On the complexity of change of order

I will discuss algorithms to change variable order, for triangular representations of varieties of dimension zero. In an attempt to keep the presentation simple, I will only talk about the bivariate case, where the main ideas are already present: duality, following the work of Kaltofen and Shoup, and trace formulas, after Diaz Toca and Gonzalez Vega.

As an application, I will point out the connection with the Rothstein-Trager integration algorithm, and discuss the complexity of rational function integration.