
    Qi{                     :   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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/m0Z0 d dl1m2Z2 d dl3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@ d dlAmBZBmCZC d d	lDmEZEmFZF d
 ZGd ZHd ZId ZJd ZKd ZLd ZMd ZNd ZOd ZPd ZQd ZRd ZSd ZTd ZUd ZVd ZWd ZXd ZYd ZZd Z[d Z\d  Z]d! Z^d" Z_d# Z`d$ Zad% Zbd& Zcd' Zdd( Zed) Zfd* Zgd+ Zhd, Zie0d-             Zjd. Zkd/ Zld0S )1    )ZZQQEXRR)ring)puiseux_ring)$_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_atanrs_atan_atanhrs_atanhrs_asinhrs_tanrs_cotrs_sinrs_cos
rs_cos_sinrs_sinhrs_coshrs_cosh_sinh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sinhcoshatanatanhasinhtanhlogsqrt)Rationalpi)expandSc                 :    d}t          | |z
            |k     sJ d S )Ng|=)abs)abtols      z/var/www/development/aibuddy-work/election-extract/venv/lib/python3.11/site-packages/sympy/polys/tests/test_ring_series.pyis_closerG      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 d S )	Nx                  x, y)r   r   r	   r   r
   )RrJ   pys       rF   test_ring_series1rU      s   R==DAq	1qAv!aA!!Q$1a4!A# 5 999991Ab1a46!1AaC!7!!;;;;;R==DAq	1qAv!aA1Aa!Q$q&1QT6!8!;ac!AAAAA62GAq!	1QT	AA1Aad1q!tAv!5!999991Aad1qs!2Q!6666666rH   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 d S )Nx, y, trK   rM      rL   )r   r   r   )rR   rJ   rT   trS   p1s         rF   
test_truncr[   %   s    i$$JAq!Q	
QqS1A	!Q		BA!Q$q
"Qq!tVAqD[A%55555555rH   c                    	 t          dt                    \  } }}d|z  z   ||z  z   t          d          D ]}t          |d          ddz  z  |dz  z  dz  |z  |dz  z  z   d|dz  z  |dz  z  z   dz  |z  z   d|z  |z  z   dz   k    sJ d|z  z   ||z  z   |dz  z  |z  z   t          |d          }|dd|z  z  z   d|z  |z  z   k    sJ t          dt                    \  }	t	          t
          	fd	           ddz  z   ddz  z  z   }ddz  z   }t          ||d          ddz  z  d
dz  z  z   dz  z   dz   k    sJ d S )NrW   rN   rL   rM   rX      rK   zc                  (    t           d          S )NrL   )r   )rS   rJ   r^   s   rF   <lambda>z test_mul_trunc.<locals>.<lambda>7   s    vaAq11 rH      )r   r   ranger   r-   
ValueError)
rR   rT   rY   irZ   R1p2rS   rJ   r^   s
          @@@rF   test_mul_truncrg   ,   s   i$$JAq!Q	AaC!A#A1XX  1aA!Q$q!tbd1fQTk)AadF1a4K7!A#a%?!A#a%G!KKKKK	AaC!A#1Qq A	1a		BQqSUQqSU"""""bMMEB
:111111222	
QqS1QT6	B	
QTB"b!Q1QT6Bq!tG#3ac#9A#=======rH   c                  2   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 d S )NrW   rN   rL   rM   rK   )r   r   r   r   )rR   rJ   rT   rY   rS   rZ   rf   s          rF   test_square_truncri   >   s    i$$JAq!Q	
QqS1Q3A	1a		B	1a		B8888	A1q!tAQ11a4!AqD&1Q3!6!:::::::rH   c                     t          dt                    \  } }}}|||z  z   }|dz  }|||fD ]-}t          ||d          }t          |d|d          }||k    s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 d S )Nx, y, z      rN   rM   rL   r   rK   Q   	   )r   r   r   r   r=   )	rR   rJ   rT   r^   p0rS   xxrZ   rf   s	            rF   test_pow_truncrs   H   s   i$$JAq!Q	
QqSB
BA!Qi  aQBB""Rxxxxx	AA	1a		BQqS====!Q1""""!RA!ac'))))	AA!Q1A!Q$q1Q3q!t8!;;;;;!a%!QA..!AqD&)ad1f2DqRSUVGW2WZ[2[[[[[[[rH   c                      t          dt                    \  } }}}|||z  z   }t          ||          sJ ||dz  z   }t          ||          rJ d|z   |dz  z   }t          ||          sJ ||z   ||z  z   }d S )Nrk   rK   rN   )r   r   r   )rR   rJ   rT   r^   rS   s        rF   test_has_constant_termru   [   s    i$$JAq!Q	AaCAa#####	AqDA!!Q'''''	A1Aa#####	A!AAArH   c                     t          dt                    \  } dz   ddz  z  z   d}t          |          }t          |z  |          dk    sJ t          dt                    \  } }dz   ddz  z  z   |z  z   dz  |z  z   t          |          }t          |z  |          dk    sJ t          dt                    \  } }dz   |z   t	          t
          fd           | j        t	          t          fd           t          dt                    \  } dz   t	          t          fd           d S )	NrJ   rL   rP   rN   rQ   c                  &    t           d          S )NrK   r   rS   rJ   s   rF   r`   z test_inversion.<locals>.<lambda>s   s    (;Aq!(D(D rH   c                  &    t           d          S NrM   rx   ry   s   rF   r`   z test_inversion.<locals>.<lambda>u   s    &9!Q&B&B rH   c                  &    t           d          S r{   rx   ry   s   rF   r`   z test_inversion.<locals>.<lambda>y   s    21a;; rH   )
r   r   r   r   r-   NotImplementedErrorzeroZeroDivisionErrorr   rc   )rR   nrZ   rT   rS   rJ   s       @@rF   test_inversionr   f   su   R==DAq	A!Q$A	A	Q1	%	%BAbD!Q1$$$$62GAq!	A!Q$1q!tAv%A	Q1	%	%BAbD!Q1$$$$62GAq!	A	A
 D D D D DEEE	A
BBBBBCCCR==DAq	AA
