ó
~9­\c           @   så  d  d l  Z  d  d l Z d  d l m Z d  d l m Z d  d l m Z d  d l m	 Z	 m
 Z
 d  d l m Z m Z m Z m Z m Z m Z d  d l m Z m Z d  d l m Z d  d	 l m Z m Z d  d
 l m Z d  d l m Z d  d l m Z m  Z  m! Z! d  d l" m# Z# d  d l$ m% Z% m& Z& m' Z' d  d l( m) Z) m* Z* d  d l+ m, Z, m- Z- m. Z. m/ Z/ m0 Z0 m1 Z1 m2 Z2 m3 Z3 m4 Z4 d  d l5 m6 Z6 m7 Z7 m8 Z8 m9 Z9 m: Z: d  d l; m< Z< m= Z= m> Z> m? Z? m@ Z@ mA ZA d  d lB mC ZC d  d lD mE ZE d  d lF mG ZG d  d lH mI ZI d  d lJ mK ZK mL ZL mM ZM mN ZN mO ZO d  d lP mQ ZQ mR ZR mS ZS mT ZT mU ZU mV ZV mW ZW d e/ e0 f d „  ƒ  YZX d „  ZY d „  ZZ d e/ e1 f d „  ƒ  YZ[ d „  Z\ d  „  Z] d! e/ e2 f d" „  ƒ  YZ^ d# „  Z_ d$ „  Z` d% e/ e3 f d& „  ƒ  YZa d' „  Zb d( „  Zc d) e/ e6 f d* „  ƒ  YZd d+ „  Ze d, „  Zf d- e/ e7 f d. „  ƒ  YZg d/ „  Zh d0 „  Zi d1 e/ e4 f d2 „  ƒ  YZj d3 e/ e8 f d4 „  ƒ  YZk d5 e/ e9 f d6 „  ƒ  YZl d7 e/ e: f d8 „  ƒ  YZm d9 „  Zn d: „  Zo d; „  Zp d< „  Zq d= „  Zr d> „  Zs d? „  Zt d@ „  Zu dA „  Zv dB „  Zw dC „  Zx dD „  Zy dE „  Zz dF „  Z{ dG „  Z| dH „  Z} dI „  Z~ dJ „  Z dK „  Z€ dL „  Z dM „  Z‚ dN „  Zƒ dO „  Z„ dP „  Z… dQ „  Z† dR „  Z‡ dS „  Zˆ dT „  Z‰ dU „  ZŠ dV „  Z‹ dW „  ZŒ dX „  Z dY „  ZŽ dZ „  Z d[ „  Z d\ „  Z‘ d] „  Z’ d^ „  Z“ d_ „  Z” d` „  Z• da „  Z– db „  Z— dc „  Z˜ dd „  Z™ de „  Zš df „  Z› dg „  Zœ dh „  Z di „  Zž dj „  ZŸ dk „  Z  dl „  Z¡ dm „  Z¢ dn „  Z£ do „  Z¤ dp „  Z¥ dq „  Z¦ dr „  Z§ ds „  Z¨ dt „  Z© du „  Zª dv „  Z« dw „  Z¬ dx „  Z­ dy „  Z® dz „  Z¯ d{ „  Z° d| „  Z± d} „  Z² d~ „  Z³ d „  Z´ d€ „  Zµ d „  Z¶ d‚ „  Z· dƒ „  Z¸ d„ „  Z¹ d… „  Zº d† „  Z» d‡ „  Z¼ eL dˆ „  ƒ Z½ d‰ „  Z¾ dŠ „  Z¿ d‹ „  ZÀ dŒ „  ZÁ d „  ZÂ d S(Ž   iÿÿÿÿN(   t   Q(   t   Add(   t   range(   t   Functiont   diff(   t   Et   Floatt   It   Integert   oot   pi(   t   Eqt   Lt(   t   S(   t   Symbolt   symbols(   t   Abs(   t   exp(   t   Maxt   Mint   sqrt(   t	   Piecewise(   t   cost   sint   tan(   t   Andt   Or(	   t
   ShapeErrort   MatrixErrort   NonSquareMatrixErrort   _MinimalMatrixt   MatrixShapingt   MatrixPropertiest   MatrixOperationst   MatrixArithmetict   MatrixSpecial(   t   MatrixDeterminantt   MatrixReductionst   MatrixSubspacest   MatrixEigent   MatrixCalculus(   t   Matrixt   diagt   eyet   matrix_multiply_elementwiset   onest   zeros(   t   Poly(   t   simplify(   t   trigsimp(   t   flatten(   t   raisest   XFAILt   slowt   skipt   warns_deprecated_sympy(   t   at   bt   ct   dt   xt   yt   zt   ShapingOnlyMatrixc           B   s   e  Z RS(    (   t   __name__t
   __module__(    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyR?   #   s   c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   t  |  | k ƒ S(   N(   t   int(   t   it   j(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   <lambda>(   t    (   R?   (   t   n(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   eye_Shaping'   s    c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   d S(   Ni    (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ,   RF   (   R?   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   zeros_Shaping+   s    t   PropertiesOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRJ   /   s   c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   t  |  | k ƒ S(   N(   RB   (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   4   RF   (   RJ   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   eye_Properties3   s    c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   d S(   Ni    (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   8   RF   (   RJ   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   zeros_Properties7   s    t   OperationsOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRM   ;   s   c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   t  |  | k ƒ S(   N(   RB   (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   @   RF   (   RM   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   eye_Operations?   s    c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   d S(   Ni    (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   D   RF   (   RM   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   zeros_OperationsC   s    t   ArithmeticOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRP   G   s   c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   t  |  | k ƒ S(   N(   RB   (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   L   RF   (   RP   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   eye_ArithmeticK   s    c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   d S(   Ni    (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   P   RF   (   RP   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   zeros_ArithmeticO   s    t   DeterminantOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRS   S   s   c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   t  |  | k ƒ S(   N(   RB   (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   X   RF   (   RS   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   eye_DeterminantW   s    c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   d S(   Ni    (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   \   RF   (   RS   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   zeros_Determinant[   s    t   ReductionsOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRV   _   s   c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   t  |  | k ƒ S(   N(   RB   (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   d   RF   (   RV   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   eye_Reductionsc   s    c         C   s   t  |  |  d „  ƒ S(   Nc         S   s   d S(   Ni    (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   h   RF   (   RV   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   zeros_Reductionsg   s    t   SpecialOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRY   k   s   t   SubspaceOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRZ   o   s   t   EigenOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyR[   s   s   t   CalculusOnlyMatrixc           B   s   e  Z RS(    (   R@   RA   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyR\   w   s   c       	   C   sK  t  d d d d d d d d g ƒ }  |  j d k s9 t ‚ |  j d k sN t ‚ |  d d k sd t ‚ |  d d k sz t ‚ t |  ƒ d d d d d d g k s¤ t ‚ t |  d d  d  … f ƒ d d d g k sÕ t ‚ t |  d  d  … d f ƒ d d g k st ‚ t |  d  d  … d  d  … f ƒ t |  ƒ k s7t ‚ |  d  d  … d  d  … f |  k s_t ‚ t  |  ƒ |  k swt ‚ t  d d d g d d d g g ƒ |  k s§t ‚ t  d d d g d d d g f ƒ |  k s×t ‚ t  d d	 g ƒ |  k sõt ‚ t  d
 d f ƒ |  k st ‚ t  d d g d d g d d g g ƒ |  k sGt ‚ d  S(   Ni   i   i   i   i   i   (   i   i   (   i   i   i   (   i   i   i   (   i   i   i   (   i   i   i   (   R   t   rowst   AssertionErrort   colst   list(   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test__MinimalMatrix{   s     $*1.4(00c          C   st   t  d d d d d d g ƒ }  |  j ƒ  } | j d k s? t ‚ x. t d ƒ D]  } | | | d k sL t ‚ qL Wd  S(   Ni   i   i   i   (   R?   t   vecR_   R^   R   (   t   mt   m_vecRC   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_vec   s
