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Jets -- compute jets of various algebraic, geometric and combinatorial objects

Description

This package enables computations with jet functors. It introduces the jets method to compute jets of polynomial rings, ideals, quotients, ring homomorphisms, and varieties. The construction of jets follows an algebraic procedure discussed in several sources, including the first three references below.

Additional features include an alternative algorithm to compute the radical of jets of monomial ideals, a function to construct jets of graphs, a method for principal components of jets, and an option for jets with "projective" gradings.

Version history:

  • 1.1: JSAG version.
  • 1.2: Improved method for principal components. Added methods for invariants of principal components of monomial ideals.

References

L. Ein and M. Mustaţă, Jet schemes and singularities.

P. Vojta, Jets via Hasse-Schmidt Derivations.

R.A. Goward and K.E. Smith, The jet scheme of a monomial scheme.

F. Galetto, E. Helmick, and M. Walsh, Jet graphs.

F. Galetto, N. Iammarino, and T. Yu, Jets and principal components of monomial ideals, and very well-covered graphs

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Package methods

Examples from the literature

Technical information

Authors

Certification a gold star

Version 1.1 of this package was accepted for publication in volume 12 of The Journal of Software for Algebra and Geometry on 20 October 2022, in the article Computing with jets (DOI: 10.2140/jsag.2022.12.43). That version can be obtained from the journal.

Version

This documentation describes version 1.2 of Jets.

Citation

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

@misc{JetsSource,
  title = {{Jets: compute jets of various algebraic, geometric and combinatorial objects. Version~1.2}},
  author = {Federico Galetto and Nicholas Iammarino},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{JetsArticle,
  title = {{Computing with jets}},
  author = {Federico Galetto and Nicholas Iammarino},
  journal = {The Journal of Software for Algebra and Geometry},
  volume = {12},
  year = {2022},
}

Exports

For the programmer

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


The source of this document is in Jets.m2:1666:0.