Quaternions

The domain contructor Quaternion implements quaternions over commutative rings. The basic operation for creating quaternions is quatern. 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.

For information on related topics, see Complex and Octonion. You can also issue the system command

to display the full list of operations defined by Quaternion.