
    sg                     >    d dl mZ d dlmZ d dlmZ d dlmZmZ d Z	y)    )approximants)symbolsbinomial)	fibonaccilucasc                  <   t        d      \  } t        d      D cg c]  }t        |       }}t        t	        |            dddz
  z  dz  dz
  dz  dz
  z  dz
  dz  z   dz
  z  gk(  sJ t        d      D cg c]  }t        |      t        |dz         z    }}t        t	        |            dddz
  z  dz  dz
  dz  dz
  z  ddz  z   dz
  z  gk(  sJ t        d      D cg c]  }t        |      dz   }}t        t	        |            d	d
d	z
  z  dz  d	z
  dz  dz
  z  dz  dz
  ddz  z  dz  z   dz
  z  ddz  z  dz  z   dz
  ddz  z  dz  z   dz
  z  dz   dz  z
  d	z   dz  ddz  z  z
  dz  z
  dz   z  gk(  sJ t        d      D cg c]#  t        fdt        dz         D              % }}t	        || d      }t        |      dk(  sJ t        |      d| dz   z  dz
  z  k(  sJ y c c}w c c}w c c}w c c}w )Nzx,t                  i#   	   %               2   ?   4      c              3   B   K   | ]  }t        |      |z  z    y w)Nr   ).0ikxs     W/var/www/html/venv/lib/python3.12/site-packages/sympy/series/tests/test_approximants.py	<genexpr>z$test_approximants.<locals>.<genexpr>   s      4AXa]1a44s   T)simplify)r   ranger   listr   r   sumnext)tr    gpyr!   s    `   @r"   test_approximantsr.      s{   5>DAq 9%aq%A%Q 	
BAJ1q1Q37+a!eadQhl-CDG G G*/)4Qq)AaC.	 4A4Q 	
BAJ1q1Q37+RAA->?B B B#Bi(q1(A(Q 	
CQK"Q$(QqS1W-1r	Bq!tGbdNQ<N/O	AqD2a4"	r!Q$wA~23
Q$1q1a4!AqD&=1Q3.23	57 7 7 ?DBiH4qs4	4HAHQD)A7a<<7b!QU)a-(((( 	& 	5 	)
 	Is   H
 !H.H%(HN)
sympy.seriesr   sympy.core.symbolr   (sympy.functions.combinatorial.factorialsr   %sympy.functions.combinatorial.numbersr   r   r.        r"   <module>r5      s    % % = D)r4   