:;;;;;<<<<<rH   c                  <   t          dt                    \  } }}t          ||d          }t          ||d|          t	          ||d          k    sJ t          ||d          }t          ||d|          d|dz  z  dz  d|dz  z  dz  z   |dz  d	z  z   |z   k    sJ d S )
NrQ   
   rm   rP      p   rM   (   rX   )r   r   r   r*   r   r   rR   rJ   rT   rS   s       rF   test_series_reversionr   |   s    62GAq!q!RAq!Q**gaA.>.>>>>>q!RAq!Q**a1fSj1QT6"9.D	1Q//      rH   c            	         t          dt                    \  } }dd|z  z   |dz  z   d|dz  z  z   }g d}t          |||d          }|                     t	          t          |                              }t          |                    ||          |d          }||k    sJ t          dt                    \  } }}g d}t          ||z   ||dd	
          }t          dd||z   z  z   d||z   dz  z  z   d||z   dz  z  z   |d          }	||	k    sJ t          dt                    \  } }d}
t          |||
          dz
  }t          ||||
          }d	}	t          |          D ]\  }}|	|t          ||||
          z  z  }	||	k    sJ d S )NrJ   rN   rL   rM   )rN   rL   r   rK   rK   rP   rQ   )rN   rM   rP   r   r   )concurr      )r   r   r   	from_listlistreversedr   composer   	enumerater   )rR   rJ   rS   crpcr1rT   rZ   rf   hrd   cxs                rF   test_series_from_listr      s   R==DAq	AaC!Q$1a4AAAq!Q''A	
T(1++&&	'	'B	"**Q""Aq	)	)B777762GAq!A	QUAq!A	6	6	6B	1q!A#w;AaC!8+a1qj81a	@	@B8888R==DAq
Aq!Q!A	Q1a	(	(B	
B1 $ $2
b1a####888888rH   c                  2   t          dt                    \  } }d|z   }t          ||d          ||dz  dz  z
  |d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                              |d          t          t          d          t          dd          z             k    sJ d S )NrJ   rN   rK   rL   rM   rp   irm   i     r      ra   rX      rP   -   $   rQ   rC   rn   r   l   K)z i^ )	r   r   r   r   r/   r   r;   r   r=   )rR   rJ   rS   rZ   rf   p3rT   rC   s           rF   test_logr      s`   R==DAq	AA!Q??a!Q$q&j1a4611111	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"9999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$q&ACDE F F F F 	A62GAq!!a%A2a1a4j>>/!Q$"6AqAvJ19L"L
Q!Q$Z..A
# "1Q3	#*,.s1vvJJ#7 7 7 7 7!ad1f*q.!Q''Bq2wKK<1+<Q+>
1a1f:q!t, 1ggadl1n,-/1!Qq!tV*~~ad/B,C
1Q3	,s1vvJJ,     	
AqD1A!Q##Aq))RA+w9W9W0W-X-XXXXXXXrH   c                  	   t          dt                    \  } }||dz  z   }dD ]C}t          d|z   ||          dz
  }t          |||          }t	          |||          }||k    sJ Dt          ||d          }|                    |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 d S )NrJ   rK   )r      rN   r      l   O$obl      LeFSX   rC   rQ   rP   rO   rM   rX   rL   )	r   r   r   r   r   coeffr/   r2   r   )
rR   rJ   rS   r   qrZ   q1precrC   rT   s
             rF   test_expr      s   R==DAq	AqDA  Aq!,,q0Aq!__B1Qwwwww	1b		B88ArE??b!;=[\\\\\\Dq1uaA	1d		BQ;;;; 	A62c!ffai=))GAq!!a%A#a&&A+b.3q66!Q$;q="@Aq!tA#Aq#!#&q66#* * * * *!ad1f*q.!Q''3q66!Q$;q!t+;A+=FF1a4KM!O,!!ffQTk"n,-/21vvad{1},=FF1a4KM,FF1a4KM,*,/FF1a4KM,:<?FF1H,EGJ1vv,N N N N N 62GAq!!a%A2c!ffRi==A#53q66!8QT8I#I
3q66!8QT$s1vvJJqL$)+-c!ff::$6 6 6 6 6!ad1f*q.!Q''2c!ffQh<<1+<QT+A
3q66!8QT!, QmmAqD0,135c!ff::ad?13D,E
3q66!8QT,s1vvJJq!tOA-,.023q66!8QT0A,B 	3q66

1, #a&&zz," " " " " " "rH   c                      t          dt                    \  } }|dz  dz
  }t          ||d          }|d|dz  z  d|dz  z  z   dz   k    sJ d S )NrJ   rL   rK   rm   )r   r   r   )rR   rJ   rS   r   s       rF   test_newtonr      sa    R==DAq	1qA!QA!Q$1a4!#######rH   c                      t          dt                    \  } }|dz  dz
  }|dz  dz
  }t          ||          |dz  d|dz  z  z
  d|dz  z  z
  d|dz  z  z   d|z  z
  dz
  k    sJ d S )	NrJ   rM   rN   rL   rX   rK   r]   r   )r   r   r   )rR   rJ   rZ   rf   s       rF   test_compose_addr      s    R==DAq	
AB	
AB"b!!QTAadF]Qq!tV%;bAg%E1%Lq%PPPPPPPrH   c                     t          dt                    \  } }}||z  |dz  |dz  z  z   |dz  |z  z   }t          |t          |d          t          ||d          k    sJ t          |t          |d          t	          ||d          k    sJ d S )NrQ   rL   rM   rP   r   )r   r   r'   r   r&   r   s       rF   test_funr      s    62GAq!	!ad1a4i!Q$q& A!VQ##vaB'7'77777!UAr""eAq"oo555555rH   c                  8	   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          |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 d S )NrQ   rN   rL   rK   r   irm   i   r   rX   rM          rP   rp         ro   r]   i   rC   d   i>  i     )r   r   r(   r/   r   r<   )rR   rJ   rT   r   rC   s        rF   test_nth_rootr      s9   62&&GAq!q1a46z1a,,AqDAd0B	!Q$q!tC1AqD&A+b.1)+,a46!8146718 8 8 8 8q1Q3wAad*Aq!44Aad
1	!Q$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!$$!R1XX+5555qsQTzAqD(!Q22aAajma2aPQ77
l6RRRRRAaC!Q$q&L1a4'Aq11ABqGGAqD $q"Qq''z"}4q"Qq''z!|BF1bQRSTgg:UUUUU 	A62&&GAq!q2a55y!Q**bBq"Q(({N1C.D.DQT.I
