  The Cox ring provides a coordinate system on a toric variety analogous to the
homogeneous coordinate ring of projective space. Rational maps between
projective spaces are described using polynomials in the coordinate ring, and
we generalise this to toric varieties, providing a unified description of
arbitrary rational maps between toric arieties in terms of their Cox
coordinates. Introducing formal roots of polynomials is necessary even in the
simplest examples.
