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Revision as of 22:00, 9 September 2013
, 22:00, 9 September 2013update
Line 7,630:
Line 7,630:
<p><math>\mathrm{T}_{11} f</math></p>+<p><math>\mathrm{E}f|_{\mathrm{d}x~\mathrm{d}y}</math></p>+<p><math>\mathrm{T}_{10} f</math></p>+<p><math>\mathrm{E}f|_{\mathrm{d}x(\mathrm{d}y)}</math></p>+<p><math>\mathrm{T}_{01} f</math></p>+<p><math>\mathrm{E}f|_{(\mathrm{d}x)\mathrm{d}y}</math></p>
−<p><math>\mathrm{T}_{00} f</math></p>
−<p><math>\mathrm{E}f|_{(\mathrm{d}x)(\mathrm{d}y)}</math></p>
f_1+f_2+f_4
−f_8
−f_3+f_6+f_9+f_5+f_7+
| || ||
| || ||
|-
|-
−| <math>f_0\!</math>
+| <math>f_{0}\!</math>
| <math>f_{0000}\!</math>
| <math>f_{0000}\!</math>
| <math>0~0~0~0</math>
| <math>0~0~0~0</math>
Line 7,826:
Line 7,826:
<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 A3.}~~\mathrm{E}f ~\text{Expanded Over Differential Features}~ \{ \mathrm{d}x, \mathrm{d}y \}</math>
+|+ style="height:30px" | <math>\text{Table A3.} ~~ \mathrm{E}f ~\text{Expanded Over Differential Features}~ \{ \mathrm{d}x, \mathrm{d}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%" |
+| style="width:18%; border-bottom:1px solid black; border-left:4px double black" |
−<math>\begin{matrix}\mathrm{T}_{11}f\\\mathrm{E}f|_{\mathrm{d}x~\mathrm{d}y}\end{matrix}</math>
−| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
−| width="18%" |
+<math>\begin{matrix}\mathrm{T}_{10}f\\\mathrm{E}f|_{\mathrm{d}x \texttt{(} \mathrm{d}y \texttt{)}}\end{matrix}</math>
−| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
−<math>\begin{matrix}\mathrm{T}_{01}f\\\mathrm{E}f|_{\texttt{(} \mathrm{d}x \texttt{)} \mathrm{d}y}\end{matrix}</math>
−| width="18%" |
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
−<math>\begin{matrix}\mathrm{T}_{00}f\\\mathrm{E}f|_{ \texttt{(} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{)}}\end{matrix}</math>
−| width="18%" |
−|-
|-
−| <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>\texttt{(~)}\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>\texttt{(~)}\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</math>
−| <math>(~)</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{(~)}\!</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}
−~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:1px solid black" |
<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:1px solid black" |
<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:1px solid black" |
<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" |
<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}
−~x~
+\texttt{~} x \texttt{~}
−\\[4pt]
+\\
−(x)
+\texttt{(} 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}
−~x~
+\texttt{~} x \texttt{~}
−\\[4pt]
+\\
−(x)
+\texttt{(} 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}
−(x)
+\texttt{(} x \texttt{)}
−\\[4pt]
+\\
−~x~
+\texttt{~} 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}
−(x)
+\texttt{(} x \texttt{)}
−\\[4pt]
+\\
−~x~
+\texttt{~} 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}
−~(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:1px solid black" |
<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:1px solid black" |
<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:1px solid black" |
<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" |
<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}
−~y~
+\texttt{~} y \texttt{~}
−\\[4pt]
+\\
−(y)
+\texttt{(} 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}
−(y)
+\texttt{(} y \texttt{)}
−\\[4pt]
+\\
−~y~
+\texttt{~} 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}
−~y~
+\texttt{~} y \texttt{~}
−\\[4pt]
+\\
−(y)
+\texttt{(} 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}
−(y)
+\texttt{(} y \texttt{)}
−\\[4pt]
+\\
−~y~
+\texttt{~} y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
|-
|-
−|
+| style="border-top:1px solid black" |
<math>\begin{matrix}
<math>\begin{matrix}
−f_{7}\\f_{11}\\f_{13}\\f_{14}
−\\[4pt]
+\end{matrix}</math>
−f_{11}
+| style="border-top:1px solid black; border-left:1px solid black" |
−\\[4pt]
−f_{13}
−\\[4pt]
−f_{14}
−\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}
−((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:1px solid black" |
<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:1px solid black" |
<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:1px solid black" |
<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>
|-
|-
−| <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>\texttt{((~))}</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>\texttt{((~))}</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
−| <math>((~))</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>\texttt{((~))}</math>
−|- style="background:#f0f0ff"
+|- style="background:ghostwhite"
−| colspan="2" | <math>\text{Fixed Point Total}\!</math>
+| style="border-top:1px solid black" colspan="2" | <math>\text{Fixed Point Total}\!</math>
−| <math>4\!</math>
+| style="border-top:1px solid black; border-left:4px double black" | <math>4\!</math>
−| <math>4\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>4\!</math>
−| <math>4\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>4\!</math>
−| <math>16\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" | <math>16\!</math>
|}
|}
