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Revision as of 02:31, 11 September 2013
, 02:31, 11 September 2013update
Line 8,498:
Line 8,498:
f_1+f_2+f_4+f_8+|+<math>\begin{matrix}
−(x)(y)
−\\
−(x)~y~
−\\
−~x~(y)
−~x~~y~
−~(\mathrm{d}x)~\mathrm{d}y~~+~(\mathrm{d}x)~\mathrm{d}y~~+~(\mathrm{d}x)~\mathrm{d}y~~+~(\mathrm{d}x)~\mathrm{d}y~~+f_3+f_6
−f_9
−f_5
−\\
−|
−<math>\begin{matrix}
−(y)
−\\
−~y~
−<math>\begin{matrix}
−\mathrm{d}y
−\\
−\mathrm{d}y
−\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−\mathrm{d}y
−\\
−\mathrm{d}y
−\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−\mathrm{d}y
−\\
−\mathrm{d}y
−\end{matrix}\!</math>
−f_7+f_{11}+f_{13}+f_{14}+((x)~y~)+((x)(y))+~(\mathrm{d}x)~\mathrm{d}y~~+((\mathrm{d}x)(\mathrm{d}y))+~~\mathrm{d}x~~\mathrm{d}y~~+~~\mathrm{d}x~(\mathrm{d}y)~+\\
−((\mathrm{d}x)(\mathrm{d}y))+~(\mathrm{d}x)~\mathrm{d}y~~+\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−~~\mathrm{d}x~~\mathrm{d}y~~
~~\mathrm{d}x~(\mathrm{d}y)~+\\+~(\mathrm{d}x)~\mathrm{d}y~~
−\\
−((\mathrm{d}x)(\mathrm{d}y))
−
<br>
<br>
−{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:80%"
+{| 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 A6.}~~\mathrm{D}f ~\text{Expanded Over Ordinary Features}~ \{ x, y \}</math>
+|+ style="height:30px" | <math>\text{Table A6.} ~~ \mathrm{D}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{D}f|_{xy}\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:4px double black" |
−| width="18%" | <math>\mathrm{D}f|_{x(y)}\!</math>
+<math>\mathrm{D}f|_{xy}\!</math>
−| width="18%" | <math>\mathrm{D}f|_{(x)y}~\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
−| width="18%" | <math>\mathrm{D}f|_{(x)(y)}\!</math>
+<math>\mathrm{D}f|_{x \texttt{(} y \texttt{)}}\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
+<math>\mathrm{D}f|_{\texttt{(} x \texttt{)} y}\!</math>
+| style="width:18%; border-bottom:1px solid black; border-left:1px solid black" |
+<math>\mathrm{D}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}f_{1}\\f_{2}\\f_{4}\\f_{8}\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{)}
\\
\\
−\texttt{(} x \texttt{)~} y \texttt{~}
\\
\\
−\texttt{~} x \texttt{~(} y \texttt{)}
\\
\\
−\texttt{~} x \texttt{~~} y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
−| style="border-top:1px solid black; border-left:4px double black" |
−\\
−\end{matrix}\!</math>
−|
<math>\begin{matrix}
<math>\begin{matrix}
−~~\mathrm{d}x~~\mathrm{d}y~~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
\\
\\
−~~\mathrm{d}x~(\mathrm{d}y)~
+\texttt{~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{)}
\\
\\
−\texttt{(} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~}
\\
\\
−((\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{)}
\\
\\
−~~\mathrm{d}x~~\mathrm{d}y~~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
\\
\\
−((\mathrm{d}x)(\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
\\
\\
−\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{~}
\\
\\
−((\mathrm{d}x)(\mathrm{d}y))
+\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
\\
\\
−~~\mathrm{d}x~~\mathrm{d}y~~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
\\
\\
−~~\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{))}
\\
\\
−\texttt{(} \mathrm{d}x \texttt{)~} \mathrm{d}y \texttt{~}
\\
\\
−~~\mathrm{d}x~(\mathrm{d}y)~
+\texttt{~} \mathrm{d}x \texttt{~(} \mathrm{d}y \texttt{)}
\\
\\
−~~\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}f_{3}\\f_{12}\end{matrix}</math>
