Changeset 118 for docs/trunk/omega-test-slides/omega-test.tex

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

  r117	r118
  4	4	\newcommand{\graph}[1]{\includegraphics[width=70mm]{#1.png}}
  5	5
  6	\newcommand{\fullframegraph}[2]{\frametitle{#1}\graph{#2}}
  7	\newcommand{\biggraph}[2]{\frametitle{#1}\graph{#2}}
  6	\newcommand{\biggraph}[1]{\includegraphics[width=100mm]{#1.png}}
  7
  8	\newcommand{\fullframegraph}[2]{\frametitle{#1}\includegraphics[width=100mm]{#2}}
  8	9
  9	10	\newcommand{\tick}[0]{\textcolor{KentGreen}{\ding{51}}}
  …	…
  139	140
  140	141	\begin{frame}[fragile]
  141	\biggraph{Inconsistent Equality}{equality-1-par}
  142	\frametitle{Inconsistent Equality}
  143	\biggraph{equality-1-par}
  142	144
  143	145	Rule: Identical coeffs but different constant $\implies$ unsolveable.
  …	…
  192	194	\end{frame}
  193	195
  194	%TODO show what happens when you don't yet have a unit coefficient(削除) (削除ここまで)
  196	%TODO show what happens when you don't yet have a unit coefficient(追記) (the substitution that is picked) (追記ここまで)
  195	197
  196	198
  …	…
  198	200
  199	201	%TODO show this maths graphically (with parallel lines):
  202	(追記) (追記ここまで)
  203	(追記) \begin{frame} (追記ここまで)
  204	(追記) \frametitle{Inequalities} (追記ここまで)
  205	(追記) \biggraph{inequality-normal} (追記ここまで)
  206	(追記) \end{frame} (追記ここまで)
  207	(追記) (追記ここまで)
  208	(追記) \begin{frame} (追記ここまで)
  209	(追記) \frametitle{Redundant Inequalities} (追記ここまで)
  210	(追記) \biggraph{inequality-redundant} (追記ここまで)
  211	(追記) \end{frame} (追記ここまで)
  212	(追記) (追記ここまで)
  213	(追記) \begin{frame} (追記ここまで)
  214	(追記) \frametitle{Unsolveable Inequalities} (追記ここまで)
  215	(追記) \biggraph{inequality-unsolveable} (追記ここまで)
  216	(追記) \end{frame} (追記ここまで)
  217	(追記) (追記ここまで)
  218	(追記) \begin{frame} (追記ここまで)
  219	(追記) \frametitle{Inequalities $\implies$ Equality} (追記ここまで)
  220	(追記) \biggraph{inequality-equality} (追記ここまで)
  221	(追記) \end{frame} (追記ここまで)
  200	222
  201	223	\begin{frame}
  …	…
  203	225	\begin{itemize}
  204	226	\item Pairs of inequalities are of interest if all their variable coeffs match, or are exact negations:
  205	\item (削除) 1: $ax + by >= c,ドル 2: (削除ここまで) $ax + by >= d$:
  227	\item (追記) $ax + by >= c,ドル (追記ここまで) $ax + by >= d$:
  206	228	\begin{itemize}
  207	229	\item $c = d \implies$ one is redundant (identical)
  …	…
  209	231	\item $c > d \implies$ eq 2 is redundant
  210	232	\end{itemize}
  211	\item (削除) 3: $ax + by >= c,ドル 4: (削除ここまで) $-ax -by >= d$ ($\implies ax + by <= -d$)
  233	\item (追記) $ax + by >= c,ドル (追記ここまで) $-ax -by >= d$ ($\implies ax + by <= -d$)
  212	234	\begin{itemize}
  213	235	\item $c = -d \implies ax + by = c$ (use as equality)
  …	…
  265	287
  266	288	\end{frame}
  267	(削除) (削除ここまで)
  268	(削除) %TODO can the above be shown *clearly* with graphics? The original paper doesn't do a good job (削除ここまで)
  269	(削除) %TODO maybe the number line? (削除ここまで)
  270	289
  271	290	\begin{frame}<1-2>[fragile]

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