We start by loading the package \verb$KnotTheory`$ --- it is only needed because it had many specific knots pre-defined:

\noindent\nbpdfInput{Snips/Implementation/1.pdf}

\noindent\nbpdfPrint{Snips/Implementation/2.pdf}

Next we quietly define the commands \verb$Rot$, used to compute rotation numbers, and \verb$PolyPlot$, used to plot polynomials as bar codes and as hexagonal QR codes. Neither is a part of the core of the computation of $\Theta$, so neither is shown; yet we do show some usage examples.

\noindent\nbpdfInput{Snips/Implementation/3.pdf}

\noindent\nbpdfInput{Snips/Implementation/4.pdf}

\noindent\nbpdfOutput{Snips/Implementation/5.pdf}

We urge the reader to compare the above output with the knot diagram in Section~\ref{ssec:OldFormulas}.

\noindent\nbpdfInput{Snips/Implementation/6.pdf}

\noindent\nbpdfInput{Snips/Implementation/7.pdf}

\noindent\nbpdfOutput{Snips/Implementation/8.pdf}

\noindent\nbpdfInput{Snips/Implementation/9.pdf}

