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dspivak committed Apr 9, 2024
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3 changes: 3 additions & 0 deletions P1-Polynomials.tex
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Expand Up @@ -1193,6 +1193,8 @@ \section{Introducing polynomial functors} \label{sec.poly.obj.intro}
\end{definition}

\index{polynomial functor!positions and directions}
\index{positions!of polynomial|seealso{polynomial functor!positions and directions}}
\index{directions!of polynomial|seealso{polynomial functor!positions and directions}}

Note that the position-set $p(\1)$ along with the $p(\1)$-indexed family of direction-sets $p[-]\colon p(\1)\to\smset$ uniquely characterize a polynomial $p$ up to isomorphism.
Throughout this book, we will often specify a polynomial by giving its positions and its directions at each position.
Expand Down Expand Up @@ -4648,6 +4650,7 @@ \section{Moore machines}\label{sec.poly.dyn_sys.moore}
\item the on-directions map $\varphi^\sharp\colon S\times A\to S$ the machine's \emph{update function}.
\end{itemize}
\end{definition}
\index{state system}

We call the codomain of a Moore machine its \emph{interface} because it encodes how an outsider interacts with the machine: an outsider observes the positions of the interface that the machine returns and feeds the directions of the interface to the machine as updates.
Rather than directly observing and changing the states, an outsider must interact with the machine via its interface.
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