Attributes of Quaternion Algebras

BaseField(A) : AlgQuat -> Fld

BaseRing(A) : AlgQuat -> Fld

The base field of the quaternion algebra A.

Basis(A) : AlgQuat -> SeqEnum

The basis of the algebra A.

Discriminant(A) : AlgQuat -> FldRatElt

Given a quaternion algebra A returns the reduced discriminant as an element of the base ring, which is well-defined up to squares. If A is defined over the rationals, then the value is a square-free integer in Q.

RamifiedPrimes(A) : AlgQuat -> SeqEnum

Given a quaternion algebra A over Q, returns the sequences of finite ramified primes, i.e. those primes dividing the discriminant. Note that the algebra is definite or indefinite, according to whether the sequence is of odd or even length.

Example AlgQuat_Ramified_Primes (H68E6)

> A := QuaternionAlgebra(-436,-503,22);
> RamifiedPrimes(A);
[ 17 ]