
    sgV`                        d dl mZmZmZ d dlmZ d dlmZmZm	Z	m
Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z& d dl'm(Z(m)Z) d dl*m+Z+ d dl,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6 d dl7m8Z8 d dl9m:Z:m;Z; d	 Z<d
 Z=d Z>d Z?d Z@d ZAd ZBd ZCd ZDd ZEd ZFd ZGd ZHd ZId ZJd ZKd ZLd ZMd ZNd ZOd ZPd ZQd ZRd  ZSd! ZTd" ZUd# ZVd$ ZWd% ZXd& ZYd' ZZd( Z[d) Z\e)d*        Z]y+),    )QQEXRR)ring) _invert_monomsrs_integraters_truncrs_mul	rs_squarers_pow_has_constant_termrs_hadamard_exprs_series_from_listrs_exprs_log	rs_newtonrs_series_inversionrs_compose_addrs_asinrs_atanrs_atanhrs_tanrs_cotrs_sinrs_cos
rs_cos_sinrs_sinhrs_coshrs_tanh_tan1rs_funrs_nth_rootrs_LambertWrs_series_reversionrs_is_puiseux	rs_series)raisesslow)symbols)
sincosexptancotatanatanhtanhlogsqrt)Rational)expandSc                 .    d}t        | |z
        |k  sJ y )Ng|=)abs)abtols      U/var/www/html/venv/lib/python3.12/site-packages/sympy/polys/tests/test_ring_series.pyis_closer=      s    
Cq1u:    c                     t        dt              \  } }|dz  d|dz  z  z   d|z  z   dz   }t        |      d|dz  z  d|dz  z  z   d|z  z   dz   k(  sJ t        |      |dz  dz  |dz  dz  z   d|z  z   dz   k(  sJ t        dt              \  } }|dz  d|dz  z  z   d|z  z   dz   }t	        ||      |dz  dz  |dz  dz  z   d|dz  z  dz  z   d|z  z   k(  sJ t        dt              \  } }}|dz  |dz  z  |z   dz   }t	        ||      |dz  |dz  z  dz  |dz  dz  z   |z   k(  sJ t	        ||      |dz  |dz  z  dz  ||z  z   |z   k(  sJ y )	Nx                  x, y)r   r   r   r   r   )Rr@   pys       r<   test_ring_series1rK      s   R=DAq	1qAv!aA!!Q$1a4!A# 5 99991Ab1a46!1AaC!7!!;;;;R=DAq	1qAv!aA1Aa!Q$q&1QT6!8!;ac!AAAA62GAq!	1QT	AA1Aad1q!tAv!5!99991Aad1qs!2Q!6666r>   c                      t        dt              \  } }}}|||z  z   dz  }t        ||d      }||dz  d|dz  z  |z  |z  z   d|dz  z  |dz  z  |dz  z  z   k(  sJ y )Nx, y, trA   rC      rB   )r   r   r	   )rH   r@   rJ   trI   p1s         r<   
test_truncrQ   !   sz    i$JAq!Q	
QqS1A	!Q	BA!Q$q
"Qq!tVAqD[A%55555r>   c                  r  	 t        dt              \  } }}d|z  z   ||z  z   t        d      D ]  }t        |d       ddz  z  |dz  z  dz  |z  |dz  z  z   d|dz  z  |dz  z  z   dz  |z  z   d|z  |z  z   dz   k(  sJ d|z  z   ||z  z   |dz  z  |z  z   t        |d      }|dd|z  z  z   d|z  |z  z   k(  sJ t        dt              \  }	t	        t
        	fd	       ddz  z   ddz  z  z   }ddz  z   }t        ||d      ddz  z  d
dz  z  z   dz  z   dz   k(  sJ y )NrM   rD   rB   rC   rN      rA   zc                       t         d      S )NrB   )r
   )rI   r@   rT   s   r<   <lambda>z test_mul_trunc.<locals>.<lambda>2   s    vaAq1 r>      )r   r   ranger
   r'   
ValueError)
rH   rJ   rO   irP   R1p2rI   r@   rT   s
          @@@r<   test_mul_truncr]   '   s   i$JAq!Q	AaC!A#A1X 1aA !Q$q!tbd1fQTk)AadF1a4K7!A#a%?!A#a%G!KKKK	AaC!A#1Qq A	1a	BQqSUQqSU""""bMEB
:12	
QqS1QT6	B	
QTB"b!Q1QT6Bq!tG#3ac#9A#====r>   c                  
   t        dt              \  } }}}d||z  z   ||z  z   dz  }t        |||d      }t        ||d      }||k(  sJ d|z   |dz  z   |dz  z   }t        ||d      d|dz  z  d|dz  z  z   d|z  z   dz   k(  sJ y )NrM   rD   rB   rC   rA   )r   r   r
   r   )rH   r@   rJ   rO   rI   rP   r\   s          r<   test_square_truncr_   8   s    i$JAq!Q	
QqS1Q3A	1a	B	1a	B8O8	A1q!tAQ11a4!AqD&1Q3!6!::::r>   c                  (   t        dt              \  } }}}|||z  z   }|dz  }|||fD ]$  }t        ||d      }t        |d|d      }||k(  r$J  d|z   }t        |d|d      }|dd|z  z   k(  sJ t        |d|d      dk(  sJ t        |d|d      dd|z  z
  k(  sJ ||z   }t        |d|d      |dz  d|dz  z  |z  z   d|z  |dz  z  z   k(  sJ t        d|z   t	        dd      |d	      d	|dz  z  d
z  |dz  dz  z
  |t	        dd      z  z   dz   k(  sJ y )Nx, y, z      rD   rC   rB   r   rA   Q   	   )r   r   r	   r   r4   )	rH   r@   rJ   rT   p0rI   xxrP   r\   s	            r<   test_pow_truncri   A   sn   i$JAq!Q	
QqSB
BA!Qi aQBB"Rxx
 	
AA	1a	BQqS==!Q1"""!RA!ac')))	AA!Q1A!Q$q1Q3q!t8!;;;;!a%!QA.!AqD&)ad1f2DqRSUVGW2WZ[2[[[[r>   c                      t        dt              \  } }}}|||z  z   }t        ||      sJ ||dz  z   }t        ||      rJ d|z   |dz  z   }t        ||      sJ ||z   ||z  z   }y )Nra   rA   rD   )r   r   r   )rH   r@   rJ   rT   rI   s        r<   test_has_constant_termrk   S   s    i$JAq!Q	AaCAa###	AqDA!!Q'''	A1Aa###	A!Ar>   c                     t        dt              \  } dz   ddz  z  z   d}t        |      }t        |z  |      dk(  sJ t        dt              \  } }dz   ddz  z  z   |z  z   dz  |z  z   t        |      }t        |z  |      dk(  sJ t        dt              \  } }dz   |z   t	        t
        fd       | j                  t	        t        fd       y )Nr@   rB   rF   rD   rG   c                      t         d      S )NrA   r   rI   r@   s   r<   rV   z test_inversion.<locals>.<lambda>j   s    (;Aq!(D r>   c                      t         d      S )NrC   rn   ro   s   r<   rV   z test_inversion.<locals>.<lambda>l   s    &9!Q&B r>   )r   r   r   r	   r'   NotImplementedErrorzeroZeroDivisionError)rH   nrP   rJ   rI   r@   s       @@r<   test_inversionru   ]   s    R=DAq	A!Q$A	A	Q1	%BAbD!Q1$$$62GAq!	A!Q$1q!tAv%A	Q1	%BAbD!Q1$$$62GAq!	A	A
 DE	A
BCr>   c                     t        dt              \  } }}t        ||d      }t        ||d|      t	        ||d      k(  sJ t        ||d      }t        ||d|      d|dz  z  dz  d|dz  z  dz  z   |dz  d	z  z   |z   k(  sJ y )