    c          C   s½   t  j t  j t t t  j g t t t t d g t t  j t t d g g }  t  j t  j t t t  j t t t t d t t  j t t d g } t d d | ƒ } | j ƒ  |  k s¹ t	 ‚ d  S(   Ni   i   i   (
   R   t   Onet   HalfR<   R=   t   ZeroR>   R?   t   tolistR^   (   t   lstt   flat_lstRc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_tolist—   s    LCc              s×  t  d d d d d d d d d d d	 g	 ƒ ‰  t t ‡  f d
 †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ ˆ  j d ƒ ˆ  j d ƒ k oÌ t d d d g d d d g g ƒ k n s× t ‚ ˆ  j d ƒ ˆ  j d ƒ k o!t d d g d d g d d g g ƒ k n s,t ‚ ˆ  j d ƒ ˆ  j d ƒ k ost d d d g d d d	 g g ƒ k n s~t ‚ ˆ  j d ƒ ˆ  j d ƒ k oÈt d d g d d g d d	 g g ƒ k n sÓt ‚ d  S(   Ni   i   i   i   i   i   i   i   i	   c              s   ˆ  j  d ƒ S(   Ni   (   t   row_del(    (   t   e(    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE       RF   c              s   ˆ  j  d ƒ S(   Niûÿÿÿ(   Rm   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ¡   RF   c              s   ˆ  j  d ƒ S(   Ni   (   t   col_del(    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ¢   RF   c              s   ˆ  j  d ƒ S(   Niûÿÿÿ(   Ro   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   £   RF   iÿÿÿÿiþÿÿÿ(   R?   R3   t
   ValueErrorRm   R)   R^   Ro   (    (    (   Rn   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_row_col_delž   s    -RURc          C   sÁ   t  d d g d d g g ƒ }  t  d t g t d g g ƒ } t  d t d g t d t g t t t g g ƒ } |  j ƒ  |  g k s‡ t ‚ | j ƒ  | g k s¢ t ‚ | j ƒ  | g k s½ t ‚ d  S(   Ni   i   i   (   R)   R<   R=   R>   t   get_diag_blocksR^   (   R8   R9   R:   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_get_diag_blocks1¬   s    0c          C   s¢  t  d d g d d g g ƒ }  t  d t g t d g g ƒ } t  d t d g t d t g t t t g g ƒ } t |  | | ƒ t |  | | ƒ t |  | | ƒ t | | | ƒ f \ } } } } t | j | j | ƒ } t | j | j | ƒ } t | j | j | ƒ } t | j | j | ƒ } | j ƒ  |  | | g k s;t	 ‚ | j ƒ  |  | | g k s\t	 ‚ | j ƒ  |  | | g k s}t	 ‚ | j ƒ  | | | g k sžt	 ‚ d  S(   Ni   i   i   (
   R)   R<   R=   R>   R*   R?   R]   R_   Rr   R^   (   R8   R9   R:   t   At   Bt   Ct   D(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_get_diag_blocks2µ   s    0N!!!c          C   s)   t  d d d d g ƒ }  |  j d k d  S(   Ni   i   i    (   i   i   (   R?   t   shape(   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_shapeÅ   s    c          C   s©   t  d ƒ }  |  j d d ƒ t d d d
 ƒ k s6 t ‚ t d d d „  ƒ } | j d d ƒ t d d d d f ƒ k s{ t ‚ | j d d	 ƒ t d d f ƒ k s¥ t ‚ d  S(   Ni   i   i	   i    i   c         S   s   |  | S(   N(    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Í   RF   i   i   i   (	   i   i    i    i    i   i    i    i    i   (   i    i   i   (   i   i   i   (   i   i   i   (   i   i   i   (   i    i   i   i   i   i   (   i   i   i   i   i   i   (   RH   t   reshapeR)   R^   R?   (   t   m0t   m1(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_reshapeÊ   s    **c          C   s‘   t  d d d d d d d d d d d	 g	 ƒ }  |  j d
 ƒ t d d d d d g ƒ k s] t ‚ |  j d
 ƒ t d d d d d g ƒ k s t ‚ d  S(   Ni   i   i   i   i   i   i   i   i	   i    (   R?   t   rowR)   R^   t   col(   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_row_colÓ   s    -0c           C   sg   t  d ƒ j t d d d g ƒ ƒ t d d d d g d d d d g d d d d g g ƒ k sc t ‚ d  S(   Ni   i   i   i    (   RH   t   row_joinR)   R^   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_row_joinÙ   s    !c           C   sm   t  d ƒ j t d d d g g ƒ ƒ t d d d g d d d g d d d g d d d g g ƒ k si t ‚ d  S(   Ni   i   i   i    (   RH   t   col_joinR)   R^   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_col_joinà   s
    $c          C   sŽ   t  d d d g g ƒ }  xo t d d ƒ D]^ } d d d g } | j | d ƒ t t d ƒ j | |  ƒ j d ƒ j ƒ  ƒ | k s( t ‚ q( Wd  S(   Ni   iüÿÿÿi   i   i    i   (	   R)   R   t   insertR2   RH   t
   row_insertR€   Ri   R^   (   t   r4RC   t   l(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_row_insertè   s
    c          C   s“  t  d d d g ƒ }  xo t d d ƒ D]^ } d d d g } | j | d ƒ t t d ƒ j | |  ƒ j d ƒ j ƒ  ƒ | k s% t ‚ q% Wt	 d ƒ j d t  d d g d d g d d g d d g d d g d d g g ƒ ƒ t  d d d d d d d d g d d d d d d d d g d d d d d d d d g d d d d d d d d g d d d d d d d d g d d d d d d d d g g ƒ k st ‚ d  S(	   Ni   iüÿÿÿi   i    i   i   i   i   (
   R)   R   R†   R2   RI   t
   col_insertR   Ri   R^   RH   (   t   c4RC   R‰   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_col_insertð   s    =Qc        
      s  t  d d d „  ƒ ‰  ˆ  j d d d g d d g ƒ t d d d d d d d d g ƒ k s` t ‚ ˆ  j d d g d d d g ƒ t d d d d d d d d	 g ƒ k s« t ‚ ˆ  j t d ƒ t d ƒ ƒ ˆ  k sÕ t ‚ t t ‡  f d
 †  ƒ t t ‡  f d †  ƒ d  S(   Ni   i   c         S   s   |  d | S(   Ni   (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   i    i   i   i	   i
   i   c              s   ˆ  j  d g d g ƒ S(   Ni   i    (   t   extract(    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   c              s   ˆ  j  d g d g ƒ S(   Ni    i   (   RŽ   (    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   (   R?   RŽ   R)   R^   R   R3   t
   IndexError(    (    (   Rc   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_extract   s    KK*c             s¿  t  d d d „  ƒ ‰  t  d d d „  ƒ ‰ ˆ  ˆ  j ˆ  ƒ k sE t ‚ ˆ  j ˆ  ˆ  ˆ  ƒ t  j ˆ  ˆ  ˆ  ƒ k oø t d d d d d d d d d g	 d d d d d d d d d g	 d	 d
 d d	 d
 d d	 d
 d g	 d d d d d d d d d g	 g ƒ k n st ‚ t t ‡  ‡ f d †  ƒ t j ƒ  t ƒ  k s7t ‚ t j d d ƒ }  t j d d ƒ } t j d d ƒ } t j d d ƒ } t  j |  | | | ƒ ‰  ˆ  j d k rµˆ  j d	 k s»t ‚ d  S(   Ni   i   c         S   s   |  d | S(   Ni   (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   
  RF   c         S   s   |  d | S(   Ni   (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   i    i   i   i   i   i   i   i	   i
   i   c              s   ˆ  j  ˆ  ˆ ƒ S(   N(   t   hstack(    (   Rc   t   m2(    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   (	   R?   R‘   R^   R)   R3   R   R.   R]   R_   (   t   M1t   M2t   M3t   M4(    (   Rc   R’   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_hstack	  s     /5c              sS  t  d d d „  ƒ ‰  t  d d d „  ƒ ‰ ˆ  ˆ  j ˆ  ƒ k sE t ‚ ˆ  j ˆ  ˆ  ˆ  ƒ t  j ˆ  ˆ  ˆ  ƒ k ot d d d g d d d g d	 d
 d g d d d g d d d g d d d g d	 d
 d g d d d g d d d g d d d g d	 d
 d g d d d g g ƒ k n st ‚ t t ‡  ‡ f d †  ƒ t j ƒ  t ƒ  k sOt ‚ d  S(   Ni   i   c         S   s   |  d | S(   Ni   (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   c         S   s   |  d | S(   Ni   (    (   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE      RF   i    i   i   i   i   i   i   i	   i
