U
    9%e                     @   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tt dtdks"ttd d td  dtd  t d  } }t | dd|ks`tt | dd|ksttdtd  td  ddt  ddt    } }t | dd|kstt | dd|kstdtd  td  ddt  d ddt  d   } }t | dd|kstt | dd|ks,tt tt d tt  td  tdt tt  tt  tt d td  tt   kstt ttd d td  ttttd dtd   tkstt td ttd ksttt dt t  td	dt dt t  tj	  } }t | tdd|ks2tt | tdd|ksJttt dt t  d	t dt t  d  } }t | tdd|kstt | tdd|kst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%   ^/var/www/html/Darija-Ai-API/env/lib/python3.8/site-packages/sympy/polys/tests/test_partfrac.py<lambda>=       ztest_apart.<locals>.<lambda>)r   AssertionErrorr   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srt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*   r)   )Mr%   r%   r&   test_apart_matrix@   s
    0r5   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s\t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std S )Nr#   r   r$   r3   r   )r   r   r   r   r   r)   r,   r%   r%   r&   test_apart_symbolicI   s(    NH&H 6r6   c                     s   ddl m   fdd} td d d td d td d  td  dt  d  td dt  d   }d| ttd d  d| ttd d   d| td td   d| td td   d| td d   d| td d   }||fS )Nr   Mulc                    s    d| ddS )Nr   F)evaluater%   )exprr7   r%   r&   mul2Y   s    z%_make_extension_example.<locals>.mul2r   r   r$   )Z
sympy.corer8   r   r   )r;   r-   r.   r%   r7   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<tt| dd|ksPtt t d t t   } ttt|  | kstt \} }ddlm	} |d" t| t t
dhd|kstW 5 Q R X d S )Nr   r   	extensionT)Zgaussianr   )dotprodsimp)r   r	   r   r)   r   r   expandr<   Zsympy.matricesr?   r   )r-   r.   r?   r%   r%   r&   test_apart_extensiong   s    

rA   c                  C   s*   t  \} }t| ttdhd|ks&td S )Nr   r=   )r<   r   r   r   r)   r,   r%   r%   r&   test_apart_extension_xfailz   s    
rB   c                  C   s  dt d d  } t| dd| ks$tt| ddtt d d tttt t  dd d s`tdt d t  d  } t| dd| kstt| ddtt d t  d tttd tdd	 ttd
d	  tdd	 t t  ddstdt d d  } t| ddtddt d dt d   dt   d t d t d  t d  t  d   tddt d   ksftt| ddtt d t d  t d  t  d tttt t  dd d tddt d   std S )Nr   r   Fr   T)autor$         	   r#   r!   r"   )r   r   r)   dummy_eqr   r   r   r
   )r-   r%   r%   r&   test_apart_full   sB    (6 
<
  rH   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st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std S )Nr   r$   rF      rD   r!   r      r#   zZZ[a,b]domain)r   r   r   r)   r   r   )pqrr%   r%   r&   test_apart_undetermined_coeffs   s    <F(rP   c               
      s8  ddl m}   fdd tdtdtd  }}}td}d	t d
td
   dtd
  dt   }t|t| dd}dttd
dtddt|d
 |ddt|d
t|| t dfgf} ||st	td
td
 d
  t| dd}dtdtddt|d
 d
 |ddt||d
 t|| t dfgf} ||s<t	dtd d
td   d
td   dtd
   t d
  }t|t| dd}dtdtddt|d
 |ddt|dt|| t dft|d
 d |ddt|d| d t|| t d
ft|d |ddt|dt|| t dfgf} ||s4t	d S )Nr   )numbered_symbolsc                    s>   t | ttfkr,t fddt| |D S | |kp<| |S )Nc                 3   s   | ]\}} ||V  qd S )Nr%   ).0r1   r2   rG   r%   r&   	<genexpr>   s     z4test_apart_list.<locals>.dummy_eq.<locals>.<genexpr>)typelisttupleallziprG   r0   rS   r%   r&   rG      s    z!test_apart_list.<locals>.dummy_eqw0w1w2r   r3   r   r$   rD   w)Zdummiesr"   ZQQrK   ZZr   $   r!   r#   )
Zsympy.utilities.iterablesrQ   r   r   r   r   r   r
   r   r)   )rQ   rZ   r[   r\   Z_ar-   gotZansr%   rS   r&   test_apart_list   s4    (," 8*6*rc   c                  C   s  dt d dt d   dt d   dt d   t  d  } t| }t|dt d  dt d d   dt d d   dt d   ksttd	}dtd
t ddtdtd gt||d t|| t  dfgf}t|dtdt td   dtdt td    kstd S )Nr_   r!   r   r#   r$   ra   r   rF   r   r   r^   rK   r"   )r   r   r   r)   r   r   r   r   )r-   Zpfdr   r%   r%   r&   test_assemble_partfrac_list   s    8DBrd   c                  C   sp   G dd dt } tttt   }ddt  }t|| | || | ksLtt|| | || | ksltd S )Nc                   @   s   e Zd ZdZdS )z3test_noncommutative_pseudomultivariate.<locals>.fooFN__name__
__module____qualname__Zis_commutativer%   r%   r%   r&   foo   s   ri   r   r   r   r   r   r)   ri   er   r%   r%   r&   &test_noncommutative_pseudomultivariate   s
     rm   c                  C   sL   G dd dt } tttt   }ddt  }t||   ||   ksHtd S )Nc                   @   s   e Zd ZdZdS )z test_noncommutative.<locals>.fooFNre   r%   r%   r%   r&   ri      s   ri   r   rj   rk   r%   r%   r&   test_noncommutative   s    rn   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std S )Nr   r   r$   )r   r   r)   r%   r%   r%   r&   test_issue_5798   s
    B2ro   N)7__doc__Zsympy.polys.partfracr   r   r   r   Zsympy.core.exprr   Zsympy.core.functionr   Zsympy.core.numbersr   r	   r
   r   Zsympy.core.relationalr   Zsympy.core.singletonr   Zsympy.core.symbolr   r   Z(sympy.functions.elementary.miscellaneousr   Zsympy.matrices.denser   Zsympy.polys.polytoolsr   r   Zsympy.polys.rationaltoolsr   Zsympy.polys.rootoftoolsr   Zsympy.testing.pytestr   r   Z	sympy.abcr   r   r   r   r   r/   r5   r6   r<   rA   rB   rH   rP   rc   rd   rm   rn   ro   r%   r%   r%   r&   <module>   s8   '	

	