÔt
 ‚ t | ƒ | k sìt
 ‚ t d t | | |  d t f t d d f ƒ } d! } t d" ƒ } t d d d d d | d | d# d d | f | d d | t f ƒ d d d | } d$ } t d% ƒ } t	 | ƒ | k s´t
 ‚ t | ƒ | k sÌt
 ‚ d  S(&   Niÿÿÿÿ(   Rï   Rû   Rü   R  R  R  i    s>     n     
 ___    
 \  `   
  \    k
  /   k 
 /__,   
k = 0   sU     n     
 ___    
 â•²      
  â•²    k
  â•±   k 
 â•±      
 â€¾â€¾â€¾    
k = 0   sE     n      
 ___     
 \  `    
  \     k
  /    k 
 /__,    
k = oo   sW     n     
 ___    
 â•²      
  â•²    k
  â•±   k 
 â•±      
 â€¾â€¾â€¾    
k = âˆž   s      n             
   n              
______            
\     `           
 \        oo      
  \        /      
   \      |       
    \     |   n   
     )    |  x  dx
    /     |       
   /     /        
  /      -oo      
 /      k         
/_____,           
 k = 0            s*     n            
  n             
______          
â•²               
 â•²      âˆž       
  â•²     âŒ        
   â•²    âŽ®   n   
    â•²   âŽ®  x  dx
    â•±   âŒ¡       
   â•±    -âˆž      
  â•±    k        
 â•±              
â•±               
â€¾â€¾â€¾â€¾â€¾â€¾          
k = 0           s¸   oo                 
  /                 
 |                  
 |   x              
 |  x  dx           
 |                  
/                   
-oo                 
 ______             
 \     `            
  \         oo      
   \         /      
    \       |       
     \      |   n   
      )     |  x  dx
     /      |       
    /      /        
   /       -oo      
  /       k         
 /_____,            
  k = 0             s   âˆž                 
âŒ                  
âŽ®   x             
âŽ®  x  dx          
âŒ¡                 
-âˆž                
 ______           
 â•²                
  â•²       âˆž       
   â•²      âŒ        
    â•²     âŽ®   n   
     â•²    âŽ®  x  dx
     â•±    âŒ¡       
    â•±     -âˆž      
   â•±     k        
  â•±               
 â•±                
 â€¾â€¾â€¾â€¾â€¾â€¾           
 k = 0            i   i   s€            oo                          
           /                          
          |                           
          |   x                       
          |  x  dx                    
          |                           
         /                            
         -oo                          
          ______                      
          \     `                     
           \                  oo      
            \                  /      
             \                |       
              \               |   n   
               )              |  x  dx
              /               |       
             /               /        
            /                -oo      
           /                k         
          /_____,                     
     2        2       1   x           
k = n  + n + x  + x + - + -           
                      x   n           sY            âˆž                          
          âŒ                           
          âŽ®   x                      
          âŽ®  x  dx                   
          âŒ¡                          
          -âˆž                         
           ______                    
           â•²                         
            â•²                âˆž       
             â•²               âŒ        
              â•²              âŽ®   n   
               â•²             âŽ®  x  dx
               â•±             âŒ¡       
              â•±              -âˆž      
             â•±              k        
            â•±                        
           â•±                         
           â€¾â€¾â€¾â€¾â€¾â€¾                    
     2        2       1   x          
k = n  + n + x  + x + â”€ + â”€          
                      x   n          s/   2        2       1   x           
n  + n + x  + x + - + -           
                  x   n           
        ______                    
        \     `                   
         \                oo      
          \                /      
           \              |       
            \             |   n   
             )            |  x  dx
            /             |       
           /             /        
          /              -oo      
         /              k         
        /_____,                   
         k = 0                    sO   2        2       1   x          
n  + n + x  + x + â”€ + â”€          
                  x   n          
         ______                  
         â•²                       
          â•²              âˆž       
           â•²             âŒ        
            â•²            âŽ®   n   
             â•²           âŽ®  x  dx
             â•±           âŒ¡       
            â•±            -âˆž      
           â•±            k        
          â•±                      
         â•±                       
         â€¾â€¾â€¾â€¾â€¾â€¾                  
         k = 0                   s/     oo   
 __    
 \ `   
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 /_,   
x = 0  sO     âˆž    
 ___   
 â•²     
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  â•±    
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 â€¾â€¾â€¾   
x = 0  s>     oo    
 ___    
 \  `   
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 /__,   
x = 0   sW     âˆž     
 ___    
 â•²      
  â•²    2
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 â•±      
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x = 0   s?     oo   
 ___   
 \  `  
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  /   2
 /__,  
x = 0  sg     âˆž    
 ____  
 â•²     
  â•²   x
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x = 0  i   sP     oo    
____    
\   `   
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 /    2 
/___,   
x = 0   ss     âˆž     
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  â•±   2 
 â•±      
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x = 0   s•     oo          
____          
\   `         
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  \   /    x\ 
   )  |    -| 
  /   | 3  2| 
 /    \x *y / 
/___,         
x = 0         sã     âˆž           
_____         
â•²             
 â•²           n
  â•²   âŽ›    xâŽž 
   â•²  âŽœ    â”€âŽŸ 
   â•±  âŽœ 3  2âŽŸ 
  â•±   âŽx â‹…y âŽ  
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â•±             
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x = 0         sP     oo    
____    
\   `   
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  /    2
 /    x 
/___,   
x = 0   ss     âˆž     
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x = 0   sb     oo      
____      
\   `     
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  /     b 
 /    y   
/___,     
x = 0     s‰     âˆž       
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 â•²        
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   â•²   â”€â”€â”€
   â•±    b 
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x = 0     s     2     oo     
____  ____     
\   ` \   `    
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  /     /    b 
 /     /    y  
/___, /___,    
y = 1 x = 0    sÍ     2     âˆž      
____  ____     
â•²     â•²        
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  â•²     â•²    â”€â”€
  â•±     â•±    b 
 â•±     â•±    y  
â•±     â•±        
â€¾â€¾â€¾â€¾  â€¾â€¾â€¾â€¾     
y = 1 x = 0    io   sŸ                 1                         
           1 + -                         
    oo         n                         
  _____    _____                         
  \    `   \    `                        
   \        \     /        1    \        
    \        \    |1 + ---------|        
     \        \   |          1  |     1  
      )        )  |    1 + -----| + -----
     /        /   |            1|       1
    /        /    |        1 + -|   1 + -
   /        /     \            k/       k
  /____,   /____,                        
      1   k = 111                        
k = -----                                
    m + 1                                s‡                 1                         
           1 + â”€                         
    âˆž          n                         
  ______   ______                        
  â•²        â•²                             
   â•²        â•²     âŽ›        1    âŽž        
    â•²        â•²    âŽœ1 + â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ        
     â•²        â•²   âŽœ          1  âŽŸ        
      â•²        â•²  âŽœ    1 + â”€â”€â”€â”€â”€âŽŸ     1  
      â•±        â•±  âŽœ            1âŽŸ + â”€â”€â”€â”€â”€
     â•±        â•±   âŽœ        1 + â”€âŽŸ       1
    â•±        â•±    âŽ            kâŽ    1 + â”€
   â•±        â•±                           k
  â•±        â•±                             
  â€¾â€¾â€¾â€¾â€¾â€¾   â€¾â€¾â€¾â€¾â€¾â€¾                        
      1   k = 111                        
k = â”€â”€â”€â”€â”€                                
    m + 1                                (   t	   sympy.abcRï   Rû   Rü   R  R  R  R'   Rî   R   R¥   R£   R/   R   Rð   (	   Rï   Rû   Rü   R  R  R  R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_sumü  s¼    .
