Changeset 116 for docs/trunk/omega-test-slides

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

  r115	r116
  245	245
  246	246	$a\beta \leq abx \leq b\alpha$
  247	(追記) \end{frame} (追記ここまで)
  248	(追記) (追記ここまで)
  249	(追記) \begin{frame}[fragile] (追記ここまで)
  250	(追記) \frametitle{Bounding Pairs} (追記ここまで)
  251	(追記) \includegraphics[width=100mm]{Omega-Test-Number-Line-2.png} (追記ここまで)
  252	(追記) (追記ここまで)
  253	(追記) $a\beta \leq abx \leq b\alpha$ (追記ここまで)
  247	254
  248	255	We can eliminate $x$ ($a\beta \leq b\alpha$) but there may be solutions to that but not the original.
  …	…
  290	297	$\neg \exists x: a\beta \leq abx \leq b\alpha \implies b\alpha - a\beta \leq ab - a - b$
  291	298
  292	(削除) \note{Using (削除ここまで):
  293
  294	(削除) (削除ここまで)$A \implies B$
  299	(追記) Using $A \implies B = \lnot B \implies \lnot A$ (追記ここまで):
  300
  301	(追記) \note{ (追記ここまで)$A \implies B$
  295	302
  296	303	$\lnot A \lor B$ (by definition)
  …	…
  377	384	%$\forall X. \operatorname{hasIntSol}(X) \implies \operatorname{hasRealSol}(X)$
  378	385
  379	$C_R$ is the real shadow of $C,ドル $X_D$ is the dark shadow of $C$
  380
  381	$\forall X. (C_R = C_D) \implies (\operatorname{hasIntSol}(C) \iff \operatorname{hasIntSol}(C_R))$
  382
  383	$\forall X. \lnot \operatorname{hasIntSol}(C_R) \implies \lnot \operatorname{hasIntSol}(C)$
  386	\begin{itemize}
  387	\item $C_R$ is the real shadow of $C,ドル $C_D$ is the dark shadow of $C$
  388	TODO insert table based on formulae:
  389	\note{
  390	$(C_R = C_D) \implies (\operatorname{hasIntSol}(C) \iff \operatorname{hasIntSol}(C_R))$
  391	$\lnot \operatorname{hasIntSol}(C_R) \implies \lnot \operatorname{hasIntSol}(C)$
  384	392	$\operatorname{hasIntSol}(C_R) \land \operatorname{hasIntSol}(C_D) \implies \operatorname{hasIntSol}(C)$
  385
  386	If $\operatorname{hasIntSol}(X_R) \wedge \neg \operatorname{hasIntSol}(X_D) \wedge (X_R \neq X_D),ドル we can't yet tell the value of $\operatorname{hasIntSol}(X$
  387
  393	If $\operatorname{hasIntSol}(C_R) \wedge \neg \operatorname{hasIntSol}(C_D) \wedge (C_R \neq C_D),ドル we can't yet tell the value of $\operatorname{hasIntSol}(C)$
  394	}
  395	\end{itemize}
  388	396	\end{frame}
  389	397

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