NrG   
   rc   rF      p   rC   (   rN   )r   r   r   r$   r   r   rH   r@   rJ   rI   s       r<   test_series_reversionr|   o   s    62GAq!q!RAq!Q*gaA.>>>>q!RAq!Q*a1fSj1QT6"9.D	1Q//   r>   c            	         t        dt              \  } }dd|z  z   |dz  z   d|dz  z  z   }g d}t        |||d      }| j                  t	        t        |                  }t        |j                  ||      |d      }||k(  sJ t        dt              \  } }}g d}t        ||z   ||dd	
      }t        dd||z   z  z   d||z   dz  z  z   d||z   dz  z  z   |d      }	||	k(  sJ t        dt              \  } }d}
t        |||
      dz
  }t        ||||
      }d	}	t        |      D ]  \  }}|	|t        ||||
      z  z  }	 ||	k(  sJ y )Nr@   rD   rB   rC   )rD   rB   r   rA   rA   rF   rG   )rD   rC   rF   rx   r   )concurrx      )r   r   r   	from_listlistreversedr	   composer   	enumerater   )rH   r@   rI   crpcr1rJ   rP   r\   hrZ   cxs                r<   test_series_from_listr   y   sn   R=DAq	AaC!Q$1a4AAAq!Q'A	
T(1+&	'B	"**Q"Aq	)B7N762GAq!A	QUAq!A	6B	1q!A#w;AaC!8+a1qj81a	@B8O8R=DAq
Aq!Q!A	Q1a	(B	
B1 $2
b1a###$8O8r>   c                  h   t        dt              \  } }d|z   }t        ||d      |dz  z  }|t        dd      |z  t        j
                  z
  |dz  z   k(  sJ d|z   d|dz  z  dz  z   }t        ||d      }|d|d	z  z  d
z  d|dz  z  dz  z   d|dz  z  dz  z
  |dz  dz  z
  d|dz  z  dz  z   |dz  dz  z
  |dz  dz  z   |z   k(  sJ t        ||d      }t        ||d      }|| k(  sJ t        dt              \  } }}d|z   d|z  |dz  z  z   }t        ||d      }|d|dz  z  |dz  z  d|dz  z  |z  z
  d|dz  z  |dz  z  z
  |dz  dz  z   d|dz  z  |z  z   |dz  dz  z
  d|dz  z  |z  z
  |dz  dz  z   d|dz  z  |z  z   |dz  dz  z
  |z   k(  sJ t        d      }t        dt              \  } }}t        ||z   |d      t        dd|dz  z  z         |dz  z  t        dd|dz  z  z        |dz  z  z   t        dd|dz  z  z        |dz  z  z
  t        d|z        |z  z   t        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d      t        |dz         |dz  z  |z  t        dd|dz  z  z        |dz  z  z   t        d|z        |dz  z  |z  z   t        dd|dz  z  z        |dz  z  z
  t        d|z        |z  z   t        t        |            z   k(  sJ ||dz  z   dz   }t        ||d      j                  |d      t        t        d      t        dd      z         k(  sJ y )Nr@   rD   rA   rB   rC   rf   rc   i     rx      rW   rN      rF   -   $   rG   r9   rd   rw   l   K)z i^ )r   r   r   r4   r6   Halfr   r)   r   r2   r   )rH   r@   rI   rP   r\   p3rJ   r9   s           r<   test_logr      s   R=DAq	AA	1aA	B!Q!AFF*QW4444	AqAvaxA	1aBQT#1a4+bAgck9AqDGC1fRiQ$q&a46"$%& & & &	Q1	%B	Aq	B"9962GAq!	A!AqDA	1aB!AqD&A+!Q$q(1QT6!Q$;6Aa?!AqD&(JQ$q&QT6!8$&'d1f-/0Avax8:;Q$q&ACDE F F F 	A62GAq!!a%A2a1a4j>/!Q$"6AqAvJ19L"L
Q!Q$Z.A
# "1Q3	#*,.s1vJ#7 7 7 7!ad1f*q.!Q'Bq2wK<1+<Q+>
1a1f:q!t, 1gadl1n,-/1!Qq!tV*~ad/B,C
1Q3	,s1vJ,    	
AqD1A!Q##Aq)RA+w9W0W-XXXXr>   c                     t        dt              \  } }||dz  z   }dD ]6  }t        d|z   ||      dz
  }t        |||      }t	        |||      }||k(  r6J  t        ||d      }|j                  |dz        t        dd      k(  sJ d	}t	        d|z   ||      }t        |||      }||dz   k(  sJ t        d
      }t        dt        t        |      |f         \  } }}	t        ||z   |d      t        |      |dz  z  dz  t        |      |dz  z  dz  z   t        |      |dz  z  dz  z   t        |      |z  z   t        |      z   k(  sJ t        ||dz  |	z  z   |z   |d      t        |      |dz  z  |	dz  z  dz  t        |      |dz  z  |	z  dz  z   t        |      |dz  z  dz  z   t        |      |dz  z  |	z  z   t        |      |dz  z  dz  z   t        |      |dz  z  |	z  z   t        |      |dz  z  dz  z   t        |      |z  z   t        |      z   k(  sJ t        dt              \  } }}	t        ||z   |d      t        t        |      dz        |dz  z  t        t        |      dz        |dz  z  z   t        t        |      dz        |dz  z  z   t        t        |            |z  z   t        t        |            z   k(  sJ t        ||dz  |	z  z   |z   |d      t        t        |      dz        |dz  z  |	dz  z  t        t        |      dz        |dz  z  |	z  z   t        t        |      dz        |dz  z  z   t        t        |            |dz  z  |	z  z   t        t        |      dz        |dz  z  z   t        t        |            |dz  z  |	z  z   t        t        |      dz        |dz  z  z   t        t        |            |z  z   t        t        |            z   k(  sJ y )Nr@   rA   )rw      rD   r      l   O$obl      LeFSX   r9   rG   rF   rE   rC   rN   rB   )	r   r   r   r   r   coeffr)   r,   r   )
rH   r@   rI   r   qrP   q1precr9   rJ   s
             r<   test_expr      s>   R=DAq	AqDA Aq!,q0Aq!_B1Qww	
 
1b	B88ArE?b!;=[\\\\Dq1uaA	1d	BQ;; 	A62c!fai=)GAq!!a%A#a&A+b.3q6!Q$;q="@Aq!tA#Aq#!#&q6#* * * *!ad1f*q.!Q'3q6!Q$;q!t+;A+=F1a4KM!O,!!fQTk"n,-/21vad{1},=F1a4KM,F1a4KM,*,/F1a4KM,:<?F1H,EGJ1v,N N N N 62GAq!!a%A2c!fRi=A#53q6!8QT8I#I
3q6!8QT$s1vJqL$)+-c!f:$6 6 6 6!ad1f*q.!Q'2c!fQh<1+<QT+A
3q6!8QT!, QmAqD0,135c!f:ad?13D,E
3q6!8QT,s1vJq!tOA-,.023q6!8QT0A,B 	3q6
1, #a&z," " " "r>   c                      t        dt              \  } }|dz  dz
