Sampling cubic rings Gundlach, Fabian <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 Society 2026 info:eu-repo/semantics/bookPart doc-type:bookPart text http://purl.org/coar/resource_type/c_3248 https://ris.uni-paderborn.de/record/65550 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1090/conm/840/16804 info:eu-repo/semantics/altIdentifier/issn/0271-4132 info:eu-repo/semantics/altIdentifier/issn/1098-3627 info:eu-repo/semantics/altIdentifier/isbn/9781470485702 info:eu-repo/semantics/altIdentifier/isbn/9781470480325 info:eu-repo/semantics/closedAccess