  The Qth-power algorithm produces a useful canonical P-module presentation for
the integral closures of certain integral extensions of
$P:=\mathbf{F}[x_n,...,x_1]$, a polyonomial ring over the finite field
$\mathbf{F}:=\mathbf{Z}_q$ of $q$ elements. Here it is shown how to use this
for several small primes $q$ to reconstruct similar integral closures over the
rationals $\mathbf{Q}$ using the Chinese remainder theorem to piece together
presentations in different positive characteristics, and the extended Euclidean
algorithm to reconstruct rational fractions to lift these to presentations over
$\mathbf{Q}$.