  }t        ||d      }|d|dz  z  d|dz  z  z   dz   k(  sJ y )Nr@   rB   rA   rc   )r   r   r   )rH   r@   rI   r   s       r<   test_newtonr      sS    R=DAq	1qA!QA!Q$1a4!####r>   c                      t        dt              \  } }|dz  dz
  }|dz  dz
  }t        ||      |dz  d|dz  z  z
  d|dz  z  z
  d|dz  z  z   d|z  z
  dz
  k(  sJ y )	Nr@   rC   rD   rB   rN   rA   rS   rx   )r   r   r   )rH   r@   rP   r\   s       r<   test_compose_addr      sx    R=DAq	
AB	
AB"b!QTAadF]Qq!tV%;bAg%E1%Lq%PPPPr>   c                      t        dt              \  } }}||z  |dz  |dz  z  z   |dz  |z  z   }t        |t        |d      t        ||d      k(  sJ t        |t        |d      t	        ||d      k(  sJ y )NrG   rB   rC   rF   rw   )r   r   r!   r   r    r{   s       r<   test_funr      s}    62GAq!	!ad1a4i!Q$q& A!VQ#vaB'7777!UAr"eAq"o555r>   c                     t        dt              \  } }}t        d|dz  |z  z   d|d      d|dz  z  |dz  z  dz  d	|d
z  z  |dz  z  dz  z   d|dz  z  |dz  z  dz  z
  |dz  |z  dz  z   dz   k(  sJ t        d||z  z   |dz  |dz  z  z   d|d      |dz   |d
z  z  dz  d|dz  z  |dz  z  dz  z   d|dz  z  |dz  z  dz  z
  d|dz  z  |dz  z  dz  z
  d|dz  z  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z
  ||z  dz  z   dz   k(  sJ t        d|z  d|d      d|t        dd      z  z  k(  sJ t        d|z  |dz  z   |dz  z   d|d      |t        dd      z  dz  d|t        dd      z  z  z   k(  sJ t        d|z  |dz  |z  z   |dz  z   d|d      }||t        d	d      z   |dz  z  dz  |t        d	d      z  dz  z   |t        dd      z  |z  dz  z   d|t        dd      z  z  z   k(  sJ t        d      }t        dt              \  } }}t        ||z   d|d      t	        dd|t        dd      z  z  z        |dz  z  t	        dd|t        dd      z  z  z        |dz  z  z
  t	        dd|t        dd      z  z  z        |z  z   t	        |t        dd      z        z   k(  sJ t        |t        dd      z  |dz  |z  z   dz   d|d      t	        t        d      dz         |t        dd      z  z  |z  t	        t        d      dz        |t        dd      z  z  z
  t	        t        d      dz        |dz  z  |z  z   t	        t        d      dz        |dz  z  z   t	        t        d      dz        |t        dd      z  z  z
  t	        t        d      dz        |t        dd      z  z  z   t	        t        d            z   k(  sJ y )NrG   rD   rB   rA   rw   irc   i   rx   rN   rC          rF   rf         re   rS   i   r9   d   i>  i     )r   r   r"   r)   r   r3   )rH   r@   rJ   r   r9   s        r<   test_nth_rootr      s   62GAq!q1a46z1a,AqDAd0B	!Q$q!tC1AqD&A+b.1)+,a46!8146718 8 8 8q1Q3wAad*Aq!4Aad
1	!Q$q!tB9AqDAc)9*,-adF1a4KM9:<=adF1a4KN9K	1QT	!9d1a4ik9"$%aCE9*,-9. . . . qsAq!$!R1X+555qsQTzAqD(!Q2aAajma2aPQ7
l6RRRRAaC!Q$q&L1a4'Aq1ABqGAqD $q"Qq'z"}4q"Qq'z!|BF1bQRSTg:UUUU 	A62GAq!q1uaA&"Q1bAh;-?*@A*E
1a2a8mad"+#%'1Q1a[=(9%:1%<+=?A!R1X++O O O Oq"Q({QT!V+a/Aq9bao=M	2a8>>475=)!R1X+5>68:472:q!t8KA8M>N
474<A> "473;2a8 ;>< 	472:q"Q({"># &(Q[>1 1 1 1r>   c            	         t        dt              \  } }}t        ||d      |dz   dz  |dz  dz  z   |dz  dz  z
  |z   k(  sJ t        ||z  |dz  |dz  z  z   |d      d|dz  z  |dz  z  |dz  |dz  z  z
  d|dz  z  |dz  z  z   |dz  |dz  z  dz  z
  |d	z  |dz  z  dz  z
  |d	z  |dz  z  z   |dz  |dz  z  z
  |dz  |dz  z  dz  z   |d
z  |dz  z  z
  |dz  |dz  z  dz  z
  |dz  |dz  z  z   ||z  z   k(  sJ t        d      }t        dt              \  } }}t        ||z   |d      t	        |dz  |z
  |dz  d
|d	z  z  z   d	|d
z  z  z   d
|dz  z  z   dz   z         |d
z  z  t	        d|dz  z  dz
  d|d	z  z  d|d
z  z  z   d|dz  z  z   dz   z        |dz  z  z   t	        ||d
z  d|dz  z  z   dz   z        |dz  z  z
  t	        d|dz  dz   z        |z  z   t	        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d
      t	        d|z  |d
z  d|dz  z  z   dz   z         |dz  z  |z  t	        d|dz  z  dz
  d|d	z  z  d|d
z  z  z   d|dz  z  z   dz   z        |dz  z  z   t	        d|dz  dz   z        |dz  z  |z  z   t	        ||d
z  d|dz  z  z   dz   z        |dz  z  z
  t	        d|dz  dz   z        |z  z   t	        t        |            z   k(  sJ y )NrG   rf   rx   rF   rC   rB   rc   rW   rN   rA   r9   rD   )r   r   r   r)   r   r/   rH   r@   rJ   r9   s       r<   	test_atanr      s$   62GAq!1a1uQwAa/!Q$q&81<<<<1Q3Aad?Aq)Qq!tVArE\AqDAI-E	!Q$q!t.d1a4ik."$%qDAIaK.023Q$q!t).<>?d1a4i.H	1QT	!.d1a4i. "#Q$q!t)A+..011QT	.:<=aC.@ @ @ @
 	A62GAq!1q5!QB1q1a4!AqD&=1QT63I	!Q$44 ( % $T$!Q$
Qq!tVa1f_	!Q$..   T$q!Q$1a4-!"345ad:$; 	1adQh<$  Q[$) ) ) ) 1q!tAv:>1a(R!QTAadF]Q5F0G-H,H	
A--a1fqj1QT6AadF?Qq!tV#;a#?@A!Q$F-G
1adQh<Aa- "$Q1qAv(9%:";AqD"@-ACEaA
J G DD- T!W+-   r>   c                     t        dt              \  } }}t        |||z  z   |d      |dz  |dz  z  dz  |dz  |dz  z  dz  z   |dz  |z  dz  z   |dz  dz  z   ||z  z   |z   k(  sJ t        ||z  |dz  |dz  z  z   |d      |dz  |dz  z  dz  d|dz  z  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  z   ||z  z   k(  sJ y )	NrG   rF   rC   rN   rB   rx   rz   rA   )r   r   r   rH   r@   rJ   s      r<   	test_asinr   
  s=   62GAq!1qs7Aq!QT!Q$Yq[1a419Q;%>Aa%I	1Q&1&&   1Q3Aad?Aq)QT!Q$Yq[1QT6!Q$;r>-I	1QT	!.d1a4ik."$%qDAI..01!.4 4 4 4r>   c            	      
   t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      z   t        dd	      |d
