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MyWikiBiz, Author Your Legacy — Friday April 04, 2025
Jump to navigationJump to search→Table A5. Ef Expanded Over Ordinary Features {x, y}
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~~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\(y~~\)+~(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\(y~~\)+~(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\(y~~\)&+~(d\(x\))~d\(y~~\)+~~d\(x\)~~d\(y~~\)&+\;d\(x\)~(d\(y\))~&+~(d\(x\))~d\(y~~\)&+0&+0&+0&+0+
$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
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\(f_{1}\)&
\(f_{1}\)&
\((x)(y)\)&
\((x)(y)\)&
−~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
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\((~x~~y~)\)&
\((~x~~y~)\)&
((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\(y\)))
\\
\\
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\(f_{15}\)&
\(f_{15}\)&
1&
1&
−1&
−1&
−1&
−1
\\
\\
\hline
\hline
