---
_id: '65550'
abstract:
- lang: eng
  text: "<p>\r\n                    We explain how to construct a uniformly random
    cubic integral domain\r\n                    <inline-formula content-type=\"math/mathml\">\r\n
    \                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"
    alttext=\"upper S\">\r\n                        <mml:semantics>\r\n                          <mml:mi>S</mml:mi>\r\n
    \                         <mml:annotation encoding=\"application/x-tex\">S</mml:annotation>\r\n
    \                       </mml:semantics>\r\n                      </mml:math>\r\n
    \                   </inline-formula>\r\n                    of given signature
    with\r\n                    <inline-formula content-type=\"math/mathml\">\r\n
    \                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"
    alttext=\"StartAbsoluteValue d i s c left-parenthesis upper S right-parenthesis
    EndAbsoluteValue less-than-or-equal-to upper T\">\r\n                        <mml:semantics>\r\n
    \                         <mml:mrow>\r\n                            <mml:mo fence=\"false\"
    stretchy=\"false\">\r\n                              |\r\n                              \r\n
    \                           </mml:mo>\r\n                            <mml:mi>d</mml:mi>\r\n
    \                           <mml:mi>i</mml:mi>\r\n                            <mml:mi>s</mml:mi>\r\n
    \                           <mml:mi>c</mml:mi>\r\n                            <mml:mo
    stretchy=\"false\">(</mml:mo>\r\n                            <mml:mi>S</mml:mi>\r\n
    \                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                            <mml:mo
    fence=\"false\" stretchy=\"false\">\r\n                              |\r\n                              \r\n
    \                           </mml:mo>\r\n                            <mml:mo>\r\n
    \                             ≤\r\n                              \r\n                            </mml:mo>\r\n
    \                           <mml:mi>T</mml:mi>\r\n                          </mml:mrow>\r\n
    \                         <mml:annotation encoding=\"application/x-tex\">\\lvert
    disc(S)\\rvert \\leq T</mml:annotation>\r\n                        </mml:semantics>\r\n
    \                     </mml:math>\r\n                    </inline-formula>\r\n
    \                   in expected time\r\n                    <inline-formula content-type=\"math/tex\">\r\n
    \                     <tex-math>\\widetilde \\mathcal {O}(\\log T)</tex-math>\r\n
    \                   </inline-formula>\r\n                    .\r\n                  </p>"
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
citation:
  ama: 'Gundlach F. Sampling cubic rings. In: <i>Contemporary Mathematics</i>. American
    Mathematical Society; 2026. doi:<a href="https://doi.org/10.1090/conm/840/16804">10.1090/conm/840/16804</a>'
  apa: Gundlach, F. (2026). Sampling cubic rings. In <i>Contemporary Mathematics</i>.
    American Mathematical Society. <a href="https://doi.org/10.1090/conm/840/16804">https://doi.org/10.1090/conm/840/16804</a>
  bibtex: '@inbook{Gundlach_2026, place={Providence, Rhode Island}, title={Sampling
    cubic rings}, DOI={<a href="https://doi.org/10.1090/conm/840/16804">10.1090/conm/840/16804</a>},
    booktitle={Contemporary Mathematics}, publisher={American Mathematical Society},
    author={Gundlach, Fabian}, year={2026} }'
  chicago: 'Gundlach, Fabian. “Sampling Cubic Rings.” In <i>Contemporary Mathematics</i>.
    Providence, Rhode Island: American Mathematical Society, 2026. <a href="https://doi.org/10.1090/conm/840/16804">https://doi.org/10.1090/conm/840/16804</a>.'
  ieee: 'F. Gundlach, “Sampling cubic rings,” in <i>Contemporary Mathematics</i>,
    Providence, Rhode Island: American Mathematical Society, 2026.'
  mla: Gundlach, Fabian. “Sampling Cubic Rings.” <i>Contemporary Mathematics</i>,
    American Mathematical Society, 2026, doi:<a href="https://doi.org/10.1090/conm/840/16804">10.1090/conm/840/16804</a>.
  short: 'F. Gundlach, in: Contemporary Mathematics, American Mathematical Society,
    Providence, Rhode Island, 2026.'
date_created: 2026-05-04T15:31:12Z
date_updated: 2026-05-04T15:32:12Z
doi: 10.1090/conm/840/16804
language:
- iso: eng
place: Providence, Rhode Island
publication: Contemporary Mathematics
publication_identifier:
  isbn:
  - '9781470485702'
  - '9781470480325'
  issn:
  - 0271-4132
  - 1098-3627
publication_status: published
publisher: American Mathematical Society
status: public
title: Sampling cubic rings
type: book_chapter
user_id: '100450'
year: '2026'
...