1a2a88mad"/#%'1Q1a[=(9%:%:1%</=?A!R1XX+/O O O O Oq"Q(({QT!V+a/Aq99baoo=M	2a88>>4775=))!R1XX+5>68:4772:q!t8KA8M>N
4774<A> "4773;2a88 ;>< 	4772:q"Q(({"># &(Q[[>1 1 1 1 1 1 1rH   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 t          dt                    \  } }|dz  d|z  z   }t          ||d          t          ||d          k    sJ t          dt                    \  } }|dz  d|z  z   }t          ||d          t          ||d          k    sJ d S )NrQ   rp   r   rP   rM   rL   rm   ra   rX   rK   rC   rN   rJ   )r   r   r   r/   r   r7   r   rR   rJ   rT   rC   rS   s        rF   	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$1a4-!"3455ad:$; 	1adQh<$  Q[[$) ) ) ) ) 1q!tAv:>1a((R!QTAadF]Q5F0G-H-H,H	
A--a1fqj1QT6AadF?Qq!tV#;a#?@AA!Q$F-G
1adQh<Aa- "$Q1qAv(9%:";";AqD"@-ACEaA
J G D DD- T!WW++-     R==DAq	1qs
AAq>>WQ1------R==DAq	1qs
AAq>>WQ1--------rH   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 d S )	NrQ   rP   rM   rX   rL   r   r   rK   )r   r   r   rR   rJ   rT   s      rF   	test_asinr   (  sZ   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 4 4 4 4rH   c            	         t          dt                    \  } }}t          ||d          ||dz  dz  z   t          dd          |dz  z  z   t          dd          |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|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                              |d          t          t          d          t          d          dz  z             k    sJ d S )NrQ   rp   rM   rL      rP      ;  r   rK   rm   ra   r   rX   rC   rN   r   l   PH]l   n)r   r   r   r/   r3   r=   r   r   r   r7   r@   r   s        rF   test_tanr   0  s   62GAq!!Q??a!Q$q&j2a88AqD=82b::ad?JJJJJ!A#1QT	/1a((AadF1b5LNR1WQT\"_,L	!Q$q!tA-1a41S(-)+,a419Q;-79:1a41Q-G	1QT	-adF1a4KN-#%&T!Q$Y-/12Aad1-=?@!tAqDy-IKLQ3-O O O O O
 	A62c!ffai=))GAq!!a%A3q6619qQ{1}#<	#a&&
$qD#FFAI#a&&!)A5AF1L#M	QSVV	QT!#"%(VVQY]A$5#68;A#? ? ? ? ? !ad1f*q.!Q''Ac!ffaiK!CFF(,BAqD+H+J	QXa^^CFFAI-	-A	>1D,EHKAPQ	TUWXZ[W[G[\]G],^	QSVV	QT!,"%(VVQY]A$5,68;A,? ? ? ? ? 62GAq!!a%A"SVVQY3q6619Q%>	#a&&
& # #qD#c!ffai!CFFAI+a-7"Q%%'ABB1a4G#H
3q6619s1vvq!t##$&(QQ&7&7&9#:<>s1vvJJ#G G G G G !ad1f*q.!Q''2aA	k	#a&&/ , ,Q$,,c!ffai!CFFAI+a-7"Q%%'ABB1a4G,H
3q6619q=!Q$q ,!#%c!ffai#a&&&8#9#9!Q$#>,? 	3q6619q=!, !Qjj,) ) ) ) )
 	
AqD1A1a$$Q++r$q''A>O<P<P= 3 0 0      rH   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 d S )NrQ   rX   r   rm   irn   rN   rL   rM   rK   rP   r   r   )r   r   r   r   s      rF   test_cotr   O  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 D D DrH   c                  j
   t          dt                    \  } }}t          ||d          ||dz  dz  z
  |dz  dz  z   |d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 d S )NrQ   rp   rM   rX   rP   x   r     rL   rm   ra   r]     rO   rK   rC   )r   r   r   r/   r0   r1   r   rR   rJ   rT   rC   s       rF   test_sinr   X  s   62GAq!!Q??a!Q$q&j1a483ad4i?????!A#1QT	/1a((AqDBJrM	1QT	#-1QT	"-%'(!tAqDy~-6891QT	!-D	1QT	"-!tAqDy{-#%&T!Q$Ys]-356T!Q$Yq[-A 	
1QT	!- d1a4i-  #$A#-& & & & & 	A62c!ffc!ffa/011GAq!!a%A#a&&A+b.3q66!Q$;q="@Aq!tA#Aq#!#&q66#* * * * *!ad1f*q.!Q''CFF71a4<1+<Q+>Aq!tAa,a&&A+b.,)+.q66!Q$;q=,9;>q66!Q$;q=,IAq!tA,Aq!tA,&(+Aq,136q66,: : : : : 62GAq!!a%A"SVVBY--1"4r#a&&(||AqD7H"H
3q66!8QT#s1vvJJqL#)+-c!ff::#6 6 6 6 6!ad1f*q.!Q''Bs1vvaxLL=A+=ad+B
3q66!8QT!, QmmAqD0,135c!ff::ad?13D,E
3q66!8QT,s1vvJJq!tOA-,.023q66!8QT0A,B 	3q66

1, #a&&zz," " " " " " "rH   c                  
   t          dt                    \  } }}t          ||d          d|dz  dz  z
  |dz  dz  z   |dz  dz  z
  |d	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 d S )NrQ   rp   rN   rL   rK   rO   rX   r   rm   逝  rM   r]   r   0   r   r   rP   rC   )r   r   r    r/   r0   r1   r   r   s       rF   test_cosr   r  s   62GAq!!Q??a!Q$q&j1a472QT#X=1U
JJJJJ!A#1QT	/1a((AqDBJrM	1QU
2-1QT	%-(*+Q$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 	A62c!ffc!ffa/011GAq!!a%A#a&&A+b.3q66!Q$;q="@Aq!tA#Aq#!#&q66#* * * * *!ad1f*q.!Q''CFF71a4<1+<Q+>Aq!tAa,a&&A+b.,)+.q66!Q$;q=,9;>q66!Q$;q=,IAq!tA,Aq!tA,&(+Aq,136q66,: : : : : 62GAq!!a%A"SVVBY--1"4r#a&&(||AqD7H"H
3q66!8QT#s1vvJJqL#)+-c!ff::#6 6 6 6 6!ad1f*q.!Q''Bs1vvaxLL=A+=ad+B
3q66!8QT!, QmmAqD0,135c!ff::ad?13D,E
3q66!8QT,s1vvJJq!tOA-,.023q66!8QT0A,B 	3q66

