book chapter published Fabian Gundlach author 100450 <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> American Mathematical Society2026 eng 0271-4132 1098-3627 9781470485702 978147048032510.1090/conm/840/16804 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> 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> 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>. F. Gundlach, in: Contemporary Mathematics, American Mathematical Society, Providence, Rhode Island, 2026. @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} } F. Gundlach, “Sampling cubic rings,” in <i>Contemporary Mathematics</i>, Providence, Rhode Island: American Mathematical Society, 2026. 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>. 655502026-05-04T15:31:12Z2026-05-04T15:32:12Z