Changeset 138

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

  r137	r138
  335	335	\subsection{Eliminating Variables}
  336	336
  337	\begin{frame}[fragile]
  338	\frametitle{Set of Inequalities}
  339	\only<1>{\biggraph{inequality-scalene-1}}
  340	\only<2>{\biggraph{inequality-scalene-2}}
  341	\only<3>{\biggraph{inequality-scalene-3}}
  342	\end{frame}
  337	\TurnLogoOff
  338
  339	\begin{frame}[fragile]
  340	\only<1>{\fullframegraph{Set of Inequalities}{inequality-scalene-1}}
  341	\only<2>{\fullframegraph{Set of Inequalities}{inequality-scalene-2}}
  342	\only<3>{\fullframegraph{Set of Inequalities}{inequality-scalene-3}}
  343	\end{frame}
  344
  345	\begin{frame}[fragile]
  346	\only<1>{\fullframegraph{Eliminate $x$}{inequality-scalene-2}}
  347	\only<2>{\fullframegraph{Eliminate $x$}{inequality-scalene-4}}
  348	\only<3>{\fullframegraph{Eliminate $x$}{inequality-scalene-5}}
  349	\only<4>{\fullframegraph{Eliminate $x$}{inequality-scalene-6}}
  350	\only<5>{\fullframegraph{Eliminate $x$}{inequality-scalene-7}}
  351	\end{frame}
  352
  353	\TurnLogoOn
  343	354
  344	355	\begin{frame}[fragile]
  345	356	\frametitle{Eliminate $x$}
  346	\only<1>{\biggraph{inequality-scalene-2}}
  347	\only<2>{\biggraph{inequality-scalene-4}}
  348	\only<3>{\biggraph{inequality-scalene-5}}
  349	\only<4>{\biggraph{inequality-scalene-6}}
  350	\only<5>{\biggraph{inequality-scalene-7}}
  351
  352	\only<6>{
  357
  353	358	$\begin{array}{llclrl}
  354	359	\text{\textcolor{KentRed}{Red}:}& y \leq 7 - 2x & \implies & & 2x & \leq 7 - y \\
  …	…
  367	372	\text{\textcolor{KentRed}{Red}}\wedge\text{\textcolor{KentBlue}{Blue}:} & 10 - 4y &\leq 2x \leq 7 - y \implies &y \geq 1
  368	373	\end{array}$
  369	}
  370	\end{frame}
  371
  372
  373
  374	%TODO talk about eliminating a variable
  374
  375	\end{frame}
  375	376
  376	377	\begin{frame}[fragile]
  377	378	\frametitle{Variable Elimination}
  378	We want to eliminate the variables one by one.
  379	Pick a variable (for illustration, $x_n$) and rephrase the set of inequalities 0ドル \leq \displaystyle\sum_{i=0}^n a_i x_i$ as:
  379	Pick a variable to eliminate (for illustration, $x_n$) and rephrase the set of inequalities 0ドル \leq \displaystyle\sum_{i=0}^n a_i x_i$ as:
  380	380
  381	381	%TODO this slide is quite dense and a little confusing.

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