special._precompute.utils

Module Contents

Functions

lagrange_inversion(a) Given a series
lagrange_inversion(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.