Peter Doyle and Curt McMullen
Last revised 1989
Version 1.0A1 dated 15 September 1994
Equations that can be solved using iterated rational maps
are characterized:
an equation is `computable'
if and only if its Galois group is within 
of solvable.
We give explicitly a new solution to the quintic polynomial,
in which the
transcendental inversion of the icosahedral map
(due to Hermite and Kronecker) is replaced by a purely iterative
algorithm.
The algorithm requires a rational map with icosahedral symmetries;
we show all rational maps with
given symmetries can be described using the classical theory of
invariant polynomials.