Computing the n-th coefficient of an algebraic power series modulo p in O(log n) operations

TL;DR

This paper pedagogically explains how to compute the n-th coefficient of an algebraic power series modulo a prime p efficiently in logarithmic time, based on a formal power series proof.

Contribution

It provides a clear exposition of a method to compute coefficients of algebraic power series modulo p in O(log n) operations, based on prior theoretical results.

Findings

Efficient algorithm for coefficient computation in algebraic power series

Logarithmic time complexity achieved for the computation

Pedagogical presentation of the formal proof

Abstract

This is an exposition, for pedagogical purposes, of the formal power series proof of Bostan, Christol and Dumas [3] of the result stated in the title (a corollary of the Christol theorem).