z  z  z   |dz  z   k(  sJ t        ||z  |dz  |d	z  z  z   |d      d|dz  z  |dz  z  d	z  d|dz  z  |dz  z  dz  z   d|dz  z  |dz  z  d	z  z   d|dz  z  |dz  z  dz  z   |dz  |dz  z  d	z  z   d|dz  z  |dz  z  d	z  z   |dz  |dz  z  z   d|dz  z  |dz  z  dz  z   |dz  |dz  z  z   |d	z  |d	z  z  d	z  z   |dz  |d	z  z  z   ||z  z   k(  sJ t	        d      }t        dt        t        |      |f         \  } }}t        ||z   |d      t        |      dz  dt        |      d	z  z  d	z  z   dt        |      z  d	z  z   |dz  z  t        |      dz  dt        |      dz  z  d	z  z   t        dd	      z   |d	z  z  z   t        |      d	z  t        |      z   |dz  z  z   t        |      dz  dz   |z  z   t        |      z   k(  sJ t        ||dz  |z  z   |z   |d      dt        |      d	z  z  dt        |      z  z   |d	z  z  |z  t        |      dz  t        dd	      t        |      dz  z  z   t        dd	      z   |d	z  z  z   t        |      dz  dz   |dz  z  |z  z   t        |      d	z  t        |      z   |dz  z  z   t        |      dz  dz   |z  z   t        |      z   k(  sJ t        dt              \  } }}t        ||z   |d      t        t        |      dz  dt        |      d	z  z  d	z  z   dt        |      z  d	z  z         |dz  z  t        t        |      dz  dt        |      dz  z  d	z  z   t        d      d	z  z         |d	z  z  z   t        t        |      d	z  t        |      z         |dz  z  z   t        t        |      dz  dz         |z  z   t        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d      t        dt        |      d	z  z  dt        |      z  z         |d	z  z  |z  t        t        |      dz  dt        |      dz  z  d	z  z   t        d      d	z  z         |d	z  z  z   t        t        |      dz  dz         |dz  z  |z  z   t        t        |      d	z  t        |      z         |dz  z  z   t        t        |      dz  dz         |z  z   t        t        |            z   k(  sJ ||dz  z   dz   }t        ||d      j                  |d      t        t        d      t        d      dz  z         k(  sJ y )NrG   rf   rF      ;  rB      rD   rC   rd   rA   rc   rW   r   rx   rN   r9   rw   l   PH]l   n)r   r   r   r4   r)   r-   r   r   r   r/   r6   rH   r@   rJ   r9   rI   s        r<   test_tanr     se   62GAq!!Q?1a4S!Q$!R08Aq>!b'3IIAPRGST T T!A#1QT	/1a(AadF1b5LNR1WQT\"_,L	!Q$q!tA-1a41S(-)+,a419Q;-79:1a41Q-G	1QT	-adF1a4KN-#%&T!Q$Y-/12Aad1-=?@!tAqDy-IKLQ3-O O O O
 	A62c!fai=)GAq!!a%A3q619qQ{1}#<	#a&
$qD#FAI#a&!)A5AF1L#M	QSV	QT!#"%(VQY]A$5#68;A#? ? ? ? !ad1f*q.!Q'Ac!faiK!CF(,BAqD+H+J	QXa^CFAI-	-A	>1D,EHKAPQ	TUWXZ[W[G[\]G],^	QSV	QT!,"%(VQY]A$5,68;A,? ? ? ? 62GAq!!a%A"SVQY3q619Q%>	#a&
& #qD#c!fai!CFAI+a-7"Q%'AB1a4G#H
3q619s1vq!t##$&(QQ&7&9#:<>s1vJ#G G G G !ad1f*q.!Q'2aA	k	#a&/ ,Q$,,c!fai!CFAI+a-7"Q%'AB1a4G,H
3q619q=!Q$q ,!#%c!fai#a&&8#9!Q$#>,? 	3q619q=!, !Qj,) ) ) )
 	
AqD1A1a$$Q+r$q'A>O<P= 3 0   r>   c                     t        dt              \  } }}t        |dz  |dz  z   |d      |dz  |dz  z
  |dz  z   |dz  z
  |d	z  z   |d
z  z
  dz   |z
  |dz  z   |dz  z
  |dz  z   |dz  z
  d|dz  z  dz  z   d|dz  z  dz  z
  k(  sJ t        ||dz  |z  z   |d      |dz   |dz  z  |dz  |z  dz  z
  |dz  |dz  z  z   |dz  dz  z
  |dz  |dz  z  z
  |dz  |z  dz  z
  ||dz  z  z   |dz  z
  |z
  |d
z  z   k(  sJ y )NrG   rN   rx   rc   ir   rd   r   rD   rB   rC   rA   rF   r   r   )r   r   r   r   s      r<   test_cotr   0  s   62GAq!!Q$A+q!$B!b'(9AG(C	B)b')G)$&')(*+),./d)356T):<=qD)ACDa4)H	!Q$q)QT6!8)    !ad1f*a#1uQTzAqDF2I'=1QT	'I	1R(Q$q!t)(d1fQh(')*1a4(023A#(689(:<=G(D D D Dr>   c                     t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      z   t        dd	      |d
z  z  z
  |dz  z   k(  sJ t        ||z  |dz  |dz  z  z   |d      |dz  |dz  z  dz  |dz  |dz  z  dz  z
  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z
  |d	z  |dz  z  d	z  z
  |d	z  |dz  z  dz  z   |dz  |dz  z  dz  z
  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z
  |dz  |dz  z  d	z  z
  |dz  |dz  z  z   ||z  z   k(  sJ t	        d      }t        dt        t        |      t        |      |f         \  } }}t        ||z   |d      t        |      |dz  z  dz  t        |      |dz  z  d	z  z
  t        |      |dz  z  dz  z
  t        |      |z  z   t        |      z   k(  sJ t        ||dz  |z  z   |z   |d      t        |       |dz  z  |dz  z  dz  t        |      |dz  z  |z  dz  z
  t        |      |dz  z  dz  z   t        |      |dz  z  |z  z
  t        |      |dz  z  d	z  z
  t        |      |dz  z  |z  z   t        |      |dz  z  dz  z
  t        |      |z  z   t        |      z   k(  sJ t        dt              \  } }}t        ||z   |d      t        t        |      dz        |dz  z  t        t        |      d	z        |dz  z  z
  t        t        |      dz        |dz  z  z
  t        t        |            |z  z   t        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d      t        t        |      dz         |dz  z  |dz  z  t        t        |      dz        |dz  z  |z  z
  t        t        |      dz        |dz  z  z   t        t        |            |dz  z  |z  z
  t        t        |      d	z        |dz  z  z
  t        t        |            |dz  z  |z  z   t        t        |      dz        |dz  z  z
  t        t        |            |z  z   t        t        |            z   k(  sJ y )NrG   rf   rF   r     rB   rD   x   rN   rd   r   rC   rc   rW   rS     rx   rE   rA   r9   )r   r   r   r4   r)   r*   r+   r   r   s       r<   test_sinr   8  s,   62GAq!!Q?1a4T1a4(1c"22Xa^AG5KKaRTgUV V V!A#1QT	/1a(AqDBJrM	1QT	#-1QT	"-%'(!tAqDy~-6891QT	!-D	1QT	"-!tAqDy{-#%&T!Q$Ys]-356T!Q$Yq[-A 	
