Changeset 164 for docs

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

  r163	r164
  511	511	\[ a\beta \leq abx \leq b\alpha \]
  512	512
  513	We can eliminate $x$ ($a\beta \leq b\alpha$(削除) (削除ここまで)) but there may be solutions to that but not the original.
  513	We can eliminate $x$ ($a\beta \leq b\alpha$(追記) ; termed $C_R,ドル the ``real'' shadow (追記ここまで)) but there may be solutions to that but not the original.
  514	514
  515	515	\begin{itemize}
  …	…
  526	526	the equation is solveable.}
  527	527
  528	\end{frame}
  529
  530	\begin{frame}<1>[fragile]
  531	\frametitle{Shadows}
  528	\note{
  532	529	\begin{itemize}
  533	530	\item Set of constraints $C_R$ ($a\beta \leq b\alpha$ for all pairs) is real shadow of constraints $C$
  …	…
  538	535	\item $\therefore$ Integer solution to $C_R$ $\land (\exists x: a\beta \leq abx \leq b\alpha) \implies $ integer solution to $C$
  539	536	\end{itemize}
  540
  537	}
  538
  539	\end{frame}
  541	540
  542	541	%Old slide:
  …	…
  560	559	}
  561	560	%$\operatorname{hasIntSol}(C_R) \land (\exists x: a\beta \leq abx \leq b\alpha) \implies \operatorname{hasIntSol}(C)$
  562	(削除) (削除ここまで)
  563	(削除) (削除ここまで)
  564	(削除) \end{frame} (削除ここまで)
  565	561
  566	562	\begin{frame}[fragile]

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