		
		7	D	!M	Q								 	,	 	$	0	P	c          C   sJ  t  }  d } t d ƒ } d } t d ƒ } d d l m } m } m } t |  ƒ t d ƒ k sd t ‚ t |  ƒ d k s| t ‚ t |  j	 | | d | d ƒ ƒ | k s­ t ‚ t |  j	 | | d | d ƒ ƒ | k sÞ t ‚ t d	 | t
 | d t | d ƒ | k st ‚ t d	 | t
 | d t | d ƒ | k sFt ‚ d  S(
   NsO                 2
kilogram*meter 
---------------
          2    
    second     so                 2
kilogramâ‹…meter 
â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€
          2    
    second     sm                       2
3*x*y*kilogram*meter 
---------------------
             2       
       second        sŸ                       2
3â‹…xâ‹…yâ‹…kilogramâ‹…meter 
â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€
             2       
       second        iÿÿÿÿ(   t   kgR  RZ  R|   i   i   (   R|   Rî   t   sympy.physics.unitsR›  R  RZ  R£   R¥   R   t
   convert_toRï   Rð   (   R¡   t
   ascii_str1t   unicode_str1t
   ascii_str2t   unicode_str2R›  R  RZ  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt
   test_units  s    			114c          C   sM  t  d ƒ }  t |  t ƒ t t d ƒ } d } t d ƒ } t | ƒ | k sR t ‚ t | ƒ | k sj t ‚ t |  t ƒ j t ƒ t d ƒ } d } t d ƒ } t | ƒ | k sµ t ‚ t | ƒ | k sÍ t ‚ t |  t ƒ j t ƒ t	 t t	 f d t
 d d ƒ f ƒ } d	 } t d
 ƒ } t | ƒ | k s1t ‚ t | ƒ | k sIt ‚ d  S(   NR™   i   s   (f(x))|     2
      |x=phi s   (f(x))â”‚   2
      â”‚x=Ï† i    s,   /d       \|   
|--(f(x))||   
\dx      /|x=0sB   âŽ›d       âŽžâ”‚   
âŽœâ”€â”€(f(x))âŽŸâ”‚   
âŽdx      âŽ â”‚x=0i   sm   /d       \|          
|--(f(x))||          
|dx      ||          
|--------||          
\   y    /|x=0, y=1/2sŸ   âŽ›d       âŽžâ”‚          
âŽœâ”€â”€(f(x))âŽŸâ”‚          
âŽœdx      âŽŸâ”‚          
âŽœâ”€â”€â”€â”€â”€â”€â”€â”€âŽŸâ”‚          
âŽ   y    âŽ â”‚x=0, y=1/2(   R	   R&   Rï   R$  Rî   R   R¥   R£   R!  Rð   R    (   R™   R¡   Rñ   R  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Subs.  s&    	!	:	c           C   sâ   t  t t t ƒ ƒ d k s! t ‚ t  t t t ƒ ƒ d k sB t ‚ t t t ƒ d t ƒd k sf t ‚ t t d t ƒd k s„ t ‚ t t	 d d t
 ƒt ƒ d t ƒd k s´ t ‚ t t	 d d t
 ƒd t ƒd	 k sÞ t ‚ d  S(
   Nu   Î³(x, y)u   Î“(x, y)R   u   Î“(x)u   Î“Rb   R  u   Î³(x)u   Î³(   R£   R–   Rï   Rð   R¥   Rj   RŸ   Rb   R¢   R1   R	   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_gammasf  s    !!$0c          C   s  t  t t t ƒ d t ƒd k s' t ‚ t  t t t ƒ d t ƒd k sN t ‚ t  t d t ƒd k sl t ‚ t  t d t ƒd k sŠ t ‚ t d ƒ }  t  |  t ƒ d t ƒd k sº t ‚ t  |  t t t ƒ d t ƒd k sä t ‚ t  |  d t ƒd	 k st ‚ d  S(
   NR   u   Î’(x, y)u   B(x, y)u   Î’u   BRW   u   Î²(x)u   beta(x, y, z)u   Î²(	   RŸ   RW   Rï   Rð   R¢   R¥   R    R	   Rú   (   t   mybeta(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt	   test_betao  s    ''$*c          C   s\   d t  f d „  ƒ  Y}  t |  d t ƒd k s4 t ‚ t |  t ƒ d t ƒd k sX t ‚ d  S(   Nt   mygammac           B   s   e  Z RS(    (   R—   R˜   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR§  |  s   R   s
   mygamma(x)(   Rb   RŸ   R¢   R¥   Rï   (   R§  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt%   test_function_subclass_different_name{  s    c           C   s¨  t  t t d t ƒ d t ƒd k s* t ‚ t  t t d t ƒ d t ƒd k sT t ‚ t  t t d t ƒ d t ƒd k s~ t ‚ t  t t t t ƒ d t ƒd k s¨ t ‚ t  t t t t ƒ d t ƒd	 k sÒ t ‚ t  t t d t ƒ d t ƒd k sü t ‚ t  t t d t ƒ d t ƒd k s&t ‚ t  t t d t ƒ d t ƒd k sPt ‚ t  t t t t ƒ d t ƒd k szt ‚ t  t t t t ƒ d t ƒd	 k s¤t ‚ d  S(
   Ni    R   s	      n
<x> i   s          n
<x - 1> iÿÿÿÿs          n
<x + 1> s           n
<-a + x> s          n
<x - y> (	   RŸ   R   Rï   R  R¢   R¥   Rû   Rð   R    (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_SingularityFunction‚  s(    c           C   s†   t  t t ƒ d t ƒd k s$ t ‚ t  t t d ƒ d t ƒt d ƒ k sQ t ‚ t  t t t d ƒ d t ƒt d ƒ k s‚ t ‚ d  S(   NR   u   Î´(x)i   s    (1)    
Î´    (x)s      (1)    
xâ‹…Î´    (x)(   RŸ   Rp   Rï   R¢   R¥   Rî   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_deltas·  s    $c          C   sO  t  d d t ƒ }  t d ƒ } d } t |  ƒ | k s< t ‚ t |  ƒ | k sT t ‚ t  d d t ƒ }  t d ƒ } d } t |  ƒ | k s t ‚ t |  ƒ | k s¨ t ‚ t  d g d g t ƒ }  t d ƒ } d } t |  ƒ | k sê t ‚ t |  ƒ | k st ‚ t  t d	 d
 t f d t ƒ }  t d ƒ } d } t |  ƒ | k sLt ‚ t |  ƒ | k sdt ‚ t  t t	 d ƒ d
 t f d t d ƒ }  t d ƒ } d } t |  ƒ | k s·t ‚ t |  ƒ | k sÏt ‚ t  d d g d	 d g d d d d t d d d ƒ }  t d ƒ } d } t |  ƒ | k s3t ‚ t |  ƒ | k sKt ‚ d  S(   NsB    â”Œâ”€  âŽ›  â”‚  âŽž
 â”œâ”€  âŽœ  â”‚ zâŽŸ
0â•µ 0 âŽ  â”‚  âŽ s3     _         
 |_  /  |  \
 |   |  | z|
0  0 \  |  /i   sB    â”Œâ”€  âŽ›  â”‚  âŽž
 â”œâ”€  âŽœ  â”‚ xâŽŸ
0â•µ 1 âŽ1 â”‚  âŽ s3     _         
 |_  /  |  \
 |   |  | x|
0  1 \1 |  /i   sB    â”Œâ”€  âŽ›2 â”‚  âŽž
 â”œâ”€  âŽœ  â”‚ xâŽŸ
1â•µ 1 âŽ1 â”‚  âŽ s3     _         
 |_  /2 |  \
 |   |  | x|
1  1 \1 |  /i   iþÿÿÿi   i   iýÿÿÿsŸ        âŽ›  Ï€         â”‚  âŽž
 â”Œâ”€  âŽœ  â”€, -2â‹…k   â”‚  âŽŸ
 â”œâ”€  âŽœ  3         â”‚ xâŽŸ
2â•µ 4 âŽœ            â”‚  âŽŸ
     âŽ3, 4, 5, -3 â”‚  âŽ s‰                         
  _  /  pi        |  \
 |_  |  --, -2*k  |  |
 |   |  3         | x|
2  4 |            |  |
     \3, 4, 5, -3 |  /s   2/3si    â”Œâ”€  âŽ›Ï€, 2/3, -2â‹…k â”‚  2âŽž
 â”œâ”€  âŽœ             â”‚ x âŽŸ
3â•µ 4 âŽ3, 4, 5, -3  â”‚   âŽ sg     _                      
 |_  /pi, 2/3, -2*k |  2\
 |   |              | x |
3  4 \ 3, 4, 5, -3  |   /ss       âŽ›     â”‚       1      âŽž
     âŽœ     â”‚ â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ
