The domain constructor Quaternion implements quaternions over commutative rings. For information on related topics see ComplexXmpPage and OctonionXmpPage . You can also issue the system command )show Quaternion to display the full list of operations defined by Quaternion.
The basic operation for creating quaternions is quatern quatern Quaternion . This is a quaternion over the rational numbers.
The four arguments are the real part, the i imaginary part, the j imaginary part, and the k imaginary part, respectively.
Because q is over the rationals (and nonzero), you can invert it.
The usual arithmetic (ring) operations are available
In general, multiplication is not commutative.
There are no predefined constants for the imaginary i, j, and k parts, but you can easily define them.
These satisfy the normal identities.
The norm is the quaternion times its conjugate.