# Chordal networks of polynomial ideals

Published in *SIAM J. Appl. Algebra Geometry*, 2017

Recommended citation: Diego Cifuentes, Pablo Parrilo (2016). "Chordal networks of polynomial ideals." *SIAM J. Appl. Algebra Geometry*. 1(1):73-170. __http://dx.doi.org/10.1137/16M106995X__

We introduce a novel representation of structured polynomial ideals: *chordal networks*.
Many interesting families of polynomial ideals admit compact chordal network representations (of size linear in the number of variables), even though the number of components is exponentially large.
Chordal networks can also be efficiently post-process to compute several properties of the underlying variety (e.g., cardinality, dimension).
We show applications in algebraic statistics and vector addition systems.

See also:

- My slides from SIAM Annual Meeting’ 17
- Pablo’s presentation at SIAM Annual Meeting’ 17
- Chordal package