Changeset 137 for docs/trunk/omega-test-slides

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

  r136	r137
  248	248
  249	249	\begin{frame}[fragile]
  250	\frametitle{(削除) Final (削除ここまで) Flow Chart}
  250	\frametitle{(追記) Equality (追記ここまで) Flow Chart}
  251	251	\biggraph{Omega-Flowchart-M4}
  252	252	\end{frame}
  …	…
  264	264	%The first one has red and green separate, so makes the ones after easier to follow
  265	265
  266	\begin{frame}
  267	\frametitle{Unsolveable Inequalities}
  268	\biggraph{inequality-unsolveable}
  269	\end{frame}
  270
  271	\begin{frame}
  272	\frametitle{Inequalities}
  273	\biggraph{inequality-normal}
  274	\end{frame}
  275
  276	\begin{frame}
  277	\frametitle{Redundant Inequalities}
  278	\biggraph{inequality-redundant}
  279	\end{frame}
  280
  281	\begin{frame}
  282	\frametitle{Inequalities $\implies$ Equality}
  283	\biggraph{inequality-equality}
  284	\end{frame}
  266	%TODO might be worth drawing over the lines (after alpha blending) in red/green to make
  267	%clearer where the inequalities start.
  268
  269	\TurnLogoOff
  270
  271	\begin{frame}
  272	\fullframegraph{Unsolveable Inequalities}{inequality-unsolveable}
  273	\end{frame}
  274
  275	\begin{frame}
  276	\fullframegraph{Inequalities}{inequality-normal}
  277	\end{frame}
  278
  279	\begin{frame}
  280	\fullframegraph{Redundant Inequalities}{inequality-redundant}
  281	\end{frame}
  282
  283	\begin{frame}
  284	\fullframegraph{Inequalities $\implies$ Equality}{inequality-equality}
  285	\end{frame}
  286
  287	\TurnLogoOn
  285	288
  286	289	\begin{frame}
  …	…
  290	293	\item $ax + by >= c,ドル $ax + by >= d$:
  291	294	\begin{itemize}
  292	(削除) \item $c = d \implies$ one is redundant (identical) (削除ここまで)
  293	295	\item $c < d \implies$ eq 1 is redundant
  294	296	\item $c > d \implies$ eq 2 is redundant
  297	(追記) \item $c = d \implies$ one is redundant (identical) (追記ここまで)
  295	298	\end{itemize}
  296	299	\item $ax + by >= c,ドル $-ax -by >= d$ ($\implies ax + by <= -d$)
  …	…
  302	305	\end{frame}
  303	306
  307	(追記) \TurnLogoOff (追記ここまで)
  308	(追記) (追記ここまで)
  309	(追記) \begin{frame}[fragile] (追記ここまで)
  310	(追記) \only<1>{\fullframegraph{Normalising Inequalities}{inequality-tightening-1}} (追記ここまで)
  311	(追記) \only<2>{\fullframegraph{Normalising Inequalities}{inequality-tightening-2}} (追記ここまで)
  312	(追記) \only<3>{\fullframegraph{Normalising Inequalities}{inequality-tightening-3}} (追記ここまで)
  313	(追記) \only<4>{\fullframegraph{Normalising Inequalities}{inequality-tightening-4}} (追記ここまで)
  314	(追記) \end{frame} (追記ここまで)
  315	(追記) (追記ここまで)
  316	(追記) \TurnLogoOn (追記ここまで)
  317	(追記) (追記ここまで)
  304	318	\begin{frame}[fragile]
  305	319	\frametitle{Normalising Inequalities}
  306	(削除) \only<1>{\biggraph{inequality-tightening-1}} (削除ここまで)
  307	(削除) \only<2>{\biggraph{inequality-tightening-2}} (削除ここまで)
  308	(削除) \only<3>{\biggraph{inequality-tightening-3}} (削除ここまで)
  309	(削除) \only<4>{\biggraph{inequality-tightening-4}} (削除ここまで)
  310	(削除) \only<5>{ (削除ここまで)
  311	320	\begin{itemize}
  312	321	\item Given an inequality in the conventional form: $\displaystyle\sum_{i=0}^n a_i x_i \geq 0$
  313	\item Normalise inequalities by finding $g,ドル the GCD of $a_1 \cdots a_n$
  314	(削除) \item Divide $a_i$ ($i \geq 1$) by $g (削除ここまで)$
  315	(削除) \item Set $a_0$ to $\lfloor a_0/g \rfloor (削除ここまで)$
  316	\end{itemize}
  317
  318	(削除) (削除ここまで)}
  319	\end{frame}(削除) (削除ここまで)
  320
  321	\begin{frame}[fragile](削除) (削除ここまで)
  322	\frametitle{F(削除) inal F (削除ここまで)low Chart}
  322	\begin{enumerate}
  323	(追記) \item Normalise inequalities by finding $g,ドル the GCD of $a_1 \cdots a_n (追記ここまで)$
  324	(追記) \item Divide each of $a_1 \cdots a_n$ by $g (追記ここまで)$
  325	\item Set $a_0$ to $\lfloor a_0/g \rfloor$
  326	\end{enumerate}
  327	(追記) \end{itemize (追記ここまで)}
  328	\end{frame}(追記) (追記ここまで)
  329
  330	\begin{frame}[fragile](追記) (追記ここまで)
  331	\frametitle{F(追記) (追記ここまで)low Chart}
  323	332	\biggraph{Omega-Flowchart-M3}
  324	333	\end{frame}

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