1, #a&&zz," " " " " " "rH   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 t          d|z   |dz  z   |d          \  }}|t          d|z   |dz  z   |d          k    sJ |t	          d|z   |dz  z   |d          k    sJ t          d          }t          dt          t          |          t          |          |f                   \  } }}t          ||z   |d          \  }}|t          ||z   |d          k    sJ |t	          ||z   |d          k    sJ t          dt                    \  } }}t          ||z   |d          \  }}|t          ||z   |d          k    sJ |t	          ||z   |d          k    sJ d S NrQ   rp   rP   rN   rL   rC   )	r   r   r!   r    r   r/   r0   r1   r   )rR   rJ   rT   r   srC   s         rF   test_cos_sinr     sG   62GAq!aADAqq!Qq!Qa!A#gq!$$DAqq1Q3w1%%%%%%q1Q3w1%%%%%% a!eadlAq))DAqq1uq!t|Q******q1uq!t|Q******A62c!ffc!ffa/011GAq!a!eQ""DAqq1ua######q1ua######62GAq!a!eQ""DAqq1ua######q1ua########rH   c            	      V   t          dt                    \  } }}t          ||d          ||dz  dz  z   |dz  dz  z   |d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                              |d          t	          t          dd          t          d          z             k    sJ t          dt                    \  } }|dz  d|z  z   }t          ||d          t          ||d          k    sJ t          dt                    \  } }|dz  d|z  z   }t          ||d          t          ||d          k    sJ d S )NrQ   rp   rM   rP   r   rL   rm   ra   rX   rK   rC   rN   r   lyY?l l    P{] rJ   )	r   r   r   r/   r   r8   r   r=   r   r   s        rF   
test_atanhr     sw   62GAq!Aq!AqDF
QT!V 3ad1f <<<<<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$1a4-!"3455ad:%;=?1a4	D
 A > >>% 588%     A1QJNAq))R!QTAadF]	6
 1 . .qD..1a4!a1fqAvo!Q$&>&BCD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<Lj3Y3Y
((4 1 1     R==CAa	1qs
A!Q??hq!Q//////
sB--CAa	1qs
A!Q??hq!Q////////rH   c                  l   t          dt                    \  } }}t          ||d          d|dz  z  d|dz  z  z   d|dz  z  z
  |z   k    sJ t          ||z  |d	z  |dz  z  z   |d          d
|dz  z  |dz  z  d|dz  z  |dz  z  z
  d
|dz  z  |dz  z  z   d|dz  z  |dz  z  z
  d|dz  z  |dz  z  z
  d|dz  z  |dz  z  z   d|dz  z  |dz  z  z
  d|dz  z  |dz  z  z   d|dz  z  |dz  z  z
  d|dz  z  |dz  z  z
  |d	z  |dz  z  z   ||z  z   k    sJ t          d          }t          dt                    \  } }}t          ||z   |d          t	          |d	|d	z  z  t          |d	z  dz             z  d	t          |d	z  dz             z  z   z             |d	z  z  t	          dt          |d	z  dz             z            |z  z   t	          t          |                    z   k    sJ t          ||d	z  |z  z   |z   |d          t	          dt          |d	z  dz             z            |d	z  z  |z  t	          |d	|d	z  z  t          |d	z  dz             z  d	t          |d	z  dz             z  z   z            |d	z  z  z
  t	          dt          |d	z  dz             z            |z  z   t	          t          |                    z   k    sJ ||d	z  z   dz   }t          ||d                              |d          t	          t          d          dt          d          z  dz  z             k    sJ d S )NrQ   rp   gm۶mۦr   g333333?rP   UUUUUU?rM   rL   g      ?rm   ra   g      ?gm۶mۦ?rX   g      ?      ?rK   rC   rN   r   l   ](~    l   |`'9 )r   r   r   r/   r   r<   r9   r   r   s        rF   
test_asinhr     s   62GAq!Aq!q!td1a4i 7#ad( BQ FFFFFAaC!Q$q!t)OQ**c!Q$hq"untAqDyA~.MAqDA/ad
1a4/(*-ad(1a4-/8:=ad(1a4-/HJMa
O KqDK/19QT>/"$'1HQTM/2471HQTM/BDEqDAI/NPQRSPS/T T T T T
 	A62GAq!AE1a  R1QT6$q!tax..+@1T!Q$QR(^^CS+S(T%U%U$U	
A%1T!Q$(^^#$$Q&%')+E!HH%6 6 6 6 6A1QJNAq))R$q!tax..0@-A-A!Q$-Fq-H2aQRSTVWSWQW	adQhRDANN*R+ O, L- L--.TL2 .246qadQh7G4H4H4J.KMOPUVWPXPX\\.Z Z Z Z Z 	
AF
QAAq"%%a,,588>NtTVxx>W? 4 1 1      rH   c                  f
   t          dt                    \  } }}t          ||d          ||dz  dz  z   |dz  dz  z   |d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          d|dz  z  t	          |          z  d|dz  z  t          |          z  z   d|d	z  z  t	          |          z  z   |t          |          z  z   t	          |          z   k    sJ t          ||d	z  |z  z   |z   |d          dt	          |          z  |dz  z  |d	z  z  dt          |          z  |dz  z  |z  z   dt	          |          z  |dz  z  z   t	          |          |dz  z  |z  z   dt          |          z  |dz  z  z   t          |          |d	z  z  |z  z   dt	          |          z  |d	z  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 d S )NrQ   rp   rM   rX   rP   r   r   r   rL   rm   ra   r]   r   rO   rK   rC   UUUUUU?r   r   )r   r   r"   r/   r5   r6   r   r   s       rF   	test_sinhr     s   62GAq!1aq1a46zAqDH4q!tDy@@@@@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#.& & & & & 	A62d1ggtAww1233GAq!1q5!Q419d1gg#6QT4779K#K O

Q$OQO $d1gg;$'*.q''$3 3 3 3 31q!tAv:>1a((CaM!Q$,>q!t,Cc4PQ77m	
AGG -Q.A%-&)-a!Q$q(8-9;>Q=A;M-N	a!Q$q-Q=A--.15a!-<?CAww-H H H H H 62GAq!1q5!Q2d1ggbj>>!Q$#6DGGAIq!t9K#K
47719ad$Q[[]$+-/Q[[$9 9 9 9 91q!tAv:>1a((BtAwwqyMM!Q$,>q!t,Cba	J
 G Ga4GG -tAwwrzNN1a4'-(*,T!WW++ad*:1*<-=?A$q''!)}}QPQT?Q-R
T!WW++ad
1
-!$q''!)}}QT1-246tAwwKKM-BDFtAwwKK-P P P P P P PrH   c                  
