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Revision as of 20:30, 10 September 2013
, 20:30, 10 September 2013update
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f_1+f_2+f_4
−f_8
−f_3+f_6+f_9+f_5+f_7+f_{11}+f_{13}+f_{14}+(~\mathrm{d}x~(\mathrm{d}y))+\\[4pt]+(~\mathrm{d}x~~\mathrm{d}y~)+\\[4pt]+((\mathrm{d}x)(\mathrm{d}y))+\\[4pt]+((\mathrm{d}x)~\mathrm{d}y~)+|
−<math>\begin{matrix}
−\\[4pt]
−
|-
|-
| style="border-top:1px solid black" | <math>f_{0}\!</math>
| style="border-top:1px solid black" | <math>f_{0}\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
−| style="border-top:1px solid black; border-left:4px double black" | <math>\texttt{(~)}\!</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>0\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
|-
|-
| style="border-top:1px solid black" |
| style="border-top:1px solid black" |
Line 8,063:
Line 8,063:
|-
|-
| style="border-top:1px solid black" | <math>f_{15}\!</math>
| style="border-top:1px solid black" | <math>f_{15}\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
−| style="border-top:1px solid black; border-left:4px double black" | <math>\texttt{((~))}</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>1\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
−| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
|- style="background:ghostwhite"
|- style="background:ghostwhite"
| style="border-top:1px solid black" colspan="2" | <math>\text{Fixed Point Total}\!</math>
| style="border-top:1px solid black" colspan="2" | <math>\text{Fixed Point Total}\!</math>
Line 8,252:
Line 8,252:
<br>
<br>
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+{| align="center" cellpadding="6" cellspacing="0" style="border-bottom:1px solid black; border-left:1px solid black; border-right:1px solid black; border-top:1px solid black; text-align:center; width:80%"
−|+ <math>\text{Table A5.}~~\mathrm{E}f ~\text{Expanded Over Ordinary Features}~ \{ x, y \}</math>
+|+ style="height:30px" | <math>\text{Table A5.} ~~ \mathrm{E}f ~\text{Expanded Over Ordinary Features}~ \{ x, y \}\!</math>
−|- style="background:#f0f0ff"
+|- style="background:ghostwhite"
−| width="10%" |
+| style="width:10%; border-bottom:1px solid black" |
−| width="18%" | <math>f\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" | <math>f\!</math>
−| width="18%" | <math>\mathrm{E}f|_{xy}</math>
+| style="width:18%; border-bottom:1px solid black; border-left:4px double black" |
−| width="18%" | <math>\mathrm{E}f|_{x(y)}</math>
+<math>\mathrm{E}f|_{xy}\!</math>
−| width="18%" | <math>\mathrm{E}f|_{(x)y}</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
−| width="18%" | <math>\mathrm{E}f|_{(x)(y)}</math>
+<math>\mathrm{E}f|_{x \texttt{(} y \texttt{)}}\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
+<math>\mathrm{E}f|_{\texttt{(} x \texttt{)} y}\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
+<math>\mathrm{E}f|_{\texttt{(} x \texttt{)(} y \texttt{)}}\!</math>
|-
|-
−| <math>f_0\!</math>
+| style="border-top:1px solid black" | <math>f_{0}\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>0\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>0\!</math>
|-
|-
−|
+| style="border-top:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−f_{1}\\f_{2}\\f_{4}\\f_{8}
−\\[4pt]
+\end{matrix}</math>
−| style="border-top:1px solid black; border-left:1px solid black" |
−\\[4pt]
−\\[4pt]
−\end{matrix}\!</math>
−|
<math>\begin{matrix}
<math>\begin{matrix}
−(x)(y)
+\texttt{(} x \texttt{)(} y \texttt{)}
−\\[4pt]
+\\
−(x)~y~
+\texttt{(} x \texttt{)~} y \texttt{~}
−\\[4pt]
+\\
−~x~(y)
+\texttt{~} x \texttt{~(} y \texttt{)}
−\\[4pt]
+\\
−~x~~y~
+\texttt{~} x \texttt{~~} y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:4px double black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~\mathrm{d}x~~\mathrm{d}y~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−~\mathrm{d}x~(\mathrm{d}y)
+\texttt{~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−(\mathrm{d}x)~\mathrm{d}y~
