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| | | |
| {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%" | | {| align="center" border="1" cellpadding="8" cellspacing="0" style="background:#f8f8ff; text-align:center; width:90%" |
− | |+ <math>\text{Table A4.}~~\operatorname{D}f ~\text{Expanded Over Differential Features}~ \{ \operatorname{d}x, \operatorname{d}y \}</math> | + | |+ <math>\text{Table A5.}~~\operatorname{E}f ~\text{Expanded Over Ordinary Features}~ \{ x, y \}</math> |
| |- style="background:#f0f0ff" | | |- style="background:#f0f0ff" |
| | width="10%" | | | | width="10%" | |
| | width="18%" | <math>f\!</math> | | | width="18%" | <math>f\!</math> |
| | width="18%" | | | | width="18%" | |
− | <math>\operatorname{D}f|_{\operatorname{d}x~\operatorname{d}y}</math> | + | <math>\operatorname{E}f|_{xy}</math> |
| | width="18%" | | | | width="18%" | |
− | <math>\operatorname{D}f|_{\operatorname{d}x(\operatorname{d}y)}</math> | + | <math>\operatorname{E}f|_{x(y)}</math> |
| | width="18%" | | | | width="18%" | |
− | <math>\operatorname{D}f|_{(\operatorname{d}x)\operatorname{d}y}</math> | + | <math>\operatorname{E}f|_{(x)y}</math> |
| | width="18%" | | | | width="18%" | |
− | <math>\operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)}</math> | + | <math>\operatorname{E}f|_{(x)(y)}</math> |
| |- | | |- |
| | <math>f_0\!</math> | | | <math>f_0\!</math> |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((x,~y))
| + | ~\operatorname{d}x~~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | ~(x,~y)~ | + | ~\operatorname{d}x~(\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | ~(x,~y)~
| + | (\operatorname{d}x)~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | ((x,~y)) | + | (\operatorname{d}x)(\operatorname{d}y) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (y) | + | ~\operatorname{d}x~(\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | ~y~ | + | ~\operatorname{d}x~~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | (y) | + | (\operatorname{d}x)(\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | ~y~ | + | (\operatorname{d}x)~\operatorname{d}y~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (x) | + | (\operatorname{d}x)~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | (x) | + | (\operatorname{d}x)(\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | ~x~ | + | ~\operatorname{d}x~~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | ~x~ | + | ~\operatorname{d}x~(\operatorname{d}y) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | (\operatorname{d}x)(\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | (~) | + | (\operatorname{d}x)~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | (~) | + | ~\operatorname{d}x~(\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | (~)
| + | ~\operatorname{d}x~~\operatorname{d}y~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((~))
| + | ~\operatorname{d}x~ |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | (\operatorname{d}x) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((~))
| + | ~\operatorname{d}x~ |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | (\operatorname{d}x) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | (\operatorname{d}x) |
| \\[4pt] | | \\[4pt] |
− | (~)
| + | ~\operatorname{d}x~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | (\operatorname{d}x) |
| \\[4pt] | | \\[4pt] |
− | (~)
| + | ~\operatorname{d}x~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | ~(\operatorname{d}x,~\operatorname{d}y)~ |
| \\[4pt] | | \\[4pt] |
− | (~) | + | ((\operatorname{d}x,~\operatorname{d}y)) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((~)) | + | ((\operatorname{d}x,~\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | ~(\operatorname{d}x,~\operatorname{d}y)~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((~)) | + | ((\operatorname{d}x,~\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | ~(\operatorname{d}x,~\operatorname{d}y)~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | ~(\operatorname{d}x,~\operatorname{d}y)~ |
| \\[4pt] | | \\[4pt] |
− | (~) | + | ((\operatorname{d}x,~\operatorname{d}y)) |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((~))
| + | ~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | (\operatorname{d}y) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | (\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | (~)
