Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2014
- DOI:
- 10.48550/arXiv.1405.6094
- arXiv:
- arXiv:1405.6094
- Bibcode:
- 2014arXiv1405.6094E
- Keywords:
-
- Computer Science - Symbolic Computation;
- 68W30;
- 03C10;
- I.1.2
- E-Print:
- H. Hong and C. Yap, eds. Mathematical Software - ICMS 2014, pp. 450-457. (Lecture Notes in Computer Science, 8592). Springer, 2014