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linearquotients

Includes scripts to find the linear orderings of an edge ideal's generators, and to verify that a given generator ordering has linear quotients.

https://github.com/mario730/linearquotients

Science Score: 44.0%

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Repository

Includes scripts to find the linear orderings of an edge ideal's generators, and to verify that a given generator ordering has linear quotients.

Basic Info
  • Host: GitHub
  • Owner: Mario730
  • Language: Macaulay2
  • Default Branch: main
  • Size: 11.7 KB
Statistics
  • Stars: 0
  • Watchers: 1
  • Forks: 0
  • Open Issues: 0
  • Releases: 0
Created almost 2 years ago · Last pushed 12 months ago
Metadata Files
Readme Citation

README.md

Methods for finding and verifying linear quotients of ideals

This repository contains the following Macaulay2 files: findLinearOrderings.m2, isLinear.m2, and getQuotients.m2. Collectively, these files consist of 3 methods for working with ideals of polynomial rings. The usage and behavior of each method are detailed below.

isLinear ( ordering, n )

Use this method to test if the given order of a list of generators yields linear quotients.

Parameters:

  • ordering: a list of generators in Q = QQ[x_1 .. x_n]
  • n: the dimension of Q, the ideal's polynomial ring

Returns:

  • true: if ordering is a linear quotients ordering
  • false: otherwise

getQuotients ( ordering )

Use this method to return the quotients of a given list of ideal generators.

Parameters:

  • ordering: a list of generators in Q = QQ[x_1 .. x_n]

Returns:

  • {quots}: a list of the linear quotients

findLinearOrderings ( edgeIdeal, n )

This method is used to find the "most linear" ordering of an ideal's generators; if an ordering exists that yields all linear quotients, it will be returned. Otherwise, an ordering will be returned that has the most linear quotients.

Parameters:

  • edgeIdeal: an edge ideal in Q = QQ[x_1 .. x_n]
  • n: the dimension of Q, the ideal's polynomial ring

Returns:

  • {order}: a list of the most linear ordering of the given ideal

Owner

  • Name: Mario
  • Login: Mario730
  • Kind: user
  • Location: Phoenix, AZ

Citation (CITATION.cff) 

cff-version: 1.2.0
title: Linear Quotients
message: >-
  If you use this software, please cite it using the
  metadata from this file.
type: software
authors:
  - given-names: Mario
    family-names: Stinson-Maas
    email: mstinson@oberlin.edu
    orcid: 'https://orcid.org/0009-0008-6283-3696'
    affiliation: Oberlin College
repository-code: 'https://github.com/Mario730/linearquotients'
date-released: '2024-07-10'

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