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.
