o
    *ήc                     @   sP  d Z ddlmZmZmZmZ ddlmZ ddlm	Z	 ddl
mZmZmZmZ ddlmZ ddlmZ ddlmZmZ dd	lmZ dd
lmZ ddlmZmZ ddlmZ ddlm Z  ddl!m"Z"m#Z# ddl$m%Z%m&Z&m'Z'm(Z(m)Z) dd Z*dd Z+dd Z,dd Z-dd Z.dd Z/dd Z0dd Z1d d! Z2d"d# Z3e#d$d% Z4d&d' Z5d(d) Z6d*S )+zOTests for algorithms for partial fraction decomposition of rational
functions.     )apart_undetermined_coeffsapart
apart_listassemble_partfrac_list)Expr)Lambda)EIRationalpi)Eq)S)DummySymbol)sqrt)Matrix)Polyfactor)together)RootSum)raisesXFAIL)xyabcc                  C   s  t ddksJ t dtdksJ td d td  dtd  t d } }t | dd|ks0J t | dd|ks:J dtd  td  ddt  ddt   } }t | dd|ks[J t | dd|kseJ dtd  td  ddt  d ddt  d  } }t | dd|ksJ t | dd|ksJ t tt d tt  td  tdt tt  tt  tt d td  tt   ksJ t ttd d td  ttttd dtd   tksJ t td ttd ksJ tt dt t  td	dt dt t  tj } }t | tdd|ksJ t | tdd|ks J tt dt t  d	t dt t  d } }t | tdd|ksCJ t | tdd|ksOJ t	t
d
d  d S )N      FfullT         c                   S   s   t dtd  td  S )Nr   r   )r   r   r    r%   r%   F/tmp/pip-target-vg8gfxp4/lib/python/sympy/polys/tests/test_partfrac.py<lambda>=       ztest_apart.<locals>.<lambda>)r   r   r   r   r   r   r
   r   Halfr   NotImplementedErrorfgr%   r%   r&   
test_apart   s.   *.6 2>6.r.   c                  C   sv   t dddd } t| t dt dtd   td d gddt  tjtd   dtd  dtd   ggks9J d S )Nr   c                 S   s   dt |  d  t |  S )Nr   )r   ijr%   r%   r&   r'   A   r(   z#test_apart_matrix.<locals>.<lambda>r   )r   r   r   r   r)   )Mr%   r%   r&   test_apart_matrix@   s
   0r4   c                  C   s  t td  dt dt  t  td   dt t t d  t td   td   dt  t dt td   t  td  } t d td  dt  t dt t d   td   dt  t t td  t d td   td   dt td  dt  t td   t  td td   }t| | tdt  dtt d   td t t t t d    ksJ tdtt  tt  tt   tdt t tt  tt   dt t tt  tt    dt t t t  t t    ksJ d S )Nr#   r   r$   r2   r   )r   r   r   r   r   r+   r%   r%   r&   test_apart_symbolicI   s(   NH&F 6r5   c                     s   ddl m   fdd} td d d td d td d  td  dt  d  td dt  d   }d| ttd d  d| ttd d   d| td td   d| td td   d| td d   d| td d   }||fS )Nr   Mulc                    s    d| ddS )Nr   F)evaluater%   )exprr6   r%   r&   mul2Y   s   z%_make_extension_example.<locals>.mul2r   r   r$   )
sympy.corer7   r   r   )r:   r,   r-   r%   r6   r&   _make_extension_exampleV   s   Rr<   c                  C   s   dt d d  } tt t  tt t   }t| td|ksJ t| dd|ks(J t t d t t   } ttt|  | ks@J t \} }ddlm} |d t| t t	dhd|ks^J W d    d S 1 siw   Y  d S )Nr   r   	extensionT)gaussianr   )dotprodsimp)
r   r	   r   r   r   expandr<   sympy.matricesr@   r   )r,   r-   r@   r%   r%   r&   test_apart_extensiong   s   

"rC   c                  C   s*   t  \} }t| ttdhd|ksJ d S )Nr   r=   )r<   r   r   r   r+   r%   r%   r&   test_apart_extension_xfailz   s   
 rD   c                  C   s  dt d d  } t| dd| ksJ t| ddtt d d tttt t  dd d s0J dt d t  d  } t| dd| ksDJ t| ddtt d t  d tttd tdd	 ttd