     âŽœ     â”‚         1    âŽŸ
 â”Œâ”€  âŽœ1, 2 â”‚ 1 + â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ
 â”œâ”€  âŽœ     â”‚           1  âŽŸ
2â•µ 2 âŽœ3, 4 â”‚     1 + â”€â”€â”€â”€â”€âŽŸ
     âŽœ     â”‚             1âŽŸ
     âŽœ     â”‚         1 + â”€âŽŸ
     âŽ     â”‚             xâŽ s                             
     /     |       1      \
     |     | -------------|
  _  |     |         1    |
 |_  |1, 2 | 1 + ---------|
 |   |     |           1  |
2  2 |3, 4 |     1 + -----|
     |     |             1|
     |     |         1 + -|
     \     |             x/(    (    (    (   i   (   i   i   i   iýÿÿÿ(   i   i   i   iýÿÿÿ(
   Rc   Rú   Rî   R   R¥   R£   Rï   R0   R  R$   (   R¡   Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt
   test_hyperÅ  sH    			 		)	:
	c       
   C   s0  t  t t t g d g d d g d d d g t ƒ }  t d ƒ } d } t |  ƒ | k s] t ‚ t |  ƒ | k su t ‚ t  d t d g d t d g g  g  t d ƒ }  t d	 ƒ } d
 } t |  ƒ | k sÎ t ‚ t |  ƒ | k sæ t ‚ t d ƒ } d } t  d g d d g d g d g t ƒ }  t |  ƒ | k s8t ‚ t |  ƒ | k sPt ‚ t  d d g d d g d g d d g d d d d t d d d ƒ }  t d ƒ } d } t |  ƒ | k sÃt ‚ t |  ƒ | k sÛt ‚ t |  t ƒ }  t d ƒ } d } t |  ƒ | k st ‚ t |  ƒ | k s,t ‚ d  S(   Ni   i    i   i   s‚   â•­â”€â•®2, 3 âŽ›Ï€, Ï€, x     1    â”‚  âŽž
â”‚â•¶â”     âŽœ                 â”‚ zâŽŸ
â•°â”€â•¯4, 5 âŽ 0, 1    1, 2, 3 â”‚  âŽ sb    __2, 3 /pi, pi, x     1    |  \
/__     |                   | z|
\_|4, 5 \  0, 1     1, 2, 3 |  /i   i   sÄ           âŽ›   Ï€          â”‚   âŽž
â•­â”€â•®0, 2 âŽœ1, â”€  2, Ï€, 5 â”‚  2âŽŸ
â”‚â•¶â”     âŽœ   7          â”‚ z âŽŸ
â•°â”€â•¯5, 0 âŽœ              â”‚   âŽŸ
        âŽ              â”‚   âŽ sš           /   pi           |   \
 __0, 2 |1, --  2, pi, 5 |  2|
/__     |   7            | z |
\_|5, 0 |                |   |
        \                |   /s³   â•­â”€â•® 1, 10 âŽ›1, 1, 1, 1, 1, 1, 1, 1, 1, 1  1 â”‚  âŽž
â”‚â•¶â”       âŽœ                                â”‚ zâŽŸ
â•°â”€â•¯11,  2 âŽ             1                1 â”‚  âŽ s    __ 1, 10 /1, 1, 1, 1, 1, 1, 1, 1, 1, 1  1 |  \
/__       |                                | z|
\_|11,  2 \             1                1 |  /i
   i   sÌ          âŽ›           â”‚       1      âŽž
        âŽœ           â”‚ â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ
        âŽœ           â”‚         1    âŽŸ
â•­â”€â•®1, 2 âŽœ1, 2  4, 3 â”‚ 1 + â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ
â”‚â•¶â”     âŽœ           â”‚           1  âŽŸ
â•°â”€â•¯4, 3 âŽœ 3    4, 5 â”‚     1 + â”€â”€â”€â”€â”€âŽŸ
        âŽœ           â”‚             1âŽŸ
        âŽœ           â”‚         1 + â”€âŽŸ
        âŽ           â”‚             xâŽ sL          /           |       1      \
        |           | -------------|
        |           |         1    |
 __1, 2 |1, 2  4, 3 | 1 + ---------|
/__     |           |           1  |
\_|4, 3 | 3    4, 5 |     1 + -----|
        |           |             1|
        |           |         1 + -|
        \           |             x/sc  âŒ                                         
âŽ®         âŽ›           â”‚       1      âŽž   
âŽ®         âŽœ           â”‚ â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ   
âŽ®         âŽœ           â”‚         1    âŽŸ   
âŽ® â•­â”€â•®1, 2 âŽœ1, 2  4, 3 â”‚ 1 + â”€â”€â”€â”€â”€â”€â”€â”€â”€âŽŸ   
âŽ® â”‚â•¶â”     âŽœ           â”‚           1  âŽŸ dx
âŽ® â•°â”€â•¯4, 3 âŽœ 3    4, 5 â”‚     1 + â”€â”€â”€â”€â”€âŽŸ   
âŽ®         âŽœ           â”‚             1âŽŸ   
âŽ®         âŽœ           â”‚         1 + â”€âŽŸ   
âŽ®         âŽ           â”‚             xâŽ    
âŒ¡                                        s.    /                                       
 |                                        
 |         /           |       1      \   
 |         |           | -------------|   
 |         |           |         1    |   
 |  __1, 2 |1, 2  4, 3 | 1 + ---------|   
 | /__     |           |           1  | dx
 | \_|4, 3 | 3    4, 5 |     1 + -----|   
 |         |           |             1|   
 |         |           |         1 + -|   
 |         \           |             x/   
 |                                        
/                                         (	   Re   R0   Rï   Rú   Rî   R   R¥   R£   R   (   R¡   Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_meijerg>  s<    3	/		(I
		c          C   ss  t  d d t ƒ\ }  } } |  | | d } d } t d ƒ } t | ƒ | k sW t ‚ t | ƒ | k so t ‚ | d |  | } d } t d ƒ } t | ƒ | k s« t ‚ t | ƒ | k sÃ t ‚ |  | d | } d } t d	 ƒ } t | ƒ | k sÿ t ‚ t | ƒ | k st ‚ |  | d | t } d
 } t d ƒ } t | ƒ | k sWt ‚ t | ƒ | k sot ‚ d  S(   Ns   A,B,Ct   commutativeiÿÿÿÿs        -1
A*B*C  s        -1
Aâ‹…Bâ‹…C  s    -1    
C  *A*Bs    -1    
C  â‹…Aâ‹…Bs      -1  
A*C  *Bs      -1  
Aâ‹…C  â‹…Bs      -1  
A*C  *B
-------
   x   s1      -1  
Aâ‹…C  â‹…B
â”€â”€â”€â”€â”€â”€â”€
   x   (   R1   R    Rî   R   R¥   R£   Rï   (   R6  R7  RJ  R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_noncommutative¹  s2    				c          C   sw   t  d ƒ \ }  } t | t d ƒ t |  ƒ ƒ } d } t d ƒ } t | ƒ | k s[ t ‚ t | ƒ | k ss t ‚ d  S(   Ns   x yiÈ   sW        /  ___         \
     |\/ 2 *y    ___|
atan2|-------, \/ x |
     \   20         /sI        âŽ›âˆš2â‹…y    âŽž
atan2âŽœâ”€â”€â”€â”€, âˆšxâŽŸ
     âŽ 20     âŽ (   R1   RV   Rg   Rî   R   R¥   R£   (   Rï   Rð   R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_special_functionsù  s    	c          C   sY   t  d d	 ƒ }  t |  ƒ d k s' t ‚ t d
