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Revision as of 17:04, 18 June 2008
, 17:04, 18 June 2008→Appendix 2 @ PlanetMath : TeX Format: update
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& & y & \operatorname{d}x & \operatorname{d}y \\+ & & (y) & \operatorname{d}x & (\operatorname{d}y) \\+ & & y & (\operatorname{d}x) & \operatorname{d}y \\+ & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\+ & & (y) & \operatorname{d}x & \operatorname{d}y \\+ & & y & \operatorname{d}x & (\operatorname{d}y) \\+ & & (y) & (\operatorname{d}x) & \operatorname{d}y \\+ & & y & (\operatorname{d}x) & (\operatorname{d}y) \\+
\begin{quote}\begin{tabular}{||c||c|c|c|c||}
\begin{quote}\begin{tabular}{||c||c|c|c|c||}
−\multicolumn{5}{c}{Table A7. Detail of Calculation for $\operatorname{D}f = \operatorname{E}f + f$} \\[6pt]
+\multicolumn{5}{c}{\textbf{Table A7. Detail of Calculation for} $\operatorname{D}f = \operatorname{E}f + f$} \\[6pt]
\hline\hline
\hline\hline
&
&
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& \operatorname{E}f|_{\operatorname{d}x\ \operatorname{d}y} \\
& \operatorname{E}f|_{\operatorname{d}x\ \operatorname{d}y} \\
+ & f|_{\operatorname{d}x\ \operatorname{d}y} \\
+ & f|_{\operatorname{d}x\ \operatorname{d}y} \\
+= & \operatorname{D}f|_{\operatorname{d}x\ \operatorname{d}y} \\
\end{array}$
\end{array}$
&
&
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& \operatorname{E}f|_{\operatorname{d}x\ (\operatorname{d}y)} \\
& \operatorname{E}f|_{\operatorname{d}x\ (\operatorname{d}y)} \\
+ & f|_{\operatorname{d}x\ (\operatorname{d}y)} \\
+ & f|_{\operatorname{d}x\ (\operatorname{d}y)} \\
+= & \operatorname{D}f|_{\operatorname{d}x\ (\operatorname{d}y)} \\
\end{array}$
\end{array}$
&
&
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& \operatorname{E}f|_{(\operatorname{d}x)\ \operatorname{d}y} \\
& \operatorname{E}f|_{(\operatorname{d}x)\ \operatorname{d}y} \\
+ & f|_{(\operatorname{d}x)\ \operatorname{d}y} \\
+ & f|_{(\operatorname{d}x)\ \operatorname{d}y} \\
+= & \operatorname{D}f|_{(\operatorname{d}x)\ \operatorname{d}y} \\
\end{array}$
\end{array}$
&
&
Line 1,006:
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& \operatorname{E}f|_{(\operatorname{d}x)(\operatorname{d}y)} \\
& \operatorname{E}f|_{(\operatorname{d}x)(\operatorname{d}y)} \\
+ & f|_{(\operatorname{d}x)(\operatorname{d}y)} \\
+ & f|_{(\operatorname{d}x)(\operatorname{d}y)} \\
+= & \operatorname{D}f|_{(\operatorname{d}x)(\operatorname{d}y)} \\
\end{array}$ \\[6pt]
\end{array}$ \\[6pt]
\hline\hline
\hline\hline
−$f_{0}$ & $0 + 0$ & $0 + 0$ & $0 + 0$ & $0 + 0$ \\[6pt]
+$f_{0}$ & $0 + 0 = 0$ & $0 + 0 = 0$ & $0 + 0 = 0$ & $0 + 0 = 0$ \\[6pt]
\hline\hline
\hline\hline
$f_{1}$
$f_{1}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & y & \operatorname{d}x & \operatorname{d}y \\
+ & x\ y & \operatorname{d}x & \operatorname{d}y \\
−+ & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\
++ & (x)(y) & \operatorname{d}x & \operatorname{d}y \\
+= & ((x, y)) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & (y) & \operatorname{d}x & (\operatorname{d}y) \\
+ & x\ (y) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\
++ & (x) (y) & \operatorname{d}x & (\operatorname{d}y) \\
+= & (y) & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & y & (\operatorname{d}x) & \operatorname{d}y \\
+ & (x)\ y & (\operatorname{d}x) & \operatorname{d}y \\
−+ & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\
++ & (x) (y) & (\operatorname{d}x) & \operatorname{d}y \\
+= & (x) & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & (x)(y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & (x) & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (x)(y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & (y) & \operatorname{d}x & \operatorname{d}y \\
+ & x\ (y) & \operatorname{d}x & \operatorname{d}y \\
−+ & (x) & y & \operatorname{d}x & \operatorname{d}y \\
++ & (x)\ y & \operatorname{d}x & \operatorname{d}y \\
+= & (x, y) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & y & \operatorname{d}x & (\operatorname{d}y) \\
+ & x\ y & \operatorname{d}x & (\operatorname{d}y) \\
−+ & (x) & y & \operatorname{d}x & (\operatorname{d}y) \\
++ & (x)\ y & \operatorname{d}x & (\operatorname{d}y) \\
+= & y & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & (y) & (\operatorname{d}x) & \operatorname{d}y \\
+ & (x) (y) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & (x) & y & (\operatorname{d}x) & \operatorname{d}y \\
++ & (x)\ y & (\operatorname{d}x) & \operatorname{d}y \\