+\texttt{(} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}x)(\mathrm{d}y)
+\texttt{(} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~\mathrm{d}x~(\mathrm{d}y)
+\texttt{~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}x~~\mathrm{d}y~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}x)(\mathrm{d}y)
+\texttt{(} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−(\mathrm{d}x)~\mathrm{d}y~
+\texttt{(} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~}
\end{matrix}\!</math>
\end{matrix}\!</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(\mathrm{d}x)~\mathrm{d}y~
+\texttt{(} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}x)(\mathrm{d}y)
+\texttt{(} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}x~~\mathrm{d}y~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−~\mathrm{d}x~(\mathrm{d}y)
+\texttt{~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(\mathrm{d}x)(\mathrm{d}y)
+\texttt{(} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−(\mathrm{d}x)~\mathrm{d}y~
+\texttt{(} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−~\mathrm{d}x~(\mathrm{d}y)
+\texttt{~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}x~~\mathrm{d}y~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
|-
|-
−|
+| style="border-top:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−f_{3}\\f_{12}
−\\[4pt]
+\end{matrix}</math>
−f_{12}
+| style="border-top:1px solid black; border-left:1px solid black" |
−\end{matrix}\!</math>
−|
<math>\begin{matrix}
<math>\begin{matrix}
−(x)
+\texttt{(} x \texttt{)}
−\\[4pt]
+\\
−~x~
+\texttt{~} x \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:4px double black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~\mathrm{d}x~
+\texttt{~} \mathrm{d}x \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}x)
+\texttt{(} \mathrm{d}x \texttt{)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~\mathrm{d}x~
+\texttt{~} \mathrm{d}x \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}x)
+\texttt{(} \mathrm{d}x \texttt{)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(\mathrm{d}x)
+\texttt{(} \mathrm{d}x \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}x~
+\texttt{~} \mathrm{d}x \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(\mathrm{d}x)
+\texttt{(} \mathrm{d}x \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}x~
+\texttt{~} \mathrm{d}x \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
|-
|-
−|
+| style="border-top:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−f_{6}\\f_{9}
−\\[4pt]
+\end{matrix}</math>
−| style="border-top:1px solid black; border-left:1px solid black" |
−\end{matrix}~</math>
−|
<math>\begin{matrix}
<math>\begin{matrix}
−~(x,~y)~
+\texttt{~(} x \texttt{,~} y \texttt{)~}
−\\[4pt]
+\\
−((x,~y))
+\texttt{((} x \texttt{,~} y \texttt{))}
−\end{matrix}~</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:4px double black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~(\mathrm{d}x,~\mathrm{d}y)~
+\texttt{~(} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{)~}
−\\[4pt]
+\\
−((\mathrm{d}x,~\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{))}
−\end{matrix}~</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−((\mathrm{d}x,~\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−~(\mathrm{d}x,~\mathrm{d}y)~
+\texttt{~(} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{)~}
−\end{matrix}~</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−((\mathrm{d}x,~\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−~(\mathrm{d}x,~\mathrm{d}y)~
+\texttt{~(} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{)~}
−\end{matrix}~</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~(\mathrm{d}x,~\mathrm{d}y)~
+\texttt{~(} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{)~}
−\\[4pt]
+\\
−((\mathrm{d}x,~\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{,~} \mathrm{d}y \texttt{))}
−\end{matrix}~</math>
+\end{matrix}</math>
|-
|-
−|