 d d t ƒ}  t |  ƒ d k sU t ‚ d  S(   Ni    i   i   s'   Segment2D(Point2D(0, 1), Point2D(0, 2))t   angleg®Gáz@s0   Ray2D(Point2D(1, 1), Point2D(2, tan(pi/50) + 1))(   i    i   (   i    i   (   i   i   (   R%   R   R¥   R!   R0   (   R  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_geometry  s    c          C   s  t  t ƒ }  d } t |  ƒ | k s* t ‚ t |  ƒ | k sB t ‚ t d t ƒ }  d } d } t |  ƒ | k su t ‚ t |  ƒ | k s t ‚ t t t ƒ ƒ d k s« t ‚ t t t ƒ ƒ d k sÉ t ‚ t t	 t ƒ ƒ d k sç t ‚ t t
 t ƒ ƒ d k st ‚ t t t ƒ ƒ d k s#t ‚ t t t ƒ ƒ d k sAt ‚ t t	 t ƒ ƒ d k s_t ‚ t t
 t ƒ ƒ d k s}t ‚ d  S(	   Ns   Ei(x)i   u   Eâ‚(z)s   expint(1, z)s   Shi(x)s   Si(x)s   Ci(x)s   Chi(x)(   RQ   Rï   R   R¥   R£   R^   Rú   RT   RU   RP   RO   (   R¡   t   stringRò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_expint  s"    c          C   s  d }  t  d ƒ } t d t d ƒ } t | ƒ |  k s> t ‚ t | ƒ | k sV t ‚ d }  t  d ƒ } t d d d t ƒ } t | ƒ |  k s— t ‚ t | ƒ | k s¯ t ‚ d }  t  d ƒ } t d t d ƒ } t | ƒ |  k sí t ‚ t | ƒ | k st ‚ d }  t  d	 ƒ } t d d d t ƒ } t | ƒ |  k sFt ‚ t | ƒ | k s^t ‚ d
 }  t  d ƒ } t d d t	 ƒ } t | ƒ |  k s›t ‚ t | ƒ | k s³t ‚ d }  t  d ƒ } t d d t	 d ƒ } t | ƒ |  k sót ‚ t | ƒ | k st ‚ d  S(   Ns    /  1  \
K|-----|
 \z + 1/s0    âŽ›  1  âŽž
KâŽœâ”€â”€â”€â”€â”€âŽŸ
 âŽz + 1âŽ i   s     / |  1  \
F|1|-----|
 \ |z + 1/s<    âŽ› â”‚  1  âŽž
FâŽœ1â”‚â”€â”€â”€â”€â”€âŽŸ
 âŽ â”‚z + 1âŽ s    /  1  \
E|-----|
 \z + 1/s0    âŽ›  1  âŽž
EâŽœâ”€â”€â”€â”€â”€âŽŸ
 âŽz + 1âŽ s     / |  1  \
E|1|-----|
 \ |z + 1/s<    âŽ› â”‚  1  âŽž
EâŽœ1â”‚â”€â”€â”€â”€â”€âŽŸ
 âŽ â”‚z + 1âŽ s     / |4\
Pi|3|-|
  \ |x/s)    âŽ› â”‚4âŽž
Î âŽœ3â”‚â”€âŽŸ
 âŽ â”‚xâŽ i   i   s      /   4| \
Pi|3; -|6|
  \   x| /s2    âŽ›   4â”‚ âŽž
Î âŽœ3; â”€â”‚6âŽŸ
 âŽ   xâ”‚ âŽ i   (
   Rî   Rl   Rú   R   R¥   R£   Rm   Rn   Ro   Rï   (   Rñ   Rò   R¡   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_elliptic_functions,  sH    						c    	      C   sÝ   d d l  m }  m } m } m } m } |  d d d ƒ } t | | d k ƒ ƒ d k s^ t ‚ | d d ƒ } t | | d	 k ƒ ƒ d
 k s‘ t ‚ | d d ƒ } | d d ƒ } t | t | | ƒ ƒ j	 ƒ d k sÙ t ‚ d  S(   Niÿÿÿÿ(   t   Normalt   Diet   Exponentialt   pspacet   wheret   x1i    i   u   Domain: 0 < xâ‚ âˆ§ xâ‚ < âˆžt   d1i   i   u   Domain: dâ‚ = 5 âˆ¨ dâ‚ = 6Rû   Rü   u3   Domain: 0 â‰¤ a âˆ§ 0 â‰¤ b âˆ§ a < âˆž âˆ§ b < âˆž(
   t   sympy.statsRµ  R¶  R·  R¸  R¹  R£   R¥   R)   t   domain(	   Rµ  R¶  R·  R¸  R¹  RA  RK  R6  R7  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_RandomDomainŽ  s    ($$c          C   s²   t  j t t ƒ }  t  j t t ƒ } |  j t t t ƒ } t | ƒ d k sS t ‚ t | ƒ d k sk t ‚ | j t t ƒ } t | ƒ d k s– t ‚ t | ƒ d k s® t ‚ d  S(   Ns	   x/(x + y)u	   x/(x + y)s   x + yu   x + y(	   R   Rƒ  Rï   Rð   R„  t   convertR   R¥   R£   (   R  t   RR¡   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_PrettyPolyœ  s    c           C   sP   t  t d d d t ƒƒ d k s' t ‚ t  t t d t ƒ ƒ d k sL t ‚ d  S(   Ni   iûÿÿÿRì   s   1 
--
 5
2 i   s   pi___
\/ x (   R   R   R    R¥   Rï   R0   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_6285©  s    'c          C   s˜  t  t t d t ƒ d ƒ d k s) t ‚ t t t d t ƒ d ƒ t d ƒ k sX t ‚ t  t t d t d d f ƒ d ƒ d k sŠ t ‚ t t t d t d d f ƒ d ƒ t d ƒ k sÂ t ‚ t  t t d t d d f ƒ d ƒ d k sô t ‚ t t t d t d d f ƒ d ƒ t d	 ƒ k s,t ‚ t d
 ƒ }  t  t	 |  t ƒ t ƒ d ƒ d k sct ‚ t t	 |  t ƒ t ƒ d ƒ t d ƒ k s”t ‚ d  S(   Ni   sS             2
/  /     \ 
| |      | 
| |  2   | 
| | x  dx| 
| |      | 
\/       / sN            2
âŽ›âŒ       âŽž 
âŽœâŽ®  2   âŽŸ 
âŽœâŽ® x  dxâŽŸ 
âŽâŒ¡      âŽ  i    i   s_             2
/  1     \ 
| ___    | 
| \  `   | 
|  \    2| 
|  /   x | 
| /__,   | 
\x = 0   / s™             2
âŽ›  1     âŽž 
âŽœ ___    âŽŸ 
âŽœ â•²      âŽŸ 
âŽœ  â•²    2âŽŸ 
âŽœ  â•±   x âŽŸ 
âŽœ â•±      âŽŸ 
âŽœ â€¾â€¾â€¾    âŽŸ 
âŽx = 0   âŽ  sZ              2
/  2      \ 
|______   | 
| |  |   2| 
| |  |  x | 
| |  |    | 
\x = 1    / sŠ              2
âŽ›  2      âŽž 
âŽœâ”€â”¬â”€â”€â”¬â”€   âŽŸ 
âŽœ â”‚  â”‚   2âŽŸ 
âŽœ â”‚  â”‚  x âŽŸ 
âŽœ â”‚  â”‚    âŽŸ 
âŽx = 1    âŽ  R™   s/             2
/d       \ 
|--(f(x))| 
\dx      / s?             2
âŽ›d       âŽž 
âŽœâ”€â”€(f(x))âŽŸ 
âŽdx      âŽ  (
   R   R   Rï   R¥   R£   Rî   R'   R   R	   R   (   R™   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_6359®  s*    	#
#
#	#c          C   sZ   d }  t  d ƒ } t d t t ƒ ƒ |  k s4 t ‚ t d t t ƒ ƒ | k sV t ‚ d  S(   Ns     1  
-----
  ___
\/ x s   1 
â”€â”€
âˆšxi   (   Rî   R   Rg   Rï   R¥   R£   (   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_6739ÿ  s
    	"c          C   s9   x2 d d g D]$ }  t  t |  ƒ ƒ |  k s t ‚ q Wd  S(   Nt   dexpr2_d1taus   dexpr2^d1tau(   R   R(   R¥   (   t	   symb_name(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt!   test_complicated_symbol_unchanged  s    c          C   s³  d d l  m }  m } m } m } m } m } |  d ƒ } |  d ƒ } |  d ƒ } | | | d ƒ }	 | | | d ƒ }
 | | ƒ } | d ƒ } t | ƒ d k s¦ t ‚ t	 | ƒ d	 k s¾ t ‚ t |	 ƒ d
 k sÖ t ‚ t	 |	 ƒ d k sî t ‚ t | ƒ d k st ‚ t	 | ƒ d k st ‚ t |
 |	 ƒ d k s:t ‚ t	 |
 |	 ƒ d k sVt ‚ t | ƒ d k snt ‚ t	 | ƒ d k s†t ‚ | ƒ  } t | ƒ d k s§t ‚ t	 | ƒ d k s¿t ‚ | i d |	 6t
 j |
 6ƒ } t | ƒ d k sôt ‚ t	 | ƒ t d ƒ k st ‚ | i d |	 6t
 j |
 6i d |
 |	 6ƒ } t | ƒ d k sUt ‚ t	 | ƒ t d ƒ k sst ‚ | | ƒ } t | ƒ d k s—t ‚ t	 | ƒ d k s¯t ‚ d  S(   Niÿÿÿÿ(   t   Objectt   IdentityMorphismt   NamedMorphismt   Categoryt   Diagramt   DiagramGridt   A1t   A2t   A3t   f1t   f2t   K1u   Aâ‚s