+= & (x) & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & y & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & (x)\ y & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & (x) & y & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (x)\ y & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & y & \operatorname{d}x & \operatorname{d}y \\
+ & (x)\ y & \operatorname{d}x & \operatorname{d}y \\
−+ & x & (y) & \operatorname{d}x & \operatorname{d}y \\
++ & x\ (y) & \operatorname{d}x & \operatorname{d}y \\
+= & (x, y) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & (y) & \operatorname{d}x & (\operatorname{d}y) \\
+ & (x) (y) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & x & (y) & \operatorname{d}x & (\operatorname{d}y) \\
++ & x\ (y) & \operatorname{d}x & (\operatorname{d}y) \\
+= & (y) & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & y & (\operatorname{d}x) & \operatorname{d}y \\
+ & x\ y & (\operatorname{d}x) & \operatorname{d}y \\
−+ & x & (y) & (\operatorname{d}x) & \operatorname{d}y \\
++ & x\ (y) & (\operatorname{d}x) & \operatorname{d}y \\
+= & x & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & x\ (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & x & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & x\ (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & (y) & \operatorname{d}x & \operatorname{d}y \\
+ & (x)(y) & \operatorname{d}x & \operatorname{d}y \\
−+ & x & y & \operatorname{d}x & \operatorname{d}y \\
++ & x\ y & \operatorname{d}x & \operatorname{d}y \\
+= & ((x, y)) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & y & \operatorname{d}x & (\operatorname{d}y) \\
+ & (x)\ y & \operatorname{d}x & (\operatorname{d}y) \\
−+ & x & y & \operatorname{d}x & (\operatorname{d}y) \\
++ & x\ y & \operatorname{d}x & (\operatorname{d}y) \\
+= & y & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & (y) & (\operatorname{d}x) & \operatorname{d}y \\
+ & x\ (y) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & x & y & (\operatorname{d}x) & \operatorname{d}y \\
++ & x\ y & (\operatorname{d}x) & \operatorname{d}y \\
+= & x & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & y & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & x\ y & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & x & y & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & x\ y & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline\hline
\hline\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & & \operatorname{d}x & \operatorname{d}y \\
+ & x & \operatorname{d}x & \operatorname{d}y \\
−+ & (x) & & \operatorname{d}x & \operatorname{d}y \\
++ & (x) & \operatorname{d}x & \operatorname{d}y \\
+= & 1 & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & & \operatorname{d}x & (\operatorname{d}y) \\
+ & x & \operatorname{d}x & (\operatorname{d}y) \\
−+ & (x) & & \operatorname{d}x & (\operatorname{d}y) \\
++ & (x) & \operatorname{d}x & (\operatorname{d}y) \\
+= & 1 & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & & (\operatorname{d}x) & \operatorname{d}y \\
+ & (x) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & (x) & & (\operatorname{d}x) & \operatorname{d}y \\
++ & (x) & (\operatorname{d}x) & \operatorname{d}y \\
+= & 0 & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & (x) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & (x) & & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (x) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & & \operatorname{d}x & \operatorname{d}y \\
+ & (x) & \operatorname{d}x & \operatorname{d}y \\
−+ & x & & \operatorname{d}x & \operatorname{d}y \\
++ & x & \operatorname{d}x & \operatorname{d}y \\
+= & 1 & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x) & & \operatorname{d}x & (\operatorname{d}y) \\
+ & (x) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & x & & \operatorname{d}x & (\operatorname{d}y) \\
++ & x & \operatorname{d}x & (\operatorname{d}y) \\
+= & 1 & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & & (\operatorname{d}x) & \operatorname{d}y \\
+ & x & (\operatorname{d}x) & \operatorname{d}y \\
−+ & x & & (\operatorname{d}x) & \operatorname{d}y \\
++ & x & (\operatorname{d}x) & \operatorname{d}y \\
+= & 0 & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & x & & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & x & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & x & & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & x & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline\hline
