# Change of basis for m-primary ideals in one and two variables

## TL;DR

This paper improves algorithms related to changing bases in polynomial ideals, extending techniques from univariate to bivariate cases, and analyzes their complexity and applications in algebraic computations.

## Contribution

It introduces a faster tangling algorithm and extends basis change techniques to bivariate polynomial ideals, providing new complexity bounds.

## Key findings

- Faster tangling algorithm for univariate polynomials
- Extension of basis change methods to bivariate ideals
- Bounds on arithmetic complexity of certain algebraic structures

## Abstract

Following recent work by van der Hoeven and Lecerf (ISSAC 2017), we discuss the complexity of linear mappings, called untangling and tangling by those authors, that arise in the context of computations with univariate polynomials. We give a slightly faster tangling algorithm and discuss new applications of these techniques. We show how to extend these ideas to bivariate settings, and use them to give bounds on the arithmetic complexity of certain algebras.