1QT	!- d1a4i-  #$A#-& & & & 	A62c!fc!fa/01GAq!!a%A#a&A+b.3q6!Q$;q="@Aq!tA#Aq#!#&q6#* * * *!ad1f*q.!Q'CF71a4<1+<Q+>Aq!tAa,a&A+b.,)+.q6!Q$;q=,9;>q6!Q$;q=,IAq!tA,Aq!tA,&(+Aq,136q6,: : : : 62GAq!!a%A"SVBY-1"4r#a&(|AqD7H"H
3q6!8QT#s1vJqL#)+-c!f:#6 6 6 6!ad1f*q.!Q'Bs1vaxL=A+=ad+B
3q6!8QT!, QmAqD0,135c!f:ad?13D,E
3q6!8QT,s1vJq!tOA-,.023q6!8QT0A,B 	3q6
1, #a&z," " " "r>   c                  .	   t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      |z  z
  t        dd      |d	z  z  z   t        j
                  |d
z  z  z
  |dz  z   k(  sJ t        ||z  |dz  |dz  z  z   |d      |dz  |dz  z  dz  |dz  |dz  z  dz  z
  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z
  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z
  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z
  |dz  |dz  z  dz  z   |dz  |dz  z  z
  |dz  |dz  z  dz  z
  dz   k(  sJ t        d      }t        dt        t        |      t        |      |f         \  } }}t        ||z   |d      t        |      |dz  z  dz  t        |      |dz  z  dz  z   t        |      |dz  z  dz  z
  t        |      |z  z
  t        |      z   k(  sJ t        ||dz  |z  z   |z   |d      t        |       |dz  z  |dz  z  dz  t        |      |dz  z  |z  dz  z   t        |      |dz  z  dz  z   t        |      |dz  z  |z  z
  t        |      |dz  z  dz  z   t        |      |dz  z  |z  z
  t        |      |dz  z  dz  z
  t        |      |z  z
  t        |      z   k(  sJ t        dt              \  } }}t        ||z   |d      t        t        |      dz        |dz  z  t        t        |      dz        |dz  z  z   t        t        |      dz        |dz  z  z
  t        t        |            |z  z
  t        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d      t        t        |      dz         |dz  z  |dz  z  t        t        |      dz        |dz  z  |z  z   t        t        |      dz        |dz  z  z   t        t        |            |dz  z  |z  z
  t        t        |      dz        |dz  z  z   t        t        |            |dz  z  |z  z
  t        t        |      dz        |dz  z  z
  t        t        |            |z  z
  t        t        |            z   k(  sJ y )NrG   rf   rF   rD   逝  rC   r   rE   r   r   r   rB   rc   rS   rw   0   rx   rN   r   rA   r9   )
r   r   r   r4   r6   r   r)   r*   r+   r   r   s       r<   test_cosr   R  sh   62GAq!!Q?1a4E1a4(1c"21"44x2q2w7NNQRQWQWXY\^X_Q__bcfhbiij j j!A#1QT	/1a(AqDBJrM	1QU
2-1QT	%-(*+Q$q"u*Q,-7	1QT	#-1QT	!-$&'d1a4im-467d1a4ik-B 	
1QT	!- d1a4il-# &'T!Q$Y-/ 23Aad1-= @A-A A A A 	A62c!fc!fa/01GAq!!a%A#a&A+b.3q6!Q$;q="@Aq!tA#Aq#!#&q6#* * * *!ad1f*q.!Q'CF71a4<1+<Q+>Aq!tAa,a&A+b.,)+.q6!Q$;q=,9;>q6!Q$;q=,IAq!tA,Aq!tA,&(+Aq,136q6,: : : : 62GAq!!a%A"SVBY-1"4r#a&(|AqD7H"H
3q6!8QT#s1vJqL#)+-c!f:#6 6 6 6!ad1f*q.!Q'Bs1vaxL=A+=ad+B
3q6!8QT!, QmAqD0,135c!f:ad?13D,E
3q6!8QT,s1vJq!tOA-,.023q6!8QT0A,B 	3q6
1, #a&z," " " "r>   c                      t        dt              \  } }}t        ||d      \  }}|t        ||d      k(  sJ |t	        ||d      k(  sJ t        |||z  z   |d      \  }}|t        |||z  z   |d      k(  sJ |t	        |||z  z   |d      k(  sJ y )NrG   rf   rF   )r   r   r   r   r   )rH   r@   rJ   r+   r*   s        r<   test_cos_sinr   l  s    62GAq!!Q"HC&Aq/!!!&Aq/!!!!ac'1a(HC&QqS!Q''''&QqS!Q''''r>   c            	         t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      z   t        dd      |dz  z  z   |d	z  z   k(  sJ t        ||z  |dz  |dz  z  z   |d      d|d
z  z  |dz  z  |d
z  |dz  z  z   d|dz  z  |dz  z  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  z   |dz  |dz  z  z   |dz  |dz  z  dz  z   |dz  |dz  z  z   |dz  |dz  z  dz  z   |dz  |dz  z  z   ||z  z   k(  sJ t	        d      }t        dt
              \  } }}t        ||z   |d      t        |dz  |z   |d
z  d|dz  z  z
  d|dz  z  z   d|dz  z  z
  dz   z        |dz  z  t        d|dz  z  dz   d|dz  z  d|dz  z  z
  d|dz  z  z   dz
  z        |dz  z  z
  t        ||dz  d|dz  z  z
  dz   z        |dz  z  z   t        d|dz  dz
  z        |z  z
  t        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d      t        d|z  |dz  d|dz  z  z
  dz   z        |dz  z  |z  t        d|dz  z  dz   d|dz  z  d|dz  z  z
  d|dz  z  z   dz
  z        |dz  z  z
  t        d|dz  dz
  z        |dz  z  |z  z
  t        ||dz  d|dz  z  z
  dz   z        |dz  z  z   t        d|dz  dz
  z        |z  z
  t        t        |            z   k(  sJ ||dz  z   dz   }t        ||d      j                  |d      t        t        dd      t        d      z         k(  sJ y )NrG   rf   rF   rD   rx   rB   rC   rd   r   rc   rW   rN   rA   r9   rw   lyY?l l    P{] )r   r   r   r4   r)   r   r0   r   r   s        r<   
test_atanhr   u  s   62GAq!Aq!QT!Xa^AqD%88Aq>%IHUVXYN[\_a[bLb%befikel%llllAaC!Q$q!t)OQ*a1fQUlQT!Q$Y.F	!Q$q!t/d1a4ik/"$%qDAIaK/023Q$q!t)/<>?d1a4i/H	1QT	!/d1a4i/ "#Q$q!t)A+/.011QT	/:<=aC/@ @ @ @
 	A62GAq!AE1a B1q1a4!AqD&=1QT63I	!Q$44 ( %T%!Q$
Qq!tVa1f_	!Q$..   T%q!Q$1a4-!"345ad:%;=?1a4	D
 A >>% 58%    A1QJNAq)R!QTAadF]	6
 1 .qD..1a4!a1fqAvo!Q$&>&BCDQTI.J
1adQh<Aa. "$Q1qAv(9%:";AqD"@.A 	1adQh<.  a\.* * * *
 	
AqD1AAq"%%a,8<Lj3Y
(4 1   r>   c                  T   t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      z   t        dd      |d	z  z  z   |d
z  z   k(  sJ t        ||z  |dz  |dz  z  z   |d      |dz  |dz  z  dz  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  z   ||z  z   k(  sJ y )NrG   rf   rF   rD   r   rB   r   rN   rd   r   rC   rc   rW   rS   r   rx   rE   rA   )r   r   r   r4   r   s      r<   	test_sinhr     s   62GAq!1aAqD HQ$5ad$:Xa=M$MPXYZ\]P^_`ce_fPf$fijmoip$pppp1Q3Aad?Aq)QT!R%Z]	1QT	#.1QT	".%'(!tAqDy~.6891QT	!.D	1QT	".!tAqDy{.#%&T!Q$Ys].356T!Q$Yq[.A 	
