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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

Version

This documentation describes version 1.0 of SCMAlgebras.

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~1.0}},
  author = {Ernesto Lax},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/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 $I$.
    • isSCM -- checks whether a module or an ideal is sequentially Cohen-Macaulay
    • minimumDimension -- computes the minimum dimension 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 $I$.
    • 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
    • minimumDimension(Ideal) -- see minimumDimension -- computes the minimum dimension of $I$.

For the programmer

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

The source of this document is in SCMAlgebras.m2:315:0.