   i   c              s   ˆ  j  ˆ  ˆ ƒ S(   N(   t   vstack(    (   Rc   R’   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   /  RF   (   R?   R˜   R^   R)   R3   R   (    (    (   Rc   R’   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_vstack  s$    /#c       	   C   s~   t  d d d d t d d t g ƒ }  |  j ƒ  t d ƒ t d ƒ t d ƒ t h k s\ t ‚ |  j t ƒ t h k sz t ‚ d  S(   Ni   i   iÿÿÿÿ(   RJ   R<   t   atomsR   R^   R   (   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_atoms4  s    &6c           C   s.   t  t g d g g ƒ j t h k s* t ‚ d  S(   Ni    (   RJ   R<   t   free_symbolsR^   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_free_symbols:  s    c          C   sŠ   t  t t f d f ƒ }  |  j t ƒ s- t ‚ |  j t ƒ sC t ‚ |  j t ƒ sX t ‚ t  d t f d f ƒ }  |  j t ƒ s† t ‚ d  S(   Ni   i   (   i   i   (   i   i   (   RJ   R<   R=   t   hasR^   R>   R   (   Rt   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_has>  s    c          C   s  t  d ƒ }  t d d d d g ƒ j ƒ  t k s6 t ‚ t d d d |  d d |  d t |  d d d |  t t |  t d g	 ƒ } | j ƒ  t k sž t ‚ | j d t ƒ t k s¼ t ‚ | j d d „  ƒ t k sÝ t ‚ t d d g  | D] }  |  j ƒ  ^ qí ƒ } | j d t ƒ t k s&t ‚ t d d g  t j	 g t
 | ƒ d D] }  |  j ƒ  ^ qJƒ } | j ƒ  t k s}t ‚ d  S(   NR<   i   i   i   i    R0   c         S   s   |  S(   N(    (   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   N  RF   (   R   RJ   t   is_anti_symmetrict   FalseR^   R=   t   Truet   expandR   Rf   R`   (   R<   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_anti_symmetricH  s    *P!+?c          C   s5  t  d d d d d d g ƒ }  |  j ƒ  s1 t ‚ |  j ƒ  sC t ‚ |  j d t ƒ s[ t ‚ t  d d d d d d g ƒ }  |  j ƒ  s‹ t ‚ t  d d t d d d ƒ ƒ }  |  j ƒ  s» t ‚ |  j ƒ  sÍ t ‚ t  d d d d d d d d d d d g	 ƒ }  |  t d d d ƒ k st ‚ t  d d t d d ƒ ƒ }  |  j ƒ  sFt ‚ |  j ƒ  sXt ‚ t  d d	 d
 f ƒ }  |  j ƒ  st ‚ t  d d f ƒ }  |  j ƒ  s£t ‚ t d d d t d d t d t	 t d d d d t	 d d g	 ƒ }  |  j ƒ  sút ‚ |  j d t ƒ st ‚ |  j
 ƒ  j d t ƒ s1t ‚ d  S(   Ni   i    i   R0   i   i   i   (   i   i    (   i    i   (   i    i    (   i   i    i    (   i    i   i    (   RJ   t   is_diagonalR^   t   is_symmetricR¡   R*   R.   R)   R<   R=   R£   (   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_diagonal_symmetricalV  s,    -Ec          C   sÒ   t  d t g t d g g ƒ }  |  j s. t ‚ t  d t t g t d g g ƒ }  |  j t k sf t ‚ t  t t g t d g g ƒ }  |  j d  k sš t ‚ t  t d g t d g g ƒ }  |  j t k sÎ t ‚ d  S(   Ni   i   (   RJ   R   t   is_hermitianR^   R¡   R<   t   None(   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_hermitianv  s    #c           C   ss   t  d ƒ j s t ‚ t t d ƒ ƒ j s1 t ‚ t t d ƒ ƒ j sM t ‚ t d d d g g ƒ j so t ‚ d  S(   Ni   i   i    (   RK   t   is_IdentityR^   RJ   R.   R-   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_Identity  s    c          C   sŠ  t  t t g t t g g ƒ }  |  j ƒ  t k s6 t ‚ t  d d d d g d d d d g g ƒ }  |  j ƒ  t k sx t ‚ t  d d d d g d d t d g g ƒ }  |  j ƒ  t k sº t ‚ t  d t d g g ƒ }  |  j ƒ  t k sê t ‚ t  d d d g g ƒ }  |  j ƒ  t k st ‚ t  d g t g d g g ƒ }  |  j ƒ  t k sPt ‚ t  d g d g d g g ƒ }  |  j ƒ  t k s†t ‚ d  S(	   Ni   i   i   i   i   i   i   i   (   RJ   R<   t   is_symbolicR¢   R^   R¡   (   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_symbolic‰  s    **c          C   sd   t  d d d g g ƒ }  |  j t k s- t ‚ t  d g d g d g g ƒ }  |  j t k s` t ‚ d  S(   Ni   i   i   (   RJ   t   is_upperR¢   R^   R¡   (   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_upperš  s    c          C   sd   t  d d d g g ƒ }  |  j t k s- t ‚ t  d g d g d g g ƒ }  |  j t k s` t ‚ d  S(   Ni   i   i   (   RJ   t   is_lowerR¡   R^   R¢   (   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_lower¡  s    c          C   sY   t  d g d g g ƒ }  t  d d g d d g g ƒ } |  j sF t ‚ | j sU t ‚ d  S(   Ni   i   (   RJ   t	   is_squareR^   (   Rc   R’   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_square¨  s    c          C   se   t  d d d d d d g ƒ }  |  j ƒ  s0 t ‚ t  d d d d d d g ƒ }  |  j ƒ  sa t ‚ d  S(   Ni   i    i   (   RJ   R¦   R^   (   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_symmetric¯  s    c          C   s  t  d d d g d d d g d d d g g ƒ }  |  j s? t ‚ t  d d d d d d d d d d d g	 ƒ }  |  j s{ t ‚ t  d d d d d d d d d d d g	 ƒ }  |  j t k s½ t ‚ |  j t k sÒ t ‚ t  d d d g d d d g d d d g g ƒ }  |  j st ‚ d  S(   Ni   i   i   i   i   i    iÿÿÿÿ(   RJ   t   is_upper_hessenbergR^   t   is_lower_hessenbergR¡   (   Rt   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_hessenberg¶  s    0--0c          C   s  t  d d g  ƒ j s t ‚ t  d d g d d g g ƒ j sB t ‚ t  t d d ƒ ƒ j s` t ‚ t  t d ƒ ƒ j s| t ‚ t  t d g d d g g ƒ j d  k s© t ‚ t  t d g d d g g ƒ j t k sÖ t ‚ t d d t	 ƒ}  t  |  d g d d g g ƒ j t k st ‚ d  S(   Ni    i   i   i   R8   t   nonzero(
   RJ   t   is_zeroR^   R.   R+   R<   R©   R¡   R   R¢   (   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_zeroÃ  s    '--c          C   s   t  t d d d d d d g ƒ j ƒ  ƒ t  d d d g ƒ k sE t ‚ t d d t ƒ}  t  t d d |  d d d g ƒ j ƒ  ƒ t  |  d g ƒ k s™ t ‚ d  S(   Ni   i    i   i   R<   t   real(   t   setRJ   t   valuesR^   R   R¢   (   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_valuesÎ  s    Ec          C   s†   t  t d ƒ ƒ }  |  j d „  ƒ t d ƒ d k s: t ‚ |  j d „  ƒ t d ƒ k s^ t ‚ |  j d „  ƒ t d ƒ k s‚ t ‚ d  S(   Ni   c         S   s   d |  S(   Ni   (    (   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ×  RF   i   c         S   s   d S(   Ni    (    (   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Ø  RF   c         S   s   d S(   Ni   (    (   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Ù  RF   (   RM   R+   t	   applyfuncR^   R.   R-   (   R|   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_applyfuncÕ  s    ($c          C   sY   d t  g d d g g }  t d d g t  d g g ƒ } | j ƒ  t |  ƒ k sU t ‚ d  S(   Ni    i   (   R   RM   t   adjointR)   R^   (   t   datt   ans(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_adjointÜ  s    c       	   C   sž   t  d d d d d d g ƒ }  t  d d d t j d d t j d d t j d d t j g ƒ } | j ƒ  \ } } | |  k sˆ t ‚ | |  k sš t ‚ d  S(   Ni   i   i   i   (   RM   R   t   ImaginaryUnitt   as_real_imagR^   (   R}   t   m3R8   R9   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_as_real_imagâ  s
    Fc          C   sÿ   t  d t d g d d d g g ƒ }  |  j t d d g t d g d d g g ƒ k sZ t ‚ |  j t d t d g d d d g g ƒ k sŽ t ‚ |  j |  j ƒ  k s© t ‚ |  j |  j j k sÄ t ‚ |  j t d d g t d g d d g g ƒ k sû t ‚ d  S(   Ni    i   i   i   (   RM   R   t   TR)   R^   Rv   t	   conjugatet   H(   t   M(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_conjugateë  s    	
c          C   sg   t  t t t d t ƒg g ƒ }  |  d d t k s; t ‚ |  j ƒ  t d t g g ƒ k sc t ‚ d  S(   Nt   evaluatei    i   (   RM   R   R<   R¡   R^   t   doitR)   (   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt	   test_doitý  s    !c              sš   t  d d t d ƒ d g ƒ ‰  t ‡  f d †  t d ƒ Dƒ ƒ sF t ‚ t ‡  f d †  t d ƒ Dƒ ƒ sn t ‚ t ‡  f d †  t d ƒ Dƒ ƒ s– t ‚ d  S(   Ni   i   i   i   c         3   s/   |  ]% } ˆ  j  ƒ  | ˆ  | j  ƒ  k Vq d  S(   N(   t   evalf(   t   .0RC   (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>  s    c         3   s5   |  ]+ } ˆ  j  d  ƒ | ˆ  | j  d  ƒ k Vq d S(   i   N(   RÒ   (   RÓ   RC   (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>  s    c         3   s5   |  ]+ } ˆ  j  d  ƒ | ˆ  | j  d  ƒ k Vq d S(   i   N(   RG   (   RÓ   RC   (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>  s    (   RM   R   t   allR   R^   (    (    (   R8   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_evalf  s    ((c          C   s  t  t t t d g t t t t t t t t t g g ƒ }  |  j ƒ  } | t t t t d d g t t d t t d t t t t d t d g g ƒ k s° t ‚ t d d t ƒ} t  d d t t	 | ƒ g ƒ j d t ƒ t t
