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QuadraticIdealExamplesByRoos -- Examples of Quadratic Ideals with Embedding Dimension Four by Jan-Erik Roos

Description

Quadratic ideals based on Main Theorem and Tables in "Homological properties of the homology algebra of the Koszul complex of a local ring: Examples and questions" by Jan-Erik Roos, Journal of Algebra 465 (2016) 399-436.

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Authors

Version

This documentation describes version 0.1 of QuadraticIdealExamplesByRoos.

Citation

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

@misc{QuadraticIdealExamplesByRoosSource,
  title = {{QuadraticIdealExamplesByRoos: A \emph{Macaulay2} package. Version~0.1}},
  author = {David Eisenbud and Michael Perlman and Ritvik Ramkumar and Deepak Sireeshan and Aleksandra Sobieska and Teresa Yu and Jacob Zoromski},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
  • Methods
    • almostKoszul(Ring,ZZ) -- see almostKoszul -- Examples discovered by Jan-Erik Roos
  • Other things
    • depthZeroTable -- Creates hashtable of Jan-Erik Roos' examples of quadratic ideals with depth zero
    • higherDepthTable -- Creates hashtable of Jan-Erik Roos' examples of quadratic ideals with positive depth
    • onedimToricIrrationalPoincare -- Produces the example of a one-dimensional toric ideal whose Poincar\'e series is irrational.
    • roosIsotopes -- Creates hashtable of Jan-Erik Roos' quadratic "isotopes"
    • roosTable -- Creates hashtable of Jan-Erik Roos' examples of quadratic ideals
    • twodimToricIrrationalPoincare -- Produces the example of a two-dimensional toric ideal whose Poincar\'e series is irrational.

For the programmer

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

The source of this document is in QuadraticIdealExamplesByRoos.m2:224:0.