PrimaryLeftAssociate[q] gives the left associate of the quaternion q with the largest scalar component.

PrimaryRightAssociate[q] gives the right associate of the quaternion q with the largest scalar component.

Quaternion[a, b, c, d] represents the quaternion a + I b + J c + K d.

QuaternionQ[q] gives True if q is a quaternion and False otherwise.

Quaternions is an option for PrimeQ which specifies whether factorization should be done over the quaternions.

RightAssociates[q] gives a list of the 24 right associates of the quaternion q.

RightGCD[a, b] gives the greatest common right divisor of the quaternions a and b.

ScalarQ[q] gives True if q is a real numeric quantity and False otherwise.

ToQuaternion[q] transforms q into a Quaternion object if possible.

UnitQuaternionQ[q] gives True if q is a unit quaternion and False otherwise.