 | ƒ t	 t | ƒ g ƒ k st ‚ d  S(   Ni   i   R8   R¼   i   t   complex(   RM   R<   R=   R£   R)   R^   R   R¢   R   R   R   R   (   R|   R}   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_expand
  s    B\(c          C   s¤  t  t t ƒ d t t d ƒ g t t d ƒ t t ƒ d t t d ƒ t t ƒ d g g ƒ }  |  j t j t ƒ t j t ƒ @ƒ } | t t d t t ƒ g t d t t ƒ t d t t ƒ g g ƒ k s× t	 ‚ |  j t j
 t ƒ t j
 t ƒ @ƒ } | t t d t g t t d t d t g g ƒ k s:t	 ‚ |  j t j t ƒ t j t ƒ @ƒ } | t t d t g t t d t d t g g ƒ k s t	 ‚ d  S(   Ni   (   RM   R   R<   R   R=   t   refineR    R¼   R)   R^   t   positivet   negative(   R|   R}   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_refine  s     B%P%>%c             sv   t  d d t ƒ\ ‰  ‰ t d d ‡ f d †  ƒ }  t d d ‡  f d †  ƒ } | j ˆ  ˆ ƒ } | |  k sr t ‚ d  S(   Ns   F, Gt   clsi   c            s   ˆ  |  | ƒ S(   N(    (   RC   RD   (   t   G(    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   &  RF   c            s   ˆ  |  | ƒ S(   N(    (   RC   RD   (   t   F(    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   '  RF   (   R   R   RM   t   replaceR^   (   t   KRÍ   t   N(    (   RÞ   RÝ   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_replace$  s
    c             sø   t  d d t ƒ\ ‰  }  t d d |  d ƒ i |  d ƒ ˆ  d ƒ 6f |  d ƒ i |  d ƒ ˆ  d ƒ 6f |  d ƒ i |  d ƒ ˆ  d ƒ 6f |  d ƒ i |  d ƒ ˆ  d ƒ 6f g ƒ } t d d ‡  f d †  ƒ } | j ˆ  |  t ƒ } | | k sô t ‚ d  S(   Ns   F, GRÜ   i   i    i   c            s   ˆ  |  | ƒ S(   N(    (   RC   RD   (   RÞ   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   0  RF   (   R   R   RM   Rß   R¢   R^   (   RÝ   Rà   RÍ   Rá   (    (   RÞ   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_replace_map,  s    YAc       
   C   sj  t  d ƒ }  t d ƒ } t d t d t t t t t g | t ƒ t | t ƒ | t ƒ d d |  t |  t ƒ |  t g g ƒ } | j ƒ  t t t t t d t g d t d d d t t |  ƒ t |  g g ƒ k sì t	 ‚ d t d } t | g g ƒ } | j ƒ  t | g g ƒ k s0t	 ‚ | j d t
 ƒ t | j d t
 ƒ g g ƒ k sft	 ‚ d  S(   NRG   t   fi   i   t   ratio(   R   R   RM   R<   R=   R   R
   R0   R)   R^   R	   (   RG   Rä   RÍ   t   eq(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_simplify5  s    $N%=$c           C   sÐ  t  d t g t d g g ƒ j t d ƒ t d d g d d g g ƒ k sN t ‚ t  t d g t t d g g ƒ j t d g t d g g ƒ t d d g d d g g ƒ k s¯ t ‚ t  t d g t t d g g ƒ j t d f t d f g ƒ t d d g d d g g ƒ k st ‚ t  t d g t t d g g ƒ j i d t 6d t 6ƒ t d d g d d g g ƒ k smt ‚ t  t t g g ƒ j i t d t 6t d t 6d t ƒt t d t d g g ƒ k sÌt ‚ d  S(	   Ni   i   i   i   iÿÿÿÿiþÿÿÿiýÿÿÿt   simultaneous(   RM   R<   t   subsR)   R^   R=   R¢   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt	   test_subsC  s    N:':'6'8c          C   sL   t  d d d g d d d g d d d g g ƒ }  |  j ƒ  d k sH t ‚ d  S(   Ni   i    i   i   i   (   RM   t   traceR^   (   RÍ   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_traceO  s    c           C   s³   t  d t g t d g g ƒ j i d t 6ƒ t d d g d d g g ƒ k sR t ‚ t  t d g t t d g g ƒ j i d t 6d t 6ƒ t d d g d d g g ƒ k s¯ t ‚ d  S(   Ni   i   i   i   iÿÿÿÿiþÿÿÿiýÿÿÿ(   RM   R<   t   xreplaceR)   R^   R=   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_xreplaceV  s    +'6c             så  t  d d d d d d d d d d d	 d
 d d g ƒ ‰  t t ‡  f d †  ƒ ˆ  j d d g d d g g ƒ }  ˆ  j d d g d d g g ƒ |  k oÒ t d d d d g d	 d
 d d g d d d d g g ƒ k n sÝ t ‚ ˆ  j d d g d d g g ƒ }  ˆ  j d d g d d g g d d ƒ|  k oit d d d d g d d d d g d
 d d	 d g g ƒ k n stt ‚ ˆ  j d d g d d g g d d ƒ}  ˆ  j d d g d d g g d d d d ƒ|  k ot d d d d g d d d d g d d	 d
 d g g ƒ k n st ‚ ˆ  j d d d d g ƒ t d d d d g d	 d
 d d g d d d d g g ƒ k sqt ‚ d d l m	 } ˆ  j | d d d d g ƒ ƒ t d d d d g d	 d
 d d g d d d d g g ƒ k sát ‚ d  S(   Ni   i   i   i   i   i   i   i   i	   i
   i   i   c              s   ˆ  j  d d g g ƒ S(   Ni    i   (   t   permute(    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   `  RF   i    t   orientationR_   t	   directiont   backwardiÿÿÿÿ(   t   Permutation(
   RM   R3   R   t   permute_rowsRï   R)   R^   t   permute_colst   sympy.combinatoricsRó   (   R9   Ró   (    (   R8   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_permute]  s8    6!,&!/&'5&!!c          C   s^   t  d d g t t g g ƒ }  t |  ƒ t  d d g t t ƒ t t ƒ g g ƒ k sZ t ‚ d  S(   Ni   iþÿÿÿi   (   RP   R<   R=   t   absR   R^   (   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_abs‚  s    c              sÅ   t  d d d g t t t g d t d t t g g ƒ ‰  ˆ  ˆ  t  d d d g d t d t d t g d t d d t t g g ƒ k s t ‚ t  d d d d g ƒ ‰ t t ‡  ‡ f d †  ƒ d  S(	   Ni   i   i   iÎÿÿÿi   i   iœÿÿÿc              s   ˆ  ˆ S(   N(    (    (   Rc   RG   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ‹  RF   (   RP   R<   R=   R>   R^   R3   R   (    (    (   Rc   RG   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_add‡  s    8Xc             sü  t  d d d f ƒ ‰  t  d d f ƒ ‰ t t ‡  ‡ f d †  ƒ t t ‡  f d †  ƒ ˆ  ˆ }  |  d d k sv t ‚ |  d d k sŒ t ‚ |  d d k s¢ t ‚ |  d d k s¸ t ‚ |  d d	 k sÎ t ‚ |  d d k sä t ‚ y t d
 ƒ Wn t k
 rn… X|  d d k st ‚ |  d d k s2t ‚ |  d d k sHt ‚ |  d d k s^t ‚ |  d d	 k stt ‚ |  d  d k sŠt ‚ ˆ  j |  ƒ } | t ˆ  |  ƒ k s´t ‚ | d! d k sÊt ‚ | d" d k sàt ‚ | d# d	 k söt ‚ | d$ d k st ‚ | d% d k s"t ‚ | d& d k s8t ‚ t t ‡  ‡ f d †  ƒ ˆ t	 d ƒ }  t
 |  t  ƒ svt ‚ |  d' t k sŒt ‚ |  d( d t k s¦t ‚ |  d) d t k sÀt ‚ |  d* d k sÖt ‚ t ˆ } |  | k sòt ‚ d ˆ }  t
 |  t  ƒ st ‚ |  d+ d k s't ‚ |  d, d- k s=t ‚ |  d. d/ k sSt ‚ |  d0 d k sit ‚ y t d ƒ Wn t k
 rŠnn Xt
 |  t  ƒ s t ‚ |  d1 d k s¶t ‚ |  d2 d3 k sÌt ‚ |  d4 d5 k sât ‚ |  d6 d k søt ‚ d  S(7   Ni   i   i   i    i   c              s   ˆ ˆ  S(   N(    (    (   R8   R9   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   š  RF   c              s   ˆ  i  S(   N(    (    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ›  RF   i   i   s	   c = a @ bi   c              s   ˆ  j  ˆ ƒ S(   N(   t   multiply_elementwise(    (   R8   R9   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ¹  RF   R<   i   s	   c = 5 @ b(   i   i   (   i   i   (   i    i   (   i   i   (   i   i    (   i    i    (   i    i   (   i   i    (   i   i   (   i   i    (   i   i   (   i    i    (   i    i   (   i   i    (   i   i   (   i   i    (   i   i   (   i    i    (   i    i   (   i   i    (   i   i   (   i   i    (   i   i   (   i    i    (   i    i   (   i   i    (   i   i   (   i    i    (   i    i   i
   (   i   i    i   (   i   i   (   i    i    (   i    i   i
   (   i   i    i   (   i   i   (   RP   R3   R   t	   TypeErrorR^   t   evalt   SyntaxErrorRû   R,   R   t
   isinstanceR<   (   R:   t   ht   c2(    (   R8   R9   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_multiplicationŽ  st    


