Complex Conjugation

HasComplexConjugate(A) : AlgEtQ -> BoolElt
Returns if the algebra A is the product of CM fields.
ComplexConjugate(x) : AlgEtQElt -> AlgEtQElt
If the algebra A of the element x is a product of CM fields, it returns the complex conjugate of the argument.
IsConjugateStable(O) : AlgEtQOrd -> BoolElt,AlgEtQOrd
Given an order O in a CM-étale algebra, it returns whether O is conjugate stable and the complex conjugate.
ComplexConjugate(O) : AlgEtQOrd -> AlgEtQOrd
Given an order O in a CM-étale algebra, it returns the complex conjugate of O.
IsConjugateStable(I) : AlgEtQIdl -> BoolElt,AlgEtQIdl
Given a fractional ideal I in a CM-étale algebra, it returns whether I is conjugate stable and the complex conjugate. Note: if the order of I is not conjugate stable, then the second output will be defined over the complex conjugate of the order.
ComplexConjugate(I) : AlgEtQIdl -> AlgEtQIdl
If A is a product of CM fields, it returns the complex conjugate of the fractional ideal I. Note: if the order of I is not conjugate stable, then the output will be defined over the complex conjugate of the order.
V2.29, 21 October 2025