  Given a pair of regular quadratic forms over $\mathbb{Q}$ which are in the
same genus and a finite set of primes $P$, we show that there is an effective
way to determine a rational equivalence between these two quadratic forms which
are integral over every prime in $P$. This answers one of the principal
questions posed by Conway and Sloane in their book {\em Sphere packings,
lattices and groups}, Grundlehren der Mathematischen Wissenschaften
[Fundamental Principles of Mathematical Sciences], Vol 290, Springer-Verlag,
New York, 1999; page 402.