c          C   s¼   t  d d g d d g g ƒ }  |  j d ƒ t k s9 t ‚ |  j d ƒ t k sT t ‚ y t d ƒ Wn! t k
 ru n t k
 r… n Xy t d ƒ Wn! t k
 r§ n t k
 r· n Xd  S(   Ni   i   i   i   s   2 @ as   a @ 2(   R)   t
   __matmul__t   NotImplementedR^   t   __rmatmul__Rý   Rþ   Rü   (   R8   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_matmulØ  s    c       
   C   s4  t  t d „  ƒ t d d g d d g g ƒ }  |  d d k sE t ‚ t d d
 d g d d d g d d d
 g g ƒ }  |  d d k sŒ t ‚ |  d t d ƒ k s¨ t ‚ |  d
 |  k s¾ t ‚ t d g g ƒ d d d k sä t ‚ t d
 d g d d g g ƒ t d ƒ t d d g d d g g ƒ k s0t ‚ d  S(    Nc           S   s   t  d ƒ d S(   Ni   i   (   i   i   (   R)   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ò  RF   i   i   i   i   iü  i¡  i,*  i7  i   i   i   i"  i  iû   iÀ  i¸  ip  i¾  iº  i±  i    id   i   i
   i   i   (   iü  i¡  i,*  i7  (	   i"  i  iû   iÀ  i¸  ip  i¾  iº  i±  (   i    i    l                (   R3   R   RP   R^   R+   R   (   Rt   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_powerñ  s    0&c          C   sA   t  d d d d g ƒ }  |  t  d d d d g ƒ k s= t ‚ d  S(   Ni   i   iÿÿÿÿiþÿÿÿ(   RP   R^   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_negþ  s    c          C   sD   t  d d d d g ƒ }  |  |  t  d d d d g ƒ k s@ t ‚ d  S(   Ni   i   i    (   RP   R^   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_sub  s    c          C   sX   t  d d d d g ƒ }  |  d t  d d t d ƒ d t d ƒ d g ƒ k sT t ‚ d  S(   Ni   i   (   RP   R   R^   (   RG   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_div  s    c             s(  t  d d d d d d d d g ƒ ‰  t t ‡  f d †  ƒ t d ƒ }  t d ƒ } |  j ƒ  d k sj t ‚ | j ƒ  d k s‚ t ‚ t d	 ƒ } t  d d g  ƒ ‰  t  d d d g ƒ } t  d d d d d d g ƒ } t  d d d d d d d d d
 d d g	 ƒ } t  d d | d d d d d d d
 d d d d d d d d g ƒ ‰ ˆ  j ƒ  d k sZt ‚ | j ƒ  d k srt ‚ | j ƒ  d k sŠt ‚ | j ƒ  d k s¢t ‚ ˆ j ƒ  d | d k sÂt ‚ ˆ j d d ƒ d | d k sèt ‚ ˆ j d d ƒ d | d k st ‚ t t ‡ f d †  ƒ d  S(   Ni   i   i   i   i   i   c              s
   ˆ  j  ƒ  S(   N(   t   det(    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   i    R<   i   i   i	   i
   i   i   i   i   iþÿÿÿi   t   methodt   bareisst	   berkowitzc              s   ˆ  j  d d ƒ S(   Nt
   iszerofunct   test(   R  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   (  RF   (	   RS   R3   R   RU   RT   R  R^   R   Rp   (   R>   t   eyR<   R9   R:   R;   (    (   R8   Rn   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_det  s(    $-B &&c             sl  t  d ƒ }  t d d |  d d d d d d d d d	 d
 d d d d d g ƒ } t d d d d g d d |  d d |  d d |  d g d d |  d d |  d d |  d g d d |  d d |  d |  d g g ƒ } | j ƒ  | k sò t ‚ | j d d ƒ | k st ‚ | j d d ƒ | k s.t ‚ t d d d d d d d d g ƒ ‰  t t ‡  f d  †  ƒ d  S(!   NR<   i   i   i   i   i   i   i   i	   i
   i   i   i   i   iøÿÿÿi    iL   iòÿÿÿiD   i   iüÿÿÿi   i†ÿÿÿi   iŽ   iëÿÿÿi0   iH   R  R  R  c              s
   ˆ  j  ƒ  S(   N(   t   adjugate(    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   9  RF   (   R   RS   R)   R  R^   R3   R   (   R<   Rn   t   adj(    (   R8   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_adjugate+  s    B'',$c             sÿ  t  d ƒ }  t d d |  d d d d d d d d d	 d
 d d d d d g ƒ ‰ t |  d d g d d	 d g d d d g g ƒ } t d d d d g d d |  d d |  d d |  d g d d |  d d |  d d |  g d d |  d d |  d d |  d g g ƒ } t |  d d g d d d g d d	 d
 g g ƒ } ˆ j d d ƒ | k sXt ‚ ˆ j d d ƒ | k svt ‚ ˆ j d d ƒ d |  d k sœt ‚ ˆ j d d ƒ d |  d k sÂt ‚ ˆ j ƒ  | k sÚt ‚ ˆ j d d  ƒ | k søt ‚ ˆ j d d! ƒ | k st ‚ t t	 ‡ f d" †  ƒ t t	 ‡ f d# †  ƒ t t	 ‡ f d$ †  ƒ t d d d d d d d d g ƒ ‰  ˆ  j d d ƒ t d d g g ƒ k s©t ‚ t t	 d% „  ƒ t t
 ‡  f d& †  ƒ t t
 ‡  f d' †  ƒ t t
 ‡  f d( †  ƒ d  S()   NR<   i   i   i   i   i   i   i   i	   i
   i   i   i   i   iL   i†ÿÿÿi0   iøÿÿÿiòÿÿÿiD   i   iŽ   iüÿÿÿiH   i   iëÿÿÿi    i   iÿÿÿÿiïÿÿÿR  R  R  c              s   ˆ  j  d d ƒ S(   Ni   i   (   t   cofactor(    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   V  RF   c              s   ˆ  j  d d ƒ S(   Ni   i   (   t   minor(    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   W  RF   c              s   ˆ  j  d d ƒ S(   Ni   i   (   t   minor_submatrix(    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   X  RF   c           S   s   t  d d g  ƒ j d d ƒ S(   Ni    (   RS   R  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ]  RF   c              s   ˆ  j  d d ƒ S(   Ni    (   R  (    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ^  RF   c              s   ˆ  j  d d ƒ S(   Ni    (   R  (    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   _  RF   c              s
   ˆ  j  ƒ  S(   N(   t   cofactor_matrix(    (   R8   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   `  RF   (   R   RS   R)   R  R^   R  R  R  R3   Rp   R   (   R<   Rc   t   cmt   sub(    (   R8   Rn   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_cofactor_and_minors<  s>    B'#0&&$-c          C   s÷   t  d ƒ t  d ƒ }  } t d d d d d d d d d	 d
 d g	 ƒ } t d ƒ j |  ƒ t |  d d |  ƒ k sx t ‚ t d ƒ j | ƒ t | d d | ƒ k sª t ‚ | j ƒ  t |  d d |  d d |  |  ƒ k sã t ‚ t t d „  ƒ d  S(   NR<   R=   i   i   i   i   i   i   i   i   i	   i   i   c           S   s   t  d g d g g ƒ j ƒ  S(   Ni   i   (   R)   t   charpoly(    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   k  RF   (   R   RS   RT   R  R/   R^   R3   R   (   R<   R=   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_charpolyc  s    -229c             s  t  d ƒ ‰  t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d	 †  ƒ t t ‡  f d
 †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ ˆ  j d d d ƒ t d d d g d d d g d d d g g ƒ k sut ‚ ˆ  j d d d ƒ t d d d g d d d g d d d g g ƒ k sÀt ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k st ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k sbt ‚ ˆ  j d d d ƒ t d d d g d d d g d d d g g ƒ k s­t ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k sþt ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k sOt ‚ ˆ  j d d d d ƒ t d d d g d d d g d d d g g ƒ k st ‚ ˆ  j d d d d d d d ƒt d d d g d d d g d d d g g ƒ k sôt ‚ ˆ  j d d d d d d d ƒt d d d g d d d g d d d g g ƒ k sKt ‚ t d d d g d ƒ }  |  j d d d ƒ t d d d g d ƒ k s˜t ‚ |  j d d d ƒ t d d d g d ƒ k sÌt ‚ |  j d d d d ƒ t d d d g d ƒ k st ‚ d  S(   Ni   c              s   ˆ  j  d ƒ S(   Nt   abc(   t   elementary_row_op(    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   q  RF   c              s