| + | ~\operatorname{d}y~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((~))
| + | ~\operatorname{d}y~ |
| \\[4pt] | | \\[4pt] |
− | ((~)) | + | (\operatorname{d}y) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | (\operatorname{d}y) |
| \\[4pt] | | \\[4pt] |
− | (~)
| + | ~\operatorname{d}y~ |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
Line 2,731: |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ~(x~~y)~ | + | (~x~~y~) |
| \\[4pt] | | \\[4pt] |
− | ~(x~(y)) | + | (~x~(y)) |
| \\[4pt] | | \\[4pt] |
− | ((x)~y)~ | + | ((x)~y~) |
| \\[4pt] | | \\[4pt] |
| ((x)(y)) | | ((x)(y)) |
Line 2,741: |
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| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ((x,~y)) | + | ((\operatorname{d}x)(\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | ~(x,~y)~
| + | ((\operatorname{d}x)~\operatorname{d}y~) |
| \\[4pt] | | \\[4pt] |
− | ~(x,~y)~ | + | (~\operatorname{d}x~(\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | ((x,~y)) | + | (~\operatorname{d}x~~\operatorname{d}y~) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ~y~ | + | ((\operatorname{d}x)~\operatorname{d}y~) |
| \\[4pt] | | \\[4pt] |
− | (y) | + | ((\operatorname{d}x)(\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | ~y~ | + | (~\operatorname{d}x~~\operatorname{d}y~) |
| \\[4pt] | | \\[4pt] |
− | (y) | + | (~\operatorname{d}x~(\operatorname{d}y)) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | ~x~ | + | (~\operatorname{d}x~(\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | ~x~ | + | (~\operatorname{d}x~~\operatorname{d}y~) |
| \\[4pt] | | \\[4pt] |
− | (x) | + | ((\operatorname{d}x)(\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | (x) | + | ((\operatorname{d}x)~\operatorname{d}y~) |
| \end{matrix}</math> | | \end{matrix}</math> |
| | | | | |
| <math>\begin{matrix} | | <math>\begin{matrix} |
− | (~) | + | (~\operatorname{d}x~~\operatorname{d}y~) |
| \\[4pt] | | \\[4pt] |
− | (~) | + | (~\operatorname{d}x~(\operatorname{d}y)) |
| \\[4pt] | | \\[4pt] |
− | (~) | + | ((\operatorname{d}x)~\operatorname{d}y~) |
| \\[4pt] | | \\[4pt] |
− | (~) | + | ((\operatorname{d}x)(\operatorname{d}y)) |
| \end{matrix}</math> | | \end{matrix}</math> |
| |- | | |- |
| | <math>f_{15}\!</math> | | | <math>f_{15}\!</math> |
| | <math>((~))</math> | | | <math>((~))</math> |
− | | <math>(~)</math> | + | | <math>((~))</math> |
− | | <math>(~)</math> | + | | <math>((~))</math> |
− | | <math>(~)</math> | + | | <math>((~))</math> |
− | | <math>(~)</math> | + | | <math>((~))</math> |
| |} | | |} |
− |
| |
− | <br>
| |
− |
| |
− | <pre>
| |
− | Table A5. Ef Expanded Over Ordinary Features {x, y}
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | | f | Ef | xy | Ef | x(y) | Ef | (x)y | Ef | (x)(y)|
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_0 | () | () | () | () | () |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_1 | (x)(y) | dx dy | dx (dy) | (dx) dy | (dx)(dy) |
| |
− | | | | | | | |
| |
− | | f_2 | (x) y | dx (dy) | dx dy | (dx)(dy) | (dx) dy |
| |
− | | | | | | | |
| |
− | | f_4 | x (y) | (dx) dy | (dx)(dy) | dx dy | dx (dy) |
| |
− | | | | | | | |
| |
− | | f_8 | x y | (dx)(dy) | (dx) dy | dx (dy) | dx dy |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_3 | (x) | dx | dx | (dx) | (dx) |
| |
− | | | | | | | |
| |
− | | f_12 | x | (dx) | (dx) | dx | dx |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_6 | (x, y) | (dx, dy) | ((dx, dy)) | ((dx, dy)) | (dx, dy) |
| |
− | | | | | | | |
| |
− | | f_9 | ((x, y)) | ((dx, dy)) | (dx, dy) | (dx, dy) | ((dx, dy)) |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_5 | (y) | dy | (dy) | dy | (dy) |
| |
− | | | | | | | |
| |
− | | f_10 | y | (dy) | dy | (dy) | dy |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_7 | (x y) | ((dx)(dy)) | ((dx) dy) | (dx (dy)) | (dx dy) |
| |
− | | | | | | | |
| |
− | | f_11 | (x (y)) | ((dx) dy) | ((dx)(dy)) | (dx dy) | (dx (dy)) |
| |
− | | | | | | | |
| |
− | | f_13 | ((x) y) | (dx (dy)) | (dx dy) | ((dx)(dy)) | ((dx) dy) |
| |
− | | | | | | | |
| |
− | | f_14 | ((x)(y)) | (dx dy) | (dx (dy)) | ((dx) dy) | ((dx)(dy)) |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | | | | | | | |
| |
− | | f_15 | (()) | (()) | (()) | (()) | (()) |
| |
− | | | | | | | |
| |
− | o------o------------o------------o------------o------------o------------o
| |
− | </pre>
| |
| | | |
| <br> | | <br> |