   f1:A1-->A2u   fâ‚:Aâ‚â€”â€”â–¶Aâ‚‚s
   id:A1-->A1u   id:Aâ‚â€”â€”â–¶Aâ‚s   f2*f1:A1-->A3u   fâ‚‚âˆ˜fâ‚:Aâ‚â€”â€”â–¶Aâ‚ƒu   Kâ‚s
   EmptySet()u   âˆ…t   uniques‘   {f2*f1:A1-->A3: EmptySet(), id:A1-->A1: EmptySet(), id:A2-->A2: EmptySet(), id:A3-->A3: EmptySet(), f1:A1-->A2: {unique}, f2:A2-->A3: EmptySet()}s´   {fâ‚‚âˆ˜fâ‚:Aâ‚â€”â€”â–¶Aâ‚ƒ: âˆ…, id:Aâ‚â€”â€”â–¶Aâ‚: âˆ…, id:Aâ‚‚â€”â€”â–¶Aâ‚‚: âˆ…, id:Aâ‚ƒâ€”â€”â–¶Aâ‚ƒ: âˆ…, fâ‚:Aâ‚â€”â€”â–¶Aâ‚‚: {unique}, fâ‚‚:Aâ‚‚â€”â€”â–¶Aâ‚ƒ: âˆ…}s¯   {f2*f1:A1-->A3: EmptySet(), id:A1-->A1: EmptySet(), id:A2-->A2: EmptySet(), id:A3-->A3: EmptySet(), f1:A1-->A2: {unique}, f2:A2-->A3: EmptySet()} ==> {f2*f1:A1-->A3: {unique}}sè   {fâ‚‚âˆ˜fâ‚:Aâ‚â€”â€”â–¶Aâ‚ƒ: âˆ…, id:Aâ‚â€”â€”â–¶Aâ‚: âˆ…, id:Aâ‚‚â€”â€”â–¶Aâ‚‚: âˆ…, id:Aâ‚ƒâ€”â€”â–¶Aâ‚ƒ: âˆ…, fâ‚:Aâ‚â€”â€”â–¶Aâ‚‚: {unique}, fâ‚‚:Aâ‚‚â€”â€”â–¶Aâ‚ƒ: âˆ…} â•â•â–¶ {fâ‚‚âˆ˜fâ‚:Aâ‚â€”â€”â–¶Aâ‚ƒ: {unique}}s   A1  A2
      
A3    u   Aâ‚  Aâ‚‚
      
Aâ‚ƒ    (   t   sympy.categoriesRÈ  RÉ  RÊ  RË  RÌ  RÍ  R   R¥   R£   R$   t   EmptySetRî   (   RÈ  RÉ  RÊ  RË  RÌ  RÍ  RÎ  RÏ  RÐ  RÑ  RÒ  t   id_A1RÓ  t   dt   grid(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_categories  s<    .	+c          C   s  t  j t t ƒ }  |  j d ƒ } | j t t g d t d g ƒ } t d ƒ } d } t | ƒ | k sm t ‚ t	 | ƒ | k s… t ‚ t d ƒ } d } t | ƒ | k s¯ t ‚ t	 | ƒ | k sÇ t ‚ |  j
 t d t ƒ } t d ƒ } d } t | ƒ | k st ‚ t	 | ƒ | k st ‚ | | } t d	 ƒ } d
 } t | ƒ | k sSt ‚ t	 | ƒ | k skt ‚ t d ƒ } d } d  S(   Ni   i   s          2
â„š[x, y] s           2
QQ[x, y] s3   â•±        âŽ¡    2âŽ¤â•²
â•²[x, y], âŽ£1, x âŽ¦â•±s#                 2  
<[x, y], [1, x ]>s   â•± 2   â•²
â•²x , yâ•±s     2    
<x , y>s               2    
     â„š[x, y]     
â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€
â•±        âŽ¡    2âŽ¤â•²
â•²[x, y], âŽ£1, x âŽ¦â•±sY               2    
    QQ[x, y]     
-----------------
              2  
<[x, y], [1, x ]>s+  â•±âŽ¡    3âŽ¤                                                â•²
â”‚âŽ¢   x âŽ¥   â•±        âŽ¡    2âŽ¤â•²           â•±        âŽ¡    2âŽ¤â•²â”‚
â”‚âŽ¢1, â”€â”€âŽ¥ + â•²[x, y], âŽ£1, x âŽ¦â•±, [2, y] + â•²[x, y], âŽ£1, x âŽ¦â•±â”‚
â•²âŽ£   2 âŽ¦                                                â•±sç         3                                                  
     x                   2                           2   
<[1, --] + <[x, y], [1, x ]>, [2, y] + <[x, y], [1, x ]>>
     2                                                   (   R   t   old_poly_ringRï   Rð   t   free_modulet	   submoduleRî   R£   R¥   R   t   ideal(   RÀ  R  R.  Rò   Rñ   R   t   Q(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_PrettyModulesM  s8    "			
			c          C   s¬   t  j t ƒ t d d g }  t d ƒ } d } t |  ƒ | k sH t ‚ t |  ƒ | k s` t ‚ t d ƒ } d } t |  j ƒ | k s t ‚ t |  j ƒ | k s¨ t ‚ d  S(   Ni   i   s=     â„š[x]  
â”€â”€â”€â”€â”€â”€â”€â”€
â•± 2    â•²
â•²x  + 1â•±s#    QQ[x]  
--------
  2     
<x  + 1>s!       â•± 2    â•²
1 + â•²x  + 1â•±s         2     
1 + <x  + 1>(   R   RÛ  Rï   Rî   R£   R¥   R   t   one(   RÀ  Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_QuotientRing§  s    		c          C   sk  d d l  m }  t j t ƒ } |  | j d ƒ | j d ƒ d g ƒ } t d ƒ } d } t | ƒ | k sp t ‚ t	 | ƒ | k sˆ t ‚ |  | j d ƒ | j d ƒ d d g ƒ } t d ƒ } d	 } t | ƒ | k sÜ t ‚ t	 | ƒ | k sô t ‚ |  | j d ƒ | j d ƒ t g g d g ƒ } t d
 ƒ } d } t | ƒ | k sOt ‚ t	 | ƒ | k sgt ‚ d  S(   Niÿÿÿÿ(   t   homomorphismi   i    s3             1         1
[0] : â„š[x]  â”€â”€> â„š[x] s/              1          1
[0] : QQ[x]  --> QQ[x] i   s^   âŽ¡0  0âŽ¤       2         2
âŽ¢    âŽ¥ : â„š[x]  â”€â”€> â„š[x] 
âŽ£0  0âŽ¦                  sP   [0  0]        2          2
[    ] : QQ[x]  --> QQ[x] 
[0  0]                    si                       1
          1     â„š[x] 
[0] : â„š[x]  â”€â”€> â”€â”€â”€â”€â”€
                <[x]>s_                         1
           1     QQ[x] 
[0] : QQ[x]  --> ------
                 <[x]> (
   t   sympy.polys.agcaRã  R   RÛ  Rï   RÜ  Rî   R£   R¥   R   (   Rã  RÀ  R¡   Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_HomomorphismÍ  s(    '	*	1	c          C   s\   t  d d t ƒ\ }  } t |  | ƒ } t | ƒ d k s@ t ‚ t | ƒ d k sX t ‚ d  S(   Ns   A BR­  s   Tr(A*B)u	   Tr(Aâ‹…B)(   R1   R    RM   R   R¥   R£   (   R6  R7  t   t(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_Tr  s    c          C   s9   t  d t d d t ƒd }  t |  ƒ d k s5 t ‚ d  S(   Niþÿÿÿi   Rì   i   s   5 - 2*(x - 2)(   R   Rï   R    R   R¥   (   t   eq(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Add  s    c           C   sR   t  t t t t ƒ ƒ ƒ d k s' t ‚ t  t t t t ƒ ƒ ƒ d k sN t ‚ d  S(   Nu   x â‡Ž yu   x â†› y(   R£   R   R   Rï   Rð   R¥   R   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_7179  s    'c           C   s%   t  t t t ƒ ƒ d k s! t ‚ d  S(   Nu   x â‡” y(   R£   R   Rï   Rð   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_7180  s    c           C   sŒ   t  t j t j ƒ d k s" t ‚ t t j t j ƒ d k sD t ‚ t  t j t j ƒ d k sf t ‚ t t j t j ƒ d k sˆ t ‚ d  S(   Ns   (-oo, oo) \ Naturalsu	   â„ \ â„•s   (-oo, oo) \ Naturals0u   â„ \ â„•â‚€(   R   R$   Rd  R_  R¥   R£   t	   Naturals0(    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Complement!  s    """c       
   C   s¡   d d l  m }  m } d d l m } t |  | d d ƒ | d d ƒ d t ƒƒ d k s_ t ‚ | t ƒ 0 t	 |  | d d ƒ | d d ƒ d t ƒƒ Wd  QXd  S(	   Niÿÿÿÿ(   t   SymmetricDifferenceR>   (   R   i   i   i   Rì   u   [2, 3] âˆ† [3, 5](
