Given a sequence of number fields returns the étale algebra corresponding to the direct product. Note: the number fields with DefiningPolynomial of degree one should be created with the parameter DoLinearExtension set to true.
We now consider the Ãùtale algebra consisting of two copies of the rational field.
> _<x> := PolynomialRing(Integers());
> QQ := NumberField(x-1:DoLinearExtension);
> A := EtaleAlgebra([QQ,QQ]);
> a := PrimitiveElement(A); a;
<1, 2>
EtaleAlgebra(f) : RngUPolElt[FldRat] -> AlgEtQ
Given a squarefree polynomial over the integers or rationals returns the product of the number fields defined by the irreducible factors.
Given a sequence of étale algebras over Q, returns their direct product, together with the natural inclusions and projections.
V2.29, 28 November 2025