Saturation -- ideal and submodule quotient, saturation, and annihilator routines

Description

This package provides various basic commutative algebra routines for working with ideals and modules.

Main functionalities

Authors

Version

This documentation describes version 0.3 of Saturation.

Citation

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

@misc{SaturationSource,
  title = {{Saturation: quotient, saturation, and annihilator routines for ideals and modules. Version~0.3}},
  author = {Justin Chen and Mahrud Sayrafi and Mike Stillman},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- annihilator -- the annihilator ideal
- isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
- saturate -- saturation of ideal or submodule
Methods
- annihilator(Ideal) -- see annihilator -- the annihilator ideal
- annihilator(Module) -- see annihilator -- the annihilator ideal
- annihilator(RingElement) -- see annihilator -- the annihilator ideal
- isSupportedInZeroLocus(Ideal,GradedModule) -- see isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
- isSupportedInZeroLocus(Ideal,Ideal) -- see isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
- isSupportedInZeroLocus(Ideal,Module) -- see isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
- Ideal : Ideal -- see quotient(Module,Module) -- ideal or submodule quotient
- Ideal : RingElement -- see quotient(Module,Module) -- ideal or submodule quotient
- Module : Ideal -- see quotient(Module,Module) -- ideal or submodule quotient
- Module : Module -- see quotient(Module,Module) -- ideal or submodule quotient
- Module : RingElement -- see quotient(Module,Module) -- ideal or submodule quotient
- MonomialIdeal : RingElement -- see quotient(Module,Module) -- ideal or submodule quotient
- quotient(Ideal,Ideal) -- see quotient(Module,Module) -- ideal or submodule quotient
- quotient(Ideal,RingElement) -- see quotient(Module,Module) -- ideal or submodule quotient
- quotient(Module,Ideal) -- see quotient(Module,Module) -- ideal or submodule quotient
- quotient(Module,Module) -- ideal or submodule quotient
- quotient(Module,RingElement) -- see quotient(Module,Module) -- ideal or submodule quotient
- quotient(MonomialIdeal,RingElement) -- see quotient(Module,Module) -- ideal or submodule quotient
- saturate(Ideal) -- see saturate -- saturation of ideal or submodule
- saturate(Ideal,Ideal) -- see saturate -- saturation of ideal or submodule
- saturate(Ideal,RingElement) -- see saturate -- saturation of ideal or submodule
- saturate(Module) -- see saturate -- saturation of ideal or submodule
- saturate(Module,Ideal) -- see saturate -- saturation of ideal or submodule
- saturate(Module,RingElement) -- see saturate -- saturation of ideal or submodule
- saturate(MonomialIdeal,RingElement) -- see saturate -- saturation of ideal or submodule
- saturate(Vector) -- see saturate -- saturation of ideal or submodule
- saturate(Vector,Ideal) -- see saturate -- saturation of ideal or submodule
- saturate(Vector,RingElement) -- see saturate -- saturation of ideal or submodule

For the programmer

The object Saturation is a package, defined in Saturation.m2, with auxiliary files in Saturation/.

The source of this document is in Saturation/doc.m2:100:0.