   Rc  Rî  R>   t   sympy.utilities.pytestR   R£   R    R¥   Ro  R   (   Rî  R>   R   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_SymmetricDifference(  s    !c           C   sL   t  t t t j ƒ ƒ d k s$ t ‚ t t t t j ƒ ƒ d k sH t ‚ d  S(   Ns   Contains(x, Integers)u	   x âˆˆ â„¤(   R   R5   Rï   R$   t   IntegersR¥   R£   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_Contains1  s    $c          C   sh   d d l  m }  |  d d t ƒ} t d ƒ } d } t | ƒ | k sL t ‚ t | ƒ | k sd t ‚ d  S(   Niÿÿÿÿ(   t   sympifys&   ((x+x**4)/(x-1))-(2*(x-1)**4/(x-1)**4)Rì   s              4    4    
  2â‹…(x - 1)    x  + x
- â”€â”€â”€â”€â”€â”€â”€â”€â”€â”€ + â”€â”€â”€â”€â”€â”€
          4    x - 1 
   (x - 1)           sm              4    4    
  2*(x - 1)    x  + x
- ---------- + ------
          4    x - 1 
   (x - 1)           (   t
   sympy.coreRó  R    Rî   R   R¥   R£   (   Ró  R  Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_82926  s    	c          C   sh   t  d ƒ }  |  t ƒ j t ƒ } t d ƒ } d } t | ƒ | k sL t ‚ t | ƒ | k sd t ‚ d  S(   NRð   s!    d       
-â”€â”€(y(x))
 dx      s      d       
- --(y(x))
  dx      (   R	   Rï   R!  Rî   R   R¥   R£   (   Rð   R¡   Rò   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_4335M  s    	c          C   sJ   d d l  m }  |  d d t ƒ} t d ƒ } t | ƒ | k sF t ‚ d  S(   Niÿÿÿÿ(   Ró  s   2*x*y**2/1**2 + 1Rì   sF        2    
2â‹…xâ‹…y     
â”€â”€â”€â”€â”€â”€ + 1
   2      
  1       (   Rô  Ró  R    Rî   R£   R¥   (   Ró  R  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_8344`  s
    	c          C   sg   t  d d d t ƒ}  t  d d d t ƒ} t |  | d t ƒ} t d ƒ } t | ƒ | k sc t ‚ d  S(   Ni   i   Rì   i
   iþÿÿÿs     3
 2 
â”€â”€â”€
  2
10 (   R   R    R   Rî   R£   R¥   (   Rï   Rð   R  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_6324n  s    	c          C   s„   t  t d ƒ t t d ƒ }  t d ƒ } t |  ƒ | k sB t ‚ t  t ƒ t d ƒ d }  t d ƒ } t |  ƒ | k s€ t ‚ d  S(   Ni   s              âŽ›xâŽž
        cosâŽœâ”€âŽŸ
           âŽ2âŽ 
âŽ›   âŽ›xâŽžâŽž      
âŽœsinâŽœâ”€âŽŸâŽŸ      
âŽ   âŽ2âŽ âŽ       i   i   s/           11
        â”€â”€
        13
(sin(x))  (   Rf   Rï   R[   Rî   R£   R¥   R$   (   R  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_7927}  s    		c          C   sÄ   d d l  m }  m } t d ƒ } |  t t | | ƒ t t t | ƒ | d d f ƒ |  t d t | | ƒ d t t d t | ƒ | d d f ƒ } t d ƒ } t	 | ƒ | k sÀ t
 ‚ d  S(   Niÿÿÿÿ(   t   lamdaRæ  R›   i    i   i   sH       1                              1                   
   2 âŒ                               âŒ                    
Î»â‹…x â‹…âŽ® 2â‹…Ï€â‹…Ï†(t)â‹…sin(2â‹…Ï€â‹…t) dt + Î»â‹…xâ‹…âŽ® Ï€â‹…Ï†(t)â‹…sin(Ï€â‹…t) dt
     âŒ¡                              âŒ¡                   
     0                              0                   (   R™  Rú  Ræ  R	   Rï   R   R0   Rf   Rî   R£   R¥   (   Rú  Ræ  R›   R  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_6134”  s    z	c    	      C   sÒ   d }  t  d d t t ƒ t  d d ƒ t t ƒ } } } t t | t | | ƒ ƒ ƒ |  k sb t ‚ d } t t ƒ t t ƒ t t	 ƒ t  d d ƒ f \ } } } } t t
 | | t | | ƒ ƒ ƒ | k sÎ t ‚ d  S(   Nu   (2, 3) âˆª ([1, 2] \ {x})i   i   i   u   {x} âˆ© {y} âˆ© ({z} \ [1, 2])(   R>   R¢   R   Rï   R£   R@   R=   R¥   Rð   Rú   R?   (	   R  Rû   Rü   Rk  R  RØ  R  R™   t   g(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_9877¤  s    2*9c          C   sr   t  t d t t d t ƒ}  t |  ƒ d k s5 t ‚ t  t d t t t d t ƒ} t | ƒ d k sn t ‚ d  S(   NiÿÿÿÿRì   s   c - (a + b)s   c - (a - b + d)(   Rk  R   Rû   Rü   R    R   R¥   RØ  (   t   expr1RS  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_13651®  s    !c          C   st   d d l  m }  d } t d ƒ } t d d t ƒ} t |  | ƒ ƒ | k sR t ‚ t |  | ƒ ƒ | k sp t ‚ d  S(   Niÿÿÿÿ(   t   primenus   nu(n)s   Î½(n)R  R  (   t   sympy.ntheory.factor_R   Rî   R1   R¢   R   R¥   R£   (   R   Rž  R  R  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_primenuµ  s    c          C   st   d d l  m }  d } t d ƒ } t d d t ƒ} t |  | ƒ ƒ | k sR t ‚ t |  | ƒ ƒ | k sp t ‚ d  S(   Niÿÿÿÿ(   t
   primeomegas   Omega(n)s   Î©(n)R  R  (   R  R  Rî   R1   R¢   R   R¥   R£   (   R  Rž  R  R  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_primeomegaÀ  s    c          C   sê  d d l  m }  d } t d ƒ } d } t d ƒ } d } t d ƒ } d } t d ƒ } d }	 t d	 ƒ }
 t d
 d t ƒ} t |  | d ƒ ƒ | k s t ‚ t |  | d ƒ ƒ | k s¾ t ‚ t |  | d d ƒ ƒ | k sã t ‚ t |  | d d ƒ ƒ | k st ‚ t |  d | d ƒ ƒ | k s-t ‚ t |  d | d ƒ ƒ | k sRt ‚ t |  | d ƒ d ƒ | k swt ‚ t |  | d ƒ d ƒ | k sœt ‚ t d |  | d ƒ ƒ |	 k sÁt ‚ t d |  | d ƒ ƒ |
 k sæt ‚ d  S(   Niÿÿÿÿ(   t   Mods   x mod 7s   (x + 1) mod 7s	   2*x mod 7s   2â‹…x mod 7s   (x mod 7) + 1s   2*(x mod 7)s   2â‹…(x mod 7)Rï   R  i   i   i   (   Rô  R  Rî   R1   R¢   R   R¥   R£   (   R  Rž  R  R   R  t
   ascii_str3t
   ucode_str3t
   ascii_str4t
   ucode_str4t
   ascii_str5t
   ucode_str5Rï   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_ModË  s,    !!%%%%%%%c           C   s@   t  t d ƒ ƒ d k s t ‚ t t d ƒ ƒ d k s< t ‚ d  S(   NR)  (   R   R(   R¥   R£   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_11801ê  s    c          C   s¼   t  d ƒ }  t d |  ƒ } t d ƒ } t | ƒ | k s@ t ‚ t d ƒ } t | d ƒ | k sh t ‚ t d ƒ } t | d ƒ | k s t ‚ t d ƒ } t |  | ƒ | k s¸ t ‚ d  S(   NRï   i   s   1
â”€
xs!      2
âŽ›1âŽž 
âŽœâ”€âŽŸ 
âŽxâŽ  i   s       1
1 + â”€
    xs     1
xâ‹…â”€