   t          dt                    \  } }}t          ||d          d|dz  dz  z   |dz  dz  z   |dz  dz  z   |d	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          dt          |          z  |dz  z  dt	          |          z  |dz  z  z   dt          |          z  |dz  z  z   t	          |          |z  z   t          |          z   k    sJ t          ||dz  |z  z   |z   |d          dt          |          z  |dz  z  |dz  z  dt	          |          z  |dz  z  |z  z   dt          |          z  |dz  z  z   t          |          |dz  z  |z  z   dt	          |          z  |dz  z  z   t	          |          |dz  z  |z  z   dt          |          z  |dz  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 d S )NrQ   rp   rN   rL   rK   rO   rX   r   rm   r   rM   r]   r   r   r   r   rP   rC   r   r   r   )r   r   r#   r/   r5   r6   r   r   s       rF   	test_coshr     s   62GAq!1aq1a46zAqDG3ad3h>AeKKKKK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$Y./ 23Aad1.= @A.A A A A A 	A62d1ggtAww1233GAq!1q5!Q4a>!Q$#6d1ggq!t9K#KT!WWad$"1ggq[$),0GG$5 5 5 5 51q!tAv:>1a((CaM!Q$,>q!t,Cc4PQ77m	
AGG -Q.A%-&)-a!Q$q(8-9;>Q=A;M-N	a!Q$q-Q=A--.15a!-<?CAww-H H H H H 62GAq!1q5!Q2d1ggbj>>!Q$#6DGGAIq!t9K#K
47719ad$Q[[]$+-/Q[[$9 9 9 9 91q!tAv:>1a((BtAwwqyMM!Q$,>q!t,Cba	J
 G Ga4GG -tAwwrzNN1a4'-(*,T!WW++ad*:1*<-=?A$q''!)}}QPQT?Q-R
T!WW++ad
1
-!$q''!)}}QT1-246tAwwKKM-BDFtAwwKK-P P P P P P PrH   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 t          d|z   |dz  z   |d          \  }}|t          d|z   |dz  z   |d          k    sJ |t	          d|z   |dz  z   |d          k    sJ t          d          }t          dt          t          |          t          |          |f                   \  } }}t          ||z   |d          \  }}|t          ||z   |d          k    sJ |t	          ||z   |d          k    sJ t          dt                    \  } }}t          ||z   |d          \  }}|t          ||z   |d          k    sJ |t	          ||z   |d          k    sJ d S r   )	r   r   r$   r#   r"   r/   r5   r6   r   )rR   rJ   rT   chshr   r   rC   s           rF   test_cosh_sinhr     sK   62GAq!!Q""FBAq!!!!!!Aq!!!!!!!ac'1a((FBQqS!Q''''''QqS!Q'''''' A1a++DAqA1a++++++A1a++++++A62d1ggtAww1233GAq!!a%A&&FBQ1%%%%%%Q1%%%%%%62GAq!!a%A&&FBQ1%%%%%%Q1%%%%%%%%rH   c            	         t          dt                    \  } }}t          ||d          |t          dd          |dz  z  z
  t          dd          |dz  z  z   t          dd	          |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|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          }|                    |d                              |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 d S )NrQ   rp   rN   rM   rL   r   rP   r   r   r   rK   rm   ra   r   rX   rC   r   iit'  i	  is'  i  )r   r   r%   r/   r   r:   r   r   s        rF   	test_tanhr   %  s   62GAq!1aq2a771a4</"Qr((1a4-?"R**QPQT/QQQQQ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2d1ggqj1T!WWaZ<>&A	$q''	!' $ $T$Q
{QtAwwz\!^;bAhhFGG1L$M
477A:Q  A%$&(*DGGQJ;?(;(;A(=$>@B477$L L L L L 	AqDF
Q1%%AIIa%%a++r%Q
2Bd1ggqj3Q
?1,3-/4T!WW}3=?A#qzz3J 0K 0K K K K K K KrH   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                              |d          } |d|z                                 |dd                                          }	t'          |                                |	                    |d                                                     t/          d|z   d|d                              |d          }d|z   t1          dd          z                      |dd                                          }	t'          |                                |	                    |d                                                     d S )NrQ   rC   rL   rP   r   rN   )r   r    r   r   r   r%   r0   r1   r3   r4   r7   r:   r   r   r/   zipr   seriesremoveOrG   as_exprsubsr   r(   r   )
rs_funcssympy_funcsrR   rJ   rT   rC   rs_func
sympy_funcrS   r   s
             rF   test_RRr   9  s|   AHS#tT2K62GAq!A"8[99 0 0GAE1a  ((A..Jq1u$$Q1--5577affQllnn..////AE1a##++Aq11A
a%"Q((	""1a++3355AQYY[[!&&A,,..**+++++rH   c                  f   t          dt                    \  } }}dd|z  z   |dz  z   d|dz  z  z   }t          ||          rJ ||t          dd          z  |z  z   }t          ||          sJ t          ||          rJ ||dz  |t          dd          z  z  |z  z   }t          ||          rJ d S )NrQ   rN   rL   rM   rP   )r   r   r+   r   s       rF   test_is_regularr   H  s    62&&GAq!	AaC!Q$1a4AQ"""""	Ar!AwwJqLAAQ"""""	AqDBqGGOAAQ"""""""rH   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  |t          dd          z  z   |z   t          dd          |t          dd          z  z  z   |t          dd          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   |z   t          dd          |t          dd          z  z  z
  t          dd          |t          dd          z  z  z
  t          dd          |t          dd          z  z  z
  t          dd          |t          dd          z  z  z
  k    sJ t          ||d          }|dt          dd          |t          dd          z  z  z
