  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.