  x(   R1   RL   Rî   R£   R¥   (   Rï   t   heRò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_UnevaluatedExprï  s    				c          C   sX   t  d d g d d g g ƒ t  d d g ƒ f }  t d ƒ } t |  ƒ | k sT t ‚ d  S(   Ni    sM   âŽ›âŽ¡0  0âŽ¤  âŽ¡0âŽ¤âŽž
âŽœâŽ¢    âŽ¥, âŽ¢ âŽ¥âŽŸ
âŽâŽ£0  0âŽ¦  âŽ£0âŽ¦âŽ (   R   Rî   R£   R¥   (   R.  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_10472  s    0	c          C   s2  t  d d d ƒ }  t  d d d ƒ } t  d d d ƒ } d } t d ƒ } t |  d ƒ | k sd t ‚ t |  d ƒ | k s€ t ‚ d	 } t d
 ƒ } t d |  d ƒ | k s² t ‚ t d |  d ƒ | k sÒ t ‚ d } t d ƒ } | d j | |  | ƒ } t | ƒ | k st ‚ t | ƒ | k s.t ‚ d  S(   NR6  i   i   R7  RJ  t   A_00s   Aâ‚€â‚€i    s   3*A_00s   3â‹…Aâ‚€â‚€s   (-B + A)[0, 0](   i    i    (   i    i    (   i    i    (   i    i    (   i    i    (   Rx   Rî   R   R¥   R£   t   subs(   R6  R7  RJ  Rž  R  R  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_MatrixElement_printing$  s       c          C   sš   d d l  m }  t d ƒ \ } } } } |  d ƒ } t d ƒ } t | | | | j ƒ | k sg t ‚ t d ƒ } t d | | j ƒ | k s– t ‚ d  S(   Niÿÿÿÿ(   R   s   x y t jR  sI   âŽ›   tâŽž    
âŽœâŽ›xâŽž âŽŸ e_j
âŽœâŽœâ”€âŽŸ âŽŸ    
âŽâŽyâŽ  âŽ     s%   âŽ›1âŽž    
âŽœâ”€âŽŸ e_j
âŽyâŽ     i   (   t   sympy.vectorR   R1   Rî   R£   R'  R¥   (   R   Rï   Rð   Ræ  R'  R  Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_12675;  s    	'	c          C   s  t  d d d ƒ }  t  d d d ƒ } t  d d d ƒ } t |  | | ƒ d k sW t ‚ t |  | ƒ d k ss t ‚ t |  | | |  | | | ƒ d k s£ t ‚ t  d t t ƒ } t  d	 t t ƒ } t | | ƒ d
 k sã t ‚ d } t t | d | | ƒ | k st ‚ d  S(   NR6  i   R7  RJ  s   -A*B*Cs   -B + As   -A*B -B*C + A*B*CRï   s   y*s   x + y*s        2     
-2*y*  -a*xiþÿÿÿ(   Rx   R   R¥   R  Rû   (   R6  R7  RJ  Rï   Rð   Rñ   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_MatrixSymbol_printingQ  s    !0c          C   sx   d t  }  t |  ƒ d k s" t ‚ t t  } t | ƒ d k sD t ‚ t t t  d t  ƒ } t | ƒ d k st t ‚ d  S(   NiZ   u   90Â°u   xÂ°u   cos(xÂ° + 90Â°)(   R}   R   R¥   Rï   R[   (   Rþ  RS  t   expr3(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_degree_printingf  s    

c          C   s±  t  d ƒ }  t t |  j |  j |  j d |  j |  j ƒ ƒ t d ƒ k sR t ‚ t t t |  j |  j ƒ ƒ t d ƒ k sƒ t ‚ t t	 |  j |  j d |  j |  j ƒ ƒ t d ƒ k sÃ t ‚ t t
 |  j |  j d |  j |  j ƒ ƒ t d ƒ k st ‚ t t |  j |  j |  j d |  j |  j ƒ ƒ t d ƒ k sIt ‚ t t |  j d |  j ƒ ƒ t d ƒ k s{t ‚ t t |  j d |  j ƒ ƒ t d	 ƒ k s­t ‚ d  S(
   NR6  i   s"   (A_i)Ã—((A_x) A_i + (3â‹…A_y) A_j)s   xâ‹…(A_i)Ã—(A_j)s    âˆ‡Ã—((A_x) A_i + (3â‹…A_y) A_j)s!   âˆ‡â‹…((A_x) A_i + (3â‹…A_y) A_j)s#   (A_i)â‹…((A_x) A_i + (3â‹…A_y) A_j)s   âˆ‡(A_x + 3â‹…A_y)s   âˆ†(A_x + 3â‹…A_y)(   R   R£   R”   R&  Rï   Rð   R'  Rî   R¥   R‘   R’   R“   R   R•   (   R6  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt    test_vector_expr_pretty_printingo  s    F1@@F2c          C   sÅ  t  d ƒ }  t d |  ƒ \ } } } t d |  ƒ } t d |  g d g g ƒ \ } } } } t d |  |  g d g d g g ƒ }	 | }
 d } t d ƒ } t |
 ƒ | k s¯ t ‚ t |
 ƒ | k sÇ t ‚ | | ƒ }
 d } t d ƒ } t |
 ƒ | k sý t ‚ t |
 ƒ | k st ‚ | | ƒ }
 d	 } t d
 ƒ } t |
 ƒ | k sKt ‚ t |
 ƒ | k sct ‚ | | ƒ }
 d } t d ƒ } t |
 ƒ | k sšt ‚ t |
 ƒ | k s²t ‚ d | | ƒ }
 d } t d ƒ } t |
 ƒ | k sít ‚ t |
 ƒ | k st ‚ |	 | | ƒ }
 d } t d ƒ } t |
 ƒ | k s?t ‚ t |
 ƒ | k sWt ‚ |	 | | ƒ }
 d } t d ƒ } t |
 ƒ | k s‘t ‚ t |
 ƒ | k s©t ‚ |	 | | ƒ | | ƒ | | ƒ }
 d } t d ƒ } t |
 ƒ | k s÷t ‚ t |
 ƒ | k st ‚ d t | | ƒ }
 d } t d ƒ } t |
 ƒ | k sMt ‚ t |
 ƒ | k set ‚ | | ƒ d | | ƒ }
 d } t d ƒ } t |
 ƒ | k s©t ‚ t |
 ƒ | k sÁt ‚ d  S(   Nt   Ls   i j kt   i_0s   A B C Di   t   Hs   -is    i
A 
  s    i_0
A   
    s    iâ‚€
A  
   s     
A 
 iiýÿÿÿs        
-3*A 
    is        
-3â‹…A 
    is    i 
H  
  js    L_0   
H      
    L_0s    Lâ‚€  
H    
   Lâ‚€s)    i     L_0  k
H    *A   *B 
  L_0        s+    i    Lâ‚€  k
H   â‹…A  â‹…B 
  Lâ‚€       s             i
(x + 1)*A 
          s"            i
(x + 1)â‹…A 
          i   s    i      i
A  + 3*B 
         s    i      i
A  + 3â‹…B 
         (   R‰   RŠ   R‹   Rî   R   R¥   R£   Rï   (   R  R&  R'  R  t   i0R6  R7  RJ  RK  R  R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_pretty_print_tensor_expr€  s‚    '$							$			c          C   s#  d d l  m }  d d l m } m } m } | d ƒ } | d | ƒ \ } } } | d | ƒ } | d | g d g g ƒ \ }	 }
 } } | d	 | | g d g d g g ƒ } |  |	 | ƒ |	 | ƒ ƒ } d
 } t d ƒ } t | ƒ | k sï t ‚ t	 | ƒ | k st ‚ |	 | ƒ |  | | | ƒ |	 | ƒ ƒ } d } t d ƒ } t | ƒ | k sZt ‚ t	 | ƒ | k srt ‚ |	 | ƒ |  |
 | ƒ | | ƒ d | | | ƒ |	 | ƒ ƒ } d } t d ƒ } t | ƒ | k sÞt ‚ t	 | ƒ | k söt ‚ |	 | ƒ |
 | ƒ |  | | ƒ | | ƒ ƒ } d } t d ƒ } t | ƒ | k sPt ‚ t	 | ƒ | k sht ‚ |	 | ƒ |
 | ƒ |  | | ƒ | | ƒ ƒ } d } t d ƒ } t | ƒ | k sÂt ‚ t	 | ƒ | k sÚt ‚ t
 | | | ƒ i d | 6ƒ } d } | } t | ƒ | k st ‚ t	 | ƒ | k s5t ‚ t
 | | | ƒ i d | 6d | 6ƒ } d } | } t | ƒ | k st ‚ t	 | ƒ | k s—t ‚ t
 | | | ƒ i d | 6ƒ } d } | } t
 | | | ƒ i d | 6ƒ } d } | } t | ƒ | k st ‚ t	 | ƒ | k st ‚ d  S(   Niÿÿÿÿ(   t   PartialDerivative(   R‰   RŠ   R‹   R  s   i j kR  s   A B C Di   R  s'    d / i\
---|A |
  j\  /
dA     
       s=    âˆ‚ âŽ› iâŽž
â”€â”€â”€âŽœA âŽŸ
  jâŽ  âŽ 
âˆ‚A     
       sO    L_0  d / k   \
A   *---|H    |
       j\  L_0/
     dA        
               sa    Lâ‚€  âˆ‚ âŽ› k  âŽž
A  â‹…â”€â”€â”€âŽœH   âŽŸ
      jâŽ  Lâ‚€âŽ 
    âˆ‚A       
             i   s‹    L_0  d / k           k   \
A   *---|B *C    + 3*H    |
       j\    L_0       L_0/
     dA                    
