SCMAlgebras -- sequentially Cohen-Macaulay modules or ideals

Description

SCMAlgebras is a package to check whether a module or an ideal is sequentially Cohen-Macaulay, by computing the modules of deficiency and the filter ideals.

Author

Ernesto Lax <erlax@unime.it>

Version

This documentation describes version 1.1 of SCMAlgebras, released May 31, 2025.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SCMAlgebrasSource,
  title = {{SCMAlgebras: sequentially Cohen-Macaulay modules or ideals. Version~1.1}},
  author = {Ernesto Lax},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- canonicalModule -- computes the canonical module of a module $M$ or an ideal $I$.
- deficiencyModule -- computes the $i$th module of deficiency of a module $M$ or an ideal $I$.
- filterIdeal -- computes the $i$th filter ideal of $I$.
- isCCM -- checks whether a module or an ideal is canonically Cohen-Macaulay
- isSCM -- checks whether a module or an ideal is sequentially Cohen-Macaulay
- isUnmixed -- checks whether an ideal is unmixed
- minimumDimension -- computes the minimum dimension of $I$.
- unmixedLayer -- computes the $i$th unmixed layer of $I$.
Methods
- canonicalModule(Ideal) -- see canonicalModule -- computes the canonical module of a module $M$ or an ideal $I$.
- canonicalModule(Module) -- see canonicalModule -- computes the canonical module of a module $M$ or an ideal $I$.
- deficiencyModule(Ideal,ZZ) -- see deficiencyModule -- computes the $i$th module of deficiency of a module $M$ or an ideal $I$.
- deficiencyModule(Module,ZZ) -- see deficiencyModule -- computes the $i$th module of deficiency of a module $M$ or an ideal $I$.
- filterIdeal(Ideal,ZZ) -- see filterIdeal -- computes the $i$th filter ideal of $I$.
- isCCM(Ideal) -- see isCCM -- checks whether a module or an ideal is canonically Cohen-Macaulay
- isCCM(Module) -- see isCCM -- checks whether a module or an ideal is canonically Cohen-Macaulay
- isSCM(Ideal) -- see isSCM -- checks whether a module or an ideal is sequentially Cohen-Macaulay
- isSCM(Module) -- see isSCM -- checks whether a module or an ideal is sequentially Cohen-Macaulay
- isUnmixed(Ideal) -- see isUnmixed -- checks whether an ideal is unmixed
- minimumDimension(Ideal) -- see minimumDimension -- computes the minimum dimension of $I$.
- unmixedLayer(Ideal,ZZ) -- see unmixedLayer -- computes the $i$th unmixed layer of $I$.

For the programmer

The object SCMAlgebras is a package, defined in SCMAlgebras.m2.

The source of this document is in SCMAlgebras.m2:481:0.