Changeset 133 for docs

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• docs/trunk/omega-test-slides/omega-test.tex

  r132	r133
  123	123	%TODO maybe to be extra clear, show a typical problem?
  124	124
  125	\section{Terms, etc}
  126
  127	\begin{frame}[fragile]
  128	\frametitle{Defining Terms}
  125	\section{The Omega Test}
  126
  127	\begin{frame}[fragile]
  128	\frametitle{The Omega Test}
  129	\begin{itemize}
  130	\item A linear integer equation solver
  131	\item Inputs:
  132	\begin{itemize}
  133	\item Set of equalities
  134	\item Set of inequalities ($\leq,\geq,ドル etc)
  135	\end{itemize}
  136	\item Output is integer solution or ``unsolveable''
  137	\item All equations are joined by $\land$ (AND); $\lor$ (OR) effectively creates multiple equation-sets.
  138	\item Integer division is not reversible (and requires rational numbers), so is avoided.
  139	\end{itemize}
  140	\end{frame}
  141
  142	\begin{frame}[fragile]
  143	\frametitle{Terms}
  129	144	\begin{itemize}
  130	145	\item General form of equations for $n$ variables ($x_1 \cdots x_n$):
  131	146	\begin{itemize}
  132	\item Equality: $\displaystyle\sum_{i=0}^n a_i x_i = 0$
  133	\item Inequality: $\displaystyle\sum_{i=0}^n a_i x_i \geq 0$
  147	\item Equality: $\displaystyle\sum_{i=0}^n a_i x_i = 0,ドル Inequality: $\displaystyle\sum_{i=0}^n a_i x_i \geq 0$
  134	148	\item $x_0 = 1, \therefore a_0$ is the constant term
  135	149	\end{itemize}
  …	…
  139	153	\end{itemize}
  140	154	\item Equations are kept normalised (GCD of coefficients $a_1 \cdots a_n$ is 1)
  141	(削除) \end{itemize} (削除ここまで)
  142	(削除) \end{frame} (削除ここまで)
  143	(削除) (削除ここまで)
  144	(削除) \begin{frame}[fragile] (削除ここまで)
  145	(削除) \frametitle{$\land$ easy $\lor$ hard} (削除ここまで)
  146	(削除) \begin{itemize} (削除ここまで)
  147	(削除) \item All equations are joined by $\land$; $\lor$ effectively creates multiple equation-sets. (削除ここまで)
  148	(削除) \item Integer division is not reversible (and requires rational numbers), so is avoided. (削除ここまで)
  149	(削除) \item We are looking for integer solutions (削除ここまで)
  150	155	\end{itemize}
  151	156	\end{frame}

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