Monomial_Ideal_Computations

title: Monomial Ideal Computations permalink: wiki/Monomial_Ideal_Computations/ layout: wiki

Goals:

Resolutions of monomial ideals
- Given a resolution an algorithm to minimize it / do one minimizing step
- compute other known resolutions (e.g. Taylor, Eliahou-Kervaire(need stable ideal) and others), see what is already in M2 and what not

Using external programs
- ~~how to read from / write to files and execute commands~~
- ~~discuss using normaliz as a library~~

Progress:

Eliahou-Kervaire resolution implemented (it is a minimal resolution for stable ideals).
Aramova-Herzog-Hibi resolution implemented (it is a minimal resolution for squarefree stable ideals).
Implemented simplicial resolutions: Given an ideal I and a simplicial complex C, compute a resolution of I supported on (the chain complex associated to) C.
Scarf complex implemented.
Several "control methods" implemented, to check: whether a chain complex is a resolution of the given ideal, whether it has nonzero scalars in the matrices, if an ideal is stable or squarefree stable, or generic. Some methods use the packages SimplicialComplexes or Chain Complex Extras.

Improve the Normaliz package: several correction including hints of the "Ask Dan & Mike" Session