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Revision as of 20:30, 10 September 2013
, 20:30, 10 September 2013update
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| 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" |
|-
|-
| 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>
<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"