   ˆ  j  ƒ  S(   N(   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   r  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n->knR   i   t   k(   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   s  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n->knR   iûÿÿÿR!  i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   t  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mt   row1i   t   row2i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   u  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mR"  i   R#  i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   v  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mR"  iûÿÿÿR#  i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   w  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mR"  i   R#  iûÿÿÿ(   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   x  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR"  i   R#  i   R!  (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   y  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR"  i   R#  i   R!  (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   z  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR"  iûÿÿÿR#  i   R!  i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   {  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR"  i   R#  iûÿÿÿR!  i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   |  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR"  i   R#  R!  i   (   R   (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   }  RF   s   n->kni    i   i   R   R!  R"  s   n<->mR#  s   n->n+kmi   i   (   RW   R3   Rp   R   R)   R^   RV   (   R8   (    (   Rn   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_row_opn  s8    KKQQKQQNWW44c             s  t  d ƒ ‰  t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d	 †  ƒ t t ‡  f d
 †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ t t ‡  f d †  ƒ ˆ  j d d d ƒ t d d d g d d d g d d d g g ƒ k sut ‚ ˆ  j d d d ƒ t d d d g d d d g d d d g g ƒ k sÀt ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k st ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k sbt ‚ ˆ  j d d d ƒ t d d d g d d d g d d d g g ƒ k s­t ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k sþt ‚ ˆ  j d d d d d ƒt d d d g d d d g d d d g g ƒ k sOt ‚ ˆ  j d d d d ƒ t d d d g d d d g d d d g g ƒ k st ‚ ˆ  j d d d d d d d ƒt d d d g d d d g d d d g g ƒ k sôt ‚ ˆ  j d d d d d d d ƒt d d d g d d d g d d d g g ƒ k sKt ‚ t d d d g d ƒ }  |  j d d d ƒ t d d d g d ƒ k s˜t ‚ |  j d d d ƒ t d d d g d ƒ k sÌt ‚ |  j d d d d ƒ t d d d g d ƒ k st ‚ d  S(   Ni   c              s   ˆ  j  d ƒ S(   NR  (   t   elementary_col_op(    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   •  RF   c              s
   ˆ  j  ƒ  S(   N(   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   –  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n->knR€   i   R!  (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   —  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n->knR€   iûÿÿÿR!  i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ˜  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mt   col1i   t   col2i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ™  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mR&  i   R'  i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   š  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mR&  iûÿÿÿR'  i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ›  RF   c              s   ˆ  j  d d d d d ƒS(   Ns   n<->mR&  i   R'  iûÿÿÿ(   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   œ  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR&  i   R'  i   R!  (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE     RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR&  i   R'  i   R!  (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ž  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR&  iûÿÿÿR'  i   R!  i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Ÿ  RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR&  i   R'  iûÿÿÿR!  i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE      RF   c              s   ˆ  j  d d d d d d d ƒS(   Ns   n->n+kmR&  i   R'  R!  i   (   R%  (    (   Rn   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ¡  RF   s   n->kni    i   i   R€   R!  R&  s   n<->mR'  s   n->n+kmi   i   (   RW   R3   Rp   R%  R)   R^   RV   (   R8   (    (   Rn   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_col_op’  s8    KKQQKQQNWW44c          C   s`  t  d ƒ }  t d ƒ } |  j s' t ‚ | j s6 t ‚ t d d g  ƒ } | j sW t ‚ t d d d d d d d d g ƒ } | j sŠ t ‚ t d d d d d d d d g ƒ } | j s¾ t ‚ t d ƒ } t d d | d d g ƒ } | j sô t ‚ t d d | | d g ƒ } | j st ‚ t d d d d d d d d d d d g	 ƒ } | j s\t ‚ d  S(   Ni   i    i   i   i   R<   (   RX   RW   t
   is_echelonR^   RV   R   (   t   zrot   identR8   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_echelon¶  s"    $$-c             sÜ  t  d ƒ }  t d ƒ } |  j ƒ  |  k s0 t ‚ | j ƒ  | k sH t ‚ t d d g  ƒ }  |  j ƒ  |  k sr t ‚ t d d d g ƒ }  |  j ƒ  |  k sŸ t ‚ ‡  f d †  } t d d d d d d d d d	 d
 d g	 ƒ }  t d g d g d g g ƒ g } g  t |  j ƒ D] } |  | d  d  … f ^ q} |  j ƒ  ‰  ˆ  j sIt ‚ | |  | | ƒ t d d d d d d d d d	 d
 d
 g	 ƒ }  g  } g  t |  j ƒ D] } |  | d  d  … f ^ qœ} |  j ƒ  ‰  ˆ  j sÙt ‚ | |  | | ƒ t d d d d d d d d d d d g	 ƒ }  t t	 d ƒ d g d g d g g ƒ t t	 d ƒ d g d g d g g ƒ g } g  t |  j ƒ D] } |  | d  d  … f ^ qx} |  j ƒ  ‰  ˆ  j sµt ‚ | |  | | ƒ t d d d d d d d d d d d g	 ƒ }  t d g d g d g g ƒ g } g  t |  j ƒ D] } |  | d  d  … f ^ q#} |  j ƒ  ‰  ˆ  j s`t ‚ | |  | | ƒ t d d d d d d d d d d d g	 ƒ }  t d g d g d g g ƒ t d g d g d g g ƒ g } g  t |  j ƒ D] } |  | d  d  … f ^ qé} |  j ƒ  ‰  ˆ  j s&t ‚ | |  | | ƒ t d d d d d d d d g ƒ }  t d g d g d g g ƒ g } g  t |  j ƒ D] } |  | d  d  … f ^ q‹} |  j ƒ  ‰  ˆ  j sÈt ‚ | |  | | ƒ d  S(   Ni   i    i   i   c            s†   x. | D]& } t  d „  ˆ  | Dƒ ƒ s t ‚ q WxN | D]F } t  d „  | Dƒ ƒ s8 t  d „  ˆ  | j ƒ  Dƒ ƒ s~ t ‚ q8 q8 Wd  S(   Nc         s   s   |  ] } | j  Vq d  S(   N(   Rº   (   RÓ   t   t(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>ç  s    c         s   s   |  ] } | j  Vq d  S(   N(   Rº   (   RÓ   R-  (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>é  s    c         s   s   |  ] } | j  Vq d  S(   N(   Rº   (   RÓ   R-  (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>ê  s    (   RÔ   R^   t	   transpose(   t   matR]   t   nullst   v(   t	   a_echelon(    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   verify_row_null_spaceå  s
    $i   i   i   i   i   i	   iþÿÿÿiýÿÿÿiÿÿÿÿ(
   RX   RW   t   echelon_formR^   RV   R)   R   R]   R)  R   (   R8   Rn   R3  R0  RC   R]   (    (   R2  sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_echelon_formÑ  sˆ    -2-2-2-2-2$2c          C   sÂ  t  d d g  ƒ }  |  j d t ƒ |  k s0 t ‚ t  d d d g ƒ }  t  d d d g ƒ } |  j d t ƒ | j d t ƒ k o‰ |  k n s” t ‚ t  d d d d d g ƒ } | j d t ƒ t d g d g d g g ƒ k så t ‚ t  d d d d d g ƒ } | j d t ƒ t d d d g g ƒ k s0t ‚ t  d d d d d d d d d	 d
 d g	 ƒ } | j d t ƒ t d d d g d d d g d d d g g ƒ k s¥t ‚ t  d d d d d d d d d d d g	 ƒ } t  d d d d d d d d d d d g	 ƒ } t  d d d d d d d d d d d g	 ƒ } t  d d d d d d d d d d d g	 ƒ } | j d t ƒ | j d t ƒ k o¶| j d t ƒ k o¶| j d t ƒ k o¶| k n sÁt ‚ t d ƒ }  t d ƒ } |  j d t ƒ |  k s÷t ‚ | j d t ƒ | k st ‚ t  d d d d d d d g d d d d d d d g d d d d d d
 d g d d d d d d d g g ƒ } | j ƒ  \ } } | t d d d d d d d g d d d d d d d g d d d d d d d g d d d d d d d g g ƒ k st ‚ | d k st ‚ t  t d ƒ d t d ƒ d d d g d d d d	 g d
