Building up from some new or lightly used theoretical tools, especially
``solvable approximation'' and ``Gaussian differential operators'',
we give a clean and efficient computer implementation of the quantum
$sl_2$ portfolio of operations. Beyond the theoretical interest and the
satisfaction that one obtains when complicated formulas come to life,
become specific, and check, we explain (and implement and prove) why
our results are valuable in knot theory.

\par 
We mean business! Page~\pageref{prog:Portfolio} displays a program
which is a complete implementation of the quantum $sl_2$ portfolio
of operations. Page~\pageref{prog:Invariant} displays a variant of that
program tailored to efficiently compute the ``Rozansky-Overbay''
invariants. Appendix~\ref{app:Tables} contains a tabulation of some of
these invariants on knots with up to 10 crossings. Much more is
at~\web{}$\coloneqq$\url{\weburl/}.