# 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.