 d d d g d d d d g g ƒ } | j d t ƒ t d d d t d ƒ d g d d d t d ƒ d g d d d t d ƒ d g d d d d g g ƒ k sùt ‚ t d ƒ } t  d d | d d t	 | ƒ | d g ƒ } xŒ t
 | j d t ƒ d d t	 | ƒ | d | t d ƒ d | d d d t	 | ƒ | d g ƒ D]% \ }	 }
 t |	 |
 ƒ j s•t ‚ q•Wd  S(   Ni    t   pivotsi   i   i   i   i   i   i   i   i	   iÿÿÿÿiûÿÿÿiùÿÿÿiþÿÿÿiýÿÿÿi   i
   i   i   i   i   i   iL   i   iî   R<   (   i    i   i   (   RV   t   rrefR¡   R^   R)   RW   RX   R   R   R   t   zipR0   Rº   (   Rn   R8   R9   R:   R;   R>   R/  t   pivot_offsetsR<   RC   RD   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt	   test_rref0  sj    :60-----+!*&!*/.c           C   s©   t  t j d d ƒ ƒ d d d d g k s0 t ‚ t  t j d ƒ ƒ d d d d g k s] t ‚ t t j d ƒ ƒ t k s~ t ‚ t t j d d t ƒƒ t k s¥ t ‚ d  S(   Ni   i   i    RÜ   (   R`   RY   R+   R^   t   typeR)   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_eyer  s    0-!c           C   så   t  t j d d ƒ ƒ d d d d g k s0 t ‚ t  t j d ƒ ƒ d d d d g k s] t ‚ t j d d ƒ t d d d g d d d g g ƒ k s™ t ‚ t t j d ƒ ƒ t k sº t ‚ t t j d d t ƒƒ t k sá t ‚ d  S(   Ni   i   i   RÜ   (   R`   RY   R-   R^   R)   R;  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt	   test_onesy  s
    0-<!c           C   så   t  t j d d ƒ ƒ d d d d g k s0 t ‚ t  t j d ƒ ƒ d d d d g k s] t ‚ t j d d ƒ t d d d g d d d g g ƒ k s™ t ‚ t t j d ƒ ƒ t k sº t ‚ t t j d d t ƒƒ t k sá t ‚ d  S(   Ni   i    i   RÜ   (   R`   RY   R.   R^   R)   R;  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_zeros  s
    0-<!c          C   s·  t  j }  t d d g d d g g ƒ } t d t g t d g g ƒ } t d t d g t d t g t t t g g ƒ } |  | | | ƒ t d d d d d d g d d d d d d g d d d t d d g d d t d d d g d d d d d t g d d d d t d g g ƒ k st ‚ |  | | | ƒ t d d d d d d d g d d d d d d d g d d d t d d d g d d t d d d d g d d d d d t d g d d d d t d t g d d d d t t t g g ƒ k sãt ‚ |  | | | ƒ t d d d d d d d g d d d d d d d g d d d t d d d g d d t d t d d g d d t t t d d g d d d d d d t g d d d d d t d g g ƒ k s¯t ‚ t t t t g ƒ } t d d g d d g g ƒ } t d d g g ƒ } |  | d | | ƒ t t d d d d d g t d d d d d g t d d d d d g d d d d d d g d d d d d d g d d d d d d g d d d d d d g g ƒ k s±t ‚ t  j d d g ƒ t d d g d d g g ƒ k sêt ‚ t  j t d d g ƒ ƒ t d g d g g ƒ k s#t ‚ t  j d d	 d d
 d ƒt d d g d d g d d g g ƒ k skt ‚ t t  j d ƒ ƒ t  k sŒt ‚ t t  j d d t ƒƒ t k s³t ‚ d  S(   Ni   i   i   i    i   i   i   i   R]   R_   RÜ   (   RY   R*   R)   R<   R=   R>   R^   R;  (   R*   R8   R9   R:   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_diag_make‰  sd    	0'**'			!c           C   sÞ  t  j d d ƒ t  j d d d ƒk o¹ t  j d d d d ƒ k o¹ t  j d d d d ƒk o¹ t  j d d d d d d ƒ k o¹ t d d d	 g d	 d d g d	 d	 d g g ƒ k n sÄ t ‚ t  j d d d d
 ƒt d d	 d	 g d d d	 g d	 d d g g ƒ k st ‚ t t d „  ƒ t t d „  ƒ t t d „  ƒ t t d „  ƒ t ƒ  5 t  j d d d d ƒ t  d d d ƒ k sŒt ‚ Wd  QXt ƒ  5 t  j d d d d ƒ t  d d d ƒ k sÌt ‚ Wd  QXt ƒ  W t  j d d ƒ t  j d d d d ƒ k o#t  j d d d d ƒ k n s.t ‚ Wd  QXt ƒ  e t  j d d d d d d ƒ t d d d	 g d	 d d g d	 d	 d g d	 d	 d	 g g ƒ k sžt ‚ Wd  QXt  j d d d d ƒ t  j d d d d ƒ k sÚt ‚ d  S(   Ni   i   t
   eigenvaluet   sizet   bandt   uppert   eigenvali   i    t   lowerc           S   s   t  j d ƒ S(   Ni   (   RY   t   jordan_block(    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Ñ  RF   c           S   s   t  j d d ƒ S(   Ng      @i   (   RY   RF  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Ó  RF   c           S   s   t  j d d ƒ S(   NR@  i   (   RY   RF  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Õ  RF   c           S   s   t  j d d d d ƒ S(   NR@  i   RD  i   (   RY   RF  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Ø  s   	R_   R]   i   (	   i   i   i    i    i   i   i    i    i   (	   i   i   i    i    i   i   i    i    i   (   RY   RF  R)   R^   R3   Rp   R7   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_jordan_blockÁ  sL    )	#

!
!
,
	$c       	   C   s  t  d d d d d g d d d d d g d d	 d
 d d g d
 d d d d g g ƒ }  |  j ƒ  } | d t d d d d
 g ƒ k sˆ t ‚ | d t d d d	 d g ƒ k s° t ‚ | d t d d d d g ƒ k sØ t ‚ t | ƒ d
 k sð t ‚ t j |  | Œ j ƒ  | k st ‚ d  S(   Ni   i   i    i   iþÿÿÿiûÿÿÿiÿÿÿÿiøÿÿÿiýÿÿÿi   i   i   iùÿÿÿ(   RZ   t   columnspaceR)   R^   t   lenR‘   (   Rc   t   basis(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_columnspaceø  s    (((c       	   C   s  t  d d d d d g d d d d d g d d	 d
 d d g d
 d d d d g g ƒ }  |  j ƒ  } | d t d d d d d g g ƒ k sŽ t ‚ | d t d d d d
 d g g ƒ k s¼ t ‚ | d t d d d d d g g ƒ k sê t ‚ t | ƒ d
 k st ‚ d  S(   Ni   i   i    i   iþÿÿÿiûÿÿÿiÿÿÿÿiøÿÿÿiýÿÿÿi   i   i   iùÿÿÿ(   RZ   t   rowspaceR)   R^   RI  (   Rc   RJ  (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_rowspace  s    ...c       	   C   s  t  d d d d d g d d d d d g d d	 d
 d d g d
 d d d d g g ƒ }  |  j ƒ  } | d t d d d d d g ƒ k s‹ t ‚ | d t d d d d d g ƒ k s¶ t ‚ t d „  |  | d Dƒ ƒ sÚ t ‚ t d „  |  | d Dƒ ƒ sþ t ‚ d  S(   Ni   i   i    i   iþÿÿÿiûÿÿÿiÿÿÿÿiøÿÿÿiýÿÿÿi   i   i   iùÿÿÿc         s   s   |  ] } | j  Vq d  S(   N(   Rº   (   RÓ   Rn   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>  s    c         s   s   |  ] } | j  Vq d  S(   N(   Rº   (   RÓ   Rn   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>   s    (   RZ   t	   nullspaceR)   R^   RÔ   (   Rc   RJ  (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_nullspace  s    ++$c          C   s—  t  d d g d d g g ƒ }  |  j t  d g d g g ƒ ƒ t  d g d g g ƒ g k s` t ‚ |  j t  d g d g g ƒ d t ƒt  d t d ƒ d g t d ƒ d g g ƒ g k sÀ t ‚ |  j t  d g d g g ƒ t  d g d g g ƒ ƒ t  d g d g g ƒ t  t d ƒ d g t d	 ƒ d g g ƒ g k sAt ‚ |  j t  d
 g d
 g g ƒ t  d g d g g ƒ ƒ t  d g d g g ƒ g k s˜t ‚ |  j t  d
 g d
 g g ƒ ƒ g  k sÅt ‚ t  d d d g d d	 d g d d d g g ƒ } t  d g d g g ƒ t  d g d g g ƒ t  d g d g g ƒ g } | j | Œ  t  d g d g g ƒ t  t d ƒ d g t d ƒ d g g ƒ g k s“t ‚ d  S(   Ni   i   i   i   t	   normalizei   iÿÿÿÿi   i   i    i	   i
   i   iûÿÿÿiþÿÿÿi   i   (   R)   t   orthogonalizeR^   R¢   R   R   (   Rc   RG   t   vecs(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_orthogonalize#  s    B`W-0Ec       
      së   t  d d d g d d d g d d d g g ƒ }  |  j ƒ  i d d t j 6d t j 6d t j 6k sk t ‚ t d d d d d g d d d d d g d d d d d g d d d d d g d d d d d g g ƒ ‰  t t ‡  f d †  ƒ d  S(   Ni    i   i   i   iýÿÿÿc              s
   ˆ  j  ƒ  S(   N(   t	   eigenvals(    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   >  RF   (	   R[   RT  R   Rf   Rh   R^   R)   R3   R   (   RÍ   (    (   Rc   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_eigenvals1  s    ;c          C   s”   t  d d d g d d d g d d d g g ƒ }  |  j ƒ  } xQ | D]I \ } } } t | ƒ d k sj t ‚ |  | d | | d k sC t ‚ qC Wd  S(   Ni    i   (   R[   t
   eigenvectsRI  R^   (   RÍ   RR  t   valt   multt   vec_list(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_eigenvectsA  s    c          C   s”   t  d d d g d d d g d d d g g ƒ }  |  j ƒ  } xQ | D]I \ } } } t | ƒ d k sj t ‚ | d |  | | d k sC t ‚ qC Wd  S(   Ni    i   (   R[   t   left_eigenvectsRI  R^   (   RÍ   RR  RW  RX  RY  (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_left_eigenvectsK  s    c             s%  t  d d d d d d g ƒ ‰  t t ‡  f d †  ƒ ˆ  j ƒ  \ }  } | j ƒ  sX t ‚ | t t d g d t g g ƒ k sƒ t ‚ t  d d d d d d g ƒ ‰  ˆ  j ƒ  \ }  } t d „  | j	 ƒ  Dƒ ƒ sÕ t ‚ t d „  |  j	 ƒ  Dƒ ƒ s÷ t ‚ ˆ  j d	 t