\hline\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x, & y) & \operatorname{d}x & \operatorname{d}y \\
+ & (x, y) & \operatorname{d}x & \operatorname{d}y \\
−+ & (x, & y) & \operatorname{d}x & \operatorname{d}y \\
++ & (x, y) & \operatorname{d}x & \operatorname{d}y \\
+= & 0 & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x, & y)) & \operatorname{d}x & (\operatorname{d}y) \\
+ & ((x, y)) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & (x, & y) & \operatorname{d}x & (\operatorname{d}y) \\
++ & (x, y) & \operatorname{d}x & (\operatorname{d}y) \\
+= & 1 & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x, & y)) & (\operatorname{d}x) & \operatorname{d}y \\
+ & ((x, y)) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & (x, & y) & (\operatorname{d}x) & \operatorname{d}y \\
++ & (x, y) & (\operatorname{d}x) & \operatorname{d}y \\
+= & 1 & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x, & y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & (x, y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & (x, & y) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (x, y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
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Line 1,199:
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\
+ & ((x, y)) & \operatorname{d}x & \operatorname{d}y \\
−+ & ((x, & y)) & \operatorname{d}x & \operatorname{d}y \\
++ & ((x, y)) & \operatorname{d}x & \operatorname{d}y \\
+= & 0 & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x, & y) & \operatorname{d}x & (\operatorname{d}y) \\
+ & (x, y) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & ((x, & y)) & \operatorname{d}x & (\operatorname{d}y) \\
++ & ((x, y)) & \operatorname{d}x & (\operatorname{d}y) \\
+= & 1 & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x, & y) & (\operatorname{d}x) & \operatorname{d}y \\
+ & (x, y) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & ((x, & y)) & (\operatorname{d}x) & \operatorname{d}y \\
++ & ((x, y)) & (\operatorname{d}x) & \operatorname{d}y \\
+= & 1 & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x, & y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & ((x, y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & ((x, & y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & ((x, y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline\hline
\hline\hline
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&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & y & \operatorname{d}x & \operatorname{d}y \\
−+ & & (y) & \operatorname{d}x & \operatorname{d}y \\
++ & (y) & \operatorname{d}x & \operatorname{d}y \\
+= & 1 & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (y) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & & (y) & \operatorname{d}x & (\operatorname{d}y) \\
++ & (y) & \operatorname{d}x & (\operatorname{d}y) \\
+= & 0 & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & y & (\operatorname{d}x) & \operatorname{d}y \\
−+ & & (y) & (\operatorname{d}x) & \operatorname{d}y \\
++ & (y) & (\operatorname{d}x) & \operatorname{d}y \\
+= & 1 & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
Line 1,211:
Line 1,251:
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (y) & \operatorname{d}x & \operatorname{d}y \\
−+ & & y & \operatorname{d}x & \operatorname{d}y \\
++ & y & \operatorname{d}x & \operatorname{d}y \\
+= & 1 & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & y & \operatorname{d}x & (\operatorname{d}y) \\
−+ & & y & \operatorname{d}x & (\operatorname{d}y) \\
++ & y & \operatorname{d}x & (\operatorname{d}y) \\
+= & 0 & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (y) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & & y & (\operatorname{d}x) & \operatorname{d}y \\
++ & y & (\operatorname{d}x) & \operatorname{d}y \\
+= & 1 & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & y & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & & y & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & y & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline\hline
\hline\hline
Line 1,233:
Line 1,277:
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & (y)) & \operatorname{d}x & \operatorname{d}y \\
+ & ((x)(y)) & \operatorname{d}x & \operatorname{d}y \\
−+ & (x & y) & \operatorname{d}x & \operatorname{d}y \\
++ & (x\ y) & \operatorname{d}x & \operatorname{d}y \\
+= & ((x, y)) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & y) & \operatorname{d}x & (\operatorname{d}y) \\
+ & ((x)\ y) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & (x & y) & \operatorname{d}x & (\operatorname{d}y) \\
