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Line 7,630: Line 7,630:  
|   ||   ||  
 
|   ||   ||  
 
|-
 
|-
| <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%" | &nbsp;
+
| style="width:10%; border-bottom:1px solid black" | &nbsp;
| 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" |
<p><math>\mathrm{T}_{11} f</math></p>
+
<math>\begin{matrix}\mathrm{T}_{11}f\\\mathrm{E}f|_{\mathrm{d}x~\mathrm{d}y}\end{matrix}</math>
<p><math>\mathrm{E}f|_{\mathrm{d}x~\mathrm{d}y}</math></p>
+
| 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>
<p><math>\mathrm{T}_{10} f</math></p>
+
| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
<p><math>\mathrm{E}f|_{\mathrm{d}x(\mathrm{d}y)}</math></p>
+
<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" |
<p><math>\mathrm{T}_{01} f</math></p>
+
<math>\begin{matrix}\mathrm{T}_{00}f\\\mathrm{E}f|_{ \texttt{(} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{)}}\end{matrix}</math>
<p><math>\mathrm{E}f|_{(\mathrm{d}x)\mathrm{d}y}</math></p>
  −
| width="18%" |
  −
<p><math>\mathrm{T}_{00} f</math></p>
  −
<p><math>\mathrm{E}f|_{(\mathrm{d}x)(\mathrm{d}y)}</math></p>
   
|-
 
|-
| <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_{1}\\f_{2}\\f_{4}\\f_{8}
\\[4pt]
+
\end{matrix}</math>
f_2
+
| style="border-top:1px solid black; border-left:1px solid black" |
\\[4pt]
  −
f_4
  −
\\[4pt]
  −
f_8
  −
\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_{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_{6}\\f_{9}
\\[4pt]
+
\end{matrix}</math>
f_9
+
| 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_{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_{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>
 
|}
 
|}
  
12,080

edits