                           sž    Lâ‚€  âˆ‚ âŽ› k          k  âŽž
A  â‹…â”€â”€â”€âŽœB â‹…C   + 3â‹…H   âŽŸ
      jâŽ    Lâ‚€       Lâ‚€âŽ 
    âˆ‚A                  
                        sm   / i    i\   d  /    \
|A  + B |*-----|C   |
\       /   L_0\ L_0/
          dD         
                     s   âŽ› i    iâŽž  âˆ‚  âŽ›   âŽž
âŽœA  + B âŽŸâ‹…â”€â”€â”€â”€âŽœC  âŽŸ
âŽ       âŽ    Lâ‚€âŽ Lâ‚€âŽ 
          âˆ‚D       
                   sw   / L_0    L_0\  d /    \
|A    + B   |*---|C   |
\           /   j\ L_0/
              dD       
                       s’   âŽ› Lâ‚€    Lâ‚€âŽž  âˆ‚ âŽ›   âŽž
âŽœA   + B  âŽŸâ‹…â”€â”€â”€âŽœC  âŽŸ
âŽ         âŽ    jâŽ Lâ‚€âŽ 
            âˆ‚D      
                    s    i=1,j
H     
      s    i=1,j=1
H       
        s    i,j=1
H     
      s       j
H    
 i=1 (   t   sympy.tensor.toperatorsR  t   sympy.tensor.tensorR‰   RŠ   R‹   Rî   R   R¥   R£   RŒ   (   R  R‰   RŠ   R‹   R  R&  R'  R  R  R6  R7  RJ  RK  R  R¡   Rñ   Rò   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt&   test_pretty_print_tensor_partial_deriv$  sn    '$	)	B	0	0	&!c          C   sG   t  d d d ƒ }  t |  t |  |  ƒ ƒ } d } | | k sC t ‚ d  S(   NRû   i   s	   a*(a x a)(   Rx   R   Rz   R¥   (   Rû   R  t   result(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_15560¿  s    c          C   sz   t  d ƒ }  t t |  d d ƒ ƒ d } d } t t |  d d ƒ ƒ | k sR t ‚ t t |  d d ƒ ƒ | k sv t ‚ d  S(   NRû   i   i   u   Î¦(a, 1, 2)s   lerchphi(a, 1, 2)(   R(   R   Rk   R¥   R£   (   Rû   t   uresultt   aresult(    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_print_lerchphiÆ  s    $c          C   sI   t  j d ƒ }  d } t |  j |  j |  j f ƒ } | | k sE t ‚ d  S(   Nt   Ns   (n_x, n_y, n_z)(   R{   t   ReferenceFrameR   Rï   Rð   Rú   R¥   (   R(  R#  R  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_issue_15583Ï  s    c    
      C   sE  d „  }  d d l  m } t d d d ƒ } |  | | ƒ ƒ d k sI t ‚ t d d d ƒ } t d d d ƒ } t d	 d d ƒ } |  | ƒ d
 k s˜ t ‚ |  | | | | ƒ d k s¼ t ‚ |  | | | | | | ƒ d k sé t ‚ t d d d ƒ } |  | ƒ d k st ‚ t d d d ƒ } |  | ƒ d k s=t ‚ t d d d ƒ } |  | ƒ d k sgt ‚ t d ƒ } t d ƒ } t d d d ƒ } t d d d ƒ }	 |  | | | | |	 ƒ d k sËt ‚ t d d d ƒ }	 t d d d ƒ } |  | | | | |	 ƒ d k st ‚ t d d d ƒ } |  | ƒ d k sAt ‚ d  S(   Nc         S   s   t  |  d t d t d d ƒS(   NR   Rž   t   mat_symbol_stylet   bold(   RŸ   R¢   R    (   R¡   (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt
   boldprettyÙ  s    iÿÿÿÿ(   t   traceR6  i   u   tr(ð€)i   R7  RJ  u   -ð€u   -ð -ð€â‹…ð + ð€u&   -ð -ð€â‹…ð -ð€â‹…ðâ‹…ð‚t   Addotu   ð€Ìˆt   omegau   Ï‰t	   omeganormu   â€–Ï‰â€–R   Rü   Rk  i   RØ  u   bâ‹…ð + Î±â‹…ðâ‹…ðœt   deltat   Betau   bâ‹…Î´ + Î±â‹…Î’â‹…ðœt   A_2u   ð€â‚‚(   Rc  R.  Rx   R¥   R(   (
   R-  R.  R6  R7  RJ  R0  Rû   Rü   Rk  RØ  (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_matrixSymbolBold×  s4    	$-((c           C   s¦   t  d d ƒ d k s t ‚ t  d d ƒ d k s6 t ‚ t  d d ƒ d k sQ t ‚ t  d d ƒ d	 k sl t ‚ t  d
 d ƒ d k s‡ t ‚ t  d d ƒ d k s¢ t ‚ d  S(   NRû   u   Ìƒu   aÌƒt   aau   aaÌƒt   aaau   aaÌƒat   aaaau   aaaÌƒat   aaaaau   aaaÌƒaat   abcdefgu   âƒœu
   abcdâƒœefg(   R€   R¥   (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_center_accentÿ  s    c              sÔ   d d l  m ‰  ˆ  d t d t ƒd k s2 t ‚ ˆ  d t d t ƒd k sT t ‚ ˆ  d t d t d d ƒd k s| t ‚ ˆ  d t d t d d ƒd	 k s¤ t ‚ t t ‡  f d
 †  ƒ t t ‡  f d †  ƒ d  S(   Niÿÿÿÿ(   R   i   R   s   1 + Iu   1 + â…ˆt   imaginary_unitR'  u   1 + â…‰c              s   ˆ  t  d t  ƒS(   NR<  (   R   (    (   R   (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR(    R)  c              s   ˆ  t  d d ƒS(   NR<  t   kkk(   R   (    (   R   (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyR(    R)  (	   Rc  R   R   R    R¥   R¢   R   R—  t
   ValueError(    (    (   R   sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   test_imaginary_unit  s    ""(((7  Rc  R    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   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   t   sympy.codegen.astRC   RD   RE   RF   RG   RH   RŠ  RI   RJ   Rî   RK   t   sympy.core.exprRL   t   sympy.core.traceRM   t   sympy.functionsRN   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   RH  Rv   Rw   Rx   Ry   Rz   t   sympy.physicsR{   Rœ  R|   R}   t   sympy.printing.prettyR~   R   RŸ   t&   sympy.printing.pretty.pretty_symbologyR€   t
   sympy.setsR   t   sympy.sets.setexprR‚   t   sympy.tensor.arrayRƒ   R„   R…   R†   R‡   t   sympy.tensor.functionsRˆ   R!  R‰   RŠ   R‹   RŒ   Rï  R   RŽ   R  R   R   R‘   R’   R“   R”   R•   t   symR–   Rû   Rü   Rk  RØ  Rï   Rð   Rú   R  R  R™   R#  R$  R   R£   R¦   R§   R©   R­   R±   R¿   RÈ   Rè   Rë   Rù   Rý   Rþ   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R"  R%  R*  R5  R8  R@  RC  RD  RF  RL  RM  RN  RP  RT  RY  R[  R^  Ra  Re  Rh  Ri  Rj  Rl  Rm  Ru  Rv  Rw  Rz  R{  R}  R€  R‚  R…  R‡  R  R‘  R”  R˜  Rš  R¢  R£  R¤  R¦  R¨  R©  Rª  R«  R¬  R®  R¯  R±  R³  R´  R¾  RÁ  RÂ  RÃ  RÄ  RÇ  RÚ  Rà  Râ  Rå  Rç  Ré  Rê  Rë  Rí  Rð  Rò  Rõ  Rö  R÷  Rø  Rù  Rû  Rý  Rÿ  R  R  R  R  R  R  R  R  R  R  R  R  R"  R$  R'  R*  R5  R;  R?  (    (    (    sF   lib/python2.7/site-packages/sympy/printing/pretty/tests/test_pretty.pyt   <module>   s8  ÿ 
.ú(("4'®								&		ÿ ›	¤		:			Y		=		<	ÿ ÿ ¸	}				9	=	V	ñ	¶	H	´			 	"			ß		Ô		$	8										\		#			 	1	@	4						ÿ ÿ 	,	8					5		y	{	@				b				Q			7	Z	&	?															
						)								¤	›					(		