++ & (x\ y) & \operatorname{d}x & (\operatorname{d}y) \\
+= & y & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & (y)) & (\operatorname{d}x) & \operatorname{d}y \\
+ & (x\ (y)) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & (x & y) & (\operatorname{d}x) & \operatorname{d}y \\
++ & (x\ y) & (\operatorname{d}x) & \operatorname{d}y \\
+= & x & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & (x\ y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & (x & y) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (x\ y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
Line 1,255:
Line 1,303:
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & y) & \operatorname{d}x & \operatorname{d}y \\
+ & ((x)\ y) & \operatorname{d}x & \operatorname{d}y \\
−+ & (x & (y)) & \operatorname{d}x & \operatorname{d}y \\
++ & (x\ (y)) & \operatorname{d}x & \operatorname{d}y \\
+= & (x, y) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & (y)) & \operatorname{d}x & (\operatorname{d}y) \\
+ & ((x) (y)) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & (x & (y)) & \operatorname{d}x & (\operatorname{d}y) \\
++ & (x\ (y)) & \operatorname{d}x & (\operatorname{d}y) \\
+= & (y) & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & y) & (\operatorname{d}x) & \operatorname{d}y \\
+ & (x\ y) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & (x & (y)) & (\operatorname{d}x) & \operatorname{d}y \\
++ & (x\ (y)) & (\operatorname{d}x) & \operatorname{d}y \\
+= & x & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & (x\ (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & (x & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & (x\ (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
Line 1,277:
Line 1,329:
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & (y)) & \operatorname{d}x & \operatorname{d}y \\
+ & (x\ (y)) & \operatorname{d}x & \operatorname{d}y \\
−+ & ((x) & y) & \operatorname{d}x & \operatorname{d}y \\
++ & ((x)\ y) & \operatorname{d}x & \operatorname{d}y \\
+= & (x, y) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & y) & \operatorname{d}x & (\operatorname{d}y) \\
+ & (x\ y) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & ((x) & y) & \operatorname{d}x & (\operatorname{d}y) \\
++ & ((x)\ y) & \operatorname{d}x & (\operatorname{d}y) \\
+= & y & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & (y)) & (\operatorname{d}x) & \operatorname{d}y \\
+ & ((x) (y)) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & ((x) & y) & (\operatorname{d}x) & \operatorname{d}y \\
++ & ((x)\ y) & (\operatorname{d}x) & \operatorname{d}y \\
+= & (x) & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & ((x)\ y) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & ((x) & y) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & ((x)\ y) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline
\hline
Line 1,299:
Line 1,355:
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & y) & \operatorname{d}x & \operatorname{d}y \\
+ & (x\ y) & \operatorname{d}x & \operatorname{d}y \\
−+ & ((x) & (y)) & \operatorname{d}x & \operatorname{d}y \\
++ & ((x)(y)) & \operatorname{d}x & \operatorname{d}y \\
+= & ((x, y)) & \operatorname{d}x & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & (x & (y)) & \operatorname{d}x & (\operatorname{d}y) \\
+ & (x\ (y)) & \operatorname{d}x & (\operatorname{d}y) \\
−+ & ((x) & (y)) & \operatorname{d}x & (\operatorname{d}y) \\
++ & ((x) (y)) & \operatorname{d}x & (\operatorname{d}y) \\
+= & (y) & \operatorname{d}x & (\operatorname{d}y) \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & y) & (\operatorname{d}x) & \operatorname{d}y \\
+ & ((x)\ y) & (\operatorname{d}x) & \operatorname{d}y \\
−+ & ((x) & (y)) & (\operatorname{d}x) & \operatorname{d}y \\
++ & ((x) (y)) & (\operatorname{d}x) & \operatorname{d}y \\
+= & (x) & (\operatorname{d}x) & \operatorname{d}y \\
\end{smallmatrix}$
\end{smallmatrix}$
&
&
$\begin{smallmatrix}
$\begin{smallmatrix}
− & ((x) & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
+ & ((x)(y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
−+ & ((x) & (y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
++ & ((x)(y)) & (\operatorname{d}x) & (\operatorname{d}y) \\
+= & 0 & (\operatorname{d}x) & (\operatorname{d}y) \\
\end{smallmatrix}$ \\[6pt]
\end{smallmatrix}$ \\[6pt]
\hline\hline
\hline\hline
−$f_{15}$ & $1 + 1$ & $1 + 1$ & $1 + 1$ & $1 + 1$ \\[6pt]
+$f_{15}$ & $1 + 1 = 0$ & $1 + 1 = 0$ & $1 + 1 = 0$ & $1 + 1 = 0$ \\[6pt]
\hline\hline
\hline\hline
\end{tabular}\end{quote}
\end{tabular}\end{quote}