+| style="border-top:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−f_{5}\\f_{10}
−\\[4pt]
+\end{matrix}</math>
−f_{10}
+| style="border-top:1px solid black; border-left:1px solid black" |
−\end{matrix}\!</math>
−|
<math>\begin{matrix}
<math>\begin{matrix}
−(y)
+\texttt{(} y \texttt{)}
−\\[4pt]
+\\
−~y~
+\texttt{~} y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:4px double black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~\mathrm{d}y~
+\texttt{~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}y)
+\texttt{(} \mathrm{d}y \texttt{)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(\mathrm{d}y)
+\texttt{(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}y~
+\texttt{~} \mathrm{d}y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−~\mathrm{d}y~
+\texttt{~} \mathrm{d}y \texttt{~}
−\\[4pt]
+\\
−(\mathrm{d}y)
+\texttt{(} \mathrm{d}y \texttt{)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(\mathrm{d}y)
+\texttt{(} \mathrm{d}y \texttt{)}
−\\[4pt]
+\\
−~\mathrm{d}y~
+\texttt{~} \mathrm{d}y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
|-
|-
−|
+| style="border-top:1px solid black" |
+<math>\begin{matrix}
+f_{7}\\f_{11}\\f_{13}\\f_{14}
+\end{matrix}</math>
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−\texttt{(~} x \texttt{~~} y \texttt{~)}
−\\[4pt]
+\\
−\texttt{(~} x \texttt{~(} y \texttt{))}
−\\[4pt]
+\\
−\texttt{((} x \texttt{)~} y \texttt{~)}
−\\[4pt]
+\\
−\texttt{((} x \texttt{)(} y \texttt{))}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:4px double black" |
<math>\begin{matrix}
<math>\begin{matrix}
−(~x~~y~)
+\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−(~x~(y))
+\texttt{((} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~)}
−\\[4pt]
+\\
−((x)~y~)
+\texttt{(~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−((x)(y))
+\texttt{(~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~)}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−((\mathrm{d}x)(\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~)}
−\\[4pt]
+\\
−((\mathrm{d}x)~\mathrm{d}y~)
+\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−(~\mathrm{d}x~(\mathrm{d}y))
+\texttt{(~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~)}
−\\[4pt]
+\\
−(~\mathrm{d}x~~\mathrm{d}y~)
+\texttt{(~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{))}
−\end{matrix}\!</math>
+\end{matrix}</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−((\mathrm{d}x)~\mathrm{d}y~)
+\texttt{(~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−((\mathrm{d}x)(\mathrm{d}y))
+\texttt{(~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~)}
−\\[4pt]
+\\
−(~\mathrm{d}x~~\mathrm{d}y~)
+\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
−\\[4pt]
+\\
−(~\mathrm{d}x~(\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~)}
\end{matrix}\!</math>
\end{matrix}\!</math>
−|
+| style="border-top:1px solid black; border-left:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−\texttt{(~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~)}
−\\
−\texttt{(~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{))}
−\\
−\texttt{((} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~)}
−\\
−\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
−\end{matrix}~\!</math>
+\end{matrix}</math>
−(~\mathrm{d}x~~\mathrm{d}y~)
−(~\mathrm{d}x~(\mathrm{d}y))
−\\[4pt]
−((\mathrm{d}x)~\mathrm{d}y~)
−\\[4pt]
−((\mathrm{d}x)(\mathrm{d}y))
−\end{matrix}\!</math>
|-
|-
−| <math>f_{15}\!</math>
+| style="border-top:1px solid black" | <math>f_{15}\!</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>1\!</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>1\!</math>
|}
|}
<br>
<br>
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%"
+{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:80%"
|+ <math>\text{Table A6.}~~\mathrm{D}f ~\text{Expanded Over Ordinary Features}~ \{ x, y \}</math>
|+ <math>\text{Table A6.}~~\mathrm{D}f ~\text{Expanded Over Ordinary Features}~ \{ x, y \}</math>
|- style="background:#f0f0ff"
|- style="background:#f0f0ff"