1QT	!. d1a4i.  #$A#.& & & &r>   c                     t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      |z  z   t        dd      |d	z  z  z   t        j
                  |d
z  z  z   |dz  z   k(  sJ t        ||z  |dz  |dz  z  z   |d      |dz  |dz  z  dz  |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  dz  z   |dz  |dz  z  z   |dz  |dz  z  dz  z   dz   k(  sJ y )NrG   rf   rF   rD   r   rC   r   rE   r   r   r   rB   rc   rS   rw   r   rx   rN   r   rA   )r   r   r   r4   r6   r   r   s      r<   	test_coshr     s   62GAq!1aAqD HQ$6q!t$;hq#>Nq>P$PS[\]_aSbcdgicjSj$j	q2w%R%! ! ! !1Q3Aad?Aq)QT!R%Z]	1QU
2.1QT	%.(*+Q$q"u*Q,.7	1QT	#.1QT	!.$&'d1a4im.467d1a4ik.B 	
1QT	!. d1a4il.# &'T!Q$Y./ 23Aad1.= @A.A A A Ar>   c            	         t        dt              \  } }}t        ||d      |dz  z  t        dd      |dz  z  t        dd      z   t        dd	      |d
z  z  z
  |dz  z   k(  sJ t        ||z  |dz  |d	z  z  z   |d      d|dz  z  |dz  z  d	z  d|dz  z  |dz  z  dz  z
  d|dz  z  |dz  z  d	z  z   d|dz  z  |dz  z  dz  z
  |dz  |dz  z  d	z  z
  d|dz  z  |dz  z  d	z  z   |dz  |dz  z  z
  d|dz  z  |dz  z  dz  z   |dz  |dz  z  z
  |d	z  |d	z  z  d	z  z
  |dz  |d	z  z  z   ||z  z   k(  sJ t	        d      }t        dt
              \  } }}t        ||z   |d      t        t        |      dz  dt        |      d	z  z  d	z  z
  dt        |      z  d	z  z         |dz  z  t        t        |      dz   dt        |      dz  z  d	z  z   t        dd	      z
        |d	z  z  z   t        t        |      d	z  t        |      z
        |dz  z  z   t        t        |      dz   dz         |z  z   t        t        |            z   k(  sJ t        ||dz  |z  z   |z   |d      }|j                  |d      j                  |d      t        dt        |      dz  z  dt        |      d	z  z  z   dt        |      dz  z  d	z  z   dt        |      z  z
  t        dd	      z         k(  sJ y )NrG   rf   rF   r   r   rB   r   rD   rC   rd   r   rA   rc   rW   r   r   rx   rN   r9   rw   iit'  i	  is'  i  )r   r   r   r4   r)   r   r1   r   r   s        r<   	test_tanhr     s   62GAq!1aAqD HS#$6q!t$;hq"o$MPXYZ\]P^_`ce_fPf$fijmoip$pppp1Q3Aad?Aq)Qq!tVArE\!^
1a41R.AqD&A+a-.(*,QT'!Q$,s*:.;=>T!Q$Yq[.I	!Q$q!tA.1QT	."$%adF1a4KN.356T!Q$Y.? 	
1QT	!. d1a4i.  #$A#.& & & & 	A62GAq!1q5!Q2d1gqj1T!WaZ<>&A	$q'	!' $T$Q
{QtAwz\!^;bAhFG1L$M
47A:Q A%$&(*DGQJ;?(;A(=$>@B47$L L L L 	AqDF
Q1%AIIa%%a+r%Q
2Bd1gqj3Q
?1,3-/4T!W}3=?A#qz3J 0K K K Kr>   c                     t         t        t        t        t        t
        g} t        t        t        t        t        t        g}t        dt              \  }}}t        d      }t        | |      D ]  \  }} |d|z   |d      j!                  |d      } |d|z         j#                  |dd      j%                         }	t'        |j)                         |	j+                  |d      j-                                 t/        d|z   d|d      j!                  |d      }d|z   t1        dd      z  j#                  |dd      j%                         }	t'        |j)                         |	j+                  |d      j-                                y )NrG   r9   rB   rF   r   rD   )r   r   r   r   r   r   r*   r+   r-   r.   r/   r1   r   r   r)   zipr   seriesremoveOr=   as_exprsubsrt   r"   r   )
rs_funcssympy_funcsrH   r@   rJ   r9   rs_func
sympy_funcrI   r   s
             r<   test_RRr     s2   AHS#tT2K62GAq!A"8[9 0AE1a ((A.q1u$$Q1-557affQlnn./0
 	AE1a#++Aq1A
a%"Q(	""1a+335AQYY[!&&A,..*+r>   c                  *   t        dt              \  } }}dd|z  z   |dz  z   d|dz  z  z   }t        ||      rJ ||t        dd      z  |z  z   }t        ||      sJ t        ||      rJ ||dz  |t        dd      z  z  |z  z   }t        ||      rJ y )NrG   rD   rB   rC   rF   )r   r   r%   r{   s       r<   test_is_regularr     s    62GAq!	AaC!Q$1a4AQ"""	Ar!AwJqLAAQ"""	AqDBqGOAAQ""""r>   c                     t        dt              \  } }}|t        dd      z  |t        dd      z  z   |z   }t        ||d      }|t        dd      z   |t        dd      z  z   d|t        d	d      z  z  z
  |t        dd      z  z   d|t        d
d      z  z  z   |t        dd      z  z
  |t        dd      z  z
  |t        dd      z  z   |t        dd      z  z
  |t        dd      z  z   }||k(  sJ t        d|z   d|d      }||t        dd      z   dz  |t        dd      z  dz  z   |t        dd      z  dz  z   dz   k(  sJ t	        d|z   |d      }||t        dd      z   dz  |t        dd      z  z   |t        dd      z  z   k(  sJ t        ||d      }||t        dd      z   |t        dd      z  z   |t        dd      z  z   k(  sJ ||t        dd      z  |z  z   }t        ||d      }||t        dd      z  |dz  z  dz  |t        dd      z  |dz  z  dz  z   |t        dd      z  |dz  z  dz  z   |t        dd      z  |z  z   dz   k(  sJ t        ||d      }||t        dd      z   |t        dd      z  z
  |t        dd      z  z
  |t        dd      z  dz  z
  |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        ||d      }||t        dd      z  |dz  z  dz  |t        dd      z  |dz  z  z   |t        d
d      z  |d
z  z  d
z  z
  |t        d
d      z  |dz  z  z
  ||dz  z  dz  z   |z   |t        dd      z  |dz  z  dz  z