−<math>\begin{matrix}
+| style="border-top:1px solid black; border-left:1px solid black" |
−<math>\begin{matrix}\texttt{(} x \texttt{)}\\\texttt{~} x \texttt{~}\end{matrix}</math>
−\\
+| style="border-top:1px solid black; border-left:4px double black" |
−f_{12}
+<math>\begin{matrix}\mathrm{d}x\\\mathrm{d}x\end{matrix}</math>
−\end{matrix}\!</math>
+| style="border-top:1px solid black; border-left:1px solid black" |
−|
+<math>\begin{matrix}\mathrm{d}x\\\mathrm{d}x\end{matrix}</math>
−<math>\begin{matrix}
+| style="border-top:1px solid black; border-left:1px solid black" |
−(x)
+<math>\begin{matrix}\mathrm{d}x\\\mathrm{d}x\end{matrix}</math>
−\\
+| style="border-top:1px solid black; border-left:1px solid black" |
−~x~
+<math>\begin{matrix}\mathrm{d}x\\\mathrm{d}x\end{matrix}</math>
−\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−\mathrm{d}x
−\\
−\mathrm{d}x
−\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−\mathrm{d}x
−\\
−\mathrm{d}x
−\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−\mathrm{d}x
−\\
−\mathrm{d}x
−\end{matrix}\!</math>
−|
−<math>\begin{matrix}
−\mathrm{d}x
−\\
−\mathrm{d}x
−\end{matrix}\!</math>
|-
|-
−|
+| style="border-top:1px solid black" | <math>\begin{matrix}f_{6}\\f_{9}\end{matrix}</math>
−<math>\begin{matrix}
+| 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{)~}
\\
\\
−((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{)}
\\
\\
−(\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{)}
\\
\\
−(\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{)}
\\
\\
−(\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{)}
\\
\\
−(\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}f_{5}\\f_{10}\end{matrix}</math>
−<math>\begin{matrix}
+| style="border-top:1px solid black; border-left:1px solid black" |
−f_{10}
−\end{matrix}\!</math>
−\end{matrix}\!</math>
−|
−|
<math>\begin{matrix}
<math>\begin{matrix}
−\mathrm{d}y
+\texttt{(} y \texttt{)}
\\
\\
−\mathrm{d}y
+\texttt{~} y \texttt{~}
−\end{matrix}\!</math>
+\end{matrix}</math>
+| style="border-top:1px solid black; border-left:4px double black" |
+<math>\begin{matrix}\mathrm{d}y\\\mathrm{d}y\end{matrix}</math>
+| style="border-top:1px solid black; border-left:1px solid black" |
+<math>\begin{matrix}\mathrm{d}y\\\mathrm{d}y\end{matrix}</math>
+| style="border-top:1px solid black; border-left:1px solid black" |
+<math>\begin{matrix}\mathrm{d}y\\\mathrm{d}y\end{matrix}</math>
+| style="border-top:1px solid black; border-left:1px solid black" |
+<math>\begin{matrix}\mathrm{d}y\\\mathrm{d}y\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{~)}
\\
\\
−\texttt{(~} x \texttt{~(} y \texttt{))}
\\
\\
−\texttt{((} x \texttt{)~} y \texttt{~)}
\\
\\
−\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{))}
\\
\\
−(~x~(y))
+\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>
−|
+| 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{~}
\\
\\
−\texttt{((} \mathrm{d}x \texttt{)(} \mathrm{d}y \texttt{))}
\\
\\
−~~\mathrm{d}x~(\mathrm{d}y)~
+\texttt{~} \mathrm{d}x \texttt{~~} \mathrm{d}y \texttt{~}
\\
\\
−~~\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{)}
\\
\\
−\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>
−|
+| 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{~}
−~~\mathrm{d}x~~\mathrm{d}y~~
\\
\\
−\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>
|-
|-
−| <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>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>
|}
|}
