
    ^Mhw                     T    	 d dl Zn# e$ r Y nw xY w	 d dlmZ n# e$ r Y nw xY wd ZdS )    Nxc                 N    t                     }t           fdt          |          D                       }t          |z                      t          d|                                          }|dz  g}t          |          D ]2}|                    |d         |z                                             3t          j	        d          g}t          d|          D ]<}|                    ||         
                    t          |dz
            |z             =d |D             }|S )a  Given a series

    f(x) = a[1]*x + a[2]*x**2 + ... + a[n-1]*x**(n - 1),

    use the Lagrange inversion formula to compute a series

    g(x) = b[1]*x + b[2]*x**2 + ... + b[n-1]*x**(n - 1)

    so that f(g(x)) = g(f(x)) = x mod x**n. We must have a[0] = 0, so
    necessarily b[0] = 0 too.

    The algorithm is naive and could be improved, but speed isn't an
    issue here and it's easy to read.

    c              3   >   K   | ]}|         t           |z  z  V  d S )Nr   ).0ias     _/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/scipy/special/_precompute/utils.py	<genexpr>z%lagrange_inversion.<locals>.<genexpr>   s/      ((!AaDAI((((((    r      c                 6    g | ]}t          j        |          S  )mpmpf)r   r   s     r
   
<listcomp>z&lagrange_inversion.<locals>.<listcomp>%   s     qr   )lensumranger   seriesremoveOappendexpandr   r   coeff)r	   nfhhpowerkbs   `      r
   lagrange_inversionr"      s     	AA((((uQxx(((((A	
1Q1%%''AdVF1XX / /vbz!|++--....	A1a[[ . .	AE**1,----AAHr   )mpmathr   ImportError	sympy.abcr   r"   r   r   r
   <module>r&      s   	 	 	 	D		 	 	 	D	    s     ""