d	  tdd	 t t  ddstJ dt d d  } t| ddtddt d dt d   dt   d t d t d  t d  t  d   tddt d   ksJ t| ddtt d t d  t d  t  d tttt t  dd d tddt d   sJ d S )Nr   r   Fr   T)autor$         	   r#   r!   r"   )r   r   dummy_eqr   r   r   r
   )r,   r%   r%   r&   test_apart_full   s>   (8
< rJ   c                  C   s
  t dt d } t td td  td  td  dtd   dt  d }td  td  td  d	 td td  dt  d  dtd   }t| ||ksRJ t dtd
d} t tt tt  td
d}dtt tt   dtt tt    }t| ||ksJ d S )Nr   r$   rH      rF   r!   r      r#   zZZ[a,b]domain)r   r   r   r   r   )pqrr%   r%   r&   test_apart_undetermined_coeffs   s   <F(rR   c               
      s6  ddl m}   fdd tdtdtd}}}td}d	t d
td
   dtd
  dt   }t|t| dd}dttd
dtddt|d
 |ddt|d
t|| t dfgf} ||sdJ td
td
 d
  t| dd}dtdtddt|d
 d
 |ddt||d
 t|| t dfgf} ||sJ dtd d
td   d
td   dtd
   t d
  }t|t| dd}dtdtddt|d
 |ddt|dt|| t dft|d
 d |ddt|d| d t|| t d
ft|d |ddt|dt|| t dfgf} ||sJ d S )Nr   )numbered_symbolsc                    s>   t | ttfv rt fddt| |D S | |kp| |S )Nc                 3   s    | ]
\}} ||V  qd S )Nr%   ).0r0   r1   rI   r%   r&   	<genexpr>   s    z4test_apart_list.<locals>.dummy_eq.<locals>.<genexpr>)typelisttupleallziprI   r/   rU   r%   r&   rI      s   z!test_apart_list.<locals>.dummy_eqw0w1w2r   r2   r   r$   rF   w)dummiesr"   QQrM   ZZr   $   r!   r#   )	sympy.utilities.iterablesrS   r   r   r   r   r   r
   r   )rS   r\   r]   r^   _ar,   gotansr%   rU   r&   test_apart_list   s2   (,"8*6*rj   c                  C   s  dt d dt d   dt d   dt d   t  d  } t| }t|dt d  dt d d   dt d d   dt d   ksBJ td	}dtd
t ddtdtd gt||d t|| t  dfgf}t|dtdt td   dtdt td    ksJ d S )Nrc   r!   r   r#   r$   re   r   rH   r   r   rb   rM   r"   )r   r   r   r   r   r   r   )r,   pfdr   r%   r%   r&   test_assemble_partfrac_list   s   8DB@rl   c                  C   sp   G dd dt } tttt   }ddt  }t|| | || | ks&J t|| | || | ks6J d S )Nc                   @      e Zd ZdZdS )z3test_noncommutative_pseudomultivariate.<locals>.fooFN__name__
__module____qualname__is_commutativer%   r%   r%   r&   foo       rs   r   r   r   r   r   rs   er   r%   r%   r&   &test_noncommutative_pseudomultivariate   s
    $rx   c                  C   sL   G dd dt } tttt   }ddt  }t||   ||   ks$J d S )Nc                   @   rm   )z test_noncommutative.<locals>.fooFNrn   r%   r%   r%   r&   rs      rt   rs   r   ru   rv   r%   r%   r&   test_noncommutative   s    ry   c                   C   s   t dt td d  td dtd d    ddtd    dt  dt d td d  d dtd  d  dt  ks@J d S )Nr   r   r$   )r   r   r%   r%   r%   r&   test_issue_5798   s
   B2rz   N)7__doc__sympy.polys.partfracr   r   r   r   sympy.core.exprr   sympy.core.functionr   sympy.core.numbersr   r	   r
   r   sympy.core.relationalr   sympy.core.singletonr   sympy.core.symbolr   r   (sympy.functions.elementary.miscellaneousr   sympy.matrices.denser   sympy.polys.polytoolsr   r   sympy.polys.rationaltoolsr   sympy.polys.rootoftoolsr   sympy.testing.pytestr   r   	sympy.abcr   r   r   r   r   r.   r4   r5   r<   rC   rD   rJ   rR   rj   rl   rx   ry   rz   r%   r%   r%   r&   <module>   s:    '	

	