12,080
edits
Changes
→Table A5. Ef Expanded Over Ordinary Features {x, y}
$latex
$latex
\begin{tabular}{|c|c||c|c|c|c|}
\begin{tabular}{|c|c||c|c|c|c|}
\multicolumn{6}{c}{Table A6. \(\mathrm{D}f\) Expanded Over Ordinary Features \(\{x, y\}\)} \\
\multicolumn{6}{c}{Table A5. \(\mathrm{E}f\) Expanded Over Ordinary Features \(\{x, y\}\)} \\
\hline
\hline
&
&
\(~~~~~~~~ f ~~~~~~~~\)&
\(~~~~~~~~ f ~~~~~~~~\)&
\(~~\mathrm{D}f|_{ x\;y }~~~\)&
\(~~\mathrm{E}f|_{ x\;y }~~~\)&
\(~~\mathrm{D}f|_{ x~(y)}\,~~\)&
\(~~\mathrm{E}f|_{ x~(y)}\,~~\)&
\(~~\mathrm{D}f|_{(x)~y }\,~~\)&
\(~~\mathrm{E}f|_{(x)~y }\,~~\)&
\(~~\mathrm{D}f|_{(x)(y)}\,~\)
\(~~\mathrm{E}f|_{(x)(y)}\;~\)
\\
\\
\hline\hline
\hline\hline
\(f_{1}\)&
\(f_{1}\)&
\((x)(y)\)&
\((x)(y)\)&
~d\(x\)~~d\(y~\)&
~d\(x\)~(d\(y\))&
(d\(x\))~d\(y~\)&
(d\(x\))(d\(y\))
\\
\\
\(f_{2}\)&
\(f_{2}\)&
\((x)~y~\)&
\((x)~y~\)&
~d\(x\)~(d\(y\))&
~d\(x\)~~d\(y~\)&
(d\(x\))(d\(y\))&
(d\(x\))~d\(y~\)
\\
\\
\(f_{4}\)&
\(f_{4}\)&
\(~x~(y)\)&
\(~x~(y)\)&
(d\(x\))~d\(y~\)&
(d\(x\))(d\(y\))&
~d\(x\)~~d\(y~\)&
~d\(x\)~(d\(y\))
\\
\\
\(f_{8}\)&
\(f_{8}\)&
\(~x~~y~\)&
\(~x~~y~\)&
(d\(x\))(d\(y\))&
(d\(x\))~d\(y~\)&
~d\(x\)~(d\(y\))&
~d\(x\)~~d\(y~\)
\\
\\
\hline
\hline
\(f_{3}\)&
\(f_{3}\)&
\((x)\)&
\((x)\)&
d\(x\)&
d\(x\) &
d\(x\)&
d\(x\) &
d\(x\)&
(d\(x\))&
d\(x\)
(d\(x\))
\\
\\
\(f_{12}\)&
\(f_{12}\)&
\( x \)&
\( x \)&
d\(x\)&
(d\(x\))&
d\(x\)&
(d\(x\))&
d\(x\)&
d\(x\) &
d\(x\)
d\(x\)
\\
\\
\hline
\hline
\(f_{6}\)&
\(f_{6}\)&
\( (x,y) \)&
\( (x,y) \)&
(d\(x\), d\(y\))&
(d\(x\), d\(y\)) &
(d\(x\), d\(y\))&
((d\(x\), d\(y\)))&
(d\(x\), d\(y\))&
((d\(x\), d\(y\)))&
(d\(x\), d\(y\))
(d\(x\), d\(y\))
\\
\\
\(f_{9}\)&
\(f_{9}\)&
\(((x,y))\)&
\(((x,y))\)&
(d\(x\), d\(y\))&
((d\(x\), d\(y\)))&
(d\(x\), d\(y\))&
(d\(x\), d\(y\)) &
(d\(x\), d\(y\))&
(d\(x\), d\(y\)) &
(d\(x\), d\(y\))
((d\(x\), d\(y\)))
\\
\\
\hline
\hline
\(f_{5}\)&
\(f_{5}\)&
\((y)\)&
\((y)\)&
d\(y\)&
d\(y\) &
d\(y\)&
(d\(y\))&
d\(y\)&
d\(y\) &
d\(y\)
(d\(y\))
\\
\\
\(f_{10}\)&
\(f_{10}\)&
\( y \)&
\( y \)&
d\(y\)&
(d\(y\))&
d\(y\)&
d\(y\) &
d\(y\)&
(d\(y\))&
d\(y\)
d\(y\)
\\
\\
\hline
\hline
\((~x~~y~)\)&
\((~x~~y~)\)&
((d\(x\))(d\(y\)))&
((d\(x\))(d\(y\)))&
((d\(x\))~d\(y\)~)&
(~d\(x\)~(d\(y\)))&
(~d\(x\)~~d\(y\)~)
\\
\\
\(f_{11}\)&
\(f_{11}\)&
\((~x~(y))\)&
\((~x~(y))\)&
((d\(x\))~d\(y\)~)&
((d\(x\))(d\(y\)))&
((d\(x\))(d\(y\)))&
(~d\(x\)~~d\(y\)~)&
(~d\(x\)~(d\(y\)))
\\
\\
\(f_{13}\)&
\(f_{13}\)&
\(((x)~y~)\)&
\(((x)~y~)\)&
(~d\(x\)~(d\(y\)))&
(~d\(x\)~~d\(y\)~)&
((d\(x\))(d\(y\)))&
((d\(x\))(d\(y\)))&
((d\(x\))~d\(y\)~)
\\
\\
\(f_{14}\)&
\(f_{14}\)&
\(((x)(y))\)&
\(((x)(y))\)&
(~d\(x\)~~d\(y\)~)&
(~d\(x\)~(d\(y\)))&
((d\(x\))~d\(y\)~)&
((d\(x\))(d\(y\)))
((d\(x\))(d\(y\)))
\\
\\
\(f_{15}\)&
\(f_{15}\)&
1&
1&
1&
1&
1&
1
\\
\\
\hline
\hline