  |t        dd      z  |z  z   k(  sJ t        ||d      }||t        dd      z  dz  |t        dd      z  dz  z   |t        dd      z  dz  z   |t        dd      z  dz  z   |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        ||d      }||t        dd      z   |t        dd      z  z   d|t        d	d      z  z  z
  d|t        dd      z  z  dz  z   d|t        d
d      z  z  z   d|t        dd      z  z  dz  z
  |t        dd      z  z
  |t        dd      z  z   |t        dd      z  z
  |t        dd      z  z   k(  sJ t        ||d      }|d   |t        dd      z  dz  |t        dd      z  z
  |t        dd      z  dz  z   |t        d
d      z  z
  |t        dd      z  dz  z
  |t        dd      z  z
  |t        dd      z  dz  z
  dz   k(  sJ |d   |t        dd      z   dz  |t        dd      z  dz  z
  |t        dd      z  dz  z
  |t        dd      z  dz  z
  |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        ||d      }||t        dd      z  |t        dd      z  z   |t        dd      z  z   |t        dd      z  dz  z   |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        ||d      }||t        dd      z  dz  |t        dd      z  dz  z   |t        dd      z  dz  z   |t        dd      z  dz  z   |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        ||d      }||t        dd      z  dz  |t        dd      z  z   |t        dd      z  dz  z   |t        d
d      z  z   |t        dd      z  dz  z   |t        dd      z  z   |t        dd      z  dz  z   dz   k(  sJ t        ||d      }||t        dd      z   |t        dd      z  z
  |t        dd      z  z
  |t        dd      z  dz  z
  |z   |t        dd      z  z   |t        dd      z  z   k(  sJ y )NrG   rB   rF   rC   rD      r   rA   rW   rx   rd   rf   rE   rN         r      rc   rb   )r   r   r   r"   r   r#   r   r   r   r   r   r   r   r   r   )rH   r@   rJ   rI   r   r   rP   s          r<   test_puiseuxr     s	   62GAq!	2a7
Q1QZ!#AAq!$A
R2Y,BqG	#a2b9n	4q"Qq'z	A	!R"X+
2a7

#%&1QZ
023R"X+
>@A2b9
M
R1X+
B 7N7AE1a#ABqGA2a7
1,q"Qq'z!|;a????q1uaABqGA2a7
*Q1QZ7777Aq!ABqGaAaj(1b1g:5555	
Q1QZ\	Br1aA2a7
1a4"Q1QZ1_Q%66BqGAqD9JJ	2a7
1    	1aA!R!W*q"R)|+aBrl:Q1QZ\I	
r!AwJBqG$ $ $ $ 	AqABqGAqD"Q1QZ1_4q"Qq'z!Q$q7HH	2a7
1a4AqD&(#%&')*BqGAqD):;=>1QZ\J J J J 	1aA2a7
1q"R)|A~-2b9Q>	2a7
1b1g:&()2a7
3 3 3 3 	q!QABr"I2a7
*Qq"R)|^;	!R!W*Q1b2h;')*1b1g:a8:;R!W*E	2a8Brl#%&2a[1 1 1 1 	1aAQ41bBi<>Ar!AwJ.BqGB>BqGK	2a7
1"R)|$&'Aajl3567 7 7 7Q4Ar!AwJ;q=1bBi<>1Ar"RyLNB	2a7
1b1g:&()2a7
3 3 3 3 	AqA2a7
Q2b	\)Ar"RyL81b1g:a<G!K	2a7
1QZ        	1aA2a7
1q"R)|A~-2b9Q>	2a7
1b1g:&()2a7
3 3 3 3 	1aA2b9QBqG+aAajm;aAajH	2a7
1"R)|$&'Aajl3567 7 7 7 	1aABqGaBrl*Q2b	\9Ar!AwJqLH	
r!AwJBqG$ $ $ $r>   c                  :   t        j                  t        d            } | j                  t        d            }t	        d      \  }}t        ||g|       \  }}}d|z   |t        dd      z  z  d|z
  |t        dd      z  z  z   }t        |      t        dd      t        d      fd|z   t        d      t        dd      fd|z
  ik(  sJ |j                         dt        d      z   |t        d      dz  z  z  dt        d      z
  |t        d      dz  z  z  z   k(  sJ y )NrB   rG   rD   rC   r   )	r   algebraic_fieldr3   
from_sympyr)   r   dictr   r6   )Ksqrt2r@   rJ   rH   xryrrI   s           r<   test_puiseux_algebraicr   	  s   
47#ALLa!E6?DAqaVQIAr2	
5"b1g+5"b1g+ 55A71Q1qwAr!Aw%HHHH99;1tAw;AaDF3q47{A!QK6OOOOOr>   c                  L   t        dt              \  } }t        ||d      |dz  z  }||dz  dz  |dz  dz  z
  |dz  d	z  z   |d
z  dz  z
  t        dd      z   |dz  dz  z
  |dz  z   k(  sJ t        ||d      }t        |d
|d      }|d|t        dd
      z  z  dz  |t        dd
      z  dz  z
  |t        dd
      z  dz  z   |t        dd
      z  dz  z
  |t        dd
      z  z   k(  sJ t        ||d      }t        |d|d      }t	        |d|d      }|d|t        dd      z  z  dz  |t        dd      z  dz  z
  d |t        d!d      z  z  d"z  z   d|t        d#d      z  z  d$z  z
  |t        dd      z  z   k(  sJ t        |t        dd
      z  |d      }||t        d#d
      z  d%z  |dz  d&z  z   |t        dd
      z  d'z  z   |dz  d(z  z   |t        dd
      z  d)z  z   |dz  d*z  z   |t        dd
      z  dz  z   |dz  d+z  z   |t        d d
      z  dz  z   |dz  d,z  z   |t        dd
      z  d	z  z   |dz  d-z  z   |t        dd
      z  dz  z   |d.z  d/z  z   |t        dd
      z  dz  z   |d
z  d0z  z   |t        d.d
      z  dz  z   |d
z  z   |t        dd
      z  z   dz   k(  sJ y )1Nr@   r   r   rc   l    LQf rN   i arA   i rB   r   rD   r   rd   r   rw   ir   i r   i^  rf   i  rF   rS   rx   i=   i:k/   iP@  rW   !   i     *   l     L.l     { l     ]
 l     nLl    Xnl    (vQ i i _7 r   rC   r   rE   )r   r   r   r"   r   r   )rH   r@   r   rI   s       r<   test1r     s   R=DAqq!RR A1Z!Q$x-/!Q$v+=1T	I
1S	rE!Ge$ $ $ $ 	q!RAAq!R AQ2a[)Ar"QxK,==	2a7
4R!W*R-(*+R!W*5 5 5 5 	q!RAAq!R Aq!QAAr"QxK	)Ar"QxK,==
1bAh;t2b8mB./12BqG< < < < 	q"Qq'z1b!A2b8..A6F1FF	2b8O#$&'d>&9:	2b8M!"$%qD$45 	
2b8J "#Ai0 34R1X+h2FG 	
1W	 "Qq'z&(	) ,-a4:	6 9:2a7
4	H
 	
1S
 b1g:c>"
 %&qDG,
 /0Aajl;
 >?qSA 	
2a7
    r>   c                     t        dt              \  } }t        d|       \  }}||t        dd      z  |z  z   }t        ||d      }||dz  dz  |dz  z   d|dz  z  z   |t        dd      z  z  |d	z  d	z  |d
z  z   |z   |t        d	d      z  z  z
  |dz  dz  |dz  z   |t        dd      z  z  z   |dz  dz  |dz  z   |t        dd      z  z  z
