{
  "abstract": "We implement a Macaulay2 package for computations involving rings of truncated Witt vectors $W_n(R)$ of a finitely generated $\\F_p$-algebra $R$. This package includes ring operations (addition, multiplication, Frobenius, Verschiebung, etc.) on elements of $W_n(R)$, conversion between tuple representatives and ghost map representatives of elements of truncated Witt vectors over polynomial rings, and explicit computation of $W_n(R)$ as a finite-type algebra over $\\Z/p^n$. This functionality is based on an algorithm we developed for performing arithmetic operations in rings of finite length $p$-typical Witt vectors over finitely generated $\\F_p$-algebras. In addition, we implement an algorithm to calculate lifts of Frobenius from $\\F_p$-algebras to flat lifts over $\\Z/p^2\\Z$, and an algorithm to find the quasi-$F$-splitting height of a local or graded complete intersection ring.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37931",
  "author_total": 5,
  "authors": [
    {
      "name": "Anne Fayolle"
    },
    {
      "name": "Abhay Goel"
    },
    {
      "name": "Devlin Mallory"
    },
    {
      "name": "Eamon Quinlan-Gallego"
    },
    {
      "name": "Teppei Takamatsu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3pv2bz54y86s1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37931",
  "fulltext_url": null,
  "id": "3pv2bz54y86s1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37931",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214929960",
  "pdf_url": "https://arxiv.org/pdf/2609.37931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3pv2bz54y86s1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The WittVectors package for Macaulay2",
  "title_text": "The WittVectors package for Macaulay2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/3pv2bz54y86s1",
  "venue": "arXiv",
  "versions": []
}