 ƒ \ } } | | k s!t ‚ d  S(
   Ni   i    iÿÿÿÿi   c              s   ˆ  j  d t ƒ S(   Nt
   reals_only(   t   diagonalizeR¢   (    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   W  RF   g      à?c         s   s   |  ] } t  | t ƒ Vq d  S(   N(   Rÿ   R   (   RÓ   Rn   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>a  s    c         s   s   |  ] } t  | t ƒ Vq d  S(   N(   Rÿ   R   (   RÓ   Rn   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>b  s    R]  (   R[   R3   R   R^  R¥   R^   R)   R   RÔ   R¾   R¢   (   t   PRw   t   _t   D2(    (   Rc   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_diagonalizeU  s    
""c          C   sÏ   t  d ƒ \ }  } } t d d |  | | | g ƒ } | j ƒ  sE t ‚ | j ƒ  sW t ‚ t d d d d d d g ƒ j ƒ  s‚ t ‚ t d d d d d d g ƒ } | j ƒ  s² t ‚ | j d t ƒ sË t ‚ d  S(   Ns   a b ci   i   i    iÿÿÿÿR]  (   R   R[   R¦   R^   t   is_diagonalizableR¢   (   R8   R9   R:   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_is_diagonalizableh  s    +c             sÿ  t  d d d d d d d d g ƒ ‰  t t ‡  f d †  ƒ t d d d d d	 d	 d	 d d d	 d	 d	 d d	 d	 d	 d	 d g ƒ ‰  ˆ  j ƒ  \ }  } ˆ  | k s  t ‚ t d d d d d	 d	 d	 d d	 d	 d	 d	 d d d	 d	 d	 d g ƒ ‰  ˆ  j ƒ  \ }  } ˆ  | k st ‚ t  d d d d	 g d
 d d	 d g d	 d	 d d g d	 d	 d
 d g g ƒ } | j ƒ  \ }  } t |  | |  j ƒ  ƒ | k s†t ‚ t d d d g ƒ j ƒ  t  d g ƒ t  d g ƒ f k sÅt ‚ t d d d g ƒ j d t ƒ t  d g ƒ k sût ‚ t  d d	 d	 d	 d g d	 d d d	 d g d	 d d	 d d	 g d	 d	 d d	 d g d d	 d	 d d	 g g ƒ ‰  t t	 ‡  f d †  ƒ t  d d d t
 d ƒ g d d t
 d ƒ d g g ƒ ‰  ˆ  j ƒ  \ }  } t d „  |  Dƒ ƒ sßt ‚ t d „  | Dƒ ƒ sût ‚ d  S(   Ni   i   iýÿÿÿi   i   i
   c              s
   ˆ  j  ƒ  S(   N(   t   jordan_form(    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   v  RF   i   i    iüÿÿÿt   calc_transformc              s
   ˆ  j  ƒ  S(   N(   Re  (    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ™  RF   g      æ?g      À?g      È?g      Ô?c         s   s*   |  ]  } t  | t ƒ p! | d  k Vq d S(   i    N(   Rÿ   R   (   RÓ   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>   s    c         s   s*   |  ]  } t  | t ƒ p! | d  k Vq d S(   i    N(   Rÿ   R   (   RÓ   R<   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pys	   <genexpr>¡  s    (   R)   R3   R   R[   Re  R^   R0   t   invR¡   R   R   RÔ   (   R_  t   JRt   (    (   Rc   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_jordan_formt  s<    $&?6f c          C   sä  t  d d t ƒ}  t d d t g d d g g ƒ } | j ƒ  d d g k sR t ‚ t d ƒ } |  | d <d | d <| j ƒ  } t | ƒ t d d t |  ƒ g ƒ k s« t ‚ t t	 |  ƒ t
 |  ƒ g t
 |  ƒ t	 |  ƒ g g ƒ } g  | j ƒ  D] } | j ƒ  ^ qï } | t d ƒ t d ƒ g k s+t ‚ t d d g d d g d d g d d g g ƒ } | j ƒ  t t d	 ƒ d
 ƒ t d
 t d	 ƒ ƒ g k s™t ‚ | j j ƒ  t t d	 ƒ d
 ƒ t d
 t d	 ƒ ƒ d d g k sàt ‚ d  S(   NR<   R¼   i    i   i   i   i   i   iÝ   i   (   i   i   (   i   i   (   R   R¢   R[   R   t   singular_valuesR^   R+   R½   R   R   R   R1   R   R   RÊ   (   R<   Rt   t   valst   sv(    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_singular_values¤  s(    "

-7%$				5c          C   s[   t  d ƒ \ }  } t d d |  | g ƒ } | j |  ƒ t d d d d g ƒ k sW t ‚ d  S(   Ns   x yi   i   i    (   R   R\   R   R)   R^   (   R<   R=   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt	   test_diffÃ  s    c          C   sg   t  d ƒ \ }  } t d d |  | g ƒ } | j |  ƒ t d d |  d d | |  g ƒ k sc t ‚ d  S(   Ns   x yi   i   (   R   R\   t	   integrateR)   R^   (   R<   R=   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_integrateË  s    c             s3  t  d ƒ \ }  } t d d |  t | ƒ |  t | ƒ |  d g ƒ } t d d |  | g ƒ } t t | ƒ |  t | ƒ g t | ƒ |  t | ƒ g d |  d g g ƒ } | j | ƒ | k sÄ t ‚ t d d d d d d g ƒ ‰  t d d d d d d g ƒ ‰ t t ‡  f d †  ƒ t t ‡  ‡ f d †  ƒ d  S(	   Ns   rho,phii   i   i   i    i   c              s   ˆ  j  t d d g ƒ ƒ S(   Ni   i   (   t   jacobianR)   (    (   Rc   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   Þ  RF   c              s   ˆ j  ˆ  ƒ S(   N(   Rq  (    (   Rc   R’   (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ß  RF   (	   R   R\   R   R   R)   Rq  R^   R3   Rü   (   t   rhot   phit   Xt   YRh  (    (   Rc   R’   sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_jacobian2Ñ  s    3c          C   sl   t  d ƒ \ }  } t d d d |  | g ƒ } | j |  d ƒ t d d t d ƒ d | g ƒ k sh t ‚ d  S(   Ns   x yi   i   i   (   R   R\   t   limitR)   R   R^   (   R<   R=   Rc   (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt
   test_limitâ  s    c              su   t  d d d g d d d g d d d	 g g ƒ ‰  d d d g ‰ t t ‡  ‡ f d
 †  ƒ t t ‡  ‡ f d †  ƒ d  S(   Ni   i   i   i   i   i   i   i   i	   c              s   ˆ  ˆ S(   N(    (    (   RÍ   R1  (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ë  RF   c              s   ˆ ˆ  S(   N(    (    (   RÍ   R1  (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyRE   ì  RF   (   R)   R3   Rü   (    (    (   RÍ   R1  sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test_issue_13774è  s    0c           C   sF   t  d d d g d d d g d d d g g ƒ i  k t k sB t ‚ d  S(   Ni    i   (   R[   R¡   R^   (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   test___eq__ï  s    (Ã   t   collectionst   randomt   sympy.assumptionsR    t   sympy.core.addR   t   sympy.core.compatibilityR   t   sympy.core.functionR   R   t   sympy.core.numbersR   R   R   R   R	   R
   t   sympy.core.relationalR   R   t   sympy.core.singletonR   t   sympy.core.symbolR   R   t$   sympy.functions.elementary.complexesR   t&   sympy.functions.elementary.exponentialR   t(   sympy.functions.elementary.miscellaneousR   R   R   t$   sympy.functions.elementary.piecewiseR   t(   sympy.functions.elementary.trigonometricR   R   R   t   sympy.logic.boolalgR   R   t   sympy.matrices.commonR   R   R   R   R   R    R!   R"   R#   t   sympy.matrices.matricesR$   R%   R&   R'   R(   t   sympy.matricesR)   R*   R+   R,   R-   R.   t   sympy.polys.polytoolsR/   t   sympy.simplify.simplifyR0   t   sympy.simplify.trigsimpR1   t   sympy.utilities.iterablesR2   t   sympy.utilities.pytestR3   R4   R5   R6   R7   t	   sympy.abcR8   R9   R:   R;   R<   R=   R>   R?   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   Ra   Re   Rl   Rq   Rs   Rx   Rz   R~   R   Rƒ   R…   RŠ   R   R   R—   R™   R›   R   RŸ   R¤   R§   Rª   R¬   R®   R°   R²   R´   Rµ   R¸   R»   R¿   RÁ   RÅ   RÉ   RÎ   RÑ   RÕ   R×   RÛ   Râ   Rã   Rç   Rê   Rì   Rî   R÷   Rù   Rú   R  R  R  R  R	  R
  R  R  R  R  R$  R(  R,  R5  R:  R<  R=  R>  R?  RG  RK  RM  RO  RS  RU  RZ  R\  Rb  Rd  Ri  Rm  Rn  Rp  Rv  Rx  Ry  Rz  (    (    (    sE   lib/python2.7/site-packages/sympy/matrices/tests/test_commonmatrix.pyt   <module>   s  .@(.(4																																		
		 																											%			J								'		$	$		_	B				8	7						
	
			0					