  The usual formulation of efficient division uses Newton iteration to compute
an inverse in a related domain where multiplicative inverses exist. On one
hand, Newton iteration allows quotients to be calculated using an efficient
multiplication method. On the other hand, working in another domain is not
always desirable and can lead to a library structure where arithmetic domains
are interdependent. This paper uses the concept of a whole shifted inverse and
modified Newton iteration to compute quotients efficiently without leaving the
original domain. The iteration is generic to domains having a suitable shift
operation, such as integers or polynomials with coefficients that do not
necessarily commute.