  |t          dd          z  z
  t          dd          |t          dd          z  z  z
  |t          d
d          z  z
  t          dd          |t          dd          z  z  z   |t          dd          z  z
  t          dd          |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  |t          dd          z  z   |z   t          dd          |t          dd          z  z  z
  t          dd          |t          dd          z  z  z
  t          dd          |t          dd          z  z  z
  t          dd          |t          dd          z  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  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          }|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 d S )NrQ   rL   rP   rM   rN      r   rK   ra   r   rn   rp   rO   rX   r      rl   rm      r   )r   r   r   r(   r   r)   r   r   r   r   r    r   r   r!   r   r   r#   r"   r$   r%   )rR   rJ   rT   rS   r   r   rZ   s          rF   test_puiseuxr   U  s   62&&GAq!	2a77
Q1QZ!#AAq!$$A
R2YY,BqGG	#a2b99n	4q"Qq''z	A	!R"XX+
2a77

#%&1QZ
023R"XX+
>@A2b99
M
R1XX+
B 7777AE1a##ABqGGA2a77
1,q"Qq''z!|;a?????q1uaABqGGA2a77
*Q1QZ77777Aq!ABqGGaAaj(1b1gg:55555	
Q1QZ\	Br1aA2a77
1a4"Q1QZ1_Q%66BqGGAqD9JJ	2a77
1     	1aA!R!WW*q"R))|+aBrl:Q1QZ\I	
r!AwwJBqGG$ $ $ $ $ 	AqABqGGAqD"Q1QZ1_4q"Qq''z!Q$q7HH	2a77
1a4AqD&(#%&')*BqGGAqD):;=>1QZ\J J J J J 	q!QA2a77
Q1QZ'!+b1ggaAaj.@@1bBii<O
R2YY,BqGG$ $ $ $ $ 	q!QA2a77
Q1QZ'!+b1ggaAaj.@@2a771
2b		L D qGGAr"RyyL()+-a771b1gg:+=> > > > > 	q!QABqGGAr!AwwJ&&Br"II51Q2a77
8JJ	2a77
"XXaAaj()+,b1gg:68:1Q2b998LM M M M M 	1aA2a77
1q"R))|A~-2b99Q>	2a77
1b1gg:&()2a77
3 3 3 3 3 	q!QABr"II2a77
*Qq"R))|^;	!R!WW*Q1b2hh;')*1b1gg:a8:;R!WW*E	2a88Brl#%&2a[1 1 1 1 1 	1aAQ41bBii<>Ar!AwwJ.BqGGB>BqGGK	2a77
1"R))|$&'Aajl3567 7 7 7 7Q4Ar!AwwJ;q=1bBii<>1Ar"RyyLNB	2a77
1b1gg:&()2a77
3 3 3 3 3 	AqA2a77
Q2b		\)Ar"RyyL81b1gg:a<G!K	2a77
1QZ          	AqA2a77
Q1QZ'!+b1ggaAaj.@@2a771
2b		L D qGGAr"RyyL()+-a771b1gg:+=> > > > > 	1aA2b99QBqGG+aAajm;aAajH	2a77
1"R))|$&'Aajl3567 7 7 7 7 	1aA2a77
1q"R))|A~-2b99Q>	2a77
1b1gg:&()2a77
3 3 3 3 3 	Q1AQ41bBii<>Ar!AwwJ.BqGGB>BqGGK	2a77
1"R))|$&'Aajl3567 7 7 7 7Q41b1gg:a<!R2YY,q.01bBii<>A	2a77
1b1gg:&()2a77
3 3 3 3 3 	1aABqGGaBrl*Q2b		\9Ar!AwwJqLH	
r!AwwJBqGG$ $ $ $ $ $ $rH   c                     t          j        t          d                    } |                     t          d                    }t	          d          \  }}t          ||g|           \  }}}d|z   |t          dd          z  z  d|z
  |t          dd          z  z  z   }|                                t          dd          t          d          fd|z   t          d          t          dd          fd|z
  ik    sJ |                                dt          d          z   |t          d          dz  z  z  dt          d          z
  |t          d          dz  z  z  z   k    sJ d S )NrL   rQ   rN   rM   r   )	r   algebraic_fieldr<   
from_sympyr/   r   to_dictr   r@   )Ksqrt2rJ   rT   rR   xryrrS   s           rF   test_puiseux_algebraicr    s7   
477##ALLa!!E6??DAqaVQ''IAr2	
5"b1gg+5"b1gg+ 55A99;;BqGGBqEE?1U7RUU2a77OAeGLLLLL99;;1tAww;AaDDF3q477{A!QK6OOOOOOOOrH   c                  H   t          dt                    \  } }t          ||d          |dz  z  }||dz  dz  |dz  dz  z
  |dz  d	z  z   |d
z  dz  z
  t          dd          z   |dz  dz  z
  |dz  z   k    sJ t          ||d          }t          |d
|d          }|d|t          dd
          z  z  dz  |t          dd
          z  dz  z
  |t          dd
          z  dz  z   |t          dd
          z  dz  z
  |t          dd
          z  z   k    sJ t          ||d          }t          |d|d          }t	          |d|d          }|d|t          dd          z  z  dz  |t          dd          z  dz  z
  d |t          d!d          z  z  d"z  z   d|t          d#d          z  z  d$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 d S )1NrJ   r   r   rm   l    LQf rX   i arK   i rL   r   rN   r   rn   r   r   ir   i r   i^  rp   i  rP   r]   r   i=   i:k/   iP@  ra   !   i     *   l     L.l     { l     ]
 l     nLl    Xnl    (vQ i i _7 r   rM   r   rO   )r   r   r   r(   r   r   )rR   rJ   r   rS   s       rF   test1r	    s   R  DAqq!RR A1Z!Q$x-/!Q$v+=1T	I
1S		rE!Ge$ $ $ $ $ 	q!RAAq!R  AQ2a[)Ar"QxxK,==	2a77
4R!WW*R-(*+R!WW*5 5 5 5 5 	q!RAAq!R  Aq!QAAr"QxxK	)Ar"QxxK,==
1bAhh;t2b88mB./12BqGG< < < < < 	q"Qq''z1b!!A2b88..A6F1FF	2b88O#$&'d>&9:	2b88M!"$%qD$45 	
2b88J "#Ai0 34R1XX+h2FG 	
1W	 "Qq''z&(	) ,-a4:	6 9:2a77
4	H
 	
1S
 b1gg:c>"
 %&qDG,
 /0Aajl;
 >?qSA 	
2a77
       rH   c                     t          dt                    \  } }t          d|                                           \  }}||t          dd          z  |z  z   }t	          ||d          }||dz  dz  |dz  z   d|dz  z  z   |t          dd          z  z  |d	z  d	z  |d
z  z   |z   |t          d	d          z  z  z
  |dz  dz  |dz  z   |t          dd          z  z  z   |dz  dz  |dz  z   |t          dd          z  z  z