  |dz  dz  dz   |z  z   |dz  |t        dd      z  z  dz  z
  ||t        dd      z  z  z   k(  sJ y )NrJ   r@   rD   rF   rC   r   rc   rB   rW   rN   rf   rA   rx   )r   r   r   )rH   rJ   r6   r@   rI   r   s         r<   test_puiseux2r   /  s]   R=DAqQ<DAq	Ar!AwJqLA1aABrAqD1QT6)1bAh;6!R%(QT/	;
bAh;: Q$q&1a4-BqG3478!tAv	18Aaj7qDFQJ>*,-qDBqGOA,=>@A!R!W*M M M Mr>   c                     t        d      \  } }}}t        ||d      j                         |k(  sJ t        t        |      |d      j                         t        |      j	                  |dd      j                         k(  sJ t        t        |      t        |      z   |d      j                         t        |      t        |      z   j	                  |dd      j                         k(  sJ t        t        |      t        |      z  |d      j                         t        |      t        |      z  j	                  |dd      j                         k(  sJ t        |      |z
  t        |dz        |dz  dz  z   z  }t        t        ||d      j                               t        |j	                  |dd      j                               k(  sJ t        |dz  dz  |dz  z         t        |dz        t        |dz        dz  z  z   }t        t        ||d      j                               t        |j	                  |dd      j                               k(  sJ t        | dz  |z         t        | dz  dz
        |z
  |dz  z
  z  }t        t        ||d      j                               t        |j	                  |dd      j                               k(  sJ t        |dz  |dz  z
  dz         dz  t        |dz  |dz  z
        z  }t        t        ||d      j                               t        |j	                  |dd      j                               k(  sJ t        ||z   |z         }t        t        ||d      j                               t        |j	                  |dd      j                               k(  sJ t        t        |dz  dz         |z   |z         }t        t        ||d	      j                               t        |j	                  |dd	      j                               k(  sJ |t        dd      z  |t        dd      z  z   |z   }t        t        |      |d      }|j                         |t        d
d      z  |t        dd      z  z   |t        dd      z  z   |t        d	d      z  dz  z   |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        t        |      |d      }|j                         |t        dd      z  dz  |t        dd      z  z   |t        dd      z  z   dz   k(  sJ t        t        |      |d      }|j                         |t        d
d      z   dz  |t        dd      z  dz  z
  |t        dd      z  dz  z
  |t        d	d      z  d	z  z
  |z   |t        dd      z  z   |t        dd      z  z   k(  sJ t        t        |      |d      }|j                         |t        dd      z  d	z  |t        dd      z  z
  |t        dd      z  dz  z   |t        dd      z  z
  |t        dd      z  dz  z
  |t        dd      z  z
  |t        dd      z  dz  z
  dz   k(  sJ t        t        |      dz  |d      j                         t        |      dz  j	                  |dd      j                         k(  sJ t        t        d| z         | d      j                         | dz   dz  | dz  dz  z   | dz  dz  z
  | z   k(  sJ t        t        dd| z  z         | d      j                         d| dz  z  d| dz  z  dz  z   d| dz  z  z
  d| z  z   k(  sJ t        t        d| z   | dz  z         | d      j                         d| d
z  z  d
z  | dz  dz  z   | dz  dz  z   | d	z  dz  z
  | dz  dz  z   | dz  dz  z   d| dz  z  dz  z
  | dz  dz  z   | z   k(  sJ t        t        d| |dz  z  z         | d      j                         | d	z   |dz  z  d	z  | dz  |dz  z  dz  z   | dz  |dz  z  dz  z
  | dz  |d	z  z  dz  z   | dz  |dz  z  dz  z
  | |dz  z  z   k(  sJ y )Nz
x, a, b, crF   r   rB   rA   rw   rC   rD   rN   rf   r   r   r   r   rc   rE   rx   rb   i@   rd   rS   )r)   r&   r   r*   r   r   r+   r5   r,   r-   r   r2   )r@   r9   r:   r   rI   r   s         r<   test_rs_seriesr   :  s   &JAq!QQ1%%'1,,,SVQ"**,Qq!	2GI  SVc!f_a+3353q6A<q!Q+ + +SVCF]Aq)113QA:q!Q+ + + 
Q!c!Q$i!Q$q&()A)Aq"%--/0F188Aq
<GI5    	AqDFQqSLC!HS1Xq[00A)Aq!$,,./6!((1a	;794    	AqD1Hs1a4!8}q(1a4/0A)Aq!$,,./6!((1a	;794    	AqD1Q3JNQs1a4!A#:.A)Aq"%--/0F188Aq
<GI5    	AEAIA)Aq!$,,./6!((1a	;794    	C1qMA!"A)Aq!$,,./6!((1a	;794    	
2a7
Q1QZ!#A#a&!QA99;!R!W*q"R)|3aBrlBQ1QZPQ\Q	
r!AwJBqG$ $ $ $ 	#a&!QA99;!R!W*Q,BqG3aAaj@1DDDD#a&!QA99;1b1g:+a-!R2Y,q.81bBi<>I	2a7
1b1g:&()2a7
3 3 3 3 	#a&!QA99;!R2Y,q.1b1g:52a7
2E2aPQ7
R	2a7
1"R)|$&'Aajl3567 7 7 7 SVAXq!$,,.3q6!82C2CAq3wy   SQZA&..0QTE!Gad1f4DqDF55   SQqS\1a(002c!Q$hAqD6JadF7qS7! ! ! !SQA&2.668Bq!tGAIqDF=T!V=$&'d1f=-/0!tAv=6891Q=?AB1a4=JqDF==    SQq!tV_a+335!Q$q"uQqDBJqL:!#$a419Q;:/12Aad1:=qDAIaK: "#AqD&:) ) ) )r>   N)^sympy.polys.domainsr   r   r   sympy.polys.ringsr   sympy.polys.ring_seriesr   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   sympy.testing.pytestr'   r(   sympy.core.symbolr)   sympy.functionsr*   r+   r,   r-   r.   r/   r0   r1   r2   r3   sympy.core.numbersr4   
sympy.corer5   r6   r=   rK   rQ   r]   r_   ri   rk   ru   r|   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r>   r<   <module>r     s'   * * "@ @ @ @ @ @ @ @ @ . %   '  76>";\$D$.Y>"@$Q61,&4>D"4"4(.&AK&,
#=$~	P4M @) @)r>   