@inbook{65550,
  abstract     = {{<p>
                    We explain how to construct a uniformly random cubic integral domain
                    <inline-formula content-type="math/mathml">
                      <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S">
                        <mml:semantics>
                          <mml:mi>S</mml:mi>
                          <mml:annotation encoding="application/x-tex">S</mml:annotation>
                        </mml:semantics>
                      </mml:math>
                    </inline-formula>
                    of given signature with
                    <inline-formula content-type="math/mathml">
                      <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">
                        <mml:semantics>
                          <mml:mrow>
                            <mml:mo fence="false" stretchy="false">
                              |
                              
                            </mml:mo>
                            <mml:mi>d</mml:mi>
                            <mml:mi>i</mml:mi>
                            <mml:mi>s</mml:mi>
                            <mml:mi>c</mml:mi>
                            <mml:mo stretchy="false">(</mml:mo>
                            <mml:mi>S</mml:mi>
                            <mml:mo stretchy="false">)</mml:mo>
                            <mml:mo fence="false" stretchy="false">
                              |
                              
                            </mml:mo>
                            <mml:mo>
                              ≤
                              
                            </mml:mo>
                            <mml:mi>T</mml:mi>
                          </mml:mrow>
                          <mml:annotation encoding="application/x-tex">\lvert disc(S)\rvert \leq T</mml:annotation>
                        </mml:semantics>
                      </mml:math>
                    </inline-formula>
                    in expected time
                    <inline-formula content-type="math/tex">
                      <tex-math>\widetilde \mathcal {O}(\log T)</tex-math>
                    </inline-formula>
                    .
                  </p>}},
  author       = {{Gundlach, Fabian}},
  booktitle    = {{Contemporary Mathematics}},
  isbn         = {{9781470485702}},
  issn         = {{0271-4132}},
  publisher    = {{American Mathematical Society}},
  title        = {{{Sampling cubic rings}}},
  doi          = {{10.1090/conm/840/16804}},
  year         = {{2026}},
}