  |dz  dz  dz   |z  z   |dz  |t          dd          z  z  dz  z
  ||t          dd          z  z  z   k    sJ d S )NrT   rJ   rN   rP   rM   r   rm   rL   ra   rX   rp   rK   r   )r   r   r   	to_domainr   )rR   rT   r@   rJ   rS   r   s         rF   test_puiseux2r    s   R==DAqQ[[]]++DAq	Ar!AwwJqLA1aABrAqD1QT6)1bAhh;6!R%(QT/	;
bAhh;: Q$q&1a4-BqGG3478!tAv	18Aaj7qDFQJ>*,-qDBqGGOA,=>@A!R!WW*M M M M M M MrH   c                  J   t          d          \  } }}}t          ||d                                          |k    sJ t          t          |          |d                                          t          |                              |dd                                          k    sJ t          t          |          t          |          z   |d                                          t          |          t          |          z                       |dd                                          k    sJ t          t          |          t          |          z  |d                                          t          |          t          |          z                      |dd                                          k    sJ t          |          |z
  t          |dz            |dz  dz  z   z  }t          t          ||d                                                    t          |                    |dd                                                    k    sJ t          |dz  dz  |dz  z             t          |dz            t          |dz            dz  z  z   }t          t          ||d                                                    t          |                    |dd                                                    k    sJ t          | dz  |z             t          | dz  dz
            |z
  |dz  z
  z  }t          t          ||d                                                    t          |                    |dd                                                    k    sJ t          |dz  |dz  z
  dz             dz  t          |dz  |dz  z
            z  }t          t          ||d                                                    t          |                    |dd                                                    k    sJ t          ||z   |z             }t          t          ||d                                                    t          |                    |dd                                                    k    sJ t          t          |dz  dz             |z   |z             }t          t          ||d	                                                    t          |                    |dd	                                                    k    sJ |t          dd          z  |t          dd          z  z   |z   }t          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          t          |          |d          }|                                |t          dd          z  dz  |t          dd          z  z   |t          dd          z  z   dz   k    sJ t          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          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          t          |          dz  |d                                          t          |          dz                      |dd                                          k    sJ d S )Nz
x, a, b, crP   r   rL   rK   r   rM   rN   rX   rp   r   r   r   r   rm   rO   r   rl   )r/   r,   r   r0   r   r   r1   r?   r2   r3   r   )rJ   rC   rD   r   rS   r   s         rF   test_rs_seriesr    s   &&JAq!QQ1%%''1,,,,SVVQ""**,,Qq!	2 2GII   SVVc!ff_a++33553q66A<q!Q+ + + +SVVCFF]Aq))1133QA:q!Q+ + + + 
Q!c!Q$ii!Q$q&()A)Aq"%%--//00F188Aq
< <GII5 5     	AqDFQqSLC!HHS1XXq[00A)Aq!$$,,..//6!((1a	; ;7994 4     	AqD1Hs1a4!8}}q(1a4/0A)Aq!$$,,..//6!((1a	; ;7994 4     	AqD1Q3JNQs1a4!A#:.A)Aq"%%--//00F188Aq
< <GII5 5     	AEAIA)Aq!$$,,..//6!((1a	; ;7994 4     	C1qMMA!""A)Aq!$$,,..//6!((1a	; ;7994 4     	
2a77
Q1QZ!#A#a&&!QA99;;!R!WW*q"R))|3aBrlBQ1QZPQ\Q	
r!AwwJBqGG$ $ $ $ $ 	#a&&!QA99;;!R!WW*Q,BqGG3aAaj@1DDDDD#a&&!QA99;;1b1gg:+a-!R2YY,q.81bBii<>I	2a77
1b1gg:&()2a77
3 3 3 3 3 	#a&&!QA99;;!R2YY,q.1b1gg:52a77
2E2aPQ77
R	2a77
1"R))|$&'Aajl3567 7 7 7 7 SVVAXq!$$,,..3q66!82C2CAq3 3wyy     rH   c                     t          d          \  } }t          t          d| z             | d                                          | 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                                          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
                                          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                                          | 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 t          t	          d| z             | d                                          | d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  z   t
