AdjustedSignIJK[q] gives the sign of the pure quaternion part of q, adjusted so its first nonzero component is positive.

IntegerQuaternionQ[q] gives True if q is an integer quaternion and False otherwise.

LeftAssociates[q] gives a list of the 24 left associates of the quaternion q.

LeftGCD[a, b] gives the greatest common left divisor of the quaternions a and b.

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.