We consider algebraic numbers defined by univariate polynomials over the rationals.
In the syntax of Maple, such numbers are expressed using the RootOf function. This
paper defines a canonical form for RootOf with respect to affine transformations.
The affine shifts of monic irreducible polynomials form a group, and the orbits of
the polynomials can be used to define a canonical form. The canonical form of the
polynomials then defines a canonical form for the corresponding algebraic numbers.
Reducing any RootOf to its canonical form has the advantage that affine relations
between algebraic numbers are readily identified. More generally, the reduction minimizes
the number of algebraic numbers appearing in a computation, and also allows the Maple
indexed RootOf to be used more easily.