          dz  z   k    sJ t          t	          d| z   | dz  z             | d                                          d| dz  z  dz  | dz  dz  z
  d| dz  z  dz  z   d| dz  z  dz  z
  | dz  dz  z   | dz  z   t
          dz  z   k    sJ t          t	          d| |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
  || z  dz  z   t
          dz  z   k    sJ t          t          d| z             | d                                          d| dz  z  t          d          dz  z  dz  | dz  t          d          dz  z  z   d| dz  z  t          d          z  dz  z   | dz  t          d          dz  z  z
  | dz  dz  z
  d| dz  z  t          d          dz  z  dz  z   | dz  t          d          z  z
  | dz  t          d          dz  z  z   | t          d          dz  z  z
  | z   t          d          z   k    sJ t          t          d| |z  z             | d                                          |dz   | dz  z  t          d          z  |dz  | dz  z  t          d          dz  z  z   || z  t          d          dz  z  z
  || z  z   t          d          z   k    sJ t          t          d| z             | d                                          | dz  t          d          z  dz  | dz  t          d          z  dz  z   | dz  t          d          z  dz  z   | t          d          z  z   t          d          z   k    sJ t          t          d| |z  z             | d                                          |dz  | dz  z  t          d          z  dz  |dz  | dz  z  t          d          z  dz  z   |dz  | dz  z  t          d          z  dz  z   || z  t          d          z  z   t          d          z   k    sJ t          t          d| z             | d                                          | dz  t          d          z  dz  | dz  t          d          z  dz  z   | dz  t          d          z  dz  z   | t          d          z  z   t          d          z   k    sJ t          t          d| |z  z             | d                                          |dz  | dz  z  t          d          z  dz  |dz  | dz  z  t          d          z  dz  z   |dz  | dz  z  t          d          z  dz  z   || z  t          d          z  z   t          d          z   k    sJ d S )Nzx arN   rP   rK   rM   rL   i@   rm   r   rn   rp   r   rX   r]   r   r   r   ir   rO   )	r/   r,   r;   r   r7   r>   r:   r5   r6   )rJ   rC   s     rF   test_rs_series_ConstantInExprr    s	   5>>DAqSQZZA&&..00QTE!Gad1f4DqDF55    SQqS\\1a((0022c!Q$hAqD6JadF7qS7    SQA&&2..6688Bq!tGAIqDF=T!V=d1f=%'(!tAv=.011Q=79:1a4=BDEqDF=KMN=O O O O OSQq!tV__a++3355!Q$q"uQqDBJqL:a419Q;:')*Aad1:578!tAqDy{:CEFq!tV:L L L L L T!a%[[!Q''//11adU3YAb5H1a4PR75Rd2g61Q6!"16%')!t6, , , , ,T!a%!Q$,''1--55773q!t8C<!Q$r';QadF2I<!Q$r	<"$%qDF<+-.qS<135a4<8 8 8 8 8T!a!e)__a++3355!Q$q!tC!Q$qRSt)TV,9Vd1a4il:T!Q$Yr\:*,-qDAIaK:8:;A#a%:@BDQ$:G G G G G T!a%[[!Q''//11R1WT!WWaZ5G5IAqDGGQJM 61a4Q)6*,-qDa!O6<>?d1f6EGHAvdSTggO HH6a4Q<6 "#Q$tAwwz/6245d1ggqjL6ACD6EGKAww6O O O O O T!a!e)__a++3355!Q$q!tDGG9KaQRdSTT O1ggqjO :Q3tAwwz>:*,-aC:026q'':: : : : : T!a%[[!Q''//11QT$q''\"_q!tDQRGG|TU~5UqDaLN6tAwwY6')-a61 1 1 1 1T!a!e)__a++3355Aad4779J29MqDAId1gga: "#Q$q!t)DGG"3A"5:689!DGG:DFJ1gg:N N N N N T!a%[[!Q''//11QT$q''\"_q!tDQRGG|TU~5UqDaLN6tAwwY6')-a61 1 1 1 1T!a!e)__a++3355Aad4779J29MqDAId1gga: "#Q$q!t)DGG"3A"5:689!DGG:DFJ1gg:N N N N N N NrH   c                  >   t          d          \  } }t          t          | t          dd          z            t	          | |t          dd          z  z             z  | d                                          | t          dd          z  t	          |t          dd          z            z  | t          dd          z  t	          |t          dd          z            z  dz  z
  | t          dd          z  t	          |t          dd          z            z  z   k    sJ d S )Nza brM   r   rX   rL   r   rp   )r/   r,   r0   r   r2   r   )rC   rD   s     rF   
test_issuer  9  s    5>>DAqSBqGG__SQ1QZ%8%88!A>>FFHH	2b88C2a77
OO#aAajQ1QZ&@&BBQ1QZPSTUWYZ[\]W^W^T^P_P_E__` ` ` ` ` `rH   N)msympy.polys.domainsr   r   r   r   sympy.polys.ringsr   sympy.polys.puiseuxr   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$   r%   r&   r'   r(   r)   r*   r+   r,   sympy.testing.pytestr-   r.   sympy.core.symbolr/   sympy.functionsr0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   sympy.core.numbersr=   r>   
sympy.corer?   r@   rG   rU   r[   rg   ri   rs   ru   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r	  r  r  r  r   rH   rF   <module>r     s6   . . . . . . . . . . . . " " " " " " , , , , , ,                                                                            . - - - - - - - % % % % % %                              + + + + + + + +                  
7 7 76 6 6> > >$; ; ;\ \ \&  = = =,    0Y Y Y>" " "B$ $ $Q Q Q6 6 61 1 1.. . .:4 4 4  >D D D" " "4" " "4$ $ $40 0 0B  (P P P2P P P0& & &2K K K(, , ,
# 
# 
#S$ S$ S$l	P 	P 	P  6M M M 5 5 5p N  N  NF` ` ` ` `rH   