Attributes

DefiningPolynomial(A): AlgEtQ -> RngUPolElt

Returns the defining polynomial of the algebra \(A\), if the corresponding number fields are distinct.

Components(A): AlgEtQ -> SeqEnum

Returns the number fields of which the algebra \(A\) is a product of, together with embeddings and projections.

Dimension(A): AlgEtQ -> RngInt

Returns the dimension of the algebra \(A\).

AbsoluteDimension(A): AlgEtQ -> RngInt

Return the dimension of the algebra \(A\) over the prime field.

HasBaseField(A): AlgEtQ -> BoolElt

Returns whether the components of the algebra \(A\) have a common base field.

BaseField(A): AlgEtQ -> FldNum, Map

Returns the common base field of the algebra \(A\), if it exists.

PrimeField(A): AlgEtQ -> FldNum

Returns the prime field of the algebra \(A\).

IsNumberField(A): AlgEtQ -> BoolElt, FldNum, Map

Returns whether \(A\) has a single component (hence is a number field). If so, also returns the number field and an isomorphism from \(A\) to it.

A1 eq A2: AlgEtQ, AlgEtQ -> BoolElt

Returns whether the algebras \(A1\) and \(A2\) are equal.