Cylindrical algebraic decomposition (CAD) is a key tool for solving problems in real algebraic geometry and beyond. In recent years a new approach has been developed, where regular chains technology is used to first build a decomposition in complex space. We consider the latest variant of this which builds the complex decomposition incrementally by polynomial and produces CADs on whose cells a sequence of formulae are truth-invariant. Like all CAD algorithms the user must provide a variable ordering which can have a profound impact on the tractability of a problem. We evaluate existing heuristics to help with the choice for this algorithm, suggest improvements and then derive a new heuristic more closely aligned with the mechanics of the new algorithm.
@article{arxiv.1405.6094,
title = {Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition},
author = {Matthew England and Russell Bradford and James H. Davenport and David Wilson},
journal= {arXiv preprint arXiv:1405.6094},
year = {2014}
}